Properties

Label 1288.1.bi.e.1189.1
Level $1288$
Weight $1$
Character 1288.1189
Analytic conductor $0.643$
Analytic rank $0$
Dimension $20$
Projective image $D_{22}$
CM discriminant -56
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1288,1,Mod(13,1288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1288, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 11, 11, 14]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1288.13");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1288 = 2^{3} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1288.bi (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: \(0.642795736271\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 11 \)
Twist minimal: yes
Projective image: \(D_{22}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{22} - \cdots)\)

Embedding invariants

Embedding label 1189.1
Root \(-0.540641 - 0.841254i\) of defining polynomial
Character \(\chi\) \(=\) 1288.1189
Dual form 1288.1.bi.e.13.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.654861 - 0.755750i) q^{2} +(-0.909632 + 0.584585i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.234072 - 0.512546i) q^{5} +(-0.153882 + 1.07028i) q^{6} +(0.959493 - 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.0702757 - 0.153882i) q^{9} +O(q^{10})\) \(q+(0.654861 - 0.755750i) q^{2} +(-0.909632 + 0.584585i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.234072 - 0.512546i) q^{5} +(-0.153882 + 1.07028i) q^{6} +(0.959493 - 0.281733i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.0702757 - 0.153882i) q^{9} +(-0.540641 - 0.158746i) q^{10} +(0.708089 + 0.817178i) q^{12} +(1.45027 + 0.425839i) q^{13} +(0.415415 - 0.909632i) q^{14} +(0.512546 + 0.329393i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.0702757 - 0.153882i) q^{18} +(-0.258908 - 1.80075i) q^{19} +(-0.474017 + 0.304632i) q^{20} +(-0.708089 + 0.817178i) q^{21} +(-0.959493 - 0.281733i) q^{23} +1.08128 q^{24} +(0.446947 - 0.515804i) q^{25} +(1.27155 - 0.817178i) q^{26} +(-0.127850 - 0.889217i) q^{27} +(-0.415415 - 0.909632i) q^{28} +(0.584585 - 0.171650i) q^{30} +(-0.415415 + 0.909632i) q^{32} +(-0.368991 - 0.425839i) q^{35} +(-0.162317 - 0.0476607i) q^{36} +(-1.53046 - 0.983568i) q^{38} +(-1.56815 + 0.460451i) q^{39} +(-0.0801894 + 0.557730i) q^{40} +(0.153882 + 1.07028i) q^{42} -0.0953214 q^{45} +(-0.841254 + 0.540641i) q^{46} +(0.708089 - 0.817178i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.0971309 - 0.675560i) q^{50} +(0.215109 - 1.49611i) q^{52} +(-0.755750 - 0.485691i) q^{54} +(-0.959493 - 0.281733i) q^{56} +(1.28820 + 1.48666i) q^{57} +(1.74557 + 0.512546i) q^{59} +(0.253098 - 0.554206i) q^{60} +(0.0240754 - 0.167448i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.121206 - 0.843008i) q^{65} +(1.03748 - 0.304632i) q^{69} -0.563465 q^{70} +(-0.857685 + 0.989821i) q^{71} +(-0.142315 + 0.0914602i) q^{72} +(-0.105026 + 0.730471i) q^{75} +(-1.74557 + 0.512546i) q^{76} +(-0.678936 + 1.48666i) q^{78} +(-0.273100 - 0.0801894i) q^{79} +(0.368991 + 0.425839i) q^{80} +(0.746902 + 0.861971i) q^{81} +(-0.822373 + 1.80075i) q^{83} +(0.909632 + 0.584585i) q^{84} +(-0.0624222 + 0.0720391i) q^{90} +1.51150 q^{91} +(-0.142315 + 0.989821i) q^{92} +(-0.862362 + 0.554206i) q^{95} +(-0.153882 - 1.07028i) q^{96} +(0.142315 - 0.989821i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 2 q^{8} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 2 q^{8} - 20 q^{9} - 2 q^{14} - 2 q^{16} + 20 q^{18} - 2 q^{23} + 2 q^{25} + 2 q^{28} + 22 q^{30} + 2 q^{32} + 2 q^{36} - 22 q^{39} + 2 q^{46} - 2 q^{49} - 2 q^{50} - 2 q^{56} - 2 q^{63} - 2 q^{64} - 18 q^{71} - 2 q^{72} + 4 q^{79} + 20 q^{81} - 2 q^{92} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1288\mathbb{Z}\right)^\times\).

