Properties

Label 3549.1.w.d.2027.1
Level 35493549
Weight 11
Character 3549.2027
Analytic conductor 1.7711.771
Analytic rank 00
Dimension 44
Projective image D3D_{3}
CM discriminant -3
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3549,1,Mod(506,3549)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3549, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 3]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3549.506");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 3549=37132 3549 = 3 \cdot 7 \cdot 13^{2}
Weight: k k == 1 1
Character orbit: [χ][\chi] == 3549.w (of order 66, degree 22, not 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: 1.771181729831.77118172983
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q(ζ12)\Q(\zeta_{12})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x2+1 x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 273)
Projective image: D3D_{3}
Projective field: Galois closure of 3.1.24843.1
Artin image: C6.C62C_6.C_6^2
Artin field: Galois closure of Q[x]/(x72)\mathbb{Q}[x]/(x^{72} - \cdots)

Embedding invariants

Embedding label 2027.1
Root 0.866025+0.500000i-0.866025 + 0.500000i of defining polynomial
Character χ\chi == 3549.2027
Dual form 3549.1.w.d.506.2

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+(0.500000+0.866025i)q3+(0.5000000.866025i)q41.00000iq7+(0.5000000.866025i)q9+(0.500000+0.866025i)q12+(0.5000000.866025i)q16+(0.866025+0.500000i)q19+(0.866025+0.500000i)q21+(0.5000000.866025i)q25+1.00000q27+(0.8660250.500000i)q28+(1.732051.00000i)q311.00000q36+(0.8660250.500000i)q37+1.00000q43+1.00000q481.00000q491.00000iq57+(0.500000+0.866025i)q61+(0.866025+0.500000i)q631.00000q64+(1.732051.00000i)q67+(0.8660250.500000i)q73+(0.500000+0.866025i)q75+1.00000iq76+(1.000001.73205i)q79+(0.500000+0.866025i)q81+(0.8660250.500000i)q84+(1.732051.00000i)q931.00000iq97+O(q100)q+(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{12} +(-0.500000 - 0.866025i) q^{16} +(-0.866025 + 0.500000i) q^{19} +(0.866025 + 0.500000i) q^{21} +(0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(-0.866025 - 0.500000i) q^{28} +(-1.73205 - 1.00000i) q^{31} -1.00000 q^{36} +(0.866025 - 0.500000i) q^{37} +1.00000 q^{43} +1.00000 q^{48} -1.00000 q^{49} -1.00000i q^{57} +(0.500000 + 0.866025i) q^{61} +(-0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(-1.73205 - 1.00000i) q^{67} +(-0.866025 - 0.500000i) q^{73} +(0.500000 + 0.866025i) q^{75} +1.00000i q^{76} +(-1.00000 - 1.73205i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(0.866025 - 0.500000i) q^{84} +(1.73205 - 1.00000i) q^{93} -1.00000i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q2q3+2q42q9+2q122q16+2q25+4q274q36+4q43+4q484q49+2q614q64+2q754q792q81+O(q100) 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} + 2 q^{12} - 2 q^{16} + 2 q^{25} + 4 q^{27} - 4 q^{36} + 4 q^{43} + 4 q^{48} - 4 q^{49} + 2 q^{61} - 4 q^{64} + 2 q^{75} - 4 q^{79} - 2 q^{81}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3549Z)×\left(\mathbb{Z}/3549\mathbb{Z}\right)^\times.

