Properties

Label 208.2.i.d.113.1
Level $208$
Weight $2$
Character 208.113
Analytic conductor $1.661$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [208,2,Mod(81,208)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(208, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("208.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 208 = 2^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 208.i (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: \(1.66088836204\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 52)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 113.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 208.113
Dual form 208.2.i.d.81.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.50000 - 2.59808i) q^{3} +2.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(1.50000 - 2.59808i) q^{3} +2.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(-2.50000 + 4.33013i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(3.00000 - 5.19615i) q^{15} +(-1.50000 - 2.59808i) q^{17} +(-1.50000 - 2.59808i) q^{19} +3.00000 q^{21} +(-0.500000 + 0.866025i) q^{23} -1.00000 q^{25} -9.00000 q^{27} +(0.500000 - 0.866025i) q^{29} +8.00000 q^{31} +(7.50000 + 12.9904i) q^{33} +(1.00000 + 1.73205i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(7.50000 + 7.79423i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-6.00000 - 10.3923i) q^{45} -4.00000 q^{47} +(3.00000 - 5.19615i) q^{49} -9.00000 q^{51} -6.00000 q^{53} +(-5.00000 + 8.66025i) q^{55} -9.00000 q^{57} +(2.50000 + 4.33013i) q^{59} +(2.50000 + 4.33013i) q^{61} +(3.00000 - 5.19615i) q^{63} +(-2.00000 + 6.92820i) q^{65} +(3.50000 - 6.06218i) q^{67} +(1.50000 + 2.59808i) q^{69} +(-5.50000 - 9.52628i) q^{71} +14.0000 q^{73} +(-1.50000 + 2.59808i) q^{75} -5.00000 q^{77} +4.00000 q^{79} +(-4.50000 + 7.79423i) q^{81} -12.0000 q^{83} +(-3.00000 - 5.19615i) q^{85} +(-1.50000 - 2.59808i) q^{87} +(4.50000 - 7.79423i) q^{89} +(-3.50000 + 0.866025i) q^{91} +(12.0000 - 20.7846i) q^{93} +(-3.00000 - 5.19615i) q^{95} +(0.500000 + 0.866025i) q^{97} +30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} + 4 q^{5} + q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{3} + 4 q^{5} + q^{7} - 6 q^{9} - 5 q^{11} - 2 q^{13} + 6 q^{15} - 3 q^{17} - 3 q^{19} + 6 q^{21} - q^{23} - 2 q^{25} - 18 q^{27} + q^{29} + 16 q^{31} + 15 q^{33} + 2 q^{35} - 3 q^{37} + 15 q^{39} - 3 q^{41} + q^{43} - 12 q^{45} - 8 q^{47} + 6 q^{49} - 18 q^{51} - 12 q^{53} - 10 q^{55} - 18 q^{57} + 5 q^{59} + 5 q^{61} + 6 q^{63} - 4 q^{65} + 7 q^{67} + 3 q^{69} - 11 q^{71} + 28 q^{73} - 3 q^{75} - 10 q^{77} + 8 q^{79} - 9 q^{81} - 24 q^{83} - 6 q^{85} - 3 q^{87} + 9 q^{89} - 7 q^{91} + 24 q^{93} - 6 q^{95} + q^{97} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/208\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(79\) \(145\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.50000 2.59808i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(4\) 0 0
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i 0.944911 0.327327i \(-0.106148\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 0 0
\(9\) −3.00000 5.19615i −1.00000 1.73205i
\(10\) 0 0
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0 0
\(13\) −1.00000 + 3.46410i −0.277350 + 0.960769i
\(14\) 0 0
\(15\) 3.00000 5.19615i 0.774597 1.34164i
\(16\) 0 0
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) −1.50000 2.59808i −0.344124 0.596040i 0.641071 0.767482i \(-0.278491\pi\)
−0.985194 + 0.171442i \(0.945157\pi\)
\(20\) 0 0
\(21\) 3.00000 0.654654
\(22\) 0 0
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −9.00000 −1.73205
\(28\) 0 0
\(29\) 0.500000 0.866025i 0.0928477 0.160817i −0.815861 0.578249i \(-0.803736\pi\)
0.908708 + 0.417432i \(0.137070\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 0 0
\(33\) 7.50000 + 12.9904i 1.30558 + 2.26134i
\(34\) 0 0
\(35\) 1.00000 + 1.73205i 0.169031 + 0.292770i
\(36\) 0 0
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) 0 0
\(39\) 7.50000 + 7.79423i 1.20096 + 1.24808i
\(40\) 0 0
\(41\) −1.50000 + 2.59808i −0.234261 + 0.405751i −0.959058 0.283211i \(-0.908600\pi\)
0.724797 + 0.688963i \(0.241934\pi\)
\(42\) 0 0
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) 0 0
\(45\) −6.00000 10.3923i −0.894427 1.54919i
\(46\) 0 0
\(47\) −4.00000 −0.583460 −0.291730 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) 0 0
\(49\) 3.00000 5.19615i 0.428571 0.742307i
\(50\) 0 0
\(51\) −9.00000 −1.26025
\(52\) 0 0
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) −5.00000 + 8.66025i −0.674200 + 1.16775i
\(56\) 0 0
\(57\) −9.00000 −1.19208
\(58\) 0 0
\(59\) 2.50000 + 4.33013i 0.325472 + 0.563735i 0.981608 0.190909i \(-0.0611434\pi\)
−0.656136 + 0.754643i \(0.727810\pi\)
\(60\) 0 0
\(61\) 2.50000 + 4.33013i 0.320092 + 0.554416i 0.980507 0.196485i \(-0.0629528\pi\)
−0.660415 + 0.750901i \(0.729619\pi\)
\(62\) 0 0
\(63\) 3.00000 5.19615i 0.377964 0.654654i
\(64\) 0 0
\(65\) −2.00000 + 6.92820i −0.248069 + 0.859338i
\(66\) 0 0
\(67\) 3.50000 6.06218i 0.427593 0.740613i −0.569066 0.822292i \(-0.692695\pi\)
0.996659 + 0.0816792i \(0.0260283\pi\)
\(68\) 0 0
\(69\) 1.50000 + 2.59808i 0.180579 + 0.312772i
\(70\) 0 0
\(71\) −5.50000 9.52628i −0.652730 1.13056i −0.982458 0.186485i \(-0.940290\pi\)
