Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (of order \(4\), 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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3599.11 | ||
Character | \(\chi\) | \(=\) | 4032.3599 |
Dual form | 4032.2.v.e.1583.11 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.0893433 | − | 0.0893433i | 0.0399555 | − | 0.0399555i | −0.686847 | − | 0.726802i | \(-0.741006\pi\) |
0.726802 | + | 0.686847i | \(0.241006\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.42480 | + | 2.42480i | 0.731106 | + | 0.731106i | 0.970839 | − | 0.239733i | \(-0.0770600\pi\) |
−0.239733 | + | 0.970839i | \(0.577060\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.86569 | + | 3.86569i | −1.07215 | + | 1.07215i | −0.0749629 | + | 0.997186i | \(0.523884\pi\) |
−0.997186 | + | 0.0749629i | \(0.976116\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.794810i | 0.192770i | 0.995344 | + | 0.0963848i | \(0.0307280\pi\) | ||||
−0.995344 | + | 0.0963848i | \(0.969272\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.65233 | + | 2.65233i | 0.608485 | + | 0.608485i | 0.942550 | − | 0.334065i | \(-0.108420\pi\) |
−0.334065 | + | 0.942550i | \(0.608420\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.92175i | 0.817741i | 0.912592 | + | 0.408871i | \(0.134077\pi\) | ||||
−0.912592 | + | 0.408871i | \(0.865923\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.98404i | 0.996807i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.47818 | − | 7.47818i | −1.38866 | − | 1.38866i | −0.828138 | − | 0.560525i | \(-0.810599\pi\) |
−0.560525 | − | 0.828138i | \(-0.689401\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.55554i | − | 0.997804i | −0.866658 | − | 0.498902i | \(-0.833737\pi\) | ||
0.866658 | − | 0.498902i | \(-0.166263\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0893433 | + | 0.0893433i | −0.0151018 | + | 0.0151018i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.35455 | − | 6.35455i | −1.04468 | − | 1.04468i | −0.998954 | − | 0.0457270i | \(-0.985440\pi\) |
−0.0457270 | − | 0.998954i | \(-0.514560\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.96091 | −1.08711 | −0.543556 | − | 0.839373i | \(-0.682922\pi\) | ||||
−0.543556 | + | 0.839373i | \(0.682922\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.25316 | − | 1.25316i | 0.191105 | − | 0.191105i | −0.605069 | − | 0.796173i | \(-0.706854\pi\) |
0.796173 | + | 0.605069i | \(0.206854\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.48295 | 0.945635 | 0.472818 | − | 0.881160i | \(-0.343237\pi\) | ||||
0.472818 | + | 0.881160i | \(0.343237\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.620687 | − | 0.620687i | 0.0852579 | − | 0.0852579i | −0.663192 | − | 0.748450i | \(-0.730799\pi\) |
0.748450 | + | 0.663192i | \(0.230799\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.433280 | 0.0584234 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.39065 | − | 3.39065i | −0.441425 | − | 0.441425i | 0.451066 | − | 0.892491i | \(-0.351044\pi\) |
−0.892491 | + | 0.451066i | \(0.851044\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.51460 | − | 7.51460i | 0.962146 | − | 0.962146i | −0.0371630 | − | 0.999309i | \(-0.511832\pi\) |
0.999309 | + | 0.0371630i | \(0.0118321\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.690747i | 0.0856766i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.22915 | − | 2.22915i | −0.272334 | − | 0.272334i | 0.557705 | − | 0.830039i | \(-0.311682\pi\) |
−0.830039 | + | 0.557705i | \(0.811682\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.95182i | 0.943707i | 0.881677 | + | 0.471853i | \(0.156415\pi\) | ||||
−0.881677 | + | 0.471853i | \(0.843585\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.9376i | − | 1.51423i | −0.653283 | − | 0.757114i | \(-0.726609\pi\) | ||
0.653283 | − | 0.757114i | \(-0.273391\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.42480 | − | 2.42480i | −0.276332 | − | 0.276332i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 10.1941i | − | 1.14693i | −0.819230 | − | 0.573465i | \(-0.805599\pi\) | ||
0.819230 | − | 0.573465i | \(-0.194401\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.2820 | + | 11.2820i | −1.23836 | + | 1.23836i | −0.277694 | + | 0.960670i | \(0.589570\pi\) |
−0.960670 | + | 0.277694i | \(0.910430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0710109 | + | 0.0710109i | 0.00770221 | + | 0.00770221i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.52785 | −0.585951 | −0.292976 | − | 0.956120i | \(-0.594645\pi\) | ||||
−0.292976 | + | 0.956120i | \(0.594645\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.86569 | − | 3.86569i | 0.405234 | − | 0.405234i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.473935 | 0.0486247 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.33616 | −0.440270 | −0.220135 | − | 0.975469i | \(-0.570650\pi\) | ||||
−0.220135 | + | 0.975469i | \(0.570650\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.66216 | + | 9.66216i | −0.961421 | + | 0.961421i | −0.999283 | − | 0.0378620i | \(-0.987945\pi\) |
0.0378620 | + | 0.999283i | \(0.487945\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.4000 | −1.61594 | −0.807969 | − | 0.589225i | \(-0.799433\pi\) | ||||
−0.807969 | + | 0.589225i | \(0.799433\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.48912 | + | 5.48912i | 0.530653 | + | 0.530653i | 0.920767 | − | 0.390114i | \(-0.127564\pi\) |
−0.390114 | + | 0.920767i | \(0.627564\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.6355 | + | 14.6355i | −1.40183 | + | 1.40183i | −0.607524 | + | 0.794301i | \(0.707837\pi\) |
