Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,2,Mod(11,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.l (of order \(6\), degree \(2\), 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: | \(0.574922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.11 |
Dual form | 72.2.l.a.59.1 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.866025 | − | 0.500000i | ||||
\(3\) | 1.72474 | − | 0.158919i | 0.995782 | − | 0.0917517i | ||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | −2.22474 | − | 1.02494i | −0.908248 | − | 0.418432i | ||||
\(7\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(8\) | − | 2.82843i | − | 1.00000i | ||||||
\(9\) | 2.94949 | − | 0.548188i | 0.983163 | − | 0.182729i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.27526 | − | 1.89097i | −0.987527 | − | 0.570149i | −0.0829925 | − | 0.996550i | \(-0.526448\pi\) |
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 2.00000 | + | 2.82843i | 0.577350 | + | 0.816497i | ||||
\(13\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | 8.02458i | 1.94625i | 0.230285 | + | 0.973123i | \(0.426034\pi\) | ||||
−0.230285 | + | 0.973123i | \(0.573966\pi\) | |||||||
\(18\) | −4.00000 | − | 1.41421i | −0.942809 | − | 0.333333i | ||||
\(19\) | −8.34847 | −1.91527 | −0.957635 | − | 0.287984i | \(-0.907015\pi\) | ||||
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.67423 | + | 4.63191i | 0.570149 | + | 0.987527i | ||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | −0.449490 | − | 4.87832i | −0.0917517 | − | 0.995782i | ||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | − | 1.41421i | 0.962250 | − | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(32\) | 4.89898 | − | 2.82843i | 0.866025 | − | 0.500000i | ||||
\(33\) | −5.94949 | − | 2.74094i | −1.03567 | − | 0.477137i | ||||
\(34\) | 5.67423 | − | 9.82806i | 0.973123 | − | 1.68550i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.89898 | + | 4.56048i | 0.649830 | + | 0.760080i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 10.2247 | + | 5.90326i | 1.65867 | + | 0.957635i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.398979 | + | 0.230351i | −0.0623101 | + | 0.0359748i | −0.530831 | − | 0.847477i | \(-0.678120\pi\) |
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.17423 | − | 2.03383i | 0.179069 | − | 0.310157i | −0.762493 | − | 0.646997i | \(-0.776025\pi\) |
0.941562 | + | 0.336840i | \(0.109358\pi\) | |||||||
\(44\) | − | 7.56388i | − | 1.14030i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | −2.89898 | + | 6.29253i | −0.418432 | + | 0.908248i | ||||
\(49\) | −3.50000 | − | 6.06218i | −0.500000 | − | 0.866025i | ||||
\(50\) | −6.12372 | + | 3.53553i | −0.866025 | + | 0.500000i | ||||
\(51\) | 1.27526 | + | 13.8404i | 0.178571 | + | 1.93804i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −7.12372 | − | 1.80348i | −0.969416 | − | 0.245423i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.3990 | + | 1.32673i | −1.90719 | + | 0.175729i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.6237 | − | 6.13361i | 1.38309 | − | 0.798528i | 0.390567 | − | 0.920575i | \(-0.372279\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.34847 | + | 7.56388i | 0.658351 | + | 0.931049i | ||||
\(67\) | 7.17423 | + | 12.4261i | 0.876472 | + | 1.51809i | 0.855186 | + | 0.518321i | \(0.173443\pi\) |
0.0212861 | + | 0.999773i | \(0.493224\pi\) | |||||||
\(68\) | −13.8990 | + | 8.02458i | −1.68550 | + | 0.973123i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −1.55051 | − | 8.34242i | −0.182729 | − | 0.983163i | ||||
\(73\) | 13.6969 | 1.60311 | 0.801553 | − | 0.597924i | \(-0.204008\pi\) | ||||
0.801553 | + | 0.597924i | \(0.204008\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.62372 | − | 7.86566i | 0.418432 | − | 0.908248i | ||||
\(76\) | −8.34847 | − | 14.4600i | −0.957635 | − | 1.65867i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.39898 | − | 3.23375i | 0.933220 | − | 0.359306i | ||||
\(82\) | 0.651531 | 0.0719495 | ||||||||
\(83\) | −2.44949 | − | 1.41421i | −0.268866 | − | 0.155230i | 0.359506 | − | 0.933143i | \(-0.382945\pi\) |
−0.628372 | + | 0.777913i | \(0.716279\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.87628 | + | 1.66062i | −0.310157 | + | 0.179069i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.34847 | + | 9.26382i | −0.570149 | + | 0.987527i | ||||
\(89\) | − | 5.65685i | − | 0.599625i | −0.953998 | − | 0.299813i | \(-0.903076\pi\) | ||
0.953998 | − | 0.299813i | \(-0.0969242\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.00000 | − | 5.65685i | 0.816497 | − | 0.577350i | ||||
\(97\) | −9.84847 | + | 17.0580i | −0.999961 | + | 1.73198i | −0.492287 | + | 0.870433i | \(0.663839\pi\) |
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 9.89949i | 1.00000i | ||||||||
\(99\) | −10.6969 | − | 3.78194i | −1.07508 | − | 0.380099i | ||||
\(100\) | 10.0000 | 1.00000 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 8.22474 | − | 17.8526i | 0.814371 | − | 1.76767i | ||||
\(103\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 4.70334i | − | 0.454689i | −0.973814 | − | 0.227345i | \(-0.926996\pi\) | ||
