Properties

Label 1368.1.dh.a.1195.1
Level 13681368
Weight 11
Character 1368.1195
Analytic conductor 0.6830.683
Analytic rank 00
Dimension 66
Projective image D9D_{9}
CM discriminant -8
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1368,1,Mod(43,1368)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1368, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 9, 12, 16]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1368.43");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 1368=233219 1368 = 2^{3} \cdot 3^{2} \cdot 19
Weight: k k == 1 1
Character orbit: [χ][\chi] == 1368.dh (of order 1818, degree 66, 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: 0.6827209372820.682720937282
Analytic rank: 00
Dimension: 66
Coefficient field: Q(ζ18)\Q(\zeta_{18})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x6x3+1 x^{6} - x^{3} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Projective image: D9D_{9}
Projective field: Galois closure of Q[x]/(x9+)\mathbb{Q}[x]/(x^{9} + \cdots)

Embedding invariants

Embedding label 1195.1
Root 0.173648+0.984808i-0.173648 + 0.984808i of defining polynomial
Character χ\chi == 1368.1195
Dual form 1368.1.dh.a.427.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.766044+0.642788i)q2+(0.5000000.866025i)q3+(0.173648+0.984808i)q4+(0.1736480.984808i)q6+(0.500000+0.866025i)q8+(0.500000+0.866025i)q9+(0.939693+1.62760i)q11+(0.7660440.642788i)q12+(0.939693+0.342020i)q16+(0.3472961.96962i)q17+(0.939693+0.342020i)q18+(0.173648+0.984808i)q19+(0.326352+1.85083i)q22+1.00000q24+(0.173648+0.984808i)q25+1.00000q27+(0.9396930.342020i)q32+(0.9396931.62760i)q33+(1.532091.28558i)q34+(0.9396930.342020i)q36+(0.500000+0.866025i)q38+(0.2660441.50881i)q41+(0.173648+0.984808i)q43+(1.43969+1.20805i)q44+(0.766044+0.642788i)q48+1.00000q49+(0.500000+0.866025i)q50+(1.87939+0.684040i)q51+(0.766044+0.642788i)q54+(0.7660440.642788i)q57+(0.326352+0.118782i)q59+(0.5000000.866025i)q64+(1.766040.642788i)q66+(1.173650.984808i)q67+2.00000q68+(0.5000000.866025i)q72+(1.439691.20805i)q73+(0.7660440.642788i)q75+(0.939693+0.342020i)q76+(0.5000000.866025i)q81+(1.173650.984808i)q821.87939q83+(0.766044+0.642788i)q861.87939q88+(0.766044+0.642788i)q89+(0.173648+0.984808i)q96+(0.266044+0.223238i)q97+(0.766044+0.642788i)q981.87939q99+O(q100)q+(0.766044 + 0.642788i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.173648 - 0.984808i) q^{6} +(-0.500000 + 0.866025i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.939693 + 1.62760i) q^{11} +(0.766044 - 0.642788i) q^{12} +(-0.939693 + 0.342020i) q^{16} +(0.347296 - 1.96962i) q^{17} +(-0.939693 + 0.342020i) q^{18} +(0.173648 + 0.984808i) q^{19} +(-0.326352 + 1.85083i) q^{22} +1.00000 q^{24} +(0.173648 + 0.984808i) q^{25} +1.00000 q^{27} +(-0.939693 - 0.342020i) q^{32} +(0.939693 - 1.62760i) q^{33} +(1.53209 - 1.28558i) q^{34} +(-0.939693 - 0.342020i) q^{36} +(-0.500000 + 0.866025i) q^{38} +(0.266044 - 1.50881i) q^{41} +(-0.173648 + 0.984808i) q^{43} +(-1.43969 + 1.20805i) q^{44} +(0.766044 + 0.642788i) q^{48} +1.00000 q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.87939 + 0.684040i) q^{51} +(0.766044 + 0.642788i) q^{54} +(0.766044 - 0.642788i) q^{57} +(-0.326352 + 0.118782i) q^{59} +(-0.500000 - 0.866025i) q^{64} +(1.76604 - 0.642788i) q^{66} +(1.17365 - 0.984808i) q^{67} +2.00000 q^{68} +(-0.500000 - 0.866025i) q^{72} +(-1.43969 - 1.20805i) q^{73} +(0.766044 - 0.642788i) q^{75} +(-0.939693 + 0.342020i) q^{76} +(-0.500000 - 0.866025i) q^{81} +(1.17365 - 0.984808i) q^{82} -1.87939 q^{83} +(-0.766044 + 0.642788i) q^{86} -1.87939 q^{88} +(-0.766044 + 0.642788i) q^{89} +(0.173648 + 0.984808i) q^{96} +(0.266044 + 0.223238i) q^{97} +(0.766044 + 0.642788i) q^{98} -1.87939 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q3q33q83q93q22+6q24+6q273q383q413q44+6q493q503q593q64+6q66+6q67+12q683q723q733q81+3q97+O(q100) 6 q - 3 q^{3} - 3 q^{8} - 3 q^{9} - 3 q^{22} + 6 q^{24} + 6 q^{27} - 3 q^{38} - 3 q^{41} - 3 q^{44} + 6 q^{49} - 3 q^{50} - 3 q^{59} - 3 q^{64} + 6 q^{66} + 6 q^{67} + 12 q^{68} - 3 q^{72} - 3 q^{73} - 3 q^{81}+ \cdots - 3 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1368Z)×\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times.