0.329728 0.944076i \(-0.393043\pi\)
\(72\) 0 0
\(73\) 14.0000 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) 0 0
\(75\) −1.50000 + 2.59808i −0.173205 + 0.300000i
\(76\) 0 0
\(77\) −5.00000 −0.569803
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) −3.00000 5.19615i −0.325396 0.563602i
\(86\) 0 0
\(87\) −1.50000 2.59808i −0.160817 0.278543i
\(88\) 0 0
\(89\) 4.50000 7.79423i 0.476999 0.826187i −0.522654 0.852545i \(-0.675058\pi\)
0.999653 + 0.0263586i \(0.00839118\pi\)
\(90\) 0 0
\(91\) −3.50000 + 0.866025i −0.366900 + 0.0907841i
\(92\) 0 0
\(93\) 12.0000 20.7846i 1.24434 2.15526i
\(94\) 0 0
\(95\) −3.00000 5.19615i −0.307794 0.533114i
\(96\) 0 0
\(97\) 0.500000 + 0.866025i 0.0507673 + 0.0879316i 0.890292 0.455389i \(-0.150500\pi\)
−0.839525 + 0.543321i \(0.817167\pi\)
\(98\) 0 0
\(99\) 30.0000 3.01511
\(100\) 0 0
\(101\) −9.50000 + 16.4545i −0.945285 + 1.63728i −0.190106 + 0.981763i \(0.560883\pi\)
−0.755179 + 0.655519i \(0.772450\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 6.00000 0.585540
\(106\) 0 0
\(107\) 5.50000 9.52628i 0.531705 0.920940i −0.467610 0.883935i \(-0.654885\pi\)
0.999315 0.0370053i \(-0.0117818\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 4.50000 + 7.79423i 0.427121 + 0.739795i
\(112\) 0 0
\(113\) −5.50000 9.52628i −0.517396 0.896157i −0.999796 0.0202056i \(-0.993568\pi\)
0.482399 0.875951i \(-0.339765\pi\)
\(114\) 0 0
\(115\) −1.00000 + 1.73205i −0.0932505 + 0.161515i
\(116\) 0 0
\(117\) 21.0000 5.19615i 1.94145 0.480384i
\(118\) 0 0
\(119\) 1.50000 2.59808i 0.137505 0.238165i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 0 0
\(123\) 4.50000 + 7.79423i 0.405751 + 0.702782i
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −2.50000 + 4.33013i −0.221839 + 0.384237i −0.955366 0.295423i \(-0.904539\pi\)
0.733527 + 0.679660i \(0.237873\pi\)
\(128\) 0 0
\(129\) 3.00000 0.264135
\(130\) 0 0
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 0 0
\(133\) 1.50000 2.59808i 0.130066 0.225282i
\(134\) 0 0
\(135\) −18.0000 −1.54919
\(136\) 0 0
\(137\) −7.50000 12.9904i −0.640768 1.10984i −0.985262 0.171054i \(-0.945283\pi\)
0.344493 0.938789i \(-0.388051\pi\)
\(138\) 0 0
\(139\) −5.50000 9.52628i −0.466504 0.808008i 0.532764 0.846264i \(-0.321153\pi\)
−0.999268 + 0.0382553i \(0.987820\pi\)
\(140\) 0 0
\(141\) −6.00000 + 10.3923i −0.505291 + 0.875190i
\(142\) 0 0
\(143\) −12.5000 12.9904i −1.04530 1.08631i
\(144\) 0 0
\(145\) 1.00000 1.73205i 0.0830455 0.143839i
\(146\) 0 0
\(147\) −9.00000 15.5885i −0.742307 1.28571i
\(148\) 0 0
\(149\) 10.5000 + 18.1865i 0.860194 + 1.48990i 0.871742 + 0.489966i \(0.162991\pi\)
−0.0115483 + 0.999933i \(0.503676\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −9.00000 + 15.5885i −0.727607 + 1.26025i
\(154\) 0 0
\(155\) 16.0000 1.28515
\(156\) 0 0
\(157\) −22.0000 −1.75579 −0.877896 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) 0 0
\(159\) −9.00000 + 15.5885i −0.713746 + 1.23625i
\(160\) 0 0
\(161\) −1.00000 −0.0788110
\(162\) 0 0
\(163\) −3.50000 6.06218i −0.274141 0.474826i 0.695777 0.718258i \(-0.255060\pi\)
−0.969918 + 0.243432i \(0.921727\pi\)
\(164\) 0 0
\(165\) 15.0000 + 25.9808i 1.16775 + 2.02260i
\(166\) 0 0
\(167\) −4.50000 + 7.79423i −0.348220 + 0.603136i −0.985933 0.167139i \(-0.946547\pi\)
0.637713 + 0.770274i \(0.279881\pi\)
\(168\) 0 0
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) 0 0
\(171\) −9.00000 + 15.5885i −0.688247 + 1.19208i
\(172\) 0 0
\(173\) −5.50000 9.52628i −0.418157 0.724270i 0.577597 0.816322i \(-0.303991\pi\)
−0.995754 + 0.0920525i \(0.970657\pi\)
\(174\) 0 0
\(175\) −0.500000 0.866025i −0.0377964 0.0654654i
\(176\) 0 0
\(177\) 15.0000 1.12747
\(178\) 0 0
\(179\) −10.5000 + 18.1865i −0.784807 + 1.35933i 0.144308 + 0.989533i \(0.453905\pi\)
−0.929114 + 0.369792i \(0.879429\pi\)
\(180\) 0 0
\(181\) 18.0000 1.33793 0.668965 0.743294i \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) 0 0
\(183\) 15.0000 1.10883
\(184\) 0 0
\(185\) −3.00000 + 5.19615i −0.220564 + 0.382029i
\(186\) 0 0
\(187\) 15.0000 1.09691
\(188\) 0 0
\(189\) −4.50000 7.79423i −0.327327 0.566947i
\(190\) 0 0
\(191\) 0.500000 + 0.866025i 0.0361787 + 0.0626634i 0.883548 0.468341i \(-0.155148\pi\)
−0.847369 + 0.531004i \(0.821815\pi\)
\(192\) 0 0
\(193\) −5.50000 + 9.52628i −0.395899 + 0.685717i −0.993215 0.116289i \(-0.962900\pi\)
0.597317 + 0.802005i \(0.296234\pi\)
\(194\) 0 0
\(195\) 15.0000 + 15.5885i 1.07417 + 1.11631i
\(196\) 0 0
\(197\) 4.50000 7.79423i 0.320612 0.555316i −0.660003 0.751263i \(-0.729445\pi\)
0.980614 + 0.195947i \(0.0627782\pi\)
\(198\) 0 0
\(199\) −9.50000 16.4545i −0.673437 1.16643i −0.976923 0.213591i \(-0.931484\pi\)
0.303486 0.952836i \(-0.401849\pi\)
\(200\) 0 0
\(201\) −10.5000 18.1865i −0.740613 1.28278i
\(202\) 0 0
\(203\) 1.00000 0.0701862
\(204\) 0 0
\(205\) −3.00000 + 5.19615i −0.209529 + 0.362915i
\(206\) 0 0
\(207\) 6.00000 0.417029
\(208\) 0 0
\(209\) 15.0000 1.03757
\(210\) 0 0
\(211\) −6.50000 + 11.2583i −0.447478 + 0.775055i −0.998221 0.0596196i \(-0.981011\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) 0 0
\(213\) −33.0000 −2.26112
\(214\) 0 0
\(215\) 1.00000 + 1.73205i 0.0681994 + 0.118125i
\(216\) 0 0
\(217\) 4.00000 + 6.92820i 0.271538 + 0.470317i
\(218\) 0 0
