Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2052,3,Mod(145,2052)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2052, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2052.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2052 = 2^{2} \cdot 3^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2052.bl (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(55.9129502467\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 684) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.3 | ||
Character | \(\chi\) | \(=\) | 2052.145 |
Dual form | 2052.3.bl.a.1585.3 |
$q$-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 \(\left(\mathbb{Z}/2052\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1027\) | \(1217\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | −8.35221 | −1.67044 | −0.835221 | − | 0.549914i | \(-0.814660\pi\) | ||||
−0.835221 | + | 0.549914i | \(0.814660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.352343 | + | 0.610277i | 0.0503348 | + | 0.0871824i | 0.890095 | − | 0.455775i | \(-0.150638\pi\) |
−0.839760 | + | 0.542957i | \(0.817305\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.3266 | + | 17.8862i | 0.938780 | + | 1.62601i | 0.767751 | + | 0.640749i | \(0.221376\pi\) |
0.171029 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.44006 | + | 4.29552i | −0.572312 | + | 0.330425i | −0.758072 | − | 0.652170i | \(-0.773859\pi\) |
0.185760 | + | 0.982595i | \(0.440525\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.72428 | − | 4.71858i | −0.160251 | − | 0.277564i | 0.774707 | − | 0.632320i | \(-0.217897\pi\) |
−0.934959 | + | 0.354756i | \(0.884564\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.849123 | − | 18.9810i | 0.0446907 | − | 0.999001i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 11.8696 | + | 20.5587i | 0.516069 | + | 0.893857i | 0.999826 | + | 0.0186548i | \(0.00593836\pi\) |
−0.483757 | + | 0.875202i | \(0.660728\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 44.7594 | 1.79038 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.37991i | 0.0820658i | 0.999158 | + | 0.0410329i | \(0.0130648\pi\) | ||||
−0.999158 | + | 0.0410329i | \(0.986935\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.32115 | + | 1.34012i | 0.0748757 | + | 0.0432295i | 0.536970 | − | 0.843601i | \(-0.319569\pi\) |
−0.462095 | + | 0.886831i | \(0.652902\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.94285 | − | 5.09716i | −0.0840813 | − | 0.145633i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 19.8089i | 0.535376i | 0.963506 | + | 0.267688i | \(0.0862596\pi\) | ||||
−0.963506 | + | 0.267688i | \(0.913740\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 75.4429i | 1.84007i | 0.391834 | + | 0.920036i | \(0.371841\pi\) | ||||
−0.391834 | + | 0.920036i | \(0.628159\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.44837 | + | 9.43685i | −0.126706 | + | 0.219462i | −0.922399 | − | 0.386239i | \(-0.873774\pi\) |
0.795692 | + | 0.605701i | \(0.207107\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −30.8259 | −0.655871 | −0.327936 | − | 0.944700i | \(-0.606353\pi\) | ||||
−0.327936 | + | 0.944700i | \(0.606353\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 24.2517 | − | 42.0052i | 0.494933 | − | 0.857249i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 76.8522 | + | 44.3706i | 1.45004 | + | 0.837182i | 0.998483 | − | 0.0550603i | \(-0.0175351\pi\) |
0.451558 | + | 0.892242i | \(0.350868\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −86.2498 | − | 149.389i | −1.56818 | − | 2.71616i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 91.5455i | − | 1.55162i | −0.630967 | − | 0.775809i | \(-0.717342\pi\) | ||
0.630967 | − | 0.775809i | \(-0.282658\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.0853 | −0.165332 | −0.0826662 | − | 0.996577i | \(-0.526344\pi\) | ||||
−0.0826662 | + | 0.996577i | \(0.526344\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 62.1410 | − | 35.8771i | 0.956015 | − | 0.551955i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.9419 | − | 8.04937i | 0.208088 | − | 0.120140i | −0.392334 | − | 0.919823i | \(-0.628332\pi\) |
0.600423 | + | 0.799683i | \(0.294999\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −67.0947 | + | 38.7371i | −0.944995 | + | 0.545593i | −0.891523 | − | 0.452976i | \(-0.850362\pi\) |
−0.0534727 | + | 0.998569i | \(0.517029\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −39.6851 | − | 68.7366i | −0.543631 | − | 0.941597i | −0.998692 | − | 0.0511363i | \(-0.983716\pi\) |
0.455061 | − | 0.890460i | \(-0.349618\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.27700 | + | 12.6041i | −0.0945065 | + | 0.163690i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −78.3707 | − | 45.2473i | −0.992034 | − | 0.572751i | −0.0861523 | − | 0.996282i | \(-0.527457\pi\) |
−0.905882 | + | 0.423531i | \(0.860791\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 31.5302 | + | 54.6119i | 0.379882 | + | 0.657975i | 0.991045 | − | 0.133530i | \(-0.0426313\pi\) |
−0.611163 | + | 0.791505i | \(0.709298\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.7537 | + | 39.4106i | 0.267691 | + | 0.463654i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 65.0621 | + | 37.5636i | 0.731035 | + | 0.422063i | 0.818801 | − | 0.574078i | \(-0.194639\pi\) |
−0.0877659 | + | 0.996141i | \(0.527973\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.24291 | − | 3.02700i | −0.0576144 | − | 0.0332637i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.09205 | + | 158.533i | −0.0746532 | + | 1.66877i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −65.4754 | − | 37.8022i | −0.675004 | − | 0.389714i | 0.122966 | − | 0.992411i | \(-0.460759\pi\) |
−0.797970 | + | 0.602697i | \(0.794093\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −84.9133 | −0.840726 | −0.420363 | − | 0.907356i | \(-0.638097\pi\) | ||||
