Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(47,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.be (of order \(18\), degree \(6\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 47.4 | ||
Character | \(\chi\) | \(=\) | 432.47 |
Dual form | 432.2.be.a.239.4 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.340461 | + | 1.69826i | 0.196565 | + | 0.980491i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.68195 | − | 0.296574i | 0.752193 | − | 0.132632i | 0.215610 | − | 0.976480i | \(-0.430826\pi\) |
0.536583 | + | 0.843848i | \(0.319715\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.981328 | + | 1.16950i | −0.370907 | + | 0.442030i | −0.918922 | − | 0.394438i | \(-0.870939\pi\) |
0.548015 | + | 0.836468i | \(0.315384\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.76817 | + | 1.15638i | −0.922724 | + | 0.385460i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.602821 | + | 3.41877i | −0.181757 | + | 1.03080i | 0.748294 | + | 0.663368i | \(0.230873\pi\) |
−0.930051 | + | 0.367430i | \(0.880238\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.74648 | + | 0.999638i | 0.761737 | + | 0.277250i | 0.693536 | − | 0.720422i | \(-0.256052\pi\) |
0.0682011 | + | 0.997672i | \(0.478274\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.07630 | + | 2.75542i | 0.277899 | + | 0.711447i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.812691 | − | 0.469208i | 0.197107 | − | 0.113800i | −0.398199 | − | 0.917299i | \(-0.630365\pi\) |
0.595305 | + | 0.803500i | \(0.297031\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.51710 | + | 0.875899i | 0.348047 | + | 0.200945i | 0.663825 | − | 0.747888i | \(-0.268932\pi\) |
−0.315778 | + | 0.948833i | \(0.602265\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.32022 | − | 1.26838i | −0.506314 | − | 0.276783i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0294832 | − | 0.0247394i | 0.00614768 | − | 0.00515851i | −0.639709 | − | 0.768618i | \(-0.720945\pi\) |
0.645856 | + | 0.763459i | \(0.276501\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.95745 | + | 0.712454i | −0.391490 | + | 0.142491i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.90629 | − | 4.30738i | −0.559316 | − | 0.828955i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.84729 | − | 5.07538i | −0.343032 | − | 0.942474i | −0.984509 | − | 0.175331i | \(-0.943900\pi\) |
0.641477 | − | 0.767142i | \(-0.278322\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.26730 | + | 5.08557i | 0.766430 | + | 0.913396i | 0.998236 | − | 0.0593663i | \(-0.0189080\pi\) |
−0.231806 | + | 0.972762i | \(0.574464\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.01119 | + | 0.140209i | −1.04641 | + | 0.0244072i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.30371 | + | 2.25808i | −0.220366 | + | 0.381686i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.09995 | + | 5.36926i | 0.509628 | + | 0.882702i | 0.999938 | + | 0.0111534i | \(0.00355030\pi\) |
−0.490310 | + | 0.871548i | \(0.663116\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.762576 | + | 5.00458i | −0.122110 | + | 0.801374i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.60794 | − | 4.41779i | 0.251119 | − | 0.689943i | −0.748521 | − | 0.663111i | \(-0.769236\pi\) |
0.999640 | − | 0.0268321i | \(-0.00854194\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.03174 | − | 1.41621i | −1.22483 | − | 0.215970i | −0.476426 | − | 0.879215i | \(-0.658068\pi\) |
−0.748403 | + | 0.663244i | \(0.769179\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.31299 | + | 2.76595i | −0.642942 | + | 0.412323i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.29137 | + | 5.27909i | 0.917691 | + | 0.770034i | 0.973567 | − | 0.228404i | \(-0.0733506\pi\) |
−0.0558757 | + | 0.998438i | \(0.517795\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.810809 | + | 4.59833i | 0.115830 | + | 0.656904i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.07353 | + | 1.22041i | 0.150324 | + | 0.170892i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 12.6923i | − | 1.74342i | −0.490020 | − | 0.871711i | \(-0.663011\pi\) | ||
0.490020 | − | 0.871711i | \(-0.336989\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.92899i | 0.799465i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.970991 | + | 2.87464i | −0.128611 | + | 0.380756i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.57645 | − | 14.6118i | −0.335425 | − | 1.90229i | −0.422997 | − | 0.906131i | \(-0.639022\pi\) |
0.0875717 | − | 0.996158i | \(-0.472089\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.6194 | + | 8.91077i | 1.35968 | + | 1.14091i | 0.976081 | + | 0.217408i | \(0.0697602\pi\) |
0.383600 | + | 0.923499i | \(0.374684\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.36410 | − | 4.37217i | 0.171860 | − | 0.550842i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.91592 | + | 0.866810i | 0.609745 | + | 0.107515i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.52189 | − | 12.4238i | 0.552437 | − | 1.51781i | −0.277937 | − | 0.960599i | \(-0.589651\pi\) |
0.830373 | − | 0.557208i | \(-0.188127\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0520517 | + | 0.0416474i | 0.00626629 | + | 0.00501376i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.81864 | − | 3.14997i | −0.215832 | − | 0.373833i | 0.737697 | − | 0.675132i | \(-0.235913\pi\) |
−0.953530 | + | 0.301299i | \(0.902580\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.02246 | + | 3.50300i | −0.236711 | + | 0.409996i | −0.959769 | − | 0.280792i | \(-0.909403\pi\) |
0.723058 | + | 0.690788i | \(0.242736\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.87637 | − | 3.08170i | −0.216664 | − | 0.355844i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.40669 | − | 4.05993i | −0.388228 | − | 0.462672i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.29234 | − | 11.7931i | −0.482926 | − | 1.32683i | −0.906973 | − | 0.421188i | \(-0.861613\pi\) |
0.424047 | − | 0.905640i | \(-0.360609\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.32557 | − | 6.40213i | 0.702841 | − | 0.711347i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.42314 | − | 1.24592i | 0.375739 | − | 0.136758i | −0.147246 | − | 0.989100i | \(-0.547041\pi\) |
0.522984 | + | 0.852342i | \(0.324819\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.22775 | − | 1.03021i | 0.133169 | − | 0.111742i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.99038 | − | 4.86514i | 0.856659 | − | 0.521597i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.61727 | + | 4.39783i | 0.807429 | + | 0.466169i | 0.846062 | − | 0.533084i | \(-0.178967\pi\) |
−0.0386332 | + | 0.999253i | \(0.512300\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.86428 | + | 2.23104i | −0.405086 | + | 0.233877i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.18377 | + | 8.97842i | −0.744923 | + | 0.931019i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.81146 | + | 1.02329i | 0.288450 | + | 0.104987i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.737508 | − | 4.18262i | 0.0748826 | − | 0.424680i | −0.924202 | − | 0.381904i | \(-0.875269\pi\) |
0.999085 | − | 0.0427765i | \(-0.0136203\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.28469 | − | 10.1608i | −0.229620 | − | 1.02120i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.83655 | − | 5.76397i | 0.481254 | − | 0.573537i | −0.469716 | − | 0.882817i | \(-0.655644\pi\) |
0.950971 | + | 0.309281i | \(0.100088\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.3823 | − | 2.18334i | 1.22007 | − | 0.215131i | 0.473713 | − | 0.880679i | \(-0.342913\pi\) |
0.746355 | + | 0.665548i | \(0.231802\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.27867 | − | 1.44524i | −0.417556 | − | 0.141041i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.0430 | −1.84096 | −0.920478 | − | 0.390794i | \(-0.872201\pi\) | ||||
−0.920478 | + | 0.390794i | \(0.872201\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.46704 | 0.427865 | 0.213933 | − | 0.976848i | \(-0.431373\pi\) | ||||