−0.794301 | + | 0.607524i | \(0.792163\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.28264i | 0.779165i | 0.920992 | + | 0.389582i | \(0.127381\pi\) | ||||
−0.920992 | + | 0.389582i | \(0.872619\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.350382 | + | 0.350382i | 0.0326733 | + | 0.0326733i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.794810i | − | 0.0728601i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.759336i | 0.0690305i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.892006 | + | 0.892006i | 0.0797835 | + | 0.0797835i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.39522i | − | 0.301277i | −0.988589 | − | 0.150638i | \(-0.951867\pi\) | ||
0.988589 | − | 0.150638i | \(-0.0481329\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.73455 | + | 8.73455i | −0.763141 | + | 0.763141i | −0.976889 | − | 0.213748i | \(-0.931433\pi\) |
0.213748 | + | 0.976889i | \(0.431433\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.65233 | − | 2.65233i | −0.229986 | − | 0.229986i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.84889 | 0.414269 | 0.207134 | − | 0.978313i | \(-0.433586\pi\) | ||||
0.207134 | + | 0.978313i | \(0.433586\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.19464 | − | 2.19464i | 0.186147 | − | 0.186147i | −0.607881 | − | 0.794028i | \(-0.707980\pi\) |
0.794028 | + | 0.607881i | \(0.207980\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.7471 | −1.56771 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.33625 | −0.110969 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.83836 | + | 2.83836i | −0.232528 | + | 0.232528i | −0.813747 | − | 0.581219i | \(-0.802576\pi\) |
0.581219 | + | 0.813747i | \(0.302576\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.9821 | 1.54474 | 0.772370 | − | 0.635172i | \(-0.219071\pi\) | ||||
0.772370 | + | 0.635172i | \(0.219071\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.496350 | − | 0.496350i | −0.0398678 | − | 0.0398678i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.3221 | + | 12.3221i | −0.983412 | + | 0.983412i | −0.999865 | − | 0.0164522i | \(-0.994763\pi\) |
0.0164522 | + | 0.999865i | \(0.494763\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.92175i | − | 0.309077i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.50400 | + | 3.50400i | 0.274454 | + | 0.274454i | 0.830890 | − | 0.556436i | \(-0.187832\pi\) |
−0.556436 | + | 0.830890i | \(0.687832\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 17.4719i | − | 1.35202i | −0.736893 | − | 0.676009i | \(-0.763708\pi\) | ||
0.736893 | − | 0.676009i | \(-0.236292\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 16.8871i | − | 1.29901i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.45528 | + | 1.45528i | 0.110643 | + | 0.110643i | 0.760261 | − | 0.649618i | \(-0.225071\pi\) |
−0.649618 | + | 0.760261i | \(0.725071\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.98404i | − | 0.376758i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.22288 | − | 2.22288i | 0.166146 | − | 0.166146i | −0.619137 | − | 0.785283i | \(-0.712518\pi\) |
0.785283 | + | 0.619137i | \(0.212518\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.13227 | + | 3.13227i | 0.232820 | + | 0.232820i | 0.813869 | − | 0.581049i | \(-0.197358\pi\) |
−0.581049 | + | 0.813869i | \(0.697358\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.13547 | −0.0834816 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.92726 | + | 1.92726i | −0.140935 | + | 0.140935i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.61134 | −0.261308 | −0.130654 | − | 0.991428i | \(-0.541708\pi\) | ||||
−0.130654 | + | 0.991428i | \(0.541708\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.01689 | −0.217160 | −0.108580 | − | 0.994088i | \(-0.534630\pi\) | ||||
−0.108580 | + | 0.994088i | \(0.534630\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.282108 | − | 0.282108i | 0.0200994 | − | 0.0200994i | −0.696986 | − | 0.717085i | \(-0.745476\pi\) |
0.717085 | + | 0.696986i | \(0.245476\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.40015 | −0.241030 | −0.120515 | − | 0.992712i | \(-0.538455\pi\) | ||||
−0.120515 | + | 0.992712i | \(0.538455\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.47818 | + | 7.47818i | 0.524865 | + | 0.524865i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.621911 | + | 0.621911i | −0.0434361 | + | 0.0434361i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.8627i | 0.889734i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.04290 | − | 6.04290i | −0.416010 | − | 0.416010i | 0.467816 | − | 0.883826i | \(-0.345041\pi\) |
−0.883826 | + | 0.467816i | \(0.845041\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 0.223922i | − | 0.0152714i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.55554i | 0.377135i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.07249 | − | 3.07249i | −0.206678 | − | 0.206678i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 22.2108i | − | 1.48734i | −0.668545 | − | 0.743672i | \(-0.733082\pi\) | ||
0.668545 | − | 0.743672i | \(-0.266918\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.1859 | + | 16.1859i | −1.07430 | + | 1.07430i | −0.0772896 | + | 0.997009i | \(0.524627\pi\) |
−0.997009 | + | 0.0772896i | \(0.975373\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.75579 | − | 7.75579i | −0.512517 | − | 0.512517i | 0.402780 | − | 0.915297i | \(-0.368044\pi\) |
−0.915297 | + | 0.402780i | \(0.868044\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.7060 | −1.22547 | −0.612734 | − | 0.790289i | \(-0.709930\pi\) | ||||
