Properties

Label 507.2.e.f.484.2
Level $507$
Weight $2$
Character 507.484
Analytic conductor $4.048$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [507,2,Mod(22,507)]
 
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, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.22");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.e (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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 484.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 507.484
Dual form 507.2.e.f.22.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +3.46410 q^{5} +(-0.866025 + 1.50000i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +3.46410 q^{5} +(-0.866025 + 1.50000i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.73205 + 3.00000i) q^{11} +2.00000 q^{12} +(1.73205 + 3.00000i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-1.73205 + 3.00000i) q^{19} +(3.46410 - 6.00000i) q^{20} -1.73205 q^{21} +(-3.00000 - 5.19615i) q^{23} +7.00000 q^{25} -1.00000 q^{27} +(1.73205 + 3.00000i) q^{28} +(-3.00000 - 5.19615i) q^{29} +1.73205 q^{31} +(-1.73205 + 3.00000i) q^{33} +(-3.00000 + 5.19615i) q^{35} +(1.00000 + 1.73205i) q^{36} +(-3.46410 - 6.00000i) q^{41} +(-0.500000 + 0.866025i) q^{43} +6.92820 q^{44} +(-1.73205 + 3.00000i) q^{45} -3.46410 q^{47} +(2.00000 - 3.46410i) q^{48} +(2.00000 + 3.46410i) q^{49} +12.0000 q^{53} +(6.00000 + 10.3923i) q^{55} -3.46410 q^{57} +(-1.73205 + 3.00000i) q^{59} +6.92820 q^{60} +(-0.500000 + 0.866025i) q^{61} +(-0.866025 - 1.50000i) q^{63} -8.00000 q^{64} +(4.33013 + 7.50000i) q^{67} +(3.00000 - 5.19615i) q^{69} +(5.19615 - 9.00000i) q^{71} -1.73205 q^{73} +(3.50000 + 6.06218i) q^{75} +(3.46410 + 6.00000i) q^{76} -6.00000 q^{77} -11.0000 q^{79} +(-6.92820 - 12.0000i) q^{80} +(-0.500000 - 0.866025i) q^{81} -13.8564 q^{83} +(-1.73205 + 3.00000i) q^{84} +(3.00000 - 5.19615i) q^{87} +(-3.46410 - 6.00000i) q^{89} -12.0000 q^{92} +(0.866025 + 1.50000i) q^{93} +(-6.00000 + 10.3923i) q^{95} +(2.59808 - 4.50000i) q^{97} -3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} + 4 q^{4} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} + 4 q^{4} - 2 q^{9} + 8 q^{12} - 8 q^{16} - 12 q^{23} + 28 q^{25} - 4 q^{27} - 12 q^{29} - 12 q^{35} + 4 q^{36} - 2 q^{43} + 8 q^{48} + 8 q^{49} + 48 q^{53} + 24 q^{55} - 2 q^{61} - 32 q^{64} + 12 q^{69} + 14 q^{75} - 24 q^{77} - 44 q^{79} - 2 q^{81} + 12 q^{87} - 48 q^{92} - 24 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 1.00000 1.73205i 0.500000 0.866025i
\(5\) 3.46410 1.54919 0.774597 0.632456i \(-0.217953\pi\)
0.774597 + 0.632456i \(0.217953\pi\)
\(6\) 0 0
\(7\) −0.866025 + 1.50000i −0.327327 + 0.566947i −0.981981 0.188982i \(-0.939481\pi\)
0.654654 + 0.755929i \(0.272814\pi\)
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.73205 + 3.00000i 0.522233 + 0.904534i 0.999665 + 0.0258656i \(0.00823419\pi\)
−0.477432 + 0.878668i \(0.658432\pi\)
\(12\) 2.00000 0.577350
\(13\) 0 0
\(14\) 0 0
\(15\) 1.73205 + 3.00000i 0.447214 + 0.774597i
\(16\) −2.00000 3.46410i −0.500000 0.866025i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) −1.73205 + 3.00000i −0.397360 + 0.688247i −0.993399 0.114708i \(-0.963407\pi\)
0.596040 + 0.802955i \(0.296740\pi\)
\(20\) 3.46410 6.00000i 0.774597 1.34164i
\(21\) −1.73205 −0.377964
\(22\) 0 0
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) 0 0
\(25\) 7.00000 1.40000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 1.73205 + 3.00000i 0.327327 + 0.566947i
\(29\) −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 0 0
\(31\) 1.73205 0.311086 0.155543 0.987829i \(-0.450287\pi\)
0.155543 + 0.987829i \(0.450287\pi\)
\(32\) 0 0
\(33\) −1.73205 + 3.00000i −0.301511 + 0.522233i
\(34\) 0 0
\(35\) −3.00000 + 5.19615i −0.507093 + 0.878310i
\(36\) 1.00000 + 1.73205i 0.166667 + 0.288675i
\(37\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.46410 6.00000i −0.541002 0.937043i −0.998847 0.0480106i \(-0.984712\pi\)
0.457845 0.889032i \(-0.348621\pi\)
\(42\) 0 0
\(43\) −0.500000 + 0.866025i −0.0762493 + 0.132068i −0.901629 0.432511i \(-0.857628\pi\)
0.825380 + 0.564578i \(0.190961\pi\)
\(44\) 6.92820 1.04447
\(45\) −1.73205 + 3.00000i −0.258199 + 0.447214i
\(46\) 0 0
\(47\) −3.46410 −0.505291 −0.252646 0.967559i \(-0.581301\pi\)
−0.252646 + 0.967559i \(0.581301\pi\)
\(48\) 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
\(57\) −3.46410 −0.458831
\(58\) 0 0
\(59\) −1.73205 + 3.00000i −0.225494 + 0.390567i −0.956467 0.291839i \(-0.905733\pi\)
0.730974 + 0.682406i \(0.239066\pi\)
\(60\) 6.92820 0.894427
\(61\) −0.500000 + 0.866025i −0.0640184 + 0.110883i −0.896258 0.443533i \(-0.853725\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) 0 0
\(63\) −0.866025 1.50000i −0.109109 0.188982i
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 4.33013 + 7.50000i 0.529009 + 0.916271i 0.999428 + 0.0338274i \(0.0107696\pi\)
−0.470418 + 0.882443i \(0.655897\pi\)
\(68\) 0 0
