Properties

Label 342.2.g.b.235.1
Level $342$
Weight $2$
Character 342.235
Analytic conductor $2.731$
Analytic rank $1$
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] = [342,2,Mod(163,342)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(342, 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("342.163");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 342.g (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.73088374913\)
Analytic rank: \(1\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 38)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 235.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 342.235
Dual form 342.2.g.b.163.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -4.00000 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -4.00000 q^{7} +1.00000 q^{8} -3.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(2.00000 + 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-3.50000 + 2.59808i) q^{19} +(1.50000 + 2.59808i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} +2.00000 q^{26} +(2.00000 - 3.46410i) q^{28} +2.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} -10.0000 q^{37} +(4.00000 + 1.73205i) q^{38} +(4.50000 + 7.79423i) q^{41} +(2.00000 + 3.46410i) q^{43} +(1.50000 - 2.59808i) q^{44} +6.00000 q^{46} +9.00000 q^{49} -5.00000 q^{50} +(-1.00000 - 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} -4.00000 q^{56} +(-4.50000 - 7.79423i) q^{59} +(2.00000 - 3.46410i) q^{61} +(-1.00000 - 1.73205i) q^{62} +1.00000 q^{64} +(3.50000 - 6.06218i) q^{67} +6.00000 q^{68} +(-3.00000 - 5.19615i) q^{71} +(0.500000 + 0.866025i) q^{73} +(5.00000 + 8.66025i) q^{74} +(-0.500000 - 4.33013i) q^{76} +12.0000 q^{77} +(2.00000 + 3.46410i) q^{79} +(4.50000 - 7.79423i) q^{82} -3.00000 q^{83} +(2.00000 - 3.46410i) q^{86} -3.00000 q^{88} +(3.00000 - 5.19615i) q^{89} +(4.00000 - 6.92820i) q^{91} +(-3.00000 - 5.19615i) q^{92} +(-8.50000 - 14.7224i) q^{97} +(-4.50000 - 7.79423i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} - 8 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{4} - 8 q^{7} + 2 q^{8} - 6 q^{11} - 2 q^{13} + 4 q^{14} - q^{16} - 6 q^{17} - 7 q^{19} + 3 q^{22} - 6 q^{23} + 5 q^{25} + 4 q^{26} + 4 q^{28} + 4 q^{31} - q^{32} - 6 q^{34} - 20 q^{37} + 8 q^{38} + 9 q^{41} + 4 q^{43} + 3 q^{44} + 12 q^{46} + 18 q^{49} - 10 q^{50} - 2 q^{52} + 6 q^{53} - 8 q^{56} - 9 q^{59} + 4 q^{61} - 2 q^{62} + 2 q^{64} + 7 q^{67} + 12 q^{68} - 6 q^{71} + q^{73} + 10 q^{74} - q^{76} + 24 q^{77} + 4 q^{79} + 9 q^{82} - 6 q^{83} + 4 q^{86} - 6 q^{88} + 6 q^{89} + 8 q^{91} - 6 q^{92} - 17 q^{97} - 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/342\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(325\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0 0
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 2.00000 + 3.46410i 0.534522 + 0.925820i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) 0 0
\(19\) −3.50000 + 2.59808i −0.802955 + 0.596040i
\(20\) 0 0
\(21\) 0 0
\(22\) 1.50000 + 2.59808i 0.319801 + 0.553912i
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0 0
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) 2.00000 3.46410i 0.377964 0.654654i
\(29\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −3.00000 + 5.19615i −0.514496 + 0.891133i
\(35\) 0 0
\(36\) 0 0
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 4.00000 + 1.73205i 0.648886 + 0.280976i
\(39\) 0 0
\(40\) 0 0
\(41\) 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i \(0.0813924\pi\)
−0.264704 + 0.964330i \(0.585274\pi\)
\(42\) 0 0
\(43\) 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i \(-0.0680112\pi\)
−0.672264 + 0.740312i \(0.734678\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) 9.00000 1.28571
\(50\) −5.00000 −0.707107
\(51\) 0 0
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −4.00000 −0.534522
\(57\) 0 0
\(58\) 0 0
\(59\) −4.50000 7.79423i −0.585850 1.01472i −0.994769 0.102151i \(-0.967427\pi\)
0.408919 0.912571i \(-0.365906\pi\)
\(60\) 0 0
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) −1.00000 1.73205i −0.127000 0.219971i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 3.50000 6.06218i 0.427593 0.740613i −0.569066 0.822292i \(-0.692695\pi\)
0.996659 + 0.0816792i \(0.0260283\pi\)
\(68\) 6.00000 0.727607
\(69\) 0 0
\(70\) 0 0
\(71\) −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i \(-0.282538\pi\)
−0.987294 + 0.158901i \(0.949205\pi\)
\(72\) 0 0
\(73\) 0.500000 + 0.866025i 0.0585206 + 0.101361i 0.893801 0.448463i \(-0.148028\pi\)
−0.835281 + 0.549823i \(0.814695\pi\)
\(74\) 5.00000 + 8.66025i 0.581238 + 1.00673i
\(75\) 0 0
\(76\) −0.500000 4.33013i −0.0573539 0.496700i
\(77\) 12.0000 1.36753
\(78\) 0 0
\(79\) 2.00000 + 3.46410i 0.225018 + 0.389742i 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 4.50000 7.79423i 0.496942 0.860729i
\(83\) −3.00000 −0.329293 −0.164646 0.986353i \(-0.552648\pi\)
−0.164646 + 0.986353i \(0.552648\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 2.00000 3.46410i 0.215666 0.373544i
