Properties

Label 3267.1.q.a.122.1
Level 32673267
Weight 11
Character 3267.122
Analytic conductor 1.6301.630
Analytic rank 00
Dimension 66
Projective image D18D_{18}
CM discriminant -11
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3267,1,Mod(122,3267)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3267, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([17, 0]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3267.122");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 3267=33112 3267 = 3^{3} \cdot 11^{2}
Weight: k k == 1 1
Character orbit: [χ][\chi] == 3267.q (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: 1.630445396271.63044539627
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,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Projective image: D18D_{18}
Projective field: Galois closure of Q[x]/(x18)\mathbb{Q}[x]/(x^{18} - \cdots)

Embedding invariants

Embedding label 122.1
Root 0.7660440.642788i-0.766044 - 0.642788i of defining polynomial
Character χ\chi == 3267.122
Dual form 3267.1.q.a.3026.1

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+(0.173648+0.984808i)q3+(0.939693+0.342020i)q4+(0.4396930.524005i)q5+(0.9396930.342020i)q9+(0.1736480.984808i)q12+(0.439693+0.524005i)q15+(0.7660440.642788i)q16+(0.233956+0.642788i)q20+(0.592396+1.62760i)q23+(0.0923963+0.524005i)q25+(0.5000000.866025i)q27+(0.3263520.118782i)q31+1.00000q36+(0.939693+1.62760i)q37+(0.592396+0.342020i)q45+(0.439693+1.20805i)q47+(0.500000+0.866025i)q48+(0.7660440.642788i)q49+1.96962iq53+(1.266041.50881i)q59+(0.5923960.342020i)q60+(0.500000+0.866025i)q64+(0.0603074+0.342020i)q67+(1.70574+0.300767i)q69+(1.11334+0.642788i)q710.532089q750.684040iq80+(0.766044+0.642788i)q81+(1.50000+0.866025i)q89+(1.113341.32683i)q92+(0.0603074+0.342020i)q93+(1.173650.984808i)q97+O(q100)q+(-0.173648 + 0.984808i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.439693 - 0.524005i) q^{5} +(-0.939693 - 0.342020i) q^{9} +(-0.173648 - 0.984808i) q^{12} +(0.439693 + 0.524005i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.233956 + 0.642788i) q^{20} +(0.592396 + 1.62760i) q^{23} +(0.0923963 + 0.524005i) q^{25} +(0.500000 - 0.866025i) q^{27} +(0.326352 - 0.118782i) q^{31} +1.00000 q^{36} +(-0.939693 + 1.62760i) q^{37} +(-0.592396 + 0.342020i) q^{45} +(-0.439693 + 1.20805i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.766044 - 0.642788i) q^{49} +1.96962i q^{53} +(1.26604 - 1.50881i) q^{59} +(-0.592396 - 0.342020i) q^{60} +(-0.500000 + 0.866025i) q^{64} +(-0.0603074 + 0.342020i) q^{67} +(-1.70574 + 0.300767i) q^{69} +(1.11334 + 0.642788i) q^{71} -0.532089 q^{75} -0.684040i q^{80} +(0.766044 + 0.642788i) q^{81} +(-1.50000 + 0.866025i) q^{89} +(-1.11334 - 1.32683i) q^{92} +(0.0603074 + 0.342020i) q^{93} +(1.17365 - 0.984808i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q3q53q156q203q25+3q27+3q31+6q36+3q47+3q48+3q593q646q67+6q759q89+6q93+6q97+O(q100) 6 q - 3 q^{5} - 3 q^{15} - 6 q^{20} - 3 q^{25} + 3 q^{27} + 3 q^{31} + 6 q^{36} + 3 q^{47} + 3 q^{48} + 3 q^{59} - 3 q^{64} - 6 q^{67} + 6 q^{75} - 9 q^{89} + 6 q^{93} + 6 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3267Z)×\left(\mathbb{Z}/3267\mathbb{Z}\right)^\times.

