Properties

Label 3267.1.q.a.848.1
Level 32673267
Weight 11
Character 3267.848
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 848.1
Root 0.939693+0.342020i0.939693 + 0.342020i of defining polynomial
Character χ\chi == 3267.848
Dual form 3267.1.q.a.2300.1

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)q3+(0.173648+0.984808i)q4+(0.673648+1.85083i)q5+(0.1736480.984808i)q9+(0.7660440.642788i)q12+(0.6736481.85083i)q15+(0.939693+0.342020i)q16+(1.939690.342020i)q20+(1.70574+0.300767i)q23+(2.205741.85083i)q25+(0.500000+0.866025i)q27+(0.2660441.50881i)q31+1.00000q36+(0.173648+0.300767i)q37+(1.70574+0.984808i)q45+(0.673648+0.118782i)q47+(0.5000000.866025i)q48+(0.939693+0.342020i)q49+1.28558iq53+(0.439693+1.20805i)q59+(1.705740.984808i)q60+(0.5000000.866025i)q64+(1.17365+0.984808i)q67+(1.113341.32683i)q69+(0.5923960.342020i)q71+2.87939q751.96962iq80+(0.9396930.342020i)q81+(1.500000.866025i)q89+(0.5923961.62760i)q92+(1.17365+0.984808i)q93+(1.766040.642788i)q97+O(q100)q+(-0.766044 + 0.642788i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.673648 + 1.85083i) q^{5} +(0.173648 - 0.984808i) q^{9} +(-0.766044 - 0.642788i) q^{12} +(-0.673648 - 1.85083i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-1.93969 - 0.342020i) q^{20} +(-1.70574 + 0.300767i) q^{23} +(-2.20574 - 1.85083i) q^{25} +(0.500000 + 0.866025i) q^{27} +(-0.266044 - 1.50881i) q^{31} +1.00000 q^{36} +(0.173648 + 0.300767i) q^{37} +(1.70574 + 0.984808i) q^{45} +(0.673648 + 0.118782i) q^{47} +(0.500000 - 0.866025i) q^{48} +(0.939693 + 0.342020i) q^{49} +1.28558i q^{53} +(-0.439693 + 1.20805i) q^{59} +(1.70574 - 0.984808i) q^{60} +(-0.500000 - 0.866025i) q^{64} +(-1.17365 + 0.984808i) q^{67} +(1.11334 - 1.32683i) q^{69} +(0.592396 - 0.342020i) q^{71} +2.87939 q^{75} -1.96962i q^{80} +(-0.939693 - 0.342020i) q^{81} +(-1.50000 - 0.866025i) q^{89} +(-0.592396 - 1.62760i) q^{92} +(1.17365 + 0.984808i) q^{93} +(1.76604 - 0.642788i) 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(1318)e\left(\frac{13}{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 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
33 −0.766044 + 0.642788i −0.766044 + 0.642788i
44 0.173648 + 0.984808i 0.173648 + 0.984808i
55 −0.673648 + 1.85083i −0.673648 + 1.85083i −0.173648 + 0.984808i 0.555556π0.555556\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
66 0 0
77 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
88 0 0
99 0.173648 0.984808i 0.173648 0.984808i
1010 0 0
1111 0 0
1212 −0.766044 0.642788i −0.766044 0.642788i
1313 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
1414 0 0
1515 −0.673648 1.85083i −0.673648 1.85083i
1616 −0.939693 + 0.342020i −0.939693 + 0.342020i
1717 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
1818 0 0
1919 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
2020 −1.93969 0.342020i −1.93969 0.342020i
2121 0 0
2222 0 0
2323 −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
2424 0 0
2525 −2.20574 1.85083i −2.20574 1.85083i
2626 0 0
2727 0.500000 + 0.866025i 0.500000 + 0.866025i
2828 0 0
2929 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
3030 0 0
3131 −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
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 1.00000 1.00000
3737 0.173648 + 0.300767i 0.173648 + 0.300767i 0.939693 0.342020i 0.111111π-0.111111\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
3838 0 0
3939 0 0
4040 0 0
4141 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
4242 0 0
4343 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
4444 0 0
4545 1.70574 + 0.984808i 1.70574 + 0.984808i
4646 0 0
4747 0.673648 + 0.118782i 0.673648 + 0.118782i 0.500000 0.866025i 0.333333π-0.333333\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
