Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(559,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.bm (of order \(6\), degree \(2\), 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 28x^{14} + 542x^{12} + 5488x^{10} + 40451x^{8} + 151312x^{6} + 395134x^{4} + 52164x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1855.8 | ||
Root | \(1.86197 + 3.22503i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1855 |
Dual form | 2736.2.bm.t.559.7 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.38255 | + | 2.39464i | 0.618294 | + | 1.07092i | 0.989797 | + | 0.142485i | \(0.0455093\pi\) |
−0.371503 | + | 0.928432i | \(0.621157\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.26278i | 1.23322i | 0.787270 | + | 0.616608i | \(0.211494\pi\) | ||||
−0.787270 | + | 0.616608i | \(0.788506\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.94197i | 0.585526i | 0.956185 | + | 0.292763i | \(0.0945746\pi\) | ||||
−0.956185 | + | 0.292763i | \(0.905425\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.96863 | + | 2.29129i | 1.10070 | + | 0.635489i | 0.936405 | − | 0.350922i | \(-0.114132\pi\) |
0.164295 | + | 0.986411i | \(0.447465\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.27533 | − | 3.94099i | −0.551848 | − | 0.955830i | −0.998141 | − | 0.0609426i | \(-0.980589\pi\) |
0.446293 | − | 0.894887i | \(-0.352744\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.43388 | + | 2.68486i | −0.787785 | + | 0.615950i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.81320 | + | 4.51095i | 1.62916 | + | 0.940599i | 0.984343 | + | 0.176266i | \(0.0564018\pi\) |
0.644822 | + | 0.764333i | \(0.276932\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.32288 | + | 2.29129i | −0.264575 | + | 0.458258i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.78556 | + | 1.03090i | 0.331571 | + | 0.191433i | 0.656538 | − | 0.754293i | \(-0.272020\pi\) |
−0.324967 | + | 0.945725i | \(0.605353\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.21645 | −0.218480 | −0.109240 | − | 0.994015i | \(-0.534842\pi\) | ||||
−0.109240 | + | 0.994015i | \(0.534842\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.81320 | + | 4.51095i | −1.32067 | + | 0.762490i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.73205i | − | 0.284747i | −0.989813 | − | 0.142374i | \(-0.954527\pi\) | ||
0.989813 | − | 0.142374i | \(-0.0454735\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.25486 | − | 1.87919i | 0.508324 | − | 0.293481i | −0.223821 | − | 0.974630i | \(-0.571853\pi\) |
0.732144 | + | 0.681149i | \(0.238520\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.82467 | + | 1.05347i | −0.278259 | + | 0.160653i | −0.632635 | − | 0.774450i | \(-0.718027\pi\) |
0.354376 | + | 0.935103i | \(0.384693\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.49499 | + | 5.48194i | 1.38499 | + | 0.799623i | 0.992745 | − | 0.120239i | \(-0.0383662\pi\) |
0.392242 | + | 0.919862i | \(0.371700\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.64575 | −0.520822 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.40250 | − | 4.27384i | −1.01681 | − | 0.587057i | −0.103633 | − | 0.994616i | \(-0.533047\pi\) |
−0.913179 | + | 0.407559i | \(0.866380\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.65032 | + | 2.68486i | −0.627049 | + | 0.362027i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.68179 | − | 2.91295i | −0.218951 | − | 0.379234i | 0.735537 | − | 0.677485i | \(-0.236930\pi\) |
−0.954488 | + | 0.298251i | \(0.903597\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.322876 | − | 0.559237i | 0.0413400 | − | 0.0716030i | −0.844615 | − | 0.535374i | \(-0.820171\pi\) |
0.885955 | + | 0.463771i | \(0.153504\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.6713i | 1.57168i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.04210 | + | 7.00112i | −0.493821 | + | 0.855323i | −0.999975 | − | 0.00712031i | \(-0.997734\pi\) |
0.506154 | + | 0.862443i | \(0.331067\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.13140 | − | 10.6199i | −0.727664 | − | 1.26035i | −0.957868 | − | 0.287208i | \(-0.907273\pi\) |
0.230204 | − | 0.973142i | \(-0.426061\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.79150 | − | 6.56708i | −0.443762 | − | 0.768618i | 0.554203 | − | 0.832381i | \(-0.313023\pi\) |
−0.997965 | + | 0.0637634i | \(0.979690\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.33622 | −0.722080 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.04308 | + | 8.73488i | 0.567391 | + | 0.982750i | 0.996823 | + | 0.0796509i | \(0.0253806\pi\) |
−0.429432 | + | 0.903099i | \(0.641286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.9639i | − | 1.20344i | −0.798707 | − | 0.601721i | \(-0.794482\pi\) | ||
0.798707 | − | 0.601721i | \(-0.205518\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.29150 | − | 10.8972i | 0.682409 | − | 1.18197i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.93321 | + | 3.42554i | 0.628919 | + | 0.363106i | 0.780333 | − | 0.625364i | \(-0.215049\pi\) |
−0.151415 | + | 0.988470i | \(0.548383\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.47597 | + | 12.9488i | −0.783695 | + | 1.35740i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.1768 | − | 4.51095i | −1.14671 | − | 0.462814i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.4059 | + | 9.47194i | −1.66576 | + | 0.961730i | −0.695883 | + | 0.718156i | \(0.744987\pi\) |
−0.969882 | + | 0.243574i | \(0.921680\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.06089 | − | 7.03367i | 0.404074 | − | 0.699877i | −0.590139 | − | 0.807301i | \(-0.700927\pi\) |
0.994213 | + | 0.107425i | \(0.0342605\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.3868 | −1.91024 | −0.955120 | − | 0.296221i | \(-0.904274\pi\) | ||||
