Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1241,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8280.1241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1241.31 | ||
Character | \(\chi\) | \(=\) | 8280.1241 |
Dual form | 8280.2.p.a.1241.18 |
$q$-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 \(\left(\mathbb{Z}/8280\mathbb{Z}\right)^\times\).
\(n\) | \(1657\) | \(2071\) | \(3961\) | \(4141\) | \(4601\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.44649i | 0.546723i | 0.961911 | + | 0.273361i | \(0.0881355\pi\) | ||||
−0.961911 | + | 0.273361i | \(0.911865\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.36137 | −0.410468 | −0.205234 | − | 0.978713i | \(-0.565795\pi\) | ||||
−0.205234 | + | 0.978713i | \(0.565795\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.07559 | −0.298314 | −0.149157 | − | 0.988814i | \(-0.547656\pi\) | ||||
−0.149157 | + | 0.988814i | \(0.547656\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.324623 | −0.0787326 | −0.0393663 | − | 0.999225i | \(-0.512534\pi\) | ||||
−0.0393663 | + | 0.999225i | \(0.512534\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.711387i | 0.163203i | 0.996665 | + | 0.0816016i | \(0.0260035\pi\) | ||||
−0.996665 | + | 0.0816016i | \(0.973996\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.999812 | − | 4.69046i | −0.208475 | − | 0.978028i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.07643i | 0.385583i | 0.981240 | + | 0.192792i | \(0.0617541\pi\) | ||||
−0.981240 | + | 0.192792i | \(0.938246\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.82838 | 1.04681 | 0.523404 | − | 0.852084i | \(-0.324662\pi\) | ||||
0.523404 | + | 0.852084i | \(0.324662\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1.44649i | − | 0.244502i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.84151i | − | 1.12474i | −0.826886 | − | 0.562369i | \(-0.809890\pi\) | ||
0.826886 | − | 0.562369i | \(-0.190110\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.86885i | 0.291865i | 0.989295 | + | 0.145933i | \(0.0466183\pi\) | ||||
−0.989295 | + | 0.145933i | \(0.953382\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.81876i | 0.887353i | 0.896187 | + | 0.443677i | \(0.146326\pi\) | ||||
−0.896187 | + | 0.443677i | \(0.853674\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 12.1813i | − | 1.77682i | −0.459047 | − | 0.888412i | \(-0.651809\pi\) | ||
0.459047 | − | 0.888412i | \(-0.348191\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.90766 | 0.701094 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.33172 | 1.00709 | 0.503544 | − | 0.863969i | \(-0.332029\pi\) | ||||
0.503544 | + | 0.863969i | \(0.332029\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.36137 | 0.183567 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.74251i | 1.26837i | 0.773183 | + | 0.634183i | \(0.218663\pi\) | ||||
−0.773183 | + | 0.634183i | \(0.781337\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.45083i | 1.21005i | 0.796205 | + | 0.605027i | \(0.206838\pi\) | ||||
−0.796205 | + | 0.605027i | \(0.793162\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.07559 | 0.133410 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.90647i | 1.21027i | 0.796124 | + | 0.605134i | \(0.206880\pi\) | ||||
−0.796124 | + | 0.605134i | \(0.793120\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5958i | 1.61353i | 0.590874 | + | 0.806764i | \(0.298783\pi\) | ||||
−0.590874 | + | 0.806764i | \(0.701217\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.12968 | −0.483342 | −0.241671 | − | 0.970358i | \(-0.577696\pi\) | ||||
−0.241671 | + | 0.970358i | \(0.577696\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.96921i | − | 0.224412i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.4503i | − | 1.28826i | −0.764918 | − | 0.644128i | \(-0.777221\pi\) | ||
0.764918 | − | 0.644128i | \(-0.222779\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.800104 | 0.0878228 | 0.0439114 | − | 0.999035i | \(-0.486018\pi\) | ||||
0.0439114 | + | 0.999035i | \(0.486018\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.324623 | 0.0352103 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.45302 | −0.896018 | −0.448009 | − | 0.894029i | \(-0.647867\pi\) | ||||
−0.448009 | + | 0.894029i | \(0.647867\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.55583i | − | 0.163095i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.711387i | − | 0.0729867i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.16643i | 0.829176i | 0.910009 | + | 0.414588i | \(0.136074\pi\) | ||||
−0.910009 | + | 0.414588i | \(0.863926\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 10.6670i | − | 1.06140i | −0.847559 | − | 0.530701i | \(-0.821929\pi\) | ||
0.847559 | − | 0.530701i | \(-0.178071\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.07517i | − | 0.500071i | −0.968237 | − | 0.250035i | \(-0.919558\pi\) | ||
0.968237 | − | 0.250035i | \(-0.0804423\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.4723 | −1.30242 | −0.651209 | − | 0.758899i | \(-0.725738\pi\) | ||||
