Properties

Label 507.2.j.b.316.1
Level $507$
Weight $2$
Character 507.316
Analytic conductor $4.048$
Analytic rank $0$
Dimension $2$
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] = [507,2,Mod(316,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.316");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.j (of order \(6\), 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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 316.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 507.316
Dual form 507.2.j.b.361.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -3.46410i q^{5} +(1.50000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -3.46410i q^{5} +(1.50000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(3.00000 + 1.73205i) q^{11} -2.00000 q^{12} +(-3.00000 - 1.73205i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(-3.00000 + 1.73205i) q^{19} +(-6.00000 + 3.46410i) q^{20} -1.73205i q^{21} +(3.00000 - 5.19615i) q^{23} -7.00000 q^{25} -1.00000 q^{27} +(-3.00000 - 1.73205i) q^{28} +(-3.00000 + 5.19615i) q^{29} -1.73205i q^{31} +(3.00000 - 1.73205i) q^{33} +(-3.00000 - 5.19615i) q^{35} +(-1.00000 + 1.73205i) q^{36} +(6.00000 + 3.46410i) q^{41} +(0.500000 + 0.866025i) q^{43} -6.92820i q^{44} +(-3.00000 + 1.73205i) q^{45} -3.46410i q^{47} +(2.00000 + 3.46410i) q^{48} +(-2.00000 + 3.46410i) q^{49} +12.0000 q^{53} +(6.00000 - 10.3923i) q^{55} +3.46410i q^{57} +(3.00000 - 1.73205i) q^{59} +6.92820i q^{60} +(-0.500000 - 0.866025i) q^{61} +(-1.50000 - 0.866025i) q^{63} +8.00000 q^{64} +(-7.50000 - 4.33013i) q^{67} +(-3.00000 - 5.19615i) q^{69} +(9.00000 - 5.19615i) q^{71} -1.73205i q^{73} +(-3.50000 + 6.06218i) q^{75} +(6.00000 + 3.46410i) q^{76} +6.00000 q^{77} -11.0000 q^{79} +(12.0000 + 6.92820i) q^{80} +(-0.500000 + 0.866025i) q^{81} +13.8564i q^{83} +(-3.00000 + 1.73205i) q^{84} +(3.00000 + 5.19615i) q^{87} +(-6.00000 - 3.46410i) q^{89} -12.0000 q^{92} +(-1.50000 - 0.866025i) q^{93} +(6.00000 + 10.3923i) q^{95} +(4.50000 - 2.59808i) q^{97} -3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} - 2 q^{4} + 3 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{3} - 2 q^{4} + 3 q^{7} - q^{9} + 6 q^{11} - 4 q^{12} - 6 q^{15} - 4 q^{16} - 6 q^{19} - 12 q^{20} + 6 q^{23} - 14 q^{25} - 2 q^{27} - 6 q^{28} - 6 q^{29} + 6 q^{33} - 6 q^{35} - 2 q^{36} + 12 q^{41} + q^{43} - 6 q^{45} + 4 q^{48} - 4 q^{49} + 24 q^{53} + 12 q^{55} + 6 q^{59} - q^{61} - 3 q^{63} + 16 q^{64} - 15 q^{67} - 6 q^{69} + 18 q^{71} - 7 q^{75} + 12 q^{76} + 12 q^{77} - 22 q^{79} + 24 q^{80} - q^{81} - 6 q^{84} + 6 q^{87} - 12 q^{89} - 24 q^{92} - 3 q^{93} + 12 q^{95} + 9 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −1.00000 1.73205i −0.500000 0.866025i
\(5\) 3.46410i 1.54919i −0.632456 0.774597i \(-0.717953\pi\)
0.632456 0.774597i \(-0.282047\pi\)
\(6\) 0 0
\(7\) 1.50000 0.866025i 0.566947 0.327327i −0.188982 0.981981i \(-0.560519\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 3.00000 + 1.73205i 0.904534 + 0.522233i 0.878668 0.477432i \(-0.158432\pi\)
0.0258656 + 0.999665i \(0.491766\pi\)
\(12\) −2.00000 −0.577350
\(13\) 0 0
\(14\) 0 0
\(15\) −3.00000 1.73205i −0.774597 0.447214i
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) −3.00000 + 1.73205i −0.688247 + 0.397360i −0.802955 0.596040i \(-0.796740\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) −6.00000 + 3.46410i −1.34164 + 0.774597i
\(21\) 1.73205i 0.377964i
\(22\) 0 0
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) 0 0
\(25\) −7.00000 −1.40000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −3.00000 1.73205i −0.566947 0.327327i
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 0 0
\(31\) 1.73205i 0.311086i −0.987829 0.155543i \(-0.950287\pi\)
0.987829 0.155543i \(-0.0497126\pi\)
\(32\) 0 0
\(33\) 3.00000 1.73205i 0.522233 0.301511i
\(34\) 0 0
\(35\) −3.00000 5.19615i −0.507093 0.878310i
\(36\) −1.00000 + 1.73205i −0.166667 + 0.288675i
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.00000 + 3.46410i 0.937043 + 0.541002i 0.889032 0.457845i \(-0.151379\pi\)
0.0480106 + 0.998847i \(0.484712\pi\)
\(42\) 0 0
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) 6.92820i 1.04447i
\(45\) −3.00000 + 1.73205i −0.447214 + 0.258199i
\(46\) 0 0
\(47\) 3.46410i 0.505291i −0.967559 0.252646i \(-0.918699\pi\)
0.967559 0.252646i \(-0.0813007\pi\)
\(48\) 2.00000 + 3.46410i 0.288675 + 0.500000i
\(49\) −2.00000 + 3.46410i −0.285714 + 0.494872i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 0 0
\(55\) 6.00000 10.3923i 0.809040 1.40130i
\(56\) 0 0
\(57\) 3.46410i 0.458831i
\(58\) 0 0
\(59\) 3.00000 1.73205i 0.390567 0.225494i −0.291839 0.956467i \(-0.594267\pi\)
0.682406 + 0.730974i \(0.260934\pi\)
\(60\) 6.92820i 0.894427i
\(61\) −0.500000 0.866025i −0.0640184 0.110883i 0.832240 0.554416i \(-0.187058\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 0 0
\(63\) −1.50000 0.866025i −0.188982 0.109109i
\(64\) 8.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −7.50000 4.33013i −0.916271 0.529009i −0.0338274 0.999428i \(-0.510770\pi\)
−0.882443 + 0.470418i \(0.844103\pi\)
\(68\) 0 0
\(69\) −3.00000 5.19615i −0.361158 0.625543i
\(70\) 0 0
\(71\) 9.00000 5.19615i 1.06810 0.616670i 0.140441 0.990089i \(-0.455148\pi\)
0.927663 + 0.373419i \(0.121815\pi\)
\(72\) 0 0
\(73\) 1.73205i 0.202721i −0.994850 0.101361i \(-0.967680\pi\)
0.994850 0.101361i \(-0.0323196\pi\)
