Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(193,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.q (of order \(3\), 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: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.961 |
Dual form | 1344.2.q.h.193.1 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | −0.732294 | − | 0.680989i | \(-0.761550\pi\) |
0.955901 | + | 0.293691i | \(0.0948835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | + | 0.866025i | 0.944911 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | 0.931505 | − | 0.363727i | \(-0.118496\pi\) |
−0.780750 | + | 0.624844i | \(0.785163\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00000 | + | 6.92820i | 0.970143 | + | 1.68034i | 0.695113 | + | 0.718900i | \(0.255354\pi\) |
0.275029 | + | 0.961436i | \(0.411312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | + | 3.46410i | −0.458831 | + | 0.794719i | −0.998899 | − | 0.0469020i | \(-0.985065\pi\) |
0.540068 | + | 0.841621i | \(0.318398\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.500000 | − | 2.59808i | −0.109109 | − | 0.566947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.50000 | − | 6.06218i | −0.628619 | − | 1.08880i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.359211 | − | 0.933257i | \(-0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.500000 | − | 0.866025i | 0.0870388 | − | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | − | 1.73205i | 0.338062 | − | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | − | 6.92820i | 0.657596 | − | 1.13899i | −0.323640 | − | 0.946180i | \(-0.604907\pi\) |
0.981236 | − | 0.192809i | \(-0.0617599\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000 | 0.624695 | 0.312348 | − | 0.949968i | \(-0.398885\pi\) | ||||
0.312348 | + | 0.949968i | \(0.398885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | + | 5.19615i | −0.437595 | + | 0.757937i | −0.997503 | − | 0.0706177i | \(-0.977503\pi\) |
0.559908 | + | 0.828554i | \(0.310836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | − | 6.92820i | 0.560112 | − | 0.970143i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.500000 | − | 0.866025i | −0.0686803 | − | 0.118958i | 0.829640 | − | 0.558298i | \(-0.188546\pi\) |
−0.898321 | + | 0.439340i | \(0.855212\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.50000 | + | 7.79423i | 0.585850 | + | 1.01472i | 0.994769 | + | 0.102151i | \(0.0325726\pi\) |
−0.408919 | + | 0.912571i | \(0.634094\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | + | 1.73205i | −0.128037 | + | 0.221766i | −0.922916 | − | 0.385002i | \(-0.874201\pi\) |
0.794879 | + | 0.606768i | \(0.207534\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.00000 | + | 1.73205i | −0.251976 | + | 0.218218i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | + | 1.73205i | 0.122169 | + | 0.211604i | 0.920623 | − | 0.390453i | \(-0.127682\pi\) |
−0.798454 | + | 0.602056i | \(0.794348\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | − | 1.73205i | −0.117041 | − | 0.202721i | 0.801553 | − | 0.597924i | \(-0.204008\pi\) |
−0.918594 | + | 0.395203i | \(0.870674\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.00000 | − | 3.46410i | 0.230940 | − | 0.400000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.500000 | + | 2.59808i | 0.0569803 | + | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.50000 | − | 7.79423i | 0.506290 | − | 0.876919i | −0.493684 | − | 0.869641i | \(-0.664350\pi\) |
0.999974 | − | 0.00727784i | \(-0.00231663\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.00000 | 0.329293 | 0.164646 | − | 0.986353i | \(-0.447352\pi\) | ||||
0.164646 | + | 0.986353i | \(0.447352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000 | 0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.50000 | − | 4.33013i | −0.268028 | − | 0.464238i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.50000 | + | 6.06218i | −0.362933 | + | 0.628619i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | + | 3.46410i | 0.205196 | + | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | −0.101535 | −0.0507673 | − | 0.998711i | \(-0.516167\pi\) | ||||
−0.0507673 | + | 0.998711i | \(0.516167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.00000 | + | 1.73205i | 0.0995037 | + | 0.172345i | 0.911479 | − | 0.411346i | \(-0.134941\pi\) |
−0.811976 | + | 0.583691i | \(0.801608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | − | 13.8564i | 0.788263 | − | 1.36531i | −0.138767 | − | 0.990325i | \(-0.544314\pi\) |
0.927030 | − | 0.374987i | \(-0.122353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.50000 | − | 0.866025i | −0.243975 | − | 0.0845154i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.50000 | − | 12.9904i | 0.725052 | − | 1.25583i | −0.233900 | − | 0.972261i | \(-0.575149\pi\) |
0.958952 | − | 0.283567i | \(-0.0915178\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | + | 8.66025i | 0.478913 | + | 0.829502i | 0.999708 | − | 0.0241802i | \(-0.00769755\pi\) |
−0.520794 | + | 0.853682i | \(0.674364\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | −0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.00000 | + | 3.46410i | 0.186501 | + | 0.323029i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.00000 | + | 20.7846i | 0.366679 | + | 1.90532i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.00000 | − | 3.46410i | −0.180334 | − | 0.312348i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.0000 | 1.15356 | 0.576782 | − | 0.816898i | \(-0.304308\pi\) | ||||
0.576782 | + | 0.816898i | \(0.304308\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.00000 | + | 8.66025i | 0.440225 | + | 0.762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.50000 | + | 16.4545i | −0.830019 | + | 1.43763i | 0.0680035 | + | 0.997685i | \(0.478337\pi\) |
−0.898022 | + | 0.439950i | \(0.854996\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | + | 6.92820i | −0.693688 | + | 0.600751i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.500000 | − | 0.866025i | 0.0430331 | − | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.00000 | − | 15.5885i | −0.768922 | − | 1.33181i | −0.938148 | − | 0.346235i | \(-0.887460\pi\) |
0.169226 | − | 0.985577i | \(-0.445873\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0000 | −0.848189 | −0.424094 | − | 0.905618i | \(-0.639408\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.50000 | − | 4.33013i | 0.207614 | − | 0.359597i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | − | 6.92820i | 0.0824786 | − | 0.571429i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.50000 | − | 6.06218i | −0.284826 | − | 0.493333i | 0.687741 | − | 0.725956i | \(-0.258602\pi\) |
