Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,3,Mod(145,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cg (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.4660106475\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 81 x^{14} - 118 x^{13} + 1960 x^{12} - 366 x^{11} + 37625 x^{10} - 83714 x^{9} + \cdots + 1148023744 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 577.5 | ||
Root | \(2.29298 - 3.14719i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.577 |
Dual form | 1008.3.cg.q.145.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.27883 | − | 0.738332i | 0.255766 | − | 0.147666i | −0.366636 | − | 0.930365i | \(-0.619490\pi\) |
0.622401 | + | 0.782698i | \(0.286157\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.08597 | − | 5.68374i | 0.583710 | − | 0.811962i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.76437 | − | 13.4483i | 0.705852 | − | 1.22257i | −0.260532 | − | 0.965465i | \(-0.583898\pi\) |
0.966383 | − | 0.257105i | \(-0.0827688\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 18.6695i | − | 1.43612i | −0.695982 | − | 0.718059i | \(-0.745031\pi\) | ||
0.695982 | − | 0.718059i | \(-0.254969\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11.8009 | − | 6.81327i | −0.694173 | − | 0.400781i | 0.111001 | − | 0.993820i | \(-0.464594\pi\) |
−0.805173 | + | 0.593040i | \(0.797928\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.20669 | + | 0.696684i | −0.0635101 | + | 0.0366676i | −0.531419 | − | 0.847109i | \(-0.678341\pi\) |
0.467909 | + | 0.883777i | \(0.345008\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20.0154 | + | 34.6678i | 0.870237 | + | 1.50729i | 0.861752 | + | 0.507330i | \(0.169368\pi\) |
0.00848505 | + | 0.999964i | \(0.497299\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.4097 | + | 19.7622i | −0.456389 | + | 0.790489i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −52.1017 | −1.79661 | −0.898305 | − | 0.439373i | \(-0.855201\pi\) | ||||
−0.898305 | + | 0.439373i | \(0.855201\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −41.5945 | − | 24.0146i | −1.34176 | − | 0.774664i | −0.354692 | − | 0.934983i | \(-0.615414\pi\) |
−0.987065 | + | 0.160319i | \(0.948748\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.02877 | − | 10.2853i | 0.0293934 | − | 0.293866i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.93414 | − | 13.7423i | −0.214436 | − | 0.371414i | 0.738662 | − | 0.674076i | \(-0.235458\pi\) |
−0.953098 | + | 0.302662i | \(0.902125\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 20.6334i | 0.503253i | 0.967824 | + | 0.251626i | \(0.0809654\pi\) | ||||
−0.967824 | + | 0.251626i | \(0.919035\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16.0549 | 0.373370 | 0.186685 | − | 0.982420i | \(-0.440226\pi\) | ||||
0.186685 | + | 0.982420i | \(0.440226\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 65.1271 | − | 37.6011i | 1.38568 | − | 0.800024i | 0.392857 | − | 0.919599i | \(-0.371487\pi\) |
0.992825 | + | 0.119575i | \(0.0381533\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.6097 | − | 46.4471i | −0.318566 | − | 0.947901i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.13459 | + | 15.8216i | −0.172351 | + | 0.298520i | −0.939241 | − | 0.343258i | \(-0.888470\pi\) |
0.766890 | + | 0.641778i | \(0.221803\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 22.9307i | − | 0.416922i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 41.7253 | + | 24.0901i | 0.707209 | + | 0.408307i | 0.810027 | − | 0.586393i | \(-0.199452\pi\) |
−0.102818 | + | 0.994700i | \(0.532786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23.2757 | − | 13.4382i | 0.381568 | − | 0.220298i | −0.296932 | − | 0.954899i | \(-0.595964\pi\) |
0.678500 | + | 0.734600i | \(0.262630\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.7843 | − | 23.8751i | −0.212066 | − | 0.367310i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.310414 | − | 0.537652i | 0.00463304 | − | 0.00802466i | −0.863700 | − | 0.504007i | \(-0.831859\pi\) |
0.868333 | + | 0.495982i | \(0.165192\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −18.7693 | −0.264356 | −0.132178 | − | 0.991226i | \(-0.542197\pi\) | ||||
−0.132178 | + | 0.991226i | \(0.542197\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −89.5780 | − | 51.7179i | −1.22710 | − | 0.708464i | −0.260674 | − | 0.965427i | \(-0.583945\pi\) |
−0.966421 | + | 0.256963i | \(0.917278\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −44.7115 | − | 99.0798i | −0.580669 | − | 1.28675i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −55.1116 | − | 95.4561i | −0.697615 | − | 1.20830i | −0.969291 | − | 0.245916i | \(-0.920911\pi\) |
0.271676 | − | 0.962389i | \(-0.412422\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 23.8805i | 0.287717i | 0.989598 | + | 0.143858i | \(0.0459510\pi\) | ||||
−0.989598 | + | 0.143858i | \(0.954049\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.1218 | −0.236727 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −114.503 | + | 66.1084i | −1.28655 | + | 0.742790i | −0.978037 | − | 0.208429i | \(-0.933165\pi\) |
−0.308513 | + | 0.951220i | \(0.599831\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −106.113 | − | 76.2831i | −1.16607 | − | 0.838276i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.02877 | + | 1.78188i | −0.0108291 | + | 0.0187566i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 72.0450i | − | 0.742732i | −0.928486 | − | 0.371366i | \(-0.878889\pi\) | ||
0.928486 | − | 0.371366i | \(-0.121111\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 145.743 | + | 84.1449i | 1.44300 | + | 0.833118i | 0.998049 | − | 0.0624354i | \(-0.0198867\pi\) |
0.444954 | + | 0.895553i | \(0.353220\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 74.2263 | − | 42.8546i | 0.720644 | − | 0.416064i | −0.0943459 | − | 0.995539i | \(-0.530076\pi\) |
0.814990 | + | 0.579476i | \(0.196743\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.54612 | + | 2.67796i | 0.0144497 | + | 0.0250277i | 0.873160 | − | 0.487434i | \(-0.162067\pi\) |