nn 11841184 15221522 33823382
χ(n)\chi(n) 1-1 e(23)e\left(\frac{2}{3}\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 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
33 −0.500000 + 0.866025i −0.500000 + 0.866025i
44 0.500000 0.866025i 0.500000 0.866025i
55 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
66 0 0
77 1.00000i 1.00000i
88 0 0
99 −0.500000 0.866025i −0.500000 0.866025i
1010 0 0
1111 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
1212 0.500000 + 0.866025i 0.500000 + 0.866025i
1313 0 0
1414 0 0
1515 0 0
1616 −0.500000 0.866025i −0.500000 0.866025i
1717 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
1818 0 0
1919 −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i 0.833333π-0.833333\pi
1.00000i 0.5π0.5\pi
2020 0 0
2121 0.866025 + 0.500000i 0.866025 + 0.500000i
2222 0 0
2323 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
2424 0 0
2525 0.500000 0.866025i 0.500000 0.866025i
2626 0 0
2727 1.00000 1.00000
2828 −0.866025 0.500000i −0.866025 0.500000i
2929 0 0 1.00000 00
−1.00000 π\pi
3030 0 0
3131 −1.73205 1.00000i −1.73205 1.00000i −0.866025 0.500000i 0.833333π-0.833333\pi
−0.866025 0.500000i 0.833333π-0.833333\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 −1.00000 −1.00000
3737 0.866025 0.500000i 0.866025 0.500000i 1.00000i 0.5π-0.5\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
3838 0 0
3939 0 0
4040 0 0
4141 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4242 0 0
4343 1.00000 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
4444 0 0
4545 0 0
4646 0 0
4747 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
4848 1.00000 1.00000
4949 −1.00000 −1.00000
5050 0 0
5151 0 0
5252 0 0
5353 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
5454 0 0
5555 0 0
5656 0 0
5757 1.00000i 1.00000i
5858 0 0
5959 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
6060 0 0
6161 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
6262 0 0
6363 −0.866025 + 0.500000i −0.866025 + 0.500000i
6464 −1.00000 −1.00000
6565 0 0
6666 0 0
6767 −1.73205 1.00000i −1.73205 1.00000i −0.866025 0.500000i 0.833333π-0.833333\pi
−0.866025 0.500000i 0.833333π-0.833333\pi
6868 0 0
6969 0 0
7070 0 0
7171 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7272 0 0
7373 −0.866025 0.500000i −0.866025 0.500000i 1.00000i 0.5π-0.5\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
7474 0 0
7575 0.500000 + 0.866025i 0.500000 + 0.866025i
7676 1.00000i 1.00000i
7777 0 0
7878 0 0
7979 −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 0.866025i 0.666667π-0.666667\pi
8080 0 0
8181 −0.500000 + 0.866025i −0.500000 + 0.866025i
8282 0 0
8383 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
8484 0.866025 0.500000i 0.866025 0.500000i
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
9090 0 0
9191 0 0
9292 0 0
9393 1.73205 1.00000i 1.73205 1.00000i
9494 0 0
9595 0 0
9696 0 0
9797 1.00000i 1.00000i −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 0.500000i 0.166667π-0.166667\pi
9898 0 0
9999 0 0
100100 −0.500000 0.866025i −0.500000 0.866025i
101101 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
102102 0 0
103103 −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i 0.333333π-0.333333\pi
−1.00000 π\pi
104104 0 0
105105 0 0
106106 0 0
107107 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
108108 0.500000 0.866025i 0.500000 0.866025i
109109 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i 0.166667π-0.166667\pi
1.00000i 0.5π0.5\pi
110110 0 0
111111 1.00000i 1.00000i
112112 −0.866025 + 0.500000i −0.866025 + 0.500000i
113113 0 0 1.00000 00
−1.00000 π\pi
114114 0 0
115115 0 0
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 0.500000 + 0.866025i 0.500000 + 0.866025i
122122 0 0
123123 0 0
124124 −1.73205 + 1.00000i −1.73205 + 1.00000i
125125 0 0
126126 0 0
127127 1.00000 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
128128 0 0
129129 −0.500000 + 0.866025i −0.500000 + 0.866025i
130130 0 0
131131 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
132132 0 0
133133 0.500000 + 0.866025i 0.500000 + 0.866025i
134134 0 0
135135 0 0
136136 0 0