−0.651209 | + | 0.758899i | \(0.725738\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.9560i | 1.81565i | 0.419345 | + | 0.907827i | \(0.362260\pi\) | ||||
−0.419345 | + | 0.907827i | \(0.637740\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.3332 | −1.63057 | −0.815285 | − | 0.579060i | \(-0.803420\pi\) | ||||
−0.815285 | + | 0.579060i | \(0.803420\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.999812 | + | 4.69046i | 0.0932329 | + | 0.437387i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.469565i | − | 0.0430449i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.14668 | −0.831516 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.4374 | 1.01490 | 0.507452 | − | 0.861680i | \(-0.330588\pi\) | ||||
0.507452 | + | 0.861680i | \(0.330588\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 20.4026i | − | 1.78258i | −0.453432 | − | 0.891291i | \(-0.649801\pi\) | ||
0.453432 | − | 0.891291i | \(-0.350199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.02902 | −0.0892269 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.2191 | 1.12938 | 0.564692 | − | 0.825302i | \(-0.308995\pi\) | ||||
0.564692 | + | 0.825302i | \(0.308995\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.49107 | −0.550566 | −0.275283 | − | 0.961363i | \(-0.588771\pi\) | ||||
−0.275283 | + | 0.961363i | \(0.588771\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.46427 | 0.122448 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.07643i | − | 0.172438i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.16983 | −0.177760 | −0.0888799 | − | 0.996042i | \(-0.528329\pi\) | ||||
−0.0888799 | + | 0.996042i | \(0.528329\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.6384 | −1.35401 | −0.677007 | − | 0.735977i | \(-0.736723\pi\) | ||||
−0.677007 | + | 0.735977i | \(0.736723\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.82838 | −0.468147 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.7007i | 1.41267i | 0.707879 | + | 0.706333i | \(0.249652\pi\) | ||||
−0.707879 | + | 0.706333i | \(0.750348\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.78471 | − | 1.44622i | 0.534710 | − | 0.113978i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.24897 | 0.0978269 | 0.0489135 | − | 0.998803i | \(-0.484424\pi\) | ||||
0.0489135 | + | 0.998803i | \(0.484424\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.14250i | 0.707468i | 0.935346 | + | 0.353734i | \(0.115088\pi\) | ||||
−0.935346 | + | 0.353734i | \(0.884912\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8431 | −0.911009 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.91436i | 0.525689i | 0.964838 | + | 0.262844i | \(0.0846606\pi\) | ||||
−0.964838 | + | 0.262844i | \(0.915339\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.44649i | 0.109345i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 8.36565i | − | 0.625278i | −0.949872 | − | 0.312639i | \(-0.898787\pi\) | ||
0.949872 | − | 0.312639i | \(-0.101213\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.04417i | 0.226272i | 0.993580 | + | 0.113136i | \(0.0360895\pi\) | ||||
−0.993580 | + | 0.113136i | \(0.963910\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.84151i | 0.502998i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.441931 | 0.0323172 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.9282 | −1.80374 | −0.901872 | − | 0.432004i | \(-0.857807\pi\) | ||||
−0.901872 | + | 0.432004i | \(0.857807\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.12064 | −0.152647 | −0.0763237 | − | 0.997083i | \(-0.524318\pi\) | ||||
−0.0763237 | + | 0.997083i | \(0.524318\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.6353i | 0.900227i | 0.892971 | + | 0.450114i | \(0.148616\pi\) | ||||
−0.892971 | + | 0.450114i | \(0.851384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.0395i | 1.49145i | 0.666255 | + | 0.745724i | \(0.267896\pi\) | ||||
−0.666255 | + | 0.745724i | \(0.732104\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.00354 | −0.210807 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1.86885i | − | 0.130526i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 0.968458i | − | 0.0669897i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.2656 | 1.60167 | 0.800836 | − | 0.598884i | \(-0.204389\pi\) | ||||
0.800836 | + | 0.598884i | \(0.204389\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 5.81876i | − | 0.396836i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.43071i | 0.572314i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.349160 | 0.0234870 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.706022 | 0.0472787 | 0.0236393 | − | 0.999721i | \(-0.492475\pi\) | ||||
0.0236393 | + | 0.999721i | \(0.492475\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.68475 | 0.244565 | 0.122283 | − | 0.992495i | \(-0.460979\pi\) | ||||
0.122283 | + | 0.992495i | \(0.460979\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.10883i | − | 0.271519i | −0.990742 | − | 0.135760i | \(-0.956653\pi\) | ||
