Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,2,Mod(881,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("1176.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.k (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: | \(9.39040727770\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.10 | ||
Character | \(\chi\) | \(=\) | 1176.881 |
Dual form | 1176.2.k.b.881.9 |
$q$-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 \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).
\(n\) | \(295\) | \(589\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.615077 | + | 1.61916i | −0.355115 | + | 0.934823i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.31193 | 0.586713 | 0.293356 | − | 0.956003i | \(-0.405228\pi\) | ||||
0.293356 | + | 0.956003i | \(0.405228\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.24336 | − | 1.99182i | −0.747786 | − | 0.663939i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.97953i | − | 1.50138i | −0.660652 | − | 0.750692i | \(-0.729720\pi\) | ||
0.660652 | − | 0.750692i | \(-0.270280\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.733252i | 0.203367i | 0.994817 | + | 0.101684i | \(0.0324230\pi\) | ||||
−0.994817 | + | 0.101684i | \(0.967577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.806939 | + | 2.12423i | −0.208351 | + | 0.548473i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.728350 | 0.176651 | 0.0883255 | − | 0.996092i | \(-0.471848\pi\) | ||||
0.0883255 | + | 0.996092i | \(0.471848\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.94457i | − | 1.59319i | −0.604511 | − | 0.796597i | \(-0.706631\pi\) | ||
0.604511 | − | 0.796597i | \(-0.293369\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.92926i | − | 1.65337i | −0.562668 | − | 0.826683i | \(-0.690225\pi\) | ||
0.562668 | − | 0.826683i | \(-0.309775\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.27884 | −0.655768 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.60491 | − | 2.40724i | 0.886216 | − | 0.463273i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.62960i | 0.859696i | 0.902901 | + | 0.429848i | \(0.141433\pi\) | ||||
−0.902901 | + | 0.429848i | \(0.858567\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.80300i | − | 0.323828i | −0.986805 | − | 0.161914i | \(-0.948233\pi\) | ||
0.986805 | − | 0.161914i | \(-0.0517668\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.06265 | + | 3.06280i | 1.40353 | + | 0.533164i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.22423 | −0.858858 | −0.429429 | − | 0.903101i | \(-0.641285\pi\) | ||||
−0.429429 | + | 0.903101i | \(0.641285\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.18725 | − | 0.451007i | −0.190112 | − | 0.0722189i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.83857 | 1.22418 | 0.612089 | − | 0.790789i | \(-0.290329\pi\) | ||||
0.612089 | + | 0.790789i | \(0.290329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.27217 | −0.194004 | −0.0970020 | − | 0.995284i | \(-0.530925\pi\) | ||||
−0.0970020 | + | 0.995284i | \(0.530925\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.94313 | − | 2.61313i | −0.438736 | − | 0.389542i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.24163 | −0.618705 | −0.309352 | − | 0.950947i | \(-0.600112\pi\) | ||||
−0.309352 | + | 0.950947i | \(0.600112\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.447992 | + | 1.17932i | −0.0627314 | + | 0.165137i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 14.4166i | − | 1.98027i | −0.140107 | − | 0.990136i | \(-0.544745\pi\) | ||
0.140107 | − | 0.990136i | \(-0.455255\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.53279i | − | 0.880882i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.2444 | + | 4.27145i | 1.48935 | + | 0.565767i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.35318 | 1.21768 | 0.608840 | − | 0.793293i | \(-0.291635\pi\) | ||||
0.608840 | + | 0.793293i | \(0.291635\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.5881i | 1.73978i | 0.493245 | + | 0.869890i | \(0.335811\pi\) | ||||
−0.493245 | + | 0.869890i | \(0.664189\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.961975i | 0.119318i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.54811 | −0.922148 | −0.461074 | − | 0.887362i | \(-0.652536\pi\) | ||||
−0.461074 | + | 0.887362i | \(0.652536\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.8387 | + | 4.87711i | 1.54560 | + | 0.587135i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.92721i | 0.822109i | 0.911611 | + | 0.411055i | \(0.134839\pi\) | ||||
−0.911611 | + | 0.411055i | \(0.865161\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.79913i | 0.444654i | 0.974972 | + | 0.222327i | \(0.0713653\pi\) | ||||
−0.974972 | + | 0.222327i | \(0.928635\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.01674 | − | 5.30897i | 0.232873 | − | 0.613027i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.5928 | 1.52931 | 0.764653 | − | 0.644442i | \(-0.222910\pi\) | ||||
0.764653 | + | 0.644442i | \(0.222910\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.06532 | + | 8.93673i | 0.118369 | + | 0.992970i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.58972 | 0.723316 | 0.361658 | − | 0.932311i | \(-0.382211\pi\) | ||||
0.361658 | + | 0.932311i | \(0.382211\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.955545 | 0.103643 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.49607 | − | 2.84757i | −0.803663 | − | 0.305291i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.37845 | −0.464115 | −0.232057 | − | 0.972702i | \(-0.574546\pi\) | ||||
−0.232057 | + | 0.972702i | \(0.574546\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.91935 | + | 1.10898i | 0.302722 | + | 0.114996i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 9.11079i | − | 0.934748i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.1510i | − | 1.53835i | −0.639039 | − | 0.769174i | \(-0.720668\pi\) | ||
0.639039 | − | 0.769174i | \(-0.279332\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.91831 | + | 11.1709i | −0.996828 | + | 1.12271i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.9959 | 1.09414 | 0.547068 | − | 0.837088i | \(-0.315744\pi\) | ||||
0.547068 | + | 0.837088i | \(0.315744\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.4292i | − | 1.02762i | −0.857903 | − | 0.513812i | \(-0.828233\pi\) | ||
0.857903 | − | 0.513812i | \(-0.171767\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.08012i | 0.297767i | 0.988855 | + | 0.148883i | \(0.0475679\pi\) | ||||