\(74\) 0 0
\(75\) −3.50000 + 6.06218i −0.404145 + 0.700000i
\(76\) 6.00000 + 3.46410i 0.688247 + 0.397360i
\(77\) 6.00000 0.683763
\(78\) 0 0
\(79\) −11.0000 −1.23760 −0.618798 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) 12.0000 + 6.92820i 1.34164 + 0.774597i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 13.8564i 1.52094i 0.649374 + 0.760469i \(0.275031\pi\)
−0.649374 + 0.760469i \(0.724969\pi\)
\(84\) −3.00000 + 1.73205i −0.327327 + 0.188982i
\(85\) 0 0
\(86\) 0 0
\(87\) 3.00000 + 5.19615i 0.321634 + 0.557086i
\(88\) 0 0
\(89\) −6.00000 3.46410i −0.635999 0.367194i 0.147073 0.989126i \(-0.453015\pi\)
−0.783072 + 0.621932i \(0.786348\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −12.0000 −1.25109
\(93\) −1.50000 0.866025i −0.155543 0.0898027i
\(94\) 0 0
\(95\) 6.00000 + 10.3923i 0.615587 + 1.06623i
\(96\) 0 0
\(97\) 4.50000 2.59808i 0.456906 0.263795i −0.253837 0.967247i \(-0.581693\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) 3.46410i 0.348155i
\(100\) 7.00000 + 12.1244i 0.700000 + 1.21244i
\(101\) 9.00000 15.5885i 0.895533 1.55111i 0.0623905 0.998052i \(-0.480128\pi\)
0.833143 0.553058i \(-0.186539\pi\)
\(102\) 0 0
\(103\) −1.00000 −0.0985329 −0.0492665 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) 0 0
\(105\) −6.00000 −0.585540
\(106\) 0 0
\(107\) 3.00000 5.19615i 0.290021 0.502331i −0.683793 0.729676i \(-0.739671\pi\)
0.973814 + 0.227345i \(0.0730044\pi\)
\(108\) 1.00000 + 1.73205i 0.0962250 + 0.166667i
\(109\) 15.5885i 1.49310i 0.665327 + 0.746552i \(0.268292\pi\)
−0.665327 + 0.746552i \(0.731708\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 6.92820i 0.654654i
\(113\) −3.00000 5.19615i −0.282216 0.488813i 0.689714 0.724082i \(-0.257736\pi\)
−0.971930 + 0.235269i \(0.924403\pi\)
\(114\) 0 0
\(115\) −18.0000 10.3923i −1.67851 0.969087i
\(116\) 12.0000 1.11417
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) 0 0
\(123\) 6.00000 3.46410i 0.541002 0.312348i
\(124\) −3.00000 + 1.73205i −0.269408 + 0.155543i
\(125\) 6.92820i 0.619677i
\(126\) 0 0
\(127\) −6.50000 + 11.2583i −0.576782 + 0.999015i 0.419064 + 0.907957i \(0.362358\pi\)
−0.995846 + 0.0910585i \(0.970975\pi\)
\(128\) 0 0
\(129\) 1.00000 0.0880451
\(130\) 0 0
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) −6.00000 3.46410i −0.522233 0.301511i
\(133\) −3.00000 + 5.19615i −0.260133 + 0.450564i
\(134\) 0 0
\(135\) 3.46410i 0.298142i
\(136\) 0 0
\(137\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(138\) 0 0
\(139\) −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i \(-0.234680\pi\)
−0.952355 + 0.304991i \(0.901346\pi\)
\(140\) −6.00000 + 10.3923i −0.507093 + 0.878310i
\(141\) −3.00000 1.73205i −0.252646 0.145865i
\(142\) 0 0
\(143\) 0 0
\(144\) 4.00000 0.333333
\(145\) 18.0000 + 10.3923i 1.49482 + 0.863034i
\(146\) 0 0
\(147\) 2.00000 + 3.46410i 0.164957 + 0.285714i
\(148\) 0 0
\(149\) 6.00000 3.46410i 0.491539 0.283790i −0.233674 0.972315i \(-0.575075\pi\)
0.725213 + 0.688525i \(0.241741\pi\)
\(150\) 0 0
\(151\) 3.46410i 0.281905i 0.990016 + 0.140952i \(0.0450164\pi\)
−0.990016 + 0.140952i \(0.954984\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −6.00000 −0.481932
\(156\) 0 0
\(157\) 11.0000 0.877896 0.438948 0.898513i \(-0.355351\pi\)
0.438948 + 0.898513i \(0.355351\pi\)
\(158\) 0 0
\(159\) 6.00000 10.3923i 0.475831 0.824163i
\(160\) 0 0
\(161\) 10.3923i 0.819028i
\(162\) 0 0
\(163\) 16.5000 9.52628i 1.29238 0.746156i 0.313304 0.949653i \(-0.398564\pi\)
0.979076 + 0.203497i \(0.0652307\pi\)
\(164\) 13.8564i 1.08200i
\(165\) −6.00000 10.3923i −0.467099 0.809040i
\(166\) 0 0
\(167\) 6.00000 + 3.46410i 0.464294 + 0.268060i 0.713848 0.700301i \(-0.246951\pi\)
−0.249554 + 0.968361i \(0.580284\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 3.00000 + 1.73205i 0.229416 + 0.132453i
\(172\) 1.00000 1.73205i 0.0762493 0.132068i
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 0 0
\(175\) −10.5000 + 6.06218i −0.793725 + 0.458258i
\(176\) −12.0000 + 6.92820i −0.904534 + 0.522233i
\(177\) 3.46410i 0.260378i
\(178\) 0 0
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 6.00000 + 3.46410i 0.447214 + 0.258199i
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) −1.00000 −0.0739221
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −6.00000 + 3.46410i −0.437595 + 0.252646i
\(189\) −1.50000 + 0.866025i −0.109109 + 0.0629941i
\(190\) 0 0
\(191\) 9.00000 + 15.5885i 0.651217 + 1.12794i 0.982828 + 0.184525i \(0.0590746\pi\)
−0.331611 + 0.943416i \(0.607592\pi\)
\(192\) 4.00000 6.92820i 0.288675 0.500000i
\(193\) 13.5000 + 7.79423i 0.971751 + 0.561041i 0.899770 0.436365i \(-0.143734\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 8.00000 0.571429
\(197\) −12.0000 6.92820i −0.854965 0.493614i 0.00735824 0.999973i \(-0.497658\pi\)
−0.862323 + 0.506359i \(0.830991\pi\)
\(198\) 0 0
\(199\) −3.50000 6.06218i −0.248108 0.429736i 0.714893 0.699234i \(-0.246476\pi\)
−0.963001 + 0.269498i \(0.913142\pi\)
\(200\) 0 0
\(201\) −7.50000 + 4.33013i −0.529009 + 0.305424i
\(202\) 0 0
\(203\) 10.3923i 0.729397i
\(204\) 0 0
\(205\) 12.0000 20.7846i 0.838116 1.45166i
\(206\) 0 0
\(207\) −6.00000 −0.417029
\(208\) 0 0
\(209\) −12.0000 −0.830057
\(210\) 0 0
\(211\) −6.50000 + 11.2583i −0.447478 + 0.775055i −0.998221 0.0596196i \(-0.981011\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) −12.0000 20.7846i −0.824163 1.42749i
