Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (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: | \(24.1467615712\) |
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 | 2881.3 | ||
Character | \(\chi\) | \(=\) | 3024.2881 |
Dual form | 3024.2.q.k.2305.3 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.26145 | + | 2.18490i | −0.564139 | + | 0.977117i | 0.432991 | + | 0.901398i | \(0.357458\pi\) |
−0.997129 | + | 0.0757184i | \(0.975875\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63136 | + | 0.275550i | −0.994562 | + | 0.104148i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.85648 | + | 4.94757i | 0.861262 | + | 1.49175i | 0.870712 | + | 0.491794i | \(0.163659\pi\) |
−0.00944971 | + | 0.999955i | \(0.503008\pi\) | |||||||
\(12\) | 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 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.49483 | + | 4.32118i | −0.605086 | + | 1.04804i | 0.386952 | + | 0.922100i | \(0.373528\pi\) |
−0.992038 | + | 0.125939i | \(0.959806\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.00383929 | + | 0.00664984i | 0.000880793 | + | 0.00152558i | 0.866465 | − | 0.499237i | \(-0.166386\pi\) |
−0.865585 | + | 0.500763i | \(0.833053\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.333877 | + | 0.578292i | −0.0696181 | + | 0.120582i | −0.898733 | − | 0.438496i | \(-0.855511\pi\) |
0.829115 | + | 0.559078i | \(0.188845\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.682524 | − | 1.18217i | −0.136505 | − | 0.236433i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.85082 | + | 6.66981i | −0.715079 | + | 1.23855i | 0.247851 | + | 0.968798i | \(0.420276\pi\) |
−0.962929 | + | 0.269754i | \(0.913058\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.76605 | 1.39482 | 0.697412 | − | 0.716671i | \(-0.254335\pi\) | ||||
0.697412 | + | 0.716671i | \(0.254335\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.71729 | − | 6.09686i | 0.459306 | − | 1.03056i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.19562 | − | 5.53498i | −0.525357 | − | 0.909946i | −0.999564 | − | 0.0295319i | \(-0.990598\pi\) |
0.474207 | − | 0.880414i | \(-0.342735\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.21159 | − | 9.02673i | −0.813913 | − | 1.40974i | −0.910106 | − | 0.414376i | \(-0.864000\pi\) |
0.0961931 | − | 0.995363i | \(-0.469333\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.16104 | 0.315220 | 0.157610 | − | 0.987501i | \(-0.449621\pi\) | ||||
0.157610 | + | 0.987501i | \(0.449621\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.84814 | − | 1.45015i | 0.978306 | − | 0.207164i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.69858 | − | 6.40613i | 0.508039 | − | 0.879950i | −0.491917 | − | 0.870642i | \(-0.663704\pi\) |
0.999957 | − | 0.00930815i | \(-0.00296292\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.4133 | −1.94348 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.523594 | −0.0681661 | −0.0340831 | − | 0.999419i | \(-0.510851\pi\) | ||||
−0.0340831 | + | 0.999419i | \(0.510851\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.99082 | −1.15116 | −0.575578 | − | 0.817747i | \(-0.695223\pi\) | ||||
−0.575578 | + | 0.817747i | \(0.695223\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.3746 | 1.53488 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.09582 | 0.622554 | 0.311277 | − | 0.950319i | \(-0.399243\pi\) | ||||
0.311277 | + | 0.950319i | \(0.399243\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.68471 | −0.674651 | −0.337325 | − | 0.941388i | \(-0.609522\pi\) | ||||
−0.337325 | + | 0.941388i | \(0.609522\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.52062 | + | 2.63379i | −0.177975 | + | 0.308262i | −0.941187 | − | 0.337887i | \(-0.890288\pi\) |
0.763212 | + | 0.646148i | \(0.223621\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.87975 | − | 12.2318i | −1.01194 | − | 1.39394i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.16230 | −0.693313 | −0.346657 | − | 0.937992i | \(-0.612683\pi\) | ||||
−0.346657 | + | 0.937992i | \(0.612683\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.258726 | + | 0.448126i | −0.0283988 | + | 0.0491882i | −0.879876 | − | 0.475204i | \(-0.842374\pi\) |
0.851477 | + | 0.524392i | \(0.175708\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.29422 | − | 10.9019i | −0.682704 | − | 1.18248i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.19093 | − | 2.06274i | −0.126238 | − | 0.218650i | 0.795978 | − | 0.605325i | \(-0.206957\pi\) |
−0.922216 | + | 0.386675i | \(0.873624\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.62377 | + | 10.5017i | 0.799188 | + | 1.10087i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0193723 | −0.00198756 | ||||||||
\(96\) | 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 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.66783 | − | 8.08492i | −0.464466 | − | 0.804479i | 0.534711 | − | 0.845035i | \(-0.320420\pi\) |
−0.999177 | + | 0.0405558i | \(0.987087\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.10926 | − | 14.0456i | 0.799029 | − | 1.38396i | −0.121220 | − | 0.992626i | \(-0.538681\pi\) |
