Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3900,2,Mod(901,3900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3900.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3900.cd (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: | \(31.1416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 26x^{10} + 239x^{8} + 924x^{6} + 1407x^{4} + 538x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 780) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.2 | ||
Root | \(3.11341i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3900.901 |
Dual form | 3900.2.cd.o.2701.2 |
$q$-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 \(\left(\mathbb{Z}/3900\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1951\) | \(3277\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.43544 | + | 0.828751i | −0.542545 | + | 0.313238i | −0.746110 | − | 0.665823i | \(-0.768081\pi\) |
0.203565 | + | 0.979061i | \(0.434747\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.23601 | + | 3.02301i | 1.57872 | + | 0.911472i | 0.995039 | + | 0.0994860i | \(0.0317199\pi\) |
0.583677 | + | 0.811986i | \(0.301613\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.95768 | + | 2.06206i | −0.820314 | + | 0.571913i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.573383 | − | 0.993129i | −0.139066 | − | 0.240869i | 0.788077 | − | 0.615576i | \(-0.211077\pi\) |
−0.927143 | + | 0.374707i | \(0.877743\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.97958 | + | 1.14291i | −0.454146 | + | 0.262201i | −0.709580 | − | 0.704625i | \(-0.751115\pi\) |
0.255433 | + | 0.966827i | \(0.417782\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.65750i | 0.361697i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.87395 | − | 6.70988i | 0.807775 | − | 1.39911i | −0.106627 | − | 0.994299i | \(-0.534005\pi\) |
0.914402 | − | 0.404808i | \(-0.132662\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.60753 | + | 6.24842i | −0.669901 | + | 1.16030i | 0.308031 | + | 0.951376i | \(0.400330\pi\) |
−0.977931 | + | 0.208926i | \(0.933003\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.26033i | − | 0.765178i | −0.923919 | − | 0.382589i | \(-0.875033\pi\) | ||
0.923919 | − | 0.382589i | \(-0.124967\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.23601 | − | 3.02301i | 0.911472 | − | 0.526239i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.74387 | − | 1.58417i | −0.451089 | − | 0.260436i | 0.257201 | − | 0.966358i | \(-0.417200\pi\) |
−0.708290 | + | 0.705922i | \(0.750533\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.306957 | + | 3.59246i | 0.0491524 | + | 0.575254i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.30618 | + | 5.37292i | 1.45338 | + | 0.839110i | 0.998671 | − | 0.0515301i | \(-0.0164098\pi\) |
0.454709 | + | 0.890640i | \(0.349743\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.23357 | + | 2.13661i | 0.188118 | + | 0.325830i | 0.944623 | − | 0.328158i | \(-0.106428\pi\) |
−0.756505 | + | 0.653988i | \(0.773095\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.5431i | 1.53787i | 0.639326 | + | 0.768935i | \(0.279213\pi\) | ||||
−0.639326 | + | 0.768935i | \(0.720787\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.12634 | + | 3.68294i | −0.303763 | + | 0.526134i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.14677 | −0.160579 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.38252 | −0.601985 | −0.300992 | − | 0.953627i | \(-0.597318\pi\) | ||||
−0.300992 | + | 0.953627i | \(0.597318\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.28582i | 0.302764i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.77915 | − | 3.33660i | 0.752382 | − | 0.434388i | −0.0741721 | − | 0.997245i | \(-0.523631\pi\) |
0.826554 | + | 0.562858i | \(0.190298\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.365010 | + | 0.632216i | 0.0467347 | + | 0.0809469i | 0.888446 | − | 0.458980i | \(-0.151785\pi\) |
−0.841712 | + | 0.539927i | \(0.818452\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.43544 | + | 0.828751i | 0.180848 | + | 0.104413i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.12741 | − | 1.80561i | −0.382075 | − | 0.220591i | 0.296646 | − | 0.954988i | \(-0.404132\pi\) |
−0.678720 | + | 0.734397i | \(0.737465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.87395 | − | 6.70988i | −0.466369 | − | 0.807775i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6742 | + | 6.16273i | −1.26679 | + | 0.731382i | −0.974379 | − | 0.224911i | \(-0.927791\pi\) |
−0.292411 | + | 0.956293i | \(0.594458\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.4953i | 1.46247i | 0.682126 | + | 0.731235i | \(0.261056\pi\) | ||||
−0.682126 | + | 0.731235i | \(0.738944\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.0213 | −1.14203 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.33438 | −0.150129 | −0.0750646 | − | 0.997179i | \(-0.523916\pi\) | ||||
−0.0750646 | + | 0.997179i | \(0.523916\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.54486i | 0.718392i | 0.933262 | + | 0.359196i | \(0.116949\pi\) | ||||
−0.933262 | + | 0.359196i | \(0.883051\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.60753 | + | 6.24842i | 0.386767 | + | 0.669901i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.19861 | + | 3.00142i | 0.551051 | + | 0.318150i | 0.749546 | − | 0.661952i | \(-0.230272\pi\) |
−0.198495 | + | 0.980102i | \(0.563605\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.53664 | − | 5.41115i | 0.265912 | − | 0.567242i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.68956 | − | 2.13017i | −0.382589 | − | 0.220888i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.17274 | + | 2.98648i | −0.525212 | + | 0.303231i | −0.739064 | − | 0.673635i | \(-0.764732\pi\) |
0.213853 | + | 0.976866i | \(0.431399\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 6.04602i | − | 0.607648i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.102016 | + | 0.176697i | −0.0101510 | + | 0.0175820i | −0.871056 | − | 0.491183i | \(-0.836565\pi\) |
0.860905 | + | 0.508765i | \(0.169898\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.25947 | −0.321165 | −0.160582 | − | 0.987022i | \(-0.551337\pi\) | ||||
−0.160582 | + | 0.987022i | \(0.551337\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.75400 | + | 3.03801i | −0.169565 | + | 0.293695i | −0.938267 | − | 0.345912i | \(-0.887570\pi\) |
0.768702 | + | 0.639607i | \(0.220903\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.5163i | 1.10307i | 0.834153 | + | 0.551533i | \(0.185957\pi\) | ||||