\(213\) 10.3923i 0.712069i
\(214\) 0 0
\(215\) 3.00000 1.73205i 0.204598 0.118125i
\(216\) 0 0
\(217\) −1.50000 2.59808i −0.101827 0.176369i
\(218\) 0 0
\(219\) −1.50000 0.866025i −0.101361 0.0585206i
\(220\) −24.0000 −1.61808
\(221\) 0 0
\(222\) 0 0
\(223\) −15.0000 8.66025i −1.00447 0.579934i −0.0949052 0.995486i \(-0.530255\pi\)
−0.909569 + 0.415553i \(0.863588\pi\)
\(224\) 0 0
\(225\) 3.50000 + 6.06218i 0.233333 + 0.404145i
\(226\) 0 0
\(227\) −18.0000 + 10.3923i −1.19470 + 0.689761i −0.959369 0.282153i \(-0.908951\pi\)
−0.235333 + 0.971915i \(0.575618\pi\)
\(228\) 6.00000 3.46410i 0.397360 0.229416i
\(229\) 27.7128i 1.83131i −0.401960 0.915657i \(-0.631671\pi\)
0.401960 0.915657i \(-0.368329\pi\)
\(230\) 0 0
\(231\) 3.00000 5.19615i 0.197386 0.341882i
\(232\) 0 0
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) −12.0000 −0.782794
\(236\) −6.00000 3.46410i −0.390567 0.225494i
\(237\) −5.50000 + 9.52628i −0.357263 + 0.618798i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 12.0000 6.92820i 0.774597 0.447214i
\(241\) −18.0000 + 10.3923i −1.15948 + 0.669427i −0.951180 0.308637i \(-0.900127\pi\)
−0.208302 + 0.978065i \(0.566794\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −1.00000 + 1.73205i −0.0640184 + 0.110883i
\(245\) 12.0000 + 6.92820i 0.766652 + 0.442627i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 12.0000 + 6.92820i 0.760469 + 0.439057i
\(250\) 0 0
\(251\) −6.00000 10.3923i −0.378717 0.655956i 0.612159 0.790735i \(-0.290301\pi\)
−0.990876 + 0.134778i \(0.956968\pi\)
\(252\) 3.46410i 0.218218i
\(253\) 18.0000 10.3923i 1.13165 0.653359i
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 6.00000 0.371391
\(262\) 0 0
\(263\) −6.00000 + 10.3923i −0.369976 + 0.640817i −0.989561 0.144112i \(-0.953967\pi\)
0.619586 + 0.784929i \(0.287301\pi\)
\(264\) 0 0
\(265\) 41.5692i 2.55358i
\(266\) 0 0
\(267\) −6.00000 + 3.46410i −0.367194 + 0.212000i
\(268\) 17.3205i 1.05802i
\(269\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 0 0
\(271\) 4.50000 + 2.59808i 0.273356 + 0.157822i 0.630412 0.776261i \(-0.282886\pi\)
−0.357056 + 0.934083i \(0.616219\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −21.0000 12.1244i −1.26635 0.731126i
\(276\) −6.00000 + 10.3923i −0.361158 + 0.625543i
\(277\) 5.00000 + 8.66025i 0.300421 + 0.520344i 0.976231 0.216731i \(-0.0695395\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(278\) 0 0
\(279\) −1.50000 + 0.866025i −0.0898027 + 0.0518476i
\(280\) 0 0
\(281\) 24.2487i 1.44656i 0.690557 + 0.723278i \(0.257366\pi\)
−0.690557 + 0.723278i \(0.742634\pi\)
\(282\) 0 0
\(283\) 5.50000 9.52628i 0.326941 0.566279i −0.654962 0.755662i \(-0.727315\pi\)
0.981903 + 0.189383i \(0.0606488\pi\)
\(284\) −18.0000 10.3923i −1.06810 0.616670i
\(285\) 12.0000 0.710819
\(286\) 0 0
\(287\) 12.0000 0.708338
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 0 0
\(291\) 5.19615i 0.304604i
\(292\) −3.00000 + 1.73205i −0.175562 + 0.101361i
\(293\) 15.0000 8.66025i 0.876309 0.505937i 0.00686959 0.999976i \(-0.497813\pi\)
0.869440 + 0.494039i \(0.164480\pi\)
\(294\) 0 0
\(295\) −6.00000 10.3923i −0.349334 0.605063i
\(296\) 0 0
\(297\) −3.00000 1.73205i −0.174078 0.100504i
\(298\) 0 0
\(299\) 0 0
\(300\) 14.0000 0.808290
\(301\) 1.50000 + 0.866025i 0.0864586 + 0.0499169i
\(302\) 0 0
\(303\) −9.00000 15.5885i −0.517036 0.895533i
\(304\) 13.8564i 0.794719i
\(305\) −3.00000 + 1.73205i −0.171780 + 0.0991769i
\(306\) 0 0
\(307\) 1.73205i 0.0988534i 0.998778 + 0.0494267i \(0.0157394\pi\)
−0.998778 + 0.0494267i \(0.984261\pi\)
\(308\) −6.00000 10.3923i −0.341882 0.592157i
\(309\) −0.500000 + 0.866025i −0.0284440 + 0.0492665i
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) 13.0000 0.734803 0.367402 0.930062i \(-0.380247\pi\)
0.367402 + 0.930062i \(0.380247\pi\)
\(314\) 0 0
\(315\) −3.00000 + 5.19615i −0.169031 + 0.292770i
\(316\) 11.0000 + 19.0526i 0.618798 + 1.07179i
\(317\) 6.92820i 0.389127i −0.980890 0.194563i \(-0.937671\pi\)
0.980890 0.194563i \(-0.0623290\pi\)
\(318\) 0 0
\(319\) −18.0000 + 10.3923i −1.00781 + 0.581857i
\(320\) 27.7128i 1.54919i
\(321\) −3.00000 5.19615i −0.167444 0.290021i
\(322\) 0 0
\(323\) 0 0
\(324\) 2.00000 0.111111
\(325\) 0 0
\(326\) 0 0
\(327\) 13.5000 + 7.79423i 0.746552 + 0.431022i
\(328\) 0 0
\(329\) −3.00000 5.19615i −0.165395 0.286473i
\(330\) 0 0
\(331\) −4.50000 + 2.59808i −0.247342 + 0.142803i −0.618547 0.785748i \(-0.712278\pi\)
0.371204 + 0.928551i \(0.378945\pi\)
\(332\) 24.0000 13.8564i 1.31717 0.760469i
\(333\) 0 0
\(334\) 0 0
\(335\) −15.0000 + 25.9808i −0.819538 + 1.41948i
\(336\) 6.00000 + 3.46410i 0.327327 + 0.188982i
\(337\) −5.00000 −0.272367 −0.136184 0.990684i \(-0.543484\pi\)
−0.136184 + 0.990684i \(0.543484\pi\)
\(338\) 0 0
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) 3.00000 5.19615i 0.162459 0.281387i
\(342\) 0 0
\(343\) 19.0526i 1.02874i
\(344\) 0 0
\(345\) −18.0000 + 10.3923i −0.969087 + 0.559503i
\(346\) 0 0
\(347\) 12.0000 + 20.7846i 0.644194 + 1.11578i 0.984487 + 0.175457i \(0.0561403\pi\)
−0.340293 + 0.940319i \(0.610526\pi\)
\(348\) 6.00000 10.3923i 0.321634 0.557086i
\(349\) 16.5000 + 9.52628i 0.883225 + 0.509930i 0.871720 0.490004i \(-0.163005\pi\)
0.0115044 + 0.999934i \(0.496338\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9.00000 5.19615i −0.479022 0.276563i 0.240987 0.970528i \(-0.422529\pi\)
