Properties

Label 1620.1.bp.b.1519.1
Level $1620$
Weight $1$
Character 1620.1519
Analytic conductor $0.808$
Analytic rank $0$
Dimension $18$
Projective image $D_{27}$
CM discriminant -20
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1620,1,Mod(79,1620)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1620, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([27, 28, 27]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1620.79");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1620.bp (of order \(54\), degree \(18\), 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: \(0.808485320465\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\Q(\zeta_{54})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - x^{9} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{27}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{27} - \cdots)\)

Embedding invariants

Embedding label 1519.1
Root \(0.0581448 - 0.998308i\) of defining polynomial
Character \(\chi\) \(=\) 1620.1519
Dual form 1620.1.bp.b.1219.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.993238 + 0.116093i) q^{2} +(-0.0581448 - 0.998308i) q^{3} +(0.973045 - 0.230616i) q^{4} +(0.893633 + 0.448799i) q^{5} +(0.173648 + 0.984808i) q^{6} +(0.479241 + 1.60078i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-0.993238 + 0.116093i) q^{9} +O(q^{10})\) \(q+(-0.993238 + 0.116093i) q^{2} +(-0.0581448 - 0.998308i) q^{3} +(0.973045 - 0.230616i) q^{4} +(0.893633 + 0.448799i) q^{5} +(0.173648 + 0.984808i) q^{6} +(0.479241 + 1.60078i) q^{7} +(-0.939693 + 0.342020i) q^{8} +(-0.993238 + 0.116093i) q^{9} +(-0.939693 - 0.342020i) q^{10} +(-0.286803 - 0.957990i) q^{12} +(-0.661840 - 1.53432i) q^{14} +(0.396080 - 0.918216i) q^{15} +(0.893633 - 0.448799i) q^{16} +(0.973045 - 0.230616i) q^{18} +(0.973045 + 0.230616i) q^{20} +(1.57020 - 0.571507i) q^{21} +(0.164512 - 0.549509i) q^{23} +(0.396080 + 0.918216i) q^{24} +(0.597159 + 0.802123i) q^{25} +(0.173648 + 0.984808i) q^{27} +(0.835488 + 1.44711i) q^{28} +(-0.543613 + 1.26024i) q^{29} +(-0.286803 + 0.957990i) q^{30} +(-0.835488 + 0.549509i) q^{32} +(-0.290162 + 1.64559i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(-0.993238 - 0.116093i) q^{40} +(-1.18624 - 0.138652i) q^{41} +(-1.49324 + 0.749932i) q^{42} +(1.57020 + 1.03274i) q^{43} +(-0.939693 - 0.342020i) q^{45} +(-0.0996057 + 0.564892i) q^{46} +(1.36320 - 1.44491i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(-1.49733 + 0.984808i) q^{49} +(-0.686242 - 0.727374i) q^{50} +(-0.286803 - 0.957990i) q^{54} +(-0.997837 - 1.34033i) q^{56} +(0.393633 - 1.31482i) q^{58} +(0.173648 - 0.984808i) q^{60} +(-0.113155 - 0.0268182i) q^{61} +(-0.661840 - 1.53432i) q^{63} +(0.766044 - 0.642788i) q^{64} +(0.313758 + 0.727374i) q^{67} +(-0.558145 - 0.132283i) q^{69} +(0.0971586 - 1.66815i) q^{70} +(0.893633 - 0.448799i) q^{72} +(0.766044 - 0.642788i) q^{75} +1.00000 q^{80} +(0.973045 - 0.230616i) q^{81} +1.19432 q^{82} +(-1.18624 + 0.138652i) q^{83} +(1.39608 - 0.918216i) q^{84} +(-1.67948 - 0.843467i) q^{86} +(1.28971 + 0.469417i) q^{87} +(1.86668 - 0.679415i) q^{89} +(0.973045 + 0.230616i) q^{90} +(0.0333522 - 0.572636i) q^{92} +(-1.18624 + 1.59340i) q^{94} +(0.597159 + 0.802123i) q^{96} +(1.37287 - 1.15198i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 18 q^{23} - 9 q^{41} - 9 q^{42} - 9 q^{48} - 9 q^{58} + 18 q^{67} - 9 q^{69} - 9 q^{70} + 18 q^{80} - 9 q^{83} + 18 q^{84} - 9 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\) \(811\) \(1297\) \(1541\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{26}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(3\) −0.0581448 0.998308i −0.0581448 0.998308i
\(4\) 0.973045 0.230616i 0.973045 0.230616i
\(5\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(6\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(7\) 0.479241 + 1.60078i 0.479241 + 1.60078i 0.766044 + 0.642788i \(0.222222\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(8\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(9\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(10\) −0.939693 0.342020i −0.939693 0.342020i
\(11\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(12\) −0.286803 0.957990i −0.286803 0.957990i
\(13\) 0 0 0.597159 0.802123i \(-0.296296\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(14\) −0.661840 1.53432i −0.661840 1.53432i
\(15\) 0.396080 0.918216i 0.396080 0.918216i
\(16\) 0.893633 0.448799i 0.893633 0.448799i
\(17\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(18\) 0.973045 0.230616i 0.973045 0.230616i
\(19\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(20\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(21\) 1.57020 0.571507i 1.57020 0.571507i
\(22\) 0 0
\(23\) 0.164512 0.549509i 0.164512 0.549509i −0.835488 0.549509i \(-0.814815\pi\)
1.00000 \(0\)
\(24\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(25\) 0.597159 + 0.802123i 0.597159 + 0.802123i
\(26\) 0 0
\(27\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(28\) 0.835488 + 1.44711i 0.835488 + 1.44711i
\(29\) −0.543613 + 1.26024i −0.543613 + 1.26024i 0.396080 + 0.918216i \(0.370370\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(30\) −0.286803 + 0.957990i −0.286803 + 0.957990i
\(31\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(32\) −0.835488 + 0.549509i −0.835488 + 0.549509i
