Properties

Label 189.2.e.b.163.1
Level 189189
Weight 22
Character 189.163
Analytic conductor 1.5091.509
Analytic rank 00
Dimension 22
CM discriminant -3
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [189,2,Mod(109,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 189=337 189 = 3^{3} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 189.e (of order 33, degree 22, 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: 1.509172598201.50917259820
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x+1 x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: U(1)[D3]\mathrm{U}(1)[D_{3}]

Embedding invariants

Embedding label 163.1
Root 0.5000000.866025i0.500000 - 0.866025i of defining polynomial
Character χ\chi == 189.163
Dual form 189.2.e.b.109.1

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+(1.00000+1.73205i)q4+(0.500000+2.59808i)q7+2.00000q13+(2.00000+3.46410i)q16+(3.500006.06218i)q19+(2.50000+4.33013i)q25+(5.00000+1.73205i)q28+(5.500009.52628i)q31+(5.000008.66025i)q3713.0000q43+(6.500002.59808i)q49+(2.00000+3.46410i)q52+(6.5000011.2583i)q618.00000q64+(8.00000+13.8564i)q67+(3.50000+6.06218i)q73+14.0000q76+(2.000003.46410i)q79+(1.00000+5.19615i)q91+5.00000q97+O(q100)q+(1.00000 + 1.73205i) q^{4} +(-0.500000 + 2.59808i) q^{7} +2.00000 q^{13} +(-2.00000 + 3.46410i) q^{16} +(3.50000 - 6.06218i) q^{19} +(2.50000 + 4.33013i) q^{25} +(-5.00000 + 1.73205i) q^{28} +(-5.50000 - 9.52628i) q^{31} +(5.00000 - 8.66025i) q^{37} -13.0000 q^{43} +(-6.50000 - 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{52} +(6.50000 - 11.2583i) q^{61} -8.00000 q^{64} +(8.00000 + 13.8564i) q^{67} +(3.50000 + 6.06218i) q^{73} +14.0000 q^{76} +(2.00000 - 3.46410i) q^{79} +(-1.00000 + 5.19615i) q^{91} +5.00000 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+2q4q7+4q134q16+7q19+5q2510q2811q31+10q3726q4313q49+4q52+13q6116q64+16q67+7q73+28q76+4q79++10q97+O(q100) 2 q + 2 q^{4} - q^{7} + 4 q^{13} - 4 q^{16} + 7 q^{19} + 5 q^{25} - 10 q^{28} - 11 q^{31} + 10 q^{37} - 26 q^{43} - 13 q^{49} + 4 q^{52} + 13 q^{61} - 16 q^{64} + 16 q^{67} + 7 q^{73} + 28 q^{76} + 4 q^{79}+ \cdots + 10 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/189Z)×\left(\mathbb{Z}/189\mathbb{Z}\right)^\times.

nn 2929 136136
χ(n)\chi(n) 11 e(13)e\left(\frac{1}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
33 0 0
44 1.00000 + 1.73205i 0.500000 + 0.866025i
55 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
66 0 0
77 −0.500000 + 2.59808i −0.188982 + 0.981981i
88 0 0
99 0 0
1010 0 0
1111 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
1212 0 0
1313 2.00000 0.554700 0.277350 0.960769i 0.410544π-0.410544\pi
0.277350 + 0.960769i 0.410544π0.410544\pi
1414 0 0
1515 0 0
1616 −2.00000 + 3.46410i −0.500000 + 0.866025i
1717 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
1818 0 0
1919 3.50000 6.06218i 0.802955 1.39076i −0.114708 0.993399i 0.536593π-0.536593\pi
0.917663 0.397360i 0.130073π-0.130073\pi
2020 0 0
2121 0 0
2222 0 0
2323 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
2424 0 0
2525 2.50000 + 4.33013i 0.500000 + 0.866025i
2626 0 0
2727 0 0
2828 −5.00000 + 1.73205i −0.944911 + 0.327327i
2929 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
3030 0 0
3131 −5.50000 9.52628i −0.987829 1.71097i −0.628619 0.777714i 0.716379π-0.716379\pi
−0.359211 0.933257i 0.616954π-0.616954\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 0 0
3737 5.00000 8.66025i 0.821995 1.42374i −0.0821995 0.996616i 0.526194π-0.526194\pi