\(n\) \(185\) \(281\) \(645\) \(967\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{11}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.654861 0.755750i 0.654861 0.755750i
\(3\) −0.909632 + 0.584585i −0.909632 + 0.584585i −0.909632 0.415415i \(-0.863636\pi\)
1.00000i \(0.5\pi\)
\(4\) −0.142315 0.989821i −0.142315 0.989821i
\(5\) −0.234072 0.512546i −0.234072 0.512546i 0.755750 0.654861i \(-0.227273\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(6\) −0.153882 + 1.07028i −0.153882 + 1.07028i
\(7\) 0.959493 0.281733i 0.959493 0.281733i
\(8\) −0.841254 0.540641i −0.841254 0.540641i
\(9\) 0.0702757 0.153882i 0.0702757 0.153882i
\(10\) −0.540641 0.158746i −0.540641 0.158746i
\(11\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(12\) 0.708089 + 0.817178i 0.708089 + 0.817178i
\(13\) 1.45027 + 0.425839i 1.45027 + 0.425839i 0.909632 0.415415i \(-0.136364\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(14\) 0.415415 0.909632i 0.415415 0.909632i
\(15\) 0.512546 + 0.329393i 0.512546 + 0.329393i
\(16\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(17\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(18\) −0.0702757 0.153882i −0.0702757 0.153882i
\(19\) −0.258908 1.80075i −0.258908 1.80075i −0.540641 0.841254i \(-0.681818\pi\)
0.281733 0.959493i \(-0.409091\pi\)
\(20\) −0.474017 + 0.304632i −0.474017 + 0.304632i
\(21\) −0.708089 + 0.817178i −0.708089 + 0.817178i
\(22\) 0 0
\(23\) −0.959493 0.281733i −0.959493 0.281733i
\(24\) 1.08128 1.08128
\(25\) 0.446947 0.515804i 0.446947 0.515804i
\(26\) 1.27155 0.817178i 1.27155 0.817178i
\(27\) −0.127850 0.889217i −0.127850 0.889217i
\(28\) −0.415415 0.909632i −0.415415 0.909632i
\(29\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(30\) 0.584585 0.171650i 0.584585 0.171650i
\(31\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(32\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(33\) 0 0
\(34\) 0 0
\(35\) −0.368991 0.425839i −0.368991 0.425839i
\(36\) −0.162317 0.0476607i −0.162317 0.0476607i
\(37\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(38\) −1.53046 0.983568i −1.53046 0.983568i
\(39\) −1.56815 + 0.460451i −1.56815 + 0.460451i
\(40\) −0.0801894 + 0.557730i −0.0801894 + 0.557730i
\(41\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(42\) 0.153882 + 1.07028i 0.153882 + 1.07028i
\(43\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(44\) 0 0
\(45\) −0.0953214 −0.0953214
\(46\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0.708089 0.817178i 0.708089 0.817178i
\(49\) 0.841254 0.540641i 0.841254 0.540641i
\(50\) −0.0971309 0.675560i −0.0971309 0.675560i
\(51\) 0 0
\(52\) 0.215109 1.49611i 0.215109 1.49611i
\(53\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(54\) −0.755750 0.485691i −0.755750 0.485691i
\(55\) 0 0
\(56\) −0.959493 0.281733i −0.959493 0.281733i
\(57\) 1.28820 + 1.48666i 1.28820 + 1.48666i
\(58\) 0 0
\(59\) 1.74557 + 0.512546i 1.74557 + 0.512546i 0.989821 0.142315i \(-0.0454545\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(60\) 0.253098 0.554206i 0.253098 0.554206i
\(61\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(62\) 0 0
\(63\) 0.0240754 0.167448i 0.0240754 0.167448i
\(64\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(65\) −0.121206 0.843008i −0.121206 0.843008i
\(66\) 0 0
\(67\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(68\) 0 0
\(69\) 1.03748 0.304632i 1.03748 0.304632i
\(70\) −0.563465 −0.563465
\(71\) −0.857685 + 0.989821i −0.857685 + 0.989821i 0.142315 + 0.989821i \(0.454545\pi\)
−1.00000 \(\pi\)
\(72\) −0.142315 + 0.0914602i −0.142315 + 0.0914602i
\(73\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(74\) 0 0
\(75\) −0.105026 + 0.730471i −0.105026 + 0.730471i
\(76\) −1.74557 + 0.512546i −1.74557 + 0.512546i
\(77\) 0 0
\(78\) −0.678936 + 1.48666i −0.678936 + 1.48666i
\(79\) −0.273100 0.0801894i −0.273100 0.0801894i 0.142315 0.989821i \(-0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(80\) 0.368991 + 0.425839i 0.368991 + 0.425839i
\(81\) 0.746902 + 0.861971i 0.746902 + 0.861971i
\(82\) 0 0
\(83\) −0.822373 + 1.80075i −0.822373 + 1.80075i −0.281733 + 0.959493i \(0.590909\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(84\) 0.909632 + 0.584585i 0.909632 + 0.584585i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(90\) −0.0624222 + 0.0720391i −0.0624222 + 0.0720391i
\(91\) 1.51150 1.51150
\(92\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(93\) 0 0
\(94\) 0 0
\(95\) −0.862362 + 0.554206i −0.862362 + 0.554206i
\(96\) −0.153882 1.07028i −0.153882 1.07028i
\(97\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(98\) 0.142315 0.989821i 0.142315 0.989821i
\(99\) 0 0
\(100\) −0.574161 0.368991i −0.574161 0.368991i
\(101\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(102\) 0 0
\(103\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(104\) −0.989821 1.14231i −0.989821 1.14231i
\(105\) 0.584585 + 0.171650i 0.584585 + 0.171650i
\(106\) 0 0
\(107\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(108\) −0.861971 + 0.253098i −0.861971 + 0.253098i
\(109\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(113\) −0.186393 + 0.215109i −0.186393 + 0.215109i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(114\) 1.96714 1.96714