\(33\) 0 0
\(34\) 0 0
\(35\) −0.290162 + 1.64559i −0.290162 + 1.64559i
\(36\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(37\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.993238 0.116093i −0.993238 0.116093i
\(41\) −1.18624 0.138652i −1.18624 0.138652i −0.500000 0.866025i \(-0.666667\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(42\) −1.49324 + 0.749932i −1.49324 + 0.749932i
\(43\) 1.57020 + 1.03274i 1.57020 + 1.03274i 0.973045 + 0.230616i \(0.0740741\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(44\) 0 0
\(45\) −0.939693 0.342020i −0.939693 0.342020i
\(46\) −0.0996057 + 0.564892i −0.0996057 + 0.564892i
\(47\) 1.36320 1.44491i 1.36320 1.44491i 0.597159 0.802123i \(-0.296296\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(48\) −0.500000 0.866025i −0.500000 0.866025i
\(49\) −1.49733 + 0.984808i −1.49733 + 0.984808i
\(50\) −0.686242 0.727374i −0.686242 0.727374i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) −0.286803 0.957990i −0.286803 0.957990i
\(55\) 0 0
\(56\) −0.997837 1.34033i −0.997837 1.34033i
\(57\) 0 0
\(58\) 0.393633 1.31482i 0.393633 1.31482i
\(59\) 0 0 −0.0581448 0.998308i \(-0.518519\pi\)
0.0581448 + 0.998308i \(0.481481\pi\)
\(60\) 0.173648 0.984808i 0.173648 0.984808i
\(61\) −0.113155 0.0268182i −0.113155 0.0268182i 0.173648 0.984808i \(-0.444444\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(62\) 0 0
\(63\) −0.661840 1.53432i −0.661840 1.53432i
\(64\) 0.766044 0.642788i 0.766044 0.642788i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.313758 + 0.727374i 0.313758 + 0.727374i 1.00000 \(0\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(68\) 0 0
\(69\) −0.558145 0.132283i −0.558145 0.132283i
\(70\) 0.0971586 1.66815i 0.0971586 1.66815i
\(71\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(72\) 0.893633 0.448799i 0.893633 0.448799i
\(73\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(74\) 0 0
\(75\) 0.766044 0.642788i 0.766044 0.642788i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.993238 0.116093i \(-0.0370370\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(80\) 1.00000 1.00000
\(81\) 0.973045 0.230616i 0.973045 0.230616i
\(82\) 1.19432 1.19432
\(83\) −1.18624 + 0.138652i −1.18624 + 0.138652i −0.686242 0.727374i \(-0.740741\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(84\) 1.39608 0.918216i 1.39608 0.918216i
\(85\) 0 0
\(86\) −1.67948 0.843467i −1.67948 0.843467i
\(87\) 1.28971 + 0.469417i 1.28971 + 0.469417i
\(88\) 0 0
\(89\) 1.86668 0.679415i 1.86668 0.679415i 0.893633 0.448799i \(-0.148148\pi\)
0.973045 0.230616i \(-0.0740741\pi\)
\(90\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(91\) 0 0
\(92\) 0.0333522 0.572636i 0.0333522 0.572636i
\(93\) 0 0
\(94\) −1.18624 + 1.59340i −1.18624 + 1.59340i
\(95\) 0 0
\(96\) 0.597159 + 0.802123i 0.597159 + 0.802123i
\(97\) 0 0 0.893633 0.448799i \(-0.148148\pi\)
−0.893633 + 0.448799i \(0.851852\pi\)
\(98\) 1.37287 1.15198i 1.37287 1.15198i
\(99\) 0 0
\(100\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(101\) 0.337935 + 0.0800921i 0.337935 + 0.0800921i 0.396080 0.918216i \(-0.370370\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(102\) 0 0
\(103\) −0.0890830 1.52950i −0.0890830 1.52950i −0.686242 0.727374i \(-0.740741\pi\)
0.597159 0.802123i \(-0.296296\pi\)
\(104\) 0 0
\(105\) 1.65968 + 0.193988i 1.65968 + 0.193988i
\(106\) 0 0
\(107\) −0.893633 + 1.54782i −0.893633 + 1.54782i −0.0581448 + 0.998308i \(0.518519\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(108\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(109\) −0.973045 1.68536i −0.973045 1.68536i −0.686242 0.727374i \(-0.740741\pi\)
−0.286803 0.957990i \(-0.592593\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.14669 + 1.21542i 1.14669 + 1.21542i
\(113\) 0 0 0.835488 0.549509i \(-0.185185\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(114\) 0 0
\(115\) 0.393633 0.417226i 0.393633 0.417226i
\(116\) −0.238329 + 1.35163i −0.238329 + 1.35163i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −0.0581448 + 0.998308i −0.0581448 + 0.998308i
\(121\) −0.993238 0.116093i −0.993238 0.116093i
\(122\) 0.115503 + 0.0135004i 0.115503 + 0.0135004i
\(123\) −0.0694434 + 1.19230i −0.0694434 + 1.19230i
\(124\) 0 0
\(125\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(126\) 0.835488 + 1.44711i 0.835488 + 1.44711i
\(127\) 0.337935 1.91652i 0.337935 1.91652i −0.0581448 0.998308i \(-0.518519\pi\)
0.396080 0.918216i \(-0.370370\pi\)
\(128\) −0.686242 + 0.727374i −0.686242 + 0.727374i
\(129\) 0.939693 1.62760i 0.939693 1.62760i
\(130\) 0 0
\(131\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.396080 0.686030i −0.396080 0.686030i
\(135\) −0.286803 + 0.957990i −0.286803 + 0.957990i
\(136\) 0 0
\(137\) 0 0 −0.597159 0.802123i \(-0.703704\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(138\) 0.569728 + 0.0665916i 0.569728 + 0.0665916i
\(139\) 0 0 0.286803 0.957990i \(-0.407407\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(140\) 0.0971586 + 1.66815i 0.0971586 + 1.66815i
\(141\) −1.52173 1.27688i −1.52173 1.27688i
\(142\) 0 0
\(143\) 0 0
\(144\) −0.835488 + 0.549509i −0.835488 + 0.549509i
\(145\) −1.05138 + 0.882215i −1.05138 + 0.882215i
\(146\) 0 0
\(147\) 1.07020 + 1.43753i 1.07020 + 1.43753i