137137 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
138138 0 0
139139 2.00000 2.00000 1.00000 00
1.00000 00
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 −0.500000 + 0.866025i −0.500000 + 0.866025i
145145 0 0
146146 0 0
147147 0.500000 0.866025i 0.500000 0.866025i
148148 1.00000i 1.00000i
149149 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
150150 0 0
151151 1.73205 + 1.00000i 1.73205 + 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
152152 0 0
153153 0 0
154154 0 0
155155 0 0
156156 0 0
157157 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i 0.666667π-0.666667\pi
1.00000 00
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 0 0
163163 0.866025 0.500000i 0.866025 0.500000i 1.00000i 0.5π-0.5\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
164164 0 0
165165 0 0
166166 0 0
167167 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
168168 0 0
169169 0 0
170170 0 0
171171 0.866025 + 0.500000i 0.866025 + 0.500000i
172172 0.500000 0.866025i 0.500000 0.866025i
173173 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
174174 0 0
175175 −0.866025 0.500000i −0.866025 0.500000i
176176 0 0
177177 0 0
178178 0 0
179179 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
180180 0 0
181181 1.00000 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
182182 0 0
183183 −1.00000 −1.00000
184184 0 0
185185 0 0
186186 0 0
187187 0 0
188188 0 0
189189 1.00000i 1.00000i
190190 0 0
191191 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
192192 0.500000 0.866025i 0.500000 0.866025i
193193 −0.866025 0.500000i −0.866025 0.500000i 1.00000i 0.5π-0.5\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
194194 0 0
195195 0 0
196196 −0.500000 + 0.866025i −0.500000 + 0.866025i
197197 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
198198 0 0
199199 −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
200200 0 0
201201 1.73205 1.00000i 1.73205 1.00000i
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 0 0
210210 0 0
211211 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
212212 0 0
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 −1.00000 + 1.73205i −1.00000 + 1.73205i
218218 0 0
219219 0.866025 0.500000i 0.866025 0.500000i
220220 0 0
221221 0 0
222222 0 0
223223 2.00000i 2.00000i 1.00000i 0.5π0.5\pi
1.00000i 0.5π0.5\pi
224224 0 0
225225 −1.00000 −1.00000
226226 0 0
227227 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
228228 −0.866025 0.500000i −0.866025 0.500000i
229229 0.866025 0.500000i 0.866025 0.500000i 1.00000i 0.5π-0.5\pi
0.866025 + 0.500000i 0.166667π0.166667\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 0
236236 0 0
237237 2.00000 2.00000
238238 0 0
239239 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
240240 0 0
241241 1.73205 + 1.00000i 1.73205 + 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
242242 0 0
243243 −0.500000 0.866025i −0.500000 0.866025i
244244 1.00000 1.00000
245245 0 0
246246 0 0
247247 0 0
248248 0 0
249249 0 0
250250 0 0
251251 0 0 1.00000 00
−1.00000 π\pi
252252 1.00000i 1.00000i
253253 0 0
254254 0 0
255255 0 0
256256 −0.500000 + 0.866025i −0.500000 + 0.866025i
257257 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
258258 0 0
259259 −0.500000 0.866025i −0.500000 0.866025i
260260 0 0
261261 0 0
262262 0 0
263263 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 −1.73205 + 1.00000i −1.73205 + 1.00000i
269269 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
270270 0 0
271271 0.866025 0.500000i 0.866025 0.500000i 1.00000i 0.5π-0.5\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 0 0
277277 −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
278278 0 0
279279 2.00000i 2.00000i
280280 0 0
281281 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
282282 0 0
283283 −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
284284 0 0
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 0.866025 + 0.500000i 0.866025 + 0.500000i
292292 −0.866025 + 0.500000i −0.866025 + 0.500000i
293293 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
294294 0 0
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 1.00000 1.00000