−0.858710 | + | 0.512462i | \(0.828734\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 46.1317 | − | 79.9024i | 0.423227 | − | 0.733050i | −0.573026 | − | 0.819537i | \(-0.694231\pi\) |
0.996253 | + | 0.0864871i | \(0.0275641\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 131.406 | 1.16289 | 0.581444 | − | 0.813586i | \(-0.302488\pi\) | ||||
0.581444 | + | 0.813586i | \(0.302488\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 51.1926 | + | 29.5561i | 0.445153 | + | 0.257009i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −86.9431 | + | 39.2346i | −0.730614 | + | 0.329702i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −60.0708 | − | 104.046i | −0.496453 | − | 0.859881i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 70.6133i | 0.564906i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −88.0157 | −0.693037 | −0.346519 | − | 0.938043i | \(-0.612636\pi\) | ||||
−0.346519 | + | 0.938043i | \(0.612636\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −28.0479 | + | 16.1935i | −0.214106 | + | 0.123614i | −0.603218 | − | 0.797576i | \(-0.706115\pi\) |
0.389112 | + | 0.921190i | \(0.372782\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.970737 | + | 9.70515i | −0.00729877 | + | 0.0729710i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 57.5739 | − | 99.7209i | 0.420247 | − | 0.727890i | −0.575716 | − | 0.817650i | \(-0.695277\pi\) |
0.995963 | + | 0.0897598i | \(0.0286099\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 206.700i | − | 1.48705i | −0.668706 | − | 0.743527i | \(-0.733152\pi\) | ||
0.668706 | − | 0.743527i | \(-0.266848\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −251.073 | − | 144.957i | −1.75576 | − | 1.01369i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −66.6291 | + | 38.4683i | −0.459511 | + | 0.265299i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −75.5206 | − | 130.806i | −0.506850 | − | 0.877890i | −0.999969 | − | 0.00792779i | \(-0.997476\pi\) |
0.493119 | − | 0.869962i | \(-0.335857\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −31.1207 | + | 53.9027i | −0.206098 | + | 0.356971i | −0.950482 | − | 0.310780i | \(-0.899410\pi\) |
0.744384 | + | 0.667751i | \(0.232743\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −70.9229 | −0.457567 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 209.429 | + | 120.914i | 1.33394 | + | 0.770153i | 0.985902 | − | 0.167325i | \(-0.0535130\pi\) |
0.348043 | + | 0.937479i | \(0.386846\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 278.825 | + | 27.8889i | 1.73183 | + | 0.173223i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.640226 | + | 1.10890i | 0.00392776 | + | 0.00680309i | 0.867983 | − | 0.496595i | \(-0.165416\pi\) |
−0.864055 | + | 0.503398i | \(0.832083\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 158.859i | − | 0.951254i | −0.879647 | − | 0.475627i | \(-0.842221\pi\) | ||
0.879647 | − | 0.475627i | \(-0.157779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −179.551 | −1.06243 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.5532 | − | 11.2890i | 0.113024 | − | 0.0652546i | −0.442422 | − | 0.896807i | \(-0.645881\pi\) |
0.555446 | + | 0.831552i | \(0.312547\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 65.7035 | + | 145.598i | 0.375449 | + | 0.831987i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 53.3082 | − | 92.3326i | 0.297811 | − | 0.515824i | −0.677824 | − | 0.735225i | \(-0.737077\pi\) |
0.975635 | + | 0.219400i | \(0.0704100\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 141.955i | − | 0.784279i | −0.919906 | − | 0.392140i | \(-0.871735\pi\) | ||
0.919906 | − | 0.392140i | \(-0.128265\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.2928 | − | 11.7161i | −0.109691 | − | 0.0633300i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −183.254 | + | 105.801i | −0.979966 | + | 0.565783i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 165.284 | + | 286.281i | 0.865363 | + | 1.49885i | 0.866686 | + | 0.498854i | \(0.166246\pi\) |
−0.00132256 | + | 0.999999i | \(0.500421\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −85.3048 | + | 147.752i | −0.441994 | + | 0.765555i | −0.997837 | − | 0.0657314i | \(-0.979062\pi\) |
0.555844 | + | 0.831287i | \(0.312395\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 291.740 | 1.48091 | 0.740457 | − | 0.672104i | \(-0.234609\pi\) | ||||
0.740457 | + | 0.672104i | \(0.234609\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 113.785 | + | 65.6941i | 0.571786 | + | 0.330121i | 0.757862 | − | 0.652414i | \(-0.226244\pi\) |
−0.186076 | + | 0.982535i | \(0.559577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −212.886 | + | 296.132i | −1.04870 | + | 1.45878i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.2343 | + | 26.3865i | 0.0743135 | + | 0.128715i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.6372i | 0.103527i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 30.5925 | 0.144988 | 0.0724942 | − | 0.997369i | \(-0.476904\pi\) | ||||
0.0724942 | + | 0.997369i | \(0.476904\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.5315 | − | 11.8538i | 0.0954952 | − | 0.0551342i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −306.446 | + | 138.289i | −1.41219 | + | 0.637278i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −127.201 | + | 220.318i | −0.575568 | + | 0.996913i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 60.1683i | 0.269813i | 0.990858 | + | 0.134906i | \(0.0430734\pi\) | ||||
−0.990858 | + | 0.134906i | \(0.956927\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −293.987 | − | 169.734i | −1.29510 | − | 0.747725i | −0.315545 | − | 0.948911i | \(-0.602187\pi\) |
−0.979553 | + | 0.201185i | \(0.935521\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 253.061 | − | 146.105i | 1.10507 | − | 0.638011i | 0.167521 | − | 0.985869i | \(-0.446424\pi\) |
0.937548 | + | 0.347857i | \(0.113091\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −54.1324 | − | 93.7601i | −0.232328 | − | 0.402404i | 0.726165 | − | 0.687521i | \(-0.241301\pi\) |
