Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(237,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.237");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 237.7 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.a.237.34 |
$q$-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 \(\left(\mathbb{Z}/4012\mathbb{Z}\right)^\times\).
\(n\) | \(2007\) | \(3129\) | \(3777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.23721i | − | 1.29166i | −0.763483 | − | 0.645828i | \(-0.776512\pi\) | ||
0.763483 | − | 0.645828i | \(-0.223488\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.538464i | 0.240809i | 0.992725 | + | 0.120404i | \(0.0384191\pi\) | ||||
−0.992725 | + | 0.120404i | \(0.961581\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.0679637i | − | 0.0256879i | −0.999918 | − | 0.0128439i | \(-0.995912\pi\) | ||
0.999918 | − | 0.0128439i | \(-0.00408847\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00513 | −0.668377 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.24868i | − | 0.376490i | −0.982122 | − | 0.188245i | \(-0.939720\pi\) | ||
0.982122 | − | 0.188245i | \(-0.0602799\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00333 | 1.11032 | 0.555162 | − | 0.831742i | \(-0.312656\pi\) | ||||
0.555162 | + | 0.831742i | \(0.312656\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.20466 | 0.311042 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.13968 | + | 3.52445i | −0.518949 | + | 0.854805i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.80395 | −0.872685 | −0.436343 | − | 0.899781i | \(-0.643726\pi\) | ||||
−0.436343 | + | 0.899781i | \(0.643726\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.152049 | −0.0331799 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.87799i | 1.64268i | 0.570442 | + | 0.821338i | \(0.306772\pi\) | ||||
−0.570442 | + | 0.821338i | \(0.693228\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.71006 | 0.942011 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.22574i | − | 0.428343i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 9.03144i | − | 1.67710i | −0.544828 | − | 0.838548i | \(-0.683405\pi\) | ||
0.544828 | − | 0.838548i | \(-0.316595\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.50639i | − | 1.34819i | −0.738646 | − | 0.674093i | \(-0.764535\pi\) | ||
0.738646 | − | 0.674093i | \(-0.235465\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.79356 | −0.486296 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0365961 | 0.00618586 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.34445i | 1.20742i | 0.797204 | + | 0.603710i | \(0.206311\pi\) | ||||
−0.797204 | + | 0.603710i | \(0.793689\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 8.95631i | − | 1.43416i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.9152i | − | 1.86083i | −0.366502 | − | 0.930417i | \(-0.619445\pi\) | ||
0.366502 | − | 0.930417i | \(-0.380555\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.82562 | −0.430903 | −0.215452 | − | 0.976515i | \(-0.569122\pi\) | ||||
−0.215452 | + | 0.976515i | \(0.569122\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.07969i | − | 0.160951i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.438627 | −0.0639803 | −0.0319902 | − | 0.999488i | \(-0.510185\pi\) | ||||
−0.0319902 | + | 0.999488i | \(0.510185\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99538 | 0.999340 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.88495 | + | 4.78693i | 1.10411 | + | 0.670304i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.43517 | 1.02130 | 0.510649 | − | 0.859789i | \(-0.329405\pi\) | ||||
0.510649 | + | 0.859789i | \(0.329405\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.672368 | 0.0906621 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.51025i | 1.12721i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 15.0300i | − | 1.92439i | −0.272357 | − | 0.962196i | \(-0.587803\pi\) | ||
0.272357 | − | 0.962196i | \(-0.412197\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.136276i | 0.0171692i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.15565i | 0.267376i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.19676 | −0.512716 | −0.256358 | − | 0.966582i | \(-0.582523\pi\) | ||||
−0.256358 | + | 0.966582i | \(0.582523\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.6248 | 2.12177 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.28442i | 0.864502i | 0.901753 | + | 0.432251i | \(0.142281\pi\) | ||||
−0.901753 | + | 0.432251i | \(0.857719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.1666i | − | 1.18991i | −0.803760 | − | 0.594954i | \(-0.797170\pi\) | ||
0.803760 | − | 0.594954i | \(-0.202830\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 10.5374i | − | 1.21675i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0848647 | −0.00967123 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.00453i | − | 0.675562i | −0.941225 | − | 0.337781i | \(-0.890324\pi\) | ||
0.941225 | − | 0.337781i | \(-0.109676\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.9948 | −1.22165 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.4552 | 1.58666 | 0.793330 | − | 0.608792i | \(-0.208345\pi\) | ||||
0.793330 | + | 0.608792i | \(0.208345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.89779 | − | 1.15214i | −0.205844 | − | 0.124967i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20.2053 | −2.16623 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.5266 | 1.53982 | 0.769908 | − | 0.638155i | \(-0.220302\pi\) | ||||
0.769908 | + | 0.638155i | \(0.220302\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.272081i | − | 0.0285219i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.7934 | −1.74139 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 2.04829i | − | 0.210150i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.93571i | 0.704215i | 0.935960 | + | 0.352108i | \(0.114535\pi\) | ||||
−0.935960 | + | 0.352108i | \(0.885465\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.50376i | 0.251637i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.29985 | −0.925369 | −0.462685 | − | 0.886523i | \(-0.653114\pi\) | ||||
−0.462685 | + | 0.886523i | \(0.653114\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.3913 | −1.81215 | −0.906076 | − | 0.423116i | \(-0.860936\pi\) | ||||
−0.906076 | + | 0.423116i | \(0.860936\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 0.0818733i | − | 0.00799001i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.66745i | 0.451219i | 0.974218 | + | 0.225610i | \(0.0724374\pi\) | ||||
−0.974218 | + | 0.225610i | \(0.927563\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 18.8258i | − | 1.80318i | −0.432589 | − | 0.901591i | \(-0.642400\pi\) | ||
