Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(1727,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.1727");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.c (of order \(2\), degree \(1\), 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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 3 x^{10} - 12 x^{9} + 73 x^{8} - 12 x^{7} + 589 x^{6} + 84 x^{5} + 2452 x^{4} + 852 x^{3} + \cdots + 9496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{12} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1727.2 | ||
Root | \(2.61836 - 1.60260i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1727 |
Dual form | 1728.4.c.j.1727.11 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 20.8488i | − 1.86477i | −0.361464 | − | 0.932386i | \(-0.617723\pi\) | ||||
0.361464 | − | 0.932386i | \(-0.382277\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.9048i | 0.750791i | 0.926865 | + | 0.375395i | \(0.122493\pi\) | ||||
−0.926865 | + | 0.375395i | \(0.877507\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −34.5116 | −0.945967 | −0.472984 | − | 0.881071i | \(-0.656823\pi\) | ||||
−0.472984 | + | 0.881071i | \(0.656823\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 31.3361 | 0.668544 | 0.334272 | − | 0.942477i | \(-0.391510\pi\) | ||||
0.334272 | + | 0.942477i | \(0.391510\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 34.4719i | − 0.491803i | −0.969295 | − | 0.245902i | \(-0.920916\pi\) | ||||
0.969295 | − | 0.245902i | \(-0.0790840\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 120.723i | 1.45767i | 0.684691 | + | 0.728833i | \(0.259937\pi\) | ||||
−0.684691 | + | 0.728833i | \(0.740063\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 137.155 | 1.24343 | 0.621714 | − | 0.783244i | \(-0.286436\pi\) | ||||
0.621714 | + | 0.783244i | \(0.286436\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −309.672 | −2.47738 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 93.1005i | − 0.596149i | −0.954543 | − | 0.298075i | \(-0.903656\pi\) | ||||
0.954543 | − | 0.298075i | \(-0.0963444\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 111.365i | 0.645217i | 0.946532 | + | 0.322609i | \(0.104560\pi\) | ||||
−0.946532 | + | 0.322609i | \(0.895440\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 289.899 | 1.40005 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 146.680 | 0.651733 | 0.325867 | − | 0.945416i | \(-0.394344\pi\) | ||||
0.325867 | + | 0.945416i | \(0.394344\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.44531i | 0.0321692i | 0.999871 | + | 0.0160846i | \(0.00512011\pi\) | ||||
−0.999871 | + | 0.0160846i | \(0.994880\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 427.523i | 1.51620i | 0.652137 | + | 0.758101i | \(0.273873\pi\) | ||||
−0.652137 | + | 0.758101i | \(0.726127\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −318.826 | −0.989481 | −0.494740 | − | 0.869041i | \(-0.664737\pi\) | ||||
−0.494740 | + | 0.869041i | \(0.664737\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 149.655 | 0.436313 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 291.451i | 0.755357i | 0.925937 | + | 0.377679i | \(0.123278\pi\) | ||||
−0.925937 | + | 0.377679i | \(0.876722\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 719.525i | 1.76401i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −364.665 | −0.804666 | −0.402333 | − | 0.915493i | \(-0.631801\pi\) | ||||
−0.402333 | + | 0.915493i | \(0.631801\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 289.983 | 0.608664 | 0.304332 | − | 0.952566i | \(-0.401567\pi\) | ||||
0.304332 | + | 0.952566i | \(0.401567\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 653.320i | − 1.24668i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 305.907i | 0.557797i | 0.960321 | + | 0.278899i | \(0.0899694\pi\) | ||||
−0.960321 | + | 0.278899i | \(0.910031\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −102.802 | −0.171836 | −0.0859178 | − | 0.996302i | \(-0.527382\pi\) | ||||
−0.0859178 | + | 0.996302i | \(0.527382\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 442.688 | 0.709764 | 0.354882 | − | 0.934911i | \(-0.384521\pi\) | ||||
0.354882 | + | 0.934911i | \(0.384521\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 479.878i | − 0.710224i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 245.350i | − 0.349419i | −0.984620 | − | 0.174709i | \(-0.944101\pi\) | ||||
0.984620 | − | 0.174709i | \(-0.0558986\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 478.981 | 0.633433 | 0.316717 | − | 0.948520i | \(-0.397420\pi\) | ||||
0.316717 | + | 0.948520i | \(0.397420\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −718.697 | −0.917101 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1417.36i | 1.68809i | 0.536273 | + | 0.844045i | \(0.319832\pi\) | ||||
−0.536273 | + | 0.844045i | \(0.680168\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 435.723i | 0.501937i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2516.92 | 2.71822 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1153.69 | 1.20762 | 0.603811 | − | 0.797128i | \(-0.293648\pi\) | ||||
