Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5184,2,Mod(2591,5184)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5184, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5184.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5184 = 2^{6} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5184.f (of order \(2\), degree \(1\), 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: | \(41.3944484078\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8x^{14} + 49x^{12} - 104x^{10} + 160x^{8} - 104x^{6} + 49x^{4} - 8x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{37}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.10 | ||
Root | \(2.04058 + 1.17813i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5184.2591 |
Dual form | 5184.2.f.e.2591.9 |
$q$-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 \(\left(\mathbb{Z}/5184\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 0.206954 | 0.0925526 | 0.0462763 | − | 0.998929i | \(-0.485265\pi\) | ||||
0.0462763 | + | 0.998929i | \(0.485265\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.03957i | 1.14885i | 0.818557 | + | 0.574425i | \(0.194774\pi\) | ||||
−0.818557 | + | 0.574425i | \(0.805226\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5.02319i | − 1.51455i | −0.653096 | − | 0.757275i | \(-0.726530\pi\) | ||||
0.653096 | − | 0.757275i | \(-0.273470\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.03957i | − 1.12037i | −0.828366 | − | 0.560187i | \(-0.810729\pi\) | ||||
0.828366 | − | 0.560187i | \(-0.189271\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.81624i | 1.16811i | 0.811714 | + | 0.584055i | \(0.198535\pi\) | ||||
−0.811714 | + | 0.584055i | \(0.801465\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.03957 | −0.238494 | −0.119247 | − | 0.992865i | \(-0.538048\pi\) | ||||
−0.119247 | + | 0.992865i | \(0.538048\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.43710 | 1.13371 | 0.566857 | − | 0.823816i | \(-0.308159\pi\) | ||||
0.566857 | + | 0.823816i | \(0.308159\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.95717 | −0.991434 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.90487 | 0.539421 | 0.269710 | − | 0.962941i | \(-0.413072\pi\) | ||||
0.269710 | + | 0.962941i | \(0.413072\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1.23898i | − 0.222528i | −0.993791 | − | 0.111264i | \(-0.964510\pi\) | ||||
0.993791 | − | 0.111264i | \(-0.0354899\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.629051i | 0.106329i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 8.77162i | − 1.44205i | −0.692911 | − | 0.721023i | \(-0.743672\pi\) | ||||
0.692911 | − | 0.721023i | \(-0.256328\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 0.979317i | − 0.152944i | −0.997072 | − | 0.0764718i | \(-0.975634\pi\) | ||||
0.997072 | − | 0.0764718i | \(-0.0243655\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.18555 | 0.485792 | 0.242896 | − | 0.970052i | \(-0.421903\pi\) | ||||
0.242896 | + | 0.970052i | \(0.421903\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.26332 | −0.476005 | −0.238002 | − | 0.971265i | \(-0.576493\pi\) | ||||
−0.238002 | + | 0.971265i | \(0.576493\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.23898 | −0.319855 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.91987 | −1.08788 | −0.543939 | − | 0.839125i | \(-0.683068\pi\) | ||||
−0.543939 | + | 0.839125i | \(0.683068\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.03957i | − 0.140176i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.8544i | 1.93388i | 0.254999 | + | 0.966941i | \(0.417925\pi\) | ||||
−0.254999 | + | 0.966941i | \(0.582075\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 9.53264i | − 1.22053i | −0.792198 | − | 0.610265i | \(-0.791063\pi\) | ||||
0.792198 | − | 0.610265i | \(-0.208937\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 0.836005i | − 0.103694i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.735311 | 0.0898326 | 0.0449163 | − | 0.998991i | \(-0.485698\pi\) | ||||
0.0449163 | + | 0.998991i | \(0.485698\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.33127 | 0.276671 | 0.138336 | − | 0.990385i | \(-0.455825\pi\) | ||||
0.138336 | + | 0.990385i | \(0.455825\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.0363 | −1.17466 | −0.587331 | − | 0.809347i | \(-0.699821\pi\) | ||||
−0.587331 | + | 0.809347i | \(0.699821\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.2683 | 1.73999 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 14.1929i | − 1.59683i | −0.602111 | − | 0.798413i | \(-0.705673\pi\) | ||||
0.602111 | − | 0.798413i | \(-0.294327\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 4.23665i | − 0.465032i | −0.972593 | − | 0.232516i | \(-0.925304\pi\) | ||||
0.972593 | − | 0.232516i | \(-0.0746959\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.996740i | 0.108112i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 11.6053i | − 1.23016i | −0.788465 | − | 0.615079i | \(-0.789124\pi\) | ||||
0.788465 | − | 0.615079i | \(-0.210876\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.2786 | 1.28714 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.215143 | −0.0220732 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.84016 | 0.491443 | 0.245722 | − | 0.969340i | \(-0.420975\pi\) | ||||
