Properties

Label 1288.1.bi.e.685.2
Level $1288$
Weight $1$
Character 1288.685
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 685.2
Root \(-0.755750 - 0.654861i\) of defining polynomial
Character \(\chi\) \(=\) 1288.685
Dual form 1288.1.bi.e.1021.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.959493 + 0.281733i) q^{2} +(0.989821 - 1.14231i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.258908 + 1.80075i) q^{5} +(1.27155 - 0.817178i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.182822 - 1.27155i) q^{9} +O(q^{10})\) \(q+(0.959493 + 0.281733i) q^{2} +(0.989821 - 1.14231i) q^{3} +(0.841254 + 0.540641i) q^{4} +(-0.258908 + 1.80075i) q^{5} +(1.27155 - 0.817178i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.182822 - 1.27155i) q^{9} +(-0.755750 + 1.65486i) q^{10} +(1.45027 - 0.425839i) q^{12} +(-0.234072 + 0.512546i) q^{13} +(-0.142315 - 0.989821i) q^{14} +(1.80075 + 2.07817i) q^{15} +(0.415415 + 0.909632i) q^{16} +(0.182822 - 1.27155i) q^{18} +(-1.66538 - 1.07028i) q^{19} +(-1.19136 + 1.37491i) q^{20} +(-1.45027 - 0.425839i) q^{21} +(0.415415 - 0.909632i) q^{23} +1.51150 q^{24} +(-2.21616 - 0.650724i) q^{25} +(-0.368991 + 0.425839i) q^{26} +(-0.361922 - 0.232593i) q^{27} +(0.142315 - 0.989821i) q^{28} +(1.14231 + 2.50132i) q^{30} +(0.142315 + 0.989821i) q^{32} +(1.74557 - 0.512546i) q^{35} +(0.533654 - 1.16854i) q^{36} +(-1.29639 - 1.49611i) q^{38} +(0.353799 + 0.774713i) q^{39} +(-1.53046 + 0.983568i) q^{40} +(-1.27155 - 0.817178i) q^{42} +2.33708 q^{45} +(0.654861 - 0.755750i) q^{46} +(1.45027 + 0.425839i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(-1.94306 - 1.24873i) q^{50} +(-0.474017 + 0.304632i) q^{52} +(-0.281733 - 0.325137i) q^{54} +(0.415415 - 0.909632i) q^{56} +(-2.87102 + 0.843008i) q^{57} +(0.822373 - 1.80075i) q^{59} +(0.391340 + 2.72183i) q^{60} +(-1.08070 + 0.694523i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(-0.862362 - 0.554206i) q^{65} +(-0.627899 - 1.37491i) q^{69} +1.81926 q^{70} +(-1.84125 - 0.540641i) q^{71} +(0.841254 - 0.970858i) q^{72} +(-2.93694 + 1.88745i) q^{75} +(-0.822373 - 1.80075i) q^{76} +(0.121206 + 0.843008i) q^{78} +(-0.698939 + 1.53046i) q^{79} +(-1.74557 + 0.512546i) q^{80} +(0.608660 - 0.178719i) q^{81} +(0.153882 + 1.07028i) q^{83} +(-0.989821 - 1.14231i) q^{84} +(2.24241 + 0.658432i) q^{90} +0.563465 q^{91} +(0.841254 - 0.540641i) q^{92} +(2.35848 - 2.72183i) q^{95} +(1.27155 + 0.817178i) q^{96} +(-0.841254 + 0.540641i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 2 q^{8} - 20 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/1288\mathbb{Z}\right)^\times\).

\(n\) \(185\) \(281\) \(645\) \(967\)
\(\chi(n)\) \(-1\) \(e\left(\frac{6}{11}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(3\) 0.989821 1.14231i 0.989821 1.14231i 1.00000i \(-0.5\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(4\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(5\) −0.258908 + 1.80075i −0.258908 + 1.80075i 0.281733 + 0.959493i \(0.409091\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(6\) 1.27155 0.817178i 1.27155 0.817178i
\(7\) −0.415415 0.909632i −0.415415 0.909632i
\(8\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(9\) −0.182822 1.27155i −0.182822 1.27155i
\(10\) −0.755750 + 1.65486i −0.755750 + 1.65486i
\(11\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(12\) 1.45027 0.425839i 1.45027 0.425839i
\(13\) −0.234072 + 0.512546i −0.234072 + 0.512546i −0.989821 0.142315i \(-0.954545\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(14\) −0.142315 0.989821i −0.142315 0.989821i
\(15\) 1.80075 + 2.07817i 1.80075 + 2.07817i
\(16\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(17\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(18\) 0.182822 1.27155i 0.182822 1.27155i
\(19\) −1.66538 1.07028i −1.66538 1.07028i −0.909632 0.415415i \(-0.863636\pi\)
−0.755750 0.654861i \(-0.772727\pi\)
\(20\) −1.19136 + 1.37491i −1.19136 + 1.37491i
\(21\) −1.45027 0.425839i −1.45027 0.425839i
\(22\) 0 0
\(23\) 0.415415 0.909632i 0.415415 0.909632i
\(24\) 1.51150 1.51150
\(25\) −2.21616 0.650724i −2.21616 0.650724i
\(26\) −0.368991 + 0.425839i −0.368991 + 0.425839i
\(27\) −0.361922 0.232593i −0.361922 0.232593i
\(28\) 0.142315 0.989821i 0.142315 0.989821i
\(29\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(30\) 1.14231 + 2.50132i 1.14231 + 2.50132i
\(31\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(32\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(33\) 0 0
\(34\) 0 0
\(35\) 1.74557 0.512546i 1.74557 0.512546i
\(36\) 0.533654 1.16854i 0.533654 1.16854i
\(37\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(38\) −1.29639 1.49611i −1.29639 1.49611i
\(39\) 0.353799 + 0.774713i 0.353799 + 0.774713i
\(40\) −1.53046 + 0.983568i −1.53046 + 0.983568i
\(41\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(42\) −1.27155 0.817178i −1.27155 0.817178i