−0.972567 | + | 0.232623i | \(0.925269\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.00000 | −0.646762 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.00000 | −0.562254 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000 | + | 17.3205i | 0.798087 | + | 1.38233i | 0.920860 | + | 0.389892i | \(0.127488\pi\) |
−0.122774 | + | 0.992435i | \(0.539179\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.500000 | + | 0.866025i | −0.0396526 | + | 0.0686803i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | + | 6.92820i | −0.630488 | + | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0000 | − | 17.3205i | 0.783260 | − | 1.35665i | −0.146772 | − | 0.989170i | \(-0.546888\pi\) |
0.930033 | − | 0.367477i | \(-0.119778\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.500000 | − | 0.866025i | −0.0389249 | − | 0.0674200i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.0000 | −1.39288 | −0.696441 | − | 0.717614i | \(-0.745234\pi\) | ||||
−0.696441 | + | 0.717614i | \(0.745234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | − | 3.46410i | −0.152944 | − | 0.264906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.00000 | + | 15.5885i | −0.684257 | + | 1.18517i | 0.289412 | + | 0.957205i | \(0.406540\pi\) |
−0.973670 | + | 0.227964i | \(0.926793\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | + | 10.3923i | 0.151186 | + | 0.785584i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.50000 | − | 7.79423i | 0.338241 | − | 0.585850i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.0000 | + | 17.3205i | 0.747435 | + | 1.29460i | 0.949048 | + | 0.315130i | \(0.102048\pi\) |
−0.201613 | + | 0.979465i | \(0.564618\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.0000 | −1.48659 | −0.743294 | − | 0.668965i | \(-0.766738\pi\) | ||||
−0.743294 | + | 0.668965i | \(0.766738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00000 | − | 6.92820i | −0.294086 | − | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | + | 6.92820i | −0.292509 | + | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.50000 | + | 0.866025i | 0.181848 | + | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.50000 | + | 9.52628i | 0.395899 | + | 0.685717i | 0.993215 | − | 0.116289i | \(-0.0370998\pi\) |
−0.597317 | + | 0.802005i | \(0.703766\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0000 | − | 17.3205i | −0.708881 | − | 1.22782i | −0.965272 | − | 0.261245i | \(-0.915867\pi\) |
0.256391 | − | 0.966573i | \(-0.417466\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | − | 1.73205i | 0.0705346 | − | 0.122169i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.5000 | + | 4.33013i | 0.877328 | + | 0.303915i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | − | 3.46410i | 0.139686 | − | 0.241943i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.00000 | − | 3.46410i | −0.139010 | − | 0.240772i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.0000 | −1.51454 | −0.757271 | − | 0.653101i | \(-0.773468\pi\) | ||||
−0.757271 | + | 0.653101i | \(0.773468\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.00000 | − | 5.19615i | −0.205557 | − | 0.356034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.00000 | + | 8.66025i | −0.340997 | + | 0.590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.50000 | − | 18.1865i | −0.237595 | − | 1.23458i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.00000 | + | 1.73205i | −0.0675737 | + | 0.117041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.0000 | −1.27233 | −0.636167 | − | 0.771551i | \(-0.719481\pi\) | ||||
−0.636167 | + | 0.771551i | \(0.719481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.50000 | + | 6.06218i | 0.232303 | + | 0.402361i | 0.958485 | − | 0.285141i | \(-0.0920405\pi\) |
−0.726182 | + | 0.687502i | \(0.758707\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0000 | − | 20.7846i | 0.792982 | − | 1.37349i | −0.131130 | − | 0.991365i | \(-0.541861\pi\) |
0.924113 | − | 0.382121i | \(-0.124806\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.00000 | − | 1.73205i | 0.131590 | − | 0.113961i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.00000 | − | 6.92820i | 0.262049 | − | 0.453882i | −0.704737 | − | 0.709468i | \(-0.748935\pi\) |
0.966786 | + | 0.255586i | \(0.0822686\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00000 | + | 5.19615i | 0.195698 | + | 0.338960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.00000 | −0.584613 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.50000 | − | 12.9904i | −0.483117 | − | 0.836784i | 0.516695 | − | 0.856170i | \(-0.327162\pi\) |
−0.999812 | + | 0.0193858i | \(0.993829\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.50000 | − | 2.59808i | 0.415270 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.50000 | − | 2.59808i | −0.0950586 | − | 0.164646i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | −0.0315597 | − | 0.999502i | \(-0.510047\pi\) | ||||
−0.0315597 | + | 0.999502i | \(0.510047\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.00000 | − | 6.92820i | −0.250490 | − | 0.433861i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.00000 | + | 15.5885i | −0.561405 | + | 0.972381i | 0.435970 | + | 0.899961i | \(0.356405\pi\) |
−0.997374 | + | 0.0724199i | \(0.976928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.0000 | − | 13.8564i | 0.994192 | − | 0.860995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.50000 | + | 4.33013i | −0.154746 | + | 0.268028i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.0000 | + | 25.9808i | 0.924940 | + | 1.60204i | 0.791658 | + | 0.610964i | \(0.209218\pi\) |
0.133281 | + | 0.991078i | \(0.457449\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.00000 | −0.0614295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.50000 | − | 14.7224i | −0.518254 | − | 0.897643i | −0.999775 | − | 0.0212079i | \(-0.993249\pi\) |
0.481521 | − | 0.876435i | \(-0.340085\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.50000 | + | 9.52628i | −0.334101 | + | 0.578680i | −0.983312 | − | 0.181928i | \(-0.941766\pi\) |
0.649211 | + | 0.760609i | \(0.275099\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.00000 | + | 3.46410i | −0.120605 | + | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.0000 | − | 20.7846i | −0.721010 | − | 1.24883i | −0.960595 | − | 0.277951i | \(-0.910345\pi\) |