nn 343343 685685 10091009 12171217
χ(n)\chi(n) 1-1 1-1 e(59)e\left(\frac{5}{9}\right) e(23)e\left(\frac{2}{3}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.766044 + 0.642788i 0.766044 + 0.642788i
33 −0.500000 0.866025i −0.500000 0.866025i
44 0.173648 + 0.984808i 0.173648 + 0.984808i
55 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
66 0.173648 0.984808i 0.173648 0.984808i
77 0 0 1.00000 00
−1.00000 π\pi
88 −0.500000 + 0.866025i −0.500000 + 0.866025i
99 −0.500000 + 0.866025i −0.500000 + 0.866025i
1010 0 0
1111 0.939693 + 1.62760i 0.939693 + 1.62760i 0.766044 + 0.642788i 0.222222π0.222222\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
1212 0.766044 0.642788i 0.766044 0.642788i
1313 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
1414 0 0
1515 0 0
1616 −0.939693 + 0.342020i −0.939693 + 0.342020i
1717 0.347296 1.96962i 0.347296 1.96962i 0.173648 0.984808i 0.444444π-0.444444\pi
0.173648 0.984808i 0.444444π-0.444444\pi
1818 −0.939693 + 0.342020i −0.939693 + 0.342020i
1919 0.173648 + 0.984808i 0.173648 + 0.984808i
2020 0 0
2121 0 0
2222 −0.326352 + 1.85083i −0.326352 + 1.85083i
2323 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
2424 1.00000 1.00000
2525 0.173648 + 0.984808i 0.173648 + 0.984808i
2626 0 0
2727 1.00000 1.00000
2828 0 0
2929 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
3030 0 0
3131 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
3232 −0.939693 0.342020i −0.939693 0.342020i
3333 0.939693 1.62760i 0.939693 1.62760i
3434 1.53209 1.28558i 1.53209 1.28558i
3535 0 0
3636 −0.939693 0.342020i −0.939693 0.342020i
3737 0 0 1.00000 00
−1.00000 π\pi
3838 −0.500000 + 0.866025i −0.500000 + 0.866025i
3939 0 0
4040 0 0
4141 0.266044 1.50881i 0.266044 1.50881i −0.500000 0.866025i 0.666667π-0.666667\pi
0.766044 0.642788i 0.222222π-0.222222\pi
4242 0 0
4343 −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i 0.222222π0.222222\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
4444 −1.43969 + 1.20805i −1.43969 + 1.20805i
4545 0 0
4646 0 0
4747 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
4848 0.766044 + 0.642788i 0.766044 + 0.642788i
4949 1.00000 1.00000
5050 −0.500000 + 0.866025i −0.500000 + 0.866025i
5151 −1.87939 + 0.684040i −1.87939 + 0.684040i
5252 0 0
5353 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
5454 0.766044 + 0.642788i 0.766044 + 0.642788i
5555 0 0
5656 0 0
5757 0.766044 0.642788i 0.766044 0.642788i
5858 0 0
5959 −0.326352 + 0.118782i −0.326352 + 0.118782i −0.500000 0.866025i 0.666667π-0.666667\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
6060 0 0
6161 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
6262 0 0
6363 0 0
6464 −0.500000 0.866025i −0.500000 0.866025i
6565 0 0
6666 1.76604 0.642788i 1.76604 0.642788i
6767 1.17365 0.984808i 1.17365 0.984808i 0.173648 0.984808i 0.444444π-0.444444\pi
1.00000 00
6868 2.00000 2.00000
6969 0 0
7070 0 0
7171 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
7272 −0.500000 0.866025i −0.500000 0.866025i
7373 −1.43969 1.20805i −1.43969 1.20805i −0.939693 0.342020i 0.888889π-0.888889\pi
−0.500000 0.866025i 0.666667π-0.666667\pi
7474 0 0
7575 0.766044 0.642788i 0.766044 0.642788i
7676 −0.939693 + 0.342020i −0.939693 + 0.342020i
7777 0 0
7878 0 0
7979 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
8080 0 0
8181 −0.500000 0.866025i −0.500000 0.866025i
8282 1.17365 0.984808i 1.17365 0.984808i
8383 −1.87939 −1.87939 −0.939693 0.342020i 0.888889π-0.888889\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
8484 0 0
8585 0 0
8686 −0.766044 + 0.642788i −0.766044 + 0.642788i
8787 0 0
8888 −1.87939 −1.87939
8989 −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i 0.888889π-0.888889\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
9090 0 0
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 0.173648 + 0.984808i 0.173648 + 0.984808i
9797 0.266044 + 0.223238i 0.266044 + 0.223238i 0.766044 0.642788i 0.222222π-0.222222\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
9898 0.766044 + 0.642788i 0.766044 + 0.642788i
9999 −1.87939 −1.87939
100100 −0.939693 + 0.342020i −0.939693 + 0.342020i
101101 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
102102 −1.87939 0.684040i −1.87939 0.684040i
103103 0 0 1.00000 00
−1.00000 π\pi
104104 0 0
105105 0 0
106106 0 0
107107 −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 0.866025i 0.666667π-0.666667\pi
108108 0.173648 + 0.984808i 0.173648 + 0.984808i
109109 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
110110 0 0
111111 0 0
112112 0 0
113113 −0.766044 1.32683i −0.766044 1.32683i −0.939693 0.342020i 0.888889π-0.888889\pi
0.173648 0.984808i 0.444444π-0.444444\pi
114114 1.00000 1.00000
115115 0 0
116116 0 0
117117 0 0
118118 −0.326352 0.118782i −0.326352 0.118782i
119119 0 0
120120 0 0
121121 −1.26604 + 2.19285i −1.26604 + 2.19285i
