Properties

Label 1380.1.bn.d.839.2
Level $1380$
Weight $1$
Character 1380.839
Analytic conductor $0.689$
Analytic rank $0$
Dimension $20$
Projective image $D_{22}$
CM discriminant -20
Inner twists $8$

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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 839.2
Root \(-0.540641 + 0.841254i\) of defining polynomial
Character \(\chi\) \(=\) 1380.839
Dual form 1380.1.bn.d.1079.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.540641 + 0.841254i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.989821 - 0.857685i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(0.142315 + 0.989821i) q^{9} +O(q^{10})\) \(q+(0.540641 + 0.841254i) q^{2} +(-0.755750 - 0.654861i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(0.142315 - 0.989821i) q^{6} +(0.989821 - 0.857685i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(0.142315 + 0.989821i) q^{9} +(0.755750 + 0.654861i) q^{10} +(0.909632 - 0.415415i) q^{12} +(1.25667 + 0.368991i) q^{14} +(-0.909632 - 0.415415i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-0.755750 + 0.654861i) q^{18} +(-0.142315 + 0.989821i) q^{20} -1.30972 q^{21} +(-0.540641 - 0.841254i) q^{23} +(0.841254 + 0.540641i) q^{24} +(0.841254 - 0.540641i) q^{25} +(0.540641 - 0.841254i) q^{27} +(0.368991 + 1.25667i) q^{28} +(0.512546 - 0.234072i) q^{29} +(-0.142315 - 0.989821i) q^{30} +(0.281733 - 0.959493i) q^{32} +(0.708089 - 1.10181i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(-0.909632 + 0.415415i) q^{40} +(0.425839 + 1.45027i) q^{41} +(-0.708089 - 1.10181i) q^{42} +(0.822373 + 0.118239i) q^{43} +(0.415415 + 0.909632i) q^{45} +(0.415415 - 0.909632i) q^{46} +1.91899i q^{47} +1.00000i q^{48} +(0.101808 - 0.708089i) q^{49} +(0.909632 + 0.415415i) q^{50} +1.00000 q^{54} +(-0.857685 + 0.989821i) q^{56} +(0.474017 + 0.304632i) q^{58} +(0.755750 - 0.654861i) q^{60} +(-1.80075 + 0.258908i) q^{61} +(0.989821 + 0.857685i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-0.153882 - 0.239446i) q^{67} +(-0.142315 + 0.989821i) q^{69} +1.30972 q^{70} +(-0.281733 - 0.959493i) q^{72} +(-0.989821 - 0.142315i) q^{75} +(-0.841254 - 0.540641i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-0.989821 + 1.14231i) q^{82} +(-1.89945 - 0.557730i) q^{83} +(0.544078 - 1.19136i) q^{84} +(0.345139 + 0.755750i) q^{86} +(-0.540641 - 0.158746i) q^{87} +(0.239446 - 1.66538i) q^{89} +(-0.540641 + 0.841254i) q^{90} +(0.989821 - 0.142315i) q^{92} +(-1.61435 + 1.03748i) q^{94} +(-0.841254 + 0.540641i) q^{96} +(0.650724 - 0.297176i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(691\) \(1201\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(e\left(\frac{9}{22}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.540641 + 0.841254i 0.540641 + 0.841254i
\(3\) −0.755750 0.654861i −0.755750 0.654861i
\(4\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(5\) 0.959493 0.281733i 0.959493 0.281733i
\(6\) 0.142315 0.989821i 0.142315 0.989821i
\(7\) 0.989821 0.857685i 0.989821 0.857685i 1.00000i \(-0.5\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(8\) −0.989821 + 0.142315i −0.989821 + 0.142315i
\(9\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(10\) 0.755750 + 0.654861i 0.755750 + 0.654861i
\(11\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(12\) 0.909632 0.415415i 0.909632 0.415415i
\(13\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(14\) 1.25667 + 0.368991i 1.25667 + 0.368991i
\(15\) −0.909632 0.415415i −0.909632 0.415415i
\(16\) −0.654861 0.755750i −0.654861 0.755750i
\(17\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(18\) −0.755750 + 0.654861i −0.755750 + 0.654861i
\(19\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(20\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(21\) −1.30972 −1.30972
\(22\) 0 0
\(23\) −0.540641 0.841254i −0.540641 0.841254i
\(24\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(25\) 0.841254 0.540641i 0.841254 0.540641i
\(26\) 0 0
\(27\) 0.540641 0.841254i 0.540641 0.841254i
\(28\) 0.368991 + 1.25667i 0.368991 + 1.25667i
\(29\) 0.512546 0.234072i 0.512546 0.234072i −0.142315 0.989821i \(-0.545455\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(30\) −0.142315 0.989821i −0.142315 0.989821i
\(31\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(32\) 0.281733 0.959493i 0.281733 0.959493i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.708089 1.10181i 0.708089 1.10181i
\(36\) −0.959493 0.281733i −0.959493 0.281733i
\(37\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.909632 + 0.415415i −0.909632 + 0.415415i
\(41\) 0.425839 + 1.45027i 0.425839 + 1.45027i 0.841254 + 0.540641i \(0.181818\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(42\) −0.708089 1.10181i −0.708089 1.10181i
\(43\) 0.822373 + 0.118239i 0.822373 + 0.118239i 0.540641 0.841254i \(-0.318182\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(44\) 0 0