−0.720009 + 0.693965i \(0.755862\pi\)
\(354\) 0 0
\(355\) −18.0000 31.1769i −0.955341 1.65470i
\(356\) 13.8564i 0.734388i
\(357\) 0 0
\(358\) 0 0
\(359\) 6.92820i 0.365657i −0.983145 0.182828i \(-0.941475\pi\)
0.983145 0.182828i \(-0.0585252\pi\)
\(360\) 0 0
\(361\) −3.50000 + 6.06218i −0.184211 + 0.319062i
\(362\) 0 0
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) −8.50000 + 14.7224i −0.443696 + 0.768505i −0.997960 0.0638362i \(-0.979666\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(368\) 12.0000 + 20.7846i 0.625543 + 1.08347i
\(369\) 6.92820i 0.360668i
\(370\) 0 0
\(371\) 18.0000 10.3923i 0.934513 0.539542i
\(372\) 3.46410i 0.179605i
\(373\) 5.50000 + 9.52628i 0.284779 + 0.493252i 0.972556 0.232671i \(-0.0747464\pi\)
−0.687776 + 0.725923i \(0.741413\pi\)
\(374\) 0 0
\(375\) 6.00000 + 3.46410i 0.309839 + 0.178885i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 19.5000 + 11.2583i 1.00165 + 0.578302i 0.908735 0.417373i \(-0.137049\pi\)
0.0929123 + 0.995674i \(0.470382\pi\)
\(380\) 12.0000 20.7846i 0.615587 1.06623i
\(381\) 6.50000 + 11.2583i 0.333005 + 0.576782i
\(382\) 0 0
\(383\) −24.0000 + 13.8564i −1.22634 + 0.708029i −0.966263 0.257558i \(-0.917082\pi\)
−0.260080 + 0.965587i \(0.583749\pi\)
\(384\) 0 0
\(385\) 20.7846i 1.05928i
\(386\) 0 0
\(387\) 0.500000 0.866025i 0.0254164 0.0440225i
\(388\) −9.00000 5.19615i −0.456906 0.263795i
\(389\) 12.0000 0.608424 0.304212 0.952604i \(-0.401607\pi\)
0.304212 + 0.952604i \(0.401607\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 3.00000 5.19615i 0.151330 0.262111i
\(394\) 0 0
\(395\) 38.1051i 1.91728i
\(396\) −6.00000 + 3.46410i −0.301511 + 0.174078i
\(397\) −13.5000 + 7.79423i −0.677546 + 0.391181i −0.798930 0.601424i \(-0.794600\pi\)
0.121384 + 0.992606i \(0.461267\pi\)
\(398\) 0 0
\(399\) 3.00000 + 5.19615i 0.150188 + 0.260133i
\(400\) 14.0000 24.2487i 0.700000 1.21244i
\(401\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −36.0000 −1.79107
\(405\) 3.00000 + 1.73205i 0.149071 + 0.0860663i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −7.50000 + 4.33013i −0.370851 + 0.214111i −0.673830 0.738886i \(-0.735352\pi\)
0.302979 + 0.952997i \(0.402019\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.00000 + 1.73205i 0.0492665 + 0.0853320i
\(413\) 3.00000 5.19615i 0.147620 0.255686i
\(414\) 0 0
\(415\) 48.0000 2.35623
\(416\) 0 0
\(417\) −5.00000 −0.244851
\(418\) 0 0
\(419\) 6.00000 10.3923i 0.293119 0.507697i −0.681426 0.731887i \(-0.738640\pi\)
0.974546 + 0.224189i \(0.0719734\pi\)
\(420\) 6.00000 + 10.3923i 0.292770 + 0.507093i
\(421\) 12.1244i 0.590905i 0.955357 + 0.295452i \(0.0954704\pi\)
−0.955357 + 0.295452i \(0.904530\pi\)
\(422\) 0 0
\(423\) −3.00000 + 1.73205i −0.145865 + 0.0842152i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.50000 0.866025i −0.0725901 0.0419099i
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) −18.0000 10.3923i −0.867029 0.500580i −0.000669521 1.00000i \(-0.500213\pi\)
−0.866360 + 0.499420i \(0.833546\pi\)
\(432\) 2.00000 3.46410i 0.0962250 0.166667i
\(433\) 11.5000 + 19.9186i 0.552655 + 0.957226i 0.998082 + 0.0619079i \(0.0197185\pi\)
−0.445427 + 0.895318i \(0.646948\pi\)
\(434\) 0 0
\(435\) 18.0000 10.3923i 0.863034 0.498273i
\(436\) 27.0000 15.5885i 1.29307 0.746552i
\(437\) 20.7846i 0.994263i
\(438\) 0 0
\(439\) −17.5000 + 30.3109i −0.835229 + 1.44666i 0.0586141 + 0.998281i \(0.481332\pi\)
−0.893843 + 0.448379i \(0.852001\pi\)
\(440\) 0 0
\(441\) 4.00000 0.190476
\(442\) 0 0
\(443\) 24.0000 1.14027 0.570137 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) 0 0
\(445\) −12.0000 + 20.7846i −0.568855 + 0.985285i
\(446\) 0 0
\(447\) 6.92820i 0.327693i
\(448\) 12.0000 6.92820i 0.566947 0.327327i
\(449\) −33.0000 + 19.0526i −1.55737 + 0.899146i −0.559859 + 0.828588i \(0.689145\pi\)
−0.997508 + 0.0705577i \(0.977522\pi\)
\(450\) 0 0
\(451\) 12.0000 + 20.7846i 0.565058 + 0.978709i
\(452\) −6.00000 + 10.3923i −0.282216 + 0.488813i
\(453\) 3.00000 + 1.73205i 0.140952 + 0.0813788i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 31.5000 + 18.1865i 1.47351 + 0.850730i 0.999555 0.0298202i \(-0.00949348\pi\)
0.473953 + 0.880550i \(0.342827\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 41.5692i 1.93817i
\(461\) 36.0000 20.7846i 1.67669 0.968036i 0.712938 0.701228i \(-0.247364\pi\)
0.963750 0.266808i \(-0.0859690\pi\)
\(462\) 0 0
\(463\) 36.3731i 1.69040i 0.534450 + 0.845200i \(0.320519\pi\)
−0.534450 + 0.845200i \(0.679481\pi\)
\(464\) −12.0000 20.7846i −0.557086 0.964901i
\(465\) −3.00000 + 5.19615i −0.139122 + 0.240966i
\(466\) 0 0
\(467\) 6.00000 0.277647 0.138823 0.990317i \(-0.455668\pi\)
0.138823 + 0.990317i \(0.455668\pi\)
\(468\) 0 0
\(469\) −15.0000 −0.692636
\(470\) 0 0
\(471\) 5.50000 9.52628i 0.253427 0.438948i
\(472\) 0 0
\(473\) 3.46410i 0.159280i
\(474\) 0 0
\(475\) 21.0000 12.1244i 0.963546 0.556304i
\(476\) 0 0
\(477\) −6.00000 10.3923i −0.274721 0.475831i
\(478\) 0 0
\(479\) −30.0000 17.3205i −1.37073 0.791394i −0.379714 0.925104i \(-0.623978\pi\)
−0.991021 + 0.133710i \(0.957311\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −9.00000 5.19615i −0.409514 0.236433i
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) −9.00000 15.5885i −0.408669 0.707835i
\(486\) 0 0
\(487\) 21.0000 12.1244i 0.951601 0.549407i 0.0580230 0.998315i \(-0.481520\pi\)
0.893578 + 0.448908i \(0.148187\pi\)
\(488\) 0 0
