Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(3005,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6012.3005");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.h (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: | \(48.0060616952\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3005.10 | ||
Character | \(\chi\) | \(=\) | 6012.3005 |
Dual form | 6012.2.h.a.3005.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6012\mathbb{Z}\right)^\times\).
\(n\) | \(3007\) | \(3341\) | \(4681\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.04368 | −1.36117 | −0.680587 | − | 0.732668i | \(-0.738275\pi\) | ||||
−0.680587 | + | 0.732668i | \(0.738275\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.233711 | 0.0883346 | 0.0441673 | − | 0.999024i | \(-0.485937\pi\) | ||||
0.0441673 | + | 0.999024i | \(0.485937\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.11221i | 0.636857i | 0.947947 | + | 0.318428i | \(0.103155\pi\) | ||||
−0.947947 | + | 0.318428i | \(0.896845\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.71375i | − | 0.475310i | −0.971350 | − | 0.237655i | \(-0.923621\pi\) | ||
0.971350 | − | 0.237655i | \(-0.0763787\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.18919 | 1.25856 | 0.629281 | − | 0.777178i | \(-0.283349\pi\) | ||||
0.629281 | + | 0.777178i | \(0.283349\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.94672 | −0.446609 | −0.223305 | − | 0.974749i | \(-0.571684\pi\) | ||||
−0.223305 | + | 0.974749i | \(0.571684\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.99706 | −0.624931 | −0.312465 | − | 0.949929i | \(-0.601155\pi\) | ||||
−0.312465 | + | 0.949929i | \(0.601155\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.26397 | 0.852793 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.73646i | 0.508149i | 0.967185 | + | 0.254074i | \(0.0817708\pi\) | ||||
−0.967185 | + | 0.254074i | \(0.918229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.50175 | −1.52696 | −0.763480 | − | 0.645832i | \(-0.776511\pi\) | ||||
−0.763480 | + | 0.645832i | \(0.776511\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.711342 | −0.120239 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8.21183i | − | 1.35002i | −0.737810 | − | 0.675008i | \(-0.764140\pi\) | ||
0.737810 | − | 0.675008i | \(-0.235860\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.33880 | 0.521433 | 0.260717 | − | 0.965415i | \(-0.416041\pi\) | ||||
0.260717 | + | 0.965415i | \(0.416041\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.222843i | 0.0339833i | 0.999856 | + | 0.0169916i | \(0.00540887\pi\) | ||||
−0.999856 | + | 0.0169916i | \(0.994591\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.47244i | 1.23583i | 0.786244 | + | 0.617916i | \(0.212023\pi\) | ||||
−0.786244 | + | 0.617916i | \(0.787977\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.94538 | −0.992197 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.15818 | 1.25797 | 0.628987 | − | 0.777416i | \(-0.283470\pi\) | ||||
0.628987 | + | 0.777416i | \(0.283470\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.42890i | − | 0.866872i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.8700 | −1.41516 | −0.707579 | − | 0.706634i | \(-0.750213\pi\) | ||||
−0.707579 | + | 0.706634i | \(0.750213\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.7341 | 1.37436 | 0.687179 | − | 0.726489i | \(-0.258849\pi\) | ||||
0.687179 | + | 0.726489i | \(0.258849\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.21611i | 0.646979i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.936932i | 0.114464i | 0.998361 | + | 0.0572322i | \(0.0182275\pi\) | ||||
−0.998361 | + | 0.0572322i | \(0.981772\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.56802 | 1.13551 | 0.567757 | − | 0.823196i | \(-0.307811\pi\) | ||||
0.567757 | + | 0.823196i | \(0.307811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.59038i | − | 1.12247i | −0.827657 | − | 0.561234i | \(-0.810327\pi\) | ||
0.827657 | − | 0.561234i | \(-0.189673\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.493649i | 0.0562565i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.20452i | 0.585554i | 0.956181 | + | 0.292777i | \(0.0945794\pi\) | ||||
−0.956181 | + | 0.292777i | \(0.905421\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.37637 | −0.370605 | −0.185303 | − | 0.982682i | \(-0.559327\pi\) | ||||
−0.185303 | + | 0.982682i | \(0.559327\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.7942 | −1.71312 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.1716i | 1.71419i | 0.515161 | + | 0.857093i | \(0.327732\pi\) | ||||
−0.515161 | + | 0.857093i | \(0.672268\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.400524i | − | 0.0419863i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.92520 | 0.607912 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.2646 | −1.14374 | −0.571872 | − | 0.820343i | \(-0.693782\pi\) | ||||
−0.571872 | + | 0.820343i | \(0.693782\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.22423 | 0.121816 | 0.0609080 | − | 0.998143i | \(-0.480600\pi\) | ||||
