Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(541,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.541");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.i (of order \(3\), 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: | \(95.5830942093\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{41})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 11x^{2} + 10x + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 540) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 541.1 | ||
Root | \(-1.35078 + 2.33962i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.541 |
Dual form | 1620.4.i.m.1081.1 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.05234 | + | 13.9471i | −0.434786 | + | 0.753071i | −0.997278 | − | 0.0737316i | \(-0.976509\pi\) |
0.562492 | + | 0.826802i | \(0.309843\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −27.7617 | + | 48.0847i | −0.760952 | + | 1.31801i | 0.181408 | + | 0.983408i | \(0.441934\pi\) |
−0.942360 | + | 0.334600i | \(0.891399\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −21.7094 | − | 37.6017i | −0.463161 | − | 0.802219i | 0.535955 | − | 0.844246i | \(-0.319952\pi\) |
−0.999116 | + | 0.0420276i | \(0.986618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −25.5234 | −0.364138 | −0.182069 | − | 0.983286i | \(-0.558279\pi\) | ||||
−0.182069 | + | 0.983286i | \(0.558279\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −103.361 | −1.24803 | −0.624016 | − | 0.781411i | \(-0.714500\pi\) | ||||
−0.624016 | + | 0.781411i | \(0.714500\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.23828 | − | 3.87682i | −0.0202919 | − | 0.0351467i | 0.855701 | − | 0.517470i | \(-0.173126\pi\) |
−0.875993 | + | 0.482324i | \(0.839793\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.23828 | + | 3.87682i | −0.0143324 | + | 0.0248244i | −0.873103 | − | 0.487536i | \(-0.837896\pi\) |
0.858770 | + | 0.512361i | \(0.171229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.5523 | + | 39.0618i | 0.130662 | + | 0.226313i | 0.923932 | − | 0.382557i | \(-0.124956\pi\) |
−0.793270 | + | 0.608870i | \(0.791623\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 80.5234 | 0.388884 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 69.5703 | 0.309116 | 0.154558 | − | 0.987984i | \(-0.450605\pi\) | ||||
0.154558 | + | 0.987984i | \(0.450605\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −241.570 | − | 418.412i | −0.920169 | − | 1.59378i | −0.799152 | − | 0.601130i | \(-0.794718\pi\) |
−0.121018 | − | 0.992650i | \(-0.538616\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −75.8664 | + | 131.404i | −0.269059 | + | 0.466023i | −0.968619 | − | 0.248550i | \(-0.920046\pi\) |
0.699560 | + | 0.714573i | \(0.253379\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 33.8086 | − | 58.5582i | 0.104925 | − | 0.181736i | −0.808782 | − | 0.588108i | \(-0.799873\pi\) |
0.913708 | + | 0.406372i | \(0.133206\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 41.8195 | + | 72.4336i | 0.121923 | + | 0.211177i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 278.953 | 0.722965 | 0.361483 | − | 0.932379i | \(-0.382271\pi\) | ||||
0.361483 | + | 0.932379i | \(0.382271\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 277.617 | 0.680616 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −128.953 | − | 223.353i | −0.284547 | − | 0.492850i | 0.687952 | − | 0.725756i | \(-0.258510\pi\) |
−0.972499 | + | 0.232906i | \(0.925176\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 244.670 | − | 423.780i | 0.513553 | − | 0.889500i | −0.486324 | − | 0.873779i | \(-0.661662\pi\) |
0.999876 | − | 0.0157208i | \(-0.00500428\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −108.547 | + | 188.009i | −0.207132 | + | 0.358763i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 386.298 | + | 669.087i | 0.704385 | + | 1.22003i | 0.966913 | + | 0.255106i | \(0.0821103\pi\) |
−0.262529 | + | 0.964924i | \(0.584556\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 536.859 | 0.897373 | 0.448687 | − | 0.893689i | \(-0.351892\pi\) | ||||
0.448687 | + | 0.893689i | \(0.351892\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −65.5703 | −0.105129 | −0.0525645 | − | 0.998618i | \(-0.516740\pi\) | ||||
−0.0525645 | + | 0.998618i | \(0.516740\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −447.094 | − | 774.389i | −0.661702 | − | 1.14610i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −374.641 | + | 648.897i | −0.533549 | + | 0.924134i | 0.465683 | + | 0.884951i | \(0.345809\pi\) |
−0.999232 | + | 0.0391822i | \(0.987525\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −630.234 | + | 1091.60i | −0.833460 | + | 1.44360i | 0.0618176 | + | 0.998087i | \(0.480310\pi\) |
−0.895278 | + | 0.445508i | \(0.853023\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 63.8086 | + | 110.520i | 0.0814237 | + | 0.141030i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1326.28 | 1.57961 | 0.789806 | − | 0.613356i | \(-0.210181\pi\) | ||||
0.789806 | + | 0.613356i | \(0.210181\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 699.245 | 0.805504 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 258.402 | + | 447.566i | 0.279069 | + | 0.483361i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.4820 | − | 28.5477i | 0.0172526 | − | 0.0298823i | −0.857270 | − | 0.514867i | \(-0.827841\pi\) |
0.874523 | + | 0.484984i | \(0.161175\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 910.090 | − | 1576.32i | 0.896607 | − | 1.55297i | 0.0648041 | − | 0.997898i | \(-0.479358\pi\) |
0.831803 | − | 0.555071i | \(-0.187309\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −687.496 | − | 1190.78i | −0.657680 | − | 1.13913i | −0.981215 | − | 0.192918i | \(-0.938205\pi\) |
0.323535 | − | 0.946216i | \(-0.395129\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1914.19 | 1.72945 | 0.864727 | − | 0.502243i | \(-0.167492\pi\) | ||||
