Properties

Label 162.2.c.a.109.1
Level $162$
Weight $2$
Character 162.109
Analytic conductor $1.294$
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] = [162,2,Mod(55,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.55");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 162.c (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: \(1.29357651274\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 162.109
Dual form 162.2.c.a.55.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +3.00000 q^{10} +(0.500000 - 0.866025i) q^{13} +(2.00000 - 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} +3.00000 q^{17} -4.00000 q^{19} +(-1.50000 - 2.59808i) q^{20} +(-2.00000 - 3.46410i) q^{25} -1.00000 q^{26} -4.00000 q^{28} +(4.50000 + 7.79423i) q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{34} -12.0000 q^{35} -1.00000 q^{37} +(2.00000 + 3.46410i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(3.00000 - 5.19615i) q^{41} +(-4.00000 - 6.92820i) q^{43} +(-6.00000 - 10.3923i) q^{47} +(-4.50000 + 7.79423i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(0.500000 + 0.866025i) q^{52} +6.00000 q^{53} +(2.00000 + 3.46410i) q^{56} +(4.50000 - 7.79423i) q^{58} +(0.500000 + 0.866025i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(1.50000 + 2.59808i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(6.00000 + 10.3923i) q^{70} +12.0000 q^{71} +11.0000 q^{73} +(0.500000 + 0.866025i) q^{74} +(2.00000 - 3.46410i) q^{76} +(8.00000 + 13.8564i) q^{79} +3.00000 q^{80} -6.00000 q^{82} +(-6.00000 - 10.3923i) q^{83} +(-4.50000 + 7.79423i) q^{85} +(-4.00000 + 6.92820i) q^{86} +3.00000 q^{89} +4.00000 q^{91} +(-6.00000 + 10.3923i) q^{94} +(6.00000 - 10.3923i) q^{95} +(-1.00000 - 1.73205i) q^{97} +9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} - 3 q^{5} + 4 q^{7} + 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - q^{4} - 3 q^{5} + 4 q^{7} + 2 q^{8} + 6 q^{10} + q^{13} + 4 q^{14} - q^{16} + 6 q^{17} - 8 q^{19} - 3 q^{20} - 4 q^{25} - 2 q^{26} - 8 q^{28} + 9 q^{29} + 4 q^{31} - q^{32} - 3 q^{34} - 24 q^{35} - 2 q^{37} + 4 q^{38} - 3 q^{40} + 6 q^{41} - 8 q^{43} - 12 q^{47} - 9 q^{49} - 4 q^{50} + q^{52} + 12 q^{53} + 4 q^{56} + 9 q^{58} + q^{61} - 8 q^{62} + 2 q^{64} + 3 q^{65} + 4 q^{67} - 3 q^{68} + 12 q^{70} + 24 q^{71} + 22 q^{73} + q^{74} + 4 q^{76} + 16 q^{79} + 6 q^{80} - 12 q^{82} - 12 q^{83} - 9 q^{85} - 8 q^{86} + 6 q^{89} + 8 q^{91} - 12 q^{94} + 12 q^{95} - 2 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 0 0
\(7\) 2.00000 + 3.46410i 0.755929 + 1.30931i 0.944911 + 0.327327i \(0.106148\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 3.00000 0.948683
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0 0
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 2.00000 3.46410i 0.534522 0.925820i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) −1.50000 2.59808i −0.335410 0.580948i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) −1.00000 −0.196116
\(27\) 0 0
\(28\) −4.00000 −0.755929
\(29\) 4.50000 + 7.79423i 0.835629 + 1.44735i 0.893517 + 0.449029i \(0.148230\pi\)
−0.0578882 + 0.998323i \(0.518437\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −1.50000 2.59808i −0.257248 0.445566i
\(35\) −12.0000 −2.02837
\(36\) 0 0
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 2.00000 + 3.46410i 0.324443 + 0.561951i
\(39\) 0 0
\(40\) −1.50000 + 2.59808i −0.237171 + 0.410792i
\(41\) 3.00000 5.19615i 0.468521 0.811503i −0.530831 0.847477i \(-0.678120\pi\)
0.999353 + 0.0359748i \(0.0114536\pi\)
\(42\) 0 0
\(43\) −4.00000 6.92820i −0.609994 1.05654i −0.991241 0.132068i \(-0.957838\pi\)
0.381246 0.924473i \(-0.375495\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.00000 10.3923i −0.875190 1.51587i −0.856560 0.516047i \(-0.827403\pi\)
−0.0186297 0.999826i \(-0.505930\pi\)
\(48\) 0 0
\(49\) −4.50000 + 7.79423i −0.642857 + 1.11346i
\(50\) −2.00000 + 3.46410i −0.282843 + 0.489898i
\(51\) 0 0
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.00000 + 3.46410i 0.267261 + 0.462910i
\(57\) 0 0
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.50000 + 2.59808i 0.186052 + 0.322252i
\(66\) 0 0
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) −1.50000 + 2.59808i −0.181902 + 0.315063i
\(69\) 0 0
\(70\) 6.00000 + 10.3923i 0.717137 + 1.24212i
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) 0.500000 + 0.866025i 0.0581238 + 0.100673i
\(75\) 0 0
\(76\) 2.00000 3.46410i 0.229416 0.397360i
\(77\) 0 0
\(78\) 0 0
\(79\) 8.00000 + 13.8564i 0.900070 + 1.55897i 0.827401 + 0.561611i \(0.189818\pi\)
0.0726692 + 0.997356i \(0.476848\pi\)
\(80\) 3.00000 0.335410
\(81\) 0 0
\(82\) −6.00000 −0.662589
\(83\) −6.00000 10.3923i −0.658586 1.14070i −0.980982 0.194099i \(-0.937822\pi\)
0.322396 0.946605i \(-0.395512\pi\)
\(84\) 0 0
\(85\) −4.50000 + 7.79423i −0.488094 + 0.845403i
\(86\) −4.00000 + 6.92820i −0.431331 + 0.747087i
\(87\) 0 0
\(88\) 0 0
\(89\) 3.00000 0.317999 0.159000 0.987279i \(-0.449173\pi\)
0.159000 + 0.987279i \(0.449173\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) 0 0
