Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(289,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.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: | \(12.0733807856\) |
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 | 289.9 | ||
Character | \(\chi\) | \(=\) | 1512.289 |
Dual form | 1512.2.t.d.361.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.52290 | 1.12828 | 0.564139 | − | 0.825680i | \(-0.309208\pi\) | ||||
0.564139 | + | 0.825680i | \(0.309208\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.07705 | − | 2.41660i | −0.407086 | − | 0.913390i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.49483 | − | 4.32118i | −0.605086 | − | 1.04804i | −0.992038 | − | 0.125939i | \(-0.959806\pi\) |
0.386952 | − | 0.922100i | \(-0.373528\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.00383929 | + | 0.00664984i | −0.000880793 | + | 0.00152558i | −0.866465 | − | 0.499237i | \(-0.833614\pi\) |
0.865585 | + | 0.500763i | \(0.166947\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 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 | 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 | ||||||||
\(31\) | 3.88302 | − | 6.72560i | 0.697412 | − | 1.20795i | −0.271949 | − | 0.962312i | \(-0.587668\pi\) |
0.969361 | − | 0.245641i | \(-0.0789984\pi\) | |||||||
\(32\) | 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 | 0.474207 | + | 0.880414i | \(0.342735\pi\) |
−0.999564 | + | 0.0295319i | \(0.990598\pi\) | |||||||
\(38\) | 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 | \(-0.597275\pi\) |
0.976332 | − | 0.216279i | \(-0.0693921\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 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 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.69858 | + | 6.40613i | 0.508039 | + | 0.879950i | 0.999957 | + | 0.00930815i | \(0.00296292\pi\) |
−0.491917 | + | 0.870642i | \(0.663704\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.4133 | 1.94348 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 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 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.18730 | − | 10.7167i | −0.767441 | − | 1.32925i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.54791 | − | 4.41311i | 0.311277 | − | 0.539147i | −0.667362 | − | 0.744733i | \(-0.732577\pi\) |
0.978639 | + | 0.205586i | \(0.0659101\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.15314 | − | 13.8060i | −0.701215 | − | 1.57334i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.08115 | − | 5.33671i | −0.346657 | − | 0.600427i | 0.638997 | − | 0.769209i | \(-0.279350\pi\) |
−0.985653 | + | 0.168783i | \(0.946016\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.19093 | + | 2.06274i | −0.126238 | + | 0.218650i | −0.922216 | − | 0.386675i | \(-0.873624\pi\) |
0.795978 | + | 0.605325i | \(0.206957\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.62377 | + | 10.5017i | −0.799188 | + | 1.10087i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.33566 | 0.928933 | 0.464466 | − | 0.885591i | \(-0.346246\pi\) | ||||
0.464466 | + | 0.885591i | \(0.346246\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.2185 | 1.59806 | 0.799029 | − | 0.601293i | \(-0.205347\pi\) | ||||
0.799029 | + | 0.601293i | \(0.205347\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 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 | 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 | ||||||||
\(115\) | −1.68468 | −0.157097 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.75551 | + | 10.6831i | −0.710947 | + | 0.979321i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.6380 | 1.96709 | ||||||||
\(122\) | 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 | \(-0.527717\pi\) | ||||
−0.0869660 | + | 0.996211i | \(0.527717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.40843 | 0.632945 | 0.316473 | − | 0.948602i | \(-0.397501\pi\) | ||||
0.316473 | + | 0.948602i | \(0.397501\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.92660 | + | 11.9972i | 0.587507 | + | 1.01759i | 0.994558 | + | 0.104186i | \(0.0332238\pi\) |
−0.407051 | + | 0.913405i | \(0.633443\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | 14.1040 | 1.15545 | 0.577724 | − | 0.816232i | \(-0.303941\pi\) | ||||
0.577724 | + | 0.816232i | \(0.303941\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.6005 | −0.862660 | −0.431330 | − | 0.902194i | \(-0.641956\pi\) | ||||
−0.431330 | + | 0.902194i | \(0.641956\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 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 | ||||||||
\(159\) | 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 | \(-0.668528\pi\) |
0.999983 | + | 0.00584647i | \(0.00186100\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 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 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.90471 | − | 13.6914i | −0.600984 | − | 1.04094i | −0.992672 | − | 0.120837i | \(-0.961442\pi\) |
