Properties

Label 1008.2.r.g.337.1
Level $1008$
Weight $2$
Character 1008.337
Analytic conductor $8.049$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(337,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.337");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 337.1
Root \(0.500000 + 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 1008.337
Dual form 1008.2.r.g.673.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.29418 + 1.15113i) q^{3} +(0.555632 - 0.962383i) q^{5} +(0.500000 + 0.866025i) q^{7} +(0.349814 - 2.97954i) q^{9} +O(q^{10})\) \(q+(-1.29418 + 1.15113i) q^{3} +(0.555632 - 0.962383i) q^{5} +(0.500000 + 0.866025i) q^{7} +(0.349814 - 2.97954i) q^{9} +(-0.944368 - 1.63569i) q^{11} +(0.500000 - 0.866025i) q^{13} +(0.388736 + 1.88510i) q^{15} -5.87636 q^{17} -7.09888 q^{19} +(-1.64400 - 0.545231i) q^{21} +(1.99381 - 3.45338i) q^{23} +(1.88255 + 3.26067i) q^{25} +(2.97710 + 4.25874i) q^{27} +(-0.493810 - 0.855304i) q^{29} +(-0.333104 + 0.576953i) q^{31} +(3.10507 + 1.02980i) q^{33} +1.11126 q^{35} -1.33379 q^{37} +(0.349814 + 1.69636i) q^{39} +(0.944368 - 1.63569i) q^{41} +(-5.43199 - 9.40848i) q^{43} +(-2.67309 - 1.99218i) q^{45} +(-5.54944 - 9.61192i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(7.60507 - 6.76443i) q^{51} -12.2101 q^{53} -2.09888 q^{55} +(9.18725 - 8.17172i) q^{57} +(2.38255 - 4.12669i) q^{59} +(-1.88255 - 3.26067i) q^{61} +(2.75526 - 1.18682i) q^{63} +(-0.555632 - 0.962383i) q^{65} +(2.04944 - 3.54974i) q^{67} +(1.39493 + 6.76443i) q^{69} +10.7651 q^{71} -3.09888 q^{73} +(-6.18980 - 2.05285i) q^{75} +(0.944368 - 1.63569i) q^{77} +(3.21565 + 5.56967i) q^{79} +(-8.75526 - 2.08457i) q^{81} +(-5.93818 - 10.2852i) q^{83} +(-3.26509 + 5.65531i) q^{85} +(1.62364 + 0.538481i) q^{87} +14.3090 q^{89} +1.00000 q^{91} +(-0.233049 - 1.13013i) q^{93} +(-3.94437 + 6.83185i) q^{95} +(-0.382546 - 0.662589i) q^{97} +(-5.20396 + 2.24159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{3} + 3 q^{5} + 3 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{3} + 3 q^{5} + 3 q^{7} - 4 q^{9} - 6 q^{11} + 3 q^{13} + 3 q^{15} - 6 q^{19} + 2 q^{21} - 6 q^{23} - 6 q^{25} + 7 q^{27} + 15 q^{29} - 3 q^{31} + 6 q^{35} - 6 q^{37} - 4 q^{39} + 6 q^{41} + 3 q^{43} - 33 q^{45} - 15 q^{47} - 3 q^{49} + 27 q^{51} - 36 q^{53} + 24 q^{55} + 7 q^{57} - 3 q^{59} + 6 q^{61} + 4 q^{63} - 3 q^{65} - 6 q^{67} + 27 q^{69} + 30 q^{71} + 18 q^{73} - 47 q^{75} + 6 q^{77} + 3 q^{79} - 40 q^{81} - 18 q^{83} + 15 q^{85} + 45 q^{87} + 12 q^{89} + 6 q^{91} + 25 q^{93} - 24 q^{95} + 15 q^{97} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.29418 + 1.15113i −0.747196 + 0.664603i
\(4\) 0 0
\(5\) 0.555632 0.962383i 0.248486 0.430391i −0.714620 0.699513i \(-0.753400\pi\)
0.963106 + 0.269122i \(0.0867336\pi\)
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 0 0
\(9\) 0.349814 2.97954i 0.116605 0.993178i
\(10\) 0 0
\(11\) −0.944368 1.63569i −0.284738 0.493180i 0.687808 0.725893i \(-0.258573\pi\)
−0.972546 + 0.232713i \(0.925240\pi\)
\(12\) 0 0
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 0 0
\(15\) 0.388736 + 1.88510i 0.100371 + 0.486731i
\(16\) 0 0
\(17\) −5.87636 −1.42523 −0.712613 0.701557i \(-0.752488\pi\)
−0.712613 + 0.701557i \(0.752488\pi\)
\(18\) 0 0
\(19\) −7.09888 −1.62860 −0.814298 0.580447i \(-0.802878\pi\)
−0.814298 + 0.580447i \(0.802878\pi\)
\(20\) 0 0
\(21\) −1.64400 0.545231i −0.358749 0.118979i
\(22\) 0 0
\(23\) 1.99381 3.45338i 0.415738 0.720080i −0.579767 0.814782i \(-0.696857\pi\)
0.995506 + 0.0947024i \(0.0301899\pi\)
\(24\) 0 0
\(25\) 1.88255 + 3.26067i 0.376509 + 0.652133i
\(26\) 0 0
\(27\) 2.97710 + 4.25874i 0.572943 + 0.819595i
\(28\) 0 0
\(29\) −0.493810 0.855304i −0.0916982 0.158826i 0.816528 0.577306i \(-0.195896\pi\)
−0.908226 + 0.418480i \(0.862563\pi\)
\(30\) 0 0
\(31\) −0.333104 + 0.576953i −0.0598272 + 0.103624i −0.894388 0.447292i \(-0.852388\pi\)
0.834561 + 0.550916i \(0.185722\pi\)
\(32\) 0 0
\(33\) 3.10507 + 1.02980i 0.540524 + 0.179265i
\(34\) 0 0
\(35\) 1.11126 0.187838
\(36\) 0 0
\(37\) −1.33379 −0.219274 −0.109637 0.993972i \(-0.534969\pi\)
−0.109637 + 0.993972i \(0.534969\pi\)
\(38\) 0 0
\(39\) 0.349814 + 1.69636i 0.0560151 + 0.271635i
\(40\) 0 0
\(41\) 0.944368 1.63569i 0.147485 0.255452i −0.782812 0.622258i \(-0.786215\pi\)
0.930297 + 0.366806i \(0.119549\pi\)
\(42\) 0 0
\(43\) −5.43199 9.40848i −0.828370 1.43478i −0.899316 0.437299i \(-0.855935\pi\)
0.0709455 0.997480i \(-0.477398\pi\)
\(44\) 0 0
\(45\) −2.67309 1.99218i −0.398480 0.296977i
\(46\) 0 0
\(47\) −5.54944 9.61192i −0.809469 1.40204i −0.913232 0.407440i \(-0.866422\pi\)
0.103763 0.994602i \(-0.466912\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0 0
\(51\) 7.60507 6.76443i 1.06492 0.947210i
\(52\) 0 0
\(53\) −12.2101 −1.67719 −0.838596 0.544753i \(-0.816623\pi\)
−0.838596 + 0.544753i \(0.816623\pi\)
\(54\) 0 0
\(55\) −2.09888 −0.283014
\(56\) 0 0
\(57\) 9.18725 8.17172i 1.21688 1.08237i
\(58\) 0 0
\(59\) 2.38255 4.12669i 0.310181 0.537249i −0.668220 0.743963i \(-0.732944\pi\)
0.978401 + 0.206714i \(0.0662770\pi\)
\(60\) 0 0
\(61\) −1.88255 3.26067i −0.241035 0.417485i 0.719974 0.694001i \(-0.244154\pi\)
−0.961009 + 0.276515i \(0.910820\pi\)
\(62\) 0 0
\(63\) 2.75526 1.18682i 0.347130 0.149525i
\(64\) 0 0
\(65\) −0.555632 0.962383i −0.0689177 0.119369i
\(66\) 0 0
\(67\) 2.04944 3.54974i 0.250379 0.433670i −0.713251 0.700909i \(-0.752778\pi\)
0.963630 + 0.267239i \(0.0861114\pi\)
\(68\) 0 0
\(69\) 1.39493 + 6.76443i 0.167929 + 0.814342i
\(70\) 0 0