−0.958493 | + | 0.285117i | \(0.907968\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 55.5242 | − | 96.1708i | 0.236273 | − | 0.409237i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.6245 | 0.0570064 | 0.0285032 | − | 0.999594i | \(-0.490926\pi\) | ||||
0.0285032 | + | 0.999594i | \(0.490926\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 161.485 | + | 93.2334i | 0.670062 | + | 0.386860i | 0.796100 | − | 0.605165i | \(-0.206893\pi\) |
−0.126038 | + | 0.992025i | \(0.540226\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −54.2556 | − | 47.8727i | −0.221451 | − | 0.195399i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.0068 | + | 22.5284i | 0.0526589 | + | 0.0912080i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 338.180i | − | 1.34733i | −0.739037 | − | 0.673665i | \(-0.764719\pi\) | ||
0.739037 | − | 0.673665i | \(-0.235281\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 621.629 | 2.45703 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −399.200 | + | 230.478i | −1.55331 | + | 0.896803i | −0.555439 | + | 0.831557i | \(0.687450\pi\) |
−0.997869 | + | 0.0652458i | \(0.979217\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −110.526 | − | 11.0552i | −0.426743 | − | 0.0426841i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −62.4410 | + | 108.151i | −0.237418 | + | 0.411221i | −0.959973 | − | 0.280093i | \(-0.909635\pi\) |
0.722554 | + | 0.691314i | \(0.242968\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.9774i | 0.101802i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 368.369 | + | 212.678i | 1.36940 | + | 0.790625i | 0.990852 | − | 0.134955i | \(-0.0430890\pi\) |
0.378551 | + | 0.925580i | \(0.376422\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 353.970 | − | 204.365i | 1.30616 | − | 0.754114i | 0.324710 | − | 0.945814i | \(-0.394733\pi\) |
0.981454 | + | 0.191700i | \(0.0614000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 177.179 | + | 306.882i | 0.644286 | + | 1.11594i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −179.920 | + | 311.630i | −0.649530 | + | 1.12502i | 0.333706 | + | 0.942677i | \(0.391701\pi\) |
−0.983235 | + | 0.182341i | \(0.941632\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −188.703 | −0.671540 | −0.335770 | − | 0.941944i | \(-0.608996\pi\) | ||||
−0.335770 | + | 0.941944i | \(0.608996\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 320.934 | + | 185.291i | 1.13404 | + | 0.654739i | 0.944948 | − | 0.327220i | \(-0.106112\pi\) |
0.189093 | + | 0.981959i | \(0.439445\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 117.275 | + | 84.3073i | 0.408622 | + | 0.293754i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −51.6586 | − | 89.4754i | −0.178750 | − | 0.309603i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 325.697i | − | 1.11159i | −0.831318 | − | 0.555796i | \(-0.812413\pi\) | ||
0.831318 | − | 0.555796i | \(-0.187587\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 71.1461 | 0.241173 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 647.231 | − | 373.679i | 2.16465 | − | 1.24976i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 65.5998 | − | 91.2519i | 0.217940 | − | 0.303162i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.8437 | − | 34.3703i | 0.0650614 | − | 0.112690i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 185.193i | 0.603236i | 0.953429 | + | 0.301618i | \(0.0975267\pi\) | ||||
−0.953429 | + | 0.301618i | \(0.902473\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 307.643 | + | 177.618i | 0.989206 | + | 0.571119i | 0.905037 | − | 0.425333i | \(-0.139843\pi\) |
0.0841694 | + | 0.996451i | \(0.473176\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −191.007 | + | 110.278i | −0.610248 | + | 0.352327i | −0.773062 | − | 0.634330i | \(-0.781276\pi\) |
0.162815 | + | 0.986657i | \(0.447943\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −228.767 | − | 396.235i | −0.721661 | − | 1.24995i | −0.960334 | − | 0.278853i | \(-0.910046\pi\) |
0.238673 | − | 0.971100i | \(-0.423288\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −404.537 | + | 700.678i | −1.26814 | + | 2.19648i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.9868 | 0.0587826 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 368.952 | + | 213.014i | 1.13524 | + | 0.655429i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 52.3922 | − | 523.802i | 0.159247 | − | 1.59210i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 159.231 | + | 275.796i | 0.481061 | + | 0.833221i | 0.999764 | − | 0.0217331i | \(-0.00691840\pi\) |
−0.518703 | + | 0.854954i | \(0.673585\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 0.916753i | − | 0.00273658i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −358.473 | −1.06372 | −0.531859 | − | 0.846833i | \(-0.678506\pi\) | ||||
−0.531859 | + | 0.846833i | \(0.678506\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −645.909 | + | 372.916i | −1.89416 | + | 1.09360i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −327.774 | − | 101.060i | −0.955610 | − | 0.294635i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.3454 | − | 30.0431i | 0.0499867 | − | 0.0865795i | −0.839949 | − | 0.542665i | \(-0.817415\pi\) |
0.889936 | + | 0.456085i | \(0.150749\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 367.693i | 1.05356i | 0.850001 | + | 0.526781i | \(0.176601\pi\) | ||||
−0.850001 | + | 0.526781i | \(0.823399\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.8743 | − | 9.16504i | −0.0449697 | − | 0.0259633i | 0.477347 | − | 0.878715i | \(-0.341599\pi\) |
−0.522316 | + | 0.852752i | \(0.674932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.0027 | + | 13.8580i | −0.0676133 | + | 0.0390365i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −82.0379 | − | 142.094i | −0.228518 | − | 0.395805i | 0.728851 | − | 0.684672i | \(-0.240055\pi\) |