0.0609080 | + | 0.998143i | \(0.480600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.764815i | − | 0.0753594i | −0.999290 | − | 0.0376797i | \(-0.988003\pi\) | ||
0.999290 | − | 0.0376797i | \(-0.0119967\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 9.90034i | − | 0.957102i | −0.878060 | − | 0.478551i | \(-0.841162\pi\) | ||
0.878060 | − | 0.478551i | \(-0.158838\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.0922689i | 0.00883776i | 0.999990 | + | 0.00441888i | \(0.00140658\pi\) | ||||
−0.999990 | + | 0.00441888i | \(0.998593\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.87054 | −0.458182 | −0.229091 | − | 0.973405i | \(-0.573575\pi\) | ||||
−0.229091 | + | 0.973405i | \(0.573575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.12209 | 0.850639 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.21277 | 0.111175 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.53855 | 0.594414 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.24025 | 0.200374 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.79810 | 0.159555 | 0.0797777 | − | 0.996813i | \(-0.474579\pi\) | ||||
0.0797777 | + | 0.996813i | \(0.474579\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.0140 | 0.962299 | 0.481150 | − | 0.876639i | \(-0.340219\pi\) | ||||
0.481150 | + | 0.876639i | \(0.340219\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.454972 | −0.0394510 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.63132i | 0.566552i | 0.959038 | + | 0.283276i | \(0.0914212\pi\) | ||||
−0.959038 | + | 0.283276i | \(0.908579\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 21.6598i | − | 1.83716i | −0.395236 | − | 0.918580i | \(-0.629337\pi\) | ||
0.395236 | − | 0.918580i | \(-0.370663\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.61981 | 0.302704 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 8.32891i | − | 0.691678i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.6000 | 1.44184 | 0.720922 | − | 0.693016i | \(-0.243718\pi\) | ||||
0.720922 | + | 0.693016i | \(0.243718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 23.5281i | − | 1.91469i | −0.288953 | − | 0.957343i | \(-0.593307\pi\) | ||
0.288953 | − | 0.957343i | \(-0.406693\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.8766 | 2.07846 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.4566 | −1.47300 | −0.736499 | − | 0.676439i | \(-0.763522\pi\) | ||||
−0.736499 | + | 0.676439i | \(0.763522\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.700448 | −0.0552030 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.5832i | 1.29889i | 0.760407 | + | 0.649447i | \(0.225000\pi\) | ||||
−0.760407 | + | 0.649447i | \(0.775000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.8060 | + | 1.73367i | −0.990960 | + | 0.134155i | ||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.0631 | 0.774081 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 25.6712i | − | 1.95175i | −0.218332 | − | 0.975874i | \(-0.570062\pi\) | ||
0.218332 | − | 0.975874i | \(-0.429938\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.996537 | 0.0753311 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 17.9325i | − | 1.34034i | −0.742208 | − | 0.670169i | \(-0.766222\pi\) | ||
0.742208 | − | 0.670169i | \(-0.233778\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.2042 | 1.57610 | 0.788049 | − | 0.615612i | \(-0.211091\pi\) | ||||
0.788049 | + | 0.615612i | \(0.211091\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.9942i | 1.83761i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.9607i | 0.801524i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 26.4287i | − | 1.91231i | −0.292856 | − | 0.956157i | \(-0.594606\pi\) | ||
0.292856 | − | 0.956157i | \(-0.405394\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 13.7744i | − | 0.991506i | −0.868464 | − | 0.495753i | \(-0.834892\pi\) | ||
0.868464 | − | 0.495753i | \(-0.165108\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.33812 | −0.665314 | −0.332657 | − | 0.943048i | \(-0.607945\pi\) | ||||
−0.332657 | + | 0.943048i | \(0.607945\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.7492 | 1.18732 | 0.593659 | − | 0.804717i | \(-0.297683\pi\) | ||||
0.593659 | + | 0.804717i | \(0.297683\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.639543i | 0.0448871i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.1622 | −0.709761 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.11190i | − | 0.284426i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.9376 | 0.959504 | 0.479752 | − | 0.877404i | \(-0.340727\pi\) | ||||
0.479752 | + | 0.877404i | \(0.340727\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 0.678263i | − | 0.0462571i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.98696 | −0.134883 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 8.89298i | − | 0.598207i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.9899 | 0.869865 | 0.434933 | − | 0.900463i | \(-0.356772\pi\) | ||||
0.434933 | + | 0.900463i | \(0.356772\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.33538 | −0.619611 | −0.309805 | − | 0.950800i | \(-0.600264\pi\) | ||||