\(115\) 0.0801894 + 0.557730i 0.0801894 + 0.557730i
\(116\) 0 0
\(117\) 0.167448 0.193245i 0.167448 0.193245i
\(118\) 1.53046 0.983568i 1.53046 0.983568i
\(119\) 0 0
\(120\) −0.253098 0.554206i −0.253098 0.554206i
\(121\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −0.909632 0.267092i −0.909632 0.267092i
\(126\) −0.110783 0.127850i −0.110783 0.127850i
\(127\) 1.25667 + 1.45027i 1.25667 + 1.45027i 0.841254 + 0.540641i \(0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(128\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(129\) 0 0
\(130\) −0.716476 0.460451i −0.716476 0.460451i
\(131\) 0.540641 0.158746i 0.540641 0.158746i 1.00000i \(-0.5\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(132\) 0 0
\(133\) −0.755750 1.65486i −0.755750 1.65486i
\(134\) 0 0
\(135\) −0.425839 + 0.273670i −0.425839 + 0.273670i
\(136\) 0 0
\(137\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(138\) 0.449181 0.983568i 0.449181 0.983568i
\(139\) −1.97964 −1.97964 −0.989821 0.142315i \(-0.954545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(140\) −0.368991 + 0.425839i −0.368991 + 0.425839i
\(141\) 0 0
\(142\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(143\) 0 0
\(144\) −0.0240754 + 0.167448i −0.0240754 + 0.167448i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.449181 + 0.983568i −0.449181 + 0.983568i
\(148\) 0 0
\(149\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(150\) 0.483276 + 0.557730i 0.483276 + 0.557730i
\(151\) −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(152\) −0.755750 + 1.65486i −0.755750 + 1.65486i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0.678936 + 1.48666i 0.678936 + 1.48666i
\(157\) 0.281733 + 1.95949i 0.281733 + 1.95949i 0.281733 + 0.959493i \(0.409091\pi\)
1.00000i \(0.500000\pi\)
\(158\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(159\) 0 0
\(160\) 0.563465 0.563465
\(161\) −1.00000 −1.00000
\(162\) 1.14055 1.14055
\(163\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0.822373 + 1.80075i 0.822373 + 1.80075i
\(167\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(168\) 1.03748 0.304632i 1.03748 0.304632i
\(169\) 1.08070 + 0.694523i 1.08070 + 0.694523i
\(170\) 0 0
\(171\) −0.295298 0.0867074i −0.295298 0.0867074i
\(172\) 0 0
\(173\) 1.29639 + 1.49611i 1.29639 + 1.49611i 0.755750 + 0.654861i \(0.227273\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(174\) 0 0
\(175\) 0.283524 0.620830i 0.283524 0.620830i
\(176\) 0 0
\(177\) −1.88745 + 0.554206i −1.88745 + 0.554206i
\(178\) 0 0
\(179\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(180\) 0.0135656 + 0.0943511i 0.0135656 + 0.0943511i
\(181\) −0.909632 + 0.584585i −0.909632 + 0.584585i −0.909632 0.415415i \(-0.863636\pi\)
1.00000i \(0.5\pi\)
\(182\) 0.989821 1.14231i 0.989821 1.14231i
\(183\) 0 0
\(184\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −0.373193 0.817178i −0.373193 0.817178i
\(190\) −0.145886 + 1.01466i −0.145886 + 1.01466i
\(191\) 1.61435 0.474017i 1.61435 0.474017i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(192\) −0.909632 0.584585i −0.909632 0.584585i
\(193\) 0.797176 1.74557i 0.797176 1.74557i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(194\) 0 0
\(195\) 0.603063 + 0.695972i 0.603063 + 0.695972i
\(196\) −0.654861 0.755750i −0.654861 0.755750i
\(197\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(198\) 0 0
\(199\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(200\) −0.654861 + 0.192284i −0.654861 + 0.192284i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.110783 + 0.127850i −0.110783 + 0.127850i
\(208\) −1.51150 −1.51150
\(209\) 0 0
\(210\) 0.512546 0.329393i 0.512546 0.329393i
\(211\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(212\) 0 0
\(213\) 0.201543 1.40176i 0.201543 1.40176i
\(214\) 0 0
\(215\) 0 0
\(216\) −0.373193 + 0.817178i −0.373193 + 0.817178i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(224\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(225\) −0.0479637 0.105026i −0.0479637 0.105026i
\(226\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(227\) 1.66538 1.07028i 1.66538 1.07028i 0.755750 0.654861i \(-0.227273\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(228\) 1.28820 1.48666i 1.28820 1.48666i
\(229\) −1.81926 −1.81926 −0.909632 0.415415i \(-0.863636\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(230\) 0.474017 + 0.304632i 0.474017 + 0.304632i
\(231\) 0 0
\(232\) 0 0
\(233\) −0.239446 + 0.153882i −0.239446 + 0.153882i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(234\) −0.0363899 0.253098i −0.0363899 0.253098i
\(235\) 0 0
\(236\) 0.258908 1.80075i 0.258908 1.80075i
\(237\) 0.295298 0.0867074i 0.295298 0.0867074i
\(238\) 0 0
\(239\) −0.797176 + 1.74557i −0.797176 + 1.74557i −0.142315 + 0.989821i \(0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(240\) −0.584585 0.171650i −0.584585 0.171650i
\(241\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(242\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(243\) −0.321330 0.0943511i −0.321330 0.0943511i
\(244\) 0 0
\(245\) −0.474017 0.304632i −0.474017 0.304632i
\(246\) 0 0
\(247\) 0.391340 2.72183i 0.391340 2.72183i
\(248\) 0 0
\(249\) −0.304632 2.11876i −0.304632 2.11876i