\(489\) 19.0526i 0.861586i
\(490\) 0 0
\(491\) −3.00000 + 5.19615i −0.135388 + 0.234499i −0.925746 0.378147i \(-0.876561\pi\)
0.790358 + 0.612646i \(0.209895\pi\)
\(492\) −12.0000 6.92820i −0.541002 0.312348i
\(493\) 0 0
\(494\) 0 0
\(495\) −12.0000 −0.539360
\(496\) 6.00000 + 3.46410i 0.269408 + 0.155543i
\(497\) 9.00000 15.5885i 0.403705 0.699238i
\(498\) 0 0
\(499\) 31.1769i 1.39567i −0.716258 0.697835i \(-0.754147\pi\)
0.716258 0.697835i \(-0.245853\pi\)
\(500\) 12.0000 6.92820i 0.536656 0.309839i
\(501\) 6.00000 3.46410i 0.268060 0.154765i
\(502\) 0 0
\(503\) 15.0000 + 25.9808i 0.668817 + 1.15842i 0.978235 + 0.207499i \(0.0665323\pi\)
−0.309418 + 0.950926i \(0.600134\pi\)
\(504\) 0 0
\(505\) −54.0000 31.1769i −2.40297 1.38735i
\(506\) 0 0
\(507\) 0 0
\(508\) 26.0000 1.15356
\(509\) 15.0000 + 8.66025i 0.664863 + 0.383859i 0.794128 0.607751i \(-0.207928\pi\)
−0.129264 + 0.991610i \(0.541262\pi\)
\(510\) 0 0
\(511\) −1.50000 2.59808i −0.0663561 0.114932i
\(512\) 0 0
\(513\) 3.00000 1.73205i 0.132453 0.0764719i
\(514\) 0 0
\(515\) 3.46410i 0.152647i
\(516\) −1.00000 1.73205i −0.0440225 0.0762493i
\(517\) 6.00000 10.3923i 0.263880 0.457053i
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) −24.0000 −1.05146 −0.525730 0.850652i \(-0.676208\pi\)
−0.525730 + 0.850652i \(0.676208\pi\)
\(522\) 0 0
\(523\) 14.0000 24.2487i 0.612177 1.06032i −0.378695 0.925521i \(-0.623627\pi\)
0.990873 0.134801i \(-0.0430394\pi\)
\(524\) −6.00000 10.3923i −0.262111 0.453990i
\(525\) 12.1244i 0.529150i
\(526\) 0 0
\(527\) 0 0
\(528\) 13.8564i 0.603023i
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) −3.00000 1.73205i −0.130189 0.0751646i
\(532\) 12.0000 0.520266
\(533\) 0 0
\(534\) 0 0
\(535\) −18.0000 10.3923i −0.778208 0.449299i
\(536\) 0 0
\(537\) 6.00000 + 10.3923i 0.258919 + 0.448461i
\(538\) 0 0
\(539\) −12.0000 + 6.92820i −0.516877 + 0.298419i
\(540\) 6.00000 3.46410i 0.258199 0.149071i
\(541\) 29.4449i 1.26593i 0.774179 + 0.632967i \(0.218163\pi\)
−0.774179 + 0.632967i \(0.781837\pi\)
\(542\) 0 0
\(543\) 7.00000 12.1244i 0.300399 0.520306i
\(544\) 0 0
\(545\) 54.0000 2.31311
\(546\) 0 0
\(547\) −19.0000 −0.812381 −0.406191 0.913788i \(-0.633143\pi\)
−0.406191 + 0.913788i \(0.633143\pi\)
\(548\) 0 0
\(549\) −0.500000 + 0.866025i −0.0213395 + 0.0369611i
\(550\) 0 0
\(551\) 20.7846i 0.885454i
\(552\) 0 0
\(553\) −16.5000 + 9.52628i −0.701651 + 0.405099i
\(554\) 0 0
\(555\) 0 0
\(556\) −5.00000 + 8.66025i −0.212047 + 0.367277i
\(557\) 24.0000 + 13.8564i 1.01691 + 0.587115i 0.913208 0.407493i \(-0.133597\pi\)
0.103704 + 0.994608i \(0.466930\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 24.0000 1.01419
\(561\) 0 0
\(562\) 0 0
\(563\) 21.0000 + 36.3731i 0.885044 + 1.53294i 0.845663 + 0.533718i \(0.179206\pi\)
0.0393818 + 0.999224i \(0.487461\pi\)
\(564\) 6.92820i 0.291730i
\(565\) −18.0000 + 10.3923i −0.757266 + 0.437208i
\(566\) 0 0
\(567\) 1.73205i 0.0727393i
\(568\) 0 0
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) −44.0000 −1.84134 −0.920671 0.390339i \(-0.872358\pi\)
−0.920671 + 0.390339i \(0.872358\pi\)
\(572\) 0 0
\(573\) 18.0000 0.751961
\(574\) 0 0
\(575\) −21.0000 + 36.3731i −0.875761 + 1.51686i
\(576\) −4.00000 6.92820i −0.166667 0.288675i
\(577\) 34.6410i 1.44212i 0.692870 + 0.721062i \(0.256346\pi\)
−0.692870 + 0.721062i \(0.743654\pi\)
\(578\) 0 0
\(579\) 13.5000 7.79423i 0.561041 0.323917i
\(580\) 41.5692i 1.72607i
\(581\) 12.0000 + 20.7846i 0.497844 + 0.862291i
\(582\) 0 0
\(583\) 36.0000 + 20.7846i 1.49097 + 0.860811i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 27.0000 + 15.5885i 1.11441 + 0.643404i 0.939968 0.341263i \(-0.110855\pi\)
0.174441 + 0.984668i \(0.444188\pi\)
\(588\) 4.00000 6.92820i 0.164957 0.285714i
\(589\) 3.00000 + 5.19615i 0.123613 + 0.214104i
\(590\) 0 0
\(591\) −12.0000 + 6.92820i −0.493614 + 0.284988i
\(592\) 0 0
\(593\) 3.46410i 0.142254i −0.997467 0.0711268i \(-0.977341\pi\)
0.997467 0.0711268i \(-0.0226595\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −12.0000 6.92820i −0.491539 0.283790i
\(597\) −7.00000 −0.286491
\(598\) 0 0
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0 0
\(601\) 13.0000 22.5167i 0.530281 0.918474i −0.469095 0.883148i \(-0.655420\pi\)
0.999376 0.0353259i \(-0.0112469\pi\)
\(602\) 0 0
\(603\) 8.66025i 0.352673i
\(604\) 6.00000 3.46410i 0.244137 0.140952i
\(605\) 3.00000 1.73205i 0.121967 0.0704179i
\(606\) 0 0
\(607\) −4.00000 6.92820i −0.162355 0.281207i 0.773358 0.633970i \(-0.218576\pi\)
−0.935713 + 0.352763i \(0.885242\pi\)
\(608\) 0 0
\(609\) 9.00000 + 5.19615i 0.364698 + 0.210559i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −7.50000 4.33013i −0.302922 0.174892i 0.340833 0.940124i \(-0.389291\pi\)
−0.643755 + 0.765232i \(0.722624\pi\)
\(614\) 0 0
\(615\) −12.0000 20.7846i −0.483887 0.838116i
\(616\) 0 0
\(617\) 9.00000 5.19615i 0.362326 0.209189i −0.307774 0.951459i \(-0.599584\pi\)
0.670101 + 0.742270i \(0.266251\pi\)
\(618\) 0 0
\(619\) 25.9808i 1.04425i −0.852867 0.522127i \(-0.825139\pi\)
0.852867 0.522127i \(-0.174861\pi\)
\(620\) 6.00000 + 10.3923i 0.240966 + 0.417365i
\(621\) −3.00000 + 5.19615i −0.120386 + 0.208514i
\(622\) 0 0
\(623\) −12.0000 −0.480770
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) 0 0
\(627\) −6.00000 + 10.3923i −0.239617 + 0.415029i
\(628\) −11.0000 19.0526i −0.438948 0.760280i
\(629\) 0 0
\(630\) 0 0