0.432589 | − | 0.901591i | \(-0.357600\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.4311 | 1.55957 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.38853i | − | 0.412838i | −0.978464 | − | 0.206419i | \(-0.933819\pi\) | ||
0.978464 | − | 0.206419i | \(-0.0661810\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.24202 | −0.395570 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.02720 | −0.742115 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.239535 | + | 0.145421i | 0.0219581 | + | 0.0133307i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.44081 | 0.858255 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −26.6568 | −2.40356 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.22852i | 0.467653i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.89783 | −0.700819 | −0.350410 | − | 0.936597i | \(-0.613958\pi\) | ||||
−0.350410 | + | 0.936597i | \(0.613958\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.32152i | 0.556579i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.178635i | 0.0156074i | 0.999970 | + | 0.00780371i | \(0.00248402\pi\) | ||||
−0.999970 | + | 0.00780371i | \(0.997516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.258531i | 0.0224174i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.19848 | 0.103149 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.423151 | −0.0361522 | −0.0180761 | − | 0.999837i | \(-0.505754\pi\) | ||||
−0.0180761 | + | 0.999837i | \(0.505754\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.07255i | − | 0.515067i | −0.966269 | − | 0.257533i | \(-0.917090\pi\) | ||
0.966269 | − | 0.257533i | \(-0.0829097\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.981303i | 0.0826406i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 4.99886i | − | 0.418026i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.86311 | 0.403859 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 15.6502i | − | 1.29080i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.23411 | −0.756488 | −0.378244 | − | 0.925706i | \(-0.623472\pi\) | ||||
−0.378244 | + | 0.925706i | \(0.623472\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.53374 | 0.531708 | 0.265854 | − | 0.964013i | \(-0.414346\pi\) | ||||
0.265854 | + | 0.964013i | \(0.414346\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.29034 | − | 7.06698i | 0.346854 | − | 0.571332i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.04192 | 0.324655 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.2750 | 1.69793 | 0.848966 | − | 0.528447i | \(-0.177226\pi\) | ||||
0.848966 | + | 0.528447i | \(0.177226\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 16.6341i | − | 1.31917i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.535418 | 0.0421969 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.11572i | 0.322368i | 0.986924 | + | 0.161184i | \(0.0515312\pi\) | ||||
−0.986924 | + | 0.161184i | \(0.948469\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 1.50423i | − | 0.117104i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.6309i | 1.28694i | 0.765472 | + | 0.643469i | \(0.222506\pi\) | ||||
−0.765472 | + | 0.643469i | \(0.777494\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.02665 | 0.232819 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.62741 | 0.583283 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 14.7350i | − | 1.12028i | −0.828398 | − | 0.560140i | \(-0.810748\pi\) | ||
0.828398 | − | 0.560140i | \(-0.189252\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.320113i | − | 0.0241983i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.23721i | 0.168159i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.37280 | 0.326838 | 0.163419 | − | 0.986557i | \(-0.447748\pi\) | ||||
0.163419 | + | 0.986557i | \(0.447748\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 12.1219i | − | 0.901015i | −0.892773 | − | 0.450507i | \(-0.851243\pi\) | ||
0.892773 | − | 0.450507i | \(-0.148757\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −33.6253 | −2.48565 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.95472 | −0.290757 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.40090 | + | 2.67177i | 0.321826 | + | 0.195379i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.151269 | −0.0110032 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.56006 | −0.112882 | −0.0564410 | − | 0.998406i | \(-0.517975\pi\) | ||||
−0.0564410 | + | 0.998406i | \(0.517975\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 17.6262i | − | 1.26876i | −0.773021 | − | 0.634381i | \(-0.781255\pi\) | ||
0.773021 | − | 0.634381i | \(-0.218745\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.82265 | 0.345357 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.0448i | − | 1.28564i | −0.766018 | − | 0.642820i | \(-0.777764\pi\) | ||
0.766018 | − | 0.642820i | \(-0.222236\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 12.8668i | − | 0.912100i | −0.889954 | − | 0.456050i | \(-0.849264\pi\) | ||
0.889954 | − | 0.456050i | \(-0.150736\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.38905i | 0.662253i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.613810 | −0.0430810 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.41589 | 0.448105 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 15.7964i | − | 1.09793i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.74990i | 0.328557i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.9691i | 1.58126i | 0.612297 | + | 0.790628i | \(0.290246\pi\) | ||||
−0.612297 | + | 0.790628i | \(0.709754\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.2968 | 1.11664 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.52150i | − | 0.103765i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.510162 | −0.0346321 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −22.7448 | −1.53695 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.56586 | + | 14.1095i | −0.576202 | + | 0.949110i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.2087 | −0.683623 | −0.341812 | − | 0.939768i | \(-0.611041\pi\) | ||||
−0.341812 | + | 0.939768i | \(0.611041\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.44428 | −0.629618 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 16.8687i | − | 1.11962i | −0.828622 | − | 0.559809i | \(-0.810875\pi\) | ||
0.828622 | − | 0.559809i | \(-0.189125\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.50455 | 0.0994236 | 0.0497118 | − | 0.998764i | \(-0.484170\pi\) | ||||