−0.834153 | + | 0.551533i | \(0.814043\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.74387 | + | 1.58417i | −0.260436 | + | 0.150363i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.0964457 | − | 0.167049i | −0.00907284 | − | 0.0157146i | 0.861453 | − | 0.507837i | \(-0.169555\pi\) |
−0.870526 | + | 0.492122i | \(0.836221\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.26464 | + | 1.53040i | 0.301816 | + | 0.141485i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.64611 | + | 0.950384i | 0.150899 | + | 0.0871215i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.7772 | + | 22.1307i | 1.16156 | + | 2.01189i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.30618 | − | 5.37292i | 0.839110 | − | 0.484460i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.63368 | − | 16.6860i | 0.854851 | − | 1.48064i | −0.0219328 | − | 0.999759i | \(-0.506982\pi\) |
0.876783 | − | 0.480885i | \(-0.159685\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.46715 | 0.217220 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.62693 | −0.316886 | −0.158443 | − | 0.987368i | \(-0.550647\pi\) | ||||
−0.158443 | + | 0.987368i | \(0.550647\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.89437 | − | 3.28115i | 0.164263 | − | 0.284512i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.78830 | − | 4.49658i | 0.665400 | − | 0.384169i | −0.128932 | − | 0.991653i | \(-0.541155\pi\) |
0.794331 | + | 0.607485i | \(0.207821\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.32861 | + | 9.22941i | 0.451966 | + | 0.782829i | 0.998508 | − | 0.0546031i | \(-0.0173894\pi\) |
−0.546542 | + | 0.837432i | \(0.684056\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.13060 | + | 5.27156i | 0.768935 | + | 0.443945i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.7201 | + | 1.85587i | −1.81633 | + | 0.155195i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.12634 | + | 3.68294i | 0.175378 | + | 0.303763i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.7162 | − | 10.8058i | 1.53329 | − | 0.885245i | 0.534083 | − | 0.845432i | \(-0.320657\pi\) |
0.999207 | − | 0.0398134i | \(-0.0126764\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.2597i | 1.40458i | 0.711892 | + | 0.702289i | \(0.247838\pi\) | ||||
−0.711892 | + | 0.702289i | \(0.752162\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.573383 | + | 0.993129i | −0.0463553 | + | 0.0802897i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.4448 | 1.71148 | 0.855741 | − | 0.517405i | \(-0.173102\pi\) | ||||
0.855741 | + | 0.517405i | \(0.173102\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.19126 | + | 3.79537i | −0.173778 | + | 0.300992i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.8422i | 1.01210i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.2954 | + | 7.09876i | −0.963051 | + | 0.556018i | −0.897111 | − | 0.441806i | \(-0.854338\pi\) |
−0.0659406 | + | 0.997824i | \(0.521005\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.51973 | + | 3.18682i | 0.427129 | + | 0.246603i | 0.698123 | − | 0.715978i | \(-0.254019\pi\) |
−0.270994 | + | 0.962581i | \(0.587352\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.49579 | − | 12.1979i | 0.345830 | − | 0.938297i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.97958 | + | 1.14291i | 0.151382 | + | 0.0874005i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.64924 | − | 14.9809i | −0.657589 | − | 1.13898i | −0.981238 | − | 0.192801i | \(-0.938243\pi\) |
0.323648 | − | 0.946177i | \(-0.395090\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 6.67319i | − | 0.501588i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.19861 | + | 9.00425i | −0.388562 | + | 0.673010i | −0.992256 | − | 0.124206i | \(-0.960361\pi\) |
0.603694 | + | 0.797216i | \(0.293695\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0711 | −0.748582 | −0.374291 | − | 0.927311i | \(-0.622114\pi\) | ||||
−0.374291 | + | 0.927311i | \(0.622114\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.730020 | 0.0539646 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.93337i | − | 0.507018i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.43544 | − | 0.828751i | 0.104413 | − | 0.0602828i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3999 | + | 18.0132i | 0.752513 | + | 1.30339i | 0.946601 | + | 0.322407i | \(0.104492\pi\) |
−0.194088 | + | 0.980984i | \(0.562175\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.8195 | + | 13.7522i | 1.71456 | + | 0.989904i | 0.928151 | + | 0.372205i | \(0.121398\pi\) |
0.786414 | + | 0.617700i | \(0.211935\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.5448 | − | 10.7068i | −1.32126 | − | 0.762831i | −0.337332 | − | 0.941386i | \(-0.609525\pi\) |
−0.983930 | + | 0.178555i | \(0.942858\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.6961 | + | 21.9903i | 0.900005 | + | 1.55885i | 0.827486 | + | 0.561487i | \(0.189770\pi\) |
0.0725188 | + | 0.997367i | \(0.476896\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.12741 | + | 1.80561i | −0.220591 | + | 0.127358i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 11.9590i | − | 0.839355i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.74791 | −0.538517 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.8201 | −0.955957 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.926303 | + | 1.60440i | −0.0637693 | + | 0.110452i | −0.896147 | − | 0.443756i | \(-0.853646\pi\) |
0.832378 | + | 0.554208i | \(0.186979\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.3255i | 0.844527i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.53075 | + | 6.11544i | 0.239683 | + | 0.415143i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.8213 | + | 6.24767i | 0.731235 | + | 0.422179i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.74378 | + | 1.75501i | 0.251834 | + | 0.118055i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.09160 | + | 5.24904i | 0.608819 | + | 0.351502i | 0.772503 | − | 0.635011i | \(-0.219005\pi\) |
−0.163684 | + | 0.986513i | \(0.552338\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.46169 | − | 4.88536i | 0.561622 | − | 0.324252i | −0.192174 | − | 0.981361i | \(-0.561554\pi\) |
0.753796 | + | 0.657108i | \(0.228221\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 16.9351i | − | 1.11910i | −0.828796 | − | 0.559550i | \(-0.810974\pi\) | ||
0.828796 | − | 0.559550i | \(-0.189026\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.01065 | + | 8.67869i | −0.329676 | + | 0.571016i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.7938 | −1.29674 | −0.648368 | − | 0.761327i | \(-0.724548\pi\) | ||||
−0.648368 | + | 0.761327i | \(0.724548\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.667188 | + | 1.15560i | −0.0433385 | + | 0.0750646i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.00847i | − | 0.0652328i | −0.999468 | − | 0.0326164i | \(-0.989616\pi\) | ||