0.920249 | − | 0.391333i | \(-0.127986\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.50171 | + | 7.79718i | 0.435196 | + | 0.753782i | 0.997312 | − | 0.0732767i | \(-0.0233456\pi\) |
−0.562115 | + | 0.827059i | \(0.690012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.71563 | − | 6.43566i | 0.355893 | − | 0.616424i | −0.631378 | − | 0.775476i | \(-0.717510\pi\) |
0.987270 | + | 0.159051i | \(0.0508435\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.14642 | − | 12.3780i | −0.672278 | − | 1.16442i | −0.977256 | − | 0.212061i | \(-0.931982\pi\) |
0.304978 | − | 0.952359i | \(-0.401351\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.842339 | − | 1.45897i | −0.0785486 | − | 0.136050i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.37411 | − | 12.0580i | 0.492644 | − | 1.10536i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8190 | + | 18.7390i | −0.983544 | + | 1.70355i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.99412 | − | 3.45392i | 0.174227 | − | 0.301771i | −0.765666 | − | 0.643238i | \(-0.777591\pi\) |
0.939894 | + | 0.341467i | \(0.110924\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0119349 | − | 0.0164402i | −0.00103489 | − | 0.00142555i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.70422 | − | 6.41589i | −0.316473 | − | 0.548147i | 0.663277 | − | 0.748374i | \(-0.269165\pi\) |
−0.979749 | + | 0.200227i | \(0.935832\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 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 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.05202 | + | 12.2144i | −0.577724 | + | 1.00065i | 0.418016 | + | 0.908440i | \(0.362726\pi\) |
−0.995740 | + | 0.0922071i | \(0.970608\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.30027 | − | 9.18034i | −0.431330 | − | 0.747086i | 0.565658 | − | 0.824640i | \(-0.308622\pi\) |
−0.996988 | + | 0.0775543i | \(0.975289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.79650 | + | 16.9680i | −0.786874 | + | 1.36291i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.259558 | −0.0207150 | −0.0103575 | − | 0.999946i | \(-0.503297\pi\) | ||||
−0.0103575 | + | 0.999946i | \(0.503297\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.719203 | − | 1.61370i | 0.0566811 | − | 0.127177i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.31882 | − | 10.9445i | −0.494928 | − | 0.857241i | 0.505055 | − | 0.863087i | \(-0.331472\pi\) |
−0.999983 | + | 0.00584647i | \(0.998139\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.74959 | − | 9.95859i | −0.444917 | − | 0.770619i | 0.553129 | − | 0.833095i | \(-0.313433\pi\) |
−0.998046 | + | 0.0624765i | \(0.980100\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.52905 | + | 9.57659i | −0.425311 | + | 0.736661i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.8094 | 1.20197 | 0.600984 | − | 0.799261i | \(-0.294775\pi\) | ||||
0.600984 | + | 0.799261i | \(0.294775\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.12171 | + | 2.92264i | 0.160387 | + | 0.220931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.49849 | + | 14.7198i | −0.635207 | + | 1.10021i | 0.351265 | + | 0.936276i | \(0.385752\pi\) |
−0.986471 | + | 0.163934i | \(0.947582\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.35841 | 0.472617 | 0.236308 | − | 0.971678i | \(-0.424062\pi\) | ||||
0.236308 | + | 0.971678i | \(0.424062\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.1245 | 1.18550 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −28.5058 | −2.08455 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.14094 | −0.299628 | −0.149814 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149814 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.69586 | −0.553960 | −0.276980 | − | 0.960876i | \(-0.589334\pi\) | ||||
−0.276980 | + | 0.960876i | \(0.589334\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.29508 | −0.234765 | −0.117383 | − | 0.993087i | \(-0.537450\pi\) | ||||
−0.117383 | + | 0.993087i | \(0.537450\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.08840 | + | 14.0095i | −0.573371 | + | 0.993108i | 0.422845 | + | 0.906202i | \(0.361031\pi\) |
−0.996216 | + | 0.0869063i | \(0.972302\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.29503 | − | 18.6118i | 0.582197 | − | 1.30629i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 26.2967 | 1.83664 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 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 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.4738 | 1.64629 | ||||||||
\(222\) | 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 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.84470 | + | 4.92716i | 0.188809 | + | 0.327027i | 0.944853 | − | 0.327493i | \(-0.106204\pi\) |
−0.756044 | + | 0.654520i | \(0.772871\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.42708 | + | 12.8641i | −0.490795 | + | 0.850082i | −0.999944 | − | 0.0105964i | \(-0.996627\pi\) |
0.509149 | + | 0.860679i | \(0.329960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.70652 | − | 11.6160i | −0.439358 | − | 0.760991i | 0.558282 | − | 0.829652i | \(-0.311461\pi\) |
