Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(193,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.t (of order \(3\), 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.2 | ||
Character | \(\chi\) | \(=\) | 1008.961 |
Dual form | 1008.2.t.k.193.2 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −1.51940 | + | 0.831519i | −0.877226 | + | 0.480078i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.52290 | −1.12828 | −0.564139 | − | 0.825680i | \(-0.690792\pi\) | ||||
−0.564139 | + | 0.825680i | \(0.690792\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.07705 | + | 2.41660i | 0.407086 | + | 0.913390i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.61715 | − | 2.52682i | 0.539050 | − | 0.842274i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.71296 | 1.72252 | 0.861262 | − | 0.508161i | \(-0.169675\pi\) | ||||
0.861262 | + | 0.508161i | \(0.169675\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.45245 | − | 4.24777i | −0.680188 | − | 1.17812i | −0.974923 | − | 0.222541i | \(-0.928565\pi\) |
0.294735 | − | 0.955579i | \(-0.404769\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.83330 | − | 2.09784i | 0.989754 | − | 0.541661i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.49483 | + | 4.32118i | 0.605086 | + | 1.04804i | 0.992038 | + | 0.125939i | \(0.0401945\pi\) |
−0.386952 | + | 0.922100i | \(0.626472\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.00383929 | − | 0.00664984i | 0.000880793 | − | 0.00152558i | −0.865585 | − | 0.500763i | \(-0.833053\pi\) |
0.866465 | + | 0.499237i | \(0.166386\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.64592 | − | 2.77620i | −0.795605 | − | 0.605816i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.667754 | −0.139236 | −0.0696181 | − | 0.997574i | \(-0.522178\pi\) | ||||
−0.0696181 | + | 0.997574i | \(0.522178\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.36505 | 0.273010 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.355997 | + | 5.18394i | −0.0685117 | + | 0.997650i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.85082 | − | 6.66981i | 0.715079 | − | 1.23855i | −0.247851 | − | 0.968798i | \(-0.579724\pi\) |
0.962929 | − | 0.269754i | \(-0.0869424\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.88302 | + | 6.72560i | −0.697412 | + | 1.20795i | 0.271949 | + | 0.962312i | \(0.412332\pi\) |
−0.969361 | + | 0.245641i | \(0.921002\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.68028 | + | 4.75044i | −1.51104 | + | 0.826946i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.71729 | − | 6.09686i | −0.459306 | − | 1.03056i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.19562 | + | 5.53498i | −0.525357 | + | 0.909946i | 0.474207 | + | 0.880414i | \(0.342735\pi\) |
−0.999564 | + | 0.0295319i | \(0.990598\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.25836 | + | 4.41480i | 1.16227 | + | 0.706934i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.21159 | + | 9.02673i | 0.813913 | + | 1.40974i | 0.910106 | + | 0.414376i | \(0.136000\pi\) |
−0.0961931 | + | 0.995363i | \(0.530667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.42935 | + | 7.67185i | −0.675469 | + | 1.16995i | 0.300863 | + | 0.953668i | \(0.402725\pi\) |
−0.976332 | + | 0.216279i | \(0.930608\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.07992 | + | 6.37493i | −0.608198 | + | 0.950318i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.08052 | + | 1.87152i | 0.157610 | + | 0.272989i | 0.934006 | − | 0.357256i | \(-0.116288\pi\) |
−0.776396 | + | 0.630245i | \(0.782954\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.67994 | + | 5.20559i | −0.668562 | + | 0.743656i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.38379 | − | 4.49109i | −1.03394 | − | 0.628879i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.69858 | − | 6.40613i | −0.508039 | − | 0.879950i | −0.999957 | − | 0.00930815i | \(-0.997037\pi\) |
0.491917 | − | 0.870642i | \(-0.336296\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.4133 | −1.94348 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.000303939 | 0.0132962i | −4.02578e−5 | 0.00176112i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.261797 | + | 0.453446i | −0.0340831 | + | 0.0590336i | −0.882564 | − | 0.470193i | \(-0.844184\pi\) |
0.848481 | + | 0.529226i | \(0.177518\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.49541 | + | 7.78628i | 0.575578 | + | 0.996931i | 0.995979 | + | 0.0895919i | \(0.0285563\pi\) |
−0.420400 | + | 0.907339i | \(0.638110\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.84807 | + | 1.18650i | 0.988764 | + | 0.149485i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.18730 | + | 10.7167i | 0.767441 | + | 1.32925i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.54791 | + | 4.41311i | −0.311277 | + | 0.539147i | −0.978639 | − | 0.205586i | \(-0.934090\pi\) |
0.667362 | + | 0.744733i | \(0.267423\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.01458 | − | 0.555250i | 0.122142 | − | 0.0668443i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.68471 | 0.674651 | 0.337325 | − | 0.941388i | \(-0.390478\pi\) | ||||
0.337325 | + | 0.941388i | \(0.390478\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.52062 | − | 2.63379i | −0.177975 | − | 0.308262i | 0.763212 | − | 0.646148i | \(-0.223621\pi\) |
−0.941187 | + | 0.337887i | \(0.890288\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.07405 | + | 1.13506i | −0.239491 | + | 0.131066i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.15314 | + | 13.8060i | 0.701215 | + | 1.57334i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.08115 | + | 5.33671i | 0.346657 | + | 0.600427i | 0.985653 | − | 0.168783i | \(-0.0539836\pi\) |
−0.638997 | + | 0.769209i | \(0.720650\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.76965 | − | 8.17250i | −0.418850 | − | 0.908056i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.258726 | − | 0.448126i | 0.0283988 | − | 0.0491882i | −0.851477 | − | 0.524392i | \(-0.824292\pi\) |
0.879876 | + | 0.475204i | \(0.157626\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.29422 | − | 10.9019i | −0.682704 | − | 1.18248i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.304852 | + | 13.3361i | −0.0326836 | + | 1.42978i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.19093 | − | 2.06274i | 0.126238 | − | 0.218650i | −0.795978 | − | 0.605325i | \(-0.793043\pi\) |
0.922216 | + | 0.386675i | \(0.126376\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.62377 | − | 10.5017i | 0.799188 | − | 1.10087i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.307402 | − | 13.4477i | 0.0318761 | − | 1.39446i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.00968615 | + | 0.0167769i | −0.000993778 | + | 0.00172127i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.32994 | − | 7.49968i | 0.439639 | − | 0.761477i | −0.558022 | − | 0.829826i | \(-0.688440\pi\) |
0.997662 | + | 0.0683485i | \(0.0217730\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.23873 | − | 14.4356i | 0.928527 | − | 1.45084i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.33566 | −0.928933 | −0.464466 | − | 0.885591i | \(-0.653754\pi\) | ||||
−0.464466 | + | 0.885591i | \(0.653754\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.2185 | −1.59806 | −0.799029 | − | 0.601293i | \(-0.794653\pi\) | ||||
−0.799029 | + | 0.601293i | \(0.794653\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.19830 | + | 7.00408i | 0.897663 | + | 0.683529i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.50171 | + | 7.79718i | −0.435196 | + | 0.753782i | −0.997312 | − | 0.0732767i | \(-0.976654\pi\) |
0.562115 | + | 0.827059i | \(0.309988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.71563 | + | 6.43566i | 0.355893 | + | 0.616424i | 0.987270 | − | 0.159051i | \(-0.0508435\pi\) |
−0.631378 | + | 0.775476i | \(0.717510\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.252984 | − | 11.0671i | 0.0240121 | − | 1.05044i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.14642 | + | 12.3780i | 0.672278 | + | 1.16442i | 0.977256 | + | 0.212061i | \(0.0680175\pi\) |