−0.309805 | + | 0.950800i | \(0.600264\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.0496 | 1.72141 | 0.860703 | − | 0.509107i | \(-0.170024\pi\) | ||||
0.860703 | + | 0.509107i | \(0.170024\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.10871i | − | 0.0726338i | −0.999340 | − | 0.0363169i | \(-0.988437\pi\) | ||
0.999340 | − | 0.0363169i | \(-0.0115626\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 25.7874i | − | 1.68218i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 12.4479i | − | 0.805184i | −0.915379 | − | 0.402592i | \(-0.868109\pi\) | ||
0.915379 | − | 0.402592i | \(-0.131891\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4845i | 0.739784i | 0.929075 | + | 0.369892i | \(0.120605\pi\) | ||||
−0.929075 | + | 0.369892i | \(0.879395\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.1395 | 1.35055 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.33620i | 0.212278i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.3240i | 1.03036i | 0.857082 | + | 0.515181i | \(0.172275\pi\) | ||||
−0.857082 | + | 0.515181i | \(0.827725\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.33044i | − | 0.397991i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.6077 | 1.16072 | 0.580359 | − | 0.814361i | \(-0.302912\pi\) | ||||
0.580359 | + | 0.814361i | \(0.302912\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.91920i | − | 0.119253i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.3510i | − | 1.00825i | −0.863631 | − | 0.504124i | \(-0.831815\pi\) | ||
0.863631 | − | 0.504124i | \(-0.168185\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −27.8745 | −1.71232 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.7864 | 1.38931 | 0.694657 | − | 0.719341i | \(-0.255556\pi\) | ||||
0.694657 | + | 0.719341i | \(0.255556\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 13.2759i | − | 0.806453i | −0.915100 | − | 0.403226i | \(-0.867889\pi\) | ||
0.915100 | − | 0.403226i | \(-0.132111\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.00641i | 0.543107i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 24.9639i | − | 1.49994i | −0.661473 | − | 0.749969i | \(-0.730068\pi\) | ||
0.661473 | − | 0.749969i | \(-0.269932\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.7440i | 0.819898i | 0.912108 | + | 0.409949i | \(0.134454\pi\) | ||||
−0.912108 | + | 0.409949i | \(0.865546\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.64056 | 0.275853 | 0.137926 | − | 0.990442i | \(-0.455956\pi\) | ||||
0.137926 | + | 0.990442i | \(0.455956\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.780316 | 0.0460606 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.92764 | 0.583979 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.10870i | − | 0.473715i | −0.971544 | − | 0.236858i | \(-0.923883\pi\) | ||
0.971544 | − | 0.236858i | \(-0.0761175\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.0849 | 1.92627 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.13622i | 0.297035i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0520810i | 0.00300190i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −32.6710 | −1.87074 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.9446i | 1.13830i | 0.822234 | + | 0.569150i | \(0.192728\pi\) | ||||
−0.822234 | + | 0.569150i | \(0.807272\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 3.07490i | − | 0.174362i | −0.996193 | − | 0.0871808i | \(-0.972214\pi\) | ||
0.996193 | − | 0.0871808i | \(-0.0277858\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8.69801i | − | 0.491641i | −0.969315 | − | 0.245820i | \(-0.920943\pi\) | ||
0.969315 | − | 0.245820i | \(-0.0790573\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 0.795282i | − | 0.0446675i | −0.999751 | − | 0.0223337i | \(-0.992890\pi\) | ||
0.999751 | − | 0.0223337i | \(-0.00710964\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.78000 | −0.323618 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.1019 | −0.562085 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 7.30738i | − | 0.405341i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.98011i | 0.109167i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 14.1043i | − | 0.775240i | −0.921819 | − | 0.387620i | \(-0.873297\pi\) | ||
0.921819 | − | 0.387620i | \(-0.126703\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 2.85172i | − | 0.155806i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.0058 | −0.653998 | −0.326999 | − | 0.945025i | \(-0.606037\pi\) | ||||
−0.326999 | + | 0.945025i | \(0.606037\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 17.9575i | − | 0.972454i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.25919 | −0.175980 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.5883 | 1.42734 | 0.713668 | − | 0.700484i | \(-0.247032\pi\) | ||||
0.713668 | + | 0.700484i | \(0.247032\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 29.7666i | − | 1.59337i | −0.604393 | − | 0.796686i | \(-0.706584\pi\) | ||