\(93\) 0 0
\(94\) −6.00000 + 10.3923i −0.618853 + 1.07188i
\(95\) 6.00000 10.3923i 0.615587 1.06623i
\(96\) 0 0
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 9.00000 0.909137
\(99\) 0 0
\(100\) 4.00000 0.400000
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 0 0
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) 0.500000 0.866025i 0.0490290 0.0849208i
\(105\) 0 0
\(106\) −3.00000 5.19615i −0.291386 0.504695i
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 0 0
\(109\) 11.0000 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.00000 3.46410i 0.188982 0.327327i
\(113\) −7.50000 + 12.9904i −0.705541 + 1.22203i 0.260955 + 0.965351i \(0.415962\pi\)
−0.966496 + 0.256681i \(0.917371\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −9.00000 −0.835629
\(117\) 0 0
\(118\) 0 0
\(119\) 6.00000 + 10.3923i 0.550019 + 0.952661i
\(120\) 0 0
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) 0.500000 0.866025i 0.0452679 0.0784063i
\(123\) 0 0
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 1.50000 2.59808i 0.131559 0.227866i
\(131\) −6.00000 + 10.3923i −0.524222 + 0.907980i 0.475380 + 0.879781i \(0.342311\pi\)
−0.999602 + 0.0281993i \(0.991023\pi\)
\(132\) 0 0
\(133\) −8.00000 13.8564i −0.693688 1.20150i
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 3.00000 0.257248
\(137\) 4.50000 + 7.79423i 0.384461 + 0.665906i 0.991694 0.128618i \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(138\) 0 0
\(139\) −10.0000 + 17.3205i −0.848189 + 1.46911i 0.0346338 + 0.999400i \(0.488974\pi\)
−0.882823 + 0.469706i \(0.844360\pi\)
\(140\) 6.00000 10.3923i 0.507093 0.878310i
\(141\) 0 0
\(142\) −6.00000 10.3923i −0.503509 0.872103i
\(143\) 0 0
\(144\) 0 0
\(145\) −27.0000 −2.24223
\(146\) −5.50000 9.52628i −0.455183 0.788400i
\(147\) 0 0
\(148\) 0.500000 0.866025i 0.0410997 0.0711868i
\(149\) 4.50000 7.79423i 0.368654 0.638528i −0.620701 0.784047i \(-0.713152\pi\)
0.989355 + 0.145519i \(0.0464853\pi\)
\(150\) 0 0
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) −4.00000 −0.324443
\(153\) 0 0
\(154\) 0 0
\(155\) 6.00000 + 10.3923i 0.481932 + 0.834730i
\(156\) 0 0
\(157\) 6.50000 11.2583i 0.518756 0.898513i −0.481006 0.876717i \(-0.659728\pi\)
0.999762 0.0217953i \(-0.00693820\pi\)
\(158\) 8.00000 13.8564i 0.636446 1.10236i
\(159\) 0 0
\(160\) −1.50000 2.59808i −0.118585 0.205396i
\(161\) 0 0
\(162\) 0 0
\(163\) 8.00000 0.626608 0.313304 0.949653i \(-0.398564\pi\)
0.313304 + 0.949653i \(0.398564\pi\)
\(164\) 3.00000 + 5.19615i 0.234261 + 0.405751i
\(165\) 0 0
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) 6.00000 10.3923i 0.464294 0.804181i −0.534875 0.844931i \(-0.679641\pi\)
0.999169 + 0.0407502i \(0.0129748\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 9.00000 0.690268
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) −1.50000 2.59808i −0.114043 0.197528i 0.803354 0.595502i \(-0.203047\pi\)
−0.917397 + 0.397974i \(0.869713\pi\)
\(174\) 0 0
\(175\) 8.00000 13.8564i 0.604743 1.04745i
\(176\) 0 0
\(177\) 0 0
\(178\) −1.50000 2.59808i −0.112430 0.194734i
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) −2.00000 3.46410i −0.148250 0.256776i
\(183\) 0 0
\(184\) 0 0
\(185\) 1.50000 2.59808i 0.110282 0.191014i
\(186\) 0 0
\(187\) 0 0
\(188\) 12.0000 0.875190
\(189\) 0 0
\(190\) −12.0000 −0.870572
\(191\) 6.00000 + 10.3923i 0.434145 + 0.751961i 0.997225 0.0744412i \(-0.0237173\pi\)
−0.563081 + 0.826402i \(0.690384\pi\)
\(192\) 0 0
\(193\) 6.50000 11.2583i 0.467880 0.810392i −0.531446 0.847092i \(-0.678351\pi\)
0.999326 + 0.0366998i \(0.0116845\pi\)
\(194\) −1.00000 + 1.73205i −0.0717958 + 0.124354i
\(195\) 0 0
\(196\) −4.50000 7.79423i −0.321429 0.556731i
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 0 0
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) −2.00000 3.46410i −0.141421 0.244949i
\(201\) 0 0
\(202\) −3.00000 + 5.19615i −0.211079 + 0.365600i
\(203\) −18.0000 + 31.1769i −1.26335 + 2.18819i
\(204\) 0 0
\(205\) 9.00000 + 15.5885i 0.628587 + 1.08875i
\(206\) −4.00000 −0.278693
\(207\) 0 0
\(208\) −1.00000 −0.0693375
\(209\) 0 0
\(210\) 0 0
\(211\) −4.00000 + 6.92820i −0.275371 + 0.476957i −0.970229 0.242190i \(-0.922134\pi\)
0.694857 + 0.719148i \(0.255467\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 0 0
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) 24.0000 1.63679
\(216\) 0 0
\(217\) 16.0000 1.08615
\(218\) −5.50000 9.52628i −0.372507 0.645201i
\(219\) 0 0
\(220\) 0 0
\(221\) 1.50000 2.59808i 0.100901 0.174766i
\(222\) 0 0
\(223\) −4.00000 6.92820i −0.267860 0.463947i 0.700449 0.713702i \(-0.252983\pi\)
−0.968309 + 0.249756i \(0.919650\pi\)
\(224\) −4.00000 −0.267261
\(225\) 0 0
\(226\) 15.0000 0.997785
\(227\) −6.00000 10.3923i −0.398234 0.689761i 0.595274 0.803523i \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) 0 0
\(229\) −11.5000 + 19.9186i −0.759941 + 1.31626i 0.182939 + 0.983124i \(0.441439\pi\)
−0.942880 + 0.333133i \(0.891894\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.50000 + 7.79423i 0.295439 + 0.511716i