0.904194 0.427121i 0.140472π-0.140472\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 −13.0000 −1.98248 −0.991241 0.132068i 0.957838π-0.957838\pi
−0.991241 + 0.132068i 0.957838π0.957838\pi
4444 0 0
4545 0 0
4646 0 0
4747 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
4848 0 0
4949 −6.50000 2.59808i −0.928571 0.371154i
5050 0 0
5151 0 0
5252 2.00000 + 3.46410i 0.277350 + 0.480384i
5353 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 0 0
5959 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
6060 0 0
6161 6.50000 11.2583i 0.832240 1.44148i −0.0640184 0.997949i 0.520392π-0.520392\pi
0.896258 0.443533i 0.146275π-0.146275\pi
6262 0 0
6363 0 0
6464 −8.00000 −1.00000
6565 0 0
6666 0 0
6767 8.00000 + 13.8564i 0.977356 + 1.69283i 0.671932 + 0.740613i 0.265465π0.265465\pi
0.305424 + 0.952217i 0.401202π0.401202\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 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i 0.0323196π-0.0323196\pi
−0.585206 + 0.810885i 0.698986π0.698986\pi
7474 0 0
7575 0 0
7676 14.0000 1.60591
7777 0 0
7878 0 0
7979 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i 0.761089π-0.761089\pi
0.956325 + 0.292306i 0.0944227π0.0944227\pi
8080 0 0
8181 0 0
8282 0 0
8383 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
8484 0 0
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
9090 0 0
9191 −1.00000 + 5.19615i −0.104828 + 0.544705i
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 0 0
9797 5.00000 0.507673 0.253837 0.967247i 0.418307π-0.418307\pi
0.253837 + 0.967247i 0.418307π0.418307\pi
9898 0 0
9999 0 0
100100 −5.00000 + 8.66025i −0.500000 + 0.866025i
101101 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
102102 0 0
103103 −10.0000 + 17.3205i −0.985329 + 1.70664i −0.344865 + 0.938652i 0.612075π0.612075\pi
−0.640464 + 0.767988i 0.721258π0.721258\pi
104104 0 0
105105 0 0
106106 0 0
107107 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
108108 0 0
109109 9.50000 + 16.4545i 0.909935 + 1.57605i 0.814152 + 0.580651i 0.197202π0.197202\pi
0.0957826 + 0.995402i 0.469465π0.469465\pi
110110 0 0
111111 0 0
112112 −8.00000 6.92820i −0.755929 0.654654i
113113 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
114114 0 0
115115 0 0
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 5.50000 9.52628i 0.500000 0.866025i
122122 0 0
123123 0 0
124124 11.0000 19.0526i 0.987829 1.71097i
125125 0 0
126126 0 0
127127 −1.00000 −0.0887357 −0.0443678 0.999015i 0.514127π-0.514127\pi
−0.0443678 + 0.999015i 0.514127π0.514127\pi
128128 0 0
129129 0 0
130130 0 0
131131 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
132132 0 0
133133 14.0000 + 12.1244i 1.21395 + 1.05131i
134134 0 0
135135 0 0
136136 0 0
137137 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
138138 0 0
139139 −16.0000 −1.35710 −0.678551 0.734553i 0.737392π-0.737392\pi
−0.678551 + 0.734553i 0.737392π0.737392\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 0 0
145145 0 0
146146 0 0
147147 0 0
148148 20.0000 1.64399
149149 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
150150 0 0
151151 −11.5000 19.9186i −0.935857 1.62095i −0.773099 0.634285i 0.781294π-0.781294\pi
−0.162758 0.986666i 0.552039π-0.552039\pi
152152 0 0
153153 0 0
154154 0 0
155155 0 0
156156 0 0
157157 −7.00000 12.1244i −0.558661 0.967629i −0.997609 0.0691164i 0.977982π-0.977982\pi
0.438948 0.898513i 0.355351π-0.355351\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 0 0
163163 −8.50000 + 14.7224i −0.665771 + 1.15315i 0.313304 + 0.949653i 0.398564π0.398564\pi
