Properties

Label 1564.1.w.c.1359.1
Level $1564$
Weight $1$
Character 1564.1359
Analytic conductor $0.781$
Analytic rank $0$
Dimension $20$
Projective image $D_{22}$
CM discriminant -68
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1564,1,Mod(271,1564)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1564, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 12]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1564.271");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1564 = 2^{2} \cdot 17 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1564.w (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: \(0.780537679758\)
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: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{22}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{22} - \cdots)\)

Embedding invariants

Embedding label 1359.1
Root \(0.540641 + 0.841254i\) of defining polynomial
Character \(\chi\) \(=\) 1564.1359
Dual form 1564.1.w.c.679.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.841254 - 0.540641i) q^{2} +(-0.215109 - 1.49611i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.627899 + 1.37491i) q^{6} +(-1.19136 + 1.37491i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-1.23259 + 0.361922i) q^{9} +O(q^{10})\) \(q+(-0.841254 - 0.540641i) q^{2} +(-0.215109 - 1.49611i) q^{3} +(0.415415 + 0.909632i) q^{4} +(-0.627899 + 1.37491i) q^{6} +(-1.19136 + 1.37491i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-1.23259 + 0.361922i) q^{9} +(1.66538 - 1.07028i) q^{11} +(1.27155 - 0.817178i) q^{12} +(0.544078 + 0.627899i) q^{13} +(1.74557 - 0.512546i) q^{14} +(-0.654861 + 0.755750i) q^{16} +(0.415415 - 0.909632i) q^{17} +(1.23259 + 0.361922i) q^{18} +(2.31329 + 1.48666i) q^{21} -1.97964 q^{22} +(-0.909632 - 0.415415i) q^{23} -1.51150 q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.118239 - 0.822373i) q^{26} +(0.178719 + 0.391340i) q^{27} +(-1.74557 - 0.512546i) q^{28} +(0.281733 - 1.95949i) q^{31} +(0.959493 - 0.281733i) q^{32} +(-1.95949 - 2.26138i) q^{33} +(-0.841254 + 0.540641i) q^{34} +(-0.841254 - 0.970858i) q^{36} +(0.822373 - 0.949069i) q^{39} +(-1.14231 - 2.50132i) q^{42} +(1.66538 + 1.07028i) q^{44} +(0.540641 + 0.841254i) q^{46} +(1.27155 + 0.817178i) q^{48} +(-0.328708 - 2.28621i) q^{49} +(-0.415415 - 0.909632i) q^{50} +(-1.45027 - 0.425839i) q^{51} +(-0.345139 + 0.755750i) q^{52} +(0.186393 - 0.215109i) q^{53} +(0.0612263 - 0.425839i) q^{54} +(1.19136 + 1.37491i) q^{56} +(-1.29639 + 1.49611i) q^{62} +(0.970858 - 2.12588i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.425839 + 2.96177i) q^{66} +1.00000 q^{68} +(-0.425839 + 1.45027i) q^{69} +(0.182822 + 1.27155i) q^{72} +(0.627899 - 1.37491i) q^{75} +(-0.512546 + 3.56484i) q^{77} +(-1.20493 + 0.353799i) q^{78} +(0.708089 + 0.817178i) q^{79} +(-0.533654 + 0.342959i) q^{81} +(-0.391340 + 2.72183i) q^{84} +(-0.822373 - 1.80075i) q^{88} +(-0.0405070 - 0.281733i) q^{89} -1.51150 q^{91} -1.00000i q^{92} -2.99223 q^{93} +(-0.627899 - 1.37491i) q^{96} +(-0.959493 + 2.10100i) q^{98} +(-1.66538 + 1.92195i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{8} + 2 q^{9} + 4 q^{13} - 2 q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{25} - 4 q^{26} + 2 q^{32} - 22 q^{33} + 2 q^{34} + 2 q^{36} - 22 q^{42} + 2 q^{49} + 2 q^{50} - 18 q^{52} - 4 q^{53} - 2 q^{64} + 20 q^{68} + 20 q^{72} - 2 q^{81} - 18 q^{89} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1564\mathbb{Z}\right)^\times\).

