Properties

Label 136.1.j.a.123.1
Level 136136
Weight 11
Character 136.123
Analytic conductor 0.0680.068
Analytic rank 00
Dimension 22
Projective image D4D_{4}
CM discriminant -8
Inner twists 44

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [136,1,Mod(115,136)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(136, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 2, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("136.115");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 136=2317 136 = 2^{3} \cdot 17
Weight: k k == 1 1
Character orbit: [χ][\chi] == 136.j (of order 44, 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: 0.06787284171810.0678728417181
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2+1 x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Projective image: D4D_{4}
Projective field: Galois closure of 4.0.314432.1
Artin image: C4C2C_4\wr C_2
Artin field: Galois closure of 8.0.20123648.1

Embedding invariants

Embedding label 123.1
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 136.123
Dual form 136.1.j.a.115.1

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+1.00000iq2+(1.00000+1.00000i)q31.00000q4+(1.000001.00000i)q61.00000iq81.00000iq9+(1.00000+1.00000i)q11+(1.000001.00000i)q12+1.00000q16+1.00000iq17+1.00000q182.00000iq19+(1.00000+1.00000i)q22+(1.00000+1.00000i)q241.00000iq25+1.00000iq322.00000q331.00000q34+1.00000iq36+2.00000q38+(1.000001.00000i)q41+(1.000001.00000i)q44+(1.00000+1.00000i)q48+1.00000iq49+1.00000q50+(1.000001.00000i)q51+(2.00000+2.00000i)q571.00000q642.00000iq661.00000iq681.00000q72+(1.00000+1.00000i)q73+(1.00000+1.00000i)q75+2.00000iq76+1.00000q81+(1.000001.00000i)q82+(1.000001.00000i)q88+(1.000001.00000i)q96+(1.000001.00000i)q971.00000q98+(1.000001.00000i)q99+O(q100)q+1.00000i q^{2} +(-1.00000 + 1.00000i) q^{3} -1.00000 q^{4} +(-1.00000 - 1.00000i) q^{6} -1.00000i q^{8} -1.00000i q^{9} +(1.00000 + 1.00000i) q^{11} +(1.00000 - 1.00000i) q^{12} +1.00000 q^{16} +1.00000i q^{17} +1.00000 q^{18} -2.00000i q^{19} +(-1.00000 + 1.00000i) q^{22} +(1.00000 + 1.00000i) q^{24} -1.00000i q^{25} +1.00000i q^{32} -2.00000 q^{33} -1.00000 q^{34} +1.00000i q^{36} +2.00000 q^{38} +(-1.00000 - 1.00000i) q^{41} +(-1.00000 - 1.00000i) q^{44} +(-1.00000 + 1.00000i) q^{48} +1.00000i q^{49} +1.00000 q^{50} +(-1.00000 - 1.00000i) q^{51} +(2.00000 + 2.00000i) q^{57} -1.00000 q^{64} -2.00000i q^{66} -1.00000i q^{68} -1.00000 q^{72} +(-1.00000 + 1.00000i) q^{73} +(1.00000 + 1.00000i) q^{75} +2.00000i q^{76} +1.00000 q^{81} +(1.00000 - 1.00000i) q^{82} +(1.00000 - 1.00000i) q^{88} +(-1.00000 - 1.00000i) q^{96} +(1.00000 - 1.00000i) q^{97} -1.00000 q^{98} +(1.00000 - 1.00000i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q32q42q6+2q11+2q12+2q16+2q182q22+2q244q332q34+4q382q412q442q48+2q502q51+4q572q64++2q99+O(q100) 2 q - 2 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{11} + 2 q^{12} + 2 q^{16} + 2 q^{18} - 2 q^{22} + 2 q^{24} - 4 q^{33} - 2 q^{34} + 4 q^{38} - 2 q^{41} - 2 q^{44} - 2 q^{48} + 2 q^{50} - 2 q^{51} + 4 q^{57} - 2 q^{64}+ \cdots + 2 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/136Z)×\left(\mathbb{Z}/136\mathbb{Z}\right)^\times.