0.603811 | + | 0.797128i | \(0.293648\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 767.096i | − 0.755732i | −0.925860 | − | 0.377866i | \(-0.876658\pi\) | ||||
0.925860 | − | 0.377866i | \(-0.123342\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1202.04i | 1.14991i | 0.818187 | + | 0.574953i | \(0.194979\pi\) | ||||
−0.818187 | + | 0.574953i | \(0.805021\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1309.28 | 1.18292 | 0.591462 | − | 0.806333i | \(-0.298551\pi\) | ||||
0.591462 | + | 0.806333i | \(0.298551\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1102.04 | −0.968407 | −0.484204 | − | 0.874955i | \(-0.660891\pi\) | ||||
−0.484204 | + | 0.874955i | \(0.660891\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 69.9098i | 0.0581997i | 0.999577 | + | 0.0290998i | \(0.00926407\pi\) | ||||
−0.999577 | + | 0.0290998i | \(0.990736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2859.52i | − 2.31871i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 479.326 | 0.369241 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −139.949 | −0.105146 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3850.19i | 2.75497i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2558.29i | − 1.78749i | −0.448574 | − | 0.893746i | \(-0.648068\pi\) | ||||
0.448574 | − | 0.893746i | \(-0.351932\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 86.6249 | 0.0577744 | 0.0288872 | − | 0.999583i | \(-0.490804\pi\) | ||||
0.0288872 | + | 0.999583i | \(0.490804\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1678.63 | −1.09440 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 699.734i | − 0.436367i | −0.975908 | − | 0.218184i | \(-0.929987\pi\) | ||||
0.975908 | − | 0.218184i | \(-0.0700131\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 789.049i | 0.481484i | 0.970589 | + | 0.240742i | \(0.0773908\pi\) | ||||
−0.970589 | + | 0.240742i | \(0.922609\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1081.46 | −0.632421 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1941.03 | −1.11168 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1593.12i | − 0.875930i | −0.898992 | − | 0.437965i | \(-0.855699\pi\) | ||||
0.898992 | − | 0.437965i | \(-0.144301\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 1502.12i | − 0.809544i | −0.914418 | − | 0.404772i | \(-0.867351\pi\) | ||||
0.914418 | − | 0.404772i | \(-0.132649\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2321.82 | 1.20318 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3596.08 | 1.82802 | 0.914008 | − | 0.405696i | \(-0.132971\pi\) | ||||
0.914008 | + | 0.405696i | \(0.132971\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1907.12i | 0.933555i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 3313.82i | − 1.59238i | −0.605044 | − | 0.796192i | \(-0.706844\pi\) | ||||
0.605044 | − | 0.796192i | \(-0.293156\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 487.046 | 0.225681 | 0.112841 | − | 0.993613i | \(-0.464005\pi\) | ||||
0.112841 | + | 0.993613i | \(0.464005\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1215.05 | −0.553049 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1752.30i | − 0.770086i | −0.922899 | − | 0.385043i | \(-0.874187\pi\) | ||||
0.922899 | − | 0.385043i | \(-0.125813\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 4305.94i | − 1.85999i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2807.62 | 1.17236 | 0.586178 | − | 0.810182i | \(-0.300632\pi\) | ||||
0.586178 | + | 0.810182i | \(0.300632\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2307.37 | 0.947546 | 0.473773 | − | 0.880647i | \(-0.342892\pi\) | ||||
0.473773 | + | 0.880647i | \(0.342892\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 3058.11i | − 1.21533i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1189.68i | 0.465230i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3375.74 | 1.27885 | 0.639425 | − | 0.768854i | \(-0.279173\pi\) | ||||
0.639425 | + | 0.768854i | \(0.279173\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 561.917 | 0.209573 | 0.104787 | − | 0.994495i | \(-0.466584\pi\) | ||||
0.104787 | + | 0.994495i | \(0.466584\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 16.7420i | − 0.00605491i | −0.999995 | − | 0.00302746i | \(-0.999036\pi\) | ||||
0.999995 | − | 0.00302746i | \(-0.000963671\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2760.01i | 0.983176i | 0.870828 | + | 0.491588i | \(0.163583\pi\) | ||||
−0.870828 | + | 0.491588i | \(0.836417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1294.55 | 0.447583 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 176.075 | 0.0599882 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 4166.33i | − 1.37890i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2766.47i | − 0.902615i | −0.892368 | − | 0.451308i | \(-0.850958\pi\) | ||||
0.892368 | − | 0.451308i | \(-0.149042\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8913.34 | 2.82737 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1548.51 | −0.484423 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1080.21i | − 0.328792i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 110.636i | − 0.0332231i | −0.999862 | − | 0.0166115i | \(-0.994712\pi\) | ||||