0.973814 | − | 0.227345i | \(-0.0730044\pi\) | |||||||
\(108\) | 7.44949 | + | 7.24604i | 0.716827 | + | 0.697251i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.79796 | − | 5.65685i | 0.921714 | − | 0.532152i | 0.0375328 | − | 0.999295i | \(-0.488050\pi\) |
0.884182 | + | 0.467143i | \(0.154717\pi\) | |||||||
\(114\) | 18.5732 | + | 8.55671i | 1.73954 | + | 0.801410i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.3485 | −1.59706 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.65153 | + | 2.86054i | 0.150139 | + | 0.260049i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.651531 | + | 0.460702i | −0.0587466 | + | 0.0415401i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 9.79796 | + | 5.65685i | 0.866025 | + | 0.500000i | ||||
\(129\) | 1.70204 | − | 3.69445i | 0.149856 | − | 0.325278i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.2474 | + | 7.07107i | −1.07006 | + | 0.617802i | −0.928199 | − | 0.372084i | \(-0.878643\pi\) |
−0.141865 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(132\) | −1.20204 | − | 13.0458i | −0.104624 | − | 1.13549i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 20.2918i | − | 1.75294i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 22.6969 | 1.94625 | ||||||||
\(137\) | −14.2980 | − | 8.25493i | −1.22156 | − | 0.705266i | −0.256307 | − | 0.966595i | \(-0.582506\pi\) |
−0.965250 | + | 0.261329i | \(0.915839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.82577 | − | 3.16232i | −0.154859 | − | 0.268224i | 0.778148 | − | 0.628080i | \(-0.216159\pi\) |
−0.933008 | + | 0.359856i | \(0.882826\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.00000 | + | 11.3137i | −0.333333 | + | 0.942809i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −16.7753 | − | 9.68520i | −1.38833 | − | 0.801553i | ||||
\(147\) | −7.00000 | − | 9.89949i | −0.577350 | − | 0.816497i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(150\) | −10.0000 | + | 7.07107i | −0.816497 | + | 0.577350i | ||||
\(151\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(152\) | 23.6130i | 1.91527i | ||||||||
\(153\) | 4.39898 | + | 23.6684i | 0.355636 | + | 1.91348i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.5732 | − | 1.97846i | −0.987845 | − | 0.155442i | ||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | −0.797959 | − | 0.460702i | −0.0623101 | − | 0.0359748i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.00000 | + | 3.46410i | 0.155230 | + | 0.268866i | ||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.50000 | + | 11.2583i | −0.500000 | + | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.6237 | + | 4.57653i | −1.88302 | + | 0.349976i | ||||
\(172\) | 4.69694 | 0.358138 | ||||||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.1010 | − | 7.56388i | 0.987527 | − | 0.570149i | ||||
\(177\) | 17.3485 | − | 12.2672i | 1.30399 | − | 0.922061i | ||||
\(178\) | −4.00000 | + | 6.92820i | −0.299813 | + | 0.519291i | ||||
\(179\) | 19.7990i | 1.47985i | 0.672692 | + | 0.739923i | \(0.265138\pi\) | ||||
−0.672692 | + | 0.739923i | \(0.734862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.1742 | − | 26.2825i | 1.10965 | − | 1.92197i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | −13.7980 | + | 1.27135i | −0.995782 | + | 0.0917517i | ||||
\(193\) | −12.8485 | − | 22.2542i | −0.924853 | − | 1.60189i | −0.791797 | − | 0.610784i | \(-0.790854\pi\) |
−0.133056 | − | 0.991109i | \(-0.542479\pi\) | |||||||
\(194\) | 24.1237 | − | 13.9278i | 1.73198 | − | 0.999961i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.00000 | − | 12.1244i | 0.500000 | − | 0.866025i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 10.4268 | + | 12.1958i | 0.740999 | + | 0.866717i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | −12.2474 | − | 7.07107i | −0.866025 | − | 0.500000i | ||||
\(201\) | 14.3485 | + | 20.2918i | 1.01206 | + | 1.43127i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −22.6969 | + | 16.0492i | −1.58910 | + | 1.12367i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.3434 | + | 15.7867i | 1.89138 | + | 1.09199i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.00000 | − | 12.1244i | −0.481900 | − | 0.834675i | 0.517884 | − | 0.855451i | \(-0.326720\pi\) |
−0.999784 | + | 0.0207756i | \(0.993386\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.32577 | + | 5.76039i | −0.227345 | + | 0.393772i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.00000 | − | 14.1421i | −0.272166 | − | 0.962250i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23.6237 | − | 2.17670i | 1.59634 | − | 0.147088i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00000 | − | 14.1421i | 0.333333 | − | 0.942809i | ||||
\(226\) | −16.0000 | −1.06430 | ||||||||
\(227\) | 23.7247 | + | 13.6975i | 1.57467 | + | 0.909134i | 0.995585 | + | 0.0938647i | \(0.0299221\pi\) |
0.579082 | + | 0.815270i | \(0.303411\pi\) | |||||||
\(228\) | −16.6969 | − | 23.6130i | −1.10578 | − | 1.56381i | ||||
\(229\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 23.1523i | − | 1.51676i | −0.651813 | − | 0.758380i | \(-0.725991\pi\) | ||