−0.979076 + 0.203497i 0.934769π0.934769\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 −9.00000 −0.692308
170170 0 0
171171 0 0
172172 −13.0000 22.5167i −0.991241 1.71688i
173173 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
174174 0 0
175175 −12.5000 + 4.33013i −0.944911 + 0.327327i
176176 0 0
177177 0 0
178178 0 0
179179 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
180180 0 0
181181 −7.00000 −0.520306 −0.260153 0.965567i 0.583773π-0.583773\pi
−0.260153 + 0.965567i 0.583773π0.583773\pi
182182 0 0
183183 0 0
184184 0 0
185185 0 0
186186 0 0
187187 0 0
188188 0 0
189189 0 0
190190 0 0
191191 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
192192 0 0
193193 −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i 0.189599π-0.189599\pi
−0.899770 + 0.436365i 0.856266π0.856266\pi
194194 0 0
195195 0 0
196196 −2.00000 13.8564i −0.142857 0.989743i
197197 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
198198 0 0
199199 −8.50000 14.7224i −0.602549 1.04365i −0.992434 0.122782i 0.960818π-0.960818\pi
0.389885 0.920864i 0.372515π-0.372515\pi
200200 0 0
201201 0 0
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 −4.00000 + 6.92820i −0.277350 + 0.480384i
209209 0 0
210210 0 0
211211 29.0000 1.99644 0.998221 0.0596196i 0.0189888π-0.0189888\pi
0.998221 + 0.0596196i 0.0189888π0.0189888\pi
212212 0 0
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 27.5000 9.52628i 1.86682 0.646686i
218218 0 0
219219 0 0
220220 0 0
221221 0 0
222222 0 0
223223 −28.0000 −1.87502 −0.937509 0.347960i 0.886874π-0.886874\pi
−0.937509 + 0.347960i 0.886874π0.886874\pi
224224 0 0
225225 0 0
226226 0 0
227227 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
228228 0 0
229229 −14.5000 + 25.1147i −0.958187 + 1.65963i −0.231287 + 0.972886i 0.574293π0.574293\pi
−0.726900 + 0.686743i 0.759040π0.759040\pi
230230 0 0
231231 0 0
232232 0 0
233233 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
234234 0 0
235235 0 0
236236 0 0
237237 0 0
238238 0 0
239239 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
240240 0 0
241241 15.5000 + 26.8468i 0.998443 + 1.72935i 0.547533 + 0.836784i 0.315567π0.315567\pi
0.450910 + 0.892570i 0.351100π0.351100\pi
242242 0 0
243243 0 0
244244 26.0000 1.66448
245245 0 0
246246 0 0
247247 7.00000 12.1244i 0.445399 0.771454i
248248 0 0
249249 0 0
250250 0 0
251251 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 −8.00000 13.8564i −0.500000 0.866025i
257257 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
258258 0 0
259259 20.0000 + 17.3205i 1.24274 + 1.07624i
260260 0 0
261261 0 0
262262 0 0
263263 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 −16.0000 + 27.7128i −0.977356 + 1.69283i
269269 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
270270 0 0
271271 0.500000 0.866025i 0.0303728 0.0526073i −0.850439 0.526073i 0.823664π-0.823664\pi
0.880812 + 0.473466i 0.156997π0.156997\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 0 0
277277 −2.50000 4.33013i −0.150210 0.260172i 0.781094 0.624413i 0.214662π-0.214662\pi
−0.931305 + 0.364241i 0.881328π0.881328\pi
278278 0 0
279279 0 0
280280 0 0
281281 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
282282 0 0
283283 12.5000 + 21.6506i 0.743048 + 1.28700i 0.951101 + 0.308879i 0.0999539π0.0999539\pi
−0.208053 + 0.978117i 0.566713π0.566713\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 8.50000 14.7224i 0.500000 0.866025i
290290 0 0
291291 0 0
292292 −7.00000 + 12.1244i −0.409644 + 0.709524i
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 0 0