0.990742 | − | 0.135760i | \(-0.0433475\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6.42318i | − | 0.420796i | −0.977616 | − | 0.210398i | \(-0.932524\pi\) | ||
0.977616 | − | 0.210398i | \(-0.0674760\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.1813i | 0.794620i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.99705i | 0.517286i | 0.965973 | + | 0.258643i | \(0.0832753\pi\) | ||||
−0.965973 | + | 0.258643i | \(0.916725\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 15.1920i | − | 0.978605i | −0.872114 | − | 0.489302i | \(-0.837251\pi\) | ||
0.872114 | − | 0.489302i | \(-0.162749\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.90766 | −0.313539 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.765157i | − | 0.0486858i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.2901 | −0.649504 | −0.324752 | − | 0.945799i | \(-0.605281\pi\) | ||||
−0.324752 | + | 0.945799i | \(0.605281\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.36111 | + | 6.38543i | 0.0855723 | + | 0.401449i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 18.4588i | − | 1.15143i | −0.817650 | − | 0.575715i | \(-0.804724\pi\) | ||
0.817650 | − | 0.575715i | \(-0.195276\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.89620 | 0.614920 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.4703 | −1.69389 | −0.846945 | − | 0.531681i | \(-0.821560\pi\) | ||||
−0.846945 | + | 0.531681i | \(0.821560\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.33172 | −0.450384 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.9569i | 0.972911i | 0.873705 | + | 0.486456i | \(0.161710\pi\) | ||||
−0.873705 | + | 0.486456i | \(0.838290\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.3919 | −1.84618 | −0.923089 | − | 0.384586i | \(-0.874344\pi\) | ||||
−0.923089 | + | 0.384586i | \(0.874344\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.36137 | −0.0820935 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.902914 | −0.0542508 | −0.0271254 | − | 0.999632i | \(-0.508635\pi\) | ||||
−0.0271254 | + | 0.999632i | \(0.508635\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.2787 | −1.44834 | −0.724172 | − | 0.689619i | \(-0.757778\pi\) | ||||
−0.724172 | + | 0.689619i | \(0.757778\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 12.5371i | − | 0.745255i | −0.927981 | − | 0.372628i | \(-0.878457\pi\) | ||
0.927981 | − | 0.372628i | \(-0.121543\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.70328 | −0.159569 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8946 | −0.993801 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.0905 | 1.52422 | 0.762112 | − | 0.647445i | \(-0.224162\pi\) | ||||
0.762112 | + | 0.647445i | \(0.224162\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.74251i | − | 0.567231i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.07538 | + | 5.04499i | 0.0621910 | + | 0.291759i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.41680 | −0.485136 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 9.45083i | − | 0.541153i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.3379 | −1.04660 | −0.523299 | − | 0.852149i | \(-0.675299\pi\) | ||||
−0.523299 | + | 0.852149i | \(0.675299\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2.54818i | − | 0.144494i | −0.997387 | − | 0.0722469i | \(-0.976983\pi\) | ||
0.997387 | − | 0.0722469i | \(-0.0230170\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.7098i | 1.84887i | 0.381340 | + | 0.924435i | \(0.375463\pi\) | ||||
−0.381340 | + | 0.924435i | \(0.624537\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 26.6634i | − | 1.49757i | −0.662815 | − | 0.748783i | \(-0.730639\pi\) | ||
0.662815 | − | 0.748783i | \(-0.269361\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.82678i | − | 0.158269i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 0.230932i | − | 0.0128494i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.07559 | −0.0596628 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.6201 | 0.971430 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.0179 | 1.04532 | 0.522660 | − | 0.852541i | \(-0.324940\pi\) | ||||
0.522660 | + | 0.852541i | \(0.324940\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 9.90647i | − | 0.541248i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.0972i | 0.713448i | 0.934210 | + | 0.356724i | \(0.116106\pi\) | ||||
−0.934210 | + | 0.356724i | \(0.883894\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.93457 | −0.429681 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2243i | 0.930027i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 6.34544i | − | 0.340641i | −0.985389 | − | 0.170320i | \(-0.945520\pi\) | ||
0.985389 | − | 0.170320i | \(-0.0544803\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.4327 | −0.986680 | −0.493340 | − | 0.869837i | \(-0.664224\pi\) | ||||
−0.493340 | + | 0.869837i | \(0.664224\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.5359i | 1.35914i | 0.733612 | + | 0.679568i | \(0.237833\pi\) | ||||
