Properties

Label 1380.1.bn.d.479.2
Level $1380$
Weight $1$
Character 1380.479
Analytic conductor $0.689$
Analytic rank $0$
Dimension $20$
Projective image $D_{22}$
CM discriminant -20
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1380,1,Mod(359,1380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1380, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 11, 21]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1380.359");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1380.bn (of order \(22\), degree \(10\), 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: \(0.688709717434\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{22})\)
Coefficient field: \(\Q(\zeta_{44})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{22}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{22} - \cdots)\)

Embedding invariants

Embedding label 479.2
Root \(-0.909632 - 0.415415i\) of defining polynomial
Character \(\chi\) \(=\) 1380.479
Dual form 1380.1.bn.d.1259.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.909632 - 0.415415i) q^{2} +(0.989821 + 0.142315i) q^{3} +(0.654861 - 0.755750i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-0.281733 + 0.0405070i) q^{7} +(0.281733 - 0.959493i) q^{8} +(0.959493 + 0.281733i) q^{9} +O(q^{10})\) \(q+(0.909632 - 0.415415i) q^{2} +(0.989821 + 0.142315i) q^{3} +(0.654861 - 0.755750i) q^{4} +(-0.841254 - 0.540641i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-0.281733 + 0.0405070i) q^{7} +(0.281733 - 0.959493i) q^{8} +(0.959493 + 0.281733i) q^{9} +(-0.989821 - 0.142315i) q^{10} +(0.755750 - 0.654861i) q^{12} +(-0.239446 + 0.153882i) q^{14} +(-0.755750 - 0.654861i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(0.989821 - 0.142315i) q^{18} +(-0.959493 + 0.281733i) q^{20} -0.284630 q^{21} +(-0.909632 + 0.415415i) q^{23} +(0.415415 - 0.909632i) q^{24} +(0.415415 + 0.909632i) q^{25} +(0.909632 + 0.415415i) q^{27} +(-0.153882 + 0.239446i) q^{28} +(-0.817178 + 0.708089i) q^{29} +(-0.959493 - 0.281733i) q^{30} +(-0.540641 - 0.841254i) q^{32} +(0.258908 + 0.118239i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-0.755750 + 0.654861i) q^{40} +(1.07028 - 1.66538i) q^{41} +(-0.258908 + 0.118239i) q^{42} +(0.368991 + 1.25667i) q^{43} +(-0.654861 - 0.755750i) q^{45} +(-0.654861 + 0.755750i) q^{46} +1.68251i q^{47} -1.00000i q^{48} +(-0.881761 + 0.258908i) q^{49} +(0.755750 + 0.654861i) q^{50} +1.00000 q^{54} +(-0.0405070 + 0.281733i) q^{56} +(-0.449181 + 0.983568i) q^{58} +(-0.989821 + 0.142315i) q^{60} +(0.425839 - 1.45027i) q^{61} +(-0.281733 - 0.0405070i) q^{63} +(-0.841254 - 0.540641i) q^{64} +(-1.74557 + 0.797176i) q^{67} +(-0.959493 + 0.281733i) q^{69} +0.284630 q^{70} +(0.540641 - 0.841254i) q^{72} +(0.281733 + 0.959493i) q^{75} +(-0.415415 + 0.909632i) q^{80} +(0.841254 + 0.540641i) q^{81} +(0.281733 - 1.95949i) q^{82} +(-0.474017 + 0.304632i) q^{83} +(-0.186393 + 0.215109i) q^{84} +(0.857685 + 0.989821i) q^{86} +(-0.909632 + 0.584585i) q^{87} +(0.797176 - 0.234072i) q^{89} +(-0.909632 - 0.415415i) q^{90} +(-0.281733 + 0.959493i) q^{92} +(0.698939 + 1.53046i) q^{94} +(-0.415415 - 0.909632i) q^{96} +(-0.694523 + 0.601808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{9} - 4 q^{14} - 2 q^{16} - 2 q^{20} - 4 q^{21} - 2 q^{24} - 2 q^{25} - 2 q^{30} - 2 q^{36} - 2 q^{45} - 2 q^{46} - 16 q^{49} + 20 q^{54} - 18 q^{56} + 2 q^{64} - 2 q^{69} + 4 q^{70} + 2 q^{80} - 2 q^{81} + 4 q^{84} + 18 q^{86} + 4 q^{89} - 4 q^{94} + 2 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(691\) \(1201\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(e\left(\frac{15}{22}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.909632 0.415415i 0.909632 0.415415i
\(3\) 0.989821 + 0.142315i 0.989821 + 0.142315i
\(4\) 0.654861 0.755750i 0.654861 0.755750i
\(5\) −0.841254 0.540641i −0.841254 0.540641i
\(6\) 0.959493 0.281733i 0.959493 0.281733i
\(7\) −0.281733 + 0.0405070i −0.281733 + 0.0405070i −0.281733 0.959493i \(-0.590909\pi\)
1.00000i \(0.5\pi\)
\(8\) 0.281733 0.959493i 0.281733 0.959493i
\(9\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(10\) −0.989821 0.142315i −0.989821 0.142315i
\(11\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(12\) 0.755750 0.654861i 0.755750 0.654861i
\(13\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(14\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(15\) −0.755750 0.654861i −0.755750 0.654861i
\(16\) −0.142315 0.989821i −0.142315 0.989821i
\(17\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(18\) 0.989821 0.142315i 0.989821 0.142315i
\(19\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(20\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(21\) −0.284630 −0.284630
\(22\) 0 0
\(23\) −0.909632 + 0.415415i −0.909632 + 0.415415i
\(24\) 0.415415 0.909632i 0.415415 0.909632i
\(25\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(26\) 0 0
\(27\) 0.909632 + 0.415415i 0.909632 + 0.415415i
\(28\) −0.153882 + 0.239446i −0.153882 + 0.239446i