−0.957369 | + | 0.288868i | \(0.906721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −179.529 | + | 310.954i | −0.497311 | + | 0.861368i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −152.740 | −0.418465 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 303.246 | + | 175.079i | 0.826284 | + | 0.477055i | 0.852579 | − | 0.522599i | \(-0.175037\pi\) |
−0.0262946 | + | 0.999654i | \(0.508371\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 52.6020 | + | 116.565i | 0.141784 | + | 0.314192i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 353.395 | + | 612.098i | 0.947440 | + | 1.64101i | 0.750790 | + | 0.660541i | \(0.229673\pi\) |
0.196650 | + | 0.980474i | \(0.436994\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 972.714i | 2.58014i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 534.245 | 1.40962 | 0.704809 | − | 0.709397i | \(-0.251033\pi\) | ||||
0.704809 | + | 0.709397i | \(0.251033\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 379.794 | − | 219.274i | 0.991630 | − | 0.572518i | 0.0858685 | − | 0.996306i | \(-0.472633\pi\) |
0.905761 | + | 0.423789i | \(0.139300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −130.332 | − | 93.6942i | −0.338525 | − | 0.243361i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −156.927 | + | 271.805i | −0.403410 | + | 0.698727i | −0.994135 | − | 0.108146i | \(-0.965509\pi\) |
0.590725 | + | 0.806873i | \(0.298842\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 545.483i | − | 1.39510i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −140.956 | − | 81.3813i | −0.356852 | − | 0.206029i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 487.980 | − | 281.736i | 1.22917 | − | 0.709661i | 0.262313 | − | 0.964983i | \(-0.415515\pi\) |
0.966856 | + | 0.255321i | \(0.0821813\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −300.808 | − | 521.014i | −0.750144 | − | 1.29929i | −0.947753 | − | 0.319006i | \(-0.896651\pi\) |
0.197609 | − | 0.980281i | \(-0.436682\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −448.341 | + | 776.549i | −1.11251 | + | 1.92692i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −246.414 | −0.605441 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −134.300 | − | 77.5382i | −0.328362 | − | 0.189580i | 0.326752 | − | 0.945110i | \(-0.394046\pi\) |
−0.655114 | + | 0.755530i | \(0.727379\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 307.410 | − | 138.724i | 0.744335 | − | 0.335894i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.6317 | + | 30.5391i | 0.0424861 | + | 0.0735881i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 539.266i | 1.28703i | 0.765433 | + | 0.643516i | \(0.222525\pi\) | ||||
−0.765433 | + | 0.643516i | \(0.777475\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 259.595 | 0.616615 | 0.308307 | − | 0.951287i | \(-0.400238\pi\) | ||||
0.308307 | + | 0.951287i | \(0.400238\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 269.291 | − | 155.475i | 0.633626 | − | 0.365824i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.7244 | − | 187.201i | 0.0438510 | − | 0.438409i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 248.827 | − | 430.981i | 0.577324 | − | 0.999955i | −0.418461 | − | 0.908235i | \(-0.637430\pi\) |
0.995785 | − | 0.0917199i | \(-0.0292364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 416.661i | − | 0.962266i | −0.876648 | − | 0.481133i | \(-0.840225\pi\) | ||
0.876648 | − | 0.481133i | \(-0.159775\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −48.3049 | − | 27.8889i | −0.110538 | − | 0.0638189i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 141.093 | − | 81.4599i | 0.321396 | − | 0.185558i | −0.330619 | − | 0.943764i | \(-0.607257\pi\) |
0.652015 | + | 0.758206i | \(0.273924\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 321.003 | + | 555.993i | 0.724611 | + | 1.25506i | 0.959134 | + | 0.282953i | \(0.0913140\pi\) |
−0.234522 | + | 0.972111i | \(0.575353\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −97.6198 | + | 169.082i | −0.219370 | + | 0.379961i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −238.462 | −0.531097 | −0.265548 | − | 0.964098i | \(-0.585553\pi\) | ||||
−0.265548 | + | 0.964098i | \(0.585553\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 277.483 | + | 160.205i | 0.615262 | + | 0.355222i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −192.022 | − | 19.2066i | −0.422027 | − | 0.0422123i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −87.9517 | − | 152.337i | −0.192454 | − | 0.333341i | 0.753609 | − | 0.657323i | \(-0.228311\pi\) |
−0.946063 | + | 0.323982i | \(0.894978\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 161.802i | 0.350980i | 0.984481 | + | 0.175490i | \(0.0561509\pi\) | ||||
−0.984481 | + | 0.175490i | \(0.943849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 88.3545 | 0.190831 | 0.0954153 | − | 0.995438i | \(-0.469582\pi\) | ||||
0.0954153 | + | 0.995438i | \(0.469582\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.32384 | − | 3.07372i | 0.0114001 | − | 0.00658184i | −0.494289 | − | 0.869298i | \(-0.664572\pi\) |
0.505689 | + | 0.862716i | \(0.331238\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.78753 | − | 3.96114i | −0.00381137 | − | 0.00844593i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 124.656 | − | 215.911i | 0.263544 | − | 0.456471i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 31.7959i | − | 0.0669387i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −518.538 | − | 299.378i | −1.08254 | − | 0.625006i | −0.150961 | − | 0.988540i | \(-0.548237\pi\) |
−0.931581 | + | 0.363534i | \(0.881570\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −256.563 | + | 148.127i | −0.533395 | + | 0.307956i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −53.1931 | − | 92.1332i | −0.109677 | − | 0.189965i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 209.892 | − | 363.544i | 0.430990 | − | 0.746496i | −0.565969 | − | 0.824427i | \(-0.691498\pi\) |
0.996959 | + | 0.0779302i | \(0.0248311\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.5914 | 0.0806341 | 0.0403171 | − | 0.999187i | \(-0.487163\pi\) | ||||