−0.733612 | + | 0.679568i | \(0.762167\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 13.5958i | − | 0.721591i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.06791 | 0.0563622 | 0.0281811 | − | 0.999603i | \(-0.491028\pi\) | ||||
0.0281811 | + | 0.999603i | \(0.491028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.4939 | 0.973365 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.12968 | 0.216157 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.3859i | 1.27293i | 0.771304 | + | 0.636467i | \(0.219605\pi\) | ||||
−0.771304 | + | 0.636467i | \(0.780395\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.6053i | 0.550598i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.0185i | 0.881185i | 0.897707 | + | 0.440592i | \(0.145232\pi\) | ||||
−0.897707 | + | 0.440592i | \(0.854768\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.23338i | − | 0.115025i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.92469i | 0.407064i | 0.979068 | + | 0.203532i | \(0.0652421\pi\) | ||||
−0.979068 | + | 0.203532i | \(0.934758\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.3980 | 0.582409 | 0.291204 | − | 0.956661i | \(-0.405944\pi\) | ||||
0.291204 | + | 0.956661i | \(0.405944\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.96921i | 0.100360i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.5063 | 0.735496 | 0.367748 | − | 0.929925i | \(-0.380129\pi\) | ||||
0.367748 | + | 0.929925i | \(0.380129\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.324562 | + | 1.52263i | 0.0164138 | + | 0.0770027i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.4503i | 0.576125i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.05311 | 0.404174 | 0.202087 | − | 0.979368i | \(-0.435228\pi\) | ||||
0.202087 | + | 0.979368i | \(0.435228\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.09759 | 0.204624 | 0.102312 | − | 0.994752i | \(-0.467376\pi\) | ||||
0.102312 | + | 0.994752i | \(0.467376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.26893 | −0.312278 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.31381i | 0.461669i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.81983 | 0.436112 | 0.218056 | − | 0.975936i | \(-0.430028\pi\) | ||||
0.218056 | + | 0.975936i | \(0.430028\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.0925 | −0.693445 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.800104 | −0.0392756 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.8862 | −1.21577 | −0.607886 | − | 0.794025i | \(-0.707982\pi\) | ||||
−0.607886 | + | 0.794025i | \(0.707982\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 39.0434i | 1.90286i | 0.307867 | + | 0.951429i | \(0.400385\pi\) | ||||
−0.307867 | + | 0.951429i | \(0.599615\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.324623 | −0.0157465 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.6706 | −0.661565 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.3323 | −0.738529 | −0.369264 | − | 0.929324i | \(-0.620390\pi\) | ||||
−0.369264 | + | 0.929324i | \(0.620390\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.4681i | 0.551121i | 0.961284 | + | 0.275560i | \(0.0888634\pi\) | ||||
−0.961284 | + | 0.275560i | \(0.911137\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.33673 | − | 0.711253i | 0.159617 | − | 0.0340238i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.49682 | 0.0714394 | 0.0357197 | − | 0.999362i | \(-0.488628\pi\) | ||||
0.0357197 | + | 0.999362i | \(0.488628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 10.3427i | − | 0.491396i | −0.969346 | − | 0.245698i | \(-0.920983\pi\) | ||
0.969346 | − | 0.245698i | \(-0.0790172\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.45302 | 0.400712 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 26.6792i | − | 1.25907i | −0.776973 | − | 0.629533i | \(-0.783246\pi\) | ||
0.776973 | − | 0.629533i | \(-0.216754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.54419i | − | 0.119801i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.55583i | 0.0729383i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 17.7567i | − | 0.830623i | −0.909679 | − | 0.415311i | \(-0.863673\pi\) | ||
0.909679 | − | 0.415311i | \(-0.136327\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.8874i | 1.67144i | 0.549152 | + | 0.835722i | \(0.314951\pi\) | ||||
−0.549152 | + | 0.835722i | \(0.685049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.2698 | −0.663172 | −0.331586 | − | 0.943425i | \(-0.607584\pi\) | ||||
−0.331586 | + | 0.943425i | \(0.607584\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.5261 | −1.69023 | −0.845113 | − | 0.534587i | \(-0.820467\pi\) | ||||
−0.845113 | + | 0.534587i | \(0.820467\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.3296 | −0.661681 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7.92148i | − | 0.364230i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.711387i | 0.0326407i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.1531 | −1.10359 | −0.551793 | − | 0.833981i | \(-0.686056\pi\) | ||||
