Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,2,Mod(271,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.271");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.bz (of order \(6\), degree \(2\), not 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: | \(8.94324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 591.8 | ||
Character | \(\chi\) | \(=\) | 1120.591 |
Dual form | 1120.2.bz.f.271.8 |
$q$-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 \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.219454 | + | 0.126702i | 0.126702 | + | 0.0731514i | 0.562011 | − | 0.827130i | \(-0.310028\pi\) |
−0.435309 | + | 0.900281i | \(0.643361\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.978876 | + | 2.45801i | 0.369980 | + | 0.929040i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.46789 | − | 2.54247i | −0.489298 | − | 0.847489i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.81455 | + | 3.14289i | −0.547106 | + | 0.947616i | 0.451365 | + | 0.892339i | \(0.350937\pi\) |
−0.998471 | + | 0.0552761i | \(0.982396\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.36097 | −1.48687 | −0.743433 | − | 0.668810i | \(-0.766804\pi\) | ||||
−0.743433 | + | 0.668810i | \(0.766804\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.253404i | 0.0654286i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.46956 | − | 2.58050i | −1.08403 | − | 0.625863i | −0.152047 | − | 0.988373i | \(-0.548586\pi\) |
−0.931980 | + | 0.362510i | \(0.881920\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.49220 | + | 3.17092i | −1.26000 | + | 0.727460i | −0.973074 | − | 0.230494i | \(-0.925966\pi\) |
−0.286924 | + | 0.957953i | \(0.592633\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0966157 | + | 0.663445i | −0.0210833 | + | 0.144776i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.231195 | − | 0.133481i | 0.0482076 | − | 0.0278326i | −0.475703 | − | 0.879606i | \(-0.657806\pi\) |
0.523910 | + | 0.851774i | \(0.324473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.50415i | − | 0.289474i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.99647i | 0.556430i | 0.960519 | + | 0.278215i | \(0.0897428\pi\) | ||||
−0.960519 | + | 0.278215i | \(0.910257\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.72336 | − | 4.71700i | 0.489130 | − | 0.847199i | −0.510791 | − | 0.859705i | \(-0.670648\pi\) |
0.999922 | + | 0.0125059i | \(0.00398086\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.796419 | + | 0.459813i | −0.138639 | + | 0.0800431i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.63926 | + | 2.07674i | −0.277085 | + | 0.351032i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.48336 | − | 4.32052i | 1.23026 | − | 0.710289i | 0.263173 | − | 0.964749i | \(-0.415231\pi\) |
0.967083 | + | 0.254460i | \(0.0818977\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.17649 | − | 0.679245i | −0.188389 | − | 0.108766i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.46796i | − | 0.541604i | −0.962635 | − | 0.270802i | \(-0.912711\pi\) | ||
0.962635 | − | 0.270802i | \(-0.0872889\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.33960 | −0.814281 | −0.407140 | − | 0.913366i | \(-0.633474\pi\) | ||||
−0.407140 | + | 0.913366i | \(0.633474\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.46789 | − | 2.54247i | 0.218821 | − | 0.379008i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.26364 | + | 3.92073i | 0.330185 | + | 0.571898i | 0.982548 | − | 0.186009i | \(-0.0595554\pi\) |
−0.652363 | + | 0.757907i | \(0.726222\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.08360 | + | 4.81217i | −0.726229 | + | 0.687453i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.653908 | − | 1.13260i | −0.0915655 | − | 0.158596i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.09705 | − | 1.78808i | −0.425413 | − | 0.245612i | 0.271978 | − | 0.962304i | \(-0.412322\pi\) |
−0.697391 | + | 0.716691i | \(0.745656\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.62909 | −0.489347 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.60705 | −0.212859 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.83489 | − | 3.94613i | −0.889827 | − | 0.513742i | −0.0159410 | − | 0.999873i | \(-0.505074\pi\) |
−0.873886 | + | 0.486131i | \(0.838408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.63069 | + | 4.55649i | 0.336825 | + | 0.583398i | 0.983834 | − | 0.179084i | \(-0.0573135\pi\) |
−0.647009 | + | 0.762483i | \(0.723980\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.81251 | − | 6.09685i | 0.606320 | − | 0.768131i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.68049 | − | 4.64274i | −0.332473 | − | 0.575861i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.963653 | + | 1.66910i | −0.117729 | + | 0.203913i | −0.918867 | − | 0.394567i | \(-0.870895\pi\) |
0.801138 | + | 0.598479i | \(0.204228\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0676490 | 0.00814398 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.9319i | 1.89077i | 0.325956 | + | 0.945385i | \(0.394314\pi\) | ||||
−0.325956 | + | 0.945385i | \(0.605686\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.12385 | + | 4.11296i | 0.833783 | + | 0.481385i | 0.855146 | − | 0.518387i | \(-0.173467\pi\) |
−0.0213629 | + | 0.999772i | \(0.506801\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.219454 | + | 0.126702i | −0.0253404 | + | 0.0146303i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.50145 | − | 1.38367i | −1.08279 | − | 0.157684i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.94273 | + | 5.74044i | −1.11864 | + | 0.645849i | −0.941054 | − | 0.338255i | \(-0.890163\pi\) |
−0.177590 | + | 0.984105i | \(0.556830\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.21310 | + | 7.29731i | −0.468122 | + | 0.810812i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.75814i | − | 0.632039i | −0.948753 | − | 0.316019i | \(-0.897654\pi\) | ||
0.948753 | − | 0.316019i | \(-0.102346\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 5.16100i | − | 0.559789i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.379658 | + | 0.657587i | −0.0407036 | + | 0.0705007i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.77496 | − | 2.75683i | 0.506145 | − | 0.292223i | −0.225103 | − | 0.974335i | \(-0.572272\pi\) |
0.731248 | + | 0.682112i | \(0.238938\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.24773 | − | 13.1773i | −0.550111 | − | 1.38136i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.19531 | − | 0.690110i | 0.123947 | − | 0.0715611i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.49220 | − | 3.17092i | −0.563488 | − | 0.325330i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.98474i | 0.810727i | 0.914156 | + | 0.405364i | \(0.132855\pi\) | ||||
−0.914156 | + | 0.405364i | \(0.867145\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.6542 | 1.07079 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.74975 | + | 8.22681i | −0.472618 | + | 0.818598i | −0.999509 | − | 0.0313347i | \(-0.990024\pi\) |
0.526891 | + | 0.849933i | \(0.323358\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.75103 | − | 6.49697i | −0.369600 | − | 0.640166i | 0.619903 | − | 0.784678i | \(-0.287172\pi\) |
−0.989503 | + | 0.144513i | \(0.953839\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.622868 | + | 0.248051i | −0.0607857 | + | 0.0242073i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.73750 | + | 6.47354i | 0.361318 | + | 0.625821i | 0.988178 | − | 0.153311i | \(-0.0489936\pi\) |
−0.626860 | + | 0.779132i | \(0.715660\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.8873 | + | 9.74989i | 1.61751 | + | 0.933870i | 0.987561 | + | 0.157234i | \(0.0502578\pi\) |
0.629949 | + | 0.776636i | \(0.283076\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.18967 | 0.207834 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.8176 | −1.95836 | −0.979179 | − | 0.202997i | \(-0.934932\pi\) | ||||