−0.988855 | + | 0.148883i | \(0.952432\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.7512 | 1.31713 | 0.658565 | − | 0.752524i | \(-0.271164\pi\) | ||||
0.658565 | + | 0.752524i | \(0.271164\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.21330 | − | 8.45886i | 0.304993 | − | 0.802879i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.6414i | − | 1.18920i | −0.804022 | − | 0.594599i | \(-0.797311\pi\) | ||
0.804022 | − | 0.594599i | \(-0.202689\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 10.4026i | − | 0.970051i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.46050 | − | 1.64495i | 0.135024 | − | 0.152075i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.7957 | −1.25415 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.82133 | + | 12.6919i | −0.434724 | + | 1.14439i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.8613 | −0.971461 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.31989 | 0.294593 | 0.147296 | − | 0.989092i | \(-0.452943\pi\) | ||||
0.147296 | + | 0.989092i | \(0.452943\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.782483 | − | 2.05985i | 0.0688937 | − | 0.181359i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.0122 | −1.39899 | −0.699497 | − | 0.714635i | \(-0.746593\pi\) | ||||
−0.699497 | + | 0.714635i | \(0.746593\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.04132 | − | 3.15813i | 0.519954 | − | 0.271808i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10.7533i | − | 0.918720i | −0.888250 | − | 0.459360i | \(-0.848079\pi\) | ||
0.888250 | − | 0.459360i | \(-0.151921\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.5535i | 1.57369i | 0.617152 | + | 0.786844i | \(0.288286\pi\) | ||||
−0.617152 | + | 0.786844i | \(0.711714\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.60893 | − | 6.86787i | 0.219711 | − | 0.578379i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.65125 | 0.305333 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.07372i | 0.504395i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 4.86849i | − | 0.398843i | −0.979914 | − | 0.199421i | \(-0.936094\pi\) | ||
0.979914 | − | 0.199421i | \(-0.0639062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.70120 | 0.138442 | 0.0692209 | − | 0.997601i | \(-0.477949\pi\) | ||||
0.0692209 | + | 0.997601i | \(0.477949\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.63395 | − | 1.45074i | −0.132097 | − | 0.117285i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.36541i | − | 0.189994i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.1776i | 1.45073i | 0.688363 | + | 0.725366i | \(0.258330\pi\) | ||||
−0.688363 | + | 0.725366i | \(0.741670\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23.3428 | + | 8.86733i | 1.85120 | + | 0.703225i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.02332 | −0.393457 | −0.196728 | − | 0.980458i | \(-0.563032\pi\) | ||||
−0.196728 | + | 0.980458i | \(0.563032\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.5776 | + | 4.01817i | 0.823468 | + | 0.312814i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.4374 | −1.27196 | −0.635982 | − | 0.771704i | \(-0.719405\pi\) | ||||
−0.635982 | + | 0.771704i | \(0.719405\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4623 | 0.958642 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.8323 | + | 15.5792i | −1.05778 | + | 1.19137i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.20447 | −0.319660 | −0.159830 | − | 0.987145i | \(-0.551095\pi\) | ||||
−0.159830 | + | 0.987145i | \(0.551095\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.75293 | + | 15.1443i | −0.432417 | + | 1.13831i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.14004i | 0.608415i | 0.952606 | + | 0.304208i | \(0.0983917\pi\) | ||||
−0.952606 | + | 0.304208i | \(0.901608\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.8884i | 1.32963i | 0.747007 | + | 0.664817i | \(0.231490\pi\) | ||||
−0.747007 | + | 0.664817i | \(0.768510\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −22.0013 | − | 8.35775i | −1.62639 | − | 0.617823i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.85382 | −0.503903 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.62684i | − | 0.265221i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.11041i | − | 0.297418i | −0.988881 | − | 0.148709i | \(-0.952488\pi\) | ||
0.988881 | − | 0.148709i | \(-0.0475119\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.22919 | −0.232442 | −0.116221 | − | 0.993223i | \(-0.537078\pi\) | ||||
−0.116221 | + | 0.993223i | \(0.537078\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.55759 | − | 0.591689i | −0.111541 | − | 0.0423717i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.70768i | − | 0.335408i | −0.985837 | − | 0.167704i | \(-0.946365\pi\) | ||
0.985837 | − | 0.167704i | \(-0.0536353\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 16.9835i | − | 1.20393i | −0.798523 | − | 0.601964i | \(-0.794385\pi\) | ||
0.798523 | − | 0.601964i | \(-0.205615\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.64267 | − | 12.2216i | 0.327469 | − | 0.862045i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.2837 | 0.718241 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.7936 | + | 17.7882i | −1.09773 | + | 1.23636i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −34.5807 | −2.39200 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.89126 | −0.130199 | −0.0650997 | − | 0.997879i | \(-0.520737\pi\) | ||||
−0.0650997 | + | 0.997879i | \(0.520737\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.2163 | − | 4.26077i | −0.768526 | − | 0.291943i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.66900 | −0.113825 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.15140 | − | 2.33676i | −0.415673 | − | 0.157904i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.534064i | 0.0359250i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.29671i | 0.622554i | 0.950319 | + | 0.311277i | \(0.100757\pi\) | ||||
−0.950319 | + | 0.311277i | \(0.899243\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.35562 | + | 6.53085i | 0.490374 | + | 0.435390i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.96994 | −0.329867 | −0.164933 | − | 0.986305i | \(-0.552741\pi\) | ||||
−0.164933 | + | 0.986305i | \(0.552741\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.33157i | 0.352320i | 0.984362 | + | 0.176160i | \(0.0563676\pi\) | ||||
−0.984362 | + | 0.176160i | \(0.943632\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.50235i | 0.229447i | 0.993397 | + | 0.114723i | \(0.0365981\pi\) | ||||