−0.955120 | + | 0.296221i | \(0.904274\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.72718 | −0.650341 | −0.325170 | − | 0.945655i | \(-0.605422\pi\) | ||||
−0.325170 | + | 0.945655i | \(0.605422\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.46863 | + | 1.42526i | −0.236452 | + | 0.136515i | −0.613545 | − | 0.789660i | \(-0.710257\pi\) |
0.377093 | + | 0.926175i | \(0.376924\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14.7330i | − | 1.38597i | −0.720953 | − | 0.692984i | \(-0.756295\pi\) | ||
0.720953 | − | 0.692984i | \(-0.243705\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.9464i | 2.32627i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.8586 | − | 7.42391i | 1.17874 | − | 0.680548i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.22876 | 0.657160 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.50972 | 0.582247 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.21645 | + | 2.10695i | −0.107942 | + | 0.186961i | −0.914936 | − | 0.403598i | \(-0.867759\pi\) |
0.806994 | + | 0.590559i | \(0.201093\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.76782 | + | 1.59800i | −0.241825 | + | 0.139618i | −0.616015 | − | 0.787734i | \(-0.711254\pi\) |
0.374190 | + | 0.927352i | \(0.377921\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.76013 | − | 11.2040i | −0.759600 | − | 0.971509i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.53019 | − | 9.57857i | 0.472476 | − | 0.818353i | −0.527028 | − | 0.849848i | \(-0.676694\pi\) |
0.999504 | + | 0.0314955i | \(0.0100270\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.47794 | + | 5.47209i | 0.803909 | + | 0.464137i | 0.844836 | − | 0.535025i | \(-0.179698\pi\) |
−0.0409275 | + | 0.999162i | \(0.513031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.44961 | + | 7.70695i | −0.372095 | + | 0.644488i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.70105i | 0.473446i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.42297 | + | 11.1249i | 0.526190 | + | 0.911388i | 0.999534 | + | 0.0305109i | \(0.00971341\pi\) |
−0.473344 | + | 0.880878i | \(0.656953\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.7355 | −1.11778 | −0.558890 | − | 0.829242i | \(-0.688772\pi\) | ||||
−0.558890 | + | 0.829242i | \(0.688772\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.68179 | − | 2.91295i | −0.135085 | − | 0.233974i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.79150 | + | 10.0312i | 0.462212 | + | 0.800575i | 0.999071 | − | 0.0430971i | \(-0.0137225\pi\) |
−0.536859 | + | 0.843672i | \(0.680389\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.7183 | + | 25.4928i | −1.15996 | + | 2.00911i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.47668i | 0.585618i | 0.956171 | + | 0.292809i | \(0.0945901\pi\) | ||||
−0.956171 | + | 0.292809i | \(0.905410\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.81320 | − | 13.5329i | 0.604603 | − | 1.04720i | −0.387511 | − | 0.921865i | \(-0.626665\pi\) |
0.992114 | − | 0.125339i | \(-0.0400017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.00000 | + | 6.92820i | 0.307692 | + | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.1617 | + | 11.6404i | −1.53287 | + | 0.885000i | −0.533638 | + | 0.845713i | \(0.679175\pi\) |
−0.999228 | + | 0.0392871i | \(0.987491\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.47597 | − | 4.31626i | −0.565131 | − | 0.326278i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.36359 | −0.251406 | −0.125703 | − | 0.992068i | \(-0.540119\pi\) | ||||
−0.125703 | + | 0.992068i | \(0.540119\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.40588 | + | 4.27579i | 0.550475 | + | 0.317817i | 0.749313 | − | 0.662215i | \(-0.230384\pi\) |
−0.198839 | + | 0.980032i | \(0.563717\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.14764 | − | 2.39464i | 0.304941 | − | 0.176058i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.65327 | − | 4.41862i | 0.559663 | − | 0.323121i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.7898i | 1.21487i | 0.794371 | + | 0.607433i | \(0.207801\pi\) | ||||
−0.794371 | + | 0.607433i | \(0.792199\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.9686 | − | 7.48744i | 0.933502 | − | 0.538958i | 0.0455847 | − | 0.998960i | \(-0.485485\pi\) |
0.887917 | + | 0.460003i | \(0.152152\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.3557 | 1.37903 | 0.689517 | − | 0.724269i | \(-0.257823\pi\) | ||||
0.689517 | + | 0.724269i | \(0.257823\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.82467 | − | 1.05347i | −0.129347 | − | 0.0746787i | 0.433930 | − | 0.900947i | \(-0.357126\pi\) |
−0.563277 | + | 0.826268i | \(0.690460\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.36359 | + | 5.82591i | −0.236078 | + | 0.408899i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | + | 5.19615i | 0.628587 | + | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.21392 | − | 6.66848i | −0.360655 | − | 0.461268i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.608223 | + | 1.05347i | 0.0418718 | + | 0.0725241i | 0.886202 | − | 0.463299i | \(-0.153335\pi\) |
−0.844330 | + | 0.535824i | \(0.820001\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.04538 | − | 2.91295i | −0.344092 | − | 0.198662i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.96900i | − | 0.269433i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 20.8537i | − | 1.40277i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.9108 | − | 20.6302i | −0.797608 | − | 1.38150i | −0.921170 | − | 0.389161i | \(-0.872765\pi\) |
0.123561 | − | 0.992337i | \(-0.460568\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.3536 | 1.48366 | 0.741829 | − | 0.670589i | \(-0.233958\pi\) | ||||
0.741829 | + | 0.670589i | \(0.233958\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.64575 | 0.439164 | 0.219582 | − | 0.975594i | \(-0.429531\pi\) | ||||