301301 1.00000i 1.00000i
302302 0 0
303303 0 0
304304 0.866025 + 0.500000i 0.866025 + 0.500000i
305305 0 0
306306 0 0
307307 2.00000i 2.00000i 1.00000i 0.5π-0.5\pi
1.00000i 0.5π-0.5\pi
308308 0 0
309309 1.00000 1.00000
310310 0 0
311311 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
312312 0 0
313313 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
314314 0 0
315315 0 0
316316 −2.00000 −2.00000
317317 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
318318 0 0
319319 0 0
320320 0 0
321321 0 0
322322 0 0
323323 0 0
324324 0.500000 + 0.866025i 0.500000 + 0.866025i
325325 0 0
326326 0 0
327327 −0.866025 + 0.500000i −0.866025 + 0.500000i
328328 0 0
329329 0 0
330330 0 0
331331 −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i 0.833333π-0.833333\pi
1.00000i 0.5π0.5\pi
332332 0 0
333333 −0.866025 0.500000i −0.866025 0.500000i
334334 0 0
335335 0 0
336336 1.00000i 1.00000i
337337 1.00000 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
338338 0 0
339339 0 0
340340 0 0
341341 0 0
342342 0 0
343343 1.00000i 1.00000i
344344 0 0
345345 0 0
346346 0 0
347347 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
348348 0 0
349349 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
350350 0 0
351351 0 0
352352 0 0
353353 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
360360 0 0
361361 0 0
362362 0 0
363363 −1.00000 −1.00000
364364 0 0
365365 0 0
366366 0 0
367367 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i 0.666667π-0.666667\pi
1.00000 00
368368 0 0
369369 0 0
370370 0 0
371371 0 0
372372 2.00000i 2.00000i
373373 −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 0.866025i 0.666667π-0.666667\pi
374374 0 0
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 2.00000i 2.00000i 1.00000i 0.5π0.5\pi
1.00000i 0.5π0.5\pi
380380 0 0
381381 −0.500000 + 0.866025i −0.500000 + 0.866025i
382382 0 0
383383 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
384384 0 0
385385 0 0
386386 0 0
387387 −0.500000 0.866025i −0.500000 0.866025i
388388 −0.866025 0.500000i −0.866025 0.500000i
389389 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
390390 0 0
391391 0 0
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 0.866025 0.500000i 0.866025 0.500000i 1.00000i 0.5π-0.5\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
398398 0 0
399399 −1.00000 −1.00000
400400 −1.00000 −1.00000
401401 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
402402 0 0
403403 0 0
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i 0.166667π-0.166667\pi
1.00000i 0.5π0.5\pi
410410 0 0
411411 0 0
412412 −1.00000 −1.00000
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 −1.00000 + 1.73205i −1.00000 + 1.73205i
418418 0 0
419419 0 0 1.00000 00
−1.00000 π\pi
420420 0 0
421421 2.00000i 2.00000i 1.00000i 0.5π0.5\pi
1.00000i 0.5π0.5\pi
422422 0 0
423423 0 0
424424 0 0
425425 0 0
426426 0 0
427427 0.866025 0.500000i 0.866025 0.500000i
428428 0 0
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 −0.500000 0.866025i −0.500000 0.866025i
433433 −2.00000 −2.00000 −1.00000 π\pi
−1.00000 π\pi
434434 0 0
435435 0 0
436436 0.866025 0.500000i 0.866025 0.500000i
437437 0 0
438438 0 0
439439 −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i 0.333333π-0.333333\pi
−1.00000 π\pi
440440 0 0
441441 0.500000 + 0.866025i 0.500000 + 0.866025i
442442 0 0
443443 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
444444 0.866025 + 0.500000i 0.866025 + 0.500000i
445445 0 0
446446 0 0
447447 0 0
448448 1.00000i 1.00000i
449449 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
450450 0 0
451451 0 0
452452 0 0
453453 −1.73205 + 1.00000i −1.73205 + 1.00000i
454454 0 0
455455 0 0
456456 0 0
457457 1.73205 1.00000i 1.73205 1.00000i 0.866025 0.500000i 0.166667π-0.166667\pi
0.866025 0.500000i 0.166667π-0.166667\pi
458458 0 0
459459 0 0
460460 0 0
461461 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
462462 0 0
463463 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
464464 0 0
465465 0 0
466466 0 0
467467 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
468468 0 0
