Properties

Label 776.1.bh.a.539.1
Level 776776
Weight 11
Character 776.539
Analytic conductor 0.3870.387
Analytic rank 00
Dimension 88
Projective image D24D_{24}
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] = [776,1,Mod(43,776)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(776, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([12, 12, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("776.43");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 776=2397 776 = 2^{3} \cdot 97
Weight: k k == 1 1
Character orbit: [χ][\chi] == 776.bh (of order 2424, degree 88, 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: 0.3872744498030.387274449803
Analytic rank: 00
Dimension: 88
Coefficient field: Q(ζ24)\Q(\zeta_{24})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8x4+1 x^{8} - x^{4} + 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: D24D_{24}
Projective field: Galois closure of Q[x]/(x24)\mathbb{Q}[x]/(x^{24} - \cdots)

Embedding invariants

Embedding label 539.1
Root 0.9659260.258819i0.965926 - 0.258819i of defining polynomial
Character χ\chi == 776.539
Dual form 776.1.bh.a.203.1

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+(0.258819+0.965926i)q2+(0.500000+0.133975i)q3+(0.866025+0.500000i)q4+(0.2588190.448288i)q6+(0.7071070.707107i)q8+(0.633975+0.366025i)q9+(0.448288+1.67303i)q11+(0.3660250.366025i)q12+(0.5000000.866025i)q16+(0.607206+0.465926i)q17+(0.5176380.517638i)q18+(1.70711+0.707107i)q191.73205q22+(0.448288+0.258819i)q24+(0.9659260.258819i)q25+(0.6339750.633975i)q27+(0.965926+0.258819i)q320.896575iq33+(0.292893+0.707107i)q34+(0.3660250.633975i)q36+(1.124841.46593i)q38+(1.83195+0.241181i)q41+(1.67303+0.965926i)q43+(0.4482881.67303i)q44+(0.133975+0.500000i)q48+(0.2588190.965926i)q491.00000iq50+(0.3660250.151613i)q51+(0.776457+0.448288i)q54+(0.7588190.582262i)q57+(0.4659260.607206i)q59+1.00000iq64+(0.8660250.232051i)q66+(1.83195+0.758819i)q67+(0.7588190.0999004i)q68+(0.707107+0.189469i)q72+0.517638q75+(1.124841.46593i)q76+(0.1339750.232051i)q81+(0.241181+1.83195i)q82+(0.965926+0.741181i)q83+(0.500000+1.86603i)q86+(1.500000.866025i)q88+(1.36603+1.36603i)q890.517638q96+(0.9659260.258819i)q97+1.00000q98+(0.3281691.22474i)q99+O(q100)q+(0.258819 + 0.965926i) q^{2} +(-0.500000 + 0.133975i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.258819 - 0.448288i) q^{6} +(-0.707107 - 0.707107i) q^{8} +(-0.633975 + 0.366025i) q^{9} +(-0.448288 + 1.67303i) q^{11} +(0.366025 - 0.366025i) q^{12} +(0.500000 - 0.866025i) q^{16} +(0.607206 + 0.465926i) q^{17} +(-0.517638 - 0.517638i) q^{18} +(-1.70711 + 0.707107i) q^{19} -1.73205 q^{22} +(0.448288 + 0.258819i) q^{24} +(-0.965926 - 0.258819i) q^{25} +(0.633975 - 0.633975i) q^{27} +(0.965926 + 0.258819i) q^{32} -0.896575i q^{33} +(-0.292893 + 0.707107i) q^{34} +(0.366025 - 0.633975i) q^{36} +(-1.12484 - 1.46593i) q^{38} +(1.83195 + 0.241181i) q^{41} +(1.67303 + 0.965926i) q^{43} +(-0.448288 - 1.67303i) q^{44} +(-0.133975 + 0.500000i) q^{48} +(0.258819 - 0.965926i) q^{49} -1.00000i q^{50} +(-0.366025 - 0.151613i) q^{51} +(0.776457 + 0.448288i) q^{54} +(0.758819 - 0.582262i) q^{57} +(-0.465926 - 0.607206i) q^{59} +1.00000i q^{64} +(0.866025 - 0.232051i) q^{66} +(-1.83195 + 0.758819i) q^{67} +(-0.758819 - 0.0999004i) q^{68} +(0.707107 + 0.189469i) q^{72} +0.517638 q^{75} +(1.12484 - 1.46593i) q^{76} +(0.133975 - 0.232051i) q^{81} +(0.241181 + 1.83195i) q^{82} +(0.965926 + 0.741181i) q^{83} +(-0.500000 + 1.86603i) q^{86} +(1.50000 - 0.866025i) q^{88} +(1.36603 + 1.36603i) q^{89} -0.517638 q^{96} +(0.965926 - 0.258819i) q^{97} +1.00000 q^{98} +(-0.328169 - 1.22474i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q4q312q94q12+4q168q19+12q278q344q368q48+4q51+4q57+4q594q68+8q81+4q824q86+12q88+4q89++8q98+O(q100) 8 q - 4 q^{3} - 12 q^{9} - 4 q^{12} + 4 q^{16} - 8 q^{19} + 12 q^{27} - 8 q^{34} - 4 q^{36} - 8 q^{48} + 4 q^{51} + 4 q^{57} + 4 q^{59} - 4 q^{68} + 8 q^{81} + 4 q^{82} - 4 q^{86} + 12 q^{88} + 4 q^{89}+ \cdots + 8 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/776Z)×\left(\mathbb{Z}/776\mathbb{Z}\right)^\times.