122122 0 0
123123 −1.43969 + 0.524005i −1.43969 + 0.524005i
124124 0 0
125125 0 0
126126 0 0
127127 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
128128 0.173648 0.984808i 0.173648 0.984808i
129129 0.939693 0.342020i 0.939693 0.342020i
130130 0 0
131131 −0.326352 + 0.118782i −0.326352 + 0.118782i −0.500000 0.866025i 0.666667π-0.666667\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
132132 1.76604 + 0.642788i 1.76604 + 0.642788i
133133 0 0
134134 1.53209 1.53209
135135 0 0
136136 1.53209 + 1.28558i 1.53209 + 1.28558i
137137 1.17365 0.984808i 1.17365 0.984808i 0.173648 0.984808i 0.444444π-0.444444\pi
1.00000 00
138138 0 0
139139 −0.326352 0.118782i −0.326352 0.118782i 0.173648 0.984808i 0.444444π-0.444444\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 0.173648 0.984808i 0.173648 0.984808i
145145 0 0
146146 −0.326352 1.85083i −0.326352 1.85083i
147147 −0.500000 0.866025i −0.500000 0.866025i
148148 0 0
149149 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
150150 1.00000 1.00000
151151 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
152152 −0.939693 0.342020i −0.939693 0.342020i
153153 1.53209 + 1.28558i 1.53209 + 1.28558i
154154 0 0
155155 0 0
156156 0 0
157157 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 0.173648 0.984808i 0.173648 0.984808i
163163 −0.173648 + 0.300767i −0.173648 + 0.300767i −0.939693 0.342020i 0.888889π-0.888889\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
164164 1.53209 1.53209
165165 0 0
166166 −1.43969 1.20805i −1.43969 1.20805i
167167 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
168168 0 0
169169 0.766044 + 0.642788i 0.766044 + 0.642788i
170170 0 0
171171 −0.939693 0.342020i −0.939693 0.342020i
172172 −1.00000 −1.00000
173173 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
174174 0 0
175175 0 0
176176 −1.43969 1.20805i −1.43969 1.20805i
177177 0.266044 + 0.223238i 0.266044 + 0.223238i
178178 −1.00000 −1.00000
179179 0.939693 1.62760i 0.939693 1.62760i 0.173648 0.984808i 0.444444π-0.444444\pi
0.766044 0.642788i 0.222222π-0.222222\pi
180180 0 0
181181 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
182182 0 0
183183 0 0
184184 0 0
185185 0 0
186186 0 0
187187 3.53209 1.28558i 3.53209 1.28558i
188188 0 0
189189 0 0
190190 0 0
191191 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
192192 −0.500000 + 0.866025i −0.500000 + 0.866025i
193193 −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i 0.222222π0.222222\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
194194 0.0603074 + 0.342020i 0.0603074 + 0.342020i
195195 0 0
196196 0.173648 + 0.984808i 0.173648 + 0.984808i
197197 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
198198 −1.43969 1.20805i −1.43969 1.20805i
199199 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
200200 −0.939693 0.342020i −0.939693 0.342020i
201201 −1.43969 0.524005i −1.43969 0.524005i
202202 0 0
203203 0 0
204204 −1.00000 1.73205i −1.00000 1.73205i
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 −1.43969 + 1.20805i −1.43969 + 1.20805i
210210 0 0
211211 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i 0.444444π-0.444444\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
212212 0 0
213213 0 0
214214 0.347296 1.96962i 0.347296 1.96962i
215215 0 0
216216 −0.500000 + 0.866025i −0.500000 + 0.866025i
217217 0 0
218218 0 0
219219 −0.326352 + 1.85083i −0.326352 + 1.85083i
220220 0 0
221221 0 0
222222 0 0
223223 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
224224 0 0
225225 −0.939693 0.342020i −0.939693 0.342020i
226226 0.266044 1.50881i 0.266044 1.50881i
227227 −0.173648 + 0.300767i −0.173648 + 0.300767i −0.939693 0.342020i 0.888889π-0.888889\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
228228 0.766044 + 0.642788i 0.766044 + 0.642788i
229229 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
230230 0 0
231231 0 0
232232 0 0
233233 1.76604 0.642788i 1.76604 0.642788i 0.766044 0.642788i 0.222222π-0.222222\pi
1.00000 00
234234 0 0
235235 0 0
236236 −0.173648 0.300767i −0.173648 0.300767i
237237 0 0
238238 0 0
239239 0 0 1.00000 00
−1.00000 π\pi
240240 0 0
241241 −0.326352 1.85083i −0.326352 1.85083i −0.500000 0.866025i 0.666667π-0.666667\pi
0.173648 0.984808i 0.444444π-0.444444\pi
242242 −2.37939 + 0.866025i −2.37939 + 0.866025i
243243 −0.500000 + 0.866025i −0.500000 + 0.866025i
244244 0 0
245245 0 0
246246 −1.43969 0.524005i −1.43969 0.524005i
247247 0 0
248248 0 0
249249 0.939693 + 1.62760i 0.939693 + 1.62760i
250250 0 0
251251 1.76604 + 0.642788i 1.76604 + 0.642788i 1.00000 00
0.766044 + 0.642788i 0.222222π0.222222\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 0.766044 0.642788i 0.766044 0.642788i
257257 −1.43969 + 1.20805i −1.43969 + 1.20805i −0.500000 + 0.866025i 0.666667π0.666667\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