0.245722 | + | 0.969340i | \(0.420975\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.3949 | −1.73085 | −0.865426 | − | 0.501036i | \(-0.832952\pi\) | ||||
−0.865426 | + | 0.501036i | \(0.832952\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 2.00000i | − 0.197066i | −0.995134 | − | 0.0985329i | \(-0.968585\pi\) | ||||
0.995134 | − | 0.0985329i | \(-0.0314150\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 11.4456i | − 1.10649i | −0.833019 | − | 0.553244i | \(-0.813390\pi\) | ||||
0.833019 | − | 0.553244i | \(-0.186610\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.80793i | 0.747864i | 0.927456 | + | 0.373932i | \(0.121991\pi\) | ||||
−0.927456 | + | 0.373932i | \(0.878009\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 19.6707i | − 1.85046i | −0.379405 | − | 0.925231i | \(-0.623871\pi\) | ||||
0.379405 | − | 0.925231i | \(-0.376129\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.12523 | 0.104928 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.6393 | −1.34198 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.2325 | −1.29386 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.06068 | −0.184312 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 7.35274i | − 0.652450i | −0.945292 | − | 0.326225i | \(-0.894223\pi\) | ||||
0.945292 | − | 0.326225i | \(-0.105777\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.0730i | 0.967449i | 0.875220 | + | 0.483725i | \(0.160716\pi\) | ||||
−0.875220 | + | 0.483725i | \(0.839284\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3.15984i | − 0.273993i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.1103i | 1.37640i | 0.725521 | + | 0.688200i | \(0.241599\pi\) | ||||
−0.725521 | + | 0.688200i | \(0.758401\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.1444 | 1.79345 | 0.896723 | − | 0.442592i | \(-0.145941\pi\) | ||||
0.896723 | + | 0.442592i | \(0.145941\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.2915 | −1.69686 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.601174 | 0.0499248 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.3437 | 1.33893 | 0.669464 | − | 0.742844i | \(-0.266524\pi\) | ||||
0.669464 | + | 0.742844i | \(0.266524\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 6.07914i | − 0.494713i | −0.968924 | − | 0.247357i | \(-0.920438\pi\) | ||||
0.968924 | − | 0.247357i | \(-0.0795619\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 0.256412i | − 0.0205955i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 14.3817i | − 1.14778i | −0.818931 | − | 0.573892i | \(-0.805433\pi\) | ||||
0.818931 | − | 0.573892i | \(-0.194567\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.5264i | 1.30247i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.8263 | 1.08296 | 0.541479 | − | 0.840714i | \(-0.317864\pi\) | ||||
0.541479 | + | 0.840714i | \(0.317864\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.97675 | 0.772024 | 0.386012 | − | 0.922494i | \(-0.373852\pi\) | ||||
0.386012 | + | 0.922494i | \(0.373852\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.31812 | −0.255240 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.8401 | −1.73650 | −0.868252 | − | 0.496123i | \(-0.834756\pi\) | ||||
−0.868252 | + | 0.496123i | \(0.834756\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 15.0677i | − 1.13901i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 15.4258i | − 1.15298i | −0.817104 | − | 0.576491i | \(-0.804422\pi\) | ||||
0.817104 | − | 0.576491i | \(-0.195578\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 14.4502i | − 1.07408i | −0.843557 | − | 0.537039i | \(-0.819543\pi\) | ||||
0.843557 | − | 0.537039i | \(-0.180457\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 1.81532i | − 0.133465i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.1929 | 1.76916 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.4190 | 1.83925 | 0.919626 | − | 0.392796i | \(-0.128492\pi\) | ||||
0.919626 | + | 0.392796i | \(0.128492\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.1583 | 1.09112 | 0.545558 | − | 0.838073i | \(-0.316318\pi\) | ||||
0.545558 | + | 0.838073i | \(0.316318\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.06068 | −0.146817 | −0.0734085 | − | 0.997302i | \(-0.523388\pi\) | ||||
−0.0734085 | + | 0.997302i | \(0.523388\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.0791389i | 0.00561001i | 0.999996 | + | 0.00280500i | \(0.000892861\pi\) | ||||
−0.999996 | + | 0.00280500i | \(0.999107\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.82955i | 0.619713i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 0.202673i | − 0.0141553i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.22196i | 0.361210i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.3527 | 1.46998 | 0.734991 | − | 0.678076i | \(-0.237186\pi\) | ||||
0.734991 | + | 0.678076i | \(0.237186\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.659262 | 0.0449613 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.76597 | 0.255651 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.4555 | 1.30872 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.4018i | 0.897448i | 0.893670 | + | 0.448724i | \(0.148121\pi\) | ||||