0.239585 | − | 0.970875i | \(-0.422989\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.00000 | 0.419079 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.00000 | − | 5.19615i | −0.178331 | − | 0.308879i | 0.762978 | − | 0.646425i | \(-0.223737\pi\) |
−0.941309 | + | 0.337546i | \(0.890403\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.00000 | − | 3.46410i | 0.118470 | − | 0.205196i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.0000 | + | 3.46410i | 0.590281 | + | 0.204479i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −23.5000 | + | 40.7032i | −1.38235 | + | 2.39431i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.500000 | + | 0.866025i | 0.0293105 | + | 0.0507673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.00000 | −0.175262 | −0.0876309 | − | 0.996153i | \(-0.527930\pi\) | ||||
−0.0876309 | + | 0.996153i | \(0.527930\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.00000 | 0.524000 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.500000 | + | 0.866025i | 0.0290129 | + | 0.0502519i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.0000 | − | 8.66025i | −1.44098 | − | 0.499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.00000 | − | 1.73205i | 0.0574485 | − | 0.0995037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.00000 | + | 1.73205i | 0.0572598 | + | 0.0991769i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.0000 | −0.910208 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.0000 | − | 24.2487i | −0.793867 | − | 1.37502i | −0.923556 | − | 0.383464i | \(-0.874731\pi\) |
0.129689 | − | 0.991555i | \(-0.458602\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.500000 | + | 0.866025i | −0.0282617 | + | 0.0489506i | −0.879810 | − | 0.475325i | \(-0.842331\pi\) |
0.851549 | + | 0.524276i | \(0.175664\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.500000 | + | 2.59808i | 0.0281718 | + | 0.146385i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.50000 | + | 4.33013i | −0.140414 | + | 0.243204i | −0.927653 | − | 0.373444i | \(-0.878177\pi\) |
0.787239 | + | 0.616649i | \(0.211510\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.50000 | + | 4.33013i | 0.139973 | + | 0.242441i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.0000 | −0.837218 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −32.0000 | −1.78053 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.00000 | − | 8.66025i | 0.276501 | − | 0.478913i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.0000 | + | 10.3923i | −0.661581 | + | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | − | 17.3205i | 0.549650 | − | 0.952021i | −0.448649 | − | 0.893708i | \(-0.648095\pi\) |
0.998298 | − | 0.0583130i | \(-0.0185721\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.00000 | + | 6.92820i | 0.219199 | + | 0.379663i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.00000 | 0.109272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.00000 | 0.0544735 | 0.0272367 | − | 0.999629i | \(-0.491329\pi\) | ||||
0.0272367 | + | 0.999629i | \(0.491329\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.00000 | − | 3.46410i | −0.108625 | − | 0.188144i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.50000 | − | 6.06218i | 0.189536 | − | 0.328285i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.00000 | − | 3.46410i | 0.107676 | − | 0.186501i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.0000 | + | 24.2487i | 0.751559 | + | 1.30174i | 0.947067 | + | 0.321037i | \(0.104031\pi\) |
−0.195507 | + | 0.980702i | \(0.562635\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.00000 | −0.321173 | −0.160586 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0000 | + | 20.7846i | 0.638696 | + | 1.10625i | 0.985719 | + | 0.168397i | \(0.0538590\pi\) |
−0.347024 | + | 0.937856i | \(0.612808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.00000 | − | 5.19615i | 0.159223 | − | 0.275783i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.0000 | − | 13.8564i | 0.846810 | − | 0.733359i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.00000 | + | 5.19615i | −0.158334 | + | 0.274242i | −0.934268 | − | 0.356572i | \(-0.883946\pi\) |
0.775934 | + | 0.630814i | \(0.217279\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.0000 | −0.524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.00000 | −0.104685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.50000 | + | 2.59808i | 0.0782994 | + | 0.135618i | 0.902516 | − | 0.430656i | \(-0.141718\pi\) |
−0.824217 | + | 0.566274i | \(0.808384\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | + | 3.46410i | −0.104116 | + | 0.180334i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.500000 | − | 2.59808i | −0.0259587 | − | 0.134885i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.00000 | + | 3.46410i | −0.103556 | + | 0.179364i | −0.913147 | − | 0.407630i | \(-0.866355\pi\) |
0.809591 | + | 0.586994i | \(0.199689\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.50000 | − | 7.79423i | −0.232379 | − | 0.402492i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.50000 | − | 11.2583i | −0.333005 | − | 0.576782i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.0000 | − | 29.4449i | 0.868659 | − | 1.50456i | 0.00529229 | − | 0.999986i | \(-0.498315\pi\) |
0.863367 | − | 0.504576i | \(-0.168351\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.50000 | + | 0.866025i | 0.127412 | + | 0.0441367i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.00000 | − | 8.66025i | 0.254164 | − | 0.440225i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.0000 | − | 29.4449i | −0.861934 | − | 1.49291i | −0.870059 | − | 0.492947i | \(-0.835920\pi\) |
0.00812520 | − | 0.999967i | \(-0.497414\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.0000 | −1.61831 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.0000 | 0.958423 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.50000 | − | 7.79423i | −0.226420 | − | 0.392170i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | − | 3.46410i | 0.100377 | − | 0.173858i | −0.811463 | − | 0.584404i | \(-0.801328\pi\) |
0.911840 | + | 0.410546i | \(0.134662\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.0000 | + | 3.46410i | 0.500626 | + | 0.173422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.0000 | − | 27.7128i | 0.799002 | − | 1.38391i | −0.121265 | − | 0.992620i | \(-0.538695\pi\) |