301301 6.50000 33.7750i 0.374654 1.94676i
302302 0 0
303303 0 0
304304 14.0000 + 24.2487i 0.802955 + 1.39076i
305305 0 0
306306 0 0
307307 −19.0000 −1.08439 −0.542194 0.840254i 0.682406π-0.682406\pi
−0.542194 + 0.840254i 0.682406π0.682406\pi
308308 0 0
309309 0 0
310310 0 0
311311 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
312312 0 0
313313 −17.5000 + 30.3109i −0.989158 + 1.71327i −0.367402 + 0.930062i 0.619753π0.619753\pi
−0.621757 + 0.783210i 0.713581π0.713581\pi
314314 0 0
315315 0 0
316316 8.00000 0.450035
317317 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
318318 0 0
319319 0 0
320320 0 0
321321 0 0
322322 0 0
323323 0 0
324324 0 0
325325 5.00000 + 8.66025i 0.277350 + 0.480384i
326326 0 0
327327 0 0
328328 0 0
329329 0 0
330330 0 0
331331 0.500000 0.866025i 0.0274825 0.0476011i −0.851957 0.523612i 0.824584π-0.824584\pi
0.879440 + 0.476011i 0.157918π0.157918\pi
332332 0 0
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 5.00000 0.272367 0.136184 0.990684i 0.456516π-0.456516\pi
0.136184 + 0.990684i 0.456516π0.456516\pi
338338 0 0
339339 0 0
340340 0 0
341341 0 0
342342 0 0
343343 10.0000 15.5885i 0.539949 0.841698i
344344 0 0
345345 0 0
346346 0 0
347347 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
348348 0 0
349349 23.0000 1.23116 0.615581 0.788074i 0.288921π-0.288921\pi
0.615581 + 0.788074i 0.288921π0.288921\pi
350350 0 0
351351 0 0
352352 0 0
353353 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
360360 0 0
361361 −15.0000 25.9808i −0.789474 1.36741i
362362 0 0
363363 0 0
364364 −10.0000 + 3.46410i −0.524142 + 0.181568i
365365 0 0
366366 0 0
367367 −17.5000 30.3109i −0.913493 1.58222i −0.809093 0.587680i 0.800041π-0.800041\pi
−0.104399 0.994535i 0.533292π-0.533292\pi
368368 0 0
369369 0 0
370370 0 0
371371 0 0
372372 0 0
373373 6.50000 11.2583i 0.336557 0.582934i −0.647225 0.762299i 0.724071π-0.724071\pi
0.983783 + 0.179364i 0.0574041π0.0574041\pi
374374 0 0
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 8.00000 0.410932 0.205466 0.978664i 0.434129π-0.434129\pi
0.205466 + 0.978664i 0.434129π0.434129\pi
380380 0 0
381381 0 0
382382 0 0
383383 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 5.00000 + 8.66025i 0.253837 + 0.439658i
389389 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
390390 0 0
391391 0 0
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 0.500000 0.866025i 0.0250943 0.0434646i −0.853206 0.521575i 0.825345π-0.825345\pi
0.878300 + 0.478110i 0.158678π0.158678\pi
398398 0 0
399399 0 0
400400 −20.0000 −1.00000
401401 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
402402 0 0
403403 −11.0000 19.0526i −0.547949 0.949076i
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 −19.0000 32.9090i −0.939490 1.62724i −0.766426 0.642333i 0.777967π-0.777967\pi
−0.173064 0.984911i 0.555367π-0.555367\pi
410410 0 0
411411 0 0
412412 −40.0000 −1.97066
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 0 0
418418 0 0
419419 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
420420 0 0
421421 −19.0000 −0.926003 −0.463002 0.886357i 0.653228π-0.653228\pi
−0.463002 + 0.886357i 0.653228π0.653228\pi
422422 0 0
423423 0 0
424424 0 0
425425 0 0
426426 0 0
427427 26.0000 + 22.5167i 1.25823 + 1.08966i
428428 0 0
429429 0 0
430430 0 0
431431 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
432432 0 0
433433 −37.0000 −1.77811 −0.889053 0.457804i 0.848636π-0.848636\pi
−0.889053 + 0.457804i 0.848636π0.848636\pi
434434 0 0
435435 0 0