0.0403171 | + | 0.999187i | \(0.487163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 614.849 | + | 354.983i | 1.24716 | + | 0.720047i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −76.6908 | + | 106.680i | −0.154307 | + | 0.214647i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −334.884 | − | 580.035i | −0.671109 | − | 1.16240i | −0.977590 | − | 0.210519i | \(-0.932485\pi\) |
0.306480 | − | 0.951877i | \(-0.400849\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 213.355i | − | 0.424166i | −0.977252 | − | 0.212083i | \(-0.931975\pi\) | ||
0.977252 | − | 0.212083i | \(-0.0680247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 248.508 | 0.492094 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 391.019 | − | 225.755i | 0.768210 | − | 0.443526i | −0.0640257 | − | 0.997948i | \(-0.520394\pi\) |
0.832236 | + | 0.554422i | \(0.187061\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −659.964 | + | 297.820i | −1.29151 | + | 0.582818i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 63.2818 | − | 109.607i | 0.122877 | − | 0.212830i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1167.80i | − | 2.25879i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 633.929 | + | 365.999i | 1.21675 | + | 0.702494i | 0.964222 | − | 0.265095i | \(-0.0854032\pi\) |
0.252532 | + | 0.967588i | \(0.418737\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 365.430 | − | 210.981i | 0.698720 | − | 0.403406i | −0.108151 | − | 0.994135i | \(-0.534493\pi\) |
0.806870 | + | 0.590728i | \(0.201160\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 327.236 | + | 566.789i | 0.620941 | + | 1.07550i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −536.736 | + | 929.654i | −1.01462 | + | 1.75738i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 385.215 | 0.722730 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.95445 | + | 2.28310i | 0.00739149 | + | 0.00426748i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −745.834 | − | 150.709i | −1.38374 | − | 0.279608i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −448.892 | − | 777.504i | −0.829745 | − | 1.43716i | −0.898238 | − | 0.439509i | \(-0.855153\pi\) |
0.0684934 | − | 0.997652i | \(-0.478181\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 136.242i | − | 0.249985i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −545.813 | −0.997829 | −0.498915 | − | 0.866651i | \(-0.666268\pi\) | ||||
−0.498915 | + | 0.866651i | \(0.666268\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 62.8707 | − | 36.2984i | 0.114103 | − | 0.0658773i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −767.731 | − | 76.7907i | −1.38830 | − | 0.138862i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 105.374 | − | 182.513i | 0.189181 | − | 0.327671i | −0.755796 | − | 0.654807i | \(-0.772750\pi\) |
0.944977 | + | 0.327135i | \(0.106083\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 299.738i | − | 0.536203i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −258.646 | − | 149.329i | −0.459407 | − | 0.265239i | 0.252388 | − | 0.967626i | \(-0.418784\pi\) |
−0.711795 | + | 0.702387i | \(0.752117\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 168.046 | − | 97.0215i | 0.297427 | − | 0.171719i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 234.818 | + | 406.717i | 0.412686 | + | 0.714793i | 0.995182 | − | 0.0980404i | \(-0.0312574\pi\) |
−0.582497 | + | 0.812833i | \(0.697924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 109.586 | − | 189.808i | 0.191919 | − | 0.332414i | −0.753967 | − | 0.656912i | \(-0.771862\pi\) |
0.945886 | + | 0.324498i | \(0.105195\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −913.483 | −1.58867 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 230.500 | + | 133.079i | 0.399480 | + | 0.230640i | 0.686260 | − | 0.727357i | \(-0.259251\pi\) |
−0.286780 | + | 0.957997i | \(0.592585\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 135.731 | + | 97.5750i | 0.233615 | + | 0.167943i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 141.849 | + | 245.689i | 0.243308 | + | 0.421422i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 209.316i | − | 0.356586i | −0.983977 | − | 0.178293i | \(-0.942943\pi\) | ||
0.983977 | − | 0.178293i | \(-0.0570575\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 66.9223 | 0.113620 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 363.251 | − | 209.723i | 0.612565 | − | 0.353665i | −0.161404 | − | 0.986888i | \(-0.551602\pi\) |
0.773969 | + | 0.633224i | \(0.218269\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −82.2171 | + | 114.367i | −0.138180 | + | 0.192214i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −350.383 | + | 606.881i | −0.584947 | + | 1.01316i | 0.409935 | + | 0.912115i | \(0.365551\pi\) |
−0.994882 | + | 0.101043i | \(0.967782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 192.210i | − | 0.319817i | −0.987132 | − | 0.159909i | \(-0.948880\pi\) | ||
0.987132 | − | 0.159909i | \(-0.0511200\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −153.640 | − | 88.7043i | −0.253951 | − | 0.146619i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −326.241 | + | 188.356i | −0.537465 | + | 0.310306i | −0.744051 | − | 0.668123i | \(-0.767098\pi\) |
0.206586 | + | 0.978428i | \(0.433765\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −701.995 | − | 1215.89i | −1.14893 | − | 1.99000i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 222.681 | − | 385.694i | 0.363264 | − | 0.629191i | −0.625232 | − | 0.780439i | \(-0.714996\pi\) |
0.988496 | + | 0.151248i | \(0.0483291\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 562.357 | 0.911437 | 0.455719 | − | 0.890124i | \(-0.349382\pi\) | ||||
0.455719 | + | 0.890124i | \(0.349382\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 351.292 | + | 202.819i | 0.567515 | + | 0.327655i | 0.756156 | − | 0.654391i | \(-0.227075\pi\) |