469469 −1.00000 + 1.73205i −1.00000 + 1.73205i
470470 0 0
471471 0.500000 + 0.866025i 0.500000 + 0.866025i
472472 0 0
473473 0 0
474474 0 0
475475 1.00000i 1.00000i
476476 0 0
477477 0 0
478478 0 0
479479 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
480480 0 0
481481 0 0
482482 0 0
483483 0 0
484484 1.00000 1.00000
485485 0 0
486486 0 0
487487 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i 0.166667π-0.166667\pi
1.00000i 0.5π0.5\pi
488488 0 0
489489 1.00000i 1.00000i
490490 0 0
491491 0 0 1.00000 00
−1.00000 π\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 2.00000i 2.00000i
497497 0 0
498498 0 0
499499 −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i 0.833333π-0.833333\pi
1.00000i 0.5π0.5\pi
500500 0 0
501501 0 0
502502 0 0
503503 0 0 1.00000 00
−1.00000 π\pi
504504 0 0
505505 0 0
506506 0 0
507507 0 0
508508 0.500000 0.866025i 0.500000 0.866025i
509509 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
510510 0 0
511511 −0.500000 + 0.866025i −0.500000 + 0.866025i
512512 0 0
513513 −0.866025 + 0.500000i −0.866025 + 0.500000i
514514 0 0
515515 0 0
516516 0.500000 + 0.866025i 0.500000 + 0.866025i
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
522522 0 0
523523 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
524524 0 0
525525 0.866025 0.500000i 0.866025 0.500000i
526526 0 0
527527 0 0
528528 0 0
529529 −0.500000 + 0.866025i −0.500000 + 0.866025i
530530 0 0
531531 0 0
532532 1.00000 1.00000
533533 0 0
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 0 0
539539 0 0
540540 0 0
541541 0.866025 0.500000i 0.866025 0.500000i 1.00000i 0.5π-0.5\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
542542 0 0
543543 −0.500000 + 0.866025i −0.500000 + 0.866025i
544544 0 0
545545 0 0
546546 0 0
547547 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
548548 0 0
549549 0.500000 0.866025i 0.500000 0.866025i
550550 0 0
551551 0 0
552552 0 0
553553 −1.73205 + 1.00000i −1.73205 + 1.00000i
554554 0 0
555555 0 0
556556 1.00000 1.73205i 1.00000 1.73205i
557557 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 0 0
563563 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
564564 0 0
565565 0 0
566566 0 0
567567 0.866025 + 0.500000i 0.866025 + 0.500000i
568568 0 0
569569 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
570570 0 0
571571 −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 0.500000 + 0.866025i 0.500000 + 0.866025i
577577 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i 0.166667π-0.166667\pi
1.00000i 0.5π0.5\pi
578578 0 0
579579 0.866025 0.500000i 0.866025 0.500000i
580580 0 0
581581 0 0
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
588588 −0.500000 0.866025i −0.500000 0.866025i
589589 2.00000 2.00000
590590 0 0
591591 0 0
592592 −0.866025 0.500000i −0.866025 0.500000i
593593 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
594594 0 0
595595 0 0
596596 0 0
597597 −0.500000 0.866025i −0.500000 0.866025i
598598 0 0
599599 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
600600 0 0
601601 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
602602 0 0
603603 2.00000i 2.00000i
604604 1.73205 1.00000i 1.73205 1.00000i
605605 0 0
606606 0 0
607607 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 0 0
613613 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i 0.166667π-0.166667\pi
1.00000i 0.5π0.5\pi
614614 0 0
615615 0 0
616616 0 0
617617 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
618618 0 0
619619 −0.866025 0.500000i −0.866025 0.500000i 1.00000i 0.5π-0.5\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 −0.500000 0.866025i −0.500000 0.866025i
626626 0 0
627627 0 0
628628 −0.500000 0.866025i −0.500000 0.866025i
629629 0 0
630630 0 0
631631 1.00000i 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
632632 0 0
633633 0.500000 0.866025i 0.500000 0.866025i
634634 0 0
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 0 0
641641 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
642642 0 0
643643 1.00000i 1.00000i −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 0.500000i 0.166667π-0.166667\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