\(69\) 3.00000 5.19615i 0.361158 0.625543i
\(70\) 0 0
\(71\) 5.19615 9.00000i 0.616670 1.06810i −0.373419 0.927663i \(-0.621815\pi\)
0.990089 0.140441i \(-0.0448520\pi\)
\(72\) 0 0
\(73\) −1.73205 −0.202721 −0.101361 0.994850i \(-0.532320\pi\)
−0.101361 + 0.994850i \(0.532320\pi\)
\(74\) 0 0
\(75\) 3.50000 + 6.06218i 0.404145 + 0.700000i
\(76\) 3.46410 + 6.00000i 0.397360 + 0.688247i
\(77\) −6.00000 −0.683763
\(78\) 0 0
\(79\) −11.0000 −1.23760 −0.618798 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) −6.92820 12.0000i −0.774597 1.34164i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −13.8564 −1.52094 −0.760469 0.649374i \(-0.775031\pi\)
−0.760469 + 0.649374i \(0.775031\pi\)
\(84\) −1.73205 + 3.00000i −0.188982 + 0.327327i
\(85\) 0 0
\(86\) 0 0
\(87\) 3.00000 5.19615i 0.321634 0.557086i
\(88\) 0 0
\(89\) −3.46410 6.00000i −0.367194 0.635999i 0.621932 0.783072i \(-0.286348\pi\)
−0.989126 + 0.147073i \(0.953015\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −12.0000 −1.25109
\(93\) 0.866025 + 1.50000i 0.0898027 + 0.155543i
\(94\) 0 0
\(95\) −6.00000 + 10.3923i −0.615587 + 1.06623i
\(96\) 0 0
\(97\) 2.59808 4.50000i 0.263795 0.456906i −0.703452 0.710742i \(-0.748359\pi\)
0.967247 + 0.253837i \(0.0816925\pi\)
\(98\) 0 0
\(99\) −3.46410 −0.348155
\(100\) 7.00000 12.1244i 0.700000 1.21244i
\(101\) −9.00000 15.5885i −0.895533 1.55111i −0.833143 0.553058i \(-0.813461\pi\)
−0.0623905 0.998052i \(-0.519872\pi\)
\(102\) 0 0
\(103\) 1.00000 0.0985329 0.0492665 0.998786i \(-0.484312\pi\)
0.0492665 + 0.998786i \(0.484312\pi\)
\(104\) 0 0
\(105\) −6.00000 −0.585540
\(106\) 0 0
\(107\) 3.00000 + 5.19615i 0.290021 + 0.502331i 0.973814 0.227345i \(-0.0730044\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(108\) −1.00000 + 1.73205i −0.0962250 + 0.166667i
\(109\) −15.5885 −1.49310 −0.746552 0.665327i \(-0.768292\pi\)
−0.746552 + 0.665327i \(0.768292\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 6.92820 0.654654
\(113\) −3.00000 + 5.19615i −0.282216 + 0.488813i −0.971930 0.235269i \(-0.924403\pi\)
0.689714 + 0.724082i \(0.257736\pi\)
\(114\) 0 0
\(115\) −10.3923 18.0000i −0.969087 1.67851i
\(116\) −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
\(123\) 3.46410 6.00000i 0.312348 0.541002i
\(124\) 1.73205 3.00000i 0.155543 0.269408i
\(125\) 6.92820 0.619677
\(126\) 0 0
\(127\) 6.50000 + 11.2583i 0.576782 + 0.999015i 0.995846 + 0.0910585i \(0.0290250\pi\)
−0.419064 + 0.907957i \(0.637642\pi\)
\(128\) 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 \(0.415581\pi\)
\(132\) 3.46410 + 6.00000i 0.301511 + 0.522233i
\(133\) −3.00000 5.19615i −0.260133 0.450564i
\(134\) 0 0
\(135\) −3.46410 −0.298142
\(136\) 0 0
\(137\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(138\) 0 0
\(139\) −2.50000 + 4.33013i −0.212047 + 0.367277i −0.952355 0.304991i \(-0.901346\pi\)
0.740308 + 0.672268i \(0.234680\pi\)
\(140\) 6.00000 + 10.3923i 0.507093 + 0.878310i
\(141\) −1.73205 3.00000i −0.145865 0.252646i
\(142\) 0 0
\(143\) 0 0
\(144\) 4.00000 0.333333
\(145\) −10.3923 18.0000i −0.863034 1.49482i
\(146\) 0 0
\(147\) −2.00000 + 3.46410i −0.164957 + 0.285714i
\(148\) 0 0
\(149\) 3.46410 6.00000i 0.283790 0.491539i −0.688525 0.725213i \(-0.741741\pi\)
0.972315 + 0.233674i \(0.0750747\pi\)
\(150\) 0 0
\(151\) 3.46410 0.281905 0.140952 0.990016i \(-0.454984\pi\)
0.140952 + 0.990016i \(0.454984\pi\)
\(152\) 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
\(161\) 10.3923 0.819028
\(162\) 0 0
\(163\) −9.52628 + 16.5000i −0.746156 + 1.29238i 0.203497 + 0.979076i \(0.434769\pi\)
−0.949653 + 0.313304i \(0.898564\pi\)
\(164\) −13.8564 −1.08200
\(165\) −6.00000 + 10.3923i −0.467099 + 0.809040i
\(166\) 0 0
\(167\) 3.46410 + 6.00000i 0.268060 + 0.464294i 0.968361 0.249554i \(-0.0802840\pi\)
−0.700301 + 0.713848i \(0.746951\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) −1.73205 3.00000i −0.132453 0.229416i
\(172\) 1.00000 + 1.73205i 0.0762493 + 0.132068i
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) 0 0
\(175\) −6.06218 + 10.5000i −0.458258 + 0.793725i
\(176\) 6.92820 12.0000i 0.522233 0.904534i
\(177\) −3.46410 −0.260378
\(178\) 0 0
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 3.46410 + 6.00000i 0.258199 + 0.447214i
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) −1.00000 −0.0739221
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −3.46410 + 6.00000i −0.252646 + 0.437595i
\(189\) 0.866025 1.50000i 0.0629941 0.109109i
\(190\) 0 0
\(191\) 9.00000 15.5885i 0.651217 1.12794i −0.331611 0.943416i \(-0.607592\pi\)
0.982828 0.184525i \(-0.0590746\pi\)
\(192\) −4.00000 6.92820i −0.288675 0.500000i
\(193\) 7.79423 + 13.5000i 0.561041 + 0.971751i 0.997406 + 0.0719816i \(0.0229323\pi\)
−0.436365 + 0.899770i \(0.643734\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 8.00000 0.571429
\(197\) 6.92820 + 12.0000i 0.493614 + 0.854965i 0.999973 0.00735824i \(-0.00234222\pi\)
−0.506359 + 0.862323i \(0.669009\pi\)