−0.304978 | + | 0.952359i | \(0.598649\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.68468 | 0.157097 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.6993 | − | 0.672380i | −1.35895 | − | 0.0621615i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.75551 | + | 10.6831i | −0.710947 | + | 0.979321i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.6380 | 1.96709 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.4244 | − | 9.38168i | −1.39077 | − | 0.845917i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.17064 | 0.820247 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.96011 | 0.173932 | 0.0869660 | − | 0.996211i | \(-0.472283\pi\) | ||||
0.0869660 | + | 0.996211i | \(0.472283\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.350652 | − | 15.3397i | 0.0308732 | − | 1.35059i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.98825 | 0.348455 | 0.174227 | − | 0.984705i | \(-0.444257\pi\) | ||||
0.174227 | + | 0.984705i | \(0.444257\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0202051 | + | 0.00211583i | 0.00175201 | + | 0.000183466i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.898147 | − | 13.0786i | 0.0773002 | − | 1.12563i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.40843 | −0.632945 | −0.316473 | − | 0.948602i | \(-0.602499\pi\) | ||||
−0.316473 | + | 0.948602i | \(0.602499\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.92660 | − | 11.9972i | −0.587507 | − | 1.01759i | −0.994558 | − | 0.104186i | \(-0.966776\pi\) |
0.407051 | − | 0.913405i | \(-0.366557\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.19795 | − | 1.94511i | −0.269316 | − | 0.163808i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.0108 | − | 24.2674i | −1.17164 | − | 2.02934i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.71524 | + | 16.8273i | −0.806807 | + | 1.39743i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.78214 | − | 11.8008i | 0.229467 | − | 0.973316i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.1040 | −1.15545 | −0.577724 | − | 0.816232i | \(-0.696059\pi\) | ||||
−0.577724 | + | 0.816232i | \(0.696059\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.6005 | 0.862660 | 0.431330 | − | 0.902194i | \(-0.358044\pi\) | ||||
0.431330 | + | 0.902194i | \(0.358044\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.9534 | + | 0.683999i | 1.20891 | + | 0.0552980i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.79650 | − | 16.9680i | 0.786874 | − | 1.36291i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.129779 | − | 0.224784i | 0.0103575 | − | 0.0179397i | −0.860800 | − | 0.508943i | \(-0.830036\pi\) |
0.871158 | + | 0.491003i | \(0.163370\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.9465 | + | 6.65803i | 0.868110 | + | 0.528016i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.719203 | − | 1.61370i | −0.0566811 | − | 0.127177i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.31882 | + | 10.9445i | −0.494928 | + | 0.857241i | −0.999983 | − | 0.00584647i | \(-0.998139\pi\) |
0.505055 | + | 0.863087i | \(0.331472\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 21.8995 | − | 11.9849i | 1.70487 | − | 0.933024i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.74959 | + | 9.95859i | 0.444917 | + | 0.770619i | 0.998046 | − | 0.0624765i | \(-0.0198999\pi\) |
−0.553129 | + | 0.833095i | \(0.686567\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.52905 | + | 9.57659i | −0.425311 | + | 0.736661i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0105942 | − | 0.0204550i | −0.000810162 | − | 0.00156423i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.90471 | + | 13.6914i | 0.600984 | + | 1.04094i | 0.992672 | + | 0.120837i | \(0.0385579\pi\) |
−0.391688 | + | 0.920098i | \(0.628109\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.47022 | + | 3.29878i | 0.111138 | + | 0.249364i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0207253 | − | 0.906654i | 0.00155781 | − | 0.0681483i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.49849 | + | 14.7198i | 0.635207 | + | 1.10021i | 0.986471 | + | 0.163934i | \(0.0524184\pi\) |
−0.351265 | + | 0.936276i | \(0.614248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.35841 | 0.472617 | 0.236308 | − | 0.971678i | \(-0.424062\pi\) | ||||
0.236308 | + | 0.971678i | \(0.424062\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.3048 | − | 8.09245i | −0.983516 | − | 0.598211i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.06225 | − | 13.9642i | 0.592749 | − | 1.02667i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.2529 | + | 24.6867i | 1.04227 | + | 1.80527i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.9110 | + | 4.72305i | −0.939134 | + | 0.343551i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.07047 | − | 3.58616i | −0.149814 | − | 0.259485i | 0.781345 | − | 0.624100i | \(-0.214534\pi\) |
−0.931159 | + | 0.364614i | \(0.881201\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.84793 | − | 6.66481i | 0.276980 | − | 0.479743i | −0.693653 | − | 0.720310i | \(-0.744000\pi\) |
0.970633 | + | 0.240566i | \(0.0773331\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18.3122 | − | 11.1381i | −1.31136 | − | 0.797618i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.29508 | 0.234765 | 0.117383 | − | 0.993087i | \(-0.462550\pi\) | ||||
0.117383 | + | 0.993087i | \(0.462550\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.08840 | − | 14.0095i | −0.573371 | − | 0.993108i | −0.996216 | − | 0.0869063i | \(-0.972302\pi\) |
0.422845 | − | 0.906202i | \(-0.361031\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.201707 | − | 8.82391i | 0.0142273 | − | 0.622391i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.2658 | + | 2.12219i | 1.42238 | + | 0.148948i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.1483 | − | 22.7736i | −0.918319 | − | 1.59058i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.07986 | + | 1.68729i | −0.0750553 | + | 0.117275i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0219337 | − | 0.0379903i | 0.00151719 | − | 0.00262784i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.9633 | + | 24.1851i | 0.961273 | + | 1.66497i | 0.719312 | + | 0.694687i | \(0.244457\pi\) |
0.241961 | + | 0.970286i | \(0.422209\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.63734 | + | 4.72694i | −0.591821 | + | 0.323885i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.1748 | − | 19.3554i | 0.762116 | − | 1.32002i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.4353 | − | 2.13994i | −1.38724 | − | 0.145268i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.50048 | + | 2.73736i | 0.304114 | + | 0.184973i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.2369 | − | 21.1950i | 0.823144 | − | 1.42573i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.1652 | − | 17.6066i | 0.680711 | − | 1.17903i | −0.294054 | − | 0.955789i | \(-0.595004\pi\) |
0.974764 | − | 0.223237i | \(-0.0716623\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.20749 | − | 3.44923i | 0.147166 | − | 0.229949i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.68939 | 0.377618 | 0.188809 | − | 0.982014i | \(-0.439537\pi\) | ||||
0.188809 | + | 0.982014i | \(0.439537\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.8542 | 0.981590 | 0.490795 | − | 0.871275i | \(-0.336706\pi\) | ||||
0.490795 | + | 0.871275i | \(0.336706\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −20.8290 | − | 15.8603i | −1.37045 | − | 1.04353i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.70652 | − | 11.6160i | 0.439358 | − | 0.760991i | −0.558282 | − | 0.829652i | \(-0.688539\pi\) |
0.997640 | + | 0.0686603i | \(0.0218725\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.72605 | − | 4.72166i | −0.177828 | − | 0.308007i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.11908 | − | 5.54656i | −0.592348 | − | 0.360288i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.33123 | + | 16.1622i | 0.603587 | + | 1.04544i | 0.992273 | + | 0.124073i | \(0.0395958\pi\) |