\(45\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(46\) 0.415415 0.909632i 0.415415 0.909632i
\(47\) 1.91899i 1.91899i 0.281733 + 0.959493i \(0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(48\) 1.00000i 1.00000i
\(49\) 0.101808 0.708089i 0.101808 0.708089i
\(50\) 0.909632 + 0.415415i 0.909632 + 0.415415i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(54\) 1.00000 1.00000
\(55\) 0 0
\(56\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(57\) 0 0
\(58\) 0.474017 + 0.304632i 0.474017 + 0.304632i
\(59\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(60\) 0.755750 0.654861i 0.755750 0.654861i
\(61\) −1.80075 + 0.258908i −1.80075 + 0.258908i −0.959493 0.281733i \(-0.909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(62\) 0 0
\(63\) 0.989821 + 0.857685i 0.989821 + 0.857685i
\(64\) 0.959493 0.281733i 0.959493 0.281733i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.153882 0.239446i −0.153882 0.239446i 0.755750 0.654861i \(-0.227273\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(68\) 0 0
\(69\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(70\) 1.30972 1.30972
\(71\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(72\) −0.281733 0.959493i −0.281733 0.959493i
\(73\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(74\) 0 0
\(75\) −0.989821 0.142315i −0.989821 0.142315i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(80\) −0.841254 0.540641i −0.841254 0.540641i
\(81\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(82\) −0.989821 + 1.14231i −0.989821 + 1.14231i
\(83\) −1.89945 0.557730i −1.89945 0.557730i −0.989821 0.142315i \(-0.954545\pi\)
−0.909632 0.415415i \(-0.863636\pi\)
\(84\) 0.544078 1.19136i 0.544078 1.19136i
\(85\) 0 0
\(86\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(87\) −0.540641 0.158746i −0.540641 0.158746i
\(88\) 0 0
\(89\) 0.239446 1.66538i 0.239446 1.66538i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(90\) −0.540641 + 0.841254i −0.540641 + 0.841254i
\(91\) 0 0
\(92\) 0.989821 0.142315i 0.989821 0.142315i
\(93\) 0 0
\(94\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(95\) 0 0
\(96\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(97\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(98\) 0.650724 0.297176i 0.650724 0.297176i
\(99\) 0 0
\(100\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(101\) 0.557730 1.89945i 0.557730 1.89945i 0.142315 0.989821i \(-0.454545\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(102\) 0 0
\(103\) −1.03748 + 1.61435i −1.03748 + 1.61435i −0.281733 + 0.959493i \(0.590909\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(104\) 0 0
\(105\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(106\) 0 0
\(107\) 0.0801894 + 0.557730i 0.0801894 + 0.557730i 0.989821 + 0.142315i \(0.0454545\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(108\) 0.540641 + 0.841254i 0.540641 + 0.841254i
\(109\) −0.983568 + 0.449181i −0.983568 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.29639 0.186393i −1.29639 0.186393i
\(113\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(114\) 0 0
\(115\) −0.755750 0.654861i −0.755750 0.654861i
\(116\) 0.563465i 0.563465i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(121\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(122\) −1.19136 1.37491i −1.19136 1.37491i
\(123\) 0.627899 1.37491i 0.627899 1.37491i
\(124\) 0 0
\(125\) 0.654861 0.755750i 0.654861 0.755750i
\(126\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(127\) 1.66538 + 1.07028i 1.66538 + 1.07028i 0.909632 + 0.415415i \(0.136364\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(128\) 0.755750 + 0.654861i 0.755750 + 0.654861i
\(129\) −0.544078 0.627899i −0.544078 0.627899i
\(130\) 0 0
\(131\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.118239 0.258908i 0.118239 0.258908i
\(135\) 0.281733 0.959493i 0.281733 0.959493i
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) −0.909632 + 0.415415i −0.909632 + 0.415415i
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0.708089 + 1.10181i 0.708089 + 1.10181i
\(141\) 1.25667 1.45027i 1.25667 1.45027i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.654861 0.755750i 0.654861 0.755750i
\(145\) 0.425839 0.368991i 0.425839 0.368991i
\(146\) 0 0
\(147\) −0.540641 + 0.468468i −0.540641 + 0.468468i
\(148\) 0 0
\(149\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(150\) −0.415415 0.909632i −0.415415 0.909632i
\(151\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 1.00000i 1.00000i
\(161\) −1.25667 0.368991i −1.25667 0.368991i
\(162\) −0.755750 0.654861i −0.755750 0.654861i
\(163\) −1.53046 + 0.983568i −1.53046 + 0.983568i −0.540641 + 0.841254i \(0.681818\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(164\) −1.49611 0.215109i −1.49611 0.215109i
\(165\) 0 0