0.864727 | + | 0.502243i | \(0.167492\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −563.978 | −0.495590 | −0.247795 | − | 0.968812i | \(-0.579706\pi\) | ||||
−0.247795 | + | 0.968812i | \(0.579706\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 620.613 | + | 1074.93i | 0.516658 | + | 0.894878i | 0.999813 | + | 0.0193433i | \(0.00615754\pi\) |
−0.483155 | + | 0.875535i | \(0.660509\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.1914 | + | 19.3841i | −0.00907483 | + | 0.0157181i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 205.523 | − | 355.977i | 0.158322 | − | 0.274222i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −875.926 | − | 1517.15i | −0.658096 | − | 1.13986i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1699.42 | −1.18740 | −0.593698 | − | 0.804688i | \(-0.702333\pi\) | ||||
−0.593698 | + | 0.804688i | \(0.702333\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −786.949 | − | 1363.04i | −0.524855 | − | 0.909076i | −0.999581 | − | 0.0289425i | \(-0.990786\pi\) |
0.474726 | − | 0.880134i | \(-0.342547\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 832.298 | − | 1441.58i | 0.542627 | − | 0.939857i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 611.859 | − | 1059.77i | 0.381567 | − | 0.660893i | −0.609719 | − | 0.792617i | \(-0.708718\pi\) |
0.991286 | + | 0.131724i | \(0.0420512\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1072.64 | + | 1857.86i | 0.654531 | + | 1.13368i | 0.982011 | + | 0.188823i | \(0.0604673\pi\) |
−0.327480 | + | 0.944858i | \(0.606199\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2410.76 | 1.40977 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.3828 | 0.0128193 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −417.996 | − | 723.990i | −0.229823 | − | 0.398064i | 0.727933 | − | 0.685648i | \(-0.240481\pi\) |
−0.957755 | + | 0.287584i | \(0.907148\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −418.244 | + | 724.419i | −0.225405 | + | 0.390413i | −0.956441 | − | 0.291926i | \(-0.905704\pi\) |
0.731036 | + | 0.682339i | \(0.239037\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 112.762 | − | 195.309i | 0.0584338 | − | 0.101210i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −705.487 | − | 1221.94i | −0.358624 | − | 0.621155i | 0.629107 | − | 0.777319i | \(-0.283421\pi\) |
−0.987731 | + | 0.156164i | \(0.950087\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 72.0937 | 0.0352906 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1926.56 | −0.925765 | −0.462883 | − | 0.886420i | \(-0.653185\pi\) | ||||
−0.462883 | + | 0.886420i | \(0.653185\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −312.094 | − | 540.562i | −0.144614 | − | 0.250479i | 0.784615 | − | 0.619983i | \(-0.212861\pi\) |
−0.929229 | + | 0.369505i | \(0.879527\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 155.906 | − | 270.038i | 0.0709633 | − | 0.122912i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1795.52 | − | 3109.94i | 0.789082 | − | 1.36673i | −0.137449 | − | 0.990509i | \(-0.543890\pi\) |
0.926530 | − | 0.376221i | \(-0.122776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −201.309 | − | 348.677i | −0.0869571 | − | 0.150614i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −424.078 | −0.177079 | −0.0885393 | − | 0.996073i | \(-0.528220\pi\) | ||||
−0.0885393 | + | 0.996073i | \(0.528220\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3492.80 | 1.43435 | 0.717177 | − | 0.696891i | \(-0.245434\pi\) | ||||
0.717177 | + | 0.696891i | \(0.245434\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −173.926 | − | 301.248i | −0.0691204 | − | 0.119720i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 708.574 | − | 1227.29i | 0.277091 | − | 0.479936i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 598.195 | − | 1036.10i | 0.226617 | − | 0.392513i | −0.730186 | − | 0.683248i | \(-0.760567\pi\) |
0.956803 | + | 0.290736i | \(0.0939000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 791.546 | + | 1371.00i | 0.295216 | + | 0.511329i | 0.975035 | − | 0.222051i | \(-0.0712750\pi\) |
−0.679819 | + | 0.733380i | \(0.737942\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2803.03 | −1.01374 | −0.506872 | − | 0.862021i | \(-0.669198\pi\) | ||||
−0.506872 | + | 0.862021i | \(0.669198\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2568.59 | 0.914989 | 0.457494 | − | 0.889213i | \(-0.348747\pi\) | ||||
0.457494 | + | 0.889213i | \(0.348747\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −36.0469 | − | 62.4350i | −0.0124630 | − | 0.0215866i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1207.85 | + | 2092.06i | −0.411512 | + | 0.712760i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2869.48 | − | 4970.08i | 0.949693 | − | 1.64492i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1168.60 | − | 2024.07i | −0.381278 | − | 0.660392i | 0.609968 | − | 0.792426i | \(-0.291182\pi\) |
−0.991245 | + | 0.132034i | \(0.957849\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 758.664 | 0.240653 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −726.397 | −0.227240 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 554.098 | + | 959.725i | 0.168654 | + | 0.292118i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1413.28 | − | 2447.88i | 0.424397 | − | 0.735077i | −0.571967 | − | 0.820277i | \(-0.693819\pi\) |
0.996364 | + | 0.0851996i | \(0.0271528\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3194.13 | − | 5532.40i | 0.933930 | − | 1.61761i | 0.157398 | − | 0.987535i | \(-0.449689\pi\) |
0.776532 | − | 0.630078i | \(-0.216977\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2380.57 | + | 4123.27i | 0.686955 | + | 1.18984i | 0.972818 | + | 0.231571i | \(0.0743864\pi\) |