4848 0.500000 0.866025i 0.500000 0.866025i
4949 0.939693 + 0.342020i 0.939693 + 0.342020i
5050 0 0
5151 0 0
5252 0 0
5353 1.28558i 1.28558i 0.766044 + 0.642788i 0.222222π0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 0 0
5959 −0.439693 + 1.20805i −0.439693 + 1.20805i 0.500000 + 0.866025i 0.333333π0.333333\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
6060 1.70574 0.984808i 1.70574 0.984808i
6161 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
6262 0 0
6363 0 0
6464 −0.500000 0.866025i −0.500000 0.866025i
6565 0 0
6666 0 0
6767 −1.17365 + 0.984808i −1.17365 + 0.984808i −0.173648 + 0.984808i 0.555556π0.555556\pi
−1.00000 π\pi
6868 0 0
6969 1.11334 1.32683i 1.11334 1.32683i
7070 0 0
7171 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
7272 0 0
7373 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
7474 0 0
7575 2.87939 2.87939
7676 0 0
7777 0 0
7878 0 0
7979 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
8080 1.96962i 1.96962i
8181 −0.939693 0.342020i −0.939693 0.342020i
8282 0 0
8383 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\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 0.666667π-0.666667\pi
−1.00000 π\pi
9090 0 0
9191 0 0
9292 −0.592396 1.62760i −0.592396 1.62760i
9393 1.17365 + 0.984808i 1.17365 + 0.984808i
9494 0 0
9595 0 0
9696 0 0
9797 1.76604 0.642788i 1.76604 0.642788i 0.766044 0.642788i 0.222222π-0.222222\pi
1.00000 00
9898 0 0
9999 0 0
100100 1.43969 2.49362i 1.43969 2.49362i
101101 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
102102 0 0
103103 −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
104104 0 0
105105 0 0
106106 0 0
107107 0 0 1.00000 00
−1.00000 π\pi
108108 −0.766044 + 0.642788i −0.766044 + 0.642788i
109109 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
110110 0 0
111111 −0.326352 0.118782i −0.326352 0.118782i
112112 0 0
113113 −0.233956 + 0.642788i −0.233956 + 0.642788i 0.766044 + 0.642788i 0.222222π0.222222\pi
−1.00000 π\pi
114114 0 0
115115 0.592396 3.35965i 0.592396 3.35965i
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 1.43969 0.524005i 1.43969 0.524005i
125125 3.20574 1.85083i 3.20574 1.85083i
126126 0 0
127127 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
128128 0 0
129129 0 0
130130 0 0
131131 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
132132 0 0
133133 0 0
134134 0 0
135135 −1.93969 + 0.342020i −1.93969 + 0.342020i
136136 0 0
137137 −0.826352 + 0.984808i −0.826352 + 0.984808i 0.173648 + 0.984808i 0.444444π0.444444\pi
−1.00000 π\pi
138138 0 0
139139 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
140140 0 0
141141 −0.592396 + 0.342020i −0.592396 + 0.342020i
142142 0 0
143143 0 0
144144 0.173648 + 0.984808i 0.173648 + 0.984808i
145145 0 0
146146 0 0
147147 −0.939693 + 0.342020i −0.939693 + 0.342020i
148148 −0.266044 + 0.223238i −0.266044 + 0.223238i
149149 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
150150 0 0
151151 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
152152 0 0
153153 0 0
154154 0 0
155155 2.97178 + 0.524005i 2.97178 + 0.524005i
156156 0 0
157157 1.43969 + 0.524005i 1.43969 + 0.524005i 0.939693 0.342020i 0.111111π-0.111111\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
158158 0 0
159159 −0.826352 0.984808i −0.826352 0.984808i
160160 0 0
161161 0 0
162162 0 0
163163 −1.87939 −1.87939 −0.939693 0.342020i 0.888889π-0.888889\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
164164 0 0
165165 0 0
166166 0 0
167167 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
168168 0 0
169169 −0.173648 + 0.984808i −0.173648 + 0.984808i
170170 0 0
171171 0 0
172172 0 0
173173 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
174174 0 0
175175 0 0
176176 0 0