\(29\) −0.817178 + 0.708089i −0.817178 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(30\) −0.959493 0.281733i −0.959493 0.281733i
\(31\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(32\) −0.540641 0.841254i −0.540641 0.841254i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.258908 + 0.118239i 0.258908 + 0.118239i
\(36\) 0.841254 0.540641i 0.841254 0.540641i
\(37\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.755750 + 0.654861i −0.755750 + 0.654861i
\(41\) 1.07028 1.66538i 1.07028 1.66538i 0.415415 0.909632i \(-0.363636\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(42\) −0.258908 + 0.118239i −0.258908 + 0.118239i
\(43\) 0.368991 + 1.25667i 0.368991 + 1.25667i 0.909632 + 0.415415i \(0.136364\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(44\) 0 0
\(45\) −0.654861 0.755750i −0.654861 0.755750i
\(46\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(47\) 1.68251i 1.68251i 0.540641 + 0.841254i \(0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(48\) 1.00000i 1.00000i
\(49\) −0.881761 + 0.258908i −0.881761 + 0.258908i
\(50\) 0.755750 + 0.654861i 0.755750 + 0.654861i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(54\) 1.00000 1.00000
\(55\) 0 0
\(56\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(57\) 0 0
\(58\) −0.449181 + 0.983568i −0.449181 + 0.983568i
\(59\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(60\) −0.989821 + 0.142315i −0.989821 + 0.142315i
\(61\) 0.425839 1.45027i 0.425839 1.45027i −0.415415 0.909632i \(-0.636364\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(62\) 0 0
\(63\) −0.281733 0.0405070i −0.281733 0.0405070i
\(64\) −0.841254 0.540641i −0.841254 0.540641i
\(65\) 0 0
\(66\) 0 0
\(67\) −1.74557 + 0.797176i −1.74557 + 0.797176i −0.755750 + 0.654861i \(0.772727\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(68\) 0 0
\(69\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(70\) 0.284630 0.284630
\(71\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(72\) 0.540641 0.841254i 0.540641 0.841254i
\(73\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(74\) 0 0
\(75\) 0.281733 + 0.959493i 0.281733 + 0.959493i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(80\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(81\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(82\) 0.281733 1.95949i 0.281733 1.95949i
\(83\) −0.474017 + 0.304632i −0.474017 + 0.304632i −0.755750 0.654861i \(-0.772727\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(84\) −0.186393 + 0.215109i −0.186393 + 0.215109i
\(85\) 0 0
\(86\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(87\) −0.909632 + 0.584585i −0.909632 + 0.584585i
\(88\) 0 0
\(89\) 0.797176 0.234072i 0.797176 0.234072i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(90\) −0.909632 0.415415i −0.909632 0.415415i
\(91\) 0 0
\(92\) −0.281733 + 0.959493i −0.281733 + 0.959493i
\(93\) 0 0
\(94\) 0.698939 + 1.53046i 0.698939 + 1.53046i
\(95\) 0 0
\(96\) −0.415415 0.909632i −0.415415 0.909632i
\(97\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(98\) −0.694523 + 0.601808i −0.694523 + 0.601808i
\(99\) 0 0
\(100\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(101\) 0.304632 + 0.474017i 0.304632 + 0.474017i 0.959493 0.281733i \(-0.0909091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(102\) 0 0
\(103\) 1.53046 + 0.698939i 1.53046 + 0.698939i 0.989821 0.142315i \(-0.0454545\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(104\) 0 0
\(105\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(106\) 0 0
\(107\) −1.03748 0.304632i −1.03748 0.304632i −0.281733 0.959493i \(-0.590909\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(108\) 0.909632 0.415415i 0.909632 0.415415i
\(109\) −1.37491 + 1.19136i −1.37491 + 1.19136i −0.415415 + 0.909632i \(0.636364\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.0801894 + 0.273100i 0.0801894 + 0.273100i
\(113\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(114\) 0 0
\(115\) 0.989821 + 0.142315i 0.989821 + 0.142315i
\(116\) 1.08128i 1.08128i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(121\) −0.654861 0.755750i −0.654861 0.755750i
\(122\) −0.215109 1.49611i −0.215109 1.49611i
\(123\) 1.29639 1.49611i 1.29639 1.49611i
\(124\) 0 0
\(125\) 0.142315 0.989821i 0.142315 0.989821i
\(126\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i
\(127\) −0.234072 + 0.512546i −0.234072 + 0.512546i −0.989821 0.142315i \(-0.954545\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(128\) −0.989821 0.142315i −0.989821 0.142315i
\(129\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(130\) 0 0
\(131\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(135\) −0.540641 0.841254i −0.540641 0.841254i
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) −0.755750 + 0.654861i −0.755750 + 0.654861i
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0.258908 0.118239i 0.258908 0.118239i