−0.551793 | + | 0.833981i | \(0.686056\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.35863i | 0.335525i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 8.16643i | − | 0.370819i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.43775 | −0.427665 | −0.213833 | − | 0.976870i | \(-0.568595\pi\) | ||||
−0.213833 | + | 0.976870i | \(0.568595\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 6.48302i | − | 0.292575i | −0.989242 | − | 0.146287i | \(-0.953268\pi\) | ||
0.989242 | − | 0.146287i | \(-0.0467324\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.674056i | − | 0.0303580i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.6663 | −0.882152 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.3397 | −0.865763 | −0.432881 | − | 0.901451i | \(-0.642503\pi\) | ||||
−0.432881 | + | 0.901451i | \(0.642503\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.4517 | −0.867309 | −0.433654 | − | 0.901079i | \(-0.642776\pi\) | ||||
−0.433654 | + | 0.901079i | \(0.642776\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.6670i | 0.474674i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.54321i | 0.378671i | 0.981912 | + | 0.189336i | \(0.0606334\pi\) | ||||
−0.981912 | + | 0.189336i | \(0.939367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 5.97355i | − | 0.264254i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.07517i | 0.223639i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.5832i | 0.729329i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.2471 | 1.28134 | 0.640669 | − | 0.767818i | \(-0.278657\pi\) | ||||
0.640669 | + | 0.767818i | \(0.278657\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 31.5199i | − | 1.37827i | −0.724634 | − | 0.689134i | \(-0.757991\pi\) | ||
0.724634 | − | 0.689134i | \(-0.242009\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.89203 | −0.0824180 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0008 | + | 9.37915i | −0.913076 | + | 0.407789i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.01011i | − | 0.0870674i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.4723 | 0.582459 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.68113 | −0.287777 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0706 | 0.991884 | 0.495942 | − | 0.868356i | \(-0.334823\pi\) | ||||
0.495942 | + | 0.868356i | \(0.334823\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 18.9560i | − | 0.811985i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.5324 | 1.77580 | 0.887899 | − | 0.460038i | \(-0.152164\pi\) | ||||
0.887899 | + | 0.460038i | \(0.152164\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.47714 | −0.0629284 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.5627 | 0.704318 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 46.2726 | 1.96063 | 0.980317 | − | 0.197428i | \(-0.0632587\pi\) | ||||
0.980317 | + | 0.197428i | \(0.0632587\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.25858i | − | 0.264710i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.6298 | −1.16446 | −0.582228 | − | 0.813026i | \(-0.697819\pi\) | ||||
−0.582228 | + | 0.813026i | \(0.697819\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.3332 | 0.729213 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −47.5737 | −1.99439 | −0.997196 | − | 0.0748375i | \(-0.976156\pi\) | ||||
−0.997196 | + | 0.0748375i | \(0.976156\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.3329i | 1.18570i | 0.805315 | + | 0.592848i | \(0.201996\pi\) | ||||
−0.805315 | + | 0.592848i | \(0.798004\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.999812 | − | 4.69046i | −0.0416950 | − | 0.195606i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.7626 | 1.19740 | 0.598702 | − | 0.800972i | \(-0.295683\pi\) | ||||
0.598702 | + | 0.800972i | \(0.295683\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.15734i | 0.0480147i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.98116 | −0.413377 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 46.1231i | − | 1.90370i | −0.306559 | − | 0.951852i | \(-0.599178\pi\) | ||
0.306559 | − | 0.951852i | \(-0.400822\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.14623i | 0.170843i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.8567i | 1.71885i | 0.511261 | + | 0.859425i | \(0.329178\pi\) | ||||
−0.511261 | + | 0.859425i | \(0.670822\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.469565i | 0.0192503i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.7755i | 1.62518i | 0.582834 | + | 0.812591i | \(0.301944\pi\) | ||||
−0.582834 | + | 0.812591i | \(0.698056\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.3403 | −1.60473 | −0.802363 | − | 0.596837i | \(-0.796424\pi\) | ||||
−0.802363 | + | 0.596837i | \(0.796424\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.14668 | 0.371865 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.7783 | 1.16807 | 0.584037 | − | 0.811727i | \(-0.301472\pi\) | ||||
0.584037 | + | 0.811727i | \(0.301472\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.1020i | 0.530051i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 21.7678i | − | 0.879193i | −0.898195 | − | 0.439597i | \(-0.855121\pi\) | ||