\(233\) −21.0000 −1.37576 −0.687878 0.725826i \(-0.741458\pi\)
−0.687878 + 0.725826i \(0.741458\pi\)
\(234\) 0 0
\(235\) 36.0000 2.34838
\(236\) 0 0
\(237\) 0 0
\(238\) 6.00000 10.3923i 0.388922 0.673633i
\(239\) 6.00000 10.3923i 0.388108 0.672222i −0.604087 0.796918i \(-0.706462\pi\)
0.992195 + 0.124696i \(0.0397955\pi\)
\(240\) 0 0
\(241\) 6.50000 + 11.2583i 0.418702 + 0.725213i 0.995809 0.0914555i \(-0.0291519\pi\)
−0.577107 + 0.816668i \(0.695819\pi\)
\(242\) −11.0000 −0.707107
\(243\) 0 0
\(244\) −1.00000 −0.0640184
\(245\) −13.5000 23.3827i −0.862483 1.49387i
\(246\) 0 0
\(247\) −2.00000 + 3.46410i −0.127257 + 0.220416i
\(248\) 2.00000 3.46410i 0.127000 0.219971i
\(249\) 0 0
\(250\) 1.50000 + 2.59808i 0.0948683 + 0.164317i
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 8.00000 + 13.8564i 0.501965 + 0.869428i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −7.50000 + 12.9904i −0.467837 + 0.810318i −0.999325 0.0367485i \(-0.988300\pi\)
0.531487 + 0.847066i \(0.321633\pi\)
\(258\) 0 0
\(259\) −2.00000 3.46410i −0.124274 0.215249i
\(260\) −3.00000 −0.186052
\(261\) 0 0
\(262\) 12.0000 0.741362
\(263\) 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) 0 0
\(265\) −9.00000 + 15.5885i −0.552866 + 0.957591i
\(266\) −8.00000 + 13.8564i −0.490511 + 0.849591i
\(267\) 0 0
\(268\) 2.00000 + 3.46410i 0.122169 + 0.211604i
\(269\) −21.0000 −1.28039 −0.640196 0.768211i \(-0.721147\pi\)
−0.640196 + 0.768211i \(0.721147\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) −1.50000 2.59808i −0.0909509 0.157532i
\(273\) 0 0
\(274\) 4.50000 7.79423i 0.271855 0.470867i
\(275\) 0 0
\(276\) 0 0
\(277\) 5.00000 + 8.66025i 0.300421 + 0.520344i 0.976231 0.216731i \(-0.0695395\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(278\) 20.0000 1.19952
\(279\) 0 0
\(280\) −12.0000 −0.717137
\(281\) −13.5000 23.3827i −0.805342 1.39489i −0.916060 0.401042i \(-0.868648\pi\)
0.110717 0.993852i \(-0.464685\pi\)
\(282\) 0 0
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) −6.00000 + 10.3923i −0.356034 + 0.616670i
\(285\) 0 0
\(286\) 0 0
\(287\) 24.0000 1.41668
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 13.5000 + 23.3827i 0.792747 + 1.37308i
\(291\) 0 0
\(292\) −5.50000 + 9.52628i −0.321863 + 0.557483i
\(293\) 4.50000 7.79423i 0.262893 0.455344i −0.704117 0.710084i \(-0.748657\pi\)
0.967009 + 0.254741i \(0.0819901\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.00000 −0.0581238
\(297\) 0 0
\(298\) −9.00000 −0.521356
\(299\) 0 0
\(300\) 0 0
\(301\) 16.0000 27.7128i 0.922225 1.59734i
\(302\) −4.00000 + 6.92820i −0.230174 + 0.398673i
\(303\) 0 0
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) −3.00000 −0.171780
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 6.00000 10.3923i 0.340777 0.590243i
\(311\) 12.0000 20.7846i 0.680458 1.17859i −0.294384 0.955687i \(-0.595114\pi\)
0.974841 0.222900i \(-0.0715523\pi\)
\(312\) 0 0
\(313\) −11.5000 19.9186i −0.650018 1.12586i −0.983118 0.182973i \(-0.941428\pi\)
0.333099 0.942892i \(-0.391906\pi\)
\(314\) −13.0000 −0.733632
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) 10.5000 + 18.1865i 0.589739 + 1.02146i 0.994266 + 0.106932i \(0.0341026\pi\)
−0.404528 + 0.914526i \(0.632564\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.50000 + 2.59808i −0.0838525 + 0.145237i
\(321\) 0 0
\(322\) 0 0
\(323\) −12.0000 −0.667698
\(324\) 0 0
\(325\) −4.00000 −0.221880
\(326\) −4.00000 6.92820i −0.221540 0.383718i
\(327\) 0 0
\(328\) 3.00000 5.19615i 0.165647 0.286910i
\(329\) 24.0000 41.5692i 1.32316 2.29179i
\(330\) 0 0
\(331\) −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i \(-0.981428\pi\)
0.448649 0.893708i \(-0.351905\pi\)
\(332\) 12.0000 0.658586
\(333\) 0 0
\(334\) −12.0000 −0.656611
\(335\) 6.00000 + 10.3923i 0.327815 + 0.567792i
\(336\) 0 0
\(337\) −1.00000 + 1.73205i −0.0544735 + 0.0943508i −0.891976 0.452082i \(-0.850681\pi\)
0.837503 + 0.546433i \(0.184015\pi\)
\(338\) 6.00000 10.3923i 0.326357 0.565267i
\(339\) 0 0
\(340\) −4.50000 7.79423i −0.244047 0.422701i
\(341\) 0 0
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) −4.00000 6.92820i −0.215666 0.373544i
\(345\) 0 0
\(346\) −1.50000 + 2.59808i −0.0806405 + 0.139673i
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 0 0
\(349\) −7.00000 12.1244i −0.374701 0.649002i 0.615581 0.788074i \(-0.288921\pi\)
−0.990282 + 0.139072i \(0.955588\pi\)
\(350\) −16.0000 −0.855236
\(351\) 0 0
\(352\) 0 0
\(353\) −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i \(-0.325675\pi\)
−0.999711 + 0.0240566i \(0.992342\pi\)
\(354\) 0 0
\(355\) −18.0000 + 31.1769i −0.955341 + 1.65470i
\(356\) −1.50000 + 2.59808i −0.0794998 + 0.137698i
\(357\) 0 0
\(358\) 6.00000 + 10.3923i 0.317110 + 0.549250i
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 5.00000 + 8.66025i 0.262794 + 0.455173i
\(363\) 0 0
\(364\) −2.00000 + 3.46410i −0.104828 + 0.181568i
\(365\) −16.5000 + 28.5788i −0.863649 + 1.49588i
\(366\) 0 0
\(367\) −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −3.00000 −0.155963