0.213933 | + | 0.976848i | \(0.431373\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.06300 | + | 7.09254i | −0.765306 | + | 0.673194i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.78707 | + | 0.315108i | −0.168113 | + | 0.0296428i | −0.257071 | − | 0.966393i | \(-0.582757\pi\) |
0.0889580 | + | 0.996035i | \(0.471646\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0422524 | − | 0.0503544i | 0.00394005 | − | 0.00469557i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.75870 | + | 0.408809i | −0.809742 | + | 0.0377944i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.248778 | + | 1.41089i | −0.0228054 | + | 0.129336i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.987967 | − | 0.359591i | −0.0898152 | − | 0.0326901i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.05000 | + | 1.22662i | 0.725844 | + | 0.110601i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4765 | + | 6.04859i | −0.937044 | + | 0.541003i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.27879 | + | 3.62506i | 0.557153 | + | 0.321672i | 0.752002 | − | 0.659161i | \(-0.229088\pi\) |
−0.194849 | + | 0.980833i | \(0.562422\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.329394 | − | 14.1221i | −0.0290015 | − | 1.24339i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3886 | − | 11.2343i | 1.16976 | − | 0.981548i | 0.169771 | − | 0.985484i | \(-0.445697\pi\) |
0.999992 | + | 0.00393578i | \(0.00125280\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.51314 | + | 0.914708i | −0.217917 | + | 0.0793152i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.16570 | − | 6.38288i | −0.530659 | − | 0.549351i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.81753 | + | 4.99361i | 0.155282 | + | 0.426633i | 0.992801 | − | 0.119774i | \(-0.0382172\pi\) |
−0.837519 | + | 0.546408i | \(0.815995\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.75657 | − | 9.24392i | −0.657904 | − | 0.784059i | 0.329179 | − | 0.944267i | \(-0.393228\pi\) |
−0.987083 | + | 0.160208i | \(0.948783\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.82330 | + | 12.4817i | −0.574625 | + | 1.05115i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.07317 | + | 8.78699i | −0.424240 | + | 0.734805i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.61227 | − | 7.98869i | −0.383028 | − | 0.663425i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.53310 | + | 2.94251i | −0.621320 | + | 0.242694i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.380050 | − | 1.04418i | 0.0311349 | − | 0.0855425i | −0.923151 | − | 0.384437i | \(-0.874396\pi\) |
0.954286 | + | 0.298894i | \(0.0966179\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.54782 | − | 1.50721i | −0.695612 | − | 0.122655i | −0.185348 | − | 0.982673i | \(-0.559341\pi\) |
−0.510264 | + | 0.860018i | \(0.670452\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.70709 | + | 2.23863i | −0.138010 | + | 0.180982i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.68565 | + | 7.28813i | 0.697648 | + | 0.585396i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.0313604 | + | 0.177853i | 0.00250283 | + | 0.0141943i | 0.986034 | − | 0.166547i | \(-0.0532616\pi\) |
−0.983531 | + | 0.180741i | \(0.942150\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.5548 | − | 4.32123i | 1.70941 | − | 0.342696i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0587581i | 0.00463079i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.6854i | 1.69853i | 0.527967 | + | 0.849265i | \(0.322955\pi\) | ||||
−0.527967 | + | 0.849265i | \(0.677045\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.0690 | + | 2.01859i | −0.783868 | + | 0.157147i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.444010 | − | 2.51811i | −0.0343585 | − | 0.194857i | 0.962797 | − | 0.270225i | \(-0.0870980\pi\) |
−0.997156 | + | 0.0753678i | \(0.975987\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.41469 | − | 2.86526i | −0.262668 | − | 0.220405i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.21247 | − | 0.670293i | −0.398608 | − | 0.0512586i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.1824 | − | 1.97176i | −0.850183 | − | 0.149910i | −0.268454 | − | 0.963293i | \(-0.586513\pi\) |
−0.581730 | + | 0.813382i | \(0.697624\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.08769 | − | 2.98839i | 0.0822213 | − | 0.225901i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.9374 | − | 9.35021i | 1.79924 | − | 0.702805i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.60767 | − | 4.51662i | −0.194907 | − | 0.337588i | 0.751963 | − | 0.659205i | \(-0.229107\pi\) |
−0.946870 | + | 0.321617i | \(0.895774\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.98011 | − | 10.3579i | 0.444498 | − | 0.769893i | −0.553519 | − | 0.832837i | \(-0.686715\pi\) |
0.998017 | + | 0.0629432i | \(0.0200487\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.5173 | + | 21.0683i | −0.851384 | + | 1.55742i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.80635 | + | 8.11149i | 0.500413 | + | 0.596369i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.11420 | + | 3.06125i | 0.0814787 | + | 0.223861i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.88950 | + | 0.828040i | 0.573877 | + | 0.0602310i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3596 | − | 3.77059i | 0.749595 | − | 0.272830i | 0.0611596 | − | 0.998128i | \(-0.480520\pi\) |
0.688435 | + | 0.725298i | \(0.258298\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.58102 | + | 5.52213i | −0.473712 | + | 0.397492i | −0.848146 | − | 0.529762i | \(-0.822281\pi\) |
0.374434 | + | 0.927253i | \(0.377837\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.201609 | + | 8.64363i | 0.0144375 | + | 0.618983i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.1886 | + | 8.76915i | 1.08214 | + | 0.624776i | 0.931474 | − | 0.363808i | \(-0.118524\pi\) |
0.150670 | + | 0.988584i | \(0.451857\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.6687 | + | 9.04633i | −1.11073 | + | 0.641278i | −0.939017 | − | 0.343870i | \(-0.888262\pi\) |
−0.171708 | + | 0.985148i | \(0.554929\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.6383 | + | 3.44953i | 1.59679 | + | 0.243311i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.74845 | + | 2.82021i | 0.543835 | + | 0.197940i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.39429 | − | 7.90739i | 0.0973812 | − | 0.552276i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.0530065 | + | 0.102577i | −0.00368421 | + | 0.00712957i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.90904 | + | 4.65861i | −0.270394 | + | 0.322243i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.8844 | − | 2.80084i | 1.09352 | − | 0.192818i | 0.402335 | − | 0.915492i | \(-0.368199\pi\) |
0.691188 | + | 0.722675i | \(0.257087\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.73029 | − | 4.16096i | 0.324114 | − | 0.285104i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.9290 | −0.949952 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.1352 | −0.688023 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.63758 | − | 2.24203i | −0.448526 | − | 0.151502i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.70108 | − | 0.476273i | 0.181694 | − | 0.0320376i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.67593 | + | 1.99730i | −0.112229 | + | 0.133749i | −0.819234 | − | 0.573459i | \(-0.805601\pi\) |
0.707005 | + | 0.707208i | \(0.250046\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.59469 | − | 4.23575i | 0.306313 | − | 0.282384i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.97284 | + | 22.5311i | −0.263686 | + | 1.49544i | 0.509063 | + | 0.860729i | \(0.329992\pi\) |
−0.772750 | + | 0.634711i | \(0.781119\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.564600 | + | 0.205498i | 0.0373098 | + | 0.0135797i | 0.360608 | − | 0.932718i | \(-0.382569\pi\) |
−0.323298 | + | 0.946297i | \(0.604792\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.73498 | − | 7.16769i | 0.377334 | − | 0.471599i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.8951 | + | 14.9505i | −1.69644 | + | 0.979441i | −0.747355 | + | 0.664425i | \(0.768676\pi\) |