436436 −19.0000 + 32.9090i −0.909935 + 1.57605i
437437 0 0
438438 0 0
439439 14.0000 24.2487i 0.668184 1.15733i −0.310228 0.950662i 0.600405π-0.600405\pi
0.978412 0.206666i 0.0662612π-0.0662612\pi
440440 0 0
441441 0 0
442442 0 0
443443 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 4.00000 20.7846i 0.188982 0.981981i
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 0 0
454454 0 0
455455 0 0
456456 0 0
457457 15.5000 26.8468i 0.725059 1.25584i −0.233890 0.972263i 0.575146π-0.575146\pi
0.958950 0.283577i 0.0915211π-0.0915211\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 23.0000 1.06890 0.534450 0.845200i 0.320519π-0.320519\pi
0.534450 + 0.845200i 0.320519π0.320519\pi
464464 0 0
465465 0 0
466466 0 0
467467 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
468468 0 0
469469 −40.0000 + 13.8564i −1.84703 + 0.639829i
470470 0 0
471471 0 0
472472 0 0
473473 0 0
474474 0 0
475475 35.0000 1.60591
476476 0 0
477477 0 0
478478 0 0
479479 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
480480 0 0
481481 10.0000 17.3205i 0.455961 0.789747i
482482 0 0
483483 0 0
484484 22.0000 1.00000
485485 0 0
486486 0 0
487487 12.5000 + 21.6506i 0.566429 + 0.981084i 0.996915 + 0.0784867i 0.0250088π0.0250088\pi
−0.430486 + 0.902597i 0.641658π0.641658\pi
488488 0 0
489489 0 0
490490 0 0
491491 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 44.0000 1.97566
497497 0 0
498498 0 0
499499 −5.50000 + 9.52628i −0.246214 + 0.426455i −0.962472 0.271380i 0.912520π-0.912520\pi
0.716258 + 0.697835i 0.245853π0.245853\pi
500500 0 0
501501 0 0
502502 0 0
503503 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
504504 0 0
505505 0 0
506506 0 0
507507 0 0
508508 −1.00000 1.73205i −0.0443678 0.0768473i
509509 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
510510 0 0
511511 −17.5000 + 6.06218i −0.774154 + 0.268175i
512512 0 0
513513 0 0
514514 0 0
515515 0 0
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
522522 0 0
523523 −4.00000 + 6.92820i −0.174908 + 0.302949i −0.940129 0.340818i 0.889296π-0.889296\pi
0.765222 + 0.643767i 0.222629π0.222629\pi
524524 0 0
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 11.5000 + 19.9186i 0.500000 + 0.866025i
530530 0 0
531531 0 0
532532 −7.00000 + 36.3731i −0.303488 + 1.57697i
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 −14.5000 + 25.1147i −0.623404 + 1.07977i 0.365444 + 0.930834i 0.380917π0.380917\pi
−0.988847 + 0.148933i 0.952416π0.952416\pi
542542 0 0
543543 0 0
544544 0 0
545545 0 0
546546 0 0
547547 41.0000 1.75303 0.876517 0.481371i 0.159861π-0.159861\pi
0.876517 + 0.481371i 0.159861π0.159861\pi
548548 0 0
549549 0 0
550550 0 0
551551 0 0
552552 0 0
553553 8.00000 + 6.92820i 0.340195 + 0.294617i
554554 0 0
555555 0 0
556556 −16.0000 27.7128i −0.678551 1.17529i
557557 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
558558 0 0
559559 −26.0000 −1.09968
560560 0 0
561561 0 0
562562 0 0
563563 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
564564 0 0
565565 0 0
566566 0 0
567567 0 0
568568 0 0
569569 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
570570 0 0
571571 15.5000 + 26.8468i 0.648655 + 1.12350i 0.983444 + 0.181210i 0.0580014π0.0580014\pi
−0.334790 + 0.942293i 0.608665π0.608665\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 0 0
577577 23.0000 + 39.8372i 0.957503 + 1.65844i 0.728535 + 0.685009i 0.240202π0.240202\pi
0.228968 + 0.973434i 0.426465π0.426465\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 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