\(250\) −0.797537 + 0.512546i −0.797537 + 0.512546i
\(251\) 0.708089 0.817178i 0.708089 0.817178i −0.281733 0.959493i \(-0.590909\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(252\) −0.169170 −0.169170
\(253\) 0 0
\(254\) 1.91899 1.91899
\(255\) 0 0
\(256\) 0.841254 0.540641i 0.841254 0.540641i
\(257\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.817178 + 0.239945i −0.817178 + 0.239945i
\(261\) 0 0
\(262\) 0.234072 0.512546i 0.234072 0.512546i
\(263\) −1.25667 0.368991i −1.25667 0.368991i −0.415415 0.909632i \(-0.636364\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −1.74557 0.512546i −1.74557 0.512546i
\(267\) 0 0
\(268\) 0 0
\(269\) −1.74557 + 0.512546i −1.74557 + 0.512546i −0.989821 0.142315i \(-0.954545\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(270\) −0.0720391 + 0.501043i −0.0720391 + 0.501043i
\(271\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(272\) 0 0
\(273\) −1.37491 + 0.883600i −1.37491 + 0.883600i
\(274\) 0.544078 0.627899i 0.544078 0.627899i
\(275\) 0 0
\(276\) −0.449181 0.983568i −0.449181 0.983568i
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) −1.29639 + 1.49611i −1.29639 + 1.49611i
\(279\) 0 0
\(280\) 0.0801894 + 0.557730i 0.0801894 + 0.557730i
\(281\) −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(282\) 0 0
\(283\) 1.45027 0.425839i 1.45027 0.425839i 0.540641 0.841254i \(-0.318182\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(284\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(285\) 0.460451 1.00825i 0.460451 1.00825i
\(286\) 0 0
\(287\) 0 0
\(288\) 0.110783 + 0.127850i 0.110783 + 0.127850i
\(289\) −0.959493 0.281733i −0.959493 0.281733i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.153882 1.07028i 0.153882 1.07028i −0.755750 0.654861i \(-0.772727\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(294\) 0.449181 + 0.983568i 0.449181 + 0.983568i
\(295\) −0.145886 1.01466i −0.145886 1.01466i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.27155 0.817178i −1.27155 0.817178i
\(300\) 0.737982 0.737982
\(301\) 0 0
\(302\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(303\) 0 0
\(304\) 0.755750 + 1.65486i 0.755750 + 1.65486i
\(305\) 0 0
\(306\) 0 0
\(307\) 1.27155 + 0.817178i 1.27155 + 0.817178i 0.989821 0.142315i \(-0.0454545\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(312\) 1.56815 + 0.460451i 1.56815 + 0.460451i
\(313\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(314\) 1.66538 + 1.07028i 1.66538 + 1.07028i
\(315\) −0.0914602 + 0.0268551i −0.0914602 + 0.0268551i
\(316\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(317\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.368991 0.425839i 0.368991 0.425839i
\(321\) 0 0
\(322\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(323\) 0 0
\(324\) 0.746902 0.861971i 0.746902 0.861971i
\(325\) 0.867845 0.557730i 0.867845 0.557730i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(332\) 1.89945 + 0.557730i 1.89945 + 0.557730i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0.449181 0.983568i 0.449181 0.983568i
\(337\) 1.10181 + 0.708089i 1.10181 + 0.708089i 0.959493 0.281733i \(-0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(338\) 1.23259 0.361922i 1.23259 0.361922i
\(339\) 0.0437995 0.304632i 0.0437995 0.304632i
\(340\) 0 0
\(341\) 0 0
\(342\) −0.258908 + 0.166390i −0.258908 + 0.166390i
\(343\) 0.654861 0.755750i 0.654861 0.755750i
\(344\) 0 0
\(345\) −0.398983 0.460451i −0.398983 0.460451i
\(346\) 1.97964 1.97964
\(347\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(348\) 0 0
\(349\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(350\) −0.283524 0.620830i −0.283524 0.620830i
\(351\) 0.193245 1.34405i 0.193245 1.34405i
\(352\) 0 0
\(353\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(354\) −0.817178 + 1.78937i −0.817178 + 1.78937i
\(355\) 0.708089 + 0.207914i 0.708089 + 0.207914i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.797176 + 1.74557i −0.797176 + 1.74557i −0.142315 + 0.989821i \(0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(360\) 0.0801894 + 0.0515346i 0.0801894 + 0.0515346i
\(361\) −2.21616 + 0.650724i −2.21616 + 0.650724i
\(362\) −0.153882 + 1.07028i −0.153882 + 1.07028i
\(363\) −0.449181 0.983568i −0.449181 0.983568i
\(364\) −0.215109 1.49611i −0.215109 1.49611i
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 1.00000 1.00000
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(374\) 0 0
\(375\) 0.983568 0.288802i 0.983568 0.288802i
\(376\) 0 0
\(377\) 0 0
\(378\) −0.861971 0.253098i −0.861971 0.253098i
\(379\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(380\) 0.671292 + 0.774713i 0.671292 + 0.774713i
\(381\) −1.99091 0.584585i −1.99091 0.584585i
\(382\) 0.698939 1.53046i 0.698939 1.53046i
\(383\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(384\) −1.03748 + 0.304632i −1.03748 + 0.304632i
\(385\) 0 0
\(386\) −0.797176 1.74557i −0.797176 1.74557i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(390\) 0.920903 0.920903
\(391\) 0 0
\(392\) −1.00000 −1.00000
\(393\) −0.398983 + 0.460451i −0.398983 + 0.460451i
\(394\) 0 0
\(395\) 0.0228243 + 0.158746i 0.0228243 + 0.158746i
\(396\) 0 0
\(397\) −0.215109 + 1.49611i −0.215109 + 1.49611i 0.540641 + 0.841254i \(0.318182\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(398\) 0 0