0.999862 | − | 0.0166115i | \(-0.00528786\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1800.57 | 0.526468 | 0.263234 | − | 0.964732i | \(-0.415211\pi\) | ||||
0.263234 | + | 0.964732i | \(0.415211\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1491.95 | 0.430528 | 0.215264 | − | 0.976556i | \(-0.430939\pi\) | ||||
0.215264 | + | 0.976556i | \(0.430939\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4545.75i | 1.27812i | 0.769157 | + | 0.639060i | \(0.220676\pi\) | ||||
−0.769157 | + | 0.639060i | \(0.779324\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6647.14i | 1.84516i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3305.97 | −0.894751 | −0.447376 | − | 0.894346i | \(-0.647641\pi\) | ||||
−0.447376 | + | 0.894346i | \(0.647641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2337.95 | −0.624898 | −0.312449 | − | 0.949934i | \(-0.601149\pi\) | ||||
−0.312449 | + | 0.949934i | \(0.601149\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3120.13i | − 0.813624i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3782.97i | 0.974514i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3625.36 | −0.911675 | −0.455838 | − | 0.890063i | \(-0.650660\pi\) | ||||
−0.455838 | + | 0.890063i | \(0.650660\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4733.45 | −1.17624 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2124.02i | 0.515537i | 0.966207 | + | 0.257768i | \(0.0829871\pi\) | ||||
−0.966207 | + | 0.257768i | \(0.917013\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2039.57i | 0.489315i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4785.87 | 1.12209 | 0.561044 | − | 0.827786i | \(-0.310400\pi\) | ||||
0.561044 | + | 0.827786i | \(0.310400\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6076.41 | 1.40857 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 241.884i | − 0.0548249i | −0.999624 | − | 0.0274125i | \(-0.991273\pi\) | ||||
0.999624 | − | 0.0274125i | \(-0.00872675\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 828.799i | − 0.185778i | −0.995676 | − | 0.0928892i | \(-0.970390\pi\) | ||||
0.995676 | − | 0.0928892i | \(-0.0296102\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10687.3 | 2.34352 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5897.19 | 1.27916 | 0.639581 | − | 0.768724i | \(-0.279108\pi\) | ||||
0.639581 | + | 0.768724i | \(0.279108\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3055.95i | 0.648763i | 0.945926 | + | 0.324382i | \(0.105156\pi\) | ||||
−0.945926 | + | 0.324382i | \(0.894844\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 196.045i | 0.0411790i | 0.999788 | + | 0.0205895i | \(0.00655430\pi\) | ||||
−0.999788 | + | 0.0205895i | \(0.993446\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −117.431 | −0.0241523 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3724.69 | 0.758130 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8748.98i | 1.74444i | 0.489114 | + | 0.872220i | \(0.337320\pi\) | ||||
−0.489114 | + | 0.872220i | \(0.662680\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7602.82i | 1.50052i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4297.91 | 0.831287 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5944.65 | −1.13835 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 6045.79i | − 1.13502i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2095.99i | − 0.389656i | −0.980837 | − | 0.194828i | \(-0.937585\pi\) | ||||
0.980837 | − | 0.194828i | \(-0.0624149\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3393.74 | 0.618783 | 0.309391 | − | 0.950935i | \(-0.399875\pi\) | ||||
0.309391 | + | 0.950935i | \(0.399875\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3579.49 | 0.646405 | 0.323203 | − | 0.946330i | \(-0.395240\pi\) | ||||
0.323203 | + | 0.946330i | \(0.395240\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4356.56i | 0.771889i | 0.922522 | + | 0.385945i | \(0.126124\pi\) | ||||
−0.922522 | + | 0.385945i | \(0.873876\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3213.05i | 0.563937i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4161.53 | 0.716885 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9703.91 | −1.65623 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 4433.23i | − 0.742893i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9191.99i | 1.52640i | 0.646164 | + | 0.763198i | \(0.276372\pi\) | ||||
−0.646164 | + | 0.763198i | \(0.723628\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6377.78 | 1.04017 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1663.33 | 0.268865 | 0.134432 | − | 0.990923i | \(-0.457079\pi\) | ||||
0.134432 | + | 0.990923i | \(0.457079\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 3843.38i | − 0.610354i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6850.30i | 1.07837i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9668.26 | 1.49573 | 0.747866 | − | 0.663850i | \(-0.231078\pi\) | ||||
0.747866 | + | 0.663850i | \(0.231078\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9928.24 | −1.52277 | −0.761384 | − | 0.648301i | \(-0.775480\pi\) | ||||