nn 244244 30263026
χ(n)\chi(n) 11 e(1718)e\left(\frac{17}{18}\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 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
33 −0.173648 + 0.984808i −0.173648 + 0.984808i
44 −0.939693 + 0.342020i −0.939693 + 0.342020i
55 0.439693 0.524005i 0.439693 0.524005i −0.500000 0.866025i 0.666667π-0.666667\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
66 0 0
77 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
88 0 0
99 −0.939693 0.342020i −0.939693 0.342020i
1010 0 0
1111 0 0
1212 −0.173648 0.984808i −0.173648 0.984808i
1313 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
1414 0 0
1515 0.439693 + 0.524005i 0.439693 + 0.524005i
1616 0.766044 0.642788i 0.766044 0.642788i
1717 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
1818 0 0
1919 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
2020 −0.233956 + 0.642788i −0.233956 + 0.642788i
2121 0 0
2222 0 0
2323 0.592396 + 1.62760i 0.592396 + 1.62760i 0.766044 + 0.642788i 0.222222π0.222222\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
2424 0 0
2525 0.0923963 + 0.524005i 0.0923963 + 0.524005i
2626 0 0
2727 0.500000 0.866025i 0.500000 0.866025i
2828 0 0
2929 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
3030 0 0
3131 0.326352 0.118782i 0.326352 0.118782i −0.173648 0.984808i 0.555556π-0.555556\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 1.00000 1.00000
3737 −0.939693 + 1.62760i −0.939693 + 1.62760i −0.173648 + 0.984808i 0.555556π0.555556\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
3838 0 0
3939 0 0
4040 0 0
4141 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
4242 0 0
4343 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
4444 0 0
4545 −0.592396 + 0.342020i −0.592396 + 0.342020i
4646 0 0
4747 −0.439693 + 1.20805i −0.439693 + 1.20805i 0.500000 + 0.866025i 0.333333π0.333333\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
4848 0.500000 + 0.866025i 0.500000 + 0.866025i
4949 −0.766044 0.642788i −0.766044 0.642788i
5050 0 0
5151 0 0
5252 0 0
5353 1.96962i 1.96962i 0.173648 + 0.984808i 0.444444π0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 0 0
5959 1.26604 1.50881i 1.26604 1.50881i 0.500000 0.866025i 0.333333π-0.333333\pi
0.766044 0.642788i 0.222222π-0.222222\pi
6060 −0.592396 0.342020i −0.592396 0.342020i
6161 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
6262 0 0
6363 0 0
6464 −0.500000 + 0.866025i −0.500000 + 0.866025i
6565 0 0
6666 0 0
6767 −0.0603074 + 0.342020i −0.0603074 + 0.342020i 0.939693 + 0.342020i 0.111111π0.111111\pi
−1.00000 π\pi
6868 0 0
6969 −1.70574 + 0.300767i −1.70574 + 0.300767i
7070 0 0
7171 1.11334 + 0.642788i 1.11334 + 0.642788i 0.939693 0.342020i 0.111111π-0.111111\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
7272 0 0
7373 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
7474 0 0
7575 −0.532089 −0.532089
7676 0 0
7777 0 0
7878 0 0
7979 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
8080 0.684040i 0.684040i
8181 0.766044 + 0.642788i 0.766044 + 0.642788i
8282 0 0
8383 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
8484 0 0
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 −1.50000 + 0.866025i −1.50000 + 0.866025i −0.500000 + 0.866025i 0.666667π0.666667\pi
−1.00000 π\pi
9090 0 0
9191 0 0
9292 −1.11334 1.32683i −1.11334 1.32683i
9393 0.0603074 + 0.342020i 0.0603074 + 0.342020i
9494 0 0
9595 0 0
9696 0 0
9797 1.17365 0.984808i 1.17365 0.984808i 0.173648 0.984808i 0.444444π-0.444444\pi
1.00000 00
9898 0 0
9999 0 0
100100 −0.266044 0.460802i −0.266044 0.460802i
101101 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
102102 0 0
103103 −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
104104 0 0
105105 0 0
106106 0 0
107107 0 0 1.00000 00
−1.00000 π\pi
108108 −0.173648 + 0.984808i −0.173648 + 0.984808i
109109 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
110110 0 0
111111 −1.43969 1.20805i −1.43969 1.20805i
112112 0 0
113113 −0.826352 + 0.984808i −0.826352 + 0.984808i 0.173648 + 0.984808i 0.444444π0.444444\pi
−1.00000 π\pi
114114 0 0
115115 1.11334 + 0.405223i 1.11334 + 0.405223i
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 0 0
122122 0 0
123123 0 0
124124 −0.266044 + 0.223238i −0.266044 + 0.223238i
125125 0.907604 + 0.524005i 0.907604 + 0.524005i