0.0497118 | + | 0.998764i | \(0.484170\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.189861i | 0.0124919i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.2873i | 0.870479i | 0.900315 | + | 0.435240i | \(0.143336\pi\) | ||||
−0.900315 | + | 0.435240i | \(0.856664\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 0.236185i | − | 0.0154070i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.4334 | −0.872595 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.2117 | −1.17802 | −0.589008 | − | 0.808127i | \(-0.700481\pi\) | ||||
−0.589008 | + | 0.808127i | \(0.700481\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.92906i | 0.188678i | 0.995540 | + | 0.0943388i | \(0.0300737\pi\) | ||||
−0.995540 | + | 0.0943388i | \(0.969926\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.9206i | 1.14961i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.76676i | 0.240650i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.2285 | −0.968964 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 32.3393i | − | 2.04942i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.2406 | 1.59317 | 0.796586 | − | 0.604525i | \(-0.206637\pi\) | ||||
0.796586 | + | 0.604525i | \(0.206637\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.83707 | 0.618451 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.57759 | + | 4.24577i | −0.161415 | + | 0.265880i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.1033 | −1.37877 | −0.689384 | − | 0.724396i | \(-0.742119\pi\) | ||||
−0.689384 | + | 0.724396i | \(0.742119\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.499156 | 0.0310160 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.1092i | 1.12093i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.6590 | −1.15056 | −0.575280 | − | 0.817956i | \(-0.695107\pi\) | ||||
−0.575280 | + | 0.817956i | \(0.695107\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.00357i | 0.245938i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 32.4991i | − | 1.98891i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 6.36955i | − | 0.388358i | −0.980966 | − | 0.194179i | \(-0.937796\pi\) | ||
0.980966 | − | 0.194179i | \(-0.0622043\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.3499 | 0.750200 | 0.375100 | − | 0.926984i | \(-0.377608\pi\) | ||||
0.375100 | + | 0.926984i | \(0.377608\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.608704 | −0.0368405 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 5.88134i | − | 0.354658i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 0.748251i | − | 0.0449581i | −0.999747 | − | 0.0224790i | \(-0.992844\pi\) | ||
0.999747 | − | 0.0224790i | \(-0.00715590\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.0513i | 0.901097i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.61078 | −0.215401 | −0.107700 | − | 0.994183i | \(-0.534349\pi\) | ||||
−0.107700 | + | 0.994183i | \(0.534349\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.96292i | 0.473346i | 0.971589 | + | 0.236673i | \(0.0760570\pi\) | ||||
−0.971589 | + | 0.236673i | \(0.923943\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.58247 | −0.271442 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.809799 | −0.0478009 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.84351 | − | 15.0824i | −0.461383 | − | 0.887201i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.5167 | 0.909604 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.19202 | −0.420162 | −0.210081 | − | 0.977684i | \(-0.567373\pi\) | ||||
−0.210081 | + | 0.977684i | \(0.567373\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 0.538464i | − | 0.0313506i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.77923 | −0.161267 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 31.5382i | 1.82390i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.192040i | 0.0110690i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.8058i | 1.19526i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.09311 | 0.463410 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.8238 | −0.617749 | −0.308874 | − | 0.951103i | \(-0.599952\pi\) | ||||
−0.308874 | + | 0.951103i | \(0.599952\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 41.1453i | 2.34068i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.2798i | 1.37678i | 0.725339 | + | 0.688392i | \(0.241683\pi\) | ||||
−0.725339 | + | 0.688392i | \(0.758317\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.5894i | 1.33335i | 0.745349 | + | 0.666675i | \(0.232283\pi\) | ||||
−0.745349 | + | 0.666675i | \(0.767717\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0733799 | −0.00413449 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.7881i | 0.830584i | 0.909688 | + | 0.415292i | \(0.136321\pi\) | ||||
−0.909688 | + | 0.415292i | \(0.863679\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.2773 | −0.631410 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.4421 | 0.582820 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.13924 | − | 13.4068i | 0.452880 | − | 0.745976i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.8559 | 1.04594 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −42.1173 | −2.32909 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.0298107i | 0.00164352i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.2912 | −0.785516 | −0.392758 | − | 0.919642i | \(-0.628479\pi\) | ||||
−0.392758 | + | 0.919642i | \(0.628479\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 14.7266i | − | 0.807011i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 2.25981i | − | 0.123466i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.9198i | 0.812733i | 0.913710 | + | 0.406367i | \(0.133204\pi\) | ||||
−0.913710 | + | 0.406367i | \(0.866796\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.81808 | −0.533245 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.37305 | −0.507579 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 0.951178i | − | 0.0513588i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.49031i | 0.510941i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.68590i | 0.197870i | 0.995094 | + | 0.0989348i | \(0.0315435\pi\) | ||||
−0.995094 | + | 0.0989348i | \(0.968456\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.68570 | 0.411406 | 0.205703 | − | 0.978614i | \(-0.434052\pi\) | ||||
0.205703 | + | 0.978614i | \(0.434052\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 8.91036i | − | 0.475600i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.6066 | 0.937105 | 0.468553 | − | 0.883436i | \(-0.344776\pi\) | ||||
0.468553 | + | 0.883436i | \(0.344776\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.92240 | −0.208179 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.325338 | − | 0.535891i | 0.0172187 | − | 0.0283624i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.8482 | −1.25866 | −0.629331 | − | 0.777138i | \(-0.716671\pi\) | ||||