0.219582 | + | 0.975594i | \(0.429531\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.01996 | − | 10.4269i | −0.394380 | − | 0.683087i | 0.598641 | − | 0.801017i | \(-0.295707\pi\) |
−0.993022 | + | 0.117930i | \(0.962374\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 30.3162i | 1.97761i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.70984i | 0.628078i | 0.949410 | + | 0.314039i | \(0.101682\pi\) | ||||
−0.949410 | + | 0.314039i | \(0.898318\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.3745 | + | 10.0312i | 1.11919 | + | 0.646165i | 0.941194 | − | 0.337866i | \(-0.109705\pi\) |
0.177996 | + | 0.984031i | \(0.443038\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.04042 | − | 8.73027i | −0.322021 | − | 0.557757i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.7796 | + | 2.78723i | −1.25854 | + | 0.177347i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.6264 | − | 9.02190i | −0.986329 | − | 0.569458i | −0.0821544 | − | 0.996620i | \(-0.526180\pi\) |
−0.904175 | + | 0.427162i | \(0.859513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.76013 | + | 15.1730i | −0.550745 | + | 0.953918i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.9736 | + | 6.33563i | 0.684516 | + | 0.395206i | 0.801554 | − | 0.597922i | \(-0.204007\pi\) |
−0.117038 | + | 0.993127i | \(0.537340\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.65131 | 0.351155 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.49499 | − | 5.48194i | 0.585486 | − | 0.338031i | −0.177824 | − | 0.984062i | \(-0.556906\pi\) |
0.763311 | + | 0.646032i | \(0.223573\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 23.6351i | − | 1.45189i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.9736 | − | 6.33563i | 0.669074 | − | 0.386290i | −0.126652 | − | 0.991947i | \(-0.540423\pi\) |
0.795726 | + | 0.605657i | \(0.207090\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.9539 | − | 9.78835i | 1.02988 | − | 0.594600i | 0.112928 | − | 0.993603i | \(-0.463977\pi\) |
0.916949 | + | 0.399003i | \(0.130644\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.44961 | − | 2.56898i | −0.268322 | − | 0.154916i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.2288 | −1.45576 | −0.727882 | − | 0.685702i | \(-0.759495\pi\) | ||||
−0.727882 | + | 0.685702i | \(0.759495\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.0949 | − | 15.0659i | −1.55669 | − | 0.898756i | −0.997570 | − | 0.0696705i | \(-0.977805\pi\) |
−0.559121 | − | 0.829086i | \(-0.688861\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.13140 | + | 10.6199i | 0.361925 | + | 0.626873i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.85425 | + | 3.21165i | −0.109073 | + | 0.188921i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.6739i | 1.55831i | 0.626833 | + | 0.779154i | \(0.284351\pi\) | ||||
−0.626833 | + | 0.779154i | \(0.715649\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.65032 | − | 8.05459i | 0.270752 | − | 0.468957i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.6718 | + | 35.8046i | 1.19548 | + | 2.07063i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.43725 | − | 5.95350i | −0.198120 | − | 0.343154i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.78556 | 0.102241 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.1694 | + | 29.7382i | 0.979908 | + | 1.69725i | 0.662682 | + | 0.748901i | \(0.269418\pi\) |
0.317226 | + | 0.948350i | \(0.397249\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.1818i | 1.31452i | 0.753665 | + | 0.657259i | \(0.228284\pi\) | ||||
−0.753665 | + | 0.657259i | \(0.771716\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.82288 | − | 3.15731i | 0.103035 | − | 0.178462i | −0.809899 | − | 0.586570i | \(-0.800478\pi\) |
0.912934 | + | 0.408108i | \(0.133811\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.61694 | + | 3.24294i | 0.315479 | + | 0.182142i | 0.649376 | − | 0.760468i | \(-0.275030\pi\) |
−0.333897 | + | 0.942610i | \(0.608364\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.00197 | + | 3.46751i | −0.112089 | + | 0.194143i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.3942 | + | 7.42391i | 1.02348 | + | 0.413077i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.5000 | + | 6.06218i | −0.582435 | + | 0.336269i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.8864 | + | 30.9801i | −0.986107 | + | 1.70799i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.3888 | −1.17563 | −0.587817 | − | 0.808994i | \(-0.700012\pi\) | ||||
−0.587817 | + | 0.808994i | \(0.700012\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −22.3536 | −1.22131 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.90588 | + | 3.40976i | −0.321714 | + | 0.185742i | −0.652156 | − | 0.758085i | \(-0.726135\pi\) |
0.330442 | + | 0.943826i | \(0.392802\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.36230i | − | 0.127926i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.9442i | 0.590930i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.5810 | + | 6.10895i | −0.568019 | + | 0.327946i | −0.756358 | − | 0.654158i | \(-0.773023\pi\) |
0.188339 | + | 0.982104i | \(0.439690\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.9373 | −1.60250 | −0.801252 | − | 0.598327i | \(-0.795832\pi\) | ||||
−0.801252 | + | 0.598327i | \(0.795832\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.8654 | 1.37668 | 0.688338 | − | 0.725390i | \(-0.258341\pi\) | ||||
0.688338 | + | 0.725390i | \(0.258341\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.9539 | − | 29.3650i | 0.899820 | − | 1.55853i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.6264 | − | 9.02190i | 0.824730 | − | 0.476158i | −0.0273150 | − | 0.999627i | \(-0.508696\pi\) |