−0.979179 | + | 0.202997i | \(0.934932\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.231195 | + | 0.133481i | 0.0215591 | + | 0.0124471i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.86933 | + | 13.6301i | 0.727520 | + | 1.26010i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.96774 | − | 13.5122i | 0.180383 | − | 1.23866i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.08515 | − | 1.87954i | −0.0986502 | − | 0.170867i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.439397 | − | 0.761058i | 0.0396191 | − | 0.0686223i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.44123i | 0.749038i | 0.927219 | + | 0.374519i | \(0.122192\pi\) | ||||
−0.927219 | + | 0.374519i | \(0.877808\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.17180 | − | 0.676537i | −0.103171 | − | 0.0595657i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.74957 | − | 2.74216i | 0.414972 | − | 0.239584i | −0.277952 | − | 0.960595i | \(-0.589656\pi\) |
0.692924 | + | 0.721011i | \(0.256322\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.1703 | − | 10.3959i | −1.14201 | − | 0.901441i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.30263 | − | 0.752075i | 0.112113 | − | 0.0647283i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.21281 | − | 7.29680i | 0.359925 | − | 0.623408i | −0.628023 | − | 0.778195i | \(-0.716136\pi\) |
0.987948 | + | 0.154787i | \(0.0494691\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.5832i | 0.982472i | 0.871027 | + | 0.491236i | \(0.163455\pi\) | ||||
−0.871027 | + | 0.491236i | \(0.836545\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.14723i | 0.0966140i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.72773 | − | 16.8489i | 0.813473 | − | 1.40898i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.59502 | + | 1.49823i | −0.215504 | + | 0.124422i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.72533 | + | 0.411949i | −0.142303 | + | 0.0339769i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.0102 | − | 5.77937i | 0.820065 | − | 0.473465i | −0.0303740 | − | 0.999539i | \(-0.509670\pi\) |
0.850439 | + | 0.526074i | \(0.176336\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.9344 | + | 8.04501i | 1.13396 | + | 0.654694i | 0.944929 | − | 0.327276i | \(-0.106131\pi\) |
0.189035 | + | 0.981970i | \(0.439464\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.1516i | 1.22493i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.44673 | 0.437492 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.07894 | + | 1.86877i | −0.0861086 | + | 0.149144i | −0.905863 | − | 0.423571i | \(-0.860777\pi\) |
0.819754 | + | 0.572715i | \(0.194110\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.453107 | − | 0.784805i | −0.0359337 | − | 0.0622391i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.554408 | + | 0.437619i | 0.0436935 | + | 0.0344892i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.598474 | − | 1.03659i | −0.0468761 | − | 0.0811918i | 0.841635 | − | 0.540046i | \(-0.181593\pi\) |
−0.888511 | + | 0.458854i | \(0.848260\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.796419 | − | 0.459813i | −0.0620011 | − | 0.0357964i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.0622 | −1.01079 | −0.505393 | − | 0.862889i | \(-0.668653\pi\) | ||||
−0.505393 | + | 0.862889i | \(0.668653\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.7400 | 1.21077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.1239 | + | 9.30916i | 1.23303 | + | 0.711889i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.3607 | − | 21.4093i | −0.939764 | − | 1.62772i | −0.765910 | − | 0.642948i | \(-0.777711\pi\) |
−0.173854 | − | 0.984771i | \(-0.555622\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.61814 | − | 0.381272i | −0.197912 | − | 0.0288215i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.999963 | − | 1.73199i | −0.0751618 | − | 0.130184i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.48006 | − | 11.2238i | 0.484342 | − | 0.838905i | −0.515496 | − | 0.856892i | \(-0.672392\pi\) |
0.999838 | + | 0.0179868i | \(0.00572569\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.5665 | −0.785403 | −0.392702 | − | 0.919666i | \(-0.628459\pi\) | ||||
−0.392702 | + | 0.919666i | \(0.628459\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.33325i | 0.0985569i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.48336 | + | 4.32052i | 0.550187 | + | 0.317651i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.2204 | − | 9.36487i | 1.18616 | − | 0.684827i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.69721 | − | 1.47238i | 0.268933 | − | 0.107100i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.42981 | − | 1.98020i | 0.248173 | − | 0.143282i | −0.370755 | − | 0.928731i | \(-0.620901\pi\) |
0.618927 | + | 0.785448i | \(0.287568\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.14531 | − | 12.3760i | 0.514330 | − | 0.890846i | −0.485531 | − | 0.874219i | \(-0.661374\pi\) |
0.999862 | − | 0.0166270i | \(-0.00529279\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 1.35849i | − | 0.0972835i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.05223i | 0.288709i | 0.989526 | + | 0.144355i | \(0.0461106\pi\) | ||||
−0.989526 | + | 0.144355i | \(0.953889\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.37120 | + | 2.37499i | −0.0972020 | + | 0.168359i | −0.910525 | − | 0.413453i | \(-0.864323\pi\) |
0.813324 | + | 0.581812i | \(0.197656\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.422955 | + | 0.244193i | −0.0298330 | + | 0.0172241i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.36534 | + | 2.93317i | −0.516946 | + | 0.205868i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00334 | − | 1.73398i | 0.209762 | − | 0.121106i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.678740 | − | 0.391871i | −0.0471757 | − | 0.0272369i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 23.0151i | − | 1.59199i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.41112 | 0.165988 | 0.0829942 | − | 0.996550i | \(-0.473552\pi\) | ||||
0.0829942 | + | 0.996550i | \(0.473552\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.01860 | + | 3.49632i | −0.138312 | + | 0.239564i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.66980 | − | 4.62422i | −0.182079 | − | 0.315370i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.2603 | + | 2.07668i | 0.968050 | + | 0.140975i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.04224 | + | 1.80521i | 0.0704279 | + | 0.121985i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.9612 | + | 13.8340i | 1.61180 | + | 0.930575i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.8843 | −1.33155 | −0.665774 | − | 0.746153i | \(-0.731899\pi\) | ||||
−0.665774 | + | 0.746153i | \(0.731899\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.93579 | 0.195719 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.4464 | − | 12.3821i | −1.42345 | − | 0.821827i | −0.426855 | − | 0.904320i | \(-0.640379\pi\) |
−0.996592 | + | 0.0824926i | \(0.973712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.98187 | − | 10.3609i | −0.395293 | − | 0.684668i | 0.597845 | − | 0.801612i | \(-0.296024\pi\) |
−0.993139 | + | 0.116943i | \(0.962690\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.90982 | − | 1.50750i | −0.125657 | − | 0.0991865i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.54956 | + | 9.61212i | 0.363564 | + | 0.629711i | 0.988545 | − | 0.150929i | \(-0.0482265\pi\) |
−0.624981 | + | 0.780640i | \(0.714893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.26364 | + | 3.92073i | −0.147663 | + | 0.255760i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.90930 | −0.188979 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.8172i | 1.60529i | 0.596455 | + | 0.802646i | \(0.296575\pi\) | ||||