\(148\) 0 0
\(149\) 1.16212 1.56100i 1.16212 1.56100i 0.396080 0.918216i \(-0.370370\pi\)
0.766044 0.642788i \(-0.222222\pi\)
\(150\) −0.686242 + 0.727374i −0.686242 + 0.727374i
\(151\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.893633 0.448799i \(-0.851852\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(161\) 0.958482 0.958482
\(162\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(163\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(164\) −1.18624 + 0.138652i −1.18624 + 0.138652i
\(165\) 0 0
\(166\) 1.16212 0.275428i 1.16212 0.275428i
\(167\) −1.22650 0.615969i −1.22650 0.615969i −0.286803 0.957990i \(-0.592593\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(168\) −1.28004 + 1.07408i −1.28004 + 1.07408i
\(169\) −0.286803 0.957990i −0.286803 0.957990i
\(170\) 0 0
\(171\) 0 0
\(172\) 1.76604 + 0.642788i 1.76604 + 0.642788i
\(173\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(174\) −1.33549 0.316516i −1.33549 0.316516i
\(175\) −0.997837 + 1.34033i −0.997837 + 1.34033i
\(176\) 0 0
\(177\) 0 0
\(178\) −1.77518 + 0.891529i −1.77518 + 0.891529i
\(179\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(180\) −0.993238 0.116093i −0.993238 0.116093i
\(181\) 1.36912 + 1.14883i 1.36912 + 1.14883i 0.973045 + 0.230616i \(0.0740741\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(182\) 0 0
\(183\) −0.0201935 + 0.114523i −0.0201935 + 0.114523i
\(184\) 0.0333522 + 0.572636i 0.0333522 + 0.572636i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0.993238 1.72034i 0.993238 1.72034i
\(189\) −1.49324 + 0.749932i −1.49324 + 0.749932i
\(190\) 0 0
\(191\) 0 0 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(192\) −0.686242 0.727374i −0.686242 0.727374i
\(193\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1.22985 + 1.30357i −1.22985 + 1.30357i
\(197\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(198\) 0 0
\(199\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(200\) −0.835488 0.549509i −0.835488 0.549509i
\(201\) 0.707900 0.355521i 0.707900 0.355521i
\(202\) −0.344948 0.0403186i −0.344948 0.0403186i
\(203\) −2.27788 0.266246i −2.27788 0.266246i
\(204\) 0 0
\(205\) −0.997837 0.656288i −0.997837 0.656288i
\(206\) 0.266044 + 1.50881i 0.266044 + 1.50881i
\(207\) −0.0996057 + 0.564892i −0.0996057 + 0.564892i
\(208\) 0 0
\(209\) 0 0
\(210\) −1.67098 −1.67098
\(211\) 0 0 0.835488 0.549509i \(-0.185185\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.707900 1.64110i 0.707900 1.64110i
\(215\) 0.939693 + 1.62760i 0.939693 + 1.62760i
\(216\) −0.500000 0.866025i −0.500000 0.866025i
\(217\) 0 0
\(218\) 1.16212 + 1.56100i 1.16212 + 1.56100i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.93293 0.458113i −1.93293 0.458113i −0.993238 0.116093i \(-0.962963\pi\)
−0.939693 0.342020i \(-0.888889\pi\)
\(224\) −1.28004 1.07408i −1.28004 1.07408i
\(225\) −0.686242 0.727374i −0.686242 0.727374i
\(226\) 0 0
\(227\) 1.36912 0.687600i 1.36912 0.687600i 0.396080 0.918216i \(-0.370370\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(228\) 0 0
\(229\) −0.543613 1.26024i −0.543613 1.26024i −0.939693 0.342020i \(-0.888889\pi\)
0.396080 0.918216i \(-0.370370\pi\)
\(230\) −0.342534 + 0.460103i −0.342534 + 0.460103i
\(231\) 0 0
\(232\) 0.0798028 1.37016i 0.0798028 1.37016i
\(233\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(234\) 0 0
\(235\) 1.86668 0.679415i 1.86668 0.679415i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.973045 0.230616i \(-0.0740741\pi\)
−0.973045 + 0.230616i \(0.925926\pi\)
\(240\) −0.0581448 0.998308i −0.0581448 0.998308i
\(241\) −1.77518 + 0.207489i −1.77518 + 0.207489i −0.939693 0.342020i \(-0.888889\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(242\) 1.00000 1.00000
\(243\) −0.286803 0.957990i −0.286803 0.957990i
\(244\) −0.116290 −0.116290
\(245\) −1.78004 + 0.208057i −1.78004 + 0.208057i
\(246\) −0.0694434 1.19230i −0.0694434 1.19230i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.207391 + 1.17617i 0.207391 + 1.17617i
\(250\) −0.286803 0.957990i −0.286803 0.957990i
\(251\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(252\) −0.997837 1.34033i −0.997837 1.34033i
\(253\) 0 0
\(254\) −0.113155 + 1.94280i −0.113155 + 1.94280i
\(255\) 0 0
\(256\) 0.597159 0.802123i 0.597159 0.802123i
\(257\) 0 0 −0.396080 0.918216i \(-0.629630\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(258\) −0.744386 + 1.72568i −0.744386 + 1.72568i
\(259\) 0 0
\(260\) 0 0
\(261\) 0.393633 1.31482i 0.393633 1.31482i
\(262\) 0 0
\(263\) 1.49079 + 0.353324i 1.49079 + 0.353324i 0.893633 0.448799i \(-0.148148\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.786803 1.82401i −0.786803 1.82401i
\(268\) 0.473045 + 0.635410i 0.473045 + 0.635410i
\(269\) −0.893633 + 1.54782i −0.893633 + 1.54782i −0.0581448 + 0.998308i \(0.518519\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(270\) 0.173648 0.984808i 0.173648 0.984808i
\(271\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −0.573606 −0.573606
\(277\) 0 0 0.686242 0.727374i \(-0.259259\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) −0.290162 1.64559i −0.290162 1.64559i
\(281\) 0.0971586 + 0.0639022i 0.0971586 + 0.0639022i 0.597159 0.802123i \(-0.296296\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(282\) 1.65968 + 1.09159i 1.65968 + 1.09159i
