Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.c (of order \(2\), degree \(1\), 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: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.22 | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.f.757.21 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.29659 | + | 0.564669i | 0.916829 | + | 0.399281i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.36230 | + | 1.46429i | 0.681149 | + | 0.732145i | ||||
\(5\) | − | 1.53368i | − | 0.685881i | −0.939357 | − | 0.342940i | \(-0.888577\pi\) | ||
0.939357 | − | 0.342940i | \(-0.111423\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.939505 | + | 2.66783i | 0.332165 | + | 0.943221i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.866019 | − | 1.98855i | 0.273859 | − | 0.628835i | ||||
\(11\) | 2.28335i | 0.688455i | 0.938886 | + | 0.344228i | \(0.111859\pi\) | ||||
−0.938886 | + | 0.344228i | \(0.888141\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 7.10447i | − | 1.97043i | −0.171333 | − | 0.985213i | \(-0.554807\pi\) | ||
0.171333 | − | 0.985213i | \(-0.445193\pi\) | |||||||
\(14\) | 1.29659 | + | 0.564669i | 0.346529 | + | 0.150914i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.288288 | + | 3.98960i | −0.0720720 | + | 0.997399i | ||||
\(17\) | 6.81307 | 1.65241 | 0.826206 | − | 0.563368i | \(-0.190495\pi\) | ||||
0.826206 | + | 0.563368i | \(0.190495\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.60676i | 0.368616i | 0.982869 | + | 0.184308i | \(0.0590044\pi\) | ||||
−0.982869 | + | 0.184308i | \(0.940996\pi\) | |||||||
\(20\) | 2.24575 | − | 2.08932i | 0.502164 | − | 0.467187i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.28934 | + | 2.96057i | −0.274887 | + | 0.631195i | ||||
\(23\) | 1.16757 | 0.243455 | 0.121727 | − | 0.992564i | \(-0.461157\pi\) | ||||
0.121727 | + | 0.992564i | \(0.461157\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.64784 | 0.529568 | ||||||||
\(26\) | 4.01168 | − | 9.21160i | 0.786754 | − | 1.80654i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.36230 | + | 1.46429i | 0.257450 | + | 0.276725i | ||||
\(29\) | − | 4.07059i | − | 0.755889i | −0.925828 | − | 0.377944i | \(-0.876631\pi\) | ||
0.925828 | − | 0.377944i | \(-0.123369\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.90568 | −1.41990 | −0.709951 | − | 0.704251i | \(-0.751283\pi\) | ||||
−0.709951 | + | 0.704251i | \(0.751283\pi\) | |||||||
\(32\) | −2.62659 | + | 5.01009i | −0.464321 | + | 0.885667i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.83376 | + | 3.84713i | 1.51498 | + | 0.659777i | ||||
\(35\) | − | 1.53368i | − | 0.259238i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.04836i | 1.15874i | 0.815063 | + | 0.579372i | \(0.196702\pi\) | ||||
−0.815063 | + | 0.579372i | \(0.803298\pi\) | |||||||
\(38\) | −0.907287 | + | 2.08331i | −0.147181 | + | 0.337958i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.09159 | − | 1.44090i | 0.646937 | − | 0.227826i | ||||
\(41\) | 10.1710 | 1.58844 | 0.794218 | − | 0.607633i | \(-0.207881\pi\) | ||||
0.794218 | + | 0.607633i | \(0.207881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.344719i | − | 0.0525691i | −0.999655 | − | 0.0262846i | \(-0.991632\pi\) | ||
0.999655 | − | 0.0262846i | \(-0.00836760\pi\) | |||||||
\(44\) | −3.34348 | + | 3.11060i | −0.504049 | + | 0.468941i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.51386 | + | 0.659289i | 0.223206 | + | 0.0972069i | ||||
\(47\) | 3.10859 | 0.453434 | 0.226717 | − | 0.973961i | \(-0.427201\pi\) | ||||
0.226717 | + | 0.973961i | \(0.427201\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.43317 | + | 1.49515i | 0.485523 | + | 0.211447i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.4030 | − | 9.67841i | 1.44264 | − | 1.34215i | ||||
\(53\) | 5.66835i | 0.778608i | 0.921109 | + | 0.389304i | \(0.127284\pi\) | ||||
−0.921109 | + | 0.389304i | \(0.872716\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.50191 | 0.472198 | ||||||||
\(56\) | 0.939505 | + | 2.66783i | 0.125547 | + | 0.356504i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.29853 | − | 5.27789i | 0.301812 | − | 0.693020i | ||||
\(59\) | 1.38165i | 0.179875i | 0.995947 | + | 0.0899374i | \(0.0286667\pi\) | ||||
−0.995947 | + | 0.0899374i | \(0.971333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5.50516i | − | 0.704863i | −0.935838 | − | 0.352431i | \(-0.885355\pi\) | ||
0.935838 | − | 0.352431i | \(-0.114645\pi\) | |||||||
\(62\) | −10.2504 | − | 4.46409i | −1.30181 | − | 0.566940i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.23466 | + | 5.01288i | −0.779333 | + | 0.626611i | ||||
\(65\) | −10.8960 | −1.35148 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.35907i | − | 1.02122i | −0.859811 | − | 0.510612i | \(-0.829419\pi\) | ||
0.859811 | − | 0.510612i | \(-0.170581\pi\) | |||||||
\(68\) | 9.28143 | + | 9.97630i | 1.12554 | + | 1.20980i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.866019 | − | 1.98855i | 0.103509 | − | 0.237677i | ||||
\(71\) | 12.2819 | 1.45759 | 0.728795 | − | 0.684732i | \(-0.240081\pi\) | ||||
0.728795 | + | 0.684732i | \(0.240081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.95132 | −0.696549 | −0.348275 | − | 0.937393i | \(-0.613232\pi\) | ||||
−0.348275 | + | 0.937393i | \(0.613232\pi\) | |||||||
\(74\) | −3.97999 | + | 9.13885i | −0.462665 | + | 1.06237i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.35276 | + | 2.18889i | −0.269880 | + | 0.251082i | ||||
\(77\) | 2.28335i | 0.260212i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.0027 | −1.68794 | −0.843968 | − | 0.536393i | \(-0.819787\pi\) | ||||
−0.843968 | + | 0.536393i | \(0.819787\pi\) | |||||||
\(80\) | 6.11875 | + | 0.442140i | 0.684097 | + | 0.0494328i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 13.1876 | + | 5.74322i | 1.45632 | + | 0.634233i | ||||
\(83\) | 14.7419i | 1.61814i | 0.587715 | + | 0.809068i | \(0.300027\pi\) | ||||
−0.587715 | + | 0.809068i | \(0.699973\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 10.4490i | − | 1.13336i | ||||||
\(86\) | 0.194652 | − | 0.446959i | 0.0209899 | − | 0.0481969i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.09159 | + | 2.14522i | −0.649366 | + | 0.228681i | ||||
\(89\) | −11.8923 | −1.26058 | −0.630290 | − | 0.776360i | \(-0.717064\pi\) | ||||
−0.630290 | + | 0.776360i | \(0.717064\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 7.10447i | − | 0.744751i | ||||||
\(92\) | 1.59058 | + | 1.70966i | 0.165829 | + | 0.178244i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.03057 | + | 1.75532i | 0.415722 | + | 0.181048i | ||||
\(95\) | 2.46425 | 0.252827 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.60256 | −0.264250 | −0.132125 | − | 0.991233i | \(-0.542180\pi\) | ||||
−0.132125 | + | 0.991233i | \(0.542180\pi\) | |||||||
\(98\) | 1.29659 | + | 0.564669i | 0.130976 | + | 0.0570402i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.60715 | + | 3.87720i | 0.360715 | + | 0.387720i | ||||
\(101\) | − | 9.58182i | − | 0.953427i | −0.879059 | − | 0.476713i | \(-0.841828\pi\) | ||
0.879059 | − | 0.476713i | \(-0.158172\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.44175 | 0.930323 | 0.465162 | − | 0.885226i | \(-0.345996\pi\) | ||||
0.465162 | + | 0.885226i | \(0.345996\pi\) | |||||||
\(104\) | 18.9535 | − | 6.67469i | 1.85855 | − | 0.654507i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.20074 | + | 7.34954i | −0.310884 | + | 0.713850i | ||||
\(107\) | − | 5.04240i | − | 0.487467i | −0.969842 | − | 0.243733i | \(-0.921628\pi\) | ||
0.969842 | − | 0.243733i | \(-0.0783722\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.35923i | 0.225973i | 0.993597 | + | 0.112987i | \(0.0360417\pi\) | ||||
−0.993597 | + | 0.112987i | \(0.963958\pi\) | |||||||
\(110\) | 4.54055 | + | 1.97742i | 0.432925 | + | 0.188540i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.288288 | + | 3.98960i | −0.0272407 | + | 0.376982i | ||||
\(113\) | −14.0317 | −1.31999 | −0.659994 | − | 0.751271i | \(-0.729441\pi\) | ||||