−0.761384 | + | 0.648301i | \(0.775480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4460.01i | 0.672471i | 0.941778 | + | 0.336236i | \(0.109154\pi\) | ||||
−0.941778 | + | 0.336236i | \(0.890846\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2143.29i | 0.320434i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2158.32 | 0.317303 | 0.158652 | − | 0.987335i | \(-0.449285\pi\) | ||||
0.158652 | + | 0.987335i | \(0.449285\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7714.95 | −1.12479 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 9229.52i | − 1.32355i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1156.43i | 0.164482i | 0.996612 | + | 0.0822411i | \(0.0262078\pi\) | ||||
−0.996612 | + | 0.0822411i | \(0.973792\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4052.59 | −0.567115 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6286.39 | 0.872647 | 0.436323 | − | 0.899790i | \(-0.356280\pi\) | ||||
0.436323 | + | 0.899790i | \(0.356280\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 2917.41i | − 0.398552i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 6921.76i | − 0.938119i | −0.883167 | − | 0.469059i | \(-0.844593\pi\) | ||||
0.883167 | − | 0.469059i | \(-0.155407\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1802.67 | −0.240502 | −0.120251 | − | 0.992744i | \(-0.538370\pi\) | ||||
−0.120251 | + | 0.992744i | \(0.538370\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10004.9 | −1.32441 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4421.02i | 0.576233i | 0.957595 | + | 0.288117i | \(0.0930291\pi\) | ||||
−0.957595 | + | 0.288117i | \(0.906971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 4728.00i | − 0.611522i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5115.26 | −0.651586 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13769.8 | 1.74077 | 0.870383 | − | 0.492375i | \(-0.163871\pi\) | ||||
0.870383 | + | 0.492375i | \(0.163871\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13534.1i | 1.68544i | 0.538350 | + | 0.842722i | \(0.319048\pi\) | ||||
−0.538350 | + | 0.842722i | \(0.680952\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3489.74i | 0.431356i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5062.18 | −0.616518 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7230.24 | 0.874114 | 0.437057 | − | 0.899434i | \(-0.356021\pi\) | ||||
0.437057 | + | 0.899434i | \(0.356021\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 5070.61i | − 0.604136i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 9986.16i | − 1.18121i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9066.85 | −1.05715 | −0.528574 | − | 0.848887i | \(-0.677273\pi\) | ||||
−0.528574 | + | 0.848887i | \(0.677273\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6017.63 | −0.696630 | −0.348315 | − | 0.937378i | \(-0.613246\pi\) | ||||
−0.348315 | + | 0.937378i | \(0.613246\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10675.0i | 1.21838i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4032.17i | 0.456979i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10533.7 | 1.17724 | 0.588619 | − | 0.808410i | \(-0.299672\pi\) | ||||
0.588619 | + | 0.808410i | \(0.299672\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −79.2056 | −0.00879071 | −0.00439536 | − | 0.999990i | \(-0.501399\pi\) | ||||
−0.00439536 | + | 0.999990i | \(0.501399\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16557.7i | 1.81250i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 9484.31i | − 1.03112i | −0.856854 | − | 0.515560i | \(-0.827584\pi\) | ||||
0.856854 | − | 0.515560i | \(-0.172416\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9734.58 | −1.04403 | −0.522013 | − | 0.852937i | \(-0.674819\pi\) | ||||
−0.522013 | + | 0.852937i | \(0.674819\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29550.3 | 3.14790 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 9270.01i | − 0.974340i | −0.873307 | − | 0.487170i | \(-0.838029\pi\) | ||||
0.873307 | − | 0.487170i | \(-0.161971\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 291.461i | − 0.0304310i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9084.31 | 0.935997 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2542.86 | −0.260285 | −0.130142 | − | 0.991495i | \(-0.541543\pi\) | ||||
−0.130142 | + | 0.991495i | \(0.541543\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10664.8i | 1.07746i | 0.842479 | + | 0.538729i | \(0.181095\pi\) | ||||
−0.842479 | + | 0.538729i | \(0.818905\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1963.48i | 0.197086i | 0.995133 | + | 0.0985428i | \(0.0314181\pi\) | ||||
−0.995133 | + | 0.0985428i | \(0.968582\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19778.8 | 1.95986 | 0.979928 | − | 0.199350i | \(-0.0638829\pi\) | ||||
0.979928 | + | 0.199350i | \(0.0638829\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4253.58 | −0.418789 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 14754.5i | − 1.43428i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 37384.4i | − 3.61119i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16062.6 | −1.53219 | −0.766095 | − | 0.642728i | \(-0.777803\pi\) | ||||