−0.997640 | + | 0.0686603i | \(0.978128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.72605 | + | 4.72166i | −0.177828 | + | 0.308007i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.33123 | − | 16.1622i | −0.603587 | − | 1.04544i | −0.992273 | − | 0.124073i | \(-0.960404\pi\) |
0.388686 | − | 0.921370i | \(-0.372929\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.7080 | + | 18.5468i | 0.689762 | + | 1.19470i | 0.971915 | + | 0.235333i | \(0.0756181\pi\) |
−0.282153 | + | 0.959369i | \(0.591049\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.47018 | + | 16.7918i | −0.349477 | + | 1.07279i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0188313 | − | 0.0326168i | 0.00119821 | − | 0.00207536i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.462898 | −0.0292179 | −0.0146089 | − | 0.999893i | \(-0.504650\pi\) | ||||
−0.0146089 | + | 0.999893i | \(0.504650\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.81485 | −0.239838 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.401256 | − | 0.694996i | 0.0250297 | − | 0.0433527i | −0.853239 | − | 0.521520i | \(-0.825365\pi\) |
0.878269 | + | 0.478167i | \(0.158699\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.93401 | + | 13.6840i | 0.617270 | + | 0.850282i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.100693 | − | 0.174406i | −0.00620902 | − | 0.0107543i | 0.862904 | − | 0.505368i | \(-0.168643\pi\) |
−0.869113 | + | 0.494613i | \(0.835310\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.33117 | + | 16.1621i | 0.573209 | + | 0.992828i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.1773 | − | 19.3596i | 0.681490 | − | 1.18038i | −0.293036 | − | 0.956101i | \(-0.594666\pi\) |
0.974526 | − | 0.224274i | \(-0.0720011\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.78925 | + | 3.09907i | 0.108689 | + | 0.188255i | 0.915240 | − | 0.402910i | \(-0.132001\pi\) |
−0.806550 | + | 0.591166i | \(0.798668\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.89924 | − | 6.75367i | 0.235133 | − | 0.407262i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.05336 | + | 8.75267i | 0.303627 | + | 0.525897i | 0.976955 | − | 0.213447i | \(-0.0684690\pi\) |
−0.673328 | + | 0.739344i | \(0.735136\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.7114 | + | 22.0167i | −0.758296 | + | 1.31341i | 0.185422 | + | 0.982659i | \(0.440635\pi\) |
−0.943719 | + | 0.330749i | \(0.892699\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.87666 | −0.230443 | −0.115222 | − | 0.993340i | \(-0.536758\pi\) | ||||
−0.115222 | + | 0.993340i | \(0.536758\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 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 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.428834 | − | 0.742762i | −0.0250527 | − | 0.0433926i | 0.853227 | − | 0.521539i | \(-0.174642\pi\) |
−0.878280 | + | 0.478147i | \(0.841309\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.660489 | − | 1.14400i | 0.0384551 | − | 0.0666063i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.27527 | 0.189414 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.54124 | − | 21.4079i | 0.549948 | − | 1.23393i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 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 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.45213 | −0.535981 | −0.267990 | − | 0.963422i | \(-0.586360\pi\) | ||||
−0.267990 | + | 0.963422i | \(0.586360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.2635 | −1.31493 | −0.657464 | − | 0.753486i | \(-0.728371\pi\) | ||||
−0.657464 | + | 0.753486i | \(0.728371\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.2354 | −0.743375 | −0.371687 | − | 0.928358i | \(-0.621221\pi\) | ||||
−0.371687 | + | 0.928358i | \(0.621221\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −43.9992 | −2.46348 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0383135 | −0.00213182 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.34772 | + | 5.79841i | −0.185698 | + | 0.321638i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.68649 | + | 0.595476i | −0.313506 | + | 0.0328297i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.4330 | 1.67275 | 0.836375 | − | 0.548158i | \(-0.184671\pi\) | ||||
0.836375 | + | 0.548158i | \(0.184671\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 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 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.6072 | −1.53571 | −0.767856 | − | 0.640622i | \(-0.778677\pi\) | ||||
−0.767856 | + | 0.640622i | \(0.778677\pi\) | |||||||
\(348\) | 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 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.29541 | + | 12.6360i | 0.388295 | + | 0.672547i | 0.992220 | − | 0.124494i | \(-0.0397307\pi\) |
−0.603925 | + | 0.797041i | \(0.706397\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.17099 | − | 12.4205i | 0.380596 | − | 0.659212i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.05831 | − | 1.83304i | −0.0558554 | − | 0.0967443i | 0.836746 | − | 0.547592i | \(-0.184455\pi\) |
−0.892601 | + | 0.450847i | \(0.851122\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.49997 | − | 16.4544i | 0.499998 | − | 0.866023i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.83638 | − | 6.64480i | −0.200805 | − | 0.347805i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.33104 | + | 5.76954i | 0.173879 | + | 0.301167i | 0.939773 | − | 0.341800i | \(-0.111036\pi\) |