−0.659994 | + | 0.751271i | \(0.729441\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.79067i | − | 0.166981i | ||||||
\(116\) | 5.96052 | − | 5.54535i | 0.553420 | − | 0.514873i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.780172 | + | 1.79143i | −0.0718207 | + | 0.164914i | ||||
\(119\) | 6.81307 | 0.624553 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.78632 | 0.526029 | ||||||||
\(122\) | 3.10859 | − | 7.13794i | 0.281439 | − | 0.646238i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.7699 | − | 11.5762i | −0.967165 | − | 1.03957i | ||||
\(125\) | − | 11.7293i | − | 1.04910i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.0218 | −1.51044 | −0.755220 | − | 0.655472i | \(-0.772470\pi\) | ||||
−0.755220 | + | 0.655472i | \(0.772470\pi\) | |||||||
\(128\) | −10.9144 | + | 2.97914i | −0.964708 | + | 0.263322i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −14.1276 | − | 6.15261i | −1.23907 | − | 0.539619i | ||||
\(131\) | 17.8861i | 1.56272i | 0.624082 | + | 0.781359i | \(0.285473\pi\) | ||||
−0.624082 | + | 0.781359i | \(0.714527\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.60676i | 0.139324i | ||||||||
\(134\) | 4.72011 | − | 10.8383i | 0.407755 | − | 0.936287i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.40091 | + | 18.1761i | 0.548874 | + | 1.55859i | ||||
\(137\) | 9.18009 | 0.784308 | 0.392154 | − | 0.919900i | \(-0.371730\pi\) | ||||
0.392154 | + | 0.919900i | \(0.371730\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 12.0518i | − | 1.02222i | −0.859516 | − | 0.511108i | \(-0.829235\pi\) | ||
0.859516 | − | 0.511108i | \(-0.170765\pi\) | |||||||
\(140\) | 2.24575 | − | 2.08932i | 0.189800 | − | 0.176580i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.9246 | + | 6.93519i | 1.33636 | + | 0.581988i | ||||
\(143\) | 16.2220 | 1.35655 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.24296 | −0.518449 | ||||||||
\(146\) | −7.71643 | − | 3.36053i | −0.638616 | − | 0.278119i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.3208 | + | 9.60197i | −0.848368 | + | 0.789277i | ||||
\(149\) | − | 7.71091i | − | 0.631702i | −0.948809 | − | 0.315851i | \(-0.897710\pi\) | ||
0.948809 | − | 0.315851i | \(-0.102290\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.91312 | 0.481203 | 0.240601 | − | 0.970624i | \(-0.422655\pi\) | ||||
0.240601 | + | 0.970624i | \(0.422655\pi\) | |||||||
\(152\) | −4.28657 | + | 1.50956i | −0.347686 | + | 0.122441i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.28934 | + | 2.96057i | −0.103898 | + | 0.238569i | ||||
\(155\) | 12.1247i | 0.973883i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 0.906198i | − | 0.0723225i | −0.999346 | − | 0.0361612i | \(-0.988487\pi\) | ||
0.999346 | − | 0.0361612i | \(-0.0115130\pi\) | |||||||
\(158\) | −19.4524 | − | 8.47156i | −1.54755 | − | 0.673961i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.68385 | + | 4.02834i | 0.607462 | + | 0.318468i | ||||
\(161\) | 1.16757 | 0.0920172 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.46083i | 0.349400i | 0.984622 | + | 0.174700i | \(0.0558955\pi\) | ||||
−0.984622 | + | 0.174700i | \(0.944105\pi\) | |||||||
\(164\) | 13.8559 | + | 14.8932i | 1.08196 | + | 1.16297i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.32430 | + | 19.1142i | −0.646091 | + | 1.48355i | ||||
\(167\) | −22.6885 | −1.75569 | −0.877845 | − | 0.478944i | \(-0.841020\pi\) | ||||
−0.877845 | + | 0.478944i | \(0.841020\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −37.4735 | −2.88258 | ||||||||
\(170\) | 5.90025 | − | 13.5481i | 0.452528 | − | 1.03909i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.504768 | − | 0.469610i | 0.0384882 | − | 0.0358074i | ||||
\(173\) | 24.2316i | 1.84229i | 0.389218 | + | 0.921145i | \(0.372745\pi\) | ||||
−0.389218 | + | 0.921145i | \(0.627255\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.64784 | 0.200158 | ||||||||
\(176\) | −9.10964 | − | 0.658262i | −0.686665 | − | 0.0496183i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.4194 | − | 6.71520i | −1.15574 | − | 0.503326i | ||||
\(179\) | 8.82249i | 0.659424i | 0.944082 | + | 0.329712i | \(0.106952\pi\) | ||||
−0.944082 | + | 0.329712i | \(0.893048\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.29583i | − | 0.319306i | −0.987173 | − | 0.159653i | \(-0.948962\pi\) | ||
0.987173 | − | 0.159653i | \(-0.0510376\pi\) | |||||||
\(182\) | 4.01168 | − | 9.21160i | 0.297365 | − | 0.682809i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.09694 | + | 3.11488i | 0.0808672 | + | 0.229632i | ||||
\(185\) | 10.8099 | 0.794760 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.5566i | 1.13761i | ||||||||
\(188\) | 4.23483 | + | 4.55188i | 0.308856 | + | 0.331980i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.19512 | + | 1.39148i | 0.231799 | + | 0.100949i | ||||
\(191\) | −0.224849 | −0.0162695 | −0.00813476 | − | 0.999967i | \(-0.502589\pi\) | ||||
−0.00813476 | + | 0.999967i | \(0.502589\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7447 | −0.845404 | −0.422702 | − | 0.906269i | \(-0.638918\pi\) | ||||
−0.422702 | + | 0.906269i | \(0.638918\pi\) | |||||||
\(194\) | −3.37446 | − | 1.46958i | −0.242272 | − | 0.105510i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.36230 | + | 1.46429i | 0.0973070 | + | 0.104592i | ||||
\(197\) | − | 14.7998i | − | 1.05444i | −0.849729 | − | 0.527220i | \(-0.823234\pi\) | ||
0.849729 | − | 0.527220i | \(-0.176766\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.6242 | −1.39112 | −0.695561 | − | 0.718467i | \(-0.744844\pi\) | ||||
−0.695561 | + | 0.718467i | \(0.744844\pi\) | |||||||
\(200\) | 2.48766 | + | 7.06399i | 0.175904 | + | 0.499500i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.41056 | − | 12.4237i | 0.380685 | − | 0.874129i | ||||
\(203\) | − | 4.07059i | − | 0.285699i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 15.5989i | − | 1.08948i | ||||||
\(206\) | 12.2421 | + | 5.33146i | 0.852947 | + | 0.371461i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 28.3440 | + | 2.04813i | 1.96530 | + | 0.142013i | ||||
\(209\) | −3.66879 | −0.253776 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 0.913482i | − | 0.0628867i | −0.999506 | − | 0.0314434i | \(-0.989990\pi\) | ||
0.999506 | − | 0.0314434i | \(-0.0100104\pi\) | |||||||
\(212\) | −8.30011 | + | 7.72199i | −0.570054 | + | 0.530348i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.84728 | − | 6.53793i | 0.194636 | − | 0.446924i | ||||
\(215\) | −0.528687 | −0.0360561 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.90568 | −0.536673 | ||||||||
\(218\) | −1.33218 | + | 3.05896i | −0.0902269 | + | 0.207179i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.77065 | + | 5.12782i | 0.321637 | + | 0.345717i | ||||
\(221\) | − | 48.4033i | − | 3.25596i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.8646 | −0.794512 | −0.397256 | − | 0.917708i | \(-0.630037\pi\) | ||||
−0.397256 | + | 0.917708i | \(0.630037\pi\) | |||||||
\(224\) | −2.62659 | + | 5.01009i | −0.175497 | + | 0.334751i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.1933 | − | 7.92324i | −1.21020 | − | 0.527046i | ||||
\(227\) | 19.2403i | 1.27702i | 0.769613 | + | 0.638510i | \(0.220449\pi\) | ||||
−0.769613 | + | 0.638510i | \(0.779551\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 7.11176i | − | 0.469958i | −0.972000 | − | 0.234979i | \(-0.924498\pi\) | ||
0.972000 | − | 0.234979i | \(-0.0755022\pi\) | |||||||
\(230\) | 1.01114 | − | 2.32177i | 0.0666723 | − | 0.153093i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.8596 | − | 3.82434i | 0.712970 | − | 0.251080i | ||||
\(233\) | −18.5527 | −1.21542 | −0.607712 | − | 0.794157i | \(-0.707913\pi\) | ||||
−0.607712 | + | 0.794157i | \(0.707913\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 4.76757i | − | 0.311002i | ||||||
\(236\) | −2.02313 | + | 1.88221i | −0.131694 | + | 0.122522i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.83376 | + | 3.84713i | 0.572608 | + | 0.249372i | ||||