\(87\) 0 0
\(88\) −3.00000 −0.319801
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) 4.00000 6.92820i 0.419314 0.726273i
\(92\) −3.00000 5.19615i −0.312772 0.541736i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −8.50000 14.7224i −0.863044 1.49484i −0.868976 0.494854i \(-0.835222\pi\)
0.00593185 0.999982i \(-0.498112\pi\)
\(98\) −4.50000 7.79423i −0.454569 0.787336i
\(99\) 0 0
\(100\) 2.50000 + 4.33013i 0.250000 + 0.433013i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) 2.00000 0.197066 0.0985329 0.995134i \(-0.468585\pi\)
0.0985329 + 0.995134i \(0.468585\pi\)
\(104\) −1.00000 + 1.73205i −0.0980581 + 0.169842i
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.00000 + 3.46410i 0.188982 + 0.327327i
\(113\) −15.0000 −1.41108 −0.705541 0.708669i \(-0.749296\pi\)
−0.705541 + 0.708669i \(0.749296\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −4.50000 + 7.79423i −0.414259 + 0.717517i
\(119\) 12.0000 + 20.7846i 1.10004 + 1.90532i
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −4.00000 −0.362143
\(123\) 0 0
\(124\) −1.00000 + 1.73205i −0.0898027 + 0.155543i
\(125\) 0 0
\(126\) 0 0
\(127\) −1.00000 + 1.73205i −0.0887357 + 0.153695i −0.906977 0.421180i \(-0.861616\pi\)
0.818241 + 0.574875i \(0.194949\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 4.50000 + 7.79423i 0.393167 + 0.680985i 0.992865 0.119241i \(-0.0380462\pi\)
−0.599699 + 0.800226i \(0.704713\pi\)
\(132\) 0 0
\(133\) 14.0000 10.3923i 1.21395 0.901127i
\(134\) −7.00000 −0.604708
\(135\) 0 0
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) 4.50000 7.79423i 0.384461 0.665906i −0.607233 0.794524i \(-0.707721\pi\)
0.991694 + 0.128618i \(0.0410540\pi\)
\(138\) 0 0
\(139\) −5.50000 + 9.52628i −0.466504 + 0.808008i −0.999268 0.0382553i \(-0.987820\pi\)
0.532764 + 0.846264i \(0.321153\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) 3.00000 5.19615i 0.250873 0.434524i
\(144\) 0 0
\(145\) 0 0
\(146\) 0.500000 0.866025i 0.0413803 0.0716728i
\(147\) 0 0
\(148\) 5.00000 8.66025i 0.410997 0.711868i
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) −3.50000 + 2.59808i −0.283887 + 0.210732i
\(153\) 0 0
\(154\) −6.00000 10.3923i −0.483494 0.837436i
\(155\) 0 0
\(156\) 0 0
\(157\) 8.00000 + 13.8564i 0.638470 + 1.10586i 0.985769 + 0.168107i \(0.0537655\pi\)
−0.347299 + 0.937754i \(0.612901\pi\)
\(158\) 2.00000 3.46410i 0.159111 0.275589i
\(159\) 0 0
\(160\) 0 0
\(161\) 12.0000 20.7846i 0.945732 1.63806i
\(162\) 0 0
\(163\) −19.0000 −1.48819 −0.744097 0.668071i \(-0.767120\pi\)
−0.744097 + 0.668071i \(0.767120\pi\)
\(164\) −9.00000 −0.702782
\(165\) 0 0
\(166\) 1.50000 + 2.59808i 0.116423 + 0.201650i
\(167\) −12.0000 + 20.7846i −0.928588 + 1.60836i −0.142901 + 0.989737i \(0.545643\pi\)
−0.785687 + 0.618624i \(0.787690\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 0 0
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) 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
\(175\) −10.0000 + 17.3205i −0.755929 + 1.30931i
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) 0 0
\(178\) −6.00000 −0.449719
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) 0 0
\(181\) −1.00000 + 1.73205i −0.0743294 + 0.128742i −0.900794 0.434246i \(-0.857015\pi\)
0.826465 + 0.562988i \(0.190348\pi\)
\(182\) −8.00000 −0.592999
\(183\) 0 0
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) 0 0
\(186\) 0 0
\(187\) 9.00000 + 15.5885i 0.658145 + 1.13994i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 0 0
\(193\) −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i \(-0.189599\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) −8.50000 + 14.7224i −0.610264 + 1.05701i
\(195\) 0 0
\(196\) −4.50000 + 7.79423i −0.321429 + 0.556731i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 5.00000 8.66025i 0.354441 0.613909i −0.632581 0.774494i \(-0.718005\pi\)
0.987022 + 0.160585i \(0.0513380\pi\)
\(200\) 2.50000 4.33013i 0.176777 0.306186i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −1.00000 1.73205i −0.0696733 0.120678i
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) 10.5000 7.79423i 0.726300 0.539138i
\(210\) 0 0
\(211\) −10.0000 17.3205i −0.688428 1.19239i −0.972346 0.233544i \(-0.924968\pi\)
0.283918 0.958849i \(-0.408366\pi\)
\(212\) 3.00000 + 5.19615i 0.206041 + 0.356873i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −8.00000 −0.543075
\(218\) 8.00000 13.8564i 0.541828 0.938474i
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) −7.00000 12.1244i −0.468755 0.811907i 0.530607 0.847618i \(-0.321964\pi\)
−0.999362 + 0.0357107i \(0.988630\pi\)
\(224\) 2.00000 3.46410i 0.133631 0.231455i
\(225\) 0 0
\(226\) 7.50000 + 12.9904i 0.498893 + 0.864107i
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 0 0
\(229\) −16.0000 −1.05731 −0.528655 0.848837i \(-0.677303\pi\)
−0.528655 + 0.848837i \(0.677303\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.50000 + 2.59808i 0.0982683 + 0.170206i 0.910968 0.412477i \(-0.135336\pi\)
−0.812700 + 0.582683i \(0.802003\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 9.00000 0.585850