−0.420363 | + | 0.907356i | \(0.638097\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 24.5788 | + | 14.1906i | 0.238629 | + | 0.137772i | 0.614546 | − | 0.788881i | \(-0.289339\pi\) |
−0.375918 | + | 0.926653i | \(0.622672\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 148.821i | − | 1.39085i | −0.718600 | − | 0.695423i | \(-0.755217\pi\) | ||
0.718600 | − | 0.695423i | \(-0.244783\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −49.6931 | + | 28.6903i | −0.455900 | + | 0.263214i | −0.710319 | − | 0.703880i | \(-0.751449\pi\) |
0.254419 | + | 0.967094i | \(0.418116\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −59.1471 | − | 34.1486i | −0.523426 | − | 0.302200i | 0.214909 | − | 0.976634i | \(-0.431054\pi\) |
−0.738335 | + | 0.674434i | \(0.764388\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −99.1372 | − | 171.711i | −0.862063 | − | 1.49314i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.91976 | − | 3.32512i | 0.0161324 | − | 0.0279422i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −152.776 | + | 264.617i | −1.26262 | + | 2.18691i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −165.035 | −1.32028 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −45.0028 | − | 25.9824i | −0.354353 | − | 0.204586i | 0.312248 | − | 0.950001i | \(-0.398918\pi\) |
−0.666601 | + | 0.745415i | \(0.732251\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −90.7869 | −0.693030 | −0.346515 | − | 0.938044i | \(-0.612635\pi\) | ||||
−0.346515 | + | 0.938044i | \(0.612635\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.8829 | − | 6.16964i | 0.0893448 | − | 0.0463882i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −232.188 | −1.69481 | −0.847403 | − | 0.530951i | \(-0.821835\pi\) | ||||
−0.847403 | + | 0.530951i | \(0.821835\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.1914 | + | 22.8482i | 0.0949022 | + | 0.164375i | 0.909568 | − | 0.415556i | \(-0.136413\pi\) |
−0.814666 | + | 0.579931i | \(0.803080\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −153.661 | − | 88.7161i | −1.07455 | − | 0.620392i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 19.8775i | − | 0.137086i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −100.867 | −0.676959 | −0.338479 | − | 0.940974i | \(-0.609913\pi\) | ||||
−0.338479 | + | 0.940974i | \(0.609913\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −201.351 | + | 116.250i | −1.33345 | + | 0.769868i | −0.985827 | − | 0.167765i | \(-0.946345\pi\) |
−0.347624 | + | 0.937634i | \(0.613012\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.3867 | − | 11.1929i | −0.125076 | − | 0.0722124i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 197.395 | 1.25729 | 0.628647 | − | 0.777691i | \(-0.283609\pi\) | ||||
0.628647 | + | 0.777691i | \(0.283609\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.36433 | + | 14.4875i | −0.0519524 | + | 0.0899842i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −238.025 | −1.46027 | −0.730137 | − | 0.683301i | \(-0.760544\pi\) | ||||
−0.730137 | + | 0.683301i | \(0.760544\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −217.700 | + | 125.689i | −1.30360 | + | 0.752631i | −0.981019 | − | 0.193912i | \(-0.937882\pi\) |
−0.322576 | + | 0.946543i | \(0.604549\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −47.5970 | + | 82.4404i | −0.281639 | + | 0.487813i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −238.033 | − | 137.428i | −1.37591 | − | 0.794384i | −0.384249 | − | 0.923229i | \(-0.625540\pi\) |
−0.991665 | + | 0.128845i | \(0.958873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.7707 | + | 27.3156i | 0.0901182 | + | 0.156089i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 106.008i | − | 0.592221i | −0.955154 | − | 0.296111i | \(-0.904310\pi\) | ||
0.955154 | − | 0.296111i | \(-0.0956897\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 155.686 | + | 89.8854i | 0.860144 | + | 0.496604i | 0.864061 | − | 0.503388i | \(-0.167913\pi\) |
−0.00391638 | + | 0.999992i | \(0.501247\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 165.448i | − | 0.894314i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 56.2649 | − | 97.4536i | 0.300882 | − | 0.521142i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 60.2220 | + | 104.308i | 0.315298 | + | 0.546113i | 0.979501 | − | 0.201440i | \(-0.0645621\pi\) |
−0.664203 | + | 0.747553i | \(0.731229\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 117.258i | 0.607555i | 0.952743 | + | 0.303778i | \(0.0982480\pi\) | ||||
−0.952743 | + | 0.303778i | \(0.901752\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −216.141 | −1.09716 | −0.548581 | − | 0.836098i | \(-0.684832\pi\) | ||||
−0.548581 | + | 0.836098i | \(0.684832\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 129.858 | − | 224.920i | 0.652551 | − | 1.13025i | −0.329950 | − | 0.943998i | \(-0.607032\pi\) |
0.982502 | − | 0.186254i | \(-0.0596347\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.45240 | + | 0.838545i | −0.00715469 | + | 0.00413076i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 630.115i | − | 3.07373i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 348.266 | − | 180.821i | 1.66634 | − | 0.865174i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 41.9123i | 0.198636i | 0.995056 | + | 0.0993182i | \(0.0316662\pi\) | ||||
−0.995056 | + | 0.0993182i | \(0.968334\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 45.5059 | − | 78.8185i | 0.211655 | − | 0.366598i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.88872i | 0.00870379i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 40.5375 | + | 23.4044i | 0.183428 | + | 0.105902i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −91.4323 | − | 52.7885i | −0.410010 | − | 0.236720i | 0.280784 | − | 0.959771i | \(-0.409406\pi\) |
−0.690794 | + | 0.723051i | \(0.742739\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 384.737 | − | 222.128i | 1.69488 | − | 0.978537i | 0.744403 | − | 0.667730i | \(-0.232734\pi\) |