\(239\) | 3.86610 | 0.250077 | 0.125039 | − | 0.992152i | \(-0.460095\pi\) | ||||
0.125039 | + | 0.992152i | \(0.460095\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5687 | −0.745205 | −0.372603 | − | 0.927991i | \(-0.621535\pi\) | ||||
−0.372603 | + | 0.927991i | \(0.621535\pi\) | |||||||
\(242\) | 7.50250 | + | 3.26736i | 0.482279 | + | 0.210034i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.06114 | − | 7.49966i | 0.516062 | − | 0.480117i | ||||
\(245\) | − | 1.53368i | − | 0.0979829i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.4152 | 0.726331 | ||||||||
\(248\) | −7.42743 | − | 21.0910i | −0.471642 | − | 1.33928i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.62317 | − | 15.2081i | 0.418886 | − | 0.961846i | ||||
\(251\) | − | 13.5653i | − | 0.856235i | −0.903723 | − | 0.428117i | \(-0.859177\pi\) | ||
0.903723 | − | 0.428117i | \(-0.140823\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.66596i | 0.167608i | ||||||||
\(254\) | −22.0703 | − | 9.61167i | −1.38481 | − | 0.603090i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.8338 | − | 2.30031i | −0.989611 | − | 0.143769i | ||||
\(257\) | 11.1567 | 0.695938 | 0.347969 | − | 0.937506i | \(-0.386871\pi\) | ||||
0.347969 | + | 0.937506i | \(0.386871\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.04836i | 0.437964i | ||||||||
\(260\) | −14.8435 | − | 15.9548i | −0.920557 | − | 0.989477i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.0997 | + | 23.1910i | −0.623964 | + | 1.43274i | ||||
\(263\) | −13.9609 | −0.860864 | −0.430432 | − | 0.902623i | \(-0.641639\pi\) | ||||
−0.430432 | + | 0.902623i | \(0.641639\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.69341 | 0.534032 | ||||||||
\(266\) | −0.907287 | + | 2.08331i | −0.0556294 | + | 0.127736i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.2401 | − | 11.3875i | 0.747683 | − | 0.695605i | ||||
\(269\) | − | 16.1185i | − | 0.982761i | −0.870945 | − | 0.491380i | \(-0.836493\pi\) | ||
0.870945 | − | 0.491380i | \(-0.163507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.91716 | 0.541679 | 0.270840 | − | 0.962624i | \(-0.412699\pi\) | ||||
0.270840 | + | 0.962624i | \(0.412699\pi\) | |||||||
\(272\) | −1.96413 | + | 27.1814i | −0.119093 | + | 1.64811i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.9028 | + | 5.18371i | 0.719076 | + | 0.313159i | ||||
\(275\) | 6.04594i | 0.364584i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.8189i | 1.61139i | 0.592328 | + | 0.805697i | \(0.298209\pi\) | ||||
−0.592328 | + | 0.805697i | \(0.701791\pi\) | |||||||
\(278\) | 6.80525 | − | 15.6262i | 0.408152 | − | 0.937197i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.09159 | − | 1.44090i | 0.244519 | − | 0.0861100i | ||||
\(281\) | −11.0688 | −0.660306 | −0.330153 | − | 0.943927i | \(-0.607100\pi\) | ||||
−0.330153 | + | 0.943927i | \(0.607100\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 21.7405i | − | 1.29234i | −0.763194 | − | 0.646170i | \(-0.776370\pi\) | ||
0.763194 | − | 0.646170i | \(-0.223630\pi\) | |||||||
\(284\) | 16.7316 | + | 17.9842i | 0.992836 | + | 1.06717i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.0333 | + | 9.16005i | 1.24372 | + | 0.541645i | ||||
\(287\) | 10.1710 | 0.600373 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.4179 | 1.73046 | ||||||||
\(290\) | −8.09456 | − | 3.52520i | −0.475329 | − | 0.207007i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.10747 | − | 8.71446i | −0.474454 | − | 0.509975i | ||||
\(293\) | − | 8.80042i | − | 0.514126i | −0.966395 | − | 0.257063i | \(-0.917245\pi\) | ||
0.966395 | − | 0.257063i | \(-0.0827548\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.11900 | 0.123373 | ||||||||
\(296\) | −18.8039 | + | 6.62197i | −1.09295 | + | 0.384894i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.35411 | − | 9.99789i | 0.252227 | − | 0.579162i | ||||
\(299\) | − | 8.29496i | − | 0.479710i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 0.344719i | − | 0.0198693i | ||||||
\(302\) | 7.66690 | + | 3.33896i | 0.441181 | + | 0.192135i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.41033 | − | 0.463210i | −0.367657 | − | 0.0265669i | ||||
\(305\) | −8.44312 | −0.483452 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.11170i | − | 0.177594i | −0.996050 | − | 0.0887971i | \(-0.971698\pi\) | ||
0.996050 | − | 0.0887971i | \(-0.0283023\pi\) | |||||||
\(308\) | −3.34348 | + | 3.11060i | −0.190513 | + | 0.177243i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.84647 | + | 15.7208i | −0.388853 | + | 0.892884i | ||||
\(311\) | 0.443815 | 0.0251664 | 0.0125832 | − | 0.999921i | \(-0.495995\pi\) | ||||
0.0125832 | + | 0.999921i | \(0.495995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.1601 | 1.08299 | 0.541497 | − | 0.840703i | \(-0.317858\pi\) | ||||
0.541497 | + | 0.840703i | \(0.317858\pi\) | |||||||
\(314\) | 0.511702 | − | 1.17497i | 0.0288770 | − | 0.0663073i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.4382 | − | 21.9683i | −1.14974 | − | 1.23581i | ||||
\(317\) | − | 11.2142i | − | 0.629854i | −0.949116 | − | 0.314927i | \(-0.898020\pi\) | ||
0.949116 | − | 0.314927i | \(-0.101980\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.29456 | 0.520396 | ||||||||
\(320\) | 7.68814 | + | 9.56195i | 0.429780 | + | 0.534529i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.51386 | + | 0.659289i | 0.0843640 | + | 0.0367408i | ||||
\(323\) | 10.9470i | 0.609105i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 18.8115i | − | 1.04347i | ||||||
\(326\) | −2.51889 | + | 5.78388i | −0.139509 | + | 0.320339i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.55566 | + | 27.1344i | 0.527623 | + | 1.49825i | ||||
\(329\) | 3.10859 | 0.171382 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 17.8007i | − | 0.978414i | −0.872168 | − | 0.489207i | \(-0.837286\pi\) | ||
0.872168 | − | 0.489207i | \(-0.162714\pi\) | |||||||
\(332\) | −21.5864 | + | 20.0829i | −1.18471 | + | 1.10219i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −29.4177 | − | 12.8115i | −1.60967 | − | 0.701014i | ||||
\(335\) | −12.8201 | −0.700437 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.46393 | −0.188692 | −0.0943461 | − | 0.995539i | \(-0.530076\pi\) | ||||
−0.0943461 | + | 0.995539i | \(0.530076\pi\) | |||||||
\(338\) | −48.5879 | − | 21.1601i | −2.64283 | − | 1.15096i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 15.3004 | − | 14.2347i | 0.829781 | − | 0.771985i | ||||
\(341\) | − | 18.0514i | − | 0.977539i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.919652 | − | 0.323865i | 0.0495843 | − | 0.0174616i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.6828 | + | 31.4184i | −0.735592 | + | 1.68906i | ||||
\(347\) | 27.3962i | 1.47070i | 0.677686 | + | 0.735352i | \(0.262983\pi\) | ||||
−0.677686 | + | 0.735352i | \(0.737017\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.62149i | 0.0867961i | 0.999058 | + | 0.0433981i | \(0.0138184\pi\) | ||||
−0.999058 | + | 0.0433981i | \(0.986182\pi\) | |||||||
\(350\) | 3.43317 | + | 1.49515i | 0.183510 | + | 0.0799193i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11.4398 | − | 5.99743i | −0.609742 | − | 0.319664i | ||||
\(353\) | −16.5882 | −0.882903 | −0.441452 | − | 0.897285i | \(-0.645536\pi\) | ||||
−0.441452 | + | 0.897285i | \(0.645536\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 18.8364i | − | 0.999732i | ||||||
\(356\) | −16.2008 | − | 17.4137i | −0.858642 | − | 0.922927i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.98178 | + | 11.4392i | −0.263296 | + | 0.604578i | ||||
\(359\) | −7.84388 | −0.413984 | −0.206992 | − | 0.978343i | \(-0.566367\pi\) | ||||
−0.206992 | + | 0.978343i | \(0.566367\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.4183 | 0.864122 | ||||||||
\(362\) | 2.42572 | − | 5.56993i | 0.127493 | − | 0.292749i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.4030 | − | 9.67841i | 0.545266 | − | 0.507287i | ||||