−0.893670 | + | 0.448724i | \(0.851879\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 9.25984i | − 0.614597i | −0.951613 | − | 0.307299i | \(-0.900575\pi\) | ||||
0.951613 | − | 0.307299i | \(-0.0994250\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 11.1717i | − 0.738246i | −0.929381 | − | 0.369123i | \(-0.879658\pi\) | ||||
0.929381 | − | 0.369123i | \(-0.120342\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.1233i | 0.925251i | 0.886554 | + | 0.462625i | \(0.153093\pi\) | ||||
−0.886554 | + | 0.462625i | \(0.846907\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.675358 | −0.0440555 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.2106 | 1.50137 | 0.750684 | − | 0.660661i | \(-0.229724\pi\) | ||||
0.750684 | + | 0.660661i | \(0.229724\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.5143 | −0.934947 | −0.467473 | − | 0.884007i | \(-0.654836\pi\) | ||||
−0.467473 | + | 0.884007i | \(0.654836\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.463366 | −0.0296034 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.19941i | 0.267202i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.03788i | 0.254869i | 0.991847 | + | 0.127434i | \(0.0406742\pi\) | ||||
−0.991847 | + | 0.127434i | \(0.959326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 27.3116i | − 1.71707i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 9.77579i | − 0.609797i | −0.952385 | − | 0.304898i | \(-0.901377\pi\) | ||||
0.952385 | − | 0.304898i | \(-0.0986225\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.6619 | 1.65669 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.5814 | −1.51576 | −0.757878 | − | 0.652396i | \(-0.773764\pi\) | ||||
−0.757878 | + | 0.652396i | \(0.773764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.63905 | −0.100686 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.02008 | −0.123167 | −0.0615833 | − | 0.998102i | \(-0.519615\pi\) | ||||
−0.0615833 | + | 0.998102i | \(0.519615\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 28.6643i | − 1.74123i | −0.491961 | − | 0.870617i | \(-0.663720\pi\) | ||||
0.491961 | − | 0.870617i | \(-0.336280\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.9008i | 1.50158i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 14.2162i | − 0.854169i | −0.904212 | − | 0.427085i | \(-0.859541\pi\) | ||||
0.904212 | − | 0.427085i | \(-0.140459\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.49178i | 0.446922i | 0.974713 | + | 0.223461i | \(0.0717356\pi\) | ||||
−0.974713 | + | 0.223461i | \(0.928264\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.6159 | −1.64159 | −0.820796 | − | 0.571221i | \(-0.806470\pi\) | ||||
−0.820796 | + | 0.571221i | \(0.806470\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.97670 | 0.175709 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.19615 | −0.364480 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.3495 | 1.53935 | 0.769677 | − | 0.638433i | \(-0.220417\pi\) | ||||
0.769677 | + | 0.638433i | \(0.220417\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.07418i | 0.178986i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 21.9635i | − 1.27018i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.68270i | 0.558102i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 1.97282i | − 0.112963i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.07418 | 0.517891 | 0.258946 | − | 0.965892i | \(-0.416625\pi\) | ||||
0.258946 | + | 0.965892i | \(0.416625\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.0661 | 1.19455 | 0.597274 | − | 0.802037i | \(-0.296250\pi\) | ||||
0.597274 | + | 0.802037i | \(0.296250\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.2325 | −1.03056 | −0.515280 | − | 0.857022i | \(-0.672312\pi\) | ||||
−0.515280 | + | 0.857022i | \(0.672312\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.60278 | 0.314684 | 0.157342 | − | 0.987544i | \(-0.449708\pi\) | ||||
0.157342 | + | 0.987544i | \(0.449708\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 14.5917i | − 0.816979i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 5.00681i | − 0.278587i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.0248i | 1.11078i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 9.91910i | − 0.546858i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.5836 | −1.62606 | −0.813032 | − | 0.582219i | \(-0.802184\pi\) | ||||
−0.813032 | + | 0.582219i | \(0.802184\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.152176 | 0.00831424 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.3116 | −1.05197 | −0.525985 | − | 0.850494i | \(-0.676303\pi\) | ||||
−0.525985 | + | 0.850494i | \(0.676303\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.22365 | −0.337029 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.4714i | 0.781385i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.2254i | 0.763659i | 0.924233 | + | 0.381829i | \(0.124706\pi\) | ||||
−0.924233 | + | 0.381829i | \(0.875294\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 12.1672i | − 0.651295i | −0.945491 | − | 0.325647i | \(-0.894418\pi\) | ||||
