Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1567,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1567");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.p (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: | \(32.1956820950\) |
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: | \( x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 1344) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.1 | ||
Root | \(1.75780 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.1567 |
Dual form | 4032.2.p.k.1567.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −3.88448 | −1.73719 | −0.868597 | − | 0.495519i | \(-0.834978\pi\) | ||||
−0.868597 | + | 0.495519i | \(0.834978\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.62383 | − | 0.339877i | −0.991715 | − | 0.128461i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.48046 | 0.446376 | 0.223188 | − | 0.974775i | \(-0.428354\pi\) | ||||
0.223188 | + | 0.974775i | \(0.428354\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.76720i | − | 0.913679i | −0.889549 | − | 0.456840i | \(-0.848981\pi\) | ||
0.889549 | − | 0.456840i | \(-0.151019\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.679754i | 0.155946i | 0.996955 | + | 0.0779731i | \(0.0248448\pi\) | ||||
−0.996955 | + | 0.0779731i | \(0.975155\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.20473i | − | 1.08526i | −0.839971 | − | 0.542631i | \(-0.817428\pi\) | ||
0.839971 | − | 0.542631i | \(-0.182572\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.0892 | 2.01784 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.03122i | − | 1.30566i | −0.757503 | − | 0.652832i | \(-0.773581\pi\) | ||
0.757503 | − | 0.652832i | \(-0.226419\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.42503 | 1.15397 | 0.576985 | − | 0.816755i | \(-0.304229\pi\) | ||||
0.576985 | + | 0.816755i | \(0.304229\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.1922 | + | 1.32025i | 1.72280 | + | 0.223162i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.71176i | 1.43220i | 0.697995 | + | 0.716102i | \(0.254076\pi\) | ||||
−0.697995 | + | 0.716102i | \(0.745924\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.16101i | 0.493666i | 0.969058 | + | 0.246833i | \(0.0793900\pi\) | ||||
−0.969058 | + | 0.246833i | \(0.920610\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.20859 | 1.25180 | 0.625899 | − | 0.779904i | \(-0.284732\pi\) | ||||
0.625899 | + | 0.779904i | \(0.284732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.88913 | −1.44248 | −0.721239 | − | 0.692686i | \(-0.756427\pi\) | ||||
−0.721239 | + | 0.692686i | \(0.756427\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.76897 | + | 1.78356i | 0.966995 | + | 0.254794i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.42503i | 0.882545i | 0.897373 | + | 0.441273i | \(0.145473\pi\) | ||||
−0.897373 | + | 0.441273i | \(0.854527\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.75084 | −0.775442 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.76897i | 1.01143i | 0.862700 | + | 0.505717i | \(0.168772\pi\) | ||||
−0.862700 | + | 0.505717i | \(0.831228\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4095 | −1.58887 | −0.794434 | − | 0.607350i | \(-0.792233\pi\) | ||||
−0.794434 | + | 0.607350i | \(0.792233\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.76897 | −0.963622 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.81478 | −1.07690 | −0.538448 | − | 0.842659i | \(-0.680989\pi\) | ||||
−0.538448 | + | 0.842659i | \(0.680989\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.9737i | − | 1.53969i | −0.638228 | − | 0.769847i | \(-0.720332\pi\) | ||
0.638228 | − | 0.769847i | \(-0.279668\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.4562i | − | 1.57493i | −0.616356 | − | 0.787467i | \(-0.711392\pi\) | ||
0.616356 | − | 0.787467i | \(-0.288608\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.88448 | − | 0.503175i | −0.442678 | − | 0.0573421i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.44872i | 0.500520i | 0.968179 | + | 0.250260i | \(0.0805161\pi\) | ||||
−0.968179 | + | 0.250260i | \(0.919484\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.4095i | 1.14259i | 0.820746 | + | 0.571293i | \(0.193558\pi\) | ||||
−0.820746 | + | 0.571293i | \(0.806442\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.6336i | 1.58724i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 10.6954i | − | 1.13371i | −0.823818 | − | 0.566855i | \(-0.808160\pi\) | ||
0.823818 | − | 0.566855i | \(-0.191840\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.24766 | − | 0.679754i | −0.550104 | − | 0.0712576i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 2.64049i | − | 0.270909i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.88913i | − | 1.00409i | −0.864842 | − | 0.502044i | \(-0.832581\pi\) | ||
0.864842 | − | 0.502044i | \(-0.167419\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.88448 | −0.386521 | −0.193260 | − | 0.981148i | \(-0.561906\pi\) | ||||
−0.193260 | + | 0.981148i | \(0.561906\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.06394 | −0.301899 | −0.150950 | − | 0.988541i | \(-0.548233\pi\) | ||||
−0.150950 | + | 0.988541i | \(0.548233\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.08665 | −0.201724 | −0.100862 | − | 0.994900i | \(-0.532160\pi\) | ||||