0.999468 | − | 0.0326164i | \(-0.0103840\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.67505 | − | 4.43119i | 0.494393 | − | 0.285438i | −0.232002 | − | 0.972715i | \(-0.574528\pi\) |
0.726395 | + | 0.687277i | \(0.241194\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.49821 | − | 7.46238i | 0.222586 | − | 0.474820i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.66801 | + | 3.27243i | 0.359196 | + | 0.207382i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.40347 | + | 2.43088i | 0.0885863 | + | 0.153436i | 0.906914 | − | 0.421316i | \(-0.138432\pi\) |
−0.818327 | + | 0.574752i | \(0.805098\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 40.5681 | − | 23.4220i | 2.55049 | − | 1.47253i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.197590 | + | 0.342236i | −0.0123253 | + | 0.0213481i | −0.872122 | − | 0.489288i | \(-0.837257\pi\) |
0.859797 | + | 0.510636i | \(0.170590\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.25154 | 0.326315 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.21505 | 0.446601 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.2704 | + | 21.2529i | −0.756623 | + | 1.31051i | 0.187940 | + | 0.982181i | \(0.439819\pi\) |
−0.944563 | + | 0.328330i | \(0.893514\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.19861 | − | 3.00142i | 0.318150 | − | 0.183684i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.07730 | − | 10.5262i | −0.370540 | − | 0.641793i | 0.619109 | − | 0.785305i | \(-0.287494\pi\) |
−0.989649 | + | 0.143512i | \(0.954161\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.19227 | − | 1.84306i | −0.193917 | − | 0.111958i | 0.399898 | − | 0.916560i | \(-0.369046\pi\) |
−0.593815 | + | 0.804602i | \(0.702379\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.41787 | − | 4.90237i | −0.206859 | − | 0.296705i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.402900 | − | 0.697843i | −0.0242079 | − | 0.0419293i | 0.853668 | − | 0.520818i | \(-0.174373\pi\) |
−0.877876 | + | 0.478889i | \(0.841040\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.68956 | + | 2.13017i | −0.220888 | + | 0.127530i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.360243i | 0.0214903i | 0.999942 | + | 0.0107452i | \(0.00342036\pi\) | ||||
−0.999942 | + | 0.0107452i | \(0.996580\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.1636 | − | 17.6039i | 0.604163 | − | 1.04644i | −0.388021 | − | 0.921651i | \(-0.626841\pi\) |
0.992183 | − | 0.124790i | \(-0.0398256\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.8113 | −1.05137 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.84246 | − | 13.5835i | 0.461321 | − | 0.799032i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.97296i | 0.350141i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.7008 | + | 8.48753i | −0.858832 | + | 0.495847i | −0.863621 | − | 0.504142i | \(-0.831809\pi\) |
0.00478898 | + | 0.999989i | \(0.498476\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.23601 | − | 3.02301i | −0.303824 | − | 0.175413i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.37827 | + | 27.8340i | 0.137539 | + | 1.60968i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.54144 | − | 2.04465i | −0.204125 | − | 0.117852i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.102016 | + | 0.176697i | 0.00586067 | + | 0.0101510i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.1770i | 0.980346i | 0.871625 | + | 0.490173i | \(0.163066\pi\) | ||||
−0.871625 | + | 0.490173i | \(0.836934\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.62973 | + | 2.82278i | −0.0927123 | + | 0.160582i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.4174 | −1.04435 | −0.522176 | − | 0.852837i | \(-0.674880\pi\) | ||||
−0.522176 | + | 0.852837i | \(0.674880\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.10571 | −0.458162 | −0.229081 | − | 0.973407i | \(-0.573572\pi\) | ||||
−0.229081 | + | 0.973407i | \(0.573572\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4.06294i | − | 0.228197i | −0.993469 | − | 0.114099i | \(-0.963602\pi\) | ||
0.993469 | − | 0.114099i | \(-0.0363980\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37.7781 | + | 21.8112i | −2.11517 | + | 1.22119i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.75400 | + | 3.03801i | 0.0978985 | + | 0.169565i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.27011 | + | 1.31065i | 0.126312 | + | 0.0729265i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.97344 | + | 5.75817i | 0.551533 | + | 0.318428i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.73761 | − | 15.1340i | −0.481720 | − | 0.834364i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.3971 | − | 10.0442i | 0.956233 | − | 0.552081i | 0.0612213 | − | 0.998124i | \(-0.480500\pi\) |
0.895012 | + | 0.446043i | \(0.147167\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.16834i | 0.173624i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.81854 | −0.208009 | −0.104005 | − | 0.994577i | \(-0.533166\pi\) | ||||
−0.104005 | + | 0.994577i | \(0.533166\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.192891 | −0.0104764 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.8790 | − | 22.3071i | 0.697438 | − | 1.20800i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.6513i | − | 1.00708i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.2317 | + | 28.1142i | 0.871365 | + | 1.50925i | 0.860585 | + | 0.509307i | \(0.170098\pi\) |
0.0107803 | + | 0.999942i | \(0.496568\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.6256 | + | 7.28941i | 0.675834 | + | 0.390193i | 0.798284 | − | 0.602282i | \(-0.205742\pi\) |
−0.122449 | + | 0.992475i | \(0.539075\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.95768 | − | 2.06206i | 0.157870 | − | 0.110065i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.8982 | − | 10.3335i | −0.952626 | − | 0.549999i | −0.0587300 | − | 0.998274i | \(-0.518705\pi\) |
−0.893896 | + | 0.448275i | \(0.852038\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.64611 | − | 0.950384i | 0.0871215 | − | 0.0502996i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.82021i | 0.307179i | 0.988135 | + | 0.153589i | \(0.0490833\pi\) | ||||
−0.988135 | + | 0.153589i | \(0.950917\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.88751 | + | 11.9295i | −0.362501 | + | 0.627870i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.5544 | 1.34126 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.11095 | − | 12.3165i | 0.371189 | − | 0.642918i | −0.618560 | − | 0.785738i | \(-0.712284\pi\) |