258258 0.939693 + 0.342020i 0.939693 + 0.342020i
259259 0 0
260260 0 0
261261 0 0
262262 −0.326352 0.118782i −0.326352 0.118782i
263263 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
264264 0.939693 + 1.62760i 0.939693 + 1.62760i
265265 0 0
266266 0 0
267267 0.939693 + 0.342020i 0.939693 + 0.342020i
268268 1.17365 + 0.984808i 1.17365 + 0.984808i
269269 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
270270 0 0
271271 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
272272 0.347296 + 1.96962i 0.347296 + 1.96962i
273273 0 0
274274 1.53209 1.53209
275275 −1.43969 + 1.20805i −1.43969 + 1.20805i
276276 0 0
277277 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
278278 −0.173648 0.300767i −0.173648 0.300767i
279279 0 0
280280 0 0
281281 0.266044 0.223238i 0.266044 0.223238i −0.500000 0.866025i 0.666667π-0.666667\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
282282 0 0
283283 −1.43969 + 0.524005i −1.43969 + 0.524005i −0.939693 0.342020i 0.888889π-0.888889\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0.766044 0.642788i 0.766044 0.642788i
289289 −2.81908 1.02606i −2.81908 1.02606i
290290 0 0
291291 0.0603074 0.342020i 0.0603074 0.342020i
292292 0.939693 1.62760i 0.939693 1.62760i
293293 0 0 1.00000 00
−1.00000 π\pi
294294 0.173648 0.984808i 0.173648 0.984808i
295295 0 0
296296 0 0
297297 0.939693 + 1.62760i 0.939693 + 1.62760i
298298 0 0
299299 0 0
300300 0.766044 + 0.642788i 0.766044 + 0.642788i
301301 0 0
302302 0 0
303303 0 0
304304 −0.500000 0.866025i −0.500000 0.866025i
305305 0 0
306306 0.347296 + 1.96962i 0.347296 + 1.96962i
307307 0.266044 + 0.223238i 0.266044 + 0.223238i 0.766044 0.642788i 0.222222π-0.222222\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
308308 0 0
309309 0 0
310310 0 0
311311 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
312312 0 0
313313 1.76604 + 0.642788i 1.76604 + 0.642788i 1.00000 00
0.766044 + 0.642788i 0.222222π0.222222\pi
314314 0 0
315315 0 0
316316 0 0
317317 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
318318 0 0
319319 0 0
320320 0 0
321321 −1.00000 + 1.73205i −1.00000 + 1.73205i
322322 0 0
323323 2.00000 2.00000
324324 0.766044 0.642788i 0.766044 0.642788i
325325 0 0
326326 −0.326352 + 0.118782i −0.326352 + 0.118782i
327327 0 0
328328 1.17365 + 0.984808i 1.17365 + 0.984808i
329329 0 0
330330 0 0
331331 −0.766044 1.32683i −0.766044 1.32683i −0.939693 0.342020i 0.888889π-0.888889\pi
0.173648 0.984808i 0.444444π-0.444444\pi
332332 −0.326352 1.85083i −0.326352 1.85083i
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 1.17365 + 0.984808i 1.17365 + 0.984808i 1.00000 00
0.173648 + 0.984808i 0.444444π0.444444\pi
338338 0.173648 + 0.984808i 0.173648 + 0.984808i
339339 −0.766044 + 1.32683i −0.766044 + 1.32683i
340340 0 0
341341 0 0
342342 −0.500000 0.866025i −0.500000 0.866025i
343343 0 0
344344 −0.766044 0.642788i −0.766044 0.642788i
345345 0 0
346346 0 0
347347 0.266044 + 0.223238i 0.266044 + 0.223238i 0.766044 0.642788i 0.222222π-0.222222\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
348348 0 0
349349 0 0 1.00000 00
−1.00000 π\pi
350350 0 0
351351 0 0
352352 −0.326352 1.85083i −0.326352 1.85083i
353353 −0.173648 0.300767i −0.173648 0.300767i 0.766044 0.642788i 0.222222π-0.222222\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
354354 0.0603074 + 0.342020i 0.0603074 + 0.342020i
355355 0 0
356356 −0.766044 0.642788i −0.766044 0.642788i
357357 0 0
358358 1.76604 0.642788i 1.76604 0.642788i
359359 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
360360 0 0
361361 −0.939693 + 0.342020i −0.939693 + 0.342020i
362362 0 0
363363 2.53209 2.53209
364364 0 0
365365 0 0
366366 0 0
367367 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
368368 0 0
369369 1.17365 + 0.984808i 1.17365 + 0.984808i
370370 0 0
371371 0 0
372372 0 0
373373 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
374374 3.53209 + 1.28558i 3.53209 + 1.28558i
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
380380 0 0
381381 0 0
382382 0 0
383383 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
384384 −0.939693 + 0.342020i −0.939693 + 0.342020i
385385 0 0
386386 −0.766044 + 0.642788i −0.766044 + 0.642788i
387387 −0.766044 0.642788i −0.766044 0.642788i
388388 −0.173648 + 0.300767i −0.173648 + 0.300767i
389389 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
390390 0 0
391391 0 0
392392 −0.500000 + 0.866025i −0.500000 + 0.866025i
393393 0.266044 + 0.223238i 0.266044 + 0.223238i
394394 0 0
395395 0 0
396396 −0.326352 1.85083i −0.326352 1.85083i
397397 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
398398 0 0
399399 0 0
400400 −0.500000 0.866025i −0.500000 0.866025i
401401 1.76604 0.642788i 1.76604 0.642788i 0.766044 0.642788i 0.222222π-0.222222\pi
1.00000 00
402402 −0.766044 1.32683i −0.766044 1.32683i
403403 0 0