nn 389389 393393 583583
χ(n)\chi(n) 1-1 e(1324)e\left(\frac{13}{24}\right) 1-1

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 0.258819 + 0.965926i 0.258819 + 0.965926i
33 −0.500000 + 0.133975i −0.500000 + 0.133975i −0.500000 0.866025i 0.666667π-0.666667\pi
1.00000i 0.5π0.5\pi
44 −0.866025 + 0.500000i −0.866025 + 0.500000i
55 0 0 0.130526 0.991445i 0.458333π-0.458333\pi
−0.130526 + 0.991445i 0.541667π0.541667\pi
66 −0.258819 0.448288i −0.258819 0.448288i
77 0 0 0.793353 0.608761i 0.208333π-0.208333\pi
−0.793353 + 0.608761i 0.791667π0.791667\pi
88 −0.707107 0.707107i −0.707107 0.707107i
99 −0.633975 + 0.366025i −0.633975 + 0.366025i
1010 0 0
1111 −0.448288 + 1.67303i −0.448288 + 1.67303i 0.258819 + 0.965926i 0.416667π0.416667\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
1212 0.366025 0.366025i 0.366025 0.366025i
1313 0 0 0.130526 0.991445i 0.458333π-0.458333\pi
−0.130526 + 0.991445i 0.541667π0.541667\pi
1414 0 0
1515 0 0
1616 0.500000 0.866025i 0.500000 0.866025i
1717 0.607206 + 0.465926i 0.607206 + 0.465926i 0.866025 0.500000i 0.166667π-0.166667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
1818 −0.517638 0.517638i −0.517638 0.517638i
1919 −1.70711 + 0.707107i −1.70711 + 0.707107i −0.707107 + 0.707107i 0.750000π0.750000\pi
−1.00000 π\pi
2020 0 0
2121 0 0
2222 −1.73205 −1.73205
2323 0 0 0.608761 0.793353i 0.291667π-0.291667\pi
−0.608761 + 0.793353i 0.708333π0.708333\pi
2424 0.448288 + 0.258819i 0.448288 + 0.258819i
2525 −0.965926 0.258819i −0.965926 0.258819i
2626 0 0
2727 0.633975 0.633975i 0.633975 0.633975i
2828 0 0
2929 0 0 −0.991445 0.130526i 0.958333π-0.958333\pi
0.991445 + 0.130526i 0.0416667π0.0416667\pi
3030 0 0
3131 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
3232 0.965926 + 0.258819i 0.965926 + 0.258819i
3333 0.896575i 0.896575i
3434 −0.292893 + 0.707107i −0.292893 + 0.707107i
3535 0 0
3636 0.366025 0.633975i 0.366025 0.633975i
3737 0 0 −0.608761 0.793353i 0.708333π-0.708333\pi
0.608761 + 0.793353i 0.291667π0.291667\pi
3838 −1.12484 1.46593i −1.12484 1.46593i
3939 0 0
4040 0 0
4141 1.83195 + 0.241181i 1.83195 + 0.241181i 0.965926 0.258819i 0.0833333π-0.0833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
4242 0 0
4343 1.67303 + 0.965926i 1.67303 + 0.965926i 0.965926 + 0.258819i 0.0833333π0.0833333\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
4444 −0.448288 1.67303i −0.448288 1.67303i
4545 0 0
4646 0 0
4747 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4848 −0.133975 + 0.500000i −0.133975 + 0.500000i
4949 0.258819 0.965926i 0.258819 0.965926i
5050 1.00000i 1.00000i
5151 −0.366025 0.151613i −0.366025 0.151613i
5252 0 0
5353 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
5454 0.776457 + 0.448288i 0.776457 + 0.448288i
5555 0 0
5656 0 0
5757 0.758819 0.582262i 0.758819 0.582262i
5858 0 0
5959 −0.465926 0.607206i −0.465926 0.607206i 0.500000 0.866025i 0.333333π-0.333333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
6060 0 0
6161 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
6262 0 0
6363 0 0
6464 1.00000i 1.00000i
6565 0 0
6666 0.866025 0.232051i 0.866025 0.232051i
6767 −1.83195 + 0.758819i −1.83195 + 0.758819i −0.866025 + 0.500000i 0.833333π0.833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
6868 −0.758819 0.0999004i −0.758819 0.0999004i
6969 0 0
7070 0 0
7171 0 0 0.991445 0.130526i 0.0416667π-0.0416667\pi
−0.991445 + 0.130526i 0.958333π0.958333\pi
7272 0.707107 + 0.189469i 0.707107 + 0.189469i
7373 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
7474 0 0
7575 0.517638 0.517638
7676 1.12484 1.46593i 1.12484 1.46593i
7777 0 0
7878 0 0
7979 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
8080 0 0
8181 0.133975 0.232051i 0.133975 0.232051i
8282 0.241181 + 1.83195i 0.241181 + 1.83195i
8383 0.965926 + 0.741181i 0.965926 + 0.741181i 0.965926 0.258819i 0.0833333π-0.0833333\pi
1.00000i 0.5π0.5\pi
8484 0 0
8585 0 0
8686 −0.500000 + 1.86603i −0.500000 + 1.86603i
8787 0 0
8888 1.50000 0.866025i 1.50000 0.866025i
8989 1.36603 + 1.36603i 1.36603 + 1.36603i 0.866025 + 0.500000i 0.166667π0.166667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
9090 0 0
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 −0.517638 −0.517638
9797 0.965926 0.258819i 0.965926 0.258819i
9898 1.00000 1.00000
9999 −0.328169 1.22474i −0.328169 1.22474i
100100 0.965926 0.258819i 0.965926 0.258819i
101101 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
102102 0.0517123 0.392794i 0.0517123 0.392794i
103103 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
104104 0 0
105105 0 0
106106 0 0
107107 1.57313 0.207107i 1.57313 0.207107i 0.707107 0.707107i 0.250000π-0.250000\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
108108 −0.232051 + 0.866025i −0.232051 + 0.866025i
109109 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
110110 0 0
111111 0 0
112112 0 0
113113 −0.965926 + 1.67303i −0.965926 + 1.67303i −0.258819 + 0.965926i 0.583333π0.583333\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