\(219\) 21.0000 36.3731i 1.41905 2.45786i
\(220\) 0 0
\(221\) 10.5000 2.59808i 0.706306 0.174766i
\(222\) 0 0
\(223\) −4.50000 + 7.79423i −0.301342 + 0.521940i −0.976440 0.215788i \(-0.930768\pi\)
0.675098 + 0.737728i \(0.264101\pi\)
\(224\) 0 0
\(225\) 3.00000 + 5.19615i 0.200000 + 0.346410i
\(226\) 0 0
\(227\) 10.5000 + 18.1865i 0.696909 + 1.20708i 0.969533 + 0.244962i \(0.0787754\pi\)
−0.272623 + 0.962121i \(0.587891\pi\)
\(228\) 0 0
\(229\) −6.00000 −0.396491 −0.198246 0.980152i \(-0.563524\pi\)
−0.198246 + 0.980152i \(0.563524\pi\)
\(230\) 0 0
\(231\) −7.50000 + 12.9904i −0.493464 + 0.854704i
\(232\) 0 0
\(233\) 22.0000 1.44127 0.720634 0.693316i \(-0.243851\pi\)
0.720634 + 0.693316i \(0.243851\pi\)
\(234\) 0 0
\(235\) −8.00000 −0.521862
\(236\) 0 0
\(237\) 6.00000 10.3923i 0.389742 0.675053i
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) 10.5000 + 18.1865i 0.676364 + 1.17150i 0.976068 + 0.217465i \(0.0697789\pi\)
−0.299704 + 0.954032i \(0.596888\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 6.00000 10.3923i 0.383326 0.663940i
\(246\) 0 0
\(247\) 10.5000 2.59808i 0.668099 0.165312i
\(248\) 0 0
\(249\) −18.0000 + 31.1769i −1.14070 + 1.97576i
\(250\) 0 0
\(251\) 4.50000 + 7.79423i 0.284037 + 0.491967i 0.972375 0.233423i \(-0.0749927\pi\)
−0.688338 + 0.725390i \(0.741659\pi\)
\(252\) 0 0
\(253\) −2.50000 4.33013i −0.157174 0.272233i
\(254\) 0 0
\(255\) −18.0000 −1.12720
\(256\) 0 0
\(257\) −1.50000 + 2.59808i −0.0935674 + 0.162064i −0.909010 0.416775i \(-0.863160\pi\)
0.815442 + 0.578838i \(0.196494\pi\)
\(258\) 0 0
\(259\) −3.00000 −0.186411
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 0 0
\(263\) 7.50000 12.9904i 0.462470 0.801021i −0.536614 0.843828i \(-0.680297\pi\)
0.999083 + 0.0428069i \(0.0136300\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) −13.5000 23.3827i −0.826187 1.43100i
\(268\) 0 0
\(269\) −7.50000 12.9904i −0.457283 0.792038i 0.541533 0.840679i \(-0.317844\pi\)
−0.998816 + 0.0486418i \(0.984511\pi\)
\(270\) 0 0
\(271\) −8.50000 + 14.7224i −0.516338 + 0.894324i 0.483482 + 0.875354i \(0.339372\pi\)
−0.999820 + 0.0189696i \(0.993961\pi\)
\(272\) 0 0
\(273\) −3.00000 + 10.3923i −0.181568 + 0.628971i
\(274\) 0 0
\(275\) 2.50000 4.33013i 0.150756 0.261116i
\(276\) 0 0
\(277\) 4.50000 + 7.79423i 0.270379 + 0.468310i 0.968959 0.247222i \(-0.0795177\pi\)
−0.698580 + 0.715532i \(0.746184\pi\)
\(278\) 0 0
\(279\) −24.0000 41.5692i −1.43684 2.48868i
\(280\) 0 0
\(281\) −2.00000 −0.119310 −0.0596550 0.998219i \(-0.519000\pi\)
−0.0596550 + 0.998219i \(0.519000\pi\)
\(282\) 0 0
\(283\) 9.50000 16.4545i 0.564716 0.978117i −0.432360 0.901701i \(-0.642319\pi\)
0.997076 0.0764162i \(-0.0243478\pi\)
\(284\) 0 0
\(285\) −18.0000 −1.06623
\(286\) 0 0
\(287\) −3.00000 −0.177084
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 3.00000 0.175863
\(292\) 0 0
\(293\) −9.50000 16.4545i −0.554996 0.961281i −0.997904 0.0647140i \(-0.979386\pi\)
0.442908 0.896567i \(-0.353947\pi\)
\(294\) 0 0
\(295\) 5.00000 + 8.66025i 0.291111 + 0.504219i
\(296\) 0 0
\(297\) 22.5000 38.9711i 1.30558 2.26134i
\(298\) 0 0
\(299\) −2.50000 2.59808i −0.144579 0.150251i
\(300\) 0 0
\(301\) −0.500000 + 0.866025i −0.0288195 + 0.0499169i
\(302\) 0 0
\(303\) 28.5000 + 49.3634i 1.63728 + 2.83586i
\(304\) 0 0
\(305\) 5.00000 + 8.66025i 0.286299 + 0.495885i
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 12.0000 20.7846i 0.682656 1.18240i
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) 14.0000 0.791327 0.395663 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) 0 0
\(315\) 6.00000 10.3923i 0.338062 0.585540i
\(316\) 0 0
\(317\) 30.0000 1.68497 0.842484 0.538721i \(-0.181092\pi\)
0.842484 + 0.538721i \(0.181092\pi\)
\(318\) 0 0
\(319\) 2.50000 + 4.33013i 0.139973 + 0.242441i
\(320\) 0 0
\(321\) −16.5000 28.5788i −0.920940 1.59512i
\(322\) 0 0
\(323\) −4.50000 + 7.79423i −0.250387 + 0.433682i
\(324\) 0 0
\(325\) 1.00000 3.46410i 0.0554700 0.192154i
\(326\) 0 0
\(327\) 15.0000 25.9808i 0.829502 1.43674i
\(328\) 0 0
\(329\) −2.00000 3.46410i −0.110264 0.190982i
\(330\) 0 0
\(331\) 8.50000 + 14.7224i 0.467202 + 0.809218i 0.999298 0.0374662i \(-0.0119287\pi\)
−0.532096 + 0.846684i \(0.678595\pi\)
\(332\) 0 0
\(333\) 18.0000 0.986394
\(334\) 0 0
\(335\) 7.00000 12.1244i 0.382451 0.662424i
\(336\) 0 0
\(337\) −10.0000 −0.544735 −0.272367 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(338\) 0 0
\(339\) −33.0000 −1.79231
\(340\) 0 0
\(341\) −20.0000 + 34.6410i −1.08306 + 1.87592i
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) 3.00000 + 5.19615i 0.161515 + 0.279751i
\(346\) 0 0
\(347\) 16.5000 + 28.5788i 0.885766 + 1.53419i 0.844833 + 0.535031i \(0.179700\pi\)
0.0409337 + 0.999162i \(0.486967\pi\)
\(348\) 0 0
\(349\) −9.50000 + 16.4545i −0.508523 + 0.880788i 0.491428 + 0.870918i \(0.336475\pi\)
−0.999951 + 0.00987003i \(0.996858\pi\)
\(350\) 0 0
\(351\) 9.00000 31.1769i 0.480384 1.66410i
\(352\) 0 0
\(353\) −3.50000 + 6.06218i −0.186286 + 0.322657i −0.944009 0.329919i \(-0.892979\pi\)
0.757723 + 0.652576i \(0.226312\pi\)
\(354\) 0 0
\(355\) −11.0000 19.0526i −0.583819 1.01120i
\(356\) 0 0
\(357\) −4.50000 7.79423i −0.238165 0.412514i
\(358\) 0 0
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) 5.00000 8.66025i 0.263158 0.455803i