0.852045 | + | 0.523469i | \(0.175362\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.58301 | − | 18.4390i | 0.241211 | − | 0.970473i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.4839 | − | 18.1586i | 0.548751 | − | 0.950464i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.82467 | + | 1.05347i | 0.0952469 | + | 0.0549908i | 0.546867 | − | 0.837220i | \(-0.315820\pi\) |
−0.451620 | + | 0.892210i | \(0.649154\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.9446 | − | 24.1528i | 0.723968 | − | 1.25395i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.85052i | − | 0.147595i | −0.997273 | − | 0.0737973i | \(-0.976488\pi\) | ||
0.997273 | − | 0.0737973i | \(-0.0235118\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.72416 | + | 8.18248i | 0.243307 | + | 0.421419i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.5191 | 0.643061 | 0.321530 | − | 0.946899i | \(-0.395803\pi\) | ||||
0.321530 | + | 0.946899i | \(0.395803\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.81320 | − | 13.5329i | −0.399236 | − | 0.691497i | 0.594396 | − | 0.804172i | \(-0.297391\pi\) |
−0.993632 | + | 0.112676i | \(0.964058\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.76013 | − | 15.1730i | −0.446458 | − | 0.773287i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.91274 | + | 11.9732i | −0.350490 | + | 0.607066i | −0.986335 | − | 0.164750i | \(-0.947318\pi\) |
0.635846 | + | 0.771816i | \(0.280652\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 41.0556i | − | 2.07627i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.9446 | + | 24.1528i | −0.701629 | + | 1.21526i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.38562 | + | 9.32817i | 0.270297 | + | 0.468167i | 0.968938 | − | 0.247305i | \(-0.0795449\pi\) |
−0.698641 | + | 0.715472i | \(0.746212\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.50433 | − | 5.48733i | 0.474624 | − | 0.274024i | −0.243549 | − | 0.969888i | \(-0.578312\pi\) |
0.718173 | + | 0.695864i | \(0.244978\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.82762 | − | 2.78723i | −0.240481 | − | 0.138842i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.36359 | 0.166727 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.4686 | − | 6.62141i | −0.567087 | − | 0.327408i | 0.188898 | − | 0.981997i | \(-0.439508\pi\) |
−0.755985 | + | 0.654589i | \(0.772842\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.50433 | − | 5.48733i | 0.467678 | − | 0.270014i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.2546 | − | 15.1581i | 1.28879 | − | 0.744081i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 16.7898i | − | 0.820234i | −0.912033 | − | 0.410117i | \(-0.865488\pi\) | ||
0.912033 | − | 0.410117i | \(-0.134512\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.4059 | − | 14.6681i | 1.23821 | − | 0.714879i | 0.269479 | − | 0.963006i | \(-0.413148\pi\) |
0.968727 | + | 0.248127i | \(0.0798151\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0399 | 0.584022 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.82467 | + | 1.05347i | 0.0883019 | + | 0.0509811i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.49499 | − | 16.4458i | 0.457358 | − | 0.792167i | −0.541463 | − | 0.840725i | \(-0.682129\pi\) |
0.998820 | + | 0.0485580i | \(0.0154626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.9686 | + | 7.48744i | 0.623232 | + | 0.359823i | 0.778126 | − | 0.628108i | \(-0.216170\pi\) |
−0.154894 | + | 0.987931i | \(0.549504\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −38.9408 | + | 5.48733i | −1.86279 | + | 0.262495i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.5612 | − | 28.6848i | −0.790421 | − | 1.36905i | −0.925707 | − | 0.378242i | \(-0.876529\pi\) |
0.135286 | − | 0.990807i | \(-0.456805\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.72718 | + | 3.88394i | 0.319618 | + | 0.184531i | 0.651222 | − | 0.758887i | \(-0.274257\pi\) |
−0.331604 | + | 0.943419i | \(0.607590\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.9439i | 0.898026i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 23.2807i | − | 1.09869i | −0.835597 | − | 0.549343i | \(-0.814878\pi\) | ||
0.835597 | − | 0.549343i | \(-0.185122\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.64934 | + | 6.32084i | 0.171841 | + | 0.297637i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −41.3436 | −1.93822 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.06275 | 0.0964912 | 0.0482456 | − | 0.998836i | \(-0.484637\pi\) | ||||
0.0482456 | + | 0.998836i | \(0.484637\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.7183 | + | 25.4928i | 0.685498 | + | 1.18732i | 0.973280 | + | 0.229621i | \(0.0737486\pi\) |
−0.287783 | + | 0.957696i | \(0.592918\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 37.7928i | − | 1.75638i | −0.478310 | − | 0.878191i | \(-0.658751\pi\) | ||
0.478310 | − | 0.878191i | \(-0.341249\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 10.9639i | − | 0.507348i | −0.967290 | − | 0.253674i | \(-0.918361\pi\) | ||
0.967290 | − | 0.253674i | \(-0.0816390\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.8431 | − | 13.1885i | −1.05480 | − | 0.608988i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.04581 | − | 3.54345i | −0.0940665 | − | 0.162928i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.60921 | − | 11.4197i | −0.0738355 | − | 0.523974i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.8586 | − | 7.42391i | −0.587524 | − | 0.339207i | 0.176594 | − | 0.984284i | \(-0.443492\pi\) |
−0.764118 | + | 0.645077i | \(0.776825\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.96863 | − | 6.87386i | 0.180954 | − | 0.313421i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −45.3638 | − | 26.1908i | −2.05987 | − | 1.18926i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.0381 | 1.13459 | 0.567293 | − | 0.823516i | \(-0.307991\pi\) | ||||