−0.949086 | + | 0.315016i | \(0.897990\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.1474 | + | 7.01332i | 0.792411 | + | 0.457499i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.5664 | − | 11.3046i | 1.20602 | − | 0.734313i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.533039 | + | 0.447273i | −0.0344794 | + | 0.0289317i | −0.659865 | − | 0.751385i | \(-0.729386\pi\) |
0.625385 | + | 0.780316i | \(0.284942\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.8422 | + | 5.40211i | −0.956069 | + | 0.347981i | −0.772492 | − | 0.635024i | \(-0.780990\pi\) |
−0.183577 | + | 0.983005i | \(0.558768\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.0261 | + | 8.56278i | 0.835623 | + | 0.549303i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.72749 | + | 7.49371i | 0.174253 | + | 0.478755i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.29111 | + | 3.92219i | 0.209408 | + | 0.249563i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.28134 | + | 5.38920i | 0.207947 | + | 0.341527i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.0929 | + | 19.2135i | −0.700180 | + | 1.21275i | 0.268223 | + | 0.963357i | \(0.413564\pi\) |
−0.968403 | + | 0.249391i | \(0.919770\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0668050 | + | 0.115710i | 0.00420000 | + | 0.00727461i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.16756 | + | 1.73430i | 0.135738 | + | 0.108606i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.17758 | + | 19.7202i | −0.447725 | + | 1.23012i | 0.486578 | + | 0.873637i | \(0.338245\pi\) |
−0.934304 | + | 0.356478i | \(0.883977\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.32143 | − | 1.64362i | −0.579205 | − | 0.102130i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.9827 | + | 11.9134i | 0.679810 | + | 0.737418i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.15049 | + | 5.16087i | 0.379256 | + | 0.318233i | 0.812410 | − | 0.583086i | \(-0.198155\pi\) |
−0.433155 | + | 0.901320i | \(0.642600\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.76421 | − | 21.3479i | −0.231233 | − | 1.31139i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.87528 | + | 14.4334i | −0.298363 | + | 0.883309i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 26.1874i | − | 1.59668i | −0.602209 | − | 0.798338i | \(-0.705713\pi\) | ||
0.602209 | − | 0.798338i | \(-0.294287\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.9170i | 0.906140i | 0.891475 | + | 0.453070i | \(0.149671\pi\) | ||||
−0.891475 | + | 0.453070i | \(0.850329\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.10452 | − | 5.80297i | −0.308940 | − | 0.351212i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.25572 | − | 7.12155i | −0.0757229 | − | 0.429446i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.2963 | − | 11.9960i | −0.858983 | − | 0.720772i | 0.102766 | − | 0.994706i | \(-0.467231\pi\) |
−0.961749 | + | 0.273933i | \(0.911675\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.6935 | − | 9.14312i | −1.05928 | − | 0.547384i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.14342 | − | 0.730597i | −0.247176 | − | 0.0435838i | 0.0486874 | − | 0.998814i | \(-0.484496\pi\) |
−0.295863 | + | 0.955230i | \(0.595607\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.667465 | + | 1.83384i | −0.0396766 | + | 0.109011i | −0.957949 | − | 0.286939i | \(-0.907362\pi\) |
0.918272 | + | 0.395950i | \(0.129585\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.780618 | + | 5.12298i | −0.0462398 | + | 0.303459i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.58869 | + | 6.21579i | 0.211834 | + | 0.366907i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.05969 | + | 13.9598i | −0.474099 | + | 0.821164i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.35426 | − | 0.171535i | 0.431114 | − | 0.0100556i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.47915 | − | 6.52979i | −0.320095 | − | 0.381474i | 0.581871 | − | 0.813281i | \(-0.302321\pi\) |
−0.901966 | + | 0.431806i | \(0.857876\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.66693 | − | 23.8122i | −0.504608 | − | 1.38640i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.4779 | − | 7.33935i | 0.956144 | − | 0.425872i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.105706 | − | 0.0384737i | 0.00611311 | − | 0.00222499i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.53804 | − | 8.00336i | 0.549763 | − | 0.461306i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.4354 | + | 6.25131i | 0.656945 | + | 0.359128i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.5041 | + | 11.8381i | 1.17406 | + | 0.677845i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.57163 | − | 4.94883i | 0.489209 | − | 0.282445i | −0.235037 | − | 0.971986i | \(-0.575521\pi\) |
0.724246 | + | 0.689542i | \(0.242188\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.92358 | + | 20.2851i | 0.450756 | + | 1.15398i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.5915 | − | 8.22263i | −1.28105 | − | 0.466262i | −0.390267 | − | 0.920702i | \(-0.627617\pi\) |
−0.890778 | + | 0.454439i | \(0.849840\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.300476 | − | 1.70409i | 0.0169839 | − | 0.0963207i | −0.975137 | − | 0.221601i | \(-0.928872\pi\) |
0.992121 | + | 0.125280i | \(0.0399829\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.997677 | − | 7.75835i | 0.0562127 | − | 0.437133i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.5341 | + | 13.7458i | −0.647819 | + | 0.772040i | −0.985583 | − | 0.169190i | \(-0.945885\pi\) |
0.337765 | + | 0.941231i | \(0.390329\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.4651 | − | 3.25590i | 1.03385 | − | 0.182295i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.48339 | − | 32.3400i | −0.361868 | − | 1.80504i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.64391 | 0.0914698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.08830 | −0.337718 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.52085 | + | 7.58620i | 0.0841033 | + | 0.419518i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.3478 | + | 2.17725i | −0.680756 | + | 0.120036i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.23357 | + | 7.42888i | −0.342628 | + | 0.408328i | −0.909651 | − | 0.415374i | \(-0.863651\pi\) |
0.567023 | + | 0.823702i | \(0.308095\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.7901 | − | 11.2783i | −0.810493 | − | 0.618049i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.92104 | − | 22.2373i | 0.214229 | − | 1.21495i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.7092 | − | 9.35737i | −1.40047 | − | 0.509728i | −0.472150 | − | 0.881518i | \(-0.656522\pi\) |
−0.928317 | + | 0.371790i | \(0.878744\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.14356 | − | 2.92762i | −0.0621097 | − | 0.159006i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.9588 | + | 11.5232i | −1.08083 | + | 0.624018i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.4284 | − | 8.90759i | −0.833055 | − | 0.480965i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0999001 | + | 0.0546118i | 0.00537844 | + | 0.00294020i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.6703 | − | 16.5053i | 1.05596 | − | 0.886052i | 0.0622488 | − | 0.998061i | \(-0.480173\pi\) |
0.993707 | + | 0.112008i | \(0.0357283\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.8555 | − | 7.59080i | 1.11637 | − | 0.406326i | 0.283045 | − | 0.959107i | \(-0.408655\pi\) |
0.833327 | + | 0.552780i | \(0.186433\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.67626 | − | 14.7354i | −0.196224 | − | 0.786516i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.49361 | + | 17.8410i | 0.345620 | + | 0.949583i | 0.983732 | + | 0.179640i | \(0.0574932\pi\) |
−0.638113 | + | 0.769943i | \(0.720285\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.99306 | − | 4.75874i | −0.211930 | − | 0.252568i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.48076 | + | 0.0578627i | −0.131296 | + | 0.00306242i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.3488 | − | 19.6567i | 0.598968 | − | 1.03744i | −0.394006 | − | 0.919108i | \(-0.628911\pi\) |