−0.612734 | + | 0.790289i | \(0.709930\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.579208 | − | 0.579208i | 0.0377834 | − | 0.0377834i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.3964 | 1.31933 | 0.659667 | − | 0.751558i | \(-0.270697\pi\) | ||||
0.659667 | + | 0.751558i | \(0.270697\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.4808 | 0.675129 | 0.337565 | − | 0.941302i | \(-0.390397\pi\) | ||||
0.337565 | + | 0.941302i | \(0.390397\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.0893433 | − | 0.0893433i | 0.00570793 | − | 0.00570793i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.5061 | −1.30477 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.2508 | − | 22.2508i | −1.40446 | − | 1.40446i | −0.785139 | − | 0.619320i | \(-0.787408\pi\) |
−0.619320 | − | 0.785139i | \(-0.712592\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.50947 | + | 9.50947i | −0.597855 | + | 0.597855i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.3780i | 1.83255i | 0.400547 | + | 0.916276i | \(0.368820\pi\) | ||||
−0.400547 | + | 0.916276i | \(0.631180\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.35455 | + | 6.35455i | 0.394852 | + | 0.394852i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.75090i | 0.539603i | 0.962916 | + | 0.269802i | \(0.0869582\pi\) | ||||
−0.962916 | + | 0.269802i | \(0.913042\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.110908i | − | 0.00681305i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.92219 | − | 8.92219i | −0.543996 | − | 0.543996i | 0.380702 | − | 0.924698i | \(-0.375682\pi\) |
−0.924698 | + | 0.380702i | \(0.875682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.36141i | 0.204191i | 0.994775 | + | 0.102096i | \(0.0325548\pi\) | ||||
−0.994775 | + | 0.102096i | \(0.967445\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.0853 | + | 12.0853i | −0.728771 | + | 0.728771i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.516082 | + | 0.516082i | 0.0310083 | + | 0.0310083i | 0.722441 | − | 0.691433i | \(-0.243020\pi\) |
−0.691433 | + | 0.722441i | \(0.743020\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.0206 | 0.776747 | 0.388373 | − | 0.921502i | \(-0.373037\pi\) | ||||
0.388373 | + | 0.921502i | \(0.373037\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.04669 | + | 7.04669i | −0.418882 | + | 0.418882i | −0.884818 | − | 0.465936i | \(-0.845718\pi\) |
0.465936 | + | 0.884818i | \(0.345718\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.96091 | 0.410890 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.3683 | 0.962840 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.61446 | + | 3.61446i | −0.211159 | + | 0.211159i | −0.804760 | − | 0.593601i | \(-0.797706\pi\) |
0.593601 | + | 0.804760i | \(0.297706\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.605864 | −0.0352747 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.1603 | − | 15.1603i | −0.876741 | − | 0.876741i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.25316 | + | 1.25316i | −0.0722308 | + | 0.0722308i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 1.34276i | − | 0.0768861i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.5015 | + | 15.5015i | 0.884715 | + | 0.884715i | 0.994009 | − | 0.109295i | \(-0.0348592\pi\) |
−0.109295 | + | 0.994009i | \(0.534859\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.6216i | 0.999227i | 0.866248 | + | 0.499613i | \(0.166525\pi\) | ||||
−0.866248 | + | 0.499613i | \(0.833475\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 18.5910i | − | 1.05083i | −0.850847 | − | 0.525414i | \(-0.823911\pi\) | ||
0.850847 | − | 0.525414i | \(-0.176089\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.0237 | − | 13.0237i | −0.731486 | − | 0.731486i | 0.239428 | − | 0.970914i | \(-0.423040\pi\) |
−0.970914 | + | 0.239428i | \(0.923040\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 36.2662i | − | 2.03052i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.10810 | + | 2.10810i | −0.117298 | + | 0.117298i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.2667 | − | 19.2667i | −1.06873 | − | 1.06873i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.48295 | −0.357417 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.844531 | − | 0.844531i | 0.0464196 | − | 0.0464196i | −0.683516 | − | 0.729936i | \(-0.739550\pi\) |
0.729936 | + | 0.683516i | \(0.239550\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.398319 | −0.0217625 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.2226 | 1.31949 | 0.659746 | − | 0.751489i | \(-0.270664\pi\) | ||||
0.659746 | + | 0.751489i | \(0.270664\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.4711 | − | 13.4711i | 0.729500 | − | 0.729500i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.75310 | − | 8.75310i | −0.469891 | − | 0.469891i | 0.431988 | − | 0.901879i | \(-0.357812\pi\) |
−0.901879 | + | 0.431988i | \(0.857812\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.87743 | + | 6.87743i | −0.368140 | + | 0.368140i | −0.866799 | − | 0.498658i | \(-0.833826\pi\) |
0.498658 | + | 0.866799i | \(0.333826\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.8780i | 1.21767i | 0.793295 | + | 0.608837i | \(0.208364\pi\) | ||||
−0.793295 | + | 0.608837i | \(0.791636\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.710441 | + | 0.710441i | 0.0377063 | + | 0.0377063i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 8.82162i | − | 0.465587i | −0.972526 | − | 0.232794i | \(-0.925213\pi\) | ||