0.950473 | − | 0.310807i | \(-0.100599\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 118.302 | − | 204.906i | 0.516604 | − | 0.894784i | −0.483210 | − | 0.875504i | \(-0.660529\pi\) |
0.999814 | − | 0.0192797i | \(-0.00613729\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 85.0481 | + | 147.308i | 0.365013 | + | 0.632222i | 0.988778 | − | 0.149390i | \(-0.0477310\pi\) |
−0.623765 | + | 0.781612i | \(0.714398\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 257.465 | 1.09559 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −221.528 | + | 383.698i | −0.926896 | + | 1.60543i | −0.138413 | + | 0.990375i | \(0.544200\pi\) |
−0.788483 | + | 0.615057i | \(0.789133\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 153.683i | − | 0.637690i | −0.947807 | − | 0.318845i | \(-0.896705\pi\) | ||
0.947807 | − | 0.318845i | \(-0.103295\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −202.555 | + | 350.836i | −0.826757 | + | 1.43198i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 75.2158 | + | 144.867i | 0.304518 | + | 0.586507i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 84.3664 | − | 146.127i | 0.336121 | − | 0.582179i | −0.647578 | − | 0.761999i | \(-0.724218\pi\) |
0.983700 | + | 0.179820i | \(0.0575515\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −245.144 | + | 424.602i | −0.968950 | + | 1.67827i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −279.805 | + | 161.545i | −1.08873 | + | 0.628581i | −0.933239 | − | 0.359256i | \(-0.883030\pi\) |
−0.155495 | + | 0.987837i | \(0.549697\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.0889 | + | 6.97953i | −0.0466753 | + | 0.0269480i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 107.182 | − | 185.645i | 0.407537 | − | 0.705875i | −0.587076 | − | 0.809532i | \(-0.699721\pi\) |
0.994613 | + | 0.103657i | \(0.0330544\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −641.885 | − | 370.593i | −2.42221 | − | 1.39846i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 339.682 | − | 196.116i | 1.26276 | − | 0.729054i | 0.289152 | − | 0.957283i | \(-0.406627\pi\) |
0.973608 | + | 0.228229i | \(0.0732935\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −89.8653 | − | 155.651i | −0.331606 | − | 0.574359i | 0.651221 | − | 0.758888i | \(-0.274257\pi\) |
−0.982827 | + | 0.184529i | \(0.940924\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 462.212 | + | 800.574i | 1.68077 | + | 2.91118i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 112.854 | + | 195.468i | 0.407414 | + | 0.705662i | 0.994599 | − | 0.103791i | \(-0.0330973\pi\) |
−0.587185 | + | 0.809453i | \(0.699764\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 138.809i | − | 0.493982i | −0.969018 | − | 0.246991i | \(-0.920558\pi\) | ||
0.969018 | − | 0.246991i | \(-0.0794418\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 45.9017 | 0.162197 | 0.0810984 | − | 0.996706i | \(-0.474157\pi\) | ||||
0.0810984 | + | 0.996706i | \(0.474157\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −46.0411 | + | 26.5818i | −0.160422 | + | 0.0926196i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 129.657 | − | 224.572i | 0.448639 | − | 0.777065i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −357.501 | − | 206.404i | −1.22014 | − | 0.704449i | −0.255193 | − | 0.966890i | \(-0.582139\pi\) |
−0.964948 | + | 0.262441i | \(0.915472\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 764.607i | 2.59189i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −176.621 | − | 101.972i | −0.590705 | − | 0.341044i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.67878 | −0.0255109 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 84.2343 | 0.276178 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 48.2502 | − | 27.8573i | 0.157167 | − | 0.0907403i | −0.419354 | − | 0.907823i | \(-0.637743\pi\) |
0.576521 | + | 0.817083i | \(0.304410\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −143.848 | + | 249.152i | −0.462534 | + | 0.801133i | −0.999086 | − | 0.0427343i | \(-0.986393\pi\) |
0.536552 | + | 0.843867i | \(0.319726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 507.327 | 1.62085 | 0.810426 | − | 0.585841i | \(-0.199236\pi\) | ||||
0.810426 | + | 0.585841i | \(0.199236\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 50.1009i | 0.158047i | 0.996873 | + | 0.0790235i | \(0.0251802\pi\) | ||||
−0.996873 | + | 0.0790235i | \(0.974820\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −42.5674 | + | 24.5763i | −0.133440 | + | 0.0770417i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −91.8767 | + | 47.7029i | −0.284448 | + | 0.147687i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −333.013 | + | 192.265i | −1.02465 | + | 0.591585i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.8613 | − | 18.8124i | −0.0330131 | − | 0.0571804i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 269.005 | − | 155.310i | 0.812705 | − | 0.469215i | −0.0351896 | − | 0.999381i | \(-0.511204\pi\) |
0.847894 | + | 0.530165i | \(0.177870\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −116.446 | + | 67.2301i | −0.347600 | + | 0.200687i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.2347i | 0.0926845i | 0.998926 | + | 0.0463423i | \(0.0147565\pi\) | ||||
−0.998926 | + | 0.0463423i | \(0.985244\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 55.3552i | 0.162332i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 68.7094 | 0.200319 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −369.111 | −1.06372 | −0.531861 | − | 0.846832i | \(-0.678507\pi\) | ||||
−0.531861 | + | 0.846832i | \(0.678507\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 182.826 | + | 316.663i | 0.523856 | + | 0.907345i | 0.999614 | + | 0.0277692i | \(0.00884035\pi\) |
−0.475758 | + | 0.879576i | \(0.657826\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −289.028 | − | 500.611i | −0.818776 | − | 1.41816i | −0.906584 | − | 0.422025i | \(-0.861319\pi\) |