−0.629331 | + | 0.777138i | \(0.716671\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.52998 | −0.238420 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 21.1211i | − | 1.10857i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.47434 | 0.286540 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 10.2109i | − | 0.533004i | −0.963834 | − | 0.266502i | \(-0.914132\pi\) | ||
0.963834 | − | 0.266502i | \(-0.0858679\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 23.8914i | 1.24374i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 0.505322i | − | 0.0262350i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.8717 | −1.70203 | −0.851017 | − | 0.525139i | \(-0.824013\pi\) | ||||
−0.851017 | + | 0.525139i | \(0.824013\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.6973 | 0.604047 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 36.1558i | − | 1.86212i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 38.3714i | − | 1.97101i | −0.169658 | − | 0.985503i | \(-0.554266\pi\) | ||
0.169658 | − | 0.985503i | \(-0.445734\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.6691i | 0.905218i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.5309 | 1.61115 | 0.805576 | − | 0.592493i | \(-0.201856\pi\) | ||||
0.805576 | + | 0.592493i | \(0.201856\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 0.0456966i | − | 0.00232892i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.66574 | 0.288006 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.2550 | 1.63539 | 0.817697 | − | 0.575649i | \(-0.195251\pi\) | ||||
0.817697 | + | 0.575649i | \(0.195251\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.7656 | − | 16.8564i | −1.40417 | − | 0.852465i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.399645 | 0.0201594 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.23323 | 0.162681 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.17555i | − | 0.0589989i | −0.999565 | − | 0.0294995i | \(-0.990609\pi\) | ||
0.999565 | − | 0.0294995i | \(-0.00939133\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.578388 | 0.0289556 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.5392i | 1.57499i | 0.616320 | + | 0.787496i | \(0.288623\pi\) | ||||
−0.616320 | + | 0.787496i | \(0.711377\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 30.0505i | − | 1.49692i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 5.92033i | − | 0.294184i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.17084 | 0.454581 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.00449 | −0.296903 | −0.148451 | − | 0.988920i | \(-0.547429\pi\) | ||||
−0.148451 | + | 0.988920i | \(0.547429\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.946679i | 0.0466962i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.0679637i | 0.00334428i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.78359i | 0.382081i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.5856 | −0.665289 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 25.5198i | − | 1.24673i | −0.781933 | − | 0.623363i | \(-0.785766\pi\) | ||
0.781933 | − | 0.623363i | \(-0.214234\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.3285 | −1.91675 | −0.958377 | − | 0.285505i | \(-0.907839\pi\) | ||||
−0.958377 | + | 0.285505i | \(0.907839\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.879505 | 0.0427630 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.0780 | + | 16.6004i | −0.488856 | + | 0.805236i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.02149 | −0.0494336 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.1835 | −0.539946 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.98939i | − | 0.0958254i | −0.998852 | − | 0.0479127i | \(-0.984743\pi\) | ||
0.998852 | − | 0.0479127i | \(-0.0152569\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.2511 | 0.540692 | 0.270346 | − | 0.962763i | \(-0.412862\pi\) | ||||
0.270346 | + | 0.962763i | \(0.412862\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 10.8798i | − | 0.521647i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 29.9675i | − | 1.43354i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.49891i | 0.357903i | 0.983858 | + | 0.178952i | \(0.0572706\pi\) | ||||
−0.983858 | + | 0.178952i | \(0.942729\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.0267 | −0.667936 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.11941 | 0.148208 | 0.0741039 | − | 0.997251i | \(-0.476390\pi\) | ||||
0.0741039 | + | 0.997251i | \(0.476390\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.82205i | 0.370801i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.6587i | 0.977122i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.9491i | − | 0.847070i | −0.905880 | − | 0.423535i | \(-0.860789\pi\) | ||
0.905880 | − | 0.423535i | \(-0.139211\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.8782 | −0.700586 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 14.6174i | − | 0.686784i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.146506 | 0.00686831 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.3936 | 1.74920 | 0.874599 | − | 0.484846i | \(-0.161124\pi\) | ||||
0.874599 | + | 0.484846i | \(0.161124\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.84450 | + | 4.76237i | 0.366150 | + | 0.222288i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.4195 | 0.625007 | 0.312504 | − | 0.949917i | \(-0.398832\pi\) | ||||
0.312504 | + | 0.949917i | \(0.398832\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.2885 | 1.12878 | 0.564391 | − | 0.825507i | \(-0.309111\pi\) | ||||
0.564391 | + | 0.825507i | \(0.309111\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 9.04265i | − | 0.419343i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.6251 | 0.769316 | 0.384658 | − | 0.923059i | \(-0.374319\pi\) | ||||
0.384658 | + | 0.923059i | \(0.374319\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.285228i | 0.0131706i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 47.5968i | − | 2.19315i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.52829i | 0.162231i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.9168 | −0.822079 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.9085 | −0.682613 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 41.1983i | − | 1.88240i | −0.337852 | − | 0.941199i | \(-0.609700\pi\) | ||
