Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(337,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.k (of order \(4\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 337.5 | ||
Character | \(\chi\) | \(=\) | 1148.337 |
Dual form | 1148.2.k.b.729.5 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −1.38781 | − | 1.38781i | −0.801250 | − | 0.801250i | 0.182041 | − | 0.983291i | \(-0.441730\pi\) |
−0.983291 | + | 0.182041i | \(0.941730\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.11167i | 0.944368i | 0.881500 | + | 0.472184i | \(0.156534\pi\) | ||||
−0.881500 | + | 0.472184i | \(0.843466\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.852014i | 0.284005i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.520395 | − | 0.520395i | −0.156905 | − | 0.156905i | 0.624289 | − | 0.781194i | \(-0.285389\pi\) |
−0.781194 | + | 0.624289i | \(0.785389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.612447 | + | 0.612447i | 0.169862 | + | 0.169862i | 0.786919 | − | 0.617057i | \(-0.211675\pi\) |
−0.617057 | + | 0.786919i | \(0.711675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.93059 | − | 2.93059i | 0.756675 | − | 0.756675i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.16252 | − | 1.16252i | 0.281954 | − | 0.281954i | −0.551934 | − | 0.833888i | \(-0.686110\pi\) |
0.833888 | + | 0.551934i | \(0.186110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.68768 | + | 2.68768i | −0.616597 | + | 0.616597i | −0.944657 | − | 0.328060i | \(-0.893605\pi\) |
0.328060 | + | 0.944657i | \(0.393605\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.96265i | − | 0.428286i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.65691 | −0.762518 | −0.381259 | − | 0.924468i | \(-0.624509\pi\) | ||||
−0.381259 | + | 0.924468i | \(0.624509\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.540846 | 0.108169 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.98099 | + | 2.98099i | −0.573692 | + | 0.573692i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.93269 | + | 3.93269i | 0.730282 | + | 0.730282i | 0.970676 | − | 0.240393i | \(-0.0772764\pi\) |
−0.240393 | + | 0.970676i | \(0.577276\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.96601 | −0.891922 | −0.445961 | − | 0.895052i | \(-0.647138\pi\) | ||||
−0.445961 | + | 0.895052i | \(0.647138\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.44442i | 0.251441i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.49318 | + | 1.49318i | −0.252393 | + | 0.252393i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.57189 | −0.258417 | −0.129208 | − | 0.991617i | \(-0.541244\pi\) | ||||
−0.129208 | + | 0.991617i | \(0.541244\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.69992i | − | 0.272204i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.38487 | + | 6.25157i | 0.216281 | + | 0.976331i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.44151i | 1.28732i | 0.765313 | + | 0.643659i | \(0.222584\pi\) | ||||
−0.765313 | + | 0.643659i | \(0.777416\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.79917 | −0.268205 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.57218 | + | 1.57218i | −0.229326 | + | 0.229326i | −0.812411 | − | 0.583085i | \(-0.801845\pi\) |
0.583085 | + | 0.812411i | \(0.301845\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.22672 | −0.451831 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.25691 | + | 2.25691i | 0.310011 | + | 0.310011i | 0.844914 | − | 0.534903i | \(-0.179652\pi\) |
−0.534903 | + | 0.844914i | \(0.679652\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.09890 | − | 1.09890i | 0.148176 | − | 0.148176i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.45997 | 0.988097 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.36540 | 0.828704 | 0.414352 | − | 0.910117i | \(-0.364008\pi\) | ||||
0.414352 | + | 0.910117i | \(0.364008\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.42809i | 1.07911i | 0.841952 | + | 0.539553i | \(0.181407\pi\) | ||||
−0.841952 | + | 0.539553i | \(0.818593\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.602465 | + | 0.602465i | −0.0759034 | + | 0.0759034i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.29329 | + | 1.29329i | −0.160413 | + | 0.160413i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.439215 | + | 0.439215i | −0.0536586 | + | 0.0536586i | −0.733427 | − | 0.679768i | \(-0.762080\pi\) |
0.679768 | + | 0.733427i | \(0.262080\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.07508 | + | 5.07508i | 0.610968 | + | 0.610968i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.13798 | − | 1.13798i | −0.135054 | − | 0.135054i | 0.636348 | − | 0.771402i | \(-0.280444\pi\) |
−0.771402 | + | 0.636348i | \(0.780444\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.278184i | 0.0325590i | 0.999867 | + | 0.0162795i | \(0.00518215\pi\) | ||||
−0.999867 | + | 0.0162795i | \(0.994818\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.750589 | − | 0.750589i | −0.0866706 | − | 0.0866706i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.735950i | − | 0.0838693i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.94424 | − | 3.94424i | −0.443762 | − | 0.443762i | 0.449512 | − | 0.893274i | \(-0.351598\pi\) |
−0.893274 | + | 0.449512i | \(0.851598\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.8301 | 1.20335 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.17699 | 0.897541 | 0.448771 | − | 0.893647i | \(-0.351862\pi\) | ||||
0.448771 | + | 0.893647i | \(0.351862\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.45487 | + | 2.45487i | 0.266268 | + | 0.266268i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 10.9156i | − | 1.17028i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.2391 | + | 11.2391i | 1.19134 | + | 1.19134i | 0.976691 | + | 0.214652i | \(0.0688617\pi\) |
0.214652 | + | 0.976691i | \(0.431138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.866131i | 0.0907952i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.89187 | + | 6.89187i | 0.714653 | + | 0.714653i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.67550 | − | 5.67550i | −0.582294 | − | 0.582294i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.32999 | + | 9.32999i | −0.947317 | + | 0.947317i | −0.998680 | − | 0.0513627i | \(-0.983644\pi\) |
0.0513627 | + | 0.998680i | \(0.483644\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.443384 | − | 0.443384i | 0.0445618 | − | 0.0445618i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.06655 | + | 8.06655i | −0.802652 | + | 0.802652i | −0.983509 | − | 0.180857i | \(-0.942113\pi\) |
0.180857 | + | 0.983509i | \(0.442113\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.71515i | 0.858729i | 0.903131 | + | 0.429364i | \(0.141262\pi\) | ||||
−0.903131 | + | 0.429364i | \(0.858738\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.14448 | 0.404460 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.4476 | 1.20336 | 0.601678 | − | 0.798738i | \(-0.294499\pi\) | ||||
0.601678 | + | 0.798738i | \(0.294499\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.538916 | + | 0.538916i | −0.0516188 | + | 0.0516188i | −0.732445 | − | 0.680826i | \(-0.761621\pi\) |
0.680826 | + | 0.732445i | \(0.261621\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.18148 | + | 2.18148i | 0.207057 | + | 0.207057i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.47377 | −0.326785 | −0.163393 | − | 0.986561i | \(-0.552244\pi\) | ||||