0.604393 | − | 0.796686i | \(-0.293416\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.1203i | 1.65637i | 0.560456 | + | 0.828184i | \(0.310626\pi\) | ||||
−0.560456 | + | 0.828184i | \(0.689374\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29.1219 | −1.54563 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 21.2836i | − | 1.12330i | −0.827374 | − | 0.561652i | \(-0.810166\pi\) | ||
0.827374 | − | 0.561652i | \(-0.189834\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2103 | −0.800540 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.1900i | 1.52787i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.18368 | 0.374985 | 0.187492 | − | 0.982266i | \(-0.439964\pi\) | ||||
0.187492 | + | 0.982266i | \(0.439964\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.14037 | 0.111123 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 12.3158i | − | 0.637689i | −0.947807 | − | 0.318844i | \(-0.896705\pi\) | ||
0.947807 | − | 0.318844i | \(-0.103295\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.68962 | 0.241528 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 12.8067i | − | 0.657834i | −0.944359 | − | 0.328917i | \(-0.893316\pi\) | ||
0.944359 | − | 0.328917i | \(-0.106684\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 26.0935i | − | 1.33332i | −0.745363 | − | 0.666659i | \(-0.767724\pi\) | ||
0.745363 | − | 0.666659i | \(-0.232276\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 1.50251i | − | 0.0765748i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.1524 | 0.768257 | 0.384129 | − | 0.923280i | \(-0.374502\pi\) | ||||
0.384129 | + | 0.923280i | \(0.374502\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.5523 | −0.786514 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 15.8409i | − | 0.797041i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.1906 | 1.06353 | 0.531764 | − | 0.846893i | \(-0.321530\pi\) | ||||
0.531764 | + | 0.846893i | \(0.321530\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0819 | −0.902965 | −0.451482 | − | 0.892280i | \(-0.649105\pi\) | ||||
−0.451482 | + | 0.892280i | \(0.649105\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.5699i | 0.725778i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.3451 | 0.859767 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.21828 | −0.109687 | −0.0548434 | − | 0.998495i | \(-0.517466\pi\) | ||||
−0.0548434 | + | 0.998495i | \(0.517466\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.54045 | −0.125007 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.2766 | 0.504458 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.24647i | 0.0608939i | 0.999536 | + | 0.0304469i | \(0.00969306\pi\) | ||||
−0.999536 | + | 0.0304469i | \(0.990307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.24823 | 0.207046 | 0.103523 | − | 0.994627i | \(-0.466988\pi\) | ||||
0.103523 | + | 0.994627i | \(0.466988\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.1265 | 1.07329 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.50867 | 0.121403 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.3570i | 1.07690i | 0.842658 | + | 0.538448i | \(0.180989\pi\) | ||||
−0.842658 | + | 0.538448i | \(0.819011\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.6183 | 0.558341 | 0.279171 | − | 0.960241i | \(-0.409940\pi\) | ||||
0.279171 | + | 0.960241i | \(0.409940\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.83445 | 0.279100 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.7712i | 1.89817i | 0.315014 | + | 0.949087i | \(0.397991\pi\) | ||||
−0.315014 | + | 0.949087i | \(0.602009\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.7204 | 0.794408 | 0.397204 | − | 0.917730i | \(-0.369981\pi\) | ||||
0.397204 | + | 0.917730i | \(0.369981\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 49.2211i | − | 2.33330i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.8333i | 0.700028i | 0.936744 | + | 0.350014i | \(0.113823\pi\) | ||||
−0.936744 | + | 0.350014i | \(0.886177\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.05226i | 0.332078i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.21906i | 0.0571506i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 29.3212i | − | 1.37159i | −0.727795 | − | 0.685794i | \(-0.759455\pi\) | ||
0.727795 | − | 0.685794i | \(-0.240545\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 0.232415i | − | 0.0108247i | −0.999985 | − | 0.00541233i | \(-0.998277\pi\) | ||
0.999985 | − | 0.00541233i | \(-0.00172281\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 27.5746i | − | 1.28150i | −0.767749 | − | 0.640750i | \(-0.778623\pi\) | ||
0.767749 | − | 0.640750i | \(-0.221377\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 11.6372i | − | 0.538507i | −0.963069 | − | 0.269254i | \(-0.913223\pi\) | ||
0.963069 | − | 0.269254i | \(-0.0867770\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.218972i | 0.0101112i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.470693 | −0.0216425 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.30076 | −0.380865 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.9459 | −0.500129 | −0.250065 | − | 0.968229i | \(-0.580452\pi\) | ||||