−0.100862 | + | 0.994900i | \(0.532160\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 17.4235i | − | 1.66887i | −0.551106 | − | 0.834435i | \(-0.685794\pi\) | ||
0.551106 | − | 0.834435i | \(-0.314206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.76897 | 0.166410 | 0.0832052 | − | 0.996532i | \(-0.473484\pi\) | ||||
0.0832052 | + | 0.996532i | \(0.473484\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.2177i | 1.88531i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.28038 | + | 9.88448i | −0.117373 | + | 0.906109i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.80823 | −0.800748 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −19.7690 | −1.76819 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0892i | 0.984009i | 0.870593 | + | 0.492004i | \(0.163736\pi\) | ||||
−0.870593 | + | 0.492004i | \(0.836264\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 1.59054i | − | 0.138966i | −0.997583 | − | 0.0694831i | \(-0.977865\pi\) | ||
0.997583 | − | 0.0694831i | \(-0.0221350\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.231033 | − | 1.78356i | 0.0200331 | − | 0.154654i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.8974 | −1.61452 | −0.807259 | − | 0.590198i | \(-0.799050\pi\) | ||||
−0.807259 | + | 0.590198i | \(0.799050\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.1784i | 0.863323i | 0.902036 | + | 0.431661i | \(0.142072\pi\) | ||||
−0.902036 | + | 0.431661i | \(0.857928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.96093 | 0.247605 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 27.3127i | 2.26819i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 4.07029i | − | 0.333451i | −0.986003 | − | 0.166726i | \(-0.946681\pi\) | ||
0.986003 | − | 0.166726i | \(-0.0533194\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.67975i | 0.706348i | 0.935558 | + | 0.353174i | \(0.114898\pi\) | ||||
−0.935558 | + | 0.353174i | \(0.885102\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.9579 | −2.00467 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.12847 | 0.249679 | 0.124840 | − | 0.992177i | \(-0.460158\pi\) | ||||
0.124840 | + | 0.992177i | \(0.460158\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.76897 | + | 13.6563i | −0.139414 | + | 1.07627i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.1759 | −0.953687 | −0.476844 | − | 0.878988i | \(-0.658219\pi\) | ||||
−0.476844 | + | 0.878988i | \(0.658219\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.56712 | −0.276032 | −0.138016 | − | 0.990430i | \(-0.544073\pi\) | ||||
−0.138016 | + | 0.990430i | \(0.544073\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.93444 | −0.375158 | −0.187579 | − | 0.982249i | \(-0.560064\pi\) | ||||
−0.187579 | + | 0.982249i | \(0.560064\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −26.4724 | − | 3.42909i | −2.00112 | − | 0.259215i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.3696 | 0.849803 | 0.424902 | − | 0.905240i | \(-0.360309\pi\) | ||||
0.424902 | + | 0.905240i | \(0.360309\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 33.8407i | − | 2.48802i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5.57720i | − | 0.407845i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.3332i | 1.61597i | 0.589200 | + | 0.807987i | \(0.299443\pi\) | ||||
−0.589200 | + | 0.807987i | \(0.700557\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.6271 | −1.48477 | −0.742387 | − | 0.669971i | \(-0.766307\pi\) | ||||
−0.742387 | + | 0.669971i | \(0.766307\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.2424i | 1.65595i | 0.560765 | + | 0.827975i | \(0.310507\pi\) | ||||
−0.560765 | + | 0.827975i | \(0.689493\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.2383 | 1.85998 | 0.929992 | − | 0.367580i | \(-0.119814\pi\) | ||||
0.929992 | + | 0.367580i | \(0.119814\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.38975 | + | 18.4487i | −0.167727 | + | 1.29485i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 12.2789i | − | 0.857594i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00635i | 0.0696107i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7821 | −0.879953 | −0.439976 | − | 0.898009i | \(-0.645013\pi\) | ||||
−0.439976 | + | 0.898009i | \(0.645013\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −31.8861 | −2.17462 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.8582 | − | 2.18372i | −1.14441 | − | 0.148240i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 7.53439i | − | 0.506818i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.03528 | −0.270222 | −0.135111 | − | 0.990830i | \(-0.543139\pi\) | ||||
−0.135111 | + | 0.990830i | \(0.543139\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.8189i | 1.38180i | 0.722950 | + | 0.690900i | \(0.242786\pi\) | ||||
−0.722950 | + | 0.690900i | \(0.757214\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.8974 | −1.77743 | −0.888717 | − | 0.458457i | \(-0.848402\pi\) | ||||
−0.888717 | + | 0.458457i | \(0.848402\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.2284 | 1.65277 | 0.826383 | − | 0.563108i | \(-0.190395\pi\) | ||||
0.826383 | + | 0.563108i | \(0.190395\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 38.4142 | 2.50586 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.74266i | 0.565516i | 0.959191 | + | 0.282758i | \(0.0912493\pi\) | ||||