−0.285863 | + | 0.958270i | \(0.592280\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1580.58 | −0.444408 | −0.222204 | − | 0.975000i | \(-0.571325\pi\) | ||||
−0.222204 | + | 0.975000i | \(0.571325\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −338.086 | −0.0938480 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 900.234 | + | 1559.25i | 0.243646 | + | 0.422007i | 0.961750 | − | 0.273929i | \(-0.0883233\pi\) |
−0.718104 | + | 0.695936i | \(0.754990\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2621.83 | + | 4541.14i | −0.700775 | + | 1.21378i | 0.267420 | + | 0.963580i | \(0.413829\pi\) |
−0.968195 | + | 0.250198i | \(0.919504\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 209.098 | − | 362.168i | 0.0545256 | − | 0.0944410i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2243.90 | + | 3886.55i | 0.578040 | + | 1.00120i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4934.37 | 1.24085 | 0.620427 | − | 0.784264i | \(-0.286959\pi\) | ||||
0.620427 | + | 0.784264i | \(0.286959\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 248.554 | 0.0617648 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2758.46 | + | 4777.80i | 0.669526 | + | 1.15965i | 0.978037 | + | 0.208433i | \(0.0668363\pi\) |
−0.308510 | + | 0.951221i | \(0.599830\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −560.204 | + | 970.302i | −0.134399 | + | 0.232786i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2598.37 | − | 4500.52i | 0.609212 | − | 1.05519i | −0.382159 | − | 0.924097i | \(-0.624819\pi\) |
0.991371 | − | 0.131089i | \(-0.0418473\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −697.383 | − | 1207.90i | −0.161660 | − | 0.280003i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −115.055 | −0.0260781 | −0.0130391 | − | 0.999915i | \(-0.504151\pi\) | ||||
−0.0130391 | + | 0.999915i | \(0.504151\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2804.16 | 0.628564 | 0.314282 | − | 0.949330i | \(-0.398236\pi\) | ||||
0.314282 | + | 0.949330i | \(0.398236\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −694.043 | − | 1202.12i | −0.152190 | − | 0.263602i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3973.19 | − | 6881.77i | 0.861827 | − | 1.49273i | −0.00833675 | − | 0.999965i | \(-0.502654\pi\) |
0.870164 | − | 0.492763i | \(-0.164013\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2806.10 | − | 4860.31i | 0.595722 | − | 1.03182i | −0.397722 | − | 0.917506i | \(-0.630199\pi\) |
0.993444 | − | 0.114316i | \(-0.0364675\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3773.25 | − | 6535.45i | −0.792566 | − | 1.37276i | −0.924373 | − | 0.381489i | \(-0.875411\pi\) |
0.131807 | − | 0.991275i | \(-0.457922\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7780.83 | 1.60031 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4261.55 | −0.867404 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1506.98 | − | 2610.17i | −0.300474 | − | 0.520437i | 0.675769 | − | 0.737113i | \(-0.263812\pi\) |
−0.976243 | + | 0.216677i | \(0.930478\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −644.766 | + | 1116.77i | −0.127253 | + | 0.220409i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −97.1835 | + | 168.327i | −0.0187969 | + | 0.0325571i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1221.80 | − | 2116.23i | −0.233966 | − | 0.405240i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2446.70 | −0.459336 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4316.35 | −0.802434 | −0.401217 | − | 0.915983i | \(-0.631413\pi\) | ||||
−0.401217 | + | 0.915983i | \(0.631413\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3815.02 | + | 6607.80i | 0.695594 | + | 1.20480i | 0.969980 | + | 0.243184i | \(0.0781920\pi\) |
−0.274386 | + | 0.961620i | \(0.588475\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3351.41 | + | 5804.81i | −0.605217 | + | 1.04827i | 0.386800 | + | 0.922164i | \(0.373580\pi\) |
−0.992017 | + | 0.126103i | \(0.959753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −892.453 | + | 1545.77i | −0.158123 | + | 0.273878i | −0.934192 | − | 0.356771i | \(-0.883878\pi\) |
0.776069 | + | 0.630649i | \(0.217211\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −124.277 | − | 215.254i | −0.0218125 | − | 0.0377804i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2638.13 | 0.454456 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1085.47 | 0.185265 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 544.477 | + | 943.061i | 0.0912400 | + | 0.158032i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3788.49 | + | 6561.85i | −0.629106 | + | 1.08964i | 0.358625 | + | 0.933482i | \(0.383246\pi\) |
−0.987731 | + | 0.156162i | \(0.950088\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1931.49 | − | 3345.44i | 0.315010 | − | 0.545614i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5390.92 | + | 9337.35i | 0.871401 | + | 1.50931i | 0.860548 | + | 0.509370i | \(0.170121\pi\) |
0.0108534 | + | 0.999941i | \(0.496545\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2504.37 | −0.397710 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6870.89 | −1.08161 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2420.41 | − | 4192.28i | −0.374451 | − | 0.648569i | 0.615793 | − | 0.787908i | \(-0.288836\pi\) |
−0.990245 | + | 0.139339i | \(0.955502\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4254.21 | − | 7368.50i | 0.652500 | − | 1.13016i | −0.330014 | − | 0.943976i | \(-0.607054\pi\) |
0.982514 | − | 0.186187i | \(-0.0596131\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4719.69 | − | 8174.74i | 0.711626 | − | 1.23257i | −0.252621 | − | 0.967565i | \(-0.581293\pi\) |
0.964247 | − | 0.265006i | \(-0.0853740\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1342.15 | − | 2324.67i | −0.200659 | − | 0.347551i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10696.6 | 1.57255 | 0.786277 | − | 0.617874i | \(-0.212006\pi\) | ||||