\(198\) 0 0
\(199\) 3.50000 6.06218i 0.248108 0.429736i −0.714893 0.699234i \(-0.753524\pi\)
0.963001 + 0.269498i \(0.0868577\pi\)
\(200\) 0 0
\(201\) −4.33013 + 7.50000i −0.305424 + 0.529009i
\(202\) 0 0
\(203\) 10.3923 0.729397
\(204\) 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 0.550743 0.834675i \(-0.314345\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) 12.0000 20.7846i 0.824163 1.42749i
\(213\) 10.3923 0.712069
\(214\) 0 0
\(215\) −1.73205 + 3.00000i −0.118125 + 0.204598i
\(216\) 0 0
\(217\) −1.50000 + 2.59808i −0.101827 + 0.176369i
\(218\) 0 0
\(219\) −0.866025 1.50000i −0.0585206 0.101361i
\(220\) 24.0000 1.61808
\(221\) 0 0
\(222\) 0 0
\(223\) 8.66025 + 15.0000i 0.579934 + 1.00447i 0.995486 + 0.0949052i \(0.0302548\pi\)
−0.415553 + 0.909569i \(0.636412\pi\)
\(224\) 0 0
\(225\) −3.50000 + 6.06218i −0.233333 + 0.404145i
\(226\) 0 0
\(227\) −10.3923 + 18.0000i −0.689761 + 1.19470i 0.282153 + 0.959369i \(0.408951\pi\)
−0.971915 + 0.235333i \(0.924382\pi\)
\(228\) −3.46410 + 6.00000i −0.229416 + 0.397360i
\(229\) −27.7128 −1.83131 −0.915657 0.401960i \(-0.868329\pi\)
−0.915657 + 0.401960i \(0.868329\pi\)
\(230\) 0 0
\(231\) −3.00000 5.19615i −0.197386 0.341882i
\(232\) 0 0
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) −12.0000 −0.782794
\(236\) 3.46410 + 6.00000i 0.225494 + 0.390567i
\(237\) −5.50000 9.52628i −0.357263 0.618798i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 6.92820 12.0000i 0.447214 0.774597i
\(241\) 10.3923 18.0000i 0.669427 1.15948i −0.308637 0.951180i \(-0.599873\pi\)
0.978065 0.208302i \(-0.0667937\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 1.00000 + 1.73205i 0.0640184 + 0.110883i
\(245\) 6.92820 + 12.0000i 0.442627 + 0.766652i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −6.92820 12.0000i −0.439057 0.760469i
\(250\) 0 0
\(251\) 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i \(-0.709699\pi\)
0.990876 + 0.134778i \(0.0430322\pi\)
\(252\) −3.46410 −0.218218
\(253\) 10.3923 18.0000i 0.653359 1.13165i
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(258\) 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 0.619586 0.784929i \(-0.287301\pi\)
−0.989561 + 0.144112i \(0.953967\pi\)
\(264\) 0 0
\(265\) 41.5692 2.55358
\(266\) 0 0
\(267\) 3.46410 6.00000i 0.212000 0.367194i
\(268\) 17.3205 1.05802
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 0 0
\(271\) 2.59808 + 4.50000i 0.157822 + 0.273356i 0.934083 0.357056i \(-0.116219\pi\)
−0.776261 + 0.630412i \(0.782886\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 12.1244 + 21.0000i 0.731126 + 1.26635i
\(276\) −6.00000 10.3923i −0.361158 0.625543i
\(277\) −5.00000 + 8.66025i −0.300421 + 0.520344i −0.976231 0.216731i \(-0.930460\pi\)
0.675810 + 0.737075i \(0.263794\pi\)
\(278\) 0 0
\(279\) −0.866025 + 1.50000i −0.0518476 + 0.0898027i
\(280\) 0 0
\(281\) 24.2487 1.44656 0.723278 0.690557i \(-0.242634\pi\)
0.723278 + 0.690557i \(0.242634\pi\)
\(282\) 0 0
\(283\) −5.50000 9.52628i −0.326941 0.566279i 0.654962 0.755662i \(-0.272685\pi\)
−0.981903 + 0.189383i \(0.939351\pi\)
\(284\) −10.3923 18.0000i −0.616670 1.06810i
\(285\) −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
\(291\) 5.19615 0.304604
\(292\) −1.73205 + 3.00000i −0.101361 + 0.175562i
\(293\) −8.66025 + 15.0000i −0.505937 + 0.876309i 0.494039 + 0.869440i \(0.335520\pi\)
−0.999976 + 0.00686959i \(0.997813\pi\)
\(294\) 0 0
\(295\) −6.00000 + 10.3923i −0.349334 + 0.605063i
\(296\) 0 0
\(297\) −1.73205 3.00000i −0.100504 0.174078i
\(298\) 0 0
\(299\) 0 0
\(300\) 14.0000 0.808290
\(301\) −0.866025 1.50000i −0.0499169 0.0864586i
\(302\) 0 0
\(303\) 9.00000 15.5885i 0.517036 0.895533i
\(304\) 13.8564 0.794719
\(305\) −1.73205 + 3.00000i −0.0991769 + 0.171780i
\(306\) 0 0
\(307\) 1.73205 0.0988534 0.0494267 0.998778i \(-0.484261\pi\)
0.0494267 + 0.998778i \(0.484261\pi\)
\(308\) −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 \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 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
\(317\) 6.92820 0.389127 0.194563 0.980890i \(-0.437671\pi\)
0.194563 + 0.980890i \(0.437671\pi\)
\(318\) 0 0
\(319\) 10.3923 18.0000i 0.581857 1.00781i
\(320\) −27.7128 −1.54919
\(321\) −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
\(327\) −7.79423 13.5000i −0.431022 0.746552i
\(328\) 0 0
\(329\) 3.00000 5.19615i 0.165395 0.286473i
\(330\) 0 0
\(331\) −2.59808 + 4.50000i −0.142803 + 0.247342i −0.928551 0.371204i \(-0.878945\pi\)
0.785748 + 0.618547i \(0.212278\pi\)
\(332\) −13.8564 + 24.0000i −0.760469 + 1.31717i
\(333\) 0 0
\(334\) 0 0
\(335\) 15.0000 + 25.9808i 0.819538 + 1.41948i
\(336\) 3.46410 + 6.00000i 0.188982 + 0.327327i
\(337\) 5.00000 0.272367 0.136184 0.990684i \(-0.456516\pi\)
0.136184 + 0.990684i \(0.456516\pi\)
\(338\) 0 0
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) 3.00000 + 5.19615i 0.162459 + 0.281387i
\(342\) 0 0
\(343\) −19.0526 −1.02874