\(141\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.142315 0.989821i 0.142315 0.989821i
\(145\) 1.07028 0.153882i 1.07028 0.153882i
\(146\) 0 0
\(147\) −0.909632 + 0.130785i −0.909632 + 0.130785i
\(148\) 0 0
\(149\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(150\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(151\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 1.00000i 1.00000i
\(161\) 0.239446 0.153882i 0.239446 0.153882i
\(162\) 0.989821 + 0.142315i 0.989821 + 0.142315i
\(163\) −0.627899 1.37491i −0.627899 1.37491i −0.909632 0.415415i \(-0.863636\pi\)
0.281733 0.959493i \(-0.409091\pi\)
\(164\) −0.557730 1.89945i −0.557730 1.89945i
\(165\) 0 0
\(166\) −0.304632 + 0.474017i −0.304632 + 0.474017i
\(167\) 0.989821 0.857685i 0.989821 0.857685i 1.00000i \(-0.5\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(168\) −0.0801894 + 0.273100i −0.0801894 + 0.273100i
\(169\) −0.959493 0.281733i −0.959493 0.281733i
\(170\) 0 0
\(171\) 0 0
\(172\) 1.19136 + 0.544078i 1.19136 + 0.544078i
\(173\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(174\) −0.584585 + 0.909632i −0.584585 + 0.909632i
\(175\) −0.153882 0.239446i −0.153882 0.239446i
\(176\) 0 0
\(177\) 0 0
\(178\) 0.627899 0.544078i 0.627899 0.544078i
\(179\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(180\) −1.00000 −1.00000
\(181\) −0.158746 0.540641i −0.158746 0.540641i 0.841254 0.540641i \(-0.181818\pi\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0.627899 1.37491i 0.627899 1.37491i
\(184\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 1.27155 + 1.10181i 1.27155 + 1.10181i
\(189\) −0.273100 0.0801894i −0.273100 0.0801894i
\(190\) 0 0
\(191\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(192\) −0.755750 0.654861i −0.755750 0.654861i
\(193\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.381761 + 0.835939i −0.381761 + 0.835939i
\(197\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(198\) 0 0
\(199\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(200\) 0.989821 0.142315i 0.989821 0.142315i
\(201\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(202\) 0.474017 + 0.304632i 0.474017 + 0.304632i
\(203\) 0.201543 0.232593i 0.201543 0.232593i
\(204\) 0 0
\(205\) −1.80075 + 0.822373i −1.80075 + 0.822373i
\(206\) 1.68251 1.68251
\(207\) −0.989821 + 0.142315i −0.989821 + 0.142315i
\(208\) 0 0
\(209\) 0 0
\(210\) 0.281733 + 0.0405070i 0.281733 + 0.0405070i
\(211\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.07028 + 0.153882i −1.07028 + 0.153882i
\(215\) 0.368991 1.25667i 0.368991 1.25667i
\(216\) 0.654861 0.755750i 0.654861 0.755750i
\(217\) 0 0
\(218\) −0.755750 + 1.65486i −0.755750 + 1.65486i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.215109 1.49611i −0.215109 1.49611i −0.755750 0.654861i \(-0.772727\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(224\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(225\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(226\) 0 0
\(227\) 1.03748 0.304632i 1.03748 0.304632i 0.281733 0.959493i \(-0.409091\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(228\) 0 0
\(229\) 1.81926i 1.81926i −0.415415 0.909632i \(-0.636364\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(230\) 0.959493 0.281733i 0.959493 0.281733i
\(231\) 0 0
\(232\) 0.449181 + 0.983568i 0.449181 + 0.983568i
\(233\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(234\) 0 0
\(235\) 0.909632 1.41542i 0.909632 1.41542i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(240\) −0.540641 + 0.841254i −0.540641 + 0.841254i
\(241\) 1.80075 + 0.822373i 1.80075 + 0.822373i 0.959493 + 0.281733i \(0.0909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(242\) −0.909632 0.415415i −0.909632 0.415415i
\(243\) 0.755750 + 0.654861i 0.755750 + 0.654861i
\(244\) −0.817178 1.27155i −0.817178 1.27155i
\(245\) 0.881761 + 0.258908i 0.881761 + 0.258908i
\(246\) 0.557730 1.89945i 0.557730 1.89945i
\(247\) 0 0
\(248\) 0 0
\(249\) −0.512546 + 0.234072i −0.512546 + 0.234072i
\(250\) −0.281733 0.959493i −0.281733 0.959493i
\(251\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(252\) −0.215109 + 0.186393i −0.215109 + 0.186393i
\(253\) 0 0
\(254\) 0.563465i 0.563465i
\(255\) 0 0
\(256\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(257\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(258\) 0.708089 + 1.10181i 0.708089 + 1.10181i
\(259\) 0 0
\(260\) 0 0
\(261\) −0.983568 + 0.449181i −0.983568 + 0.449181i
\(262\) 0 0
\(263\) 0.215109 1.49611i 0.215109 1.49611i −0.540641 0.841254i \(-0.681818\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0.822373 0.118239i 0.822373 0.118239i
\(268\) −0.540641 + 1.84125i −0.540641 + 1.84125i
\(269\) −0.557730 + 0.0801894i −0.557730 + 0.0801894i −0.415415 0.909632i \(-0.636364\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(270\) −0.841254 0.540641i −0.841254 0.540641i
\(271\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0.186393 0.215109i 0.186393 0.215109i