\(399\) 1.65486 + 1.06351i 1.65486 + 1.06351i
\(400\) −0.283524 + 0.620830i −0.283524 + 0.620830i
\(401\) −1.25667 0.368991i −1.25667 0.368991i −0.415415 0.909632i \(-0.636364\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0.266971 0.584585i 0.266971 0.584585i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(410\) 0 0
\(411\) −0.755750 + 0.485691i −0.755750 + 0.485691i
\(412\) 0 0
\(413\) 1.81926 1.81926
\(414\) 0.0240754 + 0.167448i 0.0240754 + 0.167448i
\(415\) 1.11546 1.11546
\(416\) −0.989821 + 1.14231i −0.989821 + 1.14231i
\(417\) 1.80075 1.15727i 1.80075 1.15727i
\(418\) 0 0
\(419\) −0.627899 1.37491i −0.627899 1.37491i −0.909632 0.415415i \(-0.863636\pi\)
0.281733 0.959493i \(-0.409091\pi\)
\(420\) 0.0867074 0.603063i 0.0867074 0.603063i
\(421\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) −0.927399 1.07028i −0.927399 1.07028i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0.0405070 0.281733i 0.0405070 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
1.00000 \(0\)
\(432\) 0.373193 + 0.817178i 0.373193 + 0.817178i
\(433\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.258908 + 1.80075i −0.258908 + 1.80075i
\(438\) 0 0
\(439\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(440\) 0 0
\(441\) −0.0240754 0.167448i −0.0240754 0.167448i
\(442\) 0 0
\(443\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(449\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(450\) −0.110783 0.0325288i −0.110783 0.0325288i
\(451\) 0 0
\(452\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(453\) 1.74557 0.512546i 1.74557 0.512546i
\(454\) 0.281733 1.95949i 0.281733 1.95949i
\(455\) −0.353799 0.774713i −0.353799 0.774713i
\(456\) −0.279953 1.94711i −0.279953 1.94711i
\(457\) −0.698939 + 0.449181i −0.698939 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(458\) −1.19136 + 1.37491i −1.19136 + 1.37491i
\(459\) 0 0
\(460\) 0.540641 0.158746i 0.540641 0.158746i
\(461\) 1.97964 1.97964 0.989821 0.142315i \(-0.0454545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(462\) 0 0
\(463\) 1.10181 0.708089i 1.10181 0.708089i 0.142315 0.989821i \(-0.454545\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(467\) −1.03748 + 0.304632i −1.03748 + 0.304632i −0.755750 0.654861i \(-0.772727\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(468\) −0.215109 0.138242i −0.215109 0.138242i
\(469\) 0 0
\(470\) 0 0
\(471\) −1.40176 1.61772i −1.40176 1.61772i
\(472\) −1.19136 1.37491i −1.19136 1.37491i
\(473\) 0 0
\(474\) 0.127850 0.279953i 0.127850 0.279953i
\(475\) −1.04455 0.671292i −1.04455 0.671292i
\(476\) 0 0
\(477\) 0 0
\(478\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(479\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(480\) −0.512546 + 0.329393i −0.512546 + 0.329393i
\(481\) 0 0
\(482\) 0 0
\(483\) 0.909632 0.584585i 0.909632 0.584585i
\(484\) 1.00000 1.00000
\(485\) 0 0
\(486\) −0.281733 + 0.181059i −0.281733 + 0.181059i
\(487\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −0.540641 + 0.158746i −0.540641 + 0.158746i
\(491\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −1.80075 2.07817i −1.80075 2.07817i
\(495\) 0 0
\(496\) 0 0
\(497\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(498\) −1.80075 1.15727i −1.80075 1.15727i
\(499\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(500\) −0.134919 + 0.938384i −0.134919 + 0.938384i
\(501\) 0 0
\(502\) −0.153882 1.07028i −0.153882 1.07028i
\(503\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(504\) −0.110783 + 0.127850i −0.110783 + 0.127850i
\(505\) 0 0
\(506\) 0 0
\(507\) −1.38905 −1.38905
\(508\) 1.25667 1.45027i 1.25667 1.45027i
\(509\) −0.474017 + 0.304632i −0.474017 + 0.304632i −0.755750 0.654861i \(-0.772727\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.142315 0.989821i 0.142315 0.989821i
\(513\) −1.56815 + 0.460451i −1.56815 + 0.460451i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −2.05384 0.603063i −2.05384 0.603063i
\(520\) −0.353799 + 0.774713i −0.353799 + 0.774713i
\(521\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(522\) 0 0
\(523\) −0.281733 + 1.95949i −0.281733 + 1.95949i 1.00000i \(0.5\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(524\) −0.234072 0.512546i −0.234072 0.512546i
\(525\) 0.105026 + 0.730471i 0.105026 + 0.730471i
\(526\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(527\) 0 0
\(528\) 0 0
\(529\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(530\) 0 0
\(531\) 0.201543 0.232593i 0.201543 0.232593i
\(532\) −1.53046 + 0.983568i −1.53046 + 0.983568i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −0.755750 + 1.65486i −0.755750 + 1.65486i
\(539\) 0 0
\(540\) 0.331487 + 0.382557i 0.331487 + 0.382557i
\(541\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(542\) 0 0
\(543\) 0.485691 1.06351i 0.485691 1.06351i
\(544\) 0 0
\(545\) 0 0
\(546\) −0.232593 + 1.61772i −0.232593 + 1.61772i
\(547\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(548\) −0.118239 0.822373i −0.118239 0.822373i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −1.03748 0.304632i −1.03748 0.304632i
\(553\) −0.284630 −0.284630
\(554\) 0 0
\(555\) 0 0
\(556\) 0.281733 + 1.95949i 0.281733 + 1.95949i