177177 −0.439693 1.20805i −0.439693 1.20805i
178178 0 0
179179 −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
180180 −0.673648 + 1.85083i −0.673648 + 1.85083i
181181 −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
182182 0 0
183183 0 0
184184 0 0
185185 −0.673648 + 0.118782i −0.673648 + 0.118782i
186186 0 0
187187 0 0
188188 0.684040i 0.684040i
189189 0 0
190190 0 0
191191 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
192192 0.939693 + 0.342020i 0.939693 + 0.342020i
193193 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
194194 0 0
195195 0 0
196196 −0.173648 + 0.984808i −0.173648 + 0.984808i
197197 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
198198 0 0
199199 −0.939693 1.62760i −0.939693 1.62760i −0.766044 0.642788i 0.777778π-0.777778\pi
−0.173648 0.984808i 0.555556π-0.555556\pi
200200 0 0
201201 0.266044 1.50881i 0.266044 1.50881i
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 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
212212 −1.26604 + 0.223238i −1.26604 + 0.223238i
213213 −0.233956 + 0.642788i −0.233956 + 0.642788i
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 −0.173648 + 0.984808i −0.173648 + 0.984808i 0.766044 + 0.642788i 0.222222π0.222222\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
224224 0 0
225225 −2.20574 + 1.85083i −2.20574 + 1.85083i
226226 0 0
227227 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
228228 0 0
229229 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
230230 0 0
231231 0 0
232232 0 0
233233 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
234234 0 0
235235 −0.673648 + 1.16679i −0.673648 + 1.16679i
236236 −1.26604 0.223238i −1.26604 0.223238i
237237 0 0
238238 0 0
239239 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
240240 1.26604 + 1.50881i 1.26604 + 1.50881i
241241 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
242242 0 0
243243 0.939693 0.342020i 0.939693 0.342020i
244244 0 0
245245 −1.26604 + 1.50881i −1.26604 + 1.50881i
246246 0 0
247247 0 0
248248 0 0
249249 0 0
250250 0 0
251251 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 0.766044 0.642788i 0.766044 0.642788i
257257 1.11334 + 1.32683i 1.11334 + 1.32683i 0.939693 + 0.342020i 0.111111π0.111111\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 0 0
263263 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
264264 0 0
265265 −2.37939 0.866025i −2.37939 0.866025i
266266 0 0
267267 1.70574 0.300767i 1.70574 0.300767i
268268 −1.17365 0.984808i −1.17365 0.984808i
269269 0.684040i 0.684040i −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 0.342020i 0.111111π-0.111111\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 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
278278 0 0
279279 −1.53209 −1.53209
280280 0 0
281281 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
282282 0 0
283283 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
284284 0.439693 + 0.524005i 0.439693 + 0.524005i
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 −0.939693 + 1.62760i −0.939693 + 1.62760i
292292 0 0
293293 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
294294 0 0
295295 −1.93969 1.62760i −1.93969 1.62760i
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 0.500000 + 2.83564i 0.500000 + 2.83564i
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 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
308308 0 0
309309 0.326352 0.118782i 0.326352 0.118782i
310310 0 0
311311 0.826352 + 0.984808i 0.826352 + 0.984808i 1.00000 00
−0.173648 + 0.984808i 0.555556π0.555556\pi
312312 0 0
313313 −0.939693 + 0.342020i −0.939693 + 0.342020i −0.766044 0.642788i 0.777778π-0.777778\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
314314 0 0
315315 0 0
316316 0 0