\(283\) −1.93293 0.225927i −1.93293 0.225927i −0.939693 0.342020i \(-0.888889\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.346545 1.96536i −0.346545 1.96536i
\(288\) 0.766044 0.642788i 0.766044 0.642788i
\(289\) 0.173648 0.984808i 0.173648 0.984808i
\(290\) 0.941855 0.998308i 0.941855 0.998308i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(294\) −1.22985 1.30357i −1.22985 1.30357i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −0.973045 + 1.68536i −0.973045 + 1.68536i
\(299\) 0 0
\(300\) 0.597159 0.802123i 0.597159 0.802123i
\(301\) −0.900679 + 3.00848i −0.900679 + 3.00848i
\(302\) 0 0
\(303\) 0.0603074 0.342020i 0.0603074 0.342020i
\(304\) 0 0
\(305\) −0.0890830 0.0747496i −0.0890830 0.0747496i
\(306\) 0 0
\(307\) −0.439408 + 0.368707i −0.439408 + 0.368707i −0.835488 0.549509i \(-0.814815\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(308\) 0 0
\(309\) −1.52173 + 0.177865i −1.52173 + 0.177865i
\(310\) 0 0
\(311\) 0 0 0.597159 0.802123i \(-0.296296\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(312\) 0 0
\(313\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(314\) 0 0
\(315\) 0.0971586 1.66815i 0.0971586 1.66815i
\(316\) 0 0
\(317\) 0 0 −0.286803 0.957990i \(-0.592593\pi\)
0.286803 + 0.957990i \(0.407407\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.973045 0.230616i 0.973045 0.230616i
\(321\) 1.59716 + 0.802123i 1.59716 + 0.802123i
\(322\) −0.952002 + 0.111273i −0.952002 + 0.111273i
\(323\) 0 0
\(324\) 0.893633 0.448799i 0.893633 0.448799i
\(325\) 0 0
\(326\) −0.344948 + 0.0403186i −0.344948 + 0.0403186i
\(327\) −1.62593 + 1.06939i −1.62593 + 1.06939i
\(328\) 1.16212 0.275428i 1.16212 0.275428i
\(329\) 2.96628 + 1.48972i 2.96628 + 1.48972i
\(330\) 0 0
\(331\) 0 0 −0.286803 0.957990i \(-0.592593\pi\)
0.286803 + 0.957990i \(0.407407\pi\)
\(332\) −1.12229 + 0.408481i −1.12229 + 0.408481i
\(333\) 0 0
\(334\) 1.28971 + 0.469417i 1.28971 + 0.469417i
\(335\) −0.0460600 + 0.790819i −0.0460600 + 0.790819i
\(336\) 1.14669 1.21542i 1.14669 1.21542i
\(337\) 0 0 0.597159 0.802123i \(-0.296296\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(338\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1.01400 0.850845i −1.01400 0.850845i
\(344\) −1.82873 0.433416i −1.82873 0.433416i
\(345\) −0.439408 0.368707i −0.439408 0.368707i
\(346\) 0 0
\(347\) −0.0996057 + 0.332706i −0.0996057 + 0.332706i −0.993238 0.116093i \(-0.962963\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(348\) 1.36320 + 0.159336i 1.36320 + 0.159336i
\(349\) −1.18624 1.59340i −1.18624 1.59340i −0.686242 0.727374i \(-0.740741\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(350\) 0.835488 1.44711i 0.835488 1.44711i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.65968 1.09159i 1.65968 1.09159i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(360\) 1.00000 1.00000
\(361\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(362\) −1.49324 0.982118i −1.49324 0.982118i
\(363\) −0.0581448 + 0.998308i −0.0581448 + 0.998308i
\(364\) 0 0
\(365\) 0 0
\(366\) 0.00676164 0.116093i 0.00676164 0.116093i
\(367\) 0.835488 + 0.549509i 0.835488 + 0.549509i 0.893633 0.448799i \(-0.148148\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(368\) −0.0996057 0.564892i −0.0996057 0.564892i
\(369\) 1.19432 1.19432
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.835488 0.549509i \(-0.185185\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(374\) 0 0
\(375\) 0.973045 0.230616i 0.973045 0.230616i
\(376\) −0.786803 + 1.82401i −0.786803 + 1.82401i
\(377\) 0 0
\(378\) 1.39608 0.918216i 1.39608 0.918216i
\(379\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(380\) 0 0
\(381\) −1.93293 0.225927i −1.93293 0.225927i
\(382\) 0 0
\(383\) −0.0201935 0.346709i −0.0201935 0.346709i −0.993238 0.116093i \(-0.962963\pi\)
0.973045 0.230616i \(-0.0740741\pi\)
\(384\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(385\) 0 0
\(386\) 0 0
\(387\) −1.67948 0.843467i −1.67948 0.843467i
\(388\) 0 0
\(389\) 0.707900 0.355521i 0.707900 0.355521i −0.0581448 0.998308i \(-0.518519\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.07020 1.43753i 1.07020 1.43753i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(401\) −1.82873 + 0.433416i −1.82873 + 0.433416i −0.993238 0.116093i \(-0.962963\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(402\) −0.661840 + 0.435299i −0.661840 + 0.435299i
\(403\) 0 0
\(404\) 0.347296 0.347296
\(405\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(406\) 2.29339 2.29339
\(407\) 0 0
\(408\) 0 0
\(409\) 1.49079 0.353324i 1.49079 0.353324i 0.597159 0.802123i \(-0.296296\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(410\) 1.06728 + 0.536009i 1.06728 + 0.536009i
\(411\) 0 0
\(412\) −0.439408 1.46773i −0.439408 1.46773i
\(413\) 0 0
\(414\) 0.0333522 0.572636i 0.0333522 0.572636i
\(415\) −1.12229 0.408481i −1.12229 0.408481i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.396080 0.918216i \(-0.629630\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(420\) 1.65968 0.193988i 1.65968 0.193988i
\(421\) −1.67948 + 0.843467i −1.67948 + 0.843467i −0.686242 + 0.727374i \(0.740741\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(422\) 0 0
\(423\) −1.18624 + 1.59340i −1.18624 + 1.59340i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.0112985 0.193988i −0.0112985 0.193988i