0.920267 | − | 0.391292i | \(-0.127972\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.00000 | 0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.5000 | − | 19.9186i | −0.568638 | − | 0.984911i | −0.996701 | − | 0.0811615i | \(-0.974137\pi\) |
0.428063 | − | 0.903749i | \(-0.359196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.00000 | + | 15.5885i | −0.443937 | + | 0.768922i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.50000 | + | 23.3827i | 0.221431 | + | 1.15059i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.50000 | − | 2.59808i | 0.0736321 | − | 0.127535i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.00000 | + | 8.66025i | 0.244851 | + | 0.424094i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.0000 | −1.17248 | −0.586238 | − | 0.810139i | \(-0.699392\pi\) | ||||
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | − | 5.19615i | −0.145865 | − | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.0000 | + | 27.7128i | −0.776114 | + | 1.34427i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.00000 | + | 3.46410i | −0.193574 | + | 0.167640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.0000 | 1.44171 | 0.720854 | − | 0.693087i | \(-0.243750\pi\) | ||||
0.720854 | + | 0.693087i | \(0.243750\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.00000 | −0.239732 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.00000 | − | 13.8564i | −0.382692 | − | 0.662842i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.50000 | + | 16.4545i | −0.453410 | + | 0.785330i | −0.998595 | − | 0.0529862i | \(-0.983126\pi\) |
0.545185 | + | 0.838316i | \(0.316459\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50000 | + | 2.59808i | −0.309524 | + | 0.123718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.5000 | − | 25.1147i | 0.688916 | − | 1.19324i | −0.283273 | − | 0.959039i | \(-0.591420\pi\) |
0.972189 | − | 0.234198i | \(-0.0752464\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.00000 | − | 5.19615i | −0.142214 | − | 0.246321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.00000 | −0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.0000 | −1.13263 | −0.566315 | − | 0.824189i | \(-0.691631\pi\) | ||||
−0.566315 | + | 0.824189i | \(0.691631\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.00000 | + | 3.46410i | 0.0941763 | + | 0.163118i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.50000 | + | 6.06218i | −0.164444 | + | 0.284826i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.50000 | + | 12.9904i | −0.350835 | + | 0.607664i | −0.986396 | − | 0.164386i | \(-0.947436\pi\) |
0.635561 | + | 0.772051i | \(0.280769\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.00000 | + | 6.92820i | 0.186704 | + | 0.323381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.0000 | −1.85896 | −0.929479 | − | 0.368875i | \(-0.879743\pi\) | ||||
−0.929479 | + | 0.368875i | \(0.879743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.50000 | + | 6.06218i | 0.162309 | + | 0.281127i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.00000 | + | 10.3923i | −0.277647 | + | 0.480899i | −0.970799 | − | 0.239892i | \(-0.922888\pi\) |
0.693153 | + | 0.720791i | \(0.256221\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.00000 | + | 5.19615i | 0.0461757 | + | 0.239936i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.0000 | − | 17.3205i | 0.460776 | − | 0.798087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.00000 | − | 8.66025i | −0.229900 | − | 0.398199i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.0000 | −0.734130 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.00000 | 0.0457869 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.00000 | + | 15.5885i | 0.411220 | + | 0.712255i | 0.995023 | − | 0.0996406i | \(-0.0317693\pi\) |
−0.583803 | + | 0.811895i | \(0.698436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.0000 | + | 3.46410i | 0.455016 | + | 0.157622i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.500000 | + | 0.866025i | −0.0227038 | + | 0.0393242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5000 | + | 26.8468i | 0.702372 | + | 1.21654i | 0.967632 | + | 0.252367i | \(0.0812090\pi\) |
−0.265260 | + | 0.964177i | \(0.585458\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.0000 | −0.904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.0000 | 1.21849 | 0.609246 | − | 0.792981i | \(-0.291472\pi\) | ||||
0.609246 | + | 0.792981i | \(0.291472\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000 | + | 34.6410i | 0.900755 | + | 1.56015i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.500000 | + | 0.866025i | −0.0224733 | + | 0.0389249i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.0000 | + | 5.19615i | 0.672842 | + | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.0000 | − | 29.4449i | 0.761025 | − | 1.31813i | −0.181298 | − | 0.983428i | \(-0.558030\pi\) |
0.942323 | − | 0.334705i | \(-0.108637\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.00000 | + | 15.5885i | 0.402090 | + | 0.696441i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.50000 | + | 11.2583i | 0.288675 | + | 0.500000i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.50000 | + | 7.79423i | −0.199459 | + | 0.345473i | −0.948353 | − | 0.317217i | \(-0.897252\pi\) |
0.748894 | + | 0.662690i | \(0.230585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.00000 | − | 5.19615i | −0.0442374 | − | 0.229864i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.00000 | + | 3.46410i | −0.0883022 | + | 0.152944i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.00000 | − | 13.8564i | −0.352522 | − | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.00000 | −0.263880 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.0000 | 0.790112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.00000 | − | 12.1244i | −0.306676 | − | 0.531178i | 0.670957 | − | 0.741496i | \(-0.265883\pi\) |
−0.977633 | + | 0.210318i | \(0.932550\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000 | − | 6.92820i | 0.174908 | − | 0.302949i | −0.765222 | − | 0.643767i | \(-0.777371\pi\) |