\(71\) 10.7651 1.27758 0.638791 0.769381i \(-0.279435\pi\)
0.638791 + 0.769381i \(0.279435\pi\)
\(72\) 0 0
\(73\) −3.09888 −0.362697 −0.181348 0.983419i \(-0.558046\pi\)
−0.181348 + 0.983419i \(0.558046\pi\)
\(74\) 0 0
\(75\) −6.18980 2.05285i −0.714736 0.237042i
\(76\) 0 0
\(77\) 0.944368 1.63569i 0.107621 0.186405i
\(78\) 0 0
\(79\) 3.21565 + 5.56967i 0.361789 + 0.626637i 0.988255 0.152812i \(-0.0488328\pi\)
−0.626466 + 0.779448i \(0.715499\pi\)
\(80\) 0 0
\(81\) −8.75526 2.08457i −0.972807 0.231619i
\(82\) 0 0
\(83\) −5.93818 10.2852i −0.651800 1.12895i −0.982686 0.185280i \(-0.940681\pi\)
0.330886 0.943671i \(-0.392652\pi\)
\(84\) 0 0
\(85\) −3.26509 + 5.65531i −0.354149 + 0.613404i
\(86\) 0 0
\(87\) 1.62364 + 0.538481i 0.174073 + 0.0577313i
\(88\) 0 0
\(89\) 14.3090 1.51675 0.758377 0.651816i \(-0.225993\pi\)
0.758377 + 0.651816i \(0.225993\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −0.233049 1.13013i −0.0241660 0.117189i
\(94\) 0 0
\(95\) −3.94437 + 6.83185i −0.404684 + 0.700933i
\(96\) 0 0
\(97\) −0.382546 0.662589i −0.0388417 0.0672757i 0.845951 0.533261i \(-0.179033\pi\)
−0.884793 + 0.465985i \(0.845700\pi\)
\(98\) 0 0
\(99\) −5.20396 + 2.24159i −0.523018 + 0.225288i
\(100\) 0 0
\(101\) −4.43818 7.68715i −0.441615 0.764900i 0.556194 0.831052i \(-0.312261\pi\)
−0.997810 + 0.0661523i \(0.978928\pi\)
\(102\) 0 0
\(103\) −4.98143 + 8.62809i −0.490835 + 0.850151i −0.999944 0.0105508i \(-0.996642\pi\)
0.509109 + 0.860702i \(0.329975\pi\)
\(104\) 0 0
\(105\) −1.43818 + 1.27921i −0.140352 + 0.124838i
\(106\) 0 0
\(107\) 5.22253 0.504881 0.252440 0.967612i \(-0.418767\pi\)
0.252440 + 0.967612i \(0.418767\pi\)
\(108\) 0 0
\(109\) −9.09888 −0.871515 −0.435758 0.900064i \(-0.643519\pi\)
−0.435758 + 0.900064i \(0.643519\pi\)
\(110\) 0 0
\(111\) 1.72617 1.53536i 0.163841 0.145730i
\(112\) 0 0
\(113\) 6.21015 10.7563i 0.584202 1.01187i −0.410773 0.911738i \(-0.634741\pi\)
0.994974 0.100129i \(-0.0319256\pi\)
\(114\) 0 0
\(115\) −2.21565 3.83762i −0.206610 0.357860i
\(116\) 0 0
\(117\) −2.40545 1.79272i −0.222384 0.165737i
\(118\) 0 0
\(119\) −2.93818 5.08907i −0.269342 0.466515i
\(120\) 0 0
\(121\) 3.71634 6.43689i 0.337849 0.585172i
\(122\) 0 0
\(123\) 0.660706 + 3.20397i 0.0595739 + 0.288892i
\(124\) 0 0
\(125\) 9.74033 0.871202
\(126\) 0 0
\(127\) −7.66621 −0.680266 −0.340133 0.940377i \(-0.610472\pi\)
−0.340133 + 0.940377i \(0.610472\pi\)
\(128\) 0 0
\(129\) 17.8603 + 5.92338i 1.57251 + 0.521524i
\(130\) 0 0
\(131\) −7.27128 + 12.5942i −0.635295 + 1.10036i 0.351158 + 0.936316i \(0.385788\pi\)
−0.986453 + 0.164047i \(0.947545\pi\)
\(132\) 0 0
\(133\) −3.54944 6.14781i −0.307776 0.533083i
\(134\) 0 0
\(135\) 5.75271 0.498817i 0.495115 0.0429313i
\(136\) 0 0
\(137\) −2.32072 4.01961i −0.198273 0.343419i 0.749696 0.661783i \(-0.230200\pi\)
−0.947969 + 0.318364i \(0.896867\pi\)
\(138\) 0 0
\(139\) −9.64833 + 16.7114i −0.818360 + 1.41744i 0.0885293 + 0.996074i \(0.471783\pi\)
−0.906890 + 0.421368i \(0.861550\pi\)
\(140\) 0 0
\(141\) 18.2465 + 6.05146i 1.53663 + 0.509625i
\(142\) 0 0
\(143\) −1.88874 −0.157944
\(144\) 0 0
\(145\) −1.09751 −0.0911430
\(146\) 0 0
\(147\) −0.349814 1.69636i −0.0288522 0.139913i
\(148\) 0 0
\(149\) 6.82072 11.8138i 0.558775 0.967828i −0.438824 0.898573i \(-0.644605\pi\)
0.997599 0.0692543i \(-0.0220620\pi\)
\(150\) 0 0
\(151\) 8.48143 + 14.6903i 0.690209 + 1.19548i 0.971769 + 0.235934i \(0.0758148\pi\)
−0.281560 + 0.959544i \(0.590852\pi\)
\(152\) 0 0
\(153\) −2.05563 + 17.5088i −0.166188 + 1.41550i
\(154\) 0 0
\(155\) 0.370166 + 0.641147i 0.0297325 + 0.0514981i
\(156\) 0 0
\(157\) −11.3145 + 19.5973i −0.902998 + 1.56404i −0.0794160 + 0.996842i \(0.525306\pi\)
−0.823582 + 0.567197i \(0.808028\pi\)
\(158\) 0 0
\(159\) 15.8022 14.0554i 1.25319 1.11467i
\(160\) 0 0
\(161\) 3.98762 0.314269
\(162\) 0 0
\(163\) 18.0989 1.41761 0.708807 0.705402i \(-0.249234\pi\)
0.708807 + 0.705402i \(0.249234\pi\)
\(164\) 0 0
\(165\) 2.71634 2.41608i 0.211467 0.188092i
\(166\) 0 0
\(167\) −8.61126 + 14.9151i −0.666360 + 1.15417i 0.312555 + 0.949900i \(0.398815\pi\)
−0.978915 + 0.204269i \(0.934518\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 0 0
\(171\) −2.48329 + 21.1514i −0.189902 + 1.61749i
\(172\) 0 0
\(173\) 0.431988 + 0.748226i 0.0328435 + 0.0568865i 0.881980 0.471287i \(-0.156210\pi\)
−0.849136 + 0.528174i \(0.822877\pi\)
\(174\) 0 0
\(175\) −1.88255 + 3.26067i −0.142307 + 0.246483i
\(176\) 0 0
\(177\) 1.66690 + 8.08330i 0.125292 + 0.607578i
\(178\) 0 0
\(179\) 4.67859 0.349694 0.174847 0.984596i \(-0.444057\pi\)
0.174847 + 0.984596i \(0.444057\pi\)
\(180\) 0 0
\(181\) −16.8640 −1.25349 −0.626745 0.779225i \(-0.715613\pi\)
−0.626745 + 0.779225i \(0.715613\pi\)
\(182\) 0 0
\(183\) 6.18980 + 2.05285i 0.457563 + 0.151751i
\(184\) 0 0
\(185\) −0.741098 + 1.28362i −0.0544866 + 0.0943736i
\(186\) 0 0
\(187\) 5.54944 + 9.61192i 0.405815 + 0.702893i
\(188\) 0 0
\(189\) −2.19963 + 4.70761i −0.159999 + 0.342429i
\(190\) 0 0
\(191\) −8.53087 14.7759i −0.617272 1.06915i −0.989981 0.141199i \(-0.954904\pi\)
0.372709 0.927948i \(-0.378429\pi\)
\(192\) 0 0
\(193\) −3.71634 + 6.43689i −0.267508 + 0.463337i −0.968218 0.250109i \(-0.919533\pi\)
0.700710 + 0.713446i \(0.252867\pi\)
\(194\) 0 0
\(195\) 1.82691 + 0.605896i 0.130828 + 0.0433891i
\(196\) 0 0
\(197\) −26.2953 −1.87346 −0.936730 0.350052i \(-0.886164\pi\)
−0.936730 + 0.350052i \(0.886164\pi\)
\(198\) 0 0
\(199\) −10.4327 −0.739553 −0.369776 0.929121i \(-0.620566\pi\)
−0.369776 + 0.929121i \(0.620566\pi\)
\(200\) 0 0
\(201\) 1.43385 + 6.95317i 0.101136 + 0.490439i