−0.765894 | + | 0.642967i | \(0.777703\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.96710 | + | 17.8760i | −0.413631 | + | 0.928076i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.24916 | − | 10.8239i | 0.323569 | − | 0.560438i | −0.657653 | − | 0.753321i | \(-0.728451\pi\) |
0.981222 | + | 0.192883i | \(0.0617838\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.33740 | − | 2.31644i | 0.0683379 | − | 0.118365i | −0.829832 | − | 0.558013i | \(-0.811564\pi\) |
0.898170 | + | 0.439649i | \(0.144897\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 37.9265 | − | 3.97158i | 1.93292 | − | 0.202411i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.98155 | − | 3.43214i | −0.100469 | − | 0.174017i | 0.811409 | − | 0.584478i | \(-0.198701\pi\) |
−0.911878 | + | 0.410462i | \(0.865368\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.66593 | − | 2.88548i | −0.0842499 | − | 0.145925i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.77345 | − | 13.4640i | 0.391125 | − | 0.677448i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.2978 | + | 17.8362i | 0.516829 | + | 0.895175i | 0.999809 | + | 0.0195431i | \(0.00622114\pi\) |
−0.482980 | + | 0.875632i | \(0.660446\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.91979 | + | 3.32517i | −0.0958696 | + | 0.166051i | −0.909971 | − | 0.414671i | \(-0.863897\pi\) |
0.814102 | + | 0.580722i | \(0.197230\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.0459 | − | 32.9884i | −0.948742 | − | 1.64327i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.2565 | − | 31.6212i | 0.904940 | − | 1.56740i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.4227 | −1.45486 | −0.727428 | − | 0.686184i | \(-0.759285\pi\) | ||||
−0.727428 | + | 0.686184i | \(0.759285\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 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 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.40821 | + | 7.63525i | 0.215355 | + | 0.373006i | 0.953382 | − | 0.301765i | \(-0.0975757\pi\) |
−0.738027 | + | 0.674771i | \(0.764242\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.81113 | 0.330388 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.6581 | − | 2.47742i | 1.14490 | − | 0.119891i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.8099 | + | 22.1873i | −0.617030 | + | 1.06873i | 0.372995 | + | 0.927833i | \(0.378331\pi\) |
−0.990025 | + | 0.140893i | \(0.955003\pi\) | |||||||
\(432\) | 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 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.00512739 | −0.000245277 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.9192 | −1.47569 | −0.737846 | − | 0.674969i | \(-0.764157\pi\) | ||||
−0.737846 | + | 0.674969i | \(0.764157\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.31087 | −0.442373 | −0.221186 | − | 0.975232i | \(-0.570993\pi\) | ||||
−0.221186 | + | 0.975232i | \(0.570993\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00918 | 0.284862 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.8055 | −1.12345 | −0.561724 | − | 0.827324i | \(-0.689862\pi\) | ||||
−0.561724 | + | 0.827324i | \(0.689862\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.7736 | − | 51.5694i | 1.40198 | − | 2.42831i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −32.5621 | + | 3.40983i | −1.52653 | + | 0.159855i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.8110 | −0.646053 | −0.323027 | − | 0.946390i | \(-0.604700\pi\) | ||||
−0.323027 | + | 0.946390i | \(0.604700\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.00256407 | − | 0.00444110i | 0.000119421 | − | 0.000206843i | −0.865966 | − | 0.500103i | \(-0.833295\pi\) |
0.866085 | + | 0.499897i | \(0.166629\pi\) | |||||||
\(462\) | 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 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.0484 | − | 20.8684i | −0.557532 | − | 0.965673i | −0.997702 | − | 0.0677588i | \(-0.978415\pi\) |
0.440170 | − | 0.897914i | \(-0.354918\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.4090 | + | 1.40416i | −0.619168 | + | 0.0648379i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −50.6094 | −2.32702 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.00524081 | − | 0.00907735i | 0.000240465 | − | 0.000416497i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.39114 | − | 12.8018i | −0.337710 | − | 0.584931i | 0.646292 | − | 0.763091i | \(-0.276319\pi\) |
−0.984002 | + | 0.178160i | \(0.942986\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.6742 | + | 27.1486i | −0.714683 | + | 1.23787i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.9240 | + | 18.9210i | 0.496035 | + | 0.859158i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.38360 | + | 16.2529i | −0.425211 | + | 0.736488i | −0.996440 | − | 0.0843033i | \(-0.973134\pi\) |
0.571229 | + | 0.820791i | \(0.306467\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.2871 | + | 31.6741i | 0.825284 | + | 1.42943i | 0.901702 | + | 0.432358i | \(0.142318\pi\) |