126126 0 0
127127 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
128128 0 0
129129 0 0
130130 0 0
131131 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
132132 0 0
133133 0 0
134134 0 0
135135 −0.233956 0.642788i −0.233956 0.642788i
136136 0 0
137137 −1.93969 + 0.342020i −1.93969 + 0.342020i −0.939693 + 0.342020i 0.888889π0.888889\pi
−1.00000 π\pi
138138 0 0
139139 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
140140 0 0
141141 −1.11334 0.642788i −1.11334 0.642788i
142142 0 0
143143 0 0
144144 −0.939693 + 0.342020i −0.939693 + 0.342020i
145145 0 0
146146 0 0
147147 0.766044 0.642788i 0.766044 0.642788i
148148 0.326352 1.85083i 0.326352 1.85083i
149149 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
150150 0 0
151151 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
152152 0 0
153153 0 0
154154 0 0
155155 0.0812519 0.223238i 0.0812519 0.223238i
156156 0 0
157157 −0.266044 0.223238i −0.266044 0.223238i 0.500000 0.866025i 0.333333π-0.333333\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
158158 0 0
159159 −1.93969 0.342020i −1.93969 0.342020i
160160 0 0
161161 0 0
162162 0 0
163163 1.53209 1.53209 0.766044 0.642788i 0.222222π-0.222222\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
164164 0 0
165165 0 0
166166 0 0
167167 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
168168 0 0
169169 0.939693 + 0.342020i 0.939693 + 0.342020i
170170 0 0
171171 0 0
172172 0 0
173173 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
174174 0 0
175175 0 0
176176 0 0
177177 1.26604 + 1.50881i 1.26604 + 1.50881i
178178 0 0
179179 1.70574 + 0.984808i 1.70574 + 0.984808i 0.939693 + 0.342020i 0.111111π0.111111\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
180180 0.439693 0.524005i 0.439693 0.524005i
181181 0.939693 + 1.62760i 0.939693 + 1.62760i 0.766044 + 0.642788i 0.222222π0.222222\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
182182 0 0
183183 0 0
184184 0 0
185185 0.439693 + 1.20805i 0.439693 + 1.20805i
186186 0 0
187187 0 0
188188 1.28558i 1.28558i
189189 0 0
190190 0 0
191191 −1.26604 + 0.223238i −1.26604 + 0.223238i −0.766044 0.642788i 0.777778π-0.777778\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
192192 −0.766044 0.642788i −0.766044 0.642788i
193193 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
194194 0 0
195195 0 0
196196 0.939693 + 0.342020i 0.939693 + 0.342020i
197197 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
198198 0 0
199199 0.766044 1.32683i 0.766044 1.32683i −0.173648 0.984808i 0.555556π-0.555556\pi
0.939693 0.342020i 0.111111π-0.111111\pi
200200 0 0
201201 −0.326352 0.118782i −0.326352 0.118782i
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 1.73205i 1.73205i
208208 0 0
209209 0 0
210210 0 0
211211 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
212212 −0.673648 1.85083i −0.673648 1.85083i
213213 −0.826352 + 0.984808i −0.826352 + 0.984808i
214214 0 0
215215 0 0
216216 0 0
217217 0 0
218218 0 0
219219 0 0
220220 0 0
221221 0 0
222222 0 0
223223 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
224224 0 0
225225 0.0923963 0.524005i 0.0923963 0.524005i
226226 0 0
227227 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
228228 0 0
229229 0.173648 0.984808i 0.173648 0.984808i −0.766044 0.642788i 0.777778π-0.777778\pi
0.939693 0.342020i 0.111111π-0.111111\pi
230230 0 0
231231 0 0
232232 0 0
233233 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
234234 0 0
235235 0.439693 + 0.761570i 0.439693 + 0.761570i
236236 −0.673648 + 1.85083i −0.673648 + 1.85083i
237237 0 0
238238 0 0
239239 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
240240 0.673648 + 0.118782i 0.673648 + 0.118782i
241241 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
242242 0 0
243243 −0.766044 + 0.642788i −0.766044 + 0.642788i
244244 0 0
245245 −0.673648 + 0.118782i −0.673648 + 0.118782i
246246 0 0
247247 0 0
248248 0 0
249249 0 0
250250 0 0
251251 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 0.173648 0.984808i 0.173648 0.984808i
257257 −1.70574 0.300767i −1.70574 0.300767i −0.766044 0.642788i 0.777778π-0.777778\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 0 0
263263 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
264264 0 0
265265 1.03209 + 0.866025i 1.03209 + 0.866025i
