Properties

Label 1620.1.bp.b.1159.1
Level $1620$
Weight $1$
Character 1620.1159
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 1159.1
Root \(-0.973045 - 0.230616i\) of defining polynomial
Character \(\chi\) \(=\) 1620.1159
Dual form 1620.1.bp.b.499.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.893633 - 0.448799i) q^{2} +(0.973045 - 0.230616i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-0.286803 + 0.957990i) q^{5} +(0.766044 - 0.642788i) q^{6} +(-0.543613 + 1.26024i) q^{7} +(0.173648 - 0.984808i) q^{8} +(0.893633 - 0.448799i) q^{9} +O(q^{10})\) \(q+(0.893633 - 0.448799i) q^{2} +(0.973045 - 0.230616i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-0.286803 + 0.957990i) q^{5} +(0.766044 - 0.642788i) q^{6} +(-0.543613 + 1.26024i) q^{7} +(0.173648 - 0.984808i) q^{8} +(0.893633 - 0.448799i) q^{9} +(0.173648 + 0.984808i) q^{10} +(0.396080 - 0.918216i) q^{12} +(0.0798028 + 1.37016i) q^{14} +(-0.0581448 + 0.998308i) q^{15} +(-0.286803 - 0.957990i) q^{16} +(0.597159 - 0.802123i) q^{18} +(0.597159 + 0.802123i) q^{20} +(-0.238329 + 1.35163i) q^{21} +(0.313758 + 0.727374i) q^{23} +(-0.0581448 - 0.998308i) q^{24} +(-0.835488 - 0.549509i) q^{25} +(0.766044 - 0.642788i) q^{27} +(0.686242 + 1.18861i) q^{28} +(0.115503 - 1.98312i) q^{29} +(0.396080 + 0.918216i) q^{30} +(-0.686242 - 0.727374i) q^{32} +(-1.05138 - 0.882215i) q^{35} +(0.173648 - 0.984808i) q^{36} +(0.893633 + 0.448799i) q^{40} +(-1.49324 - 0.749932i) q^{41} +(0.393633 + 1.31482i) q^{42} +(-0.238329 + 0.252614i) q^{43} +(0.173648 + 0.984808i) q^{45} +(0.606829 + 0.509190i) q^{46} +(-1.77518 + 0.207489i) q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.606439 - 0.642788i) q^{49} +(-0.993238 - 0.116093i) q^{50} +(0.396080 - 0.918216i) q^{54} +(1.14669 + 0.754192i) q^{56} +(-0.786803 - 1.82401i) q^{58} +(0.766044 + 0.642788i) q^{60} +(1.16212 + 1.56100i) q^{61} +(0.0798028 + 1.37016i) q^{63} +(-0.939693 - 0.342020i) q^{64} +(0.00676164 + 0.116093i) q^{67} +(0.473045 + 0.635410i) q^{69} +(-1.33549 - 0.316516i) q^{70} +(-0.286803 - 0.957990i) q^{72} +(-0.939693 - 0.342020i) q^{75} +1.00000 q^{80} +(0.597159 - 0.802123i) q^{81} -1.67098 q^{82} +(-1.49324 + 0.749932i) q^{83} +(0.941855 + 0.998308i) q^{84} +(-0.0996057 + 0.332706i) q^{86} +(-0.344948 - 1.95630i) q^{87} +(0.310355 - 1.76011i) q^{89} +(0.597159 + 0.802123i) q^{90} +(0.770807 + 0.182685i) q^{92} +(-1.49324 + 0.982118i) q^{94} +(-0.835488 - 0.549509i) q^{96} +(-0.830416 - 0.302247i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q+O(q^{10}) \) 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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\) \(811\) \(1297\) \(1541\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{23}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.893633 0.448799i 0.893633 0.448799i
\(3\) 0.973045 0.230616i 0.973045 0.230616i
\(4\) 0.597159 0.802123i 0.597159 0.802123i
\(5\) −0.286803 + 0.957990i −0.286803 + 0.957990i
\(6\) 0.766044 0.642788i 0.766044 0.642788i
\(7\) −0.543613 + 1.26024i −0.543613 + 1.26024i 0.396080 + 0.918216i \(0.370370\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(8\) 0.173648 0.984808i 0.173648 0.984808i
\(9\) 0.893633 0.448799i 0.893633 0.448799i
\(10\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(11\) 0 0 −0.973045 0.230616i \(-0.925926\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(12\) 0.396080 0.918216i 0.396080 0.918216i
\(13\) 0 0 0.835488 0.549509i \(-0.185185\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(14\) 0.0798028 + 1.37016i 0.0798028 + 1.37016i
\(15\) −0.0581448 + 0.998308i −0.0581448 + 0.998308i
\(16\) −0.286803 0.957990i −0.286803 0.957990i
\(17\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(18\) 0.597159 0.802123i 0.597159 0.802123i
\(19\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(20\) 0.597159 + 0.802123i 0.597159 + 0.802123i
\(21\) −0.238329 + 1.35163i −0.238329 + 1.35163i
\(22\) 0 0
\(23\) 0.313758 + 0.727374i 0.313758 + 0.727374i 1.00000 \(0\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(24\) −0.0581448 0.998308i −0.0581448 0.998308i
\(25\) −0.835488 0.549509i −0.835488 0.549509i
\(26\) 0 0
\(27\) 0.766044 0.642788i 0.766044 0.642788i
\(28\) 0.686242 + 1.18861i 0.686242 + 1.18861i
\(29\) 0.115503 1.98312i 0.115503 1.98312i −0.0581448 0.998308i \(-0.518519\pi\)
0.173648 0.984808i \(-0.444444\pi\)
\(30\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(31\) 0 0 −0.993238 0.116093i \(-0.962963\pi\)
0.993238 + 0.116093i \(0.0370370\pi\)
\(32\) −0.686242 0.727374i −0.686242 0.727374i
\(33\) 0 0
\(34\) 0 0
\(35\) −1.05138 0.882215i −1.05138 0.882215i
\(36\) 0.173648 0.984808i 0.173648 0.984808i
\(37\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(41\) −1.49324 0.749932i −1.49324 0.749932i −0.500000 0.866025i \(-0.666667\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(42\) 0.393633 + 1.31482i 0.393633 + 1.31482i
\(43\) −0.238329 + 0.252614i −0.238329 + 0.252614i −0.835488 0.549509i \(-0.814815\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(44\) 0 0
\(45\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(46\) 0.606829 + 0.509190i 0.606829 + 0.509190i
\(47\) −1.77518 + 0.207489i −1.77518 + 0.207489i −0.939693 0.342020i \(-0.888889\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(48\) −0.500000 0.866025i −0.500000 0.866025i