0.567293 | + | 0.823516i | \(0.307991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.7578 | − | 12.5619i | 0.981916 | − | 0.566909i | 0.0790678 | − | 0.996869i | \(-0.474806\pi\) |
0.902848 | + | 0.429960i | \(0.141472\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 9.38251i | − | 0.422567i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.6504 | − | 20.0054i | 1.55428 | − | 0.897367i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.4269 | − | 12.3708i | 0.959202 | − | 0.553795i | 0.0632743 | − | 0.997996i | \(-0.479846\pi\) |
0.895927 | + | 0.444201i | \(0.146512\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.8892 | − | 16.1018i | −1.24352 | − | 0.717946i | −0.273710 | − | 0.961812i | \(-0.588251\pi\) |
−0.969809 | + | 0.243867i | \(0.921584\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.4575 | 0.999346 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.6100 | − | 17.0953i | −1.31244 | − | 0.757738i | −0.329941 | − | 0.944002i | \(-0.607029\pi\) |
−0.982500 | + | 0.186264i | \(0.940362\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.4269 | − | 12.3708i | 0.947872 | − | 0.547254i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26.8032 | − | 46.4245i | −1.18109 | − | 2.04571i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.6458 | + | 18.4390i | −0.468200 | + | 0.810946i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.0645i | 0.703797i | 0.936038 | + | 0.351898i | \(0.114464\pi\) | ||||
−0.936038 | + | 0.351898i | \(0.885536\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.60921 | − | 2.78723i | 0.0703657 | − | 0.121877i | −0.828696 | − | 0.559699i | \(-0.810917\pi\) |
0.899062 | + | 0.437822i | \(0.144250\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.76782 | + | 4.79400i | 0.120568 | + | 0.208830i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.1974 | + | 50.5714i | 1.26945 | + | 2.19875i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.2231 | 0.746015 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.30064 | − | 16.1092i | −0.402102 | − | 0.696461i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 7.07994i | − | 0.304954i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.20850 | − | 9.02138i | 0.223931 | − | 0.387860i | −0.732067 | − | 0.681232i | \(-0.761444\pi\) |
0.955998 | + | 0.293373i | \(0.0947777\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.82599 | − | 3.94099i | −0.292393 | − | 0.168813i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6944 | − | 18.5232i | 0.457259 | − | 0.791996i | −0.541556 | − | 0.840665i | \(-0.682165\pi\) |
0.998815 | + | 0.0486689i | \(0.0154979\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.89922 | + | 1.25403i | −0.379120 | + | 0.0534234i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.5000 | + | 16.4545i | −1.21194 | + | 0.699716i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.33622 | + | 10.9747i | −0.268474 | + | 0.465011i | −0.968468 | − | 0.249138i | \(-0.919853\pi\) |
0.699994 | + | 0.714149i | \(0.253186\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.65524 | −0.408373 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.9800 | 1.60067 | 0.800333 | − | 0.599556i | \(-0.204656\pi\) | ||||
0.800333 | + | 0.599556i | \(0.204656\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 35.2804 | − | 20.3691i | 1.48426 | − | 0.856936i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.88197i | 0.330429i | 0.986258 | + | 0.165215i | \(0.0528317\pi\) | ||||
−0.986258 | + | 0.165215i | \(0.947168\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.57446i | 0.233284i | 0.993174 | + | 0.116642i | \(0.0372130\pi\) | ||||
−0.993174 | + | 0.116642i | \(0.962787\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.6718 | + | 11.9349i | −0.862073 | + | 0.497718i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.6458 | −1.15091 | −0.575454 | − | 0.817834i | \(-0.695175\pi\) | ||||
−0.575454 | + | 0.817834i | \(0.695175\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.7727 | 1.48410 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.29966 | − | 14.3754i | 0.343737 | − | 0.595370i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.81320 | − | 4.51095i | 0.322485 | − | 0.186187i | −0.330015 | − | 0.943976i | \(-0.607054\pi\) |
0.652500 | + | 0.757789i | \(0.273720\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.17712 | − | 3.26599i | 0.172115 | − | 0.134573i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.0345 | + | 26.0406i | −0.617394 | + | 1.06936i | 0.372566 | + | 0.928006i | \(0.378478\pi\) |
−0.989959 | + | 0.141352i | \(0.954855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 35.5552 | + | 20.5278i | 1.45762 | + | 0.841558i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.1768 | − | 19.3588i | 0.456671 | − | 0.790978i | −0.542111 | − | 0.840307i | \(-0.682375\pi\) |
0.998783 | + | 0.0493290i | \(0.0157083\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.57278i | − | 0.145737i | −0.997342 | − | 0.0728684i | \(-0.976785\pi\) | ||
0.997342 | − | 0.0728684i | \(-0.0232153\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.99410 | + | 17.3103i | 0.406318 | + | 0.703763i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.5230 | −0.670648 | −0.335324 | − | 0.942103i | \(-0.608846\pi\) | ||||
−0.335324 | + | 0.942103i | \(0.608846\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.1214 | + | 43.5115i | 1.01630 | + | 1.76029i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.76013 | + | 16.9050i | 0.394208 | + | 0.682788i | 0.993000 | − | 0.118117i | \(-0.0376856\pi\) |
−0.598792 | + | 0.800905i | \(0.704352\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.38203 | + | 14.5181i | −0.337448 | + | 0.584477i | −0.983952 | − | 0.178434i | \(-0.942897\pi\) |