266266 0 0
267267 −0.592396 1.62760i −0.592396 1.62760i
268268 −0.0603074 0.342020i −0.0603074 0.342020i
269269 1.28558i 1.28558i 0.766044 + 0.642788i 0.222222π0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
270270 0 0
271271 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 1.50000 0.866025i 1.50000 0.866025i
277277 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
278278 0 0
279279 −0.347296 −0.347296
280280 0 0
281281 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
282282 0 0
283283 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
284284 −1.26604 0.223238i −1.26604 0.223238i
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 −0.500000 0.866025i −0.500000 0.866025i
290290 0 0
291291 0.766044 + 1.32683i 0.766044 + 1.32683i
292292 0 0
293293 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
294294 0 0
295295 −0.233956 1.32683i −0.233956 1.32683i
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 0.500000 0.181985i 0.500000 0.181985i
301301 0 0
302302 0 0
303303 0 0
304304 0 0
305305 0 0
306306 0 0
307307 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
308308 0 0
309309 1.43969 1.20805i 1.43969 1.20805i
310310 0 0
311311 1.93969 + 0.342020i 1.93969 + 0.342020i 1.00000 00
0.939693 + 0.342020i 0.111111π0.111111\pi
312312 0 0
313313 0.766044 0.642788i 0.766044 0.642788i −0.173648 0.984808i 0.555556π-0.555556\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
314314 0 0
315315 0 0
316316 0 0
317317 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
318318 0 0
319319 0 0
320320 0.233956 + 0.642788i 0.233956 + 0.642788i
321321 0 0
322322 0 0
323323 0 0
324324 −0.939693 0.342020i −0.939693 0.342020i
325325 0 0
326326 0 0
327327 0 0
328328 0 0
329329 0 0
330330 0 0
331331 −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
332332 0 0
333333 1.43969 1.20805i 1.43969 1.20805i
334334 0 0
335335 0.152704 + 0.181985i 0.152704 + 0.181985i
336336 0 0
337337 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
338338 0 0
339339 −0.826352 0.984808i −0.826352 0.984808i
340340 0 0
341341 0 0
342342 0 0
343343 0 0
344344 0 0
345345 −0.592396 + 1.02606i −0.592396 + 1.02606i
346346 0 0
347347 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
348348 0 0
349349 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
350350 0 0
351351 0 0
352352 0 0
353353 1.70574 0.300767i 1.70574 0.300767i 0.766044 0.642788i 0.222222π-0.222222\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
354354 0 0
355355 0.826352 0.300767i 0.826352 0.300767i
356356 1.11334 1.32683i 1.11334 1.32683i
357357 0 0
358358 0 0
359359 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
360360 0 0
361361 0.500000 0.866025i 0.500000 0.866025i
362362 0 0
363363 0 0
364364 0 0
365365 0 0
366366 0 0
367367 1.17365 0.984808i 1.17365 0.984808i 0.173648 0.984808i 0.444444π-0.444444\pi
1.00000 00
368368 1.50000 + 0.866025i 1.50000 + 0.866025i
369369 0 0
370370 0 0
371371 0 0
372372 −0.173648 0.300767i −0.173648 0.300767i
373373 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
374374 0 0
375375 −0.673648 + 0.802823i −0.673648 + 0.802823i
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 1.26604 1.50881i 1.26604 1.50881i 0.500000 0.866025i 0.333333π-0.333333\pi
0.766044 0.642788i 0.222222π-0.222222\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 −0.766044 + 1.32683i −0.766044 + 1.32683i
389389 0.826352 + 0.984808i 0.826352 + 0.984808i 1.00000 00
−0.173648 + 0.984808i 0.555556π0.555556\pi
390390 0 0
391391 0 0
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 −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
398398 0 0
399399 0 0
400400 0.407604 + 0.342020i 0.407604 + 0.342020i
401401 −0.233956 0.642788i −0.233956 0.642788i 0.766044 0.642788i 0.222222π-0.222222\pi
−1.00000 π\pi
402402 0 0
403403 0 0
404404 0 0
405405 0.673648 0.118782i 0.673648 0.118782i
406406 0 0
407407 0 0
408408 0 0
409409 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
410410 0 0
411411 1.96962i 1.96962i
412412 1.76604 + 0.642788i 1.76604 + 0.642788i
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 0 0
418418 0 0
419419 −0.673648 0.118782i −0.673648 0.118782i −0.173648 0.984808i 0.555556π-0.555556\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
420420 0 0