\(49\) −0.606439 0.642788i −0.606439 0.642788i
\(50\) −0.993238 0.116093i −0.993238 0.116093i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 0.396080 0.918216i 0.396080 0.918216i
\(55\) 0 0
\(56\) 1.14669 + 0.754192i 1.14669 + 0.754192i
\(57\) 0 0
\(58\) −0.786803 1.82401i −0.786803 1.82401i
\(59\) 0 0 0.973045 0.230616i \(-0.0740741\pi\)
−0.973045 + 0.230616i \(0.925926\pi\)
\(60\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(61\) 1.16212 + 1.56100i 1.16212 + 1.56100i 0.766044 + 0.642788i \(0.222222\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(62\) 0 0
\(63\) 0.0798028 + 1.37016i 0.0798028 + 1.37016i
\(64\) −0.939693 0.342020i −0.939693 0.342020i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.00676164 + 0.116093i 0.00676164 + 0.116093i 1.00000 \(0\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(68\) 0 0
\(69\) 0.473045 + 0.635410i 0.473045 + 0.635410i
\(70\) −1.33549 0.316516i −1.33549 0.316516i
\(71\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(72\) −0.286803 0.957990i −0.286803 0.957990i
\(73\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(74\) 0 0
\(75\) −0.939693 0.342020i −0.939693 0.342020i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.893633 0.448799i \(-0.148148\pi\)
−0.893633 + 0.448799i \(0.851852\pi\)
\(80\) 1.00000 1.00000
\(81\) 0.597159 0.802123i 0.597159 0.802123i
\(82\) −1.67098 −1.67098
\(83\) −1.49324 + 0.749932i −1.49324 + 0.749932i −0.993238 0.116093i \(-0.962963\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(84\) 0.941855 + 0.998308i 0.941855 + 0.998308i
\(85\) 0 0
\(86\) −0.0996057 + 0.332706i −0.0996057 + 0.332706i
\(87\) −0.344948 1.95630i −0.344948 1.95630i
\(88\) 0 0
\(89\) 0.310355 1.76011i 0.310355 1.76011i −0.286803 0.957990i \(-0.592593\pi\)
0.597159 0.802123i \(-0.296296\pi\)
\(90\) 0.597159 + 0.802123i 0.597159 + 0.802123i
\(91\) 0 0
\(92\) 0.770807 + 0.182685i 0.770807 + 0.182685i
\(93\) 0 0
\(94\) −1.49324 + 0.982118i −1.49324 + 0.982118i
\(95\) 0 0
\(96\) −0.835488 0.549509i −0.835488 0.549509i
\(97\) 0 0 −0.286803 0.957990i \(-0.592593\pi\)
0.286803 + 0.957990i \(0.407407\pi\)
\(98\) −0.830416 0.302247i −0.830416 0.302247i
\(99\) 0 0
\(100\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(101\) 0.914900 + 1.22892i 0.914900 + 1.22892i 0.973045 + 0.230616i \(0.0740741\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(102\) 0 0
\(103\) −1.82873 + 0.433416i −1.82873 + 0.433416i −0.993238 0.116093i \(-0.962963\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(104\) 0 0
\(105\) −1.22650 0.615969i −1.22650 0.615969i
\(106\) 0 0
\(107\) 0.286803 0.496758i 0.286803 0.496758i −0.686242 0.727374i \(-0.740741\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(108\) −0.0581448 0.998308i −0.0581448 0.998308i
\(109\) −0.597159 1.03431i −0.597159 1.03431i −0.993238 0.116093i \(-0.962963\pi\)
0.396080 0.918216i \(-0.370370\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.36320 + 0.159336i 1.36320 + 0.159336i
\(113\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(114\) 0 0
\(115\) −0.786803 + 0.0919641i −0.786803 + 0.0919641i
\(116\) −1.52173 1.27688i −1.52173 1.27688i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(121\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(122\) 1.73909 + 0.873403i 1.73909 + 0.873403i
\(123\) −1.62593 0.385353i −1.62593 0.385353i
\(124\) 0 0
\(125\) 0.766044 0.642788i 0.766044 0.642788i
\(126\) 0.686242 + 1.18861i 0.686242 + 1.18861i
\(127\) 0.914900 + 0.767692i 0.914900 + 0.767692i 0.973045 0.230616i \(-0.0740741\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(128\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(129\) −0.173648 + 0.300767i −0.173648 + 0.300767i
\(130\) 0 0
\(131\) 0 0 −0.993238 0.116093i \(-0.962963\pi\)
0.993238 + 0.116093i \(0.0370370\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.0581448 + 0.100710i 0.0581448 + 0.100710i
\(135\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(136\) 0 0
\(137\) 0 0 −0.835488 0.549509i \(-0.814815\pi\)
0.835488 + 0.549509i \(0.185185\pi\)
\(138\) 0.707900 + 0.355521i 0.707900 + 0.355521i
\(139\) 0 0 −0.396080 0.918216i \(-0.629630\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(140\) −1.33549 + 0.316516i −1.33549 + 0.316516i
\(141\) −1.67948 + 0.611281i −1.67948 + 0.611281i
\(142\) 0 0
\(143\) 0 0
\(144\) −0.686242 0.727374i −0.686242 0.727374i
\(145\) 1.86668 + 0.679415i 1.86668 + 0.679415i
\(146\) 0 0
\(147\) −0.738329 0.485607i −0.738329 0.485607i
\(148\) 0 0
\(149\) −0.997837 + 0.656288i −0.997837 + 0.656288i −0.939693 0.342020i \(-0.888889\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(150\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(151\) 0 0 −0.973045 0.230616i \(-0.925926\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.286803 0.957990i \(-0.407407\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.893633 0.448799i 0.893633 0.448799i
\(161\) −1.08723 −1.08723
\(162\) 0.173648 0.984808i 0.173648 0.984808i
\(163\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(164\) −1.49324 + 0.749932i −1.49324 + 0.749932i
\(165\) 0 0
\(166\) −0.997837 + 1.34033i −0.997837 + 1.34033i
\(167\) 0.569728 1.90302i 0.569728 1.90302i 0.173648 0.984808i \(-0.444444\pi\)
0.396080 0.918216i \(-0.370370\pi\)