\(n\) \(783\) \(921\) \(1293\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{11}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.841254 0.540641i −0.841254 0.540641i
\(3\) −0.215109 1.49611i −0.215109 1.49611i −0.755750 0.654861i \(-0.772727\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(4\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(5\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(6\) −0.627899 + 1.37491i −0.627899 + 1.37491i
\(7\) −1.19136 + 1.37491i −1.19136 + 1.37491i −0.281733 + 0.959493i \(0.590909\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(8\) 0.142315 0.989821i 0.142315 0.989821i
\(9\) −1.23259 + 0.361922i −1.23259 + 0.361922i
\(10\) 0 0
\(11\) 1.66538 1.07028i 1.66538 1.07028i 0.755750 0.654861i \(-0.227273\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(12\) 1.27155 0.817178i 1.27155 0.817178i
\(13\) 0.544078 + 0.627899i 0.544078 + 0.627899i 0.959493 0.281733i \(-0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(14\) 1.74557 0.512546i 1.74557 0.512546i
\(15\) 0 0
\(16\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(17\) 0.415415 0.909632i 0.415415 0.909632i
\(18\) 1.23259 + 0.361922i 1.23259 + 0.361922i
\(19\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(20\) 0 0
\(21\) 2.31329 + 1.48666i 2.31329 + 1.48666i
\(22\) −1.97964 −1.97964
\(23\) −0.909632 0.415415i −0.909632 0.415415i
\(24\) −1.51150 −1.51150
\(25\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(26\) −0.118239 0.822373i −0.118239 0.822373i
\(27\) 0.178719 + 0.391340i 0.178719 + 0.391340i
\(28\) −1.74557 0.512546i −1.74557 0.512546i
\(29\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(30\) 0 0
\(31\) 0.281733 1.95949i 0.281733 1.95949i 1.00000i \(-0.5\pi\)
0.281733 0.959493i \(-0.409091\pi\)
\(32\) 0.959493 0.281733i 0.959493 0.281733i
\(33\) −1.95949 2.26138i −1.95949 2.26138i
\(34\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(35\) 0 0
\(36\) −0.841254 0.970858i −0.841254 0.970858i
\(37\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(38\) 0 0
\(39\) 0.822373 0.949069i 0.822373 0.949069i
\(40\) 0 0
\(41\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(42\) −1.14231 2.50132i −1.14231 2.50132i
\(43\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(44\) 1.66538 + 1.07028i 1.66538 + 1.07028i
\(45\) 0 0
\(46\) 0.540641 + 0.841254i 0.540641 + 0.841254i
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 1.27155 + 0.817178i 1.27155 + 0.817178i
\(49\) −0.328708 2.28621i −0.328708 2.28621i
\(50\) −0.415415 0.909632i −0.415415 0.909632i
\(51\) −1.45027 0.425839i −1.45027 0.425839i
\(52\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(53\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(54\) 0.0612263 0.425839i 0.0612263 0.425839i
\(55\) 0 0
\(56\) 1.19136 + 1.37491i 1.19136 + 1.37491i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(60\) 0 0
\(61\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(62\) −1.29639 + 1.49611i −1.29639 + 1.49611i
\(63\) 0.970858 2.12588i 0.970858 2.12588i
\(64\) −0.959493 0.281733i −0.959493 0.281733i
\(65\) 0 0
\(66\) 0.425839 + 2.96177i 0.425839 + 2.96177i
\(67\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(68\) 1.00000 1.00000
\(69\) −0.425839 + 1.45027i −0.425839 + 1.45027i
\(70\) 0 0
\(71\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(72\) 0.182822 + 1.27155i 0.182822 + 1.27155i
\(73\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(74\) 0 0
\(75\) 0.627899 1.37491i 0.627899 1.37491i
\(76\) 0 0
\(77\) −0.512546 + 3.56484i −0.512546 + 3.56484i
\(78\) −1.20493 + 0.353799i −1.20493 + 0.353799i
\(79\) 0.708089 + 0.817178i 0.708089 + 0.817178i 0.989821 0.142315i \(-0.0454545\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(80\) 0 0
\(81\) −0.533654 + 0.342959i −0.533654 + 0.342959i
\(82\) 0 0
\(83\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(84\) −0.391340 + 2.72183i −0.391340 + 2.72183i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.822373 1.80075i −0.822373 1.80075i
\(89\) −0.0405070 0.281733i −0.0405070 0.281733i 0.959493 0.281733i \(-0.0909091\pi\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) −1.51150 −1.51150
\(92\) 1.00000i 1.00000i
\(93\) −2.99223 −2.99223
\(94\) 0 0
\(95\) 0 0
\(96\) −0.627899 1.37491i −0.627899 1.37491i
\(97\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(98\) −0.959493 + 2.10100i −0.959493 + 2.10100i
\(99\) −1.66538 + 1.92195i −1.66538 + 1.92195i
\(100\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(101\) 1.61435 0.474017i 1.61435 0.474017i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(102\) 0.989821 + 1.14231i 0.989821 + 1.14231i
\(103\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(104\) 0.698939 0.449181i 0.698939 0.449181i
\(105\) 0 0
\(106\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i
\(107\) −0.0801894 + 0.557730i −0.0801894 + 0.557730i 0.909632 + 0.415415i \(0.136364\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(108\) −0.281733 + 0.325137i −0.281733 + 0.325137i