\(371\) 12.0000 + 20.7846i 0.623009 + 1.07908i
\(372\) 0 0
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −6.00000 10.3923i −0.309426 0.535942i
\(377\) 9.00000 0.463524
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 6.00000 + 10.3923i 0.307794 + 0.533114i
\(381\) 0 0
\(382\) 6.00000 10.3923i 0.306987 0.531717i
\(383\) −6.00000 + 10.3923i −0.306586 + 0.531022i −0.977613 0.210411i \(-0.932520\pi\)
0.671027 + 0.741433i \(0.265853\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −13.0000 −0.661683
\(387\) 0 0
\(388\) 2.00000 0.101535
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −4.50000 + 7.79423i −0.227284 + 0.393668i
\(393\) 0 0
\(394\) −1.50000 2.59808i −0.0755689 0.130889i
\(395\) −48.0000 −2.41514
\(396\) 0 0
\(397\) −25.0000 −1.25471 −0.627357 0.778732i \(-0.715863\pi\)
−0.627357 + 0.778732i \(0.715863\pi\)
\(398\) 2.00000 + 3.46410i 0.100251 + 0.173640i
\(399\) 0 0
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) 0 0
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) 6.00000 0.298511
\(405\) 0 0
\(406\) 36.0000 1.78665
\(407\) 0 0
\(408\) 0 0
\(409\) 12.5000 21.6506i 0.618085 1.07056i −0.371750 0.928333i \(-0.621242\pi\)
0.989835 0.142222i \(-0.0454247\pi\)
\(410\) 9.00000 15.5885i 0.444478 0.769859i
\(411\) 0 0
\(412\) 2.00000 + 3.46410i 0.0985329 + 0.170664i
\(413\) 0 0
\(414\) 0 0
\(415\) 36.0000 1.76717
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) 0 0
\(418\) 0 0
\(419\) −12.0000 + 20.7846i −0.586238 + 1.01539i 0.408481 + 0.912767i \(0.366058\pi\)
−0.994720 + 0.102628i \(0.967275\pi\)
\(420\) 0 0
\(421\) 6.50000 + 11.2583i 0.316791 + 0.548697i 0.979817 0.199899i \(-0.0640614\pi\)
−0.663026 + 0.748596i \(0.730728\pi\)
\(422\) 8.00000 0.389434
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) −6.00000 10.3923i −0.291043 0.504101i
\(426\) 0 0
\(427\) −2.00000 + 3.46410i −0.0967868 + 0.167640i
\(428\) 6.00000 10.3923i 0.290021 0.502331i
\(429\) 0 0
\(430\) −12.0000 20.7846i −0.578691 1.00232i
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 0 0
\(433\) 11.0000 0.528626 0.264313 0.964437i \(-0.414855\pi\)
0.264313 + 0.964437i \(0.414855\pi\)
\(434\) −8.00000 13.8564i −0.384012 0.665129i
\(435\) 0 0
\(436\) −5.50000 + 9.52628i −0.263402 + 0.456226i
\(437\) 0 0
\(438\) 0 0
\(439\) 14.0000 + 24.2487i 0.668184 + 1.15733i 0.978412 + 0.206666i \(0.0662612\pi\)
−0.310228 + 0.950662i \(0.600405\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −3.00000 −0.142695
\(443\) −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i \(-0.258683\pi\)
−0.972626 + 0.232377i \(0.925350\pi\)
\(444\) 0 0
\(445\) −4.50000 + 7.79423i −0.213320 + 0.369482i
\(446\) −4.00000 + 6.92820i −0.189405 + 0.328060i
\(447\) 0 0
\(448\) 2.00000 + 3.46410i 0.0944911 + 0.163663i
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −7.50000 12.9904i −0.352770 0.611016i
\(453\) 0 0
\(454\) −6.00000 + 10.3923i −0.281594 + 0.487735i
\(455\) −6.00000 + 10.3923i −0.281284 + 0.487199i
\(456\) 0 0
\(457\) 0.500000 + 0.866025i 0.0233890 + 0.0405110i 0.877483 0.479608i \(-0.159221\pi\)
−0.854094 + 0.520119i \(0.825888\pi\)
\(458\) 23.0000 1.07472
\(459\) 0 0
\(460\) 0 0
\(461\) 9.00000 + 15.5885i 0.419172 + 0.726027i 0.995856 0.0909401i \(-0.0289872\pi\)
−0.576685 + 0.816967i \(0.695654\pi\)
\(462\) 0 0
\(463\) −4.00000 + 6.92820i −0.185896 + 0.321981i −0.943878 0.330294i \(-0.892852\pi\)
0.757982 + 0.652275i \(0.226185\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) 0 0
\(466\) 10.5000 + 18.1865i 0.486403 + 0.842475i
\(467\) 24.0000 1.11059 0.555294 0.831654i \(-0.312606\pi\)
0.555294 + 0.831654i \(0.312606\pi\)
\(468\) 0 0
\(469\) 16.0000 0.738811
\(470\) −18.0000 31.1769i −0.830278 1.43808i
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 8.00000 + 13.8564i 0.367065 + 0.635776i
\(476\) −12.0000 −0.550019
\(477\) 0 0
\(478\) −12.0000 −0.548867
\(479\) −6.00000 10.3923i −0.274147 0.474837i 0.695773 0.718262i \(-0.255062\pi\)
−0.969920 + 0.243426i \(0.921729\pi\)
\(480\) 0 0
\(481\) −0.500000 + 0.866025i −0.0227980 + 0.0394874i
\(482\) 6.50000 11.2583i 0.296067 0.512803i
\(483\) 0 0
\(484\) 5.50000 + 9.52628i 0.250000 + 0.433013i
\(485\) 6.00000 0.272446
\(486\) 0 0
\(487\) −4.00000 −0.181257 −0.0906287 0.995885i \(-0.528888\pi\)
−0.0906287 + 0.995885i \(0.528888\pi\)
\(488\) 0.500000 + 0.866025i 0.0226339 + 0.0392031i
\(489\) 0 0
\(490\) −13.5000 + 23.3827i −0.609868 + 1.05632i
\(491\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(492\) 0 0
\(493\) 13.5000 + 23.3827i 0.608009 + 1.05310i
\(494\) 4.00000 0.179969
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 24.0000 + 41.5692i 1.07655 + 1.86463i
\(498\) 0 0
\(499\) 20.0000 34.6410i 0.895323 1.55074i 0.0619186 0.998081i \(-0.480278\pi\)
0.833404 0.552664i \(-0.186389\pi\)
\(500\) 1.50000 2.59808i 0.0670820 0.116190i
\(501\) 0 0
\(502\) −12.0000 20.7846i −0.535586 0.927663i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 18.0000 0.800989
\(506\) 0 0
\(507\) 0 0
\(508\) 8.00000 13.8564i 0.354943 0.614779i
