Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(37,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{37})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 10x^{2} + 9x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(-1.27069 - 2.20090i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.109 |
Dual form | 252.4.k.c.37.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(5\) | 2.58276 | + | 4.47348i | 0.231009 | + | 0.400120i | 0.958105 | − | 0.286416i | \(-0.0924639\pi\) |
−0.727096 | + | 0.686536i | \(0.759131\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.1655 | + | 3.60745i | 0.980846 | + | 0.194784i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 29.2897 | − | 50.7312i | 0.802833 | − | 1.39055i | −0.114911 | − | 0.993376i | \(-0.536658\pi\) |
0.917744 | − | 0.397172i | \(-0.130009\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −38.3311 | −0.817779 | −0.408889 | − | 0.912584i | \(-0.634084\pi\) | ||||
−0.408889 | + | 0.912584i | \(0.634084\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −26.3345 | + | 45.6126i | −0.375709 | + | 0.650747i | −0.990433 | − | 0.137996i | \(-0.955934\pi\) |
0.614724 | + | 0.788742i | \(0.289267\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 65.1241 | + | 112.798i | 0.786342 | + | 1.36198i | 0.928194 | + | 0.372097i | \(0.121361\pi\) |
−0.141852 | + | 0.989888i | \(0.545306\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 38.2897 | + | 66.3197i | 0.347128 | + | 0.601244i | 0.985738 | − | 0.168287i | \(-0.0538235\pi\) |
−0.638610 | + | 0.769531i | \(0.720490\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 49.1587 | − | 85.1453i | 0.393269 | − | 0.681163i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 288.317 | 1.84618 | 0.923089 | − | 0.384585i | \(-0.125656\pi\) | ||||
0.923089 | + | 0.384585i | \(0.125656\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 70.2897 | − | 121.745i | 0.407239 | − | 0.705358i | −0.587341 | − | 0.809340i | \(-0.699825\pi\) |
0.994579 | + | 0.103982i | \(0.0331584\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 30.7794 | + | 90.5802i | 0.148648 | + | 0.437453i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 41.2380 | + | 71.4263i | 0.183229 | + | 0.317363i | 0.942978 | − | 0.332854i | \(-0.108012\pi\) |
−0.759749 | + | 0.650216i | \(0.774678\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 282.993 | 1.07795 | 0.538977 | − | 0.842321i | \(-0.318811\pi\) | ||||
0.538977 | + | 0.842321i | \(0.318811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −172.000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 66.6207 | + | 115.390i | 0.206758 | + | 0.358116i | 0.950691 | − | 0.310138i | \(-0.100375\pi\) |
−0.743933 | + | 0.668254i | \(0.767042\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 316.973 | + | 131.062i | 0.924118 | + | 0.382106i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 18.2380 | − | 31.5892i | 0.0472676 | − | 0.0818699i | −0.841424 | − | 0.540376i | \(-0.818282\pi\) |
0.888691 | + | 0.458506i | \(0.151615\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 302.593 | 0.741848 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −126.531 | + | 219.158i | −0.279202 | + | 0.483593i | −0.971187 | − | 0.238320i | \(-0.923403\pi\) |
0.691984 | + | 0.721913i | \(0.256737\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −249.562 | − | 432.254i | −0.523822 | − | 0.907287i | −0.999615 | − | 0.0277298i | \(-0.991172\pi\) |
0.475793 | − | 0.879557i | \(-0.342161\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −99.0000 | − | 171.473i | −0.188914 | − | 0.327209i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −105.290 | + | 182.367i | −0.191988 | + | 0.332533i | −0.945909 | − | 0.324432i | \(-0.894827\pi\) |
0.753921 | + | 0.656965i | \(0.228160\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −107.365 | −0.179464 | −0.0897318 | − | 0.995966i | \(-0.528601\pi\) | ||||
−0.0897318 | + | 0.995966i | \(0.528601\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −180.672 | + | 312.934i | −0.289673 | + | 0.501728i | −0.973732 | − | 0.227699i | \(-0.926880\pi\) |
0.684059 | + | 0.729427i | \(0.260213\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 715.072 | − | 815.898i | 1.05831 | − | 1.20753i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 417.504 | + | 723.138i | 0.594593 | + | 1.02987i | 0.993604 | + | 0.112919i | \(0.0360201\pi\) |
−0.399011 | + | 0.916946i | \(0.630647\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −731.283 | −0.967093 | −0.483547 | − | 0.875319i | \(-0.660652\pi\) | ||||
−0.483547 | + | 0.875319i | \(0.660652\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −272.063 | −0.347169 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −108.983 | − | 188.764i | −0.129800 | − | 0.224819i | 0.793799 | − | 0.608180i | \(-0.208100\pi\) |
−0.923599 | + | 0.383360i | \(0.874767\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −696.304 | − | 138.277i | −0.802115 | − | 0.159290i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −336.400 | + | 582.663i | −0.363305 | + | 0.629262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 252.290 | 0.264084 | 0.132042 | − | 0.991244i | \(-0.457847\pi\) | ||||
0.132042 | + | 0.991244i | \(0.457847\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −577.886 | + | 1000.93i | −0.569325 | + | 0.986100i | 0.427308 | + | 0.904106i | \(0.359462\pi\) |
−0.996633 | + | 0.0819939i | \(0.973871\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −525.628 | − | 910.414i | −0.502831 | − | 0.870929i | −0.999995 | − | 0.00327239i | \(-0.998958\pi\) |
0.497163 | − | 0.867657i | \(-0.334375\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1037.61 | − | 1797.19i | −0.937470 | − | 1.62375i | −0.770170 | − | 0.637839i | \(-0.779828\pi\) |
−0.167300 | − | 0.985906i | \(-0.553505\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 608.079 | − | 1053.22i | 0.534343 | − | 0.925510i | −0.464851 | − | 0.885389i | \(-0.653892\pi\) |
0.999195 | − | 0.0401213i | \(-0.0127744\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1585.59 | −1.32000 | −0.659998 | − | 0.751268i | \(-0.729443\pi\) | ||||