−0.596455 | + | 0.802646i | \(0.703425\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.84971 | + | 5.68673i | 0.634475 | + | 0.366315i | 0.782483 | − | 0.622672i | \(-0.213953\pi\) |
−0.148008 | + | 0.988986i | \(0.547286\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.75706 | + | 3.32384i | −0.369316 | + | 0.213225i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.70926 | − | 1.99644i | −0.428639 | − | 0.127548i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.4435 | − | 16.9992i | 1.87345 | − | 1.08164i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.729568 | − | 1.26365i | 0.0462345 | − | 0.0800805i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.98434i | 0.567087i | 0.958959 | + | 0.283543i | \(0.0915100\pi\) | ||||
−0.958959 | + | 0.283543i | \(0.908490\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.968827i | 0.0609096i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.653908 | − | 1.13260i | 0.0409493 | − | 0.0709263i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.10401 | + | 1.21475i | −0.131244 | + | 0.0757740i | −0.564185 | − | 0.825649i | \(-0.690809\pi\) |
0.432940 | + | 0.901423i | \(0.357476\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.9451 | + | 14.1649i | 1.11506 | + | 0.880164i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.61842 | − | 4.39850i | 0.471568 | − | 0.272260i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.99243 | − | 1.15033i | −0.122858 | − | 0.0709323i | 0.437311 | − | 0.899310i | \(-0.355931\pi\) |
−0.560170 | + | 0.828378i | \(0.689264\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.57617i | − | 0.219682i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.39718 | 0.0855060 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.609154 | + | 1.05509i | −0.0371408 | + | 0.0643297i | −0.883998 | − | 0.467490i | \(-0.845158\pi\) |
0.846857 | + | 0.531820i | \(0.178492\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.1092 | + | 20.9738i | 0.735582 | + | 1.27406i | 0.954468 | + | 0.298314i | \(0.0964244\pi\) |
−0.218886 | + | 0.975750i | \(0.570242\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.517954 | − | 3.55671i | 0.0313480 | − | 0.215262i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.81455 | − | 3.14289i | −0.109421 | − | 0.189523i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.22720 | + | 4.17263i | 0.434240 | + | 0.250709i | 0.701151 | − | 0.713012i | \(-0.252670\pi\) |
−0.266911 | + | 0.963721i | \(0.586003\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.9904 | −0.957322 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.8252 | 1.18267 | 0.591337 | − | 0.806425i | \(-0.298600\pi\) | ||||
0.591337 | + | 0.806425i | \(0.298600\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.33705 | + | 4.81340i | 0.495586 | + | 0.286127i | 0.726889 | − | 0.686755i | \(-0.240965\pi\) |
−0.231303 | + | 0.972882i | \(0.574299\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.803524 | − | 1.39174i | −0.0475966 | − | 0.0824398i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.52427 | − | 3.39470i | 0.503172 | − | 0.200383i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.81796 | + | 8.34495i | 0.283409 | + | 0.490879i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.01168 | + | 1.75228i | −0.0593058 | + | 0.102721i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.487956 | −0.0285067 | −0.0142534 | − | 0.999898i | \(-0.504537\pi\) | ||||
−0.0142534 | + | 0.999898i | \(0.504537\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 7.89225i | − | 0.459505i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.72737 | + | 2.72935i | 0.274310 | + | 0.158373i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.23943 | + | 0.715586i | −0.0716782 | + | 0.0413834i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.22680 | − | 13.1248i | −0.301268 | − | 0.756499i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.08470 | + | 1.20360i | −0.119763 | + | 0.0691453i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.63069 | + | 4.55649i | −0.150633 | + | 0.260904i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.8335i | 0.675376i | 0.941258 | + | 0.337688i | \(0.109645\pi\) | ||||
−0.941258 | + | 0.337688i | \(0.890355\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1.90105i | − | 0.108147i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.29486 | − | 3.97481i | 0.130129 | − | 0.225391i | −0.793597 | − | 0.608444i | \(-0.791794\pi\) |
0.923726 | + | 0.383053i | \(0.125127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.7907 | − | 10.2714i | 1.00559 | − | 0.580577i | 0.0956913 | − | 0.995411i | \(-0.469494\pi\) |
0.909897 | + | 0.414834i | \(0.136160\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.68629 | + | 1.11933i | 0.433073 | + | 0.0630673i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.76332 | + | 3.90481i | −0.379866 | + | 0.219316i | −0.677760 | − | 0.735283i | \(-0.737049\pi\) |
0.297894 | + | 0.954599i | \(0.403716\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.41755 | − | 5.43723i | −0.527282 | − | 0.304426i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.89419i | 0.105724i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.7303 | 1.82116 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.68049 | − | 4.64274i | 0.148687 | − | 0.257533i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.47066 | + | 4.27931i | 0.136628 | + | 0.236646i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.42137 | + | 9.40195i | −0.409153 | + | 0.518346i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.35126 | − | 11.0007i | −0.349097 | − | 0.604654i | 0.636992 | − | 0.770870i | \(-0.280178\pi\) |
−0.986089 | + | 0.166216i | \(0.946845\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.9695 | − | 12.6841i | −1.20392 | − | 0.695085i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.92731 | −0.105300 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.8789 | 0.756033 | 0.378016 | − | 0.925799i | \(-0.376606\pi\) | ||||
0.378016 | + | 0.925799i | \(0.376606\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.56852 | − | 2.63763i | −0.248128 | − | 0.143257i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.88333 | + | 17.1184i | 0.535213 | + | 0.927015i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.8046 | − | 7.78501i | −0.907362 | − | 0.420351i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0338245 | + | 0.0585857i | 0.00182105 | + | 0.00315415i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.43516 | − | 11.1460i | 0.345457 | − | 0.598350i | −0.639979 | − | 0.768392i | \(-0.721057\pi\) |
0.985437 | + | 0.170042i | \(0.0543905\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.0526 | −1.12692 | −0.563460 | − | 0.826143i | \(-0.690530\pi\) | ||||
−0.563460 | + | 0.826143i | \(0.690530\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.06371i | 0.430409i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.8483 | − | 14.9235i | −1.37577 | − | 0.794298i | −0.384119 | − | 0.923284i | \(-0.625495\pi\) |
−0.991647 | + | 0.128985i | \(0.958828\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.7974 | + | 7.96595i | −0.732292 | + | 0.422789i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.14385 | − | 2.71599i | 0.113465 | − | 0.143745i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.5346 | − | 9.54628i | 0.872665 | − | 0.503833i | 0.00443178 | − | 0.999990i | \(-0.498589\pi\) |
0.868233 | + | 0.496157i | \(0.165256\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.6095 | − | 18.3762i | 0.558396 | − | 0.967169i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 0.549963i | − | 0.0288656i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.22591i | 0.430564i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.90832 | − | 8.50146i | 0.256212 | − | 0.443773i | −0.709012 | − | 0.705197i | \(-0.750859\pi\) |