\(509\) −15.0000 + 25.9808i −0.664863 + 1.15158i 0.314459 + 0.949271i \(0.398177\pi\)
−0.979322 + 0.202306i \(0.935156\pi\)
\(510\) 0 0
\(511\) 22.0000 + 38.1051i 0.973223 + 1.68567i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 15.0000 0.661622
\(515\) 6.00000 + 10.3923i 0.264392 + 0.457940i
\(516\) 0 0
\(517\) 0 0
\(518\) −2.00000 + 3.46410i −0.0878750 + 0.152204i
\(519\) 0 0
\(520\) 1.50000 + 2.59808i 0.0657794 + 0.113933i
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 0 0
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) −6.00000 10.3923i −0.262111 0.453990i
\(525\) 0 0
\(526\) 6.00000 10.3923i 0.261612 0.453126i
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 18.0000 0.781870
\(531\) 0 0
\(532\) 16.0000 0.693688
\(533\) −3.00000 5.19615i −0.129944 0.225070i
\(534\) 0 0
\(535\) 18.0000 31.1769i 0.778208 1.34790i
\(536\) 2.00000 3.46410i 0.0863868 0.149626i
\(537\) 0 0
\(538\) 10.5000 + 18.1865i 0.452687 + 0.784077i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.00000 −0.0429934 −0.0214967 0.999769i \(-0.506843\pi\)
−0.0214967 + 0.999769i \(0.506843\pi\)
\(542\) 8.00000 + 13.8564i 0.343629 + 0.595184i
\(543\) 0 0
\(544\) −1.50000 + 2.59808i −0.0643120 + 0.111392i
\(545\) −16.5000 + 28.5788i −0.706782 + 1.22418i
\(546\) 0 0
\(547\) −22.0000 38.1051i −0.940652 1.62926i −0.764231 0.644942i \(-0.776881\pi\)
−0.176421 0.984315i \(-0.556452\pi\)
\(548\) −9.00000 −0.384461
\(549\) 0 0
\(550\) 0 0
\(551\) −18.0000 31.1769i −0.766826 1.32818i
\(552\) 0 0
\(553\) −32.0000 + 55.4256i −1.36078 + 2.35694i
\(554\) 5.00000 8.66025i 0.212430 0.367939i
\(555\) 0 0
\(556\) −10.0000 17.3205i −0.424094 0.734553i
\(557\) 3.00000 0.127114 0.0635570 0.997978i \(-0.479756\pi\)
0.0635570 + 0.997978i \(0.479756\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 6.00000 + 10.3923i 0.253546 + 0.439155i
\(561\) 0 0
\(562\) −13.5000 + 23.3827i −0.569463 + 0.986339i
\(563\) 6.00000 10.3923i 0.252870 0.437983i −0.711445 0.702742i \(-0.751959\pi\)
0.964315 + 0.264758i \(0.0852922\pi\)
\(564\) 0 0
\(565\) −22.5000 38.9711i −0.946582 1.63953i
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) 12.0000 0.503509
\(569\) −7.50000 12.9904i −0.314416 0.544585i 0.664897 0.746935i \(-0.268475\pi\)
−0.979313 + 0.202350i \(0.935142\pi\)
\(570\) 0 0
\(571\) 8.00000 13.8564i 0.334790 0.579873i −0.648655 0.761083i \(-0.724668\pi\)
0.983444 + 0.181210i \(0.0580014\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −12.0000 20.7846i −0.500870 0.867533i
\(575\) 0 0
\(576\) 0 0
\(577\) −25.0000 −1.04076 −0.520382 0.853934i \(-0.674210\pi\)
−0.520382 + 0.853934i \(0.674210\pi\)
\(578\) 4.00000 + 6.92820i 0.166378 + 0.288175i
\(579\) 0 0
\(580\) 13.5000 23.3827i 0.560557 0.970913i
\(581\) 24.0000 41.5692i 0.995688 1.72458i
\(582\) 0 0
\(583\) 0 0
\(584\) 11.0000 0.455183
\(585\) 0 0
\(586\) −9.00000 −0.371787
\(587\) −12.0000 20.7846i −0.495293 0.857873i 0.504692 0.863299i \(-0.331606\pi\)
−0.999985 + 0.00542667i \(0.998273\pi\)
\(588\) 0 0
\(589\) −8.00000 + 13.8564i −0.329634 + 0.570943i
\(590\) 0 0
\(591\) 0 0
\(592\) 0.500000 + 0.866025i 0.0205499 + 0.0355934i
\(593\) −33.0000 −1.35515 −0.677574 0.735455i \(-0.736969\pi\)
−0.677574 + 0.735455i \(0.736969\pi\)
\(594\) 0 0
\(595\) −36.0000 −1.47586
\(596\) 4.50000 + 7.79423i 0.184327 + 0.319264i
\(597\) 0 0
\(598\) 0 0
\(599\) −18.0000 + 31.1769i −0.735460 + 1.27385i 0.219061 + 0.975711i \(0.429701\pi\)
−0.954521 + 0.298143i \(0.903633\pi\)
\(600\) 0 0
\(601\) −17.5000 30.3109i −0.713840 1.23641i −0.963405 0.268049i \(-0.913621\pi\)
0.249565 0.968358i \(-0.419712\pi\)
\(602\) −32.0000 −1.30422
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) 16.5000 + 28.5788i 0.670820 + 1.16190i
\(606\) 0 0
\(607\) −10.0000 + 17.3205i −0.405887 + 0.703018i −0.994424 0.105453i \(-0.966371\pi\)
0.588537 + 0.808470i \(0.299704\pi\)
\(608\) 2.00000 3.46410i 0.0811107 0.140488i
\(609\) 0 0
\(610\) 1.50000 + 2.59808i 0.0607332 + 0.105193i
\(611\) −12.0000 −0.485468
\(612\) 0 0
\(613\) 38.0000 1.53481 0.767403 0.641165i \(-0.221549\pi\)
0.767403 + 0.641165i \(0.221549\pi\)
\(614\) −10.0000 17.3205i −0.403567 0.698999i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.50000 + 2.59808i −0.0603877 + 0.104595i −0.894639 0.446790i \(-0.852567\pi\)
0.834251 + 0.551385i \(0.185900\pi\)
\(618\) 0 0
\(619\) −4.00000 6.92820i −0.160774 0.278468i 0.774373 0.632730i \(-0.218066\pi\)
−0.935146 + 0.354262i \(0.884732\pi\)
\(620\) −12.0000 −0.481932
\(621\) 0 0
\(622\) −24.0000 −0.962312
\(623\) 6.00000 + 10.3923i 0.240385 + 0.416359i
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) −11.5000 + 19.9186i −0.459632 + 0.796107i
\(627\) 0 0
\(628\) 6.50000 + 11.2583i 0.259378 + 0.449256i
\(629\) −3.00000 −0.119618
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 8.00000 + 13.8564i 0.318223 + 0.551178i
\(633\) 0 0
\(634\) 10.5000 18.1865i 0.417008 0.722280i
\(635\) 24.0000 41.5692i 0.952411 1.64962i
\(636\) 0 0
\(637\) 4.50000 + 7.79423i 0.178296 + 0.308819i
\(638\) 0 0
\(639\) 0 0
\(640\) 3.00000 0.118585