−0.388686 | + | 0.921370i | \(0.627071\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.4160 | −1.37952 | −0.689762 | − | 0.724036i | \(-0.742285\pi\) | ||||
−0.689762 | + | 0.724036i | \(0.742285\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.5232 | + | 9.28276i | 0.803363 | + | 0.595489i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.8070 | − | 13.1332i | 0.754324 | − | 0.839050i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0376627 | −0.00239642 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.0204822 | + | 0.896018i | −0.00129801 | + | 0.0567829i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.462898 | 0.0292179 | 0.0146089 | − | 0.999893i | \(-0.495350\pi\) | ||||
0.0146089 | + | 0.999893i | \(0.495350\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.81485 | −0.239838 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.6286 | + | 11.3306i | 1.16657 | + | 0.709550i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.802512 | 0.0500593 | 0.0250297 | − | 0.999687i | \(-0.492032\pi\) | ||||
0.0250297 | + | 0.999687i | \(0.492032\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.8177 | − | 1.76111i | −1.04500 | − | 0.109430i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.6261 | − | 20.5164i | −0.657737 | − | 1.26993i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.201387 | −0.0124180 | −0.00620902 | − | 0.999981i | \(-0.501976\pi\) | ||||
−0.00620902 | + | 0.999981i | \(0.501976\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.33117 | + | 16.1621i | 0.573209 | + | 0.992828i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.0942803 | + | 4.12441i | −0.00576986 | + | 0.252410i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.1773 | − | 19.3596i | −0.681490 | − | 1.18038i | −0.974526 | − | 0.224274i | \(-0.927999\pi\) |
0.293036 | − | 0.956101i | \(-0.405334\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.78925 | − | 3.09907i | 0.108689 | − | 0.188255i | −0.806550 | − | 0.591166i | \(-0.798668\pi\) |
0.915240 | + | 0.402910i | \(0.132001\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.85122 | + | 22.2955i | −0.172564 | + | 1.34939i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.79847 | 0.470266 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.1067 | −0.607254 | −0.303627 | − | 0.952791i | \(-0.598198\pi\) | ||||
−0.303627 | + | 0.952791i | \(0.598198\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.7149 | + | 20.6880i | 0.641487 | + | 1.23856i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7114 | − | 22.0167i | 0.758296 | − | 1.31341i | −0.185422 | − | 0.982659i | \(-0.559365\pi\) |
0.943719 | − | 0.330749i | \(-0.107301\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.93833 | − | 3.35728i | 0.115222 | − | 0.199570i | −0.802647 | − | 0.596455i | \(-0.796575\pi\) |
0.917868 | + | 0.396885i | \(0.129909\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.000766810 | − | 0.0335450i | 4.54219e−5 | − | 0.00198704i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.2009 | + | 22.3166i | −0.956308 | + | 1.31730i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.94838 | + | 6.83879i | −0.232257 | + | 0.402282i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.342783 | + | 14.9954i | −0.0200943 | + | 0.879049i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.428834 | + | 0.742762i | 0.0250527 | + | 0.0433926i | 0.878280 | − | 0.478147i | \(-0.158691\pi\) |
−0.853227 | + | 0.521539i | \(0.825358\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.660489 | − | 1.14400i | 0.0384551 | − | 0.0666063i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.03380 | + | 29.6157i | −0.118013 | + | 1.71848i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.63763 | + | 2.83647i | 0.0947068 | + | 0.164037i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.3104 | − | 2.44102i | −1.34359 | − | 0.140698i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.1846 | − | 7.76278i | 0.814884 | − | 0.445960i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.3415 | − | 19.6440i | −0.649412 | − | 1.12481i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.717950 | 0.0409756 | 0.0204878 | − | 0.999790i | \(-0.493478\pi\) | ||||
0.0204878 | + | 0.999790i | \(0.493478\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.6424 | − | 13.4860i | 1.40186 | − | 0.767192i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.72606 | + | 8.18578i | −0.267990 | + | 0.464173i | −0.968343 | − | 0.249624i | \(-0.919693\pi\) |
0.700352 | + | 0.713797i | \(0.253026\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.6317 | + | 20.1467i | 0.657464 | + | 1.13876i | 0.981270 | + | 0.192638i | \(0.0617043\pi\) |
−0.323806 | + | 0.946124i | \(0.604962\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −19.7999 | − | 2.99343i | −1.11560 | − | 0.168661i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.61771 | − | 11.4622i | −0.371687 | − | 0.643781i | 0.618138 | − | 0.786070i | \(-0.287887\pi\) |
−0.989825 | + | 0.142288i | \(0.954554\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.9996 | − | 38.1044i | 1.23174 | − | 2.13344i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.356380 | − | 15.5903i | 0.0198912 | − | 0.870165i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0383135 | 0.00213182 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.34772 | − | 5.79841i | −0.185698 | − | 0.321638i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.9969 | − | 6.68872i | −0.608130 | − | 0.369887i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.35894 | + | 4.62690i | −0.185184 | + | 0.255089i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.2165 | − | 26.3558i | −0.836375 | − | 1.44864i | −0.892906 | − | 0.450243i | \(-0.851338\pi\) |
0.0565316 | − | 0.998401i | \(-0.481996\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.81810 | + | 17.0257i | 0.483229 | + | 0.933001i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.42813 | − | 11.1339i | 0.351206 | − | 0.608307i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.767420 | − | 1.32921i | −0.0418041 | − | 0.0724067i | 0.844366 | − | 0.535766i | \(-0.179977\pi\) |
−0.886170 | + | 0.463360i | \(0.846644\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.1508 | − | 12.8647i | −1.14875 | − | 0.698713i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.1836 | + | 38.4231i | −1.20131 | + | 2.08073i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.6204 | − | 5.70287i | −0.951410 | − | 0.307926i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.55970 | + | 1.40084i | −0.137810 | + | 0.0754189i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.3036 | + | 24.7745i | −0.767856 | + | 1.32997i | 0.170867 | + | 0.985294i | \(0.445343\pi\) |
−0.938723 | + | 0.344672i | \(0.887990\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.05123 | + | 15.6772i | −0.484501 | + | 0.839181i | −0.999841 | − | 0.0178047i | \(-0.994332\pi\) |
0.515340 | + | 0.856986i | \(0.327666\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.8933 | − | 11.2012i | 1.22195 | − | 0.597875i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.5908 | 0.776591 | 0.388295 | − | 0.921535i | \(-0.373064\pi\) | ||||
0.388295 | + | 0.921535i | \(0.373064\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.3420 | −0.761193 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.90049 | − | 22.6808i | 0.153510 | − | 1.20040i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.05831 | − | 1.83304i | 0.0558554 | − | 0.0967443i | −0.836746 | − | 0.547592i | \(-0.815545\pi\) |
0.892601 | + | 0.450847i | \(0.148878\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.49997 | + | 16.4544i | 0.499998 | + | 0.866023i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −32.8767 | + | 17.9924i | −1.72558 | + | 0.944356i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.83638 | + | 6.64480i | 0.200805 | + | 0.347805i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.66209 | −0.347758 | −0.173879 | − | 0.984767i | \(-0.555630\pi\) | ||||