\(344\) 0 0
\(345\) 10.3923 18.0000i 0.559503 0.969087i
\(346\) 0 0
\(347\) 12.0000 20.7846i 0.644194 1.11578i −0.340293 0.940319i \(-0.610526\pi\)
0.984487 0.175457i \(-0.0561403\pi\)
\(348\) −6.00000 10.3923i −0.321634 0.557086i
\(349\) 9.52628 + 16.5000i 0.509930 + 0.883225i 0.999934 + 0.0115044i \(0.00366206\pi\)
−0.490004 + 0.871720i \(0.663005\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 5.19615 + 9.00000i 0.276563 + 0.479022i 0.970528 0.240987i \(-0.0774711\pi\)
−0.693965 + 0.720009i \(0.744138\pi\)
\(354\) 0 0
\(355\) 18.0000 31.1769i 0.955341 1.65470i
\(356\) −13.8564 −0.734388
\(357\) 0 0
\(358\) 0 0
\(359\) −6.92820 −0.365657 −0.182828 0.983145i \(-0.558525\pi\)
−0.182828 + 0.983145i \(0.558525\pi\)
\(360\) 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 0.554264 0.832341i \(-0.313000\pi\)
−0.997960 + 0.0638362i \(0.979666\pi\)
\(368\) −12.0000 + 20.7846i −0.625543 + 1.08347i
\(369\) 6.92820 0.360668
\(370\) 0 0
\(371\) −10.3923 + 18.0000i −0.539542 + 0.934513i
\(372\) 3.46410 0.179605
\(373\) 5.50000 9.52628i 0.284779 0.493252i −0.687776 0.725923i \(-0.741413\pi\)
0.972556 + 0.232671i \(0.0747464\pi\)
\(374\) 0 0
\(375\) 3.46410 + 6.00000i 0.178885 + 0.309839i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −11.2583 19.5000i −0.578302 1.00165i −0.995674 0.0929123i \(-0.970382\pi\)
0.417373 0.908735i \(-0.362951\pi\)
\(380\) 12.0000 + 20.7846i 0.615587 + 1.06623i
\(381\) −6.50000 + 11.2583i −0.333005 + 0.576782i
\(382\) 0 0
\(383\) −13.8564 + 24.0000i −0.708029 + 1.22634i 0.257558 + 0.966263i \(0.417082\pi\)
−0.965587 + 0.260080i \(0.916251\pi\)
\(384\) 0 0
\(385\) −20.7846 −1.05928
\(386\) 0 0
\(387\) −0.500000 0.866025i −0.0254164 0.0440225i
\(388\) −5.19615 9.00000i −0.263795 0.456906i
\(389\) −12.0000 −0.608424 −0.304212 0.952604i \(-0.598393\pi\)
−0.304212 + 0.952604i \(0.598393\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 3.00000 + 5.19615i 0.151330 + 0.262111i
\(394\) 0 0
\(395\) −38.1051 −1.91728
\(396\) −3.46410 + 6.00000i −0.174078 + 0.301511i
\(397\) 7.79423 13.5000i 0.391181 0.677546i −0.601424 0.798930i \(-0.705400\pi\)
0.992606 + 0.121384i \(0.0387333\pi\)
\(398\) 0 0
\(399\) 3.00000 5.19615i 0.150188 0.260133i
\(400\) −14.0000 24.2487i −0.700000 1.21244i
\(401\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −36.0000 −1.79107
\(405\) −1.73205 3.00000i −0.0860663 0.149071i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −4.33013 + 7.50000i −0.214111 + 0.370851i −0.952997 0.302979i \(-0.902019\pi\)
0.738886 + 0.673830i \(0.235352\pi\)
\(410\) 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 0.974546 0.224189i \(-0.0719734\pi\)
−0.681426 + 0.731887i \(0.738640\pi\)
\(420\) −6.00000 + 10.3923i −0.292770 + 0.507093i
\(421\) −12.1244 −0.590905 −0.295452 0.955357i \(-0.595470\pi\)
−0.295452 + 0.955357i \(0.595470\pi\)
\(422\) 0 0
\(423\) 1.73205 3.00000i 0.0842152 0.145865i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.866025 1.50000i −0.0419099 0.0725901i
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) 10.3923 + 18.0000i 0.500580 + 0.867029i 1.00000 0.000669521i \(0.000213115\pi\)
−0.499420 + 0.866360i \(0.666454\pi\)
\(432\) 2.00000 + 3.46410i 0.0962250 + 0.166667i
\(433\) −11.5000 + 19.9186i −0.552655 + 0.957226i 0.445427 + 0.895318i \(0.353052\pi\)
−0.998082 + 0.0619079i \(0.980282\pi\)
\(434\) 0 0
\(435\) 10.3923 18.0000i 0.498273 0.863034i
\(436\) −15.5885 + 27.0000i −0.746552 + 1.29307i
\(437\) 20.7846 0.994263
\(438\) 0 0
\(439\) 17.5000 + 30.3109i 0.835229 + 1.44666i 0.893843 + 0.448379i \(0.147999\pi\)
−0.0586141 + 0.998281i \(0.518668\pi\)
\(440\) 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
\(447\) 6.92820 0.327693
\(448\) 6.92820 12.0000i 0.327327 0.566947i
\(449\) 19.0526 33.0000i 0.899146 1.55737i 0.0705577 0.997508i \(-0.477522\pi\)
0.828588 0.559859i \(-0.189145\pi\)
\(450\) 0 0
\(451\) 12.0000 20.7846i 0.565058 0.978709i
\(452\) 6.00000 + 10.3923i 0.282216 + 0.488813i
\(453\) 1.73205 + 3.00000i 0.0813788 + 0.140952i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −18.1865 31.5000i −0.850730 1.47351i −0.880550 0.473953i \(-0.842827\pi\)
0.0298202 0.999555i \(-0.490507\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −41.5692 −1.93817
\(461\) 20.7846 36.0000i 0.968036 1.67669i 0.266808 0.963750i \(-0.414031\pi\)
0.701228 0.712938i \(-0.252636\pi\)
\(462\) 0 0
\(463\) 36.3731 1.69040 0.845200 0.534450i \(-0.179481\pi\)
0.845200 + 0.534450i \(0.179481\pi\)
\(464\) −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 \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) 0 0
\(469\) −15.0000 −0.692636
\(470\) 0 0
\(471\) 5.50000 + 9.52628i 0.253427 + 0.438948i
\(472\) 0 0
\(473\) −3.46410 −0.159280
\(474\) 0 0
\(475\) −12.1244 + 21.0000i −0.556304 + 0.963546i
\(476\) 0 0
\(477\) −6.00000 + 10.3923i −0.274721 + 0.475831i
\(478\) 0 0
\(479\) −17.3205 30.0000i −0.791394 1.37073i −0.925104 0.379714i \(-0.876022\pi\)