0.651813 | − | 0.758380i | \(-0.274009\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 21.2474 | + | 12.2672i | 1.38309 | + | 0.798528i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.848469 | + | 1.46959i | −0.0546547 | + | 0.0946647i | −0.892058 | − | 0.451920i | \(-0.850739\pi\) |
0.837404 | + | 0.546585i | \(0.184072\pi\) | |||||||
\(242\) | − | 4.67123i | − | 0.300278i | ||||||
\(243\) | 13.9722 | − | 6.91215i | 0.896317 | − | 0.443415i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.12372 | − | 0.103540i | 0.0716460 | − | 0.00660149i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.44949 | − | 2.04989i | −0.281975 | − | 0.129906i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.7525i | 1.30989i | 0.755678 | + | 0.654943i | \(0.227307\pi\) | ||||
−0.755678 | + | 0.654943i | \(0.772693\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −27.3990 | + | 15.8188i | −1.70910 | + | 0.986750i | −0.773427 | + | 0.633885i | \(0.781459\pi\) |
−0.935674 | + | 0.352865i | \(0.885208\pi\) | |||||||
\(258\) | −4.69694 | + | 3.32124i | −0.292419 | + | 0.206771i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 20.0000 | 1.23560 | ||||||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | −7.75255 | + | 16.8277i | −0.477137 | + | 1.03567i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.898979 | − | 9.75663i | −0.0550167 | − | 0.597096i | ||||
\(268\) | −14.3485 | + | 24.8523i | −0.876472 | + | 1.51809i | ||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −27.7980 | − | 16.0492i | −1.68550 | − | 0.973123i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.6742 | + | 20.2204i | 0.705266 | + | 1.22156i | ||||
\(275\) | −16.3763 | + | 9.45485i | −0.987527 | + | 0.570149i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(278\) | 5.16404i | 0.309719i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.4949 | − | 14.1421i | −1.46124 | − | 0.843649i | −0.462174 | − | 0.886789i | \(-0.652930\pi\) |
−0.999069 | + | 0.0431402i | \(0.986264\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0000 | + | 19.0526i | 0.653882 | + | 1.13256i | 0.982173 | + | 0.187980i | \(0.0601941\pi\) |
−0.328291 | + | 0.944577i | \(0.606473\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 12.8990 | − | 11.0280i | 0.760080 | − | 0.649830i | ||||
\(289\) | −47.3939 | −2.78788 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.2753 | + | 30.9859i | −0.836830 | + | 1.81642i | ||||
\(292\) | 13.6969 | + | 23.7238i | 0.801553 | + | 1.38833i | ||||
\(293\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(294\) | 1.57321 | + | 17.0741i | 0.0917517 | + | 0.995782i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.0505 | − | 4.82294i | −1.10542 | − | 0.279855i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 17.2474 | − | 1.58919i | 0.995782 | − | 0.0917517i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.6969 | − | 28.9199i | 0.957635 | − | 1.65867i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 11.3485 | − | 32.0983i | 0.648749 | − | 1.83494i | ||||
\(307\) | 9.65153 | 0.550842 | 0.275421 | − | 0.961324i | \(-0.411183\pi\) | ||||
0.275421 | + | 0.961324i | \(0.411183\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.1969 | − | 21.1257i | 0.689412 | − | 1.19410i | −0.282617 | − | 0.959233i | \(-0.591202\pi\) |
0.972028 | − | 0.234863i | \(-0.0754642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.747449 | − | 8.11207i | −0.0417185 | − | 0.452771i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 66.9930i | − | 3.72759i | ||||||
\(324\) | 14.0000 | + | 11.3137i | 0.777778 | + | 0.628539i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.44949 | − | 1.41421i | −0.135665 | − | 0.0783260i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.651531 | + | 1.12848i | 0.0359748 | + | 0.0623101i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0000 | + | 22.5167i | −0.714545 | + | 1.23763i | 0.248590 | + | 0.968609i | \(0.420033\pi\) |
−0.963135 | + | 0.269019i | \(0.913301\pi\) | |||||||
\(332\) | − | 5.65685i | − | 0.310460i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.1969 | + | 31.5180i | 0.991250 | + | 1.71690i | 0.609936 | + | 0.792451i | \(0.291195\pi\) |
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 15.9217 | − | 9.19239i | 0.866025 | − | 0.500000i | ||||
\(339\) | 16.0000 | − | 11.3137i | 0.869001 | − | 0.614476i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 33.3939 | + | 11.8065i | 1.80573 | + | 0.638423i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.75255 | − | 3.32124i | −0.310157 | − | 0.179069i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.4217 | + | 6.59431i | −0.613148 | + | 0.354001i | −0.774197 | − | 0.632945i | \(-0.781846\pi\) |
0.161048 | + | 0.986947i | \(0.448512\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −21.3939 | −1.14030 | ||||||||
\(353\) | 12.7020 | + | 7.33353i | 0.676061 | + | 0.390324i | 0.798369 | − | 0.602168i | \(-0.205696\pi\) |
−0.122308 | + | 0.992492i | \(0.539030\pi\) | |||||||