\(166\) −0.557730 1.89945i −0.557730 1.89945i
\(167\) −0.755750 + 0.345139i −0.755750 + 0.345139i −0.755750 0.654861i \(-0.772727\pi\)
1.00000i \(0.5\pi\)
\(168\) 1.29639 0.186393i 1.29639 0.186393i
\(169\) −0.142315 0.989821i −0.142315 0.989821i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.449181 + 0.698939i −0.449181 + 0.698939i
\(173\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(174\) −0.158746 0.540641i −0.158746 0.540641i
\(175\) 0.368991 1.25667i 0.368991 1.25667i
\(176\) 0 0
\(177\) 0 0
\(178\) 1.53046 0.698939i 1.53046 0.698939i
\(179\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(180\) −1.00000 −1.00000
\(181\) −1.95949 0.281733i −1.95949 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 1.53046 + 0.983568i 1.53046 + 0.983568i
\(184\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −1.74557 0.797176i −1.74557 0.797176i
\(189\) −0.186393 1.29639i −0.186393 1.29639i
\(190\) 0 0
\(191\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(192\) −0.909632 0.415415i −0.909632 0.415415i
\(193\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.601808 + 0.386758i 0.601808 + 0.386758i
\(197\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(198\) 0 0
\(199\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(200\) −0.755750 + 0.654861i −0.755750 + 0.654861i
\(201\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(202\) 1.89945 0.557730i 1.89945 0.557730i
\(203\) 0.306569 0.671292i 0.306569 0.671292i
\(204\) 0 0
\(205\) 0.817178 + 1.27155i 0.817178 + 1.27155i
\(206\) −1.91899 −1.91899
\(207\) 0.755750 0.654861i 0.755750 0.654861i
\(208\) 0 0
\(209\) 0 0
\(210\) −0.989821 0.857685i −0.989821 0.857685i
\(211\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.425839 + 0.368991i −0.425839 + 0.368991i
\(215\) 0.822373 0.118239i 0.822373 0.118239i
\(216\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(217\) 0 0
\(218\) −0.909632 0.584585i −0.909632 0.584585i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.19136 1.37491i −1.19136 1.37491i −0.909632 0.415415i \(-0.863636\pi\)
−0.281733 0.959493i \(-0.590909\pi\)
\(224\) −0.544078 1.19136i −0.544078 1.19136i
\(225\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(226\) 0 0
\(227\) −0.0801894 + 0.557730i −0.0801894 + 0.557730i 0.909632 + 0.415415i \(0.136364\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(228\) 0 0
\(229\) 1.08128i 1.08128i 0.841254 + 0.540641i \(0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(230\) 0.142315 0.989821i 0.142315 0.989821i
\(231\) 0 0
\(232\) −0.474017 + 0.304632i −0.474017 + 0.304632i
\(233\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(234\) 0 0
\(235\) 0.540641 + 1.84125i 0.540641 + 1.84125i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(240\) 0.281733 + 0.959493i 0.281733 + 0.959493i
\(241\) −0.817178 + 1.27155i −0.817178 + 1.27155i 0.142315 + 0.989821i \(0.454545\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(242\) −0.540641 + 0.841254i −0.540641 + 0.841254i
\(243\) 0.909632 + 0.415415i 0.909632 + 0.415415i
\(244\) 0.512546 1.74557i 0.512546 1.74557i
\(245\) −0.101808 0.708089i −0.101808 0.708089i
\(246\) 1.49611 0.215109i 1.49611 0.215109i
\(247\) 0 0
\(248\) 0 0
\(249\) 1.07028 + 1.66538i 1.07028 + 1.66538i
\(250\) 0.989821 + 0.142315i 0.989821 + 0.142315i
\(251\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(252\) −1.19136 + 0.544078i −1.19136 + 0.544078i
\(253\) 0 0
\(254\) 1.97964i 1.97964i
\(255\) 0 0
\(256\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(257\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(258\) 0.234072 0.797176i 0.234072 0.797176i
\(259\) 0 0
\(260\) 0 0
\(261\) 0.304632 + 0.474017i 0.304632 + 0.474017i
\(262\) 0 0
\(263\) 1.19136 1.37491i 1.19136 1.37491i 0.281733 0.959493i \(-0.409091\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −1.27155 + 1.10181i −1.27155 + 1.10181i
\(268\) 0.281733 0.0405070i 0.281733 0.0405070i
\(269\) −1.49611 + 1.29639i −1.49611 + 1.29639i −0.654861 + 0.755750i \(0.727273\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(270\) 0.959493 0.281733i 0.959493 0.281733i
\(271\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −0.841254 0.540641i −0.841254 0.540641i
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(281\) 0.797176 0.234072i 0.797176 0.234072i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(282\) 1.89945 + 0.273100i 1.89945 + 0.273100i
\(283\) 1.27155 1.10181i 1.27155 1.10181i 0.281733 0.959493i \(-0.409091\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.66538 + 1.07028i 1.66538 + 1.07028i
\(288\) 0.989821 + 0.142315i 0.989821 + 0.142315i
\(289\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(290\) 0.540641 + 0.158746i 0.540641 + 0.158746i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(294\) −0.686393 0.201543i −0.686393 0.201543i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 1.91899i 1.91899i