0.992974 | − | 0.118335i | \(-0.0377556\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.96560 | − | 13.7968i | −0.419242 | − | 0.726149i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.274315 | − | 1.80025i | 0.0143978 | − | 0.0944887i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.36278 | + | 6.49170i | −0.123674 | + | 0.339791i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.82713 | − | 1.38013i | −0.408573 | − | 0.0720424i | −0.0344155 | − | 0.999408i | \(-0.510957\pi\) |
−0.374157 | + | 0.927365i | \(0.622068\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.657580 | + | 14.0886i | 0.0342323 | + | 0.733423i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.8437 | + | 12.4553i | 0.770645 | + | 0.646648i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.275405 | + | 1.56190i | 0.0142599 | + | 0.0808721i | 0.991107 | − | 0.133066i | \(-0.0424821\pi\) |
−0.976847 | + | 0.213938i | \(0.931371\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.8389 | − | 15.7325i | −0.714638 | − | 0.812421i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 15.7860i | − | 0.813023i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.0092i | − | 1.23327i | −0.787249 | − | 0.616635i | \(-0.788495\pi\) | ||
0.787249 | − | 0.616635i | \(-0.211505\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.01862 | + | 11.8972i | −0.205880 | + | 0.609512i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.226558 | + | 1.28488i | 0.0115766 | + | 0.0656541i | 0.990049 | − | 0.140725i | \(-0.0449432\pi\) |
−0.978472 | + | 0.206379i | \(0.933832\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.93396 | − | 5.81829i | −0.353388 | − | 0.296527i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 23.8709 | − | 5.36743i | 1.21343 | − | 0.272842i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0139 | + | 2.64735i | 0.761234 | + | 0.134226i | 0.540772 | − | 0.841169i | \(-0.318132\pi\) |
0.220462 | + | 0.975396i | \(0.429243\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0123529 | − | 0.0339392i | 0.000624711 | − | 0.00171638i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.6371 | + | 18.9124i | 1.19233 | + | 0.954004i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.7170 | − | 18.5625i | −0.539233 | − | 0.933979i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.08632 | − | 12.2739i | 0.355652 | − | 0.616008i | −0.631577 | − | 0.775313i | \(-0.717592\pi\) |
0.987229 | + | 0.159305i | \(0.0509254\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.40904 | − | 3.95654i | −0.120603 | − | 0.198075i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.9488 | + | 23.7741i | 0.996197 | + | 1.18722i | 0.982299 | + | 0.187317i | \(0.0599793\pi\) |
0.0138970 | + | 0.999903i | \(0.495576\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.63634 | + | 18.2332i | 0.330580 | + | 0.908260i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.74061 | − | 12.6441i | 0.434324 | − | 0.628289i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.2250 | + | 7.36129i | −1.00252 | + | 0.364886i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.87431 | − | 5.76823i | 0.339913 | − | 0.285221i | −0.456812 | − | 0.889563i | \(-0.651009\pi\) |
0.796725 | + | 0.604343i | \(0.206564\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.86166 | + | 4.78676i | −0.387787 | + | 0.236114i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.6168 | + | 11.3258i | 0.965280 | + | 0.557305i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.38806 | − | 3.11080i | 0.264489 | − | 0.152703i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.0578 | − | 16.3199i | 0.639442 | − | 0.799187i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.46849 | − | 3.08228i | −0.413713 | − | 0.150579i | 0.126774 | − | 0.991932i | \(-0.459538\pi\) |
−0.540487 | + | 0.841352i | \(0.681760\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.46690 | + | 13.9905i | −0.120229 | + | 0.681855i | 0.863798 | + | 0.503838i | \(0.168079\pi\) |
−0.984027 | + | 0.178017i | \(0.943032\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −23.5202 | − | 7.33821i | −1.14359 | − | 0.356796i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.25651 | + | 1.49746i | −0.0609499 | + | 0.0726373i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.8423 | + | 3.67506i | −1.00863 | + | 0.177849i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.6498 | − | 5.62394i | −0.803860 | − | 0.271526i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.9626 | 1.29874 | 0.649372 | − | 0.760471i | \(-0.275032\pi\) | ||||
0.649372 | + | 0.760471i | \(0.275032\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.92105 | 0.188434 | 0.0942169 | − | 0.995552i | \(-0.469965\pi\) | ||||
0.0942169 | + | 0.995552i | \(0.469965\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.9966 | − | 10.5527i | 0.575192 | − | 0.505962i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0663982 | − | 0.0117078i | 0.00317626 | − | 0.000560060i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.3057 | − | 14.6654i | 0.587320 | − | 0.699941i | −0.387769 | − | 0.921757i | \(-0.626754\pi\) |
0.975089 | + | 0.221816i | \(0.0711985\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.56187 | − | 11.7914i | −0.360089 | − | 0.561493i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.58423 | + | 20.3272i | −0.170292 | + | 0.965772i | 0.773147 | + | 0.634226i | \(0.218681\pi\) |
−0.943439 | + | 0.331546i | \(0.892430\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.1162 | + | 5.13787i | 0.669171 | + | 0.243558i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.90268 | + | 0.289922i | 0.0899936 | + | 0.0137128i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.2207 | + | 7.05561i | −0.576730 | + | 0.332975i | −0.759833 | − | 0.650119i | \(-0.774719\pi\) |
0.183103 | + | 0.983094i | \(0.441386\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.1341 | + | 8.16033i | 0.665549 | + | 0.384255i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.350559 | − | 15.0296i | −0.0164707 | − | 0.706151i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.83787 | + | 4.89855i | −0.273684 | + | 0.229648i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0602 | − | 4.75353i | 0.610932 | − | 0.222361i | −0.0179791 | − | 0.999838i | \(-0.505723\pi\) |
0.628911 | + | 0.777477i | \(0.283501\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.38297 | − | 2.13691i | −0.204579 | − | 0.0997426i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.4525 | − | 31.4654i | −0.533394 | − | 1.46549i | −0.855007 | − | 0.518617i | \(-0.826447\pi\) |
0.321613 | − | 0.946871i | \(-0.395775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.5926 | + | 15.0072i | 0.585226 | + | 0.697445i | 0.974681 | − | 0.223600i | \(-0.0717810\pi\) |
−0.389455 | + | 0.921046i | \(0.627337\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.42001 | + | 17.2318i | −0.436843 | + | 0.799106i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.24674 | − | 10.8197i | 0.289065 | − | 0.500675i | −0.684522 | − | 0.728992i | \(-0.739989\pi\) |
0.973587 | + | 0.228317i | \(0.0733224\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0922 | + | 17.4802i | 0.466013 | + | 0.807159i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.291364 | + | 0.113810i | −0.0134254 | + | 0.00524409i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.68341 | − | 26.6049i | 0.445244 | − | 1.22330i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.59369 | − | 0.633664i | −0.164890 | − | 0.0290745i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.6771 | + | 35.1345i | 0.672020 | + | 1.60870i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.6447 | − | 24.8749i | −1.35450 | − | 1.13656i | −0.977638 | − | 0.210294i | \(-0.932558\pi\) |
−0.376864 | − | 0.926269i | \(-0.622998\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.14663 | + | 17.8454i | 0.143474 | + | 0.813681i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0997865 | + | 0.0200048i | −0.00454044 | + | 0.000910250i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 7.25369i | − | 0.329373i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 20.1282i | − | 0.912096i | −0.889955 | − | 0.456048i | \(-0.849264\pi\) | ||