0.0878078 | − | 0.996137i | \(-0.472014\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 560.389 | − | 323.541i | 1.57856 | − | 0.911382i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −311.123 | − | 538.882i | −0.866639 | − | 1.50106i | −0.865410 | − | 0.501064i | \(-0.832942\pi\) |
−0.00122868 | − | 0.999999i | \(-0.500391\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −359.558 | − | 32.2344i | −0.996005 | − | 0.0892921i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 331.458 | + | 574.102i | 0.908104 | + | 1.57288i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 242.198 | 0.659940 | 0.329970 | − | 0.943991i | \(-0.392961\pi\) | ||||
0.329970 | + | 0.943991i | \(0.392961\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 62.5348i | 0.168557i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −290.835 | − | 167.914i | −0.779718 | − | 0.450170i | 0.0566124 | − | 0.998396i | \(-0.481970\pi\) |
−0.836330 | + | 0.548226i | \(0.815303\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.2229 | − | 17.7067i | −0.0271166 | − | 0.0469673i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 83.3649i | 0.219960i | 0.993934 | + | 0.109980i | \(0.0350787\pi\) | ||||
−0.993934 | + | 0.109980i | \(0.964921\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.6495i | 0.0852467i | 0.999091 | + | 0.0426234i | \(0.0135715\pi\) | ||||
−0.999091 | + | 0.0426234i | \(0.986428\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 60.7791 | − | 105.272i | 0.157868 | − | 0.273435i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 253.262 | 0.651058 | 0.325529 | − | 0.945532i | \(-0.394458\pi\) | ||||
0.325529 | + | 0.945532i | \(0.394458\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 64.6720 | − | 112.015i | 0.165402 | − | 0.286484i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 654.568 | + | 377.915i | 1.65714 | + | 0.956747i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 131.950 | + | 228.543i | 0.332367 | + | 0.575676i | 0.982975 | − | 0.183737i | \(-0.0588195\pi\) |
−0.650609 | + | 0.759413i | \(0.725486\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 744.298i | − | 1.85610i | −0.372450 | − | 0.928052i | \(-0.621482\pi\) | ||
0.372450 | − | 0.928052i | \(-0.378518\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.0260 | −0.0571364 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −354.305 | + | 204.558i | −0.870529 | + | 0.502600i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −40.6985 | + | 23.4973i | −0.0995074 | + | 0.0574506i | −0.548928 | − | 0.835870i | \(-0.684964\pi\) |
0.449420 | + | 0.893320i | \(0.351631\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 55.8681 | − | 32.2555i | 0.135274 | − | 0.0781004i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −263.347 | − | 456.130i | −0.634571 | − | 1.09911i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.3570 | − | 61.2401i | 0.0843842 | − | 0.146158i | −0.820744 | − | 0.571295i | \(-0.806441\pi\) |
0.905129 | + | 0.425138i | \(0.139774\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 110.483 | + | 63.7872i | 0.262429 | + | 0.151513i | 0.625442 | − | 0.780271i | \(-0.284919\pi\) |
−0.363013 | + | 0.931784i | \(0.618252\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −121.937 | − | 211.201i | −0.286911 | − | 0.496944i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.55348 | − | 6.15481i | −0.00832197 | − | 0.0144141i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 541.149 | + | 312.432i | 1.25557 | + | 0.724901i | 0.972209 | − | 0.234113i | \(-0.0752187\pi\) |
0.283357 | + | 0.959015i | \(0.408552\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 78.5687 | + | 45.3617i | 0.181452 | + | 0.104761i | 0.587975 | − | 0.808879i | \(-0.299925\pi\) |
−0.406523 | + | 0.913641i | \(0.633259\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 400.304 | − | 207.840i | 0.916027 | − | 0.475606i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −130.860 | − | 75.5521i | −0.298087 | − | 0.172101i | 0.343496 | − | 0.939154i | \(-0.388389\pi\) |
−0.641583 | + | 0.767054i | \(0.721722\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −871.228 | −1.96666 | −0.983328 | − | 0.181842i | \(-0.941794\pi\) | ||||
−0.983328 | + | 0.181842i | \(0.941794\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −543.412 | − | 313.739i | −1.22115 | − | 0.705032i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 174.763i | − | 0.389228i | −0.980880 | − | 0.194614i | \(-0.937655\pi\) | ||
0.980880 | − | 0.194614i | \(-0.0623454\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1349.38 | + | 779.067i | −2.99198 | + | 1.72742i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 43.7899 | + | 25.2821i | 0.0962416 | + | 0.0555651i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −370.554 | − | 641.818i | −0.810840 | − | 1.40442i | −0.912277 | − | 0.409574i | \(-0.865677\pi\) |
0.101437 | − | 0.994842i | \(-0.467656\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −282.972 | + | 490.122i | −0.613822 | + | 1.06317i | 0.376768 | + | 0.926308i | \(0.377035\pi\) |
−0.990590 | + | 0.136863i | \(0.956298\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 178.485 | − | 309.146i | 0.385497 | − | 0.667701i | −0.606341 | − | 0.795205i | \(-0.707363\pi\) |
0.991838 | + | 0.127504i | \(0.0406965\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 427.161 | 0.914691 | 0.457345 | − | 0.889289i | \(-0.348800\pi\) | ||||
0.457345 | + | 0.889289i | \(0.348800\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.82469 | + | 5.67229i | 0.0209482 | + | 0.0120944i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −225.052 | −0.475797 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38.0062 | − | 849.579i | 0.0800132 | − | 1.78859i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 329.200 | 0.687266 | 0.343633 | − | 0.939104i | \(-0.388342\pi\) | ||||