\(354\) | −29.9217 | + | 2.75699i | −1.59032 | + | 0.146533i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.79796 | − | 5.65685i | 0.519291 | − | 0.299813i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.0000 | − | 24.2487i | 0.739923 | − | 1.28158i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 50.6969 | 2.66826 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.30306 | + | 4.67123i | 0.173366 | + | 0.245176i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.05051 | + | 0.898133i | −0.0546874 | + | 0.0467550i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(374\) | −37.1691 | + | 21.4596i | −1.92197 | + | 1.10965i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.3485 | −1.35343 | −0.676715 | − | 0.736245i | \(-0.736597\pi\) | ||||
−0.676715 | + | 0.736245i | \(0.736597\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | 17.7980 | + | 8.19955i | 0.908248 | + | 0.418432i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 36.3410i | 1.84971i | ||||||||
\(387\) | 2.34847 | − | 6.64247i | 0.119379 | − | 0.337656i | ||||
\(388\) | −39.3939 | −1.99992 | ||||||||
\(389\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −17.1464 | + | 9.89949i | −0.866025 | + | 0.500000i | ||||
\(393\) | −20.0000 | + | 14.1421i | −1.00887 | + | 0.713376i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.14643 | − | 22.3096i | −0.208366 | − | 1.12110i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.0000 | + | 17.3205i | 0.500000 | + | 0.866025i | ||||
\(401\) | 21.6464 | − | 12.4976i | 1.08097 | − | 0.624099i | 0.149813 | − | 0.988714i | \(-0.452133\pi\) |
0.931158 | + | 0.364615i | \(0.118800\pi\) | |||||||
\(402\) | −3.22474 | − | 34.9982i | −0.160836 | − | 1.74555i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 39.1464 | − | 3.60697i | 1.93804 | − | 0.178571i | ||||
\(409\) | 9.19694 | + | 15.9296i | 0.454759 | + | 0.787666i | 0.998674 | − | 0.0514740i | \(-0.0163919\pi\) |
−0.543915 | + | 0.839140i | \(0.683059\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.9722 | − | 11.9654i | −1.28111 | − | 0.590211i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.65153 | − | 5.16404i | −0.178816 | − | 0.252884i | ||||
\(418\) | −22.3258 | − | 38.6694i | −1.09199 | − | 1.89138i | ||||
\(419\) | 31.8434 | − | 18.3848i | 1.55565 | − | 0.898155i | 0.557986 | − | 0.829851i | \(-0.311574\pi\) |
0.997665 | − | 0.0683046i | \(-0.0217590\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(422\) | 19.7990i | 0.963800i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 34.7474 | + | 20.0614i | 1.68550 | + | 0.973123i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.14643 | − | 4.70334i | 0.393772 | − | 0.227345i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −5.10102 | + | 20.1489i | −0.245423 | + | 0.969416i | ||||
\(433\) | −4.30306 | −0.206792 | −0.103396 | − | 0.994640i | \(-0.532971\pi\) | ||||
−0.103396 | + | 0.994640i | \(0.532971\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −30.4722 | − | 14.0386i | −1.45602 | − | 0.670790i | ||||
\(439\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.6464 | − | 15.9617i | −0.649830 | − | 0.760080i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.2753 | − | 17.4794i | −1.43842 | − | 0.830473i | −0.440681 | − | 0.897664i | \(-0.645263\pi\) |
−0.997740 | + | 0.0671913i | \(0.978596\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.2015i | 1.85003i | 0.379927 | + | 0.925016i | \(0.375949\pi\) | ||||
−0.379927 | + | 0.925016i | \(0.624051\pi\) | |||||||
\(450\) | −16.1237 | + | 13.7850i | −0.760080 | + | 0.649830i | ||||
\(451\) | 1.74235 | 0.0820439 | ||||||||
\(452\) | 19.5959 | + | 11.3137i | 0.921714 | + | 0.532152i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.3712 | − | 33.5519i | −0.909134 | − | 1.57467i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.75255 | + | 40.7265i | 0.175729 | + | 1.90719i | ||||
\(457\) | 21.1969 | − | 36.7142i | 0.991551 | − | 1.71742i | 0.383437 | − | 0.923567i | \(-0.374740\pi\) |
0.608114 | − | 0.793849i | \(-0.291926\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.3485 | + | 40.1229i | 0.529701 | + | 1.87278i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.3712 | + | 28.3557i | −0.758380 | + | 1.31355i | ||||
\(467\) | − | 10.4244i | − | 0.482384i | −0.970477 | − | 0.241192i | \(-0.922462\pi\) | ||
0.970477 | − | 0.241192i | \(-0.0775384\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −17.3485 | − | 30.0484i | −0.798528 | − | 1.38309i | ||||
\(473\) | −7.69184 | + | 4.44088i | −0.353671 | + | 0.204192i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.8712 | + | 36.1499i | −0.957635 | + | 1.65867i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 2.07832 | − | 1.19992i | 0.0946647 | − | 0.0546547i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.30306 | + | 5.72107i | −0.150139 | + | 0.260049i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −22.0000 | − | 1.41421i | −0.997940 | − | 0.0641500i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.44949 | − | 0.317837i | 0.155991 | − | 0.0143731i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.6237 | − | 21.7221i | 1.69793 | − | 0.980303i | 0.750218 | − | 0.661190i | \(-0.229948\pi\) |