−0.993397 | + | 0.114723i | \(0.963402\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.56472 | −0.363002 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.36061 | + | 22.0089i | −0.543080 | + | 1.42963i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 23.4769i | − | 1.51859i | −0.650744 | − | 0.759297i | \(-0.725543\pi\) | ||
0.650744 | − | 0.759297i | \(-0.274457\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0674i | 0.648500i | 0.945971 | + | 0.324250i | \(0.105112\pi\) | ||||
−0.945971 | + | 0.324250i | \(0.894888\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.1252 | − | 3.77185i | −0.970285 | − | 0.241964i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.09212 | 0.324004 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.05319 | + | 10.6698i | −0.256860 | + | 0.676172i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.7932 | −1.24933 | −0.624666 | − | 0.780892i | \(-0.714765\pi\) | ||||
−0.624666 | + | 0.780892i | \(0.714765\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −39.4840 | −2.48234 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.587734 | + | 1.54718i | −0.0368053 | + | 0.0968882i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.6163 | −0.786984 | −0.393492 | − | 0.919328i | \(-0.628733\pi\) | ||||
−0.393492 | + | 0.919328i | \(0.628733\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.22133 | − | 10.3859i | 0.570786 | − | 0.642869i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.33199i | 0.390447i | 0.980759 | + | 0.195224i | \(0.0625433\pi\) | ||||
−0.980759 | + | 0.195224i | \(0.937457\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 18.9136i | − | 1.16185i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.69309 | − | 7.08941i | 0.164814 | − | 0.433865i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.3839 | 1.48671 | 0.743356 | − | 0.668896i | \(-0.233233\pi\) | ||||
0.743356 | + | 0.668896i | \(0.233233\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.344072i | 0.0209009i | 0.999945 | + | 0.0104504i | \(0.00332654\pi\) | ||||
−0.999945 | + | 0.0104504i | \(0.996673\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.3271i | 0.984559i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.2360 | 0.735187 | 0.367594 | − | 0.929987i | \(-0.380182\pi\) | ||||
0.367594 | + | 0.929987i | \(0.380182\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.59125 | + | 4.04478i | −0.215002 | + | 0.242155i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 16.6761i | − | 0.994810i | −0.867519 | − | 0.497405i | \(-0.834286\pi\) | ||
0.867519 | − | 0.497405i | \(-0.165714\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.10159i | 0.184371i | 0.995742 | + | 0.0921853i | \(0.0293852\pi\) | ||||
−0.995742 | + | 0.0921853i | \(0.970615\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.7518 | + | 5.60384i | 0.873823 | + | 0.331943i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4695 | −0.968794 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.5319 | + | 9.31902i | 1.43808 | + | 0.546291i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.2490 | 0.949278 | 0.474639 | − | 0.880181i | \(-0.342579\pi\) | ||||
0.474639 | + | 0.880181i | \(0.342579\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2707 | 0.714429 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.9869 | − | 22.9303i | −0.695550 | − | 1.33055i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.81415 | 0.336241 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.76334 | + | 17.8042i | −0.388544 | + | 1.02282i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.8267i | 1.02075i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.82559i | 0.161265i | 0.996744 | + | 0.0806326i | \(0.0256940\pi\) | ||||
−0.996744 | + | 0.0806326i | \(0.974306\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.8866 | + | 6.41479i | 0.960646 | + | 0.364925i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.4036 | −0.930163 | −0.465081 | − | 0.885268i | \(-0.653975\pi\) | ||||
−0.465081 | + | 0.885268i | \(0.653975\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 0.324800i | − | 0.0183588i | −0.999958 | − | 0.00917938i | \(-0.997078\pi\) | ||
0.999958 | − | 0.00917938i | \(-0.00292193\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0488i | 0.676726i | 0.941016 | + | 0.338363i | \(0.109873\pi\) | ||||
−0.941016 | + | 0.338363i | \(0.890127\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.0532 | 1.29073 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.98721 | − | 1.89451i | −0.278359 | − | 0.105742i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.05808i | − | 0.281439i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.40421i | − | 0.133362i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.45808 | + | 22.2655i | −0.467733 | + | 1.23128i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.00005 | 0.384758 | 0.192379 | − | 0.981321i | \(-0.438380\pi\) | ||||
0.192379 | + | 0.981321i | \(0.438380\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.7198 | + | 10.4057i | 0.642242 | + | 0.570229i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.90259 | −0.541036 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.2829 | −0.669094 | −0.334547 | − | 0.942379i | \(-0.608583\pi\) | ||||
−0.334547 | + | 0.942379i | \(0.608583\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.4684 | + | 7.77541i | 1.11169 | + | 0.422302i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.97809 | −0.486191 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.8435 | + | 6.39843i | 0.906826 | + | 0.344480i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 20.7785i | − | 1.11545i | −0.830027 | − | 0.557724i | \(-0.811675\pi\) | ||
0.830027 | − | 0.557724i | \(-0.188325\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.72878i | 0.0925396i | 0.998929 | + | 0.0462698i | \(0.0147334\pi\) | ||||
−0.998929 | + | 0.0462698i | \(0.985267\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.76511 | + | 3.37656i | 0.0942146 | + | 0.180227i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.6311 | 0.565837 | 0.282919 | − | 0.959144i | \(-0.408697\pi\) | ||||
0.282919 | + | 0.959144i | \(0.408697\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.08802i | 0.482342i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.22497i | 0.222985i | 0.993765 | + | 0.111493i | \(0.0355632\pi\) | ||||
−0.993765 | + | 0.111493i | \(0.964437\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −29.2271 | −1.53827 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.48542 | − | 22.3374i | 0.445369 | − | 1.17241i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.98419i | 0.260885i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.0423i | 1.25500i | 0.778617 | + | 0.627499i | \(0.215921\pi\) | ||||