−0.250065 | + | 0.968229i | \(0.580452\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.0730 | −0.641676 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 34.2857 | 1.55683 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.4976i | 0.747579i | 0.927514 | + | 0.373789i | \(0.121942\pi\) | ||||
−0.927514 | + | 0.373789i | \(0.878058\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.7588i | 1.11735i | 0.829387 | + | 0.558674i | \(0.188690\pi\) | ||||
−0.829387 | + | 0.558674i | \(0.811310\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.2000i | 0.639537i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.23615 | 0.100305 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.5947i | 1.19054i | 0.803525 | + | 0.595272i | \(0.202955\pi\) | ||||
−0.803525 | + | 0.595272i | \(0.797045\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.4288i | 1.75804i | 0.476782 | + | 0.879022i | \(0.341803\pi\) | ||||
−0.476782 | + | 0.879022i | \(0.658197\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.72617 | −0.165813 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 33.1756i | − | 1.47048i | −0.677806 | − | 0.735241i | \(-0.737069\pi\) | ||
0.677806 | − | 0.735241i | \(-0.262931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2.24138i | − | 0.0991528i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.32785i | 0.102577i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.8956 | −0.787048 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.16160 | −0.226134 | −0.113067 | − | 0.993587i | \(-0.536067\pi\) | ||||
−0.113067 | + | 0.993587i | \(0.536067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.41931 | 0.280697 | 0.140348 | − | 0.990102i | \(-0.455178\pi\) | ||||
0.140348 | + | 0.990102i | \(0.455178\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −44.1171 | −1.92177 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0176 | −0.609462 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5.72188i | − | 0.247842i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.1334i | 1.30278i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 14.6701i | − | 0.631887i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 21.4097i | − | 0.920476i | −0.887796 | − | 0.460238i | \(-0.847764\pi\) | ||
0.887796 | − | 0.460238i | \(-0.152236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 0.280837i | − | 0.0120297i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.02545i | 0.172116i | 0.996290 | + | 0.0860579i | \(0.0274270\pi\) | ||||
−0.996290 | + | 0.0860579i | \(0.972573\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 5.32714i | − | 0.226944i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.21636i | 0.0517247i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.5466i | 1.54853i | 0.632861 | + | 0.774265i | \(0.281880\pi\) | ||||
−0.632861 | + | 0.774265i | \(0.718120\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.381898 | 0.0161526 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 14.6535i | − | 0.617571i | −0.951132 | − | 0.308786i | \(-0.900077\pi\) | ||
0.951132 | − | 0.308786i | \(-0.0999225\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.8243 | 0.623665 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.3881 | 1.39970 | 0.699850 | − | 0.714290i | \(-0.253250\pi\) | ||||
0.699850 | + | 0.714290i | \(0.253250\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.9499i | 1.08597i | 0.839743 | + | 0.542984i | \(0.182706\pi\) | ||||
−0.839743 | + | 0.542984i | \(0.817294\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.7794 | −0.532936 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.5037 | 0.936840 | 0.468420 | − | 0.883506i | \(-0.344824\pi\) | ||||
0.468420 | + | 0.883506i | \(0.344824\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.789097 | −0.0327373 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.3440i | 0.801149i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.12151 | 0.128838 | 0.0644192 | − | 0.997923i | \(-0.479481\pi\) | ||||
0.0644192 | + | 0.997923i | \(0.479481\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.5506 | 0.681954 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.01684 | −0.206017 | −0.103009 | − | 0.994680i | \(-0.532847\pi\) | ||||
−0.103009 | + | 0.994680i | \(0.532847\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.69128 | −0.151328 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.9042i | 1.71216i | 0.516844 | + | 0.856080i | \(0.327107\pi\) | ||||
−0.516844 | + | 0.856080i | \(0.672893\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.0514 | −0.654751 | −0.327375 | − | 0.944894i | \(-0.606164\pi\) | ||||
−0.327375 | + | 0.944894i | \(0.606164\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.9012 | −0.809100 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.91136i | − | 0.280523i | −0.990114 | − | 0.140262i | \(-0.955206\pi\) | ||
0.990114 | − | 0.140262i | \(-0.0447944\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.5197 | 0.587403 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.9693 | 0.927723 | 0.463861 | − | 0.885908i | \(-0.346464\pi\) | ||||