−0.959191 | + | 0.282758i | \(0.908751\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 17.0234i | − | 1.09657i | −0.836291 | − | 0.548286i | \(-0.815281\pi\) | ||
0.836291 | − | 0.548286i | \(-0.184719\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −26.2939 | − | 6.92820i | −1.67986 | − | 0.442627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.35951i | 0.0865034i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.8974i | 1.57151i | 0.618536 | + | 0.785756i | \(0.287726\pi\) | ||||
−0.618536 | + | 0.785756i | \(0.712274\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.70541i | − | 0.484435i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3.56117i | − | 0.222139i | −0.993813 | − | 0.111070i | \(-0.964572\pi\) | ||
0.993813 | − | 0.111070i | \(-0.0354277\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.96093 | − | 22.8582i | 0.183983 | − | 1.42034i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.9737i | 1.53994i | 0.638078 | + | 0.769972i | \(0.279730\pi\) | ||||
−0.638078 | + | 0.769972i | \(0.720270\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 24.9579i | − | 1.53315i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.83453 | 0.172824 | 0.0864122 | − | 0.996259i | \(-0.472460\pi\) | ||||
0.0864122 | + | 0.996259i | \(0.472460\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.86426 | 0.234737 | 0.117369 | − | 0.993088i | \(-0.462554\pi\) | ||||
0.117369 | + | 0.993088i | \(0.462554\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.9367 | 0.900717 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.78356i | 0.107164i | 0.998563 | + | 0.0535818i | \(0.0170638\pi\) | ||||
−0.998563 | + | 0.0535818i | \(0.982936\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.4880 | −1.22221 | −0.611105 | − | 0.791549i | \(-0.709275\pi\) | ||||
−0.611105 | + | 0.791549i | \(0.709275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1392i | 0.721599i | 0.932643 | + | 0.360799i | \(0.117496\pi\) | ||||
−0.932643 | + | 0.360799i | \(0.882504\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.07435 | − | 8.29394i | 0.0634171 | − | 0.489576i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.80823 | 0.165190 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.93444 | −0.288273 | −0.144136 | − | 0.989558i | \(-0.546040\pi\) | ||||
−0.144136 | + | 0.989558i | \(0.546040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 30.1784i | − | 1.75706i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 10.4095i | − | 0.601995i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.5379 | − | 2.78991i | −1.24143 | − | 0.160808i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 48.2043 | 2.76017 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.4987i | − | 1.22699i | −0.789697 | − | 0.613497i | \(-0.789762\pi\) | ||
0.789697 | − | 0.613497i | \(-0.210238\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.52804 | 0.370171 | 0.185086 | − | 0.982722i | \(-0.440744\pi\) | ||||
0.185086 | + | 0.982722i | \(0.440744\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.6347i | 1.90114i | 0.310505 | + | 0.950572i | \(0.399502\pi\) | ||||
−0.310505 | + | 0.950572i | \(0.600498\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4.07029i | − | 0.228610i | −0.993446 | − | 0.114305i | \(-0.963536\pi\) | ||
0.993446 | − | 0.114305i | \(-0.0364642\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 10.4095i | − | 0.582818i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.56077 | 0.142485 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.1784 | 1.11930 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.9474 | + | 3.36109i | 1.43053 | + | 0.185303i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.1368 | 0.831993 | 0.415997 | − | 0.909366i | \(-0.363433\pi\) | ||||
0.415997 | + | 0.909366i | \(0.363433\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 34.2409 | 1.87078 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.51202 | 0.515105 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.1544 | − | 6.98037i | −0.926252 | − | 0.376905i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.61470 | −0.462461 | −0.231231 | − | 0.972899i | \(-0.574275\pi\) | ||||
−0.231231 | + | 0.972899i | \(0.574275\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.5905 | 0.834542 | 0.417271 | − | 0.908782i | \(-0.362987\pi\) | ||||
0.417271 | + | 0.908782i | \(0.362987\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.9078i | 0.633787i | 0.948461 | + | 0.316894i | \(0.102640\pi\) | ||||
−0.948461 | + | 0.316894i | \(0.897360\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 50.3961i | 2.67475i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 11.0263i | − | 0.581946i | −0.956731 | − | 0.290973i | \(-0.906021\pi\) | ||
0.956731 | − | 0.290973i | \(-0.0939790\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5379 | 0.975681 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 52.2706i | 2.73597i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.1695 | 0.583044 | 0.291522 | − | 0.956564i | \(-0.405838\pi\) | ||||
0.291522 | + | 0.956564i | \(0.405838\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.18372 | − | 16.8582i | 0.113373 | − | 0.875233i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 8.14058i | − | 0.421503i | −0.977540 | − | 0.210752i | \(-0.932409\pi\) | ||