\(202\) 0 0
\(203\) 0.493810 0.855304i 0.0346587 0.0600306i
\(204\) 0 0
\(205\) −1.04944 1.81769i −0.0732962 0.126953i
\(206\) 0 0
\(207\) −9.59201 7.14867i −0.666690 0.496867i
\(208\) 0 0
\(209\) 6.70396 + 11.6116i 0.463723 + 0.803191i
\(210\) 0 0
\(211\) 12.6978 21.9932i 0.874150 1.51407i 0.0164855 0.999864i \(-0.494752\pi\)
0.857665 0.514209i \(-0.171914\pi\)
\(212\) 0 0
\(213\) −13.9320 + 12.3920i −0.954604 + 0.849085i
\(214\) 0 0
\(215\) −12.0727 −0.823355
\(216\) 0 0
\(217\) −0.666208 −0.0452251
\(218\) 0 0
\(219\) 4.01052 3.56721i 0.271006 0.241050i
\(220\) 0 0
\(221\) −2.93818 + 5.08907i −0.197643 + 0.342328i
\(222\) 0 0
\(223\) 7.26509 + 12.5835i 0.486507 + 0.842654i 0.999880 0.0155114i \(-0.00493764\pi\)
−0.513373 + 0.858165i \(0.671604\pi\)
\(224\) 0 0
\(225\) 10.3738 4.46849i 0.691587 0.297899i
\(226\) 0 0
\(227\) 9.70396 + 16.8077i 0.644074 + 1.11557i 0.984514 + 0.175303i \(0.0560906\pi\)
−0.340440 + 0.940266i \(0.610576\pi\)
\(228\) 0 0
\(229\) 5.26509 9.11941i 0.347927 0.602627i −0.637954 0.770074i \(-0.720219\pi\)
0.985881 + 0.167447i \(0.0535523\pi\)
\(230\) 0 0
\(231\) 0.660706 + 3.20397i 0.0434713 + 0.210806i
\(232\) 0 0
\(233\) 22.6414 1.48329 0.741645 0.670792i \(-0.234046\pi\)
0.741645 + 0.670792i \(0.234046\pi\)
\(234\) 0 0
\(235\) −12.3338 −0.804568
\(236\) 0 0
\(237\) −10.5730 3.50654i −0.686792 0.227775i
\(238\) 0 0
\(239\) 2.48762 4.30868i 0.160911 0.278706i −0.774285 0.632837i \(-0.781890\pi\)
0.935196 + 0.354132i \(0.115224\pi\)
\(240\) 0 0
\(241\) −0.117454 0.203436i −0.00756588 0.0131045i 0.862218 0.506538i \(-0.169075\pi\)
−0.869784 + 0.493433i \(0.835742\pi\)
\(242\) 0 0
\(243\) 13.7305 7.38061i 0.880812 0.473466i
\(244\) 0 0
\(245\) 0.555632 + 0.962383i 0.0354980 + 0.0614844i
\(246\) 0 0
\(247\) −3.54944 + 6.14781i −0.225846 + 0.391176i
\(248\) 0 0
\(249\) 19.5247 + 6.47536i 1.23733 + 0.410359i
\(250\) 0 0
\(251\) 8.09888 0.511197 0.255599 0.966783i \(-0.417727\pi\)
0.255599 + 0.966783i \(0.417727\pi\)
\(252\) 0 0
\(253\) −7.53156 −0.473505
\(254\) 0 0
\(255\) −2.28435 11.0775i −0.143052 0.693702i
\(256\) 0 0
\(257\) −11.8764 + 20.5705i −0.740827 + 1.28315i 0.211293 + 0.977423i \(0.432233\pi\)
−0.952119 + 0.305727i \(0.901101\pi\)
\(258\) 0 0
\(259\) −0.666896 1.15510i −0.0414389 0.0717743i
\(260\) 0 0
\(261\) −2.72115 + 1.17213i −0.168435 + 0.0725529i
\(262\) 0 0
\(263\) −3.32691 5.76238i −0.205146 0.355324i 0.745033 0.667028i \(-0.232434\pi\)
−0.950179 + 0.311704i \(0.899100\pi\)
\(264\) 0 0
\(265\) −6.78435 + 11.7508i −0.416759 + 0.721848i
\(266\) 0 0
\(267\) −18.5185 + 16.4715i −1.13331 + 1.00804i
\(268\) 0 0
\(269\) 18.9876 1.15770 0.578848 0.815436i \(-0.303503\pi\)
0.578848 + 0.815436i \(0.303503\pi\)
\(270\) 0 0
\(271\) 22.3338 1.35668 0.678341 0.734748i \(-0.262699\pi\)
0.678341 + 0.734748i \(0.262699\pi\)
\(272\) 0 0
\(273\) −1.29418 + 1.15113i −0.0783275 + 0.0696694i
\(274\) 0 0
\(275\) 3.55563 6.15854i 0.214413 0.371374i
\(276\) 0 0
\(277\) 15.9134 + 27.5628i 0.956145 + 1.65609i 0.731727 + 0.681598i \(0.238715\pi\)
0.224418 + 0.974493i \(0.427952\pi\)
\(278\) 0 0
\(279\) 1.60253 + 1.19432i 0.0959407 + 0.0715021i
\(280\) 0 0
\(281\) −9.92580 17.1920i −0.592123 1.02559i −0.993946 0.109870i \(-0.964956\pi\)
0.401822 0.915718i \(-0.368377\pi\)
\(282\) 0 0
\(283\) −1.56801 + 2.71588i −0.0932086 + 0.161442i −0.908860 0.417102i \(-0.863046\pi\)
0.815651 + 0.578544i \(0.196379\pi\)
\(284\) 0 0
\(285\) −2.75959 13.3821i −0.163464 0.792688i
\(286\) 0 0
\(287\) 1.88874 0.111489
\(288\) 0 0
\(289\) 17.5316 1.03127
\(290\) 0 0
\(291\) 1.25781 + 0.417152i 0.0737340 + 0.0244539i
\(292\) 0 0
\(293\) −4.93887 + 8.55437i −0.288532 + 0.499752i −0.973459 0.228859i \(-0.926500\pi\)
0.684928 + 0.728611i \(0.259834\pi\)
\(294\) 0 0
\(295\) −2.64764 4.58584i −0.154151 0.266998i
\(296\) 0 0
\(297\) 4.15452 8.89144i 0.241069 0.515934i
\(298\) 0 0
\(299\) −1.99381 3.45338i −0.115305 0.199714i
\(300\) 0 0
\(301\) 5.43199 9.40848i 0.313095 0.542296i
\(302\) 0 0
\(303\) 14.5927 + 4.83967i 0.838328 + 0.278032i
\(304\) 0 0
\(305\) −4.18401 −0.239576
\(306\) 0 0
\(307\) −15.4313 −0.880711 −0.440355 0.897824i \(-0.645148\pi\)
−0.440355 + 0.897824i \(0.645148\pi\)
\(308\) 0 0
\(309\) −3.48515 16.9006i −0.198263 0.961440i
\(310\) 0 0
\(311\) 8.83310 15.2994i 0.500879 0.867549i −0.499120 0.866533i \(-0.666343\pi\)
0.999999 0.00101570i \(-0.000323307\pi\)
\(312\) 0 0
\(313\) −6.71634 11.6330i −0.379630 0.657538i 0.611378 0.791338i \(-0.290615\pi\)
−0.991008 + 0.133800i \(0.957282\pi\)
\(314\) 0 0
\(315\) 0.388736 3.31105i 0.0219028 0.186557i
\(316\) 0 0
\(317\) −7.93199 13.7386i −0.445505 0.771637i 0.552582 0.833458i \(-0.313642\pi\)
−0.998087 + 0.0618213i \(0.980309\pi\)
\(318\) 0 0
\(319\) −0.932677 + 1.61544i −0.0522199 + 0.0904475i
\(320\) 0 0
\(321\) −6.75890 + 6.01179i −0.377245 + 0.335546i
\(322\) 0 0
\(323\) 41.7156 2.32112
\(324\) 0 0
\(325\) 3.76509 0.208850
\(326\) 0 0
\(327\) 11.7756 10.4740i 0.651193 0.579212i
\(328\) 0 0
\(329\) 5.54944 9.61192i 0.305951 0.529922i
\(330\) 0 0
\(331\) −9.04944 15.6741i −0.497402 0.861526i 0.502593 0.864523i \(-0.332379\pi\)
−0.999996 + 0.00299694i \(0.999046\pi\)
\(332\) 0 0
\(333\) −0.466579 + 3.97408i −0.0255684 + 0.217778i
\(334\) 0 0
\(335\) −2.27747 3.94470i −0.124432 0.215522i
\(336\) 0 0
\(337\) 0.518570 0.898189i 0.0282483 0.0489275i −0.851556 0.524264i \(-0.824340\pi\)
0.879804 + 0.475337i \(0.157674\pi\)
\(338\) 0 0
\(339\) 4.34479 + 21.0693i 0.235977 + 1.14433i
\(340\) 0 0
\(341\) 1.25829 0.0681402