\(299\) 0 0
\(300\) 0.540641 0.841254i 0.540641 0.841254i
\(301\) 0.915415 0.588302i 0.915415 0.588302i
\(302\) 0 0
\(303\) −1.66538 + 1.07028i −1.66538 + 1.07028i
\(304\) 0 0
\(305\) −1.65486 + 0.755750i −1.65486 + 0.755750i
\(306\) 0 0
\(307\) 0.215109 + 1.49611i 0.215109 + 1.49611i 0.755750 + 0.654861i \(0.227273\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(308\) 0 0
\(309\) 1.84125 0.540641i 1.84125 0.540641i
\(310\) 0 0
\(311\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(312\) 0 0
\(313\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(314\) 0 0
\(315\) 1.19136 + 0.544078i 1.19136 + 0.544078i
\(316\) 0 0
\(317\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.841254 0.540641i 0.841254 0.540641i
\(321\) 0.304632 0.474017i 0.304632 0.474017i
\(322\) −0.368991 1.25667i −0.368991 1.25667i
\(323\) 0 0
\(324\) 0.142315 0.989821i 0.142315 0.989821i
\(325\) 0 0
\(326\) −1.65486 0.755750i −1.65486 0.755750i
\(327\) 1.03748 + 0.304632i 1.03748 + 0.304632i
\(328\) −0.627899 1.37491i −0.627899 1.37491i
\(329\) 1.64589 + 1.89945i 1.64589 + 1.89945i
\(330\) 0 0
\(331\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(332\) 1.29639 1.49611i 1.29639 1.49611i
\(333\) 0 0
\(334\) −0.698939 0.449181i −0.698939 0.449181i
\(335\) −0.215109 0.186393i −0.215109 0.186393i
\(336\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(337\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(338\) 0.755750 0.654861i 0.755750 0.654861i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.201543 + 0.313607i 0.201543 + 0.313607i
\(344\) −0.830830 −0.830830
\(345\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(346\) 0 0
\(347\) 0.153882 + 0.239446i 0.153882 + 0.239446i 0.909632 0.415415i \(-0.136364\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(348\) 0.368991 0.425839i 0.368991 0.425839i
\(349\) 0.544078 1.19136i 0.544078 1.19136i −0.415415 0.909632i \(-0.636364\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(350\) 1.25667 0.368991i 1.25667 0.368991i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(360\) −0.540641 0.841254i −0.540641 0.841254i
\(361\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(362\) −0.822373 1.80075i −0.822373 1.80075i
\(363\) 0.281733 0.959493i 0.281733 0.959493i
\(364\) 0 0
\(365\) 0 0
\(366\) 1.81926i 1.81926i
\(367\) 0.284630i 0.284630i −0.989821 0.142315i \(-0.954545\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(368\) −0.281733 + 0.959493i −0.281733 + 0.959493i
\(369\) −1.37491 + 0.627899i −1.37491 + 0.627899i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(374\) 0 0
\(375\) −0.989821 + 0.142315i −0.989821 + 0.142315i
\(376\) −0.273100 1.89945i −0.273100 1.89945i
\(377\) 0 0
\(378\) 0.989821 0.857685i 0.989821 0.857685i
\(379\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(380\) 0 0
\(381\) −0.557730 1.89945i −0.557730 1.89945i
\(382\) 0 0
\(383\) 0.215109 + 1.49611i 0.215109 + 1.49611i 0.755750 + 0.654861i \(0.227273\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(384\) −0.142315 0.989821i −0.142315 0.989821i
\(385\) 0 0
\(386\) 0 0
\(387\) 0.830830i 0.830830i
\(388\) 0 0
\(389\) 1.41542 0.909632i 1.41542 0.909632i 0.415415 0.909632i \(-0.363636\pi\)
1.00000 \(0\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.715370i 0.715370i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.959493 0.281733i −0.959493 0.281733i
\(401\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(402\) −0.258908 + 0.118239i −0.258908 + 0.118239i
\(403\) 0 0
\(404\) 1.49611 + 1.29639i 1.49611 + 1.29639i
\(405\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(406\) 0.730471 0.105026i 0.730471 0.105026i
\(407\) 0 0
\(408\) 0 0
\(409\) 1.84125 0.540641i 1.84125 0.540641i 0.841254 0.540641i \(-0.181818\pi\)
1.00000 \(0\)
\(410\) −0.627899 + 1.37491i −0.627899 + 1.37491i
\(411\) 0 0
\(412\) −1.03748 1.61435i −1.03748 1.61435i
\(413\) 0 0
\(414\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(415\) −1.97964 −1.97964
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(420\) 0.186393 1.29639i 0.186393 1.29639i
\(421\) 1.14231 0.989821i 1.14231 0.989821i 0.142315 0.989821i \(-0.454545\pi\)
1.00000 \(0\)
\(422\) 0 0
\(423\) −1.89945 + 0.273100i −1.89945 + 0.273100i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.56036 + 1.80075i −1.56036 + 1.80075i
\(428\) −0.540641 0.158746i −0.540641 0.158746i
\(429\) 0 0
\(430\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(431\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(432\) −0.989821 + 0.142315i −0.989821 + 0.142315i
\(433\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(434\) 0 0
\(435\) −0.563465 −0.563465
\(436\) 1.08128i 1.08128i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(440\) 0 0
\(441\) 0.715370 0.715370
\(442\) 0 0