0.977540 | − | 0.210752i | \(-0.0675912\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 14.0624i | − | 0.724252i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.4915 | −0.898479 | −0.449240 | − | 0.893411i | \(-0.648305\pi\) | ||||
−0.449240 | + | 0.893411i | \(0.648305\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.8861 | −1.62930 | −0.814652 | − | 0.579950i | \(-0.803072\pi\) | ||||
−0.814652 | + | 0.579950i | \(0.803072\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.0892 | + | 1.95458i | 0.769018 | + | 0.0996144i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 23.2424i | − | 1.17843i | −0.807975 | − | 0.589217i | \(-0.799436\pi\) | ||
0.807975 | − | 0.589217i | \(-0.200564\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.6072 | −0.991581 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 17.2810i | − | 0.869501i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.04995 | 0.153073 | 0.0765364 | − | 0.997067i | \(-0.475614\pi\) | ||||
0.0765364 | + | 0.997067i | \(0.475614\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.4594 | −0.871881 | −0.435941 | − | 0.899975i | \(-0.643584\pi\) | ||||
−0.435941 | + | 0.899975i | \(0.643584\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.8501 | 0.640107 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.8974i | 0.639302i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 17.0234i | − | 0.841751i | −0.907118 | − | 0.420876i | \(-0.861723\pi\) | ||
0.907118 | − | 0.420876i | \(-0.138277\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.64049 | − | 20.3844i | 0.129930 | − | 1.00305i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 40.4354i | − | 1.98489i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 11.3069i | − | 0.552378i | −0.961103 | − | 0.276189i | \(-0.910928\pi\) | ||
0.961103 | − | 0.276189i | \(-0.0890716\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 8.91779i | − | 0.434627i | −0.976102 | − | 0.217313i | \(-0.930271\pi\) | ||
0.976102 | − | 0.217313i | \(-0.0697293\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 38.0081i | − | 1.84366i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.5603 | + | 4.21769i | 1.57570 | + | 0.204108i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15.4617i | − | 0.744763i | −0.928080 | − | 0.372381i | \(-0.878541\pi\) | ||
0.928080 | − | 0.372381i | \(-0.121459\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 7.93455i | − | 0.381310i | −0.981657 | − | 0.190655i | \(-0.938939\pi\) | ||
0.981657 | − | 0.190655i | \(-0.0610612\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.53793 | 0.169242 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.88657 | −0.0900412 | −0.0450206 | − | 0.998986i | \(-0.514335\pi\) | ||||
−0.0450206 | + | 0.998986i | \(0.514335\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.8713 | −1.08665 | −0.543323 | − | 0.839524i | \(-0.682834\pi\) | ||||
−0.543323 | + | 0.839524i | \(0.682834\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 41.5461i | 1.96947i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.04995 | −0.332708 | −0.166354 | − | 0.986066i | \(-0.553199\pi\) | ||||
−0.166354 | + | 0.986066i | \(0.553199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.67975i | 0.220361i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 20.3844 | + | 2.64049i | 0.955638 | + | 0.123788i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.00000 | 0.0935561 | 0.0467780 | − | 0.998905i | \(-0.485105\pi\) | ||||
0.0467780 | + | 0.998905i | \(0.485105\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.57758 | −0.213199 | −0.106600 | − | 0.994302i | \(-0.533996\pi\) | ||||
−0.106600 | + | 0.994302i | \(0.533996\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.2676i | − | 1.17429i | −0.809483 | − | 0.587143i | \(-0.800252\pi\) | ||
0.809483 | − | 0.587143i | \(-0.199748\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.17843i | 0.285904i | 0.989730 | + | 0.142952i | \(0.0456594\pi\) | ||||
−0.989730 | + | 0.142952i | \(0.954341\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.1285 | + | 2.99594i | 1.06797 | + | 0.138340i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.1525 | 0.558773 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.85818i | 0.314675i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.3127 | −1.24795 | −0.623973 | − | 0.781446i | \(-0.714483\pi\) | ||||
−0.623973 | + | 0.781446i | \(0.714483\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.4235i | 0.794444i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 38.4142i | 1.74430i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.1392i | 0.912593i | 0.889828 | + | 0.456296i | \(0.150824\pi\) | ||||
−0.889828 | + | 0.456296i | \(0.849176\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.22089 | 0.416133 | 0.208066 | − | 0.978115i | \(-0.433283\pi\) | ||||
0.208066 | + | 0.978115i | \(0.433283\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.4880 | −1.19296 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.40946 | + | 34.0408i | −0.197791 | + | 1.52694i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.64147 | 0.207781 | 0.103890 | − | 0.994589i | \(-0.466871\pi\) | ||||