\(631\) −1.50000 + 0.866025i −0.0597141 + 0.0344759i −0.529560 0.848273i \(-0.677643\pi\)
0.469846 + 0.882749i \(0.344310\pi\)
\(632\) 0 0
\(633\) 6.50000 + 11.2583i 0.258352 + 0.447478i
\(634\) 0 0
\(635\) 39.0000 + 22.5167i 1.54767 + 0.893546i
\(636\) −24.0000 −0.951662
\(637\) 0 0
\(638\) 0 0
\(639\) −9.00000 5.19615i −0.356034 0.205557i
\(640\) 0 0
\(641\) −9.00000 15.5885i −0.355479 0.615707i 0.631721 0.775196i \(-0.282349\pi\)
−0.987200 + 0.159489i \(0.949015\pi\)
\(642\) 0 0
\(643\) −16.5000 + 9.52628i −0.650696 + 0.375680i −0.788723 0.614749i \(-0.789257\pi\)
0.138027 + 0.990429i \(0.455924\pi\)
\(644\) −18.0000 + 10.3923i −0.709299 + 0.409514i
\(645\) 3.46410i 0.136399i
\(646\) 0 0
\(647\) 9.00000 15.5885i 0.353827 0.612845i −0.633090 0.774078i \(-0.718214\pi\)
0.986916 + 0.161233i \(0.0515470\pi\)
\(648\) 0 0
\(649\) 12.0000 0.471041
\(650\) 0 0
\(651\) −3.00000 −0.117579
\(652\) −33.0000 19.0526i −1.29238 0.746156i
\(653\) −18.0000 + 31.1769i −0.704394 + 1.22005i 0.262515 + 0.964928i \(0.415448\pi\)
−0.966910 + 0.255119i \(0.917885\pi\)
\(654\) 0 0
\(655\) 20.7846i 0.812122i
\(656\) −24.0000 + 13.8564i −0.937043 + 0.541002i
\(657\) −1.50000 + 0.866025i −0.0585206 + 0.0337869i
\(658\) 0 0
\(659\) −24.0000 41.5692i −0.934907 1.61931i −0.774799 0.632207i \(-0.782149\pi\)
−0.160108 0.987099i \(-0.551184\pi\)
\(660\) −12.0000 + 20.7846i −0.467099 + 0.809040i
\(661\) 22.5000 + 12.9904i 0.875149 + 0.505267i 0.869056 0.494714i \(-0.164727\pi\)
0.00609283 + 0.999981i \(0.498061\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 18.0000 + 10.3923i 0.698010 + 0.402996i
\(666\) 0 0
\(667\) 18.0000 + 31.1769i 0.696963 + 1.20717i
\(668\) 13.8564i 0.536120i
\(669\) −15.0000 + 8.66025i −0.579934 + 0.334825i
\(670\) 0 0
\(671\) 3.46410i 0.133730i
\(672\) 0 0
\(673\) 0.500000 0.866025i 0.0192736 0.0333828i −0.856228 0.516599i \(-0.827198\pi\)
0.875501 + 0.483216i \(0.160531\pi\)
\(674\) 0 0
\(675\) 7.00000 0.269430
\(676\) 0 0
\(677\) 48.0000 1.84479 0.922395 0.386248i \(-0.126229\pi\)
0.922395 + 0.386248i \(0.126229\pi\)
\(678\) 0 0
\(679\) 4.50000 7.79423i 0.172694 0.299115i
\(680\) 0 0
\(681\) 20.7846i 0.796468i
\(682\) 0 0
\(683\) −21.0000 + 12.1244i −0.803543 + 0.463926i −0.844708 0.535227i \(-0.820226\pi\)
0.0411658 + 0.999152i \(0.486893\pi\)
\(684\) 6.92820i 0.264906i
\(685\) 0 0
\(686\) 0 0
\(687\) −24.0000 13.8564i −0.915657 0.528655i
\(688\) −4.00000 −0.152499
\(689\) 0 0
\(690\) 0 0
\(691\) −37.5000 21.6506i −1.42657 0.823629i −0.429719 0.902963i \(-0.641387\pi\)
−0.996848 + 0.0793336i \(0.974721\pi\)
\(692\) 6.00000 10.3923i 0.228086 0.395056i
\(693\) −3.00000 5.19615i −0.113961 0.197386i
\(694\) 0 0
\(695\) −15.0000 + 8.66025i −0.568982 + 0.328502i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −9.00000 + 15.5885i −0.340411 + 0.589610i
\(700\) 21.0000 + 12.1244i 0.793725 + 0.458258i
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 24.0000 + 13.8564i 0.904534 + 0.522233i
\(705\) −6.00000 + 10.3923i −0.225973 + 0.391397i
\(706\) 0 0
\(707\) 31.1769i 1.17253i
\(708\) −6.00000 + 3.46410i −0.225494 + 0.130189i
\(709\) 16.5000 9.52628i 0.619671 0.357767i −0.157070 0.987587i \(-0.550205\pi\)
0.776741 + 0.629821i \(0.216872\pi\)
\(710\) 0 0
\(711\) 5.50000 + 9.52628i 0.206266 + 0.357263i
\(712\) 0 0
\(713\) −9.00000 5.19615i −0.337053 0.194597i
\(714\) 0 0
\(715\) 0 0
\(716\) 24.0000 0.896922
\(717\) 0 0
\(718\) 0 0
\(719\) 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i \(-0.130979\pi\)
−0.804648 + 0.593753i \(0.797646\pi\)
\(720\) 13.8564i 0.516398i
\(721\) −1.50000 + 0.866025i −0.0558629 + 0.0322525i
\(722\) 0 0
\(723\) 20.7846i 0.772988i
\(724\) −14.0000 24.2487i −0.520306 0.901196i
\(725\) 21.0000 36.3731i 0.779920 1.35086i
\(726\) 0 0
\(727\) −35.0000 −1.29808 −0.649039 0.760755i \(-0.724829\pi\)
−0.649039 + 0.760755i \(0.724829\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 1.00000 + 1.73205i 0.0369611 + 0.0640184i
\(733\) 39.8372i 1.47142i −0.677297 0.735710i \(-0.736849\pi\)
0.677297 0.735710i \(-0.263151\pi\)
\(734\) 0 0
\(735\) 12.0000 6.92820i 0.442627 0.255551i
\(736\) 0 0
\(737\) −15.0000 25.9808i −0.552532 0.957014i
\(738\) 0 0
\(739\) −39.0000 22.5167i −1.43464 0.828289i −0.437168 0.899380i \(-0.644019\pi\)
−0.997470 + 0.0710909i \(0.977352\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 9.00000 + 5.19615i 0.330178 + 0.190628i 0.655920 0.754830i \(-0.272281\pi\)
−0.325742 + 0.945459i \(0.605614\pi\)
\(744\) 0 0
\(745\) −12.0000 20.7846i −0.439646 0.761489i
\(746\) 0 0
\(747\) 12.0000 6.92820i 0.439057 0.253490i
\(748\) 0 0
\(749\) 10.3923i 0.379727i
\(750\) 0 0
\(751\) −4.00000 + 6.92820i −0.145962 + 0.252814i −0.929731 0.368238i \(-0.879961\pi\)
0.783769 + 0.621052i \(0.213294\pi\)
\(752\) 12.0000 + 6.92820i 0.437595 + 0.252646i
\(753\) −12.0000 −0.437304
\(754\) 0 0
\(755\) 12.0000 0.436725
\(756\) 3.00000 + 1.73205i 0.109109 + 0.0629941i
\(757\) −17.0000 + 29.4449i −0.617876 + 1.07019i 0.371997 + 0.928234i \(0.378673\pi\)
−0.989873 + 0.141958i \(0.954660\pi\)
\(758\) 0 0
\(759\) 20.7846i 0.754434i
\(760\) 0 0
\(761\) 18.0000 10.3923i 0.652499 0.376721i −0.136914 0.990583i \(-0.543718\pi\)
0.789413 + 0.613862i \(0.210385\pi\)
\(762\) 0 0
\(763\) 13.5000 + 23.3827i 0.488733 + 0.846510i
\(764\) 18.0000 31.1769i 0.651217 1.12794i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −16.0000 −0.577350