\(237\) 0 0
\(238\) 12.0000 20.7846i 0.777844 1.34727i
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i \(-0.884818\pi\)
0.774202 + 0.632938i \(0.218151\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) 0 0
\(244\) 2.00000 + 3.46410i 0.128037 + 0.221766i
\(245\) 0 0
\(246\) 0 0
\(247\) −1.00000 8.66025i −0.0636285 0.551039i
\(248\) 2.00000 0.127000
\(249\) 0 0
\(250\) 0 0
\(251\) −1.50000 + 2.59808i −0.0946792 + 0.163989i −0.909475 0.415759i \(-0.863516\pi\)
0.814795 + 0.579748i \(0.196849\pi\)
\(252\) 0 0
\(253\) 9.00000 15.5885i 0.565825 0.980038i
\(254\) 2.00000 0.125491
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i \(-0.803506\pi\)
0.909010 + 0.416775i \(0.136840\pi\)
\(258\) 0 0
\(259\) 40.0000 2.48548
\(260\) 0 0
\(261\) 0 0
\(262\) 4.50000 7.79423i 0.278011 0.481529i
\(263\) −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
\(265\) 0 0
\(266\) −16.0000 6.92820i −0.981023 0.424795i
\(267\) 0 0
\(268\) 3.50000 + 6.06218i 0.213797 + 0.370306i
\(269\) 6.00000 + 10.3923i 0.365826 + 0.633630i 0.988908 0.148527i \(-0.0474530\pi\)
−0.623082 + 0.782157i \(0.714120\pi\)
\(270\) 0 0
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) −3.00000 + 5.19615i −0.181902 + 0.315063i
\(273\) 0 0
\(274\) −9.00000 −0.543710
\(275\) −7.50000 + 12.9904i −0.452267 + 0.783349i
\(276\) 0 0
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 11.0000 0.659736
\(279\) 0 0
\(280\) 0 0
\(281\) 13.5000 23.3827i 0.805342 1.39489i −0.110717 0.993852i \(-0.535315\pi\)
0.916060 0.401042i \(-0.131352\pi\)
\(282\) 0 0
\(283\) −2.50000 4.33013i −0.148610 0.257399i 0.782104 0.623148i \(-0.214146\pi\)
−0.930714 + 0.365748i \(0.880813\pi\)
\(284\) 6.00000 0.356034
\(285\) 0 0
\(286\) −6.00000 −0.354787
\(287\) −18.0000 31.1769i −1.06251 1.84032i
\(288\) 0 0
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) 0 0
\(292\) −1.00000 −0.0585206
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −10.0000 −0.581238
\(297\) 0 0
\(298\) 9.00000 15.5885i 0.521356 0.903015i
\(299\) −6.00000 10.3923i −0.346989 0.601003i
\(300\) 0 0
\(301\) −8.00000 13.8564i −0.461112 0.798670i
\(302\) 5.00000 + 8.66025i 0.287718 + 0.498342i
\(303\) 0 0
\(304\) 4.00000 + 1.73205i 0.229416 + 0.0993399i
\(305\) 0 0
\(306\) 0 0
\(307\) 3.50000 + 6.06218i 0.199756 + 0.345987i 0.948449 0.316929i \(-0.102652\pi\)
−0.748694 + 0.662916i \(0.769319\pi\)
\(308\) −6.00000 + 10.3923i −0.341882 + 0.592157i
\(309\) 0 0
\(310\) 0 0
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) 0 0
\(313\) 9.50000 16.4545i 0.536972 0.930062i −0.462093 0.886831i \(-0.652902\pi\)
0.999065 0.0432311i \(-0.0137652\pi\)
\(314\) 8.00000 13.8564i 0.451466 0.781962i
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) −24.0000 −1.33747
\(323\) 24.0000 + 10.3923i 1.33540 + 0.578243i
\(324\) 0 0
\(325\) 5.00000 + 8.66025i 0.277350 + 0.480384i
\(326\) 9.50000 + 16.4545i 0.526156 + 0.911330i
\(327\) 0 0
\(328\) 4.50000 + 7.79423i 0.248471 + 0.430364i
\(329\) 0 0
\(330\) 0 0
\(331\) 5.00000 0.274825 0.137412 0.990514i \(-0.456121\pi\)
0.137412 + 0.990514i \(0.456121\pi\)
\(332\) 1.50000 2.59808i 0.0823232 0.142588i
\(333\) 0 0
\(334\) 24.0000 1.31322
\(335\) 0 0
\(336\) 0 0
\(337\) −5.50000 9.52628i −0.299604 0.518930i 0.676441 0.736497i \(-0.263521\pi\)
−0.976045 + 0.217567i \(0.930188\pi\)
\(338\) 4.50000 7.79423i 0.244768 0.423950i
\(339\) 0 0
\(340\) 0 0
\(341\) −6.00000 −0.324918
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 2.00000 + 3.46410i 0.107833 + 0.186772i
\(345\) 0 0
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) −4.50000 7.79423i −0.241573 0.418416i 0.719590 0.694399i \(-0.244330\pi\)
−0.961162 + 0.275983i \(0.910997\pi\)
\(348\) 0 0
\(349\) −4.00000 −0.214115 −0.107058 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(350\) 20.0000 1.06904
\(351\) 0 0
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) −3.00000 −0.159674 −0.0798369 0.996808i \(-0.525440\pi\)
−0.0798369 + 0.996808i \(0.525440\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 3.00000 + 5.19615i 0.159000 + 0.275396i
\(357\) 0 0
\(358\) 4.50000 + 7.79423i 0.237832 + 0.411938i
\(359\) −3.00000 5.19615i −0.158334 0.274242i 0.775934 0.630814i \(-0.217279\pi\)
−0.934268 + 0.356572i \(0.883946\pi\)
\(360\) 0 0
\(361\) 5.50000 18.1865i 0.289474 0.957186i
\(362\) 2.00000 0.105118
\(363\) 0 0
\(364\) 4.00000 + 6.92820i 0.209657 + 0.363137i
\(365\) 0 0
\(366\) 0 0
\(367\) 11.0000 19.0526i 0.574195 0.994535i −0.421933 0.906627i \(-0.638648\pi\)
0.996129 0.0879086i \(-0.0280183\pi\)
\(368\) 6.00000 0.312772
\(369\) 0 0
\(370\) 0 0
\(371\) −12.0000 + 20.7846i −0.623009 + 1.07908i
\(372\) 0 0
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 9.00000 15.5885i 0.465379 0.806060i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 6.00000 + 10.3923i 0.306987 + 0.531717i
\(383\) −18.0000 31.1769i −0.919757 1.59307i −0.799783 0.600289i \(-0.795052\pi\)
−0.119974 0.992777i \(-0.538281\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −1.00000 + 1.73205i −0.0508987 + 0.0881591i