0.945491 | − | 0.325647i | \(-0.105582\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.419903i | 0.0223492i | 0.999938 | + | 0.0111746i | \(0.00355705\pi\) | ||||
−0.999938 | + | 0.0111746i | \(0.996443\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.482466 | 0.0256066 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.0799 | 0.743107 | 0.371554 | − | 0.928411i | \(-0.378825\pi\) | ||||
0.371554 | + | 0.928411i | \(0.378825\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.9193 | −0.943121 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.07705 | −0.108718 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 31.6248i | − 1.65080i | −0.564549 | − | 0.825400i | \(-0.690950\pi\) | ||||
0.564549 | − | 0.825400i | \(-0.309050\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 24.0730i | − 1.24981i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 33.1077i | − 1.71425i | −0.515108 | − | 0.857126i | \(-0.672248\pi\) | ||||
0.515108 | − | 0.857126i | \(-0.327752\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 11.7344i | − 0.604353i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.167186 | −0.00858775 | −0.00429387 | − | 0.999991i | \(-0.501367\pi\) | ||||
−0.00429387 | + | 0.999991i | \(0.501367\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.7432 | −1.67310 | −0.836550 | − | 0.547890i | \(-0.815431\pi\) | ||||
−0.836550 | + | 0.547890i | \(0.815431\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.15984 | 0.161041 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.4016 | 0.780893 | 0.390447 | − | 0.920626i | \(-0.372321\pi\) | ||||
0.390447 | + | 0.920626i | \(0.372321\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.1864i | 1.32430i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 2.93727i | − 0.147790i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 25.3010i | − 1.26982i | −0.772586 | − | 0.634910i | \(-0.781037\pi\) | ||||
0.772586 | − | 0.634910i | \(-0.218963\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.0391i | 0.651142i | 0.945518 | + | 0.325571i | \(0.105557\pi\) | ||||
−0.945518 | + | 0.325571i | \(0.894443\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.00496 | −0.249315 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −44.0615 | −2.18405 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.75326 | −0.383374 | −0.191687 | − | 0.981456i | \(-0.561396\pi\) | ||||
−0.191687 | + | 0.981456i | \(0.561396\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −45.1511 | −2.22174 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 0.876791i | − 0.0430400i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.2966i | 1.48009i | 0.672558 | + | 0.740044i | \(0.265195\pi\) | ||||
−0.672558 | + | 0.740044i | \(0.734805\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 18.7427i | − 0.913461i | −0.889605 | − | 0.456731i | \(-0.849020\pi\) | ||||
0.889605 | − | 0.456731i | \(-0.150980\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 23.8749i | − 1.15810i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.9751 | 1.40220 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.8198 | −0.713846 | −0.356923 | − | 0.934134i | \(-0.616174\pi\) | ||||
−0.356923 | + | 0.934134i | \(0.616174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.83364 | −0.472574 | −0.236287 | − | 0.971683i | \(-0.575931\pi\) | ||||
−0.236287 | + | 0.971683i | \(0.575931\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.65224 | −0.270383 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.79609i | 0.467542i | 0.972292 | + | 0.233771i | \(0.0751065\pi\) | ||||
−0.972292 | + | 0.233771i | \(0.924893\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.2734i | 0.583128i | 0.956551 | + | 0.291564i | \(0.0941756\pi\) | ||||
−0.956551 | + | 0.291564i | \(0.905824\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2.40176i | − 0.113854i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 8.46106i | − 0.399302i | −0.979867 | − | 0.199651i | \(-0.936019\pi\) | ||||
0.979867 | − | 0.199651i | \(-0.0639809\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.91930 | −0.231641 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.54109 | 0.119128 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.5127 | 1.09988 | 0.549939 | − | 0.835205i | \(-0.314651\pi\) | ||||
0.549939 | + | 0.835205i | \(0.314651\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.7941 | −0.875327 | −0.437664 | − | 0.899139i | \(-0.644194\pi\) | ||||
−0.437664 | + | 0.899139i | \(0.644194\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 23.7896i | − 1.10559i | −0.833316 | − | 0.552797i | \(-0.813560\pi\) | ||||
0.833316 | − | 0.552797i | \(-0.186440\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.827816i | 0.0383067i | 0.999817 | + | 0.0191534i | \(0.00609708\pi\) | ||||
−0.999817 | + | 0.0191534i | \(0.993903\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.23503i | 0.103204i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 16.0016i | − 0.735756i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.15332 | 0.236451 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.9671 | 1.04939 | 0.524696 | − | 0.851290i | \(-0.324179\pi\) | ||||