−0.188641 | + | 0.982046i | \(0.560408\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −92.1132 | + | 920.922i | −0.147854 | + | 1.47820i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −233.107 | − | 403.754i | −0.372972 | − | 0.646006i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 216.230i | 0.343768i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 369.672 | 0.585851 | 0.292926 | − | 0.956135i | \(-0.405371\pi\) | ||||
0.292926 | + | 0.956135i | \(0.405371\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −112.557 | + | 64.9848i | −0.177255 | + | 0.102338i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −867.146 | + | 291.426i | −1.36130 | + | 0.457498i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −353.414 | + | 612.132i | −0.551349 | + | 0.954964i | 0.446829 | + | 0.894619i | \(0.352553\pi\) |
−0.998178 | + | 0.0603445i | \(0.980780\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 445.022i | − | 0.692102i | −0.938216 | − | 0.346051i | \(-0.887522\pi\) | ||
0.938216 | − | 0.346051i | \(-0.112478\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 321.002 | + | 185.331i | 0.496140 | + | 0.286446i | 0.727118 | − | 0.686513i | \(-0.240859\pi\) |
−0.230978 | + | 0.972959i | \(0.574193\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 647.942 | − | 374.089i | 0.998369 | − | 0.576409i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 107.834 | + | 186.774i | 0.165136 | + | 0.286025i | 0.936704 | − | 0.350123i | \(-0.113860\pi\) |
−0.771567 | + | 0.636148i | \(0.780527\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.9123 | + | 41.4174i | −0.0365074 | + | 0.0632326i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 146.496 | 0.222301 | 0.111151 | − | 0.993804i | \(-0.464546\pi\) | ||||
0.111151 | + | 0.993804i | \(0.464546\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 792.061 | + | 457.297i | 1.19828 | + | 0.691826i | 0.960171 | − | 0.279414i | \(-0.0901401\pi\) |
0.238106 | + | 0.971239i | \(0.423473\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.92421 | + | 13.1279i | 0.00890859 | + | 0.0197413i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1042.84 | − | 1806.25i | −1.56348 | − | 2.70802i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 417.357i | − | 0.621992i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1092.50 | −1.62333 | −0.811666 | − | 0.584122i | \(-0.801439\pi\) | ||||
−0.811666 | + | 0.584122i | \(0.801439\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −151.935 | + | 87.7196i | −0.224424 | + | 0.129571i | −0.607997 | − | 0.793939i | \(-0.708027\pi\) |
0.383573 | + | 0.923510i | \(0.374693\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −409.485 | − | 294.374i | −0.603071 | − | 0.433540i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −494.398 | + | 856.322i | −0.723862 | + | 1.25377i | 0.235579 | + | 0.971855i | \(0.424301\pi\) |
−0.959441 | + | 0.281910i | \(0.909032\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 170.035i | − | 0.248226i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 295.381 | + | 170.539i | 0.428710 | + | 0.247516i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −158.527 | + | 91.5256i | −0.229417 | + | 0.132454i | −0.610303 | − | 0.792168i | \(-0.708952\pi\) |
0.380886 | + | 0.924622i | \(0.375619\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −152.614 | − | 264.334i | −0.219588 | − | 0.380337i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 140.581 | − | 243.493i | 0.201694 | − | 0.349344i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 119.325 | 0.170222 | 0.0851109 | − | 0.996371i | \(-0.472876\pi\) | ||||
0.0851109 | + | 0.996371i | \(0.472876\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.1481 | + | 11.0552i | 0.0272377 | + | 0.0157257i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1073.76 | − | 484.553i | 1.51876 | − | 0.685365i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −101.857 | − | 176.421i | −0.143662 | − | 0.248830i | 0.785211 | − | 0.619229i | \(-0.212555\pi\) |
−0.928873 | + | 0.370398i | \(0.879221\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1922.65i | − | 2.69656i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −428.106 | −0.598749 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −149.327 | + | 86.2140i | −0.207687 | + | 0.119908i | −0.600236 | − | 0.799823i | \(-0.704927\pi\) |
0.392549 | + | 0.919731i | \(0.371593\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 59.7122 | − | 596.985i | 0.0828186 | − | 0.827996i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 594.466 | − | 1029.65i | 0.819953 | − | 1.42020i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1002.21i | − | 1.37855i | −0.724499 | − | 0.689276i | \(-0.757929\pi\) | ||
0.724499 | − | 0.689276i | \(-0.242071\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −189.463 | − | 109.386i | −0.259183 | − | 0.149639i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −284.326 | + | 164.156i | −0.387894 | + | 0.223951i | −0.681247 | − | 0.732053i | \(-0.738562\pi\) |
0.293353 | + | 0.956004i | \(0.405229\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.82033 | − | 8.34906i | −0.00654048 | − | 0.0113284i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −612.564 | + | 1060.99i | −0.828910 | + | 1.43571i | 0.0699840 | + | 0.997548i | \(0.477705\pi\) |
−0.898894 | + | 0.438166i | \(0.855628\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 743.413 | 1.00056 | 0.500278 | − | 0.865865i | \(-0.333231\pi\) | ||||
0.500278 | + | 0.865865i | \(0.333231\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −193.156 | − | 111.519i | −0.259270 | − | 0.149689i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.5382 | + | 2.15432i | 0.0287560 | + | 0.00287626i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 555.950 | + | 962.934i | 0.740280 | + | 1.28220i | 0.952368 | + | 0.304952i | \(0.0986404\pi\) |
−0.212088 | + | 0.977251i | \(0.568026\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 91.9097i | 0.121735i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −716.530 | −0.946539 | −0.473270 | − | 0.880918i | \(-0.656926\pi\) | ||||