\(43\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(44\) 0 0
\(45\) 2.33708 2.33708
\(46\) 0.654861 0.755750i 0.654861 0.755750i
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 1.45027 + 0.425839i 1.45027 + 0.425839i
\(49\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(50\) −1.94306 1.24873i −1.94306 1.24873i
\(51\) 0 0
\(52\) −0.474017 + 0.304632i −0.474017 + 0.304632i
\(53\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(54\) −0.281733 0.325137i −0.281733 0.325137i
\(55\) 0 0
\(56\) 0.415415 0.909632i 0.415415 0.909632i
\(57\) −2.87102 + 0.843008i −2.87102 + 0.843008i
\(58\) 0 0
\(59\) 0.822373 1.80075i 0.822373 1.80075i 0.281733 0.959493i \(-0.409091\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(60\) 0.391340 + 2.72183i 0.391340 + 2.72183i
\(61\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(62\) 0 0
\(63\) −1.08070 + 0.694523i −1.08070 + 0.694523i
\(64\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(65\) −0.862362 0.554206i −0.862362 0.554206i
\(66\) 0 0
\(67\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(68\) 0 0
\(69\) −0.627899 1.37491i −0.627899 1.37491i
\(70\) 1.81926 1.81926
\(71\) −1.84125 0.540641i −1.84125 0.540641i −0.841254 0.540641i \(-0.818182\pi\)
−1.00000 \(\pi\)
\(72\) 0.841254 0.970858i 0.841254 0.970858i
\(73\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(74\) 0 0
\(75\) −2.93694 + 1.88745i −2.93694 + 1.88745i
\(76\) −0.822373 1.80075i −0.822373 1.80075i
\(77\) 0 0
\(78\) 0.121206 + 0.843008i 0.121206 + 0.843008i
\(79\) −0.698939 + 1.53046i −0.698939 + 1.53046i 0.142315 + 0.989821i \(0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(80\) −1.74557 + 0.512546i −1.74557 + 0.512546i
\(81\) 0.608660 0.178719i 0.608660 0.178719i
\(82\) 0 0
\(83\) 0.153882 + 1.07028i 0.153882 + 1.07028i 0.909632 + 0.415415i \(0.136364\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(84\) −0.989821 1.14231i −0.989821 1.14231i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(90\) 2.24241 + 0.658432i 2.24241 + 0.658432i
\(91\) 0.563465 0.563465
\(92\) 0.841254 0.540641i 0.841254 0.540641i
\(93\) 0 0
\(94\) 0 0
\(95\) 2.35848 2.72183i 2.35848 2.72183i
\(96\) 1.27155 + 0.817178i 1.27155 + 0.817178i
\(97\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(98\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(99\) 0 0
\(100\) −1.51255 1.74557i −1.51255 1.74557i
\(101\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(102\) 0 0
\(103\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(104\) −0.540641 + 0.158746i −0.540641 + 0.158746i
\(105\) 1.14231 2.50132i 1.14231 2.50132i
\(106\) 0 0
\(107\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(108\) −0.178719 0.391340i −0.178719 0.391340i
\(109\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.654861 0.755750i 0.654861 0.755750i
\(113\) 1.61435 + 0.474017i 1.61435 + 0.474017i 0.959493 0.281733i \(-0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(114\) −2.99223 −2.99223
\(115\) 1.53046 + 0.983568i 1.53046 + 0.983568i
\(116\) 0 0
\(117\) 0.694523 + 0.203930i 0.694523 + 0.203930i
\(118\) 1.29639 1.49611i 1.29639 1.49611i
\(119\) 0 0
\(120\) −0.391340 + 2.72183i −0.391340 + 2.72183i
\(121\) 0.841254 0.540641i 0.841254 0.540641i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0.989821 2.16741i 0.989821 2.16741i
\(126\) −1.23259 + 0.361922i −1.23259 + 0.361922i
\(127\) −0.797176 + 0.234072i −0.797176 + 0.234072i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(128\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(129\) 0 0
\(130\) −0.671292 0.774713i −0.671292 0.774713i
\(131\) 0.755750 + 1.65486i 0.755750 + 1.65486i 0.755750 + 0.654861i \(0.227273\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −0.281733 + 1.95949i −0.281733 + 1.95949i
\(134\) 0 0
\(135\) 0.512546 0.591509i 0.512546 0.591509i
\(136\) 0 0
\(137\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(138\) −0.215109 1.49611i −0.215109 1.49611i
\(139\) −1.08128 −1.08128 −0.540641 0.841254i \(-0.681818\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(140\) 1.74557 + 0.512546i 1.74557 + 0.512546i
\(141\) 0 0
\(142\) −1.61435 1.03748i −1.61435 1.03748i
\(143\) 0 0
\(144\) 1.08070 0.694523i 1.08070 0.694523i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.215109 + 1.49611i 0.215109 + 1.49611i
\(148\) 0 0
\(149\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(150\) −3.34973 + 0.983568i −3.34973 + 0.983568i
\(151\) −0.544078 + 1.19136i −0.544078 + 1.19136i 0.415415 + 0.909632i \(0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(152\) −0.281733 1.95949i −0.281733 1.95949i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.121206 + 0.843008i −0.121206 + 0.843008i
\(157\) −0.909632 0.584585i −0.909632 0.584585i 1.00000i \(-0.5\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(158\) −1.10181 + 1.27155i −1.10181 + 1.27155i