648648 0 0
649649 0 0
650650 0 0
651651 −1.00000 1.73205i −1.00000 1.73205i
652652 1.00000i 1.00000i
653653 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
654654 0 0
655655 0 0
656656 0 0
657657 1.00000i 1.00000i
658658 0 0
659659 0 0 1.00000 00
−1.00000 π\pi
660660 0 0
661661 1.73205 + 1.00000i 1.73205 + 1.00000i 0.866025 + 0.500000i 0.166667π0.166667\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 −1.73205 1.00000i −1.73205 1.00000i
670670 0 0
671671 0 0
672672 0 0
673673 1.00000 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
674674 0 0
675675 0.500000 0.866025i 0.500000 0.866025i
676676 0 0
677677 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
678678 0 0
679679 −1.00000 −1.00000
680680 0 0
681681 0 0
682682 0 0
683683 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
684684 0.866025 0.500000i 0.866025 0.500000i
685685 0 0
686686 0 0
687687 1.00000i 1.00000i
688688 −0.500000 0.866025i −0.500000 0.866025i
689689 0 0
690690 0 0
691691 −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i 0.833333π-0.833333\pi
1.00000i 0.5π0.5\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 −0.866025 + 0.500000i −0.866025 + 0.500000i
701701 0 0 1.00000 00
−1.00000 π\pi
702702 0 0
703703 −0.500000 + 0.866025i −0.500000 + 0.866025i
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 0.866025 0.500000i 0.866025 0.500000i 1.00000i 0.5π-0.5\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
710710 0 0
711711 −1.00000 + 1.73205i −1.00000 + 1.73205i
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
720720 0 0
721721 −0.866025 + 0.500000i −0.866025 + 0.500000i
722722 0 0
723723 −1.73205 + 1.00000i −1.73205 + 1.00000i
724724 0.500000 0.866025i 0.500000 0.866025i
725725 0 0
726726 0 0
727727 −2.00000 −2.00000 −1.00000 π\pi
−1.00000 π\pi
728728 0 0
729729 1.00000 1.00000
730730 0 0
731731 0 0
732732 −0.500000 + 0.866025i −0.500000 + 0.866025i
733733 1.73205 1.00000i 1.73205 1.00000i 0.866025 0.500000i 0.166667π-0.166667\pi
0.866025 0.500000i 0.166667π-0.166667\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 −0.866025 0.500000i −0.866025 0.500000i 1.00000i 0.5π-0.5\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 0
748748 0 0
749749 0 0
750750 0 0
751751 −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i 0.333333π-0.333333\pi
−1.00000 π\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 −0.866025 0.500000i −0.866025 0.500000i
757757 2.00000 2.00000 1.00000 00
1.00000 00
758758 0 0
759759 0 0
760760 0 0
761761 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
762762 0 0
763763 0.500000 0.866025i 0.500000 0.866025i
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 −0.500000 0.866025i −0.500000 0.866025i
769769 1.00000i 1.00000i −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 0.500000i 0.166667π-0.166667\pi
770770 0 0
771771 0 0
772772 −0.866025 + 0.500000i −0.866025 + 0.500000i
773773 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
774774 0 0
775775 −1.73205 + 1.00000i −1.73205 + 1.00000i
776776 0 0
777777 1.00000 1.00000
778778 0 0
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 0.500000 + 0.866025i 0.500000 + 0.866025i
785785 0 0
786786 0 0
787787 −0.866025 0.500000i −0.866025 0.500000i 1.00000i 0.5π-0.5\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 0 0
794794 0 0
795795 0 0
796796 0.500000 + 0.866025i 0.500000 + 0.866025i
797797 0 0 1.00000 00
−1.00000 π\pi
798798 0 0
799799 0 0
800800 0 0
801801 0 0
802802 0 0
803803 0 0
804804 2.00000i 2.00000i
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
810810 0 0
811811 1.00000i 1.00000i −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 0.500000i 0.166667π-0.166667\pi
812812 0 0
813813 1.00000i 1.00000i
814814 0 0
815815 0 0
816816 0 0
817817 −0.866025 + 0.500000i −0.866025 + 0.500000i
818818 0 0
819819 0 0
820820 0 0
821821 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
822822 0 0
823823 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 0.866025i 0.333333π-0.333333\pi
824824 0 0
825825 0 0
826826 0 0
827827 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