0.133710 0.991021i \(-0.457311\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 5.19615 + 9.00000i 0.236433 + 0.409514i
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 9.00000 15.5885i 0.408669 0.707835i
\(486\) 0 0
\(487\) 12.1244 21.0000i 0.549407 0.951601i −0.448908 0.893578i \(-0.648187\pi\)
0.998315 0.0580230i \(-0.0184797\pi\)
\(488\) 0 0
\(489\) −19.0526 −0.861586
\(490\) 0 0
\(491\) 3.00000 + 5.19615i 0.135388 + 0.234499i 0.925746 0.378147i \(-0.123439\pi\)
−0.790358 + 0.612646i \(0.790105\pi\)
\(492\) −6.92820 12.0000i −0.312348 0.541002i
\(493\) 0 0
\(494\) 0 0
\(495\) −12.0000 −0.539360
\(496\) −3.46410 6.00000i −0.155543 0.269408i
\(497\) 9.00000 + 15.5885i 0.403705 + 0.699238i
\(498\) 0 0
\(499\) 31.1769 1.39567 0.697835 0.716258i \(-0.254147\pi\)
0.697835 + 0.716258i \(0.254147\pi\)
\(500\) 6.92820 12.0000i 0.309839 0.536656i
\(501\) −3.46410 + 6.00000i −0.154765 + 0.268060i
\(502\) 0 0
\(503\) 15.0000 25.9808i 0.668817 1.15842i −0.309418 0.950926i \(-0.600134\pi\)
0.978235 0.207499i \(-0.0665323\pi\)
\(504\) 0 0
\(505\) −31.1769 54.0000i −1.38735 2.40297i
\(506\) 0 0
\(507\) 0 0
\(508\) 26.0000 1.15356
\(509\) −8.66025 15.0000i −0.383859 0.664863i 0.607751 0.794128i \(-0.292072\pi\)
−0.991610 + 0.129264i \(0.958738\pi\)
\(510\) 0 0
\(511\) 1.50000 2.59808i 0.0663561 0.114932i
\(512\) 0 0
\(513\) 1.73205 3.00000i 0.0764719 0.132453i
\(514\) 0 0
\(515\) 3.46410 0.152647
\(516\) −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 0.990873 + 0.134801i \(0.0430394\pi\)
−0.378695 + 0.925521i \(0.623627\pi\)
\(524\) 6.00000 10.3923i 0.262111 0.453990i
\(525\) −12.1244 −0.529150
\(526\) 0 0
\(527\) 0 0
\(528\) 13.8564 0.603023
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) −1.73205 3.00000i −0.0751646 0.130189i
\(532\) −12.0000 −0.520266
\(533\) 0 0
\(534\) 0 0
\(535\) 10.3923 + 18.0000i 0.449299 + 0.778208i
\(536\) 0 0
\(537\) −6.00000 + 10.3923i −0.258919 + 0.448461i
\(538\) 0 0
\(539\) −6.92820 + 12.0000i −0.298419 + 0.516877i
\(540\) −3.46410 + 6.00000i −0.149071 + 0.258199i
\(541\) 29.4449 1.26593 0.632967 0.774179i \(-0.281837\pi\)
0.632967 + 0.774179i \(0.281837\pi\)
\(542\) 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
\(551\) 20.7846 0.885454
\(552\) 0 0
\(553\) 9.52628 16.5000i 0.405099 0.701651i
\(554\) 0 0
\(555\) 0 0
\(556\) 5.00000 + 8.66025i 0.212047 + 0.367277i
\(557\) 13.8564 + 24.0000i 0.587115 + 1.01691i 0.994608 + 0.103704i \(0.0330696\pi\)
−0.407493 + 0.913208i \(0.633597\pi\)
\(558\) 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 −0.0393818 + 0.999224i \(0.512539\pi\)
−0.845663 + 0.533718i \(0.820794\pi\)
\(564\) −6.92820 −0.291730
\(565\) −10.3923 + 18.0000i −0.437208 + 0.757266i
\(566\) 0 0
\(567\) 1.73205 0.0727393
\(568\) 0 0
\(569\) −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) 0 0
\(571\) 44.0000 1.84134 0.920671 0.390339i \(-0.127642\pi\)
0.920671 + 0.390339i \(0.127642\pi\)
\(572\) 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
\(577\) −34.6410 −1.44212 −0.721062 0.692870i \(-0.756346\pi\)
−0.721062 + 0.692870i \(0.756346\pi\)
\(578\) 0 0
\(579\) −7.79423 + 13.5000i −0.323917 + 0.561041i
\(580\) −41.5692 −1.72607
\(581\) 12.0000 20.7846i 0.497844 0.862291i
\(582\) 0 0
\(583\) 20.7846 + 36.0000i 0.860811 + 1.49097i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −15.5885 27.0000i −0.643404 1.11441i −0.984668 0.174441i \(-0.944188\pi\)
0.341263 0.939968i \(-0.389145\pi\)
\(588\) 4.00000 + 6.92820i 0.164957 + 0.285714i
\(589\) −3.00000 + 5.19615i −0.123613 + 0.214104i
\(590\) 0 0
\(591\) −6.92820 + 12.0000i −0.284988 + 0.493614i
\(592\) 0 0
\(593\) −3.46410 −0.142254 −0.0711268 0.997467i \(-0.522659\pi\)
−0.0711268 + 0.997467i \(0.522659\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.92820 12.0000i −0.283790 0.491539i
\(597\) 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 0.999376 + 0.0353259i \(0.0112469\pi\)
−0.469095 + 0.883148i \(0.655420\pi\)
\(602\) 0 0
\(603\) −8.66025 −0.352673
\(604\) 3.46410 6.00000i 0.140952 0.244137i
\(605\) −1.73205 + 3.00000i −0.0704179 + 0.121967i
\(606\) 0 0
\(607\) −4.00000 + 6.92820i −0.162355 + 0.281207i −0.935713 0.352763i \(-0.885242\pi\)
0.773358 + 0.633970i \(0.218576\pi\)
\(608\) 0 0
\(609\) 5.19615 + 9.00000i 0.210559 + 0.364698i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 4.33013 + 7.50000i 0.174892 + 0.302922i 0.940124 0.340833i \(-0.110709\pi\)
−0.765232 + 0.643755i \(0.777376\pi\)
\(614\) 0 0
\(615\) 12.0000 20.7846i 0.483887 0.838116i
\(616\) 0 0
\(617\) 5.19615 9.00000i 0.209189 0.362326i −0.742270 0.670101i \(-0.766251\pi\)
0.951459 + 0.307774i \(0.0995842\pi\)
\(618\) 0 0
\(619\) −25.9808 −1.04425 −0.522127 0.852867i \(-0.674861\pi\)
−0.522127 + 0.852867i \(0.674861\pi\)
\(620\) 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
\(631\) 0.866025 1.50000i 0.0344759 0.0597141i −0.848273 0.529560i \(-0.822357\pi\)
0.882749 + 0.469846i \(0.155690\pi\)