0.786277 | + | 0.617874i | \(0.212006\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3824.48 | 0.557586 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 163.926 | + | 283.928i | 0.0235076 | + | 0.0407163i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3129.69 | − | 5420.79i | 0.445146 | − | 0.771016i | −0.552916 | − | 0.833237i | \(-0.686485\pi\) |
0.998062 | + | 0.0622208i | \(0.0198183\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2246.23 | + | 3890.58i | −0.314335 | + | 0.544444i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −305.050 | − | 528.363i | −0.0423456 | − | 0.0733447i | 0.844076 | − | 0.536224i | \(-0.180150\pi\) |
−0.886421 | + | 0.462879i | \(0.846816\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 194.367 | 0.0265528 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2025.74 | −0.274552 | −0.137276 | − | 0.990533i | \(-0.543835\pi\) | ||||
−0.137276 | + | 0.990533i | \(0.543835\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4562.07 | − | 7901.74i | −0.608645 | − | 1.05420i | −0.991464 | − | 0.130381i | \(-0.958380\pi\) |
0.382819 | − | 0.923823i | \(-0.374953\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2235.47 | + | 3871.95i | −0.295922 | + | 0.512552i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2547.60 | − | 4412.57i | 0.332052 | − | 0.575131i | −0.650862 | − | 0.759196i | \(-0.725592\pi\) |
0.982914 | + | 0.184065i | \(0.0589256\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 57.1287 | + | 98.9498i | 0.00738906 | + | 0.0127982i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3746.41 | 0.477221 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6140.93 | 0.776334 | 0.388167 | − | 0.921589i | \(-0.373108\pi\) | ||||
0.388167 | + | 0.921589i | \(0.373108\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1090.99 | + | 1889.65i | 0.135864 | + | 0.235324i | 0.925927 | − | 0.377702i | \(-0.123286\pi\) |
−0.790063 | + | 0.613026i | \(0.789952\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 979.194 | − | 1696.01i | 0.121035 | − | 0.209639i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1931.39 | + | 3345.27i | −0.235222 | + | 0.407417i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3546.37 | − | 6142.49i | −0.428745 | − | 0.742607i | 0.568017 | − | 0.823017i | \(-0.307711\pi\) |
−0.996762 | + | 0.0804092i | \(0.974377\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4153.50 | 0.494868 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6302.34 | 0.745470 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2883.81 | − | 4994.90i | −0.336237 | − | 0.582379i | 0.647485 | − | 0.762078i | \(-0.275821\pi\) |
−0.983722 | + | 0.179699i | \(0.942488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2233.95 | + | 3869.31i | −0.258613 | + | 0.447931i | −0.965871 | − | 0.259025i | \(-0.916599\pi\) |
0.707258 | + | 0.706956i | \(0.249932\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 319.043 | − | 552.599i | 0.0364138 | − | 0.0630705i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3940.33 | + | 6824.84i | 0.446571 | + | 0.773483i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4560.33 | 0.509660 | 0.254830 | − | 0.966986i | \(-0.417981\pi\) | ||||
0.254830 | + | 0.966986i | \(0.417981\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1412.82 | −0.156803 | −0.0784016 | − | 0.996922i | \(-0.524982\pi\) | ||||
−0.0784016 | + | 0.996922i | \(0.524982\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 231.351 | + | 400.712i | 0.0253250 | + | 0.0438642i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 976.231 | − | 1690.88i | 0.106134 | − | 0.183830i | −0.808067 | − | 0.589091i | \(-0.799486\pi\) |
0.914201 | + | 0.405261i | \(0.132819\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2078.95 | + | 3600.85i | −0.222966 | + | 0.386189i | −0.955707 | − | 0.294319i | \(-0.904907\pi\) |
0.732741 | + | 0.680508i | \(0.238241\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3315.70 | − | 5742.97i | −0.353212 | − | 0.611781i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4352.20 | −0.457446 | −0.228723 | − | 0.973492i | \(-0.573455\pi\) | ||||
−0.228723 | + | 0.973492i | \(0.573455\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26825.6 | 2.80082 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1748.11 | − | 3027.82i | −0.180116 | − | 0.311970i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1910.16 | − | 3308.50i | 0.195522 | − | 0.338655i | −0.751549 | − | 0.659677i | \(-0.770693\pi\) |
0.947072 | + | 0.321022i | \(0.104026\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5932.85 | + | 10276.0i | −0.599394 | + | 1.03818i | 0.393517 | + | 0.919317i | \(0.371258\pi\) |
−0.992911 | + | 0.118863i | \(0.962075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2653.61 | + | 4596.19i | 0.266358 | + | 0.461346i | 0.967919 | − | 0.251264i | \(-0.0808463\pi\) |
−0.701560 | + | 0.712610i | \(0.747513\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2810.91 | 0.278529 | 0.139265 | − | 0.990255i | \(-0.455526\pi\) | ||||
0.139265 | + | 0.990255i | \(0.455526\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12442.4 | −1.22503 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4212.36 | − | 7296.03i | −0.409481 | − | 0.709242i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1292.01 | − | 2237.83i | 0.124803 | − | 0.216166i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9370.19 | + | 16229.7i | −0.893810 | + | 1.54812i | −0.0585401 | + | 0.998285i | \(0.518645\pi\) |
−0.835270 | + | 0.549840i | \(0.814689\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1510.33 | − | 2615.96i | −0.143170 | − | 0.247979i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −164.820 | −0.0154312 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8260.64 | −0.768635 | −0.384318 | − | 0.923201i | \(-0.625563\pi\) | ||||