0.889955 | − | 0.456048i | \(-0.150736\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −36.8274 | + | 7.38302i | −1.66539 | + | 0.333872i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.32914 | + | 7.53795i | 0.0599834 | + | 0.340183i | 1.00000 | 0.000947128i | \(-0.000301480\pi\) | |
−0.940016 | + | 0.341130i | \(0.889190\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.88268 | − | 3.25795i | −0.174867 | − | 0.146731i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.85617 | − | 16.4125i | −0.308162 | − | 0.737686i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.46857 | + | 0.964257i | 0.245299 | + | 0.0432528i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.53447 | − | 12.4584i | 0.202991 | − | 0.557713i | −0.795868 | − | 0.605470i | \(-0.792985\pi\) |
0.998859 | + | 0.0477573i | \(0.0152074\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.12523 | − | 1.61136i | 0.184302 | − | 0.0719903i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.64136 | + | 11.5032i | 0.296124 | + | 0.512902i | 0.975246 | − | 0.221124i | \(-0.0709726\pi\) |
−0.679122 | + | 0.734026i | \(0.737639\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.42540 | − | 11.1291i | 0.285927 | − | 0.495240i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.70340 | − | 6.77454i | 0.164474 | − | 0.300868i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.3879 | − | 29.0644i | −1.08097 | − | 1.28826i | −0.955124 | − | 0.296206i | \(-0.904278\pi\) |
−0.125851 | − | 0.992049i | \(-0.540166\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.11207 | − | 5.80287i | −0.0934325 | − | 0.256704i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.636310 | − | 9.08034i | −0.0280938 | − | 0.400907i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.1790 | − | 7.34455i | 0.889193 | − | 0.323640i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.8405 | + | 18.3264i | −0.960546 | + | 0.805994i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.458608 | − | 19.6620i | −0.0201306 | − | 0.863064i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.1443 | + | 9.89824i | 0.751103 | + | 0.433650i | 0.826092 | − | 0.563535i | \(-0.190559\pi\) |
−0.0749891 | + | 0.997184i | \(0.523892\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.9712 | − | 12.1077i | 0.917007 | − | 0.529434i | 0.0343279 | − | 0.999411i | \(-0.489071\pi\) |
0.882679 | + | 0.469976i | \(0.155738\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.44538 | + | 0.829744i | 0.237656 | + | 0.0362130i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.85419 | + | 2.13075i | 0.255012 | + | 0.0928169i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.99365 | + | 22.6491i | −0.173637 | + | 0.984744i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.0288 | + | 37.4685i | 1.04276 | + | 1.62600i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.83238 | − | 10.5260i | 0.382573 | − | 0.455933i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.0294 | + | 5.64766i | −1.38475 | + | 0.244169i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.78259 | − | 5.96624i | 0.292690 | − | 0.257462i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.2094 | −0.698188 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.77906 | −0.291454 | −0.145727 | − | 0.989325i | \(-0.546552\pi\) | ||||
−0.145727 | + | 0.989325i | \(0.546552\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.6263 | + | 6.62934i | 0.842246 | + | 0.284492i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.51336 | − | 1.32481i | 0.321837 | − | 0.0567485i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.7637 | + | 19.9782i | −0.716765 | + | 0.854207i | −0.994312 | − | 0.106505i | \(-0.966034\pi\) |
0.277548 | + | 0.960712i | \(0.410478\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −39.7007 | − | 12.3864i | −1.69439 | − | 0.528640i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.64300 | − | 9.31790i | 0.0699940 | − | 0.396956i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.0043 | + | 6.55301i | 0.765619 | + | 0.278662i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.4581 | + | 14.3206i | −0.486370 | + | 0.607875i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.8803 | + | 14.3647i | −1.05421 | + | 0.608650i | −0.923826 | − | 0.382813i | \(-0.874955\pi\) |
−0.130387 | + | 0.991463i | \(0.541622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.6433 | − | 11.9184i | −0.873120 | − | 0.504096i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.81946 | + | 2.93444i | −0.203478 | + | 0.123892i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.0134 | + | 13.4368i | −0.674885 | + | 0.566296i | −0.914507 | − | 0.404571i | \(-0.867421\pi\) |
0.239622 | + | 0.970866i | \(0.422977\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.91231 | + | 1.05999i | −0.122522 | + | 0.0445943i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.27984 | + | 13.6803i | 0.0537482 | + | 0.574520i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.78377 | − | 26.8807i | −0.410157 | − | 1.12690i | −0.957108 | − | 0.289732i | \(-0.906434\pi\) |
0.546951 | − | 0.837165i | \(-0.315788\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.24820 | + | 7.44632i | 0.261479 | + | 0.311619i | 0.880771 | − | 0.473542i | \(-0.157025\pi\) |
−0.619292 | + | 0.785161i | \(0.712580\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.93048 | + | 16.3096i | 0.414852 | + | 0.681342i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.0400863 | + | 0.0694315i | −0.00167171 | + | 0.00289549i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.09107 | − | 5.35388i | −0.128683 | − | 0.222885i | 0.794484 | − | 0.607285i | \(-0.207742\pi\) |
−0.923166 | + | 0.384400i | \(0.874408\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.6186 | − | 9.29621i | −0.482852 | − | 0.386337i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.90212 | + | 5.22603i | −0.0789132 | + | 0.216812i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.3921 | + | 7.65119i | 1.79712 | + | 0.316880i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.6105 | + | 3.28520i | −0.604069 | + | 0.135826i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.60609 | − | 3.86497i | −0.190114 | − | 0.159524i | 0.542763 | − | 0.839886i | \(-0.317378\pi\) |
−0.732877 | + | 0.680362i | \(0.761823\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.01948 | + | 11.4531i | 0.0832113 | + | 0.471915i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.72117 | + | 28.7798i | −0.399875 | + | 1.18384i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 45.9763i | − | 1.88802i | −0.329915 | − | 0.944011i | \(-0.607020\pi\) | ||
0.329915 | − | 0.944011i | \(-0.392980\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.44683i | 0.100310i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.6976 | − | 23.5296i | −0.847096 | − | 0.963003i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.50094 | + | 25.5261i | 0.183903 | + | 1.04297i | 0.927356 | + | 0.374180i | \(0.122076\pi\) |
−0.743453 | + | 0.668788i | \(0.766813\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.44957 | + | 5.41183i | 0.263084 | + | 0.220753i | 0.764782 | − | 0.644289i | \(-0.222847\pi\) |
−0.501698 | + | 0.865043i | \(0.667291\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.84926 | + | 39.6202i | 0.0753077 | + | 1.61346i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.76836 | − | 0.311810i | −0.0718941 | − | 0.0126769i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.71034 | + | 15.6890i | −0.231776 | + | 0.636798i | −0.999994 | − | 0.00338920i | \(-0.998921\pi\) |
0.768219 | + | 0.640188i | \(0.221143\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.15140 | + | 14.1191i | −0.0871791 | + | 0.572133i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0020 | + | 20.7880i | 0.485548 | + | 0.840993i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.4645 | + | 21.5892i | −0.503437 | + | 0.871979i | 0.496555 | + | 0.868005i | \(0.334598\pi\) |
−0.999992 | + | 0.00397384i | \(0.998735\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.9035 | − | 0.324294i | 0.560643 | − | 0.0130768i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.56720 | − | 6.63473i | −0.224127 | − | 0.267104i | 0.642249 | − | 0.766496i | \(-0.278001\pi\) |