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 7.28504 + 2.41608i 0.392213 + 0.130077i
\(346\) 0 0
\(347\) −10.9821 + 19.0216i −0.589551 + 1.02113i 0.404740 + 0.914432i \(0.367362\pi\)
−0.994291 + 0.106701i \(0.965971\pi\)
\(348\) 0 0
\(349\) −11.7651 20.3777i −0.629771 1.09080i −0.987597 0.157007i \(-0.949815\pi\)
0.357827 0.933788i \(-0.383518\pi\)
\(350\) 0 0
\(351\) 5.17673 0.448873i 0.276313 0.0239591i
\(352\) 0 0
\(353\) −14.7713 25.5846i −0.786196 1.36173i −0.928282 0.371877i \(-0.878714\pi\)
0.142086 0.989854i \(-0.454619\pi\)
\(354\) 0 0
\(355\) 5.98143 10.3601i 0.317461 0.549859i
\(356\) 0 0
\(357\) 9.66071 + 3.20397i 0.511299 + 0.169572i
\(358\) 0 0
\(359\) −34.0741 −1.79836 −0.899182 0.437575i \(-0.855837\pi\)
−0.899182 + 0.437575i \(0.855837\pi\)
\(360\) 0 0
\(361\) 31.3942 1.65232
\(362\) 0 0
\(363\) 2.60005 + 12.6085i 0.136467 + 0.661774i
\(364\) 0 0
\(365\) −1.72184 + 2.98231i −0.0901252 + 0.156101i
\(366\) 0 0
\(367\) −13.5309 23.4362i −0.706306 1.22336i −0.966218 0.257725i \(-0.917027\pi\)
0.259912 0.965632i \(-0.416306\pi\)
\(368\) 0 0
\(369\) −4.54325 3.38597i −0.236512 0.176266i
\(370\) 0 0
\(371\) −6.10507 10.5743i −0.316960 0.548990i
\(372\) 0 0
\(373\) 5.43199 9.40848i 0.281258 0.487153i −0.690437 0.723392i \(-0.742582\pi\)
0.971695 + 0.236240i \(0.0759151\pi\)
\(374\) 0 0
\(375\) −12.6058 + 11.2124i −0.650959 + 0.579004i
\(376\) 0 0
\(377\) −0.987620 −0.0508650
\(378\) 0 0
\(379\) −0.765092 −0.0393001 −0.0196501 0.999807i \(-0.506255\pi\)
−0.0196501 + 0.999807i \(0.506255\pi\)
\(380\) 0 0
\(381\) 9.92147 8.82478i 0.508292 0.452107i
\(382\) 0 0
\(383\) 4.87704 8.44729i 0.249205 0.431636i −0.714100 0.700043i \(-0.753164\pi\)
0.963306 + 0.268407i \(0.0864973\pi\)
\(384\) 0 0
\(385\) −1.04944 1.81769i −0.0534845 0.0926379i
\(386\) 0 0
\(387\) −29.9331 + 12.8936i −1.52158 + 0.655418i
\(388\) 0 0
\(389\) 12.3269 + 21.3508i 0.624999 + 1.08253i 0.988541 + 0.150953i \(0.0482341\pi\)
−0.363542 + 0.931578i \(0.618433\pi\)
\(390\) 0 0
\(391\) −11.7163 + 20.2933i −0.592521 + 1.02628i
\(392\) 0 0
\(393\) −5.08719 24.6694i −0.256615 1.24441i
\(394\) 0 0
\(395\) 7.14687 0.359598
\(396\) 0 0
\(397\) 14.1964 0.712496 0.356248 0.934391i \(-0.384056\pi\)
0.356248 + 0.934391i \(0.384056\pi\)
\(398\) 0 0
\(399\) 11.6705 + 3.87053i 0.584258 + 0.193769i
\(400\) 0 0
\(401\) −19.4746 + 33.7309i −0.972513 + 1.68444i −0.284603 + 0.958646i \(0.591862\pi\)
−0.687910 + 0.725796i \(0.741472\pi\)
\(402\) 0 0
\(403\) 0.333104 + 0.576953i 0.0165931 + 0.0287401i
\(404\) 0 0
\(405\) −6.87085 + 7.26766i −0.341416 + 0.361133i
\(406\) 0 0
\(407\) 1.25959 + 2.18168i 0.0624356 + 0.108142i
\(408\) 0 0
\(409\) 4.09888 7.09948i 0.202677 0.351047i −0.746713 0.665146i \(-0.768369\pi\)
0.949390 + 0.314100i \(0.101703\pi\)
\(410\) 0 0
\(411\) 7.63052 + 2.53066i 0.376386 + 0.124828i
\(412\) 0 0
\(413\) 4.76509 0.234475
\(414\) 0 0
\(415\) −13.1978 −0.647853
\(416\) 0 0
\(417\) −6.75024 32.7340i −0.330561 1.60299i
\(418\) 0 0
\(419\) −0.228718 + 0.396151i −0.0111736 + 0.0193533i −0.871558 0.490292i \(-0.836890\pi\)
0.860385 + 0.509645i \(0.170223\pi\)
\(420\) 0 0
\(421\) 9.31453 + 16.1332i 0.453963 + 0.786286i 0.998628 0.0523672i \(-0.0166766\pi\)
−0.544665 + 0.838654i \(0.683343\pi\)
\(422\) 0 0
\(423\) −30.5803 + 13.1724i −1.48687 + 0.640463i
\(424\) 0 0
\(425\) −11.0625 19.1608i −0.536611 0.929437i
\(426\) 0 0
\(427\) 1.88255 3.26067i 0.0911028 0.157795i
\(428\) 0 0
\(429\) 2.44437 2.17417i 0.118015 0.104970i
\(430\) 0 0
\(431\) −10.5178 −0.506625 −0.253312 0.967385i \(-0.581520\pi\)
−0.253312 + 0.967385i \(0.581520\pi\)
\(432\) 0 0
\(433\) −2.80223 −0.134667 −0.0673333 0.997731i \(-0.521449\pi\)
−0.0673333 + 0.997731i \(0.521449\pi\)
\(434\) 0 0
\(435\) 1.42037 1.26337i 0.0681017 0.0605739i
\(436\) 0 0
\(437\) −14.1538 + 24.5151i −0.677069 + 1.17272i
\(438\) 0 0
\(439\) 2.14764 + 3.71982i 0.102501 + 0.177537i 0.912715 0.408598i \(-0.133982\pi\)
−0.810213 + 0.586135i \(0.800649\pi\)
\(440\) 0 0
\(441\) 2.40545 + 1.79272i 0.114545 + 0.0853674i
\(442\) 0 0
\(443\) 11.0989 + 19.2238i 0.527324 + 0.913352i 0.999493 + 0.0318437i \(0.0101379\pi\)
−0.472169 + 0.881508i \(0.656529\pi\)
\(444\) 0 0
\(445\) 7.95056 13.7708i 0.376893 0.652797i
\(446\) 0 0
\(447\) 4.77197 + 23.1408i 0.225706 + 1.09452i
\(448\) 0 0
\(449\) 13.4313 0.633862 0.316931 0.948449i \(-0.397348\pi\)
0.316931 + 0.948449i \(0.397348\pi\)
\(450\) 0 0
\(451\) −3.56732 −0.167979
\(452\) 0 0
\(453\) −27.8869 9.24868i −1.31024 0.434541i
\(454\) 0 0
\(455\) 0.555632 0.962383i 0.0260484 0.0451172i
\(456\) 0 0
\(457\) −7.45056 12.9047i −0.348522 0.603658i 0.637465 0.770479i \(-0.279983\pi\)
−0.985987 + 0.166821i \(0.946650\pi\)
\(458\) 0 0
\(459\) −17.4945 25.0259i −0.816573 1.16811i
\(460\) 0 0
\(461\) −3.39561 5.88138i −0.158150 0.273923i 0.776052 0.630669i \(-0.217219\pi\)
−0.934201 + 0.356746i \(0.883886\pi\)
\(462\) 0 0
\(463\) 2.21634 3.83881i 0.103002 0.178405i −0.809918 0.586543i \(-0.800489\pi\)
0.912920 + 0.408138i \(0.133822\pi\)
\(464\) 0 0
\(465\) −1.21710 0.403652i −0.0564418 0.0187189i
\(466\) 0 0
\(467\) 26.4189 1.22252 0.611261 0.791429i \(-0.290663\pi\)
0.611261 + 0.791429i \(0.290663\pi\)
\(468\) 0 0
\(469\) 4.09888 0.189269
\(470\) 0 0
\(471\) −7.91597 38.3870i −0.364748 1.76878i
\(472\) 0 0
\(473\) −10.2596 + 17.7701i −0.471736 + 0.817072i
\(474\) 0 0
\(475\) −13.3640 23.1471i −0.613181 1.06206i
\(476\) 0 0
\(477\) −4.27128 + 36.3806i −0.195569 + 1.66575i
\(478\) 0 0
\(479\) −2.75959 4.77975i −0.126089 0.218392i 0.796069 0.605206i \(-0.206909\pi\)
−0.922158 + 0.386813i \(0.873576\pi\)