−0.163393 | + | 0.986561i | \(0.552244\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 7.72218i | − | 0.720097i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.521814 | + | 0.521814i | −0.0482417 | + | 0.0482417i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.64406 | 0.150711 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.4584i | − | 0.950762i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.75403 | − | 10.5979i | 0.608991 | − | 0.955581i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.7004i | 1.04652i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.723418 | −0.0641930 | −0.0320965 | − | 0.999485i | \(-0.510218\pi\) | ||||
−0.0320965 | + | 0.999485i | \(0.510218\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.7152 | − | 11.7152i | 1.03146 | − | 1.03146i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.8945i | 1.21397i | 0.794715 | + | 0.606983i | \(0.207620\pi\) | ||||
−0.794715 | + | 0.606983i | \(0.792380\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.80096 | −0.329585 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.29487 | − | 6.29487i | −0.541776 | − | 0.541776i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.45697 | + | 1.45697i | −0.124477 | + | 0.124477i | −0.766601 | − | 0.642124i | \(-0.778053\pi\) |
0.642124 | + | 0.766601i | \(0.278053\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.798436 | −0.0677225 | −0.0338612 | − | 0.999427i | \(-0.510780\pi\) | ||||
−0.0338612 | + | 0.999427i | \(0.510780\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.36375 | 0.367494 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.637429i | − | 0.0533045i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.30455 | + | 8.30455i | −0.689655 | + | 0.689655i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.38781 | − | 1.38781i | 0.114464 | − | 0.114464i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.04524 | − | 2.04524i | 0.167553 | − | 0.167553i | −0.618350 | − | 0.785903i | \(-0.712199\pi\) |
0.785903 | + | 0.618350i | \(0.212199\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.07106 | − | 7.07106i | −0.575435 | − | 0.575435i | 0.358207 | − | 0.933642i | \(-0.383388\pi\) |
−0.933642 | + | 0.358207i | \(0.883388\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.990487 | + | 0.990487i | 0.0800762 | + | 0.0800762i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 10.4866i | − | 0.842303i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.5420 | − | 11.5420i | −0.921148 | − | 0.921148i | 0.0759626 | − | 0.997111i | \(-0.475797\pi\) |
−0.997111 | + | 0.0759626i | \(0.975797\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 6.26432i | − | 0.496793i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.58582 | − | 2.58582i | −0.203791 | − | 0.203791i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.12099 | −0.401107 | −0.200553 | − | 0.979683i | \(-0.564274\pi\) | ||||
−0.200553 | + | 0.979683i | \(0.564274\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.05013 | −0.237452 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.9884 | − | 14.9884i | −1.15984 | − | 1.15984i | −0.984511 | − | 0.175325i | \(-0.943902\pi\) |
−0.175325 | − | 0.984511i | \(-0.556098\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.2498i | − | 0.942294i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.28994 | − | 2.28994i | −0.175116 | − | 0.175116i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.58618i | 0.576767i | 0.957515 | + | 0.288383i | \(0.0931177\pi\) | ||||
−0.957515 | + | 0.288383i | \(0.906882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.382436 | + | 0.382436i | 0.0289094 | + | 0.0289094i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.83394 | − | 8.83394i | −0.664000 | − | 0.664000i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.75522 | − | 1.75522i | 0.131191 | − | 0.131191i | −0.638462 | − | 0.769653i | \(-0.720429\pi\) |
0.769653 | + | 0.638462i | \(0.220429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.764776 | − | 0.764776i | 0.0568454 | − | 0.0568454i | −0.678113 | − | 0.734958i | \(-0.737202\pi\) |
0.734958 | + | 0.678113i | \(0.237202\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.6966 | − | 11.6966i | 0.864634 | − | 0.864634i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.31931i | − | 0.244041i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.20995 | −0.0884800 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.21576 | −0.306651 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.87828 | + | 6.87828i | −0.497695 | + | 0.497695i | −0.910720 | − | 0.413025i | \(-0.864472\pi\) |
0.413025 | + | 0.910720i | \(0.364472\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.863929 | + | 0.863929i | 0.0621870 | + | 0.0621870i | 0.737516 | − | 0.675329i | \(-0.235999\pi\) |
−0.675329 | + | 0.737516i | \(0.735999\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.58966 | 0.257061 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.98320i | − | 0.640026i | −0.947413 | − | 0.320013i | \(-0.896313\pi\) | ||
0.947413 | − | 0.320013i | \(-0.103687\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.06602 | + | 1.06602i | −0.0755679 | + | 0.0755679i | −0.743881 | − | 0.668313i | \(-0.767017\pi\) |
0.668313 | + | 0.743881i | \(0.267017\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.21909 | 0.0859880 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.56166i | 0.390352i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.2013 | + | 2.92440i | −0.922016 | + | 0.204249i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 3.11574i | − | 0.216559i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.79732 | 0.193494 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.61928 | − | 9.61928i | 0.662218 | − | 0.662218i | −0.293684 | − | 0.955903i | \(-0.594881\pi\) |
0.955903 | + | 0.293684i | \(0.0948814\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.15860i | 0.216424i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.8257 | −1.21570 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.51150 | − | 3.51150i | −0.238376 | − | 0.238376i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.386065 | − | 0.386065i | 0.0260879 | − | 0.0260879i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.42397 | 0.0957866 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.4521 | −1.83833 | −0.919165 | − | 0.393873i | \(-0.871135\pi\) | ||||
−0.919165 | + | 0.393873i | \(0.871135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.460808i | 0.0307205i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.14726 | − | 4.14726i | 0.275263 | − | 0.275263i | −0.555952 | − | 0.831215i | \(-0.687646\pi\) |
0.831215 | + | 0.555952i | \(0.187646\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.45124 | + | 2.45124i | −0.161983 | + | 0.161983i | −0.783444 | − | 0.621462i | \(-0.786539\pi\) |
0.621462 | + | 0.783444i | \(0.286539\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.02136 | + | 1.02136i | −0.0672003 | + | 0.0672003i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.11812 | − | 4.11812i | −0.269787 | − | 0.269787i | 0.559227 | − | 0.829014i | \(-0.311098\pi\) |