0.989749 | + | 0.142820i | \(0.0456170\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 10.7458i | − | 0.559407i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.29083 | − | 3.63201i | 0.326604 | − | 0.188565i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.2862 | − | 28.2085i | −0.843266 | − | 1.46058i | −0.887119 | − | 0.461542i | \(-0.847296\pi\) |
0.0438524 | − | 0.999038i | \(-0.486037\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.21471 | − | 25.9198i | −0.114063 | − | 1.33494i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.5125 | − | 14.7296i | −1.31049 | − | 0.756611i | −0.328311 | − | 0.944570i | \(-0.606480\pi\) |
−0.982177 | + | 0.187959i | \(0.939813\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.63368 | − | 16.6860i | −0.493548 | − | 0.854851i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.3433 | − | 15.7867i | 1.39718 | − | 0.806660i | 0.403081 | − | 0.915164i | \(-0.367939\pi\) |
0.994096 | + | 0.108504i | \(0.0346061\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.23357 | − | 2.13661i | 0.0627061 | − | 0.108610i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.6754 | −1.14969 | −0.574843 | − | 0.818263i | \(-0.694937\pi\) | ||||
−0.574843 | + | 0.818263i | \(0.694937\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.88504 | −0.449336 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.81346 | + | 3.14101i | −0.0914772 | + | 0.158443i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.5951 | + | 6.11707i | −0.531752 | + | 0.307007i | −0.741730 | − | 0.670699i | \(-0.765994\pi\) |
0.209978 | + | 0.977706i | \(0.432661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.89437 | − | 3.28115i | −0.0948374 | − | 0.164263i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.1495 | − | 8.74659i | −0.756532 | − | 0.436784i | 0.0715175 | − | 0.997439i | \(-0.477216\pi\) |
−0.828049 | + | 0.560656i | \(0.810549\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.78507 | + | 12.6007i | 0.437616 | + | 0.627686i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.57794 | − | 16.5895i | −0.474761 | − | 0.822310i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.6025 | − | 18.2457i | 1.56264 | − | 0.902192i | 0.565654 | − | 0.824643i | \(-0.308624\pi\) |
0.996989 | − | 0.0775493i | \(-0.0247095\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 8.99316i | − | 0.443600i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.53041 | + | 9.57896i | −0.272134 | + | 0.471350i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.6572 | 0.521886 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.105105 | − | 0.182048i | 0.00513472 | − | 0.00889360i | −0.863447 | − | 0.504440i | \(-0.831699\pi\) |
0.868581 | + | 0.495547i | \(0.165032\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 8.61066i | − | 0.419658i | −0.977738 | − | 0.209829i | \(-0.932709\pi\) | ||
0.977738 | − | 0.209829i | \(-0.0672907\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.13060 | − | 5.27156i | 0.443945 | − | 0.256312i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.04790 | − | 0.605005i | −0.0507114 | − | 0.0292782i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.25282 | + | 19.7381i | −0.446730 | + | 0.952964i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.3283 | + | 8.84980i | 0.738338 | + | 0.426280i | 0.821465 | − | 0.570259i | \(-0.193157\pi\) |
−0.0831267 | + | 0.996539i | \(0.526491\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.65382 | + | 8.06065i | 0.223648 | + | 0.387370i | 0.955913 | − | 0.293650i | \(-0.0948700\pi\) |
−0.732265 | + | 0.681020i | \(0.761537\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.7103i | 0.847199i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.22475 | + | 10.7816i | −0.297091 | + | 0.514577i | −0.975469 | − | 0.220136i | \(-0.929350\pi\) |
0.678378 | + | 0.734713i | \(0.262683\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.25269 | 0.202509 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.86088 | −0.183436 | −0.0917180 | − | 0.995785i | \(-0.529236\pi\) | ||||
−0.0917180 | + | 0.995785i | \(0.529236\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 21.6116i | − | 1.02219i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.65851 | − | 5.57634i | 0.455813 | − | 0.263164i | −0.254469 | − | 0.967081i | \(-0.581901\pi\) |
0.710282 | + | 0.703917i | \(0.248567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.4848 | + | 56.2654i | 1.52965 | + | 2.64943i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.9474 | + | 8.62987i | 0.702289 | + | 0.405467i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.12068 | + | 0.647022i | 0.0524230 | + | 0.0302664i | 0.525982 | − | 0.850495i | \(-0.323698\pi\) |
−0.473559 | + | 0.880762i | \(0.657031\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.573383 | + | 0.993129i | 0.0267632 | + | 0.0463553i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.9344 | − | 8.04505i | 0.648991 | − | 0.374695i | −0.139078 | − | 0.990281i | \(-0.544414\pi\) |
0.788070 | + | 0.615586i | \(0.211081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.9707i | 0.881645i | 0.897594 | + | 0.440823i | \(0.145313\pi\) | ||||
−0.897594 | + | 0.440823i | \(0.854687\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.7236 | −1.56054 | −0.780272 | − | 0.625441i | \(-0.784919\pi\) | ||||
−0.780272 | + | 0.625441i | \(0.784919\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.98562 | 0.276390 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.7224 | − | 18.5717i | 0.494062 | − | 0.855741i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.9164i | 0.685858i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.19126 | + | 3.79537i | 0.100331 | + | 0.173778i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.68929 | − | 1.55266i | −0.122877 | − | 0.0709429i | 0.437302 | − | 0.899315i | \(-0.355934\pi\) |
−0.560179 | + | 0.828372i | \(0.689267\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.3822 | − | 0.972544i | 0.518982 | − | 0.0443442i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.1216 | + | 6.42108i | 0.506052 | + | 0.292169i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.74404 | + | 1.58427i | −0.124344 | + | 0.0717902i | −0.560882 | − | 0.827896i | \(-0.689538\pi\) |
0.436538 | + | 0.899686i | \(0.356205\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.1975i | 0.642034i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.0168 | + | 22.5458i | −0.587440 | + | 1.01748i | 0.407126 | + | 0.913372i | \(0.366531\pi\) |