nn 6969 103103 105105
χ(n)\chi(n) 1-1 1-1 e(34)e\left(\frac{3}{4}\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 1.00000i 1.00000i
33 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
44 −1.00000 −1.00000
55 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
66 −1.00000 1.00000i −1.00000 1.00000i
77 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
88 1.00000i 1.00000i
99 1.00000i 1.00000i
1010 0 0
1111 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
1212 1.00000 1.00000i 1.00000 1.00000i
1313 0 0 1.00000 00
−1.00000 π\pi
1414 0 0
1515 0 0
1616 1.00000 1.00000
1717 1.00000i 1.00000i
1818 1.00000 1.00000
1919 2.00000i 2.00000i 1.00000i 0.5π-0.5\pi
1.00000i 0.5π-0.5\pi
2020 0 0
2121 0 0
2222 −1.00000 + 1.00000i −1.00000 + 1.00000i
2323 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
2424 1.00000 + 1.00000i 1.00000 + 1.00000i
2525 1.00000i 1.00000i
2626 0 0
2727 0 0
2828 0 0
2929 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
3030 0 0
3131 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
3232 1.00000i 1.00000i
3333 −2.00000 −2.00000
3434 −1.00000 −1.00000
3535 0 0
3636 1.00000i 1.00000i
3737 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
3838 2.00000 2.00000
3939 0 0
4040 0 0
4141 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
4242 0 0
4343 0 0 1.00000 00
−1.00000 π\pi
4444 −1.00000 1.00000i −1.00000 1.00000i
4545 0 0
4646 0 0
4747 0 0 1.00000 00
−1.00000 π\pi
4848 −1.00000 + 1.00000i −1.00000 + 1.00000i
4949 1.00000i 1.00000i
5050 1.00000 1.00000
5151 −1.00000 1.00000i −1.00000 1.00000i
5252 0 0
5353 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
5454 0 0
5555 0 0
5656 0 0
5757 2.00000 + 2.00000i 2.00000 + 2.00000i
5858 0 0
5959 0 0 1.00000 00
−1.00000 π\pi
6060 0 0
6161 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
6262 0 0
6363 0 0
6464 −1.00000 −1.00000
6565 0 0
6666 2.00000i 2.00000i
6767 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
6868 1.00000i 1.00000i
6969 0 0
7070 0 0
7171 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
7272 −1.00000 −1.00000
7373 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
7474 0 0
7575 1.00000 + 1.00000i 1.00000 + 1.00000i
7676 2.00000i 2.00000i
7777 0 0
7878 0 0
7979 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
8080 0 0
8181 1.00000 1.00000
8282 1.00000 1.00000i 1.00000 1.00000i
8383 0 0 1.00000 00
−1.00000 π\pi
8484 0 0
8585 0 0
8686 0 0
8787 0 0
8888 1.00000 1.00000i 1.00000 1.00000i
8989 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
9090 0 0
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 −1.00000 1.00000i −1.00000 1.00000i
9797 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
9898 −1.00000 −1.00000
9999 1.00000 1.00000i 1.00000 1.00000i
100100 1.00000i 1.00000i
101101 0 0 1.00000 00
−1.00000 π\pi
102102 1.00000 1.00000i 1.00000 1.00000i
103103 0 0 1.00000 00
−1.00000 π\pi
104104 0 0
105105 0 0
106106 0 0
107107 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
108108 0 0
109109 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
110110 0 0
111111 0 0
112112 0 0
113113 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
114114 −2.00000 + 2.00000i −2.00000 + 2.00000i
115115 0 0
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 1.00000i 1.00000i
122122 0 0
123123 2.00000 2.00000
124124 0 0
125125 0 0
126126 0 0
127127 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
128128 1.00000i 1.00000i
129129 0 0
130130 0 0
131131 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
132132 2.00000 2.00000
133133 0 0
134134 0 0
135135 0 0
136136 1.00000 1.00000
137137 −2.00000 −2.00000 −1.00000 π\pi
−1.00000 π\pi
138138 0 0
139139 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 1.00000i 1.00000i
145145 0 0
146146 −1.00000 1.00000i −1.00000 1.00000i
147147 −1.00000 1.00000i −1.00000 1.00000i
148148 0 0
149149 0 0 1.00000 00
−1.00000 π\pi
150150 −1.00000 + 1.00000i −1.00000 + 1.00000i
151151 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
152152 −2.00000 −2.00000
153153 1.00000 1.00000
154154 0 0
155155 0 0
156156 0 0
157157 0 0 1.00000 00
−1.00000 π\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 1.00000i 1.00000i
163163 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
164164 1.00000 + 1.00000i 1.00000 + 1.00000i
165165 0 0
166166 0 0
167167 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
168168 0 0
169169 1.00000 1.00000
170170 0 0
171171 −2.00000 −2.00000
172172 0 0
173173 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
174174 0 0
175175 0 0
176176 1.00000 + 1.00000i 1.00000 + 1.00000i
177177 0 0
178178 0 0
179179 2.00000i 2.00000i 1.00000i 0.5π0.5\pi
1.00000i 0.5π0.5\pi
180180 0 0
181181 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
182182 0 0
183183 0 0
184184 0 0
185185 0 0
186186 0 0
187187 −1.00000 + 1.00000i −1.00000 + 1.00000i
188188 0 0
189189 0 0
190190 0 0
191191 0 0 1.00000 00
−1.00000 π\pi
192192 1.00000 1.00000i 1.00000 1.00000i
193193 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
194194 1.00000 + 1.00000i 1.00000 + 1.00000i
195195 0 0
196196 1.00000i 1.00000i
197197 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
198198 1.00000 + 1.00000i 1.00000 + 1.00000i