\(641\) 22.5000 + 38.9711i 0.888697 + 1.53927i 0.841417 + 0.540386i \(0.181722\pi\)
0.0472793 + 0.998882i \(0.484945\pi\)
\(642\) 0 0
\(643\) 2.00000 3.46410i 0.0788723 0.136611i −0.823891 0.566748i \(-0.808201\pi\)
0.902764 + 0.430137i \(0.141535\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.00000 + 10.3923i 0.236067 + 0.408880i
\(647\) −36.0000 −1.41531 −0.707653 0.706560i \(-0.750246\pi\)
−0.707653 + 0.706560i \(0.750246\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 2.00000 + 3.46410i 0.0784465 + 0.135873i
\(651\) 0 0
\(652\) −4.00000 + 6.92820i −0.156652 + 0.271329i
\(653\) 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) 0 0
\(655\) −18.0000 31.1769i −0.703318 1.21818i
\(656\) −6.00000 −0.234261
\(657\) 0 0
\(658\) −48.0000 −1.87123
\(659\) 6.00000 + 10.3923i 0.233727 + 0.404827i 0.958902 0.283738i \(-0.0915745\pi\)
−0.725175 + 0.688565i \(0.758241\pi\)
\(660\) 0 0
\(661\) −11.5000 + 19.9186i −0.447298 + 0.774743i −0.998209 0.0598209i \(-0.980947\pi\)
0.550911 + 0.834564i \(0.314280\pi\)
\(662\) −10.0000 + 17.3205i −0.388661 + 0.673181i
\(663\) 0 0
\(664\) −6.00000 10.3923i −0.232845 0.403300i
\(665\) 48.0000 1.86136
\(666\) 0 0
\(667\) 0 0
\(668\) 6.00000 + 10.3923i 0.232147 + 0.402090i
\(669\) 0 0
\(670\) 6.00000 10.3923i 0.231800 0.401490i
\(671\) 0 0
\(672\) 0 0
\(673\) −5.50000 9.52628i −0.212009 0.367211i 0.740334 0.672239i \(-0.234667\pi\)
−0.952343 + 0.305028i \(0.901334\pi\)
\(674\) 2.00000 0.0770371
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) −3.00000 5.19615i −0.115299 0.199704i 0.802600 0.596518i \(-0.203449\pi\)
−0.917899 + 0.396813i \(0.870116\pi\)
\(678\) 0 0
\(679\) 4.00000 6.92820i 0.153506 0.265880i
\(680\) −4.50000 + 7.79423i −0.172567 + 0.298895i
\(681\) 0 0
\(682\) 0 0
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0 0
\(685\) −27.0000 −1.03162
\(686\) 4.00000 + 6.92820i 0.152721 + 0.264520i
\(687\) 0 0
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) 3.00000 5.19615i 0.114291 0.197958i
\(690\) 0 0
\(691\) 14.0000 + 24.2487i 0.532585 + 0.922464i 0.999276 + 0.0380440i \(0.0121127\pi\)
−0.466691 + 0.884420i \(0.654554\pi\)
\(692\) 3.00000 0.114043
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −30.0000 51.9615i −1.13796 1.97101i
\(696\) 0 0
\(697\) 9.00000 15.5885i 0.340899 0.590455i
\(698\) −7.00000 + 12.1244i −0.264954 + 0.458914i
\(699\) 0 0
\(700\) 8.00000 + 13.8564i 0.302372 + 0.523723i
\(701\) 51.0000 1.92624 0.963122 0.269066i \(-0.0867150\pi\)
0.963122 + 0.269066i \(0.0867150\pi\)
\(702\) 0 0
\(703\) 4.00000 0.150863
\(704\) 0 0
\(705\) 0 0
\(706\) −9.00000 + 15.5885i −0.338719 + 0.586679i
\(707\) 12.0000 20.7846i 0.451306 0.781686i
\(708\) 0 0
\(709\) −23.5000 40.7032i −0.882561 1.52864i −0.848484 0.529221i \(-0.822484\pi\)
−0.0340772 0.999419i \(-0.510849\pi\)
\(710\) 36.0000 1.35106
\(711\) 0 0
\(712\) 3.00000 0.112430
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 6.00000 10.3923i 0.224231 0.388379i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 16.0000 0.595871
\(722\) 1.50000 + 2.59808i 0.0558242 + 0.0966904i
\(723\) 0 0
\(724\) 5.00000 8.66025i 0.185824 0.321856i
\(725\) 18.0000 31.1769i 0.668503 1.15788i
\(726\) 0 0
\(727\) 14.0000 + 24.2487i 0.519231 + 0.899335i 0.999750 + 0.0223506i \(0.00711500\pi\)
−0.480519 + 0.876984i \(0.659552\pi\)
\(728\) 4.00000 0.148250
\(729\) 0 0
\(730\) 33.0000 1.22138
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) 0 0
\(733\) −7.00000 + 12.1244i −0.258551 + 0.447823i −0.965854 0.259087i \(-0.916578\pi\)
0.707303 + 0.706910i \(0.249912\pi\)
\(734\) −4.00000 + 6.92820i −0.147643 + 0.255725i
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 1.50000 + 2.59808i 0.0551411 + 0.0955072i
\(741\) 0 0
\(742\) 12.0000 20.7846i 0.440534 0.763027i
\(743\) 6.00000 10.3923i 0.220119 0.381257i −0.734725 0.678365i \(-0.762689\pi\)
0.954844 + 0.297108i \(0.0960222\pi\)
\(744\) 0 0
\(745\) 13.5000 + 23.3827i 0.494602 + 0.856675i
\(746\) −10.0000 −0.366126
\(747\) 0 0
\(748\) 0 0
\(749\) −24.0000 41.5692i −0.876941 1.51891i
\(750\) 0 0
\(751\) −10.0000 + 17.3205i −0.364905 + 0.632034i −0.988761 0.149505i \(-0.952232\pi\)
0.623856 + 0.781540i \(0.285565\pi\)
\(752\) −6.00000 + 10.3923i −0.218797 + 0.378968i
\(753\) 0 0
\(754\) −4.50000 7.79423i −0.163880 0.283849i
\(755\) 24.0000 0.873449
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 14.0000 + 24.2487i 0.508503 + 0.880753i
\(759\) 0 0
\(760\) 6.00000 10.3923i 0.217643 0.376969i
\(761\) −7.50000 + 12.9904i −0.271875 + 0.470901i −0.969342 0.245716i \(-0.920977\pi\)
0.697467 + 0.716617i \(0.254310\pi\)
\(762\) 0 0
\(763\) 22.0000 + 38.1051i 0.796453 + 1.37950i
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) 12.0000 0.433578
\(767\) 0 0
\(768\) 0 0
\(769\) 18.5000 32.0429i 0.667127 1.15550i −0.311577 0.950221i \(-0.600857\pi\)
0.978704 0.205277i \(-0.0658095\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.50000 + 11.2583i 0.233940 + 0.405196i
\(773\) 27.0000 0.971123 0.485561 0.874203i \(-0.338615\pi\)
0.485561 + 0.874203i \(0.338615\pi\)