0.898195 | − | 0.439597i | \(-0.144879\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.0398 | 0.766512 | 0.383256 | − | 0.923642i | \(-0.374803\pi\) | ||||
0.383256 | + | 0.923642i | \(0.374803\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 15.2388i | − | 0.612498i | −0.951951 | − | 0.306249i | \(-0.900926\pi\) | ||
0.951951 | − | 0.306249i | \(-0.0990740\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 12.2272i | − | 0.489874i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.22091i | 0.0885536i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.29925i | 0.131341i | 0.997841 | + | 0.0656705i | \(0.0209186\pi\) | ||||
−0.997841 | + | 0.0656705i | \(0.979081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.4374 | −0.453879 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.27861 | −0.209146 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.41099 | 0.213721 | 0.106861 | − | 0.994274i | \(-0.465920\pi\) | ||||
0.106861 | + | 0.994274i | \(0.465920\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.9665i | 0.708530i | 0.935145 | + | 0.354265i | \(0.115269\pi\) | ||||
−0.935145 | + | 0.354265i | \(0.884731\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 32.3550i | − | 1.27201i | −0.771687 | − | 0.636003i | \(-0.780587\pi\) | ||
0.771687 | − | 0.636003i | \(-0.219413\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 13.2631i | − | 0.520623i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.8784i | 1.59970i | 0.600202 | + | 0.799848i | \(0.295087\pi\) | ||||
−0.600202 | + | 0.799848i | \(0.704913\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.4026i | 0.797195i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.9165 | 0.814793 | 0.407396 | − | 0.913251i | \(-0.366437\pi\) | ||||
0.407396 | + | 0.913251i | \(0.366437\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.6643i | 0.959331i | 0.877451 | + | 0.479665i | \(0.159242\pi\) | ||||
−0.877451 | + | 0.479665i | \(0.840758\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.02902 | 0.0399035 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.73940 | − | 2.07604i | 0.377111 | − | 0.0803845i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 12.8661i | − | 0.496688i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.52712 | −0.0974133 | −0.0487067 | − | 0.998813i | \(-0.515510\pi\) | ||||
−0.0487067 | + | 0.998813i | \(0.515510\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.1664 | −1.23626 | −0.618128 | − | 0.786077i | \(-0.712109\pi\) | ||||
−0.618128 | + | 0.786077i | \(0.712109\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.8127 | −0.453329 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.7669i | 0.526777i | 0.964690 | + | 0.263389i | \(0.0848401\pi\) | ||||
−0.964690 | + | 0.263389i | \(0.915160\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.2191 | −0.505076 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.88589 | −0.300428 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.3329 | −1.19196 | −0.595980 | − | 0.802999i | \(-0.703236\pi\) | ||||
−0.595980 | + | 0.802999i | \(0.703236\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.49107 | 0.246220 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 0.606671i | − | 0.0229793i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.30429 | 0.124801 | 0.0624006 | − | 0.998051i | \(-0.480124\pi\) | ||||
0.0624006 | + | 0.998051i | \(0.480124\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.86696 | 0.183561 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.4297 | 0.580293 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.0295i | 0.864890i | 0.901660 | + | 0.432445i | \(0.142349\pi\) | ||||
−0.901660 | + | 0.432445i | \(0.857651\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.82729 | − | 27.3378i | −0.218234 | − | 1.02381i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.46427 | −0.0547605 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.0799i | 1.38285i | 0.722449 | + | 0.691424i | \(0.243016\pi\) | ||||
−0.722449 | + | 0.691424i | \(0.756984\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.34119 | 0.273400 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.07643i | 0.0771166i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.03043i | − | 0.334920i | −0.985879 | − | 0.167460i | \(-0.946443\pi\) | ||
0.985879 | − | 0.167460i | \(-0.0535565\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.88890i | − | 0.0698636i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.8214i | 1.72939i | 0.502298 | + | 0.864695i | \(0.332488\pi\) | ||||
−0.502298 | + | 0.864695i | \(0.667512\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 13.4863i | − | 0.496776i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.6487 | 1.20100 | 0.600501 | − | 0.799624i | \(-0.294968\pi\) | ||||
0.600501 | + | 0.799624i | \(0.294968\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.9376 | 0.841499 | 0.420750 | − | 0.907177i | \(-0.361767\pi\) | ||||
