Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4140,2,Mod(1241,4140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4140.1241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4140.i (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: | \(33.0580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 62x^{14} + 1303x^{12} + 12842x^{10} + 65359x^{8} + 170834x^{6} + 207293x^{4} + 91366x^{2} + 9604 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1241.11 | ||
Root | \(-5.65286i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4140.1241 |
Dual form | 4140.2.i.b.1241.6 |
$q$-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 \(\left(\mathbb{Z}/4140\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(2071\) | \(3961\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.826970i | 0.312565i | 0.987712 | + | 0.156283i | \(0.0499511\pi\) | ||||
−0.987712 | + | 0.156283i | \(0.950049\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.34857 | 1.61265 | 0.806327 | − | 0.591469i | \(-0.201452\pi\) | ||||
0.806327 | + | 0.591469i | \(0.201452\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.20928 | −1.16744 | −0.583722 | − | 0.811953i | \(-0.698404\pi\) | ||||
−0.583722 | + | 0.811953i | \(0.698404\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.60504 | −0.874352 | −0.437176 | − | 0.899376i | \(-0.644021\pi\) | ||||
−0.437176 | + | 0.899376i | \(0.644021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.22071i | 1.19771i | 0.800857 | + | 0.598856i | \(0.204378\pi\) | ||||
−0.800857 | + | 0.598856i | \(0.795622\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.78507 | + | 0.321128i | 0.997756 | + | 0.0669598i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.68671i | − | 1.05600i | −0.849246 | − | 0.527998i | \(-0.822943\pi\) | ||
0.849246 | − | 0.527998i | \(-0.177057\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.23310 | 0.939893 | 0.469946 | − | 0.882695i | \(-0.344273\pi\) | ||||
0.469946 | + | 0.882695i | \(0.344273\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.826970i | 0.139783i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.95459i | − | 0.814530i | −0.913310 | − | 0.407265i | \(-0.866483\pi\) | ||
0.913310 | − | 0.407265i | \(-0.133517\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.4006i | 1.78047i | 0.455501 | + | 0.890235i | \(0.349460\pi\) | ||||
−0.455501 | + | 0.890235i | \(0.650540\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.85889i | 0.283478i | 0.989904 | + | 0.141739i | \(0.0452693\pi\) | ||||
−0.989904 | + | 0.141739i | \(0.954731\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.79409i | 0.261695i | 0.991403 | + | 0.130847i | \(0.0417698\pi\) | ||||
−0.991403 | + | 0.130847i | \(0.958230\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.31612 | 0.902303 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.66818 | −0.915945 | −0.457972 | − | 0.888966i | \(-0.651424\pi\) | ||||
−0.457972 | + | 0.888966i | \(0.651424\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.34857 | 0.721201 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.65007i | 0.605387i | 0.953088 | + | 0.302694i | \(0.0978859\pi\) | ||||
−0.953088 | + | 0.302694i | \(0.902114\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.82671i | 1.25818i | 0.777332 | + | 0.629090i | \(0.216573\pi\) | ||||
−0.777332 | + | 0.629090i | \(0.783427\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.20928 | −0.522097 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.81889i | − | 0.710891i | −0.934697 | − | 0.355446i | \(-0.884329\pi\) | ||
0.934697 | − | 0.355446i | \(-0.115671\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1032i | 1.31771i | 0.752269 | + | 0.658856i | \(0.228959\pi\) | ||||
−0.752269 | + | 0.658856i | \(0.771041\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.11519 | 0.715728 | 0.357864 | − | 0.933774i | \(-0.383505\pi\) | ||||
0.357864 | + | 0.933774i | \(0.383505\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.42311i | 0.504060i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.46423i | 0.164739i | 0.996602 | + | 0.0823694i | \(0.0262487\pi\) | ||||
−0.996602 | + | 0.0823694i | \(0.973751\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.97440 | 0.985069 | 0.492534 | − | 0.870293i | \(-0.336071\pi\) | ||||
0.492534 | + | 0.870293i | \(0.336071\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.60504 | −0.391022 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.0563452 | −0.00597257 | −0.00298629 | − | 0.999996i | \(-0.500951\pi\) | ||||
−0.00298629 | + | 0.999996i | \(0.500951\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.48095i | − | 0.364903i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.22071i | 0.535633i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.0241i | − | 1.52547i | −0.646714 | − | 0.762733i | \(-0.723857\pi\) | ||
0.646714 | − | 0.762733i | \(-0.276143\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.4906i | 1.93939i | 0.244324 | + | 0.969694i | \(0.421434\pi\) | ||||