\(480\) 0 0
\(481\) −0.666896 + 1.15510i −0.0304079 + 0.0526679i
\(482\) 0 0
\(483\) −5.16071 + 4.59026i −0.234820 + 0.208864i
\(484\) 0 0
\(485\) −0.850219 −0.0386065
\(486\) 0 0
\(487\) 40.4930 1.83492 0.917458 0.397834i \(-0.130238\pi\)
0.917458 + 0.397834i \(0.130238\pi\)
\(488\) 0 0
\(489\) −23.4233 + 20.8341i −1.05924 + 0.942151i
\(490\) 0 0
\(491\) 0.555632 0.962383i 0.0250753 0.0434317i −0.853215 0.521559i \(-0.825351\pi\)
0.878291 + 0.478127i \(0.158684\pi\)
\(492\) 0 0
\(493\) 2.90180 + 5.02607i 0.130691 + 0.226363i
\(494\) 0 0
\(495\) −0.734219 + 6.25370i −0.0330007 + 0.281083i
\(496\) 0 0
\(497\) 5.38255 + 9.32284i 0.241440 + 0.418187i
\(498\) 0 0
\(499\) 1.33379 2.31020i 0.0597088 0.103419i −0.834626 0.550817i \(-0.814316\pi\)
0.894335 + 0.447399i \(0.147649\pi\)
\(500\) 0 0
\(501\) −6.02468 29.2156i −0.269163 1.30526i
\(502\) 0 0
\(503\) −9.86398 −0.439813 −0.219906 0.975521i \(-0.570575\pi\)
−0.219906 + 0.975521i \(0.570575\pi\)
\(504\) 0 0
\(505\) −9.86398 −0.438941
\(506\) 0 0
\(507\) −19.7280 6.54277i −0.876149 0.290575i
\(508\) 0 0
\(509\) −4.99381 + 8.64953i −0.221347 + 0.383384i −0.955217 0.295906i \(-0.904379\pi\)
0.733870 + 0.679289i \(0.237712\pi\)
\(510\) 0 0
\(511\) −1.54944 2.68371i −0.0685433 0.118720i
\(512\) 0 0
\(513\) −21.1341 30.2323i −0.933093 1.33479i
\(514\) 0 0
\(515\) 5.53569 + 9.58809i 0.243931 + 0.422502i
\(516\) 0 0
\(517\) −10.4814 + 18.1544i −0.460973 + 0.798428i
\(518\) 0 0
\(519\) −1.42037 0.471067i −0.0623475 0.0206775i
\(520\) 0 0
\(521\) 38.7527 1.69779 0.848894 0.528564i \(-0.177269\pi\)
0.848894 + 0.528564i \(0.177269\pi\)
\(522\) 0 0
\(523\) 19.6304 0.858379 0.429190 0.903214i \(-0.358799\pi\)
0.429190 + 0.903214i \(0.358799\pi\)
\(524\) 0 0
\(525\) −1.31708 6.38694i −0.0574822 0.278749i
\(526\) 0 0
\(527\) 1.95744 3.39038i 0.0852673 0.147687i
\(528\) 0 0
\(529\) 3.54944 + 6.14781i 0.154324 + 0.267296i
\(530\) 0 0
\(531\) −11.4622 8.54245i −0.497416 0.370711i
\(532\) 0 0
\(533\) −0.944368 1.63569i −0.0409051 0.0708497i
\(534\) 0 0
\(535\) 2.90180 5.02607i 0.125456 0.217296i
\(536\) 0 0
\(537\) −6.05494 + 5.38565i −0.261290 + 0.232408i
\(538\) 0 0
\(539\) 1.88874 0.0813536
\(540\) 0 0
\(541\) −0.332415 −0.0142916 −0.00714582 0.999974i \(-0.502275\pi\)
−0.00714582 + 0.999974i \(0.502275\pi\)
\(542\) 0 0
\(543\) 21.8251 19.4126i 0.936603 0.833073i
\(544\) 0 0
\(545\) −5.05563 + 8.75661i −0.216559 + 0.375092i
\(546\) 0 0
\(547\) −13.6476 23.6384i −0.583531 1.01071i −0.995057 0.0993071i \(-0.968337\pi\)
0.411526 0.911398i \(-0.364996\pi\)
\(548\) 0 0
\(549\) −10.3738 + 4.46849i −0.442743 + 0.190710i
\(550\) 0 0
\(551\) 3.50550 + 6.07171i 0.149339 + 0.258663i
\(552\) 0 0
\(553\) −3.21565 + 5.56967i −0.136743 + 0.236846i
\(554\) 0 0
\(555\) −0.518493 2.51433i −0.0220088 0.106728i
\(556\) 0 0
\(557\) −31.4079 −1.33080 −0.665398 0.746489i \(-0.731738\pi\)
−0.665398 + 0.746489i \(0.731738\pi\)
\(558\) 0 0
\(559\) −10.8640 −0.459497
\(560\) 0 0
\(561\) −18.2465 6.05146i −0.770369 0.255493i
\(562\) 0 0
\(563\) 11.8331 20.4955i 0.498706 0.863784i −0.501293 0.865278i \(-0.667142\pi\)
0.999999 + 0.00149369i \(0.000475458\pi\)
\(564\) 0 0
\(565\) −6.90112 11.9531i −0.290332 0.502870i
\(566\) 0 0
\(567\) −2.57234 8.62456i −0.108028 0.362198i
\(568\) 0 0
\(569\) 2.36398 + 4.09453i 0.0991030 + 0.171652i 0.911314 0.411713i \(-0.135069\pi\)
−0.812211 + 0.583364i \(0.801736\pi\)
\(570\) 0 0
\(571\) 6.38255 11.0549i 0.267101 0.462633i −0.701011 0.713151i \(-0.747268\pi\)
0.968112 + 0.250518i \(0.0806009\pi\)
\(572\) 0 0
\(573\) 28.0494 + 9.30259i 1.17178 + 0.388621i
\(574\) 0 0
\(575\) 15.0138 0.626117
\(576\) 0 0
\(577\) −10.6304 −0.442551 −0.221276 0.975211i \(-0.571022\pi\)
−0.221276 + 0.975211i \(0.571022\pi\)
\(578\) 0 0
\(579\) −2.60005 12.6085i −0.108055 0.523991i
\(580\) 0 0
\(581\) 5.93818 10.2852i 0.246357 0.426703i
\(582\) 0 0
\(583\) 11.5309 + 19.9721i 0.477560 + 0.827158i
\(584\) 0 0
\(585\) −3.06182 + 1.31887i −0.126591 + 0.0545286i
\(586\) 0 0
\(587\) 1.80834 + 3.13214i 0.0746384 + 0.129277i 0.900929 0.433967i \(-0.142886\pi\)
−0.826291 + 0.563244i \(0.809553\pi\)
\(588\) 0 0
\(589\) 2.36467 4.09572i 0.0974343 0.168761i
\(590\) 0 0
\(591\) 34.0309 30.2692i 1.39984 1.24511i
\(592\) 0 0
\(593\) 22.6786 0.931298 0.465649 0.884970i \(-0.345821\pi\)
0.465649 + 0.884970i \(0.345821\pi\)
\(594\) 0 0
\(595\) −6.53018 −0.267711
\(596\) 0 0
\(597\) 13.5018 12.0093i 0.552591 0.491509i
\(598\) 0 0
\(599\) −20.2953 + 35.1524i −0.829242 + 1.43629i 0.0693908 + 0.997590i \(0.477894\pi\)
−0.898633 + 0.438701i \(0.855439\pi\)
\(600\) 0 0
\(601\) −6.59957 11.4308i −0.269202 0.466272i 0.699454 0.714678i \(-0.253427\pi\)
−0.968656 + 0.248406i \(0.920093\pi\)
\(602\) 0 0
\(603\) −9.85965 7.34813i −0.401516 0.299239i
\(604\) 0 0
\(605\) −4.12983 7.15308i −0.167902 0.290814i
\(606\) 0 0
\(607\) −0.833792 + 1.44417i −0.0338426 + 0.0586171i −0.882451 0.470405i \(-0.844108\pi\)
0.848608 + 0.529022i \(0.177441\pi\)
\(608\) 0 0
\(609\) 0.345483 + 1.67536i 0.0139997 + 0.0678889i
\(610\) 0 0
\(611\) −11.0989 −0.449013
\(612\) 0 0
\(613\) 22.9257 0.925961 0.462981 0.886368i \(-0.346780\pi\)
0.462981 + 0.886368i \(0.346780\pi\)
\(614\) 0 0
\(615\) 3.45056 + 1.14438i 0.139140 + 0.0461457i
\(616\) 0 0
\(617\) 5.37567 9.31093i 0.216416 0.374844i −0.737294 0.675573i \(-0.763897\pi\)
0.953710 + 0.300729i \(0.0972298\pi\)
\(618\) 0 0
\(619\) 12.9814 + 22.4845i 0.521768 + 0.903728i 0.999679 + 0.0253203i \(0.00806057\pi\)
−0.477912 + 0.878408i \(0.658606\pi\)
\(620\) 0 0