\(168\) 1.28971 + 0.469417i 1.28971 + 0.469417i
\(169\) 0.396080 0.918216i 0.396080 0.918216i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.0603074 + 0.342020i 0.0603074 + 0.342020i
\(173\) 0 0 −0.973045 0.230616i \(-0.925926\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(174\) −1.18624 1.59340i −1.18624 1.59340i
\(175\) 1.14669 0.754192i 1.14669 0.754192i
\(176\) 0 0
\(177\) 0 0
\(178\) −0.512593 1.71218i −0.512593 1.71218i
\(179\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(180\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(181\) 0.539014 0.196185i 0.539014 0.196185i −0.0581448 0.998308i \(-0.518519\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(182\) 0 0
\(183\) 1.49079 + 1.25092i 1.49079 + 1.25092i
\(184\) 0.770807 0.182685i 0.770807 0.182685i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.893633 + 1.54782i −0.893633 + 1.54782i
\(189\) 0.393633 + 1.31482i 0.393633 + 1.31482i
\(190\) 0 0
\(191\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(192\) −0.993238 0.116093i −0.993238 0.116093i
\(193\) 0 0 −0.993238 0.116093i \(-0.962963\pi\)
0.993238 + 0.116093i \(0.0370370\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.877735 + 0.102593i −0.877735 + 0.102593i
\(197\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(198\) 0 0
\(199\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(200\) −0.686242 + 0.727374i −0.686242 + 0.727374i
\(201\) 0.0333522 + 0.111404i 0.0333522 + 0.111404i
\(202\) 1.36912 + 0.687600i 1.36912 + 0.687600i
\(203\) 2.43641 + 1.22361i 2.43641 + 1.22361i
\(204\) 0 0
\(205\) 1.14669 1.21542i 1.14669 1.21542i
\(206\) −1.43969 + 1.20805i −1.43969 + 1.20805i
\(207\) 0.606829 + 0.509190i 0.606829 + 0.509190i
\(208\) 0 0
\(209\) 0 0
\(210\) −1.37248 −1.37248
\(211\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.0333522 0.572636i 0.0333522 0.572636i
\(215\) −0.173648 0.300767i −0.173648 0.300767i
\(216\) −0.500000 0.866025i −0.500000 0.866025i
\(217\) 0 0
\(218\) −0.997837 0.656288i −0.997837 0.656288i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.06728 + 1.43361i 1.06728 + 1.43361i 0.893633 + 0.448799i \(0.148148\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(224\) 1.28971 0.469417i 1.28971 0.469417i
\(225\) −0.993238 0.116093i −0.993238 0.116093i
\(226\) 0 0
\(227\) 0.539014 + 1.80043i 0.539014 + 1.80043i 0.597159 + 0.802123i \(0.296296\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(228\) 0 0
\(229\) 0.115503 + 1.98312i 0.115503 + 1.98312i 0.173648 + 0.984808i \(0.444444\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(230\) −0.661840 + 0.435299i −0.661840 + 0.435299i
\(231\) 0 0
\(232\) −1.93293 0.458113i −1.93293 0.458113i
\(233\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(234\) 0 0
\(235\) 0.310355 1.76011i 0.310355 1.76011i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.597159 0.802123i \(-0.296296\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(240\) 0.973045 0.230616i 0.973045 0.230616i
\(241\) −0.512593 + 0.257434i −0.512593 + 0.257434i −0.686242 0.727374i \(-0.740741\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(242\) 1.00000 1.00000
\(243\) 0.396080 0.918216i 0.396080 0.918216i
\(244\) 1.94609 1.94609
\(245\) 0.789712 0.396608i 0.789712 0.396608i
\(246\) −1.62593 + 0.385353i −1.62593 + 0.385353i
\(247\) 0 0
\(248\) 0 0
\(249\) −1.28004 + 1.07408i −1.28004 + 1.07408i
\(250\) 0.396080 0.918216i 0.396080 0.918216i
\(251\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(252\) 1.14669 + 0.754192i 1.14669 + 0.754192i
\(253\) 0 0
\(254\) 1.16212 + 0.275428i 1.16212 + 0.275428i
\(255\) 0 0
\(256\) −0.835488 + 0.549509i −0.835488 + 0.549509i
\(257\) 0 0 −0.0581448 0.998308i \(-0.518519\pi\)
0.0581448 + 0.998308i \(0.481481\pi\)
\(258\) −0.0201935 + 0.346709i −0.0201935 + 0.346709i
\(259\) 0 0
\(260\) 0 0
\(261\) −0.786803 1.82401i −0.786803 1.82401i
\(262\) 0 0
\(263\) −1.12229 1.50750i −1.12229 1.50750i −0.835488 0.549509i \(-0.814815\pi\)
−0.286803 0.957990i \(-0.592593\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.103920 1.78424i −0.103920 1.78424i
\(268\) 0.0971586 + 0.0639022i 0.0971586 + 0.0639022i
\(269\) 0.286803 0.496758i 0.286803 0.496758i −0.686242 0.727374i \(-0.740741\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(270\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(271\) 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
\(276\) 0.792160 0.792160
\(277\) 0 0 0.993238 0.116093i \(-0.0370370\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) −1.05138 + 0.882215i −1.05138 + 0.882215i
\(281\) −1.33549 + 1.41553i −1.33549 + 1.41553i −0.500000 + 0.866025i \(0.666667\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(282\) −1.22650 + 1.30001i −1.22650 + 1.30001i
\(283\) 1.06728 + 0.536009i 1.06728 + 0.536009i 0.893633 0.448799i \(-0.148148\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.75684 1.47416i 1.75684 1.47416i
\(288\) −0.939693 0.342020i −0.939693 0.342020i
\(289\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(290\) 1.97304 0.230616i 1.97304 0.230616i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.993238 0.116093i \(-0.962963\pi\)
0.993238 + 0.116093i \(0.0370370\pi\)
\(294\) −0.877735 0.102593i −0.877735 0.102593i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −0.597159 + 1.03431i −0.597159 + 1.03431i