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0.347296 1.96962i 0.347296 1.96962i
409409 0.266044 0.223238i 0.266044 0.223238i −0.500000 0.866025i 0.666667π-0.666667\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
410410 0 0
411411 −1.43969 0.524005i −1.43969 0.524005i
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 0.0603074 + 0.342020i 0.0603074 + 0.342020i
418418 −1.87939 −1.87939
419419 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
420420 0 0
421421 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
422422 0.939693 + 0.342020i 0.939693 + 0.342020i
423423 0 0
424424 0 0
425425 2.00000 2.00000
426426 0 0
427427 0 0
428428 1.53209 1.28558i 1.53209 1.28558i
429429 0 0
430430 0 0
431431 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
432432 −0.939693 + 0.342020i −0.939693 + 0.342020i
433433 0.939693 + 0.342020i 0.939693 + 0.342020i 0.766044 0.642788i 0.222222π-0.222222\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
434434 0 0
435435 0 0
436436 0 0
437437 0 0
438438 −1.43969 + 1.20805i −1.43969 + 1.20805i
439439 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
440440 0 0
441441 −0.500000 + 0.866025i −0.500000 + 0.866025i
442442 0 0
443443 0.266044 + 1.50881i 0.266044 + 1.50881i 0.766044 + 0.642788i 0.222222π0.222222\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 −0.766044 1.32683i −0.766044 1.32683i −0.939693 0.342020i 0.888889π-0.888889\pi
0.173648 0.984808i 0.444444π-0.444444\pi
450450 −0.500000 0.866025i −0.500000 0.866025i
451451 2.70574 0.984808i 2.70574 0.984808i
452452 1.17365 0.984808i 1.17365 0.984808i
453453 0 0
454454 −0.326352 + 0.118782i −0.326352 + 0.118782i
455455 0 0
456456 0.173648 + 0.984808i 0.173648 + 0.984808i
457457 −0.173648 + 0.300767i −0.173648 + 0.300767i −0.939693 0.342020i 0.888889π-0.888889\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
458458 0 0
459459 0.347296 1.96962i 0.347296 1.96962i
460460 0 0
461461 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
462462 0 0
463463 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
464464 0 0
465465 0 0
466466 1.76604 + 0.642788i 1.76604 + 0.642788i
467467 −0.766044 + 1.32683i −0.766044 + 1.32683i 0.173648 + 0.984808i 0.444444π0.444444\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 0.0603074 0.342020i 0.0603074 0.342020i
473473 −1.76604 + 0.642788i −1.76604 + 0.642788i
474474 0 0
475475 −0.939693 + 0.342020i −0.939693 + 0.342020i
476476 0 0
477477 0 0
478478 0 0
479479 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
480480 0 0
481481 0 0
482482 0.939693 1.62760i 0.939693 1.62760i
483483 0 0
484484 −2.37939 0.866025i −2.37939 0.866025i
485485 0 0
486486 −0.939693 + 0.342020i −0.939693 + 0.342020i
487487 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
488488 0 0
489489 0.347296 0.347296
490490 0 0
491491 −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i 0.222222π0.222222\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
492492 −0.766044 1.32683i −0.766044 1.32683i
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 −0.326352 + 1.85083i −0.326352 + 1.85083i
499499 0.266044 + 0.223238i 0.266044 + 0.223238i 0.766044 0.642788i 0.222222π-0.222222\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
500500 0 0
501501 0 0
502502 0.939693 + 1.62760i 0.939693 + 1.62760i
503503 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
504504 0 0
505505 0 0
506506 0 0
507507 0.173648 0.984808i 0.173648 0.984808i
508508 0 0
509509 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
510510 0 0
511511 0 0
512512 1.00000 1.00000
513513 0.173648 + 0.984808i 0.173648 + 0.984808i
514514 −1.87939 −1.87939
515515 0 0
516516 0.500000 + 0.866025i 0.500000 + 0.866025i
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 −0.766044 + 1.32683i −0.766044 + 1.32683i 0.173648 + 0.984808i 0.444444π0.444444\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
522522 0 0
523523 0.347296 + 1.96962i 0.347296 + 1.96962i 0.173648 + 0.984808i 0.444444π0.444444\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
524524 −0.173648 0.300767i −0.173648 0.300767i
525525 0 0
526526 0 0
527527 0 0
528528 −0.326352 + 1.85083i −0.326352 + 1.85083i
529529 −0.939693 + 0.342020i −0.939693 + 0.342020i
530530 0 0
531531 0.0603074 0.342020i 0.0603074 0.342020i
532532 0 0
533533 0 0
534534 0.500000 + 0.866025i 0.500000 + 0.866025i
535535 0 0
536536 0.266044 + 1.50881i 0.266044 + 1.50881i
537537 −1.87939 −1.87939
538538 0 0
539539 0.939693 + 1.62760i 0.939693 + 1.62760i
540540 0 0
541541 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
542542 0 0
543543 0 0
544544 −1.00000 + 1.73205i −1.00000 + 1.73205i
545545 0 0
546546 0 0
547547 −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i 0.888889π-0.888889\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
548548 1.17365 + 0.984808i 1.17365 + 0.984808i
549549 0 0
550550 −1.87939 −1.87939