0.420750 | + | 0.907177i | \(0.361767\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.16983 | 0.0794966 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 19.4876i | − | 0.712061i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 50.7815i | − | 1.85304i | −0.376241 | − | 0.926522i | \(-0.622784\pi\) | ||
0.376241 | − | 0.926522i | \(-0.377216\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.6384 | 0.605533 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.5700i | 0.929358i | 0.885479 | + | 0.464679i | \(0.153830\pi\) | ||||
−0.885479 | + | 0.464679i | \(0.846170\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 0.0869257i | − | 0.00315106i | −0.999999 | − | 0.00157553i | \(-0.999498\pi\) | ||
0.999999 | − | 0.00157553i | \(-0.000501506\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.4197 | −0.992659 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 10.4789i | − | 0.378371i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.3837i | 1.34809i | 0.738690 | + | 0.674045i | \(0.235445\pi\) | ||||
−0.738690 | + | 0.674045i | \(0.764555\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.32009 | −0.263285 | −0.131643 | − | 0.991297i | \(-0.542025\pi\) | ||||
−0.131643 | + | 0.991297i | \(0.542025\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.82838 | 0.209362 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.32947 | −0.0476333 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 18.5089i | − | 0.662301i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 17.7007i | − | 0.631764i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 4.62475i | − | 0.164855i | −0.996597 | − | 0.0824273i | \(-0.973733\pi\) | ||
0.996597 | − | 0.0824273i | \(-0.0262672\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 25.0723i | − | 0.891470i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 10.1652i | − | 0.360976i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.4223 | 0.935925 | 0.467963 | − | 0.883748i | \(-0.344988\pi\) | ||||
0.467963 | + | 0.883748i | \(0.344988\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.95433i | 0.139894i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.62201 | 0.198396 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.78471 | + | 1.44622i | −0.239130 | + | 0.0509726i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.6609i | 1.11314i | 0.830802 | + | 0.556568i | \(0.187882\pi\) | ||||
−0.830802 | + | 0.556568i | \(0.812118\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.97218 | −0.350171 | −0.175085 | − | 0.984553i | \(-0.556020\pi\) | ||||
−0.175085 | + | 0.984553i | \(0.556020\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.24897 | −0.0437495 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.13939 | −0.144819 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 12.3896i | − | 0.432400i | −0.976349 | − | 0.216200i | \(-0.930634\pi\) | ||
0.976349 | − | 0.216200i | \(-0.0693664\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −53.3262 | −1.85883 | −0.929417 | − | 0.369032i | \(-0.879689\pi\) | ||||
−0.929417 | + | 0.369032i | \(0.879689\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.5228 | −0.644101 | −0.322051 | − | 0.946722i | \(-0.604372\pi\) | ||||
−0.322051 | + | 0.946722i | \(0.604372\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.0760 | −1.49609 | −0.748046 | − | 0.663647i | \(-0.769008\pi\) | ||||
−0.748046 | + | 0.663647i | \(0.769008\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.59314 | −0.0551990 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 9.14250i | − | 0.316389i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.9777 | −1.27661 | −0.638306 | − | 0.769783i | \(-0.720364\pi\) | ||||
−0.638306 | + | 0.769783i | \(0.720364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.6884 | 0.851326 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.8431 | 0.407416 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 13.2306i | − | 0.454609i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.0898 | + | 6.84022i | −1.10002 | + | 0.234480i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.9154 | 1.50363 | 0.751817 | − | 0.659372i | \(-0.229178\pi\) | ||||
0.751817 | + | 0.659372i | \(0.229178\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.67247i | 0.0912897i | 0.998958 | + | 0.0456448i | \(0.0145343\pi\) | ||||
−0.998958 | + | 0.0456448i | \(0.985466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.4199 | 1.14027 | 0.570136 | − | 0.821550i | \(-0.306890\pi\) | ||||
0.570136 | + | 0.821550i | \(0.306890\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.4335i | 1.34233i | 0.741307 | + | 0.671166i | \(0.234206\pi\) | ||||
−0.741307 | + | 0.671166i | \(0.765794\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 6.91436i | − | 0.235095i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.5880i | 0.528787i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 10.6553i | − | 0.361040i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 1.44649i | − | 0.0489004i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.1216 | 1.76002 | 0.880010 | − | 0.474955i | \(-0.157536\pi\) | ||||