421421 1.43969 1.20805i 1.43969 1.20805i 0.500000 0.866025i 0.333333π-0.333333\pi
0.939693 0.342020i 0.111111π-0.111111\pi
422422 0 0
423423 0.826352 0.984808i 0.826352 0.984808i
424424 0 0
425425 0 0
426426 0 0
427427 0 0
428428 0 0
429429 0 0
430430 0 0
431431 0 0 1.00000 00
−1.00000 π\pi
432432 −0.173648 0.984808i −0.173648 0.984808i
433433 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
434434 0 0
435435 0 0
436436 0 0
437437 0 0
438438 0 0
439439 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
440440 0 0
441441 0.500000 + 0.866025i 0.500000 + 0.866025i
442442 0 0
443443 0.439693 + 0.524005i 0.439693 + 0.524005i 0.939693 0.342020i 0.111111π-0.111111\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
444444 1.76604 + 0.642788i 1.76604 + 0.642788i
445445 −0.205737 + 1.16679i −0.205737 + 1.16679i
446446 0 0
447447 0 0
448448 0 0
449449 −0.592396 0.342020i −0.592396 0.342020i 0.173648 0.984808i 0.444444π-0.444444\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
450450 0 0
451451 0 0
452452 0.439693 1.20805i 0.439693 1.20805i
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
458458 0 0
459459 0 0
460460 −1.18479 −1.18479
461461 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
462462 0 0
463463 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
464464 0 0
465465 0.205737 + 0.118782i 0.205737 + 0.118782i
466466 0 0
467467 −1.11334 + 0.642788i −1.11334 + 0.642788i −0.939693 0.342020i 0.888889π-0.888889\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
468468 0 0
469469 0 0
470470 0 0
471471 0.266044 0.223238i 0.266044 0.223238i
472472 0 0
473473 0 0
474474 0 0
475475 0 0
476476 0 0
477477 0.673648 1.85083i 0.673648 1.85083i
478478 0 0
479479 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
480480 0 0
481481 0 0
482482 0 0
483483 0 0
484484 0 0
485485 1.04801i 1.04801i
486486 0 0
487487 1.87939 1.87939 0.939693 0.342020i 0.111111π-0.111111\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
488488 0 0
489489 −0.266044 + 1.50881i −0.266044 + 1.50881i
490490 0 0
491491 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 0.173648 0.300767i 0.173648 0.300767i
497497 0 0
498498 0 0
499499 0.326352 1.85083i 0.326352 1.85083i −0.173648 0.984808i 0.555556π-0.555556\pi
0.500000 0.866025i 0.333333π-0.333333\pi
500500 −1.03209 0.181985i −1.03209 0.181985i
501501 0 0
502502 0 0
503503 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
504504 0 0
505505 0 0
506506 0 0
507507 −0.500000 + 0.866025i −0.500000 + 0.866025i
508508 0 0
509509 −0.592396 1.62760i −0.592396 1.62760i −0.766044 0.642788i 0.777778π-0.777778\pi
0.173648 0.984808i 0.444444π-0.444444\pi
510510 0 0
511511 0 0
512512 0 0
513513 0 0
514514 0 0
515515 −1.26604 + 0.223238i −1.26604 + 0.223238i
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 0.592396 0.342020i 0.592396 0.342020i −0.173648 0.984808i 0.555556π-0.555556\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
522522 0 0
523523 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
524524 0 0
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 −1.53209 + 1.28558i −1.53209 + 1.28558i
530530 0 0
531531 −1.70574 + 0.984808i −1.70574 + 0.984808i
532532 0 0
533533 0 0
534534 0 0
535535 0 0
536536 0 0
537537 −1.26604 + 1.50881i −1.26604 + 1.50881i
538538 0 0
539539 0 0
540540 0.439693 + 0.524005i 0.439693 + 0.524005i
541541 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
542542 0 0
543543 −1.76604 + 0.642788i −1.76604 + 0.642788i
544544 0 0
545545 0 0
546546 0 0
547547 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
548548 1.70574 0.984808i 1.70574 0.984808i
549549 0 0
550550 0 0
551551 0 0
552552 0 0
553553 0 0
554554 0 0
555555 −1.26604 + 0.223238i −1.26604 + 0.223238i
556556 0 0
557557 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 0 0
563563 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
564564 1.26604 + 0.223238i 1.26604 + 0.223238i
565565 0.152704 + 0.866025i 0.152704 + 0.866025i
566566 0 0
567567 0 0
568568 0 0
569569 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
570570 0 0
571571 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
572572 0 0
573573 1.28558i 1.28558i
574574 0 0
575575 −0.798133 + 0.460802i −0.798133 + 0.460802i
576576 0.766044 0.642788i 0.766044 0.642788i