0.972526 | − | 0.232794i | \(-0.0747867\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 4.93033i | − | 0.259491i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.15588 | − | 1.15588i | −0.0605017 | − | 0.0605017i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 21.0160i | − | 1.09703i | −0.836142 | − | 0.548513i | \(-0.815194\pi\) | ||
0.836142 | − | 0.548513i | \(-0.184806\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.620687 | + | 0.620687i | −0.0322245 | + | 0.0322245i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.3425 | − | 10.3425i | −0.535516 | − | 0.535516i | 0.386693 | − | 0.922209i | \(-0.373617\pi\) |
−0.922209 | + | 0.386693i | \(0.873617\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 57.8166 | 2.97771 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.1353 | + | 16.1353i | −0.828813 | + | 0.828813i | −0.987353 | − | 0.158539i | \(-0.949322\pi\) |
0.158539 | + | 0.987353i | \(0.449322\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.1083 | −0.618704 | −0.309352 | − | 0.950948i | \(-0.600112\pi\) | ||||
−0.309352 | + | 0.950948i | \(0.600112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.433280 | −0.0220820 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.7493 | + | 12.7493i | −0.646414 | + | 0.646414i | −0.952124 | − | 0.305711i | \(-0.901106\pi\) |
0.305711 | + | 0.952124i | \(0.401106\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.11704 | −0.157636 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.910778 | − | 0.910778i | −0.0458262 | − | 0.0458262i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.1299 | − | 16.1299i | 0.809534 | − | 0.809534i | −0.175029 | − | 0.984563i | \(-0.556002\pi\) |
0.984563 | + | 0.175029i | \(0.0560019\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.54744i | − | 0.0772755i | −0.999253 | − | 0.0386378i | \(-0.987698\pi\) | ||
0.999253 | − | 0.0386378i | \(-0.0123018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.4760 | + | 21.4760i | 1.06980 | + | 1.06980i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 30.8170i | − | 1.52754i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.58498i | − | 0.226712i | −0.993554 | − | 0.113356i | \(-0.963840\pi\) | ||
0.993554 | − | 0.113356i | \(-0.0361601\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.39065 | + | 3.39065i | 0.166843 | + | 0.166843i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.01595i | 0.0989589i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.8750 | − | 24.8750i | 1.21523 | − | 1.21523i | 0.245940 | − | 0.969285i | \(-0.420903\pi\) |
0.969285 | − | 0.245940i | \(-0.0790967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.42104 | + | 9.42104i | 0.459153 | + | 0.459153i | 0.898378 | − | 0.439224i | \(-0.144747\pi\) |
−0.439224 | + | 0.898378i | \(0.644747\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.96136 | −0.192154 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.51460 | + | 7.51460i | −0.363657 | + | 0.363657i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.96634 | 0.431893 | 0.215947 | − | 0.976405i | \(-0.430716\pi\) | ||||
0.215947 | + | 0.976405i | \(0.430716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.679368 | 0.0326483 | 0.0163242 | − | 0.999867i | \(-0.494804\pi\) | ||||
0.0163242 | + | 0.999867i | \(0.494804\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.4018 | + | 10.4018i | −0.497584 | + | 0.497584i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.4959 | −1.69413 | −0.847065 | − | 0.531490i | \(-0.821632\pi\) | ||||
−0.847065 | + | 0.531490i | \(0.821632\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.4369 | + | 23.4369i | 1.11352 | + | 1.11352i | 0.992670 | + | 0.120853i | \(0.0385628\pi\) |
0.120853 | + | 0.992670i | \(0.461437\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.493876 | + | 0.493876i | −0.0234120 | + | 0.0234120i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 4.45807i | − | 0.210389i | −0.994452 | − | 0.105195i | \(-0.966453\pi\) | ||
0.994452 | − | 0.105195i | \(-0.0335465\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.8788 | − | 16.8788i | −0.794793 | − | 0.794793i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 0.690747i | − | 0.0323827i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 14.9134i | − | 0.697620i | −0.937193 | − | 0.348810i | \(-0.886586\pi\) | ||
0.937193 | − | 0.348810i | \(-0.113414\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.52217 | + | 7.52217i | 0.350342 | + | 0.350342i | 0.860237 | − | 0.509895i | \(-0.170316\pi\) |
−0.509895 | + | 0.860237i | \(0.670316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.0015i | 1.85903i | 0.368787 | + | 0.929514i | \(0.379773\pi\) | ||||
−0.368787 | + | 0.929514i | \(0.620227\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.9560 | + | 18.9560i | −0.877177 | + | 0.877177i | −0.993242 | − | 0.116064i | \(-0.962972\pi\) |
0.116064 | + | 0.993242i | \(0.462972\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.22915 | + | 2.22915i | 0.102933 | + | 0.102933i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.07732 | 0.279435 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.2193 | + | 13.2193i | −0.606543 | + | 0.606543i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.3112 | 0.973733 | 0.486866 | − | 0.873476i | \(-0.338140\pi\) | ||||
0.486866 | + | 0.873476i | \(0.338140\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 49.1294 | 2.24011 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.387407 | + | 0.387407i | −0.0175912 | + | 0.0175912i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.6167 | −0.617031 | −0.308515 | − | 0.951219i | \(-0.599832\pi\) | ||||
−0.308515 | + | 0.951219i | \(0.599832\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.18965 | − | 5.18965i | −0.234206 | − | 0.234206i | 0.580240 | − | 0.814446i | \(-0.302959\pi\) |