0.646504 | + | 0.762911i | \(0.276230\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.47668i | − | 0.300513i | −0.988647 | − | 0.150256i | \(-0.951990\pi\) | ||
0.988647 | − | 0.150256i | \(-0.0480099\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.1768 | + | 19.3588i | −0.447789 | + | 0.775593i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6144 | + | 27.0449i | 0.624575 | + | 1.08180i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.82599 | + | 3.94099i | −0.272170 | + | 0.157137i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.1283 | + | 8.15696i | 0.562437 | + | 0.324723i | 0.754123 | − | 0.656733i | \(-0.228062\pi\) |
−0.191686 | + | 0.981456i | \(0.561395\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.72718 | −0.266960 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.4686 | − | 8.35347i | −0.573268 | − | 0.330976i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.2021 | + | 14.5505i | −0.995424 | + | 0.574708i | −0.906891 | − | 0.421365i | \(-0.861551\pi\) |
−0.0885329 | + | 0.996073i | \(0.528218\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.7296 | − | 18.8964i | 1.29073 | − | 0.745202i | 0.311944 | − | 0.950100i | \(-0.399020\pi\) |
0.978783 | + | 0.204899i | \(0.0656864\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 32.2037i | − | 1.26606i | −0.774128 | − | 0.633029i | \(-0.781812\pi\) | ||
0.774128 | − | 0.633029i | \(-0.218188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.65687 | − | 3.26599i | 0.222051 | − | 0.128201i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.1412 | 0.827320 | 0.413660 | − | 0.910431i | \(-0.364250\pi\) | ||||
0.413660 | + | 0.910431i | \(0.364250\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.65327 | − | 4.41862i | −0.299038 | − | 0.172650i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.5810 | + | 18.3269i | −0.412178 | + | 0.713913i | −0.995128 | − | 0.0985953i | \(-0.968565\pi\) |
0.582950 | + | 0.812508i | \(0.301898\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.0000 | + | 15.5885i | 1.05018 | + | 0.606321i | 0.922699 | − | 0.385521i | \(-0.125978\pi\) |
0.127479 | + | 0.991841i | \(0.459311\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.7183 | − | 36.4674i | 0.570750 | − | 1.41415i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.30064 | + | 16.1092i | 0.360122 | + | 0.623750i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.08602 | + | 0.627015i | 0.0419254 | + | 0.0242056i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 5.59237i | − | 0.215570i | −0.994174 | − | 0.107785i | \(-0.965624\pi\) | ||
0.994174 | − | 0.107785i | \(-0.0343758\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 25.3425i | − | 0.973992i | −0.873404 | − | 0.486996i | \(-0.838093\pi\) | ||
0.873404 | − | 0.486996i | \(-0.161907\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.9049 | − | 53.5288i | −1.18602 | − | 2.05425i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.89922 | −0.340519 | −0.170260 | − | 0.985399i | \(-0.554461\pi\) | ||||
−0.170260 | + | 0.985399i | \(0.554461\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.5830 | 1.16852 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.5852 | − | 33.9225i | −0.746136 | − | 1.29235i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.5767i | 0.744733i | 0.928086 | + | 0.372366i | \(0.121453\pi\) | ||||
−0.928086 | + | 0.372366i | \(0.878547\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30.2617i | 1.14789i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.8118 | − | 8.55157i | −0.561035 | − | 0.323914i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.4225 | + | 23.2484i | 0.506959 | + | 0.878079i | 0.999968 | + | 0.00805464i | \(0.00256390\pi\) |
−0.493008 | + | 0.870025i | \(0.664103\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.65032 | + | 5.94765i | 0.175390 | + | 0.224320i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.9493 | + | 13.2498i | 0.863099 | + | 0.498310i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.5516 | − | 30.4003i | 0.659165 | − | 1.14171i | −0.321667 | − | 0.946853i | \(-0.604243\pi\) |
0.980832 | − | 0.194855i | \(-0.0624236\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.50433 | − | 5.48733i | −0.355940 | − | 0.205502i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.6072 | −0.920257 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.68179 | + | 0.970984i | −0.0627203 | + | 0.0362116i | −0.531032 | − | 0.847352i | \(-0.678196\pi\) |
0.468312 | + | 0.883563i | \(0.344862\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 63.2549i | − | 2.35574i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.72416 | + | 2.72749i | −0.175451 | + | 0.101297i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.7786 | − | 10.8418i | 0.696459 | − | 0.402101i | −0.109568 | − | 0.993979i | \(-0.534947\pi\) |
0.806027 | + | 0.591878i | \(0.201613\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.30345 | + | 4.79400i | 0.307114 | + | 0.177312i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.3542 | −1.12116 | −0.560580 | − | 0.828100i | \(-0.689422\pi\) | ||||
−0.560580 | + | 0.828100i | \(0.689422\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.5960 | − | 7.84963i | −0.500814 | − | 0.289145i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.1283 | − | 8.15696i | 0.519717 | − | 0.300059i | −0.217102 | − | 0.976149i | \(-0.569660\pi\) |
0.736819 | + | 0.676090i | \(0.236327\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.9040 | + | 31.0106i | 0.656833 | + | 1.13767i | 0.981431 | + | 0.191816i | \(0.0614376\pi\) |
−0.324598 | + | 0.945852i | \(0.605229\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.7601 | + | 30.7614i | −0.650681 | + | 1.12701i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 21.9493i | − | 0.802011i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.9940 | − | 32.8987i | 0.693103 | − | 1.20049i | −0.277713 | − | 0.960664i | \(-0.589577\pi\) |