−0.473270 | + | 0.880918i | \(0.656926\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1022.88 | + | 590.561i | −1.34413 | + | 0.776032i | −0.987410 | − | 0.158180i | \(-0.949437\pi\) |
−0.356717 | + | 0.934212i | \(0.616104\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −265.652 | − | 588.679i | −0.348167 | − | 0.771532i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 449.751 | − | 778.992i | 0.586377 | − | 1.01564i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1046.71i | − | 1.36113i | −0.732687 | − | 0.680566i | \(-0.761734\pi\) | ||
0.732687 | − | 0.680566i | \(-0.238266\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −516.667 | − | 298.298i | −0.668391 | − | 0.385896i | 0.127075 | − | 0.991893i | \(-0.459441\pi\) |
−0.795467 | + | 0.605997i | \(0.792774\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 949.164 | − | 548.000i | 1.22473 | − | 0.707097i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.3749 | − | 24.8981i | −0.0184531 | − | 0.0319616i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −145.732 | + | 252.415i | −0.186596 | + | 0.323194i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 357.099 | 0.454903 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 858.587 | + | 495.705i | 1.09096 | + | 0.629867i | 0.933832 | − | 0.357711i | \(-0.116443\pi\) |
0.157129 | + | 0.987578i | \(0.449776\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 536.922 | − | 746.879i | 0.678789 | − | 0.944222i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −250.885 | − | 434.546i | −0.316375 | − | 0.547977i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 952.073i | 1.19457i | 0.802029 | + | 0.597285i | \(0.203754\pi\) | ||||
−0.802029 | + | 0.597285i | \(0.796246\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1024.75 | −1.28254 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1391.03 | + | 803.113i | −1.73229 | + | 1.00014i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 377.160 | − | 170.200i | 0.468522 | − | 0.211429i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −409.068 | + | 708.527i | −0.505647 | + | 0.875806i | 0.494332 | + | 0.869273i | \(0.335413\pi\) |
−0.999979 | + | 0.00653275i | \(0.997921\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1453.98i | − | 1.79282i | −0.443222 | − | 0.896412i | \(-0.646165\pi\) | ||
0.443222 | − | 0.896412i | \(-0.353835\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.63748 | + | 0.945398i | 0.00200917 | + | 0.00116000i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.3733 | + | 11.1852i | −0.0237128 | + | 0.0136906i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 305.538 | + | 529.207i | 0.372153 | + | 0.644588i | 0.989897 | − | 0.141792i | \(-0.0452864\pi\) |
−0.617744 | + | 0.786380i | \(0.711953\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 120.570 | − | 208.833i | 0.146500 | − | 0.253746i | −0.783431 | − | 0.621478i | \(-0.786532\pi\) |
0.929932 | + | 0.367732i | \(0.119866\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 868.740 | 1.05047 | 0.525236 | − | 0.850957i | \(-0.323977\pi\) | ||||
0.525236 | + | 0.850957i | \(0.323977\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −689.094 | − | 397.849i | −0.831236 | − | 0.479914i | 0.0230398 | − | 0.999735i | \(-0.492666\pi\) |
−0.854276 | + | 0.519820i | \(0.825999\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −132.248 | + | 654.473i | −0.158761 | + | 0.785682i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −117.291 | − | 203.154i | −0.140468 | − | 0.243298i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 271.638i | 0.323763i | 0.986810 | + | 0.161882i | \(0.0517563\pi\) | ||||
−0.986810 | + | 0.161882i | \(0.948244\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1873.58 | 2.22781 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −229.615 | + | 132.568i | −0.271734 | + | 0.156886i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −836.815 | − | 83.7007i | −0.987976 | − | 0.0988202i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 317.611 | − | 550.118i | 0.373221 | − | 0.646437i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 61.5771i | − | 0.0721889i | −0.999348 | − | 0.0360945i | \(-0.988508\pi\) | ||
0.999348 | − | 0.0360945i | \(-0.0114917\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −935.801 | − | 540.285i | −1.09195 | − | 0.630438i | −0.157855 | − | 0.987462i | \(-0.550458\pi\) |
−0.934095 | + | 0.357025i | \(0.883791\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 824.546 | − | 476.052i | 0.959891 | − | 0.554193i | 0.0637516 | − | 0.997966i | \(-0.479693\pi\) |
0.896140 | + | 0.443772i | \(0.146360\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 204.942 | + | 354.970i | 0.237476 | + | 0.411320i | 0.959989 | − | 0.280036i | \(-0.0903466\pi\) |
−0.722513 | + | 0.691357i | \(0.757013\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.6701 | − | 28.8735i | 0.0192718 | − | 0.0333797i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1711.63 | −1.96965 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.0377 | − | 5.79528i | −0.0115244 | − | 0.00665359i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 401.347 | + | 288.524i | 0.458683 | + | 0.329741i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −169.305 | − | 293.245i | −0.193051 | − | 0.334373i | 0.753209 | − | 0.657781i | \(-0.228505\pi\) |
−0.946260 | + | 0.323408i | \(0.895171\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 446.960i | − | 0.507333i | −0.967292 | − | 0.253666i | \(-0.918363\pi\) | ||
0.967292 | − | 0.253666i | \(-0.0816365\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 884.678 | 1.00190 | 0.500950 | − | 0.865476i | \(-0.332984\pi\) | ||||
0.500950 | + | 0.865476i | \(0.332984\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −775.206 | + | 447.565i | −0.873963 | + | 0.504583i | −0.868663 | − | 0.495403i | \(-0.835020\pi\) |