−0.766095 | + | 0.642728i | \(0.777803\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4596.39 | 0.435712 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 24053.0i | − 2.25194i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 15907.5i | − 1.48016i | −0.672519 | − | 0.740080i | \(-0.734788\pi\) | ||||
0.672519 | − | 0.740080i | \(-0.265212\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5924.49 | −0.544538 | −0.272269 | − | 0.962221i | \(-0.587774\pi\) | ||||
−0.272269 | + | 0.962221i | \(0.587774\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3209.35 | −0.293188 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 1429.44i | − 0.129013i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 5331.33i | − 0.478283i | −0.970985 | − | 0.239142i | \(-0.923134\pi\) | ||||
0.970985 | − | 0.239142i | \(-0.0768660\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2144.13 | −0.190064 | −0.0950319 | − | 0.995474i | \(-0.530295\pi\) | ||||
−0.0950319 | + | 0.995474i | \(0.530295\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15993.0 | −1.40927 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 14329.9i | − 1.24786i | −0.781481 | − | 0.623929i | \(-0.785535\pi\) | ||||
0.781481 | − | 0.623929i | \(-0.214465\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6155.51i | 0.532884i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25061.0 | 2.14431 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11003.2 | 0.936016 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 10822.8i | − 0.910087i | −0.890469 | − | 0.455043i | \(-0.849624\pi\) | ||||
0.890469 | − | 0.455043i | \(-0.150376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12111.8i | 1.01265i | 0.862344 | + | 0.506323i | \(0.168995\pi\) | ||||
−0.862344 | + | 0.506323i | \(0.831005\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3838.96 | 0.317320 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6644.58 | 0.546115 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 264.643i | 0.0215065i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 27296.9i | − 2.20588i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5164.85 | −0.412738 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22063.1 | −1.75336 | −0.876681 | − | 0.481073i | \(-0.840247\pi\) | ||||
−0.876681 | + | 0.481073i | \(0.840247\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22976.2i | 1.80586i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17842.7i | 1.39470i | 0.716731 | + | 0.697350i | \(0.245637\pi\) | ||||
−0.716731 | + | 0.697350i | \(0.754363\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11239.3 | 0.868987 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3411.56 | 0.262340 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10942.0i | 0.832365i | 0.909281 | + | 0.416183i | \(0.136632\pi\) | ||||
−0.909281 | + | 0.416183i | \(0.863368\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13396.9i | 1.01365i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1991.56 | −0.149084 | −0.0745418 | − | 0.997218i | \(-0.523749\pi\) | ||||
−0.0745418 | + | 0.997218i | \(0.523749\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1457.53 | 0.108529 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 12048.3i | − 0.887684i | −0.896105 | − | 0.443842i | \(-0.853615\pi\) | ||||
0.896105 | − | 0.443842i | \(-0.146385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 24916.7i | − 1.82615i | −0.407792 | − | 0.913075i | \(-0.633701\pi\) | ||||
0.407792 | − | 0.913075i | \(-0.366299\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −42473.2 | −3.08044 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17705.3 | −1.27743 | −0.638717 | − | 0.769441i | \(-0.720535\pi\) | ||||
−0.638717 | + | 0.769441i | \(0.720535\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6660.15i | 0.475576i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 10058.5i | − 0.714543i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22453.6 | −1.57880 | −0.789402 | − | 0.613876i | \(-0.789609\pi\) | ||||
−0.789402 | + | 0.613876i | \(0.789609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13444.3 | −0.940511 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 26839.1i | − 1.85860i | −0.369328 | − | 0.929299i | \(-0.620412\pi\) | ||||
0.369328 | − | 0.929299i | \(-0.379588\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 9993.36i | − 0.688551i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9254.44 | 0.631262 | 0.315631 | − | 0.948882i | \(-0.397784\pi\) | ||||
0.315631 | + | 0.948882i | \(0.397784\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1102.45 | 0.0748250 | 0.0374125 | − | 0.999300i | \(-0.488088\pi\) | ||||
0.0374125 | + | 0.999300i | \(0.488088\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2917.77i | 0.196073i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21383.2i | 1.42985i | 0.699202 | + | 0.714924i | \(0.253539\pi\) | ||||
−0.699202 | + | 0.714924i | \(0.746461\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9990.77 | −0.661511 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19769.0 | −1.30255 | −0.651274 | − | 0.758843i | \(-0.725765\pi\) | ||||