−0.829014 | + | 0.559227i | \(0.811098\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.31992 | − | 3.31992i | −0.216568 | − | 0.216568i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.9477i | 0.711129i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.41383 | − | 1.41383i | −0.0914532 | − | 0.0914532i | 0.659900 | − | 0.751353i | \(-0.270599\pi\) |
−0.751353 | + | 0.659900i | \(0.770599\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3.30462i | − | 0.212870i | −0.994320 | − | 0.106435i | \(-0.966056\pi\) | ||
0.994320 | − | 0.106435i | \(-0.0339435\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.08714 | − | 6.08714i | −0.390490 | − | 0.390490i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.11167 | −0.134910 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.29213 | −0.209473 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.3481 | − | 11.3481i | −0.719155 | − | 0.719155i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.78594i | 0.175847i | 0.996127 | + | 0.0879236i | \(0.0280231\pi\) | ||||
−0.996127 | + | 0.0879236i | \(0.971977\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.90304 | + | 1.90304i | 0.119643 | + | 0.119643i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 6.81377i | − | 0.426695i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.00595 | + | 1.00595i | 0.0627496 | + | 0.0627496i | 0.737785 | − | 0.675036i | \(-0.235872\pi\) |
−0.675036 | + | 0.737785i | \(0.735872\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.11149 | − | 1.11149i | −0.0690648 | − | 0.0690648i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.35071 | + | 3.35071i | −0.207404 | + | 0.207404i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.3098 | − | 15.3098i | 0.944044 | − | 0.944044i | −0.0544715 | − | 0.998515i | \(-0.517347\pi\) |
0.998515 | + | 0.0544715i | \(0.0173474\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.76586 | + | 4.76586i | −0.292764 | + | 0.292764i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 31.1954i | − | 1.90913i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.79639 | 0.414383 | 0.207192 | − | 0.978300i | \(-0.433568\pi\) | ||||
0.207192 | + | 0.978300i | \(0.433568\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.93799 | 0.542944 | 0.271472 | − | 0.962446i | \(-0.412490\pi\) | ||||
0.271472 | + | 0.962446i | \(0.412490\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.20202 | − | 1.20202i | 0.0727497 | − | 0.0727497i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.281454 | − | 0.281454i | −0.0169723 | − | 0.0169723i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.7403 | −1.00583 | −0.502914 | − | 0.864337i | \(-0.667739\pi\) | ||||
−0.502914 | + | 0.864337i | \(0.667739\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 4.23111i | − | 0.253310i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.83300 | − | 7.83300i | 0.467278 | − | 0.467278i | −0.433754 | − | 0.901032i | \(-0.642811\pi\) |
0.901032 | + | 0.433754i | \(0.142811\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.10090 | 0.422105 | 0.211052 | − | 0.977475i | \(-0.432311\pi\) | ||||
0.211052 | + | 0.977475i | \(0.432311\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.7530i | 0.933127i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.44127 | + | 5.39978i | −0.203132 | + | 0.318739i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.2971i | 0.841004i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 25.8965 | 1.51808 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.2745 | − | 17.2745i | 1.00919 | − | 1.00919i | 0.00922862 | − | 0.999957i | \(-0.497062\pi\) |
0.999957 | − | 0.00922862i | \(-0.00293760\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.4416i | 0.782602i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.10259 | 0.180030 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.23966 | − | 2.23966i | −0.129523 | − | 0.129523i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.96905 | + | 5.96905i | −0.344050 | + | 0.344050i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.3896 | 1.28625 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.7974 | −1.01907 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.19217i | − | 0.353406i | −0.984264 | − | 0.176703i | \(-0.943457\pi\) | ||
0.984264 | − | 0.176703i | \(-0.0565432\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.0949 | − | 12.0949i | 0.688057 | − | 0.688057i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.6559 | − | 12.6559i | 0.717649 | − | 0.717649i | −0.250474 | − | 0.968123i | \(-0.580587\pi\) |
0.968123 | + | 0.250474i | \(0.0805866\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.840639 | − | 0.840639i | 0.0475157 | − | 0.0475157i | −0.682950 | − | 0.730465i | \(-0.739303\pi\) |
0.730465 | + | 0.682950i | \(0.239303\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.27221 | − | 1.27221i | −0.0716808 | − | 0.0716808i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.19168 | − | 8.19168i | −0.460090 | − | 0.460090i | 0.438595 | − | 0.898685i | \(-0.355476\pi\) |
−0.898685 | + | 0.438595i | \(0.855476\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.09311i | − | 0.229170i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.2749 | − | 17.2749i | −0.964190 | − | 0.964190i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.24900i | 0.347703i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.331239 | + | 0.331239i | 0.0183739 | + | 0.0183739i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.49582 | 0.0827192 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.22339 | −0.122580 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.0714 | + | 19.0714i | 1.04826 | + | 1.04826i | 0.998775 | + | 0.0494840i | \(0.0157577\pi\) |
0.0494840 | + | 0.998775i | \(0.484242\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.33927i | − | 0.0733916i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.927477 | − | 0.927477i | −0.0506735 | − | 0.0506735i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 24.1450i | − | 1.31526i | −0.753341 | − | 0.657630i | \(-0.771559\pi\) | ||
0.753341 | − | 0.657630i | \(-0.228441\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.82093 | + | 4.82093i | 0.261837 | + | 0.261837i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.58429 | + | 2.58429i | 0.139947 | + | 0.139947i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.7169 | + | 10.7169i | −0.576978 | + | 0.576978i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.46341 | − | 8.46341i | 0.454340 | − | 0.454340i | −0.442452 | − | 0.896792i | \(-0.645891\pi\) |
0.896792 | + | 0.442452i | \(0.145891\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.1570i | 1.40015i | 0.714069 | + | 0.700075i | \(0.246850\pi\) | ||||
−0.714069 | + | 0.700075i | \(0.753150\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.65140 | −0.194897 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.1016 | 1.60215 | 0.801074 | − | 0.598565i | \(-0.204262\pi\) | ||||
0.801074 | + | 0.598565i | \(0.204262\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.40305 | − | 2.40305i | 0.127541 | − | 0.127541i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.28164 | − | 2.28164i | −0.120757 | − | 0.120757i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.71114 | 0.354200 | 0.177100 | − | 0.984193i | \(-0.443328\pi\) | ||||
0.177100 | + | 0.984193i | \(0.443328\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.55272i | 0.239617i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.5142 | + | 14.5142i | −0.761798 | + | 0.761798i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.587433 | −0.0307476 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.0624i | 0.942847i | 0.881907 | + | 0.471424i | \(0.156260\pi\) | ||||