317317 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
318318 0 0
319319 0 0
320320 1.93969 0.342020i 1.93969 0.342020i
321321 0 0
322322 0 0
323323 0 0
324324 0.173648 0.984808i 0.173648 0.984808i
325325 0 0
326326 0 0
327327 0 0
328328 0 0
329329 0 0
330330 0 0
331331 −0.326352 + 1.85083i −0.326352 + 1.85083i 0.173648 + 0.984808i 0.444444π0.444444\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
332332 0 0
333333 0.326352 0.118782i 0.326352 0.118782i
334334 0 0
335335 −1.03209 2.83564i −1.03209 2.83564i
336336 0 0
337337 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
338338 0 0
339339 −0.233956 0.642788i −0.233956 0.642788i
340340 0 0
341341 0 0
342342 0 0
343343 0 0
344344 0 0
345345 1.70574 + 2.95442i 1.70574 + 2.95442i
346346 0 0
347347 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
348348 0 0
349349 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
350350 0 0
351351 0 0
352352 0 0
353353 −1.11334 + 1.32683i −1.11334 + 1.32683i −0.173648 + 0.984808i 0.555556π0.555556\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
354354 0 0
355355 0.233956 + 1.32683i 0.233956 + 1.32683i
356356 0.592396 1.62760i 0.592396 1.62760i
357357 0 0
358358 0 0
359359 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\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 1.76604 0.642788i 1.76604 0.642788i 0.766044 0.642788i 0.222222π-0.222222\pi
1.00000 00
368368 1.50000 0.866025i 1.50000 0.866025i
369369 0 0
370370 0 0
371371 0 0
372372 −0.766044 + 1.32683i −0.766044 + 1.32683i
373373 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
374374 0 0
375375 −1.26604 + 3.47843i −1.26604 + 3.47843i
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 −0.439693 + 1.20805i −0.439693 + 1.20805i 0.500000 + 0.866025i 0.333333π0.333333\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 0.939693 + 1.62760i 0.939693 + 1.62760i
389389 0.233956 + 0.642788i 0.233956 + 0.642788i 1.00000 00
−0.766044 + 0.642788i 0.777778π0.777778\pi
390390 0 0
391391 0 0
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 −0.766044 + 1.32683i −0.766044 + 1.32683i 0.173648 + 0.984808i 0.444444π0.444444\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
398398 0 0
399399 0 0
400400 2.70574 + 0.984808i 2.70574 + 0.984808i
401401 −1.93969 + 0.342020i −1.93969 + 0.342020i −0.939693 + 0.342020i 0.888889π0.888889\pi
−1.00000 π\pi
402402 0 0
403403 0 0
404404 0 0
405405 1.26604 1.50881i 1.26604 1.50881i
406406 0 0
407407 0 0
408408 0 0
409409 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
410410 0 0
411411 1.28558i 1.28558i
412412 0.0603074 0.342020i 0.0603074 0.342020i
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 0 0
418418 0 0
419419 −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
420420 0 0
421421 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
422422 0 0
423423 0.233956 0.642788i 0.233956 0.642788i
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 −0.766044 0.642788i −0.766044 0.642788i
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 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
440440 0 0
441441 0.500000 0.866025i 0.500000 0.866025i
442442 0 0
443443 −0.673648 1.85083i −0.673648 1.85083i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.173648 0.984808i 0.555556π-0.555556\pi
444444 0.0603074 0.342020i 0.0603074 0.342020i
445445 2.61334 2.19285i 2.61334 2.19285i
446446 0 0
447447 0 0
448448 0 0
449449 1.70574 0.984808i 1.70574 0.984808i 0.766044 0.642788i 0.222222π-0.222222\pi
0.939693 0.342020i 0.111111π-0.111111\pi
450450 0 0
451451 0 0
452452 −0.673648 0.118782i −0.673648 0.118782i
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
458458 0 0
459459 0 0
460460 3.41147 3.41147
461461 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