\(387\) 0 0
\(388\) 17.0000 0.863044
\(389\) −18.0000 + 31.1769i −0.912636 + 1.58073i −0.102311 + 0.994753i \(0.532624\pi\)
−0.810326 + 0.585980i \(0.800710\pi\)
\(390\) 0 0
\(391\) 36.0000 1.82060
\(392\) 9.00000 0.454569
\(393\) 0 0
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) 0 0
\(396\) 0 0
\(397\) 5.00000 + 8.66025i 0.250943 + 0.434646i 0.963786 0.266678i \(-0.0859261\pi\)
−0.712843 + 0.701324i \(0.752593\pi\)
\(398\) −10.0000 −0.501255
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) −13.5000 23.3827i −0.674158 1.16768i −0.976714 0.214544i \(-0.931173\pi\)
0.302556 0.953131i \(-0.402160\pi\)
\(402\) 0 0
\(403\) −2.00000 + 3.46410i −0.0996271 + 0.172559i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 30.0000 1.48704
\(408\) 0 0
\(409\) −2.50000 + 4.33013i −0.123617 + 0.214111i −0.921192 0.389109i \(-0.872783\pi\)
0.797574 + 0.603220i \(0.206116\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.00000 + 1.73205i −0.0492665 + 0.0853320i
\(413\) 18.0000 + 31.1769i 0.885722 + 1.53412i
\(414\) 0 0
\(415\) 0 0
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) 0 0
\(418\) −12.0000 5.19615i −0.586939 0.254152i
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 5.00000 + 8.66025i 0.243685 + 0.422075i 0.961761 0.273890i \(-0.0883103\pi\)
−0.718076 + 0.695965i \(0.754977\pi\)
\(422\) −10.0000 + 17.3205i −0.486792 + 0.843149i
\(423\) 0 0
\(424\) 3.00000 5.19615i 0.145693 0.252347i
\(425\) −30.0000 −1.45521
\(426\) 0 0
\(427\) −8.00000 + 13.8564i −0.387147 + 0.670559i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −15.0000 + 25.9808i −0.722525 + 1.25145i 0.237460 + 0.971397i \(0.423685\pi\)
−0.959985 + 0.280052i \(0.909648\pi\)
\(432\) 0 0
\(433\) −13.0000 + 22.5167i −0.624740 + 1.08208i 0.363851 + 0.931457i \(0.381462\pi\)
−0.988591 + 0.150624i \(0.951872\pi\)
\(434\) 4.00000 + 6.92820i 0.192006 + 0.332564i
\(435\) 0 0
\(436\) −16.0000 −0.766261
\(437\) −3.00000 25.9808i −0.143509 1.24283i
\(438\) 0 0
\(439\) −7.00000 12.1244i −0.334092 0.578664i 0.649218 0.760602i \(-0.275096\pi\)
−0.983310 + 0.181938i \(0.941763\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −6.00000 10.3923i −0.285391 0.494312i
\(443\) 4.50000 7.79423i 0.213801 0.370315i −0.739100 0.673596i \(-0.764749\pi\)
0.952901 + 0.303281i \(0.0980821\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −7.00000 + 12.1244i −0.331460 + 0.574105i
\(447\) 0 0
\(448\) −4.00000 −0.188982
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) −13.5000 23.3827i −0.635690 1.10105i
\(452\) 7.50000 12.9904i 0.352770 0.611016i
\(453\) 0 0
\(454\) 1.50000 + 2.59808i 0.0703985 + 0.121934i
\(455\) 0 0
\(456\) 0 0
\(457\) 5.00000 0.233890 0.116945 0.993138i \(-0.462690\pi\)
0.116945 + 0.993138i \(0.462690\pi\)
\(458\) 8.00000 + 13.8564i 0.373815 + 0.647467i
\(459\) 0 0
\(460\) 0 0
\(461\) 3.00000 + 5.19615i 0.139724 + 0.242009i 0.927392 0.374091i \(-0.122045\pi\)
−0.787668 + 0.616100i \(0.788712\pi\)
\(462\) 0 0
\(463\) −34.0000 −1.58011 −0.790057 0.613033i \(-0.789949\pi\)
−0.790057 + 0.613033i \(0.789949\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 1.50000 2.59808i 0.0694862 0.120354i
\(467\) 27.0000 1.24941 0.624705 0.780860i \(-0.285219\pi\)
0.624705 + 0.780860i \(0.285219\pi\)
\(468\) 0 0
\(469\) −14.0000 + 24.2487i −0.646460 + 1.11970i
\(470\) 0 0
\(471\) 0 0
\(472\) −4.50000 7.79423i −0.207129 0.358758i
\(473\) −6.00000 10.3923i −0.275880 0.477839i
\(474\) 0 0
\(475\) 2.50000 + 21.6506i 0.114708 + 0.993399i
\(476\) −24.0000 −1.10004
\(477\) 0 0
\(478\) −6.00000 10.3923i −0.274434 0.475333i
\(479\) 18.0000 31.1769i 0.822441 1.42451i −0.0814184 0.996680i \(-0.525945\pi\)
0.903859 0.427830i \(-0.140722\pi\)
\(480\) 0 0
\(481\) 10.0000 17.3205i 0.455961 0.789747i
\(482\) 5.00000 0.227744
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 0 0
\(486\) 0 0
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) 2.00000 3.46410i 0.0905357 0.156813i
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −7.00000 + 5.19615i −0.314945 + 0.233786i
\(495\) 0 0
\(496\) −1.00000 1.73205i −0.0449013 0.0777714i
\(497\) 12.0000 + 20.7846i 0.538274 + 0.932317i
\(498\) 0 0
\(499\) 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i \(0.0223697\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 3.00000 0.133897
\(503\) 3.00000 5.19615i 0.133763 0.231685i −0.791361 0.611349i \(-0.790627\pi\)
0.925124 + 0.379664i \(0.123960\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −18.0000 −0.800198
\(507\) 0 0
\(508\) −1.00000 1.73205i −0.0443678 0.0768473i
\(509\) −12.0000 + 20.7846i −0.531891 + 0.921262i 0.467416 + 0.884037i \(0.345185\pi\)
−0.999307 + 0.0372243i \(0.988148\pi\)
\(510\) 0 0
\(511\) −2.00000 3.46410i −0.0884748 0.153243i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −3.00000 −0.132324
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −20.0000 34.6410i −0.878750 1.52204i
\(519\) 0 0
\(520\) 0 0
\(521\) −9.00000 −0.394297 −0.197149 0.980374i \(-0.563168\pi\)