\(774\) 0 0
\(775\) −16.0000 −0.574737
\(776\) −1.00000 1.73205i −0.0358979 0.0621770i
\(777\) 0 0
\(778\) −3.00000 + 5.19615i −0.107555 + 0.186291i
\(779\) −12.0000 + 20.7846i −0.429945 + 0.744686i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 9.00000 0.321429
\(785\) 19.5000 + 33.7750i 0.695985 + 1.20548i
\(786\) 0 0
\(787\) −16.0000 + 27.7128i −0.570338 + 0.987855i 0.426193 + 0.904632i \(0.359855\pi\)
−0.996531 + 0.0832226i \(0.973479\pi\)
\(788\) −1.50000 + 2.59808i −0.0534353 + 0.0925526i
\(789\) 0 0
\(790\) 24.0000 + 41.5692i 0.853882 + 1.47897i
\(791\) −60.0000 −2.13335
\(792\) 0 0
\(793\) 1.00000 0.0355110
\(794\) 12.5000 + 21.6506i 0.443608 + 0.768352i
\(795\) 0 0
\(796\) 2.00000 3.46410i 0.0708881 0.122782i
\(797\) −25.5000 + 44.1673i −0.903256 + 1.56449i −0.0800155 + 0.996794i \(0.525497\pi\)
−0.823241 + 0.567692i \(0.807836\pi\)
\(798\) 0 0
\(799\) −18.0000 31.1769i −0.636794 1.10296i
\(800\) 4.00000 0.141421
\(801\) 0 0
\(802\) 3.00000 0.105934
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) −2.00000 + 3.46410i −0.0704470 + 0.122018i
\(807\) 0 0
\(808\) −3.00000 5.19615i −0.105540 0.182800i
\(809\) 39.0000 1.37117 0.685583 0.727994i \(-0.259547\pi\)
0.685583 + 0.727994i \(0.259547\pi\)
\(810\) 0 0
\(811\) −16.0000 −0.561836 −0.280918 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) −18.0000 31.1769i −0.631676 1.09410i
\(813\) 0 0
\(814\) 0 0
\(815\) −12.0000 + 20.7846i −0.420342 + 0.728053i
\(816\) 0 0
\(817\) 16.0000 + 27.7128i 0.559769 + 0.969549i
\(818\) −25.0000 −0.874105
\(819\) 0 0
\(820\) −18.0000 −0.628587
\(821\) −7.50000 12.9904i −0.261752 0.453367i 0.704956 0.709251i \(-0.250967\pi\)
−0.966708 + 0.255884i \(0.917634\pi\)
\(822\) 0 0
\(823\) −22.0000 + 38.1051i −0.766872 + 1.32826i 0.172379 + 0.985031i \(0.444854\pi\)
−0.939251 + 0.343230i \(0.888479\pi\)
\(824\) 2.00000 3.46410i 0.0696733 0.120678i
\(825\) 0 0
\(826\) 0 0
\(827\) 48.0000 1.66912 0.834562 0.550914i \(-0.185721\pi\)
0.834562 + 0.550914i \(0.185721\pi\)
\(828\) 0 0
\(829\) 14.0000 0.486240 0.243120 0.969996i \(-0.421829\pi\)
0.243120 + 0.969996i \(0.421829\pi\)
\(830\) −18.0000 31.1769i −0.624789 1.08217i
\(831\) 0 0
\(832\) 0.500000 0.866025i 0.0173344 0.0300240i
\(833\) −13.5000 + 23.3827i −0.467747 + 0.810162i
\(834\) 0 0
\(835\) 18.0000 + 31.1769i 0.622916 + 1.07892i
\(836\) 0 0
\(837\) 0 0
\(838\) 24.0000 0.829066
\(839\) 12.0000 + 20.7846i 0.414286 + 0.717564i 0.995353 0.0962912i \(-0.0306980\pi\)
−0.581067 + 0.813856i \(0.697365\pi\)
\(840\) 0 0
\(841\) −26.0000 + 45.0333i −0.896552 + 1.55287i
\(842\) 6.50000 11.2583i 0.224005 0.387988i
\(843\) 0 0
\(844\) −4.00000 6.92820i −0.137686 0.238479i
\(845\) −36.0000 −1.23844
\(846\) 0 0
\(847\) 44.0000 1.51186
\(848\) −3.00000 5.19615i −0.103020 0.178437i
\(849\) 0 0
\(850\) −6.00000 + 10.3923i −0.205798 + 0.356453i
\(851\) 0 0
\(852\) 0 0
\(853\) 5.00000 + 8.66025i 0.171197 + 0.296521i 0.938839 0.344358i \(-0.111903\pi\)
−0.767642 + 0.640879i \(0.778570\pi\)
\(854\) 4.00000 0.136877
\(855\) 0 0
\(856\) −12.0000 −0.410152
\(857\) −19.5000 33.7750i −0.666107 1.15373i −0.978984 0.203938i \(-0.934626\pi\)
0.312877 0.949794i \(-0.398707\pi\)
\(858\) 0 0
\(859\) 26.0000 45.0333i 0.887109 1.53652i 0.0438309 0.999039i \(-0.486044\pi\)
0.843278 0.537478i \(-0.180623\pi\)
\(860\) −12.0000 + 20.7846i −0.409197 + 0.708749i
\(861\) 0 0
\(862\) −6.00000 10.3923i −0.204361 0.353963i
\(863\) −24.0000 −0.816970 −0.408485 0.912765i \(-0.633943\pi\)
−0.408485 + 0.912765i \(0.633943\pi\)
\(864\) 0 0
\(865\) 9.00000 0.306009
\(866\) −5.50000 9.52628i −0.186898 0.323716i
\(867\) 0 0
\(868\) −8.00000 + 13.8564i −0.271538 + 0.470317i
\(869\) 0 0
\(870\) 0 0
\(871\) −2.00000 3.46410i −0.0677674 0.117377i
\(872\) 11.0000 0.372507
\(873\) 0 0
\(874\) 0 0
\(875\) −6.00000 10.3923i −0.202837 0.351324i
\(876\) 0 0
\(877\) 12.5000 21.6506i 0.422095 0.731090i −0.574049 0.818821i \(-0.694628\pi\)
0.996144 + 0.0877308i \(0.0279615\pi\)
\(878\) 14.0000 24.2487i 0.472477 0.818354i
\(879\) 0 0
\(880\) 0 0
\(881\) −30.0000 −1.01073 −0.505363 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) 0 0
\(883\) −4.00000 −0.134611 −0.0673054 0.997732i \(-0.521440\pi\)
−0.0673054 + 0.997732i \(0.521440\pi\)
\(884\) 1.50000 + 2.59808i 0.0504505 + 0.0873828i
\(885\) 0 0
\(886\) −6.00000 + 10.3923i −0.201574 + 0.349136i
\(887\) 12.0000 20.7846i 0.402921 0.697879i −0.591156 0.806557i \(-0.701328\pi\)
0.994077 + 0.108678i \(0.0346618\pi\)
\(888\) 0 0
\(889\) −32.0000 55.4256i −1.07325 1.85892i
\(890\) 9.00000 0.301681
\(891\) 0 0
\(892\) 8.00000 0.267860
\(893\) 24.0000 + 41.5692i 0.803129 + 1.39106i
\(894\) 0 0
\(895\) 18.0000 31.1769i 0.601674 1.04213i
\(896\) 2.00000 3.46410i 0.0668153 0.115728i
\(897\) 0 0
\(898\) −9.00000 15.5885i −0.300334 0.520194i
\(899\) 36.0000 1.20067
\(900\) 0 0
\(901\) 18.0000 0.599667
\(902\) 0 0
\(903\) 0 0
\(904\) −7.50000 + 12.9904i −0.249446 + 0.432054i
\(905\) 15.0000 25.9808i 0.498617 0.863630i
\(906\) 0 0
\(907\) 8.00000 + 13.8564i 0.265636 + 0.460094i 0.967730 0.251990i \(-0.0810849\pi\)