−0.651274 | + | 0.758843i | \(0.725765\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 2702.48i | − 0.176333i | −0.996106 | − | 0.0881667i | \(-0.971899\pi\) | ||||
0.996106 | − | 0.0881667i | \(-0.0281008\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6967.79i | 0.452438i | 0.974076 | + | 0.226219i | \(0.0726365\pi\) | ||||
−0.974076 | + | 0.226219i | \(0.927364\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19708.2 | −1.26740 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 41562.7 | 2.66001 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 5056.35i | − 0.320524i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19202.4i | 1.21147i | 0.795667 | + | 0.605734i | \(0.207120\pi\) | ||||
−0.795667 | + | 0.605734i | \(0.792880\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −53337.2 | −3.33326 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4689.61 | 0.291694 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23580.8i | 1.45302i | 0.687155 | + | 0.726511i | \(0.258860\pi\) | ||||
−0.687155 | + | 0.726511i | \(0.741140\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25167.2i | 1.54354i | 0.635899 | + | 0.771772i | \(0.280629\pi\) | ||||
−0.635899 | + | 0.771772i | \(0.719371\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2247.67 | −0.136577 | −0.0682883 | − | 0.997666i | \(-0.521754\pi\) | ||||
−0.0682883 | + | 0.997666i | \(0.521754\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12585.2 | 0.761188 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 11278.6i | − 0.675906i | −0.941163 | − | 0.337953i | \(-0.890266\pi\) | ||||
0.941163 | − | 0.337953i | \(-0.109734\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1806.02i | − 0.107736i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 658.636 | 0.0389329 | 0.0194665 | − | 0.999811i | \(-0.493803\pi\) | ||||
0.0194665 | + | 0.999811i | \(0.493803\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1740.41 | −0.102412 | −0.0512060 | − | 0.998688i | \(-0.516306\pi\) | ||||
−0.0512060 | + | 0.998688i | \(0.516306\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 34997.4i | 2.04081i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 12769.2i | − 0.741269i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10007.8 | −0.575776 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −273.146 | −0.0156449 | −0.00782243 | − | 0.999969i | \(-0.502490\pi\) | ||||
−0.00782243 | + | 0.999969i | \(0.502490\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 11373.1i | − 0.645649i | −0.946459 | − | 0.322824i | \(-0.895368\pi\) | ||||
0.946459 | − | 0.322824i | \(-0.104632\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16041.8i | 0.906671i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1223.56 | 0.0685480 | 0.0342740 | − | 0.999412i | \(-0.489088\pi\) | ||||
0.0342740 | + | 0.999412i | \(0.489088\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14588.6 | −0.813725 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9132.95i | 0.504989i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9247.55i | 0.509108i | 0.967059 | + | 0.254554i | \(0.0819286\pi\) | ||||
−0.967059 | + | 0.254554i | \(0.918071\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16450.7 | 0.897858 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 291.126 | 0.0158209 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14448.0i | 0.778447i | 0.921143 | + | 0.389224i | \(0.127257\pi\) | ||||
−0.921143 | + | 0.389224i | \(0.872743\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17707.6i | 0.950009i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10666.4 | 0.567397 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7819.28 | −0.414188 | −0.207094 | − | 0.978321i | \(-0.566401\pi\) | ||||
−0.207094 | + | 0.978321i | \(0.566401\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15274.3i | 0.802281i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22547.1i | 1.17932i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7251.47 | −0.376126 | −0.188063 | − | 0.982157i | \(-0.560221\pi\) | ||||
−0.188063 | + | 0.982157i | \(0.560221\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16714.1 | −0.863338 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28830.6i | 1.47689i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 6605.59i | − 0.336985i | −0.985703 | − | 0.168492i | \(-0.946110\pi\) | ||||
0.985703 | − | 0.168492i | \(-0.0538899\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14737.5 | 0.745673 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37147.9 | 1.87188 | 0.935942 | − | 0.352155i | \(-0.114551\pi\) | ||||
0.935942 | + | 0.352155i | \(0.114551\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 10557.3i | − 0.527658i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34209.1i | 1.70285i | 0.524479 | + | 0.851423i | \(0.324260\pi\) | ||||
−0.524479 | + | 0.851423i | \(0.675740\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15746.4 | −0.777494 | −0.388747 | − | 0.921345i | \(-0.627092\pi\) | ||||
−0.388747 | + | 0.921345i | \(0.627092\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33214.6 | −1.63341 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18205.3i | 0.888128i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27773.5i | 1.34949i | 0.738049 | + | 0.674747i | \(0.235747\pi\) | ||||