−0.0764182 | + | 0.997076i | \(0.524348\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.2143 | − | 33.2801i | −0.865368 | − | 1.49886i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.9585 | − | 1.56642i | 0.670982 | − | 0.0702637i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.31591 | − | 4.01127i | 0.103674 | − | 0.179569i | −0.809521 | − | 0.587090i | \(-0.800273\pi\) |
0.913196 | + | 0.407521i | \(0.133607\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.4143 | 0.731879 | 0.365940 | − | 0.930639i | \(-0.380748\pi\) | ||||
0.365940 | + | 0.930639i | \(0.380748\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.5530 | 1.04809 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.24169 | − | 9.07888i | 0.232334 | − | 0.402414i | −0.726161 | − | 0.687525i | \(-0.758697\pi\) |
0.958495 | + | 0.285111i | \(0.0920305\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.27556 | − | 7.34947i | 0.144902 | − | 0.325121i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.4589 | + | 35.4358i | 0.901526 | + | 1.56149i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.17298 | + | 10.6919i | 0.271487 | + | 0.470230i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.0087 | − | 19.0675i | 0.482298 | − | 0.835364i | −0.517496 | − | 0.855686i | \(-0.673136\pi\) |
0.999793 | + | 0.0203215i | \(0.00646899\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.18541 | + | 2.05320i | 0.0518346 | + | 0.0897801i | 0.890778 | − | 0.454438i | \(-0.150160\pi\) |
−0.838944 | + | 0.544218i | \(0.816826\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.3750 | + | 33.5585i | −0.843988 | + | 1.46183i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2771 | + | 19.5324i | 0.490307 | + | 0.849236i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25.5623 | + | 44.2753i | −1.10723 | + | 1.91777i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.7147 | −0.982044 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.7363 | + | 29.7394i | 1.15161 | + | 1.28097i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.65209 | + | 11.5218i | 0.285996 | + | 0.495359i | 0.972850 | − | 0.231436i | \(-0.0743423\pi\) |
−0.686854 | + | 0.726795i | \(0.741009\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0591375 | −0.00251934 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.2153 | − | 1.69802i | 0.689543 | − | 0.0722074i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.09601 | + | 12.2907i | −0.300668 | + | 0.520772i | −0.976287 | − | 0.216479i | \(-0.930543\pi\) |
0.675620 | + | 0.737250i | \(0.263876\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.4511 | 1.83778 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.03971 | 0.296688 | 0.148344 | − | 0.988936i | \(-0.452606\pi\) | ||||
0.148344 | + | 0.988936i | \(0.452606\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.0595 | 1.51703 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.3016 | 0.767244 | 0.383622 | − | 0.923490i | \(-0.374677\pi\) | ||||
0.383622 | + | 0.923490i | \(0.374677\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.4383 | 1.27380 | 0.636902 | − | 0.770944i | \(-0.280215\pi\) | ||||
0.636902 | + | 0.770944i | \(0.280215\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.911516 | 0.0380128 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.65385 | − | 9.79275i | 0.235373 | − | 0.407678i | −0.724008 | − | 0.689791i | \(-0.757702\pi\) |
0.959381 | + | 0.282114i | \(0.0910356\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.557320 | − | 1.25047i | 0.0231215 | − | 0.0518784i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42.2597 | 1.75022 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.89755 | + | 17.1431i | −0.408516 | + | 0.707570i | −0.994724 | − | 0.102591i | \(-0.967287\pi\) |
0.586208 | + | 0.810161i | \(0.300620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0298161 | + | 0.0516430i | 0.00122855 | + | 0.00212791i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.69067 | − | 4.66038i | −0.110493 | − | 0.191379i | 0.805476 | − | 0.592628i | \(-0.201910\pi\) |
−0.915969 | + | 0.401249i | \(0.868576\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.5664 | + | 26.9525i | 0.802145 | + | 1.10495i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.25959 | 0.0923243 | 0.0461622 | − | 0.998934i | \(-0.485301\pi\) | ||||
0.0461622 | + | 0.998934i | \(0.485301\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.2953 | − | 47.2768i | −1.10971 | − | 1.92207i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.10803 | − | 14.0435i | 0.329095 | − | 0.570009i | −0.653238 | − | 0.757153i | \(-0.726590\pi\) |
0.982333 | + | 0.187144i | \(0.0599231\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.29985 | − | 9.17961i | −0.214409 | − | 0.371367i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.6357 | − | 37.4741i | 0.873857 | − | 1.51357i | 0.0158822 | − | 0.999874i | \(-0.494944\pi\) |
0.857975 | − | 0.513691i | \(-0.171722\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.92248 | + | 10.2580i | 0.238430 | + | 0.412973i | 0.960264 | − | 0.279093i | \(-0.0900339\pi\) |
−0.721834 | + | 0.692066i | \(0.756701\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.1644 | + | 34.9257i | 0.810475 | + | 1.40378i | 0.912532 | + | 0.409006i | \(0.134124\pi\) |