−0.659998 | + | 0.751268i | \(0.729443\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −197.786 | + | 342.576i | −0.160380 | + | 0.277786i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −642.925 | + | 733.577i | −0.495267 | + | 0.565100i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1050.27 | − | 1819.12i | −0.789083 | − | 1.36673i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1153.55 | 0.825414 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1107.37 | −0.773723 | −0.386861 | − | 0.922138i | \(-0.626441\pi\) | ||||
−0.386861 | + | 0.922138i | \(0.626441\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 442.642 | + | 766.678i | 0.295220 | + | 0.511336i | 0.975036 | − | 0.222047i | \(-0.0712738\pi\) |
−0.679816 | + | 0.733383i | \(0.737940\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 776.100 | + | 2283.97i | 0.505988 | + | 1.48906i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1076.77 | − | 1865.02i | 0.671494 | − | 1.16306i | −0.305987 | − | 0.952036i | \(-0.598986\pi\) |
0.977481 | − | 0.211025i | \(-0.0676802\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −672.580 | −0.410414 | −0.205207 | − | 0.978719i | \(-0.565787\pi\) | ||||
−0.205207 | + | 0.978719i | \(0.565787\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1122.70 | + | 1944.58i | −0.656540 | + | 1.13716i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 744.655 | + | 1289.78i | 0.426485 | + | 0.738693i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −901.666 | − | 1561.73i | −0.495754 | − | 0.858671i | 0.504234 | − | 0.863567i | \(-0.331775\pi\) |
−0.999988 | + | 0.00489580i | \(0.998442\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −557.504 | + | 965.625i | −0.300457 | + | 0.520407i | −0.976240 | − | 0.216694i | \(-0.930473\pi\) |
0.675783 | + | 0.737101i | \(0.263806\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 726.166 | 0.376304 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 839.156 | − | 1453.46i | 0.426573 | − | 0.738846i | −0.569993 | − | 0.821649i | \(-0.693054\pi\) |
0.996566 | + | 0.0828038i | \(0.0263875\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 456.307 | + | 1342.86i | 0.223367 | + | 0.657343i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −792.297 | − | 1372.30i | −0.380721 | − | 0.659428i | 0.610445 | − | 0.792059i | \(-0.290991\pi\) |
−0.991165 | + | 0.132631i | \(0.957657\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −619.669 | −0.287134 | −0.143567 | − | 0.989641i | \(-0.545857\pi\) | ||||
−0.143567 | + | 0.989641i | \(0.545857\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −727.731 | −0.331238 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1790.38 | − | 3101.03i | −0.786823 | − | 1.36282i | −0.927904 | − | 0.372819i | \(-0.878391\pi\) |
0.141082 | − | 0.989998i | \(-0.454942\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1200.15 | − | 1369.37i | 0.518416 | − | 0.591513i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −287.773 | + | 498.438i | −0.120163 | + | 0.208128i | −0.919832 | − | 0.392313i | \(-0.871675\pi\) |
0.799669 | + | 0.600441i | \(0.205008\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1556.51 | 0.639197 | 0.319598 | − | 0.947553i | \(-0.396452\pi\) | ||||
0.319598 | + | 0.947553i | \(0.396452\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −213.016 | + | 368.955i | −0.0846554 | + | 0.146627i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1542.66 | + | 2671.96i | 0.603263 | + | 1.04488i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 399.559 | + | 692.057i | 0.151367 | + | 0.262175i | 0.931730 | − | 0.363151i | \(-0.118299\pi\) |
−0.780363 | + | 0.625326i | \(0.784966\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 279.024 | − | 483.284i | 0.104065 | − | 0.180246i | −0.809291 | − | 0.587408i | \(-0.800148\pi\) |
0.913356 | + | 0.407162i | \(0.133482\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1729.59 | 0.625523 | 0.312761 | − | 0.949832i | \(-0.398746\pi\) | ||||
0.312761 | + | 0.949832i | \(0.398746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2142.77 | + | 3711.39i | −0.763302 | + | 1.32208i | 0.177837 | + | 0.984060i | \(0.443090\pi\) |
−0.941139 | + | 0.338018i | \(0.890243\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5237.44 | + | 1040.09i | 1.81082 | + | 0.359606i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 730.904 | + | 1265.96i | 0.249017 | + | 0.431311i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7629.86 | 2.52521 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 849.904 | 0.277298 | 0.138649 | − | 0.990342i | \(-0.455724\pi\) | ||||
0.138649 | + | 0.990342i | \(0.455724\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −444.235 | − | 769.438i | −0.140914 | − | 0.244071i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1716.04 | − | 1958.00i | 0.536831 | − | 0.612524i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1009.43 | − | 1748.38i | 0.307247 | − | 0.532167i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4377.66 | 1.31457 | 0.657286 | − | 0.753641i | \(-0.271704\pi\) | ||||
0.657286 | + | 0.753641i | \(0.271704\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2559.83 | + | 4433.75i | −0.748466 | + | 1.29638i | 0.200092 | + | 0.979777i | \(0.435876\pi\) |
−0.948558 | + | 0.316604i | \(0.897457\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2940.65 | − | 5093.36i | −0.848576 | − | 1.46978i | −0.882479 | − | 0.470351i | \(-0.844127\pi\) |
0.0339035 | − | 0.999425i | \(-0.489206\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 106.039 | + | 183.665i | 0.0298147 | + | 0.0516406i | 0.880548 | − | 0.473957i | \(-0.157175\pi\) |
−0.850733 | + | 0.525598i | \(0.823842\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −344.131 | + | 596.052i | −0.0955261 | + | 0.165456i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5202.95 | −1.40816 | −0.704082 | − | 0.710119i | \(-0.748641\pi\) | ||||
−0.704082 | + | 0.710119i | \(0.748641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1418.56 | + | 2457.02i | −0.379160 | + | 0.656725i | −0.990940 | − | 0.134303i | \(-0.957120\pi\) |