\(159\) 0 0
\(160\) −1.81926 −1.81926
\(161\) −1.00000 −1.00000
\(162\) 0.634356 0.634356
\(163\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −0.153882 + 1.07028i −0.153882 + 1.07028i
\(167\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(168\) −0.627899 1.37491i −0.627899 1.37491i
\(169\) 0.446947 + 0.515804i 0.446947 + 0.515804i
\(170\) 0 0
\(171\) −1.05645 + 2.31329i −1.05645 + 2.31329i
\(172\) 0 0
\(173\) 1.03748 0.304632i 1.03748 0.304632i 0.281733 0.959493i \(-0.409091\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(174\) 0 0
\(175\) 0.328708 + 2.28621i 0.328708 + 2.28621i
\(176\) 0 0
\(177\) −1.24302 2.72183i −1.24302 2.72183i
\(178\) 0 0
\(179\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(180\) 1.96608 + 1.26352i 1.96608 + 1.26352i
\(181\) 0.989821 1.14231i 0.989821 1.14231i 1.00000i \(-0.5\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(182\) 0.540641 + 0.158746i 0.540641 + 0.158746i
\(183\) 0 0
\(184\) 0.959493 0.281733i 0.959493 0.281733i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −0.0612263 + 0.425839i −0.0612263 + 0.425839i
\(190\) 3.02977 1.94711i 3.02977 1.94711i
\(191\) 0.544078 + 1.19136i 0.544078 + 1.19136i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(192\) 0.989821 + 1.14231i 0.989821 + 1.14231i
\(193\) 0.118239 + 0.822373i 0.118239 + 0.822373i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(194\) 0 0
\(195\) −1.48666 + 0.436524i −1.48666 + 0.436524i
\(196\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(197\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(198\) 0 0
\(199\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(200\) −0.959493 2.10100i −0.959493 2.10100i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.23259 0.361922i −1.23259 0.361922i
\(208\) −0.563465 −0.563465
\(209\) 0 0
\(210\) 1.80075 2.07817i 1.80075 2.07817i
\(211\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(212\) 0 0
\(213\) −2.44009 + 1.56815i −2.44009 + 1.56815i
\(214\) 0 0
\(215\) 0 0
\(216\) −0.0612263 0.425839i −0.0612263 0.425839i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(224\) 0.841254 0.540641i 0.841254 0.540641i
\(225\) −0.422268 + 2.93694i −0.422268 + 2.93694i
\(226\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(227\) −0.708089 + 0.817178i −0.708089 + 0.817178i −0.989821 0.142315i \(-0.954545\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(228\) −2.87102 0.843008i −2.87102 0.843008i
\(229\) 1.97964 1.97964 0.989821 0.142315i \(-0.0454545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(230\) 1.19136 + 1.37491i 1.19136 + 1.37491i
\(231\) 0 0
\(232\) 0 0
\(233\) −1.10181 + 1.27155i −1.10181 + 1.27155i −0.142315 + 0.989821i \(0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(234\) 0.608936 + 0.391340i 0.608936 + 0.391340i
\(235\) 0 0
\(236\) 1.66538 1.07028i 1.66538 1.07028i
\(237\) 1.05645 + 2.31329i 1.05645 + 2.31329i
\(238\) 0 0
\(239\) −0.118239 0.822373i −0.118239 0.822373i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(240\) −1.14231 + 2.50132i −1.14231 + 2.50132i
\(241\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(242\) 0.959493 0.281733i 0.959493 0.281733i
\(243\) 0.577031 1.26352i 0.577031 1.26352i
\(244\) 0 0
\(245\) −1.19136 1.37491i −1.19136 1.37491i
\(246\) 0 0
\(247\) 0.938384 0.603063i 0.938384 0.603063i
\(248\) 0 0
\(249\) 1.37491 + 0.883600i 1.37491 + 0.883600i
\(250\) 1.56036 1.80075i 1.56036 1.80075i
\(251\) 1.45027 + 0.425839i 1.45027 + 0.425839i 0.909632 0.415415i \(-0.136364\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(252\) −1.28463 −1.28463
\(253\) 0 0
\(254\) −0.830830 −0.830830
\(255\) 0 0
\(256\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(257\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.425839 0.932456i −0.425839 0.932456i
\(261\) 0 0
\(262\) 0.258908 + 1.80075i 0.258908 + 1.80075i
\(263\) 0.797176 1.74557i 0.797176 1.74557i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.822373 + 1.80075i −0.822373 + 1.80075i
\(267\) 0 0
\(268\) 0 0
\(269\) −0.822373 1.80075i −0.822373 1.80075i −0.540641 0.841254i \(-0.681818\pi\)
−0.281733 0.959493i \(-0.590909\pi\)
\(270\) 0.658432 0.423148i 0.658432 0.423148i
\(271\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(272\) 0 0
\(273\) 0.557730 0.643655i 0.557730 0.643655i
\(274\) −0.273100 0.0801894i −0.273100 0.0801894i
\(275\) 0 0
\(276\) 0.215109 1.49611i 0.215109 1.49611i
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) −1.03748 0.304632i −1.03748 0.304632i
\(279\) 0 0
\(280\) 1.53046 + 0.983568i 1.53046 + 0.983568i
\(281\) −0.118239 + 0.822373i −0.118239 + 0.822373i 0.841254 + 0.540641i \(0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(282\) 0 0
\(283\) −0.234072 0.512546i −0.234072 0.512546i 0.755750 0.654861i \(-0.227273\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(284\) −1.25667 1.45027i −1.25667 1.45027i