−0.244324 | + | 0.969694i | \(0.578566\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.247690i | 0.0244056i | 0.999926 | + | 0.0122028i | \(0.00388437\pi\) | ||||
−0.999926 | + | 0.0122028i | \(0.996116\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.00052 | −0.870113 | −0.435057 | − | 0.900403i | \(-0.643272\pi\) | ||||
−0.435057 | + | 0.900403i | \(0.643272\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.1556i | − | 0.972732i | −0.873755 | − | 0.486366i | \(-0.838322\pi\) | ||
0.873755 | − | 0.486366i | \(-0.161678\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.63519 | 0.436042 | 0.218021 | − | 0.975944i | \(-0.430040\pi\) | ||||
0.218021 | + | 0.975944i | \(0.430040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.78507 | + | 0.321128i | 0.446210 | + | 0.0299453i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.98126i | − | 0.273292i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.6072 | 1.60066 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.28911 | 0.203126 | 0.101563 | − | 0.994829i | \(-0.467616\pi\) | ||||
0.101563 | + | 0.994829i | \(0.467616\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 11.6358i | − | 1.01662i | −0.861173 | − | 0.508311i | \(-0.830270\pi\) | ||
0.861173 | − | 0.508311i | \(-0.169730\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.31737 | −0.374363 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.80437 | 0.239593 | 0.119797 | − | 0.992798i | \(-0.461776\pi\) | ||||
0.119797 | + | 0.992798i | \(0.461776\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.23304 | −0.274223 | −0.137111 | − | 0.990556i | \(-0.543782\pi\) | ||||
−0.137111 | + | 0.990556i | \(0.543782\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.5136 | −1.88269 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 5.68671i | − | 0.472255i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.32611 | 0.682101 | 0.341051 | − | 0.940045i | \(-0.389217\pi\) | ||||
0.341051 | + | 0.940045i | \(0.389217\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.72932 | −0.303488 | −0.151744 | − | 0.988420i | \(-0.548489\pi\) | ||||
−0.151744 | + | 0.988420i | \(0.548489\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.23310 | 0.420333 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.9437i | 1.19264i | 0.802747 | + | 0.596320i | \(0.203371\pi\) | ||||
−0.802747 | + | 0.596320i | \(0.796629\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.265563 | + | 3.95711i | −0.0209293 | + | 0.311864i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.8043 | 1.23789 | 0.618945 | − | 0.785434i | \(-0.287560\pi\) | ||||
0.618945 | + | 0.785434i | \(0.287560\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 0.877759i | − | 0.0679230i | −0.999423 | − | 0.0339615i | \(-0.989188\pi\) | ||
0.999423 | − | 0.0339615i | \(-0.0108124\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.71806 | 0.362927 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.84136i | 0.672196i | 0.941827 | + | 0.336098i | \(0.109107\pi\) | ||||
−0.941827 | + | 0.336098i | \(0.890893\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.826970i | 0.0625130i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.7369i | 0.952002i | 0.879445 | + | 0.476001i | \(0.157914\pi\) | ||||
−0.879445 | + | 0.476001i | \(0.842086\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0635i | 0.748017i | 0.927425 | + | 0.374008i | \(0.122017\pi\) | ||||
−0.927425 | + | 0.374008i | \(0.877983\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 4.95459i | − | 0.364269i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.2818 | −1.41003 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.9106 | −0.934177 | −0.467089 | − | 0.884210i | \(-0.654697\pi\) | ||||
−0.467089 | + | 0.884210i | \(0.654697\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.4533 | 1.90415 | 0.952074 | − | 0.305869i | \(-0.0989469\pi\) | ||||
0.952074 | + | 0.305869i | \(0.0989469\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.30018i | − | 0.591363i | −0.955287 | − | 0.295682i | \(-0.904453\pi\) | ||
0.955287 | − | 0.295682i | \(-0.0955467\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 6.61245i | − | 0.468744i | −0.972147 | − | 0.234372i | \(-0.924697\pi\) | ||
0.972147 | − | 0.234372i | \(-0.0753034\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.70274 | 0.330067 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.4006i | 0.796251i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 27.9233i | 1.93150i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.04726 | −0.140939 | −0.0704695 | − | 0.997514i | \(-0.522450\pi\) | ||||
−0.0704695 | + | 0.997514i | \(0.522450\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.85889i | 0.126775i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.32762i | 0.293778i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.1746 | 1.02076 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.3700 | −1.29711 | −0.648556 | − | 0.761167i | \(-0.724627\pi\) | ||||
−0.648556 | + | 0.761167i | \(0.724627\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.01201 | −0.598148 | −0.299074 | − | 0.954230i | \(-0.596678\pi\) | ||||