588588 0 0
589589 −77.0000 −3.17273
590590 0 0
591591 0 0
592592 20.0000 + 34.6410i 0.821995 + 1.42374i
593593 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
600600 0 0
601601 23.0000 0.938190 0.469095 0.883148i 0.344580π-0.344580\pi
0.469095 + 0.883148i 0.344580π0.344580\pi
602602 0 0
603603 0 0
604604 23.0000 39.8372i 0.935857 1.62095i
605605 0 0
606606 0 0
607607 24.5000 42.4352i 0.994424 1.72239i 0.405887 0.913923i 0.366962π-0.366962\pi
0.588537 0.808470i 0.299704π-0.299704\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 0 0
613613 18.5000 + 32.0429i 0.747208 + 1.29420i 0.949156 + 0.314806i 0.101939π0.101939\pi
−0.201948 + 0.979396i 0.564727π0.564727\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 −16.0000 27.7128i −0.643094 1.11387i −0.984738 0.174042i 0.944317π-0.944317\pi
0.341644 0.939829i 0.389016π-0.389016\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 −12.5000 + 21.6506i −0.500000 + 0.866025i
626626 0 0
627627 0 0
628628 14.0000 24.2487i 0.558661 0.967629i
629629 0 0
630630 0 0
631631 −1.00000 −0.0398094 −0.0199047 0.999802i 0.506336π-0.506336\pi
−0.0199047 + 0.999802i 0.506336π0.506336\pi
632632 0 0
633633 0 0
634634 0 0
635635 0 0
636636 0 0
637637 −13.0000 5.19615i −0.515079 0.205879i
638638 0 0
639639 0 0
640640 0 0
641641 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
642642 0 0
643643 47.0000 1.85350 0.926750 0.375680i 0.122591π-0.122591\pi
0.926750 + 0.375680i 0.122591π0.122591\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
648648 0 0
649649 0 0
650650 0 0
651651 0 0
652652 −34.0000 −1.33154
653653 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
654654 0 0
655655 0 0
656656 0 0
657657 0 0
658658 0 0
659659 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
660660 0 0
661661 24.5000 + 42.4352i 0.952940 + 1.65054i 0.739014 + 0.673690i 0.235292π0.235292\pi
0.213925 + 0.976850i 0.431375π0.431375\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 −37.0000 −1.42625 −0.713123 0.701039i 0.752720π-0.752720\pi
−0.713123 + 0.701039i 0.752720π0.752720\pi
674674 0 0
675675 0 0
676676 −9.00000 15.5885i −0.346154 0.599556i
677677 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
678678 0 0
679679 −2.50000 + 12.9904i −0.0959412 + 0.498525i
680680 0 0
681681 0 0
682682 0 0
683683 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
684684 0 0
685685 0 0
686686 0 0
687687 0 0
688688 26.0000 45.0333i 0.991241 1.71688i
689689 0 0
690690 0 0
691691 −20.5000 + 35.5070i −0.779857 + 1.35075i 0.152167 + 0.988355i 0.451375π0.451375\pi
−0.932024 + 0.362397i 0.881959π0.881959\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 −20.0000 17.3205i −0.755929 0.654654i
701701 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
702702 0 0
703703 −35.0000 60.6218i −1.32005 2.28639i
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 15.5000 26.8468i 0.582115 1.00825i −0.413114 0.910679i 0.635559π-0.635559\pi
0.995228 0.0975728i 0.0311079π-0.0311079\pi
710710 0 0
711711 0 0
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
720720 0 0
721721 −40.0000 34.6410i −1.48968 1.29010i
722722 0 0
723723 0 0
724724 −7.00000 12.1244i −0.260153 0.450598i
725725 0 0
726726 0 0
727727 5.00000 0.185440 0.0927199 0.995692i 0.470444π-0.470444\pi
0.0927199 + 0.995692i 0.470444π0.470444\pi
728728 0 0
729729 0 0
730730 0 0
731731 0 0
732732 0 0
733733 21.5000 37.2391i 0.794121 1.37546i −0.129275 0.991609i 0.541265π-0.541265\pi