\(109\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.258908 1.80075i −0.258908 1.80075i
\(113\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.897877 0.577031i −0.897877 0.577031i
\(118\) 0 0
\(119\) 0.755750 + 1.65486i 0.755750 + 1.65486i
\(120\) 0 0
\(121\) 1.21259 2.65520i 1.21259 2.65520i
\(122\) 0 0
\(123\) 0 0
\(124\) 1.89945 0.557730i 1.89945 0.557730i
\(125\) 0 0
\(126\) −1.96608 + 1.26352i −1.96608 + 1.26352i
\(127\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(128\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.368991 0.425839i 0.368991 0.425839i −0.540641 0.841254i \(-0.681818\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(132\) 1.24302 2.72183i 1.24302 2.72183i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.841254 0.540641i −0.841254 0.540641i
\(137\) −1.68251 −1.68251 −0.841254 0.540641i \(-0.818182\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(138\) 1.14231 0.989821i 1.14231 0.989821i
\(139\) −0.563465 −0.563465 −0.281733 0.959493i \(-0.590909\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.57812 + 0.463379i 1.57812 + 0.463379i
\(144\) 0.533654 1.16854i 0.533654 1.16854i
\(145\) 0 0
\(146\) 0 0
\(147\) −3.34973 + 0.983568i −3.34973 + 0.983568i
\(148\) 0 0
\(149\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(150\) −1.27155 + 0.817178i −1.27155 + 0.817178i
\(151\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(152\) 0 0
\(153\) −0.182822 + 1.27155i −0.182822 + 1.27155i
\(154\) 2.35848 2.72183i 2.35848 2.72183i
\(155\) 0 0
\(156\) 1.20493 + 0.353799i 1.20493 + 0.353799i
\(157\) −0.544078 1.19136i −0.544078 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(158\) −0.153882 1.07028i −0.153882 1.07028i
\(159\) −0.361922 0.232593i −0.361922 0.232593i
\(160\) 0 0
\(161\) 1.65486 0.755750i 1.65486 0.755750i
\(162\) 0.634356 0.634356
\(163\) 1.53046 + 0.983568i 1.53046 + 0.983568i 0.989821 + 0.142315i \(0.0454545\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.449181 0.983568i 0.449181 0.983568i −0.540641 0.841254i \(-0.681818\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(168\) 1.80075 2.07817i 1.80075 2.07817i
\(169\) 0.0440780 0.306569i 0.0440780 0.306569i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(174\) 0 0
\(175\) −1.74557 + 0.512546i −1.74557 + 0.512546i
\(176\) −0.281733 + 1.95949i −0.281733 + 1.95949i
\(177\) 0 0
\(178\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(179\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(180\) 0 0
\(181\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(182\) 1.27155 + 0.817178i 1.27155 + 0.817178i
\(183\) 0 0
\(184\) −0.540641 + 0.841254i −0.540641 + 0.841254i
\(185\) 0 0
\(186\) 2.51722 + 1.61772i 2.51722 + 1.61772i
\(187\) −0.281733 1.95949i −0.281733 1.95949i
\(188\) 0 0
\(189\) −0.750975 0.220506i −0.750975 0.220506i
\(190\) 0 0
\(191\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(192\) −0.215109 + 1.49611i −0.215109 + 1.49611i
\(193\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.94306 1.24873i 1.94306 1.24873i
\(197\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(198\) 2.44009 0.716476i 2.44009 0.716476i
\(199\) −0.215109 + 1.49611i −0.215109 + 1.49611i 0.540641 + 0.841254i \(0.318182\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(200\) 0.654861 0.755750i 0.654861 0.755750i
\(201\) 0 0
\(202\) −1.61435 0.474017i −1.61435 0.474017i
\(203\) 0 0
\(204\) −0.215109 1.49611i −0.215109 1.49611i
\(205\) 0 0
\(206\) 0 0
\(207\) 1.27155 + 0.182822i 1.27155 + 0.182822i
\(208\) −0.830830 −0.830830
\(209\) 0 0
\(210\) 0 0
\(211\) 0.449181 + 0.983568i 0.449181 + 0.983568i 0.989821 + 0.142315i \(0.0454545\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(212\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(213\) 0 0
\(214\) 0.368991 0.425839i 0.368991 0.425839i
\(215\) 0 0
\(216\) 0.412791 0.121206i 0.412791 0.121206i
\(217\) 2.35848 + 2.72183i 2.35848 + 2.72183i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.797176 0.234072i 0.797176 0.234072i
\(222\) 0 0
\(223\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(224\) −0.755750 + 1.65486i −0.755750 + 1.65486i
\(225\) −1.23259 0.361922i −1.23259 0.361922i
\(226\) 0 0
\(227\) 0.215109 + 1.49611i 0.215109 + 1.49611i 0.755750 + 0.654861i \(0.227273\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(228\) 0 0
\(229\) −0.830830 −0.830830 −0.415415 0.909632i \(-0.636364\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(230\) 0 0
\(231\) 5.44365 5.44365
\(232\) 0 0
\(233\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(234\) 0.443376 + 0.970858i 0.443376 + 0.970858i
\(235\) 0 0
\(236\) 0 0
\(237\) 1.07028 1.23516i 1.07028 1.23516i
\(238\) 0.258908 1.80075i 0.258908 1.80075i
\(239\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(240\) 0 0
\(241\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(242\) −2.45561 + 1.57812i −2.45561 + 1.57812i