−0.299074 | + | 0.954230i | \(0.596678\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.28944i | 0.547781i | 0.961761 | + | 0.273891i | \(0.0883107\pi\) | ||||
−0.961761 | + | 0.273891i | \(0.911689\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.2048i | 1.52020i | 0.649807 | + | 0.760099i | \(0.274850\pi\) | ||||
−0.649807 | + | 0.760099i | \(0.725150\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.79409i | 0.117034i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.5877i | 0.814228i | 0.913377 | + | 0.407114i | \(0.133465\pi\) | ||||
−0.913377 | + | 0.407114i | \(0.866535\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.7065i | 1.26941i | 0.772756 | + | 0.634703i | \(0.218878\pi\) | ||||
−0.772756 | + | 0.634703i | \(0.781122\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.31612 | 0.403522 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 21.9754i | − | 1.39826i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.4446 | 1.35357 | 0.676784 | − | 0.736181i | \(-0.263373\pi\) | ||||
0.676784 | + | 0.736181i | \(0.263373\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.5933 | + | 1.71758i | 1.60904 | + | 0.107983i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.5523i | 0.658234i | 0.944289 | + | 0.329117i | \(0.106751\pi\) | ||||
−0.944289 | + | 0.329117i | \(0.893249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.09730 | 0.254594 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.3888 | 0.825589 | 0.412794 | − | 0.910824i | \(-0.364553\pi\) | ||||
0.412794 | + | 0.910824i | \(0.364553\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.66818 | −0.409623 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.38744i | − | 0.206536i | −0.994654 | − | 0.103268i | \(-0.967070\pi\) | ||
0.994654 | − | 0.103268i | \(-0.0329299\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.4356 | 0.876902 | 0.438451 | − | 0.898755i | \(-0.355527\pi\) | ||||
0.438451 | + | 0.898755i | \(0.355527\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.34857 | 0.322531 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.7134 | 1.18446 | 0.592231 | − | 0.805768i | \(-0.298247\pi\) | ||||
0.592231 | + | 0.805768i | \(0.298247\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.73536 | 0.580763 | 0.290381 | − | 0.956911i | \(-0.406218\pi\) | ||||
0.290381 | + | 0.956911i | \(0.406218\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.211034i | 0.0125447i | 0.999980 | + | 0.00627234i | \(0.00199656\pi\) | ||||
−0.999980 | + | 0.00627234i | \(0.998003\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.42793 | −0.556513 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00366 | −0.235509 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.6156 | −0.853851 | −0.426925 | − | 0.904287i | \(-0.640403\pi\) | ||||
−0.426925 | + | 0.904287i | \(0.640403\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.65007i | 0.270737i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.1417 | − | 1.35172i | −1.16482 | − | 0.0781719i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.53724 | −0.0886053 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.82671i | 0.562676i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.1867 | 1.95114 | 0.975569 | − | 0.219695i | \(-0.0705064\pi\) | ||||
0.975569 | + | 0.219695i | \(0.0705064\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 29.5570i | − | 1.67602i | −0.545651 | − | 0.838012i | \(-0.683718\pi\) | ||
0.545651 | − | 0.838012i | \(-0.316282\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 32.3791i | − | 1.83018i | −0.403255 | − | 0.915088i | \(-0.632121\pi\) | ||
0.403255 | − | 0.915088i | \(-0.367879\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.62772i | 0.0914216i | 0.998955 | + | 0.0457108i | \(0.0145553\pi\) | ||||
−0.998955 | + | 0.0457108i | \(0.985445\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 30.4158i | − | 1.70296i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 18.8209i | − | 1.04722i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.20928 | −0.233489 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.48366 | −0.0817967 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.4951 | −0.741759 | −0.370880 | − | 0.928681i | \(-0.620944\pi\) | ||||
−0.370880 | + | 0.928681i | \(0.620944\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 5.81889i | − | 0.317920i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.59985i | − | 0.141623i | −0.997490 | − | 0.0708113i | \(-0.977441\pi\) | ||
0.997490 | − | 0.0708113i | \(-0.0225588\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.9896 | 1.51572 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.0120i | 0.594594i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.4803i | 1.85100i | 0.378748 | + | 0.925500i | \(0.376355\pi\) | ||||
−0.378748 | + | 0.925500i | \(0.623645\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.09741 | 0.165800 | 0.0829002 | − | 0.996558i | \(-0.473582\pi\) | ||||
0.0829002 | + | 0.996558i | \(0.473582\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.1843i | 1.76622i | 0.469162 | + | 0.883112i | \(0.344556\pi\) | ||||