\(285\) −0.774713 5.38825i −0.774713 5.38825i
\(286\) 0 0
\(287\) 0 0
\(288\) 1.23259 0.361922i 1.23259 0.361922i
\(289\) 0.415415 0.909632i 0.415415 0.909632i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.27155 + 0.817178i −1.27155 + 0.817178i −0.989821 0.142315i \(-0.954545\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(294\) −0.215109 + 1.49611i −0.215109 + 1.49611i
\(295\) 3.02977 + 1.94711i 3.02977 + 1.94711i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.368991 + 0.425839i 0.368991 + 0.425839i
\(300\) −3.49114 −3.49114
\(301\) 0 0
\(302\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(303\) 0 0
\(304\) 0.281733 1.95949i 0.281733 1.95949i
\(305\) 0 0
\(306\) 0 0
\(307\) −0.368991 0.425839i −0.368991 0.425839i 0.540641 0.841254i \(-0.318182\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(312\) −0.353799 + 0.774713i −0.353799 + 0.774713i
\(313\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(314\) −0.708089 0.817178i −0.708089 0.817178i
\(315\) −0.970858 2.12588i −0.970858 2.12588i
\(316\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(317\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.74557 0.512546i −1.74557 0.512546i
\(321\) 0 0
\(322\) −0.959493 0.281733i −0.959493 0.281733i
\(323\) 0 0
\(324\) 0.608660 + 0.178719i 0.608660 + 0.178719i
\(325\) 0.852267 0.983568i 0.852267 0.983568i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(332\) −0.449181 + 0.983568i −0.449181 + 0.983568i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −0.215109 1.49611i −0.215109 1.49611i
\(337\) −1.25667 1.45027i −1.25667 1.45027i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(338\) 0.283524 + 0.620830i 0.283524 + 0.620830i
\(339\) 2.13940 1.37491i 2.13940 1.37491i
\(340\) 0 0
\(341\) 0 0
\(342\) −1.66538 + 1.92195i −1.66538 + 1.92195i
\(343\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(344\) 0 0
\(345\) 2.63843 0.774713i 2.63843 0.774713i
\(346\) 1.08128 1.08128
\(347\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(348\) 0 0
\(349\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(350\) −0.328708 + 2.28621i −0.328708 + 2.28621i
\(351\) 0.203930 0.131058i 0.203930 0.131058i
\(352\) 0 0
\(353\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(354\) −0.425839 2.96177i −0.425839 2.96177i
\(355\) 1.45027 3.17565i 1.45027 3.17565i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.118239 0.822373i −0.118239 0.822373i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(360\) 1.53046 + 1.76625i 1.53046 + 1.76625i
\(361\) 1.21259 + 2.65520i 1.21259 + 2.65520i
\(362\) 1.27155 0.817178i 1.27155 0.817178i
\(363\) 0.215109 1.49611i 0.215109 1.49611i
\(364\) 0.474017 + 0.304632i 0.474017 + 0.304632i
\(365\) 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 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(374\) 0 0
\(375\) −1.49611 3.27603i −1.49611 3.27603i
\(376\) 0 0
\(377\) 0 0
\(378\) −0.178719 + 0.391340i −0.178719 + 0.391340i
\(379\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(380\) 3.45561 1.01466i 3.45561 1.01466i
\(381\) −0.521678 + 1.14231i −0.521678 + 1.14231i
\(382\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(383\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(384\) 0.627899 + 1.37491i 0.627899 + 1.37491i
\(385\) 0 0
\(386\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(390\) −1.54943 −1.54943
\(391\) 0 0
\(392\) −1.00000 −1.00000
\(393\) 2.63843 + 0.774713i 2.63843 + 0.774713i
\(394\) 0 0
\(395\) −2.57501 1.65486i −2.57501 1.65486i
\(396\) 0 0
\(397\) 0.474017 0.304632i 0.474017 0.304632i −0.281733 0.959493i \(-0.590909\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(398\) 0 0
\(399\) 1.95949 + 2.26138i 1.95949 + 2.26138i
\(400\) −0.328708 2.28621i −0.328708 2.28621i
\(401\) 0.797176 1.74557i 0.797176 1.74557i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0.164240 + 1.14231i 0.164240 + 1.14231i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(410\) 0 0
\(411\) −0.281733 + 0.325137i −0.281733 + 0.325137i
\(412\) 0 0
\(413\) −1.97964 −1.97964
\(414\) −1.08070 0.694523i −1.08070 0.694523i
\(415\) −1.96714 −1.96714
\(416\) −0.540641 0.158746i −0.540641 0.158746i
\(417\) −1.07028 + 1.23516i −1.07028 + 1.23516i
\(418\) 0 0
\(419\) 0.0801894 0.557730i 0.0801894 0.557730i −0.909632 0.415415i \(-0.863636\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(420\) 2.31329 1.48666i 2.31329 1.48666i
\(421\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) −2.78305 + 0.817178i −2.78305 + 0.817178i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.41542 0.909632i 1.41542 0.909632i 0.415415 0.909632i \(-0.363636\pi\)
1.00000 \(0\)
\(432\) 0.0612263 0.425839i 0.0612263 0.425839i
\(433\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.66538 + 1.07028i −1.66538 + 1.07028i
\(438\) 0 0