\(428\) −0.512593 + 1.71218i −0.512593 + 1.71218i
\(429\) 0 0
\(430\) −1.12229 1.50750i −1.12229 1.50750i
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 0.597159 + 0.802123i 0.597159 + 0.802123i
\(433\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(434\) 0 0
\(435\) 0.941855 + 0.998308i 0.941855 + 0.998308i
\(436\) −1.33549 1.41553i −1.33549 1.41553i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.686242 0.727374i \(-0.259259\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(440\) 0 0
\(441\) 1.37287 1.15198i 1.37287 1.15198i
\(442\) 0 0
\(443\) −0.661840 0.435299i −0.661840 0.435299i 0.173648 0.984808i \(-0.444444\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(444\) 0 0
\(445\) 1.97304 + 0.230616i 1.97304 + 0.230616i
\(446\) 1.97304 + 0.230616i 1.97304 + 0.230616i
\(447\) −1.62593 1.06939i −1.62593 1.06939i
\(448\) 1.39608 + 0.918216i 1.39608 + 0.918216i
\(449\) 0.0603074 + 0.342020i 0.0603074 + 0.342020i 1.00000 \(0\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(450\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −1.28004 + 0.841897i −1.28004 + 0.841897i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(458\) 0.686242 + 1.18861i 0.686242 + 1.18861i
\(459\) 0 0
\(460\) 0.286803 0.496758i 0.286803 0.496758i
\(461\) 1.06728 + 1.43361i 1.06728 + 1.43361i 0.893633 + 0.448799i \(0.148148\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(462\) 0 0
\(463\) −0.439408 + 1.46773i −0.439408 + 1.46773i 0.396080 + 0.918216i \(0.370370\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(464\) 0.0798028 + 1.37016i 0.0798028 + 1.37016i
\(465\) 0 0
\(466\) 0 0
\(467\) −1.43969 1.20805i −1.43969 1.20805i −0.939693 0.342020i \(-0.888889\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(468\) 0 0
\(469\) −1.01400 + 0.850845i −1.01400 + 0.850845i
\(470\) −1.77518 + 0.891529i −1.77518 + 0.891529i
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.286803 0.957990i \(-0.592593\pi\)
0.286803 + 0.957990i \(0.407407\pi\)
\(480\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(481\) 0 0
\(482\) 1.73909 0.412172i 1.73909 0.412172i
\(483\) −0.0557308 0.956861i −0.0557308 0.956861i
\(484\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(485\) 0 0
\(486\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(487\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 0.115503 0.0135004i 0.115503 0.0135004i
\(489\) −0.0201935 0.346709i −0.0201935 0.346709i
\(490\) 1.74385 0.413300i 1.74385 0.413300i
\(491\) 0 0 −0.893633 0.448799i \(-0.851852\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(492\) 0.207391 + 1.17617i 0.207391 + 1.17617i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.342534 1.14414i −0.342534 1.14414i
\(499\) 0 0 0.597159 0.802123i \(-0.296296\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(500\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(501\) −0.543613 + 1.26024i −0.543613 + 1.26024i
\(502\) 0 0
\(503\) −0.0890830 + 0.0747496i −0.0890830 + 0.0747496i −0.686242 0.727374i \(-0.740741\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(504\) 1.14669 + 1.21542i 1.14669 + 1.21542i
\(505\) 0.266044 + 0.223238i 0.266044 + 0.223238i
\(506\) 0 0
\(507\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(508\) −0.113155 1.94280i −0.113155 1.94280i
\(509\) 0.0333522 0.111404i 0.0333522 0.111404i −0.939693 0.342020i \(-0.888889\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(513\) 0 0
\(514\) 0 0
\(515\) 0.606829 1.40679i 0.606829 1.40679i
\(516\) 0.539014 1.80043i 0.539014 1.80043i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.0996057 + 0.564892i −0.0996057 + 0.564892i 0.893633 + 0.448799i \(0.148148\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(522\) −0.238329 + 1.35163i −0.238329 + 1.35163i
\(523\) −0.0201935 0.114523i −0.0201935 0.114523i 0.973045 0.230616i \(-0.0740741\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(524\) 0 0
\(525\) 1.39608 + 0.918216i 1.39608 + 0.918216i
\(526\) −1.52173 0.177865i −1.52173 0.177865i
\(527\) 0 0
\(528\) 0 0
\(529\) 0.560592 + 0.368707i 0.560592 + 0.368707i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0.993238 + 1.72034i 0.993238 + 1.72034i
\(535\) −1.49324 + 0.982118i −1.49324 + 0.982118i
\(536\) −0.543613 0.576196i −0.543613 0.576196i
\(537\) 0 0
\(538\) 0.707900 1.64110i 0.707900 1.64110i
\(539\) 0 0
\(540\) −0.0581448 + 0.998308i −0.0581448 + 0.998308i
\(541\) 0.0581448 0.100710i 0.0581448 0.100710i −0.835488 0.549509i \(-0.814815\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(542\) 0 0
\(543\) 1.06728 1.43361i 1.06728 1.43361i
\(544\) 0 0
\(545\) −0.113155 1.94280i −0.113155 1.94280i
\(546\) 0 0
\(547\) 0.770807 + 0.182685i 0.770807 + 0.182685i 0.597159 0.802123i \(-0.296296\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(548\) 0 0
\(549\) 0.115503 + 0.0135004i 0.115503 + 0.0135004i
\(550\) 0 0
\(551\) 0 0
\(552\) 0.569728 0.0665916i 0.569728 0.0665916i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.479241 + 1.60078i 0.479241 + 1.60078i
\(561\) 0 0
\(562\) −0.103920 0.0521907i −0.103920 0.0521907i
\(563\) 1.16212 0.275428i 1.16212 0.275428i 0.396080 0.918216i \(-0.370370\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(564\) −1.77518 0.891529i −1.77518 0.891529i