462462 0 0
463463 −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
464464 0 0
465465 −2.61334 + 1.50881i −2.61334 + 1.50881i
466466 0 0
467467 −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
468468 0 0
469469 0 0
470470 0 0
471471 −1.43969 + 0.524005i −1.43969 + 0.524005i
472472 0 0
473473 0 0
474474 0 0
475475 0 0
476476 0 0
477477 1.26604 + 0.223238i 1.26604 + 0.223238i
478478 0 0
479479 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
480480 0 0
481481 0 0
482482 0 0
483483 0 0
484484 0 0
485485 3.70167i 3.70167i
486486 0 0
487487 −0.347296 −0.347296 −0.173648 0.984808i 0.555556π-0.555556\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
488488 0 0
489489 1.43969 1.20805i 1.43969 1.20805i
490490 0 0
491491 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 0.766044 + 1.32683i 0.766044 + 1.32683i
497497 0 0
498498 0 0
499499 −0.266044 + 0.223238i −0.266044 + 0.223238i −0.766044 0.642788i 0.777778π-0.777778\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
500500 2.37939 + 2.83564i 2.37939 + 2.83564i
501501 0 0
502502 0 0
503503 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
504504 0 0
505505 0 0
506506 0 0
507507 −0.500000 0.866025i −0.500000 0.866025i
508508 0 0
509509 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
510510 0 0
511511 0 0
512512 0 0
513513 0 0
514514 0 0
515515 0.439693 0.524005i 0.439693 0.524005i
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 −1.70574 0.984808i −1.70574 0.984808i −0.939693 0.342020i 0.888889π-0.888889\pi
−0.766044 0.642788i 0.777778π-0.777778\pi
522522 0 0
523523 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
524524 0 0
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 1.87939 0.684040i 1.87939 0.684040i
530530 0 0
531531 1.11334 + 0.642788i 1.11334 + 0.642788i
532532 0 0
533533 0 0
534534 0 0
535535 0 0
536536 0 0
537537 0.439693 1.20805i 0.439693 1.20805i
538538 0 0
539539 0 0
540540 −0.673648 1.85083i −0.673648 1.85083i
541541 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
542542 0 0
543543 −0.0603074 0.342020i −0.0603074 0.342020i
544544 0 0
545545 0 0
546546 0 0
547547 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
548548 −1.11334 0.642788i −1.11334 0.642788i
549549 0 0
550550 0 0
551551 0 0
552552 0 0
553553 0 0
554554 0 0
555555 0.439693 0.524005i 0.439693 0.524005i
556556 0 0
557557 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 0 0
563563 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
564564 −0.439693 0.524005i −0.439693 0.524005i
565565 −1.03209 0.866025i −1.03209 0.866025i
566566 0 0
567567 0 0
568568 0 0
569569 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
570570 0 0
571571 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
572572 0 0
573573 0.684040i 0.684040i
574574 0 0
575575 4.31908 + 2.49362i 4.31908 + 2.49362i
576576 −0.939693 + 0.342020i −0.939693 + 0.342020i
577577 0.173648 + 0.300767i 0.173648 + 0.300767i 0.939693 0.342020i 0.111111π-0.111111\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 −1.93969 0.342020i −1.93969 0.342020i −0.939693 0.342020i 0.888889π-0.888889\pi
−1.00000 π\pi
588588 −0.500000 0.866025i −0.500000 0.866025i
589589 0 0
590590 0 0
591591 0 0
592592 −0.266044 0.223238i −0.266044 0.223238i
593593 0 0 1.00000 00
−1.00000 π\pi
594594 0 0
595595 0 0
596596 0 0
597597 1.76604 + 0.642788i 1.76604 + 0.642788i
598598 0 0
599599 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
600600 0 0
601601 0 0 −0.984808 0.173648i 0.944444π-0.944444\pi
0.984808 + 0.173648i 0.0555556π0.0555556\pi
602602 0 0
603603 0.766044 + 1.32683i 0.766044 + 1.32683i
604604 0 0
605605 0 0
606606 0 0
607607 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 0 0