−0.469162 | + | 0.883112i | \(0.655444\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.1032i | 0.589299i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.1798 | −1.43449 | −0.717247 | − | 0.696819i | \(-0.754598\pi\) | ||||
−0.717247 | + | 0.696819i | \(0.754598\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.25579 | −0.434515 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.11519 | 0.320083 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 11.6520i | − | 0.608229i | −0.952635 | − | 0.304115i | \(-0.901639\pi\) | ||
0.952635 | − | 0.304115i | \(-0.0983605\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 5.51438i | − | 0.286292i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 27.0411i | − | 1.40013i | −0.714077 | − | 0.700067i | \(-0.753153\pi\) | ||
0.714077 | − | 0.700067i | \(-0.246847\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.9370i | 1.23282i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 25.4729i | − | 1.30845i | −0.756298 | − | 0.654227i | \(-0.772994\pi\) | ||
0.756298 | − | 0.654227i | \(-0.227006\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.4529 | 0.534119 | 0.267059 | − | 0.963680i | \(-0.413948\pi\) | ||||
0.267059 | + | 0.963680i | \(0.413948\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.42311i | 0.225422i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.0966 | −0.562621 | −0.281310 | − | 0.959617i | \(-0.590769\pi\) | ||||
−0.281310 | + | 0.959617i | \(0.590769\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.2504 | − | 1.15768i | −0.872389 | − | 0.0585464i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.46423i | 0.0736735i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.5856 | 0.531274 | 0.265637 | − | 0.964073i | \(-0.414418\pi\) | ||||
0.265637 | + | 0.964073i | \(0.414418\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.2109 | −0.659720 | −0.329860 | − | 0.944030i | \(-0.607002\pi\) | ||||
−0.329860 | + | 0.944030i | \(0.607002\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.0276 | −1.09727 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 26.5000i | − | 1.31356i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.12819 | −0.303020 | −0.151510 | − | 0.988456i | \(-0.548414\pi\) | ||||
−0.151510 | + | 0.988456i | \(0.548414\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.84547 | −0.189223 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.97440 | 0.440536 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.1134 | −0.884895 | −0.442448 | − | 0.896794i | \(-0.645890\pi\) | ||||
−0.442448 | + | 0.896794i | \(0.645890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.12855i | 0.201213i | 0.994926 | + | 0.100607i | \(0.0320784\pi\) | ||||
−0.994926 | + | 0.100607i | \(0.967922\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.60504 | −0.174870 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.12639 | −0.393264 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.76534 | −0.229539 | −0.114769 | − | 0.993392i | \(-0.536613\pi\) | ||||
−0.114769 | + | 0.993392i | \(0.536613\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.2357i | 0.491897i | 0.969283 | + | 0.245949i | \(0.0790994\pi\) | ||||
−0.969283 | + | 0.245949i | \(0.920901\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.67652 | + | 24.9814i | −0.0801986 | + | 1.19502i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.5730 | 0.981895 | 0.490948 | − | 0.871189i | \(-0.336651\pi\) | ||||
0.490948 | + | 0.871189i | \(0.336651\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 16.3996i | − | 0.779169i | −0.920991 | − | 0.389584i | \(-0.872619\pi\) | ||
0.920991 | − | 0.389584i | \(-0.127381\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.0563452 | −0.00267102 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 9.82101i | − | 0.463482i | −0.972778 | − | 0.231741i | \(-0.925558\pi\) | ||
0.972778 | − | 0.231741i | \(-0.0744422\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 60.9768i | 2.87128i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 3.48095i | − | 0.163189i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 30.5414i | − | 1.42867i | −0.699805 | − | 0.714334i | \(-0.746730\pi\) | ||
0.699805 | − | 0.714334i | \(-0.253270\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.20057i | − | 0.335364i | −0.985841 | − | 0.167682i | \(-0.946372\pi\) | ||
0.985841 | − | 0.167682i | \(-0.0536282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.93798 | −0.275961 | −0.137981 | − | 0.990435i | \(-0.544061\pi\) | ||||
−0.137981 | + | 0.990435i | \(0.544061\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.4933 | 0.948317 | 0.474158 | − | 0.880440i | \(-0.342752\pi\) | ||||
0.474158 | + | 0.880440i | \(0.342752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.81205 | 0.222200 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.94239i | 0.457152i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.22071i | 0.239543i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.9538 | 1.27724 | 0.638622 | − | 0.769521i | \(-0.279505\pi\) | ||||