\(299\) 0 0
\(300\) −0.835488 + 0.549509i −0.835488 + 0.549509i
\(301\) −0.188795 0.437675i −0.188795 0.437675i
\(302\) 0 0
\(303\) 1.17365 + 0.984808i 1.17365 + 0.984808i
\(304\) 0 0
\(305\) −1.82873 + 0.665602i −1.82873 + 0.665602i
\(306\) 0 0
\(307\) −0.744386 0.270935i −0.744386 0.270935i −0.0581448 0.998308i \(-0.518519\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(308\) 0 0
\(309\) −1.67948 + 0.843467i −1.67948 + 0.843467i
\(310\) 0 0
\(311\) 0 0 0.835488 0.549509i \(-0.185185\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(312\) 0 0
\(313\) 0 0 −0.973045 0.230616i \(-0.925926\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(314\) 0 0
\(315\) −1.33549 0.316516i −1.33549 0.316516i
\(316\) 0 0
\(317\) 0 0 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.597159 0.802123i 0.597159 0.802123i
\(321\) 0.164512 0.549509i 0.164512 0.549509i
\(322\) −0.971580 + 0.487946i −0.971580 + 0.487946i
\(323\) 0 0
\(324\) −0.286803 0.957990i −0.286803 0.957990i
\(325\) 0 0
\(326\) 1.36912 0.687600i 1.36912 0.687600i
\(327\) −0.819590 0.868715i −0.819590 0.868715i
\(328\) −0.997837 + 1.34033i −0.997837 + 1.34033i
\(329\) 0.703526 2.34994i 0.703526 2.34994i
\(330\) 0 0
\(331\) 0 0 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(332\) −0.290162 + 1.64559i −0.290162 + 1.64559i
\(333\) 0 0
\(334\) −0.344948 1.95630i −0.344948 1.95630i
\(335\) −0.113155 0.0268182i −0.113155 0.0268182i
\(336\) 1.36320 0.159336i 1.36320 0.159336i
\(337\) 0 0 0.835488 0.549509i \(-0.185185\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(338\) −0.0581448 0.998308i −0.0581448 0.998308i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.149980 + 0.0545883i −0.149980 + 0.0545883i
\(344\) 0.207391 + 0.278574i 0.207391 + 0.278574i
\(345\) −0.744386 + 0.270935i −0.744386 + 0.270935i
\(346\) 0 0
\(347\) 0.606829 + 1.40679i 0.606829 + 1.40679i 0.893633 + 0.448799i \(0.148148\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(348\) −1.77518 0.891529i −1.77518 0.891529i
\(349\) −1.49324 0.982118i −1.49324 0.982118i −0.993238 0.116093i \(-0.962963\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(350\) 0.686242 1.18861i 0.686242 1.18861i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.22650 1.30001i −1.22650 1.30001i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(360\) 1.00000 1.00000
\(361\) 0.766044 0.642788i 0.766044 0.642788i
\(362\) 0.393633 0.417226i 0.393633 0.417226i
\(363\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(364\) 0 0
\(365\) 0 0
\(366\) 1.89363 + 0.448799i 1.89363 + 0.448799i
\(367\) 0.686242 0.727374i 0.686242 0.727374i −0.286803 0.957990i \(-0.592593\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(368\) 0.606829 0.509190i 0.606829 0.509190i
\(369\) −1.67098 −1.67098
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(374\) 0 0
\(375\) 0.597159 0.802123i 0.597159 0.802123i
\(376\) −0.103920 + 1.78424i −0.103920 + 1.78424i
\(377\) 0 0
\(378\) 0.941855 + 0.998308i 0.941855 + 0.998308i
\(379\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(380\) 0 0
\(381\) 1.06728 + 0.536009i 1.06728 + 0.536009i
\(382\) 0 0
\(383\) 1.49079 0.353324i 1.49079 0.353324i 0.597159 0.802123i \(-0.296296\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(384\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(385\) 0 0
\(386\) 0 0
\(387\) −0.0996057 + 0.332706i −0.0996057 + 0.332706i
\(388\) 0 0
\(389\) 0.0333522 + 0.111404i 0.0333522 + 0.111404i 0.973045 0.230616i \(-0.0740741\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.738329 + 0.485607i −0.738329 + 0.485607i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.173648 0.984808i \(-0.444444\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.286803 + 0.957990i −0.286803 + 0.957990i
\(401\) 0.207391 0.278574i 0.207391 0.278574i −0.686242 0.727374i \(-0.740741\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(402\) 0.0798028 + 0.0845860i 0.0798028 + 0.0845860i
\(403\) 0 0
\(404\) 1.53209 1.53209
\(405\) 0.597159 + 0.802123i 0.597159 + 0.802123i
\(406\) 2.72641 2.72641
\(407\) 0 0
\(408\) 0 0
\(409\) −1.12229 + 1.50750i −1.12229 + 1.50750i −0.286803 + 0.957990i \(0.592593\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(410\) 0.479241 1.60078i 0.479241 1.60078i
\(411\) 0 0
\(412\) −0.744386 + 1.72568i −0.744386 + 1.72568i
\(413\) 0 0
\(414\) 0.770807 + 0.182685i 0.770807 + 0.182685i
\(415\) −0.290162 1.64559i −0.290162 1.64559i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.0581448 0.998308i \(-0.518519\pi\)
0.0581448 + 0.998308i \(0.481481\pi\)
\(420\) −1.22650 + 0.615969i −1.22650 + 0.615969i
\(421\) −0.0996057 0.332706i −0.0996057 0.332706i 0.893633 0.448799i \(-0.148148\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(422\) 0 0
\(423\) −1.49324 + 0.982118i −1.49324 + 0.982118i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −2.59898 + 0.615969i −2.59898 + 0.615969i
\(428\) −0.227194 0.526695i −0.227194 0.526695i
\(429\) 0 0
\(430\) −0.290162 0.190842i −0.290162 0.190842i
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −0.835488 0.549509i −0.835488 0.549509i
\(433\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(434\) 0 0
\(435\) 1.97304 + 0.230616i 1.97304 + 0.230616i