114114 0.758819 + 0.582262i 0.758819 + 0.582262i
115115 0 0
116116 0 0
117117 0 0
118118 0.465926 0.607206i 0.465926 0.607206i
119119 0 0
120120 0 0
121121 −1.73205 1.00000i −1.73205 1.00000i
122122 0 0
123123 −0.948288 + 0.124844i −0.948288 + 0.124844i
124124 0 0
125125 0 0
126126 0 0
127127 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
128128 −0.965926 + 0.258819i −0.965926 + 0.258819i
129129 −0.965926 0.258819i −0.965926 0.258819i
130130 0 0
131131 0.607206 1.46593i 0.607206 1.46593i −0.258819 0.965926i 0.583333π-0.583333\pi
0.866025 0.500000i 0.166667π-0.166667\pi
132132 0.448288 + 0.776457i 0.448288 + 0.776457i
133133 0 0
134134 −1.20711 1.57313i −1.20711 1.57313i
135135 0 0
136136 −0.0999004 0.758819i −0.0999004 0.758819i
137137 0.207107 0.158919i 0.207107 0.158919i −0.500000 0.866025i 0.666667π-0.666667\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
138138 0 0
139139 −0.241181 0.0999004i −0.241181 0.0999004i 0.258819 0.965926i 0.416667π-0.416667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 0.732051i 0.732051i
145145 0 0
146146 0 0
147147 0.517638i 0.517638i
148148 0 0
149149 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
150150 0.133975 + 0.500000i 0.133975 + 0.500000i
151151 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
152152 1.70711 + 0.707107i 1.70711 + 0.707107i
153153 −0.555494 0.0731322i −0.555494 0.0731322i
154154 0 0
155155 0 0
156156 0 0
157157 0 0 −0.608761 0.793353i 0.708333π-0.708333\pi
0.608761 + 0.793353i 0.291667π0.291667\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 0.258819 + 0.0693504i 0.258819 + 0.0693504i
163163 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i 0.416667π-0.416667\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
164164 −1.70711 + 0.707107i −1.70711 + 0.707107i
165165 0 0
166166 −0.465926 + 1.12484i −0.465926 + 1.12484i
167167 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
168168 0 0
169169 −0.965926 0.258819i −0.965926 0.258819i
170170 0 0
171171 0.823443 1.07313i 0.823443 1.07313i
172172 −1.93185 −1.93185
173173 0 0 0.608761 0.793353i 0.291667π-0.291667\pi
−0.608761 + 0.793353i 0.708333π0.708333\pi
174174 0 0
175175 0 0
176176 1.22474 + 1.22474i 1.22474 + 1.22474i
177177 0.314313 + 0.241181i 0.314313 + 0.241181i
178178 −0.965926 + 1.67303i −0.965926 + 1.67303i
179179 −0.0999004 0.758819i −0.0999004 0.758819i −0.965926 0.258819i 0.916667π-0.916667\pi
0.866025 0.500000i 0.166667π-0.166667\pi
180180 0 0
181181 0 0 0.130526 0.991445i 0.458333π-0.458333\pi
−0.130526 + 0.991445i 0.541667π0.541667\pi
182182 0 0
183183 0 0
184184 0 0
185185 0 0
186186 0 0
187187 −1.05171 + 0.807007i −1.05171 + 0.807007i
188188 0 0
189189 0 0
190190 0 0
191191 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
192192 −0.133975 0.500000i −0.133975 0.500000i
193193 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
194194 0.500000 + 0.866025i 0.500000 + 0.866025i
195195 0 0
196196 0.258819 + 0.965926i 0.258819 + 0.965926i
197197 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
198198 1.09808 0.633975i 1.09808 0.633975i
199199 0 0 0.130526 0.991445i 0.458333π-0.458333\pi
−0.130526 + 0.991445i 0.541667π0.541667\pi
200200 0.500000 + 0.866025i 0.500000 + 0.866025i
201201 0.814313 0.624844i 0.814313 0.624844i
202202 0 0
203203 0 0
204204 0.392794 0.0517123i 0.392794 0.0517123i
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 −0.417738 3.17303i −0.417738 3.17303i
210210 0 0
211211 −1.57313 1.20711i −1.57313 1.20711i −0.866025 0.500000i 0.833333π-0.833333\pi
−0.707107 0.707107i 0.750000π-0.750000\pi
212212 0 0
213213 0 0
214214 0.607206 + 1.46593i 0.607206 + 1.46593i
215215 0 0
216216 −0.896575 −0.896575
217217 0 0
218218 0 0
219219 0 0
220220 0 0
221221 0 0
222222 0 0
223223 0 0 −0.991445 0.130526i 0.958333π-0.958333\pi
0.991445 + 0.130526i 0.0416667π0.0416667\pi
224224 0 0
225225 0.707107 0.189469i 0.707107 0.189469i
226226 −1.86603 0.500000i −1.86603 0.500000i
227227 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
228228 −0.366025 + 0.883663i −0.366025 + 0.883663i
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 −0.158919 1.20711i −0.158919 1.20711i −0.866025 0.500000i 0.833333π-0.833333\pi
0.707107 0.707107i 0.250000π-0.250000\pi
234234 0 0
235235 0 0
236236 0.707107 + 0.292893i 0.707107 + 0.292893i
237237 0 0
238238 0 0
239239 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
240240 0 0
241241 2.00000i 2.00000i 1.00000i 0.5π0.5\pi
1.00000i 0.5π0.5\pi
242242 0.517638 1.93185i 0.517638 1.93185i
243243 −0.267949 + 1.00000i −0.267949 + 1.00000i
244244 0 0
245245 0 0
246246 −0.366025 0.883663i −0.366025 0.883663i
247247 0 0
248248 0 0
249249 −0.582262 0.241181i −0.582262 0.241181i
250250 0 0
251251 1.46593 1.12484i 1.46593 1.12484i 0.500000 0.866025i 0.333333π-0.333333\pi
0.965926 0.258819i 0.0833333π-0.0833333\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 −0.500000 0.866025i −0.500000 0.866025i
257257 −0.607206 + 1.46593i −0.607206 + 1.46593i 0.258819 + 0.965926i 0.416667π0.416667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