0.940129 | + | 0.340818i | \(0.110704\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.00000 | − | 6.92820i | 0.349149 | − | 0.302372i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.0000 | − | 48.4974i | 1.21970 | − | 2.11258i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.00000 | −0.390567 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.50000 | − | 12.9904i | −0.324253 | − | 0.561623i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.0000 | − | 17.3205i | 0.431532 | − | 0.747435i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | + | 6.92820i | −0.0430730 | + | 0.298419i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0000 | − | 19.0526i | 0.472927 | − | 0.819133i | −0.526593 | − | 0.850118i | \(-0.676531\pi\) |
0.999520 | + | 0.0309841i | \(0.00986412\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.0000 | + | 17.3205i | 0.429141 | + | 0.743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.0000 | 0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.0000 | + | 17.3205i | −0.426014 | + | 0.737878i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.0000 | − | 15.5885i | 0.765438 | − | 0.662889i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.00000 | + | 6.92820i | −0.169791 | + | 0.294086i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.50000 | + | 7.79423i | 0.190671 | + | 0.330252i | 0.945473 | − | 0.325701i | \(-0.105600\pi\) |
−0.754802 | + | 0.655953i | \(0.772267\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.5000 | + | 25.1147i | 0.611102 | + | 1.05846i | 0.991055 | + | 0.133454i | \(0.0426069\pi\) |
−0.379953 | + | 0.925006i | \(0.624060\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00000 | − | 3.46410i | 0.0841406 | − | 0.145736i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.500000 | − | 2.59808i | −0.0209980 | − | 0.109109i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00000 | − | 10.3923i | 0.251533 | − | 0.435668i | −0.712415 | − | 0.701758i | \(-0.752399\pi\) |
0.963948 | + | 0.266090i | \(0.0857319\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.00000 | + | 12.1244i | 0.292941 | + | 0.507388i | 0.974504 | − | 0.224371i | \(-0.0720328\pi\) |
−0.681563 | + | 0.731760i | \(0.738699\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.0000 | −0.667246 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.5000 | − | 19.9186i | −0.478751 | − | 0.829222i | 0.520952 | − | 0.853586i | \(-0.325577\pi\) |
−0.999703 | + | 0.0243645i | \(0.992244\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.50000 | − | 9.52628i | 0.228572 | − | 0.395899i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.50000 | + | 2.59808i | 0.311152 | + | 0.107786i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.500000 | − | 0.866025i | 0.0207079 | − | 0.0358671i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.0000 | −0.619116 | −0.309558 | − | 0.950881i | \(-0.600181\pi\) | ||||
−0.309558 | + | 0.950881i | \(0.600181\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.0000 | 1.15372 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | + | 15.5885i | 0.370211 | + | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.0000 | − | 31.1769i | 0.739171 | − | 1.28028i | −0.213697 | − | 0.976900i | \(-0.568551\pi\) |
0.952869 | − | 0.303383i | \(-0.0981160\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.0000 | + | 6.92820i | 0.819920 | + | 0.284029i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.0000 | + | 17.3205i | −0.409273 | + | 0.708881i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.0000 | − | 25.9808i | −0.612883 | − | 1.06155i | −0.990752 | − | 0.135686i | \(-0.956676\pi\) |
0.377869 | − | 0.925859i | \(-0.376657\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.0000 | 0.775026 | 0.387513 | − | 0.921864i | \(-0.373334\pi\) | ||||
0.387513 | + | 0.921864i | \(0.373334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.00000 | −0.0814463 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.00000 | − | 8.66025i | −0.203279 | − | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.5000 | + | 21.6506i | −0.507359 | + | 0.878772i | 0.492604 | + | 0.870253i | \(0.336045\pi\) |
−0.999964 | + | 0.00851879i | \(0.997288\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.50000 | − | 12.9904i | −0.101305 | − | 0.526397i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.0000 | + | 38.1051i | 0.888572 | + | 1.53905i | 0.841564 | + | 0.540157i | \(0.181635\pi\) |
0.0470071 | + | 0.998895i | \(0.485032\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.00000 | −0.161296 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.00000 | − | 8.66025i | −0.200967 | − | 0.348085i | 0.747873 | − | 0.663842i | \(-0.231075\pi\) |
−0.948840 | + | 0.315757i | \(0.897742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | + | 3.46410i | −0.0802572 | + | 0.139010i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0000 | − | 10.3923i | 0.480770 | − | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.00000 | + | 3.46410i | 0.0798723 | + | 0.138343i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 64.0000 | 2.55185 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.0000 | 1.31371 | 0.656855 | − | 0.754017i | \(-0.271887\pi\) | ||||
0.656855 | + | 0.754017i | \(0.271887\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.0000 | + | 19.0526i | 0.437211 | + | 0.757271i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.50000 | − | 11.2583i | 0.257945 | − | 0.446773i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.00000 | + | 5.19615i | −0.118678 | + | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.0000 | − | 32.9090i | −0.750455 | − | 1.29983i | −0.947602 | − | 0.319452i | \(-0.896501\pi\) |
0.197148 | − | 0.980374i | \(-0.436832\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.00000 | −0.0788723 | −0.0394362 | − | 0.999222i | \(-0.512556\pi\) | ||||
−0.0394362 | + | 0.999222i | \(0.512556\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.0000 | 0.393750 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.00000 | − | 8.66025i | −0.196570 | − | 0.340470i | 0.750844 | − | 0.660480i | \(-0.229647\pi\) |
−0.947414 | + | 0.320010i | \(0.896314\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.50000 | + | 7.79423i | −0.176640 | + | 0.305950i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.0000 | + | 12.1244i | −0.548703 | + | 0.475191i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.5000 | + | 26.8468i | −0.606562 | + | 1.05060i | 0.385241 | + | 0.922816i | \(0.374118\pi\) |
−0.991803 | + | 0.127780i | \(0.959215\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.50000 | + | 16.4545i | 0.371196 | + | 0.642930i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | 0.0780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.0000 | −0.623272 | −0.311636 | − | 0.950202i | \(-0.600877\pi\) | ||||