\(365\) | 9.12740i | 0.477750i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.761448 | 0.0397472 | 0.0198736 | − | 0.999803i | \(-0.493674\pi\) | ||||
0.0198736 | + | 0.999803i | \(0.493674\pi\) | |||||||
\(368\) | −0.336596 | + | 4.65813i | −0.0175463 | + | 0.242822i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 14.0160 | + | 6.10402i | 0.728659 | + | 0.317333i | ||||
\(371\) | 5.66835i | 0.294286i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 13.3240i | − | 0.689888i | −0.938623 | − | 0.344944i | \(-0.887898\pi\) | ||
0.938623 | − | 0.344944i | \(-0.112102\pi\) | |||||||
\(374\) | −8.78433 | + | 20.1706i | −0.454227 | + | 1.04299i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.92054 | + | 8.29320i | 0.150615 | + | 0.427689i | ||||
\(377\) | −28.9194 | −1.48942 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 13.6595i | − | 0.701640i | −0.936443 | − | 0.350820i | \(-0.885903\pi\) | ||
0.936443 | − | 0.350820i | \(-0.114097\pi\) | |||||||
\(380\) | 3.35704 | + | 3.60837i | 0.172213 | + | 0.185106i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.291538 | − | 0.126965i | −0.0149164 | − | 0.00649612i | ||||
\(383\) | 9.70332 | 0.495816 | 0.247908 | − | 0.968784i | \(-0.420257\pi\) | ||||
0.247908 | + | 0.968784i | \(0.420257\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.50191 | 0.178474 | ||||||||
\(386\) | −15.2281 | − | 6.63188i | −0.775090 | − | 0.337554i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.54546 | − | 3.81090i | −0.179994 | − | 0.193469i | ||||
\(389\) | 24.7223i | 1.25347i | 0.779233 | + | 0.626734i | \(0.215609\pi\) | ||||
−0.779233 | + | 0.626734i | \(0.784391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.95472 | 0.402287 | ||||||||
\(392\) | 0.939505 | + | 2.66783i | 0.0474522 | + | 0.134746i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.35697 | − | 19.1892i | 0.421018 | − | 0.966740i | ||||
\(395\) | 23.0093i | 1.15772i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.1070i | 1.46084i | 0.682999 | + | 0.730420i | \(0.260675\pi\) | ||||
−0.682999 | + | 0.730420i | \(0.739325\pi\) | |||||||
\(398\) | −25.4446 | − | 11.0812i | −1.27542 | − | 0.555449i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.763340 | + | 10.5638i | −0.0381670 | + | 0.528191i | ||||
\(401\) | −13.7247 | −0.685380 | −0.342690 | − | 0.939449i | \(-0.611338\pi\) | ||||
−0.342690 | + | 0.939449i | \(0.611338\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 56.1657i | 2.79781i | ||||||||
\(404\) | 14.0306 | − | 13.0533i | 0.698046 | − | 0.649426i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.29853 | − | 5.27789i | 0.114074 | − | 0.261937i | ||||
\(407\) | −16.0939 | −0.797743 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.1707 | 0.898486 | 0.449243 | − | 0.893410i | \(-0.351694\pi\) | ||||
0.449243 | + | 0.893410i | \(0.351694\pi\) | |||||||
\(410\) | 8.80824 | − | 20.2255i | 0.435008 | − | 0.998864i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.8625 | + | 13.8255i | 0.633689 | + | 0.681131i | ||||
\(413\) | 1.38165i | 0.0679863i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.6093 | 1.10985 | ||||||||
\(416\) | 35.5941 | + | 18.6606i | 1.74514 | + | 0.914909i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.75692 | − | 2.07165i | −0.232669 | − | 0.101328i | ||||
\(419\) | − | 32.9489i | − | 1.60966i | −0.593507 | − | 0.804829i | \(-0.702257\pi\) | ||
0.593507 | − | 0.804829i | \(-0.297743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.5222i | 1.34135i | 0.741751 | + | 0.670675i | \(0.233996\pi\) | ||||
−0.741751 | + | 0.670675i | \(0.766004\pi\) | |||||||
\(422\) | 0.515815 | − | 1.18441i | 0.0251095 | − | 0.0576563i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.1222 | + | 5.32545i | −0.734400 | + | 0.258626i | ||||
\(425\) | 18.0399 | 0.875064 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5.50516i | − | 0.266413i | ||||||
\(428\) | 7.38353 | − | 6.86925i | 0.356896 | − | 0.332038i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.685491 | − | 0.298533i | −0.0330573 | − | 0.0143965i | ||||
\(431\) | 40.3524 | 1.94371 | 0.971855 | − | 0.235582i | \(-0.0756996\pi\) | ||||
0.971855 | + | 0.235582i | \(0.0756996\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.5928 | −1.85465 | −0.927327 | − | 0.374253i | \(-0.877899\pi\) | ||||
−0.927327 | + | 0.374253i | \(0.877899\pi\) | |||||||
\(434\) | −10.2504 | − | 4.46409i | −0.492037 | − | 0.214283i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.45460 | + | 3.21397i | −0.165445 | + | 0.153921i | ||||
\(437\) | 1.87600i | 0.0897413i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.68908 | −0.0806152 | −0.0403076 | − | 0.999187i | \(-0.512834\pi\) | ||||
−0.0403076 | + | 0.999187i | \(0.512834\pi\) | |||||||
\(440\) | 3.29007 | + | 9.34252i | 0.156848 | + | 0.445387i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 27.3318 | − | 62.7592i | 1.30004 | − | 2.98515i | ||||
\(443\) | − | 18.3190i | − | 0.870361i | −0.900343 | − | 0.435180i | \(-0.856685\pi\) | ||
0.900343 | − | 0.435180i | \(-0.143315\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.2389i | 0.864607i | ||||||||
\(446\) | −15.3835 | − | 6.69956i | −0.728431 | − | 0.317234i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.23466 | + | 5.01288i | −0.294560 | + | 0.236837i | ||||
\(449\) | −34.2644 | −1.61704 | −0.808518 | − | 0.588471i | \(-0.799730\pi\) | ||||
−0.808518 | + | 0.588471i | \(0.799730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.2238i | 1.09357i | ||||||||
\(452\) | −19.1153 | − | 20.5464i | −0.899108 | − | 0.966422i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.8644 | + | 24.9467i | −0.509890 | + | 1.17081i | ||||
\(455\) | −10.8960 | −0.510810 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.08541 | 0.144330 | 0.0721648 | − | 0.997393i | \(-0.477009\pi\) | ||||
0.0721648 | + | 0.997393i | \(0.477009\pi\) | |||||||
\(458\) | 4.01579 | − | 9.22104i | 0.187645 | − | 0.430871i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.62206 | − | 2.43943i | 0.122254 | − | 0.113739i | ||||
\(461\) | 8.62369i | 0.401645i | 0.979628 | + | 0.200823i | \(0.0643615\pi\) | ||||
−0.979628 | + | 0.200823i | \(0.935639\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.29178 | 0.152982 | 0.0764910 | − | 0.997070i | \(-0.475628\pi\) | ||||
0.0764910 | + | 0.997070i | \(0.475628\pi\) | |||||||
\(464\) | 16.2400 | + | 1.17350i | 0.753923 | + | 0.0544784i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.0552 | − | 10.4761i | −1.11434 | − | 0.485296i | ||||
\(467\) | − | 31.3473i | − | 1.45058i | −0.688443 | − | 0.725290i | \(-0.741706\pi\) | ||
0.688443 | − | 0.725290i | \(-0.258294\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 8.35907i | − | 0.385986i | ||||||
\(470\) | 2.69210 | − | 6.18159i | 0.124177 | − | 0.285135i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.68600 | + | 1.29806i | −0.169662 | + | 0.0597482i | ||||
\(473\) | 0.787113 | 0.0361915 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.25444i | 0.195207i | ||||||||
\(476\) | 9.28143 | + | 9.97630i | 0.425414 | + | 0.457263i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.01275 | + | 2.18307i | 0.229278 | + | 0.0998512i | ||||
\(479\) | 23.7139 | 1.08351 | 0.541757 | − | 0.840535i | \(-0.317759\pi\) | ||||
0.541757 | + | 0.840535i | \(0.317759\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.0749 | 2.28322 | ||||||||
\(482\) | −14.9999 | − | 6.53248i | −0.683225 | − | 0.297546i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.88270 | + | 8.47285i | 0.358304 | + | 0.385130i | ||||
\(485\) | 3.99148i | 0.181244i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.7317 | 1.61916 | 0.809580 | − | 0.587010i | \(-0.199695\pi\) | ||||
0.809580 | + | 0.587010i | \(0.199695\pi\) | |||||||
\(488\) | 14.6868 | − | 5.17212i | 0.664842 | − | 0.234131i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.866019 | − | 1.98855i | 0.0391227 | − | 0.0898335i | ||||
\(491\) | 40.3543i | 1.82116i | 0.413330 | + | 0.910581i | \(0.364366\pi\) | ||||