0.638622 | + | 0.769521i | \(0.279505\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.8553i | 0.950919i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 15.0241i | − | 0.682209i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.2625 | −1.23538 | −0.617690 | − | 0.786422i | \(-0.711931\pi\) | ||||
−0.617690 | + | 0.786422i | \(0.711931\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 37.4663i | − | 1.69083i | −0.534110 | − | 0.845415i | \(-0.679353\pi\) | ||
0.534110 | − | 0.845415i | \(-0.320647\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.5008i | 0.923311i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.18204 | −0.411871 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.3473 | −1.35853 | −0.679266 | − | 0.733892i | \(-0.737702\pi\) | ||||
−0.679266 | + | 0.733892i | \(0.737702\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.08858 | 0.316064 | 0.158032 | − | 0.987434i | \(-0.449485\pi\) | ||||
0.158032 | + | 0.987434i | \(0.449485\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.4906i | 0.867320i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 23.4017i | − | 1.03726i | −0.854999 | − | 0.518630i | \(-0.826442\pi\) | ||
0.854999 | − | 0.518630i | \(-0.173558\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.05707i | 0.223712i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.247690i | 0.0109145i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.59582i | 0.422024i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.74404 | 0.339273 | 0.169636 | − | 0.985507i | \(-0.445741\pi\) | ||||
0.169636 | + | 0.985507i | \(0.445741\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.9918i | 0.961634i | 0.876821 | + | 0.480817i | \(0.159660\pi\) | ||||
−0.876821 | + | 0.480817i | \(0.840340\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.8656 | −0.821797 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.7938 | + | 3.07324i | 0.991033 | + | 0.133619i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 47.9882i | − | 2.07860i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.00052 | −0.389127 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 33.7822 | 1.45510 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6968 | −0.459892 | −0.229946 | − | 0.973203i | \(-0.573855\pi\) | ||||
−0.229946 | + | 0.973203i | \(0.573855\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 10.1556i | − | 0.435019i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.4632 | 1.17424 | 0.587122 | − | 0.809499i | \(-0.300261\pi\) | ||||
0.587122 | + | 0.809499i | \(0.300261\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.6886 | 1.26478 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.21088 | −0.0514916 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.1611 | 0.642398 | 0.321199 | − | 0.947012i | \(-0.395914\pi\) | ||||
0.321199 | + | 0.947012i | \(0.395914\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.82458i | − | 0.330945i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.3602 | −1.11095 | −0.555475 | − | 0.831533i | \(-0.687464\pi\) | ||||
−0.555475 | + | 0.831533i | \(0.687464\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.63519 | 0.195004 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.2551 | −1.26836 | −0.634179 | − | 0.773186i | \(-0.718662\pi\) | ||||
−0.634179 | + | 0.773186i | \(0.718662\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.0330i | 1.75903i | 0.475874 | + | 0.879513i | \(0.342132\pi\) | ||||
−0.475874 | + | 0.879513i | \(0.657868\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.78507 | + | 0.321128i | 0.199551 | + | 0.0133920i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.2284 | 0.883750 | 0.441875 | − | 0.897077i | \(-0.354314\pi\) | ||||
0.441875 | + | 0.897077i | \(0.354314\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.42156i | 0.307898i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.6652 | −1.47710 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.0478i | 0.744911i | 0.928050 | + | 0.372455i | \(0.121484\pi\) | ||||
−0.928050 | + | 0.372455i | \(0.878516\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.3205i | 1.12572i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.6934i | 0.972973i | 0.873688 | + | 0.486486i | \(0.161722\pi\) | ||||
−0.873688 | + | 0.486486i | \(0.838278\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 2.98126i | − | 0.122220i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 14.1037i | − | 0.576261i | −0.957591 | − | 0.288131i | \(-0.906966\pi\) | ||
0.957591 | − | 0.288131i | \(-0.0930337\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.8218 | 1.33883 | 0.669415 | − | 0.742889i | \(-0.266545\pi\) | ||||
0.669415 | + | 0.742889i | \(0.266545\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.6072 | 0.715835 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.9134 | −0.970616 | −0.485308 | − | 0.874343i | \(-0.661293\pi\) | ||||
−0.485308 | + | 0.874343i | \(0.661293\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 7.55183i | − | 0.305514i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 37.1500i | − | 1.50047i | −0.661170 | − | 0.750237i | \(-0.729940\pi\) | ||