\(439\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(440\) 0 0
\(441\) 1.08070 + 0.694523i 1.08070 + 0.694523i
\(442\) 0 0
\(443\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.959493 0.281733i 0.959493 0.281733i
\(449\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(450\) −1.23259 + 2.69900i −1.23259 + 2.69900i
\(451\) 0 0
\(452\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(453\) 0.822373 + 1.80075i 0.822373 + 1.80075i
\(454\) −0.909632 + 0.584585i −0.909632 + 0.584585i
\(455\) −0.145886 + 1.01466i −0.145886 + 1.01466i
\(456\) −2.51722 1.61772i −2.51722 1.61772i
\(457\) −0.186393 + 0.215109i −0.186393 + 0.215109i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(458\) 1.89945 + 0.557730i 1.89945 + 0.557730i
\(459\) 0 0
\(460\) 0.755750 + 1.65486i 0.755750 + 1.65486i
\(461\) 1.08128 1.08128 0.540641 0.841254i \(-0.318182\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(462\) 0 0
\(463\) −1.25667 + 1.45027i −1.25667 + 1.45027i −0.415415 + 0.909632i \(0.636364\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(467\) 0.627899 + 1.37491i 0.627899 + 1.37491i 0.909632 + 0.415415i \(0.136364\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(468\) 0.474017 + 0.547045i 0.474017 + 0.547045i
\(469\) 0 0
\(470\) 0 0
\(471\) −1.56815 + 0.460451i −1.56815 + 0.460451i
\(472\) 1.89945 0.557730i 1.89945 0.557730i
\(473\) 0 0
\(474\) 0.361922 + 2.51722i 0.361922 + 2.51722i
\(475\) 2.99430 + 3.45561i 2.99430 + 3.45561i
\(476\) 0 0
\(477\) 0 0
\(478\) 0.118239 0.822373i 0.118239 0.822373i
\(479\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(480\) −1.80075 + 2.07817i −1.80075 + 2.07817i
\(481\) 0 0
\(482\) 0 0
\(483\) −0.989821 + 1.14231i −0.989821 + 1.14231i
\(484\) 1.00000 1.00000
\(485\) 0 0
\(486\) 0.909632 1.04977i 0.909632 1.04977i
\(487\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −0.755750 1.65486i −0.755750 1.65486i
\(491\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 1.07028 0.314261i 1.07028 0.314261i
\(495\) 0 0
\(496\) 0 0
\(497\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(498\) 1.07028 + 1.23516i 1.07028 + 1.23516i
\(499\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(500\) 2.00448 1.28820i 2.00448 1.28820i
\(501\) 0 0
\(502\) 1.27155 + 0.817178i 1.27155 + 0.817178i
\(503\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(504\) −1.23259 0.361922i −1.23259 0.361922i
\(505\) 0 0
\(506\) 0 0
\(507\) 1.03161 1.03161
\(508\) −0.797176 0.234072i −0.797176 0.234072i
\(509\) −1.19136 + 1.37491i −1.19136 + 1.37491i −0.281733 + 0.959493i \(0.590909\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(513\) 0.353799 + 0.774713i 0.353799 + 0.774713i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0.678936 1.48666i 0.678936 1.48666i
\(520\) −0.145886 1.01466i −0.145886 1.01466i
\(521\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(522\) 0 0
\(523\) 0.909632 0.584585i 0.909632 0.584585i 1.00000i \(-0.5\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(524\) −0.258908 + 1.80075i −0.258908 + 1.80075i
\(525\) 2.93694 + 1.88745i 2.93694 + 1.88745i
\(526\) 1.25667 1.45027i 1.25667 1.45027i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.654861 0.755750i −0.654861 0.755750i
\(530\) 0 0
\(531\) −2.44009 0.716476i −2.44009 0.716476i
\(532\) −1.29639 + 1.49611i −1.29639 + 1.49611i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −0.281733 1.95949i −0.281733 1.95949i
\(539\) 0 0
\(540\) 0.750975 0.220506i 0.750975 0.220506i
\(541\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(542\) 0 0
\(543\) −0.325137 2.26138i −0.325137 2.26138i
\(544\) 0 0
\(545\) 0 0
\(546\) 0.716476 0.460451i 0.716476 0.460451i
\(547\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(548\) −0.239446 0.153882i −0.239446 0.153882i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0.627899 1.37491i 0.627899 1.37491i
\(553\) 1.68251 1.68251
\(554\) 0 0
\(555\) 0 0
\(556\) −0.909632 0.584585i −0.909632 0.584585i
\(557\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.19136 + 1.37491i 1.19136 + 1.37491i
\(561\) 0 0
\(562\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(563\) −0.540641 + 0.158746i −0.540641 + 0.158746i −0.540641 0.841254i \(-0.681818\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) −1.27155 + 2.78431i −1.27155 + 2.78431i
\(566\) −0.0801894 0.557730i −0.0801894 0.557730i
\(567\) −0.415415 0.479414i −0.415415 0.479414i
\(568\) −0.797176 1.74557i −0.797176 1.74557i
\(569\) 1.10181 0.708089i 1.10181 0.708089i 0.142315 0.989821i \(-0.454545\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(570\) 0.774713 5.38825i 0.774713 5.38825i
\(571\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(572\) 0 0
\(573\) 1.89945 + 0.557730i 1.89945 + 0.557730i
\(574\) 0 0
\(575\) −1.51255 + 1.74557i −1.51255 + 1.74557i
\(576\) 1.28463 1.28463