−0.778617 | + | 0.627499i | \(0.784079\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.5847 | − | 15.6130i | −0.915424 | − | 0.812780i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.5901 | 1.68745 | 0.843727 | − | 0.536773i | \(-0.180357\pi\) | ||||
0.843727 | + | 0.536773i | \(0.180357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.68052 | − | 17.5861i | 0.344980 | − | 0.908143i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.39466 | −0.174834 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.2333 | 0.987948 | 0.493974 | − | 0.869477i | \(-0.335544\pi\) | ||||
0.493974 | + | 0.869477i | \(0.335544\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.04199 | + | 5.37544i | −0.104614 | + | 0.275392i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.9404 | −1.32549 | −0.662745 | − | 0.748845i | \(-0.730609\pi\) | ||||
−0.662745 | + | 0.748845i | \(0.730609\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.85393 | + | 2.53393i | 0.145074 | + | 0.128807i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.5765i | 1.14467i | 0.820019 | + | 0.572336i | \(0.193963\pi\) | ||||
−0.820019 | + | 0.572336i | \(0.806037\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.77528i | − | 0.292069i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.84876 | − | 25.9264i | 0.496804 | − | 1.30781i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.8328 | 0.897264 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 6.72959i | − | 0.337748i | −0.985638 | − | 0.168874i | \(-0.945987\pi\) | ||
0.985638 | − | 0.168874i | \(-0.0540132\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.54640i | 0.326911i | 0.986551 | + | 0.163456i | \(0.0522641\pi\) | ||||
−0.986551 | + | 0.163456i | \(0.947736\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.32205 | 0.0658562 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.39763 | + | 11.7244i | 0.0694487 | + | 0.582588i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.0142i | 1.28948i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 20.2168i | − | 0.999654i | −0.866125 | − | 0.499827i | \(-0.833397\pi\) | ||
0.866125 | − | 0.499827i | \(-0.166603\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.4114 | + | 6.61414i | 0.858840 | + | 0.326251i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.64525 | 0.424379 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.0411 | − | 11.4118i | −1.47112 | − | 0.558840i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.0519 | 0.637627 | 0.318813 | − | 0.947817i | \(-0.396716\pi\) | ||||
0.318813 | + | 0.947817i | \(0.396716\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.1602 | −1.61613 | −0.808065 | − | 0.589093i | \(-0.799485\pi\) | ||||
−0.808065 | + | 0.589093i | \(0.799485\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.51549 | + | 8.44855i | 0.462659 | + | 0.410782i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.38814 | −0.115842 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.24580 | + | 5.91195i | −0.108428 | + | 0.285432i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.12004i | 0.0539506i | 0.999636 | + | 0.0269753i | \(0.00858755\pi\) | ||||
−0.999636 | + | 0.0269753i | \(0.991412\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 29.9594i | − | 1.43976i | −0.694100 | − | 0.719878i | \(-0.744198\pi\) | ||
0.694100 | − | 0.719878i | \(-0.255802\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.83432 | − | 3.73581i | −0.471520 | − | 0.179118i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −55.0653 | −2.63413 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 21.6375i | − | 1.03270i | −0.856378 | − | 0.516350i | \(-0.827290\pi\) | ||
0.856378 | − | 0.516350i | \(-0.172710\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 7.88010i | − | 0.374395i | −0.982322 | − | 0.187198i | \(-0.940060\pi\) | ||
0.982322 | − | 0.187198i | \(-0.0599404\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.74422 | −0.272302 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.88287 | + | 2.99450i | 0.372847 | + | 0.141635i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.5174i | 1.39301i | 0.717550 | + | 0.696507i | \(0.245263\pi\) | ||||
−0.717550 | + | 0.696507i | \(0.754737\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 39.0324i | − | 1.83796i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.04637 | + | 2.75452i | −0.0491628 | + | 0.129419i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.57745 | 0.120568 | 0.0602839 | − | 0.998181i | \(-0.480799\pi\) | ||||
0.0602839 | + | 0.998181i | \(0.480799\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.35399 | − | 1.75331i | 0.156551 | − | 0.0818376i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.8387 | 1.43630 | 0.718151 | − | 0.695888i | \(-0.244989\pi\) | ||||
0.718151 | + | 0.695888i | \(0.244989\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.6548 | 1.70349 | 0.851745 | − | 0.523956i | \(-0.175544\pi\) | ||||
0.851745 | + | 0.523956i | \(0.175544\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.82998 | + | 1.45491i | 0.177611 | + | 0.0674699i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.0771 | 1.62318 | 0.811588 | − | 0.584231i | \(-0.198604\pi\) | ||||
0.811588 | + | 0.584231i | \(0.198604\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −29.4325 | − | 11.1806i | −1.35618 | − | 0.515177i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.33480i | 0.291274i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.7701i | 1.04477i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28.7152 | + | 32.3416i | −1.31478 | + | 1.48082i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.7683 | 1.31446 | 0.657228 | − | 0.753691i | \(-0.271729\pi\) | ||||
0.657228 | + | 0.753691i | \(0.271729\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 3.83067i | − | 0.174664i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 19.8770i | − | 0.902569i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.0750 | 1.63471 | 0.817356 | − | 0.576133i | \(-0.195439\pi\) | ||||
0.817356 | + | 0.576133i | \(0.195439\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.08973 | − | 8.13356i | 0.139723 | − | 0.367812i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 26.0949i | − | 1.17764i | −0.808263 | − | 0.588822i | \(-0.799592\pi\) | ||