613613 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
614614 0 0
615615 0 0
616616 0 0
617617 1.26604 0.223238i 1.26604 0.223238i 0.500000 0.866025i 0.333333π-0.333333\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
618618 0 0
619619 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
620620 3.01763i 3.01763i
621621 −1.11334 1.32683i −1.11334 1.32683i
622622 0 0
623623 0 0
624624 0 0
625625 0.766044 + 4.34445i 0.766044 + 4.34445i
626626 0 0
627627 0 0
628628 −0.266044 + 1.50881i −0.266044 + 1.50881i
629629 0 0
630630 0 0
631631 0.766044 + 1.32683i 0.766044 + 1.32683i 0.939693 + 0.342020i 0.111111π0.111111\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
632632 0 0
633633 0 0
634634 0 0
635635 0 0
636636 0.826352 0.984808i 0.826352 0.984808i
637637 0 0
638638 0 0
639639 −0.233956 0.642788i −0.233956 0.642788i
640640 0 0
641641 −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
642642 0 0
643643 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
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 −0.326352 1.85083i −0.326352 1.85083i
653653 −0.673648 + 1.85083i −0.673648 + 1.85083i −0.173648 + 0.984808i 0.555556π0.555556\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
654654 0 0
655655 0 0
656656 0 0
657657 0 0
658658 0 0
659659 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
660660 0 0
661661 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
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 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
674674 0 0
675675 0.500000 2.83564i 0.500000 2.83564i
676676 −1.00000 −1.00000
677677 0 0 −0.766044 0.642788i 0.777778π-0.777778\pi
0.766044 + 0.642788i 0.222222π0.222222\pi
678678 0 0
679679 0 0
680680 0 0
681681 0 0
682682 0 0
683683 −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
684684 0 0
685685 −1.26604 2.19285i −1.26604 2.19285i
686686 0 0
687687 −0.173648 + 0.984808i −0.173648 + 0.984808i
688688 0 0
689689 0 0
690690 0 0
691691 −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
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 −0.233956 1.32683i −0.233956 1.32683i
706706 0 0
707707 0 0
708708 1.11334 0.642788i 1.11334 0.642788i
709709 −0.0603074 + 0.342020i −0.0603074 + 0.342020i 0.939693 + 0.342020i 0.111111π0.111111\pi
−1.00000 π\pi
710710 0 0
711711 0 0
712712 0 0
713713 0.907604 + 2.49362i 0.907604 + 2.49362i
714714 0 0
715715 0 0
716716 −0.826352 0.984808i −0.826352 0.984808i
717717 0 0
718718 0 0
719719 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
720720 −1.93969 0.342020i −1.93969 0.342020i
721721 0 0
722722 0 0
723723 0 0
724724 −0.326352 0.118782i −0.326352 0.118782i
725725 0 0
726726 0 0
727727 1.43969 + 1.20805i 1.43969 + 1.20805i 0.939693 + 0.342020i 0.111111π0.111111\pi
0.500000 + 0.866025i 0.333333π0.333333\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 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
734734 0 0
735735 1.96962i 1.96962i
736736 0 0
737737 0 0
738738 0 0
739739 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
740740 −0.233956 0.642788i −0.233956 0.642788i
741741 0 0
742742 0 0
743743 0 0 0.766044 0.642788i 0.222222π-0.222222\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
744744 0 0
745745 0 0
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 −1.76604 0.642788i −1.76604 0.642788i −0.766044 0.642788i 0.777778π-0.777778\pi
−1.00000 π\pi
752752 −0.673648 + 0.118782i −0.673648 + 0.118782i
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 −1.53209 −1.53209 −0.766044 0.642788i 0.777778π-0.777778\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
758758 0 0
759759 0 0
760760 0 0
761761 0 0 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
762762 0 0
763763 0 0