\(632\) 0 0
\(633\) 6.50000 11.2583i 0.258352 0.447478i
\(634\) 0 0
\(635\) 22.5167 + 39.0000i 0.893546 + 1.54767i
\(636\) 24.0000 0.951662
\(637\) 0 0
\(638\) 0 0
\(639\) 5.19615 + 9.00000i 0.205557 + 0.356034i
\(640\) 0 0
\(641\) 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) 0 0
\(643\) −9.52628 + 16.5000i −0.375680 + 0.650696i −0.990429 0.138027i \(-0.955924\pi\)
0.614749 + 0.788723i \(0.289257\pi\)
\(644\) 10.3923 18.0000i 0.409514 0.709299i
\(645\) −3.46410 −0.136399
\(646\) 0 0
\(647\) −9.00000 15.5885i −0.353827 0.612845i 0.633090 0.774078i \(-0.281786\pi\)
−0.986916 + 0.161233i \(0.948453\pi\)
\(648\) 0 0
\(649\) −12.0000 −0.471041
\(650\) 0 0
\(651\) −3.00000 −0.117579
\(652\) 19.0526 + 33.0000i 0.746156 + 1.29238i
\(653\) −18.0000 31.1769i −0.704394 1.22005i −0.966910 0.255119i \(-0.917885\pi\)
0.262515 0.964928i \(-0.415448\pi\)
\(654\) 0 0
\(655\) 20.7846 0.812122
\(656\) −13.8564 + 24.0000i −0.541002 + 0.937043i
\(657\) 0.866025 1.50000i 0.0337869 0.0585206i
\(658\) 0 0
\(659\) −24.0000 + 41.5692i −0.934907 + 1.61931i −0.160108 + 0.987099i \(0.551184\pi\)
−0.774799 + 0.632207i \(0.782149\pi\)
\(660\) 12.0000 + 20.7846i 0.467099 + 0.809040i
\(661\) 12.9904 + 22.5000i 0.505267 + 0.875149i 0.999981 + 0.00609283i \(0.00193942\pi\)
−0.494714 + 0.869056i \(0.664727\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −10.3923 18.0000i −0.402996 0.698010i
\(666\) 0 0
\(667\) −18.0000 + 31.1769i −0.696963 + 1.20717i
\(668\) 13.8564 0.536120
\(669\) −8.66025 + 15.0000i −0.334825 + 0.579934i
\(670\) 0 0
\(671\) −3.46410 −0.133730
\(672\) 0 0
\(673\) −0.500000 0.866025i −0.0192736 0.0333828i 0.856228 0.516599i \(-0.172802\pi\)
−0.875501 + 0.483216i \(0.839469\pi\)
\(674\) 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
\(681\) −20.7846 −0.796468
\(682\) 0 0
\(683\) 12.1244 21.0000i 0.463926 0.803543i −0.535227 0.844708i \(-0.679774\pi\)
0.999152 + 0.0411658i \(0.0131072\pi\)
\(684\) −6.92820 −0.264906
\(685\) 0 0
\(686\) 0 0
\(687\) −13.8564 24.0000i −0.528655 0.915657i
\(688\) 4.00000 0.152499
\(689\) 0 0
\(690\) 0 0
\(691\) 21.6506 + 37.5000i 0.823629 + 1.42657i 0.902963 + 0.429719i \(0.141387\pi\)
−0.0793336 + 0.996848i \(0.525279\pi\)
\(692\) 6.00000 + 10.3923i 0.228086 + 0.395056i
\(693\) 3.00000 5.19615i 0.113961 0.197386i
\(694\) 0 0
\(695\) −8.66025 + 15.0000i −0.328502 + 0.568982i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 9.00000 + 15.5885i 0.340411 + 0.589610i
\(700\) 12.1244 + 21.0000i 0.458258 + 0.793725i
\(701\) 12.0000 0.453234 0.226617 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −13.8564 24.0000i −0.522233 0.904534i
\(705\) −6.00000 10.3923i −0.225973 0.391397i
\(706\) 0 0
\(707\) 31.1769 1.17253
\(708\) −3.46410 + 6.00000i −0.130189 + 0.225494i
\(709\) −9.52628 + 16.5000i −0.357767 + 0.619671i −0.987587 0.157070i \(-0.949795\pi\)
0.629821 + 0.776741i \(0.283128\pi\)
\(710\) 0 0
\(711\) 5.50000 9.52628i 0.206266 0.357263i
\(712\) 0 0
\(713\) −5.19615 9.00000i −0.194597 0.337053i
\(714\) 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 \(-0.869021\pi\)
0.804648 + 0.593753i \(0.202354\pi\)
\(720\) 13.8564 0.516398
\(721\) −0.866025 + 1.50000i −0.0322525 + 0.0558629i
\(722\) 0 0
\(723\) 20.7846 0.772988
\(724\) −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 \(-0.275171\pi\)
0.649039 + 0.760755i \(0.275171\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) −1.00000 + 1.73205i −0.0369611 + 0.0640184i
\(733\) 39.8372 1.47142 0.735710 0.677297i \(-0.236849\pi\)
0.735710 + 0.677297i \(0.236849\pi\)
\(734\) 0 0
\(735\) −6.92820 + 12.0000i −0.255551 + 0.442627i
\(736\) 0 0
\(737\) −15.0000 + 25.9808i −0.552532 + 0.957014i
\(738\) 0 0
\(739\) −22.5167 39.0000i −0.828289 1.43464i −0.899380 0.437168i \(-0.855981\pi\)
0.0710909 0.997470i \(-0.477352\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −5.19615 9.00000i −0.190628 0.330178i 0.754830 0.655920i \(-0.227719\pi\)
−0.945459 + 0.325742i \(0.894386\pi\)
\(744\) 0 0
\(745\) 12.0000 20.7846i 0.439646 0.761489i
\(746\) 0 0
\(747\) 6.92820 12.0000i 0.253490 0.439057i
\(748\) 0 0
\(749\) −10.3923 −0.379727
\(750\) 0 0
\(751\) 4.00000 + 6.92820i 0.145962 + 0.252814i 0.929731 0.368238i \(-0.120039\pi\)
−0.783769 + 0.621052i \(0.786706\pi\)
\(752\) 6.92820 + 12.0000i 0.252646 + 0.437595i
\(753\) 12.0000 0.437304
\(754\) 0 0
\(755\) 12.0000 0.436725
\(756\) −1.73205 3.00000i −0.0629941 0.109109i
\(757\) −17.0000 29.4449i −0.617876 1.07019i −0.989873 0.141958i \(-0.954660\pi\)
0.371997 0.928234i \(-0.378673\pi\)
\(758\) 0 0
\(759\) 20.7846 0.754434
\(760\) 0 0
\(761\) −10.3923 + 18.0000i −0.376721 + 0.652499i −0.990583 0.136914i \(-0.956282\pi\)
0.613862 + 0.789413i \(0.289615\pi\)
\(762\) 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
\(769\) −3.46410 6.00000i −0.124919 0.216366i 0.796782 0.604266i \(-0.206534\pi\)
−0.921701 + 0.387901i \(0.873200\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 31.1769 1.12208