−0.197149 + 0.980374i \(0.563168\pi\)
\(522\) 0 0
\(523\) 14.0000 24.2487i 0.612177 1.06032i −0.378695 0.925521i \(-0.623627\pi\)
0.990873 0.134801i \(-0.0430394\pi\)
\(524\) −9.00000 −0.393167
\(525\) 0 0
\(526\) −6.00000 + 10.3923i −0.261612 + 0.453126i
\(527\) −6.00000 10.3923i −0.261364 0.452696i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) 0 0
\(532\) 2.00000 + 17.3205i 0.0867110 + 0.750939i
\(533\) −18.0000 −0.779667
\(534\) 0 0
\(535\) 0 0
\(536\) 3.50000 6.06218i 0.151177 0.261846i
\(537\) 0 0
\(538\) 6.00000 10.3923i 0.258678 0.448044i
\(539\) −27.0000 −1.16297
\(540\) 0 0
\(541\) −22.0000 + 38.1051i −0.945854 + 1.63827i −0.191821 + 0.981430i \(0.561439\pi\)
−0.754032 + 0.656837i \(0.771894\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) 0 0
\(544\) 6.00000 0.257248
\(545\) 0 0
\(546\) 0 0
\(547\) 2.00000 3.46410i 0.0855138 0.148114i −0.820096 0.572226i \(-0.806080\pi\)
0.905610 + 0.424111i \(0.139413\pi\)
\(548\) 4.50000 + 7.79423i 0.192230 + 0.332953i
\(549\) 0 0
\(550\) 15.0000 0.639602
\(551\) 0 0
\(552\) 0 0
\(553\) −8.00000 13.8564i −0.340195 0.589234i
\(554\) −4.00000 6.92820i −0.169944 0.294351i
\(555\) 0 0
\(556\) −5.50000 9.52628i −0.233252 0.404004i
\(557\) 12.0000 20.7846i 0.508456 0.880672i −0.491496 0.870880i \(-0.663550\pi\)
0.999952 0.00979220i \(-0.00311700\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) −27.0000 −1.13893
\(563\) 21.0000 0.885044 0.442522 0.896758i \(-0.354084\pi\)
0.442522 + 0.896758i \(0.354084\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −2.50000 + 4.33013i −0.105083 + 0.182009i
\(567\) 0 0
\(568\) −3.00000 5.19615i −0.125877 0.218026i
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 0 0
\(571\) −7.00000 −0.292941 −0.146470 0.989215i \(-0.546791\pi\)
−0.146470 + 0.989215i \(0.546791\pi\)
\(572\) 3.00000 + 5.19615i 0.125436 + 0.217262i
\(573\) 0 0
\(574\) −18.0000 + 31.1769i −0.751305 + 1.30130i
\(575\) 15.0000 + 25.9808i 0.625543 + 1.08347i
\(576\) 0 0
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) 19.0000 0.790296
\(579\) 0 0
\(580\) 0 0
\(581\) 12.0000 0.497844
\(582\) 0 0
\(583\) −9.00000 + 15.5885i −0.372742 + 0.645608i
\(584\) 0.500000 + 0.866025i 0.0206901 + 0.0358364i
\(585\) 0 0
\(586\) 12.0000 + 20.7846i 0.495715 + 0.858604i
\(587\) −6.00000 10.3923i −0.247647 0.428936i 0.715226 0.698893i \(-0.246324\pi\)
−0.962872 + 0.269957i \(0.912990\pi\)
\(588\) 0 0
\(589\) −7.00000 + 5.19615i −0.288430 + 0.214104i
\(590\) 0 0
\(591\) 0 0
\(592\) 5.00000 + 8.66025i 0.205499 + 0.355934i
\(593\) −10.5000 + 18.1865i −0.431183 + 0.746831i −0.996976 0.0777165i \(-0.975237\pi\)
0.565792 + 0.824548i \(0.308570\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) −6.00000 + 10.3923i −0.245358 + 0.424973i
\(599\) −3.00000 + 5.19615i −0.122577 + 0.212309i −0.920783 0.390075i \(-0.872449\pi\)
0.798206 + 0.602384i \(0.205782\pi\)
\(600\) 0 0
\(601\) −13.0000 −0.530281 −0.265141 0.964210i \(-0.585418\pi\)
−0.265141 + 0.964210i \(0.585418\pi\)
\(602\) −8.00000 + 13.8564i −0.326056 + 0.564745i
\(603\) 0 0
\(604\) 5.00000 8.66025i 0.203447 0.352381i
\(605\) 0 0
\(606\) 0 0
\(607\) 20.0000 0.811775 0.405887 0.913923i \(-0.366962\pi\)
0.405887 + 0.913923i \(0.366962\pi\)
\(608\) −0.500000 4.33013i −0.0202777 0.175610i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) 3.50000 6.06218i 0.141249 0.244650i
\(615\) 0 0
\(616\) 12.0000 0.483494
\(617\) 1.50000 2.59808i 0.0603877 0.104595i −0.834251 0.551385i \(-0.814100\pi\)
0.894639 + 0.446790i \(0.147433\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −15.0000 25.9808i −0.601445 1.04173i
\(623\) −12.0000 + 20.7846i −0.480770 + 0.832718i
\(624\) 0 0
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) −19.0000 −0.759393
\(627\) 0 0
\(628\) −16.0000 −0.638470
\(629\) 30.0000 + 51.9615i 1.19618 + 2.07184i
\(630\) 0 0
\(631\) 14.0000 24.2487i 0.557331 0.965326i −0.440387 0.897808i \(-0.645159\pi\)
0.997718 0.0675178i \(-0.0215080\pi\)
\(632\) 2.00000 + 3.46410i 0.0795557 + 0.137795i
\(633\) 0 0
\(634\) 18.0000 0.714871
\(635\) 0 0
\(636\) 0 0
\(637\) −9.00000 + 15.5885i −0.356593 + 0.617637i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −19.5000 33.7750i −0.770204 1.33403i −0.937451 0.348117i \(-0.886821\pi\)
0.167247 0.985915i \(-0.446512\pi\)
\(642\) 0 0
\(643\) 21.5000 + 37.2391i 0.847877 + 1.46857i 0.883099 + 0.469187i \(0.155453\pi\)
−0.0352216 + 0.999380i \(0.511214\pi\)
\(644\) 12.0000 + 20.7846i 0.472866 + 0.819028i
\(645\) 0 0
\(646\) −3.00000 25.9808i −0.118033 1.02220i
\(647\) −18.0000 −0.707653 −0.353827 0.935311i \(-0.615120\pi\)
−0.353827 + 0.935311i \(0.615120\pi\)
\(648\) 0 0
\(649\) 13.5000 + 23.3827i 0.529921 + 0.917851i
\(650\) 5.00000 8.66025i 0.196116 0.339683i
\(651\) 0 0
\(652\) 9.50000 16.4545i 0.372049 0.644407i
\(653\) 12.0000 0.469596 0.234798 0.972044i \(-0.424557\pi\)
0.234798 + 0.972044i \(0.424557\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 4.50000 7.79423i 0.175695 0.304314i
\(657\) 0 0
\(658\) 0 0
\(659\) 18.0000 31.1769i 0.701180 1.21448i −0.266872 0.963732i \(-0.585990\pi\)