−0.994566 | + | 0.104105i | \(0.966802\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.27398 | 0.372641 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.2147 | − | 17.6924i | 0.458194 | − | 0.793615i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.4095i | 0.868888i | 0.900699 | + | 0.434444i | \(0.143055\pi\) | ||||
−0.900699 | + | 0.434444i | \(0.856945\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.51973 | − | 3.18682i | 0.246603 | − | 0.142376i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.0723 | − | 33.0342i | −0.850391 | − | 1.47292i | −0.880856 | − | 0.473385i | \(-0.843032\pi\) |
0.0304646 | − | 0.999536i | \(-0.490301\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.31576 | − | 9.99240i | −0.369316 | − | 0.443778i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.6333 | + | 20.5729i | 1.57942 | + | 0.911878i | 0.994940 | + | 0.100470i | \(0.0320345\pi\) |
0.584479 | + | 0.811409i | \(0.301299\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.3555 | − | 17.9363i | −0.458102 | − | 0.793455i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.97958 | − | 1.14291i | 0.0874005 | − | 0.0504607i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.8719 | + | 55.2038i | −1.40173 | + | 2.42786i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.2985 | −0.759319 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.4270 | 1.33303 | 0.666516 | − | 0.745490i | \(-0.267785\pi\) | ||||
0.666516 | + | 0.745490i | \(0.267785\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.60990 | + | 11.4487i | −0.289031 | + | 0.500616i | −0.973579 | − | 0.228352i | \(-0.926666\pi\) |
0.684548 | + | 0.728968i | \(0.260000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.23106 | + | 2.44280i | −0.184308 | + | 0.106410i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.5150 | − | 32.0690i | −0.805001 | − | 1.39430i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.77915 | − | 3.33660i | −0.250794 | − | 0.144796i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −38.6040 | + | 3.29851i | −1.67213 | + | 0.142874i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.19861 | + | 9.00425i | 0.224337 | + | 0.388562i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.2671 | + | 12.8559i | −0.959112 | + | 0.553744i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 13.9179i | − | 0.598378i | −0.954194 | − | 0.299189i | \(-0.903284\pi\) | ||
0.954194 | − | 0.299189i | \(-0.0967161\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.03557 | + | 8.72186i | −0.216097 | + | 0.374291i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.7737 | 0.888219 | 0.444109 | − | 0.895973i | \(-0.353520\pi\) | ||||
0.444109 | + | 0.895973i | \(0.353520\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.365010 | − | 0.632216i | 0.0155782 | − | 0.0269823i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 16.4923i | − | 0.702596i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.91542 | − | 1.10587i | 0.0814518 | − | 0.0470262i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.6876 | − | 7.90255i | −0.579963 | − | 0.334842i | 0.181156 | − | 0.983454i | \(-0.442016\pi\) |
−0.761119 | + | 0.648613i | \(0.775350\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.05435 | − | 3.77572i | −0.340663 | − | 0.159696i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.00448 | − | 3.46669i | −0.253509 | − | 0.146364i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.1334 | + | 34.8721i | 0.848521 | + | 1.46968i | 0.882528 | + | 0.470261i | \(0.155840\pi\) |
−0.0340062 | + | 0.999422i | \(0.510827\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.65750i | − | 0.0696085i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.65461 | − | 13.2582i | 0.320898 | − | 0.555812i | −0.659775 | − | 0.751463i | \(-0.729349\pi\) |
0.980674 | + | 0.195651i | \(0.0626819\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.13351 | −0.131133 | −0.0655666 | − | 0.997848i | \(-0.520885\pi\) | ||||
−0.0655666 | + | 0.997848i | \(0.520885\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.7999 | 0.868927 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.1801i | 1.21478i | 0.794403 | + | 0.607391i | \(0.207784\pi\) | ||||
−0.794403 | + | 0.607391i | \(0.792216\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 23.8195 | − | 13.7522i | 0.989904 | − | 0.571522i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.42406 | − | 9.39474i | −0.225028 | − | 0.389760i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.9469 | − | 13.2484i | −0.950363 | − | 0.548692i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.93311 | + | 2.27078i | 0.162337 | + | 0.0937252i | 0.578967 | − | 0.815351i | \(-0.303456\pi\) |
−0.416631 | + | 0.909076i | \(0.636789\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.86917 | + | 8.43366i | 0.200631 | + | 0.347503i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.5448 | + | 10.7068i | −0.762831 | + | 0.440421i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 3.21321i | − | 0.131951i | −0.997821 | − | 0.0659754i | \(-0.978984\pi\) | ||
0.997821 | − | 0.0659754i | \(-0.0210159\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.3923 | 1.03924 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.32402 | −0.176675 | −0.0883373 | − | 0.996091i | \(-0.528155\pi\) | ||||
−0.0883373 | + | 0.996091i | \(0.528155\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.14660 | − | 1.98597i | 0.0467709 | − | 0.0810096i | −0.841692 | − | 0.539958i | \(-0.818440\pi\) |
0.888463 | + | 0.458948i | \(0.151774\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.61123i | 0.147061i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.77184 | + | 4.80097i | 0.112506 | + | 0.194865i | 0.916780 | − | 0.399393i | \(-0.130779\pi\) |
−0.804274 | + | 0.594258i | \(0.797446\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.3568 | − | 5.97948i | −0.419677 | − | 0.242301i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.7406 | − | 31.1832i | −0.879529 | − | 1.26154i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.35569 | + | 3.66946i | 0.256704 | + | 0.148208i | 0.622830 | − | 0.782357i | \(-0.285983\pi\) |
−0.366126 | + | 0.930565i | \(0.619316\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.3650 | + | 16.9539i | −1.18219 | + | 0.682537i | −0.956520 | − | 0.291667i | \(-0.905790\pi\) |
−0.225669 | + | 0.974204i | \(0.572457\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 44.9279i | − | 1.80580i | −0.429847 | − | 0.902902i | \(-0.641432\pi\) | ||