\(773\) 25.9808 45.0000i 0.934463 1.61854i 0.158874 0.987299i \(-0.449213\pi\)
0.775589 0.631239i \(-0.217453\pi\)
\(774\) 0 0
\(775\) 12.1244 0.435520
\(776\) 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
\(785\) 38.1051 1.36003
\(786\) 0 0
\(787\) 16.4545 28.5000i 0.586539 1.01592i −0.408143 0.912918i \(-0.633823\pi\)
0.994682 0.102997i \(-0.0328433\pi\)
\(788\) 27.7128 0.987228
\(789\) 6.00000 10.3923i 0.213606 0.369976i
\(790\) 0 0
\(791\) −5.19615 9.00000i −0.184754 0.320003i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 20.7846 + 36.0000i 0.737154 + 1.27679i
\(796\) −7.00000 12.1244i −0.248108 0.429736i
\(797\) 6.00000 10.3923i 0.212531 0.368114i −0.739975 0.672634i \(-0.765163\pi\)
0.952506 + 0.304520i \(0.0984960\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 6.92820 0.244796
\(802\) 0 0
\(803\) −3.00000 5.19615i −0.105868 0.183368i
\(804\) 8.66025 + 15.0000i 0.305424 + 0.529009i
\(805\) 36.0000 1.26883
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −6.00000 10.3923i −0.210949 0.365374i 0.741063 0.671436i \(-0.234322\pi\)
−0.952012 + 0.306062i \(0.900989\pi\)
\(810\) 0 0
\(811\) −25.9808 −0.912308 −0.456154 0.889901i \(-0.650773\pi\)
−0.456154 + 0.889901i \(0.650773\pi\)
\(812\) 10.3923 18.0000i 0.364698 0.631676i
\(813\) −2.59808 + 4.50000i −0.0911185 + 0.157822i
\(814\) 0 0
\(815\) −33.0000 + 57.1577i −1.15594 + 2.00215i
\(816\) 0 0
\(817\) −1.73205 3.00000i −0.0605968 0.104957i
\(818\) 0 0
\(819\) 0 0
\(820\) −48.0000 −1.67623
\(821\) 12.1244 + 21.0000i 0.423143 + 0.732905i 0.996245 0.0865789i \(-0.0275935\pi\)
−0.573102 + 0.819484i \(0.694260\pi\)
\(822\) 0 0
\(823\) 16.0000 27.7128i 0.557725 0.966008i −0.439961 0.898017i \(-0.645008\pi\)
0.997686 0.0679910i \(-0.0216589\pi\)
\(824\) 0 0
\(825\) −12.1244 + 21.0000i −0.422116 + 0.731126i
\(826\) 0 0
\(827\) −48.4974 −1.68642 −0.843210 0.537584i \(-0.819337\pi\)
−0.843210 + 0.537584i \(0.819337\pi\)
\(828\) 6.00000 10.3923i 0.208514 0.361158i
\(829\) 15.5000 + 26.8468i 0.538337 + 0.932427i 0.998994 + 0.0448490i \(0.0142807\pi\)
−0.460657 + 0.887578i \(0.652386\pi\)
\(830\) 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
\(837\) −1.73205 −0.0598684
\(838\) 0 0
\(839\) 15.5885 27.0000i 0.538173 0.932144i −0.460829 0.887489i \(-0.652448\pi\)
0.999002 0.0446547i \(-0.0142187\pi\)
\(840\) 0 0
\(841\) −3.50000 + 6.06218i −0.120690 + 0.209041i
\(842\) 0 0
\(843\) 12.1244 + 21.0000i 0.417585 + 0.723278i
\(844\) −26.0000 −0.894957
\(845\) 0 0
\(846\) 0 0
\(847\) −0.866025 1.50000i −0.0297570 0.0515406i
\(848\) −24.0000 41.5692i −0.824163 1.42749i
\(849\) 5.50000 9.52628i 0.188760 0.326941i
\(850\) 0 0
\(851\) 0 0
\(852\) 10.3923 18.0000i 0.356034 0.616670i
\(853\) 25.9808 0.889564 0.444782 0.895639i \(-0.353281\pi\)
0.444782 + 0.895639i \(0.353281\pi\)
\(854\) 0 0
\(855\) −6.00000 10.3923i −0.205196 0.355409i
\(856\) 0 0
\(857\) −18.0000 −0.614868 −0.307434 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(858\) 0 0
\(859\) 13.0000 0.443554 0.221777 0.975097i \(-0.428814\pi\)
0.221777 + 0.975097i \(0.428814\pi\)
\(860\) 3.46410 + 6.00000i 0.118125 + 0.204598i
\(861\) 6.00000 + 10.3923i 0.204479 + 0.354169i
\(862\) 0 0
\(863\) −17.3205 −0.589597 −0.294798 0.955559i \(-0.595253\pi\)
−0.294798 + 0.955559i \(0.595253\pi\)
\(864\) 0 0
\(865\) −10.3923 + 18.0000i −0.353349 + 0.612018i
\(866\) 0 0
\(867\) −8.50000 + 14.7224i −0.288675 + 0.500000i
\(868\) 3.00000 + 5.19615i 0.101827 + 0.176369i
\(869\) −19.0526 33.0000i −0.646314 1.11945i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 2.59808 + 4.50000i 0.0879316 + 0.152302i
\(874\) 0 0
\(875\) −6.00000 + 10.3923i −0.202837 + 0.351324i
\(876\) −3.46410 −0.117041
\(877\) −20.7846 + 36.0000i −0.701846 + 1.21563i 0.265971 + 0.963981i \(0.414307\pi\)
−0.967818 + 0.251653i \(0.919026\pi\)
\(878\) 0 0
\(879\) −17.3205 −0.584206
\(880\) 24.0000 41.5692i 0.809040 1.40130i
\(881\) −6.00000 10.3923i −0.202145 0.350126i 0.747074 0.664741i \(-0.231458\pi\)
−0.949219 + 0.314615i \(0.898125\pi\)
\(882\) 0 0
\(883\) 5.00000 0.168263 0.0841317 0.996455i \(-0.473188\pi\)
0.0841317 + 0.996455i \(0.473188\pi\)
\(884\) 0 0
\(885\) −12.0000 −0.403376
\(886\) 0 0
\(887\) 21.0000 + 36.3731i 0.705111 + 1.22129i 0.966651 + 0.256096i \(0.0824362\pi\)
−0.261540 + 0.965193i \(0.584230\pi\)
\(888\) 0 0
\(889\) −22.5167 −0.755185
\(890\) 0 0
\(891\) 1.73205 3.00000i 0.0580259 0.100504i
\(892\) 34.6410 1.15987
\(893\) 6.00000 10.3923i 0.200782 0.347765i
\(894\) 0 0
\(895\) 20.7846 + 36.0000i 0.694753 + 1.20335i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −5.19615 9.00000i −0.173301 0.300167i
\(900\) 7.00000 + 12.1244i 0.233333 + 0.404145i
\(901\) 0 0
\(902\) 0 0
\(903\) 0.866025 1.50000i 0.0288195 0.0499169i
\(904\) 0 0
\(905\) −48.4974 −1.61211
\(906\) 0 0
\(907\) −22.0000 38.1051i −0.730498 1.26526i −0.956671 0.291172i \(-0.905955\pi\)
0.226173 0.974087i \(-0.427379\pi\)