\(443\) 0.755750 0.345139i 0.755750 0.345139i 1.00000i \(-0.5\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(444\) 0 0
\(445\) −0.239446 1.66538i −0.239446 1.66538i
\(446\) 0.512546 1.74557i 0.512546 1.74557i
\(447\) 0.540641 + 1.84125i 0.540641 + 1.84125i
\(448\) 0.708089 1.10181i 0.708089 1.10181i
\(449\) −0.584585 + 0.909632i −0.584585 + 0.909632i 0.415415 + 0.909632i \(0.363636\pi\)
−1.00000 \(1.00000\pi\)
\(450\) −0.281733 + 0.959493i −0.281733 + 0.959493i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −0.512546 + 0.234072i −0.512546 + 0.234072i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(458\) −0.909632 + 0.584585i −0.909632 + 0.584585i
\(459\) 0 0
\(460\) 0.909632 0.415415i 0.909632 0.415415i
\(461\) 1.08128i 1.08128i −0.841254 0.540641i \(-0.818182\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(462\) 0 0
\(463\) 0.215109 1.49611i 0.215109 1.49611i −0.540641 0.841254i \(-0.681818\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(464\) −0.512546 0.234072i −0.512546 0.234072i
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(468\) 0 0
\(469\) −0.357685 0.105026i −0.357685 0.105026i
\(470\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(471\) 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 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(480\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(481\) 0 0
\(482\) −1.51150 −1.51150
\(483\) 0.708089 + 1.10181i 0.708089 + 1.10181i
\(484\) −1.00000 −1.00000
\(485\) 0 0
\(486\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(487\) 0.627899 1.37491i 0.627899 1.37491i −0.281733 0.959493i \(-0.590909\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(488\) 1.74557 0.512546i 1.74557 0.512546i
\(489\) 1.80075 + 0.258908i 1.80075 + 0.258908i
\(490\) 0.540641 0.468468i 0.540641 0.468468i
\(491\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(492\) 0.989821 + 1.14231i 0.989821 + 1.14231i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.822373 + 1.80075i −0.822373 + 1.80075i
\(499\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(500\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(501\) 0.797176 + 0.234072i 0.797176 + 0.234072i
\(502\) 0 0
\(503\) 0.153882 1.07028i 0.153882 1.07028i −0.755750 0.654861i \(-0.772727\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(504\) −1.10181 0.708089i −1.10181 0.708089i
\(505\) 1.97964i 1.97964i
\(506\) 0 0
\(507\) −0.540641 + 0.841254i −0.540641 + 0.841254i
\(508\) −1.66538 + 1.07028i −1.66538 + 1.07028i
\(509\) 1.80075 + 0.258908i 1.80075 + 0.258908i 0.959493 0.281733i \(-0.0909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.909632 + 0.415415i −0.909632 + 0.415415i
\(513\) 0 0
\(514\) 0 0
\(515\) −0.540641 + 1.84125i −0.540641 + 1.84125i
\(516\) 0.797176 0.234072i 0.797176 0.234072i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i \(0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(522\) −0.234072 + 0.512546i −0.234072 + 0.512546i
\(523\) 0.258908 0.118239i 0.258908 0.118239i −0.281733 0.959493i \(-0.590909\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(524\) 0 0
\(525\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(526\) 1.80075 + 0.258908i 1.80075 + 0.258908i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −1.61435 0.474017i −1.61435 0.474017i
\(535\) 0.234072 + 0.512546i 0.234072 + 0.512546i
\(536\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(537\) 0 0
\(538\) −1.89945 0.557730i −1.89945 0.557730i
\(539\) 0 0
\(540\) 0.755750 + 0.654861i 0.755750 + 0.654861i
\(541\) 0.239446 + 0.153882i 0.239446 + 0.153882i 0.654861 0.755750i \(-0.272727\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(542\) 0 0
\(543\) 1.29639 + 1.49611i 1.29639 + 1.49611i
\(544\) 0 0
\(545\) −0.817178 + 0.708089i −0.817178 + 0.708089i
\(546\) 0 0
\(547\) −0.540641 + 0.158746i −0.540641 + 0.158746i −0.540641 0.841254i \(-0.681818\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) −0.512546 1.74557i −0.512546 1.74557i
\(550\) 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 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −1.29639 + 0.186393i −1.29639 + 0.186393i
\(561\) 0 0
\(562\) 0.627899 + 0.544078i 0.627899 + 0.544078i
\(563\) 1.27155 + 0.817178i 1.27155 + 0.817178i 0.989821 0.142315i \(-0.0454545\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(564\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(565\) 0 0
\(566\) 1.61435 + 0.474017i 1.61435 + 0.474017i
\(567\) −0.708089 + 1.10181i −0.708089 + 1.10181i
\(568\) 0 0
\(569\) −0.118239 0.258908i −0.118239 0.258908i 0.841254 0.540641i \(-0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(570\) 0 0
\(571\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 1.97964i 1.97964i
\(575\) −0.909632 0.415415i −0.909632 0.415415i