0.947717 | − | 0.319113i | \(-0.103385\pi\) | |||||||
\(492\) | −1.44949 | − | 0.667783i | −0.0653480 | − | 0.0301060i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.00000 | + | 5.65685i | 0.179244 | + | 0.253490i | ||||
\(499\) | −14.8712 | − | 25.7576i | −0.665725 | − | 1.15307i | −0.979088 | − | 0.203436i | \(-0.934789\pi\) |
0.313363 | − | 0.949633i | \(-0.398544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.6742 | − | 25.4165i | 0.654943 | − | 1.13439i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.42168 | + | 20.4507i | −0.418432 | + | 0.908248i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274i | 1.00000i | ||||||||
\(513\) | −41.7423 | + | 11.8065i | −1.84297 | + | 0.521271i | ||||
\(514\) | 44.7423 | 1.97350 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.10102 | − | 0.746431i | 0.356628 | − | 0.0328598i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 17.4313i | − | 0.763678i | −0.924229 | − | 0.381839i | \(-0.875291\pi\) | ||
0.924229 | − | 0.381839i | \(-0.124709\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.0000 | 1.66162 | 0.830812 | − | 0.556553i | \(-0.187876\pi\) | ||||
0.830812 | + | 0.556553i | \(0.187876\pi\) | |||||||
\(524\) | −24.4949 | − | 14.1421i | −1.07006 | − | 0.617802i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 21.3939 | − | 15.1278i | 0.931049 | − | 0.658351i | ||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.9722 | − | 23.9148i | 1.21389 | − | 1.03781i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −5.79796 | + | 12.5851i | −0.250902 | + | 0.544609i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 35.1464 | − | 20.2918i | 1.51809 | − | 0.876472i | ||||
\(537\) | 3.14643 | + | 34.1482i | 0.135778 | + | 1.47360i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.4736i | 1.14030i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 22.6969 | + | 39.3123i | 0.973123 | + | 1.68550i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.82577 | + | 13.5546i | −0.334606 | + | 0.579554i | −0.983409 | − | 0.181402i | \(-0.941936\pi\) |
0.648803 | + | 0.760956i | \(0.275270\pi\) | |||||||
\(548\) | − | 33.0197i | − | 1.41053i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 26.7423 | 1.14030 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.65153 | − | 6.32464i | 0.154859 | − | 0.268224i | ||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.9949 | − | 47.7422i | 0.928625 | − | 2.01568i | ||||
\(562\) | 20.0000 | + | 34.6410i | 0.843649 | + | 1.46124i | ||||
\(563\) | −38.4217 | + | 22.1828i | −1.61928 | + | 0.934892i | −0.632175 | + | 0.774826i | \(0.717837\pi\) |
−0.987106 | + | 0.160066i | \(0.948829\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 31.1127i | − | 1.30776i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.2980 | − | 23.8434i | −1.73130 | − | 0.999567i | −0.880366 | − | 0.474295i | \(-0.842703\pi\) |
−0.850935 | − | 0.525271i | \(-0.823964\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.8712 | − | 41.3461i | −0.998978 | − | 1.73028i | −0.538642 | − | 0.842535i | \(-0.681062\pi\) |
−0.460336 | − | 0.887745i | \(-0.652271\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −23.5959 | + | 4.38551i | −0.983163 | + | 0.182729i | ||||
\(577\) | −12.3939 | −0.515964 | −0.257982 | − | 0.966150i | \(-0.583058\pi\) | ||||
−0.257982 | + | 0.966150i | \(0.583058\pi\) | |||||||
\(578\) | 58.0454 | + | 33.5125i | 2.41437 | + | 1.39394i | ||||
\(579\) | −25.6969 | − | 36.3410i | −1.06793 | − | 1.51028i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 39.3939 | − | 27.8557i | 1.63293 | − | 1.15465i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 38.7408i | − | 1.60311i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.3207 | − | 14.6189i | −1.04510 | − | 0.603386i | −0.123823 | − | 0.992304i | \(-0.539516\pi\) |
−0.921272 | + | 0.388918i | \(0.872849\pi\) | |||||||
\(588\) | 10.1464 | − | 22.0239i | 0.418432 | − | 0.908248i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 45.2548i | 1.85839i | 0.369586 | + | 0.929197i | \(0.379500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | 19.9217 | + | 19.3776i | 0.817397 | + | 0.795073i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | −22.2474 | − | 10.2494i | −0.908248 | − | 0.418432i | ||||
\(601\) | −18.8485 | + | 32.6465i | −0.768845 | + | 1.33168i | 0.169344 | + | 0.985557i | \(0.445835\pi\) |
−0.938190 | + | 0.346122i | \(0.887498\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.9722 | + | 32.7179i | 1.13912 | + | 1.33238i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(608\) | −40.8990 | + | 23.6130i | −1.65867 | + | 0.957635i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −36.5959 | + | 31.2877i | −1.47930 | + | 1.26473i | ||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | −11.8207 | − | 6.82466i | −0.477043 | − | 0.275421i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.35357 | + | 3.09089i | −0.215527 | + | 0.124434i | −0.603877 | − | 0.797077i | \(-0.706378\pi\) |
0.388351 | + | 0.921512i | \(0.373045\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.8712 | + | 20.5615i | −0.477143 | + | 0.826435i | −0.999657 | − | 0.0261952i | \(-0.991661\pi\) |