−0.311636 | + | 0.950202i | \(0.600877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.00000 | + | 15.5885i | 0.350059 | + | 0.606321i | 0.986260 | − | 0.165203i | \(-0.0528281\pi\) |
−0.636200 | + | 0.771524i | \(0.719495\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.00000 | + | 10.3923i | 0.0775567 | + | 0.402996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.0000 | + | 17.3205i | −0.387202 | + | 0.670653i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.50000 | + | 16.4545i | 0.367291 | + | 0.636167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.0000 | −0.732396 | −0.366198 | − | 0.930537i | \(-0.619341\pi\) | ||||
−0.366198 | + | 0.930537i | \(0.619341\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.00000 | + | 3.46410i | 0.0769800 | + | 0.133333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.5000 | + | 23.3827i | −0.518847 | + | 0.898670i | 0.480913 | + | 0.876768i | \(0.340305\pi\) |
−0.999760 | + | 0.0219013i | \(0.993028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.50000 | − | 0.866025i | −0.0959412 | − | 0.0332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.50000 | − | 6.06218i | 0.134120 | − | 0.232303i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.5000 | − | 32.0429i | −0.707883 | − | 1.22609i | −0.965641 | − | 0.259880i | \(-0.916317\pi\) |
0.257758 | − | 0.966209i | \(-0.417016\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0000 | −0.687745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.0000 | −0.915657 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.00000 | + | 10.3923i | −0.228251 | + | 0.395342i | −0.957290 | − | 0.289130i | \(-0.906634\pi\) |
0.729039 | + | 0.684472i | \(0.239967\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.50000 | − | 0.866025i | −0.0949671 | − | 0.0328976i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.00000 | + | 8.66025i | −0.189661 | + | 0.328502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.0000 | + | 27.7128i | 0.606043 | + | 1.04970i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.00000 | −0.302588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.0000 | −1.01978 | −0.509888 | − | 0.860241i | \(-0.670313\pi\) | ||||
−0.509888 | + | 0.860241i | \(0.670313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0000 | + | 27.7128i | 0.603451 | + | 1.04521i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.00000 | − | 5.19615i | 0.112987 | − | 0.195698i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.00000 | + | 5.19615i | 0.0376089 | + | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.00000 | − | 12.1244i | 0.262891 | − | 0.455340i | −0.704118 | − | 0.710083i | \(-0.748658\pi\) |
0.967009 | + | 0.254743i | \(0.0819909\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.50000 | + | 7.79423i | 0.168763 | + | 0.292306i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.0000 | 1.04861 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.00000 | − | 10.3923i | −0.224074 | − | 0.388108i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.00000 | + | 8.66025i | −0.186469 | + | 0.322973i | −0.944070 | − | 0.329744i | \(-0.893038\pi\) |
0.757602 | + | 0.652717i | \(0.226371\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.0000 | − | 27.7128i | 1.19174 | − | 1.03208i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.50000 | + | 12.9904i | −0.278928 | + | 0.483117i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.0000 | + | 17.3205i | 0.371391 | + | 0.643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.0000 | 0.704671 | 0.352335 | − | 0.935874i | \(-0.385388\pi\) | ||||
0.352335 | + | 0.935874i | \(0.385388\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.0000 | − | 69.2820i | −1.47945 | − | 2.56249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.00000 | + | 12.1244i | −0.258551 | + | 0.447823i | −0.965854 | − | 0.259087i | \(-0.916578\pi\) |
0.707303 | + | 0.706910i | \(0.249912\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.50000 | − | 4.33013i | −0.202871 | − | 0.159719i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.00000 | + | 1.73205i | −0.0368355 | + | 0.0638009i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.0000 | + | 29.4449i | 0.625355 | + | 1.08315i | 0.988472 | + | 0.151403i | \(0.0483792\pi\) |
−0.363117 | + | 0.931744i | \(0.618287\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.0000 | −1.39408 | −0.697042 | − | 0.717030i | \(-0.745501\pi\) | ||||
−0.697042 | + | 0.717030i | \(0.745501\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.00000 | − | 5.19615i | −0.109911 | − | 0.190372i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.50000 | + | 2.59808i | −0.0548821 | + | 0.0950586i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.0000 | − | 25.9808i | 1.09618 | − | 0.949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.50000 | − | 6.06218i | 0.127717 | − | 0.221212i | −0.795075 | − | 0.606511i | \(-0.792568\pi\) |
0.922792 | + | 0.385299i | \(0.125902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.500000 | + | 0.866025i | 0.0182210 | + | 0.0315597i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.00000 | −0.254756 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.00000 | + | 3.46410i | 0.0725954 | + | 0.125739i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.00000 | + | 25.9808i | 0.181012 | + | 0.940567i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.00000 | + | 6.92820i | −0.144620 | + | 0.250490i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.0000 | −0.685158 | −0.342579 | − | 0.939489i | \(-0.611300\pi\) | ||||
−0.342579 | + | 0.939489i | \(0.611300\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000 | 0.648254 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.00000 | + | 15.5885i | 0.323708 | + | 0.560678i | 0.981250 | − | 0.192740i | \(-0.0617373\pi\) |
−0.657542 | + | 0.753418i | \(0.728404\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.0000 | − | 24.2487i | 0.502895 | − | 0.871039i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −20.0000 | − | 6.92820i | −0.717496 | − | 0.248548i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.00000 | + | 13.8564i | −0.286630 | + | 0.496457i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.00000 | + | 5.19615i | 0.107348 | + | 0.185933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.00000 | 0.178685 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.0000 | 0.713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.0000 | − | 32.9090i | −0.677277 | − | 1.17308i | −0.975798 | − | 0.218675i | \(-0.929827\pi\) |