0.968052 0.250748i \(-0.0806766\pi\)
\(660\) 0 0
\(661\) 20.0000 34.6410i 0.777910 1.34738i −0.155235 0.987878i \(-0.549613\pi\)
0.933144 0.359502i \(-0.117053\pi\)
\(662\) −2.50000 4.33013i −0.0971653 0.168295i
\(663\) 0 0
\(664\) −3.00000 −0.116423
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −12.0000 20.7846i −0.464294 0.804181i
\(669\) 0 0
\(670\) 0 0
\(671\) −6.00000 + 10.3923i −0.231627 + 0.401190i
\(672\) 0 0
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) −5.50000 + 9.52628i −0.211852 + 0.366939i
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) 42.0000 1.61419 0.807096 0.590421i \(-0.201038\pi\)
0.807096 + 0.590421i \(0.201038\pi\)
\(678\) 0 0
\(679\) 34.0000 + 58.8897i 1.30480 + 2.25998i
\(680\) 0 0
\(681\) 0 0
\(682\) 3.00000 + 5.19615i 0.114876 + 0.198971i
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 4.00000 + 6.92820i 0.152721 + 0.264520i
\(687\) 0 0
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) 0 0
\(691\) 44.0000 1.67384 0.836919 0.547326i \(-0.184354\pi\)
0.836919 + 0.547326i \(0.184354\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −4.50000 + 7.79423i −0.170818 + 0.295865i
\(695\) 0 0
\(696\) 0 0
\(697\) 27.0000 46.7654i 1.02270 1.77136i
\(698\) 2.00000 + 3.46410i 0.0757011 + 0.131118i
\(699\) 0 0
\(700\) −10.0000 17.3205i −0.377964 0.654654i
\(701\) −12.0000 20.7846i −0.453234 0.785024i 0.545351 0.838208i \(-0.316396\pi\)
−0.998585 + 0.0531839i \(0.983063\pi\)
\(702\) 0 0
\(703\) 35.0000 25.9808i 1.32005 0.979883i
\(704\) −3.00000 −0.113067
\(705\) 0 0
\(706\) 1.50000 + 2.59808i 0.0564532 + 0.0977799i
\(707\) 0 0
\(708\) 0 0
\(709\) −7.00000 + 12.1244i −0.262891 + 0.455340i −0.967009 0.254743i \(-0.918009\pi\)
0.704118 + 0.710083i \(0.251342\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) −6.00000 + 10.3923i −0.224702 + 0.389195i
\(714\) 0 0
\(715\) 0 0
\(716\) 4.50000 7.79423i 0.168173 0.291284i
\(717\) 0 0
\(718\) −3.00000 + 5.19615i −0.111959 + 0.193919i
\(719\) 15.0000 + 25.9808i 0.559406 + 0.968919i 0.997546 + 0.0700124i \(0.0223039\pi\)
−0.438141 + 0.898906i \(0.644363\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) −18.5000 + 4.33013i −0.688499 + 0.161151i
\(723\) 0 0
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) 0 0
\(726\) 0 0
\(727\) −16.0000 27.7128i −0.593407 1.02781i −0.993770 0.111454i \(-0.964449\pi\)
0.400362 0.916357i \(-0.368884\pi\)
\(728\) 4.00000 6.92820i 0.148250 0.256776i
\(729\) 0 0
\(730\) 0 0
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) 0 0
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) −22.0000 −0.812035
\(735\) 0 0
\(736\) −3.00000 5.19615i −0.110581 0.191533i
\(737\) −10.5000 + 18.1865i −0.386772 + 0.669910i
\(738\) 0 0
\(739\) −17.5000 30.3109i −0.643748 1.11500i −0.984589 0.174883i \(-0.944045\pi\)
0.340841 0.940121i \(-0.389288\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 24.0000 0.881068
\(743\) −9.00000 15.5885i −0.330178 0.571885i 0.652369 0.757902i \(-0.273775\pi\)
−0.982547 + 0.186017i \(0.940442\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 2.00000 + 3.46410i 0.0732252 + 0.126830i
\(747\) 0 0
\(748\) −18.0000 −0.658145
\(749\) 0 0
\(750\) 0 0
\(751\) −19.0000 + 32.9090i −0.693320 + 1.20087i 0.277424 + 0.960748i \(0.410519\pi\)
−0.970744 + 0.240118i \(0.922814\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 5.00000 + 8.66025i 0.181728 + 0.314762i 0.942469 0.334293i \(-0.108498\pi\)
−0.760741 + 0.649056i \(0.775164\pi\)
\(758\) 14.0000 + 24.2487i 0.508503 + 0.880753i
\(759\) 0 0
\(760\) 0 0
\(761\) 39.0000 1.41375 0.706874 0.707339i \(-0.250105\pi\)
0.706874 + 0.707339i \(0.250105\pi\)
\(762\) 0 0
\(763\) −32.0000 55.4256i −1.15848 2.00654i
\(764\) 6.00000 10.3923i 0.217072 0.375980i
\(765\) 0 0
\(766\) −18.0000 + 31.1769i −0.650366 + 1.12647i
\(767\) 18.0000 0.649942
\(768\) 0 0
\(769\) −1.00000 + 1.73205i −0.0360609 + 0.0624593i −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 2.00000 0.0719816
\(773\) −24.0000 + 41.5692i −0.863220 + 1.49514i 0.00558380 + 0.999984i \(0.498223\pi\)
−0.868804 + 0.495156i \(0.835111\pi\)
\(774\) 0 0
\(775\) 5.00000 8.66025i 0.179605 0.311086i
\(776\) −8.50000 14.7224i −0.305132 0.528505i
\(777\) 0 0
\(778\) 36.0000 1.29066
\(779\) −36.0000 15.5885i −1.28983 0.558514i
\(780\) 0 0
\(781\) 9.00000 + 15.5885i 0.322045 + 0.557799i
\(782\) −18.0000 31.1769i −0.643679 1.11488i
\(783\) 0 0
\(784\) −4.50000 7.79423i −0.160714 0.278365i
\(785\) 0 0
\(786\) 0 0
\(787\) −7.00000 −0.249523 −0.124762 0.992187i \(-0.539817\pi\)
−0.124762 + 0.992187i \(0.539817\pi\)
\(788\) 9.00000 15.5885i 0.320612 0.555316i
\(789\) 0 0
\(790\) 0 0
\(791\) 60.0000 2.13335
\(792\) 0 0
\(793\) 4.00000 + 6.92820i 0.142044 + 0.246028i
\(794\) 5.00000 8.66025i 0.177443 0.307341i
\(795\) 0 0
\(796\) 5.00000 + 8.66025i 0.177220 + 0.306955i
\(797\) −6.00000 −0.212531 −0.106265 0.994338i \(-0.533889\pi\)
−0.106265 + 0.994338i \(0.533889\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 2.50000 + 4.33013i 0.0883883 + 0.153093i