\(769\) 6.00000 + 3.46410i 0.216366 + 0.124919i 0.604266 0.796782i \(-0.293466\pi\)
−0.387901 + 0.921701i \(0.626800\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 31.1769i 1.12208i
\(773\) 45.0000 25.9808i 1.61854 0.934463i 0.631239 0.775589i \(-0.282547\pi\)
0.987299 0.158874i \(-0.0507865\pi\)
\(774\) 0 0
\(775\) 12.1244i 0.435520i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 36.0000 1.28818
\(782\) 0 0
\(783\) 3.00000 5.19615i 0.107211 0.185695i
\(784\) −8.00000 13.8564i −0.285714 0.494872i
\(785\) 38.1051i 1.36003i
\(786\) 0 0
\(787\) −28.5000 + 16.4545i −1.01592 + 0.586539i −0.912918 0.408143i \(-0.866177\pi\)
−0.102997 + 0.994682i \(0.532843\pi\)
\(788\) 27.7128i 0.987228i
\(789\) 6.00000 + 10.3923i 0.213606 + 0.369976i
\(790\) 0 0
\(791\) −9.00000 5.19615i −0.320003 0.184754i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −36.0000 20.7846i −1.27679 0.737154i
\(796\) −7.00000 + 12.1244i −0.248108 + 0.429736i
\(797\) −6.00000 10.3923i −0.212531 0.368114i 0.739975 0.672634i \(-0.234837\pi\)
−0.952506 + 0.304520i \(0.901504\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 6.92820i 0.244796i
\(802\) 0 0
\(803\) 3.00000 5.19615i 0.105868 0.183368i
\(804\) 15.0000 + 8.66025i 0.529009 + 0.305424i
\(805\) −36.0000 −1.26883
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −6.00000 + 10.3923i −0.210949 + 0.365374i −0.952012 0.306062i \(-0.900989\pi\)
0.741063 + 0.671436i \(0.234322\pi\)
\(810\) 0 0
\(811\) 25.9808i 0.912308i 0.889901 + 0.456154i \(0.150773\pi\)
−0.889901 + 0.456154i \(0.849227\pi\)
\(812\) 18.0000 10.3923i 0.631676 0.364698i
\(813\) 4.50000 2.59808i 0.157822 0.0911185i
\(814\) 0 0
\(815\) −33.0000 57.1577i −1.15594 2.00215i
\(816\) 0 0
\(817\) −3.00000 1.73205i −0.104957 0.0605968i
\(818\) 0 0
\(819\) 0 0
\(820\) −48.0000 −1.67623
\(821\) −21.0000 12.1244i −0.732905 0.423143i 0.0865789 0.996245i \(-0.472407\pi\)
−0.819484 + 0.573102i \(0.805740\pi\)
\(822\) 0 0
\(823\) −16.0000 27.7128i −0.557725 0.966008i −0.997686 0.0679910i \(-0.978341\pi\)
0.439961 0.898017i \(-0.354992\pi\)
\(824\) 0 0
\(825\) −21.0000 + 12.1244i −0.731126 + 0.422116i
\(826\) 0 0
\(827\) 48.4974i 1.68642i −0.537584 0.843210i \(-0.680663\pi\)
0.537584 0.843210i \(-0.319337\pi\)
\(828\) 6.00000 + 10.3923i 0.208514 + 0.361158i
\(829\) −15.5000 + 26.8468i −0.538337 + 0.932427i 0.460657 + 0.887578i \(0.347614\pi\)
−0.998994 + 0.0448490i \(0.985719\pi\)
\(830\) 0 0
\(831\) 10.0000 0.346896
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 12.0000 20.7846i 0.415277 0.719281i
\(836\) 12.0000 + 20.7846i 0.415029 + 0.718851i
\(837\) 1.73205i 0.0598684i
\(838\) 0 0
\(839\) −27.0000 + 15.5885i −0.932144 + 0.538173i −0.887489 0.460829i \(-0.847552\pi\)
−0.0446547 + 0.999002i \(0.514219\pi\)
\(840\) 0 0
\(841\) −3.50000 6.06218i −0.120690 0.209041i
\(842\) 0 0
\(843\) 21.0000 + 12.1244i 0.723278 + 0.417585i
\(844\) 26.0000 0.894957
\(845\) 0 0
\(846\) 0 0
\(847\) 1.50000 + 0.866025i 0.0515406 + 0.0297570i
\(848\) −24.0000 + 41.5692i −0.824163 + 1.42749i
\(849\) −5.50000 9.52628i −0.188760 0.326941i
\(850\) 0 0
\(851\) 0 0
\(852\) −18.0000 + 10.3923i −0.616670 + 0.356034i
\(853\) 25.9808i 0.889564i 0.895639 + 0.444782i \(0.146719\pi\)
−0.895639 + 0.444782i \(0.853281\pi\)
\(854\) 0 0
\(855\) 6.00000 10.3923i 0.205196 0.355409i
\(856\) 0 0
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 0 0
\(859\) 13.0000 0.443554 0.221777 0.975097i \(-0.428814\pi\)
0.221777 + 0.975097i \(0.428814\pi\)
\(860\) −6.00000 3.46410i −0.204598 0.118125i
\(861\) 6.00000 10.3923i 0.204479 0.354169i
\(862\) 0 0
\(863\) 17.3205i 0.589597i 0.955559 + 0.294798i \(0.0952525\pi\)
−0.955559 + 0.294798i \(0.904747\pi\)
\(864\) 0 0
\(865\) 18.0000 10.3923i 0.612018 0.353349i
\(866\) 0 0
\(867\) −8.50000 14.7224i −0.288675 0.500000i
\(868\) −3.00000 + 5.19615i −0.101827 + 0.176369i
\(869\) −33.0000 19.0526i −1.11945 0.646314i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −4.50000 2.59808i −0.152302 0.0879316i
\(874\) 0 0
\(875\) 6.00000 + 10.3923i 0.202837 + 0.351324i
\(876\) 3.46410i 0.117041i
\(877\) −36.0000 + 20.7846i −1.21563 + 0.701846i −0.963981 0.265971i \(-0.914307\pi\)
−0.251653 + 0.967818i \(0.580974\pi\)
\(878\) 0 0
\(879\) 17.3205i 0.584206i
\(880\) 24.0000 + 41.5692i 0.809040 + 1.40130i
\(881\) 6.00000 10.3923i 0.202145 0.350126i −0.747074 0.664741i \(-0.768542\pi\)
0.949219 + 0.314615i \(0.101875\pi\)
\(882\) 0 0
\(883\) −5.00000 −0.168263 −0.0841317 0.996455i \(-0.526812\pi\)
−0.0841317 + 0.996455i \(0.526812\pi\)
\(884\) 0 0
\(885\) −12.0000 −0.403376
\(886\) 0 0
\(887\) 21.0000 36.3731i 0.705111 1.22129i −0.261540 0.965193i \(-0.584230\pi\)
0.966651 0.256096i \(-0.0824362\pi\)
\(888\) 0 0
\(889\) 22.5167i 0.755185i
\(890\) 0 0
\(891\) −3.00000 + 1.73205i −0.100504 + 0.0580259i
\(892\) 34.6410i 1.15987i
\(893\) 6.00000 + 10.3923i 0.200782 + 0.347765i
\(894\) 0 0
\(895\) 36.0000 + 20.7846i 1.20335 + 0.694753i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 9.00000 + 5.19615i 0.300167 + 0.173301i
\(900\) 7.00000 12.1244i 0.233333 0.404145i
\(901\) 0 0
\(902\) 0 0
\(903\) 1.50000 0.866025i 0.0499169 0.0288195i
\(904\) 0 0
\(905\) 48.4974i 1.61211i
\(906\) 0 0
\(907\) 22.0000 38.1051i 0.730498 1.26526i −0.226173 0.974087i \(-0.572621\pi\)
0.956671 0.291172i \(-0.0940453\pi\)
\(908\) 36.0000 + 20.7846i 1.19470 + 0.689761i
\(909\) −18.0000 −0.597022