\(565\) 0 0
\(566\) 1.94609 1.94609
\(567\) 0.835488 + 1.44711i 0.835488 + 1.44711i
\(568\) 0 0
\(569\) 1.86668 0.218183i 1.86668 0.218183i 0.893633 0.448799i \(-0.148148\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(570\) 0 0
\(571\) 0 0 0.973045 0.230616i \(-0.0740741\pi\)
−0.973045 + 0.230616i \(0.925926\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.572366 + 1.91184i 0.572366 + 1.91184i
\(575\) 0.539014 0.196185i 0.539014 0.196185i
\(576\) −0.686242 + 0.727374i −0.686242 + 0.727374i
\(577\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(578\) −0.0581448 + 0.998308i −0.0581448 + 0.998308i
\(579\) 0 0
\(580\) −0.819590 + 1.10090i −0.819590 + 1.10090i
\(581\) −0.790446 1.83246i −0.790446 1.83246i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −0.113155 0.0268182i −0.113155 0.0268182i 0.173648 0.984808i \(-0.444444\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(588\) 1.37287 + 1.15198i 1.37287 + 1.15198i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.770807 1.78693i 0.770807 1.78693i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.835488 0.549509i \(-0.185185\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(600\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(601\) 1.28971 1.36702i 1.28971 1.36702i 0.396080 0.918216i \(-0.370370\pi\)
0.893633 0.448799i \(-0.148148\pi\)
\(602\) 0.545326 3.09270i 0.545326 3.09270i
\(603\) −0.396080 0.686030i −0.396080 0.686030i
\(604\) 0 0
\(605\) −0.835488 0.549509i −0.835488 0.549509i
\(606\) −0.0201935 + 0.346709i −0.0201935 + 0.346709i
\(607\) 1.36320 + 0.159336i 1.36320 + 0.159336i 0.766044 0.642788i \(-0.222222\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(608\) 0 0
\(609\) −0.133349 + 2.28951i −0.133349 + 2.28951i
\(610\) 0.0971586 + 0.0639022i 0.0971586 + 0.0639022i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(614\) 0.393633 0.417226i 0.393633 0.417226i
\(615\) −0.597159 + 1.03431i −0.597159 + 1.03431i
\(616\) 0 0
\(617\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(618\) 1.49079 0.353324i 1.49079 0.353324i
\(619\) 0 0 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(620\) 0 0
\(621\) 0.569728 + 0.0665916i 0.569728 + 0.0665916i
\(622\) 0 0
\(623\) 1.98218 + 2.66253i 1.98218 + 2.66253i
\(624\) 0 0
\(625\) −0.286803 + 0.957990i −0.286803 + 0.957990i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0.0971586 + 1.66815i 0.0971586 + 1.66815i
\(631\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.16212 1.56100i 1.16212 1.56100i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(641\) −0.512593 1.71218i −0.512593 1.71218i −0.686242 0.727374i \(-0.740741\pi\)
0.173648 0.984808i \(-0.444444\pi\)
\(642\) −1.67948 0.611281i −1.67948 0.611281i
\(643\) −1.22650 0.615969i −1.22650 0.615969i −0.286803 0.957990i \(-0.592593\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(644\) 0.932646 0.221041i 0.932646 0.221041i
\(645\) 1.57020 1.03274i 1.57020 1.03274i
\(646\) 0 0
\(647\) 1.94609 1.94609 0.973045 0.230616i \(-0.0740741\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(648\) −0.835488 + 0.549509i −0.835488 + 0.549509i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.337935 0.0800921i 0.337935 0.0800921i
\(653\) 0 0 −0.893633 0.448799i \(-0.851852\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(654\) 1.49079 1.25092i 1.49079 1.25092i
\(655\) 0 0
\(656\) −1.12229 + 0.408481i −1.12229 + 0.408481i
\(657\) 0 0
\(658\) −3.11917 1.13529i −3.11917 1.13529i
\(659\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(660\) 0 0
\(661\) 0.914900 1.22892i 0.914900 1.22892i −0.0581448 0.998308i \(-0.518519\pi\)
0.973045 0.230616i \(-0.0740741\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 1.06728 0.536009i 1.06728 0.536009i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.603080 + 0.506044i 0.603080 + 0.506044i
\(668\) −1.33549 0.316516i −1.33549 0.316516i
\(669\) −0.344948 + 1.95630i −0.344948 + 1.95630i
\(670\) −0.0460600 0.790819i −0.0460600 0.790819i
\(671\) 0 0
\(672\) −0.997837 + 1.34033i −0.997837 + 1.34033i
\(673\) 0 0 −0.597159 0.802123i \(-0.703704\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(674\) 0 0
\(675\) −0.686242 + 0.727374i −0.686242 + 0.727374i
\(676\) −0.500000 0.866025i −0.500000 0.866025i
\(677\) 0 0 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −0.766044 1.32683i −0.766044 1.32683i
\(682\) 0 0
\(683\) −0.326352 + 1.85083i −0.326352 + 1.85083i 0.173648 + 0.984808i \(0.444444\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.10592 + 0.727374i 1.10592 + 0.727374i
\(687\) −1.22650 + 0.615969i −1.22650 + 0.615969i
\(688\) 1.86668 + 0.218183i 1.86668 + 0.218183i
\(689\) 0 0
\(690\) 0.479241 + 0.315202i 0.479241 + 0.315202i
\(691\) 0 0 −0.835488 0.549509i \(-0.814815\pi\)
0.835488 + 0.549509i \(0.185185\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.0603074 0.342020i 0.0603074 0.342020i
\(695\) 0 0
\(696\) −1.37248 −1.37248
\(697\) 0 0
\(698\) 1.36320 + 1.44491i 1.36320 + 1.44491i
\(699\) 0 0
\(700\) −0.661840 + 1.53432i −0.661840 + 1.53432i
\(701\) 0.993238 + 1.72034i 0.993238 + 1.72034i 0.597159 + 0.802123i \(0.296296\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −0.786803 1.82401i −0.786803 1.82401i
\(706\) 0 0
\(707\) 0.0337428 + 0.579342i 0.0337428 + 0.579342i
\(708\) 0 0