−0.881907 | + | 0.471424i | \(0.843740\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.32642 | + | 1.17993i | −0.277283 | + | 0.0614248i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.19176i | 0.165708i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.3347 | 0.794000 | 0.397000 | − | 0.917819i | \(-0.370051\pi\) | ||||
0.397000 | + | 0.917819i | \(0.370051\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.2380 | − | 16.2380i | 0.838524 | − | 0.838524i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.81713i | 0.248095i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.86104 | −0.403794 | −0.201897 | − | 0.979407i | \(-0.564711\pi\) | ||||
−0.201897 | + | 0.979407i | \(0.564711\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.00396 | + | 1.00396i | 0.0514346 | + | 0.0514346i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.82055 | + | 7.82055i | −0.399612 | + | 0.399612i | −0.878096 | − | 0.478484i | \(-0.841186\pi\) |
0.478484 | + | 0.878096i | \(0.341186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.55408 | 0.0792035 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.19228 | −0.365604 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.90513i | 0.299402i | 0.988731 | + | 0.149701i | \(0.0478311\pi\) | ||||
−0.988731 | + | 0.149701i | \(0.952169\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.25124 | + | 4.25124i | −0.214995 | + | 0.214995i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.2828 | − | 19.2828i | 0.972691 | − | 0.972691i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.32894 | − | 8.32894i | 0.419075 | − | 0.419075i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.3757 | − | 20.3757i | −1.02263 | − | 1.02263i | −0.999738 | − | 0.0228914i | \(-0.992713\pi\) |
−0.0228914 | − | 0.999738i | \(-0.507287\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.27499 | + | 5.27499i | 0.264080 | + | 0.264080i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.3889i | 0.518798i | 0.965770 | + | 0.259399i | \(0.0835245\pi\) | ||||
−0.965770 | + | 0.259399i | \(0.916476\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.04142 | − | 3.04142i | −0.151504 | − | 0.151504i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 22.8696i | 1.13640i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.818004 | + | 0.818004i | 0.0405469 | + | 0.0405469i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.8922 | 1.13195 | 0.565974 | − | 0.824423i | \(-0.308500\pi\) | ||||
0.565974 | + | 0.824423i | \(0.308500\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.04397 | 0.199474 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.50102 | + | 4.50102i | 0.221481 | + | 0.221481i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.2671i | 0.847609i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.10808 | + | 1.10808i | 0.0542627 | + | 0.0542627i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.91881i | 0.289153i | 0.989494 | + | 0.144576i | \(0.0461819\pi\) | ||||
−0.989494 | + | 0.144576i | \(0.953818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.46517 | − | 4.46517i | −0.217619 | − | 0.217619i | 0.589875 | − | 0.807494i | \(-0.299177\pi\) |
−0.807494 | + | 0.589875i | \(0.799177\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.33952 | − | 1.33952i | −0.0651295 | − | 0.0651295i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.628746 | − | 0.628746i | 0.0304987 | − | 0.0304987i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.95956 | + | 5.95956i | −0.288403 | + | 0.288403i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.884629 | + | 0.884629i | −0.0427103 | + | 0.0427103i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.00868i | 0.433933i | 0.976179 | + | 0.216966i | \(0.0696162\pi\) | ||||
−0.976179 | + | 0.216966i | \(0.930384\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.47139 | −0.407109 | −0.203555 | − | 0.979064i | \(-0.565249\pi\) | ||||
−0.203555 | + | 0.979064i | \(0.565249\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.0502 | 1.10517 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.82861 | − | 9.82861i | 0.470166 | − | 0.470166i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.29786 | − | 2.29786i | −0.109671 | − | 0.109671i | 0.650142 | − | 0.759813i | \(-0.274709\pi\) |
−0.759813 | + | 0.650142i | \(0.774709\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.852014 | −0.0405721 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 1.31899i | − | 0.0626673i | −0.999509 | − | 0.0313336i | \(-0.990025\pi\) | ||
0.999509 | − | 0.0313336i | \(-0.00997544\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.7333 | + | 23.7333i | −1.12507 | + | 1.12507i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.67680 | −0.268504 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 20.9279i | − | 0.987649i | −0.869561 | − | 0.493825i | \(-0.835598\pi\) | ||
0.869561 | − | 0.493825i | \(-0.164402\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.53261 | − | 3.97397i | 0.119256 | − | 0.187127i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.6265i | 0.922135i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.82898 | −0.0857441 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.6067 | − | 13.6067i | 0.636493 | − | 0.636493i | −0.313196 | − | 0.949689i | \(-0.601400\pi\) |
0.949689 | + | 0.313196i | \(0.101400\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.93095i | 0.323509i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.5007 | 1.37398 | 0.686992 | − | 0.726665i | \(-0.258931\pi\) | ||||
0.686992 | + | 0.726665i | \(0.258931\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.4091 | − | 20.4091i | −0.948490 | − | 0.948490i | 0.0502464 | − | 0.998737i | \(-0.483999\pi\) |
−0.998737 | + | 0.0502464i | \(0.983999\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.5534 | + | 14.5534i | −0.674896 | + | 0.674896i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.6883 | 0.725969 | 0.362984 | − | 0.931795i | \(-0.381758\pi\) | ||||
0.362984 | + | 0.931795i | \(0.381758\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.621143 | −0.0286817 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.0360i | 1.47614i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.39292 | − | 4.39292i | 0.201987 | − | 0.201987i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.45362 | + | 1.45362i | −0.0666967 | + | 0.0666967i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.92292 | + | 1.92292i | −0.0880446 | + | 0.0880446i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.85693 | − | 7.85693i | −0.358992 | − | 0.358992i | 0.504449 | − | 0.863441i | \(-0.331696\pi\) |
−0.863441 | + | 0.504449i | \(0.831696\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.962699 | − | 0.962699i | −0.0438953 | − | 0.0438953i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.17725i | 0.326576i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.7019 | − | 19.7019i | −0.894616 | − | 0.894616i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.60885i | − | 0.299476i | −0.988726 | − | 0.149738i | \(-0.952157\pi\) | ||