\(577\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(578\) 0.654861 0.755750i 0.654861 0.755750i
\(579\) 1.05645 + 0.678936i 1.05645 + 0.678936i
\(580\) 0 0
\(581\) 0.909632 0.584585i 0.909632 0.584585i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −0.547045 + 1.19786i −0.547045 + 1.19786i
\(586\) −1.45027 + 0.425839i −1.45027 + 0.425839i
\(587\) 0.540641 0.158746i 0.540641 0.158746i 1.00000i \(-0.5\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(588\) −0.627899 + 1.37491i −0.627899 + 1.37491i
\(589\) 0 0
\(590\) 2.35848 + 2.72183i 2.35848 + 2.72183i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0.234072 + 0.512546i 0.234072 + 0.512546i
\(599\) 1.30972 1.30972 0.654861 0.755750i \(-0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(600\) −3.34973 0.983568i −3.34973 0.983568i
\(601\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(605\) 0.755750 + 1.65486i 0.755750 + 1.65486i
\(606\) 0 0
\(607\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(608\) 0.822373 1.80075i 0.822373 1.80075i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(614\) −0.234072 0.512546i −0.234072 0.512546i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.698939 0.449181i −0.698939 0.449181i 0.142315 0.989821i \(-0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(618\) 0 0
\(619\) −1.03748 0.304632i −1.03748 0.304632i −0.281733 0.959493i \(-0.590909\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(620\) 0 0
\(621\) −0.361922 + 0.232593i −0.361922 + 0.232593i
\(622\) 0 0
\(623\) 0 0
\(624\) −0.557730 + 0.643655i −0.557730 + 0.643655i
\(625\) 1.70362 + 1.09485i 1.70362 + 1.09485i
\(626\) 0 0
\(627\) 0 0
\(628\) −0.449181 0.983568i −0.449181 0.983568i
\(629\) 0 0
\(630\) −0.332601 2.31329i −0.332601 2.31329i
\(631\) 0.544078 1.19136i 0.544078 1.19136i −0.415415 0.909632i \(-0.636364\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(632\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(633\) 0 0
\(634\) 0 0
\(635\) −0.215109 1.49611i −0.215109 1.49611i
\(636\) 0 0
\(637\) −0.234072 0.512546i −0.234072 0.512546i
\(638\) 0 0
\(639\) −0.350833 + 2.44009i −0.350833 + 2.44009i
\(640\) −1.53046 0.983568i −1.53046 0.983568i
\(641\) 0.544078 0.627899i 0.544078 0.627899i −0.415415 0.909632i \(-0.636364\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(642\) 0 0
\(643\) −1.51150 −1.51150 −0.755750 0.654861i \(-0.772727\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(644\) −0.841254 0.540641i −0.841254 0.540641i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(648\) 0.533654 + 0.342959i 0.533654 + 0.342959i
\(649\) 0 0
\(650\) 1.09485 0.703616i 1.09485 0.703616i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(654\) 0 0
\(655\) −3.17565 + 0.932456i −3.17565 + 0.932456i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(660\) 0 0
\(661\) −0.474017 + 0.304632i −0.474017 + 0.304632i −0.755750 0.654861i \(-0.772727\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.708089 + 0.817178i −0.708089 + 0.817178i
\(665\) −3.45561 1.01466i −3.45561 1.01466i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0.215109 1.49611i 0.215109 1.49611i
\(673\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(674\) −0.797176 1.74557i −0.797176 1.74557i
\(675\) 0.650724 + 0.750975i 0.650724 + 0.750975i
\(676\) 0.0971309 + 0.675560i 0.0971309 + 0.675560i
\(677\) 0.449181 0.983568i 0.449181 0.983568i −0.540641 0.841254i \(-0.681818\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(678\) 2.44009 0.716476i 2.44009 0.716476i
\(679\) 0 0
\(680\) 0 0
\(681\) 0.232593 + 1.61772i 0.232593 + 1.61772i
\(682\) 0 0
\(683\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(684\) −2.13940 + 1.37491i −2.13940 + 1.37491i
\(685\) 0.0736930 0.512546i 0.0736930 0.512546i
\(686\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(687\) 1.95949 2.26138i 1.95949 2.26138i
\(688\) 0 0
\(689\) 0 0
\(690\) 2.74982 2.74982
\(691\) −1.97964 −1.97964 −0.989821 0.142315i \(-0.954545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(692\) 1.03748 + 0.304632i 1.03748 + 0.304632i
\(693\) 0 0
\(694\) 0 0
\(695\) 0.279953 1.94711i 0.279953 1.94711i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0.361922 + 2.51722i 0.361922 + 2.51722i
\(700\) −0.959493 + 2.10100i −0.959493 + 2.10100i
\(701\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(702\) 0.232593 0.0682955i 0.232593 0.0682955i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0.425839 2.96177i 0.425839 2.96177i
\(709\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(710\) 2.28621 2.63843i 2.28621 2.63843i
\(711\) 2.07385 + 0.608936i 2.07385 + 0.608936i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −1.05645 0.678936i −1.05645 0.678936i
\(718\) 0.118239 0.822373i 0.118239 0.822373i
\(719\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(720\) 0.970858 + 2.12588i 0.970858 + 2.12588i
\(721\) 0 0
\(722\) 0.415415 + 2.88927i 0.415415 + 2.88927i