0.923396 0.383849i 0.125402π-0.125402\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 18.5000 + 32.0429i 0.680534 + 1.17872i 0.974818 + 0.223001i 0.0715853π0.0715853\pi
−0.294285 + 0.955718i 0.595081π0.595081\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 −20.5000 + 35.5070i −0.748056 + 1.29567i 0.200698 + 0.979653i 0.435679π0.435679\pi
−0.948753 + 0.316017i 0.897654π0.897654\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 −55.0000 −1.99901 −0.999505 0.0314762i 0.989979π-0.989979\pi
−0.999505 + 0.0314762i 0.989979π0.989979\pi
758758 0 0
759759 0 0
760760 0 0
761761 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
762762 0 0
763763 −47.5000 + 16.4545i −1.71962 + 0.595692i
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 0 0
769769 −49.0000 −1.76699 −0.883493 0.468445i 0.844814π-0.844814\pi
−0.883493 + 0.468445i 0.844814π0.844814\pi
770770 0 0
771771 0 0
772772 2.00000 3.46410i 0.0719816 0.124676i
773773 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
774774 0 0
775775 27.5000 47.6314i 0.987829 1.71097i
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 22.0000 17.3205i 0.785714 0.618590i
785785 0 0
786786 0 0
787787 12.5000 + 21.6506i 0.445577 + 0.771762i 0.998092 0.0617409i 0.0196653π-0.0196653\pi
−0.552515 + 0.833503i 0.686332π0.686332\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 13.0000 22.5167i 0.461644 0.799590i
794794 0 0
795795 0 0
796796 17.0000 29.4449i 0.602549 1.04365i
797797 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
798798 0 0
799799 0 0
800800 0 0
801801 0 0
802802 0 0
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
810810 0 0
811811 56.0000 1.96643 0.983213 0.182462i 0.0584065π-0.0584065\pi
0.983213 + 0.182462i 0.0584065π0.0584065\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 0 0
817817 −45.5000 + 78.8083i −1.59184 + 2.75715i
818818 0 0
819819 0 0
820820 0 0
821821 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
822822 0 0
823823 −23.5000 40.7032i −0.819159 1.41882i −0.906303 0.422628i 0.861108π-0.861108\pi
0.0871445 0.996196i 0.472226π-0.472226\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 3.50000 + 6.06218i 0.121560 + 0.210548i 0.920383 0.391018i 0.127877π-0.127877\pi
−0.798823 + 0.601566i 0.794544π0.794544\pi
830830 0 0
831831 0 0
832832 −16.0000 −0.554700
833833 0 0
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0 0
839839 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
840840 0 0
841841 −29.0000 −1.00000
842842 0 0
843843 0 0
844844 29.0000 + 50.2295i 0.998221 + 1.72897i
845845 0 0
846846 0 0
847847 22.0000 + 19.0526i 0.755929 + 0.654654i
848848 0 0
849849 0 0
850850 0 0
851851 0 0
852852 0 0
853853 35.0000 1.19838 0.599189 0.800608i 0.295490π-0.295490\pi
0.599189 + 0.800608i 0.295490π0.295490\pi
854854 0 0
855855 0 0
856856 0 0
857857 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
858858 0 0
859859 21.5000 37.2391i 0.733571 1.27058i −0.221777 0.975097i 0.571186π-0.571186\pi
0.955348 0.295484i 0.0954809π-0.0954809\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
864864 0 0
865865 0 0
866866 0 0
867867 0 0
868868 44.0000 + 38.1051i 1.49346 + 1.29337i
869869 0 0
870870 0 0
871871 16.0000 + 27.7128i 0.542139 + 0.939013i
872872 0 0
873873 0 0
874874 0 0
875875 0 0
876876 0 0
877877 12.5000 21.6506i 0.422095 0.731090i −0.574049 0.818821i 0.694628π-0.694628\pi
0.996144 + 0.0877308i 0.0279615π0.0279615\pi
878878 0 0
879879 0 0
880880 0 0
881881 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
882882 0 0
883883 47.0000 1.58168 0.790838 0.612026i 0.209645π-0.209645\pi
0.790838 + 0.612026i 0.209645π0.209645\pi