0.611780 | + | 0.791028i | \(0.290454\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 232.360 | + | 1756.47i | 0.0605916 | + | 0.458028i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2496.28 | − | 4323.68i | −0.643054 | − | 1.11380i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4697.05 | 1.18118 | 0.590588 | − | 0.806973i | \(-0.298896\pi\) | ||||
0.590588 | + | 0.806973i | \(0.298896\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4485.97 | 1.11474 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3501.86 | + | 6065.40i | 0.849961 | + | 1.47218i | 0.881242 | + | 0.472665i | \(0.156708\pi\) |
−0.0312810 | + | 0.999511i | \(0.509959\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 491.443 | + | 1446.26i | 0.117903 | + | 0.346974i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 614.153 | − | 1063.74i | 0.143994 | − | 0.249404i | −0.785003 | − | 0.619491i | \(-0.787339\pi\) |
0.928997 | + | 0.370087i | \(0.120672\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 188.418 | 0.0436770 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 70.9423 | − | 122.876i | 0.0160797 | − | 0.0278508i | −0.857874 | − | 0.513861i | \(-0.828215\pi\) |
0.873953 | + | 0.486010i | \(0.161548\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 182.387 | + | 315.904i | 0.0408828 | + | 0.0708111i | 0.885743 | − | 0.464176i | \(-0.153650\pi\) |
−0.844860 | + | 0.534988i | \(0.820316\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2879.68 | − | 4987.76i | −0.631460 | − | 1.09372i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −994.238 | + | 1722.07i | −0.215661 | + | 0.373535i | −0.953477 | − | 0.301467i | \(-0.902524\pi\) |
0.737816 | + | 0.675002i | \(0.235857\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4903.93 | −1.04108 | −0.520541 | − | 0.853837i | \(-0.674270\pi\) | ||||
−0.520541 | + | 0.853837i | \(0.674270\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1630.04 | + | 2823.31i | −0.342387 | + | 0.593032i | −0.984876 | − | 0.173263i | \(-0.944569\pi\) |
0.642488 | + | 0.766296i | \(0.277902\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5140.72 | + | 1020.88i | 1.05731 | + | 0.209968i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1069.49 | + | 1852.41i | 0.217686 | + | 0.377043i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1613.67 | −0.321746 | −0.160873 | − | 0.986975i | \(-0.551431\pi\) | ||||
−0.160873 | + | 0.986975i | \(0.551431\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1307.20 | −0.257993 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1467.68 | − | 2542.10i | −0.283874 | − | 0.491684i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3124.47 | − | 620.481i | −0.598311 | − | 0.118817i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1289.12 | − | 2232.82i | 0.242016 | − | 0.419183i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2846.16 | −0.529116 | −0.264558 | − | 0.964370i | \(-0.585226\pi\) | ||||
−0.264558 | + | 0.964370i | \(0.585226\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1391.70 | − | 2410.49i | 0.253749 | − | 0.439506i | −0.710806 | − | 0.703388i | \(-0.751670\pi\) |
0.964555 | + | 0.263882i | \(0.0850030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1501.07 | + | 2599.92i | 0.271071 | + | 0.469509i | 0.969136 | − | 0.246525i | \(-0.0792887\pi\) |
−0.698065 | + | 0.716034i | \(0.745955\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1886.91 | − | 3268.22i | −0.334319 | − | 0.579058i | 0.649035 | − | 0.760759i | \(-0.275173\pi\) |
−0.983354 | + | 0.181701i | \(0.941840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8444.72 | − | 14626.7i | 1.48217 | − | 2.56720i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6860.04 | −1.18174 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1884.30 | + | 3263.71i | −0.321607 | + | 0.557040i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 793.935 | + | 2336.46i | 0.133043 | + | 0.391529i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 487.939 | + | 845.135i | 0.0810259 | + | 0.140341i | 0.903691 | − | 0.428186i | \(-0.140847\pi\) |
−0.822665 | + | 0.568526i | \(0.807514\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1087.75 | −0.177404 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3563.93 | −0.576083 | −0.288041 | − | 0.957618i | \(-0.593004\pi\) | ||||
−0.288041 | + | 0.957618i | \(0.593004\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4117.52 | − | 7131.76i | −0.653890 | − | 1.13257i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5285.17 | + | 3524.28i | 0.831990 | + | 0.554791i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −577.677 | + | 1000.57i | −0.0893698 | + | 0.154793i | −0.907245 | − | 0.420603i | \(-0.861819\pi\) |
0.817875 | + | 0.575396i | \(0.195152\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4693.29 | −0.719845 | −0.359922 | − | 0.932982i | \(-0.617197\pi\) | ||||
−0.359922 | + | 0.932982i | \(0.617197\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6628.54 | + | 11481.0i | −0.999439 | + | 1.73108i | −0.470704 | + | 0.882291i | \(0.656000\pi\) |
−0.528734 | + | 0.848787i | \(0.677333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −277.299 | − | 480.296i | −0.0414578 | − | 0.0718070i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −893.312 | − | 1547.26i | −0.131329 | − | 0.227469i | 0.792860 | − | 0.609404i | \(-0.208591\pi\) |
−0.924189 | + | 0.381935i | \(0.875258\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5052.81 | + | 8751.72i | −0.736668 | + | 1.27595i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1866.54 | −0.267668 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3201.75 | + | 5545.60i | −0.455395 | + | 0.788768i | −0.998711 | − | 0.0507606i | \(-0.983835\pi\) |
0.543315 | + | 0.839529i | \(0.317169\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 445.259 | − | 508.041i | 0.0623092 | − | 0.0710948i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6085.11 | − | 10539.7i | −0.844705 | − | 1.46307i | −0.885877 | − | 0.463920i | \(-0.846442\pi\) |