\(243\) 0.909632 + 1.04977i 0.909632 + 1.04977i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −1.89945 0.557730i −1.89945 0.557730i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(252\) 2.33708 2.33708
\(253\) −1.95949 + 0.281733i −1.95949 + 0.281733i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.142315 0.989821i −0.142315 0.989821i
\(257\) 0.544078 + 1.19136i 0.544078 + 1.19136i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.540641 + 0.158746i −0.540641 + 0.158746i
\(263\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(264\) −2.51722 + 1.61772i −2.51722 + 1.61772i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.412791 + 0.121206i −0.412791 + 0.121206i
\(268\) 0 0
\(269\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(270\) 0 0
\(271\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(272\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(273\) 0.325137 + 2.26138i 0.325137 + 2.26138i
\(274\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(275\) 1.97964 1.97964
\(276\) −1.49611 + 0.215109i −1.49611 + 0.215109i
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0.474017 + 0.304632i 0.474017 + 0.304632i
\(279\) 0.361922 + 2.51722i 0.361922 + 2.51722i
\(280\) 0 0
\(281\) 1.84125 + 0.540641i 1.84125 + 0.540641i 1.00000 \(0\)
0.841254 + 0.540641i \(0.181818\pi\)
\(282\) 0 0
\(283\) −0.708089 + 0.817178i −0.708089 + 0.817178i −0.989821 0.142315i \(-0.954545\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −1.07708 1.24302i −1.07708 1.24302i
\(287\) 0 0
\(288\) −1.08070 + 0.694523i −1.08070 + 0.694523i
\(289\) −0.654861 0.755750i −0.654861 0.755750i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(294\) 3.34973 + 0.983568i 3.34973 + 0.983568i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.716476 + 0.460451i 0.716476 + 0.460451i
\(298\) 1.30972 1.30972
\(299\) −0.234072 0.797176i −0.234072 0.797176i
\(300\) 1.51150 1.51150
\(301\) 0 0
\(302\) 0 0
\(303\) −1.05645 2.31329i −1.05645 2.31329i
\(304\) 0 0
\(305\) 0 0
\(306\) 0.841254 0.970858i 0.841254 0.970858i
\(307\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(308\) −3.45561 + 1.01466i −3.45561 + 1.01466i
\(309\) 0 0
\(310\) 0 0
\(311\) −1.53046 + 0.983568i −1.53046 + 0.983568i −0.540641 + 0.841254i \(0.681818\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(312\) −0.822373 0.949069i −0.822373 0.949069i
\(313\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(314\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(315\) 0 0
\(316\) −0.449181 + 0.983568i −0.449181 + 0.983568i
\(317\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(318\) 0.178719 + 0.391340i 0.178719 + 0.391340i
\(319\) 0 0
\(320\) 0 0
\(321\) 0.851677 0.851677
\(322\) −1.80075 0.258908i −1.80075 0.258908i
\(323\) 0 0
\(324\) −0.533654 0.342959i −0.533654 0.342959i
\(325\) 0.118239 + 0.822373i 0.118239 + 0.822373i
\(326\) −0.755750 1.65486i −0.755750 1.65486i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −0.909632 + 0.584585i −0.909632 + 0.584585i
\(335\) 0 0
\(336\) −2.63843 + 0.774713i −2.63843 + 0.774713i
\(337\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(338\) −0.202824 + 0.234072i −0.202824 + 0.234072i
\(339\) 0 0
\(340\) 0 0
\(341\) −1.62801 3.56484i −1.62801 3.56484i
\(342\) 0 0
\(343\) 2.00448 + 1.28820i 2.00448 + 1.28820i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.66538 1.07028i −1.66538 1.07028i −0.909632 0.415415i \(-0.863636\pi\)
−0.755750 0.654861i \(-0.772727\pi\)
\(348\) 0 0
\(349\) 0.345139 + 0.755750i 0.345139 + 0.755750i 1.00000 \(0\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(350\) 1.74557 + 0.512546i 1.74557 + 0.512546i
\(351\) −0.148485 + 0.325137i −0.148485 + 0.325137i
\(352\) 1.29639 1.49611i 1.29639 1.49611i
\(353\) 0.273100 1.89945i 0.273100 1.89945i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.239446 0.153882i 0.239446 0.153882i
\(357\) 2.31329 1.48666i 2.31329 1.48666i
\(358\) 0 0
\(359\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(360\) 0 0
\(361\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(362\) 0 0
\(363\) −4.23333 1.24302i −4.23333 1.24302i
\(364\) −0.627899 1.37491i −0.627899 1.37491i
\(365\) 0 0
\(366\) 0 0
\(367\) 0.563465 0.563465 0.281733 0.959493i \(-0.409091\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(368\) 0.909632 0.415415i 0.909632 0.415415i
\(369\) 0 0
\(370\) 0 0
\(371\) 0.0736930 + 0.512546i 0.0736930 + 0.512546i
\(372\) −1.24302 2.72183i −1.24302 2.72183i
\(373\) 1.61435 + 0.474017i 1.61435 + 0.474017i 0.959493 0.281733i \(-0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(374\) −0.822373 + 1.80075i −0.822373 + 1.80075i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0.512546 + 0.591509i 0.512546 + 0.591509i
\(379\) −0.474017 + 0.304632i −0.474017 + 0.304632i −0.755750 0.654861i \(-0.772727\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(384\) 0.989821 1.14231i 0.989821 1.14231i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1.10181 + 0.708089i 1.10181 + 0.708089i 0.959493 0.281733i \(-0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(390\) 0 0