0.988726 | − | 0.149738i | \(-0.0478430\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.10694 | + | 7.10694i | 0.321387 | + | 0.321387i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.0898 | −0.590733 | −0.295367 | − | 0.955384i | \(-0.595442\pi\) | ||||
−0.295367 | + | 0.955384i | \(0.595442\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.14370 | 0.411812 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.936282 | + | 0.936282i | 0.0420827 | + | 0.0420827i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.60935i | − | 0.0721893i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.6689 | + | 18.6689i | 0.835734 | + | 0.835734i | 0.988294 | − | 0.152560i | \(-0.0487518\pi\) |
−0.152560 | + | 0.988294i | \(0.548752\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 41.6019i | 1.85864i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.7586 | − | 28.7586i | −1.28228 | − | 1.28228i | −0.939367 | − | 0.342914i | \(-0.888586\pi\) |
−0.342914 | − | 0.939367i | \(-0.611414\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.0339 | − | 17.0339i | −0.757999 | − | 0.757999i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.0004 | + | 17.0004i | −0.755013 | + | 0.755013i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.29529 | − | 1.29529i | 0.0574128 | − | 0.0574128i | −0.677817 | − | 0.735230i | \(-0.737074\pi\) |
0.735230 | + | 0.677817i | \(0.237074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.196706 | + | 0.196706i | −0.00870175 | + | 0.00870175i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 16.0239i | − | 0.707473i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.4035 | −0.810956 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.63631 | 0.0719647 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.5282 | − | 10.5282i | 0.462135 | − | 0.462135i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.6591 | + | 10.6591i | 0.466983 | + | 0.466983i | 0.900936 | − | 0.433953i | \(-0.142882\pi\) |
−0.433953 | + | 0.900936i | \(0.642882\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.5879 | −0.900245 | −0.450123 | − | 0.892967i | \(-0.648620\pi\) | ||||
−0.450123 | + | 0.892967i | \(0.648620\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.06149i | − | 0.0463274i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.77311 | + | 5.77311i | −0.251481 | + | 0.251481i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.62703 | −0.418567 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.42341i | 0.235356i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.98059 | + | 4.67692i | −0.129104 | + | 0.202580i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.2853i | 1.13641i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.87180 | −0.210234 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.520395 | − | 0.520395i | 0.0224150 | − | 0.0224150i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.2711i | 0.957508i | 0.877949 | + | 0.478754i | \(0.158911\pi\) | ||||
−0.877949 | + | 0.478754i | \(0.841089\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.12272 | −0.0910948 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.13801 | − | 1.13801i | −0.0487472 | − | 0.0487472i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.8837 | + | 28.8837i | −1.23498 | + | 1.23498i | −0.272951 | + | 0.962028i | \(0.588000\pi\) |
−0.962028 | + | 0.272951i | \(0.912000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.18085 | −0.306471 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.1397 | −0.900580 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 5.57800i | − | 0.237201i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.60656 | + | 4.60656i | −0.195538 | + | 0.195538i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.69310 | − | 5.69310i | 0.241224 | − | 0.241224i | −0.576132 | − | 0.817357i | \(-0.695439\pi\) |
0.817357 | + | 0.576132i | \(0.195439\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.16998 | + | 5.16998i | −0.218667 | + | 0.218667i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.67917 | + | 1.67917i | 0.0708946 | + | 0.0708946i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.2253 | + | 17.2253i | 0.725960 | + | 0.725960i | 0.969812 | − | 0.243852i | \(-0.0784111\pi\) |
−0.243852 | + | 0.969812i | \(0.578411\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 7.33547i | − | 0.308605i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.65805 | + | 7.65805i | 0.321608 | + | 0.321608i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.3445i | 1.77517i | 0.460640 | + | 0.887587i | \(0.347620\pi\) | ||||
−0.460640 | + | 0.887587i | \(0.652380\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.34409 | − | 5.34409i | −0.223643 | − | 0.223643i | 0.586388 | − | 0.810031i | \(-0.300550\pi\) |
−0.810031 | + | 0.586388i | \(0.800550\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.0914 | 0.797557 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.97782 | −0.0824809 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.9190 | − | 32.9190i | −1.37044 | − | 1.37044i | −0.859790 | − | 0.510648i | \(-0.829406\pi\) |
−0.510648 | − | 0.859790i | \(-0.670594\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 2.39793i | − | 0.0996547i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.78201 | + | 5.78201i | 0.239878 | + | 0.239878i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.34898i | − | 0.0972846i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.10190 | − | 1.10190i | −0.0455579 | − | 0.0455579i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.6815 | − | 20.6815i | −0.853616 | − | 0.853616i | 0.136960 | − | 0.990577i | \(-0.456267\pi\) |
−0.990577 | + | 0.136960i | \(0.956267\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.3471 | − | 13.3471i | 0.549957 | − | 0.549957i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.4669 | + | 12.4669i | −0.512822 | + | 0.512822i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.00333 | − | 4.00333i | 0.164397 | − | 0.164397i | −0.620114 | − | 0.784511i | \(-0.712914\pi\) |
0.784511 | + | 0.620114i | \(0.212914\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.47171i | 0.142326i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.95885 | 0.121098 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 47.6272 | 1.94600 | 0.972998 | − | 0.230812i | \(-0.0741383\pi\) | ||||
0.972998 | + | 0.230812i | \(0.0741383\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.81011 | + | 8.81011i | −0.359372 | + | 0.359372i | −0.863581 | − | 0.504210i | \(-0.831784\pi\) |
0.504210 | + | 0.863581i | \(0.331784\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.374217 | − | 0.374217i | −0.0152393 | − | 0.0152393i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.0847 | 0.897869 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 36.5165i | − | 1.48216i | −0.671418 | − | 0.741078i | \(-0.734315\pi\) | ||
0.671418 | − | 0.741078i | \(-0.265685\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.71851 | − | 7.71851i | 0.312770 | − | 0.312770i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.92575 | −0.0779075 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.2352i | 1.30197i | 0.759092 | + | 0.650984i | \(0.225643\pi\) | ||||
−0.759092 | + | 0.650984i | \(0.774357\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 22.3793 | + | 14.2623i | 0.902420 | + | 0.575111i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 18.8966i | − | 0.760749i | −0.924833 | − | 0.380374i | \(-0.875795\pi\) | ||