0.965224 | + | 0.261424i | \(0.0841921\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.81717 | + | 5.09059i | −0.459003 | + | 0.265006i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.36349 | − | 9.36290i | 0.0707890 | − | 0.486097i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.2929 | − | 11.7161i | 1.05072 | − | 0.606636i | 0.127873 | − | 0.991791i | \(-0.459185\pi\) |
0.922852 | + | 0.385154i | \(0.125852\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.219454 | − | 0.126702i | −0.0113326 | − | 0.00654286i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 16.0640i | − | 0.827337i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.7259 | −0.550954 | −0.275477 | − | 0.961308i | \(-0.588836\pi\) | ||||
−0.275477 | + | 0.961308i | \(0.588836\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.06952 | + | 1.85246i | −0.0547932 | + | 0.0949046i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.700673 | + | 1.21360i | 0.0358027 | + | 0.0620122i | 0.883372 | − | 0.468673i | \(-0.155268\pi\) |
−0.847569 | + | 0.530686i | \(0.821935\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.55243 | − | 8.92033i | −0.181049 | − | 0.454622i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.83796 | + | 13.5757i | 0.398426 | + | 0.690094i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.49049 | − | 1.43789i | −0.126273 | − | 0.0729037i | 0.435533 | − | 0.900173i | \(-0.356560\pi\) |
−0.561806 | + | 0.827269i | \(0.689893\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.37779 | −0.0696777 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.38975 | 0.0701036 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.94273 | − | 5.74044i | −0.500273 | − | 0.288833i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.26251 | + | 2.18672i | 0.0633633 | + | 0.109749i | 0.895967 | − | 0.444121i | \(-0.146484\pi\) |
−0.832603 | + | 0.553870i | \(0.813151\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.57310 | − | 3.95014i | −0.0787536 | − | 0.197754i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.3792 | − | 33.5657i | −0.967749 | − | 1.67619i | −0.702041 | − | 0.712136i | \(-0.747728\pi\) |
−0.265707 | − | 0.964054i | \(-0.585606\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.5999 | + | 25.2877i | −0.727271 | + | 1.25967i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.42620 | −0.418701 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.3591i | 1.55441i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.68850 | + | 1.55221i | 0.132938 | + | 0.0767518i | 0.564994 | − | 0.825095i | \(-0.308878\pi\) |
−0.432056 | + | 0.901847i | \(0.642212\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.84904 | − | 1.06754i | 0.0912062 | − | 0.0526579i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.00909 | − | 20.6630i | 0.148068 | − | 1.01676i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.98670 | − | 2.87907i | 0.244787 | − | 0.141328i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.46761 | + | 2.54197i | −0.0718691 | + | 0.124481i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 11.1649i | − | 0.545441i | −0.962093 | − | 0.272720i | \(-0.912077\pi\) | ||
0.962093 | − | 0.272720i | \(-0.0879234\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.1106i | 1.71119i | 0.517648 | + | 0.855594i | \(0.326808\pi\) | ||||
−0.517648 | + | 0.855594i | \(0.673192\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.64555 | − | 11.5104i | 0.323118 | − | 0.559656i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.46956 | − | 2.58050i | 0.216805 | − | 0.125173i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.62476 | + | 10.9265i | −0.417381 | + | 0.528770i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.26958 | − | 2.46504i | 0.206137 | − | 0.119013i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.4675 | − | 7.19809i | −0.600536 | − | 0.346720i | 0.168716 | − | 0.985665i | \(-0.446038\pi\) |
−0.769253 | + | 0.638945i | \(0.779371\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.8668i | 1.77171i | 0.463967 | + | 0.885853i | \(0.346426\pi\) | ||||
−0.463967 | + | 0.885853i | \(0.653574\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.759316 | −0.0364064 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.846514 | + | 1.46621i | −0.0404943 | + | 0.0701381i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.4785 | + | 32.0057i | 0.881930 | + | 1.52755i | 0.849193 | + | 0.528083i | \(0.177089\pi\) |
0.0327369 | + | 0.999464i | \(0.489578\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.6970 | + | 5.86113i | 0.937951 | + | 0.279101i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.7895 | − | 18.6880i | −0.512626 | − | 0.887895i | −0.999893 | − | 0.0146414i | \(-0.995339\pi\) |
0.487267 | − | 0.873253i | \(-0.337994\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.77496 | + | 2.75683i | 0.226355 | + | 0.130686i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.92903 | 0.138538 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.7876 | −1.50015 | −0.750075 | − | 0.661353i | \(-0.769983\pi\) | ||||
−0.750075 | + | 0.661353i | \(0.769983\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.8994 | + | 6.29277i | 0.513233 | + | 0.296315i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.03864 | + | 3.53102i | 0.0957835 | + | 0.165902i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.78802 | − | 11.1333i | 0.411989 | − | 0.521938i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5642 | + | 20.0298i | 0.540950 | + | 0.936954i | 0.998850 | + | 0.0479496i | \(0.0152687\pi\) |
−0.457899 | + | 0.889004i | \(0.651398\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.88146 | + | 6.72289i | −0.181171 | + | 0.313797i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.98126 | 0.464874 | 0.232437 | − | 0.972611i | \(-0.425330\pi\) | ||||
0.232437 | + | 0.972611i | \(0.425330\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.3501i | − | 1.13165i | −0.824527 | − | 0.565823i | \(-0.808558\pi\) | ||
0.824527 | − | 0.565823i | \(-0.191442\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.19531 | + | 0.690110i | 0.0554310 | + | 0.0320031i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.6077 | − | 13.0525i | 1.04616 | − | 0.604000i | 0.124587 | − | 0.992209i | \(-0.460239\pi\) |
0.921571 | + | 0.388209i | \(0.126906\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.04595 | − | 0.734828i | −0.233000 | − | 0.0339312i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.473554 | + | 0.273407i | −0.0218202 | + | 0.0125979i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.68894 | − | 16.7817i | 0.445498 | − | 0.771625i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.34185i | − | 0.290984i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.4989i | 0.480710i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.24704 | − | 5.62403i | 0.148361 | − | 0.256969i | −0.782261 | − | 0.622951i | \(-0.785934\pi\) |
0.930622 | + | 0.365982i | \(0.119267\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40.1181 | + | 23.1622i | −1.82923 | + | 1.05610i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.0662200 | + | 0.166282i | 0.00301311 | + | 0.00756608i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.91499 | + | 3.99237i | −0.313993 | + | 0.181284i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.244780 | − | 0.141324i | −0.0110921 | − | 0.00640400i | 0.494444 | − | 0.869210i | \(-0.335372\pi\) |
−0.505536 | + | 0.862806i | \(0.668705\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 0.303311i | − | 0.0137162i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.1902 | −0.820912 | −0.410456 | − | 0.911880i | \(-0.634630\pi\) | ||||