0.808263 | − | 0.588822i | \(-0.200408\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.37197i | 0.151866i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.0121 | + | 14.6554i | −0.584852 | + | 0.658711i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.5440 | −0.830143 | −0.415072 | − | 0.909789i | \(-0.636243\pi\) | ||||
−0.415072 | + | 0.909789i | \(0.636243\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.1103 | − | 26.6148i | 0.451694 | − | 1.18906i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.2682 | 0.859126 | 0.429563 | − | 0.903037i | \(-0.358668\pi\) | ||||
0.429563 | + | 0.903037i | \(0.358668\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.4259 | 0.641943 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.66531 | + | 20.1785i | −0.340428 | + | 0.896160i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.9311 | 1.14938 | 0.574688 | − | 0.818373i | \(-0.305123\pi\) | ||||
0.574688 | + | 0.818373i | \(0.305123\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.7172 | − | 31.9791i | −0.738084 | − | 1.41191i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 13.6824i | − | 0.602920i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.1213i | 0.928914i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.58607 | − | 6.80771i | 0.113516 | − | 0.298825i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.0717 | 0.485059 | 0.242530 | − | 0.970144i | \(-0.422023\pi\) | ||||
0.242530 | + | 0.970144i | \(0.422023\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.4586i | 1.55050i | 0.631656 | + | 0.775249i | \(0.282376\pi\) | ||||
−0.631656 | + | 0.775249i | \(0.717624\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.31322i | − | 0.0572046i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −39.8732 | −1.73362 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.9825 | − | 18.6298i | −0.910565 | − | 0.808466i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.74764i | 0.248958i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.04091i | 0.174704i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.1800 | − | 5.00676i | −0.568760 | − | 0.216057i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.04913 | −0.346059 | −0.173029 | − | 0.984917i | \(-0.555356\pi\) | ||||
−0.173029 | + | 0.984917i | \(0.555356\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −28.9642 | − | 11.0027i | −1.24297 | − | 0.472173i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.0407 | 0.772777 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.3821 | 0.657690 | 0.328845 | − | 0.944384i | \(-0.393341\pi\) | ||||
0.328845 | + | 0.944384i | \(0.393341\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.0651 | − | 30.4830i | 1.15511 | − | 1.30098i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.1506 | 1.36966 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.21563 | − | 11.0974i | 0.178944 | − | 0.471060i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 34.1048i | − | 1.44507i | −0.691336 | − | 0.722534i | \(-0.742977\pi\) | ||
0.691336 | − | 0.722534i | \(-0.257023\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.932820i | − | 0.0394541i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.87244 | + | 2.23079i | 0.247934 | + | 0.0941840i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.6655 | −1.37669 | −0.688343 | − | 0.725385i | \(-0.741662\pi\) | ||||
−0.688343 | + | 0.725385i | \(0.741662\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 16.5846i | − | 0.697718i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 23.9380i | − | 1.00353i | −0.865004 | − | 0.501766i | \(-0.832684\pi\) | ||
0.865004 | − | 0.501766i | \(-0.167316\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.9501 | −1.04413 | −0.522065 | − | 0.852906i | \(-0.674838\pi\) | ||||
−0.522065 | + | 0.852906i | \(0.674838\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.65540 | + | 2.52822i | 0.278034 | + | 0.105618i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 25.9988i | 1.08422i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.7925i | 0.865601i | 0.901490 | + | 0.432801i | \(0.142475\pi\) | ||||
−0.901490 | + | 0.432801i | \(0.857525\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.98620 | − | 5.22858i | 0.0825438 | − | 0.217292i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −71.7879 | −2.97315 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.91608 | − | 2.15806i | 0.0792201 | − | 0.0892246i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.7010 | 0.482951 | 0.241475 | − | 0.970407i | \(-0.422369\pi\) | ||||
0.241475 | + | 0.970407i | \(0.422369\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.5211 | −0.515922 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.62249 | + | 2.89559i | 0.313547 | + | 0.119109i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.6454 | 1.38165 | 0.690826 | − | 0.723021i | \(-0.257247\pi\) | ||||
0.690826 | + | 0.723021i | \(0.257247\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27.4990 | + | 10.4462i | 1.12546 | + | 0.427533i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.2044i | 0.457800i | 0.973450 | + | 0.228900i | \(0.0735129\pi\) | ||||
−0.973450 | + | 0.228900i | \(0.926487\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.08245i | − | 0.248108i | −0.992275 | − | 0.124054i | \(-0.960410\pi\) | ||
0.992275 | − | 0.124054i | \(-0.0395897\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.9331 | + | 15.0345i | 0.689570 | + | 0.612251i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.0990 | −0.735829 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.92845i | − | 0.281217i | −0.990065 | − | 0.140608i | \(-0.955094\pi\) | ||
0.990065 | − | 0.140608i | \(-0.0449059\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3.11018i | − | 0.125824i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.5231 | 0.546194 | 0.273097 | − | 0.961987i | \(-0.411952\pi\) | ||||
0.273097 | + | 0.961987i | \(0.411952\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.32524 | + | 16.6509i | −0.255058 | + | 0.671428i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.82786i | 0.154104i | 0.997027 | + | 0.0770519i | \(0.0245507\pi\) | ||||
−0.997027 | + | 0.0770519i | \(0.975449\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.89220i | 0.236827i | 0.992964 | + | 0.118414i | \(0.0377809\pi\) | ||||
−0.992964 | + | 0.118414i | \(0.962219\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.0876 | − | 36.5136i | −0.765959 | − | 1.46524i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.14498 | 0.0857994 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.2698 | − | 55.9917i | 0.849434 | − | 2.23609i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.80507 | −0.151718 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.83697 | −0.152747 | −0.0763737 | − | 0.997079i | \(-0.524334\pi\) | ||||