−0.866376 | + | 0.499392i | \(0.833557\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.19615 | + | 17.0238i | 0.249044 | + | 0.684244i | 0.999722 | + | 0.0235754i | \(0.00750497\pi\) |
−0.750678 | + | 0.660669i | \(0.770273\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.192248 | − | 0.0550956i | −0.00771466 | − | 0.00221091i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.6183 | + | 4.59269i | −0.505542 | + | 0.184002i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.84845 | + | 6.58563i | −0.313938 | + | 0.263425i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.24240 | − | 5.05249i | −0.369106 | − | 0.201777i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.03860 | + | 2.90904i | 0.200902 | + | 0.115991i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.2093 | + | 22.6375i | −1.56090 | + | 0.901185i | −0.563732 | + | 0.825958i | \(0.690635\pi\) |
−0.997166 | + | 0.0752273i | \(0.976032\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.1645 | + | 26.0222i | 0.404005 | + | 1.03429i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.6357 | + | 4.23506i | 0.461750 | + | 0.168063i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.36979 | + | 13.4397i | −0.0938944 | + | 0.532502i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.67687 | + | 6.61663i | 0.343252 | + | 0.261750i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.21101 | − | 10.9773i | 0.363813 | − | 0.433576i | −0.552823 | − | 0.833299i | \(-0.686449\pi\) |
0.916636 | + | 0.399723i | \(0.130894\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.8469 | + | 4.38119i | −0.979867 | + | 0.172777i | −0.640568 | − | 0.767901i | \(-0.721301\pi\) |
−0.339299 | + | 0.940678i | \(0.610190\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.74228 | − | 23.6551i | −0.186727 | − | 0.931419i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.8495 | 1.44870 | 0.724352 | − | 0.689430i | \(-0.242139\pi\) | ||||
0.724352 | + | 0.689430i | \(0.242139\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 51.5074 | 2.02184 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.45064 | − | 17.2122i | −0.135241 | − | 0.674600i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.3576 | − | 5.52920i | 1.22712 | − | 0.216374i | 0.477732 | − | 0.878506i | \(-0.341459\pi\) |
0.749387 | + | 0.662132i | \(0.230348\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.1871 | − | 22.8663i | 0.749703 | − | 0.893461i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.54771 | − | 12.0357i | 0.0603820 | − | 0.469556i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.52273 | − | 14.3071i | 0.0982717 | − | 0.557326i | −0.895424 | − | 0.445215i | \(-0.853127\pi\) |
0.993696 | − | 0.112112i | \(-0.0357615\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.12471 | + | 2.22921i | 0.238224 | + | 0.0867063i | 0.458373 | − | 0.888760i | \(-0.348432\pi\) |
−0.220150 | + | 0.975466i | \(0.570655\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.72845 | + | 4.42498i | 0.0671273 | + | 0.171852i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.95571 | + | 2.28383i | −0.153396 | + | 0.0885630i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.180025 | − | 0.103938i | −0.00697061 | − | 0.00402449i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.96252 | − | 2.16617i | −0.153200 | − | 0.0837489i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36.8655 | + | 30.9338i | −1.42318 | + | 1.19419i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.8218 | − | 6.48661i | 0.686980 | − | 0.250040i | 0.0251385 | − | 0.999684i | \(-0.491997\pi\) |
0.661842 | + | 0.749644i | \(0.269775\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.75772 | + | 6.36088i | 0.337085 | + | 0.244830i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.86289 | + | 27.0981i | 0.379062 | + | 1.04146i | 0.971746 | + | 0.236029i | \(0.0758459\pi\) |
−0.592684 | + | 0.805435i | \(0.701932\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.16784 | + | 4.96703i | 0.159947 | + | 0.190617i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −39.6162 | + | 0.924033i | −1.51810 | + | 0.0354090i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.473868 | − | 0.820764i | 0.0181321 | − | 0.0314057i | −0.856817 | − | 0.515621i | \(-0.827561\pi\) |
0.874949 | + | 0.484215i | \(0.160895\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.53797 | + | 7.86000i | 0.173387 | + | 0.300315i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.156764 | + | 1.02880i | −0.00598094 | + | 0.0392513i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.6877 | − | 34.8592i | 0.483363 | − | 1.32803i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.8003 | + | 3.84398i | 0.829321 | + | 0.146232i | 0.572165 | − | 0.820138i | \(-0.306104\pi\) |
0.257156 | + | 0.966370i | \(0.417215\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.1251 | + | 7.29917i | 0.536570 | + | 0.277273i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.7877 | − | 13.2475i | −0.598862 | − | 0.502505i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.766098 | − | 4.34476i | −0.0290180 | − | 0.164569i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −34.2061 | − | 38.8865i | −1.29379 | − | 1.47082i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 37.6486i | − | 1.42197i | −0.703209 | − | 0.710983i | \(-0.748250\pi\) | ||
0.703209 | − | 0.710983i | \(-0.251750\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.8610i | 0.409629i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.77473 | + | 23.0173i | −0.292813 | + | 0.866880i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.99473 | + | 11.3127i | 0.0750197 | + | 0.425458i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.0912 | + | 20.2150i | 0.904766 | + | 0.759189i | 0.971116 | − | 0.238608i | \(-0.0766911\pi\) |
−0.0663503 | + | 0.997796i | \(0.521135\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.5193 | + | 27.6818i | 0.957048 | + | 1.03815i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.251628 | + | 0.0443687i | 0.00942353 | + | 0.00166162i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.92684 | + | 16.2839i | −0.221651 | + | 0.608982i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.941064 | − | 0.752960i | −0.0351447 | − | 0.0281198i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.2799 | + | 17.8053i | 0.383375 | + | 0.664025i | 0.991542 | − | 0.129784i | \(-0.0414283\pi\) |
−0.608167 | + | 0.793809i | \(0.708095\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.59772 | + | 16.6237i | −0.357438 | + | 0.619100i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.2274 | − | 23.3667i | −0.529122 | − | 0.869016i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.23194 | + | 8.61869i | 0.268588 | + | 0.320090i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.7919 | + | 46.1353i | 0.622776 | + | 1.71106i | 0.700089 | + | 0.714056i | \(0.253144\pi\) |
−0.0773130 | + | 0.997007i | \(0.524634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.1070 | + | 25.0370i | −0.374332 | + | 0.927295i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.19182 | + | 2.61761i | −0.265999 | + | 0.0968158i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.2847 | − | 26.2510i | 1.15553 | − | 0.969603i | 0.155694 | − | 0.987805i | \(-0.450239\pi\) |
0.999834 | + | 0.0182021i | \(0.00579423\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.7977 | + | 7.18329i | −0.435163 | + | 0.264960i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39.7482 | + | 22.9486i | 1.46414 | + | 0.845323i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.5124 | − | 19.9257i | 1.26956 | − | 0.732981i | 0.294655 | − | 0.955604i | \(-0.404795\pi\) |
0.974905 | + | 0.222623i | \(0.0714619\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.54041 | + | 6.92451i | −0.203532 | + | 0.254378i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.8926 | + | 9.06017i | 0.913221 | + | 0.332385i | 0.755538 | − | 0.655104i | \(-0.227375\pi\) |