−0.410456 | + | 0.911880i | \(0.634630\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.73239 | − | 13.3929i | 0.348249 | − | 0.603185i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.32712 | + | 9.22684i | 0.239436 | + | 0.414716i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −39.1607 | + | 15.5954i | −1.75660 | + | 0.699548i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.608016 | + | 1.05312i | 0.0272185 | + | 0.0471439i | 0.879314 | − | 0.476243i | \(-0.158002\pi\) |
−0.852095 | + | 0.523387i | \(0.824668\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.86656 | − | 1.65501i | −0.128069 | − | 0.0739404i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.9355 | −1.69146 | −0.845729 | − | 0.533612i | \(-0.820834\pi\) | ||||
−0.845729 | + | 0.533612i | \(0.820834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.49950 | −0.422722 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.45421 | + | 1.99429i | 0.153407 | + | 0.0885695i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.30256 | + | 9.18430i | 0.235032 | + | 0.407087i | 0.959282 | − | 0.282450i | \(-0.0911473\pi\) |
−0.724250 | + | 0.689537i | \(0.757814\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.13631 | + | 21.5365i | −0.138742 | + | 0.952721i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.76955 | + | 8.26110i | 0.210581 | + | 0.364736i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.75103 | − | 6.49697i | 0.165290 | − | 0.286291i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.4299 | −0.722585 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 6.26448i | − | 0.274980i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.18563 | − | 0.684522i | −0.0519432 | − | 0.0299894i | 0.473803 | − | 0.880631i | \(-0.342881\pi\) |
−0.525747 | + | 0.850641i | \(0.676214\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.24052 | − | 0.716212i | 0.0542439 | − | 0.0313178i | −0.472633 | − | 0.881259i | \(-0.656696\pi\) |
0.526877 | + | 0.849942i | \(0.323363\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.526253 | − | 0.415394i | −0.0229675 | − | 0.0181293i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.3445 | + | 14.0553i | −1.06046 | + | 0.612257i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4644 | + | 19.8569i | −0.498451 | + | 0.863342i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 23.1700i | 1.00549i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.5916i | 0.805293i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.73750 | + | 6.47354i | −0.161586 | + | 0.279876i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.84415 | − | 1.64207i | 0.122734 | − | 0.0708606i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.89967 | − | 24.7091i | −0.254117 | − | 1.06430i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.20272 | − | 0.694390i | 0.0517089 | − | 0.0298542i | −0.473923 | − | 0.880566i | \(-0.657162\pi\) |
0.525632 | + | 0.850712i | \(0.323829\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.31887 | − | 1.33880i | −0.0995120 | − | 0.0574533i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.4998i | 0.835279i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.0700 | −1.84154 | −0.920770 | − | 0.390106i | \(-0.872438\pi\) | ||||
−0.920770 | + | 0.390106i | \(0.872438\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.72314 | − | 13.3769i | 0.329616 | − | 0.570911i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.50157 | − | 16.4572i | −0.404781 | − | 0.701100i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.8427 | − | 18.8201i | −1.01390 | − | 0.800313i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.09484 | + | 1.89631i | 0.0464732 | + | 0.0804939i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.0779 | + | 11.5920i | 0.850727 | + | 0.491167i | 0.860896 | − | 0.508781i | \(-0.169904\pi\) |
−0.0101693 | + | 0.999948i | \(0.503237\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.6254 | 1.21073 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.74619 | 0.200384 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.3256 | − | 11.7350i | −0.856620 | − | 0.494570i | 0.00625865 | − | 0.999980i | \(-0.498008\pi\) |
−0.862879 | + | 0.505410i | \(0.831341\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.4088 | − | 18.0286i | −0.437902 | − | 0.758469i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.0609 | − | 3.21268i | −0.926472 | − | 0.134920i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.75158 | + | 3.03382i | 0.0734300 | + | 0.127185i | 0.900402 | − | 0.435058i | \(-0.143272\pi\) |
−0.826972 | + | 0.562242i | \(0.809939\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.67971 | − | 11.5696i | 0.279537 | − | 0.484172i | −0.691733 | − | 0.722154i | \(-0.743152\pi\) |
0.971270 | + | 0.237981i | \(0.0764857\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.00358 | 0.0419252 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.266961i | 0.0111331i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.5233 | − | 17.0453i | −1.22907 | − | 0.709604i | −0.262234 | − | 0.965004i | \(-0.584459\pi\) |
−0.966835 | + | 0.255401i | \(0.917793\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.13613 | − | 1.81065i | 0.130333 | − | 0.0752479i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.1536 | − | 5.63651i | 0.587189 | − | 0.233842i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.2395 | − | 6.48912i | 0.465492 | − | 0.268752i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.86933 | + | 13.6301i | −0.325357 | + | 0.563535i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.77581i | − | 0.362216i | −0.983463 | − | 0.181108i | \(-0.942032\pi\) | ||
0.983463 | − | 0.181108i | \(-0.0579684\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.5423i | 1.42329i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.513425 | + | 0.889277i | −0.0211195 | + | 0.0365800i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.54851 | + | 3.20343i | −0.227850 | + | 0.131549i | −0.609580 | − | 0.792725i | \(-0.708662\pi\) |
0.381730 | + | 0.924274i | \(0.375328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.6858 | − | 5.05198i | 0.520066 | − | 0.207111i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.601832 | + | 0.347468i | −0.0246313 | + | 0.0142209i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.6488 | + | 7.88017i | 0.557677 | + | 0.321975i | 0.752213 | − | 0.658921i | \(-0.228987\pi\) |
−0.194536 | + | 0.980895i | \(0.562320\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.5644i | 0.961213i | 0.876936 | + | 0.480606i | \(0.159583\pi\) | ||||
−0.876936 | + | 0.480606i | \(0.840417\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.65816 | 0.230418 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.08515 | − | 1.87954i | 0.0441177 | − | 0.0764141i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.5467 | − | 40.7841i | −0.955733 | − | 1.65538i | −0.732683 | − | 0.680570i | \(-0.761732\pi\) |
−0.223050 | − | 0.974807i | \(-0.571601\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.98799 | − | 0.289506i | −0.0805575 | − | 0.0117314i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.1353 | − | 21.0189i | −0.490941 | − | 0.850335i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.4900 | + | 16.4487i | 1.15070 | + | 0.664357i | 0.949058 | − | 0.315102i | \(-0.102039\pi\) |
0.201642 | + | 0.979459i | \(0.435372\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.878794 | 0.0354364 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.76738 | 0.272444 | 0.136222 | − | 0.990678i | \(-0.456504\pi\) | ||||
0.136222 | + | 0.990678i | \(0.456504\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.7468 | − | 7.93673i | −0.552531 | − | 0.319004i | 0.197611 | − | 0.980281i | \(-0.436682\pi\) |