−0.814446 | + | 0.580240i | \(0.802959\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.94373 | − | 5.94373i | 0.267692 | − | 0.267692i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 7.95182i | − | 0.356688i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.15618 | + | 7.15618i | 0.320355 | + | 0.320355i | 0.848903 | − | 0.528548i | \(-0.177264\pi\) |
−0.528548 | + | 0.848903i | \(0.677264\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.5554i | 1.49616i | 0.663607 | + | 0.748081i | \(0.269025\pi\) | ||||
−0.663607 | + | 0.748081i | \(0.730975\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.72650i | 0.0768282i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.615168 | − | 0.615168i | −0.0272669 | − | 0.0272669i | 0.693342 | − | 0.720609i | \(-0.256138\pi\) |
−0.720609 | + | 0.693342i | \(0.756138\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.9376i | 0.572324i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.46523 | + | 1.46523i | −0.0645656 | + | 0.0645656i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.7199 | + | 15.7199i | 0.691359 | + | 0.691359i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.91593 | −0.259182 | −0.129591 | − | 0.991568i | \(-0.541366\pi\) | ||||
−0.129591 | + | 0.991568i | \(0.541366\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.7110 | + | 17.7110i | −0.774449 | + | 0.774449i | −0.978881 | − | 0.204432i | \(-0.934465\pi\) |
0.204432 | + | 0.978881i | \(0.434465\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.41560 | 0.192346 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.61988 | 0.331299 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.9087 | − | 26.9087i | 1.16555 | − | 1.16555i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.980831 | 0.0424050 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.42480 | + | 2.42480i | 0.104444 | + | 0.104444i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.13769 | + | 9.13769i | −0.392860 | + | 0.392860i | −0.875706 | − | 0.482846i | \(-0.839603\pi\) |
0.482846 | + | 0.875706i | \(0.339603\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.61516i | 0.112021i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.1099 | + | 30.1099i | 1.28741 | + | 1.28741i | 0.936356 | + | 0.351052i | \(0.114176\pi\) |
0.351052 | + | 0.936356i | \(0.385824\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 39.6691i | − | 1.68996i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.1941i | 0.433499i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.3306 | − | 16.3306i | −0.691950 | − | 0.691950i | 0.270711 | − | 0.962661i | \(-0.412741\pi\) |
−0.962661 | + | 0.270711i | \(0.912741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.68863i | 0.409785i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.288759 | + | 0.288759i | −0.0121697 | + | 0.0121697i | −0.713165 | − | 0.700996i | \(-0.752739\pi\) |
0.700996 | + | 0.713165i | \(0.252739\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.739998 | + | 0.739998i | 0.0311319 | + | 0.0311319i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.8386 | −0.999365 | −0.499683 | − | 0.866209i | \(-0.666550\pi\) | ||||
−0.499683 | + | 0.866209i | \(0.666550\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.86113 | + | 1.86113i | −0.0778857 | + | 0.0778857i | −0.744976 | − | 0.667091i | \(-0.767539\pi\) |
0.667091 | + | 0.744976i | \(0.267539\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.5461 | −0.815130 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.0148 | −1.33279 | −0.666396 | − | 0.745598i | \(-0.732164\pi\) | ||||
−0.666396 | + | 0.745598i | \(0.732164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.2820 | − | 11.2820i | 0.468057 | − | 0.468057i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.01009 | 0.124665 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.73084 | + | 1.73084i | 0.0714394 | + | 0.0714394i | 0.741924 | − | 0.670484i | \(-0.233914\pi\) |
−0.670484 | + | 0.741924i | \(0.733914\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.7351 | − | 14.7351i | 0.607149 | − | 0.607149i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.8985i | 0.940328i | 0.882579 | + | 0.470164i | \(0.155805\pi\) | ||||
−0.882579 | + | 0.470164i | \(0.844195\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0710109 | − | 0.0710109i | −0.00291116 | − | 0.00291116i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 26.0002i | − | 1.06234i | −0.847266 | − | 0.531169i | \(-0.821753\pi\) | ||
0.847266 | − | 0.531169i | \(-0.178247\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 21.0502i | − | 0.858654i | −0.903149 | − | 0.429327i | \(-0.858751\pi\) | ||
0.903149 | − | 0.429327i | \(-0.141249\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.0678415 | + | 0.0678415i | 0.00275815 | + | 0.00275815i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.7336i | 1.32861i | 0.747460 | + | 0.664307i | \(0.231273\pi\) | ||||
−0.747460 | + | 0.664307i | \(0.768727\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.0611 | + | 25.0611i | −1.01386 | + | 1.01386i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.14939 | + | 7.14939i | 0.288761 | + | 0.288761i | 0.836590 | − | 0.547829i | \(-0.184546\pi\) |
−0.547829 | + | 0.836590i | \(0.684546\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.8667 | −0.638769 | −0.319384 | − | 0.947625i | \(-0.603476\pi\) | ||||
−0.319384 | + | 0.947625i | \(0.603476\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.4351 | − | 20.4351i | 0.821355 | − | 0.821355i | −0.164947 | − | 0.986302i | \(-0.552745\pi\) |