−0.413330 | + | 0.910581i | \(0.635634\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 27.7332i | − | 1.24904i | ||||||
\(494\) | 14.8008 | + | 6.44580i | 0.665921 | + | 0.290010i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.27911 | − | 31.5405i | 0.102335 | − | 1.41621i | ||||
\(497\) | 12.2819 | 0.550917 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.0646i | 1.83831i | 0.393902 | + | 0.919153i | \(0.371125\pi\) | ||||
−0.393902 | + | 0.919153i | \(0.628875\pi\) | |||||||
\(500\) | 17.1751 | − | 15.9788i | 0.768094 | − | 0.714594i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.65991 | − | 17.5887i | 0.341879 | − | 0.785021i | ||||
\(503\) | 13.5744 | 0.605252 | 0.302626 | − | 0.953109i | \(-0.402137\pi\) | ||||
0.302626 | + | 0.953109i | \(0.402137\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.6954 | −0.653937 | ||||||||
\(506\) | −1.50539 | + | 3.45667i | −0.0669226 | + | 0.153668i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23.1887 | − | 24.9248i | −1.02883 | − | 1.10586i | ||||
\(509\) | 13.3591i | 0.592132i | 0.955167 | + | 0.296066i | \(0.0956749\pi\) | ||||
−0.955167 | + | 0.296066i | \(0.904325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.95132 | −0.263271 | ||||||||
\(512\) | −19.2310 | − | 11.9234i | −0.849899 | − | 0.526945i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.4657 | + | 6.29986i | 0.638056 | + | 0.277875i | ||||
\(515\) | − | 14.4806i | − | 0.638091i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.09799i | 0.312169i | ||||||||
\(518\) | −3.97999 | + | 9.13885i | −0.174871 | + | 0.401538i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.2368 | − | 29.0686i | −0.448914 | − | 1.27474i | ||||
\(521\) | −20.5338 | −0.899600 | −0.449800 | − | 0.893129i | \(-0.648505\pi\) | ||||
−0.449800 | + | 0.893129i | \(0.648505\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.37298i | 0.191217i | 0.995419 | + | 0.0956086i | \(0.0304797\pi\) | ||||
−0.995419 | + | 0.0956086i | \(0.969520\pi\) | |||||||
\(524\) | −26.1905 | + | 24.3662i | −1.14414 | + | 1.06444i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.1015 | − | 7.88327i | −0.789264 | − | 0.343727i | ||||
\(527\) | −53.8619 | −2.34626 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6368 | −0.940730 | ||||||||
\(530\) | 11.2718 | + | 4.90890i | 0.489616 | + | 0.213229i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.35276 | + | 2.18889i | −0.102005 | + | 0.0949002i | ||||
\(533\) | − | 72.2593i | − | 3.12990i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.73340 | −0.334344 | ||||||||
\(536\) | 22.3006 | − | 7.85339i | 0.963239 | − | 0.339215i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.10160 | − | 20.8991i | 0.392398 | − | 0.901023i | ||||
\(539\) | 2.28335i | 0.0983507i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.8762i | 0.510598i | 0.966862 | + | 0.255299i | \(0.0821740\pi\) | ||||
−0.966862 | + | 0.255299i | \(0.917826\pi\) | |||||||
\(542\) | 11.5619 | + | 5.03525i | 0.496627 | + | 0.216282i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −17.8952 | + | 34.1341i | −0.767249 | + | 1.46349i | ||||
\(545\) | 3.61829 | 0.154991 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5.50044i | − | 0.235182i | −0.993062 | − | 0.117591i | \(-0.962483\pi\) | ||
0.993062 | − | 0.117591i | \(-0.0375171\pi\) | |||||||
\(548\) | 12.5060 | + | 13.4423i | 0.534231 | + | 0.574227i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.41395 | + | 7.83911i | −0.145571 | + | 0.334261i | ||||
\(551\) | 6.54045 | 0.278633 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.0027 | −0.637980 | ||||||||
\(554\) | −15.1438 | + | 34.7732i | −0.643399 | + | 1.47737i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.6473 | − | 16.4181i | 0.748410 | − | 0.696282i | ||||
\(557\) | 8.19596i | 0.347274i | 0.984810 | + | 0.173637i | \(0.0555519\pi\) | ||||
−0.984810 | + | 0.173637i | \(0.944448\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.44905 | −0.103584 | ||||||||
\(560\) | 6.11875 | + | 0.442140i | 0.258564 | + | 0.0186838i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.3516 | − | 6.25018i | −0.605388 | − | 0.263648i | ||||
\(563\) | 0.145215i | 0.00612008i | 0.999995 | + | 0.00306004i | \(0.000974043\pi\) | ||||
−0.999995 | + | 0.00306004i | \(0.999026\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.5200i | 0.905354i | ||||||||
\(566\) | 12.2762 | − | 28.1886i | 0.516007 | − | 1.18485i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.5389 | + | 32.7660i | 0.484160 | + | 1.37483i | ||||
\(569\) | 5.09548 | 0.213613 | 0.106807 | − | 0.994280i | \(-0.465937\pi\) | ||||
0.106807 | + | 0.994280i | \(0.465937\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.3061i | 1.05903i | 0.848301 | + | 0.529514i | \(0.177626\pi\) | ||||
−0.848301 | + | 0.529514i | \(0.822374\pi\) | |||||||
\(572\) | 22.0992 | + | 23.7537i | 0.924013 | + | 0.993191i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 13.1876 | + | 5.74322i | 0.550439 | + | 0.239717i | ||||
\(575\) | 3.09153 | 0.128926 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.5004 | 0.811814 | 0.405907 | − | 0.913914i | \(-0.366956\pi\) | ||||
0.405907 | + | 0.913914i | \(0.366956\pi\) | |||||||
\(578\) | 38.1430 | + | 16.6114i | 1.58654 | + | 0.690942i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.50477 | − | 9.14150i | −0.353141 | − | 0.379580i | ||||
\(581\) | 14.7419i | 0.611598i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.9428 | −0.536037 | ||||||||
\(584\) | −5.59130 | − | 15.8771i | −0.231369 | − | 0.657000i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.96932 | − | 11.4105i | 0.205281 | − | 0.471365i | ||||
\(587\) | 36.0783i | 1.48911i | 0.667561 | + | 0.744555i | \(0.267338\pi\) | ||||
−0.667561 | + | 0.744555i | \(0.732662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 12.7025i | − | 0.523399i | ||||||
\(590\) | 2.74747 | + | 1.19653i | 0.113112 | + | 0.0492604i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −28.1201 | − | 2.03196i | −1.15573 | − | 0.0835130i | ||||
\(593\) | 16.7669 | 0.688535 | 0.344268 | − | 0.938872i | \(-0.388127\pi\) | ||||
0.344268 | + | 0.938872i | \(0.388127\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 10.4490i | − | 0.428369i | ||||||
\(596\) | 11.2910 | − | 10.5046i | 0.462497 | − | 0.430283i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.68390 | − | 10.7552i | 0.191539 | − | 0.439811i | ||||
\(599\) | 31.1008 | 1.27074 | 0.635372 | − | 0.772206i | \(-0.280847\pi\) | ||||
0.635372 | + | 0.772206i | \(0.280847\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.1858 | 0.701022 | 0.350511 | − | 0.936559i | \(-0.386008\pi\) | ||||
0.350511 | + | 0.936559i | \(0.386008\pi\) | |||||||
\(602\) | 0.194652 | − | 0.446959i | 0.00793342 | − | 0.0182167i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.05543 | + | 8.65852i | 0.327771 | + | 0.352310i | ||||
\(605\) | − | 8.87434i | − | 0.360793i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.9692 | 0.526404 | 0.263202 | − | 0.964741i | \(-0.415221\pi\) | ||||
0.263202 | + | 0.964741i | \(0.415221\pi\) | |||||||
\(608\) | −8.05001 | − | 4.22030i | −0.326471 | − | 0.171156i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.9473 | − | 4.76757i | −0.443242 | − | 0.193033i | ||||
\(611\) | − | 22.0849i | − | 0.893459i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 26.5265i | − | 1.07139i | −0.844410 | − | 0.535697i | \(-0.820049\pi\) | ||
0.844410 | − | 0.535697i | \(-0.179951\pi\) | |||||||
\(614\) | 1.75708 | − | 4.03460i | 0.0709100 | − | 0.162823i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.09159 | + | 2.14522i | −0.245437 | + | 0.0864332i | ||||
\(617\) | 37.3263 | 1.50270 | 0.751350 | − | 0.659904i | \(-0.229403\pi\) | ||||
0.751350 | + | 0.659904i | \(0.229403\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.8774i | − | 0.437200i | −0.975815 | − | 0.218600i | \(-0.929851\pi\) | ||
0.975815 | − | 0.218600i | \(-0.0701489\pi\) | |||||||