−0.750142 | + | 0.661276i | \(0.770015\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.200775 | − | 0.347752i | −0.00805682 | − | 0.0139548i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.4504 | + | 9.03830i | 0.458750 | + | 0.362112i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.91606 | − | 5.05077i | 0.116456 | − | 0.201708i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −44.5964 | −1.77817 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.6006i | 0.740479i | 0.928936 | + | 0.370240i | \(0.120724\pi\) | ||||
−0.928936 | + | 0.370240i | \(0.879276\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.529130 | + | 0.305493i | 0.0210310 | + | 0.0121423i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.31032 | + | 4.22062i | −0.290101 | + | 0.167490i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.2530 | − | 25.7979i | 1.07980 | − | 1.02215i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 40.5063 | − | 23.3863i | 1.60241 | − | 0.925149i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.77857 | + | 6.54468i | −0.149245 | + | 0.258499i | −0.930948 | − | 0.365151i | \(-0.881018\pi\) |
0.781704 | + | 0.623650i | \(0.214351\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 21.9243i | − | 0.864609i | −0.901728 | − | 0.432305i | \(-0.857701\pi\) | ||
0.901728 | − | 0.432305i | \(-0.142299\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.35307i | − | 0.0532772i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.3244 | + | 19.6144i | −0.445207 | + | 0.771120i | −0.998067 | − | 0.0621538i | \(-0.980203\pi\) |
0.552860 | + | 0.833274i | \(0.313536\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.8044 | − | 14.3208i | 0.973659 | − | 0.562143i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.86635 | + | 2.26254i | 0.112341 | + | 0.0886759i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.05556 | − | 1.76413i | 0.119573 | − | 0.0690357i | −0.439020 | − | 0.898477i | \(-0.644674\pi\) |
0.558594 | + | 0.829441i | \(0.311341\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.74957 | + | 2.74216i | 0.185581 | + | 0.107145i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 24.1495i | − | 0.942162i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.5143 | −1.46135 | −0.730676 | − | 0.682725i | \(-0.760795\pi\) | ||||
−0.730676 | + | 0.682725i | \(0.760795\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.6573 | − | 25.3871i | 0.570102 | − | 0.987445i | −0.426453 | − | 0.904510i | \(-0.640237\pi\) |
0.996555 | − | 0.0829357i | \(-0.0264296\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.50558 | + | 6.07185i | 0.136146 | + | 0.235811i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.41797 | − | 16.6038i | 0.0937648 | − | 0.643868i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.399971 | + | 0.692769i | 0.0154869 | + | 0.0268241i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.36368 | − | 2.51937i | −0.168710 | − | 0.0974046i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.0940 | −0.737116 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.3062 | −0.628558 | −0.314279 | − | 0.949331i | \(-0.601763\pi\) | ||||
−0.314279 | + | 0.949331i | \(0.601763\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.30263 | + | 0.752075i | 0.0501383 | + | 0.0289474i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.9655 | − | 31.1171i | −0.690469 | − | 1.19593i | −0.971684 | − | 0.236282i | \(-0.924071\pi\) |
0.281216 | − | 0.959645i | \(-0.409262\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.6265 | + | 7.81607i | −0.753198 | + | 0.299953i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.13766 | − | 5.43459i | −0.120236 | − | 0.208254i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.9429 | + | 24.1497i | −0.533509 | + | 0.924064i | 0.465725 | + | 0.884929i | \(0.345794\pi\) |
−0.999234 | + | 0.0391349i | \(0.987540\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.42562 | 0.321926 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3.03166i | − | 0.115665i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.6032 | + | 9.58587i | 0.632532 | + | 0.365193i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.9094 | + | 12.0721i | −0.795432 | + | 0.459243i | −0.841871 | − | 0.539678i | \(-0.818546\pi\) |
0.0464394 | + | 0.998921i | \(0.485213\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.4292 | + | 26.1882i | 0.396172 | + | 0.994807i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.0313 | + | 5.79158i | −0.380510 | + | 0.219687i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.94907 | + | 15.5002i | −0.338970 | + | 0.587113i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.81256i | 0.106381i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 14.4688i | − | 0.546481i | −0.961946 | − | 0.273240i | \(-0.911905\pi\) | ||
0.961946 | − | 0.273240i | \(-0.0880954\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.4001 | + | 47.4583i | −1.03341 | + | 1.78992i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.993528 | + | 0.573614i | −0.0374184 | + | 0.0216035i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.8710 | − | 3.62189i | −0.935369 | − | 0.136215i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.2208 | + | 9.36506i | −0.609183 | + | 0.351712i | −0.772646 | − | 0.634837i | \(-0.781067\pi\) |
0.163462 | + | 0.986550i | \(0.447734\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.1897 | + | 16.8527i | 1.09470 | + | 0.632025i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.45407i | − | 0.0544552i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.4555 | 0.727593 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.14439 | + | 5.44624i | −0.117429 | + | 0.203394i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.8589 | − | 25.7364i | −0.554145 | − | 0.959807i | −0.997970 | − | 0.0636936i | \(-0.979712\pi\) |
0.443824 | − | 0.896114i | \(-0.353621\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.2978 | − | 15.5798i | 0.457994 | − | 0.580221i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.44104 | + | 2.49595i | 0.0535928 | + | 0.0928255i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.59502 | − | 1.49823i | −0.0963765 | − | 0.0556430i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.23594 | 0.268366 | 0.134183 | − | 0.990957i | \(-0.457159\pi\) | ||||
0.134183 | + | 0.990957i | \(0.457159\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.5941 | 0.873854 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.8656 | + | 13.7788i | 0.882702 | + | 0.509628i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.4471 | + | 19.8270i | 0.422810 | + | 0.732328i | 0.996213 | − | 0.0869452i | \(-0.0277105\pi\) |
−0.573403 | + | 0.819273i | \(0.694377\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.21942 | − | 1.28820i | −0.0449791 | − | 0.0475161i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.49719 | − | 6.05730i | −0.128821 | − | 0.223124i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.9700 | − | 34.5891i | 0.734610 | − | 1.27238i | −0.220284 | − | 0.975436i | \(-0.570699\pi\) |
0.954894 | − | 0.296946i | \(-0.0959682\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.61534 | 0.316492 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.99702i | 0.293382i | 0.989182 | + | 0.146691i | \(0.0468623\pi\) | ||||
−0.989182 | + | 0.146691i | \(0.953138\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0102 | + | 5.77937i | 0.366744 | + | 0.211740i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.6399 | + | 8.45234i | −0.535645 | + | 0.309255i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.2535 | + | 15.5236i | −0.447732 | + | 0.567220i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.9662 | − | 6.90868i | 0.436652 | − | 0.252101i | −0.265524 | − | 0.964104i | \(-0.585545\pi\) |