\(709\) 0.770807 + 0.182685i 0.770807 + 0.182685i 0.597159 0.802123i \(-0.296296\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.52173 + 1.27688i −1.52173 + 1.27688i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(720\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(721\) 2.40569 0.875600i 2.40569 0.875600i
\(722\) −0.286803 0.957990i −0.286803 0.957990i
\(723\) 0.310355 + 1.76011i 0.310355 + 1.76011i
\(724\) 1.59716 + 0.802123i 1.59716 + 0.802123i
\(725\) −1.33549 + 0.316516i −1.33549 + 0.316516i
\(726\) −0.0581448 0.998308i −0.0581448 0.998308i
\(727\) 0.115503 0.0135004i 0.115503 0.0135004i −0.0581448 0.998308i \(-0.518519\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(728\) 0 0
\(729\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.00676164 + 0.116093i 0.00676164 + 0.116093i
\(733\) 0 0 0.973045 0.230616i \(-0.0740741\pi\)
−0.973045 + 0.230616i \(0.925926\pi\)
\(734\) −0.893633 0.448799i −0.893633 0.448799i
\(735\) 0.311205 + 1.76493i 0.311205 + 1.76493i
\(736\) 0.164512 + 0.549509i 0.164512 + 0.549509i
\(737\) 0 0
\(738\) −1.18624 + 0.138652i −1.18624 + 0.138652i
\(739\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.786803 1.82401i −0.786803 1.82401i −0.500000 0.866025i \(-0.666667\pi\)
−0.286803 0.957990i \(-0.592593\pi\)
\(744\) 0 0
\(745\) 1.73909 0.873403i 1.73909 0.873403i
\(746\) 0 0
\(747\) 1.16212 0.275428i 1.16212 0.275428i
\(748\) 0 0
\(749\) −2.90598 0.688729i −2.90598 0.688729i
\(750\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(751\) 0 0 −0.0581448 0.998308i \(-0.518519\pi\)
0.0581448 + 0.998308i \(0.481481\pi\)
\(752\) 0.569728 1.90302i 0.569728 1.90302i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −1.28004 + 1.07408i −1.28004 + 1.07408i
\(757\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.661840 + 0.435299i −0.661840 + 0.435299i −0.835488 0.549509i \(-0.814815\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(762\) 1.94609 1.94609
\(763\) 2.23157 2.36532i 2.23157 2.36532i
\(764\) 0 0
\(765\) 0 0
\(766\) 0.0603074 + 0.342020i 0.0603074 + 0.342020i
\(767\) 0 0
\(768\) −0.835488 0.549509i −0.835488 0.549509i
\(769\) 1.65968 + 0.193988i 1.65968 + 0.193988i 0.893633 0.448799i \(-0.148148\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(774\) 1.76604 + 0.642788i 1.76604 + 0.642788i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −0.661840 + 0.435299i −0.661840 + 0.435299i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −1.33549 0.316516i −1.33549 0.316516i
\(784\) −0.896080 + 1.55206i −0.896080 + 1.55206i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.286803 0.957990i 0.286803 0.957990i −0.686242 0.727374i \(-0.740741\pi\)
0.973045 0.230616i \(-0.0740741\pi\)
\(788\) 0 0
\(789\) 0.266044 1.50881i 0.266044 1.50881i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.597159 0.802123i \(-0.296296\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.939693 0.342020i −0.939693 0.342020i
\(801\) −1.77518 + 0.891529i −1.77518 + 0.891529i
\(802\) 1.76604 0.642788i 1.76604 0.642788i
\(803\) 0 0
\(804\) 0.606829 0.509190i 0.606829 0.509190i
\(805\) 0.856531 + 0.430166i 0.856531 + 0.430166i
\(806\) 0 0
\(807\) 1.59716 + 0.802123i 1.59716 + 0.802123i
\(808\) −0.344948 + 0.0403186i −0.344948 + 0.0403186i
\(809\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(810\) −0.993238 0.116093i −0.993238 0.116093i
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) −2.27788 + 0.266246i −2.27788 + 0.266246i
\(813\) 0 0
\(814\) 0 0
\(815\) 0.310355 + 0.155866i 0.310355 + 0.155866i
\(816\) 0 0
\(817\) 0 0
\(818\) −1.43969 + 0.524005i −1.43969 + 0.524005i
\(819\) 0 0
\(820\) −1.12229 0.408481i −1.12229 0.408481i
\(821\) 0.0333522 0.572636i 0.0333522 0.572636i −0.939693 0.342020i \(-0.888889\pi\)
0.973045 0.230616i \(-0.0740741\pi\)
\(822\) 0 0
\(823\) −0.0694434 + 0.0932786i −0.0694434 + 0.0932786i −0.835488 0.549509i \(-0.814815\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(824\) 0.606829 + 1.40679i 0.606829 + 1.40679i
\(825\) 0 0
\(826\) 0 0
\(827\) −1.05138 + 0.882215i −1.05138 + 0.882215i −0.993238 0.116093i \(-0.962963\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(828\) 0.0333522 + 0.572636i 0.0333522 + 0.572636i
\(829\) −0.439408 0.368707i −0.439408 0.368707i 0.396080 0.918216i \(-0.370370\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(830\) 1.16212 + 0.275428i 1.16212 + 0.275428i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −0.819590 1.10090i −0.819590 1.10090i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(840\) −1.62593 + 0.385353i −1.62593 + 0.385353i
\(841\) −0.606439 0.642788i −0.606439 0.642788i
\(842\) 1.57020 1.03274i 1.57020 1.03274i
\(843\) 0.0581448 0.100710i 0.0581448 0.100710i
\(844\) 0 0
\(845\) 0.173648 0.984808i 0.173648 0.984808i
\(846\) 0.993238 1.72034i 0.993238 1.72034i
\(847\) −0.290162 1.64559i −0.290162 1.64559i
\(848\) 0 0
\(849\) −0.113155 + 1.94280i −0.113155 + 1.94280i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.835488 0.549509i \(-0.814815\pi\)
0.835488 + 0.549509i \(0.185185\pi\)
\(854\) 0.0337428 + 0.191365i 0.0337428 + 0.191365i
\(855\) 0 0
\(856\) 0.310355 1.76011i 0.310355 1.76011i
\(857\) 0 0 0.686242 0.727374i \(-0.259259\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(858\) 0 0