0.103890 | + | 0.994589i | \(0.466871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.7455 | 1.05876 | 0.529381 | − | 0.848384i | \(-0.322424\pi\) | ||||
0.529381 | + | 0.848384i | \(0.322424\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.0892 | 0.671461 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.16547 | 0.406252 | 0.203126 | − | 0.979153i | \(-0.434890\pi\) | ||||
0.203126 | + | 0.979153i | \(0.434890\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.57347 | + | 35.3069i | −0.202318 | + | 1.56189i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.9018 | 0.524457 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.6405 | −0.643888 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 18.8360i | − | 0.825219i | −0.910908 | − | 0.412610i | \(-0.864617\pi\) | ||
0.910908 | − | 0.412610i | \(-0.135383\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 41.2543i | − | 1.80392i | −0.431815 | − | 0.901962i | \(-0.642127\pi\) | ||
0.431815 | − | 0.901962i | \(-0.357873\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 24.2043i | − | 1.05436i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.08921 | −0.177792 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.32201i | 0.273837i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.10557 | 0.350434 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.0212 | + | 2.64049i | 0.431644 | + | 0.113734i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.8430i | 1.62700i | 0.581567 | + | 0.813499i | \(0.302440\pi\) | ||||
−0.581567 | + | 0.813499i | \(0.697560\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 67.6814i | 2.89915i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.9541 | −1.36626 | −0.683130 | − | 0.730297i | \(-0.739382\pi\) | ||||
−0.683130 | + | 0.730297i | \(0.739382\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.77950 | 0.203613 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.51202 | − | 11.6727i | 0.0642975 | − | 0.496373i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 17.7207i | − | 0.750849i | −0.926853 | − | 0.375424i | \(-0.877497\pi\) | ||
0.926853 | − | 0.375424i | \(-0.122503\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.4172 | 0.694372 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.12847i | 0.216139i | 0.994143 | + | 0.108070i | \(0.0344670\pi\) | ||||
−0.994143 | + | 0.108070i | \(0.965533\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.87153 | −0.289087 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.4095 | −1.19099 | −0.595493 | − | 0.803360i | \(-0.703043\pi\) | ||||
−0.595493 | + | 0.803360i | \(0.703043\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.8118 | −1.28943 | −0.644716 | − | 0.764422i | \(-0.723024\pi\) | ||||
−0.644716 | + | 0.764422i | \(0.723024\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 52.5116i | − | 2.18989i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.0594i | 1.50117i | 0.660772 | + | 0.750587i | \(0.270229\pi\) | ||||
−0.660772 | + | 0.750587i | \(0.729771\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.53793 | − | 27.3127i | 0.146778 | − | 1.13312i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.51202i | 0.393948i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.1784i | 0.750304i | 0.926963 | + | 0.375152i | \(0.122409\pi\) | ||||
−0.926963 | + | 0.375152i | \(0.877591\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.36744i | 0.179957i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.9014i | 0.447668i | 0.974627 | + | 0.223834i | \(0.0718574\pi\) | ||||
−0.974627 | + | 0.223834i | \(0.928143\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.97363 | − | 38.3961i | 0.203899 | − | 1.57409i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.74532i | 0.234747i | 0.993088 | + | 0.117374i | \(0.0374475\pi\) | ||||
−0.993088 | + | 0.117374i | \(0.962552\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 35.9894i | − | 1.46804i | −0.679129 | − | 0.734019i | \(-0.737642\pi\) | ||
0.679129 | − | 0.734019i | \(-0.262358\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 34.2154 | 1.39105 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.4652 | 0.911832 | 0.455916 | − | 0.890023i | \(-0.349312\pi\) | ||||
0.455916 | + | 0.890023i | \(0.349312\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.7783 | −0.800143 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 36.1954i | − | 1.46192i | −0.682420 | − | 0.730960i | \(-0.739073\pi\) | ||
0.682420 | − | 0.730960i | \(-0.260927\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.8974 | −1.24388 | −0.621942 | − | 0.783063i | \(-0.713656\pi\) | ||||
−0.621942 | + | 0.783063i | \(0.713656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.45941i | − | 0.299819i | −0.988700 | − | 0.149910i | \(-0.952102\pi\) | ||
0.988700 | − | 0.149910i | \(-0.0478982\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.63512 | + | 28.0629i | −0.145638 | + | 1.12432i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 26.3462 | 1.05385 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.8189 | 1.30858 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.2676i | 0.687414i | 0.939077 | + | 0.343707i | \(0.111683\pi\) | ||||