\(362\) 0 0
\(363\) −42.0000 −2.20443
\(364\) 0 0
\(365\) 28.0000 1.46559
\(366\) 0 0
\(367\) 11.5000 19.9186i 0.600295 1.03974i −0.392481 0.919760i \(-0.628383\pi\)
0.992776 0.119982i \(-0.0382835\pi\)
\(368\) 0 0
\(369\) 18.0000 0.937043
\(370\) 0 0
\(371\) −3.00000 5.19615i −0.155752 0.269771i
\(372\) 0 0
\(373\) −11.5000 19.9186i −0.595447 1.03135i −0.993484 0.113975i \(-0.963641\pi\)
0.398036 0.917370i \(-0.369692\pi\)
\(374\) 0 0
\(375\) −18.0000 + 31.1769i −0.929516 + 1.60997i
\(376\) 0 0
\(377\) 2.50000 + 2.59808i 0.128757 + 0.133808i
\(378\) 0 0
\(379\) −2.50000 + 4.33013i −0.128416 + 0.222424i −0.923063 0.384648i \(-0.874323\pi\)
0.794647 + 0.607072i \(0.207656\pi\)
\(380\) 0 0
\(381\) 7.50000 + 12.9904i 0.384237 + 0.665517i
\(382\) 0 0
\(383\) 4.50000 + 7.79423i 0.229939 + 0.398266i 0.957790 0.287469i \(-0.0928139\pi\)
−0.727851 + 0.685736i \(0.759481\pi\)
\(384\) 0 0
\(385\) −10.0000 −0.509647
\(386\) 0 0
\(387\) 3.00000 5.19615i 0.152499 0.264135i
\(388\) 0 0
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 0 0
\(391\) 3.00000 0.151717
\(392\) 0 0
\(393\) 6.00000 10.3923i 0.302660 0.524222i
\(394\) 0 0
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) 12.5000 + 21.6506i 0.627357 + 1.08661i 0.988080 + 0.153941i \(0.0491966\pi\)
−0.360723 + 0.932673i \(0.617470\pi\)
\(398\) 0 0
\(399\) −4.50000 7.79423i −0.225282 0.390199i
\(400\) 0 0
\(401\) −13.5000 + 23.3827i −0.674158 + 1.16768i 0.302556 + 0.953131i \(0.402160\pi\)
−0.976714 + 0.214544i \(0.931173\pi\)
\(402\) 0 0
\(403\) −8.00000 + 27.7128i −0.398508 + 1.38047i
\(404\) 0 0
\(405\) −9.00000 + 15.5885i −0.447214 + 0.774597i
\(406\) 0 0
\(407\) −7.50000 12.9904i −0.371761 0.643909i
\(408\) 0 0
\(409\) 2.50000 + 4.33013i 0.123617 + 0.214111i 0.921192 0.389109i \(-0.127217\pi\)
−0.797574 + 0.603220i \(0.793884\pi\)
\(410\) 0 0
\(411\) −45.0000 −2.21969
\(412\) 0 0
\(413\) −2.50000 + 4.33013i −0.123017 + 0.213072i
\(414\) 0 0
\(415\) −24.0000 −1.17811
\(416\) 0 0
\(417\) −33.0000 −1.61602
\(418\) 0 0
\(419\) 7.50000 12.9904i 0.366399 0.634622i −0.622601 0.782540i \(-0.713924\pi\)
0.989000 + 0.147918i \(0.0472572\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) 12.0000 + 20.7846i 0.583460 + 1.01058i
\(424\) 0 0
\(425\) 1.50000 + 2.59808i 0.0727607 + 0.126025i
\(426\) 0 0
\(427\) −2.50000 + 4.33013i −0.120983 + 0.209550i
\(428\) 0 0
\(429\) −52.5000 + 12.9904i −2.53472 + 0.627182i
\(430\) 0 0
\(431\) 1.50000 2.59808i 0.0722525 0.125145i −0.827636 0.561266i \(-0.810315\pi\)
0.899888 + 0.436121i \(0.143648\pi\)
\(432\) 0 0
\(433\) −9.50000 16.4545i −0.456541 0.790752i 0.542234 0.840227i \(-0.317578\pi\)
−0.998775 + 0.0494752i \(0.984245\pi\)
\(434\) 0 0
\(435\) −3.00000 5.19615i −0.143839 0.249136i
\(436\) 0 0
\(437\) 3.00000 0.143509
\(438\) 0 0
\(439\) −6.50000 + 11.2583i −0.310228 + 0.537331i −0.978412 0.206666i \(-0.933739\pi\)
0.668184 + 0.743996i \(0.267072\pi\)
\(440\) 0 0
\(441\) −36.0000 −1.71429
\(442\) 0 0
\(443\) −12.0000 −0.570137 −0.285069 0.958507i \(-0.592016\pi\)
−0.285069 + 0.958507i \(0.592016\pi\)
\(444\) 0 0
\(445\) 9.00000 15.5885i 0.426641 0.738964i
\(446\) 0 0
\(447\) 63.0000 2.97980
\(448\) 0 0
\(449\) 2.50000 + 4.33013i 0.117982 + 0.204351i 0.918968 0.394332i \(-0.129024\pi\)
−0.800986 + 0.598684i \(0.795691\pi\)
\(450\) 0 0
\(451\) −7.50000 12.9904i −0.353161 0.611693i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −7.00000 + 1.73205i −0.328165 + 0.0811998i
\(456\) 0 0
\(457\) 8.50000 14.7224i 0.397613 0.688686i −0.595818 0.803120i \(-0.703172\pi\)
0.993431 + 0.114433i \(0.0365053\pi\)
\(458\) 0 0
\(459\) 13.5000 + 23.3827i 0.630126 + 1.09141i
\(460\) 0 0
\(461\) 4.50000 + 7.79423i 0.209586 + 0.363013i 0.951584 0.307388i \(-0.0994551\pi\)
−0.741998 + 0.670402i \(0.766122\pi\)
\(462\) 0 0
\(463\) −40.0000 −1.85896 −0.929479 0.368875i \(-0.879743\pi\)
−0.929479 + 0.368875i \(0.879743\pi\)
\(464\) 0 0
\(465\) 24.0000 41.5692i 1.11297 1.92773i
\(466\) 0 0
\(467\) 16.0000 0.740392 0.370196 0.928954i \(-0.379291\pi\)
0.370196 + 0.928954i \(0.379291\pi\)
\(468\) 0 0
\(469\) 7.00000 0.323230
\(470\) 0 0
\(471\) −33.0000 + 57.1577i −1.52056 + 2.63369i
\(472\) 0 0
\(473\) −5.00000 −0.229900
\(474\) 0 0
\(475\) 1.50000 + 2.59808i 0.0688247 + 0.119208i
\(476\) 0 0
\(477\) 18.0000 + 31.1769i 0.824163 + 1.42749i
\(478\) 0 0
\(479\) 1.50000 2.59808i 0.0685367 0.118709i −0.829721 0.558179i \(-0.811500\pi\)
0.898257 + 0.439470i \(0.144834\pi\)
\(480\) 0 0
\(481\) −7.50000 7.79423i −0.341971 0.355386i
\(482\) 0 0
\(483\) −1.50000 + 2.59808i −0.0682524 + 0.118217i
\(484\) 0 0
\(485\) 1.00000 + 1.73205i 0.0454077 + 0.0786484i
\(486\) 0 0
\(487\) 14.5000 + 25.1147i 0.657058 + 1.13806i 0.981374 + 0.192109i \(0.0615326\pi\)
−0.324316 + 0.945949i \(0.605134\pi\)
\(488\) 0 0
\(489\) −21.0000 −0.949653
\(490\) 0 0
\(491\) 15.5000 26.8468i 0.699505 1.21158i −0.269133 0.963103i \(-0.586737\pi\)
0.968638 0.248476i \(-0.0799296\pi\)
\(492\) 0 0
\(493\) −3.00000 −0.135113
\(494\) 0 0
\(495\) 60.0000 2.69680
\(496\) 0 0
\(497\) 5.50000 9.52628i 0.246709 0.427312i
\(498\) 0 0
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) 13.5000 + 23.3827i 0.603136 + 1.04466i
\(502\) 0 0
\(503\) −11.5000 19.9186i −0.512760 0.888126i −0.999891 0.0147968i \(-0.995290\pi\)