828828 0 0
829829 −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
830830 0 0
831831 −0.500000 0.866025i −0.500000 0.866025i
832832 0 0
833833 0 0
834834 0 0
835835 0 0
836836 0 0
837837 −1.73205 1.00000i −1.73205 1.00000i
838838 0 0
839839 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
840840 0 0
841841 1.00000 1.00000
842842 0 0
843843 0 0
844844 −0.500000 + 0.866025i −0.500000 + 0.866025i
845845 0 0
846846 0 0
847847 0.866025 0.500000i 0.866025 0.500000i
848848 0 0
849849 −0.500000 0.866025i −0.500000 0.866025i
850850 0 0
851851 0 0
852852 0 0
853853 2.00000i 2.00000i 1.00000i 0.5π-0.5\pi
1.00000i 0.5π-0.5\pi
854854 0 0
855855 0 0
856856 0 0
857857 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
858858 0 0
859859 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
864864 0 0
865865 0 0
866866 0 0
867867 1.00000 1.00000
868868 1.00000 + 1.73205i 1.00000 + 1.73205i
869869 0 0
870870 0 0
871871 0 0
872872 0 0
873873 −0.866025 + 0.500000i −0.866025 + 0.500000i
874874 0 0
875875 0 0
876876 1.00000i 1.00000i
877877 1.73205 1.00000i 1.73205 1.00000i 0.866025 0.500000i 0.166667π-0.166667\pi
0.866025 0.500000i 0.166667π-0.166667\pi
878878 0 0
879879 0 0
880880 0 0
881881 0 0 1.00000 00
−1.00000 π\pi
882882 0 0
883883 1.00000 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
884884 0 0
885885 0 0
886886 0 0
887887 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
888888 0 0
889889 1.00000i 1.00000i
890890 0 0
891891 0 0
892892 1.73205 + 1.00000i 1.73205 + 1.00000i
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 −0.500000 + 0.866025i −0.500000 + 0.866025i
901901 0 0
902902 0 0
903903 0.866025 + 0.500000i 0.866025 + 0.500000i
904904 0 0
905905 0 0
906906 0 0
907907 −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
908908 0 0
909909 0 0
910910 0 0
911911 0 0 1.00000 00
−1.00000 π\pi
912912 −0.866025 + 0.500000i −0.866025 + 0.500000i
913913 0 0
914914 0 0
915915 0 0
916916 1.00000i 1.00000i
917917 0 0
918918 0 0
919919 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 00
−0.500000 + 0.866025i 0.666667π0.666667\pi
920920 0 0
921921 1.73205 + 1.00000i 1.73205 + 1.00000i
922922 0 0
923923 0 0
924924 0 0
925925 1.00000i 1.00000i
926926 0 0
927927 −0.500000 + 0.866025i −0.500000 + 0.866025i
928928 0 0
929929 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
930930 0 0
931931 0.866025 0.500000i 0.866025 0.500000i
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 −1.00000 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
938938 0 0
939939 −1.00000 −1.00000
940940 0 0
941941 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
948948 1.00000 1.73205i 1.00000 1.73205i
949949 0 0
950950 0 0
951951 0 0
952952 0 0
953953 0 0 1.00000 00
−1.00000 π\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 1.50000 + 2.59808i 1.50000 + 2.59808i
962962 0 0
963963 0 0
964964 1.73205 1.00000i 1.73205 1.00000i
965965 0 0
966966 0 0
967967 1.00000i 1.00000i −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 0.500000i 0.166667π-0.166667\pi
968968 0 0
969969 0 0
970970 0 0
971971 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
972972 −1.00000 −1.00000
973973 2.00000i 2.00000i
974974 0 0
975975 0 0
976976 0.500000 0.866025i 0.500000 0.866025i
977977 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
978978 0 0
979979 0 0
980980 0 0
981981 1.00000i 1.00000i
982982 0 0
983983 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\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 0.666667π-0.666667\pi
1.00000 00
992992 0 0
993993 1.00000i 1.00000i
994994 0 0
995995 0 0
996996 0 0
997997 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i 0.666667π-0.666667\pi
1.00000 00
998998 0 0
999999 0.866025 0.500000i 0.866025 0.500000i
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 3549.1.w.d.2027.1 4
3.2 odd 2 CM 3549.1.w.d.2027.1 4
7.2 even 3 inner 3549.1.w.d.506.1 4
13.2 odd 12 273.1.s.a.74.1 2
13.3 even 3 3549.1.bp.c.2006.1 4
13.4 even 6 3549.1.x.c.1544.1 4
13.5 odd 4 3549.1.bk.b.1691.1 2
13.6 odd 12 273.1.bm.a.263.1 yes 2
13.7 odd 12 3549.1.bm.a.2174.1 2
13.8 odd 4 3549.1.bk.a.1691.1 2