\(801\) 0 0
\(802\) −13.5000 + 23.3827i −0.476702 + 0.825671i
\(803\) −1.50000 2.59808i −0.0529339 0.0916841i
\(804\) 0 0
\(805\) 0 0
\(806\) 4.00000 0.140894
\(807\) 0 0
\(808\) 0 0
\(809\) −45.0000 −1.58212 −0.791058 0.611741i \(-0.790469\pi\)
−0.791058 + 0.611741i \(0.790469\pi\)
\(810\) 0 0
\(811\) 8.00000 13.8564i 0.280918 0.486564i −0.690693 0.723148i \(-0.742694\pi\)
0.971611 + 0.236584i \(0.0760278\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −15.0000 25.9808i −0.525750 0.910625i
\(815\) 0 0
\(816\) 0 0
\(817\) −16.0000 6.92820i −0.559769 0.242387i
\(818\) 5.00000 0.174821
\(819\) 0 0
\(820\) 0 0
\(821\) 9.00000 15.5885i 0.314102 0.544041i −0.665144 0.746715i \(-0.731630\pi\)
0.979246 + 0.202674i \(0.0649632\pi\)
\(822\) 0 0
\(823\) −7.00000 + 12.1244i −0.244005 + 0.422628i −0.961851 0.273573i \(-0.911795\pi\)
0.717847 + 0.696201i \(0.245128\pi\)
\(824\) 2.00000 0.0696733
\(825\) 0 0
\(826\) 18.0000 31.1769i 0.626300 1.08478i
\(827\) −19.5000 + 33.7750i −0.678081 + 1.17447i 0.297477 + 0.954729i \(0.403855\pi\)
−0.975558 + 0.219742i \(0.929478\pi\)
\(828\) 0 0
\(829\) 44.0000 1.52818 0.764092 0.645108i \(-0.223188\pi\)
0.764092 + 0.645108i \(0.223188\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.00000 + 1.73205i −0.0346688 + 0.0600481i
\(833\) −27.0000 46.7654i −0.935495 1.62032i
\(834\) 0 0
\(835\) 0 0
\(836\) 1.50000 + 12.9904i 0.0518786 + 0.449282i
\(837\) 0 0
\(838\) −6.00000 10.3923i −0.207267 0.358996i
\(839\) −6.00000 10.3923i −0.207143 0.358782i 0.743670 0.668546i \(-0.233083\pi\)
−0.950813 + 0.309764i \(0.899750\pi\)
\(840\) 0 0
\(841\) 14.5000 + 25.1147i 0.500000 + 0.866025i
\(842\) 5.00000 8.66025i 0.172311 0.298452i
\(843\) 0 0
\(844\) 20.0000 0.688428
\(845\) 0 0
\(846\) 0 0
\(847\) 8.00000 0.274883
\(848\) −6.00000 −0.206041
\(849\) 0 0
\(850\) 15.0000 + 25.9808i 0.514496 + 0.891133i
\(851\) 30.0000 51.9615i 1.02839 1.78122i
\(852\) 0 0
\(853\) 11.0000 + 19.0526i 0.376633 + 0.652347i 0.990570 0.137008i \(-0.0437485\pi\)
−0.613937 + 0.789355i \(0.710415\pi\)
\(854\) 16.0000 0.547509
\(855\) 0 0
\(856\) 0 0
\(857\) −1.50000 2.59808i −0.0512390 0.0887486i 0.839268 0.543718i \(-0.182984\pi\)
−0.890507 + 0.454969i \(0.849650\pi\)
\(858\) 0 0
\(859\) 21.5000 37.2391i 0.733571 1.27058i −0.221777 0.975097i \(-0.571186\pi\)
0.955348 0.295484i \(-0.0954809\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 30.0000 1.02180
\(863\) −18.0000 −0.612727 −0.306364 0.951915i \(-0.599112\pi\)
−0.306364 + 0.951915i \(0.599112\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 26.0000 0.883516
\(867\) 0 0
\(868\) 4.00000 6.92820i 0.135769 0.235159i
\(869\) −6.00000 10.3923i −0.203536 0.352535i
\(870\) 0 0
\(871\) 7.00000 + 12.1244i 0.237186 + 0.410818i
\(872\) 8.00000 + 13.8564i 0.270914 + 0.469237i
\(873\) 0 0
\(874\) −21.0000 + 15.5885i −0.710336 + 0.527287i
\(875\) 0 0
\(876\) 0 0
\(877\) −10.0000 17.3205i −0.337676 0.584872i 0.646319 0.763067i \(-0.276307\pi\)
−0.983995 + 0.178195i \(0.942974\pi\)
\(878\) −7.00000 + 12.1244i −0.236239 + 0.409177i
\(879\) 0 0
\(880\) 0 0
\(881\) 9.00000 0.303218 0.151609 0.988441i \(-0.451555\pi\)
0.151609 + 0.988441i \(0.451555\pi\)
\(882\) 0 0
\(883\) 9.50000 16.4545i 0.319700 0.553737i −0.660725 0.750628i \(-0.729751\pi\)
0.980425 + 0.196891i \(0.0630844\pi\)
\(884\) −6.00000 + 10.3923i −0.201802 + 0.349531i
\(885\) 0 0
\(886\) −9.00000 −0.302361
\(887\) 24.0000 41.5692i 0.805841 1.39576i −0.109881 0.993945i \(-0.535047\pi\)
0.915722 0.401813i \(-0.131620\pi\)
\(888\) 0 0
\(889\) 4.00000 6.92820i 0.134156 0.232364i
\(890\) 0 0
\(891\) 0 0
\(892\) 14.0000 0.468755
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 2.00000 + 3.46410i 0.0668153 + 0.115728i
\(897\) 0 0
\(898\) 4.50000 + 7.79423i 0.150167 + 0.260097i
\(899\) 0 0
\(900\) 0 0
\(901\) −36.0000 −1.19933
\(902\) −13.5000 + 23.3827i −0.449501 + 0.778558i
\(903\) 0 0
\(904\) −15.0000 −0.498893
\(905\) 0 0
\(906\) 0 0
\(907\) −8.50000 14.7224i −0.282238 0.488850i 0.689698 0.724097i \(-0.257743\pi\)
−0.971936 + 0.235247i \(0.924410\pi\)
\(908\) 1.50000 2.59808i 0.0497792 0.0862202i
\(909\) 0 0
\(910\) 0 0
\(911\) −30.0000 −0.993944 −0.496972 0.867766i \(-0.665555\pi\)
−0.496972 + 0.867766i \(0.665555\pi\)
\(912\) 0 0
\(913\) 9.00000 0.297857
\(914\) −2.50000 4.33013i −0.0826927 0.143228i
\(915\) 0 0
\(916\) 8.00000 13.8564i 0.264327 0.457829i
\(917\) −18.0000 31.1769i −0.594412 1.02955i
\(918\) 0 0
\(919\) −10.0000 −0.329870 −0.164935 0.986304i \(-0.552741\pi\)
−0.164935 + 0.986304i \(0.552741\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 3.00000 5.19615i 0.0987997 0.171126i
\(923\) 12.0000 0.394985
\(924\) 0 0
\(925\) −25.0000 + 43.3013i −0.821995 + 1.42374i
\(926\) 17.0000 + 29.4449i 0.558655 + 0.967618i
\(927\) 0 0
\(928\) 0 0
\(929\) −1.50000 2.59808i −0.0492134 0.0852401i 0.840369 0.542014i \(-0.182338\pi\)
−0.889583 + 0.456774i \(0.849005\pi\)
\(930\) 0 0
\(931\) −31.5000 + 23.3827i −1.03237 + 0.766337i
\(932\) −3.00000 −0.0982683
\(933\) 0 0