\(576\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(577\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(578\) −0.989821 0.142315i −0.989821 0.142315i
\(579\) 0 0
\(580\) 0.158746 + 0.540641i 0.158746 + 0.540641i
\(581\) −2.35848 + 1.07708i −2.35848 + 1.07708i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.449181 0.698939i 0.449181 0.698939i −0.540641 0.841254i \(-0.681818\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(588\) −0.201543 0.686393i −0.201543 0.686393i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.61435 1.03748i 1.61435 1.03748i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 1.00000 1.00000
\(601\) −0.239446 + 1.66538i −0.239446 + 1.66538i 0.415415 + 0.909632i \(0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(602\) 0.989821 + 0.452036i 0.989821 + 0.452036i
\(603\) 0.215109 0.186393i 0.215109 0.186393i
\(604\) 0 0
\(605\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(606\) −1.80075 0.822373i −1.80075 0.822373i
\(607\) −1.74557 0.512546i −1.74557 0.512546i −0.755750 0.654861i \(-0.772727\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(608\) 0 0
\(609\) −0.671292 + 0.306569i −0.671292 + 0.306569i
\(610\) −1.53046 0.983568i −1.53046 0.983568i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(614\) −1.14231 + 0.989821i −1.14231 + 0.989821i
\(615\) 0.215109 1.49611i 0.215109 1.49611i
\(616\) 0 0
\(617\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(618\) 1.45027 + 1.25667i 1.45027 + 1.25667i
\(619\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(620\) 0 0
\(621\) −1.00000 −1.00000
\(622\) 0 0
\(623\) −1.19136 1.85380i −1.19136 1.85380i
\(624\) 0 0
\(625\) 0.415415 0.909632i 0.415415 0.909632i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(631\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.89945 + 0.557730i 1.89945 + 0.557730i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0.909632 + 0.415415i 0.909632 + 0.415415i
\(641\) 0.273100 1.89945i 0.273100 1.89945i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(642\) 0.563465 0.563465
\(643\) 0.830830i 0.830830i −0.909632 0.415415i \(-0.863636\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(644\) 0.857685 0.989821i 0.857685 0.989821i
\(645\) −0.698939 0.449181i −0.698939 0.449181i
\(646\) 0 0
\(647\) −0.281733 0.0405070i −0.281733 0.0405070i 1.00000i \(-0.5\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(648\) 0.909632 0.415415i 0.909632 0.415415i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.258908 1.80075i −0.258908 1.80075i
\(653\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(654\) 0.304632 + 1.03748i 0.304632 + 1.03748i
\(655\) 0 0
\(656\) 0.817178 1.27155i 0.817178 1.27155i
\(657\) 0 0
\(658\) −0.708089 + 2.41153i −0.708089 + 2.41153i
\(659\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(660\) 0 0
\(661\) 0.512546 0.234072i 0.512546 0.234072i −0.142315 0.989821i \(-0.545455\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 1.95949 + 0.281733i 1.95949 + 0.281733i
\(665\) 0 0
\(666\) 0 0
\(667\) −0.474017 0.304632i −0.474017 0.304632i
\(668\) 0.830830i 0.830830i
\(669\) 1.81926i 1.81926i
\(670\) 0.0405070 0.281733i 0.0405070 0.281733i
\(671\) 0 0
\(672\) −0.368991 + 1.25667i −0.368991 + 1.25667i
\(673\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(674\) 0 0
\(675\) 1.00000i 1.00000i
\(676\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(677\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.425839 0.368991i 0.425839 0.368991i
\(682\) 0 0
\(683\) −0.989821 + 0.857685i −0.989821 + 0.857685i −0.989821 0.142315i \(-0.954545\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.154861 + 0.339098i −0.154861 + 0.339098i
\(687\) 0.708089 0.817178i 0.708089 0.817178i
\(688\) −0.449181 0.698939i −0.449181 0.698939i
\(689\) 0 0
\(690\) −0.755750 + 0.654861i −0.755750 + 0.654861i
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(695\) 0 0
\(696\) 0.557730 + 0.0801894i 0.557730 + 0.0801894i
\(697\) 0 0
\(698\) 1.29639 0.186393i 1.29639 0.186393i
\(699\) 0 0
\(700\) 0.989821 + 0.857685i 0.989821 + 0.857685i
\(701\) 0.698939 + 0.449181i 0.698939 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0.797176 1.74557i 0.797176 1.74557i
\(706\) 0 0
\(707\) −1.07708 2.35848i −1.07708 2.35848i
\(708\) 0 0
\(709\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.68251i 1.68251i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(720\) 0.415415 0.909632i 0.415415 0.909632i
\(721\) 0.357685 + 2.48775i 0.357685 + 2.48775i
\(722\) −0.281733 + 0.959493i −0.281733 + 0.959493i
\(723\) 1.45027 0.425839i 1.45027 0.425839i
\(724\) 1.07028 1.66538i 1.07028 1.66538i
\(725\) 0.304632 0.474017i 0.304632 0.474017i
\(726\) 0.959493 0.281733i 0.959493 0.281733i
\(727\) 0.540641 1.84125i 0.540641 1.84125i 1.00000i \(-0.5\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(728\) 0 0
\(729\) −0.415415 0.909632i −0.415415 0.909632i