0.343633 | + | 0.939104i | \(0.388342\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −85.0895 | − | 147.379i | −0.176901 | − | 0.306402i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 546.864 | + | 315.732i | 1.12756 | + | 0.650994i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 788.052i | 1.61818i | 0.587687 | + | 0.809088i | \(0.300039\pi\) | ||||
−0.587687 | + | 0.809088i | \(0.699961\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 781.176 | 1.59099 | 0.795495 | − | 0.605960i | \(-0.207211\pi\) | ||||
0.795495 | + | 0.605960i | \(0.207211\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.2298 | − | 6.48352i | 0.0227785 | − | 0.0131512i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −47.2807 | − | 27.2975i | −0.0951323 | − | 0.0549246i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 233.501 | 0.467938 | 0.233969 | − | 0.972244i | \(-0.424829\pi\) | ||||
0.233969 | + | 0.972244i | \(0.424829\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −402.390 | + | 696.960i | −0.799980 | + | 1.38561i | 0.119649 | + | 0.992816i | \(0.461823\pi\) |
−0.919628 | + | 0.392789i | \(0.871510\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 709.214 | 1.40438 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 98.8113 | − | 57.0487i | 0.194128 | − | 0.112080i | −0.399785 | − | 0.916609i | \(-0.630915\pi\) |
0.593914 | + | 0.804529i | \(0.297582\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.9655 | − | 48.4377i | 0.0547271 | − | 0.0947901i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −205.287 | − | 118.523i | −0.398616 | − | 0.230141i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −318.327 | − | 551.358i | −0.615719 | − | 1.06646i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 330.381i | − | 0.634130i | −0.948404 | − | 0.317065i | \(-0.897303\pi\) | ||
0.948404 | − | 0.317065i | \(-0.102697\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 223.871 | + | 129.252i | 0.428052 | + | 0.247136i | 0.698517 | − | 0.715594i | \(-0.253844\pi\) |
−0.270464 | + | 0.962730i | \(0.587177\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 14.6034i | − | 0.0277104i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.2737 | + | 29.9189i | −0.0326535 | + | 0.0565575i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −324.067 | − | 561.300i | −0.608005 | − | 1.05310i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1242.98i | 2.32333i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1001.75 | 1.85853 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 307.180 | − | 532.051i | 0.567800 | − | 0.983458i | −0.428983 | − | 0.903312i | \(-0.641128\pi\) |
0.996783 | − | 0.0801456i | \(-0.0255385\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 415.047 | − | 239.628i | 0.761555 | − | 0.439684i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 321.852i | 0.588394i | 0.955745 | + | 0.294197i | \(0.0950522\pi\) | ||||
−0.955745 | + | 0.294197i | \(0.904948\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 45.1731 | + | 2.02083i | 0.0819838 | + | 0.00366758i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 63.7704i | − | 0.115317i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 257.207 | − | 445.496i | 0.461772 | − | 0.799813i | −0.537277 | − | 0.843406i | \(-0.680547\pi\) |
0.999049 | + | 0.0435927i | \(0.0138804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 93.6143i | − | 0.167467i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −378.199 | − | 218.353i | −0.671756 | − | 0.387839i | 0.124986 | − | 0.992159i | \(-0.460112\pi\) |
−0.796742 | + | 0.604320i | \(0.793445\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 494.009 | + | 285.216i | 0.874353 | + | 0.504808i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −734.219 | + | 423.901i | −1.29037 | + | 0.744994i | −0.978719 | − | 0.205204i | \(-0.934214\pi\) |
−0.311648 | + | 0.950198i | \(0.600881\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −393.820 | + | 682.116i | −0.689702 | + | 1.19460i | 0.282232 | + | 0.959346i | \(0.408925\pi\) |
−0.971934 | + | 0.235253i | \(0.924408\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 531.275 | + | 920.196i | 0.923957 | + | 1.60034i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 291.421 | 0.505062 | 0.252531 | − | 0.967589i | \(-0.418737\pi\) | ||||
0.252531 | + | 0.967589i | \(0.418737\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.2189 | + | 38.4843i | −0.0382425 | + | 0.0662380i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1832.79i | 3.14372i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 449.526 | − | 778.603i | 0.765803 | − | 1.32641i | −0.174018 | − | 0.984743i | \(-0.555675\pi\) |
0.939821 | − | 0.341667i | \(-0.110992\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.4077 | − | 42.9198i | 0.0465326 | − | 0.0728690i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −272.320 | + | 471.672i | −0.459224 | + | 0.795400i | −0.998920 | − | 0.0464601i | \(-0.985206\pi\) |
0.539696 | + | 0.841860i | \(0.318539\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.0342 | + | 27.7721i | −0.0269483 | + | 0.0466758i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −372.742 | + | 215.203i | −0.622274 | + | 0.359270i | −0.777754 | − | 0.628569i | \(-0.783641\pi\) |
0.155480 | + | 0.987839i | \(0.450308\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −640.942 | + | 370.048i | −1.06646 | + | 0.615721i | −0.927212 | − | 0.374537i | \(-0.877802\pi\) |
−0.139247 | + | 0.990258i | \(0.544468\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1276.02 | − | 2210.13i | 2.10913 | − | 3.65311i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −452.418 | − | 261.204i | −0.745334 | − | 0.430319i | 0.0786715 | − | 0.996901i | \(-0.474932\pi\) |
−0.824006 | + | 0.566582i | \(0.808266\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 229.347 | − | 132.413i | 0.375363 | − | 0.216716i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −129.627 | − | 224.520i | −0.211463 | − | 0.366264i | 0.740710 | − | 0.671825i | \(-0.234489\pi\) |