0.391688 | − | 0.920098i | \(-0.371891\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.47022 | − | 3.29878i | −0.111138 | − | 0.249364i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 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 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 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 | 0.996216 | + | 0.0869063i | \(0.0276981\pi\) |
−0.422845 | + | 0.906202i | \(0.638969\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 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 | ||||||||
\(207\) | 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 | \(-0.755543\pi\) |
−0.241961 | − | 0.970286i | \(-0.577791\pi\) | |||||||
\(212\) | 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 | ||||||||
\(221\) | −12.2369 | + | 21.1950i | −0.823144 | + | 1.42573i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.1652 | + | 17.6066i | −0.680711 | + | 1.17903i | 0.294054 | + | 0.955789i | \(0.404996\pi\) |
−0.974764 | + | 0.223237i | \(0.928338\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 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 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.70652 | + | 11.6160i | −0.439358 | + | 0.760991i | −0.997640 | − | 0.0686603i | \(-0.978128\pi\) |
0.558282 | + | 0.829652i | \(0.311461\pi\) | |||||||
\(234\) | 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 | \(0.0395958\pi\) |
−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 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.8070 | + | 13.1332i | −0.754324 | + | 0.839050i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0376627 | 0.00239642 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.802512 | −0.0500593 | −0.0250297 | − | 0.999687i | \(-0.507968\pi\) | ||||
−0.0250297 | + | 0.999687i | \(0.507968\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.8177 | + | 1.76111i | 1.04500 | + | 0.109430i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 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 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.1773 | + | 19.3596i | 0.681490 | + | 1.18038i | 0.974526 | + | 0.224274i | \(0.0720011\pi\) |
−0.293036 | + | 0.956101i | \(0.594666\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.78925 | + | 3.09907i | −0.108689 | + | 0.188255i | −0.915240 | − | 0.402910i | \(-0.867999\pi\) |
0.806550 | + | 0.591166i | \(0.201332\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | 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 | ||||||||
\(283\) | −1.93833 | + | 3.35728i | −0.115222 | + | 0.199570i | −0.917868 | − | 0.396885i | \(-0.870091\pi\) |
0.802647 | + | 0.596455i | \(0.203425\pi\) | |||||||
\(284\) | 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 | ||||||||
\(299\) | 1.63763 | + | 2.83647i | 0.0947068 | + | 0.164037i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.3104 | − | 2.44102i | −1.34359 | − | 0.140698i | ||||
\(302\) | 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 | \(-0.506522\pi\) | ||||
−0.0204878 | + | 0.999790i | \(0.506522\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.61771 | + | 11.4622i | 0.371687 | + | 0.643781i | 0.989825 | − | 0.142288i | \(-0.0454460\pi\) |
−0.618138 | + | 0.786070i | \(0.712113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.9996 | + | 38.1044i | −1.23174 | + | 2.13344i | ||||
\(320\) | 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 | ||||||||
\(329\) | 3.35894 | − | 4.62690i | 0.185184 | − | 0.255089i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.2165 | + | 26.3558i | 0.836375 | + | 1.44864i | 0.892906 | + | 0.450243i | \(0.148662\pi\) |
−0.0565316 | + | 0.998401i | \(0.518004\pi\) | |||||||
\(332\) | 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 | ||||||||
\(347\) | −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 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.5908 | −0.776591 | −0.388295 | − | 0.921535i | \(-0.626936\pi\) | ||||
−0.388295 | + | 0.921535i | \(0.626936\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.3420 | 0.761193 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.83638 | − | 6.64480i | −0.200805 | − | 0.347805i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.66209 | 0.347758 | 0.173879 | − | 0.984767i | \(-0.444370\pi\) | ||||
0.173879 | + | 0.984767i | \(0.444370\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 37.7758 | 1.94555 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.5504 | −1.00423 | −0.502117 | − | 0.864800i | \(-0.667445\pi\) | ||||
−0.502117 | + | 0.864800i | \(0.667445\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.96310 | 0.200937 | 0.100469 | − | 0.994940i | \(-0.467966\pi\) | ||||
0.100469 | + | 0.994940i | \(0.467966\pi\) | |||||||
\(390\) | 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 | −0.482980 | − | 0.875632i | \(-0.660446\pi\) |
0.999809 | − | 0.0195431i | \(-0.00622114\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.83957 | 0.191739 | 0.0958696 | − | 0.995394i | \(-0.469437\pi\) | ||||