−0.173879 | + | 0.984767i | \(0.555630\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 31.2368 | + | 1.42884i | 1.62613 | + | 0.0743825i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.4975 | − | 15.8377i | 0.596922 | − | 0.822253i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.4983 | −0.647138 | −0.323569 | − | 0.946205i | \(-0.604883\pi\) | ||||
−0.323569 | + | 0.946205i | \(0.604883\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.9339 | + | 7.62556i | −0.719542 | + | 0.393782i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −37.7758 | −1.94555 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.5504 | 1.00423 | 0.502117 | − | 0.864800i | \(-0.332555\pi\) | ||||
0.502117 | + | 0.864800i | \(0.332555\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.97820 | + | 1.62987i | −0.152578 | + | 0.0835009i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.67480 | 0.136676 | 0.0683379 | − | 0.997662i | \(-0.478230\pi\) | ||||
0.0683379 | + | 0.997662i | \(0.478230\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.5238 | − | 34.8311i | −0.791165 | − | 1.77516i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.2225 | + | 23.5987i | 0.621304 | + | 1.19959i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.96310 | −0.200937 | −0.100469 | − | 0.994940i | \(-0.532034\pi\) | ||||
−0.100469 | + | 0.994940i | \(0.532034\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.66593 | − | 2.88548i | −0.0842499 | − | 0.145925i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.05974 | + | 3.31631i | −0.305673 | + | 0.167285i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.77345 | − | 13.4640i | −0.391125 | − | 0.677448i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.2978 | − | 17.8362i | 0.516829 | − | 0.895175i | −0.482980 | − | 0.875632i | \(-0.660446\pi\) |
0.999809 | − | 0.0195431i | \(-0.00622114\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0324590 | + | 0.0135861i | −0.00162498 | + | 0.000680158i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.83957 | −0.191739 | −0.0958696 | − | 0.995394i | \(-0.530563\pi\) | ||||
−0.0958696 | + | 0.995394i | \(0.530563\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.0917 | 1.89748 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.51046 | + | 20.6184i | 0.472579 | + | 1.02454i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.2565 | + | 31.6212i | −0.904940 | + | 1.56740i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.7113 | − | 25.4808i | 0.727428 | − | 1.25994i | −0.230538 | − | 0.973063i | \(-0.574049\pi\) |
0.957967 | − | 0.286880i | \(-0.0926180\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.2564 | − | 6.16026i | 0.555236 | − | 0.303863i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.37777 | − | 0.144276i | −0.0677954 | − | 0.00709938i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.652741 | + | 1.13058i | −0.0320418 | + | 0.0554980i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.5002 | + | 12.4690i | 1.00390 | + | 0.610609i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.40821 | − | 7.63525i | −0.215355 | − | 0.373006i | 0.738027 | − | 0.674771i | \(-0.235758\pi\) |
−0.953382 | + | 0.301765i | \(0.902424\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.6437 | + | 30.5597i | −0.859899 | + | 1.48939i | 0.0121255 | + | 0.999926i | \(0.496140\pi\) |
−0.872024 | + | 0.489462i | \(0.837193\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.47635 | + | 0.296242i | 0.314891 | + | 0.0144038i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.40557 | + | 5.89861i | 0.165194 | + | 0.286125i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.9746 | + | 19.2498i | −0.676277 | + | 0.931564i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 41.4668 | + | 25.2216i | 2.00203 | + | 1.21771i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.8099 | + | 22.1873i | 0.617030 | + | 1.06873i | 0.990025 | + | 0.140893i | \(0.0449975\pi\) |
−0.372995 | + | 0.927833i | \(0.621669\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.8556 | 0.810030 | 0.405015 | − | 0.914310i | \(-0.367266\pi\) | ||||
0.405015 | + | 0.914310i | \(0.367266\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.769113 | − | 33.6458i | 0.0368762 | − | 1.61319i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.00256370 | + | 0.00444045i | −0.000122638 | + | 0.000212416i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.4596 | + | 26.7768i | 0.737846 | + | 1.27799i | 0.953463 | + | 0.301509i | \(0.0974902\pi\) |
−0.215618 | + | 0.976478i | \(0.569176\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.58544 | + | 20.2436i | 0.265973 | + | 0.963980i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.65544 | − | 8.06345i | −0.221186 | − | 0.383106i | 0.733982 | − | 0.679169i | \(-0.237660\pi\) |
−0.955169 | + | 0.296063i | \(0.904326\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.00459 | + | 5.20410i | −0.142431 | + | 0.246698i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.4297 | − | 11.7278i | 1.01359 | − | 0.554705i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.8055 | 1.12345 | 0.561724 | − | 0.827324i | \(-0.310138\pi\) | ||||
0.561724 | + | 0.827324i | \(0.310138\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.7736 | + | 51.5694i | 1.40198 | + | 2.42831i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.1065 | + | 8.81456i | −0.756748 | + | 0.414144i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −19.2340 | + | 26.4947i | −0.901706 | + | 1.24209i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.90552 | + | 11.9607i | 0.323027 | + | 0.559498i | 0.981111 | − | 0.193446i | \(-0.0619663\pi\) |
−0.658084 | + | 0.752944i | \(0.728633\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −23.2889 | + | 11.3947i | −1.08703 | + | 0.531861i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.00256407 | + | 0.00444110i | −0.000119421 | + | 0.000206843i | −0.866085 | − | 0.499897i | \(-0.833371\pi\) |
0.865966 | + | 0.500103i | \(0.166705\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.9682 | − | 22.4616i | −0.602685 | − | 1.04388i | −0.992413 | − | 0.122951i | \(-0.960764\pi\) |
0.389728 | − | 0.920930i | \(-0.372569\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.775546 | + | 33.9272i | −0.0359651 | + | 1.57334i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0484 | − | 20.8684i | 0.557532 | − | 0.965673i | −0.440170 | − | 0.897914i | \(-0.645082\pi\) |
0.997702 | − | 0.0677588i | \(-0.0215848\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.4090 | − | 1.40416i | −0.619168 | − | 0.0648379i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0102740 | + | 0.449450i | −0.000473402 | + | 0.0207095i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25.3047 | + | 43.8290i | −1.16351 | + | 2.01526i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.00524081 | − | 0.00907735i | 0.000240465 | − | 0.000416497i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.1683 | − | 1.01403i | −1.01502 | − | 0.0464291i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.7823 | −0.675420 | −0.337710 | − | 0.941250i | \(-0.609652\pi\) | ||||
−0.337710 | + | 0.941250i | \(0.609652\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.3485 | 1.42937 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.43458 | + | 1.85382i | 0.110777 | + | 0.0843516i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.9240 | + | 18.9210i | −0.496035 | + | 0.859158i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.38360 | − | 16.2529i | −0.425211 | − | 0.736488i | 0.571229 | − | 0.820791i | \(-0.306467\pi\) |
−0.996440 | + | 0.0843033i | \(0.973134\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.500234 | − | 21.8833i | 0.0226213 | − | 0.989598i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.2871 | − | 31.6741i | −0.825284 | − | 1.42943i | −0.901702 | − | 0.432358i | \(-0.857682\pi\) |
0.0764182 | − | 0.997076i | \(-0.475652\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.4286 | 1.73074 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −23.3084 | + | 36.4197i | −1.04764 | + | 1.63695i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.12270 | + | 13.7377i | 0.274641 | + | 0.616219i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.63182 | −0.207349 | −0.103674 | − | 0.994611i | \(-0.533060\pi\) | ||||