0.702177 | + | 0.712003i | \(0.252212\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.13833 | + | 1.97165i | −0.0414832 | + | 0.0718509i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0900i | 0.585576i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.8579i | 0.394636i | 0.980340 | + | 0.197318i | \(0.0632232\pi\) | ||||
−0.980340 | + | 0.197318i | \(0.936777\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.122752 | + | 0.212613i | −0.00445562 | + | 0.00771736i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.6101 | + | 22.8689i | −1.43586 | + | 0.828996i | −0.997559 | − | 0.0698299i | \(-0.977754\pi\) |
−0.438305 | + | 0.898826i | \(0.644421\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.43472 | + | 51.0531i | −0.269155 | + | 1.84825i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.1217 | + | 7.57580i | −0.474415 | + | 0.273904i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.6416 | + | 21.1551i | 1.32305 | + | 0.763865i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5.29591i | − | 0.190976i | −0.995431 | − | 0.0954878i | \(-0.969559\pi\) | ||
0.995431 | − | 0.0954878i | \(-0.0304411\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.615644 | −0.0221719 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.85880 | + | 15.3439i | −0.318629 | + | 0.551882i | −0.980202 | − | 0.197999i | \(-0.936556\pi\) |
0.661573 | + | 0.749881i | \(0.269889\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.72336 | + | 4.71700i | 0.0978261 | + | 0.169440i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.14342 | + | 5.38223i | 0.0768947 | + | 0.193086i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.9966 | + | 19.0467i | 0.393995 | + | 0.682420i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −50.0722 | − | 28.9092i | −1.79172 | − | 1.03445i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.50714 | 0.161072 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.15787 | −0.0770179 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.1625 | + | 15.6823i | 0.968240 | + | 0.559013i | 0.898699 | − | 0.438566i | \(-0.144513\pi\) |
0.0695406 | + | 0.997579i | \(0.477847\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.291498 | − | 0.504889i | −0.0103776 | − | 0.0179745i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.3779 | − | 51.1699i | −0.724554 | − | 1.81939i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.1030 | − | 24.4272i | −0.500814 | − | 0.867435i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.453107 | − | 0.784805i | 0.0160701 | − | 0.0278342i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.8746 | −0.456040 | −0.228020 | − | 0.973656i | \(-0.573225\pi\) | ||||
−0.228020 | + | 0.973656i | \(0.573225\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 23.3652i | − | 0.826603i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.0183 | − | 8.09345i | −0.495311 | − | 0.285968i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.8531 | + | 14.9263i | −0.912336 | + | 0.526737i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.101785 | + | 0.698941i | −0.00358745 | + | 0.0246344i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.267363 | + | 0.154362i | −0.00941162 | + | 0.00543380i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.22687 | + | 5.58910i | −0.113451 | + | 0.196502i | −0.917159 | − | 0.398521i | \(-0.869524\pi\) |
0.803709 | + | 0.595023i | \(0.202857\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.3882i | 0.856385i | 0.903688 | + | 0.428192i | \(0.140849\pi\) | ||||
−0.903688 | + | 0.428192i | \(0.859151\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.13703i | 0.215235i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.598474 | − | 1.03659i | 0.0209636 | − | 0.0363101i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.3261 | − | 16.9314i | 1.02599 | − | 0.592356i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.7997 | + | 32.6850i | −0.901516 | + | 1.14211i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.5027 | + | 8.95047i | −0.541047 | + | 0.312373i | −0.745503 | − | 0.666502i | \(-0.767791\pi\) |
0.204456 | + | 0.978876i | \(0.434457\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.0780 | + | 13.3241i | 0.804449 | + | 0.464449i | 0.845024 | − | 0.534728i | \(-0.179586\pi\) |
−0.0405758 | + | 0.999176i | \(0.512919\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 0.919625i | − | 0.0320172i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.2259 | 1.32924 | 0.664622 | − | 0.747179i | \(-0.268592\pi\) | ||||
0.664622 | + | 0.747179i | \(0.268592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.10978 | + | 5.38630i | −0.108007 | + | 0.187074i | −0.914963 | − | 0.403538i | \(-0.867780\pi\) |
0.806956 | + | 0.590612i | \(0.201114\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.05736 | + | 1.83140i | 0.0366794 | + | 0.0635305i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.1393 | − | 8.39004i | 1.21750 | − | 0.290698i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.53112 | − | 11.3122i | −0.226019 | − | 0.391476i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.09508 | − | 4.09635i | −0.245242 | − | 0.141590i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.919692 | 0.0317513 | 0.0158757 | − | 0.999874i | \(-0.494946\pi\) | ||||
0.0158757 | + | 0.999874i | \(0.494946\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0212 | 0.690386 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.35073 | + | 2.51189i | 0.149847 | + | 0.0865142i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.87001 | + | 13.6312i | 0.270736 | + | 0.468929i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.55769 | − | 4.50715i | 0.122244 | − | 0.154867i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.21973 | + | 2.11264i | 0.0418611 | + | 0.0725056i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.15341 | − | 1.99777i | 0.0395384 | − | 0.0684826i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.0382 | 1.09697 | 0.548484 | − | 0.836161i | \(-0.315205\pi\) | ||||
0.548484 | + | 0.836161i | \(0.315205\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.6183i | 0.636733i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.8577 | − | 8.57808i | −0.507529 | − | 0.293022i | 0.224289 | − | 0.974523i | \(-0.427994\pi\) |
−0.731817 | + | 0.681501i | \(0.761327\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.5226 | − | 26.2825i | 1.55321 | − | 0.896747i | 0.555333 | − | 0.831628i | \(-0.312591\pi\) |
0.997878 | − | 0.0651185i | \(-0.0207425\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.30080 | + | 0.335059i | 0.0784111 | + | 0.0114188i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.80096 | + | 5.08124i | −0.299588 | + | 0.172967i | −0.642258 | − | 0.766489i | \(-0.722002\pi\) |
0.342670 | + | 0.939456i | \(0.388669\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.3607 | − | 21.4093i | 0.420275 | − | 0.727938i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.44178i | 0.0829271i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 41.6651i | − | 1.41339i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.16612 | − | 8.94798i | 0.175047 | − | 0.303191i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.3009 | − | 11.7207i | 0.687082 | − | 0.396687i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.978876 | − | 2.45801i | −0.0330921 | − | 0.0830958i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.0621 | − | 18.5111i | 1.08266 | − | 0.625074i | 0.151047 | − | 0.988527i | \(-0.451736\pi\) |
0.931613 | + | 0.363453i | \(0.118402\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.107084 | − | 0.0618250i | −0.00361185 | − | 0.00208531i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 46.4428i | − | 1.56470i | −0.622841 | − | 0.782348i | \(-0.714022\pi\) | ||