551551 0 0
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 0.0603074 0.342020i 0.0603074 0.342020i
557557 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
558558 0 0
559559 0 0
560560 0 0
561561 −2.87939 2.41609i −2.87939 2.41609i
562562 0.347296 0.347296
563563 0.939693 1.62760i 0.939693 1.62760i 0.173648 0.984808i 0.444444π-0.444444\pi
0.766044 0.642788i 0.222222π-0.222222\pi
564564 0 0
565565 0 0
566566 −1.43969 0.524005i −1.43969 0.524005i
567567 0 0
568568 0 0
569569 −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i 0.666667π0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
570570 0 0
571571 −0.766044 1.32683i −0.766044 1.32683i −0.939693 0.342020i 0.888889π-0.888889\pi
0.173648 0.984808i 0.444444π-0.444444\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 1.00000 1.00000
577577 −0.173648 0.300767i −0.173648 0.300767i 0.766044 0.642788i 0.222222π-0.222222\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
578578 −1.50000 2.59808i −1.50000 2.59808i
579579 0.939693 0.342020i 0.939693 0.342020i
580580 0 0
581581 0 0
582582 0.266044 0.223238i 0.266044 0.223238i
583583 0 0
584584 1.76604 0.642788i 1.76604 0.642788i
585585 0 0
586586 0 0
587587 −0.766044 0.642788i −0.766044 0.642788i 0.173648 0.984808i 0.444444π-0.444444\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
588588 0.766044 0.642788i 0.766044 0.642788i
589589 0 0
590590 0 0
591591 0 0
592592 0 0
593593 −1.43969 0.524005i −1.43969 0.524005i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
594594 −0.326352 + 1.85083i −0.326352 + 1.85083i
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
600600 0.173648 + 0.984808i 0.173648 + 0.984808i
601601 0.347296 0.347296 0.173648 0.984808i 0.444444π-0.444444\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
602602 0 0
603603 0.266044 + 1.50881i 0.266044 + 1.50881i
604604 0 0
605605 0 0
606606 0 0
607607 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
608608 0.173648 0.984808i 0.173648 0.984808i
609609 0 0
610610 0 0
611611 0 0
612612 −1.00000 + 1.73205i −1.00000 + 1.73205i
613613 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
614614 0.0603074 + 0.342020i 0.0603074 + 0.342020i
615615 0 0
616616 0 0
617617 0.266044 0.223238i 0.266044 0.223238i −0.500000 0.866025i 0.666667π-0.666667\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
618618 0 0
619619 −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 0.866025i 0.666667π-0.666667\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 −0.939693 + 0.342020i −0.939693 + 0.342020i
626626 0.939693 + 1.62760i 0.939693 + 1.62760i
627627 1.76604 + 0.642788i 1.76604 + 0.642788i
628628 0 0
629629 0 0
630630 0 0
631631 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
632632 0 0
633633 −0.766044 0.642788i −0.766044 0.642788i
634634 0 0
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 0 0
641641 0.0603074 0.342020i 0.0603074 0.342020i −0.939693 0.342020i 0.888889π-0.888889\pi
1.00000 00
642642 −1.87939 + 0.684040i −1.87939 + 0.684040i
643643 0.266044 1.50881i 0.266044 1.50881i −0.500000 0.866025i 0.666667π-0.666667\pi
0.766044 0.642788i 0.222222π-0.222222\pi
644644 0 0
645645 0 0
646646 1.53209 + 1.28558i 1.53209 + 1.28558i
647647 0 0 1.00000 00
−1.00000 π\pi
648648 1.00000 1.00000
649649 −0.500000 0.419550i −0.500000 0.419550i
650650 0 0
651651 0 0
652652 −0.326352 0.118782i −0.326352 0.118782i
653653 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
654654 0 0
655655 0 0
656656 0.266044 + 1.50881i 0.266044 + 1.50881i
657657 1.76604 0.642788i 1.76604 0.642788i
658658 0 0
659659 −0.173648 0.984808i −0.173648 0.984808i −0.939693 0.342020i 0.888889π-0.888889\pi
0.766044 0.642788i 0.222222π-0.222222\pi
660660 0 0
661661 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
662662 0.266044 1.50881i 0.266044 1.50881i
663663 0 0
664664 0.939693 1.62760i 0.939693 1.62760i
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
674674 0.266044 + 1.50881i 0.266044 + 1.50881i
675675 0.173648 + 0.984808i 0.173648 + 0.984808i
676676 −0.500000 + 0.866025i −0.500000 + 0.866025i
677677 0 0 1.00000 00
−1.00000 π\pi
678678 −1.43969 + 0.524005i −1.43969 + 0.524005i
679679 0 0
680680 0 0
681681 0.347296 0.347296
682682 0 0
683683 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
684684 0.173648 0.984808i 0.173648 0.984808i
685685 0 0
686686 0 0
687687 0 0
688688 −0.173648 0.984808i −0.173648 0.984808i
689689 0 0
690690 0 0
691691 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
692692 0 0
693693 0 0
694694 0.0603074 + 0.342020i 0.0603074 + 0.342020i
695695 0 0
696696 0 0
697697 −2.87939 1.04801i −2.87939 1.04801i
698698 0 0
699699 −1.43969 1.20805i −1.43969 1.20805i
700700 0 0
701701 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
702702 0 0
703703 0 0
704704 0.939693 1.62760i 0.939693 1.62760i
705705 0 0