0.0411720 | − | 0.999152i | \(-0.486891\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11051.5 | −1.50977 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2565.68 | −0.347732 | −0.173866 | − | 0.984769i | \(-0.555626\pi\) | ||||
−0.173866 | + | 0.984769i | \(0.555626\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3304.58 | − | 5723.70i | −0.440878 | − | 0.763623i | 0.556877 | − | 0.830595i | \(-0.311999\pi\) |
−0.997755 | + | 0.0669723i | \(0.978666\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5496.76 | + | 1091.59i | 0.727639 | + | 0.144500i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4443.74 | − | 7696.79i | 0.579195 | − | 1.00319i | −0.416377 | − | 0.909192i | \(-0.636700\pi\) |
0.995572 | − | 0.0940027i | \(-0.0299662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4033.35 | −0.521676 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2156.63 | + | 3735.39i | −0.274713 | + | 0.475817i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4435.95 | − | 7683.29i | −0.560791 | − | 0.971318i | −0.997428 | − | 0.0716802i | \(-0.977164\pi\) |
0.436637 | − | 0.899638i | \(-0.356169\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −641.120 | − | 1110.45i | −0.0798404 | − | 0.138288i | 0.823341 | − | 0.567548i | \(-0.192108\pi\) |
−0.903181 | + | 0.429260i | \(0.858774\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2694.28 | + | 4666.62i | −0.333031 | + | 0.576827i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4831.39 | 0.588411 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3843.32 | − | 6656.82i | 0.464645 | − | 0.804788i | −0.534541 | − | 0.845143i | \(-0.679515\pi\) |
0.999185 | + | 0.0403544i | \(0.0128487\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3089.11 | + | 3524.67i | −0.368051 | + | 0.419946i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1888.73 | − | 3271.38i | −0.223408 | − | 0.386953i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13364.1 | 1.55818 | 0.779092 | − | 0.626909i | \(-0.215680\pi\) | ||||
0.779092 | + | 0.626909i | \(0.215680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1781.20 | 0.206201 | 0.103100 | − | 0.994671i | \(-0.467124\pi\) | ||||
0.103100 | + | 0.994671i | \(0.467124\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2589.14 | + | 4484.51i | 0.295509 | + | 0.511837i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2974.09 | − | 8752.41i | −0.337064 | − | 0.991941i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3791.18 | + | 6566.51i | −0.423700 | + | 0.733869i | −0.996298 | − | 0.0859668i | \(-0.972602\pi\) |
0.572598 | + | 0.819836i | \(0.305935\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8642.25 | 0.959169 | 0.479585 | − | 0.877496i | \(-0.340787\pi\) | ||||
0.479585 | + | 0.877496i | \(0.340787\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4987.16 | + | 8638.02i | −0.545923 | + | 0.945567i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7106.31 | + | 12308.5i | 0.772586 | + | 1.33816i | 0.936141 | + | 0.351625i | \(0.114371\pi\) |
−0.163555 | + | 0.986534i | \(0.552296\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3884.78 | − | 6728.64i | −0.416640 | − | 0.721642i | 0.578959 | − | 0.815357i | \(-0.303459\pi\) |
−0.995599 | + | 0.0937150i | \(0.970126\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 562.954 | − | 975.065i | 0.0599698 | − | 0.103871i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7691.17 | 0.808393 | 0.404197 | − | 0.914672i | \(-0.367551\pi\) | ||||
0.404197 | + | 0.914672i | \(0.367551\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8288.78 | − | 14356.6i | 0.865417 | − | 1.49895i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1179.81 | − | 3472.04i | −0.121561 | − | 0.357740i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6692.10 | + | 11591.1i | 0.684996 | + | 1.18645i | 0.973438 | + | 0.228951i | \(0.0735295\pi\) |
−0.288442 | + | 0.957497i | \(0.593137\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5451.80 | 0.550793 | 0.275396 | − | 0.961331i | \(-0.411191\pi\) | ||||
0.275396 | + | 0.961331i | \(0.411191\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13193.4 | −1.32430 | −0.662148 | − | 0.749373i | \(-0.730355\pi\) | ||||
−0.662148 | + | 0.749373i | \(0.730355\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1169.09 | + | 2024.93i | 0.115844 | + | 0.200648i | 0.918117 | − | 0.396310i | \(-0.129709\pi\) |
−0.802273 | + | 0.596958i | \(0.796376\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2570.52 | + | 2932.97i | −0.253082 | + | 0.288767i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5037.82 | + | 8725.77i | −0.489724 | + | 0.848226i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12805.7 | 1.23698 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9262.11 | − | 16042.5i | 0.883501 | − | 1.53027i | 0.0360779 | − | 0.999349i | \(-0.488514\pi\) |
0.847423 | − | 0.530919i | \(-0.178153\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1580.70 | − | 2737.85i | −0.149841 | − | 0.259532i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 651.605 | + | 1128.61i | 0.0610059 | + | 0.105665i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2878.54 | + | 4985.77i | −0.267842 | + | 0.463916i | −0.968304 | − | 0.249774i | \(-0.919644\pi\) |
0.700462 | + | 0.713689i | \(0.252977\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10593.6 | 0.973692 | 0.486846 | − | 0.873488i | \(-0.338147\pi\) | ||||
0.486846 | + | 0.873488i | \(0.338147\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7592.69 | + | 13150.9i | −0.693626 | + | 1.20139i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1950.35 | − | 387.315i | −0.176026 | − | 0.0349566i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1548.31 | + | 2681.75i | 0.138901 | + | 0.240584i | 0.927081 | − | 0.374861i | \(-0.122310\pi\) |
−0.788180 | + | 0.615445i | \(0.788976\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3149.14 | 0.279151 | 0.139576 | − | 0.990211i | \(-0.455426\pi\) | ||||