0.463861 | + | 0.885908i | \(0.346464\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.885982i | 0.0356683i | 0.999841 | + | 0.0178342i | \(0.00567709\pi\) | ||||
−0.999841 | + | 0.0178342i | \(0.994323\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.5451i | 0.665005i | 0.943102 | + | 0.332503i | \(0.107893\pi\) | ||||
−0.943102 | + | 0.332503i | \(0.892107\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.77949i | 0.151422i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.1384 | −1.12554 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 42.6127i | − | 1.69908i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.2675 | −1.28455 | −0.642274 | − | 0.766475i | \(-0.722009\pi\) | ||||
−0.642274 | + | 0.766475i | \(0.722009\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.47283 | −0.217183 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.9027i | 0.471601i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.26760 | −0.287053 | −0.143526 | − | 0.989646i | \(-0.545844\pi\) | ||||
−0.143526 | + | 0.989646i | \(0.545844\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.1194i | − | 0.438507i | −0.975668 | − | 0.219254i | \(-0.929638\pi\) | ||
0.975668 | − | 0.219254i | \(-0.0703622\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.0483 | −1.49583 | −0.747917 | − | 0.663792i | \(-0.768946\pi\) | ||||
−0.747917 | + | 0.663792i | \(0.768946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 22.9598i | − | 0.901253i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 49.0410i | − | 1.91912i | −0.281498 | − | 0.959562i | \(-0.590831\pi\) | ||
0.281498 | − | 0.959562i | \(-0.409169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33.5231 | −1.30986 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.928331 | −0.0361626 | −0.0180813 | − | 0.999837i | \(-0.505756\pi\) | ||||
−0.0180813 | + | 0.999837i | \(0.505756\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.60700i | 0.256983i | 0.991711 | + | 0.128491i | \(0.0410134\pi\) | ||||
−0.991711 | + | 0.128491i | \(0.958987\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.38479 | 0.0536997 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 8.20135i | − | 0.317558i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.6727i | 0.875268i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 18.6494i | − | 0.718881i | −0.933168 | − | 0.359440i | \(-0.882968\pi\) | ||
0.933168 | − | 0.359440i | \(-0.117032\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.2712i | 1.54775i | 0.633340 | + | 0.773874i | \(0.281684\pi\) | ||||
−0.633340 | + | 0.773874i | \(0.718316\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.63266 | −0.101032 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.3335 | −0.586720 | −0.293360 | − | 0.956002i | \(-0.594773\pi\) | ||||
−0.293360 | + | 0.956002i | \(0.594773\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 20.1836i | − | 0.771175i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 15.6949i | − | 0.597927i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 20.9822i | − | 0.798201i | −0.916907 | − | 0.399101i | \(-0.869322\pi\) | ||
0.916907 | − | 0.399101i | \(-0.130678\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 65.9254i | 2.50069i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.3257 | 0.656256 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8.00186i | − | 0.302226i | −0.988516 | − | 0.151113i | \(-0.951714\pi\) | ||
0.988516 | − | 0.151113i | \(-0.0482858\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.9862i | 0.602930i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.286118 | 0.0107606 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 19.1316i | − | 0.718502i | −0.933241 | − | 0.359251i | \(-0.883032\pi\) | ||
0.933241 | − | 0.359251i | \(-0.116968\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.4803 | 0.954243 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.0175 | −0.412033 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.562268 | 0.0209691 | 0.0104845 | − | 0.999945i | \(-0.496663\pi\) | ||||
0.0104845 | + | 0.999945i | \(0.496663\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 0.178746i | − | 0.00665684i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.6682i | 0.433346i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 23.7745i | − | 0.881747i | −0.897569 | − | 0.440874i | \(-0.854669\pi\) | ||
0.897569 | − | 0.440874i | \(-0.145331\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.15638i | 0.0427701i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.6661 | 0.541705 | 0.270853 | − | 0.962621i | \(-0.412694\pi\) | ||||
0.270853 | + | 0.962621i | \(0.412694\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.97900 | −0.0728974 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 11.2062i | − | 0.412225i | −0.978528 | − | 0.206113i | \(-0.933919\pi\) | ||
0.978528 | − | 0.206113i | \(-0.0660813\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.3715i | 0.673985i | 0.941507 | + | 0.336992i | \(0.109410\pi\) | ||||