\(391\) −0.755750 + 0.654861i −0.755750 + 0.654861i
\(392\) −2.30972 −2.30972
\(393\) −0.716476 0.460451i −0.716476 0.460451i
\(394\) 0 0
\(395\) 0 0
\(396\) −2.44009 0.716476i −2.44009 0.716476i
\(397\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(398\) 0.989821 1.14231i 0.989821 1.14231i
\(399\) 0 0
\(400\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(401\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(402\) 0 0
\(403\) 1.38365 0.889217i 1.38365 0.889217i
\(404\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.627899 + 1.37491i −0.627899 + 1.37491i
\(409\) −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(410\) 0 0
\(411\) 0.361922 + 2.51722i 0.361922 + 2.51722i
\(412\) 0 0
\(413\) 0 0
\(414\) −0.970858 0.841254i −0.970858 0.841254i
\(415\) 0 0
\(416\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(417\) 0.121206 + 0.843008i 0.121206 + 0.843008i
\(418\) 0 0
\(419\) 1.89945 + 0.557730i 1.89945 + 0.557730i 0.989821 + 0.142315i \(0.0454545\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(420\) 0 0
\(421\) −0.857685 + 0.989821i −0.857685 + 0.989821i 0.142315 + 0.989821i \(0.454545\pi\)
−1.00000 \(\pi\)
\(422\) 0.153882 1.07028i 0.153882 1.07028i
\(423\) 0 0
\(424\) −0.186393 0.215109i −0.186393 0.215109i
\(425\) 0.841254 0.540641i 0.841254 0.540641i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.540641 + 0.158746i −0.540641 + 0.158746i
\(429\) 0.353799 2.46073i 0.353799 2.46073i
\(430\) 0 0
\(431\) −0.627899 + 1.37491i −0.627899 + 1.37491i 0.281733 + 0.959493i \(0.409091\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(432\) −0.412791 0.121206i −0.412791 0.121206i
\(433\) 0.797176 + 1.74557i 0.797176 + 1.74557i 0.654861 + 0.755750i \(0.272727\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(434\) −0.512546 3.56484i −0.512546 3.56484i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 1.66538 + 1.07028i 1.66538 + 1.07028i 0.909632 + 0.415415i \(0.136364\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(440\) 0 0
\(441\) 1.23259 + 2.69900i 1.23259 + 2.69900i
\(442\) −0.797176 0.234072i −0.797176 0.234072i
\(443\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.29639 + 1.49611i 1.29639 + 1.49611i
\(448\) 1.53046 0.983568i 1.53046 0.983568i
\(449\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(450\) 0.841254 + 0.970858i 0.841254 + 0.970858i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.627899 1.37491i 0.627899 1.37491i
\(455\) 0 0
\(456\) 0 0
\(457\) 0.118239 + 0.822373i 0.118239 + 0.822373i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(458\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(459\) 0.430218 0.430218
\(460\) 0 0
\(461\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(462\) −4.57949 2.94306i −4.57949 2.94306i
\(463\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(468\) 0.151894 1.05645i 0.151894 1.05645i
\(469\) 0 0
\(470\) 0 0
\(471\) −1.66538 + 1.07028i −1.66538 + 1.07028i
\(472\) 0 0
\(473\) 0 0
\(474\) −1.56815 + 0.460451i −1.56815 + 0.460451i
\(475\) 0 0
\(476\) −1.19136 + 1.37491i −1.19136 + 1.37491i
\(477\) −0.151894 + 0.332601i −0.151894 + 0.332601i
\(478\) 0 0
\(479\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −1.48666 2.31329i −1.48666 2.31329i
\(484\) 2.91899 2.91899
\(485\) 0 0
\(486\) −0.197682 1.37491i −0.197682 1.37491i
\(487\) −0.755750 1.65486i −0.755750 1.65486i −0.755750 0.654861i \(-0.772727\pi\)
1.00000i \(-0.5\pi\)
\(488\) 0 0
\(489\) 1.14231 2.50132i 1.14231 2.50132i
\(490\) 0 0
\(491\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.29639 + 1.49611i 1.29639 + 1.49611i
\(497\) 0 0
\(498\) 0 0
\(499\) −1.19136 + 1.37491i −1.19136 + 1.37491i −0.281733 + 0.959493i \(0.590909\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(500\) 0 0
\(501\) −1.56815 0.460451i −1.56815 0.460451i
\(502\) 0 0
\(503\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(504\) −1.96608 1.26352i −1.96608 1.26352i
\(505\) 0 0
\(506\) 1.80075 + 0.822373i 1.80075 + 0.822373i
\(507\) −0.468144 −0.468144
\(508\) 0 0
\(509\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i 1.00000 \(0\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(513\) 0 0
\(514\) 0.186393 1.29639i 0.186393 1.29639i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(522\) 0 0
\(523\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(524\) 0.540641 + 0.158746i 0.540641 + 0.158746i
\(525\) 1.14231 + 2.50132i 1.14231 + 2.50132i
\(526\) 0 0
\(527\) −1.66538 1.07028i −1.66538 1.07028i
\(528\) 2.99223 2.99223
\(529\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0.412791 + 0.121206i 0.412791 + 0.121206i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.99430 3.45561i −2.99430 3.45561i
\(540\) 0 0
\(541\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.142315 0.989821i 0.142315 0.989821i
\(545\) 0 0
\(546\) 0.949069 2.07817i 0.949069 2.07817i