\(436\) −1.18624 0.138652i −1.18624 0.138652i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.993238 0.116093i \(-0.0370370\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(440\) 0 0
\(441\) −0.830416 0.302247i −0.830416 0.302247i
\(442\) 0 0
\(443\) 0.0798028 0.0845860i 0.0798028 0.0845860i −0.686242 0.727374i \(-0.740741\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(444\) 0 0
\(445\) 1.59716 + 0.802123i 1.59716 + 0.802123i
\(446\) 1.59716 + 0.802123i 1.59716 + 0.802123i
\(447\) −0.819590 + 0.868715i −0.819590 + 0.868715i
\(448\) 0.941855 0.998308i 0.941855 0.998308i
\(449\) 1.17365 0.984808i 1.17365 0.984808i 0.173648 0.984808i \(-0.444444\pi\)
1.00000 \(0\)
\(450\) −0.939693 + 0.342020i −0.939693 + 0.342020i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 1.28971 + 1.36702i 1.28971 + 1.36702i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(458\) 0.993238 + 1.72034i 0.993238 + 1.72034i
\(459\) 0 0
\(460\) −0.396080 + 0.686030i −0.396080 + 0.686030i
\(461\) 0.479241 + 0.315202i 0.479241 + 0.315202i 0.766044 0.642788i \(-0.222222\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(462\) 0 0
\(463\) −0.744386 1.72568i −0.744386 1.72568i −0.686242 0.727374i \(-0.740741\pi\)
−0.0581448 0.998308i \(-0.518519\pi\)
\(464\) −1.93293 + 0.458113i −1.93293 + 0.458113i
\(465\) 0 0
\(466\) 0 0
\(467\) −0.326352 + 0.118782i −0.326352 + 0.118782i −0.500000 0.866025i \(-0.666667\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(468\) 0 0
\(469\) −0.149980 0.0545883i −0.149980 0.0545883i
\(470\) −0.512593 1.71218i −0.512593 1.71218i
\(471\) 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 0.396080 0.918216i \(-0.370370\pi\)
−0.396080 + 0.918216i \(0.629630\pi\)
\(480\) 0.766044 0.642788i 0.766044 0.642788i
\(481\) 0 0
\(482\) −0.342534 + 0.460103i −0.342534 + 0.460103i
\(483\) −1.05792 + 0.250732i −1.05792 + 0.250732i
\(484\) 0.893633 0.448799i 0.893633 0.448799i
\(485\) 0 0
\(486\) −0.0581448 0.998308i −0.0581448 0.998308i
\(487\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 1.73909 0.873403i 1.73909 0.873403i
\(489\) 1.49079 0.353324i 1.49079 0.353324i
\(490\) 0.527715 0.708845i 0.527715 0.708845i
\(491\) 0 0 0.286803 0.957990i \(-0.407407\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(492\) −1.28004 + 1.07408i −1.28004 + 1.07408i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.661840 + 1.53432i −0.661840 + 1.53432i
\(499\) 0 0 0.835488 0.549509i \(-0.185185\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(500\) −0.0581448 0.998308i −0.0581448 0.998308i
\(501\) 0.115503 1.98312i 0.115503 1.98312i
\(502\) 0 0
\(503\) −1.82873 0.665602i −1.82873 0.665602i −0.993238 0.116093i \(-0.962963\pi\)
−0.835488 0.549509i \(-0.814815\pi\)
\(504\) 1.36320 + 0.159336i 1.36320 + 0.159336i
\(505\) −1.43969 + 0.524005i −1.43969 + 0.524005i
\(506\) 0 0
\(507\) 0.173648 0.984808i 0.173648 0.984808i
\(508\) 1.16212 0.275428i 1.16212 0.275428i
\(509\) 0.770807 + 1.78693i 0.770807 + 1.78693i 0.597159 + 0.802123i \(0.296296\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(513\) 0 0
\(514\) 0 0
\(515\) 0.109277 1.87621i 0.109277 1.87621i
\(516\) 0.137557 + 0.318893i 0.137557 + 0.318893i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.606829 + 0.509190i 0.606829 + 0.509190i 0.893633 0.448799i \(-0.148148\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(522\) −1.52173 1.27688i −1.52173 1.27688i
\(523\) 1.49079 1.25092i 1.49079 1.25092i 0.597159 0.802123i \(-0.296296\pi\)
0.893633 0.448799i \(-0.148148\pi\)
\(524\) 0 0
\(525\) 0.941855 0.998308i 0.941855 0.998308i
\(526\) −1.67948 0.843467i −1.67948 0.843467i
\(527\) 0 0
\(528\) 0 0
\(529\) 0.255614 0.270935i 0.255614 0.270935i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.893633 1.54782i −0.893633 1.54782i
\(535\) 0.393633 + 0.417226i 0.393633 + 0.417226i
\(536\) 0.115503 + 0.0135004i 0.115503 + 0.0135004i
\(537\) 0 0
\(538\) 0.0333522 0.572636i 0.0333522 0.572636i
\(539\) 0 0
\(540\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(541\) −0.973045 + 1.68536i −0.973045 + 1.68536i −0.286803 + 0.957990i \(0.592593\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(542\) 0 0
\(543\) 0.479241 0.315202i 0.479241 0.315202i
\(544\) 0 0
\(545\) 1.16212 0.275428i 1.16212 0.275428i
\(546\) 0 0
\(547\) −0.0694434 0.0932786i −0.0694434 0.0932786i 0.766044 0.642788i \(-0.222222\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(548\) 0 0
\(549\) 1.73909 + 0.873403i 1.73909 + 0.873403i
\(550\) 0 0
\(551\) 0 0
\(552\) 0.707900 0.355521i 0.707900 0.355521i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −0.543613 + 1.26024i −0.543613 + 1.26024i
\(561\) 0 0
\(562\) −0.558145 + 1.86433i −0.558145 + 1.86433i
\(563\) −0.997837 + 1.34033i −0.997837 + 1.34033i −0.0581448 + 0.998308i \(0.518519\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(564\) −0.512593 + 1.71218i −0.512593 + 1.71218i
\(565\) 0 0
\(566\) 1.19432 1.19432
\(567\) 0.686242 + 1.18861i 0.686242 + 1.18861i
\(568\) 0 0
\(569\) 0.310355 0.155866i 0.310355 0.155866i −0.286803 0.957990i \(-0.592593\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(570\) 0 0
\(571\) 0 0 0.597159 0.802123i \(-0.296296\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.908364 2.10582i 0.908364 2.10582i
\(575\) 0.137557 0.780125i 0.137557 0.780125i