0.487131 0.873329i \(-0.338043\pi\)
\(504\) 0 0
\(505\) −19.0000 + 32.9090i −0.845489 + 1.46443i
\(506\) 0 0
\(507\) −34.5000 + 18.1865i −1.53220 + 0.807692i
\(508\) 0 0
\(509\) 2.50000 4.33013i 0.110811 0.191930i −0.805287 0.592886i \(-0.797989\pi\)
0.916097 + 0.400956i \(0.131322\pi\)
\(510\) 0 0
\(511\) 7.00000 + 12.1244i 0.309662 + 0.536350i
\(512\) 0 0
\(513\) 13.5000 + 23.3827i 0.596040 + 1.03237i
\(514\) 0 0
\(515\) 16.0000 0.705044
\(516\) 0 0
\(517\) 10.0000 17.3205i 0.439799 0.761755i
\(518\) 0 0
\(519\) −33.0000 −1.44854
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) 7.50000 12.9904i 0.327952 0.568030i −0.654153 0.756362i \(-0.726975\pi\)
0.982105 + 0.188332i \(0.0603082\pi\)
\(524\) 0 0
\(525\) −3.00000 −0.130931
\(526\) 0 0
\(527\) −12.0000 20.7846i −0.522728 0.905392i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0 0
\(531\) 15.0000 25.9808i 0.650945 1.12747i
\(532\) 0 0
\(533\) −7.50000 7.79423i −0.324861 0.337606i
\(534\) 0 0
\(535\) 11.0000 19.0526i 0.475571 0.823714i
\(536\) 0 0
\(537\) 31.5000 + 54.5596i 1.35933 + 2.35442i
\(538\) 0 0
\(539\) 15.0000 + 25.9808i 0.646096 + 1.11907i
\(540\) 0 0
\(541\) −34.0000 −1.46177 −0.730887 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) 0 0
\(543\) 27.0000 46.7654i 1.15868 2.00689i
\(544\) 0 0
\(545\) 20.0000 0.856706
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) 15.0000 25.9808i 0.640184 1.10883i
\(550\) 0 0
\(551\) −3.00000 −0.127804
\(552\) 0 0
\(553\) 2.00000 + 3.46410i 0.0850487 + 0.147309i
\(554\) 0 0
\(555\) 9.00000 + 15.5885i 0.382029 + 0.661693i
\(556\) 0 0
\(557\) 16.5000 28.5788i 0.699127 1.21092i −0.269642 0.962961i \(-0.586905\pi\)
0.968769 0.247964i \(-0.0797613\pi\)
\(558\) 0 0
\(559\) −3.50000 + 0.866025i −0.148034 + 0.0366290i
\(560\) 0 0
\(561\) 22.5000 38.9711i 0.949951 1.64536i
\(562\) 0 0
\(563\) −9.50000 16.4545i −0.400377 0.693474i 0.593394 0.804912i \(-0.297788\pi\)
−0.993771 + 0.111438i \(0.964454\pi\)
\(564\) 0 0
\(565\) −11.0000 19.0526i −0.462773 0.801547i
\(566\) 0 0
\(567\) −9.00000 −0.377964
\(568\) 0 0
\(569\) −3.50000 + 6.06218i −0.146728 + 0.254140i −0.930016 0.367519i \(-0.880207\pi\)
0.783289 + 0.621658i \(0.213541\pi\)
\(570\) 0 0
\(571\) −12.0000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) 0 0
\(573\) 3.00000 0.125327
\(574\) 0 0
\(575\) 0.500000 0.866025i 0.0208514 0.0361158i
\(576\) 0 0
\(577\) 6.00000 0.249783 0.124892 0.992170i \(-0.460142\pi\)
0.124892 + 0.992170i \(0.460142\pi\)
\(578\) 0 0
\(579\) 16.5000 + 28.5788i 0.685717 + 1.18770i
\(580\) 0 0
\(581\) −6.00000 10.3923i −0.248922 0.431145i
\(582\) 0 0
\(583\) 15.0000 25.9808i 0.621237 1.07601i
\(584\) 0 0
\(585\) 42.0000 10.3923i 1.73649 0.429669i
\(586\) 0 0
\(587\) −12.5000 + 21.6506i −0.515930 + 0.893617i 0.483899 + 0.875124i \(0.339220\pi\)
−0.999829 + 0.0184934i \(0.994113\pi\)
\(588\) 0 0
\(589\) −12.0000 20.7846i −0.494451 0.856415i
\(590\) 0 0
\(591\) −13.5000 23.3827i −0.555316 0.961835i
\(592\) 0 0
\(593\) −34.0000 −1.39621 −0.698106 0.715994i \(-0.745974\pi\)
−0.698106 + 0.715994i \(0.745974\pi\)
\(594\) 0 0
\(595\) 3.00000 5.19615i 0.122988 0.213021i
\(596\) 0 0
\(597\) −57.0000 −2.33285
\(598\) 0 0
\(599\) 20.0000 0.817178 0.408589 0.912719i \(-0.366021\pi\)
0.408589 + 0.912719i \(0.366021\pi\)
\(600\) 0 0
\(601\) −9.50000 + 16.4545i −0.387513 + 0.671192i −0.992114 0.125336i \(-0.959999\pi\)
0.604601 + 0.796528i \(0.293332\pi\)
\(602\) 0 0
\(603\) −42.0000 −1.71037
\(604\) 0 0
\(605\) −14.0000 24.2487i −0.569181 0.985850i
\(606\) 0 0
\(607\) −13.5000 23.3827i −0.547948 0.949074i −0.998415 0.0562808i \(-0.982076\pi\)
0.450467 0.892793i \(-0.351258\pi\)
\(608\) 0 0
\(609\) 1.50000 2.59808i 0.0607831 0.105279i
\(610\) 0 0
\(611\) 4.00000 13.8564i 0.161823 0.560570i
\(612\) 0 0
\(613\) −5.50000 + 9.52628i −0.222143 + 0.384763i −0.955458 0.295126i \(-0.904638\pi\)
0.733316 + 0.679888i \(0.237972\pi\)
\(614\) 0 0
\(615\) 9.00000 + 15.5885i 0.362915 + 0.628587i
\(616\) 0 0
\(617\) −3.50000 6.06218i −0.140905 0.244054i 0.786933 0.617039i \(-0.211668\pi\)
−0.927838 + 0.372985i \(0.878334\pi\)
\(618\) 0 0
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) 4.50000 7.79423i 0.180579 0.312772i
\(622\) 0 0
\(623\) 9.00000 0.360577
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 0 0
\(627\) 22.5000 38.9711i 0.898563 1.55636i
\(628\) 0 0
\(629\) 9.00000 0.358854
\(630\) 0 0
\(631\) 18.5000 + 32.0429i 0.736473 + 1.27561i 0.954074 + 0.299571i \(0.0968437\pi\)
−0.217601 + 0.976038i \(0.569823\pi\)
\(632\) 0 0
\(633\) 19.5000 + 33.7750i 0.775055 + 1.34244i
\(634\) 0 0
\(635\) −5.00000 + 8.66025i −0.198419 + 0.343672i
\(636\) 0 0
\(637\) 15.0000 + 15.5885i 0.594322 + 0.617637i
\(638\) 0 0
\(639\) −33.0000 + 57.1577i −1.30546 + 2.26112i
\(640\) 0 0
\(641\) 2.50000 + 4.33013i 0.0987441 + 0.171030i 0.911165 0.412042i \(-0.135184\pi\)
−0.812421 + 0.583071i \(0.801851\pi\)
\(642\) 0 0
\(643\) −15.5000 26.8468i −0.611260 1.05873i −0.991028 0.133652i \(-0.957330\pi\)
0.379768 0.925082i \(-0.376004\pi\)
\(644\) 0 0
\(645\) 6.00000 0.236250
\(646\) 0 0
\(647\) −14.5000 + 25.1147i −0.570054 + 0.987362i 0.426506 + 0.904485i \(0.359744\pi\)
−0.996560 + 0.0828774i \(0.973589\pi\)
\(648\) 0 0
\(649\) −25.0000 −0.981336