0.970816 | − | 0.239825i | \(-0.0770901\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.9900 | − | 32.8916i | −0.691116 | − | 1.19705i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.6144 | + | 28.7769i | 0.603860 | + | 1.04592i | 0.992231 | + | 0.124413i | \(0.0397047\pi\) |
−0.388371 | + | 0.921503i | \(0.626962\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.4365 | 1.06707 | 0.533536 | − | 0.845777i | \(-0.320863\pi\) | ||||
0.533536 | + | 0.845777i | \(0.320863\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.65032 | − | 8.05459i | −0.168353 | − | 0.291596i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 15.4139i | − | 0.556564i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.0203 | + | 36.4082i | −0.758010 | + | 1.31291i | 0.185854 | + | 0.982577i | \(0.440495\pi\) |
−0.943864 | + | 0.330334i | \(0.892838\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.9263 | + | 17.2779i | 1.07637 | + | 0.621445i | 0.929916 | − | 0.367772i | \(-0.119879\pi\) |
0.146458 | + | 0.989217i | \(0.453213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.60921 | − | 2.78723i | 0.0578044 | − | 0.100120i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.13140 | + | 15.1918i | −0.219680 | + | 0.544302i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.6235 | − | 11.9070i | 0.737968 | − | 0.426066i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.0141 | + | 27.7372i | −0.571566 | + | 0.989982i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.9920 | 1.49685 | 0.748427 | − | 0.663217i | \(-0.230809\pi\) | ||||
0.748427 | + | 0.663217i | \(0.230809\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.0707 | 1.70920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.56275 | − | 1.47960i | 0.0910058 | − | 0.0525422i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.75839i | 0.133129i | 0.997782 | + | 0.0665645i | \(0.0212038\pi\) | ||||
−0.997782 | + | 0.0665645i | \(0.978796\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 49.8929i | − | 1.76508i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.7531 | − | 7.36298i | 0.450046 | − | 0.259834i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −81.3948 | −2.86879 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.4979 | 0.931617 | 0.465809 | − | 0.884885i | \(-0.345764\pi\) | ||||
0.465809 | + | 0.884885i | \(0.345764\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.21841 | − | 5.57446i | 0.113014 | − | 0.195746i | −0.803970 | − | 0.594670i | \(-0.797283\pi\) |
0.916984 | + | 0.398924i | \(0.130616\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.9040 | + | 10.3369i | −0.627149 | + | 0.362084i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.43725 | − | 8.51648i | 0.120254 | − | 0.297954i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.7845 | − | 27.3396i | 0.550884 | − | 0.954159i | −0.447327 | − | 0.894371i | \(-0.647624\pi\) |
0.998211 | − | 0.0597889i | \(-0.0190427\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.5552 | − | 20.5278i | −1.23938 | − | 0.715554i | −0.270410 | − | 0.962745i | \(-0.587159\pi\) |
−0.968967 | + | 0.247191i | \(0.920492\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.7172 | + | 44.5434i | −0.894273 | + | 1.54893i | −0.0595722 | + | 0.998224i | \(0.518974\pi\) |
−0.834701 | + | 0.550703i | \(0.814360\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 48.1714i | − | 1.67306i | −0.547920 | − | 0.836531i | \(-0.684580\pi\) | ||
0.547920 | − | 0.836531i | \(-0.315420\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.29529 | + | 14.3679i | 0.287415 | + | 0.497817i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 43.2085 | 1.49529 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.81320 | − | 13.5329i | −0.269742 | − | 0.467206i | 0.699053 | − | 0.715069i | \(-0.253605\pi\) |
−0.968795 | + | 0.247863i | \(0.920272\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.3745 | − | 21.4333i | −0.426707 | − | 0.739078i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.0604 | + | 19.1571i | −0.380489 | + | 0.659026i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.5859i | 0.810420i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.81320 | − | 13.5329i | 0.267833 | − | 0.463900i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.8542 | + | 23.9963i | 0.474360 | + | 0.821616i | 0.999569 | − | 0.0293572i | \(-0.00934602\pi\) |
−0.525209 | + | 0.850974i | \(0.676013\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.66275 | + | 4.42409i | −0.261755 | + | 0.151124i | −0.625135 | − | 0.780517i | \(-0.714956\pi\) |
0.363380 | + | 0.931641i | \(0.381623\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.3828 | − | 23.3150i | −1.37784 | − | 0.795499i | −0.385944 | − | 0.922522i | \(-0.626124\pi\) |
−0.991900 | + | 0.127023i | \(0.959458\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.4443 | 1.10442 | 0.552209 | − | 0.833706i | \(-0.313785\pi\) | ||||
0.552209 | + | 0.833706i | \(0.313785\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −55.7490 | − | 32.1867i | −1.89552 | − | 1.09438i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.9629 | + | 9.79351i | −0.575425 | + | 0.332222i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.0832 | + | 18.5232i | −1.08710 | + | 0.627635i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21.2398i | 0.718037i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.625492 | − | 0.361128i | 0.0211214 | − | 0.0121944i | −0.489402 | − | 0.872058i | \(-0.662785\pi\) |
0.510524 | + | 0.859864i | \(0.329452\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.37716 | 0.147470 | 0.0737351 | − | 0.997278i | \(-0.476508\pi\) | ||||
0.0737351 | + | 0.997278i | \(0.476508\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.7766 | + | 9.68598i | 0.564578 | + | 0.325959i | 0.754981 | − | 0.655747i | \(-0.227646\pi\) |