0.924833 | − | 0.380374i | \(-0.124205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.32834 | −0.294551 | −0.147275 | − | 0.989096i | \(-0.547050\pi\) | ||||
−0.147275 | + | 0.989096i | \(0.547050\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.9012 | − | 10.9012i | 0.437450 | − | 0.437450i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.8945i | 0.636799i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.0033 | −0.880130 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.88213 | − | 3.88213i | −0.155037 | − | 0.155037i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.82736 | + | 1.82736i | −0.0728616 | + | 0.0728616i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.8793 | 1.58757 | 0.793785 | − | 0.608198i | \(-0.208107\pi\) | ||||
0.793785 | + | 0.608198i | \(0.208107\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.6994 | −1.06121 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 1.52762i | − | 0.0606218i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.612447 | + | 0.612447i | −0.0242660 | + | 0.0242660i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.969578 | − | 0.969578i | 0.0383559 | − | 0.0383559i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.47633 | + | 9.47633i | −0.374292 | + | 0.374292i | −0.869038 | − | 0.494745i | \(-0.835261\pi\) |
0.494745 | + | 0.869038i | \(0.335261\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.2664 | + | 14.2664i | 0.562614 | + | 0.562614i | 0.930049 | − | 0.367435i | \(-0.119764\pi\) |
−0.367435 | + | 0.930049i | \(0.619764\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.7386 | + | 24.7386i | 0.974081 | + | 0.974081i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 17.0892i | − | 0.671846i | −0.941889 | − | 0.335923i | \(-0.890952\pi\) | ||
0.941889 | − | 0.335923i | \(-0.109048\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.31252 | − | 3.31252i | −0.130028 | − | 0.130028i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.74657i | 0.381998i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.1468 | + | 11.1468i | 0.436207 | + | 0.436207i | 0.890733 | − | 0.454526i | \(-0.150191\pi\) |
−0.454526 | + | 0.890733i | \(0.650191\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.3406 | −1.14643 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.237017 | −0.00924690 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.418356 | + | 0.418356i | 0.0162968 | + | 0.0162968i | 0.715208 | − | 0.698911i | \(-0.246332\pi\) |
−0.698911 | + | 0.715208i | \(0.746332\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 5.10196i | − | 0.198443i | −0.995065 | − | 0.0992216i | \(-0.968365\pi\) | ||
0.995065 | − | 0.0992216i | \(-0.0316353\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.97620 | − | 1.97620i | −0.0767491 | − | 0.0767491i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 8.02637i | − | 0.311249i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.3815 | − | 14.3815i | −0.556853 | − | 0.556853i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 38.0982 | + | 38.0982i | 1.47296 | + | 1.47296i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.38594 | − | 4.38594i | 0.169317 | − | 0.169317i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.9106 | − | 18.9106i | 0.728952 | − | 0.728952i | −0.241459 | − | 0.970411i | \(-0.577626\pi\) |
0.970411 | + | 0.241459i | \(0.0776261\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.61225 | + | 1.61225i | −0.0620557 | + | 0.0620557i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 22.4278i | − | 0.861969i | −0.902359 | − | 0.430984i | \(-0.858166\pi\) | ||
0.902359 | − | 0.430984i | \(-0.141834\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.1946 | −0.506362 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.5112 | −0.441109 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.6486 | − | 16.6486i | 0.637040 | − | 0.637040i | −0.312784 | − | 0.949824i | \(-0.601262\pi\) |
0.949824 | + | 0.312784i | \(0.101262\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.07663 | − | 3.07663i | −0.117552 | − | 0.117552i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.80370 | 0.259577 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.76448i | 0.105318i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.3720 | + | 19.3720i | −0.736945 | + | 0.736945i | −0.971986 | − | 0.235040i | \(-0.924478\pi\) |
0.235040 | + | 0.971986i | \(0.424478\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.627040 | 0.0238193 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 1.68603i | − | 0.0639549i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.87756 | + | 5.65765i | 0.336261 | + | 0.214299i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.4303i | 0.432334i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.05364 | 0.266412 | 0.133206 | − | 0.991088i | \(-0.457473\pi\) | ||||
0.133206 | + | 0.991088i | \(0.457473\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.22474 | − | 4.22474i | 0.159339 | − | 0.159339i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.21481i | 0.347050i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.4078 | −0.429036 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.3339 | − | 13.3339i | −0.500767 | − | 0.500767i | 0.410909 | − | 0.911676i | \(-0.365211\pi\) |
−0.911676 | + | 0.410909i | \(0.865211\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.36055 | − | 3.36055i | 0.126030 | − | 0.126030i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.1603 | 0.680107 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.34604 | 0.0503391 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.92425i | 0.146554i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.6670 | − | 21.6670i | 0.808044 | − | 0.808044i | −0.176294 | − | 0.984338i | \(-0.556411\pi\) |
0.984338 | + | 0.176294i | \(0.0564109\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.16254 | + | 6.16254i | −0.229505 | + | 0.229505i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.58618 | + | 4.58618i | −0.170562 | + | 0.170562i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.12698 | + | 2.12698i | 0.0789940 | + | 0.0789940i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.23623 | + | 4.23623i | 0.157113 | + | 0.157113i | 0.781286 | − | 0.624173i | \(-0.214564\pi\) |
−0.624173 | + | 0.781286i | \(0.714564\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 15.5948i | − | 0.577585i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.81346 | + | 9.81346i | 0.362964 | + | 0.362964i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.0360i | 1.77425i | 0.461531 | + | 0.887124i | \(0.347300\pi\) | ||||
−0.461531 | + | 0.887124i | \(0.652700\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.93059 | + | 2.93059i | 0.108096 | + | 0.108096i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.457131 | 0.0168386 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.0807 | 0.922608 | 0.461304 | − | 0.887242i | \(-0.347382\pi\) | ||||
0.461304 | + | 0.887242i | \(0.347382\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.56884 | + | 4.56884i | 0.167840 | + | 0.167840i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.1665i | 0.849897i | 0.905218 | + | 0.424948i | \(0.139708\pi\) | ||||