−0.102057 | + | 0.994779i | \(0.532542\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.70215 | + | 5.09967i | 0.148323 | + | 0.204314i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.9809 | − | 25.9478i | 0.599238 | − | 1.03791i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.47259 | + | 4.28265i | −0.0981217 | + | 0.169952i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.9546 | − | 25.5329i | −0.909496 | − | 1.01165i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.76975 | + | 15.1896i | 0.346384 | + | 0.599955i | 0.985604 | − | 0.169069i | \(-0.0540761\pi\) |
−0.639220 | + | 0.769024i | \(0.720743\pi\) | |||||||
\(642\) | 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 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.3252 | − | 19.6159i | 0.445240 | − | 0.771179i | −0.552828 | − | 0.833295i | \(-0.686452\pi\) |
0.998069 | + | 0.0621160i | \(0.0197849\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.49564 | − | 2.59052i | −0.0587089 | − | 0.101687i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.392054 | + | 0.679058i | −0.0153423 | + | 0.0265736i | −0.873595 | − | 0.486654i | \(-0.838217\pi\) |
0.858252 | + | 0.513228i | \(0.171550\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.03098 | + | 8.71392i | 0.196577 | + | 0.340481i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.7219 | + | 28.9632i | −0.651392 | + | 1.12824i | 0.331393 | + | 0.943493i | \(0.392481\pi\) |
−0.982785 | + | 0.184752i | \(0.940852\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.06516 | 0.119221 | 0.0596104 | − | 0.998222i | \(-0.481014\pi\) | ||||
0.0596104 | + | 0.998222i | \(0.481014\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 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 | 0 | ||||||||
\(670\) | 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 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.7164 | 0.450296 | 0.225148 | − | 0.974325i | \(-0.427713\pi\) | ||||
0.225148 | + | 0.974325i | \(0.427713\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.32711 | + | 20.9275i | −0.357942 | + | 0.803124i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.7190 | − | 35.8864i | 0.792791 | − | 1.37315i | −0.131441 | − | 0.991324i | \(-0.541960\pi\) |
0.924232 | − | 0.381831i | \(-0.124706\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.6908 | 0.714138 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.2824 | −1.38225 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.91350 | 0.263002 | 0.131501 | − | 0.991316i | \(-0.458020\pi\) | ||||
0.131501 | + | 0.991316i | \(0.458020\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 34.9503 | 1.32574 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 52.0081 | 1.96995 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.1954 | −1.48039 | −0.740195 | − | 0.672392i | \(-0.765267\pi\) | ||||
−0.740195 | + | 0.672392i | \(0.765267\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0245378 | − | 0.0425008i | 0.000925462 | − | 0.00160295i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.5106 | + | 19.9881i | 0.545726 | + | 0.751731i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.4871 | 0.769409 | 0.384705 | − | 0.923040i | \(-0.374303\pi\) | ||||
0.384705 | + | 0.923040i | \(0.374303\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 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 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.1300 | + | 29.6700i | 0.638840 | + | 1.10650i | 0.985688 | + | 0.168582i | \(0.0539187\pi\) |
−0.346848 | + | 0.937921i | \(0.612748\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.4681 | + | 39.1937i | −0.650547 | + | 1.45965i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.5131 | 0.390447 | ||||||||
\(726\) | 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 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.1010 | − | 38.2800i | −0.817433 | − | 1.41584i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.7887 | + | 34.2750i | −0.730911 | + | 1.26597i | 0.225584 | + | 0.974224i | \(0.427571\pi\) |
−0.956494 | + | 0.291751i | \(0.905762\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.5561 | + | 25.2119i | 0.536182 | + | 0.928694i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.8407 | + | 18.7767i | −0.398783 | + | 0.690712i | −0.993576 | − | 0.113167i | \(-0.963901\pi\) |
0.594793 | + | 0.803879i | \(0.297234\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.5692 | + | 28.6987i | 0.607864 | + | 1.05285i | 0.991592 | + | 0.129406i | \(0.0413069\pi\) |
−0.383727 | + | 0.923446i | \(0.625360\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.7916 | − | 30.8159i | −0.651832 | − | 1.12901i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.9941 | − | 19.2768i | −0.511335 | − | 0.704358i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.9662 | + | 22.4581i | −0.473144 | + | 0.819509i | −0.999527 | − | 0.0307381i | \(-0.990214\pi\) |
0.526384 | + | 0.850247i | \(0.323548\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.2648 | + | 31.6355i | −0.662097 | + | 1.14679i | 0.317967 | + | 0.948102i | \(0.397000\pi\) |