0.337852 | − | 0.941199i | \(-0.390300\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.4022i | 1.34063i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 1.19785i | − | 0.0545038i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.73464 | −0.169581 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.1704i | 1.54841i | 0.632935 | + | 0.774205i | \(0.281850\pi\) | ||||
−0.632935 | + | 0.774205i | \(0.718150\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.20774 | 0.416388 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.00943 | −0.271202 | −0.135601 | − | 0.990764i | \(-0.543296\pi\) | ||||
−0.135601 | + | 0.990764i | \(0.543296\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.8309 | + | 19.3244i | 1.43359 | + | 0.870328i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.34819 | −0.0605964 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.495077 | 0.0222072 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 21.5072i | − | 0.962796i | −0.876502 | − | 0.481398i | \(-0.840129\pi\) | ||
0.876502 | − | 0.481398i | \(-0.159871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 37.2069 | 1.66228 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.7335i | 1.01364i | 0.862052 | + | 0.506819i | \(0.169179\pi\) | ||||
−0.862052 | + | 0.506819i | \(0.830821\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 5.00764i | − | 0.222837i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 6.77127i | − | 0.300723i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.3585 | −0.680755 | −0.340377 | − | 0.940289i | \(-0.610555\pi\) | ||||
−0.340377 | + | 0.940289i | \(0.610555\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.690958 | −0.0305662 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.46659i | 0.373809i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 9.90308i | − | 0.436382i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.547703i | 0.0240880i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.9653 | −1.44702 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.5216i | 0.811448i | 0.913996 | + | 0.405724i | \(0.132981\pi\) | ||||
−0.913996 | + | 0.405724i | \(0.867019\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.6431 | −0.465391 | −0.232695 | − | 0.972550i | \(-0.574755\pi\) | ||||
−0.232695 | + | 0.972550i | \(0.574755\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.716162 | −0.0312559 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.4559 | + | 16.0613i | 1.15244 | + | 0.699641i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −39.0628 | −1.69838 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.00513 | 0.0870152 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 47.7003i | − | 2.06613i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.51325 | −0.108657 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 9.78288i | − | 0.422163i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 8.73497i | − | 0.376242i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 13.3166i | − | 0.572524i | −0.958151 | − | 0.286262i | \(-0.907587\pi\) | ||
0.958151 | − | 0.286262i | \(-0.0924128\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −27.1193 | −1.16380 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.1370 | 0.434222 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.5686i | 0.494636i | 0.968934 | + | 0.247318i | \(0.0795493\pi\) | ||||
−0.968934 | + | 0.247318i | \(0.920451\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.1371i | 1.28622i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.3551i | 1.46358i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.408090 | −0.0173538 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.84757i | 0.375558i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.5416 | 1.25172 | 0.625859 | − | 0.779936i | \(-0.284748\pi\) | ||||
0.625859 | + | 0.779936i | \(0.284748\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.3119 | −0.478442 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.97733 | − | 9.84576i | 0.252363 | − | 0.415688i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.38299 | 0.353301 | 0.176650 | − | 0.984274i | \(-0.443474\pi\) | ||||
0.176650 | + | 0.984274i | \(0.443474\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.36307 | 0.0994149 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.747251i | 0.0313816i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.9209 | 1.12858 | 0.564292 | − | 0.825576i | \(-0.309149\pi\) | ||||
0.564292 | + | 0.825576i | \(0.309149\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.6553i | 1.40843i | 0.709986 | + | 0.704216i | \(0.248701\pi\) | ||||
−0.709986 | + | 0.704216i | \(0.751299\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.49019i | 0.145805i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 37.1058i | 1.54742i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.0192 | 1.04156 | 0.520781 | − | 0.853690i | \(-0.325641\pi\) | ||||
0.520781 | + | 0.853690i | \(0.325641\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −39.4336 | −1.63880 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 0.982427i | − | 0.0407579i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 9.28412i | − | 0.384509i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 4.32236i | − | 0.178708i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.91456 | −0.0790224 | −0.0395112 | − | 0.999219i | \(-0.512580\pi\) | ||||
−0.0395112 | + | 0.999219i | \(0.512580\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.5539i | 1.17654i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −40.3701 | −1.66060 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.0382 | 0.987131 | 0.493565 | − | 0.869709i | \(-0.335693\pi\) | ||||
0.493565 | + | 0.869709i | \(0.335693\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0783040 | + | 0.128981i | −0.00321015 | + | 0.00528771i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.7857 | −1.17812 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.8609 | 1.34266 | 0.671331 | − | 0.741158i | \(-0.265723\pi\) | ||||
0.671331 | + | 0.741158i | \(0.265723\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.59752i | 0.309909i | 0.987922 | + | 0.154955i | \(0.0495231\pi\) | ||||
−0.987922 | + | 0.154955i | \(0.950477\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.41505 | 0.342687 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.08354i | 0.206675i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 19.0717i | − | 0.774096i | −0.922060 | − | 0.387048i | \(-0.873495\pi\) | ||
0.922060 | − | 0.387048i | \(-0.126505\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.37323i | 0.0556459i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.75597 | −0.0710389 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.921264 | −0.0372095 | −0.0186047 | − | 0.999827i | \(-0.505922\pi\) | ||||