−0.939077 | + | 0.343707i | \(0.888317\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 43.0759i | − | 1.70941i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.5379 | + | 3.56712i | 0.536393 | + | 0.141334i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.09990 | −0.319927 | −0.159963 | − | 0.987123i | \(-0.551138\pi\) | ||||
−0.159963 | + | 0.987123i | \(0.551138\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 24.2177i | − | 0.955052i | −0.878618 | − | 0.477526i | \(-0.841534\pi\) | ||
0.878618 | − | 0.477526i | \(-0.158466\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.14058 | 0.320039 | 0.160020 | − | 0.987114i | \(-0.448844\pi\) | ||||
0.160020 | + | 0.987114i | \(0.448844\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.5017i | 0.451480i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.3502i | 1.38336i | 0.722204 | + | 0.691681i | \(0.243129\pi\) | ||||
−0.722204 | + | 0.691681i | \(0.756871\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.17843i | 0.241411i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.5480 | −1.22894 | −0.614468 | − | 0.788942i | \(-0.710629\pi\) | ||||
−0.614468 | + | 0.788942i | \(0.710629\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.3096 | 0.400995 | 0.200498 | − | 0.979694i | \(-0.435744\pi\) | ||||
0.200498 | + | 0.979694i | \(0.435744\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.897442 | + | 6.92820i | −0.0348013 | + | 0.268664i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −36.5956 | −1.41699 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.3717 | −0.709233 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.0892 | −0.967118 | −0.483559 | − | 0.875312i | \(-0.660656\pi\) | ||||
−0.483559 | + | 0.875312i | \(0.660656\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.1414 | 1.00470 | 0.502348 | − | 0.864665i | \(-0.332469\pi\) | ||||
0.502348 | + | 0.864665i | \(0.332469\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.36109 | + | 25.9474i | −0.128987 | + | 0.995770i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.6886 | 1.51864 | 0.759321 | − | 0.650716i | \(-0.225531\pi\) | ||||
0.759321 | + | 0.650716i | \(0.225531\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 73.4068 | 2.80473 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.8501i | 0.489548i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.4354i | 0.777398i | 0.921365 | + | 0.388699i | \(0.127075\pi\) | ||||
−0.921365 | + | 0.388699i | \(0.872925\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 39.5379i | − | 1.49976i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.9081 | 0.451053 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23.0482i | − | 0.870520i | −0.900305 | − | 0.435260i | \(-0.856657\pi\) | ||
0.900305 | − | 0.435260i | \(-0.143343\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.92185 | −0.223347 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.1922 | + | 1.32025i | 0.383318 | + | 0.0496530i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 6.72217i | − | 0.252457i | −0.992001 | − | 0.126228i | \(-0.959713\pi\) | ||
0.992001 | − | 0.126228i | \(-0.0402872\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 33.4405i | − | 1.25236i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.5017 | −0.430138 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.6686 | 0.547047 | 0.273524 | − | 0.961865i | \(-0.411811\pi\) | ||||
0.273524 | + | 0.961865i | \(0.411811\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.03926 | + | 1.04136i | 0.299398 | + | 0.0387824i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 70.9395i | − | 2.63463i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.99214 | −0.370588 | −0.185294 | − | 0.982683i | \(-0.559324\pi\) | ||||
−0.185294 | + | 0.982683i | \(0.559324\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 30.9234i | − | 1.14374i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.45941 | −0.349391 | −0.174696 | − | 0.984622i | \(-0.555894\pi\) | ||||
−0.174696 | + | 0.984622i | \(0.555894\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.0500 | −0.480701 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.3119 | −0.452899 | −0.226450 | − | 0.974023i | \(-0.572712\pi\) | ||||
−0.226450 | + | 0.974023i | \(0.572712\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.51429i | − | 0.0555537i | −0.999614 | − | 0.0277769i | \(-0.991157\pi\) | ||
0.999614 | − | 0.0277769i | \(-0.00884279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.8110i | 0.579270i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.47502 | + | 0.709205i | 0.200053 | + | 0.0259138i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.5745i | 1.91847i | 0.282606 | + | 0.959236i | \(0.408801\pi\) | ||||
−0.282606 | + | 0.959236i | \(0.591199\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 33.7164i | − | 1.22706i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.2030i | 0.806982i | 0.914984 | + | 0.403491i | \(0.132203\pi\) | ||||
−0.914984 | + | 0.403491i | \(0.867797\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 11.3016i | − | 0.409682i | −0.978795 | − | 0.204841i | \(-0.934332\pi\) | ||
0.978795 | − | 0.204841i | \(-0.0656678\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.92185 | + | 45.7164i | −0.214385 | + | 1.65504i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.5379i | 0.561042i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.4923i | 1.17170i | 0.810419 | + | 0.585851i | \(0.199240\pi\) | ||||