−0.905218 | + | 0.424948i | \(0.860292\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.31888 | + | 4.31888i | 0.158232 | + | 0.158232i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.96691i | 0.254906i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.80180 | + | 8.80180i | 0.321611 | + | 0.321611i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.4974 | + | 22.4974i | 0.820942 | + | 0.820942i | 0.986243 | − | 0.165301i | \(-0.0528595\pi\) |
−0.165301 | + | 0.986243i | \(0.552860\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.86635 | − | 3.86635i | 0.140898 | − | 0.140898i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.9318 | − | 14.9318i | 0.543422 | − | 0.543422i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.62170 | + | 8.62170i | −0.313361 | + | 0.313361i | −0.846210 | − | 0.532849i | \(-0.821121\pi\) |
0.532849 | + | 0.846210i | \(0.321121\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5.28210i | − | 0.191728i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.67890 | −0.169610 | −0.0848049 | − | 0.996398i | \(-0.527027\pi\) | ||||
−0.0848049 | + | 0.996398i | \(0.527027\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.762143 | −0.0275914 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.09158 | + | 2.09158i | −0.0756214 | + | 0.0756214i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.89847 | + | 3.89847i | 0.140766 | + | 0.140766i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.68935 | 0.277285 | 0.138643 | − | 0.990342i | \(-0.455726\pi\) | ||||
0.138643 | + | 0.990342i | \(0.455726\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 2.79214i | − | 0.100556i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.51065 | − | 6.51065i | 0.234172 | − | 0.234172i | −0.580260 | − | 0.814432i | \(-0.697049\pi\) |
0.814432 | + | 0.580260i | \(0.197049\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.68585 | −0.0964785 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.08507i | 0.110676i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.5243 | − | 13.0801i | −0.735361 | − | 0.468644i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.18440i | 0.0423813i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23.4466 | −0.837914 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.3728 | − | 24.3728i | 0.869903 | − | 0.869903i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.8016i | 1.38313i | 0.722314 | + | 0.691565i | \(0.243078\pi\) | ||||
−0.722314 | + | 0.691565i | \(0.756922\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −42.4941 | −1.51283 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.45633 | − | 2.45633i | −0.0873370 | − | 0.0873370i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.16176 | + | 5.16176i | −0.183299 | + | 0.183299i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.2282 | 0.469155 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.6615 | −1.40488 | −0.702441 | − | 0.711742i | \(-0.747907\pi\) | ||||
−0.702441 | + | 0.711742i | \(0.747907\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.65539i | 0.129318i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.57587 | + | 9.57587i | −0.338347 | + | 0.338347i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.144766 | − | 0.144766i | 0.00510867 | − | 0.00510867i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.46041 | − | 5.46041i | 0.192454 | − | 0.192454i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.43208 | − | 9.43208i | −0.332025 | − | 0.332025i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.2934 | + | 30.2934i | 1.06506 | + | 1.06506i | 0.997731 | + | 0.0673269i | \(0.0214470\pi\) |
0.0673269 | + | 0.997731i | \(0.478553\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.5648i | 0.862587i | 0.902212 | + | 0.431294i | \(0.141943\pi\) | ||||
−0.902212 | + | 0.431294i | \(0.858057\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.4042 | − | 12.4042i | −0.435034 | − | 0.435034i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 10.8138i | − | 0.378792i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.6881 | − | 22.6881i | −0.793756 | − | 0.793756i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.737956 | −0.0257863 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.37822 | 0.0481001 | 0.0240500 | − | 0.999711i | \(-0.492344\pi\) | ||||
0.0240500 | + | 0.999711i | \(0.492344\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.51453 | − | 3.51453i | −0.122509 | − | 0.122509i | 0.643194 | − | 0.765703i | \(-0.277609\pi\) |
−0.765703 | + | 0.643194i | \(0.777609\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.781206i | 0.0271981i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.56446 | + | 8.56446i | 0.297815 | + | 0.297815i | 0.840158 | − | 0.542342i | \(-0.182462\pi\) |
−0.542342 | + | 0.840158i | \(0.682462\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 29.0041i | − | 1.00735i | −0.863892 | − | 0.503677i | \(-0.831980\pi\) | ||
0.863892 | − | 0.503677i | \(-0.168020\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.2323 | + | 23.2323i | 0.805920 | + | 0.805920i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.16252 | + | 1.16252i | 0.0402791 | + | 0.0402791i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31.6505 | − | 31.6505i | 1.09531 | − | 1.09531i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.8036 | − | 14.8036i | 0.511688 | − | 0.511688i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.7499 | + | 26.7499i | −0.923510 | + | 0.923510i | −0.997276 | − | 0.0737653i | \(-0.976498\pi\) |
0.0737653 | + | 0.997276i | \(0.476498\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.93211i | 0.0666246i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.7414 | −0.748813 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.8676 | 0.889872 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.39519 | − | 7.39519i | 0.254102 | − | 0.254102i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.85468 | − | 9.85468i | −0.338212 | − | 0.338212i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.74825 | 0.197047 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.9534i | 0.751670i | 0.926687 | + | 0.375835i | \(0.122644\pi\) | ||||
−0.926687 | + | 0.375835i | \(0.877356\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.83561 | − | 4.83561i | 0.165374 | − | 0.165374i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.9767 | 0.477434 | 0.238717 | − | 0.971089i | \(-0.423273\pi\) | ||||
0.238717 | + | 0.971089i | \(0.423273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 15.6320i | − | 0.533357i | −0.963786 | − | 0.266679i | \(-0.914074\pi\) | ||
0.963786 | − | 0.266679i | \(-0.0859262\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.2697 | − | 2.71803i | 0.418149 | − | 0.0926302i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 55.7402i | 1.89742i | 0.316151 | + | 0.948709i | \(0.397610\pi\) | ||||
−0.316151 | + | 0.948709i | \(0.602390\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.0195 | −0.544680 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.8416 | − | 19.8416i | 0.673855 | − | 0.673855i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.10513i | 0.139257i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.537991 | −0.0182291 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.94929 | − | 7.94929i | −0.269043 | − | 0.269043i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.27346 | + | 8.27346i | −0.279694 | + | 0.279694i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 57.2454 | 1.93304 | 0.966519 | − | 0.256594i | \(-0.0826004\pi\) | ||||