−0.980064 | + | 0.198684i | \(0.936333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.00382 | + | 17.9584i | −0.289758 | + | 0.650138i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.28409 | + | 2.22411i | 0.0463658 | + | 0.0803079i | ||||
\(768\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.1309 | + | 27.9395i | −0.580187 | + | 1.00491i | 0.415270 | + | 0.909698i | \(0.363687\pi\) |
−0.995457 | + | 0.0952148i | \(0.969646\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.30051 | − | 9.18076i | −0.190400 | − | 0.329783i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0400175 | − | 0.0693124i | 0.00143378 | − | 0.00248337i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.2383 | − | 28.1255i | −0.581051 | − | 1.00641i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.327420 | − | 0.567107i | 0.0116861 | − | 0.0202409i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.7676 | −1.09675 | −0.548373 | − | 0.836234i | \(-0.684753\pi\) | ||||
−0.548373 | + | 0.836234i | \(0.684753\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 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 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.59378 | + | 6.22460i | 0.127298 | + | 0.220487i | 0.922629 | − | 0.385689i | \(-0.126036\pi\) |
−0.795331 | + | 0.606176i | \(0.792703\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.39144 | + | 9.33824i | −0.190735 | + | 0.330363i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.3745 | −0.613133 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.61852 | + | 3.60699i | 0.0922908 | + | 0.127130i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.3886 | − | 40.5103i | 0.822301 | − | 1.42427i | −0.0816637 | − | 0.996660i | \(-0.526023\pi\) |
0.903965 | − | 0.427607i | \(-0.140643\pi\) | |||||||
\(810\) | 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 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.8836 | 1.11683 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.0680221 | −0.00237979 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.2215 | 0.601034 | 0.300517 | − | 0.953776i | \(-0.402841\pi\) | ||||
0.300517 | + | 0.953776i | \(0.402841\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.5434 | −0.402378 | −0.201189 | − | 0.979552i | \(-0.564480\pi\) | ||||
−0.201189 | + | 0.979552i | \(0.564480\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.1448 | −0.700503 | −0.350251 | − | 0.936656i | \(-0.613904\pi\) | ||||
−0.350251 | + | 0.936656i | \(0.613904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.01358 | + | 6.95172i | −0.139397 | + | 0.241443i | −0.927269 | − | 0.374397i | \(-0.877850\pi\) |
0.787871 | + | 0.615840i | \(0.211183\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.8186 | + | 33.2099i | −0.374843 | + | 1.15066i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.0114 | 1.00398 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.59341 | + | 7.95603i | −0.158582 | + | 0.274673i | −0.934358 | − | 0.356337i | \(-0.884026\pi\) |
0.775775 | + | 0.631009i | \(0.217359\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.1576 | − | 26.2537i | −0.522675 | − | 0.905299i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 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 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.26778 | 0.146298 | ||||||||
\(852\) | 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 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.0326 | + | 20.8410i | 0.411024 | + | 0.711915i | 0.995002 | − | 0.0998547i | \(-0.0318378\pi\) |
−0.583978 | + | 0.811770i | \(0.698504\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.15861 | + | 14.1311i | −0.278368 | + | 0.482148i | −0.970979 | − | 0.239163i | \(-0.923127\pi\) |
0.692611 | + | 0.721311i | \(0.256460\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.64675 | − | 16.7087i | −0.328379 | − | 0.568770i | 0.653811 | − | 0.756658i | \(-0.273169\pi\) |
−0.982190 | + | 0.187888i | \(0.939836\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.9428 | + | 34.5420i | −0.678077 | + | 1.17446i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.6025 | − | 30.4884i | −0.597124 | − | 1.03425i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.4973 | − | 21.6459i | −0.423453 | − | 0.733443i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.1313 | − | 2.52697i | 0.815786 | − | 0.0854273i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.1464 | + | 26.2343i | −0.511457 | + | 0.885870i | 0.488454 | + | 0.872589i | \(0.337561\pi\) |
−0.999912 | + | 0.0132808i | \(0.995772\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.4943 | −0.656779 | −0.328390 | − | 0.944542i | \(-0.606506\pi\) | ||||
−0.328390 | + | 0.944542i | \(0.606506\pi\) | |||||||
\(882\) | 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 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.05946 | − | 3.56709i | 0.0691499 | − | 0.119771i | −0.829377 | − | 0.558689i | \(-0.811305\pi\) |
0.898527 | + | 0.438918i | \(0.144638\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.15777 | + | 0.540110i | −0.172986 | + | 0.0181147i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.00829686 | + | 0.0143706i | 0.000277644 | + | 0.000480893i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.4409 | − | 37.1367i | −0.716689 | − | 1.24134i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.02083 | + | 13.8925i | −0.266621 | + | 0.461802i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.07084 | + | 7.05090i | 0.135170 | + | 0.234121i | 0.925662 | − | 0.378351i | \(-0.123509\pi\) |