−0.0186047 | + | 0.999827i | \(0.505922\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 14.3537i | − | 0.578798i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.5651i | 1.27076i | 0.772198 | + | 0.635382i | \(0.219158\pi\) | ||||
−0.772198 | + | 0.635382i | \(0.780842\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0416i | 0.885927i | 0.896540 | + | 0.442963i | \(0.146073\pi\) | ||||
−0.896540 | + | 0.442963i | \(0.853927\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.5343 | 0.703629 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 0.987281i | − | 0.0395546i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.7349 | 0.829396 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.6265 | 0.424383 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.8851 | − | 15.7148i | −1.03211 | − | 0.626590i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.7630 | 1.90141 | 0.950707 | − | 0.310089i | \(-0.100359\pi\) | ||||
0.950707 | + | 0.310089i | \(0.100359\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 51.3867 | 2.04244 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 4.25270i | − | 0.168763i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.0048 | 1.10959 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 14.6062i | − | 0.577813i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 6.92689i | − | 0.273596i | −0.990599 | − | 0.136798i | \(-0.956319\pi\) | ||
0.990599 | − | 0.136798i | \(-0.0436811\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 22.1869i | − | 0.874965i | −0.899227 | − | 0.437482i | \(-0.855870\pi\) | ||
0.899227 | − | 0.437482i | \(-0.144130\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.40391 | −0.134029 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.7351 | −0.500668 | −0.250334 | − | 0.968159i | \(-0.580540\pi\) | ||||
−0.250334 | + | 0.968159i | \(0.580540\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.24868i | 0.0490148i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.14134i | 0.0447327i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.8049i | 0.814160i | 0.913393 | + | 0.407080i | \(0.133453\pi\) | ||||
−0.913393 | + | 0.407080i | \(0.866547\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0961887 | −0.00375840 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.3853i | 0.795306i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.4677 | 1.77117 | 0.885585 | − | 0.464477i | \(-0.153758\pi\) | ||||
0.885585 | + | 0.464477i | \(0.153758\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.3461 | 0.985848 | 0.492924 | − | 0.870072i | \(-0.335928\pi\) | ||||
0.492924 | + | 0.870072i | \(0.335928\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 31.5661 | + | 19.1637i | 1.22592 | + | 0.744255i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.139210 | −0.00539831 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 71.1496 | 2.75492 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.8390i | 0.883007i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.7676 | −0.724515 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 41.0320i | − | 1.58167i | −0.612031 | − | 0.790834i | \(-0.709647\pi\) | ||
0.612031 | − | 0.790834i | \(-0.290353\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 10.4833i | − | 0.403504i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.9598i | 0.728683i | 0.931265 | + | 0.364341i | \(0.118706\pi\) | ||||
−0.931265 | + | 0.364341i | \(0.881294\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.471377 | 0.0180898 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −37.7390 | −1.44616 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.11620i | 0.272294i | 0.990689 | + | 0.136147i | \(0.0434719\pi\) | ||||
−0.990689 | + | 0.136147i | \(0.956528\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 0.227852i | − | 0.00870576i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3.36601i | − | 0.128421i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.7654 | 1.13397 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.0448i | 0.496249i | 0.968728 | + | 0.248124i | \(0.0798142\pi\) | ||||
−0.968728 | + | 0.248124i | \(0.920186\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.170165 | 0.00646403 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.26985 | 0.124033 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41.9944 | + | 25.4947i | 1.59065 | + | 0.965679i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.7265 | 1.12436 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.8484 | 1.16513 | 0.582563 | − | 0.812785i | \(-0.302050\pi\) | ||||
0.582563 | + | 0.812785i | \(0.302050\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 27.9379i | − | 1.05370i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.528397 | −0.0199006 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.632052i | 0.0237708i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.4982i | 1.59605i | 0.602622 | + | 0.798027i | \(0.294123\pi\) | ||||
−0.602622 | + | 0.798027i | \(0.705877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0399i | 0.451530i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 59.1353 | 2.21463 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.69171 | 0.100664 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 40.7434i | 1.52159i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.2016i | 1.49927i | 0.661853 | + | 0.749633i | \(0.269770\pi\) | ||||
−0.661853 | + | 0.749633i | \(0.730230\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.24994i | 0.0465503i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.55295 | 0.243707 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 42.5386i | − | 1.57984i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.5800 | 1.57920 | 0.789602 | − | 0.613619i | \(-0.210287\pi\) | ||||
0.789602 | + | 0.613619i | \(0.210287\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.10774 | 0.263250 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.04593 | − | 9.95876i | 0.223617 | − | 0.368338i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.9773 | 1.29192 | 0.645958 | − | 0.763373i | \(-0.276458\pi\) | ||||
0.645958 | + | 0.763373i | \(0.276458\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.42706 | 0.310837 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.24039i | 0.193032i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.18760 | −0.337971 | −0.168986 | − | 0.985619i | \(-0.554049\pi\) | ||||
−0.168986 | + | 0.985619i | \(0.554049\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 34.0693i | 1.25157i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 0.293179i | − | 0.0107557i | −0.999986 | − | 0.00537784i | \(-0.998288\pi\) | ||