0.298521 | − | 0.954403i | \(-0.403507\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.0000 | − | 25.9808i | 0.534014 | − | 0.924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.0000 | + | 3.46410i | 0.355559 | + | 0.123169i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.500000 | + | 0.866025i | 0.0177332 | + | 0.0307148i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 51.0000 | 1.80651 | 0.903256 | − | 0.429101i | \(-0.141170\pi\) | ||||
0.903256 | + | 0.429101i | \(0.141170\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.0000 | −1.69812 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.00000 | + | 5.19615i | 0.106000 | + | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.00000 | − | 1.73205i | 0.0352892 | − | 0.0611227i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.00000 | + | 10.3923i | 0.0704907 | + | 0.366281i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.50000 | + | 14.7224i | −0.299214 | + | 0.518254i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.0000 | + | 27.7128i | 0.562530 | + | 0.974331i | 0.997275 | + | 0.0737769i | \(0.0235053\pi\) |
−0.434745 | + | 0.900554i | \(0.643161\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.0000 | 0.385787 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.0000 | − | 17.3205i | −0.350285 | − | 0.606711i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.0000 | − | 34.6410i | 0.699711 | − | 1.21194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.500000 | + | 0.866025i | −0.0174501 | + | 0.0302245i | −0.874619 | − | 0.484812i | \(-0.838888\pi\) |
0.857168 | + | 0.515036i | \(0.172221\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | − | 13.8564i | −0.278862 | − | 0.483004i | 0.692240 | − | 0.721668i | \(-0.256624\pi\) |
−0.971102 | + | 0.238664i | \(0.923291\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.00000 | 0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.0000 | 1.49526 | 0.747628 | − | 0.664117i | \(-0.231193\pi\) | ||||
0.747628 | + | 0.664117i | \(0.231193\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.0000 | − | 17.3205i | −0.347314 | − | 0.601566i | 0.638457 | − | 0.769657i | \(-0.279573\pi\) |
−0.985771 | + | 0.168091i | \(0.946240\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.0000 | + | 20.7846i | −0.416275 | + | 0.721010i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.00000 | + | 55.4256i | −0.277184 | + | 1.92038i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.00000 | + | 15.5885i | −0.311458 | + | 0.539461i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.50000 | − | 6.06218i | −0.120978 | − | 0.209540i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.00000 | −0.276191 | −0.138095 | − | 0.990419i | \(-0.544098\pi\) | ||||
−0.138095 | + | 0.990419i | \(0.544098\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.00000 | − | 5.19615i | −0.103325 | − | 0.178965i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.50000 | + | 11.2583i | −0.223607 | + | 0.387298i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.0000 | − | 17.3205i | 0.687208 | − | 0.595140i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.00000 | + | 5.19615i | −0.102960 | + | 0.178331i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.0000 | + | 27.7128i | 0.548473 | + | 0.949983i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.0000 | −1.43805 | −0.719026 | − | 0.694983i | \(-0.755412\pi\) | ||||
−0.719026 | + | 0.694983i | \(0.755412\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.00000 | + | 5.19615i | 0.102478 | + | 0.177497i | 0.912705 | − | 0.408619i | \(-0.133990\pi\) |
−0.810227 | + | 0.586116i | \(0.800656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.00000 | + | 15.5885i | −0.307076 | + | 0.531871i | −0.977721 | − | 0.209907i | \(-0.932684\pi\) |
0.670645 | + | 0.741778i | \(0.266017\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.00000 | − | 10.3923i | −0.0681598 | − | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.0000 | − | 39.8372i | 0.782929 | − | 1.35607i | −0.147299 | − | 0.989092i | \(-0.547058\pi\) |
0.930228 | − | 0.366981i | \(-0.119609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | + | 15.5885i | 0.306009 | + | 0.530023i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 47.0000 | 1.59620 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.00000 | 0.305304 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.500000 | − | 0.866025i | 0.0169224 | − | 0.0293105i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.5000 | + | 7.79423i | 0.760639 | + | 0.263493i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.0000 | − | 27.7128i | 0.540282 | − | 0.935795i | −0.458606 | − | 0.888640i | \(-0.651651\pi\) |
0.998888 | − | 0.0471555i | \(-0.0150156\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.50000 | + | 2.59808i | 0.0505937 | + | 0.0876309i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000 | 0.942275 | 0.471138 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471138 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.50000 | − | 7.79423i | −0.151266 | − | 0.262000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.00000 | + | 3.46410i | −0.0671534 | + | 0.116313i | −0.897647 | − | 0.440715i | \(-0.854725\pi\) |
0.830494 | + | 0.557028i | \(0.188058\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.5000 | + | 11.2583i | 1.09002 | + | 0.377592i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.500000 | − | 0.866025i | 0.0167506 | − | 0.0290129i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.0000 | − | 20.7846i | −0.401565 | − | 0.695530i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.0000 | 0.668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.5000 | − | 30.3109i | −0.583658 | − | 1.01092i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00000 | − | 6.92820i | 0.133259 | − | 0.230812i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.00000 | + | 25.9808i | 0.166390 | + | 0.864586i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.0000 | + | 17.3205i | −0.332411 | + | 0.575753i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.00000 | − | 10.3923i | −0.199227 | − | 0.345071i | 0.749051 | − | 0.662512i | \(-0.230510\pi\) |