0.0958696 | + | 0.995394i | \(0.469437\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.0917 | −1.89748 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | 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 | 0.738027 | − | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 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 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | 0 | ||||||||
\(436\) | 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 | \(-0.902510\pi\) |
0.215618 | − | 0.976478i | \(-0.430824\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 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 | ||||||||
\(447\) | 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 | ||||||||
\(455\) | −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 | ||||||||
\(459\) | 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 | \(0.0392358\pi\) |
−0.389728 | + | 0.920930i | \(0.627431\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 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 | 0 | ||||||||
\(472\) | 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 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 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 | \(-0.0268664\pi\) |
−0.571229 | + | 0.820791i | \(0.693533\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.12270 | − | 13.7377i | −0.274641 | − | 0.616219i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.63182 | 0.207349 | 0.103674 | − | 0.994611i | \(-0.466940\pi\) | ||||
0.103674 | + | 0.994611i | \(0.466940\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.4834 | −0.464668 | −0.232334 | − | 0.972636i | \(-0.574636\pi\) | ||||
−0.232334 | + | 0.972636i | \(0.574636\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.72705 | + | 6.51145i | −0.209112 | + | 0.288050i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 40.9178 | 1.80305 | ||||||||
\(516\) | 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 | 0.999793 | − | 0.0203215i | \(-0.00646899\pi\) |
−0.517496 | + | 0.855686i | \(0.673136\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.18541 | + | 2.05320i | −0.0518346 | + | 0.0897801i | −0.890778 | − | 0.454438i | \(-0.849840\pi\) |
0.838944 | + | 0.544218i | \(0.183174\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −38.7500 | −1.68798 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5541 | −0.980613 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 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 | ||||||||
\(537\) | 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 | −0.686854 | − | 0.726795i | \(-0.741009\pi\) |
0.972850 | + | 0.231436i | \(0.0743423\pi\) | |||||||
\(542\) | 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 | −0.913408 | − | 0.407046i | \(-0.866559\pi\) |
0.809216 | + | 0.587512i | \(0.199892\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 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 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.09601 | − | 12.2907i | −0.300668 | − | 0.520772i | 0.675620 | − | 0.737250i | \(-0.263876\pi\) |
−0.976287 | + | 0.216479i | \(0.930543\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −43.4511 | −1.83778 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 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 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.15081 | − | 15.8497i | −0.383622 | − | 0.664453i | 0.607955 | − | 0.793972i | \(-0.291990\pi\) |
−0.991577 | + | 0.129519i | \(0.958657\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.2192 | − | 26.3604i | 0.636902 | − | 1.10315i | −0.349206 | − | 0.937046i | \(-0.613549\pi\) |
0.986109 | − | 0.166102i | \(-0.0531180\pi\) | |||||||
\(572\) | 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 | 0.959381 | − | 0.282114i | \(-0.0910356\pi\) |
−0.724008 | + | 0.689791i | \(0.757702\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 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 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.69067 | + | 4.66038i | −0.110493 | + | 0.191379i | −0.915969 | − | 0.401249i | \(-0.868576\pi\) |
0.805476 | + | 0.592628i | \(0.201910\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.5664 | + | 26.9525i | −0.802145 | + | 1.10495i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 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 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 54.5905 | 2.21942 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.2161 | 0.658190 | 0.329095 | − | 0.944297i | \(-0.393256\pi\) | ||||
0.329095 | + | 0.944297i | \(0.393256\pi\) | |||||||
\(608\) | 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 | 0.857975 | + | 0.513691i | \(0.171722\pi\) |
0.0158822 | + | 0.999874i | \(0.494944\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | 40.3288 | 1.62095 | 0.810475 | − | 0.585773i | \(-0.199209\pi\) | ||||