764764 0.592396 + 0.342020i 0.592396 + 0.342020i
765765 0 0
766766 0 0
767767 0 0
768768 −0.173648 + 0.984808i −0.173648 + 0.984808i
769769 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
770770 0 0
771771 −1.70574 0.300767i −1.70574 0.300767i
772772 0 0
773773 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
774774 0 0
775775 −2.20574 + 3.82045i −2.20574 + 3.82045i
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 −1.93969 + 2.31164i −1.93969 + 2.31164i
786786 0 0
787787 0 0 0.984808 0.173648i 0.0555556π-0.0555556\pi
−0.984808 + 0.173648i 0.944444π0.944444\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 0 0
794794 0 0
795795 2.37939 0.866025i 2.37939 0.866025i
796796 1.43969 1.20805i 1.43969 1.20805i
797797 −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
798798 0 0
799799 0 0
800800 0 0
801801 −1.11334 + 1.32683i −1.11334 + 1.32683i
802802 0 0
803803 0 0
804804 1.53209 1.53209
805805 0 0
806806 0 0
807807 0.439693 + 0.524005i 0.439693 + 0.524005i
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 1.26604 3.47843i 1.26604 3.47843i
816816 0 0
817817 0 0
818818 0 0
819819 0 0
820820 0 0
821821 0 0 0.939693 0.342020i 0.111111π-0.111111\pi
−0.939693 + 0.342020i 0.888889π0.888889\pi
822822 0 0
823823 −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
824824 0 0
825825 0 0
826826 0 0
827827 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
828828 −1.70574 + 0.300767i −1.70574 + 0.300767i
829829 −0.766044 + 1.32683i −0.766044 + 1.32683i 0.173648 + 0.984808i 0.444444π0.444444\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 1.17365 0.984808i 1.17365 0.984808i
838838 0 0
839839 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
840840 0 0
841841 0.173648 + 0.984808i 0.173648 + 0.984808i
842842 0 0
843843 0 0
844844 0 0
845845 −1.70574 0.984808i −1.70574 0.984808i
846846 0 0
847847 0 0
848848 −0.439693 1.20805i −0.439693 1.20805i
849849 0 0
850850 0 0
851851 −0.386659 0.460802i −0.386659 0.460802i
852852 −0.673648 0.118782i −0.673648 0.118782i
853853 0 0 −0.342020 0.939693i 0.611111π-0.611111\pi
0.342020 + 0.939693i 0.388889π0.388889\pi
854854 0 0
855855 0 0
856856 0 0
857857 0 0 0.173648 0.984808i 0.444444π-0.444444\pi
−0.173648 + 0.984808i 0.555556π0.555556\pi
858858 0 0
859859 1.76604 + 0.642788i 1.76604 + 0.642788i 1.00000 00
0.766044 + 0.642788i 0.222222π0.222222\pi
860860 0 0
861861 0 0
862862 0 0
863863 1.73205i 1.73205i 0.500000 + 0.866025i 0.333333π0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
864864 0 0
865865 0 0
866866 0 0
867867 −0.173648 0.984808i −0.173648 0.984808i
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0 0
873873 −0.326352 1.85083i −0.326352 1.85083i
874874 0 0
875875 0 0
876876 0 0
877877 0 0 −0.642788 0.766044i 0.722222π-0.722222\pi
0.642788 + 0.766044i 0.277778π0.277778\pi
878878 0 0
879879 0 0
880880 0 0
881881 −0.592396 + 0.342020i −0.592396 + 0.342020i −0.766044 0.642788i 0.777778π-0.777778\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
882882 0 0
883883 −0.939693 + 1.62760i −0.939693 + 1.62760i −0.173648 + 0.984808i 0.555556π0.555556\pi
−0.766044 + 0.642788i 0.777778π0.777778\pi
884884 0 0
885885 2.53209 2.53209
886886 0 0
887887 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\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 −0.439693 2.49362i −0.439693 2.49362i
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 −2.20574 1.85083i −2.20574 1.85083i
901901 0 0
902902 0 0
903903 0 0
904904 0 0
905905 −0.439693 0.524005i −0.439693 0.524005i
906906 0 0
907907 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
908908 0 0
909909 0 0
910910 0 0
911911 1.93969 + 0.342020i 1.93969 + 0.342020i 1.00000 00
0.939693 + 0.342020i 0.111111π0.111111\pi
912912 0 0
913913 0 0
914914 0 0