0.999986 | − | 0.00537784i | \(-0.00171183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 4.97224i | − | 0.182169i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −28.9845 | −1.06049 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.317217 | 0.0115909 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 34.6526i | − | 1.26449i | −0.774769 | − | 0.632245i | \(-0.782134\pi\) | ||
0.774769 | − | 0.632245i | \(-0.217866\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 56.4686i | − | 2.05783i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.51819i | 0.128040i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.4889 | −1.65332 | −0.826661 | − | 0.562701i | \(-0.809762\pi\) | ||||
−0.826661 | + | 0.562701i | \(0.809762\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 22.0076i | − | 0.798826i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −51.3442 | −1.86123 | −0.930614 | − | 0.366003i | \(-0.880726\pi\) | ||||
−0.930614 | + | 0.366003i | \(0.880726\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.27947 | −0.0463199 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.80532 | + | 2.31020i | 0.137582 | + | 0.0835254i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.00333 | −0.144552 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.1432 | −0.906687 | −0.453344 | − | 0.891336i | \(-0.649769\pi\) | ||||
−0.453344 | + | 0.891336i | \(0.649769\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 49.4499i | 1.78089i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.148731 | 0.00534947 | 0.00267473 | − | 0.999996i | \(-0.499149\pi\) | ||||
0.00267473 | + | 0.999996i | \(0.499149\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 35.3555i | − | 1.27001i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 1.11672i | − | 0.0400621i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 45.3246i | 1.62392i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.09588 | 0.325476 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.1016 | −0.718373 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.4558i | 0.408877i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 49.7135i | − | 1.77209i | −0.463595 | − | 0.886047i | \(-0.653441\pi\) | ||
0.463595 | − | 0.886047i | \(-0.346559\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 41.7441i | 1.48613i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.298261 | −0.0106049 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 60.1700i | − | 2.13670i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.95686 | 0.317667 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.7889 | −0.523851 | −0.261926 | − | 0.965088i | \(-0.584358\pi\) | ||||
−0.261926 | + | 0.965088i | \(0.584358\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.938523 | − | 1.54592i | 0.0332026 | − | 0.0546907i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29.1277 | −1.02918 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.6948 | −0.447988 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.288304i | 0.0101614i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.2500 | −0.501625 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 36.9850i | − | 1.30032i | −0.759796 | − | 0.650161i | \(-0.774701\pi\) | ||
0.759796 | − | 0.650161i | \(-0.225299\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 27.8127i | − | 0.976634i | −0.872666 | − | 0.488317i | \(-0.837611\pi\) | ||
0.872666 | − | 0.488317i | \(-0.162389\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 27.6293i | − | 0.969001i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.21617 | −0.0776289 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.7485 | 0.376043 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.545558i | 0.0190634i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.9216i | 1.74228i | 0.491038 | + | 0.871138i | \(0.336618\pi\) | ||||
−0.491038 | + | 0.871138i | \(0.663382\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.824220i | 0.0287305i | 0.999897 | + | 0.0143653i | \(0.00457276\pi\) | ||||
−0.999897 | + | 0.0143653i | \(0.995427\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.1578 | −0.458096 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.6915i | 0.615195i | 0.951517 | + | 0.307597i | \(0.0995250\pi\) | ||||
−0.951517 | + | 0.307597i | \(0.900475\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.2134 | −0.632578 | −0.316289 | − | 0.948663i | \(-0.602437\pi\) | ||||
−0.316289 | + | 0.948663i | \(0.602437\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.67400 | −0.0580704 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.9679 | + | 24.6549i | −0.518607 | + | 0.854241i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.95516 | −0.309906 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.7072 | −0.577487 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 21.6765i | − | 0.748355i | −0.927357 | − | 0.374177i | \(-0.877925\pi\) | ||
0.927357 | − | 0.374177i | \(-0.122075\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −52.5669 | −1.81265 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.07809i | 0.278224i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.62974i | 0.0560649i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 0.641633i | − | 0.0220468i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.8148 | 0.611401 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −57.8595 | −1.98340 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.5140i | 0.976302i | 0.872759 | + | 0.488151i | \(0.162328\pi\) | ||||
−0.872759 | + | 0.488151i | \(0.837672\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.10709i | 0.140460i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 33.4831i | − | 1.14376i | −0.820337 | − | 0.571881i | \(-0.806214\pi\) | ||
0.820337 | − | 0.571881i | \(-0.193786\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.6618 | 1.31912 | 0.659562 | − | 0.751650i | \(-0.270742\pi\) | ||||
0.659562 | + | 0.751650i | \(0.270742\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.81169i | 0.0617423i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.31401 | −0.146851 | −0.0734253 | − | 0.997301i | \(-0.523393\pi\) | ||||
−0.0734253 | + | 0.997301i | \(0.523393\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.93426 | 0.269773 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −33.7426 | + | 17.5476i | −1.14596 | + | 0.595948i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.49771 | −0.254343 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.8010 | −0.569281 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 13.9070i | − | 0.470681i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.355350 | 0.0120130 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.6885i | 1.03628i | 0.855297 | + | 0.518138i | \(0.173375\pi\) | ||||