−0.738049 | + | 0.674747i | \(0.764253\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31317.5 | −1.50961 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12694.0 | 0.609471 | 0.304736 | − | 0.952437i | \(-0.401432\pi\) | ||||
0.304736 | + | 0.952437i | \(0.401432\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 18061.4i | − 0.860349i | −0.902746 | − | 0.430175i | \(-0.858452\pi\) | ||||
0.902746 | − | 0.430175i | \(-0.141548\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 15323.7i | − 0.727071i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11427.2 | −0.537955 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32615.8 | 1.52946 | 0.764731 | − | 0.644350i | \(-0.222872\pi\) | ||||
0.764731 | + | 0.644350i | \(0.222872\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8518.40i | 0.396359i | 0.980166 | + | 0.198179i | \(0.0635029\pi\) | ||||
−0.980166 | + | 0.198179i | \(0.936497\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 34486.6i | − 1.59844i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1019.54 | −0.0468919 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3547.86 | 0.162551 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 74973.9i | − 3.40883i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12371.2i | 0.560338i | 0.959951 | + | 0.280169i | \(0.0903906\pi\) | ||||
−0.959951 | + | 0.280169i | \(0.909609\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −972.085 | −0.0436958 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9086.93 | 0.406919 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 37675.0i | − 1.67443i | −0.546877 | − | 0.837213i | \(-0.684184\pi\) | ||||
0.546877 | − | 0.837213i | \(-0.315816\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10990.5i | 0.486630i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15277.9 | −0.671413 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 39761.2 | 1.74087 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41809.2i | 1.81697i | 0.417914 | + | 0.908487i | \(0.362761\pi\) | ||||
−0.417914 | + | 0.908487i | \(0.637239\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19357.2i | 0.838129i | 0.907956 | + | 0.419065i | \(0.137642\pi\) | ||||
−0.907956 | + | 0.419065i | \(0.862358\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −69089.2 | −2.96943 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −51611.7 | −2.21012 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 24774.0i | − 1.05313i | −0.850135 | − | 0.526565i | \(-0.823480\pi\) | ||||
0.850135 | − | 0.526565i | \(-0.176520\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10955.1i | 0.463997i | 0.972716 | + | 0.231999i | \(0.0745265\pi\) | ||||
−0.972716 | + | 0.231999i | \(0.925474\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15446.2 | −0.649475 | −0.324738 | − | 0.945804i | \(-0.605276\pi\) | ||||
−0.324738 | + | 0.945804i | \(0.605276\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4599.69 | −0.192707 | −0.0963533 | − | 0.995347i | \(-0.530718\pi\) | ||||
−0.0963533 | + | 0.995347i | \(0.530718\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 5158.90i | − 0.214580i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 10154.3i | − 0.420844i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26299.3 | −1.08219 | −0.541093 | − | 0.840963i | \(-0.681989\pi\) | ||||
−0.541093 | + | 0.840963i | \(0.681989\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15721.3 | 0.644606 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25332.3i | 1.03131i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1945.97i | − 0.0789426i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20118.0 | 0.810384 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26223.5 | −1.05261 | −0.526305 | − | 0.850296i | \(-0.676423\pi\) | ||||
−0.526305 | + | 0.850296i | \(0.676423\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13156.2i | 0.524396i | 0.965014 | + | 0.262198i | \(0.0844473\pi\) | ||||
−0.965014 | + | 0.262198i | \(0.915553\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 33557.9i | − 1.33292i | −0.745539 | − | 0.666462i | \(-0.767808\pi\) | ||||
0.745539 | − | 0.666462i | \(-0.232192\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16298.7 | 0.642889 | 0.321445 | − | 0.946928i | \(-0.395832\pi\) | ||||
0.321445 | + | 0.946928i | \(0.395832\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36533.3 | −1.43603 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8467.44i | 0.330539i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9585.92i | 0.372912i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −53536.2 | −2.06841 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28884.4 | 1.11215 | 0.556075 | − | 0.831132i | \(-0.312307\pi\) | ||||
0.556075 | + | 0.831132i | \(0.312307\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47233.0i | 1.80626i | 0.429362 | + | 0.903132i | \(0.358738\pi\) | ||||
−0.429362 | + | 0.903132i | \(0.641262\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 12998.5i | − 0.495394i | −0.968838 | − | 0.247697i | \(-0.920326\pi\) | ||||