\(620\) | −17.7541 | + | 16.5175i | −0.713023 | + | 0.663360i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.575446 | + | 0.250608i | 0.0230733 | + | 0.0100485i | ||||
\(623\) | −11.8923 | −0.476454 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.74975 | −0.189990 | ||||||||
\(626\) | 24.8428 | + | 10.8191i | 0.992920 | + | 0.432419i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.32694 | − | 1.23451i | 0.0529505 | − | 0.0492624i | ||||
\(629\) | 48.0210i | 1.91472i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.2943 | −0.967140 | −0.483570 | − | 0.875306i | \(-0.660660\pi\) | ||||
−0.483570 | + | 0.875306i | \(0.660660\pi\) | |||||||
\(632\) | −14.0951 | − | 40.0247i | −0.560674 | − | 1.59210i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.33233 | − | 14.5403i | 0.251489 | − | 0.577468i | ||||
\(635\) | 26.1059i | 1.03598i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 7.10447i | − | 0.281489i | ||||||
\(638\) | 12.0512 | + | 5.24835i | 0.477113 | + | 0.207784i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.56904 | + | 16.7392i | 0.180607 | + | 0.661675i | ||||
\(641\) | 16.5765 | 0.654731 | 0.327365 | − | 0.944898i | \(-0.393839\pi\) | ||||
0.327365 | + | 0.944898i | \(0.393839\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.15319i | − | 0.282094i | −0.990003 | − | 0.141047i | \(-0.954953\pi\) | ||
0.990003 | − | 0.141047i | \(-0.0450469\pi\) | |||||||
\(644\) | 1.59058 | + | 1.70966i | 0.0626775 | + | 0.0673699i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.18141 | + | 14.1937i | −0.243204 | + | 0.558445i | ||||
\(647\) | 7.94968 | 0.312534 | 0.156267 | − | 0.987715i | \(-0.450054\pi\) | ||||
0.156267 | + | 0.987715i | \(0.450054\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.15478 | −0.123836 | ||||||||
\(650\) | 10.6223 | − | 24.3908i | 0.416640 | − | 0.956687i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.53195 | + | 6.07699i | −0.255811 | + | 0.237993i | ||||
\(653\) | − | 7.45217i | − | 0.291626i | −0.989312 | − | 0.145813i | \(-0.953420\pi\) | ||
0.989312 | − | 0.145813i | \(-0.0465798\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.4315 | 1.07184 | ||||||||
\(656\) | −2.93216 | + | 40.5780i | −0.114482 | + | 1.58431i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.03057 | + | 1.75532i | 0.157128 | + | 0.0684297i | ||||
\(659\) | 26.2741i | 1.02349i | 0.859136 | + | 0.511747i | \(0.171001\pi\) | ||||
−0.859136 | + | 0.511747i | \(0.828999\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.98821i | 0.155123i | 0.996988 | + | 0.0775617i | \(0.0247135\pi\) | ||||
−0.996988 | + | 0.0775617i | \(0.975287\pi\) | |||||||
\(662\) | 10.0515 | − | 23.0802i | 0.390662 | − | 0.897038i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −39.3290 | + | 13.8501i | −1.52626 | + | 0.537488i | ||||
\(665\) | 2.46425 | 0.0955594 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 4.75268i | − | 0.184025i | ||||||
\(668\) | −30.9085 | − | 33.2226i | −1.19589 | − | 1.28542i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.6224 | − | 7.23911i | −0.642181 | − | 0.279671i | ||||
\(671\) | 12.5702 | 0.485267 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.5709 | 1.17842 | 0.589211 | − | 0.807979i | \(-0.299439\pi\) | ||||
0.589211 | + | 0.807979i | \(0.299439\pi\) | |||||||
\(674\) | −4.49130 | − | 1.95597i | −0.172998 | − | 0.0753413i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −51.0501 | − | 54.8721i | −1.96347 | − | 2.11047i | ||||
\(677\) | − | 21.9032i | − | 0.841808i | −0.907105 | − | 0.420904i | \(-0.861713\pi\) | ||
0.907105 | − | 0.420904i | \(-0.138287\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.60256 | −0.0998770 | ||||||||
\(680\) | 27.8763 | − | 9.81692i | 1.06901 | − | 0.376462i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.1931 | − | 23.4053i | 0.390313 | − | 0.896236i | ||||
\(683\) | − | 13.0423i | − | 0.499051i | −0.968368 | − | 0.249525i | \(-0.919725\pi\) | ||
0.968368 | − | 0.249525i | \(-0.0802746\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 14.0793i | − | 0.537942i | ||||||
\(686\) | 1.29659 | + | 0.564669i | 0.0495041 | + | 0.0215592i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.37529 | + | 0.0993783i | 0.0524324 | + | 0.00378876i | ||||
\(689\) | 40.2707 | 1.53419 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.25399i | − | 0.123788i | −0.998083 | − | 0.0618938i | \(-0.980286\pi\) | ||
0.998083 | − | 0.0618938i | \(-0.0197140\pi\) | |||||||
\(692\) | −35.4820 | + | 33.0106i | −1.34882 | + | 1.25487i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.4698 | + | 35.5216i | −0.587224 | + | 1.34838i | ||||
\(695\) | −18.4835 | −0.701118 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 69.2954 | 2.62475 | ||||||||
\(698\) | −0.915603 | + | 2.10240i | −0.0346561 | + | 0.0795772i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.60715 | + | 3.87720i | 0.136337 | + | 0.146545i | ||||
\(701\) | − | 2.70404i | − | 0.102130i | −0.998695 | − | 0.0510650i | \(-0.983738\pi\) | ||
0.998695 | − | 0.0510650i | \(-0.0162616\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.3250 | −0.427132 | ||||||||
\(704\) | −11.4462 | − | 14.2359i | −0.431393 | − | 0.536536i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.5082 | − | 9.36687i | −0.809471 | − | 0.352527i | ||||
\(707\) | − | 9.58182i | − | 0.360361i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.0447i | 1.84191i | 0.389668 | + | 0.920955i | \(0.372590\pi\) | ||||
−0.389668 | + | 0.920955i | \(0.627410\pi\) | |||||||
\(710\) | 10.6363 | − | 24.4231i | 0.399174 | − | 0.916583i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.1729 | − | 31.7266i | −0.418721 | − | 1.18901i | ||||
\(713\) | −9.23042 | −0.345682 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 24.8793i | − | 0.930431i | ||||||
\(716\) | −12.9187 | + | 12.0189i | −0.482794 | + | 0.449166i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.1703 | − | 4.42920i | −0.379553 | − | 0.165296i | ||||
\(719\) | 21.3291 | 0.795442 | 0.397721 | − | 0.917506i | \(-0.369801\pi\) | ||||
0.397721 | + | 0.917506i | \(0.369801\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.44175 | 0.351629 | ||||||||
\(722\) | 21.2879 | + | 9.27092i | 0.792252 | + | 0.345028i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.29033 | − | 5.85219i | 0.233778 | − | 0.217495i | ||||
\(725\) | − | 10.7783i | − | 0.400294i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.5713 | −0.874210 | −0.437105 | − | 0.899411i | \(-0.643996\pi\) | ||||
−0.437105 | + | 0.899411i | \(0.643996\pi\) | |||||||
\(728\) | 18.9535 | − | 6.67469i | 0.702465 | − | 0.247380i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.15396 | + | 11.8345i | −0.190756 | + | 0.438015i | ||||
\(731\) | − | 2.34859i | − | 0.0868658i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.28803i | 0.0845105i | 0.999107 | + | 0.0422552i | \(0.0134543\pi\) | ||||
−0.999107 | + | 0.0422552i | \(0.986546\pi\) | |||||||
\(734\) | 0.987286 | + | 0.429966i | 0.0364414 | + | 0.0158703i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.06673 | + | 5.84962i | −0.113041 | + | 0.215620i | ||||
\(737\) | 19.0867 | 0.703067 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.6953i | 1.23950i | 0.784798 | + | 0.619751i | \(0.212766\pi\) | ||||
−0.784798 | + | 0.619751i | \(0.787234\pi\) | |||||||
\(740\) | 14.7263 | + | 15.8288i | 0.541350 | + | 0.581879i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.20074 | + | 7.34954i | −0.117503 | + | 0.269810i | ||||
\(743\) | −35.7898 | −1.31300 | −0.656501 | − | 0.754326i | \(-0.727964\pi\) | ||||
−0.656501 | + | 0.754326i | \(0.727964\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.8260 | −0.433272 | ||||||||
\(746\) | 7.52362 | − | 17.2757i | 0.275459 | − | 0.632509i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22.7794 | + | 21.1927i | −0.832896 | + | 0.774883i | ||||
\(749\) | − | 5.04240i | − | 0.184245i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.35858 | 0.268518 | 0.134259 | − | 0.990946i | \(-0.457135\pi\) | ||||