0.986302 | + | 0.164947i | \(0.0527453\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.52785 | 0.221469 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.7608 | −0.990432 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.05066 | − | 5.05066i | 0.201383 | − | 0.201383i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.1876 | −1.56003 | −0.780017 | − | 0.625758i | \(-0.784790\pi\) | ||||
−0.780017 | + | 0.625758i | \(0.784790\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.303340 | − | 0.303340i | −0.0120377 | − | 0.0120377i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.86569 | + | 3.86569i | −0.153164 | + | 0.153164i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 32.1293i | − | 1.26903i | −0.772911 | − | 0.634515i | \(-0.781200\pi\) | ||
0.772911 | − | 0.634515i | \(-0.218800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.7452 | − | 13.7452i | −0.542059 | − | 0.542059i | 0.382073 | − | 0.924132i | \(-0.375210\pi\) |
−0.924132 | + | 0.382073i | \(0.875210\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.78120i | 0.227282i | 0.993522 | + | 0.113641i | \(0.0362514\pi\) | ||||
−0.993522 | + | 0.113641i | \(0.963749\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 16.4433i | − | 0.645457i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.9854 | − | 13.9854i | −0.547293 | − | 0.547293i | 0.378364 | − | 0.925657i | \(-0.376487\pi\) |
−0.925657 | + | 0.378364i | \(0.876487\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.56075i | 0.0609834i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.6810 | − | 19.6810i | 0.766661 | − | 0.766661i | −0.210856 | − | 0.977517i | \(-0.567625\pi\) |
0.977517 | + | 0.210856i | \(0.0676251\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.7655 | + | 12.7655i | 0.496519 | + | 0.496519i | 0.910353 | − | 0.413833i | \(-0.135810\pi\) |
−0.413833 | + | 0.910353i | \(0.635810\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.473935 | −0.0183784 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.3275 | − | 29.3275i | 1.13557 | − | 1.13557i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.4429 | 1.40686 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.7910 | 1.68802 | 0.844010 | − | 0.536328i | \(-0.180189\pi\) | ||||
0.844010 | + | 0.536328i | \(0.180189\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.0415 | + | 25.0415i | −0.962422 | + | 0.962422i | −0.999319 | − | 0.0368968i | \(-0.988253\pi\) |
0.0368968 | + | 0.999319i | \(0.488253\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.33616 | 0.166407 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.6770 | + | 12.6770i | 0.485071 | + | 0.485071i | 0.906747 | − | 0.421676i | \(-0.138558\pi\) |
−0.421676 | + | 0.906747i | \(0.638558\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.433216 | − | 0.433216i | 0.0165523 | − | 0.0165523i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.79877i | 0.182818i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.5147 | − | 11.5147i | −0.438041 | − | 0.438041i | 0.453312 | − | 0.891352i | \(-0.350243\pi\) |
−0.891352 | + | 0.453312i | \(0.850243\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 0.392153i | − | 0.0148752i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 5.53260i | − | 0.209562i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.5725 | + | 24.5725i | 0.928089 | + | 0.928089i | 0.997582 | − | 0.0694930i | \(-0.0221382\pi\) |
−0.0694930 | + | 0.997582i | \(0.522138\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 33.7087i | − | 1.27135i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.66216 | − | 9.66216i | 0.363383 | − | 0.363383i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.9488 | − | 11.9488i | −0.448745 | − | 0.448745i | 0.446192 | − | 0.894937i | \(-0.352780\pi\) |
−0.894937 | + | 0.446192i | \(0.852780\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.7874 | 0.815946 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.67492 | + | 1.67492i | −0.0626386 | + | 0.0626386i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.8496 | −0.777559 | −0.388779 | − | 0.921331i | \(-0.627103\pi\) | ||||
−0.388779 | + | 0.921331i | \(0.627103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.4000 | 0.610767 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 37.2715 | − | 37.2715i | 1.38423 | − | 1.38423i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.4099 | 1.83251 | 0.916257 | − | 0.400592i | \(-0.131195\pi\) | ||||
0.916257 | + | 0.400592i | \(0.131195\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.996021 | + | 0.996021i | 0.0368392 | + | 0.0368392i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.8419 | + | 22.8419i | −0.843686 | + | 0.843686i | −0.989336 | − | 0.145650i | \(-0.953473\pi\) |
0.145650 | + | 0.989336i | \(0.453473\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 10.8105i | − | 0.398210i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.95695 | + | 3.95695i | 0.145559 | + | 0.145559i | 0.776131 | − | 0.630572i | \(-0.217180\pi\) |
−0.630572 | + | 0.776131i | \(0.717180\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.72532i | − | 0.0632958i | −0.999499 | − | 0.0316479i | \(-0.989924\pi\) | ||
0.999499 | − | 0.0316479i | \(-0.0100755\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.507177i | 0.0185815i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.48912 | − | 5.48912i | −0.200568 | − | 0.200568i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 28.0700i | − | 1.02429i | −0.858900 | − | 0.512144i | \(-0.828852\pi\) | ||