0.429847 | − | 0.902902i | \(-0.358568\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.87395 | + | 6.70988i | −0.155456 | + | 0.269258i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.94971 | −0.398627 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.91006 | + | 11.9686i | −0.275961 | + | 0.477979i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.63335i | 0.144871i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.6730 | + | 20.0185i | −1.38031 | + | 0.796923i | −0.992196 | − | 0.124688i | \(-0.960207\pi\) |
−0.388115 | + | 0.921611i | \(0.626874\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.926303 | + | 1.60440i | 0.0368172 | + | 0.0637693i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.30539 | − | 15.2776i | −0.0517215 | − | 0.605321i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.6742 | + | 6.16273i | 0.422263 | + | 0.243794i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.7186 | − | 23.7614i | −0.541854 | − | 0.938519i | −0.998798 | − | 0.0490230i | \(-0.984389\pi\) |
0.456944 | − | 0.889496i | \(-0.348944\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.6665 | − | 6.73564i | 0.460081 | − | 0.265628i | −0.251998 | − | 0.967728i | \(-0.581087\pi\) |
0.712078 | + | 0.702100i | \(0.247754\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.9621 | − | 29.3793i | 0.666851 | − | 1.15502i | −0.311929 | − | 0.950105i | \(-0.600975\pi\) |
0.978780 | − | 0.204914i | \(-0.0656914\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.3463 | 1.58373 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.06151 | 0.276762 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.57766 | + | 2.73259i | −0.0617386 | + | 0.106934i | −0.895243 | − | 0.445579i | \(-0.852998\pi\) |
0.833504 | + | 0.552513i | \(0.186331\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.8213 | − | 6.24767i | 0.422179 | − | 0.243745i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.37780 | − | 9.31463i | −0.209489 | − | 0.362846i | 0.742064 | − | 0.670329i | \(-0.233847\pi\) |
−0.951554 | + | 0.307482i | \(0.900514\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.5544 | − | 19.3727i | −1.30512 | − | 0.753509i | −0.323839 | − | 0.946112i | \(-0.604974\pi\) |
−0.981277 | + | 0.192603i | \(0.938307\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.39177 | − | 2.36470i | 0.131726 | − | 0.0918375i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.9508 | + | 48.4122i | 1.08226 | + | 1.87453i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.09160 | − | 5.24904i | 0.351502 | − | 0.202940i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.41372i | 0.170390i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.90782 | + | 17.1608i | −0.381918 | + | 0.661502i | −0.991336 | − | 0.131347i | \(-0.958070\pi\) |
0.609418 | + | 0.792849i | \(0.291403\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.5883 | 0.752841 | 0.376421 | − | 0.926449i | \(-0.377155\pi\) | ||||
0.376421 | + | 0.926449i | \(0.377155\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.95010 | − | 8.57382i | 0.189967 | − | 0.329033i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 9.77071i | − | 0.374415i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.5656 | + | 13.0282i | −0.863447 | + | 0.498511i | −0.865165 | − | 0.501487i | \(-0.832786\pi\) |
0.00171806 | + | 0.999999i | \(0.499453\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.6662 | − | 8.46753i | −0.559550 | − | 0.323057i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.9621 | − | 9.03702i | 0.493817 | − | 0.344283i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.99020 | − | 4.03579i | −0.265920 | − | 0.153529i | 0.361112 | − | 0.932522i | \(-0.382397\pi\) |
−0.627032 | + | 0.778994i | \(0.715730\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.01065 | + | 8.67869i | 0.190339 | + | 0.329676i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.3230i | − | 0.466766i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.89691 | + | 17.1419i | −0.374335 | + | 0.648368i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.9799 | −0.603551 | −0.301775 | − | 0.953379i | \(-0.597579\pi\) | ||||
−0.301775 | + | 0.953379i | \(0.597579\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.24226 | 0.273147 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 0.338183i | − | 0.0127187i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.5086 | + | 12.4180i | −0.807772 | + | 0.466367i | −0.846181 | − | 0.532895i | \(-0.821104\pi\) |
0.0384099 | + | 0.999262i | \(0.487771\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.667188 | + | 1.15560i | 0.0250215 | + | 0.0433385i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.5863 | − | 16.5043i | −1.07057 | − | 0.618092i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.873364 | − | 0.504237i | −0.0326164 | − | 0.0188311i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.8491 | − | 18.7912i | −0.404603 | − | 0.700794i | 0.589672 | − | 0.807643i | \(-0.299257\pi\) |
−0.994275 | + | 0.106849i | \(0.965924\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.67877 | − | 2.70129i | 0.174246 | − | 0.100601i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 8.86238i | − | 0.329596i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.2453 | −1.27009 | −0.635044 | − | 0.772476i | \(-0.719018\pi\) | ||||
−0.635044 | + | 0.772476i | \(0.719018\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.41462 | − | 2.45019i | 0.0523216 | − | 0.0906237i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 16.9049i | − | 0.624397i | −0.950017 | − | 0.312199i | \(-0.898935\pi\) | ||
0.950017 | − | 0.312199i | \(-0.101065\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.9168 | − | 18.9084i | −0.402125 | − | 0.696501i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.0843 | − | 9.86363i | −0.628456 | − | 0.362839i | 0.151698 | − | 0.988427i | \(-0.451526\pi\) |
−0.780154 | + | 0.625588i | \(0.784859\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.71350 | − | 6.76073i | −0.173155 | − | 0.248362i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.0040 | − | 12.7040i | −0.807247 | − | 0.466064i | 0.0387519 | − | 0.999249i | \(-0.487662\pi\) |
−0.845999 | + | 0.533185i | \(0.820995\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.66801 | − | 3.27243i | 0.207382 | − | 0.119732i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 5.81450i | − | 0.212457i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.0169 | − | 38.1343i | 0.803407 | − | 1.39154i | −0.113954 | − | 0.993486i | \(-0.536352\pi\) |
0.917361 | − | 0.398056i | \(-0.130315\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.80694 | 0.102291 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.2160 | − | 17.6946i | 0.371306 | − | 0.643121i | −0.618461 | − | 0.785816i | \(-0.712243\pi\) |