−0.0763737 | + | 0.997079i | \(0.524334\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.16327 | − | 3.06225i | 0.0462358 | − | 0.121713i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.35547 | 0.172841 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.7977 | − | 15.5402i | 0.545830 | − | 0.614762i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.98598i | 0.157437i | 0.996897 | + | 0.0787183i | \(0.0250828\pi\) | ||||
−0.996897 | + | 0.0787183i | \(0.974917\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 15.4887i | − | 0.610814i | −0.952222 | − | 0.305407i | \(-0.901207\pi\) | ||
0.952222 | − | 0.305407i | \(-0.0987925\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.02656 | − | 2.70237i | 0.0404209 | − | 0.106406i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.6256 | −0.810874 | −0.405437 | − | 0.914123i | \(-0.632881\pi\) | ||||
−0.405437 | + | 0.914123i | \(0.632881\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 46.5744i | − | 1.82821i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 50.2427i | − | 1.96615i | −0.183203 | − | 0.983075i | \(-0.558646\pi\) | ||
0.183203 | − | 0.983075i | \(-0.441354\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.0069 | −0.820808 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.56717 | − | 8.52281i | 0.295224 | − | 0.332507i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.6160i | 1.34845i | 0.738528 | + | 0.674223i | \(0.235521\pi\) | ||||
−0.738528 | + | 0.674223i | \(0.764479\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.98831i | 0.388500i | 0.980952 | + | 0.194250i | \(0.0622274\pi\) | ||||
−0.980952 | + | 0.194250i | \(0.937773\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.864736 | − | 0.328491i | −0.0335835 | − | 0.0127575i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.7093 | 1.42139 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.0529 | − | 5.71819i | −0.581977 | − | 0.221078i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 67.6624 | 2.61208 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.78901 | −0.338791 | −0.169396 | − | 0.985548i | \(-0.554182\pi\) | ||||
−0.169396 | + | 0.985548i | \(0.554182\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.0988 | + | 7.89294i | −0.581152 | + | 0.303799i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.75875 | −0.182894 | −0.0914468 | − | 0.995810i | \(-0.529149\pi\) | ||||
−0.0914468 | + | 0.995810i | \(0.529149\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.05690 | − | 8.04714i | 0.117141 | − | 0.308367i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.0958i | 0.998529i | 0.866450 | + | 0.499265i | \(0.166396\pi\) | ||||
−0.866450 | + | 0.499265i | \(0.833604\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 14.1076i | − | 0.539025i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.63267 | − | 3.27933i | −0.329357 | − | 0.125114i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.5710 | 0.402723 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.6050i | 1.16427i | 0.813093 | + | 0.582134i | \(0.197782\pi\) | ||||
−0.813093 | + | 0.582134i | \(0.802218\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24.3409i | 0.923303i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.70922 | 0.216252 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.67087 | − | 2.15422i | −0.214492 | − | 0.0814800i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.8510i | 1.73177i | 0.500246 | + | 0.865884i | \(0.333243\pi\) | ||||
−0.500246 | + | 0.865884i | \(0.666757\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.2800i | 1.36833i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.42273 | − | 9.01017i | 0.128908 | − | 0.339343i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.32458 | −0.275080 | −0.137540 | − | 0.990496i | \(-0.543920\pi\) | ||||
−0.137540 | + | 0.990496i | \(0.543920\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.4935 | − | 27.0743i | −1.14359 | − | 1.01537i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.2965 | −0.535407 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.79018 | 0.179143 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 38.0128 | + | 14.4401i | 1.41962 | + | 0.539276i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.6425 | 0.695246 | 0.347623 | − | 0.937634i | \(-0.386989\pi\) | ||||
0.347623 | + | 0.937634i | \(0.386989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.3008 | − | 6.19225i | −0.606233 | − | 0.230292i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 15.1797i | − | 0.563761i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.44113i | 0.164712i | 0.996603 | + | 0.0823562i | \(0.0262445\pi\) | ||||
−0.996603 | + | 0.0823562i | \(0.973755\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.4104 | − | 22.1702i | 0.570757 | − | 0.821119i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.926585 | −0.0342710 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.3288i | 1.37877i | 0.724395 | + | 0.689385i | \(0.242119\pi\) | ||||
−0.724395 | + | 0.689385i | \(0.757881\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 37.5860i | 1.38450i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.7067 | 0.577780 | 0.288890 | − | 0.957362i | \(-0.406714\pi\) | ||||
0.288890 | + | 0.957362i | \(0.406714\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.13205 | + | 8.24496i | −0.115059 | + | 0.302886i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 41.4427i | − | 1.52039i | −0.649697 | − | 0.760193i | \(-0.725104\pi\) | ||
0.649697 | − | 0.760193i | \(-0.274896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 6.38712i | − | 0.234006i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.7831 | − | 13.1255i | −0.540886 | − | 0.480238i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.9195 | 0.434948 | 0.217474 | − | 0.976066i | \(-0.430218\pi\) | ||||
0.217474 | + | 0.976066i | \(0.430218\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.1743 | − | 32.0483i | 0.443657 | − | 1.16790i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.23186 | 0.0812256 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.9855 | 0.762731 | 0.381365 | − | 0.924424i | \(-0.375454\pi\) | ||||
0.381365 | + | 0.924424i | \(0.375454\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 24.2857 | − | 63.9309i | 0.881516 | − | 2.32054i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.4963 | −0.960489 | −0.480245 | − | 0.877135i | \(-0.659452\pi\) | ||||