258258 1.00000i 1.00000i
259259 0 0
260260 0 0
261261 0 0
262262 1.57313 + 0.207107i 1.57313 + 0.207107i
263263 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
264264 −0.633975 + 0.633975i −0.633975 + 0.633975i
265265 0 0
266266 0 0
267267 −0.866025 0.500000i −0.866025 0.500000i
268268 1.20711 1.57313i 1.20711 1.57313i
269269 0 0 1.00000 00
−1.00000 π\pi
270270 0 0
271271 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
272272 0.707107 0.292893i 0.707107 0.292893i
273273 0 0
274274 0.207107 + 0.158919i 0.207107 + 0.158919i
275275 0.866025 1.50000i 0.866025 1.50000i
276276 0 0
277277 0 0 −0.793353 0.608761i 0.791667π-0.791667\pi
0.793353 + 0.608761i 0.208333π0.208333\pi
278278 0.0340742 0.258819i 0.0340742 0.258819i
279279 0 0
280280 0 0
281281 −1.96593 + 0.258819i −1.96593 + 0.258819i −0.965926 + 0.258819i 0.916667π0.916667\pi
−1.00000 π\pi
282282 0 0
283283 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 −0.707107 + 0.189469i −0.707107 + 0.189469i
289289 −0.107206 0.400100i −0.107206 0.400100i
290290 0 0
291291 −0.448288 + 0.258819i −0.448288 + 0.258819i
292292 0 0
293293 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
294294 −0.500000 + 0.133975i −0.500000 + 0.133975i
295295 0 0
296296 0 0
297297 0.776457 + 1.34486i 0.776457 + 1.34486i
298298 0 0
299299 0 0
300300 −0.448288 + 0.258819i −0.448288 + 0.258819i
301301 0 0
302302 0 0
303303 0 0
304304 −0.241181 + 1.83195i −0.241181 + 1.83195i
305305 0 0
306306 −0.0731322 0.555494i −0.0731322 0.555494i
307307 0.258819 0.448288i 0.258819 0.448288i −0.707107 0.707107i 0.750000π-0.750000\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
308308 0 0
309309 0 0
310310 0 0
311311 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
312312 0 0
313313 −1.93185 −1.93185 −0.965926 0.258819i 0.916667π-0.916667\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
314314 0 0
315315 0 0
316316 0 0
317317 0 0 0.991445 0.130526i 0.0416667π-0.0416667\pi
−0.991445 + 0.130526i 0.958333π0.958333\pi
318318 0 0
319319 0 0
320320 0 0
321321 −0.758819 + 0.314313i −0.758819 + 0.314313i
322322 0 0
323323 −1.36603 0.366025i −1.36603 0.366025i
324324 0.267949i 0.267949i
325325 0 0
326326 0.500000 + 0.866025i 0.500000 + 0.866025i
327327 0 0
328328 −1.12484 1.46593i −1.12484 1.46593i
329329 0 0
330330 0 0
331331 −0.207107 + 0.158919i −0.207107 + 0.158919i −0.707107 0.707107i 0.750000π-0.750000\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
332332 −1.20711 0.158919i −1.20711 0.158919i
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 1.12484 + 0.465926i 1.12484 + 0.465926i 0.866025 0.500000i 0.166667π-0.166667\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
338338 1.00000i 1.00000i
339339 0.258819 0.965926i 0.258819 0.965926i
340340 0 0
341341 0 0
342342 1.24969 + 0.517638i 1.24969 + 0.517638i
343343 0 0
344344 −0.500000 1.86603i −0.500000 1.86603i
345345 0 0
346346 0 0
347347 1.20711 + 0.158919i 1.20711 + 0.158919i 0.707107 0.707107i 0.250000π-0.250000\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
348348 0 0
349349 0 0 −0.130526 0.991445i 0.541667π-0.541667\pi
0.130526 + 0.991445i 0.458333π0.458333\pi
350350 0 0
351351 0 0
352352 −0.866025 + 1.50000i −0.866025 + 1.50000i
353353 1.00000 + 1.73205i 1.00000 + 1.73205i 0.500000 + 0.866025i 0.333333π0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
354354 −0.151613 + 0.366025i −0.151613 + 0.366025i
355355 0 0
356356 −1.86603 0.500000i −1.86603 0.500000i
357357 0 0
358358 0.707107 0.292893i 0.707107 0.292893i
359359 0 0 −0.991445 0.130526i 0.958333π-0.958333\pi
0.991445 + 0.130526i 0.0416667π0.0416667\pi
360360 0 0
361361 1.70711 1.70711i 1.70711 1.70711i
362362 0 0
363363 1.00000 + 0.267949i 1.00000 + 0.267949i
364364 0 0
365365 0 0
366366 0 0
367367 0 0 0.608761 0.793353i 0.291667π-0.291667\pi
−0.608761 + 0.793353i 0.708333π0.708333\pi
368368 0 0
369369 −1.24969 + 0.517638i −1.24969 + 0.517638i
370370 0 0
371371 0 0
372372 0 0
373373 0 0 −0.130526 0.991445i 0.541667π-0.541667\pi
0.130526 + 0.991445i 0.458333π0.458333\pi
374374 −1.05171 0.807007i −1.05171 0.807007i
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 0.866025 0.500000i 0.866025 0.500000i 1.00000i 0.5π-0.5\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
380380 0 0
381381 0 0
382382 0 0
383383 0 0 0.130526 0.991445i 0.458333π-0.458333\pi
−0.130526 + 0.991445i 0.541667π0.541667\pi
384384 0.448288 0.258819i 0.448288 0.258819i
385385 0 0
386386 −0.258819 0.965926i −0.258819 0.965926i
387387 −1.41421 −1.41421
388388 −0.707107 + 0.707107i −0.707107 + 0.707107i
389389 0 0 1.00000 00
−1.00000 π\pi
390390 0 0
391391 0 0
392392 −0.866025 + 0.500000i −0.866025 + 0.500000i
393393 −0.107206 + 0.814313i −0.107206 + 0.814313i
394394 0 0
395395 0 0
396396 0.896575 + 0.896575i 0.896575 + 0.896575i
397397 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
398398 0 0
399399 0 0
400400 −0.707107 + 0.707107i −0.707107 + 0.707107i
401401 −0.0340742 + 0.258819i −0.0340742 + 0.258819i 0.965926 + 0.258819i 0.0833333π0.0833333\pi