\(281\) 1.10181 + 0.708089i 1.10181 + 0.708089i 0.959493 0.281733i \(-0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(282\) 0.474017 + 1.61435i 0.474017 + 1.61435i
\(283\) −0.822373 + 0.118239i −0.822373 + 0.118239i −0.540641 0.841254i \(-0.681818\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.234072 + 0.512546i −0.234072 + 0.512546i
\(288\) −0.281733 0.959493i −0.281733 0.959493i
\(289\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(290\) 0.909632 0.584585i 0.909632 0.584585i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(294\) −0.773100 + 0.496841i −0.773100 + 0.496841i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 1.68251i 1.68251i
\(299\) 0 0
\(300\) 0.909632 + 0.415415i 0.909632 + 0.415415i
\(301\) −0.154861 0.339098i −0.154861 0.339098i
\(302\) 0 0
\(303\) 0.234072 + 0.512546i 0.234072 + 0.512546i
\(304\) 0 0
\(305\) −1.14231 + 0.989821i −1.14231 + 0.989821i
\(306\) 0 0
\(307\) −1.89945 0.557730i −1.89945 0.557730i −0.989821 0.142315i \(-0.954545\pi\)
−0.909632 0.415415i \(-0.863636\pi\)
\(308\) 0 0
\(309\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(310\) 0 0
\(311\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(312\) 0 0
\(313\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(314\) 0 0
\(315\) 0.215109 + 0.186393i 0.215109 + 0.186393i
\(316\) 0 0
\(317\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(321\) −0.983568 0.449181i −0.983568 0.449181i
\(322\) 0.153882 0.239446i 0.153882 0.239446i
\(323\) 0 0
\(324\) 0.959493 0.281733i 0.959493 0.281733i
\(325\) 0 0
\(326\) −1.14231 0.989821i −1.14231 0.989821i
\(327\) −1.53046 + 0.983568i −1.53046 + 0.983568i
\(328\) −1.29639 1.49611i −1.29639 1.49611i
\(329\) −0.0681534 0.474017i −0.0681534 0.474017i
\(330\) 0 0
\(331\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(332\) −0.0801894 + 0.557730i −0.0801894 + 0.557730i
\(333\) 0 0
\(334\) 0.544078 1.19136i 0.544078 1.19136i
\(335\) 1.89945 + 0.273100i 1.89945 + 0.273100i
\(336\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(337\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(338\) −0.989821 + 0.142315i −0.989821 + 0.142315i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.496841 0.226900i 0.496841 0.226900i
\(344\) 1.30972 1.30972
\(345\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(346\) 0 0
\(347\) 1.74557 0.797176i 1.74557 0.797176i 0.755750 0.654861i \(-0.227273\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(348\) −0.153882 + 1.07028i −0.153882 + 1.07028i
\(349\) −0.186393 + 0.215109i −0.186393 + 0.215109i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(350\) −0.239446 0.153882i −0.239446 0.153882i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.345139 0.755750i 0.345139 0.755750i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(360\) −0.909632 + 0.415415i −0.909632 + 0.415415i
\(361\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(362\) −0.368991 0.425839i −0.368991 0.425839i
\(363\) −0.540641 0.841254i −0.540641 0.841254i
\(364\) 0 0
\(365\) 0 0
\(366\) 1.51150i 1.51150i
\(367\) 1.91899i 1.91899i 0.281733 + 0.959493i \(0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(368\) 0.540641 + 0.841254i 0.540641 + 0.841254i
\(369\) 1.49611 1.29639i 1.49611 1.29639i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(374\) 0 0
\(375\) 0.281733 0.959493i 0.281733 0.959493i
\(376\) 1.61435 + 0.474017i 1.61435 + 0.474017i
\(377\) 0 0
\(378\) −0.281733 + 0.0405070i −0.281733 + 0.0405070i
\(379\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(380\) 0 0
\(381\) −0.304632 + 0.474017i −0.304632 + 0.474017i
\(382\) 0 0
\(383\) −1.89945 0.557730i −1.89945 0.557730i −0.989821 0.142315i \(-0.954545\pi\)
−0.909632 0.415415i \(-0.863636\pi\)
\(384\) −0.959493 0.281733i −0.959493 0.281733i
\(385\) 0 0
\(386\) 0 0
\(387\) 1.30972i 1.30972i
\(388\) 0 0
\(389\) 0.345139 + 0.755750i 0.345139 + 0.755750i 1.00000 \(0\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.918986i 0.918986i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.841254 0.540641i 0.841254 0.540641i
\(401\) 0.273100 1.89945i 0.273100 1.89945i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(402\) −1.45027 + 1.25667i −1.45027 + 1.25667i
\(403\) 0 0
\(404\) 0.557730 + 0.0801894i 0.557730 + 0.0801894i
\(405\) −0.415415 0.909632i −0.415415 0.909632i
\(406\) 0.0867074 0.295298i 0.0867074 0.295298i
\(407\) 0 0
\(408\) 0 0
\(409\) 1.41542 + 0.909632i 1.41542 + 0.909632i 1.00000 \(0\)
0.415415 + 0.909632i \(0.363636\pi\)
\(410\) −1.29639 + 1.49611i −1.29639 + 1.49611i
\(411\) 0 0
\(412\) 1.53046 0.698939i 1.53046 0.698939i
\(413\) 0 0
\(414\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(415\) 0.563465 0.563465
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(420\) 0.273100 0.0801894i 0.273100 0.0801894i
\(421\) 1.95949 0.281733i 1.95949 0.281733i 0.959493 0.281733i \(-0.0909091\pi\)
1.00000 \(0\)
\(422\) 0 0