−0.480245 | + | 0.877135i | \(0.659452\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.14363 | − | 1.90327i | −0.0775031 | − | 0.0688129i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.85823i | 0.247636i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 49.5271i | − | 1.78599i | −0.450062 | − | 0.892997i | \(-0.648598\pi\) | ||
0.450062 | − | 0.892997i | \(-0.351402\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.76001 | − | 20.4278i | 0.279470 | − | 0.735690i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.37448 | 0.265242 | 0.132621 | − | 0.991167i | \(-0.457661\pi\) | ||||
0.132621 | + | 0.991167i | \(0.457661\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.91175i | 0.212356i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 54.4355i | − | 1.95035i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.4943 | 1.23430 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.1445 | + | 21.3189i | 0.398274 | + | 0.761876i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.8478i | 0.851164i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 36.1045i | − | 1.28699i | −0.765452 | − | 0.643493i | \(-0.777484\pi\) | ||
0.765452 | − | 0.643493i | \(-0.222516\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.2525 | − | 3.89467i | −0.364999 | − | 0.138654i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.96351 | −0.353815 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 30.6241 | + | 11.6333i | 1.08613 | + | 0.412591i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.6502 | 0.908576 | 0.454288 | − | 0.890855i | \(-0.349894\pi\) | ||||
0.454288 | + | 0.890855i | \(0.349894\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.08939 | −0.109295 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.82244 | + | 8.72108i | 0.347059 | + | 0.308144i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.9179 | 0.667597 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.9980 | + | 39.4814i | −0.527954 | + | 1.38981i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.6220i | 1.14693i | 0.819230 | + | 0.573464i | \(0.194401\pi\) | ||||
−0.819230 | + | 0.573464i | \(0.805599\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 12.7234i | − | 0.446779i | −0.974729 | − | 0.223390i | \(-0.928288\pi\) | ||
0.974729 | − | 0.223390i | \(-0.0717122\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.557107 | − | 0.211631i | −0.0195386 | − | 0.00742221i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.59025 | −0.230846 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.83467i | 0.309086i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.7965i | 1.84261i | 0.388842 | + | 0.921305i | \(0.372875\pi\) | ||||
−0.388842 | + | 0.921305i | \(0.627125\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.6738 | 0.441783 | 0.220891 | − | 0.975298i | \(-0.429103\pi\) | ||||
0.220891 | + | 0.975298i | \(0.429103\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −26.4361 | − | 10.0424i | −0.920388 | − | 0.349632i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.4839i | 1.06003i | 0.847988 | + | 0.530015i | \(0.177814\pi\) | ||||
−0.847988 | + | 0.530015i | \(0.822186\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 7.95851i | − | 0.276410i | −0.990404 | − | 0.138205i | \(-0.955867\pi\) | ||
0.990404 | − | 0.138205i | \(-0.0441334\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.52606 | + | 19.8120i | −0.261076 | + | 0.687270i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.5647 | −0.746278 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.34025 | − | 8.30266i | −0.150021 | − | 0.286982i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.9255 | 0.549808 | 0.274904 | − | 0.961472i | \(-0.411354\pi\) | ||||
0.274904 | + | 0.961472i | \(0.411354\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.56677 | 0.260923 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.0012 | + | 10.2571i | 0.929971 | + | 0.353272i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.3497 | 0.562448 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.02198 | − | 1.90772i | −0.172354 | − | 0.0654728i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 41.4243i | 1.42001i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.3170i | 0.832597i | 0.909228 | + | 0.416298i | \(0.136673\pi\) | ||||
−0.909228 | + | 0.416298i | \(0.863327\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.1470 | + | 20.4388i | −0.620616 | + | 0.698992i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.2919 | −1.51298 | −0.756491 | − | 0.654005i | \(-0.773088\pi\) | ||||
−0.756491 | + | 0.654005i | \(0.773088\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.8833i | 0.780769i | 0.920652 | + | 0.390385i | \(0.127658\pi\) | ||||
−0.920652 | + | 0.390385i | \(0.872342\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.6628i | 0.805490i | 0.915312 | + | 0.402745i | \(0.131944\pi\) | ||||
−0.915312 | + | 0.402745i | \(0.868056\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.51597 | −0.187549 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.1300 | − | 26.6668i | 0.344034 | − | 0.905651i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 67.6856i | − | 2.29608i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 5.53466i | − | 0.187535i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −30.1780 | + | 33.9891i | −1.02137 | + | 1.15036i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.5159 | 0.996680 | 0.498340 | − | 0.866982i | \(-0.333943\pi\) | ||||
0.498340 | + | 0.866982i | \(0.333943\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.99441 | + | 26.3098i | −0.337103 | + | 0.887406i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.0113 | 0.404673 | 0.202336 | − | 0.979316i | \(-0.435147\pi\) | ||||
0.202336 | + | 0.979316i | \(0.435147\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.4428 | −0.889871 | −0.444935 | − | 0.895563i | \(-0.646773\pi\) | ||||
−0.444935 | + | 0.895563i | \(0.646773\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.54744 | + | 19.8683i | −0.253704 | + | 0.667864i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.12476 | 0.104919 | 0.0524596 | − | 0.998623i | \(-0.483294\pi\) | ||||
0.0524596 | + | 0.998623i | \(0.483294\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 44.5007 | − | 5.30480i | 1.49083 | − | 0.177718i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.4563i | 0.985717i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.6792i | 0.356965i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.57615 | + | 9.41403i | −0.119404 | + | 0.314325i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.34718 | 0.278394 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 10.5003i | − | 0.349817i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.4683i | 0.780113i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −57.9808 | −1.92522 | −0.962610 | − | 0.270890i | \(-0.912682\pi\) | ||||