\(576\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(577\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(578\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(579\) 0 0
\(580\) 1.65968 1.09159i 1.65968 1.09159i
\(581\) −0.133349 2.28951i −0.133349 2.28951i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.16212 + 1.56100i 1.16212 + 1.56100i 0.766044 + 0.642788i \(0.222222\pi\)
0.396080 + 0.918216i \(0.370370\pi\)
\(588\) −0.830416 + 0.302247i −0.830416 + 0.302247i
\(589\) 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
\(596\) −0.0694434 + 1.19230i −0.0694434 + 1.19230i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(600\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(601\) −0.344948 + 0.0403186i −0.344948 + 0.0403186i −0.286803 0.957990i \(-0.592593\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(602\) −0.365142 0.306390i −0.365142 0.306390i
\(603\) 0.0581448 + 0.100710i 0.0581448 + 0.100710i
\(604\) 0 0
\(605\) −0.686242 + 0.727374i −0.686242 + 0.727374i
\(606\) 1.49079 + 0.353324i 1.49079 + 0.353324i
\(607\) −1.77518 0.891529i −1.77518 0.891529i −0.939693 0.342020i \(-0.888889\pi\)
−0.835488 0.549509i \(-0.814815\pi\)
\(608\) 0 0
\(609\) 2.65292 + 0.628753i 2.65292 + 0.628753i
\(610\) −1.33549 + 1.41553i −1.33549 + 1.41553i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(614\) −0.786803 + 0.0919641i −0.786803 + 0.0919641i
\(615\) 0.835488 1.44711i 0.835488 1.44711i
\(616\) 0 0
\(617\) 0 0 −0.993238 0.116093i \(-0.962963\pi\)
0.993238 + 0.116093i \(0.0370370\pi\)
\(618\) −1.12229 + 1.50750i −1.12229 + 1.50750i
\(619\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(620\) 0 0
\(621\) 0.707900 + 0.355521i 0.707900 + 0.355521i
\(622\) 0 0
\(623\) 2.04944 + 1.34794i 2.04944 + 1.34794i
\(624\) 0 0
\(625\) 0.396080 + 0.918216i 0.396080 + 0.918216i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −1.33549 + 0.316516i −1.33549 + 0.316516i
\(631\) 0 0 −0.939693 0.342020i \(-0.888889\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −0.997837 + 0.656288i −0.997837 + 0.656288i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0.173648 0.984808i 0.173648 0.984808i
\(641\) −0.227194 + 0.526695i −0.227194 + 0.526695i −0.993238 0.116093i \(-0.962963\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(642\) −0.0996057 0.564892i −0.0996057 0.564892i
\(643\) 0.569728 1.90302i 0.569728 1.90302i 0.173648 0.984808i \(-0.444444\pi\)
0.396080 0.918216i \(-0.370370\pi\)
\(644\) −0.649246 + 0.872089i −0.649246 + 0.872089i
\(645\) −0.238329 0.252614i −0.238329 0.252614i
\(646\) 0 0
\(647\) 1.19432 1.19432 0.597159 0.802123i \(-0.296296\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(648\) −0.686242 0.727374i −0.686242 0.727374i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.914900 1.22892i 0.914900 1.22892i
\(653\) 0 0 0.286803 0.957990i \(-0.407407\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(654\) −1.12229 0.408481i −1.12229 0.408481i
\(655\) 0 0
\(656\) −0.290162 + 1.64559i −0.290162 + 1.64559i
\(657\) 0 0
\(658\) −0.425958 2.41573i −0.425958 2.41573i
\(659\) 0 0 −0.973045 0.230616i \(-0.925926\pi\)
0.973045 + 0.230616i \(0.0740741\pi\)
\(660\) 0 0
\(661\) 1.57020 1.03274i 1.57020 1.03274i 0.597159 0.802123i \(-0.296296\pi\)
0.973045 0.230616i \(-0.0740741\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.479241 + 1.60078i 0.479241 + 1.60078i
\(665\) 0 0
\(666\) 0 0
\(667\) 1.47871 0.538205i 1.47871 0.538205i
\(668\) −1.18624 1.59340i −1.18624 1.59340i
\(669\) 1.36912 + 1.14883i 1.36912 + 1.14883i
\(670\) −0.113155 + 0.0268182i −0.113155 + 0.0268182i
\(671\) 0 0
\(672\) 1.14669 0.754192i 1.14669 0.754192i
\(673\) 0 0 −0.835488 0.549509i \(-0.814815\pi\)
0.835488 + 0.549509i \(0.185185\pi\)
\(674\) 0 0
\(675\) −0.993238 + 0.116093i −0.993238 + 0.116093i
\(676\) −0.500000 0.866025i −0.500000 0.866025i
\(677\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.939693 + 1.62760i 0.939693 + 1.62760i
\(682\) 0 0
\(683\) 0.266044 + 0.223238i 0.266044 + 0.223238i 0.766044 0.642788i \(-0.222222\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.109528 + 0.116093i −0.109528 + 0.116093i
\(687\) 0.569728 + 1.90302i 0.569728 + 1.90302i
\(688\) 0.310355 + 0.155866i 0.310355 + 0.155866i
\(689\) 0 0
\(690\) −0.543613 + 0.576196i −0.543613 + 0.576196i
\(691\) 0 0 0.686242 0.727374i \(-0.259259\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.17365 + 0.984808i 1.17365 + 0.984808i
\(695\) 0 0
\(696\) −1.98648 −1.98648
\(697\) 0 0
\(698\) −1.77518 0.207489i −1.77518 0.207489i
\(699\) 0 0
\(700\) 0.0798028 1.37016i 0.0798028 1.37016i
\(701\) −0.893633 1.54782i −0.893633 1.54782i −0.835488 0.549509i \(-0.814815\pi\)
−0.0581448 0.998308i \(-0.518519\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −0.103920 1.78424i −0.103920 1.78424i
\(706\) 0 0
\(707\) −2.04609 + 0.484931i −2.04609 + 0.484931i
\(708\) 0 0
\(709\) −0.0694434 0.0932786i −0.0694434 0.0932786i 0.766044 0.642788i \(-0.222222\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.67948 0.611281i −1.67948 0.611281i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(720\) 0.893633 0.448799i 0.893633 0.448799i
\(721\) 0.447912 2.54024i 0.447912 2.54024i
\(722\) 0.396080 0.918216i 0.396080 0.918216i
\(723\) −0.439408 + 0.368707i −0.439408 + 0.368707i