\(423\) −0.474017 + 1.61435i −0.474017 + 1.61435i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.0612263 + 0.425839i −0.0612263 + 0.425839i
\(428\) −0.909632 + 0.584585i −0.909632 + 0.584585i
\(429\) 0 0
\(430\) −0.186393 1.29639i −0.186393 1.29639i
\(431\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(432\) 0.281733 0.959493i 0.281733 0.959493i
\(433\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(434\) 0 0
\(435\) 1.08128 1.08128
\(436\) 1.81926i 1.81926i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(440\) 0 0
\(441\) −0.918986 −0.918986
\(442\) 0 0
\(443\) −0.989821 + 0.857685i −0.989821 + 0.857685i −0.989821 0.142315i \(-0.954545\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) −0.797176 0.234072i −0.797176 0.234072i
\(446\) −0.817178 1.27155i −0.817178 1.27155i
\(447\) 0.909632 1.41542i 0.909632 1.41542i
\(448\) 0.258908 + 0.118239i 0.258908 + 0.118239i
\(449\) −1.65486 0.755750i −1.65486 0.755750i −0.654861 0.755750i \(-0.727273\pi\)
−1.00000 \(\pi\)
\(450\) 0.540641 + 0.841254i 0.540641 + 0.841254i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.817178 0.708089i 0.817178 0.708089i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(458\) −0.755750 1.65486i −0.755750 1.65486i
\(459\) 0 0
\(460\) 0.755750 0.654861i 0.755750 0.654861i
\(461\) 1.81926i 1.81926i 0.415415 + 0.909632i \(0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(462\) 0 0
\(463\) −1.89945 + 0.557730i −1.89945 + 0.557730i −0.909632 + 0.415415i \(0.863636\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(464\) 0.817178 + 0.708089i 0.817178 + 0.708089i
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(468\) 0 0
\(469\) 0.459493 0.295298i 0.459493 0.295298i
\(470\) 0.239446 1.66538i 0.239446 1.66538i
\(471\) 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 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(480\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(481\) 0 0
\(482\) 1.97964 1.97964
\(483\) 0.258908 0.118239i 0.258908 0.118239i
\(484\) −1.00000 −1.00000
\(485\) 0 0
\(486\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(487\) 1.29639 1.49611i 1.29639 1.49611i 0.540641 0.841254i \(-0.318182\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(488\) −1.27155 0.817178i −1.27155 0.817178i
\(489\) −0.425839 1.45027i −0.425839 1.45027i
\(490\) 0.909632 0.130785i 0.909632 0.130785i
\(491\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(492\) −0.281733 1.95949i −0.281733 1.95949i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.368991 + 0.425839i −0.368991 + 0.425839i
\(499\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(500\) −0.654861 0.755750i −0.654861 0.755750i
\(501\) 1.10181 0.708089i 1.10181 0.708089i
\(502\) 0 0
\(503\) 1.74557 0.512546i 1.74557 0.512546i 0.755750 0.654861i \(-0.227273\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(504\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(505\) 0.563465i 0.563465i
\(506\) 0 0
\(507\) −0.909632 0.415415i −0.909632 0.415415i
\(508\) 0.234072 + 0.512546i 0.234072 + 0.512546i
\(509\) −0.425839 1.45027i −0.425839 1.45027i −0.841254 0.540641i \(-0.818182\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.755750 + 0.654861i −0.755750 + 0.654861i
\(513\) 0 0
\(514\) 0 0
\(515\) −0.909632 1.41542i −0.909632 1.41542i
\(516\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(522\) −0.708089 + 0.817178i −0.708089 + 0.817178i
\(523\) 1.45027 1.25667i 1.45027 1.25667i 0.540641 0.841254i \(-0.318182\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(524\) 0 0
\(525\) −0.118239 0.258908i −0.118239 0.258908i
\(526\) −0.425839 1.45027i −0.425839 1.45027i
\(527\) 0 0
\(528\) 0 0
\(529\) 0.654861 0.755750i 0.654861 0.755750i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0.698939 0.449181i 0.698939 0.449181i
\(535\) 0.708089 + 0.817178i 0.708089 + 0.817178i
\(536\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(537\) 0 0
\(538\) −0.474017 + 0.304632i −0.474017 + 0.304632i
\(539\) 0 0
\(540\) −0.989821 0.142315i −0.989821 0.142315i
\(541\) 0.797176 1.74557i 0.797176 1.74557i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(542\) 0 0
\(543\) −0.0801894 0.557730i −0.0801894 0.557730i
\(544\) 0 0
\(545\) 1.80075 0.258908i 1.80075 0.258908i
\(546\) 0 0
\(547\) −0.909632 0.584585i −0.909632 0.584585i 1.00000i \(-0.5\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(548\) 0 0
\(549\) 0.817178 1.27155i 0.817178 1.27155i
\(550\) 0 0
\(551\) 0 0
\(552\) 1.00000i 1.00000i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.0801894 0.273100i 0.0801894 0.273100i
\(561\) 0 0
\(562\) 1.29639 + 0.186393i 1.29639 + 0.186393i
\(563\) −0.822373 + 1.80075i −0.822373 + 1.80075i −0.281733 + 0.959493i \(0.590909\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(564\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(565\) 0 0
\(566\) −0.698939 + 0.449181i −0.698939 + 0.449181i
\(567\) −0.258908 0.118239i −0.258908 0.118239i
\(568\) 0 0