0.661170 | − | 0.750237i | \(-0.270060\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.1226 | −0.488036 | −0.244018 | − | 0.969771i | \(-0.578466\pi\) | ||||
−0.244018 | + | 0.969771i | \(0.578466\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 13.1429i | − | 0.528256i | −0.964488 | − | 0.264128i | \(-0.914916\pi\) | ||
0.964488 | − | 0.264128i | \(-0.0850842\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 0.0465957i | − | 0.00186682i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.8615i | 0.712186i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.82487i | − | 0.112456i | −0.998418 | − | 0.0562282i | \(-0.982093\pi\) | ||
0.998418 | − | 0.0562282i | \(-0.0179075\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.28911 | 0.0908405 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.5863 | −1.05339 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.81398 | −0.0716478 | −0.0358239 | − | 0.999358i | \(-0.511406\pi\) | ||||
−0.0358239 | + | 0.999358i | \(0.511406\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.7415i | 0.975711i | 0.872924 | + | 0.487855i | \(0.162221\pi\) | ||||
−0.872924 | + | 0.487855i | \(0.837779\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 41.3075i | − | 1.62397i | −0.583681 | − | 0.811983i | \(-0.698388\pi\) | ||
0.583681 | − | 0.811983i | \(-0.301612\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.8712i | 0.976281i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.5923i | 0.492774i | 0.969172 | + | 0.246387i | \(0.0792434\pi\) | ||||
−0.969172 | + | 0.246387i | \(0.920757\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 11.6358i | − | 0.454647i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.4875 | 0.798080 | 0.399040 | − | 0.916934i | \(-0.369344\pi\) | ||||
0.399040 | + | 0.916934i | \(0.369344\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 40.3876i | − | 1.57090i | −0.618927 | − | 0.785449i | \(-0.712432\pi\) | ||
0.618927 | − | 0.785449i | \(-0.287568\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.31737 | −0.167420 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.82616 | − | 27.2113i | 0.0707092 | − | 1.05363i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 52.5588i | 2.02901i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −47.1930 | −1.81915 | −0.909577 | − | 0.415535i | \(-0.863594\pi\) | ||||
−0.909577 | + | 0.415535i | \(0.863594\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −47.4443 | −1.82343 | −0.911716 | − | 0.410821i | \(-0.865242\pi\) | ||||
−0.911716 | + | 0.410821i | \(0.865242\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.4245 | 0.476807 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 30.1260i | − | 1.15274i | −0.817188 | − | 0.576371i | \(-0.804469\pi\) | ||
0.817188 | − | 0.576371i | \(-0.195531\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.80437 | 0.107149 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.0682 | 1.06931 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.3816 | −1.57423 | −0.787115 | − | 0.616806i | \(-0.788426\pi\) | ||||
−0.787115 | + | 0.616806i | \(0.788426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.23304 | −0.122636 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 41.0996i | − | 1.55676i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.1046 | 0.910418 | 0.455209 | − | 0.890385i | \(-0.349565\pi\) | ||||
0.455209 | + | 0.890385i | \(0.349565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.8665 | 0.975573 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.1181 | −0.606185 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 41.1005i | − | 1.54356i | −0.635890 | − | 0.771780i | \(-0.719367\pi\) | ||
0.635890 | − | 0.771780i | \(-0.280633\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.0407 | + | 1.68050i | 0.937783 | + | 0.0629350i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.5136 | −0.841963 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 19.0130i | − | 0.709065i | −0.935044 | − | 0.354532i | \(-0.884640\pi\) | ||
0.935044 | − | 0.354532i | \(-0.115360\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.204832 | −0.00762835 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 5.68671i | − | 0.211199i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 0.332437i | − | 0.0123294i | −0.999981 | − | 0.00616470i | \(-0.998038\pi\) | ||
0.999981 | − | 0.00616470i | \(-0.00196230\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 6.70137i | − | 0.247859i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.37626i | 0.161641i | 0.996729 | + | 0.0808203i | \(0.0257540\pi\) | ||||
−0.996729 | + | 0.0808203i | \(0.974246\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 31.1228i | − | 1.14642i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.49427 | 0.312467 | 0.156233 | − | 0.987720i | \(-0.450065\pi\) | ||||
0.156233 | + | 0.987720i | \(0.450065\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.8899 | −0.729689 | −0.364844 | − | 0.931068i | \(-0.618878\pi\) | ||||