706706 0.0603074 0.342020i 0.0603074 0.342020i
707707 0 0
708708 −0.173648 + 0.300767i −0.173648 + 0.300767i
709709 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
710710 0 0
711711 0 0
712712 −0.173648 0.984808i −0.173648 0.984808i
713713 0 0
714714 0 0
715715 0 0
716716 1.76604 + 0.642788i 1.76604 + 0.642788i
717717 0 0
718718 0 0
719719 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
720720 0 0
721721 0 0
722722 −0.939693 0.342020i −0.939693 0.342020i
723723 −1.43969 + 1.20805i −1.43969 + 1.20805i
724724 0 0
725725 0 0
726726 1.93969 + 1.62760i 1.93969 + 1.62760i
727727 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
728728 0 0
729729 1.00000 1.00000
730730 0 0
731731 1.87939 + 0.684040i 1.87939 + 0.684040i
732732 0 0
733733 0 0 1.00000 00
−1.00000 π\pi
734734 0 0
735735 0 0
736736 0 0
737737 2.70574 + 0.984808i 2.70574 + 0.984808i
738738 0.266044 + 1.50881i 0.266044 + 1.50881i
739739 0.266044 1.50881i 0.266044 1.50881i −0.500000 0.866025i 0.666667π-0.666667\pi
0.766044 0.642788i 0.222222π-0.222222\pi
740740 0 0
741741 0 0
742742 0 0
743743 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
744744 0 0
745745 0 0
746746 0 0
747747 0.939693 1.62760i 0.939693 1.62760i
748748 1.87939 + 3.25519i 1.87939 + 3.25519i
749749 0 0
750750 0 0
751751 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
752752 0 0
753753 −0.326352 1.85083i −0.326352 1.85083i
754754 0 0
755755 0 0
756756 0 0
757757 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
758758 −0.766044 0.642788i −0.766044 0.642788i
759759 0 0
760760 0 0
761761 −0.173648 0.300767i −0.173648 0.300767i 0.766044 0.642788i 0.222222π-0.222222\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 −0.939693 0.342020i −0.939693 0.342020i
769769 −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i 0.888889π-0.888889\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
770770 0 0
771771 1.76604 + 0.642788i 1.76604 + 0.642788i
772772 −1.00000 −1.00000
773773 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
774774 −0.173648 0.984808i −0.173648 0.984808i
775775 0 0
776776 −0.326352 + 0.118782i −0.326352 + 0.118782i
777777 0 0
778778 0 0
779779 1.53209 1.53209
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 −0.939693 + 0.342020i −0.939693 + 0.342020i
785785 0 0
786786 0.0603074 + 0.342020i 0.0603074 + 0.342020i
787787 1.53209 1.53209 0.766044 0.642788i 0.222222π-0.222222\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0.939693 1.62760i 0.939693 1.62760i
793793 0 0
794794 0 0
795795 0 0
796796 0 0
797797 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
798798 0 0
799799 0 0
800800 0.173648 0.984808i 0.173648 0.984808i
801801 −0.173648 0.984808i −0.173648 0.984808i
802802 1.76604 + 0.642788i 1.76604 + 0.642788i
803803 0.613341 3.47843i 0.613341 3.47843i
804804 0.266044 1.50881i 0.266044 1.50881i
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 −0.173648 + 0.300767i −0.173648 + 0.300767i −0.939693 0.342020i 0.888889π-0.888889\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
810810 0 0
811811 −0.766044 + 0.642788i −0.766044 + 0.642788i −0.939693 0.342020i 0.888889π-0.888889\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 1.53209 1.28558i 1.53209 1.28558i
817817 −1.00000 −1.00000
818818 0.347296 0.347296
819819 0 0
820820 0 0
821821 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
822822 −0.766044 1.32683i −0.766044 1.32683i
823823 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
824824 0 0
825825 1.76604 + 0.642788i 1.76604 + 0.642788i
826826 0 0
827827 0.266044 + 1.50881i 0.266044 + 1.50881i 0.766044 + 0.642788i 0.222222π0.222222\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
828828 0 0
829829 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
830830 0 0
831831 0 0
832832 0 0
833833 0.347296 1.96962i 0.347296 1.96962i
834834 −0.173648 + 0.300767i −0.173648 + 0.300767i
835835 0 0
836836 −1.43969 1.20805i −1.43969 1.20805i
837837 0 0
838838 −0.173648 + 0.984808i −0.173648 + 0.984808i
839839 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
840840 0 0
841841 0.766044 + 0.642788i 0.766044 + 0.642788i
842842 0 0
843843 −0.326352 0.118782i −0.326352 0.118782i
844844 0.500000 + 0.866025i 0.500000 + 0.866025i
845845 0 0
846846 0 0
847847 0 0
848848 0 0
849849 1.17365 + 0.984808i 1.17365 + 0.984808i
850850 1.53209 + 1.28558i 1.53209 + 1.28558i
851851 0 0
852852 0 0
853853 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
854854 0 0
855855 0 0
856856 2.00000 2.00000
857857 0.266044 + 0.223238i 0.266044 + 0.223238i 0.766044 0.642788i 0.222222π-0.222222\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
858858 0 0
859859 −0.326352 1.85083i −0.326352 1.85083i −0.500000 0.866025i 0.666667π-0.666667\pi
0.173648 0.984808i 0.444444π-0.444444\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