\(569\) 1.25667 + 1.45027i 1.25667 + 1.45027i 0.841254 + 0.540641i \(0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(570\) 0 0
\(571\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.563465i 0.563465i
\(575\) −0.755750 0.654861i −0.755750 0.654861i
\(576\) −0.654861 0.755750i −0.654861 0.755750i
\(577\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(578\) 0.281733 + 0.959493i 0.281733 + 0.959493i
\(579\) 0 0
\(580\) 0.584585 0.909632i 0.584585 0.909632i
\(581\) 0.121206 0.105026i 0.121206 0.105026i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.19136 0.544078i −1.19136 0.544078i −0.281733 0.959493i \(-0.590909\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(588\) −0.496841 + 0.773100i −0.496841 + 0.773100i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.698939 1.53046i −0.698939 1.53046i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 1.00000 1.00000
\(601\) −0.797176 + 0.234072i −0.797176 + 0.234072i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(602\) −0.281733 0.244123i −0.281733 0.244123i
\(603\) −1.89945 + 0.273100i −1.89945 + 0.273100i
\(604\) 0 0
\(605\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(606\) 0.425839 + 0.368991i 0.425839 + 0.368991i
\(607\) 1.27155 0.817178i 1.27155 0.817178i 0.281733 0.959493i \(-0.409091\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(608\) 0 0
\(609\) 0.232593 0.201543i 0.232593 0.201543i
\(610\) −0.627899 + 1.37491i −0.627899 + 1.37491i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(614\) −1.95949 + 0.281733i −1.95949 + 0.281733i
\(615\) −1.89945 + 0.557730i −1.89945 + 0.557730i
\(616\) 0 0
\(617\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(618\) 1.66538 + 0.239446i 1.66538 + 0.239446i
\(619\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(620\) 0 0
\(621\) −1.00000 −1.00000
\(622\) 0 0
\(623\) −0.215109 + 0.0982369i −0.215109 + 0.0982369i
\(624\) 0 0
\(625\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(631\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.474017 0.304632i 0.474017 0.304632i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0.755750 + 0.654861i 0.755750 + 0.654861i
\(641\) −1.61435 + 0.474017i −1.61435 + 0.474017i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(642\) −1.08128 −1.08128
\(643\) 1.30972i 1.30972i −0.755750 0.654861i \(-0.772727\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(644\) 0.0405070 0.281733i 0.0405070 0.281733i
\(645\) 0.544078 1.19136i 0.544078 1.19136i
\(646\) 0 0
\(647\) 0.540641 + 1.84125i 0.540641 + 1.84125i 0.540641 + 0.841254i \(0.318182\pi\)
1.00000i \(0.5\pi\)
\(648\) 0.755750 0.654861i 0.755750 0.654861i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −1.45027 0.425839i −1.45027 0.425839i
\(653\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(654\) −0.983568 + 1.53046i −0.983568 + 1.53046i
\(655\) 0 0
\(656\) −1.80075 0.822373i −1.80075 0.822373i
\(657\) 0 0
\(658\) −0.258908 0.402869i −0.258908 0.402869i
\(659\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(660\) 0 0
\(661\) −0.817178 + 0.708089i −0.817178 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.158746 + 0.540641i 0.158746 + 0.540641i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.449181 0.983568i 0.449181 0.983568i
\(668\) 1.30972i 1.30972i
\(669\) 1.51150i 1.51150i
\(670\) 1.84125 0.540641i 1.84125 0.540641i
\(671\) 0 0
\(672\) 0.153882 + 0.239446i 0.153882 + 0.239446i
\(673\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(674\) 0 0
\(675\) 1.00000i 1.00000i
\(676\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(677\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.07028 0.153882i 1.07028 0.153882i
\(682\) 0 0
\(683\) 0.281733 0.0405070i 0.281733 0.0405070i 1.00000i \(-0.5\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.357685 0.412791i 0.357685 0.412791i
\(687\) 0.258908 1.80075i 0.258908 1.80075i
\(688\) 1.19136 0.544078i 1.19136 0.544078i
\(689\) 0 0
\(690\) 0.989821 0.142315i 0.989821 0.142315i
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.25667 1.45027i 1.25667 1.45027i
\(695\) 0 0
\(696\) 0.304632 + 1.03748i 0.304632 + 1.03748i
\(697\) 0 0
\(698\) −0.0801894 + 0.273100i −0.0801894 + 0.273100i
\(699\) 0 0
\(700\) −0.281733 0.0405070i −0.281733 0.0405070i
\(701\) −0.544078 + 1.19136i −0.544078 + 1.19136i 0.415415 + 0.909632i \(0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 1.10181 1.27155i 1.10181 1.27155i
\(706\) 0 0
\(707\) −0.105026 0.121206i −0.105026 0.121206i
\(708\) 0 0
\(709\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.830830i 0.830830i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(720\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(721\) −0.459493 0.134919i −0.459493 0.134919i
\(722\) 0.540641 + 0.841254i 0.540641 + 0.841254i
\(723\) 1.66538 + 1.07028i 1.66538 + 1.07028i
\(724\) −0.512546 0.234072i −0.512546 0.234072i
\(725\) −0.983568 0.449181i −0.983568 0.449181i
\(726\) −0.841254 0.540641i −0.841254 0.540641i