−0.384318 | + | 0.923201i | \(0.625563\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7462.29 | − | 12925.1i | −0.685883 | − | 1.18798i | −0.973159 | − | 0.230136i | \(-0.926083\pi\) |
0.287276 | − | 0.957848i | \(-0.407250\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 57.1287 | − | 98.9498i | 0.00521896 | − | 0.00903950i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4322.98 | + | 7487.61i | −0.390165 | + | 0.675786i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2967.06 | + | 5139.10i | 0.266180 | + | 0.461037i | 0.967872 | − | 0.251443i | \(-0.0809051\pi\) |
−0.701692 | + | 0.712480i | \(0.747572\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2704.62 | −0.239747 | −0.119874 | − | 0.992789i | \(-0.538249\pi\) | ||||
−0.119874 | + | 0.992789i | \(0.538249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9100.90 | −0.801950 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1383.25 | + | 2395.85i | 0.120454 | + | 0.208633i | 0.919947 | − | 0.392043i | \(-0.128232\pi\) |
−0.799493 | + | 0.600676i | \(0.794898\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 527.995 | − | 914.513i | 0.0457086 | − | 0.0791696i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3437.48 | + | 5953.89i | −0.294123 | + | 0.509436i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1877.17 | + | 3251.35i | 0.159686 | + | 0.276585i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1502.48 | 0.126344 | 0.0631718 | − | 0.998003i | \(-0.479878\pi\) | ||||
0.0631718 | + | 0.998003i | \(0.479878\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23380.0 | −1.95475 | −0.977377 | − | 0.211504i | \(-0.932164\pi\) | ||||
−0.977377 | + | 0.211504i | \(0.932164\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −575.613 | − | 996.991i | −0.0475789 | − | 0.0824092i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6073.48 | − | 10519.6i | 0.499176 | − | 0.864599i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10488.7 | + | 18166.9i | −0.852374 | + | 1.47635i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4785.47 | − | 8288.67i | −0.386717 | − | 0.669814i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4643.93 | −0.371110 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18343.1 | 1.45773 | 0.728865 | − | 0.684657i | \(-0.240048\pi\) | ||||
0.728865 | + | 0.684657i | \(0.240048\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1409.95 | + | 2442.10i | 0.110817 | + | 0.191941i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2856.60 | + | 4947.78i | −0.223290 | + | 0.386749i | −0.955805 | − | 0.294002i | \(-0.905013\pi\) |
0.732515 | + | 0.680751i | \(0.238346\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 231.351 | − | 400.712i | 0.0178873 | − | 0.0309817i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6033.47 | − | 10450.3i | −0.463959 | − | 0.803600i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20519.3 | −1.56092 | −0.780460 | − | 0.625206i | \(-0.785015\pi\) | ||||
−0.780460 | + | 0.625206i | \(0.785015\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6588.05 | 0.498470 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12722.9 | + | 22036.7i | 0.952408 | + | 1.64962i | 0.740192 | + | 0.672396i | \(0.234735\pi\) |
0.212216 | + | 0.977223i | \(0.431932\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3103.07 | − | 5374.67i | 0.231057 | − | 0.400202i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3657.47 | − | 6334.92i | 0.269471 | − | 0.466738i | −0.699254 | − | 0.714873i | \(-0.746484\pi\) |
0.968725 | + | 0.248135i | \(0.0798178\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3796.52 | − | 6575.76i | −0.278247 | − | 0.481939i | 0.692702 | − | 0.721224i | \(-0.256420\pi\) |
−0.970949 | + | 0.239285i | \(0.923087\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 111.914 | 0.00811677 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19291.2 | −1.39186 | −0.695929 | − | 0.718110i | \(-0.745007\pi\) | ||||
−0.695929 | + | 0.718110i | \(0.745007\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10149.7 | − | 17579.8i | −0.724753 | − | 1.25531i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7744.22 | + | 13413.4i | −0.550142 | + | 0.952874i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10151.2 | − | 17582.4i | 0.713773 | − | 1.23629i | −0.249657 | − | 0.968334i | \(-0.580318\pi\) |
0.963431 | − | 0.267957i | \(-0.0863487\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2331.03 | − | 4037.46i | −0.163070 | − | 0.282446i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11878.2 | −0.822562 | −0.411281 | − | 0.911509i | \(-0.634918\pi\) | ||||
−0.411281 | + | 0.911509i | \(0.634918\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2055.23 | −0.141607 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −804.093 | − | 1392.73i | −0.0548487 | − | 0.0950007i | 0.837297 | − | 0.546748i | \(-0.184134\pi\) |
−0.892146 | + | 0.451747i | \(0.850801\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9517.75 | + | 16485.2i | −0.645985 | + | 1.11888i | 0.338088 | + | 0.941115i | \(0.390220\pi\) |
−0.984073 | + | 0.177765i | \(0.943113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4379.63 | + | 7585.74i | −0.294309 | + | 0.509759i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3082.24 | + | 5338.59i | 0.206102 | + | 0.356980i | 0.950483 | − | 0.310775i | \(-0.100589\pi\) |
−0.744381 | + | 0.667755i | \(0.767255\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2935.85 | −0.194389 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10601.8 | −0.698538 | −0.349269 | − | 0.937023i | \(-0.613570\pi\) | ||||
−0.349269 | + | 0.937023i | \(0.613570\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7086.92 | − | 12274.9i | −0.462413 | − | 0.800923i | 0.536668 | − | 0.843794i | \(-0.319683\pi\) |