\(724\) 0.164512 0.549509i 0.164512 0.549509i
\(725\) −1.18624 + 1.59340i −1.18624 + 1.59340i
\(726\) 0.973045 0.230616i 0.973045 0.230616i
\(727\) 1.73909 0.873403i 1.73909 0.873403i 0.766044 0.642788i \(-0.222222\pi\)
0.973045 0.230616i \(-0.0740741\pi\)
\(728\) 0 0
\(729\) 0.173648 0.984808i 0.173648 0.984808i
\(730\) 0 0
\(731\) 0 0
\(732\) 1.89363 0.448799i 1.89363 0.448799i
\(733\) 0 0 0.597159 0.802123i \(-0.296296\pi\)
−0.597159 + 0.802123i \(0.703704\pi\)
\(734\) 0.286803 0.957990i 0.286803 0.957990i
\(735\) 0.676961 0.568038i 0.676961 0.568038i
\(736\) 0.313758 0.727374i 0.313758 0.727374i
\(737\) 0 0
\(738\) −1.49324 + 0.749932i −1.49324 + 0.749932i
\(739\) 0 0 −0.173648 0.984808i \(-0.555556\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.103920 1.78424i −0.103920 1.78424i −0.500000 0.866025i \(-0.666667\pi\)
0.396080 0.918216i \(-0.370370\pi\)
\(744\) 0 0
\(745\) −0.342534 1.14414i −0.342534 1.14414i
\(746\) 0 0
\(747\) −0.997837 + 1.34033i −0.997837 + 1.34033i
\(748\) 0 0
\(749\) 0.470122 + 0.631484i 0.470122 + 0.631484i
\(750\) 0.173648 0.984808i 0.173648 0.984808i
\(751\) 0 0 0.973045 0.230616i \(-0.0740741\pi\)
−0.973045 + 0.230616i \(0.925926\pi\)
\(752\) 0.707900 + 1.64110i 0.707900 + 1.64110i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.28971 + 0.469417i 1.28971 + 0.469417i
\(757\) 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
\(761\) 0.0798028 + 0.0845860i 0.0798028 + 0.0845860i 0.766044 0.642788i \(-0.222222\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(762\) 1.19432 1.19432
\(763\) 1.62810 0.190297i 1.62810 0.190297i
\(764\) 0 0
\(765\) 0 0
\(766\) 1.17365 0.984808i 1.17365 0.984808i
\(767\) 0 0
\(768\) −0.686242 + 0.727374i −0.686242 + 0.727374i
\(769\) −1.22650 0.615969i −1.22650 0.615969i −0.286803 0.957990i \(-0.592593\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.766044 0.642788i \(-0.222222\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(774\) 0.0603074 + 0.342020i 0.0603074 + 0.342020i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.0798028 + 0.0845860i 0.0798028 + 0.0845860i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −1.18624 1.59340i −1.18624 1.59340i
\(784\) −0.441855 + 0.765316i −0.441855 + 0.765316i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.396080 0.918216i −0.396080 0.918216i −0.993238 0.116093i \(-0.962963\pi\)
0.597159 0.802123i \(-0.296296\pi\)
\(788\) 0 0
\(789\) −1.43969 1.20805i −1.43969 1.20805i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.835488 0.549509i \(-0.185185\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.173648 + 0.984808i 0.173648 + 0.984808i
\(801\) −0.512593 1.71218i −0.512593 1.71218i
\(802\) 0.0603074 0.342020i 0.0603074 0.342020i
\(803\) 0 0
\(804\) 0.109277 + 0.0397734i 0.109277 + 0.0397734i
\(805\) 0.311820 1.04155i 0.311820 1.04155i
\(806\) 0 0
\(807\) 0.164512 0.549509i 0.164512 0.549509i
\(808\) 1.36912 0.687600i 1.36912 0.687600i
\(809\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(810\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 2.43641 1.22361i 2.43641 1.22361i
\(813\) 0 0
\(814\) 0 0
\(815\) −0.439408 + 1.46773i −0.439408 + 1.46773i
\(816\) 0 0
\(817\) 0 0
\(818\) −0.326352 + 1.85083i −0.326352 + 1.85083i
\(819\) 0 0
\(820\) −0.290162 1.64559i −0.290162 1.64559i
\(821\) 0.770807 + 0.182685i 0.770807 + 0.182685i 0.597159 0.802123i \(-0.296296\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(822\) 0 0
\(823\) −1.62593 + 1.06939i −1.62593 + 1.06939i −0.686242 + 0.727374i \(0.740741\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(824\) 0.109277 + 1.87621i 0.109277 + 1.87621i
\(825\) 0 0
\(826\) 0 0
\(827\) 1.86668 + 0.679415i 1.86668 + 0.679415i 0.973045 + 0.230616i \(0.0740741\pi\)
0.893633 + 0.448799i \(0.148148\pi\)
\(828\) 0.770807 0.182685i 0.770807 0.182685i
\(829\) −0.744386 + 0.270935i −0.744386 + 0.270935i −0.686242 0.727374i \(-0.740741\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(830\) −0.997837 1.34033i −0.997837 1.34033i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 1.65968 + 1.09159i 1.65968 + 1.09159i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.0581448 0.998308i \(-0.481481\pi\)
−0.0581448 + 0.998308i \(0.518519\pi\)
\(840\) −0.819590 + 1.10090i −0.819590 + 1.10090i
\(841\) −2.92617 0.342020i −2.92617 0.342020i
\(842\) −0.238329 0.252614i −0.238329 0.252614i
\(843\) −0.973045 + 1.68536i −0.973045 + 1.68536i
\(844\) 0 0
\(845\) 0.766044 + 0.642788i 0.766044 + 0.642788i
\(846\) −0.893633 + 1.54782i −0.893633 + 1.54782i
\(847\) −1.05138 + 0.882215i −1.05138 + 0.882215i
\(848\) 0 0
\(849\) 1.16212 + 0.275428i 1.16212 + 0.275428i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 0.686242 0.727374i \(-0.259259\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(854\) −2.04609 + 1.71687i −2.04609 + 1.71687i
\(855\) 0 0
\(856\) −0.439408 0.368707i −0.439408 0.368707i
\(857\) 0 0 0.993238 0.116093i \(-0.0370370\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(858\) 0 0
\(859\) 0 0 −0.686242 0.727374i \(-0.740741\pi\)
0.686242 + 0.727374i \(0.259259\pi\)
\(860\) −0.344948 0.0403186i −0.344948 0.0403186i
\(861\) 1.36952 1.83958i 1.36952 1.83958i
\(862\) 0 0
\(863\) 0.286803 + 0.496758i 0.286803 + 0.496758i 0.973045 0.230616i \(-0.0740741\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(864\) −0.993238 0.116093i −0.993238 0.116093i