0.858900 | − | 0.512144i | \(-0.171148\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.69592 | − | 1.69592i | 0.0617209 | − | 0.0617209i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.3781 | − | 21.3781i | −0.777001 | − | 0.777001i | 0.202319 | − | 0.979320i | \(-0.435152\pi\) |
−0.979320 | + | 0.202319i | \(0.935152\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.0483 | 0.618001 | 0.309001 | − | 0.951062i | \(-0.400005\pi\) | ||||
0.309001 | + | 0.951062i | \(0.400005\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.6355 | − | 14.6355i | 0.529840 | − | 0.529840i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.2144 | 0.946547 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.6693 | 0.637172 | 0.318586 | − | 0.947894i | \(-0.396792\pi\) | ||||
0.318586 | + | 0.947894i | \(0.396792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.41723 | + | 3.41723i | −0.122909 | + | 0.122909i | −0.765886 | − | 0.642977i | \(-0.777699\pi\) |
0.642977 | + | 0.765886i | \(0.277699\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.6890 | 0.994618 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.4626 | − | 18.4626i | −0.661492 | − | 0.661492i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.2816 | + | 19.2816i | −0.689949 | + | 0.689949i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.20180i | 0.0785855i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.5567 | + | 16.5567i | 0.590183 | + | 0.590183i | 0.937681 | − | 0.347498i | \(-0.112969\pi\) |
−0.347498 | + | 0.937681i | \(0.612969\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 8.28264i | − | 0.294497i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 58.0982i | 2.06313i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.4377 | + | 15.4377i | 0.546833 | + | 0.546833i | 0.925523 | − | 0.378691i | \(-0.123626\pi\) |
−0.378691 | + | 0.925523i | \(0.623626\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.15271i | 0.182290i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.3710 | − | 31.3710i | 1.10706 | − | 1.10706i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.350382 | − | 0.350382i | −0.0123493 | − | 0.0123493i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.9730 | 1.75696 | 0.878478 | − | 0.477782i | \(-0.158559\pi\) | ||||
0.878478 | + | 0.477782i | \(0.158559\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.3832 | + | 34.3832i | −1.20736 | + | 1.20736i | −0.235477 | + | 0.971880i | \(0.575665\pi\) |
−0.971880 | + | 0.235477i | \(0.924335\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.626117 | 0.0219319 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.64756 | 0.232569 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.59874 | + | 1.59874i | −0.0557963 | + | 0.0557963i | −0.734454 | − | 0.678658i | \(-0.762562\pi\) |
0.678658 | + | 0.734454i | \(0.262562\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.9226 | 1.32190 | 0.660949 | − | 0.750431i | \(-0.270154\pi\) | ||||
0.660949 | + | 0.750431i | \(0.270154\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.5300 | + | 34.5300i | 1.20073 | + | 1.20073i | 0.973946 | + | 0.226779i | \(0.0728196\pi\) |
0.226779 | + | 0.973946i | \(0.427180\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.0890 | + | 16.0890i | −0.558795 | + | 0.558795i | −0.928964 | − | 0.370169i | \(-0.879300\pi\) |
0.370169 | + | 0.928964i | \(0.379300\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.794810i | 0.0275385i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.56100 | − | 1.56100i | −0.0540206 | − | 0.0540206i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 27.2955i | − | 0.942344i | −0.882041 | − | 0.471172i | \(-0.843831\pi\) | ||
0.882041 | − | 0.471172i | \(-0.156169\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 82.8462i | 2.85677i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.50875 | − | 1.50875i | −0.0519025 | − | 0.0519025i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 0.759336i | − | 0.0260911i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.9209 | − | 24.9209i | 0.854279 | − | 0.854279i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.1407 | + | 18.1407i | 0.621125 | + | 0.621125i | 0.945819 | − | 0.324694i | \(-0.105261\pi\) |
−0.324694 | + | 0.945819i | \(0.605261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43.2364 | −1.47693 | −0.738464 | − | 0.674293i | \(-0.764449\pi\) | ||||
−0.738464 | + | 0.674293i | \(0.764449\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.72658 | + | 5.72658i | −0.195388 | + | 0.195388i | −0.798020 | − | 0.602631i | \(-0.794119\pi\) |
0.602631 | + | 0.798020i | \(0.294119\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.7413 | 0.740082 | 0.370041 | − | 0.929015i | \(-0.379344\pi\) | ||||
0.370041 | + | 0.929015i | \(0.379344\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.260040 | 0.00884162 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.7188 | − | 24.7188i | 0.838527 | − | 0.838527i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.2344 | 0.583966 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.892006 | − | 0.892006i | −0.0301553 | − | 0.0301553i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.9822 | + | 23.9822i | −0.809822 | + | 0.809822i | −0.984607 | − | 0.174785i | \(-0.944077\pi\) |
0.174785 | + | 0.984607i | \(0.444077\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 35.2047i | − | 1.18608i | −0.805175 | − | 0.593038i | \(-0.797929\pi\) | ||
0.805175 | − | 0.593038i | \(-0.202071\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0728 | + | 29.0728i | 0.978377 | + | 0.978377i | 0.999771 | − | 0.0213942i | \(-0.00681049\pi\) |