−1.00000 1.00000π1.00000\pi
402402 0.814313 + 0.624844i 0.814313 + 0.624844i
403403 0 0
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0.151613 + 0.366025i 0.151613 + 0.366025i
409409 0.741181 0.965926i 0.741181 0.965926i −0.258819 0.965926i 0.583333π-0.583333\pi
1.00000 00
410410 0 0
411411 −0.0822623 + 0.107206i −0.0822623 + 0.107206i
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 0.133975 + 0.0176381i 0.133975 + 0.0176381i
418418 2.95680 1.22474i 2.95680 1.22474i
419419 −0.500000 + 0.133975i −0.500000 + 0.133975i −0.500000 0.866025i 0.666667π-0.666667\pi
1.00000i 0.5π0.5\pi
420420 0 0
421421 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
422422 0.758819 1.83195i 0.758819 1.83195i
423423 0 0
424424 0 0
425425 −0.465926 0.607206i −0.465926 0.607206i
426426 0 0
427427 0 0
428428 −1.25882 + 0.965926i −1.25882 + 0.965926i
429429 0 0
430430 0 0
431431 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
432432 −0.232051 0.866025i −0.232051 0.866025i
433433 0.758819 + 1.83195i 0.758819 + 1.83195i 0.500000 + 0.866025i 0.333333π0.333333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
434434 0 0
435435 0 0
436436 0 0
437437 0 0
438438 0 0
439439 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
440440 0 0
441441 0.189469 + 0.707107i 0.189469 + 0.707107i
442442 0 0
443443 0.241181 + 0.0999004i 0.241181 + 0.0999004i 0.500000 0.866025i 0.333333π-0.333333\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 −0.258819 + 0.448288i −0.258819 + 0.448288i −0.965926 0.258819i 0.916667π-0.916667\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
450450 0.366025 + 0.633975i 0.366025 + 0.633975i
451451 −1.22474 + 2.95680i −1.22474 + 2.95680i
452452 1.93185i 1.93185i
453453 0 0
454454 −0.965926 + 0.258819i −0.965926 + 0.258819i
455455 0 0
456456 −0.948288 0.124844i −0.948288 0.124844i
457457 0.607206 1.46593i 0.607206 1.46593i −0.258819 0.965926i 0.583333π-0.583333\pi
0.866025 0.500000i 0.166667π-0.166667\pi
458458 0 0
459459 0.680339 0.0895683i 0.680339 0.0895683i
460460 0 0
461461 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
462462 0 0
463463 0 0 1.00000 00
−1.00000 π\pi
464464 0 0
465465 0 0
466466 1.12484 0.465926i 1.12484 0.465926i
467467 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 −0.0999004 + 0.758819i −0.0999004 + 0.758819i
473473 −2.36603 + 2.36603i −2.36603 + 2.36603i
474474 0 0
475475 1.83195 0.241181i 1.83195 0.241181i
476476 0 0
477477 0 0
478478 0 0
479479 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
480480 0 0
481481 0 0
482482 −1.93185 + 0.517638i −1.93185 + 0.517638i
483483 0 0
484484 2.00000 2.00000
485485 0 0
486486 −1.03528 −1.03528
487487 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
488488 0 0
489489 −0.448288 + 0.258819i −0.448288 + 0.258819i
490490 0 0
491491 −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i 0.333333π-0.333333\pi
−1.00000 π\pi
492492 0.758819 0.582262i 0.758819 0.582262i
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0.0822623 0.624844i 0.0822623 0.624844i
499499 1.46593 + 1.12484i 1.46593 + 1.12484i 0.965926 + 0.258819i 0.0833333π0.0833333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
500500 0 0
501501 0 0
502502 1.46593 + 1.12484i 1.46593 + 1.12484i
503503 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
504504 0 0
505505 0 0
506506 0 0
507507 0.517638 0.517638
508508 0 0
509509 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
510510 0 0
511511 0 0
512512 0.707107 0.707107i 0.707107 0.707107i
513513 −0.633975 + 1.53055i −0.633975 + 1.53055i
514514 −1.57313 0.207107i −1.57313 0.207107i
515515 0 0
516516 0.965926 0.258819i 0.965926 0.258819i
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i 0.666667π-0.666667\pi
1.00000 00
522522 0 0
523523 0.741181 + 0.965926i 0.741181 + 0.965926i 1.00000 00
−0.258819 + 0.965926i 0.583333π0.583333\pi
524524 0.207107 + 1.57313i 0.207107 + 1.57313i
525525 0 0
526526 0 0
527527 0 0
528528 −0.776457 0.448288i −0.776457 0.448288i
529529 −0.258819 0.965926i −0.258819 0.965926i
530530 0 0
531531 0.517638 + 0.214413i 0.517638 + 0.214413i
532532 0 0
533533 0 0
534534 0.258819 0.965926i 0.258819 0.965926i
535535 0 0
536536 1.83195 + 0.758819i 1.83195 + 0.758819i
537537 0.151613 + 0.366025i 0.151613 + 0.366025i
538538 0 0
539539 1.50000 + 0.866025i 1.50000 + 0.866025i
540540 0 0
541541 0 0 −0.991445 0.130526i 0.958333π-0.958333\pi
0.991445 + 0.130526i 0.0416667π0.0416667\pi
542542 0 0
543543 0 0
544544 0.465926 + 0.607206i 0.465926 + 0.607206i
545545 0 0
546546 0 0
547547 −0.965926 1.67303i −0.965926 1.67303i −0.707107 0.707107i 0.750000π-0.750000\pi
−0.258819 0.965926i 0.583333π-0.583333\pi
548548 −0.0999004 + 0.241181i −0.0999004 + 0.241181i
549549 0 0
550550 1.67303 + 0.448288i 1.67303 + 0.448288i
551551 0 0
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 0.258819 0.0340742i 0.258819 0.0340742i
557557 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
558558 0 0
559559 0 0
560560 0 0