\(547\) 1.03748 + 0.304632i 1.03748 + 0.304632i 0.755750 0.654861i \(-0.227273\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(548\) −0.698939 1.53046i −0.698939 1.53046i
\(549\) 0 0
\(550\) −1.66538 1.07028i −1.66538 1.07028i
\(551\) 0 0
\(552\) 1.37491 + 0.627899i 1.37491 + 0.627899i
\(553\) −1.96714 −1.96714
\(554\) 0 0
\(555\) 0 0
\(556\) −0.234072 0.512546i −0.234072 0.512546i
\(557\) −1.84125 0.540641i −1.84125 0.540641i −0.841254 0.540641i \(-0.818182\pi\)
−1.00000 \(\pi\)
\(558\) 1.05645 2.31329i 1.05645 2.31329i
\(559\) 0 0
\(560\) 0 0
\(561\) −2.87102 + 0.843008i −2.87102 + 0.843008i
\(562\) −1.25667 1.45027i −1.25667 1.45027i
\(563\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.03748 0.304632i 1.03748 0.304632i
\(567\) 0.164240 1.14231i 0.164240 1.14231i
\(568\) 0 0
\(569\) −0.544078 + 1.19136i −0.544078 + 1.19136i 0.415415 + 0.909632i \(0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(570\) 0 0
\(571\) 0.449181 + 0.983568i 0.449181 + 0.983568i 0.989821 + 0.142315i \(0.0454545\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(572\) 0.234072 + 1.62801i 0.234072 + 1.62801i
\(573\) 0 0
\(574\) 0 0
\(575\) −0.540641 0.841254i −0.540641 0.841254i
\(576\) 1.28463 1.28463
\(577\) −1.41542 0.909632i −1.41542 0.909632i −0.415415 0.909632i \(-0.636364\pi\)
−1.00000 \(\pi\)
\(578\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.0801894 0.557730i 0.0801894 0.557730i
\(584\) 0 0
\(585\) 0 0
\(586\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(587\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(588\) −2.28621 2.63843i −2.28621 2.63843i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(594\) −0.353799 0.774713i −0.353799 0.774713i
\(595\) 0 0
\(596\) −1.10181 0.708089i −1.10181 0.708089i
\(597\) 2.28463 2.28463
\(598\) −0.234072 + 0.797176i −0.234072 + 0.797176i
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) −1.27155 0.817178i −1.27155 0.817178i
\(601\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) −0.361922 + 2.51722i −0.361922 + 2.51722i
\(607\) 1.03748 0.304632i 1.03748 0.304632i 0.281733 0.959493i \(-0.409091\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −1.23259 + 0.361922i −1.23259 + 0.361922i
\(613\) −0.239446 + 1.66538i −0.239446 + 1.66538i 0.415415 + 0.909632i \(0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 3.45561 + 1.01466i 3.45561 + 1.01466i
\(617\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(618\) 0 0
\(619\) −0.474017 0.304632i −0.474017 0.304632i 0.281733 0.959493i \(-0.409091\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(620\) 0 0
\(621\) 0.430218i 0.430218i
\(622\) 1.81926 1.81926
\(623\) 0.435615 + 0.279953i 0.435615 + 0.279953i
\(624\) 0.178719 + 1.24302i 0.178719 + 1.24302i
\(625\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.857685 0.989821i 0.857685 0.989821i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(632\) 0.909632 0.584585i 0.909632 0.584585i
\(633\) 1.37491 0.883600i 1.37491 0.883600i
\(634\) 0 0
\(635\) 0 0
\(636\) 0.0612263 0.425839i 0.0612263 0.425839i
\(637\) 1.25667 1.45027i 1.25667 1.45027i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(642\) −0.716476 0.460451i −0.716476 0.460451i
\(643\) −1.81926 −1.81926 −0.909632 0.415415i \(-0.863636\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(644\) 1.37491 + 1.19136i 1.37491 + 1.19136i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(648\) 0.263521 + 0.577031i 0.263521 + 0.577031i
\(649\) 0 0
\(650\) 0.345139 0.755750i 0.345139 0.755750i
\(651\) 3.56484 4.11404i 3.56484 4.11404i
\(652\) −0.258908 + 1.80075i −0.258908 + 1.80075i
\(653\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(660\) 0 0
\(661\) −0.797176 + 1.74557i −0.797176 + 1.74557i −0.142315 + 0.989821i \(0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(662\) 0 0
\(663\) −0.521678 1.14231i −0.521678 1.14231i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.08128 1.08128
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 2.63843 + 0.774713i 2.63843 + 0.774713i
\(673\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(674\) 0 0
\(675\) −0.0612263 + 0.425839i −0.0612263 + 0.425839i
\(676\) 0.297176 0.0872586i 0.297176 0.0872586i
\(677\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 2.19209 0.643655i 2.19209 0.643655i
\(682\) −0.557730 + 3.87910i −0.557730 + 3.87910i
\(683\) −0.708089 + 0.817178i −0.708089 + 0.817178i −0.989821 0.142315i \(-0.954545\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.989821 2.16741i −0.989821 2.16741i
\(687\) 0.178719 + 1.24302i 0.178719 + 1.24302i
\(688\) 0 0
\(689\) 0.236479 0.236479
\(690\) 0 0
\(691\) −1.81926 −1.81926 −0.909632 0.415415i \(-0.863636\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(692\) 0 0
\(693\) −0.658432 4.57949i −0.658432 4.57949i
\(694\) 0.822373 + 1.80075i 0.822373 + 1.80075i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0.118239 0.822373i 0.118239 0.822373i
\(699\) 0 0
\(700\) −1.19136 1.37491i −1.19136 1.37491i