0.134259 | + | 0.990946i | \(0.457135\pi\) | |||||||
\(752\) | −0.896169 | + | 12.4020i | −0.0326799 | + | 0.452255i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −37.4966 | − | 16.3299i | −1.36555 | − | 0.594699i | ||||
\(755\) | − | 9.06881i | − | 0.330048i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 23.2086i | − | 0.843530i | −0.906705 | − | 0.421765i | \(-0.861411\pi\) | ||
0.906705 | − | 0.421765i | \(-0.138589\pi\) | |||||||
\(758\) | 7.71308 | − | 17.7108i | 0.280152 | − | 0.643283i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.31517 | + | 6.57420i | 0.0839802 | + | 0.238471i | ||||
\(761\) | 22.1491 | 0.802902 | 0.401451 | − | 0.915880i | \(-0.368506\pi\) | ||||
0.401451 | + | 0.915880i | \(0.368506\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.35923i | 0.0854099i | ||||||||
\(764\) | −0.306312 | − | 0.329245i | −0.0110820 | − | 0.0119117i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.5812 | + | 5.47916i | 0.454579 | + | 0.197970i | ||||
\(767\) | 9.81586 | 0.354430 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.4818 | −0.991020 | −0.495510 | − | 0.868602i | \(-0.665019\pi\) | ||||
−0.495510 | + | 0.868602i | \(0.665019\pi\) | |||||||
\(770\) | 4.54055 | + | 1.97742i | 0.163630 | + | 0.0712613i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.9998 | − | 17.1977i | −0.575846 | − | 0.618958i | ||||
\(773\) | 39.9693i | 1.43760i | 0.695219 | + | 0.718798i | \(0.255308\pi\) | ||||
−0.695219 | + | 0.718798i | \(0.744692\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.9330 | −0.751935 | ||||||||
\(776\) | −2.44512 | − | 6.94319i | −0.0877746 | − | 0.249246i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13.9599 | + | 32.0547i | −0.500487 | + | 1.14922i | ||||
\(779\) | 16.3423i | 0.585523i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.0438i | 1.00348i | ||||||||
\(782\) | 10.3140 | + | 4.49178i | 0.368829 | + | 0.160626i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.288288 | + | 3.98960i | −0.0102960 | + | 0.142486i | ||||
\(785\) | −1.38981 | −0.0496046 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.5651i | 1.23211i | 0.787702 | + | 0.616057i | \(0.211271\pi\) | ||||
−0.787702 | + | 0.616057i | \(0.788729\pi\) | |||||||
\(788\) | 21.6711 | − | 20.1617i | 0.772002 | − | 0.718230i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.9926 | + | 29.8336i | −0.462257 | + | 1.06143i | ||||
\(791\) | −14.0317 | −0.498908 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.1112 | −1.38888 | ||||||||
\(794\) | −16.4358 | + | 37.7399i | −0.583286 | + | 1.33934i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26.7340 | − | 28.7355i | −0.947562 | − | 1.01850i | ||||
\(797\) | 16.9968i | 0.602059i | 0.953615 | + | 0.301029i | \(0.0973302\pi\) | ||||
−0.953615 | + | 0.301029i | \(0.902670\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.1790 | 0.749260 | ||||||||
\(800\) | −6.95480 | + | 13.2659i | −0.245889 | + | 0.469021i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17.7953 | − | 7.74992i | −0.628376 | − | 0.273659i | ||||
\(803\) | − | 13.5889i | − | 0.479543i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 1.79067i | − | 0.0631128i | ||||||
\(806\) | −31.7150 | + | 72.8239i | −1.11711 | + | 2.56511i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 25.5627 | − | 9.00217i | 0.899292 | − | 0.316695i | ||||
\(809\) | −2.33018 | −0.0819249 | −0.0409624 | − | 0.999161i | \(-0.513042\pi\) | ||||
−0.0409624 | + | 0.999161i | \(0.513042\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.79524i | − | 0.308843i | −0.988005 | − | 0.154421i | \(-0.950649\pi\) | ||
0.988005 | − | 0.154421i | \(-0.0493513\pi\) | |||||||
\(812\) | 5.96052 | − | 5.54535i | 0.209173 | − | 0.194604i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.8672 | − | 9.08771i | −0.731394 | − | 0.318524i | ||||
\(815\) | 6.84147 | 0.239646 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.553880 | 0.0193778 | ||||||||
\(818\) | 23.5600 | + | 10.2605i | 0.823757 | + | 0.358748i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 22.8414 | − | 21.2504i | 0.797655 | − | 0.742097i | ||||
\(821\) | 14.1689i | 0.494497i | 0.968952 | + | 0.247249i | \(0.0795265\pi\) | ||||
−0.968952 | + | 0.247249i | \(0.920474\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.53482 | 0.192932 | 0.0964659 | − | 0.995336i | \(-0.469246\pi\) | ||||
0.0964659 | + | 0.995336i | \(0.469246\pi\) | |||||||
\(824\) | 8.87057 | + | 25.1890i | 0.309021 | + | 0.877501i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.780172 | + | 1.79143i | −0.0271457 | + | 0.0623318i | ||||
\(827\) | 7.32030i | 0.254552i | 0.991867 | + | 0.127276i | \(0.0406234\pi\) | ||||
−0.991867 | + | 0.127276i | \(0.959377\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.7046i | 1.13588i | 0.823071 | + | 0.567939i | \(0.192259\pi\) | ||||
−0.823071 | + | 0.567939i | \(0.807741\pi\) | |||||||
\(830\) | 29.3150 | + | 12.7668i | 1.01754 | + | 0.443141i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 35.6139 | + | 44.2940i | 1.23469 | + | 1.53562i | ||||
\(833\) | 6.81307 | 0.236059 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.7968i | 1.20419i | ||||||||
\(836\) | −4.99799 | − | 5.37217i | −0.172859 | − | 0.185800i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.6052 | − | 42.7212i | 0.642706 | − | 1.47578i | ||||
\(839\) | 19.2836 | 0.665744 | 0.332872 | − | 0.942972i | \(-0.391982\pi\) | ||||
0.332872 | + | 0.942972i | \(0.391982\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.4303 | 0.428632 | ||||||||
\(842\) | −15.5409 | + | 35.6851i | −0.535576 | + | 1.22979i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.33760 | − | 1.24444i | 0.0460422 | − | 0.0428352i | ||||
\(845\) | 57.4723i | 1.97711i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.78632 | 0.198820 | ||||||||
\(848\) | −22.6144 | − | 1.63412i | −0.776583 | − | 0.0561158i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 23.3904 | + | 10.1866i | 0.802284 | + | 0.349397i | ||||
\(851\) | 8.22944i | 0.282102i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.5003i | 0.838874i | 0.907784 | + | 0.419437i | \(0.137772\pi\) | ||||
−0.907784 | + | 0.419437i | \(0.862228\pi\) | |||||||
\(854\) | 3.10859 | − | 7.13794i | 0.106374 | − | 0.244255i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.4523 | − | 4.73736i | 0.459789 | − | 0.161920i | ||||
\(857\) | −24.0113 | −0.820211 | −0.410105 | − | 0.912038i | \(-0.634508\pi\) | ||||
−0.410105 | + | 0.912038i | \(0.634508\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.15328i | − | 0.0734689i | −0.999325 | − | 0.0367344i | \(-0.988304\pi\) | ||
0.999325 | − | 0.0367344i | \(-0.0116956\pi\) | |||||||
\(860\) | −0.720229 | − | 0.774151i | −0.0245596 | − | 0.0263983i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 52.3206 | + | 22.7858i | 1.78205 | + | 0.776087i | ||||
\(863\) | −6.94727 | −0.236488 | −0.118244 | − | 0.992985i | \(-0.537726\pi\) | ||||
−0.118244 | + | 0.992985i | \(0.537726\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.1633 | 1.26359 | ||||||||
\(866\) | −50.0391 | − | 21.7922i | −1.70040 | − | 0.740528i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.7699 | − | 11.5762i | −0.365554 | − | 0.392922i | ||||
\(869\) | − | 34.2564i | − | 1.16207i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −59.3868 | −2.01225 | ||||||||
\(872\) | −6.29403 | + | 2.21651i | −0.213143 | + | 0.0750604i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.05932 | + | 2.43241i | −0.0358320 | + | 0.0822774i | ||||
\(875\) | − | 11.7293i | − | 0.396523i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 24.2307i | − | 0.818211i | −0.912487 | − | 0.409106i | \(-0.865841\pi\) | ||
0.912487 | − | 0.409106i | \(-0.134159\pi\) | |||||||
\(878\) | −2.19004 | − | 0.953769i | −0.0739103 | − | 0.0321881i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00956 | + | 13.9712i | −0.0340323 | + | 0.470970i | ||||
\(881\) | −42.4462 | −1.43005 | −0.715024 | − | 0.699100i | \(-0.753584\pi\) | ||||