\(557\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.474017 + 0.304632i 0.474017 + 0.304632i
\(561\) 0 0
\(562\) −1.84125 0.540641i −1.84125 0.540641i
\(563\) −0.989821 1.14231i −0.989821 1.14231i −0.989821 0.142315i \(-0.954545\pi\)
1.00000i \(-0.5\pi\)
\(564\) 0 0
\(565\) 0.153882 + 0.0451840i 0.153882 + 0.0451840i
\(566\) 0.627899 1.37491i 0.627899 1.37491i
\(567\) 0.959493 + 0.616629i 0.959493 + 0.616629i
\(568\) 1.25667 0.368991i 1.25667 0.368991i
\(569\) 0.239446 1.66538i 0.239446 1.66538i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(570\) −0.460451 1.00825i −0.460451 1.00825i
\(571\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(572\) 0 0
\(573\) −1.19136 + 1.37491i −1.19136 + 1.37491i
\(574\) 0 0
\(575\) −0.574161 + 0.368991i −0.574161 + 0.368991i
\(576\) 0.169170 0.169170
\(577\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(578\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(579\) 0.295298 + 2.05384i 0.295298 + 2.05384i
\(580\) 0 0
\(581\) −0.281733 + 1.95949i −0.281733 + 1.95949i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −0.138242 0.0405915i −0.138242 0.0405915i
\(586\) −0.708089 0.817178i −0.708089 0.817178i
\(587\) 0.989821 + 1.14231i 0.989821 + 1.14231i 0.989821 + 0.142315i \(0.0454545\pi\)
1.00000i \(0.500000\pi\)
\(588\) 1.03748 + 0.304632i 1.03748 + 0.304632i
\(589\) 0 0
\(590\) −0.862362 0.554206i −0.862362 0.554206i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −1.45027 + 0.425839i −1.45027 + 0.425839i
\(599\) −1.68251 −1.68251 −0.841254 0.540641i \(-0.818182\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(600\) 0.483276 0.557730i 0.483276 0.557730i
\(601\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(605\) 0.540641 0.158746i 0.540641 0.158746i
\(606\) 0 0
\(607\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(608\) 1.74557 + 0.512546i 1.74557 + 0.512546i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(614\) 1.45027 0.425839i 1.45027 0.425839i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.273100 1.89945i −0.273100 1.89945i −0.415415 0.909632i \(-0.636364\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(618\) 0 0
\(619\) −1.29639 + 1.49611i −1.29639 + 1.49611i −0.540641 + 0.841254i \(0.681818\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(620\) 0 0
\(621\) −0.127850 + 0.889217i −0.127850 + 0.889217i
\(622\) 0 0
\(623\) 0 0
\(624\) 1.37491 0.883600i 1.37491 0.883600i
\(625\) −0.0211086 0.146813i −0.0211086 0.146813i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.89945 0.557730i 1.89945 0.557730i
\(629\) 0 0
\(630\) −0.0395979 + 0.0867074i −0.0395979 + 0.0867074i
\(631\) 1.61435 + 0.474017i 1.61435 + 0.474017i 0.959493 0.281733i \(-0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(632\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(633\) 0 0
\(634\) 0 0
\(635\) 0.449181 0.983568i 0.449181 0.983568i
\(636\) 0 0
\(637\) 1.45027 0.425839i 1.45027 0.425839i
\(638\) 0 0
\(639\) 0.0920417 + 0.201543i 0.0920417 + 0.201543i
\(640\) −0.0801894 0.557730i −0.0801894 0.557730i
\(641\) 1.61435 1.03748i 1.61435 1.03748i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(642\) 0 0
\(643\) −1.08128 −1.08128 −0.540641 0.841254i \(-0.681818\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(644\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(648\) −0.162317 1.12894i −0.162317 1.12894i
\(649\) 0 0
\(650\) 0.146813 1.02111i 0.146813 1.02111i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(654\) 0 0
\(655\) −0.207914 0.239945i −0.207914 0.239945i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(660\) 0 0
\(661\) 0.215109 1.49611i 0.215109 1.49611i −0.540641 0.841254i \(-0.681818\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 1.66538 1.07028i 1.66538 1.07028i
\(665\) −0.671292 + 0.774713i −0.671292 + 0.774713i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −0.449181 0.983568i −0.449181 0.983568i
\(673\) −0.239446 + 1.66538i −0.239446 + 1.66538i 0.415415 + 0.909632i \(0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(674\) 1.25667 0.368991i 1.25667 0.368991i
\(675\) −0.515804 0.331487i −0.515804 0.331487i
\(676\) 0.533654 1.16854i 0.533654 1.16854i
\(677\) −1.89945 0.557730i −1.89945 0.557730i −0.989821 0.142315i \(-0.954545\pi\)
−0.909632 0.415415i \(-0.863636\pi\)
\(678\) −0.201543 0.232593i −0.201543 0.232593i
\(679\) 0 0
\(680\) 0 0
\(681\) −0.889217 + 1.94711i −0.889217 + 1.94711i
\(682\) 0 0
\(683\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(684\) −0.0437995 + 0.304632i −0.0437995 + 0.304632i
\(685\) −0.194474 0.425839i −0.194474 0.425839i
\(686\) −0.142315 0.989821i −0.142315 0.989821i
\(687\) 1.65486 1.06351i 1.65486 1.06351i
\(688\) 0 0
\(689\) 0 0
\(690\) −0.609264 −0.609264
\(691\) 1.81926 1.81926 0.909632 0.415415i \(-0.136364\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(692\) 1.29639 1.49611i 1.29639 1.49611i
\(693\) 0 0
\(694\) 0 0
\(695\) 0.463379 + 1.01466i 0.463379 + 1.01466i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0.127850 0.279953i 0.127850 0.279953i
\(700\) −0.654861 0.192284i −0.654861 0.192284i
\(701\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(702\) −0.889217 1.02621i −0.889217 1.02621i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0.817178 + 1.78937i 0.817178 + 1.78937i