\(621\) 20.6428 1.78994i 0.828368 0.0718277i
\(622\) 0 0
\(623\) 7.15452 + 12.3920i 0.286640 + 0.496474i
\(624\) 0 0
\(625\) −4.00069 + 6.92940i −0.160028 + 0.277176i
\(626\) 0 0
\(627\) −22.0426 7.31041i −0.880295 0.291950i
\(628\) 0 0
\(629\) 7.83784 0.312515
\(630\) 0 0
\(631\) −3.00138 −0.119483 −0.0597415 0.998214i \(-0.519028\pi\)
−0.0597415 + 0.998214i \(0.519028\pi\)
\(632\) 0 0
\(633\) 8.88372 + 43.0799i 0.353096 + 1.71227i
\(634\) 0 0
\(635\) −4.25959 + 7.37783i −0.169037 + 0.292780i
\(636\) 0 0
\(637\) 0.500000 + 0.866025i 0.0198107 + 0.0343132i
\(638\) 0 0
\(639\) 3.76578 32.0750i 0.148972 1.26887i
\(640\) 0 0
\(641\) −6.77266 11.7306i −0.267504 0.463330i 0.700713 0.713444i \(-0.252866\pi\)
−0.968217 + 0.250113i \(0.919532\pi\)
\(642\) 0 0
\(643\) 17.4814 30.2787i 0.689400 1.19408i −0.282632 0.959228i \(-0.591207\pi\)
0.972032 0.234848i \(-0.0754592\pi\)
\(644\) 0 0
\(645\) 15.6243 13.8973i 0.615207 0.547204i
\(646\) 0 0
\(647\) −25.9890 −1.02173 −0.510866 0.859660i \(-0.670675\pi\)
−0.510866 + 0.859660i \(0.670675\pi\)
\(648\) 0 0
\(649\) −9.00000 −0.353281
\(650\) 0 0
\(651\) 0.862194 0.766889i 0.0337920 0.0300568i
\(652\) 0 0
\(653\) 2.93818 5.08907i 0.114980 0.199151i −0.802792 0.596259i \(-0.796653\pi\)
0.917772 + 0.397108i \(0.129986\pi\)
\(654\) 0 0
\(655\) 8.08031 + 13.9955i 0.315724 + 0.546850i
\(656\) 0 0
\(657\) −1.08403 + 9.23324i −0.0422922 + 0.360223i
\(658\) 0 0
\(659\) −20.6359 35.7425i −0.803862 1.39233i −0.917056 0.398758i \(-0.869441\pi\)
0.113194 0.993573i \(-0.463892\pi\)
\(660\) 0 0
\(661\) 18.4814 32.0108i 0.718844 1.24507i −0.242614 0.970123i \(-0.578005\pi\)
0.961458 0.274952i \(-0.0886619\pi\)
\(662\) 0 0
\(663\) −2.05563 9.96840i −0.0798341 0.387141i
\(664\) 0 0
\(665\) −7.88874 −0.305912
\(666\) 0 0
\(667\) −3.93825 −0.152490
\(668\) 0 0
\(669\) −23.8876 7.92231i −0.923547 0.306294i
\(670\) 0 0
\(671\) −3.55563 + 6.15854i −0.137264 + 0.237748i
\(672\) 0 0
\(673\) −22.6971 39.3125i −0.874908 1.51539i −0.856861 0.515548i \(-0.827588\pi\)
−0.0180476 0.999837i \(-0.505745\pi\)
\(674\) 0 0
\(675\) −8.28180 + 17.7246i −0.318767 + 0.682220i
\(676\) 0 0
\(677\) −1.14764 1.98777i −0.0441073 0.0763961i 0.843129 0.537711i \(-0.180711\pi\)
−0.887236 + 0.461315i \(0.847378\pi\)
\(678\) 0 0
\(679\) 0.382546 0.662589i 0.0146808 0.0254278i
\(680\) 0 0
\(681\) −31.9065 10.5818i −1.22266 0.405495i
\(682\) 0 0
\(683\) −32.1483 −1.23012 −0.615059 0.788481i \(-0.710868\pi\)
−0.615059 + 0.788481i \(0.710868\pi\)
\(684\) 0 0
\(685\) −5.15787 −0.197072
\(686\) 0 0
\(687\) 3.68361 + 17.8630i 0.140538 + 0.681514i
\(688\) 0 0
\(689\) −6.10507 + 10.5743i −0.232585 + 0.402849i
\(690\) 0 0
\(691\) −3.40180 5.89210i −0.129411 0.224146i 0.794038 0.607869i \(-0.207975\pi\)
−0.923448 + 0.383723i \(0.874642\pi\)
\(692\) 0 0
\(693\) −4.54325 3.38597i −0.172584 0.128622i
\(694\) 0 0
\(695\) 10.7218 + 18.5708i 0.406703 + 0.704429i
\(696\) 0 0
\(697\) −5.54944 + 9.61192i −0.210200 + 0.364077i
\(698\) 0 0
\(699\) −29.3022 + 26.0632i −1.10831 + 0.985800i
\(700\) 0 0
\(701\) 42.5933 1.60873 0.804363 0.594137i \(-0.202507\pi\)
0.804363 + 0.594137i \(0.202507\pi\)
\(702\) 0 0
\(703\) 9.46844 0.357109
\(704\) 0 0
\(705\) 15.9622 14.1978i 0.601170 0.534719i
\(706\) 0 0
\(707\) 4.43818 7.68715i 0.166915 0.289105i
\(708\) 0 0
\(709\) 2.56732 + 4.44673i 0.0964178 + 0.167001i 0.910199 0.414170i \(-0.135928\pi\)
−0.813782 + 0.581171i \(0.802595\pi\)
\(710\) 0 0
\(711\) 17.7199 7.63279i 0.664548 0.286252i
\(712\) 0 0
\(713\) 1.32829 + 2.30067i 0.0497449 + 0.0861607i
\(714\) 0 0
\(715\) −1.04944 + 1.81769i −0.0392469 + 0.0679776i
\(716\) 0 0
\(717\) 1.74041 + 8.43979i 0.0649968 + 0.315190i
\(718\) 0 0
\(719\) −23.6057 −0.880344 −0.440172 0.897914i \(-0.645082\pi\)
−0.440172 + 0.897914i \(0.645082\pi\)
\(720\) 0 0
\(721\) −9.96286 −0.371036
\(722\) 0 0
\(723\) 0.386188 + 0.128079i 0.0143625 + 0.00476332i
\(724\) 0 0
\(725\) 1.85924 3.22030i 0.0690505 0.119599i
\(726\) 0 0
\(727\) 0.000688709 0.00119288i 2.55428e−5 4.42414e-5i 0.866038 0.499978i \(-0.166659\pi\)
−0.866013 + 0.500022i \(0.833325\pi\)
\(728\) 0 0
\(729\) −9.27375 + 25.3574i −0.343472 + 0.939163i
\(730\) 0 0
\(731\) 31.9203 + 55.2876i 1.18061 + 2.04488i
\(732\) 0 0
\(733\) 10.6978 18.5291i 0.395131 0.684387i −0.597987 0.801506i \(-0.704032\pi\)
0.993118 + 0.117119i \(0.0373658\pi\)
\(734\) 0 0
\(735\) −1.82691 0.605896i −0.0673867 0.0223488i
\(736\) 0 0
\(737\) −7.74171 −0.285170
\(738\) 0 0
\(739\) 32.0232 1.17799 0.588997 0.808135i \(-0.299523\pi\)
0.588997 + 0.808135i \(0.299523\pi\)
\(740\) 0 0
\(741\) −2.48329 12.0422i −0.0912259 0.442383i
\(742\) 0 0
\(743\) −25.2596 + 43.7509i −0.926685 + 1.60506i −0.137855 + 0.990452i \(0.544021\pi\)
−0.788829 + 0.614612i \(0.789312\pi\)
\(744\) 0 0
\(745\) −7.57963 13.1283i −0.277696 0.480984i
\(746\) 0 0
\(747\) −32.7225 + 14.0951i −1.19725 + 0.515713i
\(748\) 0 0
\(749\) 2.61126 + 4.52284i 0.0954135 + 0.165261i
\(750\) 0 0
\(751\) 20.3145 35.1858i 0.741288 1.28395i −0.210621 0.977568i \(-0.567549\pi\)
0.951909 0.306381i \(-0.0991180\pi\)
\(752\) 0 0
\(753\) −10.4814 + 9.32284i −0.381965 + 0.339743i
\(754\) 0 0
\(755\) 18.8502 0.686030
\(756\) 0 0
\(757\) −7.90112 −0.287171 −0.143585 0.989638i \(-0.545863\pi\)
−0.143585 + 0.989638i \(0.545863\pi\)
\(758\) 0 0
\(759\) 9.74721 8.66978i 0.353801 0.314693i
\(760\) 0 0
\(761\) −11.0124 + 19.0740i −0.399198 + 0.691432i −0.993627 0.112716i \(-0.964045\pi\)
0.594429 + 0.804148i \(0.297378\pi\)
\(762\) 0 0
\(763\) −4.54944 7.87987i −0.164701 0.285270i
\(764\) 0 0