0.139576 | + | 0.990211i | \(0.455426\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5970.17 | −0.526078 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4566.92 | − | 7910.14i | −0.397692 | − | 0.688823i | 0.595749 | − | 0.803171i | \(-0.296855\pi\) |
−0.993441 | + | 0.114348i | \(0.963522\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4410.90 | + | 5032.84i | −0.381853 | + | 0.435694i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2715.14 | − | 4702.76i | 0.232317 | − | 0.402386i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7805.20 | 0.663969 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2558.89 | + | 4432.12i | −0.215176 | + | 0.372696i | −0.953327 | − | 0.301939i | \(-0.902366\pi\) |
0.738151 | + | 0.674636i | \(0.235699\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2934.26 | − | 5082.28i | −0.245327 | − | 0.424919i | 0.716896 | − | 0.697180i | \(-0.245562\pi\) |
−0.962224 | + | 0.272261i | \(0.912229\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3702.08 | + | 6412.20i | 0.306006 | + | 0.530018i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3151.30 | − | 5458.22i | 0.259004 | − | 0.448608i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10847.4 | −0.881527 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5359.79 | − | 9283.42i | 0.433128 | − | 0.750200i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15933.0 | − | 12241.6i | 1.27325 | − | 0.978263i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4140.16 | + | 7170.97i | 0.329019 | + | 0.569878i | 0.982318 | − | 0.187223i | \(-0.0599486\pi\) |
−0.653298 | + | 0.757101i | \(0.726615\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6282.10 | 0.493753 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16832.7 | 1.31575 | 0.657875 | − | 0.753127i | \(-0.271455\pi\) | ||||
0.657875 | + | 0.753127i | \(0.271455\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18776.4 | + | 32521.7i | 1.45173 | + | 2.51447i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4975.49 | + | 14642.3i | 0.382603 | + | 1.12596i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5254.65 | − | 9101.32i | 0.399725 | − | 0.692344i | −0.593967 | − | 0.804489i | \(-0.702439\pi\) |
0.993692 | + | 0.112146i | \(0.0357724\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6592.94 | 0.498840 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 166.502 | − | 288.390i | 0.0124640 | − | 0.0215883i | −0.859726 | − | 0.510755i | \(-0.829366\pi\) |
0.872190 | + | 0.489167i | \(0.162699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4095.19 | − | 7093.08i | −0.304931 | − | 0.528156i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7544.12 | + | 13066.8i | 0.555828 | + | 0.962722i | 0.997839 | + | 0.0657121i | \(0.0209319\pi\) |
−0.442011 | + | 0.897010i | \(0.645735\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 917.219 | − | 1588.67i | 0.0672232 | − | 0.116434i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) |
0.897678 | + | 0.440652i | \(0.145253\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7529.08 | 0.546060 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4258.15 | + | 7375.33i | −0.307225 | + | 0.532130i | −0.977754 | − | 0.209753i | \(-0.932734\pi\) |
0.670529 | + | 0.741883i | \(0.266067\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13284.1 | − | 2638.07i | −0.948570 | − | 0.188374i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1068.37 | − | 1850.47i | −0.0758960 | − | 0.131456i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23957.0 | −1.68452 | −0.842258 | − | 0.539074i | \(-0.818774\pi\) | ||||
−0.842258 | + | 0.539074i | \(0.818774\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18310.2 | 1.28092 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5865.45 | + | 10159.3i | 0.406181 | + | 0.703525i | 0.994458 | − | 0.105134i | \(-0.0335270\pi\) |
−0.588277 | + | 0.808659i | \(0.700194\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4942.16 | − | 981.453i | −0.340519 | − | 0.0676229i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2315.67 | − | 4010.86i | 0.157956 | − | 0.273588i | −0.776175 | − | 0.630517i | \(-0.782843\pi\) |
0.934132 | + | 0.356929i | \(0.116176\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25359.8 | −1.72121 | −0.860606 | − | 0.509272i | \(-0.829915\pi\) | ||||
−0.860606 | + | 0.509272i | \(0.829915\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5425.19 | − | 9396.71i | 0.364571 | − | 0.631456i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −62.3696 | − | 108.027i | −0.00417052 | − | 0.00722355i | 0.863933 | − | 0.503607i | \(-0.167994\pi\) |
−0.868103 | + | 0.496384i | \(0.834661\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2553.64 | − | 4423.04i | −0.169082 | − | 0.292859i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8592.54 | − | 14882.7i | 0.566149 | − | 0.980599i | −0.430793 | − | 0.902451i | \(-0.641766\pi\) |
0.996942 | − | 0.0781479i | \(-0.0249006\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25988.1 | 1.69569 | 0.847844 | − | 0.530246i | \(-0.177900\pi\) | ||||
0.847844 | + | 0.530246i | \(0.177900\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9442.62 | − | 16355.1i | 0.613135 | − | 1.06198i | −0.377573 | − | 0.925980i | \(-0.623241\pi\) |
0.990709 | − | 0.136002i | \(-0.0434254\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1298.77 | − | 3822.15i | −0.0835222 | − | 0.245796i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3165.49 | − | 5482.78i | −0.202591 | − | 0.350898i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4343.93 | −0.275364 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6552.95 | −0.413421 | −0.206710 | − | 0.978402i | \(-0.566276\pi\) | ||||
−0.206710 | + | 0.978402i | \(0.566276\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2860.06 | − | 4953.77i | −0.178737 | − | 0.309582i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12149.9 | − | 5023.76i | −0.755724 | − | 0.312478i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13835.5 | + | 23963.8i | −0.852525 | + | 1.47662i | 0.0263968 | + | 0.999652i | \(0.491597\pi\) |