−0.103674 | + | 0.994611i | \(0.533060\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.0167 | − | 10.3502i | −0.760250 | − | 0.462412i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.4143 | −0.731879 | −0.365940 | − | 0.930639i | \(-0.619252\pi\) | ||||
−0.365940 | + | 0.930639i | \(0.619252\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.5530 | 1.04809 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.437711 | − | 19.1482i | 0.0194394 | − | 0.850401i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.4834 | 0.464668 | 0.232334 | − | 0.972636i | \(-0.425364\pi\) | ||||
0.232334 | + | 0.972636i | \(0.425364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.72705 | − | 6.51145i | 0.209112 | − | 0.288050i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.0331056 | + | 0.0222700i | 0.00146165 | + | 0.000983243i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 40.9178 | 1.80305 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.17298 | + | 10.6919i | 0.271487 | + | 0.470230i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.3951 | − | 14.2297i | −1.02693 | − | 0.624616i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.0087 | − | 19.0675i | −0.482298 | − | 0.835364i | 0.517496 | − | 0.855686i | \(-0.326864\pi\) |
−0.999793 | + | 0.0203215i | \(0.993531\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.18541 | − | 2.05320i | 0.0518346 | − | 0.0897801i | −0.838944 | − | 0.544218i | \(-0.816826\pi\) |
0.890778 | + | 0.454438i | \(0.150160\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.97685 | − | 3.78964i | −0.217208 | − | 0.165394i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −38.7500 | −1.68798 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5541 | −0.980613 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.722411 | + | 1.39480i | 0.0313500 | + | 0.0605293i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.5623 | − | 44.2753i | 1.10723 | − | 1.91777i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.3574 | − | 19.6715i | 0.491022 | − | 0.850475i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −25.1524 | − | 15.2986i | −1.08541 | − | 0.660184i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.7363 | + | 29.7394i | −1.15161 | + | 1.28097i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.65209 | − | 11.5218i | 0.285996 | − | 0.495359i | −0.686854 | − | 0.726795i | \(-0.741009\pi\) |
0.972850 | + | 0.231436i | \(0.0743423\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.66096 | + | 5.28714i | −0.414592 | + | 0.226893i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.37418 | − | 16.2366i | −0.401546 | − | 0.695498i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.43685 | − | 4.22074i | 0.104192 | − | 0.180466i | −0.809216 | − | 0.587512i | \(-0.800108\pi\) |
0.913408 | + | 0.407046i | \(0.133441\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 26.9443 | + | 1.23249i | 1.14995 | + | 0.0526014i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0295688 | − | 0.0512146i | −0.00125967 | − | 0.00218182i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.57816 | + | 13.1938i | −0.407305 | + | 0.561058i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.638254 | + | 27.9212i | −0.0270924 | + | 1.18519i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.09601 | + | 12.2907i | 0.300668 | + | 0.520772i | 0.976287 | − | 0.216479i | \(-0.0694572\pi\) |
−0.675620 | + | 0.737250i | \(0.736124\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.4511 | 1.83778 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −42.1833 | − | 25.6575i | −1.78098 | − | 1.08326i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.51985 | − | 6.09657i | 0.148344 | − | 0.256940i | −0.782271 | − | 0.622938i | \(-0.785939\pi\) |
0.930616 | + | 0.365998i | \(0.119272\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0297 | − | 31.2284i | −0.758516 | − | 1.31379i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.6896 | − | 17.9119i | 0.658901 | − | 0.752230i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.15081 | + | 15.8497i | 0.383622 | + | 0.664453i | 0.991577 | − | 0.129519i | \(-0.0413432\pi\) |
−0.607955 | + | 0.793972i | \(0.708010\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.2192 | + | 26.3604i | −0.636902 | + | 1.10315i | 0.349206 | + | 0.937046i | \(0.386451\pi\) |
−0.986109 | + | 0.166102i | \(0.946882\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.12783 | + | 3.72717i | 0.255994 | + | 0.155705i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.911516 | −0.0380128 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.65385 | + | 9.79275i | 0.235373 | + | 0.407678i | 0.959381 | − | 0.282114i | \(-0.0910356\pi\) |
−0.724008 | + | 0.689791i | \(0.757702\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.304624 | + | 13.3261i | −0.0126597 | + | 0.553815i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.36160 | + | 0.142584i | 0.0564888 | + | 0.00591538i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.1299 | − | 36.5980i | −0.875110 | − | 1.51573i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 37.0850 | + | 1.69635i | 1.53328 | + | 0.0701354i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.89755 | − | 17.1431i | 0.408516 | − | 0.707570i | −0.586208 | − | 0.810161i | \(-0.699380\pi\) |
0.994724 | + | 0.102591i | \(0.0327132\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0298161 | + | 0.0516430i | 0.00122855 | + | 0.00212791i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.00655 | + | 2.73993i | −0.205942 | + | 0.112706i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.69067 | − | 4.66038i | 0.110493 | − | 0.191379i | −0.805476 | − | 0.592628i | \(-0.798090\pi\) |
0.915969 | + | 0.401249i | \(0.131424\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.5664 | − | 26.9525i | 0.802145 | − | 1.10495i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.9387 | + | 14.5604i | 0.979746 | + | 0.595917i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.12979 | − | 1.95686i | 0.0461622 | − | 0.0799552i | −0.842021 | − | 0.539445i | \(-0.818634\pi\) |
0.888183 | + | 0.459489i | \(0.151968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.1873 | − | 31.5013i | 0.741875 | − | 1.28496i | −0.209766 | − | 0.977752i | \(-0.567270\pi\) |
0.951641 | − | 0.307213i | \(-0.0993964\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.03078 | + | 13.5748i | 0.286316 | + | 0.552808i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −54.5905 | −2.21942 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.2161 | −0.658190 | −0.329095 | − | 0.944297i | \(-0.606744\pi\) | ||||
−0.329095 | + | 0.944297i | \(0.606744\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −32.5565 | + | 13.6269i | −1.31925 | + | 0.552192i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.29985 | − | 9.17961i | 0.214409 | − | 0.371367i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.6357 | + | 37.4741i | 0.873857 | + | 1.51357i | 0.857975 | + | 0.513691i | \(0.171722\pi\) |
0.0158822 | + | 0.999874i | \(0.494944\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 38.9142 | + | 23.6691i | 1.56917 | + | 0.954429i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.92248 | − | 10.2580i | −0.238430 | − | 0.412973i | 0.721834 | − | 0.692066i | \(-0.243299\pi\) |
−0.960264 | + | 0.279093i | \(0.909966\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.3288 | −1.62095 | −0.810475 | − | 0.585773i | \(-0.800791\pi\) | ||||