\(650\) 0 0
\(651\) 24.0000 0.940634
\(652\) 0 0
\(653\) −1.50000 + 2.59808i −0.0586995 + 0.101671i −0.893882 0.448303i \(-0.852029\pi\)
0.835182 + 0.549973i \(0.185362\pi\)
\(654\) 0 0
\(655\) 8.00000 0.312586
\(656\) 0 0
\(657\) −42.0000 72.7461i −1.63858 2.83810i
\(658\) 0 0
\(659\) 16.5000 + 28.5788i 0.642749 + 1.11327i 0.984817 + 0.173598i \(0.0555394\pi\)
−0.342068 + 0.939675i \(0.611127\pi\)
\(660\) 0 0
\(661\) 18.5000 32.0429i 0.719567 1.24633i −0.241605 0.970375i \(-0.577674\pi\)
0.961172 0.275951i \(-0.0889928\pi\)
\(662\) 0 0
\(663\) 9.00000 31.1769i 0.349531 1.21081i
\(664\) 0 0
\(665\) 3.00000 5.19615i 0.116335 0.201498i
\(666\) 0 0
\(667\) 0.500000 + 0.866025i 0.0193601 + 0.0335326i
\(668\) 0 0
\(669\) 13.5000 + 23.3827i 0.521940 + 0.904027i
\(670\) 0 0
\(671\) −25.0000 −0.965114
\(672\) 0 0
\(673\) −3.50000 + 6.06218i −0.134915 + 0.233680i −0.925565 0.378589i \(-0.876409\pi\)
0.790650 + 0.612268i \(0.209743\pi\)
\(674\) 0 0
\(675\) 9.00000 0.346410
\(676\) 0 0
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) 0 0
\(679\) −0.500000 + 0.866025i −0.0191882 + 0.0332350i
\(680\) 0 0
\(681\) 63.0000 2.41417
\(682\) 0 0
\(683\) −5.50000 9.52628i −0.210452 0.364513i 0.741404 0.671059i \(-0.234160\pi\)
−0.951856 + 0.306546i \(0.900827\pi\)
\(684\) 0 0
\(685\) −15.0000 25.9808i −0.573121 0.992674i
\(686\) 0 0
\(687\) −9.00000 + 15.5885i −0.343371 + 0.594737i
\(688\) 0 0
\(689\) 6.00000 20.7846i 0.228582 0.791831i
\(690\) 0 0
\(691\) −2.50000 + 4.33013i −0.0951045 + 0.164726i −0.909652 0.415371i \(-0.863652\pi\)
0.814548 + 0.580097i \(0.196985\pi\)
\(692\) 0 0
\(693\) 15.0000 + 25.9808i 0.569803 + 0.986928i
\(694\) 0 0
\(695\) −11.0000 19.0526i −0.417254 0.722705i
\(696\) 0 0
\(697\) 9.00000 0.340899
\(698\) 0 0
\(699\) 33.0000 57.1577i 1.24817 2.16190i
\(700\) 0 0
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 0 0
\(703\) 9.00000 0.339441
\(704\) 0 0
\(705\) −12.0000 + 20.7846i −0.451946 + 0.782794i
\(706\) 0 0
\(707\) −19.0000 −0.714569
\(708\) 0 0
\(709\) 0.500000 + 0.866025i 0.0187779 + 0.0325243i 0.875262 0.483650i \(-0.160689\pi\)
−0.856484 + 0.516174i \(0.827356\pi\)
\(710\) 0 0
\(711\) −12.0000 20.7846i −0.450035 0.779484i
\(712\) 0 0
\(713\) −4.00000 + 6.92820i −0.149801 + 0.259463i
\(714\) 0 0
\(715\) −25.0000 25.9808i −0.934947 0.971625i
\(716\) 0 0
\(717\) −36.0000 + 62.3538i −1.34444 + 2.32865i
\(718\) 0 0
\(719\) 8.50000 + 14.7224i 0.316997 + 0.549054i 0.979860 0.199686i \(-0.0639923\pi\)
−0.662863 + 0.748740i \(0.730659\pi\)
\(720\) 0 0
\(721\) 4.00000 + 6.92820i 0.148968 + 0.258020i
\(722\) 0 0
\(723\) 63.0000 2.34300
\(724\) 0 0
\(725\) −0.500000 + 0.866025i −0.0185695 + 0.0321634i
\(726\) 0 0
\(727\) 8.00000 0.296704 0.148352 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 1.50000 2.59808i 0.0554795 0.0960933i
\(732\) 0 0
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) 0 0
\(735\) −18.0000 31.1769i −0.663940 1.14998i
\(736\) 0 0
\(737\) 17.5000 + 30.3109i 0.644621 + 1.11652i
\(738\) 0 0
\(739\) 7.50000 12.9904i 0.275892 0.477859i −0.694468 0.719524i \(-0.744360\pi\)
0.970360 + 0.241665i \(0.0776935\pi\)
\(740\) 0 0
\(741\) 9.00000 31.1769i 0.330623 1.14531i
\(742\) 0 0
\(743\) −14.5000 + 25.1147i −0.531953 + 0.921370i 0.467351 + 0.884072i \(0.345209\pi\)
−0.999304 + 0.0372984i \(0.988125\pi\)
\(744\) 0 0
\(745\) 21.0000 + 36.3731i 0.769380 + 1.33261i
\(746\) 0 0
\(747\) 36.0000 + 62.3538i 1.31717 + 2.28141i
\(748\) 0 0
\(749\) 11.0000 0.401931
\(750\) 0 0
\(751\) −4.50000 + 7.79423i −0.164207 + 0.284415i −0.936374 0.351005i \(-0.885840\pi\)
0.772166 + 0.635421i \(0.219173\pi\)
\(752\) 0 0
\(753\) 27.0000 0.983935
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.50000 + 2.59808i −0.0545184 + 0.0944287i −0.891997 0.452042i \(-0.850696\pi\)
0.837478 + 0.546471i \(0.184029\pi\)
\(758\) 0 0
\(759\) −15.0000 −0.544466
\(760\) 0 0
\(761\) −13.5000 23.3827i −0.489375 0.847622i 0.510551 0.859848i \(-0.329442\pi\)
−0.999925 + 0.0122260i \(0.996108\pi\)
\(762\) 0 0
\(763\) 5.00000 + 8.66025i 0.181012 + 0.313522i
\(764\) 0 0
\(765\) −18.0000 + 31.1769i −0.650791 + 1.12720i
\(766\) 0 0
\(767\) −17.5000 + 4.33013i −0.631888 + 0.156352i
\(768\) 0 0
\(769\) 10.5000 18.1865i 0.378640 0.655823i −0.612225 0.790684i \(-0.709725\pi\)
0.990865 + 0.134860i \(0.0430586\pi\)
\(770\) 0 0
\(771\) 4.50000 + 7.79423i 0.162064 + 0.280702i
\(772\) 0 0
\(773\) 0.500000 + 0.866025i 0.0179838 + 0.0311488i 0.874877 0.484345i \(-0.160942\pi\)
−0.856893 + 0.515494i \(0.827609\pi\)
\(774\) 0 0
\(775\) −8.00000 −0.287368
\(776\) 0 0
\(777\) −4.50000 + 7.79423i −0.161437 + 0.279616i
\(778\) 0 0
\(779\) 9.00000 0.322458
\(780\) 0 0
\(781\) 55.0000 1.96805
\(782\) 0 0
\(783\) −4.50000 + 7.79423i −0.160817 + 0.278543i
\(784\) 0 0
\(785\) −44.0000 −1.57043
\(786\) 0 0
\(787\) −3.50000 6.06218i −0.124762 0.216093i 0.796878 0.604140i \(-0.206483\pi\)
−0.921640 + 0.388047i \(0.873150\pi\)
\(788\) 0 0
\(789\) −22.5000 38.9711i −0.801021 1.38741i
\(790\) 0 0
\(791\) 5.50000 9.52628i 0.195557 0.338716i
\(792\) 0 0
\(793\) −17.5000 + 4.33013i −0.621443 + 0.153767i
\(794\) 0 0
\(795\) −18.0000 + 31.1769i −0.638394 + 1.10573i
\(796\) 0 0
\(797\) −13.5000 23.3827i −0.478195 0.828257i 0.521493 0.853256i \(-0.325375\pi\)