0.966519 | + | 0.256594i | \(0.0826004\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −47.9473 | −1.61722 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 39.8961i | − | 1.34413i | −0.740491 | − | 0.672066i | \(-0.765407\pi\) | ||
0.740491 | − | 0.672066i | \(-0.234593\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.151721 | − | 0.151721i | 0.00510581 | − | 0.00510581i | −0.704549 | − | 0.709655i | \(-0.748851\pi\) |
0.709655 | + | 0.704549i | \(0.248851\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.6544 | − | 18.6544i | 0.627060 | − | 0.627060i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.81787 | − | 6.81787i | 0.228922 | − | 0.228922i | −0.583320 | − | 0.812242i | \(-0.698247\pi\) |
0.812242 | + | 0.583320i | \(0.198247\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.511534 | − | 0.511534i | −0.0171563 | − | 0.0171563i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.63594 | − | 5.63594i | −0.188811 | − | 0.188811i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 8.45103i | − | 0.282803i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.70644 | + | 3.70644i | 0.123893 | + | 0.123893i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.21644i | 0.207561i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.5298 | − | 19.5298i | −0.651355 | − | 0.651355i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.24744 | 0.174817 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.5678 | 0.551341 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.61496 | + | 1.61496i | 0.0536830 | + | 0.0536830i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 31.0676i | − | 1.03158i | −0.856714 | − | 0.515791i | \(-0.827498\pi\) | ||
0.856714 | − | 0.515791i | \(-0.172502\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.87282 | − | 6.87282i | −0.227957 | − | 0.227957i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.9756i | 1.82142i | 0.413042 | + | 0.910712i | \(0.364466\pi\) | ||||
−0.413042 | + | 0.910712i | \(0.635534\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.25527 | − | 4.25527i | −0.140829 | − | 0.140829i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.6993 | + | 24.6993i | 0.816533 | + | 0.816533i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.82488 | + | 9.82488i | −0.324446 | + | 0.324446i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.2472 | − | 14.2472i | 0.469972 | − | 0.469972i | −0.431934 | − | 0.901905i | \(-0.642169\pi\) |
0.901905 | + | 0.431934i | \(0.142169\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.59354 | + | 8.59354i | −0.283167 | + | 0.283167i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.39391i | − | 0.0458811i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.850149 | −0.0279527 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.42543 | −0.243883 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.08578 | − | 6.08578i | 0.199668 | − | 0.199668i | −0.600190 | − | 0.799858i | \(-0.704908\pi\) |
0.799858 | + | 0.600190i | \(0.204908\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.68768 | − | 2.68768i | −0.0880853 | − | 0.0880853i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −35.1278 | −1.15003 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2.55501i | − | 0.0835576i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.41689 | + | 1.41689i | −0.0462878 | + | 0.0462878i | −0.729872 | − | 0.683584i | \(-0.760420\pi\) |
0.683584 | + | 0.729872i | \(0.260420\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.33329 | −0.0761440 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 14.4776i | − | 0.471956i | −0.971758 | − | 0.235978i | \(-0.924171\pi\) | ||
0.971758 | − | 0.235978i | \(-0.0758294\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.06436 | − | 22.8614i | −0.164918 | − | 0.744470i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 8.90229i | − | 0.289591i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.27765 | −0.0415182 | −0.0207591 | − | 0.999785i | \(-0.506608\pi\) | ||||
−0.0207591 | + | 0.999785i | \(0.506608\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.170373 | + | 0.170373i | −0.00553054 | + | 0.00553054i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.7369i | 0.737295i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.6253 | −0.506154 | −0.253077 | − | 0.967446i | \(-0.581443\pi\) | ||||
−0.253077 | + | 0.967446i | \(0.581443\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.5247 | − | 14.5247i | −0.470007 | − | 0.470007i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.68044 | + | 5.68044i | −0.183623 | + | 0.183623i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.06046 | −0.0665357 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.33870 | −0.204474 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.6055i | 0.341759i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.82433 | + | 1.82433i | −0.0587274 | + | 0.0587274i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.9846 | − | 16.9846i | 0.546187 | − | 0.546187i | −0.379149 | − | 0.925336i | \(-0.623783\pi\) |
0.925336 | + | 0.379149i | \(0.123783\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.67240 | − | 8.67240i | 0.278598 | − | 0.278598i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.218722 | − | 0.218722i | −0.00701914 | − | 0.00701914i | 0.703589 | − | 0.710608i | \(-0.251580\pi\) |
−0.710608 | + | 0.703589i | \(0.751580\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.564580 | − | 0.564580i | −0.0180996 | − | 0.0180996i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 0.919392i | − | 0.0294441i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.9439 | − | 33.9439i | −1.08596 | − | 1.08596i | −0.995940 | − | 0.0900206i | \(-0.971307\pi\) |
−0.0900206 | − | 0.995940i | \(-0.528693\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 11.6976i | − | 0.373855i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.459164 | − | 0.459164i | −0.0146600 | − | 0.0146600i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.5678 | −0.368957 | −0.184478 | − | 0.982837i | \(-0.559060\pi\) | ||||
−0.184478 | + | 0.982837i | \(0.559060\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.9696 | 0.604421 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.08564 | + | 3.08564i | 0.0982170 | + | 0.0982170i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 30.8698i | − | 0.981602i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.7912 | + | 22.7912i | 0.723988 | + | 0.723988i | 0.969415 | − | 0.245427i | \(-0.0789283\pi\) |
−0.245427 | + | 0.969415i | \(0.578928\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 52.9348i | − | 1.67984i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.25107 | − | 2.25107i | −0.0713639 | − | 0.0713639i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.1411 | − | 27.1411i | −0.859569 | − | 0.859569i | 0.131719 | − | 0.991287i | \(-0.457950\pi\) |
−0.991287 | + | 0.131719i | \(0.957950\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.68578 | − | 4.68578i | 0.148252 | − | 0.148252i |
(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 | 1148.2.k.b.337.5 | ✓ | 36 | |
41.32 | even | 4 | inner | 1148.2.k.b.729.5 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.k.b.337.5 | ✓ | 36 | 1.1 | even | 1 | trivial | |
1148.2.k.b.729.5 | yes | 36 | 41.32 | even | 4 | inner |