0.524696 | + | 0.851290i | \(0.324179\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −35.4336 | −1.61563 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.00169 | 0.0454844 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.4665i | 1.51651i | 0.651957 | + | 0.758256i | \(0.273948\pi\) | ||||
−0.651957 | + | 0.758256i | \(0.726052\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 19.8776i | − 0.897065i | −0.893767 | − | 0.448532i | \(-0.851947\pi\) | ||||
0.893767 | − | 0.448532i | \(-0.148053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.9905i | 0.630102i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.08606i | 0.317853i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.04452 | 0.270590 | 0.135295 | − | 0.990805i | \(-0.456802\pi\) | ||||
0.135295 | + | 0.990805i | \(0.456802\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.252024 | 0.0112372 | 0.00561859 | − | 0.999984i | \(-0.498212\pi\) | ||||
0.00561859 | + | 0.999984i | \(0.498212\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.59993 | −0.160195 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.1848 | −1.20495 | −0.602473 | − | 0.798139i | \(-0.705818\pi\) | ||||
−0.602473 | + | 0.798139i | \(0.705818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 30.5061i | − 1.34951i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 0.413908i | − 0.0182390i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.3923i | 0.720933i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.6451i | 1.64926i | 0.565671 | + | 0.824631i | \(0.308617\pi\) | ||||
−0.565671 | + | 0.824631i | \(0.691383\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.20180 | 0.0962780 | 0.0481390 | − | 0.998841i | \(-0.484671\pi\) | ||||
0.0481390 | + | 0.998841i | \(0.484671\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.96723 | 0.259937 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.56206 | 0.285307 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.95602 | −0.171354 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 2.36871i | − 0.102408i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.2468i | 0.484436i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.04196i | 0.345751i | 0.984944 | + | 0.172875i | \(0.0553058\pi\) | ||||
−0.984944 | + | 0.172875i | \(0.944694\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.61588i | 0.0692168i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.1745 | −0.905357 | −0.452679 | − | 0.891674i | \(-0.649532\pi\) | ||||
−0.452679 | + | 0.891674i | \(0.649532\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.01981 | −0.128648 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 43.1403 | 1.83451 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.5871 | 0.787562 | 0.393781 | − | 0.919204i | \(-0.371167\pi\) | ||||
0.393781 | + | 0.919204i | \(0.371167\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 12.8682i | − 0.544269i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 19.0085i | − 0.801115i | −0.916272 | − | 0.400557i | \(-0.868817\pi\) | ||||
0.916272 | − | 0.400557i | \(-0.131183\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 4.07092i | − 0.171265i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 3.82654i | − 0.160417i | −0.996778 | − | 0.0802084i | \(-0.974441\pi\) | ||||
0.996778 | − | 0.0802084i | \(-0.0255586\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.6174 | −0.611720 | −0.305860 | − | 0.952076i | \(-0.598944\pi\) | ||||
−0.305860 | + | 0.952076i | \(0.598944\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.9526 | −1.12400 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.28305 | −0.0534142 | −0.0267071 | − | 0.999643i | \(-0.508502\pi\) | ||||
−0.0267071 | + | 0.999643i | \(0.508502\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.8776 | 0.534252 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 39.7830i | 1.64765i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.45348i | 0.225089i | 0.993647 | + | 0.112545i | \(0.0359001\pi\) | ||||
−0.993647 | + | 0.112545i | \(0.964100\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.28801i | 0.0530715i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 25.7774i | − 1.05855i | −0.848450 | − | 0.529276i | \(-0.822464\pi\) | ||||
0.848450 | − | 0.529276i | \(-0.177536\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.02966 | −0.124204 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.6141 | 1.61859 | 0.809295 | − | 0.587403i | \(-0.199849\pi\) | ||||
0.809295 | + | 0.587403i | \(0.199849\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.44785 | 0.140641 | 0.0703204 | − | 0.997524i | \(-0.477598\pi\) | ||||
0.0703204 | + | 0.997524i | \(0.477598\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.94546 | −0.119750 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.0029i | 0.933660i | 0.884347 | + | 0.466830i | \(0.154604\pi\) | ||||
−0.884347 | + | 0.466830i | \(0.845396\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.1824i | 0.533304i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.82786i | 0.275775i | 0.990448 | + | 0.137887i | \(0.0440312\pi\) | ||||