−0.941507 | + | 0.336992i | \(0.890590\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −53.5686 | −1.96260 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 2.31382i | − | 0.0845453i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 28.1684i | − | 1.02788i | −0.857826 | − | 0.513940i | \(-0.828185\pi\) | ||
0.857826 | − | 0.513940i | \(-0.171815\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 71.6118i | 2.60622i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.5297 | 0.600783 | 0.300392 | − | 0.953816i | \(-0.402883\pi\) | ||||
0.300392 | + | 0.953816i | \(0.402883\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.7874i | 0.789792i | 0.918726 | + | 0.394896i | \(0.129219\pi\) | ||||
−0.918726 | + | 0.394896i | \(0.870781\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.0215643i | 0.000780680i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.6285i | 0.672638i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.7462i | 1.72177i | 0.508799 | + | 0.860885i | \(0.330090\pi\) | ||||
−0.508799 | + | 0.860885i | \(0.669910\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.34511 | −0.0843478 | −0.0421739 | − | 0.999110i | \(-0.513428\pi\) | ||||
−0.0421739 | + | 0.999110i | \(0.513428\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36.2512 | −1.30218 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.49972 | −0.232877 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.2097i | 0.723160i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 56.1759 | 2.00500 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 28.3179i | − | 1.00942i | −0.863288 | − | 0.504711i | \(-0.831599\pi\) | ||
0.863288 | − | 0.504711i | \(-0.168401\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.13830 | −0.0404733 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 18.3955i | − | 0.653245i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.3671 | 0.402642 | 0.201321 | − | 0.979525i | \(-0.435477\pi\) | ||||
0.201321 | + | 0.979525i | \(0.435477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.9651i | 1.55537i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.2569 | 0.714852 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.13194 | 0.0751409 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.1713i | 0.955292i | 0.878552 | + | 0.477646i | \(0.158510\pi\) | ||||
−0.878552 | + | 0.477646i | \(0.841490\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.0530i | 0.598812i | 0.954126 | + | 0.299406i | \(0.0967885\pi\) | ||||
−0.954126 | + | 0.299406i | \(0.903211\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 50.4738i | − | 1.76802i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 0.433814i | − | 0.0151772i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.44058 | −0.189878 | −0.0949388 | − | 0.995483i | \(-0.530266\pi\) | ||||
−0.0949388 | + | 0.995483i | \(0.530266\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 23.9319i | − | 0.834214i | −0.908857 | − | 0.417107i | \(-0.863044\pi\) | ||
0.908857 | − | 0.417107i | \(-0.136956\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.7390 | −1.20799 | −0.603997 | − | 0.796987i | \(-0.706426\pi\) | ||||
−0.603997 | + | 0.796987i | \(0.706426\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.6778i | 1.82958i | 0.403934 | + | 0.914788i | \(0.367643\pi\) | ||||
−0.403934 | + | 0.914788i | \(0.632357\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −36.0409 | −1.24874 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 38.9774 | − | 5.27672i | 1.34887 | − | 0.182608i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.3802i | 0.461937i | 0.972961 | + | 0.230969i | \(0.0741895\pi\) | ||||
−0.972961 | + | 0.230969i | \(0.925811\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.5118 | 0.741785 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30.6287 | −1.05366 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.52813 | 0.0525073 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.6114i | 0.843667i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.8527 | −0.953658 | −0.476829 | − | 0.878996i | \(-0.658214\pi\) | ||||
−0.476829 | + | 0.878996i | \(0.658214\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 44.3918i | − | 1.51640i | −0.652024 | − | 0.758198i | \(-0.726080\pi\) | ||
0.652024 | − | 0.758198i | \(-0.273920\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.2278 | 0.553685 | 0.276842 | − | 0.960915i | \(-0.410712\pi\) | ||||
0.276842 | + | 0.960915i | \(0.410712\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 41.3503i | − | 1.40758i | −0.710407 | − | 0.703791i | \(-0.751489\pi\) | ||
0.710407 | − | 0.703791i | \(-0.248511\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 78.1350i | 2.65667i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.9931 | −0.372914 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.60567 | 0.0544060 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.523572 | 0.0177000 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.5337 | 1.09858 | 0.549292 | − | 0.835631i | \(-0.314898\pi\) | ||||