−0.702094 + 0.712084i \(0.747752\pi\)
\(908\) 12.0000 0.398234
\(909\) 0 0
\(910\) 12.0000 0.397796
\(911\) 12.0000 + 20.7846i 0.397578 + 0.688625i 0.993426 0.114472i \(-0.0365176\pi\)
−0.595849 + 0.803097i \(0.703184\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.500000 0.866025i 0.0165385 0.0286456i
\(915\) 0 0
\(916\) −11.5000 19.9186i −0.379971 0.658129i
\(917\) −48.0000 −1.58510
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 9.00000 15.5885i 0.296399 0.513378i
\(923\) 6.00000 10.3923i 0.197492 0.342067i
\(924\) 0 0
\(925\) 2.00000 + 3.46410i 0.0657596 + 0.113899i
\(926\) 8.00000 0.262896
\(927\) 0 0
\(928\) −9.00000 −0.295439
\(929\) −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
\(931\) 18.0000 31.1769i 0.589926 1.02178i
\(932\) 10.5000 18.1865i 0.343939 0.595720i
\(933\) 0 0
\(934\) −12.0000 20.7846i −0.392652 0.680093i
\(935\) 0 0
\(936\) 0 0
\(937\) −37.0000 −1.20874 −0.604369 0.796705i \(-0.706575\pi\)
−0.604369 + 0.796705i \(0.706575\pi\)
\(938\) −8.00000 13.8564i −0.261209 0.452428i
\(939\) 0 0
\(940\) −18.0000 + 31.1769i −0.587095 + 1.01688i
\(941\) −13.5000 + 23.3827i −0.440087 + 0.762254i −0.997695 0.0678506i \(-0.978386\pi\)
0.557608 + 0.830104i \(0.311719\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −6.00000 10.3923i −0.194974 0.337705i 0.751918 0.659256i \(-0.229129\pi\)
−0.946892 + 0.321552i \(0.895796\pi\)
\(948\) 0 0
\(949\) 5.50000 9.52628i 0.178538 0.309236i
\(950\) 8.00000 13.8564i 0.259554 0.449561i
\(951\) 0 0
\(952\) 6.00000 + 10.3923i 0.194461 + 0.336817i
\(953\) −9.00000 −0.291539 −0.145769 0.989319i \(-0.546566\pi\)
−0.145769 + 0.989319i \(0.546566\pi\)
\(954\) 0 0
\(955\) −36.0000 −1.16493
\(956\) 6.00000 + 10.3923i 0.194054 + 0.336111i
\(957\) 0 0
\(958\) −6.00000 + 10.3923i −0.193851 + 0.335760i
\(959\) −18.0000 + 31.1769i −0.581250 + 1.00676i
\(960\) 0 0
\(961\) 7.50000 + 12.9904i 0.241935 + 0.419045i
\(962\) 1.00000 0.0322413
\(963\) 0 0
\(964\) −13.0000 −0.418702
\(965\) 19.5000 + 33.7750i 0.627727 + 1.08726i
\(966\) 0 0
\(967\) 2.00000 3.46410i 0.0643157 0.111398i −0.832075 0.554664i \(-0.812847\pi\)
0.896390 + 0.443266i \(0.146180\pi\)
\(968\) 5.50000 9.52628i 0.176777 0.306186i
\(969\) 0 0
\(970\) −3.00000 5.19615i −0.0963242 0.166838i
\(971\) 36.0000 1.15529 0.577647 0.816286i \(-0.303971\pi\)
0.577647 + 0.816286i \(0.303971\pi\)
\(972\) 0 0
\(973\) −80.0000 −2.56468
\(974\) 2.00000 + 3.46410i 0.0640841 + 0.110997i
\(975\) 0 0
\(976\) 0.500000 0.866025i 0.0160046 0.0277208i
\(977\) −9.00000 + 15.5885i −0.287936 + 0.498719i −0.973317 0.229465i \(-0.926302\pi\)
0.685381 + 0.728184i \(0.259636\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 27.0000 0.862483
\(981\) 0 0
\(982\) 0 0
\(983\) 24.0000 + 41.5692i 0.765481 + 1.32585i 0.939992 + 0.341197i \(0.110832\pi\)
−0.174511 + 0.984655i \(0.555834\pi\)
\(984\) 0 0
\(985\) −4.50000 + 7.79423i −0.143382 + 0.248345i
\(986\) 13.5000 23.3827i 0.429928 0.744656i
\(987\) 0 0
\(988\) −2.00000 3.46410i −0.0636285 0.110208i
\(989\) 0 0
\(990\) 0 0
\(991\) −52.0000 −1.65183 −0.825917 0.563791i \(-0.809342\pi\)
−0.825917 + 0.563791i \(0.809342\pi\)
\(992\) 2.00000 + 3.46410i 0.0635001 + 0.109985i
\(993\) 0 0
\(994\) 24.0000 41.5692i 0.761234 1.31850i
\(995\) 6.00000 10.3923i 0.190213 0.329458i
\(996\) 0 0
\(997\) 18.5000 + 32.0429i 0.585901 + 1.01481i 0.994762 + 0.102214i \(0.0325925\pi\)
−0.408862 + 0.912596i \(0.634074\pi\)
\(998\) −40.0000 −1.26618
\(999\) 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 162.2.c.a.109.1 2
3.2 odd 2 162.2.c.d.109.1 2
4.3 odd 2 1296.2.i.b.433.1 2
9.2 odd 6 162.2.c.d.55.1 2
9.4 even 3 162.2.a.d.1.1 yes 1
9.5 odd 6 162.2.a.a.1.1 1
9.7 even 3 inner 162.2.c.a.55.1 2
12.11 even 2 1296.2.i.n.433.1 2
36.7 odd 6 1296.2.i.b.865.1 2
36.11 even 6 1296.2.i.n.865.1 2
36.23 even 6 1296.2.a.c.1.1 1
36.31 odd 6 1296.2.a.l.1.1 1
45.4 even 6 4050.2.a.r.1.1 1
45.13 odd 12 4050.2.c.n.649.1 2
45.14 odd 6 4050.2.a.bh.1.1 1
45.22 odd 12 4050.2.c.n.649.2 2
45.23 even 12 4050.2.c.g.649.2 2
45.32 even 12 4050.2.c.g.649.1 2
63.13 odd 6 7938.2.a.s.1.1 1
63.41 even 6 7938.2.a.n.1.1 1
72.5 odd 6 5184.2.a.y.1.1 1
72.13 even 6 5184.2.a.c.1.1 1
72.59 even 6 5184.2.a.bd.1.1 1
72.67 odd 6 5184.2.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
162.2.a.a.1.1 1 9.5 odd 6
162.2.a.d.1.1 yes 1 9.4 even 3
162.2.c.a.55.1 2 9.7 even 3 inner
162.2.c.a.109.1 2 1.1 even 1 trivial
162.2.c.d.55.1 2 9.2 odd 6
162.2.c.d.109.1 2 3.2 odd 2
1296.2.a.c.1.1 1 36.23 even 6
1296.2.a.l.1.1 1 36.31 odd 6
1296.2.i.b.433.1 2 4.3 odd 2
1296.2.i.b.865.1 2 36.7 odd 6
1296.2.i.n.433.1 2 12.11 even 2
1296.2.i.n.865.1 2 36.11 even 6
4050.2.a.r.1.1 1 45.4 even 6
4050.2.a.bh.1.1 1 45.14 odd 6
4050.2.c.g.649.1 2 45.32 even 12
4050.2.c.g.649.2 2 45.23 even 12
4050.2.c.n.649.1 2 45.13 odd 12
4050.2.c.n.649.2 2 45.22 odd 12
5184.2.a.c.1.1 1 72.13 even 6
5184.2.a.h.1.1 1 72.67 odd 6
5184.2.a.y.1.1 1 72.5 odd 6
5184.2.a.bd.1.1 1 72.59 even 6
7938.2.a.n.1.1 1 63.41 even 6
7938.2.a.s.1.1 1 63.13 odd 6