−0.364844 | + | 0.931068i | \(0.618878\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.32611 | 0.305045 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 7.44316i | − | 0.271967i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 4.99053i | − | 0.182107i | −0.995846 | − | 0.0910535i | \(-0.970977\pi\) | ||
0.995846 | − | 0.0910535i | \(-0.0290234\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.72932 | −0.135724 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 38.7722i | − | 1.40920i | −0.709606 | − | 0.704599i | \(-0.751127\pi\) | ||
0.709606 | − | 0.704599i | \(-0.248873\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 13.7993i | − | 0.500224i | −0.968217 | − | 0.250112i | \(-0.919533\pi\) | ||
0.968217 | − | 0.250112i | \(-0.0804674\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.39839 | 0.304042 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 19.5734i | − | 0.706756i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 12.0874i | − | 0.435883i | −0.975962 | − | 0.217942i | \(-0.930066\pi\) | ||
0.975962 | − | 0.217942i | \(-0.0699342\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.7194 | −1.28474 | −0.642368 | − | 0.766396i | \(-0.722048\pi\) | ||||
−0.642368 | + | 0.766396i | \(0.722048\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.23310 | 0.187979 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −59.5191 | −2.13249 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 59.3865i | 2.12501i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.9437i | 0.533365i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 21.0986i | − | 0.752082i | −0.926603 | − | 0.376041i | \(-0.877285\pi\) | ||
0.926603 | − | 0.376041i | \(-0.122715\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.83316i | 0.136292i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 41.3634i | − | 1.46886i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.8022 | −1.48071 | −0.740355 | − | 0.672216i | \(-0.765343\pi\) | ||||
−0.740355 | + | 0.672216i | \(0.765343\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6.46777i | − | 0.228813i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.7075 | 1.15422 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.265563 | + | 3.95711i | −0.00935987 | + | 0.139470i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 27.2362i | − | 0.957573i | −0.877931 | − | 0.478786i | \(-0.841077\pi\) | ||
0.877931 | − | 0.478786i | \(-0.158923\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.3116 | 1.45065 | 0.725323 | − | 0.688408i | \(-0.241690\pi\) | ||||
0.725323 | + | 0.688408i | \(0.241690\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.8043 | 0.553602 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.70471 | −0.339525 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 2.54365i | − | 0.0887741i | −0.999014 | − | 0.0443870i | \(-0.985867\pi\) | ||
0.999014 | − | 0.0443870i | \(-0.0141335\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.4594 | −1.06175 | −0.530873 | − | 0.847451i | \(-0.678136\pi\) | ||||
−0.530873 | + | 0.847451i | \(0.678136\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −51.1175 | −1.77753 | −0.888764 | − | 0.458365i | \(-0.848435\pi\) | ||||
−0.888764 | + | 0.458365i | \(0.848435\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.5460 | −1.65134 | −0.825670 | − | 0.564153i | \(-0.809203\pi\) | ||||
−0.825670 | + | 0.564153i | \(0.809203\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.7699 | −0.788930 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 0.877759i | − | 0.0303761i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.8450 | −0.926792 | −0.463396 | − | 0.886151i | \(-0.653369\pi\) | ||||
−0.463396 | + | 0.886151i | \(0.653369\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.33865 | −0.115126 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.71806 | 0.162306 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.5606i | 0.500309i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.59106 | − | 23.7081i | 0.0545408 | − | 0.812702i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.4644 | −1.11156 | −0.555780 | − | 0.831330i | \(-0.687580\pi\) | ||||
−0.555780 | + | 0.831330i | \(0.687580\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 10.4155i | − | 0.355787i | −0.984050 | − | 0.177893i | \(-0.943072\pi\) | ||
0.984050 | − | 0.177893i | \(-0.0569282\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.1733 | −1.16598 | −0.582989 | − | 0.812480i | \(-0.698117\pi\) | ||||
−0.582989 | + | 0.812480i | \(0.698117\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 18.6417i | − | 0.634572i | −0.948330 | − | 0.317286i | \(-0.897229\pi\) | ||
0.948330 | − | 0.317286i | \(-0.102771\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.84136i | 0.300615i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.83154i | 0.265667i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.4934i | 0.829926i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.826970i | 0.0279567i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.2978 | −1.42830 | −0.714148 | − | 0.699995i | \(-0.753186\pi\) | ||||