0.622841 | − | 0.782348i | \(-0.285978\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.4744 | 0.890935 | 0.445468 | − | 0.895298i | \(-0.353037\pi\) | ||||
0.445468 | + | 0.895298i | \(0.353037\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.999963 | − | 1.73199i | 0.0336134 | − | 0.0582201i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.77822 | + | 10.0082i | 0.194014 | + | 0.336041i | 0.946577 | − | 0.322479i | \(-0.104516\pi\) |
−0.752563 | + | 0.658520i | \(0.771183\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.7486 | + | 8.26293i | −0.695886 | + | 0.277130i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.2897 | − | 26.4826i | −0.512225 | − | 0.887200i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.8647 | − | 14.3556i | −0.832065 | − | 0.480393i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.9601 | 0.433209 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.362664 | −0.0121090 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.1343 | + | 8.16047i | 0.471407 | + | 0.272167i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.22831 | + | 15.9839i | 0.307439 | + | 0.532501i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.515889 | − | 3.54253i | 0.0171677 | − | 0.117888i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.28326 | − | 9.15087i | −0.175621 | − | 0.304185i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.9712 | + | 34.5911i | −0.663131 | + | 1.14858i | 0.316657 | + | 0.948540i | \(0.397440\pi\) |
−0.979788 | + | 0.200037i | \(0.935894\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27.8885 | 0.925003 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 46.6862i | − | 1.54678i | −0.633929 | − | 0.773391i | \(-0.718559\pi\) | ||
0.633929 | − | 0.773391i | \(-0.281441\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0972 | + | 10.4484i | 0.598930 | + | 0.345792i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.15463 | + | 0.666626i | −0.0381709 | + | 0.0220380i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.3895 | + | 8.99023i | 0.376114 | + | 0.296884i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.20385 | − | 4.15914i | 0.237633 | − | 0.137198i | −0.376455 | − | 0.926435i | \(-0.622857\pi\) |
0.614088 | + | 0.789237i | \(0.289524\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.49933 | + | 2.59692i | −0.0494046 | + | 0.0855714i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 85.4105i | − | 2.81132i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.64104i | 0.284116i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.0122 | + | 19.0737i | −0.361689 | + | 0.626463i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.5169 | − | 13.5775i | 0.771565 | − | 0.445463i | −0.0618674 | − | 0.998084i | \(-0.519706\pi\) |
0.833433 | + | 0.552621i | \(0.186372\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.6611 | − | 42.5491i | 0.414952 | − | 1.39449i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.00723 | − | 0.581525i | 0.0329753 | − | 0.0190383i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.2204 | + | 9.36487i | 0.530465 | + | 0.306264i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 36.9312i | − | 1.20649i | −0.797556 | − | 0.603245i | \(-0.793874\pi\) | ||
0.797556 | − | 0.603245i | \(-0.206126\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.20565 | 0.169880 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.58723 | + | 13.1415i | −0.247336 | + | 0.428399i | −0.962786 | − | 0.270265i | \(-0.912889\pi\) |
0.715449 | + | 0.698664i | \(0.246222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.462905 | − | 0.801776i | −0.0150743 | − | 0.0261094i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.12372 | + | 2.46569i | 0.101615 | + | 0.0802090i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.7591 | + | 29.0275i | 0.544596 | + | 0.943268i | 0.998632 | + | 0.0522848i | \(0.0166503\pi\) |
−0.454036 | + | 0.890983i | \(0.650016\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.1907 | − | 22.0494i | −1.23972 | − | 0.715755i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.97899 | −0.0641730 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.60332 | −0.0843298 | −0.0421649 | − | 0.999111i | \(-0.513425\pi\) | ||||
−0.0421649 | + | 0.999111i | \(0.513425\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.42981 | + | 1.98020i | 0.110986 | + | 0.0640779i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.37781 | − | 2.38644i | −0.0445384 | − | 0.0771428i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.0594 | + | 3.21245i | 0.712335 | + | 0.103736i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.666587 | + | 1.15456i | 0.0215028 | + | 0.0372439i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.9725 | − | 19.0049i | 0.353584 | − | 0.612426i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.2906 | 0.460031 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 43.0328i | − | 1.38384i | −0.721973 | − | 0.691921i | \(-0.756764\pi\) | ||
0.721973 | − | 0.691921i | \(-0.243236\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.18279 | + | 4.14699i | 0.230744 | + | 0.133220i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.5453 | + | 29.1823i | −1.62208 | + | 0.936506i | −0.635712 | + | 0.771927i | \(0.719293\pi\) |
−0.986364 | + | 0.164579i | \(0.947373\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.4715 | + | 11.3385i | −0.912755 | + | 0.363495i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.17649 | − | 0.679245i | 0.0376777 | − | 0.0217532i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.680919 | − | 1.17939i | 0.0217845 | − | 0.0377319i | −0.854928 | − | 0.518747i | \(-0.826399\pi\) |
0.876712 | + | 0.481015i | \(0.159732\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0095i | 0.639508i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 57.2472i | − | 1.82776i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.32160 | − | 9.21728i | 0.169733 | − | 0.293986i | −0.768593 | − | 0.639738i | \(-0.779043\pi\) |
0.938326 | + | 0.345752i | \(0.112376\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.50933 | + | 2.02611i | −0.111817 | + | 0.0645573i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.81989 | + | 1.12299i | −0.0897582 | + | 0.0357453i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.23449 | + | 0.712733i | −0.0392545 | + | 0.0226636i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.2678 | − | 19.7845i | −1.08855 | − | 0.628476i | −0.155361 | − | 0.987858i | \(-0.549654\pi\) |
−0.933191 | + | 0.359382i | \(0.882987\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 3.21887i | − | 0.102148i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.74240 | −0.0869401 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.3520 | − | 17.9301i | 0.327850 | − | 0.567852i | −0.654235 | − | 0.756291i | \(-0.727009\pi\) |
0.982085 | + | 0.188439i | \(0.0603427\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.49871 | − | 11.2561i | −0.205610 | − | 0.356127i |
(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 | 1120.2.bz.f.591.8 | 24 | ||
4.3 | odd | 2 | 280.2.bj.e.171.6 | yes | 24 | ||
7.5 | odd | 6 | 1120.2.bz.e.271.8 | 24 | |||
8.3 | odd | 2 | 1120.2.bz.e.591.8 | 24 | |||
8.5 | even | 2 | 280.2.bj.f.171.3 | yes | 24 | ||
28.19 | even | 6 | 280.2.bj.f.131.3 | yes | 24 | ||
56.5 | odd | 6 | 280.2.bj.e.131.6 | ✓ | 24 | ||
56.19 | even | 6 | inner | 1120.2.bz.f.271.8 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bj.e.131.6 | ✓ | 24 | 56.5 | odd | 6 | ||
280.2.bj.e.171.6 | yes | 24 | 4.3 | odd | 2 | ||
280.2.bj.f.131.3 | yes | 24 | 28.19 | even | 6 | ||
280.2.bj.f.171.3 | yes | 24 | 8.5 | even | 2 | ||
1120.2.bz.e.271.8 | 24 | 7.5 | odd | 6 | |||
1120.2.bz.e.591.8 | 24 | 8.3 | odd | 2 | |||
1120.2.bz.f.271.8 | 24 | 56.19 | even | 6 | inner | ||
1120.2.bz.f.591.8 | 24 | 1.1 | even | 1 | trivial |