−0.952172 | + | 0.305561i | \(0.901156\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.6423 | + | 44.4138i | 0.0415596 | + | 0.0719834i | 0.886057 | − | 0.463576i | \(-0.153434\pi\) |
−0.844497 | + | 0.535560i | \(0.820101\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −338.509 | − | 586.315i | −0.546865 | − | 0.947197i | −0.998487 | − | 0.0549882i | \(-0.982488\pi\) |
0.451622 | − | 0.892209i | \(-0.350845\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 52.9412i | 0.0849778i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 259.420 | 0.415072 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 93.4699 | − | 53.9649i | 0.148601 | − | 0.0857947i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −174.679 | + | 302.553i | −0.276829 | + | 0.479481i | −0.970595 | − | 0.240719i | \(-0.922617\pi\) |
0.693766 | + | 0.720200i | \(0.255950\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 375.873 | + | 217.010i | 0.591926 | + | 0.341748i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 416.695i | 0.654152i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 289.836 | + | 167.337i | 0.452162 | + | 0.261056i | 0.708743 | − | 0.705467i | \(-0.249263\pi\) |
−0.256581 | + | 0.966523i | \(0.582596\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −59.1079 | −0.0919252 | −0.0459626 | − | 0.998943i | \(-0.514636\pi\) | ||||
−0.0459626 | + | 0.998943i | \(0.514636\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −157.684 | −0.243716 | −0.121858 | − | 0.992548i | \(-0.538885\pi\) | ||||
−0.121858 | + | 0.992548i | \(0.538885\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1637.40 | − | 945.352i | 2.52295 | − | 1.45663i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −199.103 | + | 344.856i | −0.304905 | + | 0.528111i | −0.977240 | − | 0.212136i | \(-0.931958\pi\) |
0.672335 | + | 0.740247i | \(0.265291\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 758.271 | 1.15767 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1062.19i | 1.61182i | 0.592041 | + | 0.805908i | \(0.298322\pi\) | ||||
−0.592041 | + | 0.805908i | \(0.701678\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −352.363 | + | 203.437i | −0.533076 | + | 0.307772i | −0.742268 | − | 0.670103i | \(-0.766250\pi\) |
0.209192 | + | 0.977875i | \(0.432917\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −99.2481 | + | 51.5301i | −0.149245 | + | 0.0774889i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.9278 | + | 28.2485i | −0.0733551 | + | 0.0423516i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −104.146 | − | 180.387i | −0.155211 | − | 0.268833i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 376.962 | − | 217.639i | 0.560122 | − | 0.323387i | −0.193072 | − | 0.981185i | \(-0.561845\pi\) |
0.753195 | + | 0.657798i | \(0.228512\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −396.408 | + | 228.866i | −0.585536 | + | 0.338059i | −0.763330 | − | 0.646008i | \(-0.776437\pi\) |
0.177794 | + | 0.984068i | \(0.443104\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 53.2775i | − | 0.0784646i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 332.751i | − | 0.487190i | −0.969877 | − | 0.243595i | \(-0.921673\pi\) | ||
0.969877 | − | 0.243595i | \(-0.0783267\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1939.29 | 2.83107 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −762.380 | −1.10650 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.6760 | + | 73.9170i | 0.0617598 | + | 0.106971i | 0.895252 | − | 0.445560i | \(-0.146995\pi\) |
−0.833492 | + | 0.552531i | \(0.813662\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −110.177 | − | 190.833i | −0.158529 | − | 0.274580i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 355.984 | − | 205.527i | 0.510737 | − | 0.294874i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 264.113 | + | 457.458i | 0.376766 | + | 0.652579i | 0.990590 | − | 0.136865i | \(-0.0437026\pi\) |
−0.613823 | + | 0.789443i | \(0.710369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 375.993 | + | 16.8202i | 0.534841 | + | 0.0239263i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.9187 | − | 51.8206i | −0.0423178 | − | 0.0732965i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1202.26 | −1.69571 | −0.847854 | − | 0.530229i | \(-0.822106\pi\) | ||||
−0.847854 | + | 0.530229i | \(0.822106\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 63.6264i | 0.0892376i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1283.41 | + | 740.975i | 1.79497 | + | 1.03633i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −346.447 | − | 600.064i | −0.481846 | − | 0.834581i | 0.517937 | − | 0.855419i | \(-0.326700\pi\) |
−0.999783 | + | 0.0208376i | \(0.993367\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.9998i | 0.0277390i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 106.523i | 0.146929i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −654.043 | + | 1132.84i | −0.899646 | + | 1.55823i | −0.0716995 | + | 0.997426i | \(0.522842\pi\) |
−0.827947 | + | 0.560807i | \(0.810491\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 59.3714 | 0.0812194 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −216.509 | + | 375.004i | −0.295374 | + | 0.511602i | −0.975072 | − | 0.221890i | \(-0.928777\pi\) |
0.679698 | + | 0.733492i | \(0.262111\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 287.945 | + | 166.245i | 0.390698 | + | 0.225570i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 617.926 | + | 1070.28i | 0.836165 | + | 1.44828i | 0.893078 | + | 0.449901i | \(0.148541\pi\) |
−0.0569131 | + | 0.998379i | \(0.518126\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 947.212i | 1.27485i | 0.770513 | + | 0.637424i | \(0.220000\pi\) | ||||
−0.770513 | + | 0.637424i | \(0.780000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 842.461 | 1.13082 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 90.8217 | − | 52.4359i | 0.121257 | − | 0.0700079i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1219.16 | − | 703.884i | 1.62339 | − | 0.937263i | 0.637382 | − | 0.770548i | \(-0.280017\pi\) |