−0.190403 | + | 0.981706i | \(0.560979\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.6718 | + | 35.8046i | −0.694090 | + | 1.20220i | 0.276396 | + | 0.961044i | \(0.410860\pi\) |
−0.970486 | + | 0.241156i | \(0.922473\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.87451 | − | 3.96900i | −0.230564 | − | 0.133116i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −47.3229 | + | 6.66848i | −1.58360 | + | 0.223152i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.65032 | − | 8.05459i | −0.155443 | − | 0.269235i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.17204 | − | 1.25403i | −0.0724417 | − | 0.0418242i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.8976i | 1.29587i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.6459i | 0.786017i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.3888 | + | 37.0464i | 0.710203 | + | 1.23011i | 0.964781 | + | 0.263055i | \(0.0847300\pi\) |
−0.254578 | + | 0.967052i | \(0.581937\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.2628 | 0.406285 | 0.203142 | − | 0.979149i | \(-0.434885\pi\) | ||||
0.203142 | + | 0.979149i | \(0.434885\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.2915 | 0.704646 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.21392 | − | 9.03078i | −0.172179 | − | 0.298223i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 22.8395i | − | 0.753405i | −0.926334 | − | 0.376702i | \(-0.877058\pi\) | ||
0.926334 | − | 0.376702i | \(-0.122942\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 56.1952i | − | 1.84969i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.96863 | + | 2.29129i | 0.130488 | + | 0.0753371i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.7792 | − | 32.5264i | −0.616124 | − | 1.06716i | −0.990186 | − | 0.139754i | \(-0.955369\pi\) |
0.374062 | − | 0.927404i | \(-0.377965\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.5191 | − | 9.78835i | 0.410296 | − | 0.320800i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.1620 | + | 12.2179i | 0.692072 | + | 0.399568i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.90588 | − | 8.49723i | 0.160268 | − | 0.277593i | −0.774697 | − | 0.632333i | \(-0.782097\pi\) |
0.934965 | + | 0.354740i | \(0.115431\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.9078 | 1.10419 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.3842 | + | 21.5838i | −1.21482 | + | 0.701379i | −0.963806 | − | 0.266604i | \(-0.914098\pi\) |
−0.251017 | + | 0.967983i | \(0.580765\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 34.7497i | − | 1.12802i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.576515 | − | 0.332851i | 0.0186752 | − | 0.0107821i | −0.490633 | − | 0.871366i | \(-0.663235\pi\) |
0.509309 | + | 0.860584i | \(0.329901\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.2055 | + | 23.2127i | −1.30102 | + | 0.751144i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.2528 | + | 18.0438i | 1.00921 | + | 0.582665i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5203 | −0.952266 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.8595 | + | 20.7035i | 1.15436 | + | 0.666469i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.4299 | + | 14.1046i | −0.785612 | + | 0.453573i | −0.838416 | − | 0.545031i | \(-0.816518\pi\) |
0.0528033 | + | 0.998605i | \(0.483184\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.4850 | + | 49.3374i | 0.914127 | + | 1.58331i | 0.808175 | + | 0.588942i | \(0.200455\pi\) |
0.105951 | + | 0.994371i | \(0.466211\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.8542 | + | 30.9245i | −0.572381 | + | 0.991393i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.55057i | 0.209571i | 0.994495 | + | 0.104786i | \(0.0334156\pi\) | ||||
−0.994495 | + | 0.104786i | \(0.966584\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.65229 | + | 11.5221i | −0.212608 | + | 0.368248i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.04538 | − | 8.73886i | −0.160923 | − | 0.278726i | 0.774277 | − | 0.632847i | \(-0.218114\pi\) |
−0.935200 | + | 0.354120i | \(0.884780\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.7601 | + | 46.3499i | 0.852649 | + | 1.47683i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.0087 | −0.604440 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.90887 | + | 17.1627i | 0.314766 | + | 0.545190i | 0.979388 | − | 0.201990i | \(-0.0647408\pi\) |
−0.664622 | + | 0.747180i | \(0.731407\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 5.82591i | − | 0.184694i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.7915 | − | 30.8158i | 0.563463 | − | 0.975946i | −0.433728 | − | 0.901044i | \(-0.642802\pi\) |
0.997191 | − | 0.0749021i | \(-0.0238644\pi\) | |||||||
\(998\) | 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 | 2736.2.bm.t.1855.8 | yes | 16 | |
3.2 | odd | 2 | inner | 2736.2.bm.t.1855.2 | yes | 16 | |
4.3 | odd | 2 | inner | 2736.2.bm.t.1855.7 | yes | 16 | |
12.11 | even | 2 | inner | 2736.2.bm.t.1855.1 | yes | 16 | |
19.8 | odd | 6 | inner | 2736.2.bm.t.559.8 | yes | 16 | |
57.8 | even | 6 | inner | 2736.2.bm.t.559.2 | yes | 16 | |
76.27 | even | 6 | inner | 2736.2.bm.t.559.7 | yes | 16 | |
228.179 | odd | 6 | inner | 2736.2.bm.t.559.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.bm.t.559.1 | ✓ | 16 | 228.179 | odd | 6 | inner | |
2736.2.bm.t.559.2 | yes | 16 | 57.8 | even | 6 | inner | |
2736.2.bm.t.559.7 | yes | 16 | 76.27 | even | 6 | inner | |
2736.2.bm.t.559.8 | yes | 16 | 19.8 | odd | 6 | inner | |
2736.2.bm.t.1855.1 | yes | 16 | 12.11 | even | 2 | inner | |
2736.2.bm.t.1855.2 | yes | 16 | 3.2 | odd | 2 | inner | |
2736.2.bm.t.1855.7 | yes | 16 | 4.3 | odd | 2 | inner | |
2736.2.bm.t.1855.8 | yes | 16 | 1.1 | even | 1 | trivial |