561561 0.417738 0.544406i 0.417738 0.544406i
562562 −0.758819 1.83195i −0.758819 1.83195i
563563 0.707107 0.292893i 0.707107 0.292893i 1.00000i 0.5π-0.5\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
564564 0 0
565565 0 0
566566 0 0
567567 0 0
568568 0 0
569569 −0.258819 + 1.96593i −0.258819 + 1.96593i 1.00000i 0.5π0.5\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
570570 0 0
571571 −0.133975 + 0.500000i −0.133975 + 0.500000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−1.00000 π\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 −0.366025 0.633975i −0.366025 0.633975i
577577 0.258819 1.96593i 0.258819 1.96593i 1.00000i 0.5π-0.5\pi
0.258819 0.965926i 0.416667π-0.416667\pi
578578 0.358719 0.207107i 0.358719 0.207107i
579579 0.500000 0.133975i 0.500000 0.133975i
580580 0 0
581581 0 0
582582 −0.366025 0.366025i −0.366025 0.366025i
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 0.0340742 0.258819i 0.0340742 0.258819i −0.965926 0.258819i 0.916667π-0.916667\pi
1.00000 00
588588 −0.258819 0.448288i −0.258819 0.448288i
589589 0 0
590590 0 0
591591 0 0
592592 0 0
593593 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i 0.750000π-0.750000\pi
0.965926 0.258819i 0.0833333π-0.0833333\pi
594594 −1.09808 + 1.09808i −1.09808 + 1.09808i
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 0 0 −0.793353 0.608761i 0.791667π-0.791667\pi
0.793353 + 0.608761i 0.208333π0.208333\pi
600600 −0.366025 0.366025i −0.366025 0.366025i
601601 −0.707107 + 0.292893i −0.707107 + 0.292893i −0.707107 0.707107i 0.750000π-0.750000\pi
1.00000i 0.5π0.5\pi
602602 0 0
603603 0.883663 1.15161i 0.883663 1.15161i
604604 0 0
605605 0 0
606606 0 0
607607 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
608608 −1.83195 + 0.241181i −1.83195 + 0.241181i
609609 0 0
610610 0 0
611611 0 0
612612 0.517638 0.214413i 0.517638 0.214413i
613613 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
614614 0.500000 + 0.133975i 0.500000 + 0.133975i
615615 0 0
616616 0 0
617617 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i 0.0833333π0.0833333\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
618618 0 0
619619 −1.12484 1.46593i −1.12484 1.46593i −0.866025 0.500000i 0.833333π-0.833333\pi
−0.258819 0.965926i 0.583333π-0.583333\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 0.866025 + 0.500000i 0.866025 + 0.500000i
626626 −0.500000 1.86603i −0.500000 1.86603i
627627 0.633975 + 1.53055i 0.633975 + 1.53055i
628628 0 0
629629 0 0
630630 0 0
631631 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
632632 0 0
633633 0.948288 + 0.392794i 0.948288 + 0.392794i
634634 0 0
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 0 0
641641 0.158919 + 0.207107i 0.158919 + 0.207107i 0.866025 0.500000i 0.166667π-0.166667\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
642642 −0.500000 0.651613i −0.500000 0.651613i
643643 0.707107 1.22474i 0.707107 1.22474i −0.258819 0.965926i 0.583333π-0.583333\pi
0.965926 0.258819i 0.0833333π-0.0833333\pi
644644 0 0
645645 0 0
646646 1.41421i 1.41421i
647647 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
648648 −0.258819 + 0.0693504i −0.258819 + 0.0693504i
649649 1.22474 0.507306i 1.22474 0.507306i
650650 0 0
651651 0 0
652652 −0.707107 + 0.707107i −0.707107 + 0.707107i
653653 0 0 0.991445 0.130526i 0.0416667π-0.0416667\pi
−0.991445 + 0.130526i 0.958333π0.958333\pi
654654 0 0
655655 0 0
656656 1.12484 1.46593i 1.12484 1.46593i
657657 0 0
658658 0 0
659659 −0.607206 1.46593i −0.607206 1.46593i −0.866025 0.500000i 0.833333π-0.833333\pi
0.258819 0.965926i 0.416667π-0.416667\pi
660660 0 0
661661 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
662662 −0.207107 0.158919i −0.207107 0.158919i
663663 0 0
664664 −0.158919 1.20711i −0.158919 1.20711i
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 0.258819 + 0.448288i 0.258819 + 0.448288i 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
674674 −0.158919 + 1.20711i −0.158919 + 1.20711i
675675 −0.776457 + 0.448288i −0.776457 + 0.448288i
676676 0.965926 0.258819i 0.965926 0.258819i
677677 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
678678 1.00000 1.00000
679679 0 0
680680 0 0
681681 −0.133975 0.500000i −0.133975 0.500000i
682682 0 0
683683 −0.448288 + 0.258819i −0.448288 + 0.258819i −0.707107 0.707107i 0.750000π-0.750000\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
684684 −0.176557 + 1.34108i −0.176557 + 1.34108i
685685 0 0
686686 0 0
687687 0 0
688688 1.67303 0.965926i 1.67303 0.965926i
689689 0 0
690690 0 0
691691 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
692692 0 0
693693 0 0
694694 0.158919 + 1.20711i 0.158919 + 1.20711i
695695 0 0
696696 0 0
697697 1.00000 + 1.00000i 1.00000 + 1.00000i
698698 0 0
699699 0.241181 + 0.582262i 0.241181 + 0.582262i
700700 0 0
701701 0 0 1.00000 00
−1.00000 π\pi
702702 0 0
703703 0 0
704704 −1.67303 0.448288i −1.67303 0.448288i
705705 0 0
706706 −1.41421 + 1.41421i −1.41421 + 1.41421i
707707 0 0
708708 −0.392794 0.0517123i −0.392794 0.0517123i