0.986005 | − | 0.166715i | \(-0.0533160\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1681.73 | − | 970.946i | 2.22745 | − | 1.28602i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −325.685 | − | 564.102i | −0.430231 | − | 0.745182i | 0.566662 | − | 0.823950i | \(-0.308234\pi\) |
−0.996893 | + | 0.0787687i | \(0.974901\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −261.899 | + | 453.622i | −0.344151 | + | 0.596087i | −0.985199 | − | 0.171414i | \(-0.945167\pi\) |
0.641048 | + | 0.767501i | \(0.278500\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.0181 | − | 20.2177i | −0.0458952 | − | 0.0264976i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 393.236 | + | 681.104i | 0.512693 | + | 0.888010i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 92.2444 | + | 159.772i | 0.119954 | + | 0.207766i | 0.919749 | − | 0.392507i | \(-0.128392\pi\) |
−0.799795 | + | 0.600273i | \(0.795059\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −152.283 | − | 87.9206i | −0.197002 | − | 0.113739i | 0.398254 | − | 0.917275i | \(-0.369616\pi\) |
−0.595257 | + | 0.803536i | \(0.702950\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 103.893 | + | 59.9828i | 0.134056 | + | 0.0773971i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1431.98 | + | 64.0603i | 1.83823 | + | 0.0822341i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1385.72 | − | 800.044i | −1.77429 | − | 1.02438i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1648.68 | −2.10024 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −80.0272 | − | 46.2037i | −0.101686 | − | 0.0587087i | 0.448294 | − | 0.893886i | \(-0.352032\pi\) |
−0.549981 | + | 0.835177i | \(0.685365\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 48.1281i | − | 0.0608447i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 75.0350 | − | 43.3215i | 0.0946217 | − | 0.0546299i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 769.440 | + | 444.236i | 0.965420 | + | 0.557385i | 0.897837 | − | 0.440328i | \(-0.145138\pi\) |
0.0675830 | + | 0.997714i | \(0.478471\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 83.9783 | + | 145.455i | 0.105104 | + | 0.182046i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 819.622 | − | 1419.63i | 1.02070 | − | 1.76790i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 69.8607 | − | 121.002i | 0.0867834 | − | 0.150313i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 939.940 | 1.16185 | 0.580927 | − | 0.813956i | \(-0.302690\pi\) | ||||
0.580927 | + | 0.813956i | \(0.302690\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 361.756 | + | 208.860i | 0.446062 | + | 0.257534i | 0.706166 | − | 0.708047i | \(-0.250423\pi\) |
−0.260104 | + | 0.965581i | \(0.583757\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1988.03 | 2.43930 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 174.495 | + | 111.429i | 0.213580 | + | 0.136387i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 560.135 | 0.682260 | 0.341130 | − | 0.940016i | \(-0.389190\pi\) | ||||
0.341130 | + | 0.940016i | \(0.389190\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 623.961 | + | 1080.73i | 0.758154 | + | 1.31316i | 0.943791 | + | 0.330542i | \(0.107232\pi\) |
−0.185637 | + | 0.982618i | \(0.559435\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −496.644 | − | 286.737i | −0.600537 | − | 0.346720i | 0.168716 | − | 0.985665i | \(-0.446038\pi\) |
−0.769253 | + | 0.638945i | \(0.779371\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 921.847i | − | 1.11200i | −0.831183 | − | 0.555999i | \(-0.812336\pi\) | ||
0.831183 | − | 0.555999i | \(-0.187664\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −264.273 | −0.317255 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1818.28 | − | 1049.78i | 2.17758 | − | 1.25723i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 431.746 | + | 249.269i | 0.514596 | + | 0.297102i | 0.734721 | − | 0.678369i | \(-0.237313\pi\) |
−0.220125 | + | 0.975472i | \(0.570646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 835.336 | 0.993265 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 397.540 | − | 688.560i | 0.470462 | − | 0.814864i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −215.319 | −0.254214 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −407.245 | + | 235.123i | −0.478549 | + | 0.276291i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −681.852 | + | 1181.00i | −0.799358 | + | 1.38453i | 0.120677 | + | 0.992692i | \(0.461493\pi\) |
−0.920035 | + | 0.391837i | \(0.871840\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1159.34 | − | 669.347i | −1.35279 | − | 0.781036i | −0.364153 | − | 0.931339i | \(-0.618642\pi\) |
−0.988640 | + | 0.150303i | \(0.951975\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −316.285 | − | 547.822i | −0.368202 | − | 0.637744i | 0.621083 | − | 0.783745i | \(-0.286693\pi\) |
−0.989284 | + | 0.146001i | \(0.953360\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 731.113i | − | 0.847176i | −0.905855 | − | 0.423588i | \(-0.860770\pi\) | ||
0.905855 | − | 0.423588i | \(-0.139230\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1988.10 | + | 1147.83i | 2.29838 | + | 1.32697i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1869.00i | − | 2.15075i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −69.1525 | + | 119.776i | −0.0793944 | + | 0.137515i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −58.1489 | − | 100.717i | −0.0664559 | − | 0.115105i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1157.72i | − | 1.32009i | −0.751224 | − | 0.660047i | \(-0.770536\pi\) | ||
0.751224 | − | 0.660047i | \(-0.229464\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0365 | −0.0204728 | −0.0102364 | − | 0.999948i | \(-0.503258\pi\) | ||||
−0.0102364 | + | 0.999948i | \(0.503258\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 494.516 | − | 856.527i | 0.560041 | − | 0.970019i | −0.437451 | − | 0.899242i | \(-0.644119\pi\) |