577577 −0.939693 + 1.62760i −0.939693 + 1.62760i −0.173648 + 0.984808i 0.555556π0.555556\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
578578 0 0
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 −0.233956 + 0.642788i −0.233956 + 0.642788i 0.766044 + 0.642788i 0.222222π0.222222\pi
−1.00000 π\pi
588588 −0.500000 + 0.866025i −0.500000 + 0.866025i
589589 0 0
590590 0 0
591591 0 0
592592 0.326352 + 1.85083i 0.326352 + 1.85083i
593593 0 0 1.00000 00
−1.00000 π\pi
594594 0 0
595595 0 0
596596 0 0
597597 1.17365 + 0.984808i 1.17365 + 0.984808i
598598 0 0
599599 1.11334 1.32683i 1.11334 1.32683i 0.173648 0.984808i 0.444444π-0.444444\pi
0.939693 0.342020i 0.111111π-0.111111\pi
600600 0 0
601601 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
602602 0 0
603603 0.173648 0.300767i 0.173648 0.300767i
604604 0 0
605605 0 0
606606 0 0
607607 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 0 0
613613 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
614614 0 0
615615 0 0
616616 0 0
617617 0.673648 + 1.85083i 0.673648 + 1.85083i 0.500000 + 0.866025i 0.333333π0.333333\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
618618 0 0
619619 −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
620620 0.237565i 0.237565i
621621 1.70574 + 0.300767i 1.70574 + 0.300767i
622622 0 0
623623 0 0
624624 0 0
625625 0.173648 0.0632028i 0.173648 0.0632028i
626626 0 0
627627 0 0
628628 0.326352 + 0.118782i 0.326352 + 0.118782i
629629 0 0
630630 0 0
631631 0.173648 0.300767i 0.173648 0.300767i −0.766044 0.642788i 0.777778π-0.777778\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
632632 0 0
633633 0 0
634634 0 0
635635 0 0
636636 1.93969 0.342020i 1.93969 0.342020i
637637 0 0
638638 0 0
639639 −0.826352 0.984808i −0.826352 0.984808i
640640 0 0
641641 0.592396 1.62760i 0.592396 1.62760i −0.173648 0.984808i 0.555556π-0.555556\pi
0.766044 0.642788i 0.222222π-0.222222\pi
642642 0 0
643643 −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
644644 0 0
645645 0 0
646646 0 0
647647 0 0 1.00000 00
−1.00000 π\pi
648648 0 0
649649 0 0
650650 0 0
651651 0 0
652652 −1.43969 + 0.524005i −1.43969 + 0.524005i
653653 0.439693 0.524005i 0.439693 0.524005i −0.500000 0.866025i 0.666667π-0.666667\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
654654 0 0
655655 0 0
656656 0 0
657657 0 0
658658 0 0
659659 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
660660 0 0
661661 −0.266044 + 1.50881i −0.266044 + 1.50881i 0.500000 + 0.866025i 0.333333π0.333333\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 −0.500000 + 0.866025i −0.500000 + 0.866025i
670670 0 0
671671 0 0
672672 0 0
673673 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
674674 0 0
675675 0.500000 + 0.181985i 0.500000 + 0.181985i
676676 −1.00000 −1.00000
677677 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
678678 0 0
679679 0 0
680680 0 0
681681 0 0
682682 0 0
683683 −1.11334 + 0.642788i −1.11334 + 0.642788i −0.939693 0.342020i 0.888889π-0.888889\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
684684 0 0
685685 −0.673648 + 1.16679i −0.673648 + 1.16679i
686686 0 0
687687 0.939693 + 0.342020i 0.939693 + 0.342020i
688688 0 0
689689 0 0
690690 0 0
691691 −1.43969 + 1.20805i −1.43969 + 1.20805i −0.500000 + 0.866025i 0.666667π0.666667\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 0 0
698698 0 0
699699 0 0
700700 0 0
701701 0 0 1.00000 00
−1.00000 π\pi
702702 0 0
703703 0 0
704704 0 0
705705 −0.826352 + 0.300767i −0.826352 + 0.300767i
706706 0 0
707707 0 0
708708 −1.70574 0.984808i −1.70574 0.984808i
709709 −1.76604 0.642788i −1.76604 0.642788i −0.766044 0.642788i 0.777778π-0.777778\pi
−1.00000 π\pi
710710 0 0
711711 0 0
712712 0 0
713713 0.386659 + 0.460802i 0.386659 + 0.460802i
714714 0 0
715715 0 0
716716 −1.93969 0.342020i −1.93969 0.342020i
717717 0 0
718718 0 0
719719 1.11334 + 0.642788i 1.11334 + 0.642788i 0.939693 0.342020i 0.111111π-0.111111\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
720720 −0.233956 + 0.642788i −0.233956 + 0.642788i
721721 0 0
722722 0 0
723723 0 0
724724 −1.43969 1.20805i −1.43969 1.20805i
725725 0 0
726726 0 0
727727 −0.266044 1.50881i −0.266044 1.50881i −0.766044 0.642788i 0.777778π-0.777778\pi
0.500000 0.866025i 0.333333π-0.333333\pi
728728 0 0