0.989767 | + | 0.142695i | \(0.0455767\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 46.8440i | − | 1.70033i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.4379 | + | 6.60370i | −0.414625 | + | 0.239384i | −0.692775 | − | 0.721154i | \(-0.743612\pi\) |
0.278150 | + | 0.960538i | \(0.410279\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.54418 | − | 16.5310i | −0.345522 | − | 0.598462i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.2126 | + | 21.7856i | −0.368757 | + | 0.786632i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.23441 | + | 4.75414i | 0.296940 | + | 0.171439i | 0.641068 | − | 0.767484i | \(-0.278492\pi\) |
−0.344127 | + | 0.938923i | \(0.611825\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.197590 | + | 0.342236i | 0.00711604 | + | 0.0123253i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.39516 | − | 3.11490i | 0.194050 | − | 0.112035i | −0.399827 | − | 0.916591i | \(-0.630930\pi\) |
0.593877 | + | 0.804556i | \(0.297596\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.62577 | − | 4.54796i | 0.0941989 | − | 0.163157i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −24.5631 | −0.880063 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −74.5200 | −2.66654 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.60753 | − | 6.24842i | 0.128922 | − | 0.223300i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.4276 | − | 22.7635i | 1.40544 | − | 0.811433i | 0.410499 | − | 0.911861i | \(-0.365355\pi\) |
0.994944 | + | 0.100428i | \(0.0320213\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.2704 | + | 21.2529i | 0.436837 | + | 0.756623i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.276884 | + | 0.159859i | 0.00984485 | + | 0.00568393i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.38325 | − | 1.11722i | −0.0846318 | − | 0.0396737i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.5541 | + | 20.0123i | 0.409267 | + | 0.708871i | 0.994808 | − | 0.101772i | \(-0.0324511\pi\) |
−0.585541 | + | 0.810643i | \(0.699118\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.4707 | − | 6.04524i | 0.370426 | − | 0.213865i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 6.00284i | − | 0.212100i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37.7736 | + | 65.4257i | −1.33300 | + | 2.30882i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.1546 | −0.427862 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.03014 | − | 6.98041i | 0.141692 | − | 0.245418i | −0.786442 | − | 0.617664i | \(-0.788079\pi\) |
0.928134 | + | 0.372246i | \(0.121412\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 48.6471i | − | 1.70823i | −0.520084 | − | 0.854115i | \(-0.674099\pi\) | ||
0.520084 | − | 0.854115i | \(-0.325901\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.19227 | + | 1.84306i | −0.111958 | + | 0.0646389i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.88391 | − | 2.81973i | −0.170866 | − | 0.0986497i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.95451 | + | 0.508781i | −0.208067 | + | 0.0177783i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.7461 | − | 24.1021i | −1.45695 | − | 0.841169i | −0.458088 | − | 0.888907i | \(-0.651465\pi\) |
−0.998860 | + | 0.0477380i | \(0.984799\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.3042 | + | 42.0960i | 0.847190 | + | 1.46738i | 0.883706 | + | 0.468043i | \(0.155041\pi\) |
−0.0365160 | + | 0.999333i | \(0.511626\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.1081i | 0.699229i | 0.936894 | + | 0.349614i | \(0.113687\pi\) | ||||
−0.936894 | + | 0.349614i | \(0.886313\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.5726 | − | 18.3123i | 0.367203 | − | 0.636014i | −0.621924 | − | 0.783077i | \(-0.713649\pi\) |
0.989127 | + | 0.147063i | \(0.0469821\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.805800 | −0.0279529 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.87684 | 0.168972 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.26033i | 0.147259i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.3127 | − | 7.10874i | 0.425082 | − | 0.245421i | −0.272167 | − | 0.962250i | \(-0.587740\pi\) |
0.697249 | + | 0.716829i | \(0.254407\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.5285 | − | 19.9679i | −0.397534 | − | 0.688549i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.311980 | + | 0.180122i | 0.0107452 | + | 0.00620372i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.6817 | − | 21.1782i | −1.26040 | − | 0.727692i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.1636 | − | 17.6039i | −0.348813 | − | 0.604163i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.2592 | + | 12.2740i | −0.728757 | + | 0.420748i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 26.1008i | − | 0.893676i | −0.894615 | − | 0.446838i | \(-0.852550\pi\) | ||
0.894615 | − | 0.446838i | \(-0.147450\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.1782 | 0.928390 | 0.464195 | − | 0.885733i | \(-0.346344\pi\) | ||||
0.464195 | + | 0.885733i | \(0.346344\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.8502 | −1.15495 | −0.577477 | − | 0.816407i | \(-0.695963\pi\) | ||||
−0.577477 | + | 0.816407i | \(0.695963\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.90563 | + | 15.4250i | −0.303503 | + | 0.525683i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 49.9350i | − | 1.69981i | −0.526938 | − | 0.849904i | \(-0.676660\pi\) | ||
0.526938 | − | 0.849904i | \(-0.323340\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.84246 | − | 13.5835i | −0.266344 | − | 0.461321i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.98681 | − | 4.03384i | −0.237011 | − | 0.136839i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.9732 | − | 1.10849i | 0.439580 | − | 0.0375598i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.17274 | + | 2.98648i | 0.175071 | + | 0.101077i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.9224 | + | 6.88339i | −0.402590 | + | 0.232436i | −0.687601 | − | 0.726089i | \(-0.741336\pi\) |
0.285011 | + | 0.958524i | \(0.408003\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.9751i | 0.572555i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.98061 | + | 12.0908i | −0.235183 | + | 0.407348i | −0.959326 | − | 0.282302i | \(-0.908902\pi\) |
0.724143 | + | 0.689650i | \(0.242235\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.95089 | 0.200263 | 0.100132 | − | 0.994974i | \(-0.468074\pi\) | ||||
0.100132 | + | 0.994974i | \(0.468074\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.86299 | + | 17.0832i | −0.331167 | + | 0.573598i | −0.982741 | − | 0.184987i | \(-0.940776\pi\) |