\(723\) 0 0
\(724\) 1.45027 0.425839i 1.45027 0.425839i
\(725\) 0 0
\(726\) 0.627899 1.37491i 0.627899 1.37491i
\(727\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(728\) 0.368991 + 0.425839i 0.368991 + 0.425839i
\(729\) −0.608660 1.33278i −0.608660 1.33278i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.368991 + 0.425839i −0.368991 + 0.425839i −0.909632 0.415415i \(-0.863636\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(734\) 0 0
\(735\) −2.74982 −2.74982
\(736\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(740\) 0 0
\(741\) 0.239945 1.66886i 0.239945 1.66886i
\(742\) 0 0
\(743\) 0.345139 + 0.755750i 0.345139 + 0.755750i 1.00000 \(0\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.33278 0.391340i 1.33278 0.391340i
\(748\) 0 0
\(749\) 0 0
\(750\) −0.512546 3.56484i −0.512546 3.56484i
\(751\) 0.186393 + 0.215109i 0.186393 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(752\) 0 0
\(753\) 1.92195 1.23516i 1.92195 1.23516i
\(754\) 0 0
\(755\) −2.00448 1.28820i −2.00448 1.28820i
\(756\) −0.281733 + 0.325137i −0.281733 + 0.325137i
\(757\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 3.60149 3.60149
\(761\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(762\) −0.822373 + 0.949069i −0.822373 + 0.949069i
\(763\) 0 0
\(764\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(765\) 0 0
\(766\) 0 0
\(767\) 0.730471 + 0.843008i 0.730471 + 0.843008i
\(768\) 0.215109 + 1.49611i 0.215109 + 1.49611i
\(769\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(773\) 0.258908 + 1.80075i 0.258908 + 1.80075i 0.540641 + 0.841254i \(0.318182\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −1.48666 0.436524i −1.48666 0.436524i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.959493 0.281733i −0.959493 0.281733i
\(785\) 1.28820 1.48666i 1.28820 1.48666i
\(786\) 2.31329 + 1.48666i 2.31329 + 1.48666i
\(787\) −0.281733 + 1.95949i −0.281733 + 1.95949i 1.00000i \(0.5\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(788\) 0 0
\(789\) −1.20493 2.63843i −1.20493 2.63843i
\(790\) −2.00448 2.31329i −2.00448 2.31329i
\(791\) −0.239446 1.66538i −0.239446 1.66538i
\(792\) 0 0
\(793\) 0 0
\(794\) 0.540641 0.158746i 0.540641 0.158746i
\(795\) 0 0
\(796\) 0 0
\(797\) 0.368991 + 0.425839i 0.368991 + 0.425839i 0.909632 0.415415i \(-0.136364\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(798\) 1.24302 + 2.72183i 1.24302 + 2.72183i
\(799\) 0 0
\(800\) 0.328708 2.28621i 0.328708 2.28621i
\(801\) 0 0
\(802\) 1.25667 1.45027i 1.25667 1.45027i
\(803\) 0 0
\(804\) 0 0
\(805\) 0.258908 1.80075i 0.258908 1.80075i
\(806\) 0 0
\(807\) −2.87102 0.843008i −2.87102 0.843008i
\(808\) 0 0
\(809\) −1.41542 0.909632i −1.41542 0.909632i −0.415415 0.909632i \(-0.636364\pi\)
−1.00000 \(\pi\)
\(810\) −0.164240 + 1.14231i −0.164240 + 1.14231i
\(811\) 1.66538 1.07028i 1.66538 1.07028i 0.755750 0.654861i \(-0.227273\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) −0.103014 0.716476i −0.103014 0.716476i
\(820\) 0 0
\(821\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(822\) −0.361922 + 0.232593i −0.361922 + 0.232593i
\(823\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i 0.959493 + 0.281733i \(0.0909091\pi\)
−1.00000 \(1.00000\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −1.89945 0.557730i −1.89945 0.557730i
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) −0.841254 0.970858i −0.841254 0.970858i
\(829\) −1.81926 −1.81926 −0.909632 0.415415i \(-0.863636\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(830\) −1.88745 0.554206i −1.88745 0.554206i
\(831\) 0 0
\(832\) −0.474017 0.304632i −0.474017 0.304632i
\(833\) 0 0
\(834\) −1.37491 + 0.883600i −1.37491 + 0.883600i
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0.234072 0.512546i 0.234072 0.512546i
\(839\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(840\) 2.63843 0.774713i 2.63843 0.774713i
\(841\) 0.415415 0.909632i 0.415415 0.909632i
\(842\) 0 0
\(843\) 0.822373 + 0.949069i 0.822373 + 0.949069i
\(844\) 0 0
\(845\) −1.04455 + 0.671292i −1.04455 + 0.671292i
\(846\) 0 0
\(847\) −0.841254 0.540641i −0.841254 0.540641i
\(848\) 0 0
\(849\) −0.817178 0.239945i −0.817178 0.239945i
\(850\) 0 0
\(851\) 0 0
\(852\) −2.90055 −2.90055
\(853\) −1.03748 0.304632i −1.03748 0.304632i −0.281733 0.959493i \(-0.590909\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(854\) 0 0
\(855\) −3.89213 2.50132i −3.89213 2.50132i
\(856\) 0 0
\(857\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(858\) 0 0
\(859\) 1.19136 + 1.37491i 1.19136 + 1.37491i 0.909632 + 0.415415i \(0.136364\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 1.61435 0.474017i 1.61435 0.474017i
\(863\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i −0.415415 0.909632i \(-0.636364\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(864\) 0.178719 0.391340i 0.178719 0.391340i