0.810475 | + | 0.585773i | \(0.199209\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.26751 | + | 0.656320i | 0.251103 | + | 0.0262949i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.9619 | −1.19848 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.8902 | 1.27154 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.9489 | 0.555298 | 0.277649 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277649 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.94518 | −0.196243 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.5895 | + | 7.11283i | 1.33086 | + | 0.281821i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.5395 | −0.692768 | −0.346384 | − | 0.938093i | \(-0.612591\pi\) | ||||
−0.346384 | + | 0.938093i | \(0.612591\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.5329 | − | 23.4397i | −0.533686 | − | 0.924371i | −0.999226 | − | 0.0393443i | \(-0.987473\pi\) |
0.465540 | − | 0.885027i | \(-0.345860\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.784108 | 0.0306845 | 0.0153423 | − | 0.999882i | \(-0.495116\pi\) | ||||
0.0153423 | + | 0.999882i | \(0.495116\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.0620 | 0.393154 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 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 | 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 | ||||||||
\(677\) | −5.85818 | − | 10.1467i | −0.225148 | − | 0.389968i | 0.731216 | − | 0.682146i | \(-0.238953\pi\) |
−0.956364 | + | 0.292178i | \(0.905620\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.7873 | − | 2.38624i | −0.874497 | − | 0.0915753i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 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 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.1412 | − | 31.4215i | 0.691125 | − | 1.19706i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.45675 | + | 5.98727i | 0.131501 | + | 0.227766i | 0.924255 | − | 0.381775i | \(-0.124687\pi\) |
−0.792754 | + | 0.609541i | \(0.791354\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 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 | 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 | ||||||||
\(707\) | −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 | ||||||||
\(711\) | 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 | 0.346848 | + | 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 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.25655 | + | 9.10461i | −0.195223 | + | 0.338137i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.18914 | − | 12.4520i | 0.266631 | − | 0.461818i | −0.701359 | − | 0.712808i | \(-0.747423\pi\) |
0.967990 | + | 0.250991i | \(0.0807563\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | 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 | \(-0.0360995\pi\) |
−0.594793 | + | 0.803879i | \(0.702766\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 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 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.6912 | + | 2.48089i | 0.865659 | + | 0.0906499i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.9324 | −0.946288 | −0.473144 | − | 0.880985i | \(-0.656881\pi\) | ||||
−0.473144 | + | 0.880985i | \(0.656881\pi\) | |||||||
\(752\) | 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 | ||||||||
\(761\) | 36.5295 | 1.32419 | 0.662097 | − | 0.749418i | \(-0.269667\pi\) | ||||
0.662097 | + | 0.749418i | \(0.269667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.5505 | − | 15.9107i | 0.418157 | − | 0.576007i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.1309 | − | 27.9395i | −0.580187 | − | 1.00491i | −0.995457 | − | 0.0952148i | \(-0.969646\pi\) |
0.415270 | − | 0.909698i | \(-0.363687\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.30051 | − | 9.18076i | 0.190400 | − | 0.329783i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0800351 | 0.00286755 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.4765 | 1.16210 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 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 | \(0.351419\pi\) |
−0.998386 | + | 0.0567879i | \(0.981914\pi\) | |||||||
\(788\) | 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 | ||||||||
\(803\) | −8.68725 | − | 15.0468i | −0.306566 | − | 0.530989i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.81448 | + | 4.07120i | 0.0639520 | + | 0.143491i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.3886 | + | 40.5103i | 0.822301 | + | 1.42427i | 0.903965 | + | 0.427607i | \(0.140643\pi\) |
−0.0816637 | + | 0.996660i | \(0.526023\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.6946 | 0.621341 | 0.310671 | − | 0.950518i | \(-0.399446\pi\) | ||||
0.310671 | + | 0.950518i | \(0.399446\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.61075 | − | 14.9143i | −0.300517 | − | 0.520511i | 0.675736 | − | 0.737144i | \(-0.263826\pi\) |
−0.976253 | + | 0.216633i | \(0.930493\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.77170 | + | 9.99688i | −0.201189 | + | 0.348469i | −0.948912 | − | 0.315542i | \(-0.897814\pi\) |