0.522514 | + | 0.852631i | \(0.324994\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | −29.8763 | + | 17.2491i | −1.19410 | + | 0.689412i | ||||
\(627\) | 49.6691 | + | 22.8827i | 1.98359 | + | 0.913845i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.0000 | − | 19.7990i | −0.556450 | − | 0.786939i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.2526 | − | 11.1155i | −0.760430 | − | 0.439034i | 0.0690201 | − | 0.997615i | \(-0.478013\pi\) |
−0.829450 | + | 0.558581i | \(0.811346\pi\) | |||||||
\(642\) | −4.82066 | + | 10.4637i | −0.190256 | + | 0.412971i | ||||
\(643\) | 16.1742 | + | 28.0146i | 0.637850 | + | 1.10479i | 0.985904 | + | 0.167313i | \(0.0535092\pi\) |
−0.348054 | + | 0.937474i | \(0.613157\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −47.3712 | + | 82.0493i | −1.86379 | + | 3.22819i | ||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | −9.14643 | − | 23.7559i | −0.359306 | − | 0.933220i | ||||
\(649\) | −46.3939 | −1.82112 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.00000 | + | 3.46410i | 0.0783260 | + | 0.135665i | ||||
\(653\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1.84281i | − | 0.0719495i | ||||||
\(657\) | 40.3990 | − | 7.50850i | 1.57611 | − | 0.292934i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.6413 | + | 24.0416i | 1.62212 | + | 0.936529i | 0.986353 | + | 0.164644i | \(0.0526477\pi\) |
0.635763 | + | 0.771885i | \(0.280686\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(662\) | 31.8434 | − | 18.3848i | 1.23763 | − | 0.714545i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.00000 | + | 6.92820i | −0.155230 | + | 0.268866i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.00000 | − | 8.66025i | 0.192736 | − | 0.333828i | −0.753420 | − | 0.657539i | \(-0.771597\pi\) |
0.946156 | + | 0.323711i | \(0.104931\pi\) | |||||||
\(674\) | − | 51.4687i | − | 1.98250i | ||||||
\(675\) | 6.37628 | − | 25.1862i | 0.245423 | − | 0.969416i | ||||
\(676\) | −26.0000 | −1.00000 | ||||||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | −27.5959 | + | 2.54270i | −1.05981 | + | 0.0976517i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 43.0959 | + | 19.8544i | 1.65144 | + | 0.760821i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 51.9294i | 1.98702i | 0.113728 | + | 0.993512i | \(0.463721\pi\) | ||||
−0.113728 | + | 0.993512i | \(0.536279\pi\) | |||||||
\(684\) | −32.5505 | − | 38.0730i | −1.24460 | − | 1.45576i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.69694 | + | 8.13534i | 0.179069 | + | 0.310157i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.0000 | − | 39.8372i | 0.874961 | − | 1.51548i | 0.0181572 | − | 0.999835i | \(-0.494220\pi\) |
0.856804 | − | 0.515642i | \(-0.172447\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.6515 | 0.708002 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.84847 | − | 3.20164i | −0.0700158 | − | 0.121271i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.67934 | − | 39.9319i | −0.139165 | − | 1.51036i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 26.2020 | + | 15.1278i | 0.987527 | + | 0.570149i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.3712 | − | 17.9634i | −0.390324 | − | 0.676061i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 38.5959 | + | 17.7812i | 1.45052 | + | 0.668259i | ||||
\(709\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.0000 | −0.599625 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −34.2929 | + | 19.7990i | −1.28158 | + | 0.739923i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −62.0908 | − | 35.8481i | −2.31078 | − | 1.33413i | ||||
\(723\) | −1.22985 | + | 2.66951i | −0.0457385 | + | 0.0992801i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.742346 | − | 8.05669i | −0.0275510 | − | 0.299012i | ||||
\(727\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.3207 | + | 9.42274i | 0.603642 | + | 0.348513i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 54.2650i | − | 1.99888i | ||||||
\(738\) | 1.92168 | − | 0.357161i | 0.0707381 | − | 0.0131473i | ||||
\(739\) | 53.7423 | 1.97694 | 0.988472 | − | 0.151403i | \(-0.0483792\pi\) | ||||
0.988472 | + | 0.151403i | \(0.0483792\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.00000 | − | 2.82843i | −0.292705 | − | 0.103487i | ||||
\(748\) | 60.6969 | 2.21930 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.29796 | + | 35.7928i | 0.120184 | + | 1.30436i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 32.2702 | + | 18.6312i | 1.17210 | + | 0.676715i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.79796 | − | 5.65685i | 0.355176 | − | 0.205061i | −0.311787 | − | 0.950152i | \(-0.600927\pi\) |
0.666962 | + | 0.745091i | \(0.267594\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −16.0000 | − | 22.6274i | −0.577350 | − | 0.816497i | ||||
\(769\) | 11.0000 | + | 19.0526i | 0.396670 | + | 0.687053i | 0.993313 | − | 0.115454i | \(-0.0368323\pi\) |
−0.596643 | + | 0.802507i | \(0.703499\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.7423 | + | 31.6376i | −1.61136 | + | 1.13940i | ||||