\(859\) 0 0 0.835488 0.549509i \(-0.185185\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(860\) 1.28971 + 1.36702i 1.28971 + 1.36702i
\(861\) −1.94188 + 0.460234i −1.94188 + 0.460234i
\(862\) 0 0
\(863\) −0.893633 1.54782i −0.893633 1.54782i −0.835488 0.549509i \(-0.814815\pi\)
−0.0581448 0.998308i \(-0.518519\pi\)
\(864\) −0.686242 0.727374i −0.686242 0.727374i
\(865\) 0 0
\(866\) 0 0
\(867\) −0.993238 0.116093i −0.993238 0.116093i
\(868\) 0 0
\(869\) 0 0
\(870\) −1.05138 0.882215i −1.05138 0.882215i
\(871\) 0 0
\(872\) 1.49079 + 1.25092i 1.49079 + 1.25092i
\(873\) 0 0
\(874\) 0 0
\(875\) −1.49324 + 0.749932i −1.49324 + 0.749932i
\(876\) 0 0
\(877\) 0 0 −0.396080 0.918216i \(-0.629630\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.82873 0.665602i −1.82873 0.665602i −0.993238 0.116093i \(-0.962963\pi\)
−0.835488 0.549509i \(-0.814815\pi\)
\(882\) −1.22985 + 1.30357i −1.22985 + 1.30357i
\(883\) −1.12229 + 0.408481i −1.12229 + 0.408481i −0.835488 0.549509i \(-0.814815\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0.707900 + 0.355521i 0.707900 + 0.355521i
\(887\) 0.337935 0.0800921i 0.337935 0.0800921i −0.0581448 0.998308i \(-0.518519\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(888\) 0 0
\(889\) 3.22988 0.377519i 3.22988 0.377519i
\(890\) −1.98648 −1.98648
\(891\) 0 0
\(892\) −1.98648 −1.98648
\(893\) 0 0
\(894\) 1.73909 + 0.873403i 1.73909 + 0.873403i
\(895\) 0 0
\(896\) −1.49324 0.749932i −1.49324 0.749932i
\(897\) 0 0
\(898\) −0.0996057 0.332706i −0.0996057 0.332706i
\(899\) 0 0
\(900\) −0.835488 0.549509i −0.835488 0.549509i
\(901\) 0 0
\(902\) 0 0
\(903\) 3.05576 + 0.724228i 3.05576 + 0.724228i
\(904\) 0 0
\(905\) 0.707900 + 1.64110i 0.707900 + 1.64110i
\(906\) 0 0
\(907\) 1.59716 0.802123i 1.59716 0.802123i 0.597159 0.802123i \(-0.296296\pi\)
1.00000 \(0\)
\(908\) 1.17365 0.984808i 1.17365 0.984808i
\(909\) −0.344948 0.0403186i −0.344948 0.0403186i
\(910\) 0 0
\(911\) 0 0 −0.973045 0.230616i \(-0.925926\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −0.0694434 + 0.0932786i −0.0694434 + 0.0932786i
\(916\) −0.819590 1.10090i −0.819590 1.10090i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(920\) −0.227194 + 0.526695i −0.227194 + 0.526695i
\(921\) 0.393633 + 0.417226i 0.393633 + 0.417226i
\(922\) −1.22650 1.30001i −1.22650 1.30001i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0.266044 1.50881i 0.266044 1.50881i
\(927\) 0.266044 + 1.50881i 0.266044 + 1.50881i
\(928\) −0.238329 1.35163i −0.238329 1.35163i
\(929\) 1.57020 + 1.03274i 1.57020 + 1.03274i 0.973045 + 0.230616i \(0.0740741\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 1.57020 + 1.03274i 1.57020 + 1.03274i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(938\) 0.908364 0.962809i 0.908364 0.962809i
\(939\) 0 0
\(940\) 1.65968 1.09159i 1.65968 1.09159i
\(941\) −0.819590 0.868715i −0.819590 0.868715i 0.173648 0.984808i \(-0.444444\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(942\) 0 0
\(943\) −0.271342 + 0.629041i −0.271342 + 0.629041i
\(944\) 0 0
\(945\) −1.67098 −1.67098
\(946\) 0 0
\(947\) 0.713197 + 0.957990i 0.713197 + 0.957990i 1.00000 \(0\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −0.286803 0.957990i −0.286803 0.957990i
\(961\) −0.0581448 + 0.998308i −0.0581448 + 0.998308i
\(962\) 0 0
\(963\) 0.707900 1.64110i 0.707900 1.64110i
\(964\) −1.67948 + 0.611281i −1.67948 + 0.611281i
\(965\) 0 0
\(966\) 0.166439 + 0.943921i 0.166439 + 0.943921i
\(967\) −0.512593 0.257434i −0.512593 0.257434i 0.173648 0.984808i \(-0.444444\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(968\) 0.973045 0.230616i 0.973045 0.230616i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −0.500000 0.866025i −0.500000 0.866025i
\(973\) 0 0
\(974\) 0.993238 0.116093i 0.993238 0.116093i
\(975\) 0 0
\(976\) −0.113155 + 0.0268182i −0.113155 + 0.0268182i
\(977\) 0 0 −0.893633 0.448799i \(-0.851852\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(978\) 0.0603074 + 0.342020i 0.0603074 + 0.342020i
\(979\) 0 0
\(980\) −1.68408 + 0.612955i −1.68408 + 0.612955i
\(981\) 1.16212 + 1.56100i 1.16212 + 1.56100i
\(982\) 0 0
\(983\) 0.0971586 1.66815i 0.0971586 1.66815i −0.500000 0.866025i \(-0.666667\pi\)
0.597159 0.802123i \(-0.296296\pi\)
\(984\) −0.342534 1.14414i −0.342534 1.14414i
\(985\) 0 0
\(986\) 0 0
\(987\) 1.31473 3.04788i 1.31473 3.04788i
\(988\) 0 0
\(989\) 0.825817 0.692943i 0.825817 0.692943i
\(990\) 0 0
\(991\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0.473045 + 1.09664i 0.473045 + 1.09664i
\(997\) 0 0 −0.597159 0.802123i \(-0.703704\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1620.1.bp.b.1519.1 yes 18
4.3 odd 2 1620.1.bp.a.1519.1 yes 18
5.4 even 2 1620.1.bp.a.1519.1 yes 18
20.19 odd 2 CM 1620.1.bp.b.1519.1 yes 18
81.4 even 27 inner 1620.1.bp.b.1219.1 yes 18
324.247 odd 54 1620.1.bp.a.1219.1 18
405.4 even 54 1620.1.bp.a.1219.1 18
1620.1219 odd 54 inner 1620.1.bp.b.1219.1 yes 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1620.1.bp.a.1219.1 18 324.247 odd 54
1620.1.bp.a.1219.1 18 405.4 even 54
1620.1.bp.a.1519.1 yes 18 4.3 odd 2
1620.1.bp.a.1519.1 yes 18 5.4 even 2
1620.1.bp.b.1219.1 yes 18 81.4 even 27 inner
1620.1.bp.b.1219.1 yes 18 1620.1219 odd 54 inner
1620.1.bp.b.1519.1 yes 18 1.1 even 1 trivial
1620.1.bp.b.1519.1 yes 18 20.19 odd 2 CM