0.880010 | + | 0.474955i | \(0.157536\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.2070 | −1.38830 | −0.694149 | − | 0.719831i | \(-0.744219\pi\) | ||||
−0.694149 | + | 0.719831i | \(0.744219\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.8335 | −1.10493 | −0.552467 | − | 0.833535i | \(-0.686313\pi\) | ||||
−0.552467 | + | 0.833535i | \(0.686313\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 43.0506i | − | 1.44550i | −0.691112 | − | 0.722748i | \(-0.742879\pi\) | ||
0.691112 | − | 0.722748i | \(-0.257121\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.5441i | 0.554871i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.66561 | 0.289984 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.36565i | 0.279633i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.1022i | 0.403632i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.38004 | −0.0792907 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 3.04417i | − | 0.101192i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.0912i | 0.600709i | 0.953828 | + | 0.300354i | \(0.0971050\pi\) | ||||
−0.953828 | + | 0.300354i | \(0.902895\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.6612 | −0.419483 | −0.209742 | − | 0.977757i | \(-0.567262\pi\) | ||||
−0.209742 | + | 0.977757i | \(0.567262\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.08924 | −0.0360484 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.5122 | 0.974578 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 10.9121i | − | 0.359958i | −0.983670 | − | 0.179979i | \(-0.942397\pi\) | ||
0.983670 | − | 0.179979i | \(-0.0576030\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 14.6235i | − | 0.481337i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 6.84151i | − | 0.224948i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.6243i | 1.16879i | 0.811468 | + | 0.584397i | \(0.198669\pi\) | ||||
−0.811468 | + | 0.584397i | \(0.801331\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.49124i | 0.114421i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.441931 | −0.0144527 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 20.2708i | − | 0.662219i | −0.943592 | − | 0.331110i | \(-0.892577\pi\) | ||
0.943592 | − | 0.331110i | \(-0.107423\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 58.8664 | 1.91899 | 0.959495 | − | 0.281724i | \(-0.0909063\pi\) | ||||
0.959495 | + | 0.281724i | \(0.0909063\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.76575 | − | 1.86850i | 0.285452 | − | 0.0608466i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 33.9338i | − | 1.10270i | −0.834273 | − | 0.551351i | \(-0.814113\pi\) | ||
0.834273 | − | 0.551351i | \(-0.185887\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.44182 | 0.144188 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.8700 | 1.03237 | 0.516185 | − | 0.856477i | \(-0.327352\pi\) | ||||
0.516185 | + | 0.856477i | \(0.327352\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.9282 | 0.806659 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.1213i | 0.617460i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.97006 | 0.0958085 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.12064 | 0.0682660 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.0561 | 0.837908 | 0.418954 | − | 0.908008i | \(-0.362397\pi\) | ||||
0.418954 | + | 0.908008i | \(0.362397\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.0161 | 0.642349 | 0.321174 | − | 0.947020i | \(-0.395922\pi\) | ||||
0.321174 | + | 0.947020i | \(0.395922\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 9.38929i | − | 0.301007i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.2242 | −0.775000 | −0.387500 | − | 0.921870i | \(-0.626661\pi\) | ||||
−0.387500 | + | 0.921870i | \(0.626661\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.5077 | 0.367787 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.1667 | −0.866482 | −0.433241 | − | 0.901278i | \(-0.642630\pi\) | ||||
−0.433241 | + | 0.901278i | \(0.642630\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 12.6353i | − | 0.402594i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.2927 | − | 5.81767i | 0.867856 | − | 0.184991i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.8974 | 0.409700 | 0.204850 | − | 0.978793i | \(-0.434329\pi\) | ||||
0.204850 | + | 0.978793i | \(0.434329\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 21.0395i | − | 0.666996i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.1967 | 0.449614 | 0.224807 | − | 0.974403i | \(-0.427825\pi\) | ||||
0.224807 | + | 0.974403i | \(0.427825\pi\) | |||||||
\(998\) | 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 | 8280.2.p.a.1241.31 | yes | 48 | |
3.2 | odd | 2 | 8280.2.p.b.1241.31 | yes | 48 | ||
23.22 | odd | 2 | 8280.2.p.b.1241.18 | yes | 48 | ||
69.68 | even | 2 | inner | 8280.2.p.a.1241.18 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8280.2.p.a.1241.18 | ✓ | 48 | 69.68 | even | 2 | inner | |
8280.2.p.a.1241.31 | yes | 48 | 1.1 | even | 1 | trivial | |
8280.2.p.b.1241.18 | yes | 48 | 23.22 | odd | 2 | ||
8280.2.p.b.1241.31 | yes | 48 | 3.2 | odd | 2 |