−0.790492 | + | 0.612472i | \(0.790175\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.6454 | + | 42.6871i | −0.816540 | + | 1.41429i | 0.0916774 | + | 0.995789i | \(0.470777\pi\) |
−0.908217 | + | 0.418499i | \(0.862556\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.95618 | −0.0978354 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.29553 | + | 9.63801i | −0.141851 | + | 0.318275i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.71585 | + | 8.16809i | 0.155561 | + | 0.269440i | 0.933263 | − | 0.359193i | \(-0.116948\pi\) |
−0.777702 | + | 0.628633i | \(0.783615\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 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 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.4739 | −0.967006 | −0.483503 | − | 0.875343i | \(-0.660636\pi\) | ||||
−0.483503 | + | 0.875343i | \(0.660636\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0359352 | + | 0.0399715i | 0.00117773 | + | 0.00131001i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.98173 | 0.0972017 | 0.0486008 | − | 0.998818i | \(-0.484524\pi\) | ||||
0.0486008 | + | 0.998818i | \(0.484524\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.96011 | 0.226652 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.3292 | 0.985567 | 0.492783 | − | 0.870152i | \(-0.335979\pi\) | ||||
0.492783 | + | 0.870152i | \(0.335979\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.9170 | 0.484226 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.380127 | −0.0123135 | −0.00615676 | − | 0.999981i | \(-0.501960\pi\) | ||||
−0.00615676 | + | 0.999981i | \(0.501960\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.22360 | − | 9.04754i | 0.169032 | − | 0.292771i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.5150 | + | 15.8618i | 0.371840 | + | 0.512206i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.3115 | 0.945533 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.3746 | − | 47.4141i | −0.878491 | − | 1.52159i | −0.852996 | − | 0.521917i | \(-0.825217\pi\) |
−0.0254951 | − | 0.999675i | \(-0.508116\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.5323 | + | 29.6604i | 0.690292 | + | 0.950870i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.71311 | −0.0868001 | −0.0434001 | − | 0.999058i | \(-0.513819\pi\) | ||||
−0.0434001 | + | 0.999058i | \(0.513819\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.80371 | − | 11.7844i | 0.217448 | − | 0.376630i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.3828 | − | 37.0361i | −0.682006 | − | 1.18127i | −0.974368 | − | 0.224961i | \(-0.927774\pi\) |
0.292362 | − | 0.956308i | \(-0.405559\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.15659 | − | 7.19943i | 0.132440 | − | 0.229393i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.95771 | − | 5.12291i | −0.0940498 | − | 0.162899i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.6731 | + | 51.3954i | −0.942598 | + | 1.63263i | −0.182107 | + | 0.983279i | \(0.558292\pi\) |
−0.760491 | + | 0.649349i | \(0.775042\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.4063 | − | 35.3447i | −0.646922 | − | 1.12050i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.0320 | − | 38.1606i | −0.697762 | − | 1.20856i | −0.969241 | − | 0.246114i | \(-0.920846\pi\) |
0.271479 | − | 0.962444i | \(-0.412487\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3024.2.q.k.2881.3 | 22 | ||
3.2 | odd | 2 | 1008.2.q.k.529.9 | 22 | |||
4.3 | odd | 2 | 1512.2.q.c.1369.3 | 22 | |||
7.2 | even | 3 | 3024.2.t.l.289.9 | 22 | |||
9.4 | even | 3 | 3024.2.t.l.1873.9 | 22 | |||
9.5 | odd | 6 | 1008.2.t.k.193.2 | 22 | |||
12.11 | even | 2 | 504.2.q.d.25.3 | ✓ | 22 | ||
21.2 | odd | 6 | 1008.2.t.k.961.2 | 22 | |||
28.23 | odd | 6 | 1512.2.t.d.289.9 | 22 | |||
36.23 | even | 6 | 504.2.t.d.193.10 | yes | 22 | ||
36.31 | odd | 6 | 1512.2.t.d.361.9 | 22 | |||
63.23 | odd | 6 | 1008.2.q.k.625.9 | 22 | |||
63.58 | even | 3 | inner | 3024.2.q.k.2305.3 | 22 | ||
84.23 | even | 6 | 504.2.t.d.457.10 | yes | 22 | ||
252.23 | even | 6 | 504.2.q.d.121.3 | yes | 22 | ||
252.247 | odd | 6 | 1512.2.q.c.793.3 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.3 | ✓ | 22 | 12.11 | even | 2 | ||
504.2.q.d.121.3 | yes | 22 | 252.23 | even | 6 | ||
504.2.t.d.193.10 | yes | 22 | 36.23 | even | 6 | ||
504.2.t.d.457.10 | yes | 22 | 84.23 | even | 6 | ||
1008.2.q.k.529.9 | 22 | 3.2 | odd | 2 | |||
1008.2.q.k.625.9 | 22 | 63.23 | odd | 6 | |||
1008.2.t.k.193.2 | 22 | 9.5 | odd | 6 | |||
1008.2.t.k.961.2 | 22 | 21.2 | odd | 6 | |||
1512.2.q.c.793.3 | 22 | 252.247 | odd | 6 | |||
1512.2.q.c.1369.3 | 22 | 4.3 | odd | 2 | |||
1512.2.t.d.289.9 | 22 | 28.23 | odd | 6 | |||
1512.2.t.d.361.9 | 22 | 36.31 | odd | 6 | |||
3024.2.q.k.2305.3 | 22 | 63.58 | even | 3 | inner | ||
3024.2.q.k.2881.3 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.t.l.289.9 | 22 | 7.2 | even | 3 | |||
3024.2.t.l.1873.9 | 22 | 9.4 | even | 3 |