0.651574 | + | 0.758585i | \(0.274109\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.9357i | 1.07109i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.23601 | + | 3.02301i | −0.175413 | + | 0.101275i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.0498 | − | 20.8709i | −0.403232 | − | 0.698418i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.2941 | + | 11.8574i | 0.844546 | + | 0.395906i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.6203 | + | 15.3693i | 0.887838 | + | 0.512593i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.51286 | + | 4.35240i | 0.0837155 | + | 0.145000i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.54144 | + | 2.04465i | −0.117852 | + | 0.0680417i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.07493 | − | 13.9862i | 0.268124 | − | 0.464404i | −0.700254 | − | 0.713894i | \(-0.746930\pi\) |
0.968377 | + | 0.249490i | \(0.0802631\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.204032 | 0.00676732 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.1748 | 1.16539 | 0.582696 | − | 0.812690i | \(-0.301998\pi\) | ||||
0.582696 | + | 0.812690i | \(0.301998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.7852 | + | 34.2689i | −0.654794 | + | 1.13414i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.20623 | − | 3.00582i | 0.171925 | − | 0.0992610i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.24395 | − | 12.5469i | −0.238956 | − | 0.413884i | 0.721459 | − | 0.692457i | \(-0.243472\pi\) |
−0.960415 | + | 0.278573i | \(0.910139\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.8758 | + | 8.58852i | 0.490173 | + | 0.283001i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.8629 | − | 40.2382i | 0.620879 | − | 1.32446i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.62973 | + | 2.82278i | 0.0535275 | + | 0.0927123i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.4260 | − | 18.7212i | 1.06386 | − | 0.614222i | 0.137365 | − | 0.990520i | \(-0.456137\pi\) |
0.926499 | + | 0.376298i | \(0.122803\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 9.72088i | − | 0.318589i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.20868 | + | 15.9499i | −0.301479 | + | 0.522176i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.2285 | 1.83690 | 0.918452 | − | 0.395533i | \(-0.129440\pi\) | ||||
0.918452 | + | 0.395533i | \(0.129440\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.05286 | + | 7.01975i | −0.132260 | + | 0.229081i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 37.7863i | − | 1.23180i | −0.787826 | − | 0.615898i | \(-0.788793\pi\) | ||
0.787826 | − | 0.615898i | \(-0.211207\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 72.1034 | − | 41.6289i | 2.34801 | − | 1.35562i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.68360 | − | 5.01348i | −0.282179 | − | 0.162916i | 0.352230 | − | 0.935913i | \(-0.385423\pi\) |
−0.634409 | + | 0.772997i | \(0.718757\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.7662 | − | 36.9573i | −0.836406 | − | 1.19968i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.51861 | − | 2.03147i | −0.114099 | − | 0.0658749i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.289497 | − | 0.501424i | −0.00937773 | − | 0.0162427i | 0.861298 | − | 0.508099i | \(-0.169652\pi\) |
−0.870676 | + | 0.491857i | \(0.836318\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 43.6224i | 1.41011i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.45309 | + | 12.9091i | −0.240673 | + | 0.416857i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.8496 | 0.414502 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.50799 | 0.113043 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17.0784i | − | 0.549205i | −0.961558 | − | 0.274602i | \(-0.911454\pi\) | ||
0.961558 | − | 0.274602i | \(-0.0885462\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.27011 | − | 1.31065i | 0.0729265 | − | 0.0421042i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.5819 | − | 37.3810i | −0.692597 | − | 1.19961i | −0.970984 | − | 0.239144i | \(-0.923133\pi\) |
0.278387 | − | 0.960469i | \(-0.410200\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.2978 | − | 8.83217i | −0.490424 | − | 0.283146i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.9032 | − | 21.3061i | −1.18064 | − | 0.681641i | −0.224476 | − | 0.974480i | \(-0.572067\pi\) |
−0.956162 | + | 0.292838i | \(0.905400\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.1466 | + | 31.4309i | 0.579969 | + | 1.00454i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.97344 | − | 5.75817i | 0.318428 | − | 0.183844i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.6346i | 1.45552i | 0.685834 | + | 0.727758i | \(0.259438\pi\) | ||||
−0.685834 | + | 0.727758i | \(0.740562\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.4752 | −0.556243 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.1152 | 0.607829 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.76168 | − | 6.51542i | 0.119494 | − | 0.206969i | −0.800073 | − | 0.599902i | \(-0.795206\pi\) |
0.919567 | + | 0.392933i | \(0.128540\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 20.0885i | − | 0.637489i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.4852 | − | 30.2852i | −0.553760 | − | 0.959141i | −0.997999 | − | 0.0632324i | \(-0.979859\pi\) |
0.444239 | − | 0.895909i | \(-0.353474\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.74387 | + | 1.58417i | 0.0868121 | + | 0.0501210i |
(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 | 3900.2.cd.o.901.2 | 12 | ||
5.2 | odd | 4 | 780.2.bv.a.589.4 | yes | 24 | ||
5.3 | odd | 4 | 780.2.bv.a.589.9 | yes | 24 | ||
5.4 | even | 2 | 3900.2.cd.n.901.5 | 12 | |||
13.10 | even | 6 | inner | 3900.2.cd.o.2701.2 | 12 | ||
15.2 | even | 4 | 2340.2.cr.b.1369.5 | 24 | |||
15.8 | even | 4 | 2340.2.cr.b.1369.8 | 24 | |||
65.23 | odd | 12 | 780.2.bv.a.49.4 | ✓ | 24 | ||
65.49 | even | 6 | 3900.2.cd.n.2701.5 | 12 | |||
65.62 | odd | 12 | 780.2.bv.a.49.9 | yes | 24 | ||
195.23 | even | 12 | 2340.2.cr.b.829.5 | 24 | |||
195.62 | even | 12 | 2340.2.cr.b.829.8 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
780.2.bv.a.49.4 | ✓ | 24 | 65.23 | odd | 12 | ||
780.2.bv.a.49.9 | yes | 24 | 65.62 | odd | 12 | ||
780.2.bv.a.589.4 | yes | 24 | 5.2 | odd | 4 | ||
780.2.bv.a.589.9 | yes | 24 | 5.3 | odd | 4 | ||
2340.2.cr.b.829.5 | 24 | 195.23 | even | 12 | |||
2340.2.cr.b.829.8 | 24 | 195.62 | even | 12 | |||
2340.2.cr.b.1369.5 | 24 | 15.2 | even | 4 | |||
2340.2.cr.b.1369.8 | 24 | 15.8 | even | 4 | |||
3900.2.cd.n.901.5 | 12 | 5.4 | even | 2 | |||
3900.2.cd.n.2701.5 | 12 | 65.49 | even | 6 | |||
3900.2.cd.o.901.2 | 12 | 1.1 | even | 1 | trivial | ||
3900.2.cd.o.2701.2 | 12 | 13.10 | even | 6 | inner |