−0.810475 | + | 0.585773i | \(0.800791\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.237718 | − | 3.46160i | 0.00953931 | − | 0.138909i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.26751 | + | 0.656320i | 0.251103 | + | 0.0262949i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.9619 | −1.19848 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.00173640 | + | 0.0759607i | −6.93450e−5 | + | 0.00303358i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.8902 | −1.27154 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.9489 | −0.555298 | −0.277649 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277649 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −41.3262 | − | 25.1361i | −1.64257 | − | 0.999072i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.94518 | −0.196243 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.5895 | + | 7.11283i | 1.33086 | + | 0.281821i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.19303 | − | 14.3642i | 0.363671 | − | 0.568240i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.5395 | 0.692768 | 0.346384 | − | 0.938093i | \(-0.387409\pi\) | ||||
0.346384 | + | 0.938093i | \(0.387409\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.5329 | + | 23.4397i | 0.533686 | + | 0.924371i | 0.999226 | + | 0.0393443i | \(0.0125269\pi\) |
−0.465540 | + | 0.885027i | \(0.654140\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.884662 | + | 38.7006i | −0.0348335 | + | 1.52383i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.3252 | − | 19.6159i | −0.445240 | − | 0.771179i | 0.552828 | − | 0.833295i | \(-0.313548\pi\) |
−0.998069 | + | 0.0621160i | \(0.980215\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.49564 | + | 2.59052i | −0.0587089 | + | 0.101687i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.8288 | − | 13.7409i | 1.28666 | − | 0.538549i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.784108 | −0.0306845 | −0.0153423 | − | 0.999882i | \(-0.504884\pi\) | ||||
−0.0153423 | + | 0.999882i | \(0.504884\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.0620 | −0.393154 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.11419 | − | 0.416903i | −0.355578 | − | 0.0162649i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.7219 | − | 28.9632i | 0.651392 | − | 1.12824i | −0.331393 | − | 0.943493i | \(-0.607519\pi\) |
0.982785 | − | 0.184752i | \(-0.0591481\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.53258 | + | 2.65450i | −0.0596104 | + | 0.103248i | −0.894291 | − | 0.447487i | \(-0.852319\pi\) |
0.834680 | + | 0.550735i | \(0.185652\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.968743 | + | 42.3788i | −0.0376229 | + | 1.64586i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0509756 | − | 0.00533805i | −0.00197675 | − | 0.000207001i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.57140 | + | 4.45379i | −0.0995649 | + | 0.172451i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.804733 | + | 35.2040i | −0.0311128 | + | 1.36107i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.6821 | + | 44.4827i | 0.991447 | + | 1.71724i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.4618 | − | 25.0487i | 0.557463 | − | 0.965555i | −0.440244 | − | 0.897878i | \(-0.645108\pi\) |
0.997707 | − | 0.0676766i | \(-0.0215586\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.485953 | + | 7.07633i | −0.0187044 | + | 0.272368i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.85818 | + | 10.1467i | 0.225148 | + | 0.389968i | 0.956364 | − | 0.292178i | \(-0.0943801\pi\) |
−0.731216 | + | 0.682146i | \(0.761047\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.7873 | + | 2.38624i | 0.874497 | + | 0.0915753i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.64446 | + | 4.73084i | −0.331256 | + | 0.181286i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.7190 | − | 35.8864i | −0.792791 | − | 1.37315i | −0.924232 | − | 0.381831i | \(-0.875294\pi\) |
0.131441 | − | 0.991324i | \(-0.458040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.6908 | 0.714138 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22.5694 | + | 12.3515i | −0.861076 | + | 0.471240i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.1412 | + | 31.4215i | −0.691125 | + | 1.19706i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.45675 | − | 5.98727i | −0.131501 | − | 0.227766i | 0.792754 | − | 0.609541i | \(-0.208646\pi\) |
−0.924255 | + | 0.381775i | \(0.875313\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 44.8358 | + | 6.77845i | 1.70317 | + | 0.257492i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.4752 | + | 30.2679i | 0.662871 | + | 1.14813i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.0041 | + | 45.0404i | −0.984974 | + | 1.70603i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.530926 | + | 23.2260i | −0.0200815 | + | 0.878487i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.1954 | 1.48039 | 0.740195 | − | 0.672392i | \(-0.234733\pi\) | ||||
0.740195 | + | 0.672392i | \(0.234733\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0245378 | + | 0.0425008i | 0.000925462 | + | 0.00160295i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.06811 | + | 4.90732i | 0.303863 | + | 0.184820i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.0550 | − | 22.5606i | −0.378155 | − | 0.848478i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.2436 | − | 17.7424i | −0.384705 | − | 0.666328i | 0.607023 | − | 0.794684i | \(-0.292363\pi\) |
−0.991728 | + | 0.128356i | \(0.959030\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.4676 | + | 0.844748i | 0.692589 | + | 0.0316805i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.59290 | − | 4.49104i | 0.0971050 | − | 0.168191i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.3479 | + | 61.2243i | 1.32193 | + | 2.28966i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.6170 | − | 16.7977i | −1.03138 | − | 0.627321i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.1300 | + | 29.6700i | −0.638840 | + | 1.10650i | 0.346848 | + | 0.937921i | \(0.387252\pi\) |
−0.985688 | + | 0.168582i | \(0.946081\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.4681 | − | 39.1937i | −0.650547 | − | 1.45965i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.5394 | − | 17.8078i | 1.21015 | − | 0.662279i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.25655 | − | 9.10461i | 0.195223 | − | 0.338137i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.18914 | + | 12.4520i | −0.266631 | + | 0.461818i | −0.967990 | − | 0.250991i | \(-0.919244\pi\) |
0.701359 | + | 0.712808i | \(0.252577\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.7465 | − | 3.69094i | −0.990612 | − | 0.136701i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −44.2019 | −1.63487 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.5773 | 1.46182 | 0.730911 | − | 0.682473i | \(-0.239096\pi\) | ||||
0.730911 | + | 0.682473i | \(0.239096\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.01907 | + | 29.7724i | −0.258902 | + | 1.09817i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.5561 | + | 25.2119i | −0.536182 | + | 0.928694i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.8407 | − | 18.7767i | −0.398783 | − | 0.690712i | 0.594793 | − | 0.803879i | \(-0.297234\pi\) |
−0.993576 | + | 0.113167i | \(0.963901\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0572246 | − | 0.0313172i | 0.00210220 | − | 0.00115047i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.5692 | − | 28.6987i | −0.607864 | − | 1.05285i | −0.991592 | − | 0.129406i | \(-0.958693\pi\) |
0.383727 | − | 0.923446i | \(-0.374640\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.5831 | 1.30366 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.713936 | − | 1.37844i | −0.0261216 | − | 0.0504345i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.6912 | − | 2.48089i | −0.865659 | − | 0.0906499i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.9324 | 0.946288 | 0.473144 | − | 0.880985i | \(-0.343119\pi\) | ||||
0.473144 | + | 0.880985i | \(0.343119\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.703328 | + | 0.384909i | −0.0256307 | + | 0.0140269i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26.7442 | −0.973320 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.5846 | −1.11162 | −0.555808 | − | 0.831311i | \(-0.687591\pi\) | ||||
−0.555808 | + | 0.831311i | \(0.687591\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.79629 | − | 3.17212i | 0.210392 | − | 0.115141i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.5295 | −1.32419 | −0.662097 | − | 0.749418i | \(-0.730333\pi\) | ||||