−0.715024 | + | 0.699100i | \(0.753584\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.397509i | 0.0133773i | 0.999978 | + | 0.00668863i | \(0.00212907\pi\) | ||||
−0.999978 | + | 0.00668863i | \(0.997871\pi\) | |||||||
\(884\) | 70.8764 | − | 65.9397i | 2.38383 | − | 2.21779i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.3442 | − | 23.7522i | 0.347519 | − | 0.797971i | ||||
\(887\) | −36.3698 | −1.22118 | −0.610590 | − | 0.791947i | \(-0.709068\pi\) | ||||
−0.610590 | + | 0.791947i | \(0.709068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.0218 | −0.570892 | ||||||||
\(890\) | −10.2989 | + | 23.6484i | −0.345221 | + | 0.792696i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.1631 | − | 17.3732i | −0.541181 | − | 0.581698i | ||||
\(893\) | 4.99476i | 0.167143i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.5308 | 0.452286 | ||||||||
\(896\) | −10.9144 | + | 2.97914i | −0.364625 | + | 0.0995262i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −44.4269 | − | 19.3480i | −1.48254 | − | 0.645652i | ||||
\(899\) | 32.1807i | 1.07329i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38.6189i | 1.28658i | ||||||||
\(902\) | −13.1138 | + | 30.1118i | −0.436641 | + | 1.00261i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.1828 | − | 37.4341i | −0.438454 | − | 1.24504i | ||||
\(905\) | −6.58840 | −0.219006 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 52.1212i | − | 1.73066i | −0.501205 | − | 0.865329i | \(-0.667110\pi\) | ||
0.501205 | − | 0.865329i | \(-0.332890\pi\) | |||||||
\(908\) | −28.1733 | + | 26.2110i | −0.934964 | + | 0.869841i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −14.1276 | − | 6.15261i | −0.468325 | − | 0.203957i | ||||
\(911\) | 25.8160 | 0.855322 | 0.427661 | − | 0.903939i | \(-0.359338\pi\) | ||||
0.427661 | + | 0.903939i | \(0.359338\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.6609 | −1.11401 | ||||||||
\(914\) | 4.00052 | + | 1.74224i | 0.132326 | + | 0.0576281i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.4137 | − | 9.68833i | 0.344077 | − | 0.320112i | ||||
\(917\) | 17.8861i | 0.590652i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.71609 | −0.155569 | −0.0777847 | − | 0.996970i | \(-0.524785\pi\) | ||||
−0.0777847 | + | 0.996970i | \(0.524785\pi\) | |||||||
\(920\) | 4.77721 | − | 1.68234i | 0.157500 | − | 0.0554652i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.86953 | + | 11.1814i | −0.160369 | + | 0.368240i | ||||
\(923\) | − | 87.2562i | − | 2.87207i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.6629i | 0.613634i | ||||||||
\(926\) | 4.26810 | + | 1.85877i | 0.140258 | + | 0.0610829i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 20.3940 | + | 10.6918i | 0.669466 | + | 0.350975i | ||||
\(929\) | 48.4774 | 1.59049 | 0.795246 | − | 0.606287i | \(-0.207342\pi\) | ||||
0.795246 | + | 0.606287i | \(0.207342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.60676i | 0.0526594i | ||||||||
\(932\) | −25.2742 | − | 27.1665i | −0.827885 | − | 0.889867i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.7008 | − | 40.6446i | 0.579189 | − | 1.32993i | ||||
\(935\) | 23.8588 | 0.780266 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.5193 | 0.376319 | 0.188159 | − | 0.982138i | \(-0.439748\pi\) | ||||
0.188159 | + | 0.982138i | \(0.439748\pi\) | |||||||
\(938\) | 4.72011 | − | 10.8383i | 0.154117 | − | 0.353883i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.98110 | − | 6.49485i | 0.227698 | − | 0.211839i | ||||
\(941\) | − | 32.3390i | − | 1.05422i | −0.849796 | − | 0.527111i | \(-0.823275\pi\) | ||
0.849796 | − | 0.527111i | \(-0.176725\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.8753 | 0.386712 | ||||||||
\(944\) | −5.51221 | − | 0.398312i | −0.179407 | − | 0.0129639i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.02056 | + | 0.444458i | 0.0331814 | + | 0.0144506i | ||||
\(947\) | − | 37.4382i | − | 1.21658i | −0.793715 | − | 0.608289i | \(-0.791856\pi\) | ||
0.793715 | − | 0.608289i | \(-0.208144\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.2810i | 1.37250i | ||||||||
\(950\) | −2.40235 | + | 5.51627i | −0.0779426 | + | 0.178972i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.40091 | + | 18.1761i | 0.207455 | + | 0.589092i | ||||
\(953\) | −18.4974 | −0.599190 | −0.299595 | − | 0.954066i | \(-0.596852\pi\) | ||||
−0.299595 | + | 0.954066i | \(0.596852\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.344846i | 0.0111590i | ||||||||
\(956\) | 5.26678 | + | 5.66109i | 0.170340 | + | 0.183093i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.7472 | + | 13.3905i | 0.993397 | + | 0.432627i | ||||
\(959\) | 9.18009 | 0.296441 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.4998 | 1.01612 | ||||||||
\(962\) | 64.9267 | + | 28.2757i | 2.09332 | + | 0.911647i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.7600 | − | 16.9399i | −0.507596 | − | 0.545598i | ||||
\(965\) | 18.0126i | 0.579846i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.4221 | 1.42852 | 0.714259 | − | 0.699882i | \(-0.246764\pi\) | ||||
0.714259 | + | 0.699882i | \(0.246764\pi\) | |||||||
\(968\) | 5.43628 | + | 15.4369i | 0.174729 | + | 0.496162i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.25387 | + | 5.17532i | −0.0723672 | + | 0.166169i | ||||
\(971\) | − | 37.5434i | − | 1.20482i | −0.798185 | − | 0.602412i | \(-0.794206\pi\) | ||
0.798185 | − | 0.602412i | \(-0.205794\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 12.0518i | − | 0.386361i | ||||||
\(974\) | 46.3295 | + | 20.1766i | 1.48449 | + | 0.646500i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.9634 | + | 1.58707i | 0.703030 | + | 0.0508009i | ||||
\(977\) | −6.89949 | −0.220734 | −0.110367 | − | 0.993891i | \(-0.535203\pi\) | ||||
−0.110367 | + | 0.993891i | \(0.535203\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 27.1542i | − | 0.867853i | ||||||
\(980\) | 2.24575 | − | 2.08932i | 0.0717377 | − | 0.0667410i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −22.7868 | + | 52.3230i | −0.727156 | + | 1.66969i | ||||
\(983\) | 28.9252 | 0.922571 | 0.461285 | − | 0.887252i | \(-0.347388\pi\) | ||||
0.461285 | + | 0.887252i | \(0.347388\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.6980 | −0.723220 | ||||||||
\(986\) | 15.6601 | − | 35.9586i | 0.498718 | − | 1.14515i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.5509 | + | 16.7151i | 0.494739 | + | 0.531779i | ||||
\(989\) | − | 0.402483i | − | 0.0127982i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.7278 | 1.19846 | 0.599232 | − | 0.800575i | \(-0.295473\pi\) | ||||
0.599232 | + | 0.800575i | \(0.295473\pi\) | |||||||
\(992\) | 20.7650 | − | 39.6082i | 0.659290 | − | 1.25756i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.9246 | + | 6.93519i | 0.505096 | + | 0.219971i | ||||
\(995\) | 30.0971i | 0.954144i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 53.0914i | − | 1.68142i | −0.541484 | − | 0.840711i | \(-0.682137\pi\) | ||
0.541484 | − | 0.840711i | \(-0.317863\pi\) | |||||||
\(998\) | −23.1879 | + | 53.2440i | −0.734001 | + | 1.68541i | ||||
\(999\) | 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.c.f.757.22 | yes | 24 | |
3.2 | odd | 2 | inner | 1512.2.c.f.757.3 | ✓ | 24 | |
4.3 | odd | 2 | 6048.2.c.g.3025.9 | 24 | |||
8.3 | odd | 2 | 6048.2.c.g.3025.16 | 24 | |||
8.5 | even | 2 | inner | 1512.2.c.f.757.21 | yes | 24 | |
12.11 | even | 2 | 6048.2.c.g.3025.15 | 24 | |||
24.5 | odd | 2 | inner | 1512.2.c.f.757.4 | yes | 24 | |
24.11 | even | 2 | 6048.2.c.g.3025.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.f.757.3 | ✓ | 24 | 3.2 | odd | 2 | inner | |
1512.2.c.f.757.4 | yes | 24 | 24.5 | odd | 2 | inner | |
1512.2.c.f.757.21 | yes | 24 | 8.5 | even | 2 | inner | |
1512.2.c.f.757.22 | yes | 24 | 1.1 | even | 1 | trivial | |
6048.2.c.g.3025.9 | 24 | 4.3 | odd | 2 | |||
6048.2.c.g.3025.10 | 24 | 24.11 | even | 2 | |||
6048.2.c.g.3025.15 | 24 | 12.11 | even | 2 | |||
6048.2.c.g.3025.16 | 24 | 8.3 | odd | 2 |