709709 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
710710 0 0
711711 0 0
712712 1.93185i 1.93185i
713713 0 0
714714 0 0
715715 0 0
716716 0.465926 + 0.607206i 0.465926 + 0.607206i
717717 0 0
718718 0 0
719719 0 0 0.793353 0.608761i 0.208333π-0.208333\pi
−0.793353 + 0.608761i 0.791667π0.791667\pi
720720 0 0
721721 0 0
722722 2.09077 + 1.20711i 2.09077 + 1.20711i
723723 −0.267949 1.00000i −0.267949 1.00000i
724724 0 0
725725 0 0
726726 1.03528i 1.03528i
727727 0 0 0.258819 0.965926i 0.416667π-0.416667\pi
−0.258819 + 0.965926i 0.583333π0.583333\pi
728728 0 0
729729 0.267949i 0.267949i
730730 0 0
731731 0.565826 + 1.36603i 0.565826 + 1.36603i
732732 0 0
733733 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
734734 0 0
735735 0 0
736736 0 0
737737 −0.448288 3.40508i −0.448288 3.40508i
738738 −0.823443 1.07313i −0.823443 1.07313i
739739 −0.158919 0.207107i −0.158919 0.207107i 0.707107 0.707107i 0.250000π-0.250000\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
740740 0 0
741741 0 0
742742 0 0
743743 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
744744 0 0
745745 0 0
746746 0 0
747747 −0.883663 0.116337i −0.883663 0.116337i
748748 0.507306 1.22474i 0.507306 1.22474i
749749 0 0
750750 0 0
751751 0 0 −0.965926 0.258819i 0.916667π-0.916667\pi
0.965926 + 0.258819i 0.0833333π0.0833333\pi
752752 0 0
753753 −0.582262 + 0.758819i −0.582262 + 0.758819i
754754 0 0
755755 0 0
756756 0 0
757757 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
758758 0.707107 + 0.707107i 0.707107 + 0.707107i
759759 0 0
760760 0 0
761761 0.0999004 + 0.758819i 0.0999004 + 0.758819i 0.965926 + 0.258819i 0.0833333π0.0833333\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 0.366025 + 0.366025i 0.366025 + 0.366025i
769769 1.46593 1.12484i 1.46593 1.12484i 0.500000 0.866025i 0.333333π-0.333333\pi
0.965926 0.258819i 0.0833333π-0.0833333\pi
770770 0 0
771771 0.107206 0.814313i 0.107206 0.814313i
772772 0.866025 0.500000i 0.866025 0.500000i
773773 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
774774 −0.366025 1.36603i −0.366025 1.36603i
775775 0 0
776776 −0.866025 0.500000i −0.866025 0.500000i
777777 0 0
778778 0 0
779779 −3.29788 + 0.883663i −3.29788 + 0.883663i
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 −0.707107 0.707107i −0.707107 0.707107i
785785 0 0
786786 −0.814313 + 0.107206i −0.814313 + 0.107206i
787787 0.366025 1.36603i 0.366025 1.36603i −0.500000 0.866025i 0.666667π-0.666667\pi
0.866025 0.500000i 0.166667π-0.166667\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 −0.633975 + 1.09808i −0.633975 + 1.09808i
793793 0 0
794794 0 0
795795 0 0
796796 0 0
797797 0 0 0.608761 0.793353i 0.291667π-0.291667\pi
−0.608761 + 0.793353i 0.708333π0.708333\pi
798798 0 0
799799 0 0
800800 −0.866025 0.500000i −0.866025 0.500000i
801801 −1.36603 0.366025i −1.36603 0.366025i
802802 −0.258819 + 0.0340742i −0.258819 + 0.0340742i
803803 0 0
804804 −0.392794 + 0.948288i −0.392794 + 0.948288i
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 1.41421i 1.41421i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
810810 0 0
811811 0.965926 + 1.67303i 0.965926 + 1.67303i 0.707107 + 0.707107i 0.250000π0.250000\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 −0.314313 + 0.241181i −0.314313 + 0.241181i
817817 −3.53906 0.465926i −3.53906 0.465926i
818818 1.12484 + 0.465926i 1.12484 + 0.465926i
819819 0 0
820820 0 0
821821 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
822822 −0.124844 0.0517123i −0.124844 0.0517123i
823823 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
824824 0 0
825825 −0.232051 + 0.866025i −0.232051 + 0.866025i
826826 0 0
827827 −1.83195 0.758819i −1.83195 0.758819i −0.965926 0.258819i 0.916667π-0.916667\pi
−0.866025 0.500000i 0.833333π-0.833333\pi
828828 0 0
829829 0 0 −0.258819 0.965926i 0.583333π-0.583333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
830830 0 0
831831 0 0
832832 0 0
833833 0.607206 0.465926i 0.607206 0.465926i
834834 0.0176381 + 0.133975i 0.0176381 + 0.133975i
835835 0 0
836836 1.94829 + 2.53906i 1.94829 + 2.53906i
837837 0 0
838838 −0.258819 0.448288i −0.258819 0.448288i
839839 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
840840 0 0
841841 0.965926 + 0.258819i 0.965926 + 0.258819i
842842 0 0
843843 0.948288 0.392794i 0.948288 0.392794i
844844 1.96593 + 0.258819i 1.96593 + 0.258819i
845845 0 0
846846 0 0
847847 0 0
848848 0 0
849849 0 0
850850 0.465926 0.607206i 0.465926 0.607206i
851851 0 0
852852 0 0
853853 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
854854 0 0
855855 0 0
856856 −1.25882 0.965926i −1.25882 0.965926i
857857 0.866025 1.50000i 0.866025 1.50000i 1.00000i 0.5π-0.5\pi
0.866025 0.500000i 0.166667π-0.166667\pi
858858 0 0
859859 1.25882 + 0.965926i 1.25882 + 0.965926i 1.00000 00
0.258819 + 0.965926i 0.416667π0.416667\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 0.991445 0.130526i 0.0416667π-0.0416667\pi
−0.991445 + 0.130526i 0.958333π0.958333\pi
864864 0.776457 0.448288i 0.776457 0.448288i
865865 0 0