−0.810419 | + | 0.585851i | \(0.800760\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.6535 | −1.28237 | −0.641183 | − | 0.767388i | \(-0.721556\pi\) | ||||
−0.641183 | + | 0.767388i | \(0.721556\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 64.8235 | 2.32853 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.14871 | −0.0769854 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 19.2071i | − | 0.687283i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.1525 | −0.433742 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.00000i | 0.142585i | 0.997455 | + | 0.0712923i | \(0.0227123\pi\) | ||||
−0.997455 | + | 0.0712923i | \(0.977288\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.64147 | − | 0.601231i | −0.165032 | − | 0.0213773i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.8189 | −0.881346 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −44.8604 | −1.58904 | −0.794519 | − | 0.607239i | \(-0.792277\pi\) | ||||
−0.794519 | + | 0.607239i | \(0.792277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.2543i | 1.31796i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 19.9215i | − | 0.703014i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.87153 | − | 53.0478i | 0.242189 | − | 1.86969i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.2284 | −0.886983 | −0.443491 | − | 0.896279i | \(-0.646260\pi\) | ||||
−0.443491 | + | 0.896279i | \(0.646260\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.0785226i | 0.00275730i | 0.999999 | + | 0.00137865i | \(0.000438839\pi\) | ||||
−0.999999 | + | 0.00137865i | \(0.999561\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 47.2969 | 1.65674 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.57982i | 0.195213i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 26.4093i | − | 0.921692i | −0.887480 | − | 0.460846i | \(-0.847546\pi\) | ||
0.887480 | − | 0.460846i | \(-0.152454\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 6.54863i | − | 0.228271i | −0.993465 | − | 0.114135i | \(-0.963590\pi\) | ||
0.993465 | − | 0.114135i | \(-0.0364098\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.0043 | −1.56495 | −0.782476 | − | 0.622681i | \(-0.786043\pi\) | ||||
−0.782476 | + | 0.622681i | \(0.786043\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.4354 | 0.501361 | 0.250681 | − | 0.968070i | \(-0.419346\pi\) | ||||
0.250681 | + | 0.968070i | \(0.419346\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.71902 | − | 25.5000i | 0.232800 | − | 0.883524i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.8564 | 0.479521 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.5420 | 1.53776 | 0.768881 | − | 0.639392i | \(-0.220814\pi\) | ||||
0.768881 | + | 0.639392i | \(0.220814\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.4380 | −0.704760 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 34.9604 | 1.20267 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.1113 | + | 2.99371i | 0.794113 | + | 0.102865i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.3424 | 1.55432 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.4095 | −1.24664 | −0.623318 | − | 0.781968i | \(-0.714216\pi\) | ||||
−0.623318 | + | 0.781968i | \(0.714216\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 50.4579i | 1.72361i | 0.507239 | + | 0.861805i | \(0.330666\pi\) | ||||
−0.507239 | + | 0.861805i | \(0.669334\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 13.0366i | − | 0.444803i | −0.974955 | − | 0.222402i | \(-0.928610\pi\) | ||
0.974955 | − | 0.222402i | \(-0.0713896\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 53.4091i | 1.81807i | 0.416724 | + | 0.909033i | \(0.363178\pi\) | ||||
−0.416724 | + | 0.909033i | \(0.636822\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.1677 | 0.651723 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.58617i | 0.223420i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.6296 | −0.597355 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 51.8704 | + | 6.71902i | 1.75354 | + | 0.227144i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 11.7077i | − | 0.395341i | −0.980269 | − | 0.197670i | \(-0.936662\pi\) | ||
0.980269 | − | 0.197670i | \(-0.0633376\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.0798i | 1.04711i | 0.851993 | + | 0.523553i | \(0.175394\pi\) | ||||
−0.851993 | + | 0.523553i | \(0.824606\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.4834 | 0.790279 | 0.395140 | − | 0.918621i | \(-0.370696\pi\) | ||||
0.395140 | + | 0.918621i | \(0.370696\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.27659 | −0.277901 | −0.138950 | − | 0.990299i | \(-0.544373\pi\) | ||||
−0.138950 | + | 0.990299i | \(0.544373\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.76897 | − | 29.0962i | 0.126407 | − | 0.975856i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 6.72217i | − | 0.224949i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −44.1650 | −1.47627 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 45.1758i | − | 1.50670i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.2043 | 0.806364 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.76897 | 0.258249 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.7600 | −1.05457 | −0.527287 | − | 0.849687i | \(-0.676791\pi\) | ||||