\(730\) 0 0
\(731\) 0 0
\(732\) −1.53046 + 0.983568i −1.53046 + 0.983568i
\(733\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(734\) 0.239446 0.153882i 0.239446 0.153882i
\(735\) −0.386758 + 0.601808i −0.386758 + 0.601808i
\(736\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(737\) 0 0
\(738\) −1.27155 0.817178i −1.27155 0.817178i
\(739\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.368991 0.425839i −0.368991 0.425839i 0.540641 0.841254i \(-0.318182\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(744\) 0 0
\(745\) −1.84125 0.540641i −1.84125 0.540641i
\(746\) 0 0
\(747\) 0.281733 1.95949i 0.281733 1.95949i
\(748\) 0 0
\(749\) 0.557730 + 0.483276i 0.557730 + 0.483276i
\(750\) −0.654861 0.755750i −0.654861 0.755750i
\(751\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(752\) 1.45027 1.25667i 1.45027 1.25667i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.25667 + 0.368991i 1.25667 + 0.368991i
\(757\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.817178 + 1.27155i 0.817178 + 1.27155i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(762\) 1.29639 1.49611i 1.29639 1.49611i
\(763\) −0.588302 + 1.28820i −0.588302 + 1.28820i
\(764\) 0 0
\(765\) 0 0
\(766\) −1.14231 + 0.989821i −1.14231 + 0.989821i
\(767\) 0 0
\(768\) 0.755750 0.654861i 0.755750 0.654861i
\(769\) −1.37491 1.19136i −1.37491 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(774\) −0.698939 + 0.449181i −0.698939 + 0.449181i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 1.53046 + 0.698939i 1.53046 + 0.698939i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0.0801894 0.557730i 0.0801894 0.557730i
\(784\) −0.601808 + 0.386758i −0.601808 + 0.386758i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.474017 1.61435i −0.474017 1.61435i −0.755750 0.654861i \(-0.772727\pi\)
0.281733 0.959493i \(-0.409091\pi\)
\(788\) 0 0
\(789\) −1.80075 + 0.258908i −1.80075 + 0.258908i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.281733 0.959493i −0.281733 0.959493i
\(801\) 1.68251 1.68251
\(802\) 0.281733 + 0.0405070i 0.281733 + 0.0405070i
\(803\) 0 0
\(804\) −0.239446 0.153882i −0.239446 0.153882i
\(805\) −1.30972 −1.30972
\(806\) 0 0
\(807\) 1.97964 1.97964
\(808\) −0.281733 + 1.95949i −0.281733 + 1.95949i
\(809\) 0.983568 + 0.449181i 0.983568 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(810\) −0.909632 0.415415i −0.909632 0.415415i
\(811\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(812\) 0.483276 + 0.557730i 0.483276 + 0.557730i
\(813\) 0 0
\(814\) 0 0
\(815\) −1.19136 + 1.37491i −1.19136 + 1.37491i
\(816\) 0 0
\(817\) 0 0
\(818\) 1.45027 + 1.25667i 1.45027 + 1.25667i
\(819\) 0 0
\(820\) −1.49611 + 0.215109i −1.49611 + 0.215109i
\(821\) −0.425839 + 0.368991i −0.425839 + 0.368991i −0.841254 0.540641i \(-0.818182\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(822\) 0 0
\(823\) 1.45027 0.425839i 1.45027 0.425839i 0.540641 0.841254i \(-0.318182\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(824\) 0.797176 1.74557i 0.797176 1.74557i
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0.281733 + 0.959493i 0.281733 + 0.959493i
\(829\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(830\) −1.07028 1.66538i −1.07028 1.66538i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −0.627899 + 0.544078i −0.627899 + 0.544078i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(840\) 1.19136 0.544078i 1.19136 0.544078i
\(841\) −0.446947 + 0.515804i −0.446947 + 0.515804i
\(842\) 1.45027 + 0.425839i 1.45027 + 0.425839i
\(843\) −0.755750 0.345139i −0.755750 0.345139i
\(844\) 0 0
\(845\) −0.415415 0.909632i −0.415415 0.909632i
\(846\) −1.25667 1.45027i −1.25667 1.45027i
\(847\) 1.19136 + 0.544078i 1.19136 + 0.544078i
\(848\) 0 0
\(849\) −1.68251 −1.68251
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(854\) −2.35848 0.339098i −2.35848 0.339098i
\(855\) 0 0
\(856\) −0.158746 0.540641i −0.158746 0.540641i
\(857\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(858\) 0 0
\(859\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(860\) −0.234072 + 0.797176i −0.234072 + 0.797176i
\(861\) −0.557730 1.89945i −0.557730 1.89945i
\(862\) 0 0
\(863\) −0.708089 + 1.10181i −0.708089 + 1.10181i 0.281733 + 0.959493i \(0.409091\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(864\) −0.654861 0.755750i −0.654861 0.755750i
\(865\) 0 0
\(866\) 0 0
\(867\) 0.989821 0.142315i 0.989821 0.142315i
\(868\) 0 0
\(869\) 0 0
\(870\) −0.304632 0.474017i −0.304632 0.474017i
\(871\) 0 0
\(872\) 0.909632 0.584585i 0.909632 0.584585i
\(873\) 0 0
\(874\) 0 0
\(875\) 1.30972i 1.30972i
\(876\) 0 0
\(877\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −0.186393 0.215109i −0.186393 0.215109i 0.654861 0.755750i \(-0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(882\) 0.386758 + 0.601808i 0.386758 + 0.601808i