−0.878922 | + | 0.476965i | \(0.841737\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27154.8 | −1.66544 | −0.832722 | − | 0.553691i | \(-0.813219\pi\) | ||||
−0.832722 | + | 0.553691i | \(0.813219\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13661.3 | − | 23662.1i | 0.830110 | − | 1.43779i | −0.0678409 | − | 0.997696i | \(-0.521611\pi\) |
0.897951 | − | 0.440096i | \(-0.145056\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7412.11 | + | 12838.1i | 0.448306 | + | 0.776489i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 716.430 | + | 1240.89i | 0.0429342 | + | 0.0743643i | 0.886694 | − | 0.462357i | \(-0.152996\pi\) |
−0.843760 | + | 0.536721i | \(0.819663\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2286.48 | + | 3960.30i | −0.136397 | + | 0.236247i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12914.0 | −0.763367 | −0.381684 | − | 0.924293i | \(-0.624656\pi\) | ||||
−0.381684 | + | 0.924293i | \(0.624656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5034.42 | − | 8719.87i | 0.296243 | − | 0.513107i | −0.679031 | − | 0.734110i | \(-0.737600\pi\) |
0.975273 | + | 0.221003i | \(0.0709330\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8212.82 | + | 9370.82i | −0.478916 | + | 0.546444i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11039.6 | + | 19121.1i | 0.640861 | + | 1.11000i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29238.4 | −1.68217 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1686.86 | −0.0966174 | −0.0483087 | − | 0.998832i | \(-0.515383\pi\) | ||||
−0.0483087 | + | 0.998832i | \(0.515383\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11267.5 | − | 19515.9i | −0.639654 | − | 1.10791i | −0.985509 | − | 0.169625i | \(-0.945744\pi\) |
0.345855 | − | 0.938288i | \(-0.387589\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4582.98 | + | 910.124i | 0.259026 | + | 0.0514394i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14703.1 | + | 25466.4i | −0.823714 | + | 1.42671i | 0.0791844 | + | 0.996860i | \(0.474768\pi\) |
−0.902898 | + | 0.429854i | \(0.858565\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11124.2 | 0.620485 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −699.082 | + | 1210.85i | −0.0386544 | + | 0.0669515i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −125.763 | − | 217.828i | −0.00692365 | − | 0.0119921i | 0.862543 | − | 0.505984i | \(-0.168871\pi\) |
−0.869466 | + | 0.493992i | \(0.835537\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1737.11 | − | 3008.77i | −0.0948093 | − | 0.164215i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7452.48 | + | 12908.1i | −0.404997 | + | 0.701475i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6188.42 | 0.333429 | 0.166714 | − | 0.986005i | \(-0.446684\pi\) | ||||
0.166714 | + | 0.986005i | \(0.446684\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5371.18 | + | 9303.16i | −0.288162 | + | 0.499111i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14108.4 | + | 16097.7i | −0.750497 | + | 0.856317i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13719.7 | − | 23763.2i | −0.726734 | − | 1.25874i | −0.958256 | − | 0.285911i | \(-0.907704\pi\) |
0.231522 | − | 0.972830i | \(-0.425629\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10765.5 | 0.565456 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11598.7 | −0.606667 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6139.25 | − | 10633.5i | −0.318436 | − | 0.551547i | 0.661726 | − | 0.749746i | \(-0.269824\pi\) |
−0.980162 | + | 0.198199i | \(0.936491\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6264.03 | − | 18434.3i | −0.323557 | − | 0.952191i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14173.3 | − | 24548.9i | 0.726046 | − | 1.25755i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8576.11 | 0.437510 | 0.218755 | − | 0.975780i | \(-0.429800\pi\) | ||||
0.218755 | + | 0.975780i | \(0.429800\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4529.53 | − | 7845.38i | 0.229180 | − | 0.396952i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6437.42 | + | 11149.9i | 0.324381 | + | 0.561845i | 0.981387 | − | 0.192041i | \(-0.0615106\pi\) |
−0.657006 | + | 0.753886i | \(0.728177\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6167.80 | + | 10682.9i | 0.308268 | + | 0.533937i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9958.63 | + | 17248.9i | −0.495716 | + | 0.858606i | −0.999988 | − | 0.00493950i | \(-0.998428\pi\) |
0.504272 | + | 0.863545i | \(0.331761\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22672.6 | −1.11948 | −0.559741 | − | 0.828667i | \(-0.689100\pi\) | ||||
−0.559741 | + | 0.828667i | \(0.689100\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4657.58 | − | 8067.16i | 0.229048 | − | 0.396722i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12365.4 | − | 36390.0i | −0.603234 | − | 1.77525i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10476.8 | + | 18146.3i | 0.509059 | + | 0.881716i | 0.999945 | + | 0.0104920i | \(0.00333977\pi\) |
−0.490886 | + | 0.871224i | \(0.663327\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5759.60 | −0.277633 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12684.5 | −0.609018 | −0.304509 | − | 0.952510i | \(-0.598492\pi\) | ||||
−0.304509 | + | 0.952510i | \(0.598492\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16831.8 | − | 29153.6i | −0.801779 | − | 1.38872i | −0.918444 | − | 0.395550i | \(-0.870554\pi\) |
0.116666 | − | 0.993171i | \(-0.462779\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14845.5 | − | 16938.8i | 0.704383 | − | 0.803701i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4850.07 | − | 8400.57i | 0.228326 | − | 0.395472i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20358.4 | −0.954672 | −0.477336 | − | 0.878721i | \(-0.658398\pi\) | ||||
−0.477336 | + | 0.878721i | \(0.658398\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −165.421 | + | 286.517i | −0.00769698 | + | 0.0133316i | −0.869848 | − | 0.493319i | \(-0.835783\pi\) |