−0.855297 | + | 0.518138i | \(0.826625\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.0901i | 0.542706i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.1195i | 1.31797i | 0.752157 | + | 0.658985i | \(0.229014\pi\) | ||||
−0.752157 | + | 0.658985i | \(0.770986\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.0135 | 1.71674 | 0.858370 | − | 0.513032i | \(-0.171478\pi\) | ||||
0.858370 | + | 0.513032i | \(0.171478\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.20466 | −0.0404942 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.9687i | 0.737637i | 0.929501 | + | 0.368818i | \(0.120238\pi\) | ||||
−0.929501 | + | 0.368818i | \(0.879762\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.536766i | 0.0180026i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.7290i | 0.459939i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.66851 | 0.0558347 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.35460i | 0.0787054i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 70.5578 | 2.35585 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −67.7935 | −2.26104 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.9089 | + | 26.2049i | −0.530002 | + | 0.873011i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.429634 | 0.0142973 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.52722 | 0.216972 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 46.1535i | − | 1.53250i | −0.642542 | − | 0.766250i | \(-0.722120\pi\) | ||
0.642542 | − | 0.766250i | \(-0.277880\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.6474 | 0.618495 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 22.6987i | − | 0.752040i | −0.926611 | − | 0.376020i | \(-0.877292\pi\) | ||
0.926611 | − | 0.376020i | \(-0.122708\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 18.0498i | − | 0.597362i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 18.1060i | − | 0.598567i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.0121407 | 0.000400922 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.3839 | 1.20019 | 0.600096 | − | 0.799928i | \(-0.295129\pi\) | ||||
0.600096 | + | 0.799928i | \(0.295129\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.2152i | 0.797919i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.1619i | 0.959877i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.5928i | 1.13740i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 36.8770 | 1.21120 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.99217i | 0.163788i | 0.996641 | + | 0.0818939i | \(0.0260969\pi\) | ||||
−0.996641 | + | 0.0818939i | \(0.973903\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.6101 | −0.872110 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 54.3192 | 1.77833 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.43865 | + | 2.36973i | −0.0470490 | + | 0.0774984i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.7810 | −1.65894 | −0.829471 | − | 0.558550i | \(-0.811358\pi\) | ||||
−0.829471 | + | 0.558550i | \(0.811358\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 52.7745 | 1.72223 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.8096i | 0.841370i | 0.907207 | + | 0.420685i | \(0.138210\pi\) | ||||
−0.907207 | + | 0.420685i | \(0.861790\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 93.8675 | 3.05675 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 0.0814532i | − | 0.00264967i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 30.3908i | − | 0.987570i | −0.869584 | − | 0.493785i | \(-0.835613\pi\) | ||
0.869584 | − | 0.493785i | \(-0.164387\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 40.7001i | − | 1.32118i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.0842 | 1.07283 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.58660 | 0.213361 | 0.106681 | − | 0.994293i | \(-0.465978\pi\) | ||||
0.106681 | + | 0.994293i | \(0.465978\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 0.840037i | − | 0.0271830i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.2298i | 0.815565i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.0287589i | 0.000928673i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.3458 | −0.817608 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 9.35884i | − | 0.301584i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.49108 | 0.305529 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8556 | 0.413409 | 0.206704 | − | 0.978403i | \(-0.433726\pi\) | ||||
0.206704 | + | 0.978403i | \(0.433726\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29.9940 | − | 18.2092i | −0.963545 | − | 0.584965i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.175222 | 0.00562314 | 0.00281157 | − | 0.999996i | \(-0.499105\pi\) | ||||
0.00281157 | + | 0.999996i | \(0.499105\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.412713 | −0.0132310 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 42.1847i | − | 1.35099i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.8868 | −1.50004 | −0.750020 | − | 0.661415i | \(-0.769956\pi\) | ||||
−0.750020 | + | 0.661415i | \(0.769956\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 18.1390i | − | 0.579725i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.7481i | 1.20521i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.1430i | 1.28036i | 0.768224 | + | 0.640181i | \(0.221141\pi\) | ||||
−0.768224 | + | 0.640181i | \(0.778859\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.71649 | 0.309593 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.0666930 | 0.00212286 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 22.2602i | − | 0.707834i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 52.6000i | − | 1.67089i | −0.549572 | − | 0.835446i | \(-0.685209\pi\) | ||
0.549572 | − | 0.835446i | \(-0.314791\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 31.9725i | 1.01462i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.92829 | 0.219642 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.61292i | 0.272774i | 0.990656 | + | 0.136387i | \(0.0435490\pi\) | ||||
−0.990656 | + | 0.136387i | \(0.956451\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.3468 | 0.517190 |
(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 | 4012.2.b.a.237.7 | ✓ | 40 | |
17.16 | even | 2 | inner | 4012.2.b.a.237.34 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.a.237.7 | ✓ | 40 | 1.1 | even | 1 | trivial | |
4012.2.b.a.237.34 | yes | 40 | 17.16 | even | 2 | inner |