−0.662097 | + | 0.749418i | \(0.730333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.5505 | + | 15.9107i | −0.418157 | + | 0.576007i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −37.7259 | − | 1.72566i | −1.36398 | − | 0.0623915i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.56818 | 0.0927315 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.3107 | − | 36.9113i | −0.768485 | − | 1.33105i | −0.938384 | − | 0.345593i | \(-0.887678\pi\) |
0.169900 | − | 0.985461i | \(-0.445656\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.21934 | + | 0.667305i | −0.0439134 | + | 0.0240324i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.1309 | + | 27.9395i | 0.580187 | + | 1.00491i | 0.995457 | + | 0.0952148i | \(0.0303538\pi\) |
−0.415270 | + | 0.909698i | \(0.636313\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.30051 | + | 9.18076i | −0.190400 | + | 0.329783i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27.0172 | − | 11.3084i | 0.969236 | − | 0.405687i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0800351 | 0.00286755 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.4765 | 1.16210 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33.2050 | + | 22.3368i | 1.18665 | + | 0.798254i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.327420 | + | 0.567107i | −0.0116861 | + | 0.0202409i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.3838 | − | 26.6455i | 0.548373 | − | 0.949810i | −0.450013 | − | 0.893022i | \(-0.648581\pi\) |
0.998386 | − | 0.0567879i | \(-0.0180859\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.305987 | − | 0.167457i | 0.0108934 | − | 0.00596163i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.2156 | + | 30.6017i | −0.789895 | + | 1.08807i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.0496 | − | 38.1910i | 0.783003 | − | 1.35620i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27.6169 | − | 16.7976i | −0.979469 | − | 0.595749i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.59378 | − | 6.22460i | −0.127298 | − | 0.220487i | 0.795331 | − | 0.606176i | \(-0.207297\pi\) |
−0.922629 | + | 0.385689i | \(0.873964\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.39144 | + | 9.33824i | −0.190735 | + | 0.330363i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.28628 | − | 6.34502i | −0.116115 | − | 0.224190i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.68725 | − | 15.0468i | −0.306566 | − | 0.530989i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.81448 | + | 4.07120i | 0.0639520 | + | 0.143491i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.0806 | + | 20.1208i | 1.16449 | + | 0.708287i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.3886 | − | 40.5103i | −0.822301 | − | 1.42427i | −0.903965 | − | 0.427607i | \(-0.859357\pi\) |
0.0816637 | − | 0.996660i | \(-0.473977\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.6946 | −0.621341 | −0.310671 | − | 0.950518i | \(-0.600554\pi\) | ||||
−0.310671 | + | 0.950518i | \(0.600554\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.141647 | + | 6.19653i | −0.00496779 | + | 0.217322i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.9418 | − | 27.6120i | 0.558416 | − | 0.967205i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0340111 | + | 0.0589089i | 0.00118990 | + | 0.00206096i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.2070 | − | 36.2467i | −0.496434 | − | 1.26656i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.61075 | + | 14.9143i | 0.300517 | + | 0.520511i | 0.976253 | − | 0.216633i | \(-0.0695074\pi\) |
−0.675736 | + | 0.737144i | \(0.736174\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.77170 | − | 9.99688i | 0.201189 | − | 0.348469i | −0.747723 | − | 0.664011i | \(-0.768853\pi\) |
0.948912 | + | 0.315542i | \(0.102186\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.8490 | + | 6.48458i | −0.412529 | + | 0.225764i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.1448 | 0.700503 | 0.350251 | − | 0.936656i | \(-0.386096\pi\) | ||||
0.350251 | + | 0.936656i | \(0.386096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.01358 | − | 6.95172i | −0.139397 | − | 0.241443i | 0.787871 | − | 0.615840i | \(-0.211183\pi\) |
−0.927269 | + | 0.374397i | \(0.877850\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.3561 | − | 8.40393i | 0.532699 | − | 0.291529i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34.1699 | − | 7.23574i | −1.18392 | − | 0.250704i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.5057 | − | 25.1246i | −0.501990 | − | 0.869472i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −33.4828 | − | 22.5237i | −1.15733 | − | 0.778532i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.59341 | − | 7.95603i | 0.158582 | − | 0.274673i | −0.775775 | − | 0.631009i | \(-0.782641\pi\) |
0.934358 | + | 0.356337i | \(0.115974\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.1576 | − | 26.2537i | −0.522675 | − | 0.905299i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.00630 | + | 44.0220i | −0.0346589 | + | 1.51620i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.9493 | − | 24.1608i | 0.479869 | − | 0.831158i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.3051 | + | 52.2904i | 0.800774 | + | 1.79672i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.153449 | + | 6.71281i | −0.00526636 | + | 0.230383i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.13389 | − | 3.69600i | 0.0731488 | − | 0.126697i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.7925 | + | 18.6931i | −0.369527 | + | 0.640040i | −0.989492 | − | 0.144590i | \(-0.953814\pi\) |
0.619964 | + | 0.784630i | \(0.287147\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0267283 | + | 0.0516060i | 0.000914088 | + | 0.00176489i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.0651 | 0.822049 | 0.411024 | − | 0.911624i | \(-0.365171\pi\) | ||||
0.411024 | + | 0.911624i | \(0.365171\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.3172 | 0.556737 | 0.278368 | − | 0.960474i | \(-0.410206\pi\) | ||||
0.278368 | + | 0.960474i | \(0.410206\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.05898 | − | 47.3791i | 0.206490 | − | 1.61468i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.64675 | − | 16.7087i | 0.328379 | − | 0.568770i | −0.653811 | − | 0.756658i | \(-0.726831\pi\) |
0.982190 | + | 0.187888i | \(0.0601643\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.9428 | − | 34.5420i | −0.678077 | − | 1.17446i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.312576 | − | 13.6740i | 0.0106156 | − | 0.464393i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.6025 | + | 30.4884i | 0.597124 | + | 1.03425i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.9945 | 0.846907 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.9482 | − | 23.0691i | −0.404385 | − | 0.780771i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.87722 | + | 22.1618i | 0.333911 | + | 0.749205i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.2928 | 1.02291 | 0.511457 | − | 0.859309i | \(-0.329106\pi\) | ||||
0.511457 | + | 0.859309i | \(0.329106\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.26919 | − | 0.771968i | −0.0428087 | − | 0.0260378i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.4943 | 0.656779 | 0.328390 | − | 0.944542i | \(-0.393494\pi\) | ||||
0.328390 | + | 0.944542i | \(0.393494\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.5302 | −1.59952 | −0.799759 | − | 0.600321i | \(-0.795040\pi\) | ||||
−0.799759 | + | 0.600321i | \(0.795040\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.0522880 | + | 2.28740i | −0.00175764 | + | 0.0768902i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.11892 | 0.138300 | 0.0691499 | − | 0.997606i | \(-0.477971\pi\) | ||||