\(883\) 1.03748 + 0.304632i 1.03748 + 0.304632i 0.755750 0.654861i \(-0.227273\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(887\) −1.27155 1.10181i −1.27155 1.10181i −0.989821 0.142315i \(-0.954545\pi\)
−0.281733 0.959493i \(-0.590909\pi\)
\(888\) 0 0
\(889\) 2.56639 0.368991i 2.56639 0.368991i
\(890\) 1.27155 1.10181i 1.27155 1.10181i
\(891\) 0 0
\(892\) 1.74557 0.512546i 1.74557 0.512546i
\(893\) 0 0
\(894\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(895\) 0 0
\(896\) 1.30972 1.30972
\(897\) 0 0
\(898\) −1.08128 −1.08128
\(899\) 0 0
\(900\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(901\) 0 0
\(902\) 0 0
\(903\) −1.07708 0.154861i −1.07708 0.154861i
\(904\) 0 0
\(905\) −1.95949 + 0.281733i −1.95949 + 0.281733i
\(906\) 0 0
\(907\) 1.27155 + 1.10181i 1.27155 + 1.10181i 0.989821 + 0.142315i \(0.0454545\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(908\) −0.474017 0.304632i −0.474017 0.304632i
\(909\) 1.95949 + 0.281733i 1.95949 + 0.281733i
\(910\) 0 0
\(911\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 1.74557 + 0.512546i 1.74557 + 0.512546i
\(916\) −0.983568 0.449181i −0.983568 0.449181i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(921\) 0.817178 1.27155i 0.817178 1.27155i
\(922\) 0.909632 0.584585i 0.909632 0.584585i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 1.37491 0.627899i 1.37491 0.627899i
\(927\) −1.74557 0.797176i −1.74557 0.797176i
\(928\) −0.0801894 0.557730i −0.0801894 0.557730i
\(929\) 0.158746 0.540641i 0.158746 0.540641i −0.841254 0.540641i \(-0.818182\pi\)
1.00000 \(0\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(938\) −0.105026 0.357685i −0.105026 0.357685i
\(939\) 0 0
\(940\) −1.89945 0.273100i −1.89945 0.273100i
\(941\) −0.698939 + 0.449181i −0.698939 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(942\) 0 0
\(943\) 0.989821 1.14231i 0.989821 1.14231i
\(944\) 0 0
\(945\) −0.544078 1.19136i −0.544078 1.19136i
\(946\) 0 0
\(947\) 1.53046 + 0.698939i 1.53046 + 0.698939i 0.989821 0.142315i \(-0.0454545\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −0.989821 0.142315i −0.989821 0.142315i
\(961\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(962\) 0 0
\(963\) −0.540641 + 0.158746i −0.540641 + 0.158746i
\(964\) −0.817178 1.27155i −0.817178 1.27155i
\(965\) 0 0
\(966\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(967\) 1.08128 1.08128 0.540641 0.841254i \(-0.318182\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(968\) −0.540641 0.841254i −0.540641 0.841254i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(972\) −0.755750 + 0.654861i −0.755750 + 0.654861i
\(973\) 0 0
\(974\) 1.49611 0.215109i 1.49611 0.215109i
\(975\) 0 0
\(976\) 1.37491 + 1.19136i 1.37491 + 1.19136i
\(977\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(978\) 0.755750 + 1.65486i 0.755750 + 1.65486i
\(979\) 0 0
\(980\) 0.686393 + 0.201543i 0.686393 + 0.201543i
\(981\) −0.584585 0.909632i −0.584585 0.909632i
\(982\) 0 0
\(983\) 0.449181 + 0.983568i 0.449181 + 0.983568i 0.989821 + 0.142315i \(0.0454545\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(984\) −0.425839 + 1.45027i −0.425839 + 1.45027i
\(985\) 0 0
\(986\) 0 0
\(987\) 2.51334i 2.51334i
\(988\) 0 0
\(989\) −0.345139 0.755750i −0.345139 0.755750i
\(990\) 0 0
\(991\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) −1.95949 + 0.281733i −1.95949 + 0.281733i
\(997\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(998\) 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.839.2 yes 20
3.2 odd 2 1380.1.bn.a.839.1 20
4.3 odd 2 inner 1380.1.bn.d.839.1 yes 20
5.4 even 2 inner 1380.1.bn.d.839.1 yes 20
12.11 even 2 1380.1.bn.a.839.2 yes 20
15.14 odd 2 1380.1.bn.a.839.2 yes 20
20.19 odd 2 CM 1380.1.bn.d.839.2 yes 20
23.21 odd 22 1380.1.bn.a.1079.1 yes 20
60.59 even 2 1380.1.bn.a.839.1 20
69.44 even 22 inner 1380.1.bn.d.1079.2 yes 20
92.67 even 22 1380.1.bn.a.1079.2 yes 20
115.44 odd 22 1380.1.bn.a.1079.2 yes 20
276.251 odd 22 inner 1380.1.bn.d.1079.1 yes 20
345.44 even 22 inner 1380.1.bn.d.1079.1 yes 20
460.159 even 22 1380.1.bn.a.1079.1 yes 20
1380.1079 odd 22 inner 1380.1.bn.d.1079.2 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1380.1.bn.a.839.1 20 3.2 odd 2
1380.1.bn.a.839.1 20 60.59 even 2
1380.1.bn.a.839.2 yes 20 12.11 even 2
1380.1.bn.a.839.2 yes 20 15.14 odd 2
1380.1.bn.a.1079.1 yes 20 23.21 odd 22
1380.1.bn.a.1079.1 yes 20 460.159 even 22
1380.1.bn.a.1079.2 yes 20 92.67 even 22
1380.1.bn.a.1079.2 yes 20 115.44 odd 22
1380.1.bn.d.839.1 yes 20 4.3 odd 2 inner
1380.1.bn.d.839.1 yes 20 5.4 even 2 inner
1380.1.bn.d.839.2 yes 20 1.1 even 1 trivial
1380.1.bn.d.839.2 yes 20 20.19 odd 2 CM
1380.1.bn.d.1079.1 yes 20 276.251 odd 22 inner
1380.1.bn.d.1079.1 yes 20 345.44 even 22 inner
1380.1.bn.d.1079.2 yes 20 69.44 even 22 inner
1380.1.bn.d.1079.2 yes 20 1380.1079 odd 22 inner