\(701\) −0.698939 + 0.449181i −0.698939 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(702\) 0.300696 0.193245i 0.300696 0.193245i
\(703\) 0 0
\(704\) −1.89945 + 0.557730i −1.89945 + 0.557730i
\(705\) 0 0
\(706\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(707\) −1.27155 + 2.78431i −1.27155 + 2.78431i
\(708\) 0 0
\(709\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(710\) 0 0
\(711\) −1.16854 0.750975i −1.16854 0.750975i
\(712\) −0.284630 −0.284630
\(713\) −1.07028 + 1.66538i −1.07028 + 1.66538i
\(714\) −2.74982 −2.74982
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0.755750 1.65486i 0.755750 1.65486i 1.00000i \(-0.5\pi\)
0.755750 0.654861i \(-0.227273\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.959493 0.281733i 0.959493 0.281733i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 2.88927 + 3.33440i 2.88927 + 3.33440i
\(727\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(728\) −0.215109 + 1.49611i −0.215109 + 1.49611i
\(729\) 0.959493 1.10731i 0.959493 1.10731i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.118239 0.822373i −0.118239 0.822373i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(734\) −0.474017 0.304632i −0.474017 0.304632i
\(735\) 0 0
\(736\) −0.989821 0.142315i −0.989821 0.142315i
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.215109 0.471022i 0.215109 0.471022i
\(743\) −0.989821 + 1.14231i −0.989821 + 1.14231i 1.00000i \(0.5\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(744\) −0.425839 + 2.96177i −0.425839 + 2.96177i
\(745\) 0 0
\(746\) −1.10181 1.27155i −1.10181 1.27155i
\(747\) 0 0
\(748\) 1.66538 1.07028i 1.66538 1.07028i
\(749\) −0.671292 0.774713i −0.671292 0.774713i
\(750\) 0 0
\(751\) 0.258908 1.80075i 0.258908 1.80075i −0.281733 0.959493i \(-0.590909\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.111387 0.774713i −0.111387 0.774713i
\(757\) −0.698939 0.449181i −0.698939 0.449181i 0.142315 0.989821i \(-0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(758\) 0.563465 0.563465
\(759\) 0.843008 + 2.87102i 0.843008 + 2.87102i
\(760\) 0 0
\(761\) −0.698939 0.449181i −0.698939 0.449181i 0.142315 0.989821i \(-0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −1.45027 + 0.425839i −1.45027 + 0.425839i
\(769\) −0.857685 0.989821i −0.857685 0.989821i 0.142315 0.989821i \(-0.454545\pi\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 1.66538 1.07028i 1.66538 1.07028i
\(772\) 0 0
\(773\) 1.61435 0.474017i 1.61435 0.474017i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(774\) 0 0
\(775\) 1.29639 1.49611i 1.29639 1.49611i
\(776\) 0 0
\(777\) 0 0
\(778\) −0.544078 1.19136i −0.544078 1.19136i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0.989821 0.142315i 0.989821 0.142315i
\(783\) 0 0
\(784\) 1.94306 + 1.24873i 1.94306 + 1.24873i
\(785\) 0 0
\(786\) 0.353799 + 0.774713i 0.353799 + 0.774713i
\(787\) 1.74557 + 0.512546i 1.74557 + 0.512546i 0.989821 0.142315i \(-0.0454545\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 1.66538 + 1.92195i 1.66538 + 1.92195i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −1.45027 + 0.425839i −1.45027 + 0.425839i
\(797\) −0.118239 + 0.822373i −0.118239 + 0.822373i 0.841254 + 0.540641i \(0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(801\) 0.151894 + 0.332601i 0.151894 + 0.332601i
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) −1.64475 −1.64475
\(807\) 0 0
\(808\) −0.239446 1.66538i −0.239446 1.66538i
\(809\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(810\) 0 0
\(811\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 1.27155 0.817178i 1.27155 0.817178i
\(817\) 0 0
\(818\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(819\) 1.86306 0.547045i 1.86306 0.547045i
\(820\) 0 0
\(821\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(822\) 1.05645 2.31329i 1.05645 2.31329i
\(823\) −0.540641 0.158746i −0.540641 0.158746i 1.00000i \(-0.5\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(824\) 0 0
\(825\) −0.425839 2.96177i −0.425839 2.96177i
\(826\) 0 0
\(827\) 1.08128 1.08128 0.540641 0.841254i \(-0.318182\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(828\) 0.361922 + 1.23259i 0.361922 + 1.23259i
\(829\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −0.345139 0.755750i −0.345139 0.755750i
\(833\) −2.21616 0.650724i −2.21616 0.650724i
\(834\) 0.353799 0.774713i 0.353799 0.774713i
\(835\) 0 0
\(836\) 0 0
\(837\) 0.817178 0.239945i 0.817178 0.239945i
\(838\) −1.29639 1.49611i −1.29639 1.49611i
\(839\) 0.474017 0.304632i 0.474017 0.304632i −0.281733 0.959493i \(-0.590909\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(840\) 0 0
\(841\) −0.654861 0.755750i −0.654861 0.755750i
\(842\) 1.25667 0.368991i 1.25667 0.368991i
\(843\) 0.412791 2.87102i 0.412791 2.87102i
\(844\) −0.708089 + 0.817178i −0.708089 + 0.817178i
\(845\) 0 0
\(846\) 0 0
\(847\) 2.20602 + 4.83052i 2.20602 + 4.83052i
\(848\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(849\) 1.37491 + 0.883600i 1.37491 + 0.883600i
\(850\) −1.00000 −1.00000