−0.999081 | + | 0.0428709i | \(0.986350\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1111.12 | − | 1924.51i | 0.0721479 | − | 0.124964i | −0.827695 | − | 0.561179i | \(-0.810348\pi\) |
0.899842 | + | 0.436215i | \(0.143681\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10679.7 | + | 18497.7i | −0.686793 | + | 1.18956i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1775.67 | −0.112561 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20385.1 | 1.28608 | 0.643041 | − | 0.765832i | \(-0.277672\pi\) | ||||
0.643041 | + | 0.765832i | \(0.277672\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4248.55 | + | 7358.71i | 0.265510 | + | 0.459877i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1815.75 | − | 3144.97i | 0.112940 | − | 0.195618i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6379.38 | − | 11049.4i | 0.393090 | − | 0.680851i | −0.599766 | − | 0.800176i | \(-0.704740\pi\) |
0.992855 | + | 0.119324i | \(0.0380729\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6652.21 | + | 11522.0i | 0.407990 | + | 0.706660i | 0.994664 | − | 0.103163i | \(-0.0328964\pi\) |
−0.586674 | + | 0.809823i | \(0.699563\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24988.8 | 1.51841 | 0.759206 | − | 0.650851i | \(-0.225588\pi\) | ||||
0.759206 | + | 0.650851i | \(0.225588\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14319.8 | 0.866106 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7394.11 | + | 12807.0i | 0.443115 | + | 0.767497i | 0.997919 | − | 0.0644840i | \(-0.0205402\pi\) |
−0.554804 | + | 0.831981i | \(0.687207\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3934.75 | + | 6815.18i | −0.234723 | + | 0.406551i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1500.94 | + | 2599.70i | −0.0887226 | + | 0.153672i | −0.906971 | − | 0.421192i | \(-0.861612\pi\) |
0.818249 | + | 0.574864i | \(0.194945\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9242.46 | + | 16008.4i | 0.543858 | + | 0.941989i | 0.998678 | + | 0.0514058i | \(0.0163702\pi\) |
−0.454820 | + | 0.890583i | \(0.650296\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8322.98 | −0.485340 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.0397 | 0.00116333 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13584.9 | + | 23529.7i | 0.781578 | + | 1.35373i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −463.411 | + | 802.651i | −0.0265426 | + | 0.0459732i | −0.878992 | − | 0.476837i | \(-0.841783\pi\) |
0.852449 | + | 0.522810i | \(0.175116\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16802.3 | + | 29102.5i | −0.953865 | + | 1.65214i | −0.216920 | + | 0.976189i | \(0.569601\pi\) |
−0.736945 | + | 0.675953i | \(0.763732\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 265.438 | + | 459.752i | 0.0150023 | + | 0.0259848i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6468.33 | 0.362377 | 0.181189 | − | 0.983448i | \(-0.442006\pi\) | ||||
0.181189 | + | 0.983448i | \(0.442006\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6118.59 | −0.341284 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6055.90 | − | 10489.1i | −0.334850 | − | 0.579976i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15760.2 | − | 27297.4i | 0.867649 | − | 1.50281i | 0.00325629 | − | 0.999995i | \(-0.498963\pi\) |
0.864393 | − | 0.502817i | \(-0.167703\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5363.18 | − | 9289.31i | 0.292715 | − | 0.506998i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6165.70 | + | 10679.3i | 0.335068 | + | 0.580355i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32088.9 | −1.72893 | −0.864465 | − | 0.502693i | \(-0.832343\pi\) | ||||
−0.864465 | + | 0.502693i | \(0.832343\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7190.85 | −0.385787 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14656.7 | + | 25386.2i | 0.779664 | + | 1.35042i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4338.98 | + | 7515.34i | −0.229836 | + | 0.398088i | −0.957759 | − | 0.287571i | \(-0.907152\pi\) |
0.727923 | + | 0.685659i | \(0.240486\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 100.957 | − | 174.863i | 0.00530277 | − | 0.00918466i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6026.89 | − | 10438.9i | −0.315235 | − | 0.546003i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22564.2 | −1.17038 | −0.585190 | − | 0.810896i | \(-0.698980\pi\) | ||||
−0.585190 | + | 0.810896i | \(0.698980\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22143.8 | 1.14380 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −55.9571 | − | 96.9205i | −0.00286648 | − | 0.00496488i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 423.322 | − | 733.215i | 0.0215958 | − | 0.0374050i | −0.855026 | − | 0.518586i | \(-0.826459\pi\) |
0.876621 | + | 0.481181i | \(0.159792\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1936.37 | − | 3353.89i | 0.0979744 | − | 0.169697i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14590.7 | − | 25271.8i | −0.735225 | − | 1.27345i | −0.954625 | − | 0.297812i | \(-0.903743\pi\) |
0.219400 | − | 0.975635i | \(-0.429590\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −42897.1 | −2.14401 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5544.59 | 0.275996 | 0.137998 | − | 0.990432i | \(-0.455933\pi\) | ||||
0.137998 | + | 0.990432i | \(0.455933\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10048.0 | + | 17403.6i | 0.496131 | + | 0.859324i | 0.999990 | − | 0.00446196i | \(-0.00142029\pi\) |
−0.503859 | + | 0.863786i | \(0.668087\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2089.98 | + | 3619.95i | −0.102780 | + | 0.178020i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15413.7 | + | 26697.3i | −0.751941 | + | 1.30240i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19589.0 | + | 33929.2i | 0.951817 | + | 1.64860i | 0.741490 | + | 0.670964i | \(0.234120\pi\) |