729729 −0.500000 0.866025i −0.500000 0.866025i
730730 0 0
731731 0 0
732732 0 0
733733 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
734734 0 0
735735 0.684040i 0.684040i
736736 0 0
737737 0 0
738738 0 0
739739 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
740740 −0.826352 0.984808i −0.826352 0.984808i
741741 0 0
742742 0 0
743743 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
744744 0 0
745745 0 0
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 −1.17365 0.984808i −1.17365 0.984808i −0.173648 0.984808i 0.555556π-0.555556\pi
−1.00000 π\pi
752752 0.439693 + 1.20805i 0.439693 + 1.20805i
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 −0.347296 −0.347296 −0.173648 0.984808i 0.555556π-0.555556\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
758758 0 0
759759 0 0
760760 0 0
761761 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
762762 0 0
763763 0 0
764764 1.11334 0.642788i 1.11334 0.642788i
765765 0 0
766766 0 0
767767 0 0
768768 0.939693 + 0.342020i 0.939693 + 0.342020i
769769 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
770770 0 0
771771 0.592396 1.62760i 0.592396 1.62760i
772772 0 0
773773 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
774774 0 0
775775 0.0923963 + 0.160035i 0.0923963 + 0.160035i
776776 0 0
777777 0 0
778778 0 0
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 −1.00000 −1.00000
785785 −0.233956 + 0.0412527i −0.233956 + 0.0412527i
786786 0 0
787787 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 0 0
794794 0 0
795795 −1.03209 + 0.866025i −1.03209 + 0.866025i
796796 −0.266044 + 1.50881i −0.266044 + 1.50881i
797797 −0.673648 0.118782i −0.673648 0.118782i −0.173648 0.984808i 0.555556π-0.555556\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
798798 0 0
799799 0 0
800800 0 0
801801 1.70574 0.300767i 1.70574 0.300767i
802802 0 0
803803 0 0
804804 0.347296 0.347296
805805 0 0
806806 0 0
807807 −1.26604 0.223238i −1.26604 0.223238i
808808 0 0
809809 0 0 1.00000 00
−1.00000 π\pi
810810 0 0
811811 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
812812 0 0
813813 0 0
814814 0 0
815815 0.673648 0.802823i 0.673648 0.802823i
816816 0 0
817817 0 0
818818 0 0
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 0
823823 −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i 0.222222π0.222222\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
824824 0 0
825825 0 0
826826 0 0
827827 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
828828 0.592396 + 1.62760i 0.592396 + 1.62760i
829829 −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
830830 0 0
831831 0 0
832832 0 0
833833 0 0
834834 0 0
835835 0 0
836836 0 0
837837 0.0603074 0.342020i 0.0603074 0.342020i
838838 0 0
839839 −1.70574 + 0.300767i −1.70574 + 0.300767i −0.939693 0.342020i 0.888889π-0.888889\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
840840 0 0
841841 −0.939693 + 0.342020i −0.939693 + 0.342020i
842842 0 0
843843 0 0
844844 0 0
845845 0.592396 0.342020i 0.592396 0.342020i
846846 0 0
847847 0 0
848848 1.26604 + 1.50881i 1.26604 + 1.50881i
849849 0 0
850850 0 0
851851 −3.20574 0.565258i −3.20574 0.565258i
852852 0.439693 1.20805i 0.439693 1.20805i
853853 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
854854 0 0
855855 0 0
856856 0 0
857857 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
858858 0 0
859859 1.17365 + 0.984808i 1.17365 + 0.984808i 1.00000 00
0.173648 + 0.984808i 0.444444π0.444444\pi
860860 0 0
861861 0 0
862862 0 0
863863 1.73205i 1.73205i −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 0.866025i 0.333333π-0.333333\pi
864864 0 0
865865 0 0
866866 0 0
867867 0.939693 0.342020i 0.939693 0.342020i
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0 0
873873 −1.43969 + 0.524005i −1.43969 + 0.524005i
874874 0 0
875875 0 0
876876 0 0
877877 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
878878 0 0
879879 0 0
880880 0 0
881881 −1.11334 0.642788i −1.11334 0.642788i −0.173648 0.984808i 0.555556π-0.555556\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
882882 0 0
883883 0.766044 + 1.32683i 0.766044 + 1.32683i 0.939693 + 0.342020i 0.111111π0.111111\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
884884 0 0
885885 1.34730 1.34730
886886 0 0
887887 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