−0.990448 | + | 0.137887i | \(0.955969\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 21.9201i | − 0.882469i | −0.897392 | − | 0.441235i | \(-0.854541\pi\) | ||||
0.897392 | − | 0.441235i | \(-0.145459\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.0131 | 1.48768 | 0.743841 | − | 0.668356i | \(-0.233002\pi\) | ||||
0.743841 | + | 0.668356i | \(0.233002\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.2751 | 1.41327 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.3594 | 0.974375 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.2462 | 1.68447 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 25.2815i | − 1.00644i | −0.864158 | − | 0.503220i | \(-0.832149\pi\) | ||||
0.864158 | − | 0.503220i | \(-0.167851\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.52168i | − 0.0603859i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.04452i | 0.358357i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.6465i | 0.775988i | 0.921662 | + | 0.387994i | \(0.126832\pi\) | ||||
−0.921662 | + | 0.387994i | \(0.873168\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.2089 | −0.678652 | −0.339326 | − | 0.940669i | \(-0.610199\pi\) | ||||
−0.339326 | + | 0.940669i | \(0.610199\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.9988 | 1.33663 | 0.668315 | − | 0.743879i | \(-0.267016\pi\) | ||||
0.668315 | + | 0.743879i | \(0.267016\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 74.6167 | 2.92896 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.5636 | 0.804718 | 0.402359 | − | 0.915482i | \(-0.368190\pi\) | ||||
0.402359 | + | 0.915482i | \(0.368190\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.29159i | 0.0895400i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.4586i | 0.874864i | 0.899251 | + | 0.437432i | \(0.144112\pi\) | ||||
−0.899251 | + | 0.437432i | \(0.855888\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.1362i | 0.666521i | 0.942835 | + | 0.333260i | \(0.108149\pi\) | ||||
−0.942835 | + | 0.333260i | \(0.891851\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 0.653942i | − 0.0253588i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.7941 | 0.611549 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −47.8843 | −1.84855 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.7595 | −1.18569 | −0.592845 | − | 0.805317i | \(-0.701995\pi\) | ||||
−0.592845 | + | 0.805317i | \(0.701995\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.3157 | −0.511764 | −0.255882 | − | 0.966708i | \(-0.582366\pi\) | ||||
−0.255882 | + | 0.966708i | \(0.582366\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.7120i | 0.564594i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 27.4006i | − 1.04846i | −0.851578 | − | 0.524228i | \(-0.824354\pi\) | ||||
0.851578 | − | 0.524228i | \(-0.175646\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.33410i | 0.127389i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 31.9929i | 1.21883i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.1790 | 0.653521 | 0.326761 | − | 0.945107i | \(-0.394043\pi\) | ||||
0.326761 | + | 0.945107i | \(0.394043\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.37592 | 0.165988 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.71662 | 0.178655 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.7770 | 1.61567 | 0.807833 | − | 0.589412i | \(-0.200640\pi\) | ||||
0.807833 | + | 0.589412i | \(0.200640\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.11871i | 0.343919i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 52.8729i | − 1.98849i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 51.9018i | 1.94921i | 0.223928 | + | 0.974606i | \(0.428112\pi\) | ||||
−0.223928 | + | 0.974606i | \(0.571888\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 6.73647i | − 0.252283i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.19941 | −0.157049 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.6166 | −1.10451 | −0.552257 | − | 0.833674i | \(-0.686233\pi\) | ||||
−0.552257 | + | 0.833674i | \(0.686233\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.07914 | 0.226399 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.3999 | −0.534800 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.8177i | 1.18005i | 0.807384 | + | 0.590026i | \(0.200882\pi\) | ||||
−0.807384 | + | 0.590026i | \(0.799118\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.3424i | 0.567458i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.4062i | 0.864527i | 0.901747 | + | 0.432263i | \(0.142285\pi\) | ||||
−0.901747 | + | 0.432263i | \(0.857715\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 3.69361i | − 0.136056i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.0424 | 0.516558 | 0.258279 | − | 0.966070i | \(-0.416845\pi\) | ||||
0.258279 | + | 0.966070i | \(0.416845\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.8612 | −0.471832 | −0.235916 | − | 0.971773i | \(-0.575809\pi\) | ||||
−0.235916 | + | 0.971773i | \(0.575809\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.38239 | 0.123921 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 34.7897 | 1.27119 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 39.4254i | − 1.43865i | −0.694673 | − | 0.719326i | \(-0.744451\pi\) | ||||