0.210327 | + | 0.977631i | \(0.432547\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4182.44 | 0.201609 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37739.2 | 1.81196 | 0.905980 | − | 0.423322i | \(-0.139136\pi\) | ||||
0.905980 | + | 0.423322i | \(0.139136\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4556.30 | + | 7891.74i | 0.217038 | + | 0.375920i | 0.953901 | − | 0.300122i | \(-0.0970272\pi\) |
−0.736863 | + | 0.676042i | \(0.763694\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4541.35 | − | 7865.84i | 0.215475 | − | 0.373214i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5598.98 | + | 9697.72i | −0.263582 | + | 0.456538i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15504.9 | + | 26855.3i | 0.727076 | + | 1.25933i | 0.958114 | + | 0.286388i | \(0.0924548\pi\) |
−0.231037 | + | 0.972945i | \(0.574212\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13117.9 | −0.610372 | −0.305186 | − | 0.952293i | \(-0.598719\pi\) | ||||
−0.305186 | + | 0.952293i | \(0.598719\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1127.62 | −0.0522648 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24968.9 | + | 43247.5i | 1.14840 | + | 1.98909i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14904.1 | + | 25814.7i | −0.682858 | + | 1.18274i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3527.43 | + | 6109.69i | −0.160382 | + | 0.277789i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4334.37 | − | 7507.35i | −0.196320 | − | 0.340036i | 0.751013 | − | 0.660288i | \(-0.229566\pi\) |
−0.947332 | + | 0.320252i | \(0.896232\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19989.6 | −0.898542 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21246.5 | −0.951431 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12589.3 | − | 21805.3i | −0.559519 | − | 0.969115i | −0.997537 | − | 0.0701484i | \(-0.977653\pi\) |
0.438018 | − | 0.898966i | \(-0.355681\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −862.911 | + | 1494.61i | −0.0382073 | + | 0.0661769i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1820.34 | − | 3152.93i | 0.0799982 | − | 0.138561i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −180.234 | − | 312.175i | −0.00789121 | − | 0.0136680i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21442.3 | −0.931856 | −0.465928 | − | 0.884823i | \(-0.654279\pi\) | ||||
−0.465928 | + | 0.884823i | \(0.654279\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23957.5 | −1.03731 | −0.518656 | − | 0.854983i | \(-0.673568\pi\) | ||||
−0.518656 | + | 0.854983i | \(0.673568\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4816.40 | + | 8342.25i | 0.207007 | + | 0.358547i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7841.62 | − | 13582.1i | 0.335794 | − | 0.581612i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10332.2 | + | 17895.8i | −0.439214 | + | 0.760742i | −0.997629 | − | 0.0688203i | \(-0.978076\pi\) |
0.558415 | + | 0.829562i | \(0.311410\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22979.2 | − | 39801.2i | −0.973276 | − | 1.68576i | −0.685512 | − | 0.728062i | \(-0.740421\pi\) |
−0.287764 | − | 0.957701i | \(-0.592912\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22841.3 | −0.960423 | −0.480211 | − | 0.877153i | \(-0.659440\pi\) | ||||
−0.480211 | + | 0.877153i | \(0.659440\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28412.5 | −1.19036 | −0.595179 | − | 0.803594i | \(-0.702919\pi\) | ||||
−0.595179 | + | 0.803594i | \(0.702919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1067.38 | − | 1848.75i | −0.0443967 | − | 0.0768974i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1560.47 | + | 2702.81i | −0.0646733 | + | 0.112018i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10331.0 | − | 17893.9i | 0.425110 | − | 0.736312i | −0.571321 | − | 0.820727i | \(-0.693569\pi\) |
0.996431 | + | 0.0844151i | \(0.0269022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12184.5 | + | 21104.1i | 0.499589 | + | 0.865314i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1559.06 | −0.0634715 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28213.0 | 1.14452 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −155.718 | − | 269.712i | −0.00627256 | − | 0.0108644i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11777.1 | + | 20398.6i | −0.472733 | + | 0.818798i | −0.999513 | − | 0.0312037i | \(-0.990066\pi\) |
0.526780 | + | 0.850002i | \(0.323399\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19445.5 | − | 33680.6i | 0.775084 | − | 1.34248i | −0.159664 | − | 0.987171i | \(-0.551041\pi\) |
0.934747 | − | 0.355313i | \(-0.115626\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14971.0 | − | 25930.5i | −0.594649 | − | 1.02996i | −0.993596 | − | 0.112988i | \(-0.963958\pi\) |
0.398947 | − | 0.916974i | \(-0.369376\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11036.3 | −0.435318 | −0.217659 | − | 0.976025i | \(-0.569842\pi\) | ||||
−0.217659 | + | 0.976025i | \(0.569842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17955.2 | −0.705776 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20801.3 | − | 36029.0i | −0.812010 | − | 1.40644i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16772.6 | − | 29050.9i | 0.652487 | − | 1.13014i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1006.54 | + | 1743.38i | −0.0388884 | + | 0.0673567i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12433.7 | + | 21535.8i | 0.478742 | + | 0.829205i | 0.999703 | − | 0.0243754i | \(-0.00775970\pi\) |
−0.520961 | + | 0.853580i | \(0.674426\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10250.2 | −0.391983 | −0.195991 | − | 0.980606i | \(-0.562792\pi\) | ||||