0.157683 | + | 0.987490i | \(0.449598\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.329550 | − | 1.86897i | 0.0120738 | − | 0.0684739i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.03509 | + | 7.40738i | −0.293989 | + | 0.271022i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.6874 | − | 22.2708i | 0.682824 | − | 0.813758i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.30283 | − | 1.11136i | 0.229994 | − | 0.0405541i | −0.0574634 | − | 0.998348i | \(-0.518301\pi\) |
0.287457 | + | 0.957794i | \(0.407190\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −36.4063 | − | 12.2972i | −1.32672 | − | 0.448136i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.8240 | −0.539502 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.3500 | −0.848671 | −0.424336 | − | 0.905505i | \(-0.639492\pi\) | ||||
−0.424336 | + | 0.905505i | \(0.639492\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.173761 | + | 0.152847i | −0.00630711 | + | 0.00554799i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.5181 | + | 8.20240i | −1.68628 | + | 0.297337i | −0.932870 | − | 0.360213i | \(-0.882704\pi\) |
−0.753411 | + | 0.657550i | \(0.771593\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.38363 | + | 5.22421i | −0.158698 | + | 0.189129i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.20732 | + | 4.27155i | −0.0798060 | + | 0.154438i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.53030 | − | 42.7065i | 0.271903 | − | 1.54204i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.1294 | + | 8.05443i | 0.798006 | + | 0.290450i | 0.708660 | − | 0.705550i | \(-0.249300\pi\) |
0.0893459 | + | 0.996001i | \(0.471522\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.9338 | − | 5.47543i | −1.29412 | − | 0.197193i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.0923 | − | 6.98148i | 0.434929 | − | 0.251106i | −0.266515 | − | 0.963831i | \(-0.585872\pi\) |
0.701444 | + | 0.712724i | \(0.252539\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.9763 | − | 6.91450i | −0.430200 | − | 0.248376i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.382286 | − | 16.3898i | −0.0137144 | − | 0.587980i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.30895 | − | 5.29384i | 0.226042 | − | 0.189671i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.8653 | − | 4.31863i | 0.424575 | − | 0.154533i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.4928 | + | 22.7075i | −0.589405 | + | 0.811498i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.105493 | + | 0.289841i | 0.00376522 | + | 0.0103449i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.1852 | − | 39.5486i | −1.18292 | − | 1.40975i | −0.891416 | − | 0.453186i | \(-0.850287\pi\) |
−0.291508 | − | 0.956568i | \(-0.594157\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.67051 | + | 12.2022i | −0.237476 | + | 0.434410i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.38518 | − | 2.39920i | 0.0492513 | − | 0.0853057i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.2586 | + | 35.0889i | 0.719403 | + | 1.24604i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 34.9727 | − | 13.6607i | 1.24035 | − | 0.484495i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.4781 | + | 34.2834i | −0.441998 | + | 1.21438i | 0.496178 | + | 0.868221i | \(0.334736\pi\) |
−0.938176 | + | 0.346159i | \(0.887486\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.58993 | + | 1.33831i | 0.268512 | + | 0.0473460i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −26.1715 | − | 3.36550i | −0.924724 | − | 0.118914i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.7568 | − | 9.02601i | −0.379598 | − | 0.318521i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0174261 | + | 0.0988284i | 0.000614190 | + | 0.00348324i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 44.4731 | − | 8.91579i | 1.56553 | − | 0.313851i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 40.9070i | − | 1.43821i | −0.694899 | − | 0.719107i | \(-0.744551\pi\) | ||
0.694899 | − | 0.719107i | \(-0.255449\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 39.1807i | − | 1.37582i | −0.725795 | − | 0.687911i | \(-0.758528\pi\) | ||
0.725795 | − | 0.687911i | \(-0.241472\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.3329 | + | 5.07863i | −0.888462 | + | 0.178115i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.43132 | + | 36.4738i | 0.225279 | + | 1.27762i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.9445 | − | 9.18353i | −0.382900 | − | 0.321291i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.11706 | − | 10.6445i | 0.283633 | − | 0.371949i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.39112 | − | 1.30325i | −0.257952 | − | 0.0454839i | 0.0431766 | − | 0.999067i | \(-0.486252\pi\) |
−0.301129 | + | 0.953584i | \(0.597363\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.86470 | + | 27.1030i | −0.343862 | + | 0.944753i | 0.640401 | + | 0.768041i | \(0.278768\pi\) |
−0.984263 | + | 0.176712i | \(0.943454\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.6667 | − | 4.55715i | 0.406183 | − | 0.158660i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.3147 | − | 35.1861i | −0.706411 | − | 1.22354i | −0.966180 | − | 0.257869i | \(-0.916980\pi\) |
0.259769 | − | 0.965671i | \(-0.416354\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.83592 | − | 15.3043i | 0.306884 | − | 0.531539i | −0.670795 | − | 0.741643i | \(-0.734047\pi\) |
0.977679 | + | 0.210104i | \(0.0673802\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.5051 | − | 28.3630i | 0.537864 | − | 0.983903i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.81651 | + | 3.35658i | 0.0975862 | + | 0.116299i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.49361 | − | 4.10366i | −0.0516885 | − | 0.142013i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.50345 | − | 33.1610i | 0.328487 | − | 1.14621i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.2749 | + | 4.10375i | −0.389254 | + | 0.141677i | −0.529231 | − | 0.848478i | \(-0.677520\pi\) |
0.139977 | + | 0.990155i | \(0.455297\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.131685 | + | 0.110497i | −0.00454086 | + | 0.00381023i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.169928 | − | 7.28535i | −0.00585263 | − | 0.250921i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.59311 | − | 3.80653i | −0.226810 | − | 0.130949i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.39006 | − | 0.802553i | 0.0477631 | − | 0.0275760i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.34159 | − | 0.509177i | −0.114683 | − | 0.0174749i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.224229 | + | 0.0816125i | 0.00768646 | + | 0.00279764i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.26964 | − | 12.8718i | 0.0777110 | − | 0.440721i | −0.920982 | − | 0.389606i | \(-0.872611\pi\) |
0.998693 | − | 0.0511152i | \(-0.0162776\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.96593 | + | 0.418482i | −0.306628 | + | 0.0143118i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.7920 | + | 14.0531i | −0.402807 | + | 0.480046i | −0.928874 | − | 0.370397i | \(-0.879222\pi\) |
0.526067 | + | 0.850443i | \(0.323666\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.0233 | + | 7.76250i | −1.50206 | + | 0.264853i | −0.863353 | − | 0.504600i | \(-0.831640\pi\) |
−0.638704 | + | 0.769453i | \(0.720529\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.33423 | + | 8.21076i | −0.318110 | + | 0.279822i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 56.2127 | 1.91350 | 0.956751 | − | 0.290908i | \(-0.0939572\pi\) | ||||
0.956751 | + | 0.290908i | \(0.0939572\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.3931 | −0.659385 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.4514 | − | 8.93469i | −0.898335 | − | 0.303438i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.9054 | − | 7.56539i | 1.45547 | − | 0.256638i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.8386 | − | 29.6015i | 0.841623 | − | 1.00301i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.79515 | + | 12.4310i | 0.0946014 | + | 0.420727i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.20702 | − | 18.1879i | 0.108417 | − | 0.614863i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.6889 | − | 18.0853i | −1.67788 | − | 0.610697i | −0.684860 | − | 0.728675i | \(-0.740137\pi\) |