13.9 even 3 3549.1.x.c.1544.2 4
13.10 even 6 3549.1.bp.c.2006.2 4
13.11 odd 12 3549.1.s.a.1712.1 2
13.12 even 2 inner 3549.1.w.d.2027.2 4
21.2 odd 6 inner 3549.1.w.d.506.1 4
39.2 even 12 273.1.s.a.74.1 2
39.5 even 4 3549.1.bk.b.1691.1 2
39.8 even 4 3549.1.bk.a.1691.1 2
39.11 even 12 3549.1.s.a.1712.1 2
39.17 odd 6 3549.1.x.c.1544.1 4
39.20 even 12 3549.1.bm.a.2174.1 2
39.23 odd 6 3549.1.bp.c.2006.2 4
39.29 odd 6 3549.1.bp.c.2006.1 4
39.32 even 12 273.1.bm.a.263.1 yes 2
39.35 odd 6 3549.1.x.c.1544.2 4
39.38 odd 2 inner 3549.1.w.d.2027.2 4
91.2 odd 12 273.1.bm.a.191.1 yes 2
91.6 even 12 1911.1.bm.a.263.1 2
91.9 even 3 3549.1.bp.c.23.2 4
91.16 even 3 3549.1.x.c.485.1 4
91.19 even 12 1911.1.s.a.1745.1 2
91.23 even 6 3549.1.x.c.485.2 4
91.30 even 6 3549.1.bp.c.23.1 4
91.32 odd 12 1911.1.be.a.1667.1 2
91.37 odd 12 3549.1.bm.a.191.1 2
91.41 even 12 1911.1.s.a.1439.1 2
91.44 odd 12 3549.1.bk.b.170.1 2
91.45 even 12 1911.1.be.b.1667.1 2
91.51 even 6 inner 3549.1.w.d.506.2 4
91.54 even 12 1911.1.bm.a.1010.1 2
91.58 odd 12 273.1.s.a.107.1 yes 2
91.67 odd 12 1911.1.be.a.932.1 2
91.72 odd 12 3549.1.s.a.653.1 2
91.80 even 12 1911.1.be.b.932.1 2
91.86 odd 12 3549.1.bk.a.170.1 2
273.2 even 12 273.1.bm.a.191.1 yes 2
273.23 odd 6 3549.1.x.c.485.2 4
273.32 even 12 1911.1.be.a.1667.1 2
273.41 odd 12 1911.1.s.a.1439.1 2
273.44 even 12 3549.1.bk.b.170.1 2
273.80 odd 12 1911.1.be.b.932.1 2
273.86 even 12 3549.1.bk.a.170.1 2
273.107 odd 6 3549.1.x.c.485.1 4
273.110 odd 12 1911.1.s.a.1745.1 2
273.128 even 12 3549.1.bm.a.191.1 2
273.149 even 12 273.1.s.a.107.1 yes 2
273.158 even 12 1911.1.be.a.932.1 2
273.188 odd 12 1911.1.bm.a.263.1 2
273.191 odd 6 3549.1.bp.c.23.2 4
273.212 odd 6 3549.1.bp.c.23.1 4
273.227 odd 12 1911.1.be.b.1667.1 2
273.233 odd 6 inner 3549.1.w.d.506.2 4
273.236 odd 12 1911.1.bm.a.1010.1 2
273.254 even 12 3549.1.s.a.653.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.1.s.a.74.1 2 13.2 odd 12
273.1.s.a.74.1 2 39.2 even 12
273.1.s.a.107.1 yes 2 91.58 odd 12
273.1.s.a.107.1 yes 2 273.149 even 12
273.1.bm.a.191.1 yes 2 91.2 odd 12
273.1.bm.a.191.1 yes 2 273.2 even 12
273.1.bm.a.263.1 yes 2 13.6 odd 12
273.1.bm.a.263.1 yes 2 39.32 even 12
1911.1.s.a.1439.1 2 91.41 even 12
1911.1.s.a.1439.1 2 273.41 odd 12
1911.1.s.a.1745.1 2 91.19 even 12
1911.1.s.a.1745.1 2 273.110 odd 12
1911.1.be.a.932.1 2 91.67 odd 12
1911.1.be.a.932.1 2 273.158 even 12
1911.1.be.a.1667.1 2 91.32 odd 12
1911.1.be.a.1667.1 2 273.32 even 12
1911.1.be.b.932.1 2 91.80 even 12
1911.1.be.b.932.1 2 273.80 odd 12
1911.1.be.b.1667.1 2 91.45 even 12
1911.1.be.b.1667.1 2 273.227 odd 12
1911.1.bm.a.263.1 2 91.6 even 12
1911.1.bm.a.263.1 2 273.188 odd 12
1911.1.bm.a.1010.1 2 91.54 even 12
1911.1.bm.a.1010.1 2 273.236 odd 12
3549.1.s.a.653.1 2 91.72 odd 12
3549.1.s.a.653.1 2 273.254 even 12
3549.1.s.a.1712.1 2 13.11 odd 12
3549.1.s.a.1712.1 2 39.11 even 12
3549.1.w.d.506.1 4 7.2 even 3 inner
3549.1.w.d.506.1 4 21.2 odd 6 inner
3549.1.w.d.506.2 4 91.51 even 6 inner
3549.1.w.d.506.2 4 273.233 odd 6 inner
3549.1.w.d.2027.1 4 1.1 even 1 trivial
3549.1.w.d.2027.1 4 3.2 odd 2 CM
3549.1.w.d.2027.2 4 13.12 even 2 inner
3549.1.w.d.2027.2 4 39.38 odd 2 inner
3549.1.x.c.485.1 4 91.16 even 3
3549.1.x.c.485.1 4 273.107 odd 6
3549.1.x.c.485.2 4 91.23 even 6
3549.1.x.c.485.2 4 273.23 odd 6
3549.1.x.c.1544.1 4 13.4 even 6
3549.1.x.c.1544.1 4 39.17 odd 6
3549.1.x.c.1544.2 4 13.9 even 3
3549.1.x.c.1544.2 4 39.35 odd 6
3549.1.bk.a.170.1 2 91.86 odd 12
3549.1.bk.a.170.1 2 273.86 even 12
3549.1.bk.a.1691.1 2 13.8 odd 4
3549.1.bk.a.1691.1 2 39.8 even 4
3549.1.bk.b.170.1 2 91.44 odd 12
3549.1.bk.b.170.1 2 273.44 even 12
3549.1.bk.b.1691.1 2 13.5 odd 4
3549.1.bk.b.1691.1 2 39.5 even 4
3549.1.bm.a.191.1 2 91.37 odd 12
3549.1.bm.a.191.1 2 273.128 even 12
3549.1.bm.a.2174.1 2 13.7 odd 12
3549.1.bm.a.2174.1 2 39.20 even 12
3549.1.bp.c.23.1 4 91.30 even 6
3549.1.bp.c.23.1 4 273.212 odd 6
3549.1.bp.c.23.2 4 91.9 even 3
3549.1.bp.c.23.2 4 273.191 odd 6
3549.1.bp.c.2006.1 4 13.3 even 3
3549.1.bp.c.2006.1 4 39.29 odd 6
3549.1.bp.c.2006.2 4 13.10 even 6
3549.1.bp.c.2006.2 4 39.23 odd 6