−0.0213942 | + | 0.999771i | \(0.506810\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.4222i | 0.887172i | 0.896232 | + | 0.443586i | \(0.146294\pi\) | ||||
−0.896232 | + | 0.443586i | \(0.853706\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.39522i | 0.113872i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.1949 | + | 17.1949i | 0.575405 | + | 0.575405i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 0.397198i | − | 0.0132769i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.5453 | + | 41.5453i | −1.38561 | + | 1.38561i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.493328 | + | 0.493328i | 0.0164351 | + | 0.0164351i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.559694 | 0.0186049 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.8359 | − | 13.8359i | 0.459413 | − | 0.459413i | −0.439050 | − | 0.898463i | \(-0.644685\pi\) |
0.898463 | + | 0.439050i | \(0.144685\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.8417 | 1.08809 | 0.544047 | − | 0.839055i | \(-0.316891\pi\) | ||||
0.544047 | + | 0.839055i | \(0.316891\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.7134 | −1.81075 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.73455 | − | 8.73455i | 0.288440 | − | 0.288440i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.13244 | −0.0373559 | −0.0186779 | − | 0.999826i | \(-0.505946\pi\) | ||||
−0.0186779 | + | 0.999826i | \(0.505946\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.7393 | − | 30.7393i | −1.01179 | − | 1.01179i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31.6713 | − | 31.6713i | 1.04135 | − | 1.04135i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 47.3464i | − | 1.55338i | −0.629880 | − | 0.776692i | \(-0.716896\pi\) | ||
0.629880 | − | 0.776692i | \(-0.283104\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.65233 | + | 2.65233i | 0.0869265 | + | 0.0869265i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.344375i | 0.0112623i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 52.0425i | − | 1.70015i | −0.526658 | − | 0.850077i | \(-0.676555\pi\) | ||
0.526658 | − | 0.850077i | \(-0.323445\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.8877 | − | 21.8877i | −0.713520 | − | 0.713520i | 0.253750 | − | 0.967270i | \(-0.418336\pi\) |
−0.967270 | + | 0.253750i | \(0.918336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 27.2989i | − | 0.888976i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.2385 | − | 27.2385i | 0.885132 | − | 0.885132i | −0.108919 | − | 0.994051i | \(-0.534739\pi\) |
0.994051 | + | 0.108919i | \(0.0347389\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.0126 | + | 50.0126i | 1.62348 | + | 1.62348i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.7540 | 1.32015 | 0.660076 | − | 0.751199i | \(-0.270524\pi\) | ||||
0.660076 | + | 0.751199i | \(0.270524\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.322649 | + | 0.322649i | −0.0104407 | + | 0.0104407i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.84889 | −0.156579 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.135984 | 0.00438657 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.269538 | + | 0.269538i | −0.00867675 | + | 0.00867675i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.9910 | −0.932287 | −0.466143 | − | 0.884709i | \(-0.654357\pi\) | ||||
−0.466143 | + | 0.884709i | \(0.654357\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.5270 | + | 16.5270i | 0.530377 | + | 0.530377i | 0.920685 | − | 0.390308i | \(-0.127631\pi\) |
−0.390308 | + | 0.920685i | \(0.627631\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.19464 | + | 2.19464i | −0.0703569 | + | 0.0703569i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.6420i | 1.01232i | 0.862440 | + | 0.506159i | \(0.168935\pi\) | ||||
−0.862440 | + | 0.506159i | \(0.831065\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.4040 | − | 13.4040i | −0.428392 | − | 0.428392i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.2993i | 0.360390i | 0.983631 | + | 0.180195i | \(0.0576729\pi\) | ||||
−0.983631 | + | 0.180195i | \(0.942327\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 0.0504089i | − | 0.00160616i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.91457 | + | 4.91457i | 0.156274 | + | 0.156274i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.9518i | 0.951451i | 0.879594 | + | 0.475725i | \(0.157814\pi\) | ||||
−0.879594 | + | 0.475725i | \(0.842186\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.303780 | + | 0.303780i | −0.00963048 | + | 0.00963048i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.9968 | − | 11.9968i | −0.379941 | − | 0.379941i | 0.491139 | − | 0.871081i | \(-0.336581\pi\) |
−0.871081 | + | 0.491139i | \(0.836581\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 4032.2.v.e.3599.11 | 40 | ||
3.2 | odd | 2 | inner | 4032.2.v.e.3599.10 | 40 | ||
4.3 | odd | 2 | 1008.2.v.e.827.10 | yes | 40 | ||
12.11 | even | 2 | 1008.2.v.e.827.11 | yes | 40 | ||
16.3 | odd | 4 | inner | 4032.2.v.e.1583.10 | 40 | ||
16.13 | even | 4 | 1008.2.v.e.323.11 | yes | 40 | ||
48.29 | odd | 4 | 1008.2.v.e.323.10 | ✓ | 40 | ||
48.35 | even | 4 | inner | 4032.2.v.e.1583.11 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.e.323.10 | ✓ | 40 | 48.29 | odd | 4 | ||
1008.2.v.e.323.11 | yes | 40 | 16.13 | even | 4 | ||
1008.2.v.e.827.10 | yes | 40 | 4.3 | odd | 2 | ||
1008.2.v.e.827.11 | yes | 40 | 12.11 | even | 2 | ||
4032.2.v.e.1583.10 | 40 | 16.3 | odd | 4 | inner | ||
4032.2.v.e.1583.11 | 40 | 48.35 | even | 4 | inner | ||
4032.2.v.e.3599.10 | 40 | 3.2 | odd | 2 | inner | ||
4032.2.v.e.3599.11 | 40 | 1.1 | even | 1 | trivial |