−0.993016 | + | 0.117977i | \(0.962359\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.22385 | − | 11.5281i | 0.311113 | − | 0.388835i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.9275 | + | 10.3504i | −0.603992 | + | 0.348715i | −0.770610 | − | 0.637306i | \(-0.780049\pi\) |
0.166618 | + | 0.986021i | \(0.446715\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.8565 | − | 9.15473i | −0.533612 | − | 0.308081i | 0.208874 | − | 0.977943i | \(-0.433020\pi\) |
−0.742486 | + | 0.669861i | \(0.766354\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 37.4886 | − | 22.8258i | 1.26016 | − | 0.767282i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.9691 | + | 12.5606i | −0.502615 | + | 0.421744i | −0.858521 | − | 0.512778i | \(-0.828616\pi\) |
0.355907 | + | 0.934521i | \(0.384172\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.4011 | + | 3.78568i | −0.348841 | + | 0.126968i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.0742 | + | 25.4850i | 0.605509 | + | 0.853779i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.92070 | + | 13.5195i | 0.164665 | + | 0.452413i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.72550 | − | 6.82338i | −0.191382 | − | 0.228081i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.101327 | + | 0.166417i | 0.00338321 | + | 0.00555649i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.9283 | − | 31.0527i | 0.597941 | − | 1.03566i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.95533 | − | 10.3149i | −0.198401 | − | 0.343640i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.8391 | + | 13.4732i | 0.560371 | + | 0.448361i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.98640 | − | 19.1950i | 0.232236 | − | 0.638063i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.2190 | + | 6.91536i | 1.30224 | + | 0.229621i | 0.781400 | − | 0.624030i | \(-0.214506\pi\) |
0.520845 | + | 0.853651i | \(0.325617\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.72305 | + | 21.5486i | −0.222990 | + | 0.714721i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.5751 | − | 30.6901i | −1.21179 | − | 1.01681i | −0.999213 | − | 0.0396634i | \(-0.987371\pi\) |
−0.212572 | − | 0.977145i | \(-0.568184\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.19598 | + | 12.4540i | 0.0726762 | + | 0.412167i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.1233 | + | 38.8517i | −0.433841 | + | 1.28440i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.6825i | 0.881133i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 45.4710i | − | 1.49995i | −0.661466 | − | 0.749975i | \(-0.730066\pi\) | ||
0.661466 | − | 0.749975i | \(-0.269934\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.3227 | + | 12.8720i | 0.373096 | + | 0.424146i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.84602 | − | 10.4693i | −0.0607626 | − | 0.344602i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.89334 | − | 8.30150i | −0.325291 | − | 0.272952i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −31.7517 | + | 20.3626i | −1.04286 | + | 0.668794i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.7888 | − | 5.07625i | −0.944531 | − | 0.166546i | −0.319887 | − | 0.947456i | \(-0.603645\pi\) |
−0.624644 | + | 0.780909i | \(0.714756\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.79759 | + | 7.68631i | −0.0916873 | + | 0.251909i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.27265 | − | 41.1657i | 0.205357 | − | 1.34770i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.78193 | + | 4.81844i | 0.0909788 | + | 0.157580i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.92824 | − | 3.33982i | 0.0629930 | − | 0.109107i | −0.832809 | − | 0.553560i | \(-0.813269\pi\) |
0.895802 | + | 0.444453i | \(0.146602\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.99628 | − | 0.0698872i | 0.0977800 | − | 0.00228068i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.70135 | − | 7.98635i | −0.218458 | − | 0.260348i | 0.645674 | − | 0.763613i | \(-0.276576\pi\) |
−0.864132 | + | 0.503265i | \(0.832132\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.0618859 | − | 0.170030i | −0.00201528 | − | 0.00553694i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.5154 | − | 0.947096i | 0.439655 | − | 0.0308090i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.2753 | + | 7.37959i | −0.658858 | + | 0.239805i | −0.649743 | − | 0.760154i | \(-0.725124\pi\) |
−0.00911453 | + | 0.999958i | \(0.502901\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.05639 | + | 7.59921i | −0.293983 | + | 0.246681i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.2708 | − | 14.9080i | −0.884317 | − | 0.483424i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.4831 | − | 17.5994i | −0.987446 | − | 0.570102i | −0.0829360 | − | 0.996555i | \(-0.526430\pi\) |
−0.904510 | + | 0.426453i | \(0.859763\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.3061 | − | 9.41434i | 0.527654 | − | 0.304641i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.8160 | + | 30.2501i | 0.381957 | + | 0.977846i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.62363 | − | 2.77477i | −0.246180 | − | 0.0896021i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.27009 | + | 12.8743i | −0.0732285 | + | 0.415300i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 52.7143 | − | 22.0210i | 1.69870 | − | 0.709616i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.43125 | + | 11.2397i | −0.303603 | + | 0.361820i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.0342 | − | 1.76930i | 0.322678 | − | 0.0568968i | −0.00996311 | − | 0.999950i | \(-0.503171\pi\) |
0.332641 | + | 0.943054i | \(0.392060\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.559688 | + | 2.79179i | 0.0179798 | + | 0.0896853i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.24359 | 0.296641 | 0.148321 | − | 0.988939i | \(-0.452613\pi\) | ||||
0.148321 | + | 0.988939i | \(0.452613\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.4225 | 0.590599 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.07283 | − | 10.3395i | −0.0663836 | − | 0.331130i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.13934 | + | 1.08253i | −0.196415 | + | 0.0346332i | −0.270990 | − | 0.962582i | \(-0.587351\pi\) |
0.0745752 | + | 0.997215i | \(0.476240\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.6270 | + | 23.3906i | −0.627283 | + | 0.747566i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.3655 | + | 5.16560i | −0.394802 | + | 0.164925i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.20795 | + | 12.5219i | −0.0704228 | + | 0.399388i | 0.929137 | + | 0.369735i | \(0.120551\pi\) |
−0.999560 | + | 0.0296531i | \(0.990560\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.1472 | + | 10.2448i | 0.896846 | + | 0.326425i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.90148 | − | 20.2285i | −0.251507 | − | 0.643880i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.271838 | + | 0.156946i | −0.00864394 | + | 0.00499058i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.84640 | − | 3.37542i | −0.185717 | − | 0.107224i | 0.404259 | − | 0.914645i | \(-0.367529\pi\) |
−0.589976 | + | 0.807421i | \(0.700863\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.7385 | − | 8.05698i | −0.467711 | − | 0.255681i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.6711 | + | 19.8624i | −0.750425 | + | 0.629682i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.9552 | + | 20.0021i | −1.74045 | + | 0.633472i | −0.999283 | − | 0.0378501i | \(-0.987949\pi\) |
−0.741166 | + | 0.671322i | \(0.765727\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.1181 | − | 28.9573i | 0.446677 | − | 0.916167i |
(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 | 432.2.be.a.47.4 | yes | 36 | |
4.3 | odd | 2 | inner | 432.2.be.a.47.3 | ✓ | 36 | |
27.23 | odd | 18 | inner | 432.2.be.a.239.3 | yes | 36 | |
108.23 | even | 18 | inner | 432.2.be.a.239.4 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.be.a.47.3 | ✓ | 36 | 4.3 | odd | 2 | inner | |
432.2.be.a.47.4 | yes | 36 | 1.1 | even | 1 | trivial | |
432.2.be.a.239.3 | yes | 36 | 27.23 | odd | 18 | inner | |
432.2.be.a.239.4 | yes | 36 | 108.23 | even | 18 | inner |