\(709\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(710\) 0.620830 0.398983i 0.620830 0.398983i
\(711\) −0.0315321 + 0.0363899i −0.0315321 + 0.0363899i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −0.295298 2.05384i −0.295298 2.05384i
\(718\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(719\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(720\) 0.0914602 0.0268551i 0.0914602 0.0268551i
\(721\) 0 0
\(722\) −0.959493 + 2.10100i −0.959493 + 2.10100i
\(723\) 0 0
\(724\) 0.708089 + 0.817178i 0.708089 + 0.817178i
\(725\) 0 0
\(726\) −1.03748 0.304632i −1.03748 0.304632i
\(727\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(728\) −1.27155 0.817178i −1.27155 0.817178i
\(729\) −0.746902 + 0.219310i −0.746902 + 0.219310i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 1.27155 0.817178i 1.27155 0.817178i 0.281733 0.959493i \(-0.409091\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(734\) 0 0
\(735\) 0.609264 0.609264
\(736\) 0.654861 0.755750i 0.654861 0.755750i
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(740\) 0 0
\(741\) 1.23516 + 2.70463i 1.23516 + 2.70463i
\(742\) 0 0
\(743\) 1.84125 0.540641i 1.84125 0.540641i 0.841254 0.540641i \(-0.181818\pi\)
1.00000 \(0\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.219310 + 0.253098i 0.219310 + 0.253098i
\(748\) 0 0
\(749\) 0 0
\(750\) 0.425839 0.932456i 0.425839 0.932456i
\(751\) 0.698939 + 0.449181i 0.698939 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(752\) 0 0
\(753\) −0.166390 + 1.15727i −0.166390 + 1.15727i
\(754\) 0 0
\(755\) 0.134919 + 0.938384i 0.134919 + 0.938384i
\(756\) −0.755750 + 0.485691i −0.755750 + 0.485691i
\(757\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 1.02509 1.02509
\(761\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(762\) −1.74557 + 1.12181i −1.74557 + 1.12181i
\(763\) 0 0
\(764\) −0.698939 1.53046i −0.698939 1.53046i
\(765\) 0 0
\(766\) 0 0
\(767\) 2.31329 + 1.48666i 2.31329 + 1.48666i
\(768\) −0.449181 + 0.983568i −0.449181 + 0.983568i
\(769\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.84125 0.540641i −1.84125 0.540641i
\(773\) 0.234072 0.512546i 0.234072 0.512546i −0.755750 0.654861i \(-0.772727\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0.603063 0.695972i 0.603063 0.695972i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(785\) 0.938384 0.603063i 0.938384 0.603063i
\(786\) 0.0867074 + 0.603063i 0.0867074 + 0.603063i
\(787\) −0.755750 1.65486i −0.755750 1.65486i −0.755750 0.654861i \(-0.772727\pi\)
1.00000i \(-0.5\pi\)
\(788\) 0 0
\(789\) 1.35881 0.398983i 1.35881 0.398983i
\(790\) 0.134919 + 0.0867074i 0.134919 + 0.0867074i
\(791\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(792\) 0 0
\(793\) 0 0
\(794\) 0.989821 + 1.14231i 0.989821 + 1.14231i
\(795\) 0 0
\(796\) 0 0
\(797\) −1.27155 0.817178i −1.27155 0.817178i −0.281733 0.959493i \(-0.590909\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(798\) 1.88745 0.554206i 1.88745 0.554206i
\(799\) 0 0
\(800\) 0.283524 + 0.620830i 0.283524 + 0.620830i
\(801\) 0 0
\(802\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(803\) 0 0
\(804\) 0 0
\(805\) 0.234072 + 0.512546i 0.234072 + 0.512546i
\(806\) 0 0
\(807\) 1.28820 1.48666i 1.28820 1.48666i
\(808\) 0 0
\(809\) −0.0405070 0.281733i −0.0405070 0.281733i 0.959493 0.281733i \(-0.0909091\pi\)
−1.00000 \(\pi\)
\(810\) −0.266971 0.584585i −0.266971 0.584585i
\(811\) 0.258908 1.80075i 0.258908 1.80075i −0.281733 0.959493i \(-0.590909\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0.106222 0.232593i 0.106222 0.232593i
\(820\) 0 0
\(821\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(822\) −0.127850 + 0.889217i −0.127850 + 0.889217i
\(823\) −0.345139 0.755750i −0.345139 0.755750i 0.654861 0.755750i \(-0.272727\pi\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 1.19136 1.37491i 1.19136 1.37491i
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0.142315 + 0.0914602i 0.142315 + 0.0914602i
\(829\) 0.563465 0.563465 0.281733 0.959493i \(-0.409091\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(830\) 0.730471 0.843008i 0.730471 0.843008i
\(831\) 0 0
\(832\) 0.215109 + 1.49611i 0.215109 + 1.49611i
\(833\) 0 0
\(834\) 0.304632 2.11876i 0.304632 2.11876i
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) −1.45027 0.425839i −1.45027 0.425839i
\(839\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(840\) −0.398983 0.460451i −0.398983 0.460451i
\(841\) −0.959493 0.281733i −0.959493 0.281733i
\(842\) 0 0
\(843\) 1.74557 + 1.12181i 1.74557 + 1.12181i
\(844\) 0 0
\(845\) 0.103014 0.716476i 0.103014 0.716476i
\(846\) 0 0
\(847\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(848\) 0 0
\(849\) −1.07028 + 1.23516i −1.07028 + 1.23516i
\(850\) 0 0
\(851\) 0 0
\(852\) −1.41618 −1.41618
\(853\) −1.29639 + 1.49611i −1.29639 + 1.49611i −0.540641 + 0.841254i \(0.681818\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(854\) 0 0
\(855\) 0.0246795 + 0.171650i 0.0246795 + 0.171650i
\(856\) 0 0
\(857\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(858\) 0 0
\(859\) 0.474017 + 0.304632i 0.474017 + 0.304632i 0.755750 0.654861i \(-0.227273\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −0.186393 0.215109i −0.186393 0.215109i