\(772\) | 25.6969 | − | 44.5084i | 0.924853 | − | 1.60189i | ||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | −7.57321 | + | 6.47472i | −0.272214 | + | 0.232729i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 48.2474 | + | 27.8557i | 1.73198 | + | 0.999961i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.33087 | − | 1.92308i | 0.119341 | − | 0.0689014i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 34.4949 | − | 3.17837i | 1.23039 | − | 0.113369i | ||||
\(787\) | −25.0000 | − | 43.3013i | −0.891154 | − | 1.54352i | −0.838494 | − | 0.544911i | \(-0.816563\pi\) |
−0.0526599 | − | 0.998613i | \(-0.516770\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.6969 | + | 30.2555i | −0.380099 | + | 1.07508i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | − | 28.2843i | − | 1.00000i | ||||||
\(801\) | −3.10102 | − | 16.6848i | −0.109569 | − | 0.589530i | ||||
\(802\) | −35.3485 | −1.24820 | ||||||||
\(803\) | −44.8610 | − | 25.9005i | −1.58311 | − | 0.914009i | ||||
\(804\) | −20.7980 | + | 45.1441i | −0.733487 | + | 1.59211i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.4804i | 1.17711i | 0.808458 | + | 0.588555i | \(0.200303\pi\) | ||||
−0.808458 | + | 0.588555i | \(0.799697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.7423 | 0.623018 | 0.311509 | − | 0.950243i | \(-0.399166\pi\) | ||||
0.311509 | + | 0.950243i | \(0.399166\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −50.4949 | − | 23.2631i | −1.76767 | − | 0.814371i | ||||
\(817\) | −9.80306 | + | 16.9794i | −0.342966 | + | 0.594034i | ||||
\(818\) | − | 26.0129i | − | 0.909519i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(822\) | 23.3485 | + | 33.0197i | 0.814371 | + | 1.15170i | ||||
\(823\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −26.7423 | + | 18.9097i | −0.931049 | + | 0.658351i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.7990i | 0.688478i | 0.938882 | + | 0.344239i | \(0.111863\pi\) | ||||
−0.938882 | + | 0.344239i | \(0.888137\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 48.6464 | − | 28.0860i | 1.68550 | − | 0.973123i | ||||
\(834\) | 0.820663 | + | 8.90666i | 0.0284172 | + | 0.308412i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 63.1468i | 2.18398i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −52.0000 | −1.79631 | ||||||||
\(839\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.5000 | + | 25.1147i | 0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −44.4949 | − | 20.4989i | −1.53249 | − | 0.706019i | ||||
\(844\) | 14.0000 | − | 24.2487i | 0.481900 | − | 0.834675i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.0000 | + | 31.1127i | 0.755038 | + | 1.06779i | ||||
\(850\) | −28.3712 | − | 49.1403i | −0.973123 | − | 1.68550i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.3031 | −0.454689 | ||||||||
\(857\) | 19.5959 | + | 11.3137i | 0.669384 | + | 0.386469i | 0.795843 | − | 0.605503i | \(-0.207028\pi\) |
−0.126459 | + | 0.991972i | \(0.540361\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.8258 | − | 18.7508i | −0.369370 | − | 0.639768i | 0.620097 | − | 0.784525i | \(-0.287093\pi\) |
−0.989467 | + | 0.144757i | \(0.953760\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 20.4949 | − | 21.0703i | 0.697251 | − | 0.716827i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.27015 | + | 3.04272i | 0.179087 | + | 0.103396i | ||||
\(867\) | −81.7423 | + | 7.53177i | −2.77612 | + | 0.255792i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.6969 | + | 55.7114i | −0.666640 | + | 1.88554i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 27.3939 | + | 38.7408i | 0.925553 | + | 1.30893i | ||||
\(877\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 56.5685i | − | 1.90584i | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||
0.303218 | − | 0.952921i | \(-0.401939\pi\) | |||||||
\(882\) | 5.42679 | + | 29.1985i | 0.182729 | + | 0.983163i | ||||
\(883\) | −52.4393 | −1.76472 | −0.882361 | − | 0.470573i | \(-0.844047\pi\) | ||||
−0.882361 | + | 0.470573i | \(0.844047\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.7196 | + | 42.8157i | 0.830473 | + | 1.43842i | ||||
\(887\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.6237 | − | 5.29085i | −1.12644 | − | 0.177250i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 27.7196 | − | 48.0118i | 0.925016 | − | 1.60218i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 29.4949 | − | 5.48188i | 0.983163 | − | 0.182729i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −2.13393 | − | 1.23202i | −0.0710521 | − | 0.0410219i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.0000 | − | 27.7128i | −0.532152 | − | 0.921714i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.2196 | − | 40.2176i | 0.770996 | − | 1.33540i | −0.166022 | − | 0.986122i | \(-0.553092\pi\) |
0.937018 | − | 0.349281i | \(-0.113574\pi\) | |||||||
\(908\) | 54.7900i | 1.81827i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(912\) | 24.2020 | − | 52.5330i | 0.801410 | − | 1.73954i | ||||
\(913\) | 5.34847 | + | 9.26382i | 0.177008 | + | 0.306588i | ||||