0.862151 | + | 0.506651i | \(0.169117\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6910.69 | − | 11969.7i | −0.320309 | − | 0.554791i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18429.7 | + | 31921.2i | 0.847641 | + | 1.46816i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3144.69 | + | 5446.77i | −0.144079 | + | 0.249553i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8669.36 | 0.394169 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3381.10 | + | 5856.24i | −0.153143 | + | 0.265251i | −0.932381 | − | 0.361477i | \(-0.882273\pi\) |
0.779239 | + | 0.626727i | \(0.215606\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28803.0 | − | 5719.93i | −1.29471 | − | 0.257114i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9565.98 | + | 16568.8i | 0.428371 | + | 0.741960i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23848.2 | −1.05991 | −0.529954 | − | 0.848027i | \(-0.677791\pi\) | ||||
−0.529954 | + | 0.848027i | \(0.677791\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7017.69 | −0.310723 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10583.7 | + | 18331.5i | 0.465118 | + | 0.805608i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4828.72 | + | 5509.57i | −0.211416 | + | 0.241226i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −463.570 | + | 802.926i | −0.0201462 | + | 0.0348942i | −0.875923 | − | 0.482451i | \(-0.839746\pi\) |
0.855777 | + | 0.517346i | \(0.173080\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4288.65 | −0.185690 | −0.0928451 | − | 0.995681i | \(-0.529596\pi\) | ||||
−0.0928451 | + | 0.995681i | \(0.529596\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4092.63 | − | 7088.64i | 0.175900 | − | 0.304668i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11201.4 | − | 19401.3i | −0.479664 | − | 0.830803i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13876.0 | + | 24034.0i | 0.589862 | + | 1.02167i | 0.994250 | + | 0.107083i | \(0.0341510\pi\) |
−0.404389 | + | 0.914587i | \(0.632516\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4345.08 | + | 7525.89i | −0.184034 | + | 0.318756i | −0.943251 | − | 0.332082i | \(-0.892249\pi\) |
0.759217 | + | 0.650838i | \(0.225582\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29503.0 | −1.24053 | −0.620267 | − | 0.784391i | \(-0.712976\pi\) | ||||
−0.620267 | + | 0.784391i | \(0.712976\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10138.2 | − | 17559.8i | 0.424744 | − | 0.735678i | −0.571653 | − | 0.820496i | \(-0.693697\pi\) |
0.996396 | + | 0.0848178i | \(0.0270308\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14325.4 | + | 11006.5i | −0.595854 | + | 0.457806i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1600.46 | − | 2772.07i | −0.0663307 | − | 0.114888i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5229.63 | −0.215193 | −0.107596 | − | 0.994195i | \(-0.534315\pi\) | ||||
−0.107596 | + | 0.994195i | \(0.534315\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58737.9 | 2.40838 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1879.56 | − | 3255.49i | −0.0765191 | − | 0.132535i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12516.3 | − | 36834.1i | −0.507751 | − | 1.49425i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3157.98 | + | 5469.78i | −0.127208 | + | 0.220331i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16423.9 | −0.659255 | −0.329628 | − | 0.944111i | \(-0.606923\pi\) | ||||
−0.329628 | + | 0.944111i | \(0.606923\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15495.9 | − | 26839.7i | 0.617655 | − | 1.06981i | −0.372258 | − | 0.928129i | \(-0.621416\pi\) |
0.989913 | − | 0.141680i | \(-0.0452504\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16257.1 | + | 28158.2i | 0.645735 | + | 1.11845i | 0.984131 | + | 0.177442i | \(0.0567823\pi\) |
−0.338396 | + | 0.941004i | \(0.609884\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8682.78 | + | 15039.0i | 0.342486 | + | 0.593203i | 0.984894 | − | 0.173160i | \(-0.0553978\pi\) |
−0.642408 | + | 0.766363i | \(0.722065\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9248.27 | − | 16018.5i | 0.363527 | − | 0.629647i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48914.2 | 1.90944 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4035.86 | − | 6990.32i | 0.157003 | − | 0.271938i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20954.9 | + | 4161.38i | 0.809604 | + | 0.160777i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10303.2 | + | 17845.6i | 0.396709 | + | 0.687119i | 0.993318 | − | 0.115413i | \(-0.0368190\pi\) |
−0.596609 | + | 0.802532i | \(0.703486\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4704.88 | 0.179922 | 0.0899610 | − | 0.995945i | \(-0.471326\pi\) | ||||
0.0899610 | + | 0.995945i | \(0.471326\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13075.1 | −0.498313 | −0.249157 | − | 0.968463i | \(-0.580153\pi\) | ||||
−0.249157 | + | 0.968463i | \(0.580153\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22284.6 | + | 38598.1i | 0.843568 | + | 1.46110i | 0.886859 | + | 0.462039i | \(0.152882\pi\) |
−0.0432918 | + | 0.999062i | \(0.513785\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20115.9 | − | 3994.77i | −0.758903 | − | 0.150709i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8677.23 | + | 15029.4i | −0.325165 | + | 0.563203i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2973.00 | −0.111035 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20265.7 | − | 35101.3i | 0.751835 | − | 1.30222i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 960.577 | + | 1663.77i | 0.0355177 | + | 0.0615185i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4020.10 | + | 6963.02i | 0.147660 | + | 0.255755i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8001.65 | − | 13859.3i | 0.292933 | − | 0.507375i | −0.681569 | − | 0.731754i | \(-0.738702\pi\) |
0.974502 | + | 0.224379i | \(0.0720353\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10072.4 | −0.366315 | −0.183157 | − | 0.983084i | \(-0.558632\pi\) | ||||