\(863\) 0.544078 + 0.627899i 0.544078 + 0.627899i 0.959493 0.281733i \(-0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(864\) 0.861971 + 0.253098i 0.861971 + 0.253098i
\(865\) 0.463379 1.01466i 0.463379 1.01466i
\(866\) 0 0
\(867\) 1.03748 0.304632i 1.03748 0.304632i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 1.19136 + 1.37491i 1.19136 + 1.37491i
\(875\) −0.948034 −0.948034
\(876\) 0 0
\(877\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(878\) 0 0
\(879\) 0.485691 + 1.06351i 0.485691 + 1.06351i
\(880\) 0 0
\(881\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(882\) −0.142315 0.0914602i −0.142315 0.0914602i
\(883\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(884\) 0 0
\(885\) 0.725856 + 0.837683i 0.725856 + 0.837683i
\(886\) 0 0
\(887\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(888\) 0 0
\(889\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 1.00000
\(897\) 1.63436 1.63436
\(898\) −0.830830 −0.830830
\(899\) 0 0
\(900\) −0.0971309 + 0.0624222i −0.0971309 + 0.0624222i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0.273100 0.0801894i 0.273100 0.0801894i
\(905\) 0.512546 + 0.329393i 0.512546 + 0.329393i
\(906\) 0.755750 1.65486i 0.755750 1.65486i
\(907\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(908\) −1.29639 1.49611i −1.29639 1.49611i
\(909\) 0 0
\(910\) −0.817178 0.239945i −0.817178 0.239945i
\(911\) −0.118239 + 0.258908i −0.118239 + 0.258908i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(912\) −1.65486 1.06351i −1.65486 1.06351i
\(913\) 0 0
\(914\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(915\) 0 0
\(916\) 0.258908 + 1.80075i 0.258908 + 1.80075i
\(917\) 0.474017 0.304632i 0.474017 0.304632i
\(918\) 0 0
\(919\) 1.30972 1.30972 0.654861 0.755750i \(-0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(920\) 0.234072 0.512546i 0.234072 0.512546i
\(921\) −1.63436 −1.63436
\(922\) 1.29639 1.49611i 1.29639 1.49611i
\(923\) −1.66538 + 1.07028i −1.66538 + 1.07028i
\(924\) 0 0
\(925\) 0 0
\(926\) 0.186393 1.29639i 0.186393 1.29639i
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(930\) 0 0
\(931\) −1.19136 1.37491i −1.19136 1.37491i
\(932\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(933\) 0 0
\(934\) −0.449181 + 0.983568i −0.449181 + 0.983568i
\(935\) 0 0
\(936\) −0.245343 + 0.0720391i −0.245343 + 0.0720391i
\(937\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.29639 1.49611i 1.29639 1.49611i 0.540641 0.841254i \(-0.318182\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(942\) −2.14055 −2.14055
\(943\) 0 0
\(944\) −1.81926 −1.81926
\(945\) −0.331487 + 0.382557i −0.331487 + 0.382557i
\(946\) 0 0
\(947\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(948\) −0.127850 0.279953i −0.127850 0.279953i
\(949\) 0 0
\(950\) −1.19136 + 0.349816i −1.19136 + 0.349816i
\(951\) 0 0
\(952\) 0 0
\(953\) 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(954\) 0 0
\(955\) −0.620830 0.716476i −0.620830 0.716476i
\(956\) 1.84125 + 0.540641i 1.84125 + 0.540641i
\(957\) 0 0
\(958\) 0 0
\(959\) 0.797176 0.234072i 0.797176 0.234072i
\(960\) −0.0867074 + 0.603063i −0.0867074 + 0.603063i
\(961\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.08128 −1.08128
\(966\) 0.153882 1.07028i 0.153882 1.07028i
\(967\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(968\) 0.654861 0.755750i 0.654861 0.755750i
\(969\) 0 0
\(970\) 0 0
\(971\) 0.234072 + 0.512546i 0.234072 + 0.512546i 0.989821 0.142315i \(-0.0454545\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(972\) −0.0476607 + 0.331487i −0.0476607 + 0.331487i
\(973\) −1.89945 + 0.557730i −1.89945 + 0.557730i
\(974\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(975\) −0.463379 + 1.01466i −0.463379 + 1.01466i
\(976\) 0 0
\(977\) 1.25667 + 1.45027i 1.25667 + 1.45027i 0.841254 + 0.540641i \(0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −0.234072 + 0.512546i −0.234072 + 0.512546i
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −2.74982 −2.74982
\(989\) 0 0
\(990\) 0 0
\(991\) −1.25667 + 1.45027i −1.25667 + 1.45027i −0.415415 + 0.909632i \(0.636364\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0.544078 + 1.19136i 0.544078 + 1.19136i
\(995\) 0 0
\(996\) −2.05384 + 0.603063i −2.05384 + 0.603063i
\(997\) −0.474017 0.304632i −0.474017 0.304632i 0.281733 0.959493i \(-0.409091\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(998\) 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 1288.1.bi.e.1189.1 yes 20
7.6 odd 2 inner 1288.1.bi.e.1189.2 yes 20
8.5 even 2 inner 1288.1.bi.e.1189.2 yes 20
23.13 even 11 inner 1288.1.bi.e.13.1 20
56.13 odd 2 CM 1288.1.bi.e.1189.1 yes 20
161.13 odd 22 inner 1288.1.bi.e.13.2 yes 20
184.13 even 22 inner 1288.1.bi.e.13.2 yes 20
1288.13 odd 22 inner 1288.1.bi.e.13.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1288.1.bi.e.13.1 20 23.13 even 11 inner
1288.1.bi.e.13.1 20 1288.13 odd 22 inner
1288.1.bi.e.13.2 yes 20 161.13 odd 22 inner
1288.1.bi.e.13.2 yes 20 184.13 even 22 inner
1288.1.bi.e.1189.1 yes 20 1.1 even 1 trivial
1288.1.bi.e.1189.1 yes 20 56.13 odd 2 CM
1288.1.bi.e.1189.2 yes 20 7.6 odd 2 inner
1288.1.bi.e.1189.2 yes 20 8.5 even 2 inner