−0.714148 | + | 0.699995i | \(0.753186\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.8656 | 1.51156 | 0.755780 | − | 0.654826i | \(-0.227258\pi\) | ||||
0.755780 | + | 0.654826i | \(0.227258\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.4176 | −0.350579 | −0.175289 | − | 0.984517i | \(-0.556086\pi\) | ||||
−0.175289 | + | 0.984517i | \(0.556086\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 48.0868i | − | 1.61460i | −0.590145 | − | 0.807298i | \(-0.700929\pi\) | ||
0.590145 | − | 0.807298i | \(-0.299071\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.89302i | 0.0634900i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.36642 | −0.313435 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.7369i | 0.425748i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 29.7591i | − | 0.992522i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0391 | 0.800858 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.0635i | 0.334523i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 18.0597i | − | 0.599661i | −0.953993 | − | 0.299830i | \(-0.903070\pi\) | ||
0.953993 | − | 0.299830i | \(-0.0969301\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.3139 | 1.53445 | 0.767225 | − | 0.641379i | \(-0.221637\pi\) | ||||
0.767225 | + | 0.641379i | \(0.221637\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.0002 | 1.58858 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.62243 | 0.317761 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.917053i | 0.0302508i | 0.999886 | + | 0.0151254i | \(0.00481474\pi\) | ||||
−0.999886 | + | 0.0151254i | \(0.995185\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 46.7367i | − | 1.53836i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 4.95459i | − | 0.162906i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.70815i | 0.0888516i | 0.999013 | + | 0.0444258i | \(0.0141458\pi\) | ||||
−0.999013 | + | 0.0444258i | \(0.985854\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.9746i | 1.08070i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19.2818 | −0.630583 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 58.5686i | − | 1.91335i | −0.291154 | − | 0.956676i | \(-0.594039\pi\) | ||
0.291154 | − | 0.956676i | \(-0.405961\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.0376 | −0.490213 | −0.245107 | − | 0.969496i | \(-0.578823\pi\) | ||||
−0.245107 | + | 0.969496i | \(0.578823\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.66104 | + | 54.5525i | −0.119220 | + | 1.77647i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.78805i | 0.0581037i | 0.999578 | + | 0.0290518i | \(0.00924879\pi\) | ||||
−0.999578 | + | 0.0290518i | \(0.990751\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.7405 | −0.835573 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.9100 | 0.709736 | 0.354868 | − | 0.934916i | \(-0.384526\pi\) | ||||
0.354868 | + | 0.934916i | \(0.384526\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.9106 | −0.417777 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.31913i | 0.0748885i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.61464 | −0.116601 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.4533 | 0.851561 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.3740 | −1.52344 | −0.761722 | − | 0.647904i | \(-0.775646\pi\) | ||||
−0.761722 | + | 0.647904i | \(0.775646\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.8635 | 0.637449 | 0.318725 | − | 0.947847i | \(-0.396745\pi\) | ||||
0.318725 | + | 0.947847i | \(0.396745\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.67362i | − | 0.0857125i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.0169 | −0.928332 | −0.464166 | − | 0.885748i | \(-0.653646\pi\) | ||||
−0.464166 | + | 0.885748i | \(0.653646\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.301366 | −0.00963170 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.9587 | 1.30638 | 0.653190 | − | 0.757194i | \(-0.273430\pi\) | ||||
0.653190 | + | 0.757194i | \(0.273430\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 8.30018i | − | 0.264466i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.596941 | + | 8.89490i | −0.0189816 | + | 0.282842i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.6334 | 1.19546 | 0.597732 | − | 0.801696i | \(-0.296069\pi\) | ||||
0.597732 | + | 0.801696i | \(0.296069\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 6.61245i | − | 0.209629i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.7183 | −0.877849 | −0.438924 | − | 0.898524i | \(-0.644640\pi\) | ||||
−0.438924 | + | 0.898524i | \(0.644640\pi\) | |||||||
\(998\) | 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 | 4140.2.i.b.1241.11 | yes | 16 | |
3.2 | odd | 2 | 4140.2.i.a.1241.11 | yes | 16 | ||
23.22 | odd | 2 | 4140.2.i.a.1241.6 | ✓ | 16 | ||
69.68 | even | 2 | inner | 4140.2.i.b.1241.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4140.2.i.a.1241.6 | ✓ | 16 | 23.22 | odd | 2 | ||
4140.2.i.a.1241.11 | yes | 16 | 3.2 | odd | 2 | ||
4140.2.i.b.1241.6 | yes | 16 | 69.68 | even | 2 | inner | |
4140.2.i.b.1241.11 | yes | 16 | 1.1 | even | 1 | trivial |