0.747723 | + | 0.664011i | \(0.231147\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 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 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 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 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 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 | ||||||||
\(851\) | 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 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.0651 | −0.822049 | −0.411024 | − | 0.911624i | \(-0.634829\pi\) | ||||
−0.411024 | + | 0.911624i | \(0.634829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.3172 | −0.556737 | −0.278368 | − | 0.960474i | \(-0.589794\pi\) | ||||
−0.278368 | + | 0.960474i | \(0.589794\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 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 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.6025 | − | 30.4884i | −0.597124 | − | 1.03425i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.9945 | −0.846907 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 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 | ||||||||
\(879\) | 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 | \(-0.204960\pi\) | ||||
0.799759 | + | 0.600321i | \(0.204960\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0165937 | −0.000555287 | ||||||||
\(894\) | 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 | ||||||||
\(905\) | 16.0417 | 0.533243 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.14168 | 0.270340 | 0.135170 | − | 0.990822i | \(-0.456842\pi\) | ||||
0.135170 | + | 0.990822i | \(0.456842\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | 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 | \(-0.883052\pi\) |
0.777702 | + | 0.628633i | \(0.216385\pi\) | |||||||
\(920\) | 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 | ||||||||
\(929\) | 14.7369 | + | 25.5251i | 0.483503 | + | 0.837452i | 0.999821 | − | 0.0189453i | \(-0.00603083\pi\) |
−0.516317 | + | 0.856397i | \(0.672697\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0166487 | − | 0.0511066i | −0.000545641 | − | 0.00167495i | ||||
\(932\) | 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 | ||||||||
\(941\) | −1.49087 | + | 2.58226i | −0.0486008 | + | 0.0841791i | −0.889302 | − | 0.457320i | \(-0.848810\pi\) |
0.840702 | + | 0.541499i | \(0.182143\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.48005 | + | 6.02763i | 0.113326 | + | 0.196287i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 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 | ||||||||
\(951\) | 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 | ||||||||
\(959\) | −7.97924 | − | 17.9032i | −0.257663 | − | 0.578126i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.6558 | − | 25.3845i | −0.472766 | − | 0.818855i | ||||
\(962\) | 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 | \(-0.906578\pi\) |
0.228078 | − | 0.973643i | \(-0.426756\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.35656 | − | 2.34962i | 0.0434001 | − | 0.0751711i | −0.843509 | − | 0.537114i | \(-0.819514\pi\) |
0.886909 | + | 0.461943i | \(0.152848\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.80371 | + | 11.7844i | −0.217448 | + | 0.376630i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 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 | 0.760491 | + | 0.649349i | \(0.224958\pi\) |
0.182107 | + | 0.983279i | \(0.441708\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | 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 | 1512.2.t.d.289.9 | 22 | ||
3.2 | odd | 2 | 504.2.t.d.457.10 | yes | 22 | ||
4.3 | odd | 2 | 3024.2.t.l.289.9 | 22 | |||
7.4 | even | 3 | 1512.2.q.c.1369.3 | 22 | |||
9.4 | even | 3 | 1512.2.q.c.793.3 | 22 | |||
9.5 | odd | 6 | 504.2.q.d.121.3 | yes | 22 | ||
12.11 | even | 2 | 1008.2.t.k.961.2 | 22 | |||
21.11 | odd | 6 | 504.2.q.d.25.3 | ✓ | 22 | ||
28.11 | odd | 6 | 3024.2.q.k.2881.3 | 22 | |||
36.23 | even | 6 | 1008.2.q.k.625.9 | 22 | |||
36.31 | odd | 6 | 3024.2.q.k.2305.3 | 22 | |||
63.4 | even | 3 | inner | 1512.2.t.d.361.9 | 22 | ||
63.32 | odd | 6 | 504.2.t.d.193.10 | yes | 22 | ||
84.11 | even | 6 | 1008.2.q.k.529.9 | 22 | |||
252.67 | odd | 6 | 3024.2.t.l.1873.9 | 22 | |||
252.95 | even | 6 | 1008.2.t.k.193.2 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.3 | ✓ | 22 | 21.11 | odd | 6 | ||
504.2.q.d.121.3 | yes | 22 | 9.5 | odd | 6 | ||
504.2.t.d.193.10 | yes | 22 | 63.32 | odd | 6 | ||
504.2.t.d.457.10 | yes | 22 | 3.2 | odd | 2 | ||
1008.2.q.k.529.9 | 22 | 84.11 | even | 6 | |||
1008.2.q.k.625.9 | 22 | 36.23 | even | 6 | |||
1008.2.t.k.193.2 | 22 | 252.95 | even | 6 | |||
1008.2.t.k.961.2 | 22 | 12.11 | even | 2 | |||
1512.2.q.c.793.3 | 22 | 9.4 | even | 3 | |||
1512.2.q.c.1369.3 | 22 | 7.4 | even | 3 | |||
1512.2.t.d.289.9 | 22 | 1.1 | even | 1 | trivial | ||
1512.2.t.d.361.9 | 22 | 63.4 | even | 3 | inner | ||
3024.2.q.k.2305.3 | 22 | 36.31 | odd | 6 | |||
3024.2.q.k.2881.3 | 22 | 28.11 | odd | 6 | |||
3024.2.t.l.289.9 | 22 | 4.3 | odd | 2 | |||
3024.2.t.l.1873.9 | 22 | 252.67 | odd | 6 |