\(865\) 0 0
\(866\) 0 0
\(867\) 0.893633 + 0.448799i 0.893633 + 0.448799i
\(868\) 0 0
\(869\) 0 0
\(870\) 1.86668 0.679415i 1.86668 0.679415i
\(871\) 0 0
\(872\) −1.12229 + 0.408481i −1.12229 + 0.408481i
\(873\) 0 0
\(874\) 0 0
\(875\) 0.393633 + 1.31482i 0.393633 + 1.31482i
\(876\) 0 0
\(877\) 0 0 −0.0581448 0.998308i \(-0.518519\pi\)
0.0581448 + 0.998308i \(0.481481\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0.207391 + 1.17617i 0.207391 + 1.17617i 0.893633 + 0.448799i \(0.148148\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(882\) −0.877735 + 0.102593i −0.877735 + 0.102593i
\(883\) −0.290162 + 1.64559i −0.290162 + 1.64559i 0.396080 + 0.918216i \(0.370370\pi\)
−0.686242 + 0.727374i \(0.740741\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0.0333522 0.111404i 0.0333522 0.111404i
\(887\) 0.914900 1.22892i 0.914900 1.22892i −0.0581448 0.998308i \(-0.518519\pi\)
0.973045 0.230616i \(-0.0740741\pi\)
\(888\) 0 0
\(889\) −1.46483 + 0.735663i −1.46483 + 0.735663i
\(890\) 1.78727 1.78727
\(891\) 0 0
\(892\) 1.78727 1.78727
\(893\) 0 0
\(894\) −0.342534 + 1.14414i −0.342534 + 1.14414i
\(895\) 0 0
\(896\) 0.393633 1.31482i 0.393633 1.31482i
\(897\) 0 0
\(898\) 0.606829 1.40679i 0.606829 1.40679i
\(899\) 0 0
\(900\) −0.686242 + 0.727374i −0.686242 + 0.727374i
\(901\) 0 0
\(902\) 0 0
\(903\) −0.284641 0.382339i −0.284641 0.382339i
\(904\) 0 0
\(905\) 0.0333522 + 0.572636i 0.0333522 + 0.572636i
\(906\) 0 0
\(907\) 0.164512 + 0.549509i 0.164512 + 0.549509i 1.00000 \(0\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(908\) 1.76604 + 0.642788i 1.76604 + 0.642788i
\(909\) 1.36912 + 0.687600i 1.36912 + 0.687600i
\(910\) 0 0
\(911\) 0 0 −0.597159 0.802123i \(-0.703704\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −1.62593 + 1.06939i −1.62593 + 1.06939i
\(916\) 1.65968 + 1.09159i 1.65968 + 1.09159i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(920\) −0.0460600 + 0.790819i −0.0460600 + 0.790819i
\(921\) −0.786803 0.0919641i −0.786803 0.0919641i
\(922\) 0.569728 + 0.0665916i 0.569728 + 0.0665916i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) −1.43969 1.20805i −1.43969 1.20805i
\(927\) −1.43969 + 1.20805i −1.43969 + 1.20805i
\(928\) −1.52173 + 1.27688i −1.52173 + 1.27688i
\(929\) −0.238329 + 0.252614i −0.238329 + 0.252614i −0.835488 0.549509i \(-0.814815\pi\)
0.597159 + 0.802123i \(0.296296\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) −0.238329 + 0.252614i −0.238329 + 0.252614i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 −0.766044 0.642788i \(-0.777778\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(938\) −0.158526 + 0.0185291i −0.158526 + 0.0185291i
\(939\) 0 0
\(940\) −1.22650 1.30001i −1.22650 1.30001i
\(941\) 1.65968 + 0.193988i 1.65968 + 0.193988i 0.893633 0.448799i \(-0.148148\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(942\) 0 0
\(943\) 0.0769651 1.32144i 0.0769651 1.32144i
\(944\) 0 0
\(945\) −1.37248 −1.37248
\(946\) 0 0
\(947\) 1.39608 + 0.918216i 1.39608 + 0.918216i 1.00000 \(0\)
0.396080 + 0.918216i \(0.370370\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0.396080 0.918216i 0.396080 0.918216i
\(961\) 0.973045 + 0.230616i 0.973045 + 0.230616i
\(962\) 0 0
\(963\) 0.0333522 0.572636i 0.0333522 0.572636i
\(964\) −0.0996057 + 0.564892i −0.0996057 + 0.564892i
\(965\) 0 0
\(966\) −0.832863 + 0.698855i −0.832863 + 0.698855i
\(967\) −0.227194 + 0.758881i −0.227194 + 0.758881i 0.766044 + 0.642788i \(0.222222\pi\)
−0.993238 + 0.116093i \(0.962963\pi\)
\(968\) 0.597159 0.802123i 0.597159 0.802123i
\(969\) 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
\(974\) −0.893633 + 0.448799i −0.893633 + 0.448799i
\(975\) 0 0
\(976\) 1.16212 1.56100i 1.16212 1.56100i
\(977\) 0 0 0.286803 0.957990i \(-0.407407\pi\)
−0.286803 + 0.957990i \(0.592593\pi\)
\(978\) 1.17365 0.984808i 1.17365 0.984808i
\(979\) 0 0
\(980\) 0.153455 0.870285i 0.153455 0.870285i
\(981\) −0.997837 0.656288i −0.997837 0.656288i
\(982\) 0 0
\(983\) −1.33549 0.316516i −1.33549 0.316516i −0.500000 0.866025i \(-0.666667\pi\)
−0.835488 + 0.549509i \(0.814815\pi\)
\(984\) −0.661840 + 1.53432i −0.661840 + 1.53432i
\(985\) 0 0
\(986\) 0 0
\(987\) 0.142629 2.44884i 0.142629 2.44884i
\(988\) 0 0
\(989\) −0.258523 0.0940946i −0.258523 0.0940946i
\(990\) 0 0
\(991\) 0 0 0.939693 0.342020i \(-0.111111\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0.0971586 + 1.66815i 0.0971586 + 1.66815i
\(997\) 0 0 −0.835488 0.549509i \(-0.814815\pi\)
0.835488 + 0.549509i \(0.185185\pi\)
\(998\) 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.1159.1 yes 18
4.3 odd 2 1620.1.bp.a.1159.1 yes 18
5.4 even 2 1620.1.bp.a.1159.1 yes 18
20.19 odd 2 CM 1620.1.bp.b.1159.1 yes 18
81.13 even 27 inner 1620.1.bp.b.499.1 yes 18
324.175 odd 54 1620.1.bp.a.499.1 18
405.94 even 54 1620.1.bp.a.499.1 18
1620.499 odd 54 inner 1620.1.bp.b.499.1 yes 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1620.1.bp.a.499.1 18 324.175 odd 54
1620.1.bp.a.499.1 18 405.94 even 54
1620.1.bp.a.1159.1 yes 18 4.3 odd 2
1620.1.bp.a.1159.1 yes 18 5.4 even 2
1620.1.bp.b.499.1 yes 18 81.13 even 27 inner
1620.1.bp.b.499.1 yes 18 1620.499 odd 54 inner
1620.1.bp.b.1159.1 yes 18 1.1 even 1 trivial
1620.1.bp.b.1159.1 yes 18 20.19 odd 2 CM