−0.00530011 | + | 0.999986i | \(0.501687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −359.629 | + | 500.258i | −0.404533 | + | 0.562720i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −52.3922 | + | 90.7460i | −0.0586699 | + | 0.101619i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 157.437i | − | 0.175907i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2167.14 | + | 1251.20i | 2.41061 | + | 1.39177i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 215.593 | − | 124.473i | 0.239282 | − | 0.138150i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −104.810 | − | 181.535i | −0.115812 | − | 0.200592i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −702.978 | + | 1217.59i | −0.775059 | + | 1.34244i | 0.159703 | + | 0.987165i | \(0.448946\pi\) |
−0.934761 | + | 0.355276i | \(0.884387\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 709.400 | 0.778704 | 0.389352 | − | 0.921089i | \(-0.372699\pi\) | ||||
0.389352 | + | 0.921089i | \(0.372699\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 321.152 | + | 185.417i | 0.351754 | + | 0.203085i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.5635 | + | 225.583i | −0.0246058 | + | 0.246001i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.5829 | − | 20.0622i | −0.0126039 | − | 0.0218305i | 0.859655 | − | 0.510876i | \(-0.170679\pi\) |
−0.872259 | + | 0.489045i | \(0.837345\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 350.414i | 0.379647i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 362.106 | 0.391466 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1051.65 | − | 607.168i | 1.13202 | − | 0.653572i | 0.187577 | − | 0.982250i | \(-0.439936\pi\) |
0.944442 | + | 0.328678i | \(0.106603\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51.1951 | + | 45.1723i | 0.0549894 | + | 0.0485202i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −156.233 | + | 270.604i | −0.167094 | + | 0.289416i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 465.914i | 0.497240i | 0.968601 | + | 0.248620i | \(0.0799770\pi\) | ||||
−0.968601 | + | 0.248620i | \(0.920023\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1354.48 | − | 782.009i | −1.43940 | − | 0.831041i | −0.441597 | − | 0.897214i | \(-0.645588\pi\) |
−0.997808 | + | 0.0661729i | \(0.978921\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −715.313 | + | 412.986i | −0.758550 | + | 0.437949i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.1548 | + | 45.3015i | 0.0276186 | + | 0.0478369i | 0.879504 | − | 0.475891i | \(-0.157874\pi\) |
−0.851886 | + | 0.523728i | \(0.824541\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −965.548 | + | 1672.38i | −1.01744 | + | 1.76225i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −248.105 | −0.260341 | −0.130170 | − | 0.991492i | \(-0.541552\pi\) | ||||
−0.130170 | + | 0.991492i | \(0.541552\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 422.741 | + | 244.069i | 0.442660 | + | 0.255570i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −331.542 | − | 734.691i | −0.345717 | − | 0.766102i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 672.900 | + | 1165.50i | 0.700208 | + | 1.21280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 251.933i | 0.261070i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 944.970 | 0.977218 | 0.488609 | − | 0.872503i | \(-0.337505\pi\) | ||||
0.488609 | + | 0.872503i | \(0.337505\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 896.377 | − | 517.523i | 0.923148 | − | 0.532980i | 0.0385102 | − | 0.999258i | \(-0.487739\pi\) |
0.884638 | + | 0.466278i | \(0.154405\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1174.83 | − | 844.572i | −1.20743 | − | 0.868008i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −128.007 | + | 221.715i | −0.131020 | + | 0.226934i | −0.924070 | − | 0.382223i | \(-0.875159\pi\) |
0.793050 | + | 0.609157i | \(0.208492\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2053.16i | 2.09720i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 547.281 | + | 315.973i | 0.556746 | + | 0.321437i | 0.751838 | − | 0.659348i | \(-0.229167\pi\) |
−0.195093 | + | 0.980785i | \(0.562501\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 373.085 | − | 215.401i | 0.378767 | − | 0.218681i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 321.346 | + | 556.588i | 0.324920 | + | 0.562778i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −130.255 | + | 225.608i | −0.131438 | + | 0.227657i | −0.924231 | − | 0.381834i | \(-0.875293\pi\) |
0.792793 | + | 0.609491i | \(0.208626\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 194.016 | 0.194991 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −592.313 | − | 341.972i | −0.594096 | − | 0.343001i | 0.172620 | − | 0.984989i | \(-0.444777\pi\) |
−0.766715 | + | 0.641987i | \(0.778110\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.3.cg.q.577.5 | 16 | ||
3.2 | odd | 2 | inner | 1008.3.cg.q.577.4 | 16 | ||
4.3 | odd | 2 | 504.3.by.d.73.5 | yes | 16 | ||
7.5 | odd | 6 | inner | 1008.3.cg.q.145.5 | 16 | ||
12.11 | even | 2 | 504.3.by.d.73.4 | ✓ | 16 | ||
21.5 | even | 6 | inner | 1008.3.cg.q.145.4 | 16 | ||
28.3 | even | 6 | 3528.3.f.i.2449.8 | 16 | |||
28.11 | odd | 6 | 3528.3.f.i.2449.10 | 16 | |||
28.19 | even | 6 | 504.3.by.d.145.5 | yes | 16 | ||
84.11 | even | 6 | 3528.3.f.i.2449.7 | 16 | |||
84.47 | odd | 6 | 504.3.by.d.145.4 | yes | 16 | ||
84.59 | odd | 6 | 3528.3.f.i.2449.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.3.by.d.73.4 | ✓ | 16 | 12.11 | even | 2 | ||
504.3.by.d.73.5 | yes | 16 | 4.3 | odd | 2 | ||
504.3.by.d.145.4 | yes | 16 | 84.47 | odd | 6 | ||
504.3.by.d.145.5 | yes | 16 | 28.19 | even | 6 | ||
1008.3.cg.q.145.4 | 16 | 21.5 | even | 6 | inner | ||
1008.3.cg.q.145.5 | 16 | 7.5 | odd | 6 | inner | ||
1008.3.cg.q.577.4 | 16 | 3.2 | odd | 2 | inner | ||
1008.3.cg.q.577.5 | 16 | 1.1 | even | 1 | trivial | ||
3528.3.f.i.2449.7 | 16 | 84.11 | even | 6 | |||
3528.3.f.i.2449.8 | 16 | 28.3 | even | 6 | |||
3528.3.f.i.2449.9 | 16 | 84.59 | odd | 6 | |||
3528.3.f.i.2449.10 | 16 | 28.11 | odd | 6 |