884884 0 0
885885 0 0
886886 0 0
887887 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
888888 0 0
889889 0.500000 2.59808i 0.0167695 0.0871367i
890890 0 0
891891 0 0
892892 −28.0000 48.4974i −0.937509 1.62381i
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 0 0
901901 0 0
902902 0 0
903903 0 0
904904 0 0
905905 0 0
906906 0 0
907907 20.0000 + 34.6410i 0.664089 + 1.15024i 0.979531 + 0.201291i 0.0645138π0.0645138\pi
−0.315442 + 0.948945i 0.602153π0.602153\pi
908908 0 0
909909 0 0
910910 0 0
911911 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
912912 0 0
913913 0 0
914914 0 0
915915 0 0
916916 −58.0000 −1.91637
917917 0 0
918918 0 0
919919 −26.5000 + 45.8993i −0.874154 + 1.51408i −0.0164935 + 0.999864i 0.505250π0.505250\pi
−0.857661 + 0.514216i 0.828083π0.828083\pi
920920 0 0
921921 0 0
922922 0 0
923923 0 0
924924 0 0
925925 50.0000 1.64399
926926 0 0
927927 0 0
928928 0 0
929929 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
930930 0 0
931931 −38.5000 + 30.3109i −1.26179 + 0.993399i
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 26.0000 0.849383 0.424691 0.905338i 0.360383π-0.360383\pi
0.424691 + 0.905338i 0.360383π0.360383\pi
938938 0 0
939939 0 0
940940 0 0
941941 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
948948 0 0
949949 7.00000 + 12.1244i 0.227230 + 0.393573i
950950 0 0
951951 0 0
952952 0 0
953953 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 −45.0000 + 77.9423i −1.45161 + 2.51427i
962962 0 0
963963 0 0
964964 −31.0000 + 53.6936i −0.998443 + 1.72935i
965965 0 0
966966 0 0
967967 20.0000 0.643157 0.321578 0.946883i 0.395787π-0.395787\pi
0.321578 + 0.946883i 0.395787π0.395787\pi
968968 0 0
969969 0 0
970970 0 0
971971 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
972972 0 0
973973 8.00000 41.5692i 0.256468 1.33265i
974974 0 0
975975 0 0
976976 26.0000 + 45.0333i 0.832240 + 1.44148i
977977 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
978978 0 0
979979 0 0
980980 0 0
981981 0 0
982982 0 0
983983 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 28.0000 0.890799
989989 0 0
990990 0 0
991991 −22.0000 38.1051i −0.698853 1.21045i −0.968864 0.247592i 0.920361π-0.920361\pi
0.270011 0.962857i 0.412973π-0.412973\pi
992992 0 0
993993 0 0
994994 0 0
995995 0 0
996996 0 0
997997 −29.5000 51.0955i −0.934274 1.61821i −0.775923 0.630828i 0.782715π-0.782715\pi
−0.158352 0.987383i 0.550618π-0.550618\pi
998998 0 0
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 189.2.e.b.163.1 yes 2
3.2 odd 2 CM 189.2.e.b.163.1 yes 2
7.2 even 3 1323.2.a.k.1.1 1
7.4 even 3 inner 189.2.e.b.109.1 2
7.5 odd 6 1323.2.a.j.1.1 1
9.2 odd 6 567.2.h.d.352.1 2
9.4 even 3 567.2.g.c.541.1 2
9.5 odd 6 567.2.g.c.541.1 2
9.7 even 3 567.2.h.d.352.1 2
21.2 odd 6 1323.2.a.k.1.1 1
21.5 even 6 1323.2.a.j.1.1 1
21.11 odd 6 inner 189.2.e.b.109.1 2
63.4 even 3 567.2.h.d.298.1 2
63.11 odd 6 567.2.g.c.109.1 2
63.25 even 3 567.2.g.c.109.1 2
63.32 odd 6 567.2.h.d.298.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.e.b.109.1 2 7.4 even 3 inner
189.2.e.b.109.1 2 21.11 odd 6 inner
189.2.e.b.163.1 yes 2 1.1 even 1 trivial
189.2.e.b.163.1 yes 2 3.2 odd 2 CM
567.2.g.c.109.1 2 63.11 odd 6
567.2.g.c.109.1 2 63.25 even 3
567.2.g.c.541.1 2 9.4 even 3
567.2.g.c.541.1 2 9.5 odd 6
567.2.h.d.298.1 2 63.4 even 3
567.2.h.d.298.1 2 63.32 odd 6
567.2.h.d.352.1 2 9.2 odd 6
567.2.h.d.352.1 2 9.7 even 3
1323.2.a.j.1.1 1 7.5 odd 6
1323.2.a.j.1.1 1 21.5 even 6
1323.2.a.k.1.1 1 7.2 even 3
1323.2.a.k.1.1 1 21.2 odd 6