0.997492 | − | 0.0707772i | \(-0.0225479\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1048.59 | + | 605.403i | −1.18217 | + | 0.682528i | −0.956516 | − | 0.291678i | \(-0.905786\pi\) |
−0.225657 | + | 0.974207i | \(0.572453\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 36.6189i | − | 0.0411911i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.1750 | + | 585.108i | −0.0293113 | + | 0.655216i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 885.398i | 0.989271i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.18935 | + | 5.52412i | −0.00354767 | + | 0.00614474i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 483.511i | − | 0.536638i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1300.32 | − | 750.742i | −1.43682 | − | 0.829549i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 279.508 | + | 161.374i | 0.308168 | + | 0.177921i | 0.646106 | − | 0.763247i | \(-0.276396\pi\) |
−0.337938 | + | 0.941168i | \(0.609730\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −567.038 | + | 327.380i | −0.622435 | + | 0.359363i | −0.777816 | − | 0.628492i | \(-0.783673\pi\) |
0.155382 | + | 0.987855i | \(0.450339\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −651.198 | + | 1127.91i | −0.713251 | + | 1.23539i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −31.9882 | − | 55.4051i | −0.0348835 | − | 0.0604200i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1299.09 | −1.41359 | −0.706796 | − | 0.707417i | \(-0.749860\pi\) | ||||
−0.706796 | + | 0.707417i | \(0.749860\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 332.792 | − | 576.413i | 0.360555 | − | 0.624500i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 886.635i | 0.958524i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 260.771 | − | 451.669i | 0.280701 | − | 0.486188i | −0.690857 | − | 0.722992i | \(-0.742767\pi\) |
0.971558 | + | 0.236804i | \(0.0760998\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −776.709 | − | 495.990i | −0.834273 | − | 0.532749i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −469.936 | + | 813.953i | −0.502606 | + | 0.870538i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −625.318 | + | 1083.08i | −0.667362 | + | 1.15590i | 0.311277 | + | 0.950319i | \(0.399243\pi\) |
−0.978639 | + | 0.205586i | \(0.934090\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −165.450 | + | 95.5225i | −0.175823 | + | 0.101512i | −0.585329 | − | 0.810796i | \(-0.699035\pi\) |
0.409505 | + | 0.912308i | \(0.365701\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1551.01 | + | 895.476i | −1.64476 | + | 0.949603i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −292.243 | + | 506.180i | −0.308599 | + | 0.534509i | −0.978056 | − | 0.208342i | \(-0.933193\pi\) |
0.669457 | + | 0.742851i | \(0.266527\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 590.519 | + | 340.936i | 0.622254 | + | 0.359258i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −221.454 | + | 127.856i | −0.232375 | + | 0.134162i | −0.611667 | − | 0.791115i | \(-0.709501\pi\) |
0.379292 | + | 0.925277i | \(0.376168\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −502.987 | − | 871.198i | −0.526688 | − | 0.912250i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −81.8100 | − | 141.699i | −0.0853076 | − | 0.147757i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −476.908 | − | 826.029i | −0.496262 | − | 0.859552i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 979.365i | − | 1.01489i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −775.857 | −0.802334 | −0.401167 | − | 0.916005i | \(-0.631395\pi\) | ||||
−0.401167 | + | 0.916005i | \(0.631395\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −618.028 | + | 356.819i | −0.636486 | + | 0.367476i | −0.783260 | − | 0.621695i | \(-0.786445\pi\) |
0.146773 | + | 0.989170i | \(0.453111\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.29581 | + | 16.1008i | −0.00955376 | + | 0.0165476i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 749.812 | + | 432.904i | 0.767463 | + | 0.443095i | 0.831969 | − | 0.554822i | \(-0.187214\pi\) |
−0.0645057 | + | 0.997917i | \(0.520547\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1551.61i | 1.58490i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1367.55 | − | 789.558i | −1.39120 | − | 0.803212i | −0.397756 | − | 0.917491i | \(-0.630211\pi\) |
−0.993449 | + | 0.114279i | \(0.963544\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1805.25 | 1.83274 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −258.679 | −0.261556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 208.038 | − | 120.111i | 0.209927 | − | 0.121202i | −0.391350 | − | 0.920242i | \(-0.627992\pi\) |
0.601278 | + | 0.799040i | \(0.294659\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1084.60 | + | 1878.58i | −1.09005 | + | 1.88802i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −454.623 | −0.455991 | −0.227995 | − | 0.973662i | \(-0.573217\pi\) | ||||
−0.227995 | + | 0.973662i | \(0.573217\pi\) | |||||||
\(998\) | 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 | 2052.3.bl.a.145.3 | 80 | ||
3.2 | odd | 2 | 684.3.bl.a.373.11 | yes | 80 | ||
9.2 | odd | 6 | 684.3.s.a.601.24 | yes | 80 | ||
9.7 | even | 3 | 2052.3.s.a.829.38 | 80 | |||
19.8 | odd | 6 | 2052.3.s.a.901.38 | 80 | |||
57.8 | even | 6 | 684.3.s.a.445.24 | ✓ | 80 | ||
171.65 | even | 6 | 684.3.bl.a.673.11 | yes | 80 | ||
171.160 | odd | 6 | inner | 2052.3.bl.a.1585.3 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.s.a.445.24 | ✓ | 80 | 57.8 | even | 6 | ||
684.3.s.a.601.24 | yes | 80 | 9.2 | odd | 6 | ||
684.3.bl.a.373.11 | yes | 80 | 3.2 | odd | 2 | ||
684.3.bl.a.673.11 | yes | 80 | 171.65 | even | 6 | ||
2052.3.s.a.829.38 | 80 | 9.7 | even | 3 | |||
2052.3.s.a.901.38 | 80 | 19.8 | odd | 6 | |||
2052.3.bl.a.145.3 | 80 | 1.1 | even | 1 | trivial | ||
2052.3.bl.a.1585.3 | 80 | 171.160 | odd | 6 | inner |