−0.183157 | + | 0.983084i | \(0.558632\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21419.0 | + | 37098.9i | −0.776415 | + | 1.34479i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5275.07 | + | 15523.9i | 0.189965 | + | 0.559046i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22639.1 | − | 39212.0i | −0.812617 | − | 1.40749i | −0.911027 | − | 0.412347i | \(-0.864709\pi\) |
0.0984103 | − | 0.995146i | \(-0.468624\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4115.42 | 0.146761 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8108.82 | 0.288234 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4068.29 | − | 7046.48i | −0.143677 | − | 0.248856i | 0.785201 | − | 0.619240i | \(-0.212559\pi\) |
−0.928879 | + | 0.370384i | \(0.879226\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5858.94 | + | 44289.3i | 0.206250 | + | 1.55910i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7968.63 | + | 13802.1i | −0.278719 | + | 0.482755i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34741.9 | 1.21128 | 0.605640 | − | 0.795739i | \(-0.292917\pi\) | ||||
0.605640 | + | 0.795739i | \(0.292917\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18728.8 | − | 32439.2i | 0.648822 | − | 1.12379i | −0.334583 | − | 0.942366i | \(-0.608595\pi\) |
0.983405 | − | 0.181426i | \(-0.0580713\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10835.7 | + | 18768.0i | 0.374188 | + | 0.648113i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3776.15 | − | 6540.48i | −0.129576 | − | 0.224432i | 0.793937 | − | 0.608001i | \(-0.208028\pi\) |
−0.923512 | + | 0.383569i | \(0.874695\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6925.36 | − | 11995.1i | 0.236888 | − | 0.410302i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25745.6 | 0.875111 | 0.437556 | − | 0.899191i | \(-0.355844\pi\) | ||||
0.437556 | + | 0.899191i | \(0.355844\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2063.93 | + | 3574.84i | −0.0699343 | + | 0.121130i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26288.0 | − | 29994.7i | 0.885178 | − | 1.00999i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5014.22 | + | 8684.89i | 0.168313 | + | 0.291527i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2882.61 | 0.0961601 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31718.6 | 1.05481 | 0.527406 | − | 0.849614i | \(-0.323165\pi\) | ||||
0.527406 | + | 0.849614i | \(0.323165\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19654.4 | + | 34042.4i | 0.649578 | + | 1.12510i | 0.983224 | + | 0.182404i | \(0.0583877\pi\) |
−0.333646 | + | 0.942699i | \(0.608279\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12217.8 | − | 2426.30i | −0.402553 | − | 0.0799420i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2619.30 | + | 4536.77i | −0.0857717 | + | 0.148561i | −0.905720 | − | 0.423877i | \(-0.860669\pi\) |
0.819948 | + | 0.572438i | \(0.194002\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12768.3 | −0.416830 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12581.8 | + | 21792.2i | −0.408236 | + | 0.707085i | −0.994692 | − | 0.102896i | \(-0.967189\pi\) |
0.586456 | + | 0.809981i | \(0.300523\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4467.11 | + | 7737.26i | 0.144502 | + | 0.250284i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6585.82 | − | 11407.0i | −0.211746 | − | 0.366755i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21780.6 | + | 37725.1i | −0.698166 | + | 1.20926i | 0.270935 | + | 0.962598i | \(0.412667\pi\) |
−0.969102 | + | 0.246662i | \(0.920666\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22137.1 | −0.705320 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25420.2 | − | 44029.0i | 0.807487 | − | 1.39861i | −0.107112 | − | 0.994247i | \(-0.534160\pi\) |
0.914599 | − | 0.404362i | \(-0.132506\pi\) | |||||||
\(998\) | 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 | 252.4.k.c.109.2 | 4 | ||
3.2 | odd | 2 | 28.4.e.a.25.2 | yes | 4 | ||
7.2 | even | 3 | inner | 252.4.k.c.37.2 | 4 | ||
7.3 | odd | 6 | 1764.4.a.n.1.2 | 2 | |||
7.4 | even | 3 | 1764.4.a.z.1.1 | 2 | |||
7.5 | odd | 6 | 1764.4.k.ba.1549.1 | 4 | |||
7.6 | odd | 2 | 1764.4.k.ba.361.1 | 4 | |||
12.11 | even | 2 | 112.4.i.d.81.1 | 4 | |||
15.2 | even | 4 | 700.4.r.d.249.2 | 8 | |||
15.8 | even | 4 | 700.4.r.d.249.3 | 8 | |||
15.14 | odd | 2 | 700.4.i.g.501.1 | 4 | |||
21.2 | odd | 6 | 28.4.e.a.9.2 | ✓ | 4 | ||
21.5 | even | 6 | 196.4.e.g.177.1 | 4 | |||
21.11 | odd | 6 | 196.4.a.e.1.1 | 2 | |||
21.17 | even | 6 | 196.4.a.g.1.2 | 2 | |||
21.20 | even | 2 | 196.4.e.g.165.1 | 4 | |||
24.5 | odd | 2 | 448.4.i.h.193.1 | 4 | |||
24.11 | even | 2 | 448.4.i.g.193.2 | 4 | |||
84.11 | even | 6 | 784.4.a.u.1.2 | 2 | |||
84.23 | even | 6 | 112.4.i.d.65.1 | 4 | |||
84.59 | odd | 6 | 784.4.a.ba.1.1 | 2 | |||
105.2 | even | 12 | 700.4.r.d.149.3 | 8 | |||
105.23 | even | 12 | 700.4.r.d.149.2 | 8 | |||
105.44 | odd | 6 | 700.4.i.g.401.1 | 4 | |||
168.107 | even | 6 | 448.4.i.g.65.2 | 4 | |||
168.149 | odd | 6 | 448.4.i.h.65.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.4.e.a.9.2 | ✓ | 4 | 21.2 | odd | 6 | ||
28.4.e.a.25.2 | yes | 4 | 3.2 | odd | 2 | ||
112.4.i.d.65.1 | 4 | 84.23 | even | 6 | |||
112.4.i.d.81.1 | 4 | 12.11 | even | 2 | |||
196.4.a.e.1.1 | 2 | 21.11 | odd | 6 | |||
196.4.a.g.1.2 | 2 | 21.17 | even | 6 | |||
196.4.e.g.165.1 | 4 | 21.20 | even | 2 | |||
196.4.e.g.177.1 | 4 | 21.5 | even | 6 | |||
252.4.k.c.37.2 | 4 | 7.2 | even | 3 | inner | ||
252.4.k.c.109.2 | 4 | 1.1 | even | 1 | trivial | ||
448.4.i.g.65.2 | 4 | 168.107 | even | 6 | |||
448.4.i.g.193.2 | 4 | 24.11 | even | 2 | |||
448.4.i.h.65.1 | 4 | 168.149 | odd | 6 | |||
448.4.i.h.193.1 | 4 | 24.5 | odd | 2 | |||
700.4.i.g.401.1 | 4 | 105.44 | odd | 6 | |||
700.4.i.g.501.1 | 4 | 15.14 | odd | 2 | |||
700.4.r.d.149.2 | 8 | 105.23 | even | 12 | |||
700.4.r.d.149.3 | 8 | 105.2 | even | 12 | |||
700.4.r.d.249.2 | 8 | 15.2 | even | 4 | |||
700.4.r.d.249.3 | 8 | 15.8 | even | 4 | |||
784.4.a.u.1.2 | 2 | 84.11 | even | 6 | |||
784.4.a.ba.1.1 | 2 | 84.59 | odd | 6 | |||
1764.4.a.n.1.2 | 2 | 7.3 | odd | 6 | |||
1764.4.a.z.1.1 | 2 | 7.4 | even | 3 | |||
1764.4.k.ba.361.1 | 4 | 7.6 | odd | 2 | |||
1764.4.k.ba.1549.1 | 4 | 7.5 | odd | 6 |