−0.999687 + 0.0249984i \(0.992042\pi\)
\(798\) 0 0
\(799\) 6.00000 + 10.3923i 0.212265 + 0.367653i
\(800\) 0 0
\(801\) −54.0000 −1.90800
\(802\) 0 0
\(803\) −35.0000 + 60.6218i −1.23512 + 2.13930i
\(804\) 0 0
\(805\) −2.00000 −0.0704907
\(806\) 0 0
\(807\) −45.0000 −1.58408
\(808\) 0 0
\(809\) 22.5000 38.9711i 0.791058 1.37015i −0.134255 0.990947i \(-0.542864\pi\)
0.925312 0.379206i \(-0.123803\pi\)
\(810\) 0 0
\(811\) 40.0000 1.40459 0.702295 0.711886i \(-0.252159\pi\)
0.702295 + 0.711886i \(0.252159\pi\)
\(812\) 0 0
\(813\) 25.5000 + 44.1673i 0.894324 + 1.54901i
\(814\) 0 0
\(815\) −7.00000 12.1244i −0.245199 0.424698i
\(816\) 0 0
\(817\) 1.50000 2.59808i 0.0524784 0.0908952i
\(818\) 0 0
\(819\) 15.0000 + 15.5885i 0.524142 + 0.544705i
\(820\) 0 0
\(821\) −23.5000 + 40.7032i −0.820156 + 1.42055i 0.0854103 + 0.996346i \(0.472780\pi\)
−0.905566 + 0.424205i \(0.860553\pi\)
\(822\) 0 0
\(823\) −1.50000 2.59808i −0.0522867 0.0905632i 0.838697 0.544598i \(-0.183318\pi\)
−0.890984 + 0.454034i \(0.849984\pi\)
\(824\) 0 0
\(825\) −7.50000 12.9904i −0.261116 0.452267i
\(826\) 0 0
\(827\) −36.0000 −1.25184 −0.625921 0.779886i \(-0.715277\pi\)
−0.625921 + 0.779886i \(0.715277\pi\)
\(828\) 0 0
\(829\) −15.5000 + 26.8468i −0.538337 + 0.932427i 0.460657 + 0.887578i \(0.347614\pi\)
−0.998994 + 0.0448490i \(0.985719\pi\)
\(830\) 0 0
\(831\) 27.0000 0.936620
\(832\) 0 0
\(833\) −18.0000 −0.623663
\(834\) 0 0
\(835\) −9.00000 + 15.5885i −0.311458 + 0.539461i
\(836\) 0 0
\(837\) −72.0000 −2.48868
\(838\) 0 0
\(839\) −21.5000 37.2391i −0.742262 1.28564i −0.951463 0.307763i \(-0.900419\pi\)
0.209200 0.977873i \(-0.432914\pi\)
\(840\) 0 0
\(841\) 14.0000 + 24.2487i 0.482759 + 0.836162i
\(842\) 0 0
\(843\) −3.00000 + 5.19615i −0.103325 + 0.178965i
\(844\) 0 0
\(845\) −22.0000 13.8564i −0.756823 0.476675i
\(846\) 0 0
\(847\) 7.00000 12.1244i 0.240523 0.416598i
\(848\) 0 0
\(849\) −28.5000 49.3634i −0.978117 1.69415i
\(850\) 0 0
\(851\) −1.50000 2.59808i −0.0514193 0.0890609i
\(852\) 0 0
\(853\) 10.0000 0.342393 0.171197 0.985237i \(-0.445237\pi\)
0.171197 + 0.985237i \(0.445237\pi\)
\(854\) 0 0
\(855\) −18.0000 + 31.1769i −0.615587 + 1.06623i
\(856\) 0 0
\(857\) −2.00000 −0.0683187 −0.0341593 0.999416i \(-0.510875\pi\)
−0.0341593 + 0.999416i \(0.510875\pi\)
\(858\) 0 0
\(859\) 28.0000 0.955348 0.477674 0.878537i \(-0.341480\pi\)
0.477674 + 0.878537i \(0.341480\pi\)
\(860\) 0 0
\(861\) −4.50000 + 7.79423i −0.153360 + 0.265627i
\(862\) 0 0
\(863\) −16.0000 −0.544646 −0.272323 0.962206i \(-0.587792\pi\)
−0.272323 + 0.962206i \(0.587792\pi\)
\(864\) 0 0
\(865\) −11.0000 19.0526i −0.374011 0.647806i
\(866\) 0 0
\(867\) −12.0000 20.7846i −0.407541 0.705882i
\(868\) 0 0
\(869\) −10.0000 + 17.3205i −0.339227 + 0.587558i
\(870\) 0 0
\(871\) 17.5000 + 18.1865i 0.592965 + 0.616227i
\(872\) 0 0
\(873\) 3.00000 5.19615i 0.101535 0.175863i
\(874\) 0 0
\(875\) −6.00000 10.3923i −0.202837 0.351324i
\(876\) 0 0
\(877\) 22.5000 + 38.9711i 0.759771 + 1.31596i 0.942967 + 0.332886i \(0.108022\pi\)
−0.183196 + 0.983076i \(0.558644\pi\)
\(878\) 0 0
\(879\) −57.0000 −1.92256
\(880\) 0 0
\(881\) −25.5000 + 44.1673i −0.859117 + 1.48803i 0.0136556 + 0.999907i \(0.495653\pi\)
−0.872772 + 0.488127i \(0.837680\pi\)
\(882\) 0 0
\(883\) 44.0000 1.48072 0.740359 0.672212i \(-0.234656\pi\)
0.740359 + 0.672212i \(0.234656\pi\)
\(884\) 0 0
\(885\) 30.0000 1.00844
\(886\) 0 0
\(887\) −26.5000 + 45.8993i −0.889783 + 1.54115i −0.0496513 + 0.998767i \(0.515811\pi\)
−0.840132 + 0.542383i \(0.817522\pi\)
\(888\) 0 0
\(889\) −5.00000 −0.167695
\(890\) 0 0
\(891\) −22.5000 38.9711i −0.753778 1.30558i
\(892\) 0 0
\(893\) 6.00000 + 10.3923i 0.200782 + 0.347765i
\(894\) 0 0
\(895\) −21.0000 + 36.3731i −0.701953 + 1.21582i
\(896\) 0 0
\(897\) −10.5000 + 2.59808i −0.350585 + 0.0867472i
\(898\) 0 0
\(899\) 4.00000 6.92820i 0.133407 0.231069i
\(900\) 0 0
\(901\) 9.00000 + 15.5885i 0.299833 + 0.519327i
\(902\) 0 0
\(903\) 1.50000 + 2.59808i 0.0499169 + 0.0864586i
\(904\) 0 0
\(905\) 36.0000 1.19668
\(906\) 0 0
\(907\) 1.50000 2.59808i 0.0498067 0.0862677i −0.840047 0.542513i \(-0.817473\pi\)
0.889854 + 0.456246i \(0.150806\pi\)
\(908\) 0 0
\(909\) 114.000 3.78114
\(910\) 0 0
\(911\) 48.0000 1.59031 0.795155 0.606406i \(-0.207389\pi\)
0.795155 + 0.606406i \(0.207389\pi\)
\(912\) 0 0
\(913\) 30.0000 51.9615i 0.992855 1.71968i
\(914\) 0 0
\(915\) 30.0000 0.991769
\(916\) 0 0
\(917\) 2.00000 + 3.46410i 0.0660458 + 0.114395i
\(918\) 0 0
\(919\) 16.5000 + 28.5788i 0.544285 + 0.942729i 0.998652 + 0.0519142i \(0.0165322\pi\)
−0.454367 + 0.890815i \(0.650134\pi\)
\(920\) 0 0
\(921\) 6.00000 10.3923i 0.197707 0.342438i
\(922\) 0 0
\(923\) 38.5000 9.52628i 1.26724 0.313561i
\(924\) 0 0
\(925\) 1.50000 2.59808i 0.0493197 0.0854242i
\(926\) 0 0
\(927\) −24.0000 41.5692i −0.788263 1.36531i
\(928\) 0 0
\(929\) 10.5000 + 18.1865i 0.344494 + 0.596681i 0.985262 0.171054i \(-0.0547172\pi\)
−0.640768 + 0.767735i \(0.721384\pi\)
\(930\) 0 0
\(931\) −18.0000 −0.589926
\(932\) 0 0
\(933\) 36.0000 62.3538i 1.17859 2.04137i
\(934\) 0 0
\(935\) 30.0000 0.981105
\(936\) 0 0
\(937\) −18.0000 −0.588034 −0.294017 0.955800i \(-0.594992\pi\)
−0.294017 + 0.955800i \(0.594992\pi\)
\(938\) 0 0
\(939\) 21.0000 36.3731i 0.685309 1.18699i
\(940\) 0 0