866866 −1.57313 + 1.20711i −1.57313 + 1.20711i
867867 0.107206 + 0.185687i 0.107206 + 0.185687i
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0 0
873873 −0.517638 + 0.517638i −0.517638 + 0.517638i
874874 0 0
875875 0 0
876876 0 0
877877 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
878878 0 0
879879 0 0
880880 0 0
881881 −0.707107 0.707107i −0.707107 0.707107i 0.258819 0.965926i 0.416667π-0.416667\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
882882 −0.633975 + 0.366025i −0.633975 + 0.366025i
883883 1.57313 0.207107i 1.57313 0.207107i 0.707107 0.707107i 0.250000π-0.250000\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
884884 0 0
885885 0 0
886886 −0.0340742 + 0.258819i −0.0340742 + 0.258819i
887887 0 0 −0.793353 0.608761i 0.791667π-0.791667\pi
0.793353 + 0.608761i 0.208333π0.208333\pi
888888 0 0
889889 0 0
890890 0 0
891891 0.328169 + 0.328169i 0.328169 + 0.328169i
892892 0 0
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 −0.500000 0.133975i −0.500000 0.133975i
899899 0 0
900900 −0.517638 + 0.517638i −0.517638 + 0.517638i
901901 0 0
902902 −3.17303 0.417738i −3.17303 0.417738i
903903 0 0
904904 1.86603 0.500000i 1.86603 0.500000i
905905 0 0
906906 0 0
907907 0.465926 1.12484i 0.465926 1.12484i −0.500000 0.866025i 0.666667π-0.666667\pi
0.965926 0.258819i 0.0833333π-0.0833333\pi
908908 −0.500000 0.866025i −0.500000 0.866025i
909909 0 0
910910 0 0
911911 0 0 −0.608761 0.793353i 0.708333π-0.708333\pi
0.608761 + 0.793353i 0.291667π0.291667\pi
912912 −0.124844 0.948288i −0.124844 0.948288i
913913 −1.67303 + 1.28376i −1.67303 + 1.28376i
914914 1.57313 + 0.207107i 1.57313 + 0.207107i
915915 0 0
916916 0 0
917917 0 0
918918 0.262601 + 0.633975i 0.262601 + 0.633975i
919919 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
920920 0 0
921921 −0.0693504 + 0.258819i −0.0693504 + 0.258819i
922922 0 0
923923 0 0
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 0 0
929929 1.57313 + 0.207107i 1.57313 + 0.207107i 0.866025 0.500000i 0.166667π-0.166667\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
930930 0 0
931931 0.241181 + 1.83195i 0.241181 + 1.83195i
932932 0.741181 + 0.965926i 0.741181 + 0.965926i
933933 0 0
934934 −0.707107 + 1.22474i −0.707107 + 1.22474i
935935 0 0
936936 0 0
937937 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
938938 0 0
939939 0.965926 0.258819i 0.965926 0.258819i
940940 0 0
941941 0 0 −0.991445 0.130526i 0.958333π-0.958333\pi
0.991445 + 0.130526i 0.0416667π0.0416667\pi
942942 0 0
943943 0 0
944944 −0.758819 + 0.0999004i −0.758819 + 0.0999004i
945945 0 0
946946 −2.89778 1.67303i −2.89778 1.67303i
947947 −0.741181 + 0.965926i −0.741181 + 0.965926i 0.258819 + 0.965926i 0.416667π0.416667\pi
−1.00000 π\pi
948948 0 0
949949 0 0
950950 0.707107 + 1.70711i 0.707107 + 1.70711i
951951 0 0
952952 0 0
953953 −0.607206 0.465926i −0.607206 0.465926i 0.258819 0.965926i 0.416667π-0.416667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 0.866025 0.500000i 0.866025 0.500000i
962962 0 0
963963 −0.921519 + 0.707107i −0.921519 + 0.707107i
964964 −1.00000 1.73205i −1.00000 1.73205i
965965 0 0
966966 0 0
967967 0 0 0.965926 0.258819i 0.0833333π-0.0833333\pi
−0.965926 + 0.258819i 0.916667π0.916667\pi
968968 0.517638 + 1.93185i 0.517638 + 1.93185i
969969 0.732051 0.732051
970970 0 0
971971 −1.41421 −1.41421 −0.707107 0.707107i 0.750000π-0.750000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
972972 −0.267949 1.00000i −0.267949 1.00000i
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 −0.607206 + 0.465926i −0.607206 + 0.465926i −0.866025 0.500000i 0.833333π-0.833333\pi
0.258819 + 0.965926i 0.416667π0.416667\pi
978978 −0.366025 0.366025i −0.366025 0.366025i
979979 −2.89778 + 1.67303i −2.89778 + 1.67303i
980980 0 0
981981 0 0
982982 0.707107 0.707107i 0.707107 0.707107i
983983 0 0 0.130526 0.991445i 0.458333π-0.458333\pi
−0.130526 + 0.991445i 0.541667π0.541667\pi
984984 0.758819 + 0.582262i 0.758819 + 0.582262i
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 0 0 0.608761 0.793353i 0.291667π-0.291667\pi
−0.608761 + 0.793353i 0.708333π0.708333\pi
992992 0 0
993993 0.0822623 0.107206i 0.0822623 0.107206i
994994 0 0
995995 0 0
996996 0.624844 0.0822623i 0.624844 0.0822623i
997997 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
998998 −0.707107 + 1.70711i −0.707107 + 1.70711i
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 776.1.bh.a.539.1 yes 8
4.3 odd 2 3104.1.dr.a.2479.1 8
8.3 odd 2 CM 776.1.bh.a.539.1 yes 8
8.5 even 2 3104.1.dr.a.2479.1 8
97.9 even 24 inner 776.1.bh.a.203.1 8
388.203 odd 24 3104.1.dr.a.591.1 8
776.203 odd 24 inner 776.1.bh.a.203.1 8
776.397 even 24 3104.1.dr.a.591.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
776.1.bh.a.203.1 8 97.9 even 24 inner
776.1.bh.a.203.1 8 776.203 odd 24 inner
776.1.bh.a.539.1 yes 8 1.1 even 1 trivial
776.1.bh.a.539.1 yes 8 8.3 odd 2 CM
3104.1.dr.a.591.1 8 388.203 odd 24
3104.1.dr.a.591.1 8 776.397 even 24
3104.1.dr.a.2479.1 8 4.3 odd 2
3104.1.dr.a.2479.1 8 8.5 even 2