\(727\) 0.909632 + 1.41542i 0.909632 + 1.41542i 0.909632 + 0.415415i \(0.136364\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.627899 1.37491i −0.627899 1.37491i
\(733\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(734\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(735\) 0.835939 + 0.381761i 0.835939 + 0.381761i
\(736\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(737\) 0 0
\(738\) 0.822373 1.80075i 0.822373 1.80075i
\(739\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.153882 + 1.07028i 0.153882 + 1.07028i 0.909632 + 0.415415i \(0.136364\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(744\) 0 0
\(745\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(746\) 0 0
\(747\) −0.540641 + 0.158746i −0.540641 + 0.158746i
\(748\) 0 0
\(749\) 0.304632 + 0.0437995i 0.304632 + 0.0437995i
\(750\) −0.142315 0.989821i −0.142315 0.989821i
\(751\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(752\) 1.66538 0.239446i 1.66538 0.239446i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(757\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.80075 + 0.822373i −1.80075 + 0.822373i −0.841254 + 0.540641i \(0.818182\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(762\) −0.0801894 + 0.557730i −0.0801894 + 0.557730i
\(763\) 0.339098 0.391340i 0.339098 0.391340i
\(764\) 0 0
\(765\) 0 0
\(766\) −1.95949 + 0.281733i −1.95949 + 0.281733i
\(767\) 0 0
\(768\) −0.989821 + 0.142315i −0.989821 + 0.142315i
\(769\) 1.49611 + 0.215109i 1.49611 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(774\) 0.544078 + 1.19136i 0.544078 + 1.19136i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.627899 + 0.544078i 0.627899 + 0.544078i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −1.03748 + 0.304632i −1.03748 + 0.304632i
\(784\) 0.381761 + 0.835939i 0.381761 + 0.835939i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.449181 0.698939i 0.449181 0.698939i −0.540641 0.841254i \(-0.681818\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(788\) 0 0
\(789\) 0.425839 1.45027i 0.425839 1.45027i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.540641 0.841254i 0.540641 0.841254i
\(801\) 0.830830 0.830830
\(802\) −0.540641 1.84125i −0.540641 1.84125i
\(803\) 0 0
\(804\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(805\) −0.284630 −0.284630
\(806\) 0 0
\(807\) −0.563465 −0.563465
\(808\) 0.540641 0.158746i 0.540641 0.158746i
\(809\) 1.37491 + 1.19136i 1.37491 + 1.19136i 0.959493 + 0.281733i \(0.0909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(810\) −0.755750 0.654861i −0.755750 0.654861i
\(811\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(812\) −0.0437995 0.304632i −0.0437995 0.304632i
\(813\) 0 0
\(814\) 0 0
\(815\) −0.215109 + 1.49611i −0.215109 + 1.49611i
\(816\) 0 0
\(817\) 0 0
\(818\) 1.66538 + 0.239446i 1.66538 + 0.239446i
\(819\) 0 0
\(820\) −0.557730 + 1.89945i −0.557730 + 1.89945i
\(821\) −1.07028 + 0.153882i −1.07028 + 0.153882i −0.654861 0.755750i \(-0.727273\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(822\) 0 0
\(823\) 1.66538 + 1.07028i 1.66538 + 1.07028i 0.909632 + 0.415415i \(0.136364\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(824\) 1.10181 1.27155i 1.10181 1.27155i
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) −0.540641 + 0.841254i −0.540641 + 0.841254i
\(829\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(830\) 0.512546 0.234072i 0.512546 0.234072i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −1.29639 + 0.186393i −1.29639 + 0.186393i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(840\) 0.215109 0.186393i 0.215109 0.186393i
\(841\) 0.0240754 0.167448i 0.0240754 0.167448i
\(842\) 1.66538 1.07028i 1.66538 1.07028i
\(843\) 0.989821 + 0.857685i 0.989821 + 0.857685i
\(844\) 0 0
\(845\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(846\) 0.239446 + 1.66538i 0.239446 + 1.66538i
\(847\) 0.215109 + 0.186393i 0.215109 + 0.186393i
\(848\) 0 0
\(849\) −0.830830 −0.830830
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(854\) 0.121206 + 0.412791i 0.121206 + 0.412791i
\(855\) 0 0
\(856\) −0.584585 + 0.909632i −0.584585 + 0.909632i
\(857\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(858\) 0 0
\(859\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(860\) −0.708089 1.10181i −0.708089 1.10181i
\(861\) −0.304632 + 0.474017i −0.304632 + 0.474017i
\(862\) 0 0
\(863\) −0.258908 0.118239i −0.258908 0.118239i 0.281733 0.959493i \(-0.409091\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(864\) −0.142315 0.989821i −0.142315 0.989821i
\(865\) 0 0
\(866\) 0 0
\(867\) −0.281733 + 0.959493i −0.281733 + 0.959493i
\(868\) 0 0
\(869\) 0 0
\(870\) 0.983568 0.449181i 0.983568 0.449181i
\(871\) 0 0
\(872\) 0.755750 + 1.65486i 0.755750 + 1.65486i
\(873\) 0 0
\(874\) 0 0
\(875\) 0.284630i 0.284630i
\(876\) 0 0
\(877\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −0.273100 1.89945i −0.273100 1.89945i −0.415415 0.909632i \(-0.636364\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(882\) −0.835939 + 0.381761i −0.835939 + 0.381761i