915915 0 0
916916 0.766044 + 0.642788i 0.766044 + 0.642788i
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 0.173648 0.984808i 0.173648 0.984808i
926926 0 0
927927 −0.173648 + 0.300767i −0.173648 + 0.300767i
928928 0 0
929929 0.439693 + 1.20805i 0.439693 + 1.20805i 0.939693 + 0.342020i 0.111111π0.111111\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
930930 0 0
931931 0 0
932932 0 0
933933 −1.26604 0.223238i −1.26604 0.223238i
934934 0 0
935935 0 0
936936 0 0
937937 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
938938 0 0
939939 0.500000 0.866025i 0.500000 0.866025i
940940 −1.26604 0.460802i −1.26604 0.460802i
941941 0 0 −0.173648 0.984808i 0.555556π-0.555556\pi
0.173648 + 0.984808i 0.444444π0.444444\pi
942942 0 0
943943 0 0
944944 1.28558i 1.28558i
945945 0 0
946946 0 0
947947 0.826352 0.984808i 0.826352 0.984808i −0.173648 0.984808i 0.555556π-0.555556\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 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
954954 0 0
955955 0.673648 + 1.16679i 0.673648 + 1.16679i
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 −1.26604 + 1.50881i −1.26604 + 1.50881i
961961 −1.26604 + 0.460802i −1.26604 + 0.460802i
962962 0 0
963963 0 0
964964 0 0
965965 0 0
966966 0 0
967967 0 0 0.342020 0.939693i 0.388889π-0.388889\pi
−0.342020 + 0.939693i 0.611111π0.611111\pi
968968 0 0
969969 0 0
970970 0 0
971971 1.73205i 1.73205i −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 0.866025i 0.333333π-0.333333\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 −0.939693 0.342020i 0.888889π-0.888889\pi
0.939693 + 0.342020i 0.111111π0.111111\pi
978978 0 0
979979 0 0
980980 −1.70574 0.984808i −1.70574 0.984808i
981981 0 0
982982 0 0
983983 −0.439693 1.20805i −0.439693 1.20805i −0.939693 0.342020i 0.888889π-0.888889\pi
0.500000 0.866025i 0.333333π-0.333333\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 0.333333π0.333333\pi
−1.00000 π\pi
992992 0 0
993993 −0.939693 1.62760i −0.939693 1.62760i
994994 0 0
995995 3.64543 0.642788i 3.64543 0.642788i
996996 0 0
997997 0 0 0.642788 0.766044i 0.277778π-0.277778\pi
−0.642788 + 0.766044i 0.722222π0.722222\pi
998998 0 0
999999 −0.173648 + 0.300767i −0.173648 + 0.300767i
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.848.1 6
11.2 odd 10 3267.1.be.a.686.1 24
11.3 even 5 3267.1.be.a.2792.1 24
11.4 even 5 3267.1.be.a.632.1 24
11.5 even 5 3267.1.be.a.1334.1 24
11.6 odd 10 3267.1.be.a.1334.1 24
11.7 odd 10 3267.1.be.a.632.1 24
11.8 odd 10 3267.1.be.a.2792.1 24
11.9 even 5 3267.1.be.a.686.1 24
11.10 odd 2 CM 3267.1.q.a.848.1 6
27.5 odd 18 inner 3267.1.q.a.2300.1 yes 6
297.5 odd 90 3267.1.be.a.2786.1 24
297.32 even 18 inner 3267.1.q.a.2300.1 yes 6
297.59 odd 90 3267.1.be.a.2084.1 24
297.86 odd 90 3267.1.be.a.2138.1 24
297.113 odd 90 3267.1.be.a.977.1 24
297.140 even 90 3267.1.be.a.977.1 24
297.167 even 90 3267.1.be.a.2138.1 24
297.194 even 90 3267.1.be.a.2084.1 24
297.248 even 90 3267.1.be.a.2786.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3267.1.q.a.848.1 6 1.1 even 1 trivial
3267.1.q.a.848.1 6 11.10 odd 2 CM
3267.1.q.a.2300.1 yes 6 27.5 odd 18 inner
3267.1.q.a.2300.1 yes 6 297.32 even 18 inner
3267.1.be.a.632.1 24 11.4 even 5
3267.1.be.a.632.1 24 11.7 odd 10
3267.1.be.a.686.1 24 11.2 odd 10
3267.1.be.a.686.1 24 11.9 even 5
3267.1.be.a.977.1 24 297.113 odd 90
3267.1.be.a.977.1 24 297.140 even 90
3267.1.be.a.1334.1 24 11.5 even 5
3267.1.be.a.1334.1 24 11.6 odd 10
3267.1.be.a.2084.1 24 297.59 odd 90
3267.1.be.a.2084.1 24 297.194 even 90
3267.1.be.a.2138.1 24 297.86 odd 90
3267.1.be.a.2138.1 24 297.167 even 90
3267.1.be.a.2786.1 24 297.5 odd 90
3267.1.be.a.2786.1 24 297.248 even 90
3267.1.be.a.2792.1 24 11.3 even 5
3267.1.be.a.2792.1 24 11.8 odd 10