\(765\) 15.7080 + 11.7068i 0.567924 + 0.423259i
\(766\) 0 0
\(767\) −2.38255 4.12669i −0.0860287 0.149006i
\(768\) 0 0
\(769\) 24.4127 42.2841i 0.880346 1.52480i 0.0293884 0.999568i \(-0.490644\pi\)
0.850957 0.525235i \(-0.176023\pi\)
\(770\) 0 0
\(771\) −8.30903 40.2931i −0.299243 1.45112i
\(772\) 0 0
\(773\) 34.4807 1.24018 0.620092 0.784529i \(-0.287095\pi\)
0.620092 + 0.784529i \(0.287095\pi\)
\(774\) 0 0
\(775\) −2.50833 −0.0901020
\(776\) 0 0
\(777\) 2.19275 + 0.727225i 0.0786645 + 0.0260891i
\(778\) 0 0
\(779\) −6.70396 + 11.6116i −0.240194 + 0.416029i
\(780\) 0 0
\(781\) −10.1662 17.6084i −0.363776 0.630078i
\(782\) 0 0
\(783\) 2.17240 4.64934i 0.0776351 0.166154i
\(784\) 0 0
\(785\) 12.5734 + 21.7778i 0.448765 + 0.777284i
\(786\) 0 0
\(787\) 5.86329 10.1555i 0.209004 0.362005i −0.742397 0.669960i \(-0.766311\pi\)
0.951401 + 0.307955i \(0.0996446\pi\)
\(788\) 0 0
\(789\) 10.9389 + 3.62787i 0.389434 + 0.129156i
\(790\) 0 0
\(791\) 12.4203 0.441615
\(792\) 0 0
\(793\) −3.76509 −0.133702
\(794\) 0 0
\(795\) −4.74652 23.0174i −0.168342 0.816342i
\(796\) 0 0
\(797\) 26.1236 45.2473i 0.925344 1.60274i 0.134338 0.990936i \(-0.457109\pi\)
0.791007 0.611808i \(-0.209557\pi\)
\(798\) 0 0
\(799\) 32.6105 + 56.4830i 1.15368 + 1.99823i
\(800\) 0 0
\(801\) 5.00550 42.6343i 0.176861 1.50641i
\(802\) 0 0
\(803\) 2.92649 + 5.06882i 0.103273 + 0.178875i
\(804\) 0 0
\(805\) 2.21565 3.83762i 0.0780914 0.135258i
\(806\) 0 0
\(807\) −24.5734 + 21.8572i −0.865026 + 0.769408i
\(808\) 0 0
\(809\) −30.5439 −1.07387 −0.536934 0.843624i \(-0.680418\pi\)
−0.536934 + 0.843624i \(0.680418\pi\)
\(810\) 0 0
\(811\) 27.9629 0.981909 0.490954 0.871185i \(-0.336648\pi\)
0.490954 + 0.871185i \(0.336648\pi\)
\(812\) 0 0
\(813\) −28.9040 + 25.7090i −1.01371 + 0.901655i
\(814\) 0 0
\(815\) 10.0563 17.4181i 0.352258 0.610128i
\(816\) 0 0
\(817\) 38.5611 + 66.7897i 1.34908 + 2.33668i
\(818\) 0 0
\(819\) 0.349814 2.97954i 0.0122235 0.104113i
\(820\) 0 0
\(821\) 3.78435 + 6.55469i 0.132075 + 0.228760i 0.924476 0.381240i \(-0.124503\pi\)
−0.792401 + 0.610000i \(0.791169\pi\)
\(822\) 0 0
\(823\) −18.1978 + 31.5195i −0.634334 + 1.09870i 0.352321 + 0.935879i \(0.385392\pi\)
−0.986656 + 0.162820i \(0.947941\pi\)
\(824\) 0 0
\(825\) 2.48762 + 12.0632i 0.0866078 + 0.419988i
\(826\) 0 0
\(827\) 2.36955 0.0823975 0.0411987 0.999151i \(-0.486882\pi\)
0.0411987 + 0.999151i \(0.486882\pi\)
\(828\) 0 0
\(829\) −22.2335 −0.772202 −0.386101 0.922456i \(-0.626178\pi\)
−0.386101 + 0.922456i \(0.626178\pi\)
\(830\) 0 0
\(831\) −52.3232 17.3530i −1.81507 0.601968i
\(832\) 0 0
\(833\) 2.93818 5.08907i 0.101802 0.176326i
\(834\) 0 0
\(835\) 9.56939 + 16.5747i 0.331162 + 0.573590i
\(836\) 0 0
\(837\) −3.44878 + 0.299043i −0.119207 + 0.0103364i
\(838\) 0 0
\(839\) −6.05494 10.4875i −0.209040 0.362068i 0.742372 0.669987i \(-0.233701\pi\)
−0.951412 + 0.307920i \(0.900367\pi\)
\(840\) 0 0
\(841\) 14.0123 24.2700i 0.483183 0.836897i
\(842\) 0 0
\(843\) 32.6359 + 10.8237i 1.12404 + 0.372788i
\(844\) 0 0
\(845\) 13.3352 0.458744
\(846\) 0 0
\(847\) 7.43268 0.255390
\(848\) 0 0
\(849\) −1.09703 5.31982i −0.0376498 0.182576i
\(850\) 0 0
\(851\) −2.65933 + 4.60609i −0.0911606 + 0.157895i
\(852\) 0 0
\(853\) 16.5494 + 28.6645i 0.566642 + 0.981453i 0.996895 + 0.0787444i \(0.0250911\pi\)
−0.430253 + 0.902708i \(0.641576\pi\)
\(854\) 0 0
\(855\) 18.9759 + 14.1423i 0.648963 + 0.483655i
\(856\) 0 0
\(857\) −8.77128 15.1923i −0.299621 0.518959i 0.676428 0.736509i \(-0.263527\pi\)
−0.976049 + 0.217549i \(0.930194\pi\)
\(858\) 0 0
\(859\) 6.93130 12.0054i 0.236493 0.409618i −0.723213 0.690625i \(-0.757335\pi\)
0.959705 + 0.281008i \(0.0906687\pi\)
\(860\) 0 0
\(861\) −2.44437 + 2.17417i −0.0833038 + 0.0740957i
\(862\) 0 0
\(863\) 10.9890 0.374070 0.187035 0.982353i \(-0.440112\pi\)
0.187035 + 0.982353i \(0.440112\pi\)
\(864\) 0 0
\(865\) 0.960106 0.0326446
\(866\) 0 0
\(867\) −22.6890 + 20.1811i −0.770560 + 0.685384i
\(868\) 0 0
\(869\) 6.07351 10.5196i 0.206030 0.356854i
\(870\) 0 0
\(871\) −2.04944 3.54974i −0.0694427 0.120278i
\(872\) 0 0
\(873\) −2.10803 + 0.908026i −0.0713459 + 0.0307320i
\(874\) 0 0
\(875\) 4.87017 + 8.43538i 0.164642 + 0.285168i
\(876\) 0 0
\(877\) −12.2472 + 21.2128i −0.413559 + 0.716305i −0.995276 0.0970861i \(-0.969048\pi\)
0.581717 + 0.813391i \(0.302381\pi\)
\(878\) 0 0
\(879\) −3.45537 16.7562i −0.116547 0.565172i
\(880\) 0 0
\(881\) −19.9243 −0.671268 −0.335634 0.941992i \(-0.608951\pi\)
−0.335634 + 0.941992i \(0.608951\pi\)
\(882\) 0 0
\(883\) −39.5316 −1.33034 −0.665171 0.746691i \(-0.731642\pi\)
−0.665171 + 0.746691i \(0.731642\pi\)
\(884\) 0 0
\(885\) 8.70541 + 2.88715i 0.292629 + 0.0970505i
\(886\) 0 0
\(887\) −20.5378 + 35.5724i −0.689590 + 1.19441i 0.282380 + 0.959303i \(0.408876\pi\)
−0.971971 + 0.235103i \(0.924457\pi\)
\(888\) 0 0
\(889\) −3.83310 6.63913i −0.128558 0.222669i
\(890\) 0 0
\(891\) 4.85848 + 16.2895i 0.162765 + 0.545719i
\(892\) 0 0
\(893\) 39.3948 + 68.2339i 1.31830 + 2.28336i
\(894\) 0 0
\(895\) 2.59957 4.50259i 0.0868941 0.150505i
\(896\) 0 0
\(897\) 6.55563 + 2.17417i 0.218886 + 0.0725936i
\(898\) 0 0
\(899\) 0.657960 0.0219442
\(900\) 0 0
\(901\) 71.7512 2.39038
\(902\) 0 0
\(903\) 3.80037 + 18.4292i 0.126468 + 0.613285i
\(904\) 0 0
\(905\) −9.37017 + 16.2296i −0.311475 + 0.539490i
\(906\) 0 0
\(907\) −5.83242 10.1020i −0.193662 0.335433i 0.752799 0.658250i \(-0.228703\pi\)
−0.946461 + 0.322818i \(0.895370\pi\)
\(908\) 0 0
\(909\) −24.4567 + 10.5346i −0.811177 + 0.349412i
\(910\) 0 0
\(911\) −20.8028 36.0316i −0.689229 1.19378i −0.972088 0.234618i \(-0.924616\pi\)