\(934\) −13.5000 23.3827i −0.441733 0.765105i
\(935\) 0 0
\(936\) 0 0
\(937\) −17.5000 + 30.3109i −0.571700 + 0.990214i 0.424691 + 0.905338i \(0.360383\pi\)
−0.996392 + 0.0848755i \(0.972951\pi\)
\(938\) 28.0000 0.914232
\(939\) 0 0
\(940\) 0 0
\(941\) −21.0000 + 36.3731i −0.684580 + 1.18573i 0.288988 + 0.957333i \(0.406681\pi\)
−0.973568 + 0.228395i \(0.926652\pi\)
\(942\) 0 0
\(943\) −54.0000 −1.75848
\(944\) −4.50000 + 7.79423i −0.146463 + 0.253681i
\(945\) 0 0
\(946\) −6.00000 + 10.3923i −0.195077 + 0.337883i
\(947\) 30.0000 + 51.9615i 0.974869 + 1.68852i 0.680367 + 0.732872i \(0.261821\pi\)
0.294502 + 0.955651i \(0.404846\pi\)
\(948\) 0 0
\(949\) −2.00000 −0.0649227
\(950\) 17.5000 12.9904i 0.567775 0.421464i
\(951\) 0 0
\(952\) 12.0000 + 20.7846i 0.388922 + 0.673633i
\(953\) −7.50000 12.9904i −0.242949 0.420800i 0.718604 0.695419i \(-0.244781\pi\)
−0.961553 + 0.274620i \(0.911448\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −6.00000 + 10.3923i −0.194054 + 0.336111i
\(957\) 0 0
\(958\) −36.0000 −1.16311
\(959\) −18.0000 + 31.1769i −0.581250 + 1.00676i
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) −20.0000 −0.644826
\(963\) 0 0
\(964\) −2.50000 4.33013i −0.0805196 0.139464i
\(965\) 0 0
\(966\) 0 0
\(967\) 17.0000 + 29.4449i 0.546683 + 0.946883i 0.998499 + 0.0547717i \(0.0174431\pi\)
−0.451816 + 0.892111i \(0.649224\pi\)
\(968\) −2.00000 −0.0642824
\(969\) 0 0
\(970\) 0 0
\(971\) 10.5000 + 18.1865i 0.336961 + 0.583634i 0.983860 0.178942i \(-0.0572676\pi\)
−0.646899 + 0.762576i \(0.723934\pi\)
\(972\) 0 0
\(973\) 22.0000 38.1051i 0.705288 1.22159i
\(974\) −1.00000 1.73205i −0.0320421 0.0554985i
\(975\) 0 0
\(976\) −4.00000 −0.128037
\(977\) −33.0000 −1.05576 −0.527882 0.849318i \(-0.677014\pi\)
−0.527882 + 0.849318i \(0.677014\pi\)
\(978\) 0 0
\(979\) −9.00000 + 15.5885i −0.287641 + 0.498209i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 12.0000 + 20.7846i 0.382741 + 0.662926i 0.991453 0.130465i \(-0.0416470\pi\)
−0.608712 + 0.793391i \(0.708314\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 8.00000 + 3.46410i 0.254514 + 0.110208i
\(989\) −24.0000 −0.763156
\(990\) 0 0
\(991\) −4.00000 6.92820i −0.127064 0.220082i 0.795474 0.605988i \(-0.207222\pi\)
−0.922538 + 0.385906i \(0.873889\pi\)
\(992\) −1.00000 + 1.73205i −0.0317500 + 0.0549927i
\(993\) 0 0
\(994\) 12.0000 20.7846i 0.380617 0.659248i
\(995\) 0 0
\(996\) 0 0
\(997\) 2.00000 3.46410i 0.0633406 0.109709i −0.832616 0.553851i \(-0.813158\pi\)
0.895957 + 0.444141i \(0.146491\pi\)
\(998\) 12.5000 21.6506i 0.395681 0.685339i
\(999\) 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 342.2.g.b.235.1 2
3.2 odd 2 38.2.c.a.7.1 2
4.3 odd 2 2736.2.s.m.577.1 2
12.11 even 2 304.2.i.c.273.1 2
15.2 even 4 950.2.j.e.349.1 4
15.8 even 4 950.2.j.e.349.2 4
15.14 odd 2 950.2.e.d.501.1 2
19.7 even 3 6498.2.a.s.1.1 1
19.11 even 3 inner 342.2.g.b.163.1 2
19.12 odd 6 6498.2.a.e.1.1 1
24.5 odd 2 1216.2.i.h.577.1 2
24.11 even 2 1216.2.i.d.577.1 2
57.2 even 18 722.2.e.i.389.1 6
57.5 odd 18 722.2.e.j.99.1 6
57.8 even 6 722.2.c.b.429.1 2
57.11 odd 6 38.2.c.a.11.1 yes 2
57.14 even 18 722.2.e.i.99.1 6
57.17 odd 18 722.2.e.j.389.1 6
57.23 odd 18 722.2.e.j.245.1 6
57.26 odd 6 722.2.a.c.1.1 1
57.29 even 18 722.2.e.i.415.1 6
57.32 even 18 722.2.e.i.423.1 6
57.35 odd 18 722.2.e.j.595.1 6
57.41 even 18 722.2.e.i.595.1 6
57.44 odd 18 722.2.e.j.423.1 6
57.47 odd 18 722.2.e.j.415.1 6
57.50 even 6 722.2.a.d.1.1 1
57.53 even 18 722.2.e.i.245.1 6
57.56 even 2 722.2.c.b.653.1 2
76.11 odd 6 2736.2.s.m.1873.1 2
228.11 even 6 304.2.i.c.49.1 2
228.83 even 6 5776.2.a.g.1.1 1
228.107 odd 6 5776.2.a.n.1.1 1
285.68 even 12 950.2.j.e.49.1 4
285.182 even 12 950.2.j.e.49.2 4
285.239 odd 6 950.2.e.d.201.1 2
456.11 even 6 1216.2.i.d.961.1 2
456.125 odd 6 1216.2.i.h.961.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.2.c.a.7.1 2 3.2 odd 2
38.2.c.a.11.1 yes 2 57.11 odd 6
304.2.i.c.49.1 2 228.11 even 6
304.2.i.c.273.1 2 12.11 even 2
342.2.g.b.163.1 2 19.11 even 3 inner
342.2.g.b.235.1 2 1.1 even 1 trivial
722.2.a.c.1.1 1 57.26 odd 6
722.2.a.d.1.1 1 57.50 even 6
722.2.c.b.429.1 2 57.8 even 6
722.2.c.b.653.1 2 57.56 even 2
722.2.e.i.99.1 6 57.14 even 18
722.2.e.i.245.1 6 57.53 even 18
722.2.e.i.389.1 6 57.2 even 18
722.2.e.i.415.1 6 57.29 even 18
722.2.e.i.423.1 6 57.32 even 18
722.2.e.i.595.1 6 57.41 even 18
722.2.e.j.99.1 6 57.5 odd 18
722.2.e.j.245.1 6 57.23 odd 18
722.2.e.j.389.1 6 57.17 odd 18
722.2.e.j.415.1 6 57.47 odd 18
722.2.e.j.423.1 6 57.44 odd 18
722.2.e.j.595.1 6 57.35 odd 18
950.2.e.d.201.1 2 285.239 odd 6
950.2.e.d.501.1 2 15.14 odd 2
950.2.j.e.49.1 4 285.68 even 12
950.2.j.e.49.2 4 285.182 even 12
950.2.j.e.349.1 4 15.2 even 4
950.2.j.e.349.2 4 15.8 even 4
1216.2.i.d.577.1 2 24.11 even 2
1216.2.i.d.961.1 2 456.11 even 6
1216.2.i.h.577.1 2 24.5 odd 2
1216.2.i.h.961.1 2 456.125 odd 6
2736.2.s.m.577.1 2 4.3 odd 2
2736.2.s.m.1873.1 2 76.11 odd 6
5776.2.a.g.1.1 1 228.83 even 6
5776.2.a.n.1.1 1 228.107 odd 6
6498.2.a.e.1.1 1 19.12 odd 6
6498.2.a.s.1.1 1 19.7 even 3