−0.527287 | + | 0.849687i | \(0.676791\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 48.9737i | − | 1.62257i | −0.584650 | − | 0.811285i | \(-0.698768\pi\) | ||
0.584650 | − | 0.811285i | \(-0.301232\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.4108i | 0.510024i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.540588 | + | 4.17331i | −0.0178518 | + | 0.137815i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.0366i | 0.693934i | 0.937877 | + | 0.346967i | \(0.112788\pi\) | ||||
−0.937877 | + | 0.346967i | \(0.887212\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 25.9474i | − | 0.854069i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 87.8948i | 2.88996i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.6173i | 0.545194i | 0.962128 | + | 0.272597i | \(0.0878826\pi\) | ||||
−0.962128 | + | 0.272597i | \(0.912117\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.21238 | + | 4.60123i | −0.0397342 | + | 0.150799i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.6645i | 0.708506i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.2018i | 1.21533i | 0.794194 | + | 0.607665i | \(0.207894\pi\) | ||||
−0.794194 | + | 0.607665i | \(0.792106\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.6535 | 1.55346 | 0.776729 | − | 0.629835i | \(-0.216877\pi\) | ||||
0.776729 | + | 0.629835i | \(0.216877\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.4522 | 0.535757 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.3305 | −0.465679 | −0.232840 | − | 0.972515i | \(-0.574802\pi\) | ||||
−0.232840 | + | 0.972515i | \(0.574802\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 26.9125i | − | 0.873616i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.71636 | 0.120385 | 0.0601924 | − | 0.998187i | \(-0.480829\pi\) | ||||
0.0601924 | + | 0.998187i | \(0.480829\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 86.7530i | − | 2.80726i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 49.5837 | + | 6.42280i | 1.60114 | + | 0.207403i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.2810 | 0.331645 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 80.1258 | 2.57934 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.1651i | 0.841412i | 0.907197 | + | 0.420706i | \(0.138218\pi\) | ||||
−0.907197 | + | 0.420706i | \(0.861782\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 25.7949i | − | 0.827797i | −0.910323 | − | 0.413899i | \(-0.864167\pi\) | ||
0.910323 | − | 0.413899i | \(-0.135833\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.45941 | − | 26.7065i | 0.110904 | − | 0.856170i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.69310 | 0.214131 | 0.107066 | − | 0.994252i | \(-0.465855\pi\) | ||||
0.107066 | + | 0.994252i | \(0.465855\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 15.8341i | − | 0.506062i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52.6826 | −1.68031 | −0.840157 | − | 0.542343i | \(-0.817538\pi\) | ||||
−0.840157 | + | 0.542343i | \(0.817538\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 90.2846i | − | 2.87671i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 42.7235i | − | 1.35853i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 18.9367i | − | 0.601544i | −0.953696 | − | 0.300772i | \(-0.902756\pi\) | ||
0.953696 | − | 0.300772i | \(-0.0972444\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −101.922 | −3.23115 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.33359 | 0.0422352 | 0.0211176 | − | 0.999777i | \(-0.493278\pi\) | ||||
0.0211176 | + | 0.999777i | \(0.493278\pi\) | |||||||
\(998\) | 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 | 4032.2.p.k.1567.1 | 12 | ||
3.2 | odd | 2 | 1344.2.p.d.223.11 | yes | 12 | ||
4.3 | odd | 2 | inner | 4032.2.p.k.1567.4 | 12 | ||
7.6 | odd | 2 | 4032.2.p.j.1567.11 | 12 | |||
8.3 | odd | 2 | 4032.2.p.j.1567.12 | 12 | |||
8.5 | even | 2 | 4032.2.p.j.1567.9 | 12 | |||
12.11 | even | 2 | 1344.2.p.d.223.6 | yes | 12 | ||
21.20 | even | 2 | 1344.2.p.c.223.2 | yes | 12 | ||
24.5 | odd | 2 | 1344.2.p.c.223.1 | ✓ | 12 | ||
24.11 | even | 2 | 1344.2.p.c.223.8 | yes | 12 | ||
28.27 | even | 2 | 4032.2.p.j.1567.10 | 12 | |||
56.13 | odd | 2 | inner | 4032.2.p.k.1567.3 | 12 | ||
56.27 | even | 2 | inner | 4032.2.p.k.1567.2 | 12 | ||
84.83 | odd | 2 | 1344.2.p.c.223.7 | yes | 12 | ||
168.83 | odd | 2 | 1344.2.p.d.223.5 | yes | 12 | ||
168.125 | even | 2 | 1344.2.p.d.223.12 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.2.p.c.223.1 | ✓ | 12 | 24.5 | odd | 2 | ||
1344.2.p.c.223.2 | yes | 12 | 21.20 | even | 2 | ||
1344.2.p.c.223.7 | yes | 12 | 84.83 | odd | 2 | ||
1344.2.p.c.223.8 | yes | 12 | 24.11 | even | 2 | ||
1344.2.p.d.223.5 | yes | 12 | 168.83 | odd | 2 | ||
1344.2.p.d.223.6 | yes | 12 | 12.11 | even | 2 | ||
1344.2.p.d.223.11 | yes | 12 | 3.2 | odd | 2 | ||
1344.2.p.d.223.12 | yes | 12 | 168.125 | even | 2 | ||
4032.2.p.j.1567.9 | 12 | 8.5 | even | 2 | |||
4032.2.p.j.1567.10 | 12 | 28.27 | even | 2 | |||
4032.2.p.j.1567.11 | 12 | 7.6 | odd | 2 | |||
4032.2.p.j.1567.12 | 12 | 8.3 | odd | 2 | |||
4032.2.p.k.1567.1 | 12 | 1.1 | even | 1 | trivial | ||
4032.2.p.k.1567.2 | 12 | 56.27 | even | 2 | inner | ||
4032.2.p.k.1567.3 | 12 | 56.13 | odd | 2 | inner | ||
4032.2.p.k.1567.4 | 12 | 4.3 | odd | 2 | inner |