\(914\) | −51.9217 | + | 29.9770i | −1.71742 | + | 0.991551i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 14.4722 | − | 57.1649i | 0.477654 | − | 1.88672i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.6464 | − | 1.53381i | 0.548518 | − | 0.0505407i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.4949 | − | 14.1421i | −0.803652 | − | 0.463988i | 0.0410949 | − | 0.999155i | \(-0.486915\pi\) |
−0.844746 | + | 0.535167i | \(0.820249\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.2196 | + | 50.6099i | 0.957635 | + | 1.65867i | ||||
\(932\) | 40.1010 | − | 23.1523i | 1.31355 | − | 0.758380i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.37117 | + | 12.7672i | −0.241192 | + | 0.417757i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.6793 | − | 38.3748i | 0.576943 | − | 1.25231i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 49.0689i | 1.59706i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.5607 | 0.408384 | ||||||||
\(947\) | 45.7702 | + | 26.4254i | 1.48733 | + | 0.858710i | 0.999896 | − | 0.0144491i | \(-0.00459946\pi\) |
0.487435 | + | 0.873160i | \(0.337933\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 51.1237 | − | 29.5163i | 1.65867 | − | 0.957635i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.7456i | 0.445265i | 0.974902 | + | 0.222633i | \(0.0714650\pi\) | ||||
−0.974902 | + | 0.222633i | \(0.928535\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.5000 | + | 26.8468i | −0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.57832 | − | 13.8725i | −0.0830851 | − | 0.447034i | ||||
\(964\) | −3.39388 | −0.109309 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(968\) | 8.09082 | − | 4.67123i | 0.260049 | − | 0.150139i | ||||
\(969\) | −10.6464 | − | 115.546i | −0.342013 | − | 3.71186i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 31.1127i | − | 0.998454i | −0.866471 | − | 0.499227i | \(-0.833617\pi\) | ||
0.866471 | − | 0.499227i | \(-0.166383\pi\) | |||||||
\(972\) | 25.9444 | + | 17.2884i | 0.832167 | + | 0.554526i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.4444 | + | 12.9583i | −0.718060 | + | 0.414572i | −0.814038 | − | 0.580812i | \(-0.802735\pi\) |
0.0959785 | + | 0.995383i | \(0.469402\pi\) | |||||||
\(978\) | −4.44949 | − | 2.04989i | −0.142279 | − | 0.0655482i | ||||
\(979\) | −10.6969 | + | 18.5276i | −0.341876 | + | 0.592146i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −61.4393 | −1.96061 | ||||||||
\(983\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(984\) | 1.30306 | + | 1.84281i | 0.0415401 | + | 0.0587466i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.8434 | + | 40.9014i | −0.597976 | + | 1.29797i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.898979 | − | 9.75663i | −0.0284853 | − | 0.309151i | ||||
\(997\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(998\) | 42.0620i | 1.33145i | ||||||||
\(999\) | 0 | 0 |
(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 | 72.2.l.a.11.1 | ✓ | 4 | |
3.2 | odd | 2 | 216.2.l.a.35.2 | 4 | |||
4.3 | odd | 2 | 288.2.p.a.47.1 | 4 | |||
8.3 | odd | 2 | CM | 72.2.l.a.11.1 | ✓ | 4 | |
8.5 | even | 2 | 288.2.p.a.47.1 | 4 | |||
9.2 | odd | 6 | 648.2.f.a.323.1 | 4 | |||
9.4 | even | 3 | 216.2.l.a.179.2 | 4 | |||
9.5 | odd | 6 | inner | 72.2.l.a.59.1 | yes | 4 | |
9.7 | even | 3 | 648.2.f.a.323.4 | 4 | |||
12.11 | even | 2 | 864.2.p.a.143.2 | 4 | |||
24.5 | odd | 2 | 864.2.p.a.143.2 | 4 | |||
24.11 | even | 2 | 216.2.l.a.35.2 | 4 | |||
36.7 | odd | 6 | 2592.2.f.a.1295.2 | 4 | |||
36.11 | even | 6 | 2592.2.f.a.1295.3 | 4 | |||
36.23 | even | 6 | 288.2.p.a.239.1 | 4 | |||
36.31 | odd | 6 | 864.2.p.a.719.2 | 4 | |||
72.5 | odd | 6 | 288.2.p.a.239.1 | 4 | |||
72.11 | even | 6 | 648.2.f.a.323.1 | 4 | |||
72.13 | even | 6 | 864.2.p.a.719.2 | 4 | |||
72.29 | odd | 6 | 2592.2.f.a.1295.3 | 4 | |||
72.43 | odd | 6 | 648.2.f.a.323.4 | 4 | |||
72.59 | even | 6 | inner | 72.2.l.a.59.1 | yes | 4 | |
72.61 | even | 6 | 2592.2.f.a.1295.2 | 4 | |||
72.67 | odd | 6 | 216.2.l.a.179.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.l.a.11.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
72.2.l.a.11.1 | ✓ | 4 | 8.3 | odd | 2 | CM | |
72.2.l.a.59.1 | yes | 4 | 9.5 | odd | 6 | inner | |
72.2.l.a.59.1 | yes | 4 | 72.59 | even | 6 | inner | |
216.2.l.a.35.2 | 4 | 3.2 | odd | 2 | |||
216.2.l.a.35.2 | 4 | 24.11 | even | 2 | |||
216.2.l.a.179.2 | 4 | 9.4 | even | 3 | |||
216.2.l.a.179.2 | 4 | 72.67 | odd | 6 | |||
288.2.p.a.47.1 | 4 | 4.3 | odd | 2 | |||
288.2.p.a.47.1 | 4 | 8.5 | even | 2 | |||
288.2.p.a.239.1 | 4 | 36.23 | even | 6 | |||
288.2.p.a.239.1 | 4 | 72.5 | odd | 6 | |||
648.2.f.a.323.1 | 4 | 9.2 | odd | 6 | |||
648.2.f.a.323.1 | 4 | 72.11 | even | 6 | |||
648.2.f.a.323.4 | 4 | 9.7 | even | 3 | |||
648.2.f.a.323.4 | 4 | 72.43 | odd | 6 | |||
864.2.p.a.143.2 | 4 | 12.11 | even | 2 | |||
864.2.p.a.143.2 | 4 | 24.5 | odd | 2 | |||
864.2.p.a.719.2 | 4 | 36.31 | odd | 6 | |||
864.2.p.a.719.2 | 4 | 72.13 | even | 6 | |||
2592.2.f.a.1295.2 | 4 | 36.7 | odd | 6 | |||
2592.2.f.a.1295.2 | 4 | 72.61 | even | 6 | |||
2592.2.f.a.1295.3 | 4 | 36.11 | even | 6 | |||
2592.2.f.a.1295.3 | 4 | 72.29 | odd | 6 |