864864 −0.939693 0.342020i −0.939693 0.342020i
865865 0 0
866866 0.500000 + 0.866025i 0.500000 + 0.866025i
867867 0.520945 + 2.95442i 0.520945 + 2.95442i
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0 0
873873 −0.326352 + 0.118782i −0.326352 + 0.118782i
874874 0 0
875875 0 0
876876 −1.87939 −1.87939
877877 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
878878 0 0
879879 0 0
880880 0 0
881881 0.939693 + 1.62760i 0.939693 + 1.62760i 0.766044 + 0.642788i 0.222222π0.222222\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
882882 −0.939693 + 0.342020i −0.939693 + 0.342020i
883883 0.266044 + 1.50881i 0.266044 + 1.50881i 0.766044 + 0.642788i 0.222222π0.222222\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
884884 0 0
885885 0 0
886886 −0.766044 + 1.32683i −0.766044 + 1.32683i
887887 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
888888 0 0
889889 0 0
890890 0 0
891891 0.939693 1.62760i 0.939693 1.62760i
892892 0 0
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0.266044 1.50881i 0.266044 1.50881i
899899 0 0
900900 0.173648 0.984808i 0.173648 0.984808i
901901 0 0
902902 2.70574 + 0.984808i 2.70574 + 0.984808i
903903 0 0
904904 1.53209 1.53209
905905 0 0
906906 0 0
907907 0.0603074 0.342020i 0.0603074 0.342020i −0.939693 0.342020i 0.888889π-0.888889\pi
1.00000 00
908908 −0.326352 0.118782i −0.326352 0.118782i
909909 0 0
910910 0 0
911911 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
912912 −0.500000 + 0.866025i −0.500000 + 0.866025i
913913 −1.76604 3.05888i −1.76604 3.05888i
914914 −0.326352 + 0.118782i −0.326352 + 0.118782i
915915 0 0
916916 0 0
917917 0 0
918918 1.53209 1.28558i 1.53209 1.28558i
919919 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
920920 0 0
921921 0.0603074 0.342020i 0.0603074 0.342020i
922922 0 0
923923 0 0
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 0 0
929929 1.17365 + 0.984808i 1.17365 + 0.984808i 1.00000 00
0.173648 + 0.984808i 0.444444π0.444444\pi
930930 0 0
931931 0.173648 + 0.984808i 0.173648 + 0.984808i
932932 0.939693 + 1.62760i 0.939693 + 1.62760i
933933 0 0
934934 −1.43969 + 0.524005i −1.43969 + 0.524005i
935935 0 0
936936 0 0
937937 0.266044 0.223238i 0.266044 0.223238i −0.500000 0.866025i 0.666667π-0.666667\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
938938 0 0
939939 −0.326352 1.85083i −0.326352 1.85083i
940940 0 0
941941 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
942942 0 0
943943 0 0
944944 0.266044 0.223238i 0.266044 0.223238i
945945 0 0
946946 −1.76604 0.642788i −1.76604 0.642788i
947947 0.939693 0.342020i 0.939693 0.342020i 0.173648 0.984808i 0.444444π-0.444444\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
948948 0 0
949949 0 0
950950 −0.939693 0.342020i −0.939693 0.342020i
951951 0 0
952952 0 0
953953 −1.43969 1.20805i −1.43969 1.20805i −0.939693 0.342020i 0.888889π-0.888889\pi
−0.500000 0.866025i 0.666667π-0.666667\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 −0.500000 0.866025i −0.500000 0.866025i
962962 0 0
963963 2.00000 2.00000
964964 1.76604 0.642788i 1.76604 0.642788i
965965 0 0
966966 0 0
967967 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
968968 −1.26604 2.19285i −1.26604 2.19285i
969969 −1.00000 1.73205i −1.00000 1.73205i
970970 0 0
971971 0.0603074 0.342020i 0.0603074 0.342020i −0.939693 0.342020i 0.888889π-0.888889\pi
1.00000 00
972972 −0.939693 0.342020i −0.939693 0.342020i
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 −1.87939 −1.87939 −0.939693 0.342020i 0.888889π-0.888889\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
978978 0.266044 + 0.223238i 0.266044 + 0.223238i
979979 −1.76604 0.642788i −1.76604 0.642788i
980980 0 0
981981 0 0
982982 −0.766044 + 0.642788i −0.766044 + 0.642788i
983983 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
984984 0.266044 1.50881i 0.266044 1.50881i
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
992992 0 0
993993 −0.766044 + 1.32683i −0.766044 + 1.32683i
994994 0 0
995995 0 0
996996 −1.43969 + 1.20805i −1.43969 + 1.20805i
997997 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
998998 0.0603074 + 0.342020i 0.0603074 + 0.342020i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1368.1.dh.a.1195.1 yes 6
8.3 odd 2 CM 1368.1.dh.a.1195.1 yes 6
9.4 even 3 1368.1.en.a.283.1 yes 6
19.9 even 9 1368.1.en.a.1339.1 yes 6
72.67 odd 6 1368.1.en.a.283.1 yes 6
152.123 odd 18 1368.1.en.a.1339.1 yes 6
171.85 even 9 inner 1368.1.dh.a.427.1 6
1368.427 odd 18 inner 1368.1.dh.a.427.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1368.1.dh.a.427.1 6 171.85 even 9 inner
1368.1.dh.a.427.1 6 1368.427 odd 18 inner
1368.1.dh.a.1195.1 yes 6 1.1 even 1 trivial
1368.1.dh.a.1195.1 yes 6 8.3 odd 2 CM
1368.1.en.a.283.1 yes 6 9.4 even 3
1368.1.en.a.283.1 yes 6 72.67 odd 6
1368.1.en.a.1339.1 yes 6 19.9 even 9
1368.1.en.a.1339.1 yes 6 152.123 odd 18