0.282859 0.959162i \(-0.408717\pi\)
\(912\) 0 0
\(913\) −11.2156 + 19.4261i −0.371184 + 0.642909i
\(914\) 0 0
\(915\) 5.41487 4.81633i 0.179010 0.159223i
\(916\) 0 0
\(917\) −14.5426 −0.480238
\(918\) 0 0
\(919\) 28.3338 0.934646 0.467323 0.884087i \(-0.345219\pi\)
0.467323 + 0.884087i \(0.345219\pi\)
\(920\) 0 0
\(921\) 19.9709 17.7634i 0.658064 0.585323i
\(922\) 0 0
\(923\) 5.38255 9.32284i 0.177169 0.306865i
\(924\) 0 0
\(925\) −2.51093 4.34905i −0.0825587 0.142996i
\(926\) 0 0
\(927\) 23.9651 + 17.8606i 0.787118 + 0.586618i
\(928\) 0 0
\(929\) −14.9127 25.8296i −0.489271 0.847442i 0.510653 0.859787i \(-0.329404\pi\)
−0.999924 + 0.0123450i \(0.996070\pi\)
\(930\) 0 0
\(931\) 3.54944 6.14781i 0.116328 0.201486i
\(932\) 0 0
\(933\) 6.17989 + 29.9682i 0.202320 + 0.981115i
\(934\) 0 0
\(935\) 12.3338 0.403358
\(936\) 0 0
\(937\) −2.56870 −0.0839158 −0.0419579 0.999119i \(-0.513360\pi\)
−0.0419579 + 0.999119i \(0.513360\pi\)
\(938\) 0 0
\(939\) 22.0833 + 7.32391i 0.720660 + 0.239007i
\(940\) 0 0
\(941\) −2.33448 + 4.04344i −0.0761019 + 0.131812i −0.901565 0.432644i \(-0.857581\pi\)
0.825463 + 0.564456i \(0.190914\pi\)
\(942\) 0 0
\(943\) −3.76578 6.52252i −0.122631 0.212403i
\(944\) 0 0
\(945\) 3.30834 + 4.73259i 0.107620 + 0.153951i
\(946\) 0 0
\(947\) 15.8454 + 27.4450i 0.514907 + 0.891844i 0.999850 + 0.0172990i \(0.00550671\pi\)
−0.484944 + 0.874545i \(0.661160\pi\)
\(948\) 0 0
\(949\) −1.54944 + 2.68371i −0.0502970 + 0.0871170i
\(950\) 0 0
\(951\) 26.0803 + 8.64953i 0.845712 + 0.280480i
\(952\) 0 0
\(953\) 13.0604 0.423067 0.211533 0.977371i \(-0.432154\pi\)
0.211533 + 0.977371i \(0.432154\pi\)
\(954\) 0 0
\(955\) −18.9601 −0.613535
\(956\) 0 0
\(957\) −0.652527 3.16431i −0.0210932 0.102288i
\(958\) 0 0
\(959\) 2.32072 4.01961i 0.0749401 0.129800i
\(960\) 0 0
\(961\) 15.2781 + 26.4624i 0.492841 + 0.853626i
\(962\) 0 0
\(963\) 1.82691 15.5607i 0.0588715 0.501437i
\(964\) 0 0
\(965\) 4.12983 + 7.15308i 0.132944 + 0.230266i
\(966\) 0 0
\(967\) −4.48074 + 7.76087i −0.144091 + 0.249573i −0.929033 0.369996i \(-0.879359\pi\)
0.784942 + 0.619569i \(0.212692\pi\)
\(968\) 0 0
\(969\) −53.9875 + 48.0199i −1.73433 + 1.54262i
\(970\) 0 0
\(971\) −0.543941 −0.0174559 −0.00872795 0.999962i \(-0.502778\pi\)
−0.00872795 + 0.999962i \(0.502778\pi\)
\(972\) 0 0
\(973\) −19.2967 −0.618622
\(974\) 0 0
\(975\) −4.87271 + 4.33410i −0.156052 + 0.138802i
\(976\) 0 0
\(977\) −18.2280 + 31.5717i −0.583164 + 1.01007i 0.411938 + 0.911212i \(0.364852\pi\)
−0.995102 + 0.0988575i \(0.968481\pi\)
\(978\) 0 0
\(979\) −13.5130 23.4052i −0.431877 0.748033i
\(980\) 0 0
\(981\) −3.18292 + 27.1104i −0.101623 + 0.865570i
\(982\) 0 0
\(983\) −18.1916 31.5087i −0.580221 1.00497i −0.995453 0.0952569i \(-0.969633\pi\)
0.415231 0.909716i \(-0.363701\pi\)
\(984\) 0 0
\(985\) −14.6105 + 25.3061i −0.465529 + 0.806320i
\(986\) 0 0
\(987\) 3.88255 + 18.8277i 0.123583 + 0.599292i
\(988\) 0 0
\(989\) −43.3214 −1.37754
\(990\) 0 0
\(991\) 31.9642 1.01538 0.507689 0.861541i \(-0.330500\pi\)
0.507689 + 0.861541i \(0.330500\pi\)
\(992\) 0 0
\(993\) 29.7545 + 9.86807i 0.944230 + 0.313154i
\(994\) 0 0
\(995\) −5.79673 + 10.0402i −0.183769 + 0.318297i
\(996\) 0 0
\(997\) −13.0000 22.5167i −0.411714 0.713110i 0.583363 0.812211i \(-0.301736\pi\)
−0.995077 + 0.0991016i \(0.968403\pi\)
\(998\) 0 0
\(999\) −3.97083 5.68028i −0.125632 0.179716i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1008.2.r.g.337.1 6
3.2 odd 2 3024.2.r.i.1009.2 6
4.3 odd 2 252.2.j.b.85.3 6
9.2 odd 6 3024.2.r.i.2017.2 6
9.4 even 3 9072.2.a.bt.1.2 3
9.5 odd 6 9072.2.a.bz.1.2 3
9.7 even 3 inner 1008.2.r.g.673.1 6
12.11 even 2 756.2.j.a.253.2 6
28.3 even 6 1764.2.i.e.373.3 6
28.11 odd 6 1764.2.i.f.373.1 6
28.19 even 6 1764.2.l.g.949.1 6
28.23 odd 6 1764.2.l.d.949.3 6
28.27 even 2 1764.2.j.d.589.1 6
36.7 odd 6 252.2.j.b.169.3 yes 6
36.11 even 6 756.2.j.a.505.2 6
36.23 even 6 2268.2.a.j.1.2 3
36.31 odd 6 2268.2.a.g.1.2 3
84.11 even 6 5292.2.i.d.1549.2 6
84.23 even 6 5292.2.l.g.361.2 6
84.47 odd 6 5292.2.l.d.361.2 6
84.59 odd 6 5292.2.i.g.1549.2 6
84.83 odd 2 5292.2.j.e.1765.2 6
252.11 even 6 5292.2.l.g.3313.2 6
252.47 odd 6 5292.2.i.g.2125.2 6
252.79 odd 6 1764.2.i.f.1537.1 6
252.83 odd 6 5292.2.j.e.3529.2 6
252.115 even 6 1764.2.l.g.961.1 6
252.151 odd 6 1764.2.l.d.961.3 6
252.187 even 6 1764.2.i.e.1537.3 6
252.191 even 6 5292.2.i.d.2125.2 6
252.223 even 6 1764.2.j.d.1177.1 6
252.227 odd 6 5292.2.l.d.3313.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.j.b.85.3 6 4.3 odd 2
252.2.j.b.169.3 yes 6 36.7 odd 6
756.2.j.a.253.2 6 12.11 even 2
756.2.j.a.505.2 6 36.11 even 6
1008.2.r.g.337.1 6 1.1 even 1 trivial
1008.2.r.g.673.1 6 9.7 even 3 inner
1764.2.i.e.373.3 6 28.3 even 6
1764.2.i.e.1537.3 6 252.187 even 6
1764.2.i.f.373.1 6 28.11 odd 6
1764.2.i.f.1537.1 6 252.79 odd 6
1764.2.j.d.589.1 6 28.27 even 2
1764.2.j.d.1177.1 6 252.223 even 6
1764.2.l.d.949.3 6 28.23 odd 6
1764.2.l.d.961.3 6 252.151 odd 6
1764.2.l.g.949.1 6 28.19 even 6
1764.2.l.g.961.1 6 252.115 even 6
2268.2.a.g.1.2 3 36.31 odd 6
2268.2.a.j.1.2 3 36.23 even 6
3024.2.r.i.1009.2 6 3.2 odd 2
3024.2.r.i.2017.2 6 9.2 odd 6
5292.2.i.d.1549.2 6 84.11 even 6
5292.2.i.d.2125.2 6 252.191 even 6
5292.2.i.g.1549.2 6 84.59 odd 6
5292.2.i.g.2125.2 6 252.47 odd 6
5292.2.j.e.1765.2 6 84.83 odd 2
5292.2.j.e.3529.2 6 252.83 odd 6
5292.2.l.d.361.2 6 84.47 odd 6
5292.2.l.d.3313.2 6 252.227 odd 6
5292.2.l.g.361.2 6 84.23 even 6
5292.2.l.g.3313.2 6 252.11 even 6
9072.2.a.bt.1.2 3 9.4 even 3
9072.2.a.bz.1.2 3 9.5 odd 6