−0.962610 | + | 0.270890i | \(0.912682\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.6678 | − | 21.9019i | −0.818180 | − | 0.726439i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 0.434872i | − | 0.0144079i | −0.999974 | − | 0.00720397i | \(-0.997707\pi\) | ||
0.999974 | − | 0.00720397i | \(-0.00229312\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 32.8137i | − | 1.08597i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −28.8642 | − | 10.9648i | −0.954222 | − | 0.362485i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.1535 | 1.32454 | 0.662271 | − | 0.749264i | \(-0.269593\pi\) | ||||
0.662271 | + | 0.749264i | \(0.269593\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.57509 | − | 1.73796i | −0.150754 | − | 0.0572677i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.07939 | −0.167190 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.1294 | 0.563211 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.7732 | + | 23.3965i | −0.682280 | + | 0.768443i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.1366 | 0.923132 | 0.461566 | − | 0.887106i | \(-0.347288\pi\) | ||||
0.461566 | + | 0.887106i | \(0.347288\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.0895 | − | 26.5600i | 0.330315 | − | 0.869537i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 4.75816i | − | 0.155609i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.1209i | 1.86606i | 0.359801 | + | 0.933029i | \(0.382844\pi\) | ||||
−0.359801 | + | 0.933029i | \(0.617156\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.525902 | + | 0.199777i | 0.0171622 | + | 0.00651947i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.0352 | 0.327138 | 0.163569 | − | 0.986532i | \(-0.447699\pi\) | ||||
0.163569 | + | 0.986532i | \(0.447699\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 62.1541i | − | 2.02401i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.9443i | 0.583110i | 0.956554 | + | 0.291555i | \(0.0941726\pi\) | ||||
−0.956554 | + | 0.291555i | \(0.905827\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.78572 | −0.0904282 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.5089 | − | 7.41092i | −0.632618 | − | 0.240316i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.76188i | 0.0570730i | 0.999593 | + | 0.0285365i | \(0.00908469\pi\) | ||||
−0.999593 | + | 0.0285365i | \(0.990915\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 5.39256i | − | 0.174499i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.1795 | + | 37.3269i | −0.458359 | + | 1.20661i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.7492 | 0.895135 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.13505 | − | 6.90983i | 0.197699 | − | 0.222666i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.23647 | −0.136377 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.8379 | −0.670102 | −0.335051 | − | 0.942200i | \(-0.608754\pi\) | ||||
−0.335051 | + | 0.942200i | \(0.608754\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.18985 | + | 3.11111i | 0.263096 | + | 0.0999433i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.7633 | −0.730509 | −0.365254 | − | 0.930908i | \(-0.619018\pi\) | ||||
−0.365254 | + | 0.930908i | \(0.619018\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.89281 | + | 1.47878i | 0.124670 | + | 0.0473588i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 0.531619i | − | 0.0170080i | −0.999964 | − | 0.00850401i | \(-0.997293\pi\) | ||
0.999964 | − | 0.00850401i | \(-0.00270694\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.8026i | 0.696815i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.8490 | − | 27.3900i | −0.984932 | − | 0.874495i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.67319 | 0.308527 | 0.154263 | − | 0.988030i | \(-0.450700\pi\) | ||||
0.154263 | + | 0.988030i | \(0.450700\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 6.17615i | − | 0.196788i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.0874i | 0.320759i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.14717 | 0.131739 | 0.0658695 | − | 0.997828i | \(-0.479018\pi\) | ||||
0.0658695 | + | 0.997828i | \(0.479018\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.30557 | + | 11.3342i | −0.136633 | + | 0.359680i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 22.2812i | − | 0.706361i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 4.38581i | − | 0.138900i | −0.997585 | − | 0.0694500i | \(-0.977876\pi\) | ||
0.997585 | − | 0.0694500i | \(-0.0221244\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24.0571 | + | 12.5759i | −0.761133 | + | 0.397885i |
(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 | 1176.2.k.b.881.10 | yes | 24 | |
3.2 | odd | 2 | inner | 1176.2.k.b.881.16 | yes | 24 | |
4.3 | odd | 2 | 2352.2.k.j.881.15 | 24 | |||
7.2 | even | 3 | 1176.2.u.c.521.6 | 48 | |||
7.3 | odd | 6 | 1176.2.u.c.1097.2 | 48 | |||
7.4 | even | 3 | 1176.2.u.c.1097.23 | 48 | |||
7.5 | odd | 6 | 1176.2.u.c.521.19 | 48 | |||
7.6 | odd | 2 | inner | 1176.2.k.b.881.15 | yes | 24 | |
12.11 | even | 2 | 2352.2.k.j.881.9 | 24 | |||
21.2 | odd | 6 | 1176.2.u.c.521.2 | 48 | |||
21.5 | even | 6 | 1176.2.u.c.521.23 | 48 | |||
21.11 | odd | 6 | 1176.2.u.c.1097.19 | 48 | |||
21.17 | even | 6 | 1176.2.u.c.1097.6 | 48 | |||
21.20 | even | 2 | inner | 1176.2.k.b.881.9 | ✓ | 24 | |
28.27 | even | 2 | 2352.2.k.j.881.10 | 24 | |||
84.83 | odd | 2 | 2352.2.k.j.881.16 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.2.k.b.881.9 | ✓ | 24 | 21.20 | even | 2 | inner | |
1176.2.k.b.881.10 | yes | 24 | 1.1 | even | 1 | trivial | |
1176.2.k.b.881.15 | yes | 24 | 7.6 | odd | 2 | inner | |
1176.2.k.b.881.16 | yes | 24 | 3.2 | odd | 2 | inner | |
1176.2.u.c.521.2 | 48 | 21.2 | odd | 6 | |||
1176.2.u.c.521.6 | 48 | 7.2 | even | 3 | |||
1176.2.u.c.521.19 | 48 | 7.5 | odd | 6 | |||
1176.2.u.c.521.23 | 48 | 21.5 | even | 6 | |||
1176.2.u.c.1097.2 | 48 | 7.3 | odd | 6 | |||
1176.2.u.c.1097.6 | 48 | 21.17 | even | 6 | |||
1176.2.u.c.1097.19 | 48 | 21.11 | odd | 6 | |||
1176.2.u.c.1097.23 | 48 | 7.4 | even | 3 | |||
2352.2.k.j.881.9 | 24 | 12.11 | even | 2 | |||
2352.2.k.j.881.10 | 24 | 28.27 | even | 2 | |||
2352.2.k.j.881.15 | 24 | 4.3 | odd | 2 | |||
2352.2.k.j.881.16 | 24 | 84.83 | odd | 2 |