\(910\) 0 0
\(911\) −12.0000 −0.397578 −0.198789 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(912\) −12.0000 6.92820i −0.397360 0.229416i
\(913\) −24.0000 + 41.5692i −0.794284 + 1.37574i
\(914\) 0 0
\(915\) 3.46410i 0.114520i
\(916\) −48.0000 + 27.7128i −1.58596 + 0.915657i
\(917\) 9.00000 5.19615i 0.297206 0.171592i
\(918\) 0 0
\(919\) 16.0000 + 27.7128i 0.527791 + 0.914161i 0.999475 + 0.0323936i \(0.0103130\pi\)
−0.471684 + 0.881768i \(0.656354\pi\)
\(920\) 0 0
\(921\) 1.50000 + 0.866025i 0.0494267 + 0.0285365i
\(922\) 0 0
\(923\) 0 0
\(924\) −12.0000 −0.394771
\(925\) 0 0
\(926\) 0 0
\(927\) 0.500000 + 0.866025i 0.0164222 + 0.0284440i
\(928\) 0 0
\(929\) 18.0000 10.3923i 0.590561 0.340960i −0.174758 0.984611i \(-0.555914\pi\)
0.765319 + 0.643651i \(0.222581\pi\)
\(930\) 0 0
\(931\) 13.8564i 0.454125i
\(932\) 18.0000 + 31.1769i 0.589610 + 1.02123i
\(933\) −12.0000 + 20.7846i −0.392862 + 0.680458i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −14.0000 −0.457360 −0.228680 0.973502i \(-0.573441\pi\)
−0.228680 + 0.973502i \(0.573441\pi\)
\(938\) 0 0
\(939\) 6.50000 11.2583i 0.212119 0.367402i
\(940\) 12.0000 + 20.7846i 0.391397 + 0.677919i
\(941\) 10.3923i 0.338779i 0.985549 + 0.169390i \(0.0541797\pi\)
−0.985549 + 0.169390i \(0.945820\pi\)
\(942\) 0 0
\(943\) 36.0000 20.7846i 1.17232 0.676840i
\(944\) 13.8564i 0.450988i
\(945\) 3.00000 + 5.19615i 0.0975900 + 0.169031i
\(946\) 0 0
\(947\) 42.0000 + 24.2487i 1.36482 + 0.787977i 0.990260 0.139227i \(-0.0444618\pi\)
0.374556 + 0.927204i \(0.377795\pi\)
\(948\) 22.0000 0.714527
\(949\) 0 0
\(950\) 0 0
\(951\) −6.00000 3.46410i −0.194563 0.112331i
\(952\) 0 0
\(953\) −3.00000 5.19615i −0.0971795 0.168320i 0.813337 0.581793i \(-0.197649\pi\)
−0.910516 + 0.413473i \(0.864315\pi\)
\(954\) 0 0
\(955\) 54.0000 31.1769i 1.74740 1.00886i
\(956\) 0 0
\(957\) 20.7846i 0.671871i
\(958\) 0 0
\(959\) 0 0
\(960\) −24.0000 13.8564i −0.774597 0.447214i
\(961\) 28.0000 0.903226
\(962\) 0 0
\(963\) −6.00000 −0.193347
\(964\) 36.0000 + 20.7846i 1.15948 + 0.669427i
\(965\) 27.0000 46.7654i 0.869161 1.50543i
\(966\) 0 0
\(967\) 24.2487i 0.779786i 0.920860 + 0.389893i \(0.127488\pi\)
−0.920860 + 0.389893i \(0.872512\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −18.0000 31.1769i −0.577647 1.00051i −0.995748 0.0921142i \(-0.970638\pi\)
0.418101 0.908401i \(-0.362696\pi\)
\(972\) 1.00000 1.73205i 0.0320750 0.0555556i
\(973\) −7.50000 4.33013i −0.240439 0.138817i
\(974\) 0 0
\(975\) 0 0
\(976\) 4.00000 0.128037
\(977\) 24.0000 + 13.8564i 0.767828 + 0.443306i 0.832099 0.554627i \(-0.187139\pi\)
−0.0642712 + 0.997932i \(0.520472\pi\)
\(978\) 0 0
\(979\) −12.0000 20.7846i −0.383522 0.664279i
\(980\) 27.7128i 0.885253i
\(981\) 13.5000 7.79423i 0.431022 0.248851i
\(982\) 0 0
\(983\) 10.3923i 0.331463i 0.986171 + 0.165732i \(0.0529985\pi\)
−0.986171 + 0.165732i \(0.947001\pi\)
\(984\) 0 0
\(985\) −24.0000 + 41.5692i −0.764704 + 1.32451i
\(986\) 0 0
\(987\) −6.00000 −0.190982
\(988\) 0 0
\(989\) 6.00000 0.190789
\(990\) 0 0
\(991\) 8.00000 13.8564i 0.254128 0.440163i −0.710530 0.703667i \(-0.751545\pi\)
0.964658 + 0.263504i \(0.0848781\pi\)
\(992\) 0 0
\(993\) 5.19615i 0.164895i
\(994\) 0 0
\(995\) −21.0000 + 12.1244i −0.665745 + 0.384368i
\(996\) 27.7128i 0.878114i
\(997\) −17.5000 30.3109i −0.554231 0.959955i −0.997963 0.0637961i \(-0.979679\pi\)
0.443732 0.896159i \(-0.353654\pi\)
\(998\) 0 0
\(999\) 0 0
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 507.2.j.b.316.1 2
13.2 odd 12 507.2.e.f.484.1 4
13.3 even 3 39.2.j.a.10.1 yes 2
13.4 even 6 507.2.b.c.337.2 2
13.5 odd 4 507.2.e.f.22.1 4
13.6 odd 12 507.2.a.e.1.1 2
13.7 odd 12 507.2.a.e.1.2 2
13.8 odd 4 507.2.e.f.22.2 4
13.9 even 3 507.2.b.c.337.1 2
13.10 even 6 inner 507.2.j.b.361.1 2
13.11 odd 12 507.2.e.f.484.2 4
13.12 even 2 39.2.j.a.4.1 2
39.17 odd 6 1521.2.b.f.1351.1 2
39.20 even 12 1521.2.a.h.1.1 2
39.29 odd 6 117.2.q.a.10.1 2
39.32 even 12 1521.2.a.h.1.2 2
39.35 odd 6 1521.2.b.f.1351.2 2
39.38 odd 2 117.2.q.a.82.1 2
52.3 odd 6 624.2.bv.b.49.1 2
52.7 even 12 8112.2.a.bu.1.2 2
52.19 even 12 8112.2.a.bu.1.1 2
52.51 odd 2 624.2.bv.b.433.1 2
65.3 odd 12 975.2.w.d.49.1 4
65.12 odd 4 975.2.w.d.199.1 4
65.29 even 6 975.2.bc.c.751.1 2
65.38 odd 4 975.2.w.d.199.2 4
65.42 odd 12 975.2.w.d.49.2 4
65.64 even 2 975.2.bc.c.901.1 2
156.107 even 6 1872.2.by.f.1297.1 2
156.155 even 2 1872.2.by.f.433.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.j.a.4.1 2 13.12 even 2
39.2.j.a.10.1 yes 2 13.3 even 3
117.2.q.a.10.1 2 39.29 odd 6
117.2.q.a.82.1 2 39.38 odd 2
507.2.a.e.1.1 2 13.6 odd 12
507.2.a.e.1.2 2 13.7 odd 12
507.2.b.c.337.1 2 13.9 even 3
507.2.b.c.337.2 2 13.4 even 6
507.2.e.f.22.1 4 13.5 odd 4
507.2.e.f.22.2 4 13.8 odd 4
507.2.e.f.484.1 4 13.2 odd 12
507.2.e.f.484.2 4 13.11 odd 12
507.2.j.b.316.1 2 1.1 even 1 trivial
507.2.j.b.361.1 2 13.10 even 6 inner
624.2.bv.b.49.1 2 52.3 odd 6
624.2.bv.b.433.1 2 52.51 odd 2
975.2.w.d.49.1 4 65.3 odd 12
975.2.w.d.49.2 4 65.42 odd 12
975.2.w.d.199.1 4 65.12 odd 4
975.2.w.d.199.2 4 65.38 odd 4
975.2.bc.c.751.1 2 65.29 even 6
975.2.bc.c.901.1 2 65.64 even 2
1521.2.a.h.1.1 2 39.20 even 12
1521.2.a.h.1.2 2 39.32 even 12
1521.2.b.f.1351.1 2 39.17 odd 6
1521.2.b.f.1351.2 2 39.35 odd 6
1872.2.by.f.433.1 2 156.155 even 2
1872.2.by.f.1297.1 2 156.107 even 6
8112.2.a.bu.1.1 2 52.19 even 12
8112.2.a.bu.1.2 2 52.7 even 12