0.0691499 | + | 0.997606i | \(0.477971\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.11114 | + | 4.73682i | 0.0708052 | + | 0.158868i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.5359 | − | 46.6892i | −0.721479 | − | 1.56415i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.0165937 | 0.000555287 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.4409 | − | 37.1367i | −0.716689 | − | 1.24134i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.84680 | − | 2.94800i | −0.161830 | − | 0.0984309i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29.9056 | + | 51.7981i | 0.997408 | + | 1.72756i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.4547 | − | 31.9645i | 0.614815 | − | 1.06489i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 37.4476 | − | 15.6742i | 1.24618 | − | 0.521605i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.0417 | −0.533243 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.14168 | −0.270340 | −0.135170 | − | 0.990822i | \(-0.543158\pi\) | ||||
−0.135170 | + | 0.990822i | \(0.543158\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.0972 | + | 23.5895i | −0.500741 | + | 0.782415i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.6454 | − | 42.6871i | 0.816540 | − | 1.41429i | −0.0916774 | − | 0.995789i | \(-0.529223\pi\) |
0.908217 | − | 0.418499i | \(-0.137444\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.47809 | − | 2.56013i | 0.0489177 | − | 0.0847279i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 33.5667 | + | 20.4165i | 1.10968 | + | 0.674948i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.29553 | + | 9.63801i | 0.141851 | + | 0.318275i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.71585 | − | 8.16809i | 0.155561 | − | 0.269440i | −0.777702 | − | 0.628633i | \(-0.783615\pi\) |
0.933263 | + | 0.359193i | \(0.116948\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.09085 | + | 0.596989i | −0.0359448 | + | 0.0196715i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.9415 | − | 24.1473i | −0.458889 | − | 0.794819i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.36218 | + | 7.55552i | −0.143428 | + | 0.248424i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −26.2278 | + | 40.9813i | −0.861433 | + | 1.34600i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.7369 | − | 25.5251i | −0.483503 | − | 0.837452i | 0.516317 | − | 0.856397i | \(-0.327303\pi\) |
−0.999821 | + | 0.0189453i | \(0.993969\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0166487 | + | 0.0511066i | 0.000545641 | + | 0.00167495i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.374142 | − | 16.3673i | 0.0122489 | − | 0.535841i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −35.9587 | − | 62.2823i | −1.17597 | − | 2.03685i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.3451 | −1.77538 | −0.887688 | − | 0.460445i | \(-0.847690\pi\) | ||||
−0.887688 | + | 0.460445i | \(0.847690\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34.4257 | − | 20.9390i | −1.12344 | − | 0.683317i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.49087 | − | 2.58226i | 0.0486008 | − | 0.0841791i | −0.840702 | − | 0.541499i | \(-0.817857\pi\) |
0.889302 | + | 0.457320i | \(0.151190\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.48005 | − | 6.02763i | −0.113326 | − | 0.196287i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 32.5731 | − | 11.9158i | 1.05960 | − | 0.387621i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.1646 | + | 26.2659i | 0.492783 | + | 0.853526i | 0.999965 | − | 0.00831303i | \(-0.00264615\pi\) |
−0.507182 | + | 0.861839i | \(0.669313\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.45850 | + | 12.9185i | −0.242113 | + | 0.419352i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.5860 | + | 11.9129i | 0.635119 | + | 0.386303i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.380127 | 0.0123135 | 0.00615676 | − | 0.999981i | \(-0.498040\pi\) | ||||
0.00615676 | + | 0.999981i | \(0.498040\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.22360 | + | 9.04754i | 0.169032 | + | 0.292771i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.74161 | + | 76.1889i | −0.0562983 | + | 2.46284i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.97924 | − | 17.9032i | −0.257663 | − | 0.578126i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.6558 | − | 25.3845i | −0.472766 | − | 0.818855i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.4221 | + | 23.9842i | 0.400298 | + | 0.772881i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.70796 | + | 16.8147i | −0.312510 | + | 0.541284i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.6744 | + | 39.2732i | 0.729160 | + | 1.26294i | 0.957239 | + | 0.289300i | \(0.0934224\pi\) |
−0.228078 | + | 0.973643i | \(0.573244\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.0582135 | + | 0.0318584i | −0.00187009 | + | 0.00102344i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.3746 | − | 47.4141i | 0.878491 | − | 1.52159i | 0.0254951 | − | 0.999675i | \(-0.491884\pi\) |
0.852996 | − | 0.521917i | \(-0.174783\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.5323 | − | 29.6604i | 0.690292 | − | 0.950870i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.90801 | + | 6.02642i | 0.317310 | + | 0.193000i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.35656 | + | 2.34962i | −0.0434001 | + | 0.0751711i | −0.886909 | − | 0.461943i | \(-0.847152\pi\) |
0.843509 | + | 0.537114i | \(0.180486\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.80371 | − | 11.7844i | 0.217448 | − | 0.376630i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.2705 | + | 1.01870i | 0.711042 | + | 0.0325246i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.7656 | −1.36401 | −0.682006 | − | 0.731347i | \(-0.738892\pi\) | ||||
−0.682006 | + | 0.731347i | \(0.738892\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.31318 | −0.264880 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.25621 | − | 9.82314i | 0.0399857 | − | 0.312674i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.95771 | − | 5.12291i | 0.0940498 | − | 0.162899i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.6731 | − | 51.3954i | −0.942598 | − | 1.63263i | −0.760491 | − | 0.649349i | \(-0.775042\pi\) |
−0.182107 | − | 0.983279i | \(-0.558292\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 45.0353 | + | 27.3921i | 1.42915 | + | 0.869262i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.4063 | + | 35.3447i | 0.646922 | + | 1.12050i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.0641 | 1.39552 | 0.697762 | − | 0.716330i | \(-0.254179\pi\) | ||||
0.697762 | + | 0.716330i | \(0.254179\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.5554 | − | 18.5364i | −0.871814 | − | 0.586465i |
(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 | 1008.2.t.k.961.2 | 22 | ||
3.2 | odd | 2 | 3024.2.t.l.289.9 | 22 | |||
4.3 | odd | 2 | 504.2.t.d.457.10 | yes | 22 | ||
7.4 | even | 3 | 1008.2.q.k.529.9 | 22 | |||
9.4 | even | 3 | 1008.2.q.k.625.9 | 22 | |||
9.5 | odd | 6 | 3024.2.q.k.2305.3 | 22 | |||
12.11 | even | 2 | 1512.2.t.d.289.9 | 22 | |||
21.11 | odd | 6 | 3024.2.q.k.2881.3 | 22 | |||
28.11 | odd | 6 | 504.2.q.d.25.3 | ✓ | 22 | ||
36.23 | even | 6 | 1512.2.q.c.793.3 | 22 | |||
36.31 | odd | 6 | 504.2.q.d.121.3 | yes | 22 | ||
63.4 | even | 3 | inner | 1008.2.t.k.193.2 | 22 | ||
63.32 | odd | 6 | 3024.2.t.l.1873.9 | 22 | |||
84.11 | even | 6 | 1512.2.q.c.1369.3 | 22 | |||
252.67 | odd | 6 | 504.2.t.d.193.10 | yes | 22 | ||
252.95 | even | 6 | 1512.2.t.d.361.9 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.3 | ✓ | 22 | 28.11 | odd | 6 | ||
504.2.q.d.121.3 | yes | 22 | 36.31 | odd | 6 | ||
504.2.t.d.193.10 | yes | 22 | 252.67 | odd | 6 | ||
504.2.t.d.457.10 | yes | 22 | 4.3 | odd | 2 | ||
1008.2.q.k.529.9 | 22 | 7.4 | even | 3 | |||
1008.2.q.k.625.9 | 22 | 9.4 | even | 3 | |||
1008.2.t.k.193.2 | 22 | 63.4 | even | 3 | inner | ||
1008.2.t.k.961.2 | 22 | 1.1 | even | 1 | trivial | ||
1512.2.q.c.793.3 | 22 | 36.23 | even | 6 | |||
1512.2.q.c.1369.3 | 22 | 84.11 | even | 6 | |||
1512.2.t.d.289.9 | 22 | 12.11 | even | 2 | |||
1512.2.t.d.361.9 | 22 | 252.95 | even | 6 | |||
3024.2.q.k.2305.3 | 22 | 9.5 | odd | 6 | |||
3024.2.q.k.2881.3 | 22 | 21.11 | odd | 6 | |||
3024.2.t.l.289.9 | 22 | 3.2 | odd | 2 | |||
3024.2.t.l.1873.9 | 22 | 63.32 | odd | 6 |