\(883\) −1.53046 + 0.983568i −1.53046 + 0.983568i −0.540641 + 0.841254i \(0.681818\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(887\) 0.822373 + 0.118239i 0.822373 + 0.118239i 0.540641 0.841254i \(-0.318182\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(888\) 0 0
\(889\) 0.0451840 0.153882i 0.0451840 0.153882i
\(890\) −0.822373 + 0.118239i −0.822373 + 0.118239i
\(891\) 0 0
\(892\) −1.27155 0.817178i −1.27155 0.817178i
\(893\) 0 0
\(894\) 0.239446 1.66538i 0.239446 1.66538i
\(895\) 0 0
\(896\) 0.284630 0.284630
\(897\) 0 0
\(898\) −1.81926 −1.81926
\(899\) 0 0
\(900\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(901\) 0 0
\(902\) 0 0
\(903\) −0.105026 0.357685i −0.105026 0.357685i
\(904\) 0 0
\(905\) −0.158746 + 0.540641i −0.158746 + 0.540641i
\(906\) 0 0
\(907\) −0.822373 0.118239i −0.822373 0.118239i −0.281733 0.959493i \(-0.590909\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(908\) 0.449181 0.983568i 0.449181 0.983568i
\(909\) 0.158746 + 0.540641i 0.158746 + 0.540641i
\(910\) 0 0
\(911\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −1.27155 + 0.817178i −1.27155 + 0.817178i
\(916\) −1.37491 1.19136i −1.37491 1.19136i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0.415415 0.909632i 0.415415 0.909632i
\(921\) −1.80075 0.822373i −1.80075 0.822373i
\(922\) 0.755750 + 1.65486i 0.755750 + 1.65486i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) −1.49611 + 1.29639i −1.49611 + 1.29639i
\(927\) 1.27155 + 1.10181i 1.27155 + 1.10181i
\(928\) 1.03748 + 0.304632i 1.03748 + 0.304632i
\(929\) 0.584585 + 0.909632i 0.584585 + 0.909632i 1.00000 \(0\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(938\) 0.295298 0.459493i 0.295298 0.459493i
\(939\) 0 0
\(940\) −0.474017 1.61435i −0.474017 1.61435i
\(941\) 0.544078 + 1.19136i 0.544078 + 1.19136i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(942\) 0 0
\(943\) −0.281733 + 1.95949i −0.281733 + 1.95949i
\(944\) 0 0
\(945\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(946\) 0 0
\(947\) 0.627899 + 0.544078i 0.627899 + 0.544078i 0.909632 0.415415i \(-0.136364\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0.281733 + 0.959493i 0.281733 + 0.959493i
\(961\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(962\) 0 0
\(963\) −0.909632 0.584585i −0.909632 0.584585i
\(964\) 1.80075 0.822373i 1.80075 0.822373i
\(965\) 0 0
\(966\) 0.186393 0.215109i 0.186393 0.215109i
\(967\) 1.81926 1.81926 0.909632 0.415415i \(-0.136364\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(968\) −0.909632 + 0.415415i −0.909632 + 0.415415i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(972\) 0.989821 0.142315i 0.989821 0.142315i
\(973\) 0 0
\(974\) 0.557730 1.89945i 0.557730 1.89945i
\(975\) 0 0
\(976\) −1.49611 0.215109i −1.49611 0.215109i
\(977\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(978\) −0.989821 1.14231i −0.989821 1.14231i
\(979\) 0 0
\(980\) 0.773100 0.496841i 0.773100 0.496841i
\(981\) −1.65486 + 0.755750i −1.65486 + 0.755750i
\(982\) 0 0
\(983\) −1.19136 1.37491i −1.19136 1.37491i −0.909632 0.415415i \(-0.863636\pi\)
−0.281733 0.959493i \(-0.590909\pi\)
\(984\) −1.07028 1.66538i −1.07028 1.66538i
\(985\) 0 0
\(986\) 0 0
\(987\) 0.478891i 0.478891i
\(988\) 0 0
\(989\) −0.857685 0.989821i −0.857685 0.989821i
\(990\) 0 0
\(991\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) −0.158746 + 0.540641i −0.158746 + 0.540641i
\(997\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(998\) 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 1380.1.bn.d.479.2 yes 20
3.2 odd 2 1380.1.bn.a.479.1 20
4.3 odd 2 inner 1380.1.bn.d.479.1 yes 20
5.4 even 2 inner 1380.1.bn.d.479.1 yes 20
12.11 even 2 1380.1.bn.a.479.2 yes 20
15.14 odd 2 1380.1.bn.a.479.2 yes 20
20.19 odd 2 CM 1380.1.bn.d.479.2 yes 20
23.17 odd 22 1380.1.bn.a.1259.1 yes 20
60.59 even 2 1380.1.bn.a.479.1 20
69.17 even 22 inner 1380.1.bn.d.1259.2 yes 20
92.63 even 22 1380.1.bn.a.1259.2 yes 20
115.109 odd 22 1380.1.bn.a.1259.2 yes 20
276.155 odd 22 inner 1380.1.bn.d.1259.1 yes 20
345.224 even 22 inner 1380.1.bn.d.1259.1 yes 20
460.339 even 22 1380.1.bn.a.1259.1 yes 20
1380.1259 odd 22 inner 1380.1.bn.d.1259.2 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1380.1.bn.a.479.1 20 3.2 odd 2
1380.1.bn.a.479.1 20 60.59 even 2
1380.1.bn.a.479.2 yes 20 12.11 even 2
1380.1.bn.a.479.2 yes 20 15.14 odd 2
1380.1.bn.a.1259.1 yes 20 23.17 odd 22
1380.1.bn.a.1259.1 yes 20 460.339 even 22
1380.1.bn.a.1259.2 yes 20 92.63 even 22
1380.1.bn.a.1259.2 yes 20 115.109 odd 22
1380.1.bn.d.479.1 yes 20 4.3 odd 2 inner
1380.1.bn.d.479.1 yes 20 5.4 even 2 inner
1380.1.bn.d.479.2 yes 20 1.1 even 1 trivial
1380.1.bn.d.479.2 yes 20 20.19 odd 2 CM
1380.1.bn.d.1259.1 yes 20 276.155 odd 22 inner
1380.1.bn.d.1259.1 yes 20 345.224 even 22 inner
1380.1.bn.d.1259.2 yes 20 69.17 even 22 inner
1380.1.bn.d.1259.2 yes 20 1380.1259 odd 22 inner