−0.948278 | + | 0.317441i | \(0.897176\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.00000 | −0.0663358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.50000 | + | 2.59808i | 0.0496428 | + | 0.0859838i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.00000 | − | 1.73205i | 0.0330590 | − | 0.0572598i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −38.0000 | + | 32.9090i | −1.25487 | + | 1.08675i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0000 | − | 27.7128i | 0.527791 | − | 0.914161i | −0.471684 | − | 0.881768i | \(-0.656354\pi\) |
0.999475 | − | 0.0323936i | \(-0.0103130\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.00000 | − | 3.46410i | −0.0659022 | − | 0.114146i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.0000 | 1.05215 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.00000 | + | 13.8564i | 0.262754 | + | 0.455104i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.0000 | + | 29.4449i | −0.557752 | + | 0.966055i | 0.439932 | + | 0.898031i | \(0.355003\pi\) |
−0.997684 | + | 0.0680235i | \(0.978331\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.0000 | + | 10.3923i | −0.852116 | + | 0.340594i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.0000 | + | 24.2487i | −0.458339 | + | 0.793867i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.00000 | + | 6.92820i | 0.130814 | + | 0.226576i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.0000 | −0.947389 | −0.473694 | − | 0.880689i | \(-0.657080\pi\) | ||||
−0.473694 | + | 0.880689i | \(0.657080\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.00000 | 0.0326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.5000 | − | 44.1673i | −0.831276 | − | 1.43981i | −0.897027 | − | 0.441977i | \(-0.854277\pi\) |
0.0657503 | − | 0.997836i | \(-0.479056\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.00000 | + | 13.8564i | −0.260516 | + | 0.451227i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.00000 | − | 1.73205i | 0.0650600 | − | 0.0563436i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.0000 | − | 34.6410i | 0.649913 | − | 1.12568i | −0.333231 | − | 0.942845i | \(-0.608139\pi\) |
0.983143 | − | 0.182836i | \(-0.0585279\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.00000 | 0.162136 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.00000 | −0.194359 | −0.0971795 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971795 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.50000 | − | 4.33013i | 0.0808135 | − | 0.139973i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.00000 | − | 46.7654i | −0.290625 | − | 1.51013i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | + | 15.5885i | −0.290323 | + | 0.502853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.50000 | + | 12.9904i | 0.241684 | + | 0.418609i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.0000 | 0.354103 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.00000 | 0.225105 | 0.112552 | − | 0.993646i | \(-0.464097\pi\) | ||||
0.112552 | + | 0.993646i | \(0.464097\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.0000 | + | 27.7128i | 0.513994 | + | 0.890264i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.5000 | − | 51.0955i | 0.946700 | − | 1.63973i | 0.194389 | − | 0.980925i | \(-0.437728\pi\) |
0.752311 | − | 0.658808i | \(-0.228939\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.0000 | − | 8.66025i | −0.801463 | − | 0.277635i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.0000 | − | 43.3013i | −0.799821 | − | 1.38533i | −0.919732 | − | 0.392546i | \(-0.871594\pi\) |
0.119912 | − | 0.992785i | \(-0.461739\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.0000 | + | 20.7846i | 0.382741 | + | 0.662926i | 0.991453 | − | 0.130465i | \(-0.0416470\pi\) |
−0.608712 | + | 0.793391i | \(0.708314\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.00000 | + | 15.5885i | −0.286764 | + | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.0000 | + | 5.19615i | 0.477455 | + | 0.165395i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.0000 | − | 34.6410i | 0.635963 | − | 1.10152i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.50000 | + | 4.33013i | 0.0794151 | + | 0.137551i | 0.902998 | − | 0.429645i | \(-0.141361\pi\) |
−0.823583 | + | 0.567196i | \(0.808028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.0000 | −0.634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.0000 | −0.634043 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.00000 | + | 8.66025i | 0.158352 | + | 0.274273i | 0.934274 | − | 0.356555i | \(-0.116049\pi\) |
−0.775923 | + | 0.630828i | \(0.782715\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.00000 | − | 6.92820i | 0.126554 | − | 0.219199i |
(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 | 1344.2.q.h.961.1 | 2 | ||
4.3 | odd | 2 | 1344.2.q.r.961.1 | 2 | |||
7.2 | even | 3 | 9408.2.a.cg.1.1 | 1 | |||
7.4 | even | 3 | inner | 1344.2.q.h.193.1 | 2 | ||
7.5 | odd | 6 | 9408.2.a.bb.1.1 | 1 | |||
8.3 | odd | 2 | 672.2.q.b.289.1 | yes | 2 | ||
8.5 | even | 2 | 672.2.q.g.289.1 | yes | 2 | ||
24.5 | odd | 2 | 2016.2.s.j.289.1 | 2 | |||
24.11 | even | 2 | 2016.2.s.i.289.1 | 2 | |||
28.11 | odd | 6 | 1344.2.q.r.193.1 | 2 | |||
28.19 | even | 6 | 9408.2.a.cp.1.1 | 1 | |||
28.23 | odd | 6 | 9408.2.a.o.1.1 | 1 | |||
56.5 | odd | 6 | 4704.2.a.w.1.1 | 1 | |||
56.11 | odd | 6 | 672.2.q.b.193.1 | ✓ | 2 | ||
56.19 | even | 6 | 4704.2.a.f.1.1 | 1 | |||
56.37 | even | 6 | 4704.2.a.l.1.1 | 1 | |||
56.51 | odd | 6 | 4704.2.a.bc.1.1 | 1 | |||
56.53 | even | 6 | 672.2.q.g.193.1 | yes | 2 | ||
168.11 | even | 6 | 2016.2.s.i.865.1 | 2 | |||
168.53 | odd | 6 | 2016.2.s.j.865.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.q.b.193.1 | ✓ | 2 | 56.11 | odd | 6 | ||
672.2.q.b.289.1 | yes | 2 | 8.3 | odd | 2 | ||
672.2.q.g.193.1 | yes | 2 | 56.53 | even | 6 | ||
672.2.q.g.289.1 | yes | 2 | 8.5 | even | 2 | ||
1344.2.q.h.193.1 | 2 | 7.4 | even | 3 | inner | ||
1344.2.q.h.961.1 | 2 | 1.1 | even | 1 | trivial | ||
1344.2.q.r.193.1 | 2 | 28.11 | odd | 6 | |||
1344.2.q.r.961.1 | 2 | 4.3 | odd | 2 | |||
2016.2.s.i.289.1 | 2 | 24.11 | even | 2 | |||
2016.2.s.i.865.1 | 2 | 168.11 | even | 6 | |||
2016.2.s.j.289.1 | 2 | 24.5 | odd | 2 | |||
2016.2.s.j.865.1 | 2 | 168.53 | odd | 6 | |||
4704.2.a.f.1.1 | 1 | 56.19 | even | 6 | |||
4704.2.a.l.1.1 | 1 | 56.37 | even | 6 | |||
4704.2.a.w.1.1 | 1 | 56.5 | odd | 6 | |||
4704.2.a.bc.1.1 | 1 | 56.51 | odd | 6 | |||
9408.2.a.o.1.1 | 1 | 28.23 | odd | 6 | |||
9408.2.a.bb.1.1 | 1 | 7.5 | odd | 6 | |||
9408.2.a.cg.1.1 | 1 | 7.2 | even | 3 | |||
9408.2.a.cp.1.1 | 1 | 28.19 | even | 6 |