0.549292 | + | 0.835631i | \(0.314898\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.7864 | 0.767692 | 0.383846 | − | 0.923397i | \(-0.374599\pi\) | ||||
0.383846 | + | 0.923397i | \(0.374599\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.41110 | −0.148445 | −0.0742227 | − | 0.997242i | \(-0.523648\pi\) | ||||
−0.0742227 | + | 0.997242i | \(0.523648\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.3070 | −1.48768 | −0.743842 | − | 0.668355i | \(-0.766999\pi\) | ||||
−0.743842 | + | 0.668355i | \(0.766999\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.420236 | 0.0140943 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 16.4935i | − | 0.551934i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 54.5807i | 1.82443i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 23.2647i | − | 0.775922i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.5235 | 1.58324 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −64.5388 | −2.14534 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.2595 | −0.871931 | −0.435966 | − | 0.899963i | \(-0.643593\pi\) | ||||
−0.435966 | + | 0.899963i | \(0.643593\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 19.4779i | − | 0.645332i | −0.946513 | − | 0.322666i | \(-0.895421\pi\) | ||
0.946513 | − | 0.322666i | \(-0.104579\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 7.13162i | − | 0.236022i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.57410 | 0.0850043 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.9731 | −0.559889 | −0.279945 | − | 0.960016i | \(-0.590316\pi\) | ||||
−0.279945 | + | 0.960016i | \(0.590316\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 16.3972i | − | 0.539721i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 35.0150i | − | 1.15128i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 16.0513i | − | 0.526625i | −0.964711 | − | 0.263312i | \(-0.915185\pi\) | ||
0.964711 | − | 0.263312i | \(-0.0848150\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.5207 | 0.443124 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 33.3607i | − | 1.09101i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 10.4512i | − | 0.341426i | −0.985321 | − | 0.170713i | \(-0.945393\pi\) | ||
0.985321 | − | 0.170713i | \(-0.0546071\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.4202 | −1.18726 | −0.593632 | − | 0.804736i | \(-0.702307\pi\) | ||||
−0.593632 | + | 0.804736i | \(0.702307\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.0066 | −0.325860 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 24.1342i | − | 0.784257i | −0.919910 | − | 0.392129i | \(-0.871739\pi\) | ||
0.919910 | − | 0.392129i | \(-0.128261\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.4355 | −0.533520 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.15154 | 0.0696953 | 0.0348476 | − | 0.999393i | \(-0.488905\pi\) | ||||
0.0348476 | + | 0.999393i | \(0.488905\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 80.4404i | 2.60299i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.54981i | 0.0500461i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.2797 | 1.33160 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 41.9249i | 1.34961i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.2527 | −1.74465 | −0.872324 | − | 0.488929i | \(-0.837388\pi\) | ||||
−0.872324 | + | 0.488929i | \(0.837388\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.3533 | −1.07036 | −0.535180 | − | 0.844738i | \(-0.679756\pi\) | ||||
−0.535180 | + | 0.844738i | \(0.679756\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 5.06214i | − | 0.162285i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.8130 | −0.473909 | −0.236955 | − | 0.971521i | \(-0.576149\pi\) | ||||
−0.236955 | + | 0.971521i | \(0.576149\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.1579 | −1.09169 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.3384 | 0.967644 | 0.483822 | − | 0.875166i | \(-0.339248\pi\) | ||||
0.483822 | + | 0.875166i | \(0.339248\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.4222 | 0.905607 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 0.667875i | − | 0.0212372i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.4997i | 0.937088i | 0.883440 | + | 0.468544i | \(0.155221\pi\) | ||||
−0.883440 | + | 0.468544i | \(0.844779\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −50.9790 | −1.61614 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.6928 | −1.03539 | −0.517696 | − | 0.855565i | \(-0.673210\pi\) | ||||
−0.517696 | + | 0.855565i | \(0.673210\pi\) | |||||||
\(998\) | 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 | 6012.2.h.a.3005.10 | yes | 56 | |
3.2 | odd | 2 | inner | 6012.2.h.a.3005.47 | yes | 56 | |
167.166 | odd | 2 | inner | 6012.2.h.a.3005.48 | yes | 56 | |
501.500 | even | 2 | inner | 6012.2.h.a.3005.9 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6012.2.h.a.3005.9 | ✓ | 56 | 501.500 | even | 2 | inner | |
6012.2.h.a.3005.10 | yes | 56 | 1.1 | even | 1 | trivial | |
6012.2.h.a.3005.47 | yes | 56 | 3.2 | odd | 2 | inner | |
6012.2.h.a.3005.48 | yes | 56 | 167.166 | odd | 2 | inner |