−0.195991 | + | 0.980606i | \(0.562792\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39991.9 | −1.52416 | −0.762081 | − | 0.647481i | \(-0.775822\pi\) | ||||
−0.762081 | + | 0.647481i | \(0.775822\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12121.9 | + | 20995.8i | 0.458867 | + | 0.794780i | 0.998901 | − | 0.0468624i | \(-0.0149222\pi\) |
−0.540035 | + | 0.841643i | \(0.681589\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13684.3 | − | 23702.0i | 0.516263 | − | 0.894193i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3494.49 | + | 6052.63i | −0.130950 | + | 0.226812i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1060.19 | + | 1836.31i | 0.0395960 | + | 0.0685822i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −201.914 | −0.00749079 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7119.84 | −0.263259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8732.01 | − | 15124.3i | −0.320731 | − | 0.555523i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5503.94 | + | 9533.10i | −0.201494 | + | 0.348998i | −0.949010 | − | 0.315246i | \(-0.897913\pi\) |
0.747516 | + | 0.664244i | \(0.231246\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6056.53 | + | 10490.2i | −0.220265 | + | 0.381511i | −0.954889 | − | 0.296965i | \(-0.904026\pi\) |
0.734623 | + | 0.678475i | \(0.237359\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34992.8 | − | 60609.3i | −1.26845 | − | 2.19701i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 25347.1 | 0.912799 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5343.49 | 0.191801 | 0.0959007 | − | 0.995391i | \(-0.469427\pi\) | ||||
0.0959007 | + | 0.995391i | \(0.469427\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11654.9 | − | 20186.8i | −0.415628 | − | 0.719890i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −869.629 | + | 1506.24i | −0.0309116 | + | 0.0535404i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3995.65 | + | 6920.67i | −0.141112 | + | 0.244413i | −0.927916 | − | 0.372790i | \(-0.878401\pi\) |
0.786804 | + | 0.617203i | \(0.211734\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4322.51 | − | 7486.80i | −0.152164 | − | 0.263555i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7085.74 | −0.247838 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33059.7 | 1.15263 | 0.576315 | − | 0.817227i | \(-0.304490\pi\) | ||||
0.576315 | + | 0.817227i | \(0.304490\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11880.5 | − | 20577.6i | −0.411576 | − | 0.712871i | 0.583486 | − | 0.812123i | \(-0.301688\pi\) |
−0.995062 | + | 0.0992521i | \(0.968355\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1081.41 | + | 1873.05i | −0.0373440 | + | 0.0646818i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17484.1 | + | 30283.3i | −0.599953 | + | 1.03915i | 0.392874 | + | 0.919592i | \(0.371481\pi\) |
−0.992827 | + | 0.119557i | \(0.961852\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1423.49 | + | 2465.56i | 0.0486917 | + | 0.0843365i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −50724.6 | −1.72417 | −0.862084 | − | 0.506766i | \(-0.830841\pi\) | ||||
−0.862084 | + | 0.506766i | \(0.830841\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5981.95 | −0.202693 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9853.80 | + | 17067.3i | 0.331800 | + | 0.574694i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13878.3 | − | 24037.9i | 0.465855 | − | 0.806884i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3957.73 | − | 6854.99i | 0.132025 | − | 0.228673i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7558.50 | − | 13091.7i | −0.251360 | − | 0.435368i | 0.712541 | − | 0.701631i | \(-0.247544\pi\) |
−0.963900 | + | 0.266263i | \(0.914211\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48459.4 | 1.60158 | 0.800792 | − | 0.598943i | \(-0.204412\pi\) | ||||
0.800792 | + | 0.598943i | \(0.204412\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34549.0 | −1.13832 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10306.0 | + | 17850.5i | 0.337481 | + | 0.584534i | 0.983958 | − | 0.178399i | \(-0.0570919\pi\) |
−0.646477 | + | 0.762933i | \(0.723759\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36819.8 | + | 63773.8i | −1.20201 | + | 2.08194i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4545.20 | − | 7872.52i | 0.147476 | − | 0.255437i | −0.782818 | − | 0.622251i | \(-0.786218\pi\) |
0.930294 | + | 0.366814i | \(0.119552\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7007.58 | + | 12137.5i | 0.226680 | + | 0.392622i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 679.242 | 0.0218389 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29334.8 | 0.940312 | 0.470156 | − | 0.882583i | \(-0.344198\pi\) | ||||
0.470156 | + | 0.882583i | \(0.344198\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6421.48 | − | 11122.3i | −0.204598 | − | 0.354374i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1141.47 | − | 1977.09i | 0.0362595 | − | 0.0628034i | −0.847326 | − | 0.531073i | \(-0.821789\pi\) |
0.883586 | + | 0.468270i | \(0.155122\pi\) | |||||||
\(998\) | 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 | 1620.4.i.m.541.1 | 4 | ||
3.2 | odd | 2 | 1620.4.i.p.541.1 | 4 | |||
9.2 | odd | 6 | 540.4.a.g.1.2 | ✓ | 2 | ||
9.4 | even | 3 | inner | 1620.4.i.m.1081.1 | 4 | ||
9.5 | odd | 6 | 1620.4.i.p.1081.1 | 4 | |||
9.7 | even | 3 | 540.4.a.j.1.2 | yes | 2 | ||
36.7 | odd | 6 | 2160.4.a.z.1.1 | 2 | |||
36.11 | even | 6 | 2160.4.a.u.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
540.4.a.g.1.2 | ✓ | 2 | 9.2 | odd | 6 | ||
540.4.a.j.1.2 | yes | 2 | 9.7 | even | 3 | ||
1620.4.i.m.541.1 | 4 | 1.1 | even | 1 | trivial | ||
1620.4.i.m.1081.1 | 4 | 9.4 | even | 3 | inner | ||
1620.4.i.p.541.1 | 4 | 3.2 | odd | 2 | |||
1620.4.i.p.1081.1 | 4 | 9.5 | odd | 6 | |||
2160.4.a.u.1.1 | 2 | 36.11 | even | 6 | |||
2160.4.a.z.1.1 | 2 | 36.7 | odd | 6 |