0.694673 | − | 0.719326i | \(-0.255549\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1.25810i | − 0.0457870i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.4992i | 0.526981i | 0.964662 | + | 0.263491i | \(0.0848738\pi\) | ||||
−0.964662 | + | 0.263491i | \(0.915126\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.6306i | 1.69036i | 0.534482 | + | 0.845180i | \(0.320507\pi\) | ||||
−0.534482 | + | 0.845180i | \(0.679493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.7327 | −0.859183 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 60.0055 | 2.16667 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.7055 | 0.854841 | 0.427421 | − | 0.904053i | \(-0.359422\pi\) | ||||
0.427421 | + | 0.904053i | \(0.359422\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.1631 | −0.869085 | −0.434542 | − | 0.900651i | \(-0.643090\pi\) | ||||
−0.434542 | + | 0.900651i | \(0.643090\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.14185i | 0.220622i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.01807i | 0.0364761i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 11.7104i | − 0.419032i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 2.97635i | − 0.106230i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.5199 | −0.980979 | −0.490490 | − | 0.871447i | \(-0.663182\pi\) | ||||
−0.490490 | + | 0.871447i | \(0.663182\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 59.7904 | 2.12590 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.5078 | −1.36745 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.6199 | −0.447019 | −0.223510 | − | 0.974702i | \(-0.571751\pi\) | ||||
−0.223510 | + | 0.974702i | \(0.571751\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 15.7169i | − 0.556026i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 50.4143i | 1.77908i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.42021i | 0.120547i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.5226i | 0.545744i | 0.962050 | + | 0.272872i | \(0.0879736\pi\) | ||||
−0.962050 | + | 0.272872i | \(0.912026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.4347 | −1.70077 | −0.850386 | − | 0.526159i | \(-0.823632\pi\) | ||||
−0.850386 | + | 0.526159i | \(0.823632\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.86141 | 0.100231 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.31160 | −0.115858 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.0891 | 0.421912 | 0.210956 | − | 0.977496i | \(-0.432342\pi\) | ||||
0.210956 | + | 0.977496i | \(0.432342\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.10430i | 0.177925i | 0.996035 | + | 0.0889623i | \(0.0283551\pi\) | ||||
−0.996035 | + | 0.0889623i | \(0.971645\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.40603i | 0.222760i | 0.993778 | + | 0.111380i | \(0.0355270\pi\) | ||||
−0.993778 | + | 0.111380i | \(0.964473\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.1518i | 1.46399i | 0.681309 | + | 0.731996i | \(0.261411\pi\) | ||||
−0.681309 | + | 0.731996i | \(0.738589\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 10.7835i | − 0.373625i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.06473 | 0.0714528 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.3893 | −1.80868 | −0.904340 | − | 0.426813i | \(-0.859636\pi\) | ||||
−0.904340 | + | 0.426813i | \(0.859636\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5617 | −0.709025 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.686698 | −0.0236231 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 43.2606i | − 1.48645i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 47.6922i | − 1.63487i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.2920i | 0.968698i | 0.874875 | + | 0.484349i | \(0.160944\pi\) | ||||
−0.874875 | + | 0.484349i | \(0.839056\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.5139i | 1.11065i | 0.831632 | + | 0.555327i | \(0.187407\pi\) | ||||
−0.831632 | + | 0.555327i | \(0.812593\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.9453 | 1.39703 | 0.698517 | − | 0.715593i | \(-0.253843\pi\) | ||||
0.698517 | + | 0.715593i | \(0.253843\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.23907 | −0.314502 | −0.157251 | − | 0.987559i | \(-0.550263\pi\) | ||||
−0.157251 | + | 0.987559i | \(0.550263\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.72686 | −0.160718 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −71.2936 | −2.41847 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 2.97034i | − 0.100646i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 6.26357i | − 0.211747i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.01556i | − 0.0342930i | −0.999853 | − | 0.0171465i | \(-0.994542\pi\) | ||||
0.999853 | − | 0.0171465i | \(-0.00545816\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 49.9531i | − 1.68296i | −0.540285 | − | 0.841482i | \(-0.681684\pi\) | ||||
0.540285 | − | 0.841482i | \(-0.318316\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.0726 | −1.34855 | −0.674275 | − | 0.738480i | \(-0.735544\pi\) | ||||