\(865\) 0.279953 + 1.94711i 0.279953 + 1.94711i
\(866\) 0 0
\(867\) −0.627899 1.37491i −0.627899 1.37491i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) −1.89945 + 0.557730i −1.89945 + 0.557730i
\(875\) −2.38273 −2.38273
\(876\) 0 0
\(877\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(878\) 0 0
\(879\) −0.325137 + 2.26138i −0.325137 + 2.26138i
\(880\) 0 0
\(881\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(882\) 0.841254 + 0.970858i 0.841254 + 0.970858i
\(883\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(884\) 0 0
\(885\) 5.22315 1.53365i 5.22315 1.53365i
\(886\) 0 0
\(887\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(888\) 0 0
\(889\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 1.00000
\(897\) 0.851677 0.851677
\(898\) 0.284630 0.284630
\(899\) 0 0
\(900\) −1.94306 + 2.24241i −1.94306 + 2.24241i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0.698939 + 1.53046i 0.698939 + 1.53046i
\(905\) 1.80075 + 2.07817i 1.80075 + 2.07817i
\(906\) 0.281733 + 1.95949i 0.281733 + 1.95949i
\(907\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(908\) −1.03748 + 0.304632i −1.03748 + 0.304632i
\(909\) 0 0
\(910\) −0.425839 + 0.932456i −0.425839 + 0.932456i
\(911\) −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(912\) −1.95949 2.26138i −1.95949 2.26138i
\(913\) 0 0
\(914\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(915\) 0 0
\(916\) 1.66538 + 1.07028i 1.66538 + 1.07028i
\(917\) 1.19136 1.37491i 1.19136 1.37491i
\(918\) 0 0
\(919\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(920\) 0.258908 + 1.80075i 0.258908 + 1.80075i
\(921\) −0.851677 −0.851677
\(922\) 1.03748 + 0.304632i 1.03748 + 0.304632i
\(923\) 0.708089 0.817178i 0.708089 0.817178i
\(924\) 0 0
\(925\) 0 0
\(926\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(930\) 0 0
\(931\) 1.89945 0.557730i 1.89945 0.557730i
\(932\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(933\) 0 0
\(934\) 0.215109 + 1.49611i 0.215109 + 1.49611i
\(935\) 0 0
\(936\) 0.300696 + 0.658432i 0.300696 + 0.658432i
\(937\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.03748 + 0.304632i 1.03748 + 0.304632i 0.755750 0.654861i \(-0.227273\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(942\) −1.63436 −1.63436
\(943\) 0 0
\(944\) 1.97964 1.97964
\(945\) −0.750975 0.220506i −0.750975 0.220506i
\(946\) 0 0
\(947\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(948\) −0.361922 + 2.51722i −0.361922 + 2.51722i
\(949\) 0 0
\(950\) 1.89945 + 4.15922i 1.89945 + 4.15922i
\(951\) 0 0
\(952\) 0 0
\(953\) −0.797176 + 1.74557i −0.797176 + 1.74557i −0.142315 + 0.989821i \(0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(954\) 0 0
\(955\) −2.28621 + 0.671292i −2.28621 + 0.671292i
\(956\) 0.345139 0.755750i 0.345139 0.755750i
\(957\) 0 0
\(958\) 0 0
\(959\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(960\) −2.31329 + 1.48666i −2.31329 + 1.48666i
\(961\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.51150 −1.51150
\(966\) −1.27155 + 0.817178i −1.27155 + 0.817178i
\(967\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(968\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(969\) 0 0
\(970\) 0 0
\(971\) 0.258908 1.80075i 0.258908 1.80075i −0.281733 0.959493i \(-0.590909\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(972\) 1.16854 0.750975i 1.16854 0.750975i
\(973\) 0.449181 + 0.983568i 0.449181 + 0.983568i
\(974\) −1.25667 1.45027i −1.25667 1.45027i
\(975\) −0.279953 1.94711i −0.279953 1.94711i
\(976\) 0 0
\(977\) −0.797176 + 0.234072i −0.797176 + 0.234072i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −0.258908 1.80075i −0.258908 1.80075i
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 1.11546 1.11546
\(989\) 0 0
\(990\) 0 0
\(991\) 0.797176 + 0.234072i 0.797176 + 0.234072i 0.654861 0.755750i \(-0.272727\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(995\) 0 0
\(996\) 0.678936 + 1.48666i 0.678936 + 1.48666i
\(997\) −1.19136 1.37491i −1.19136 1.37491i −0.909632 0.415415i \(-0.863636\pi\)
−0.281733 0.959493i \(-0.590909\pi\)
\(998\) 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.685.2 yes 20
7.6 odd 2 inner 1288.1.bi.e.685.1 20
8.5 even 2 inner 1288.1.bi.e.685.1 20
23.9 even 11 inner 1288.1.bi.e.1021.2 yes 20
56.13 odd 2 CM 1288.1.bi.e.685.2 yes 20
161.55 odd 22 inner 1288.1.bi.e.1021.1 yes 20
184.101 even 22 inner 1288.1.bi.e.1021.1 yes 20
1288.1021 odd 22 inner 1288.1.bi.e.1021.2 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1288.1.bi.e.685.1 20 7.6 odd 2 inner
1288.1.bi.e.685.1 20 8.5 even 2 inner
1288.1.bi.e.685.2 yes 20 1.1 even 1 trivial
1288.1.bi.e.685.2 yes 20 56.13 odd 2 CM
1288.1.bi.e.1021.1 yes 20 161.55 odd 22 inner
1288.1.bi.e.1021.1 yes 20 184.101 even 22 inner
1288.1.bi.e.1021.2 yes 20 23.9 even 11 inner
1288.1.bi.e.1021.2 yes 20 1288.1021 odd 22 inner