0.968838 | − | 0.247697i | \(-0.0796738\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16177.5 | 0.612386 | 0.306193 | − | 0.951970i | \(-0.400945\pi\) | ||||
0.306193 | + | 0.951970i | \(0.400945\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35572.6 | 1.34203 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 38489.5i | − 1.44233i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 58535.6i | − 2.18618i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10368.1 | 0.384646 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10046.9 | 0.371487 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 48106.0i | − 1.76696i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41803.5i | 1.53039i | 0.643800 | + | 0.765194i | \(0.277357\pi\) | ||||
−0.643800 | + | 0.765194i | \(0.722643\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25834.2 | −0.939543 | −0.469772 | − | 0.882788i | \(-0.655664\pi\) | ||||
−0.469772 | + | 0.882788i | \(0.655664\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16530.4 | −0.599207 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1204.51i | 0.0433765i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18742.0i | 0.672734i | 0.941731 | + | 0.336367i | \(0.109198\pi\) | ||||
−0.941731 | + | 0.336367i | \(0.890802\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3221.41 | −0.114880 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −45422.8 | −1.61459 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9052.31i | 0.319695i | 0.987142 | + | 0.159847i | \(0.0511002\pi\) | ||||
−0.987142 | + | 0.159847i | \(0.948900\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18066.8i | 0.635999i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24803.4 | 0.867547 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28189.2 | −0.982819 | −0.491409 | − | 0.870929i | \(-0.663518\pi\) | ||||
−0.491409 | + | 0.870929i | \(0.663518\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11490.8i | 0.398074i | 0.979992 | + | 0.199037i | \(0.0637814\pi\) | ||||
−0.979992 | + | 0.199037i | \(0.936219\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1158.32i | 0.0400001i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15309.8 | −0.525344 | −0.262672 | − | 0.964885i | \(-0.584604\pi\) | ||||
−0.262672 | + | 0.964885i | \(0.584604\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13872.1 | 0.474508 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 9896.90i | − 0.336403i | −0.985753 | − | 0.168201i | \(-0.946204\pi\) | ||||
0.985753 | − | 0.168201i | \(-0.0537959\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 70380.1i | − 2.38476i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9729.69 | 0.327620 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17388.9 | 0.583695 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 11715.3i | − 0.390807i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 16779.4i | − 0.558003i | −0.960291 | − | 0.279001i | \(-0.909997\pi\) | ||||
0.960291 | − | 0.279001i | \(-0.0900034\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53400.1 | −1.76487 | −0.882437 | − | 0.470431i | \(-0.844098\pi\) | ||||
−0.882437 | + | 0.470431i | \(0.844098\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10971.6 | −0.361494 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9474.13i | 0.310240i | 0.987896 | + | 0.155120i | \(0.0495764\pi\) | ||||
−0.987896 | + | 0.155120i | \(0.950424\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 48915.4i | − 1.59688i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56693.6 | 1.83952 | 0.919758 | − | 0.392485i | \(-0.128385\pi\) | ||||
0.919758 | + | 0.392485i | \(0.128385\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −349.050 | −0.0112910 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 58637.1i | 1.88529i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 38944.6i | − 1.24835i | −0.781285 | − | 0.624175i | \(-0.785435\pi\) | ||||
0.781285 | − | 0.624175i | \(-0.214565\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 57542.9 | 1.83340 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33995.1 | 1.07987 | 0.539937 | − | 0.841705i | \(-0.318448\pi\) | ||||
0.539937 | + | 0.841705i | \(0.318448\pi\) | |||||||
\(998\) | 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 | 1728.4.c.j.1727.2 | 12 | ||
3.2 | odd | 2 | inner | 1728.4.c.j.1727.12 | 12 | ||
4.3 | odd | 2 | inner | 1728.4.c.j.1727.1 | 12 | ||
8.3 | odd | 2 | 108.4.b.b.107.1 | ✓ | 12 | ||
8.5 | even | 2 | 108.4.b.b.107.11 | yes | 12 | ||
12.11 | even | 2 | inner | 1728.4.c.j.1727.11 | 12 | ||
24.5 | odd | 2 | 108.4.b.b.107.2 | yes | 12 | ||
24.11 | even | 2 | 108.4.b.b.107.12 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.b.b.107.1 | ✓ | 12 | 8.3 | odd | 2 | ||
108.4.b.b.107.2 | yes | 12 | 24.5 | odd | 2 | ||
108.4.b.b.107.11 | yes | 12 | 8.5 | even | 2 | ||
108.4.b.b.107.12 | yes | 12 | 24.11 | even | 2 | ||
1728.4.c.j.1727.1 | 12 | 4.3 | odd | 2 | inner | ||
1728.4.c.j.1727.2 | 12 | 1.1 | even | 1 | trivial | ||
1728.4.c.j.1727.11 | 12 | 12.11 | even | 2 | inner | ||
1728.4.c.j.1727.12 | 12 | 3.2 | odd | 2 | inner |