−0.674275 | + | 0.738480i | \(0.735544\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.4591 | −0.989141 | −0.494570 | − | 0.869138i | \(-0.664675\pi\) | ||||
−0.494570 | + | 0.869138i | \(0.664675\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.3491 | 0.749566 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.39245 | 0.113524 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 3.19244i | − 0.106711i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 3.59908i | − 0.120036i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 38.1440i | − 1.27076i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 2.99053i | − 0.0994087i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.3557 | −1.20717 | −0.603585 | − | 0.797299i | \(-0.706262\pi\) | ||||
−0.603585 | + | 0.797299i | \(0.706262\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.3465 | 0.939162 | 0.469581 | − | 0.882889i | \(-0.344405\pi\) | ||||
0.469581 | + | 0.882889i | \(0.344405\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.2815 | −0.704314 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33.6570 | −1.11145 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.7435i | 1.93777i | 0.247514 | + | 0.968884i | \(0.420386\pi\) | ||||
−0.247514 | + | 0.968884i | \(0.579614\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 9.41733i | − 0.309975i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43.4824i | 1.42969i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 24.7981i | − 0.813599i | −0.913517 | − | 0.406800i | \(-0.866645\pi\) | ||||
0.913517 | − | 0.406800i | \(-0.133355\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.32758 | 0.0762833 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.00681 | 0.163740 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.1819 | 0.822656 | 0.411328 | − | 0.911487i | \(-0.365065\pi\) | ||||
0.411328 | + | 0.911487i | \(0.365065\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.6929 | −1.19615 | −0.598077 | − | 0.801439i | \(-0.704068\pi\) | ||||
−0.598077 | + | 0.801439i | \(0.704068\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 5.32464i | − 0.173394i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.7134i | 0.705590i | 0.935701 | + | 0.352795i | \(0.114769\pi\) | ||||
−0.935701 | + | 0.352795i | \(0.885231\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.5424i | 1.31606i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 16.5469i | − 0.536005i | −0.963418 | − | 0.268003i | \(-0.913636\pi\) | ||||
0.963418 | − | 0.268003i | \(-0.0863636\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.26055 | 0.170228 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −48.9685 | −1.58128 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.4649 | 0.950481 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.13707 | 0.100986 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.0566i | 0.870083i | 0.900410 | + | 0.435041i | \(0.143266\pi\) | ||||
−0.900410 | + | 0.435041i | \(0.856734\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.0968i | 1.31886i | 0.751766 | + | 0.659430i | \(0.229202\pi\) | ||||
−0.751766 | + | 0.659430i | \(0.770798\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 64.2699i | 2.06040i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46.7497i | 1.49566i | 0.663892 | + | 0.747828i | \(0.268903\pi\) | ||||
−0.663892 | + | 0.747828i | \(0.731097\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −58.2956 | −1.86314 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.5184 | −1.45181 | −0.725906 | − | 0.687794i | \(-0.758579\pi\) | ||||
−0.725906 | + | 0.687794i | \(0.758579\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.426465 | −0.0135883 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.3202 | 0.550749 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.8381i | 0.725477i | 0.931891 | + | 0.362739i | \(0.118158\pi\) | ||||
−0.931891 | + | 0.362739i | \(0.881842\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.0163781i | 0 0.000519221i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 43.7357i | − 1.38512i | −0.721358 | − | 0.692562i | \(-0.756482\pi\) | ||||
0.721358 | − | 0.692562i | \(-0.243518\pi\) | |||||||
\(998\) | 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 | 5184.2.f.e.2591.10 | yes | 16 | |
3.2 | odd | 2 | inner | 5184.2.f.e.2591.8 | yes | 16 | |
4.3 | odd | 2 | 5184.2.f.b.2591.9 | yes | 16 | ||
8.3 | odd | 2 | inner | 5184.2.f.e.2591.7 | yes | 16 | |
8.5 | even | 2 | 5184.2.f.b.2591.8 | yes | 16 | ||
12.11 | even | 2 | 5184.2.f.b.2591.7 | ✓ | 16 | ||
24.5 | odd | 2 | 5184.2.f.b.2591.10 | yes | 16 | ||
24.11 | even | 2 | inner | 5184.2.f.e.2591.9 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5184.2.f.b.2591.7 | ✓ | 16 | 12.11 | even | 2 | ||
5184.2.f.b.2591.8 | yes | 16 | 8.5 | even | 2 | ||
5184.2.f.b.2591.9 | yes | 16 | 4.3 | odd | 2 | ||
5184.2.f.b.2591.10 | yes | 16 | 24.5 | odd | 2 | ||
5184.2.f.e.2591.7 | yes | 16 | 8.3 | odd | 2 | inner | |
5184.2.f.e.2591.8 | yes | 16 | 3.2 | odd | 2 | inner | |
5184.2.f.e.2591.9 | yes | 16 | 24.11 | even | 2 | inner | |
5184.2.f.e.2591.10 | yes | 16 | 1.1 | even | 1 | trivial |