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0.540641 + 0.158746i 0.540641 + 0.158746i
\(857\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(858\) −1.62801 + 1.87882i −1.62801 + 1.87882i
\(859\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 1.27155 0.817178i 1.27155 0.817178i
\(863\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(864\) 0.281733 + 0.325137i 0.281733 + 0.325137i
\(865\) 0 0
\(866\) 0.273100 1.89945i 0.273100 1.89945i
\(867\) −0.989821 + 1.14231i −0.989821 + 1.14231i
\(868\) −1.49611 + 3.27603i −1.49611 + 3.27603i
\(869\) 2.05384 + 0.603063i 2.05384 + 0.603063i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(878\) −0.822373 1.80075i −0.822373 1.80075i
\(879\) −2.44009 0.716476i −2.44009 0.716476i
\(880\) 0 0
\(881\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(882\) 0.422268 2.93694i 0.422268 2.93694i
\(883\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(884\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(885\) 0 0
\(886\) 0 0
\(887\) −0.368991 0.425839i −0.368991 0.425839i 0.540641 0.841254i \(-0.318182\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −0.521678 + 1.14231i −0.521678 + 1.14231i
\(892\) 0 0
\(893\) 0 0
\(894\) −0.281733 1.95949i −0.281733 1.95949i
\(895\) 0 0
\(896\) −1.81926 −1.81926
\(897\) −1.14231 + 0.521678i −1.14231 + 0.521678i
\(898\) 0 0
\(899\) 0 0
\(900\) −0.182822 1.27155i −0.182822 1.27155i
\(901\) −0.118239 0.258908i −0.118239 0.258908i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0.989821 + 1.14231i 0.989821 + 1.14231i 0.989821 + 0.142315i \(0.0454545\pi\)
1.00000i \(0.500000\pi\)
\(908\) −1.27155 + 0.817178i −1.27155 + 0.817178i
\(909\) −1.81828 + 1.16854i −1.81828 + 1.16854i
\(910\) 0 0
\(911\) −1.03748 + 0.304632i −1.03748 + 0.304632i −0.755750 0.654861i \(-0.772727\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.345139 0.755750i 0.345139 0.755750i
\(915\) 0 0
\(916\) −0.345139 0.755750i −0.345139 0.755750i
\(917\) 0.145886 + 1.01466i 0.145886 + 1.01466i
\(918\) −0.361922 0.232593i −0.361922 0.232593i
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(923\) 0 0
\(924\) 2.26138 + 4.95172i 2.26138 + 4.95172i
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 1.80075 + 2.07817i 1.80075 + 2.07817i
\(934\) 0 0
\(935\) 0 0
\(936\) −0.698939 + 0.806618i −0.698939 + 0.806618i
\(937\) −0.118239 + 0.258908i −0.118239 + 0.258908i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(942\) 1.97964 1.97964
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0.234072 + 0.512546i 0.234072 + 0.512546i 0.989821 0.142315i \(-0.0454545\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(948\) 1.56815 + 0.460451i 1.56815 + 0.460451i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 1.74557 0.512546i 1.74557 0.512546i
\(953\) 1.30972 + 1.51150i 1.30972 + 1.51150i 0.654861 + 0.755750i \(0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(954\) 0.307599 0.197682i 0.307599 0.197682i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 2.00448 2.31329i 2.00448 2.31329i
\(960\) 0 0
\(961\) −2.80075 0.822373i −2.80075 0.822373i
\(962\) 0 0
\(963\) −0.103014 0.716476i −0.103014 0.716476i
\(964\) 0 0
\(965\) 0 0
\(966\) 2.74982i 2.74982i
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −2.45561 1.57812i −2.45561 1.57812i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(972\) −0.577031 + 1.26352i −0.577031 + 1.26352i
\(973\) 0.671292 0.774713i 0.671292 0.774713i
\(974\) −0.258908 + 1.80075i −0.258908 + 1.80075i
\(975\) 1.20493 0.353799i 1.20493 0.353799i
\(976\) 0 0
\(977\) −1.61435 + 1.03748i −1.61435 + 1.03748i −0.654861 + 0.755750i \(0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(978\) −2.31329 + 1.48666i −2.31329 + 1.48666i
\(979\) −0.368991 0.425839i −0.368991 0.425839i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0.627899 1.37491i 0.627899 1.37491i −0.281733 0.959493i \(-0.590909\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0.909632 + 0.584585i 0.909632 + 0.584585i 0.909632 0.415415i \(-0.136364\pi\)
1.00000i \(0.5\pi\)
\(992\) −0.281733 1.95949i −0.281733 1.95949i
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(998\) 1.74557 0.512546i 1.74557 0.512546i
\(999\) 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 1564.1.w.c.1359.1 yes 20
4.3 odd 2 inner 1564.1.w.c.1359.2 yes 20
17.16 even 2 inner 1564.1.w.c.1359.2 yes 20
23.12 even 11 inner 1564.1.w.c.679.1 20
68.67 odd 2 CM 1564.1.w.c.1359.1 yes 20
92.35 odd 22 inner 1564.1.w.c.679.2 yes 20
391.288 even 22 inner 1564.1.w.c.679.2 yes 20
1564.679 odd 22 inner 1564.1.w.c.679.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1564.1.w.c.679.1 20 23.12 even 11 inner
1564.1.w.c.679.1 20 1564.679 odd 22 inner
1564.1.w.c.679.2 yes 20 92.35 odd 22 inner
1564.1.w.c.679.2 yes 20 391.288 even 22 inner
1564.1.w.c.1359.1 yes 20 1.1 even 1 trivial
1564.1.w.c.1359.1 yes 20 68.67 odd 2 CM
1564.1.w.c.1359.2 yes 20 4.3 odd 2 inner
1564.1.w.c.1359.2 yes 20 17.16 even 2 inner