\(908\) 20.7846 + 36.0000i 0.689761 + 1.19470i
\(909\) 18.0000 0.597022
\(910\) 0 0
\(911\) −12.0000 −0.397578 −0.198789 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(912\) 6.92820 + 12.0000i 0.229416 + 0.397360i
\(913\) −24.0000 41.5692i −0.794284 1.37574i
\(914\) 0 0
\(915\) −3.46410 −0.114520
\(916\) −27.7128 + 48.0000i −0.915657 + 1.58596i
\(917\) −5.19615 + 9.00000i −0.171592 + 0.297206i
\(918\) 0 0
\(919\) 16.0000 27.7128i 0.527791 0.914161i −0.471684 0.881768i \(-0.656354\pi\)
0.999475 0.0323936i \(-0.0103130\pi\)
\(920\) 0 0
\(921\) 0.866025 + 1.50000i 0.0285365 + 0.0494267i
\(922\) 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
\(929\) 10.3923 18.0000i 0.340960 0.590561i −0.643651 0.765319i \(-0.722581\pi\)
0.984611 + 0.174758i \(0.0559144\pi\)
\(930\) 0 0
\(931\) −13.8564 −0.454125
\(932\) 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
\(941\) −10.3923 −0.338779 −0.169390 0.985549i \(-0.554180\pi\)
−0.169390 + 0.985549i \(0.554180\pi\)
\(942\) 0 0
\(943\) −20.7846 + 36.0000i −0.676840 + 1.17232i
\(944\) 13.8564 0.450988
\(945\) 3.00000 5.19615i 0.0975900 0.169031i
\(946\) 0 0
\(947\) 24.2487 + 42.0000i 0.787977 + 1.36482i 0.927204 + 0.374556i \(0.122205\pi\)
−0.139227 + 0.990260i \(0.544462\pi\)
\(948\) −22.0000 −0.714527
\(949\) 0 0
\(950\) 0 0
\(951\) 3.46410 + 6.00000i 0.112331 + 0.194563i
\(952\) 0 0
\(953\) 3.00000 5.19615i 0.0971795 0.168320i −0.813337 0.581793i \(-0.802351\pi\)
0.910516 + 0.413473i \(0.135685\pi\)
\(954\) 0 0
\(955\) 31.1769 54.0000i 1.00886 1.74740i
\(956\) 0 0
\(957\) 20.7846 0.671871
\(958\) 0 0
\(959\) 0 0
\(960\) −13.8564 24.0000i −0.447214 0.774597i
\(961\) −28.0000 −0.903226
\(962\) 0 0
\(963\) −6.00000 −0.193347
\(964\) −20.7846 36.0000i −0.669427 1.15948i
\(965\) 27.0000 + 46.7654i 0.869161 + 1.50543i
\(966\) 0 0
\(967\) −24.2487 −0.779786 −0.389893 0.920860i \(-0.627488\pi\)
−0.389893 + 0.920860i \(0.627488\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −18.0000 + 31.1769i −0.577647 + 1.00051i 0.418101 + 0.908401i \(0.362696\pi\)
−0.995748 + 0.0921142i \(0.970638\pi\)
\(972\) −1.00000 1.73205i −0.0320750 0.0555556i
\(973\) −4.33013 7.50000i −0.138817 0.240439i
\(974\) 0 0
\(975\) 0 0
\(976\) 4.00000 0.128037
\(977\) −13.8564 24.0000i −0.443306 0.767828i 0.554627 0.832099i \(-0.312861\pi\)
−0.997932 + 0.0642712i \(0.979528\pi\)
\(978\) 0 0
\(979\) 12.0000 20.7846i 0.383522 0.664279i
\(980\) 27.7128 0.885253
\(981\) 7.79423 13.5000i 0.248851 0.431022i
\(982\) 0 0
\(983\) 10.3923 0.331463 0.165732 0.986171i \(-0.447001\pi\)
0.165732 + 0.986171i \(0.447001\pi\)
\(984\) 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 0.964658 0.263504i \(-0.0848781\pi\)
−0.710530 + 0.703667i \(0.751545\pi\)
\(992\) 0 0
\(993\) −5.19615 −0.164895
\(994\) 0 0
\(995\) 12.1244 21.0000i 0.384368 0.665745i
\(996\) −27.7128 −0.878114
\(997\) −17.5000 + 30.3109i −0.554231 + 0.959955i 0.443732 + 0.896159i \(0.353654\pi\)
−0.997963 + 0.0637961i \(0.979679\pi\)
\(998\) 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.e.f.484.2 4
13.2 odd 12 507.2.b.c.337.1 2
13.3 even 3 507.2.a.e.1.2 2
13.4 even 6 inner 507.2.e.f.22.1 4
13.5 odd 4 39.2.j.a.10.1 yes 2
13.6 odd 12 507.2.j.b.316.1 2
13.7 odd 12 39.2.j.a.4.1 2
13.8 odd 4 507.2.j.b.361.1 2
13.9 even 3 inner 507.2.e.f.22.2 4
13.10 even 6 507.2.a.e.1.1 2
13.11 odd 12 507.2.b.c.337.2 2
13.12 even 2 inner 507.2.e.f.484.1 4
39.2 even 12 1521.2.b.f.1351.2 2
39.5 even 4 117.2.q.a.10.1 2
39.11 even 12 1521.2.b.f.1351.1 2
39.20 even 12 117.2.q.a.82.1 2
39.23 odd 6 1521.2.a.h.1.2 2
39.29 odd 6 1521.2.a.h.1.1 2
52.3 odd 6 8112.2.a.bu.1.2 2
52.7 even 12 624.2.bv.b.433.1 2
52.23 odd 6 8112.2.a.bu.1.1 2
52.31 even 4 624.2.bv.b.49.1 2
65.7 even 12 975.2.w.d.199.1 4
65.18 even 4 975.2.w.d.49.1 4
65.33 even 12 975.2.w.d.199.2 4
65.44 odd 4 975.2.bc.c.751.1 2
65.57 even 4 975.2.w.d.49.2 4
65.59 odd 12 975.2.bc.c.901.1 2
156.59 odd 12 1872.2.by.f.433.1 2
156.83 odd 4 1872.2.by.f.1297.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.j.a.4.1 2 13.7 odd 12
39.2.j.a.10.1 yes 2 13.5 odd 4
117.2.q.a.10.1 2 39.5 even 4
117.2.q.a.82.1 2 39.20 even 12
507.2.a.e.1.1 2 13.10 even 6
507.2.a.e.1.2 2 13.3 even 3
507.2.b.c.337.1 2 13.2 odd 12
507.2.b.c.337.2 2 13.11 odd 12
507.2.e.f.22.1 4 13.4 even 6 inner
507.2.e.f.22.2 4 13.9 even 3 inner
507.2.e.f.484.1 4 13.12 even 2 inner
507.2.e.f.484.2 4 1.1 even 1 trivial
507.2.j.b.316.1 2 13.6 odd 12
507.2.j.b.361.1 2 13.8 odd 4
624.2.bv.b.49.1 2 52.31 even 4
624.2.bv.b.433.1 2 52.7 even 12
975.2.w.d.49.1 4 65.18 even 4
975.2.w.d.49.2 4 65.57 even 4
975.2.w.d.199.1 4 65.7 even 12
975.2.w.d.199.2 4 65.33 even 12
975.2.bc.c.751.1 2 65.44 odd 4
975.2.bc.c.901.1 2 65.59 odd 12
1521.2.a.h.1.1 2 39.29 odd 6
1521.2.a.h.1.2 2 39.23 odd 6
1521.2.b.f.1351.1 2 39.11 even 12
1521.2.b.f.1351.2 2 39.2 even 12
1872.2.by.f.433.1 2 156.59 odd 12
1872.2.by.f.1297.1 2 156.83 odd 4
8112.2.a.bu.1.1 2 52.23 odd 6
8112.2.a.bu.1.2 2 52.3 odd 6