888888 0 0
889889 0 0
890890 0 0
891891 0 0
892892 −1.00000 −1.00000
893893 0 0
894894 0 0
895895 1.26604 0.460802i 1.26604 0.460802i
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 0.0923963 + 0.524005i 0.0923963 + 0.524005i
901901 0 0
902902 0 0
903903 0 0
904904 0 0
905905 1.26604 + 0.223238i 1.26604 + 0.223238i
906906 0 0
907907 −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
908908 0 0
909909 0 0
910910 0 0
911911 0.233956 0.642788i 0.233956 0.642788i −0.766044 0.642788i 0.777778π-0.777778\pi
1.00000 00
912912 0 0
913913 0 0
914914 0 0
915915 0 0
916916 0.173648 + 0.984808i 0.173648 + 0.984808i
917917 0 0
918918 0 0
919919 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
920920 0 0
921921 0 0
922922 0 0
923923 0 0
924924 0 0
925925 −0.939693 0.342020i −0.939693 0.342020i
926926 0 0
927927 0.939693 + 1.62760i 0.939693 + 1.62760i
928928 0 0
929929 −1.26604 1.50881i −1.26604 1.50881i −0.766044 0.642788i 0.777778π-0.777778\pi
−0.500000 0.866025i 0.666667π-0.666667\pi
930930 0 0
931931 0 0
932932 0 0
933933 −0.673648 + 1.85083i −0.673648 + 1.85083i
934934 0 0
935935 0 0
936936 0 0
937937 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
938938 0 0
939939 0.500000 + 0.866025i 0.500000 + 0.866025i
940940 −0.673648 0.565258i −0.673648 0.565258i
941941 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
942942 0 0
943943 0 0
944944 1.96962i 1.96962i
945945 0 0
946946 0 0
947947 1.93969 0.342020i 1.93969 0.342020i 0.939693 0.342020i 0.111111π-0.111111\pi
1.00000 00
948948 0 0
949949 0 0
950950 0 0
951951 0 0
952952 0 0
953953 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
954954 0 0
955955 −0.439693 + 0.761570i −0.439693 + 0.761570i
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 −0.673648 + 0.118782i −0.673648 + 0.118782i
961961 −0.673648 + 0.565258i −0.673648 + 0.565258i
962962 0 0
963963 0 0
964964 0 0
965965 0 0
966966 0 0
967967 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
968968 0 0
969969 0 0
970970 0 0
971971 1.73205i 1.73205i 0.500000 + 0.866025i 0.333333π0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
972972 0.500000 0.866025i 0.500000 0.866025i
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
978978 0 0
979979 0 0
980980 0.592396 0.342020i 0.592396 0.342020i
981981 0 0
982982 0 0
983983 1.26604 + 1.50881i 1.26604 + 1.50881i 0.766044 + 0.642788i 0.222222π0.222222\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i 0.333333π-0.333333\pi
−1.00000 π\pi
992992 0 0
993993 0.766044 1.32683i 0.766044 1.32683i
994994 0 0
995995 −0.358441 0.984808i −0.358441 0.984808i
996996 0 0
997997 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
998998 0 0
999999 0.939693 + 1.62760i 0.939693 + 1.62760i
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 3267.1.q.a.122.1 6
11.2 odd 10 3267.1.be.a.3227.1 24
11.3 even 5 3267.1.be.a.2066.1 24
11.4 even 5 3267.1.be.a.3173.1 24
11.5 even 5 3267.1.be.a.608.1 24
11.6 odd 10 3267.1.be.a.608.1 24
11.7 odd 10 3267.1.be.a.3173.1 24
11.8 odd 10 3267.1.be.a.2066.1 24
11.9 even 5 3267.1.be.a.3227.1 24
11.10 odd 2 CM 3267.1.q.a.122.1 6
27.2 odd 18 inner 3267.1.q.a.3026.1 yes 6
297.2 even 90 3267.1.be.a.2864.1 24
297.29 even 90 3267.1.be.a.2810.1 24
297.83 even 90 3267.1.be.a.245.1 24
297.137 odd 90 3267.1.be.a.245.1 24
297.164 even 18 inner 3267.1.q.a.3026.1 yes 6
297.191 odd 90 3267.1.be.a.2810.1 24
297.218 odd 90 3267.1.be.a.2864.1 24
297.245 odd 90 3267.1.be.a.1703.1 24
297.272 even 90 3267.1.be.a.1703.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3267.1.q.a.122.1 6 1.1 even 1 trivial
3267.1.q.a.122.1 6 11.10 odd 2 CM
3267.1.q.a.3026.1 yes 6 27.2 odd 18 inner
3267.1.q.a.3026.1 yes 6 297.164 even 18 inner
3267.1.be.a.245.1 24 297.83 even 90
3267.1.be.a.245.1 24 297.137 odd 90
3267.1.be.a.608.1 24 11.5 even 5
3267.1.be.a.608.1 24 11.6 odd 10
3267.1.be.a.1703.1 24 297.245 odd 90
3267.1.be.a.1703.1 24 297.272 even 90
3267.1.be.a.2066.1 24 11.3 even 5
3267.1.be.a.2066.1 24 11.8 odd 10
3267.1.be.a.2810.1 24 297.29 even 90
3267.1.be.a.2810.1 24 297.191 odd 90
3267.1.be.a.2864.1 24 297.2 even 90
3267.1.be.a.2864.1 24 297.218 odd 90
3267.1.be.a.3173.1 24 11.4 even 5
3267.1.be.a.3173.1 24 11.7 odd 10
3267.1.be.a.3227.1 24 11.2 odd 10
3267.1.be.a.3227.1 24 11.9 even 5