\(941\) −50.0000 −1.62995 −0.814977 0.579494i \(-0.803250\pi\)
−0.814977 + 0.579494i \(0.803250\pi\)
\(942\) 0 0
\(943\) −1.50000 2.59808i −0.0488467 0.0846050i
\(944\) 0 0
\(945\) −9.00000 15.5885i −0.292770 0.507093i
\(946\) 0 0
\(947\) 13.5000 23.3827i 0.438691 0.759835i −0.558898 0.829237i \(-0.688776\pi\)
0.997589 + 0.0694014i \(0.0221089\pi\)
\(948\) 0 0
\(949\) −14.0000 + 48.4974i −0.454459 + 1.57429i
\(950\) 0 0
\(951\) 45.0000 77.9423i 1.45922 2.52745i
\(952\) 0 0
\(953\) 0.500000 + 0.866025i 0.0161966 + 0.0280533i 0.874010 0.485908i \(-0.161511\pi\)
−0.857814 + 0.513961i \(0.828178\pi\)
\(954\) 0 0
\(955\) 1.00000 + 1.73205i 0.0323592 + 0.0560478i
\(956\) 0 0
\(957\) 15.0000 0.484881
\(958\) 0 0
\(959\) 7.50000 12.9904i 0.242188 0.419481i
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 0 0
\(963\) −66.0000 −2.12682
\(964\) 0 0
\(965\) −11.0000 + 19.0526i −0.354103 + 0.613324i
\(966\) 0 0
\(967\) −32.0000 −1.02905 −0.514525 0.857475i \(-0.672032\pi\)
−0.514525 + 0.857475i \(0.672032\pi\)
\(968\) 0 0
\(969\) 13.5000 + 23.3827i 0.433682 + 0.751160i
\(970\) 0 0
\(971\) −7.50000 12.9904i −0.240686 0.416881i 0.720224 0.693742i \(-0.244039\pi\)
−0.960910 + 0.276861i \(0.910706\pi\)
\(972\) 0 0
\(973\) 5.50000 9.52628i 0.176322 0.305398i
\(974\) 0 0
\(975\) −7.50000 7.79423i −0.240192 0.249615i
\(976\) 0 0
\(977\) −19.5000 + 33.7750i −0.623860 + 1.08056i 0.364900 + 0.931047i \(0.381103\pi\)
−0.988760 + 0.149511i \(0.952230\pi\)
\(978\) 0 0
\(979\) 22.5000 + 38.9711i 0.719103 + 1.24552i
\(980\) 0 0
\(981\) −30.0000 51.9615i −0.957826 1.65900i
\(982\) 0 0
\(983\) 16.0000 0.510321 0.255160 0.966899i \(-0.417872\pi\)
0.255160 + 0.966899i \(0.417872\pi\)
\(984\) 0 0
\(985\) 9.00000 15.5885i 0.286764 0.496690i
\(986\) 0 0
\(987\) −12.0000 −0.381964
\(988\) 0 0
\(989\) −1.00000 −0.0317982
\(990\) 0 0
\(991\) 13.5000 23.3827i 0.428842 0.742775i −0.567929 0.823078i \(-0.692255\pi\)
0.996771 + 0.0803021i \(0.0255885\pi\)
\(992\) 0 0
\(993\) 51.0000 1.61844
\(994\) 0 0
\(995\) −19.0000 32.9090i −0.602340 1.04328i
\(996\) 0 0
\(997\) −17.5000 30.3109i −0.554231 0.959955i −0.997963 0.0637961i \(-0.979679\pi\)
0.443732 0.896159i \(-0.353654\pi\)
\(998\) 0 0
\(999\) 13.5000 23.3827i 0.427121 0.739795i
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 208.2.i.d.113.1 2
3.2 odd 2 1872.2.t.f.1153.1 2
4.3 odd 2 52.2.e.a.9.1 2
8.3 odd 2 832.2.i.j.321.1 2
8.5 even 2 832.2.i.a.321.1 2
12.11 even 2 468.2.l.a.217.1 2
13.3 even 3 inner 208.2.i.d.81.1 2
13.4 even 6 2704.2.a.a.1.1 1
13.6 odd 12 2704.2.f.a.337.1 2
13.7 odd 12 2704.2.f.a.337.2 2
13.9 even 3 2704.2.a.b.1.1 1
20.3 even 4 1300.2.bb.f.1049.1 4
20.7 even 4 1300.2.bb.f.1049.2 4
20.19 odd 2 1300.2.i.f.1101.1 2
28.3 even 6 2548.2.l.a.373.1 2
28.11 odd 6 2548.2.l.h.373.1 2
28.19 even 6 2548.2.i.h.165.1 2
28.23 odd 6 2548.2.i.a.165.1 2
28.27 even 2 2548.2.k.d.1569.1 2
39.29 odd 6 1872.2.t.f.289.1 2
52.3 odd 6 52.2.e.a.29.1 yes 2
52.7 even 12 676.2.d.d.337.2 2
52.11 even 12 676.2.h.b.361.2 4
52.15 even 12 676.2.h.b.361.1 4
52.19 even 12 676.2.d.d.337.1 2
52.23 odd 6 676.2.e.a.653.1 2
52.31 even 4 676.2.h.b.485.1 4
52.35 odd 6 676.2.a.e.1.1 1
52.43 odd 6 676.2.a.d.1.1 1
52.47 even 4 676.2.h.b.485.2 4
52.51 odd 2 676.2.e.a.529.1 2
104.3 odd 6 832.2.i.j.705.1 2
104.29 even 6 832.2.i.a.705.1 2
156.35 even 6 6084.2.a.f.1.1 1
156.59 odd 12 6084.2.b.l.4393.1 2
156.71 odd 12 6084.2.b.l.4393.2 2
156.95 even 6 6084.2.a.k.1.1 1
156.107 even 6 468.2.l.a.289.1 2
260.3 even 12 1300.2.bb.f.549.2 4
260.107 even 12 1300.2.bb.f.549.1 4
260.159 odd 6 1300.2.i.f.601.1 2
364.3 even 6 2548.2.i.h.1745.1 2
364.55 even 6 2548.2.k.d.393.1 2
364.107 odd 6 2548.2.l.h.1537.1 2
364.159 even 6 2548.2.l.a.1537.1 2
364.263 odd 6 2548.2.i.a.1745.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
52.2.e.a.9.1 2 4.3 odd 2
52.2.e.a.29.1 yes 2 52.3 odd 6
208.2.i.d.81.1 2 13.3 even 3 inner
208.2.i.d.113.1 2 1.1 even 1 trivial
468.2.l.a.217.1 2 12.11 even 2
468.2.l.a.289.1 2 156.107 even 6
676.2.a.d.1.1 1 52.43 odd 6
676.2.a.e.1.1 1 52.35 odd 6
676.2.d.d.337.1 2 52.19 even 12
676.2.d.d.337.2 2 52.7 even 12
676.2.e.a.529.1 2 52.51 odd 2
676.2.e.a.653.1 2 52.23 odd 6
676.2.h.b.361.1 4 52.15 even 12
676.2.h.b.361.2 4 52.11 even 12
676.2.h.b.485.1 4 52.31 even 4
676.2.h.b.485.2 4 52.47 even 4
832.2.i.a.321.1 2 8.5 even 2
832.2.i.a.705.1 2 104.29 even 6
832.2.i.j.321.1 2 8.3 odd 2
832.2.i.j.705.1 2 104.3 odd 6
1300.2.i.f.601.1 2 260.159 odd 6
1300.2.i.f.1101.1 2 20.19 odd 2
1300.2.bb.f.549.1 4 260.107 even 12
1300.2.bb.f.549.2 4 260.3 even 12
1300.2.bb.f.1049.1 4 20.3 even 4
1300.2.bb.f.1049.2 4 20.7 even 4
1872.2.t.f.289.1 2 39.29 odd 6
1872.2.t.f.1153.1 2 3.2 odd 2
2548.2.i.a.165.1 2 28.23 odd 6
2548.2.i.a.1745.1 2 364.263 odd 6
2548.2.i.h.165.1 2 28.19 even 6
2548.2.i.h.1745.1 2 364.3 even 6
2548.2.k.d.393.1 2 364.55 even 6
2548.2.k.d.1569.1 2 28.27 even 2
2548.2.l.a.373.1 2 28.3 even 6
2548.2.l.a.1537.1 2 364.159 even 6
2548.2.l.h.373.1 2 28.11 odd 6
2548.2.l.h.1537.1 2 364.107 odd 6
2704.2.a.a.1.1 1 13.4 even 6
2704.2.a.b.1.1 1 13.9 even 3
2704.2.f.a.337.1 2 13.6 odd 12
2704.2.f.a.337.2 2 13.7 odd 12
6084.2.a.f.1.1 1 156.35 even 6
6084.2.a.k.1.1 1 156.95 even 6
6084.2.b.l.4393.1 2 156.59 odd 12
6084.2.b.l.4393.2 2 156.71 odd 12