199199 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
200200 −1.00000 −1.00000
201201 0 0
202202 0 0
203203 0 0
204204 1.00000 + 1.00000i 1.00000 + 1.00000i
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 2.00000 2.00000i 2.00000 2.00000i
210210 0 0
211211 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
212212 0 0
213213 0 0
214214 1.00000 + 1.00000i 1.00000 + 1.00000i
215215 0 0
216216 0 0
217217 0 0
218218 0 0
219219 2.00000i 2.00000i
220220 0 0
221221 0 0
222222 0 0
223223 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
224224 0 0
225225 −1.00000 −1.00000
226226 1.00000 1.00000i 1.00000 1.00000i
227227 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
228228 −2.00000 2.00000i −2.00000 2.00000i
229229 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
230230 0 0
231231 0 0
232232 0 0
233233 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
234234 0 0
235235 0 0
236236 0 0
237237 0 0
238238 0 0
239239 0 0 1.00000 00
−1.00000 π\pi
240240 0 0
241241 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
242242 −1.00000 −1.00000
243243 −1.00000 + 1.00000i −1.00000 + 1.00000i
244244 0 0
245245 0 0
246246 2.00000i 2.00000i
247247 0 0
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 1.00000 1.00000
257257 0 0 1.00000 00
−1.00000 π\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 −1.00000 1.00000i −1.00000 1.00000i
263263 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
264264 2.00000i 2.00000i
265265 0 0
266266 0 0
267267 0 0
268268 0 0
269269 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
270270 0 0
271271 0 0 1.00000 00
−1.00000 π\pi
272272 1.00000i 1.00000i
273273 0 0
274274 2.00000i 2.00000i
275275 1.00000 1.00000i 1.00000 1.00000i
276276 0 0
277277 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
278278 −1.00000 1.00000i −1.00000 1.00000i
279279 0 0
280280 0 0
281281 2.00000i 2.00000i 1.00000i 0.5π0.5\pi
1.00000i 0.5π0.5\pi
282282 0 0
283283 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 1.00000 1.00000
289289 −1.00000 −1.00000
290290 0 0
291291 2.00000i 2.00000i
292292 1.00000 1.00000i 1.00000 1.00000i
293293 0 0 1.00000 00
−1.00000 π\pi
294294 1.00000 1.00000i 1.00000 1.00000i
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 −1.00000 1.00000i −1.00000 1.00000i
301301 0 0
302302 0 0
303303 0 0
304304 2.00000i 2.00000i
305305 0 0
306306 1.00000i 1.00000i
307307 2.00000 2.00000 1.00000 00
1.00000 00
308308 0 0
309309 0 0
310310 0 0
311311 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
312312 0 0
313313 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
314314 0 0
315315 0 0
316316 0 0
317317 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
318318 0 0
319319 0 0
320320 0 0
321321 2.00000i 2.00000i
322322 0 0
323323 2.00000 2.00000
324324 −1.00000 −1.00000
325325 0 0
326326 −1.00000 + 1.00000i −1.00000 + 1.00000i
327327 0 0
328328 −1.00000 + 1.00000i −1.00000 + 1.00000i
329329 0 0
330330 0 0
331331 0 0 1.00000 00
−1.00000 π\pi
332332 0 0
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
338338 1.00000i 1.00000i
339339 2.00000 2.00000
340340 0 0
341341 0 0
342342 2.00000i 2.00000i
343343 0 0
344344 0 0
345345 0 0
346346 0 0
347347 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
348348 0 0
349349 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
350350 0 0
351351 0 0
352352 −1.00000 + 1.00000i −1.00000 + 1.00000i
353353 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 −2.00000 −2.00000
359359 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
360360 0 0
361361 −3.00000 −3.00000
362362 0 0
363363 −1.00000 1.00000i −1.00000 1.00000i
364364 0 0
365365 0 0
366366 0 0
367367 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
368368 0 0
369369 −1.00000 + 1.00000i −1.00000 + 1.00000i
370370 0 0
371371 0 0
372372 0 0
373373 0 0 1.00000 00
−1.00000 π\pi
374374 −1.00000 1.00000i −1.00000 1.00000i
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
380380 0 0
381381 0 0
382382 0 0
383383 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
384384 1.00000 + 1.00000i 1.00000 + 1.00000i
385385 0 0
386386 1.00000 1.00000i 1.00000 1.00000i
387387 0 0
388388 −1.00000 + 1.00000i −1.00000 + 1.00000i
389389 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
390390 0 0
391391 0 0
392392 1.00000 1.00000
393393 2.00000i 2.00000i
394394 0 0
395395 0 0
396396 −1.00000 + 1.00000i −1.00000 + 1.00000i
397397 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
398398 0 0
399399 0 0
400400 1.00000i 1.00000i
401401 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
402402 0 0
403403 0 0
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 −1.00000 + 1.00000i −1.00000 + 1.00000i
409409 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
410410 0 0
411411 2.00000 2.00000i 2.00000 2.00000i
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 2.00000i 2.00000i
418418 2.00000 + 2.00000i 2.00000 + 2.00000i
419419 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
420420 0 0
421421 0 0 1.00000 00
−1.00000 π\pi
422422 1.00000 1.00000i 1.00000 1.00000i
423423 0 0
424424 0 0
425425 1.00000 1.00000
426426 0 0
427427 0 0
428428 −1.00000 + 1.00000i −1.00000 + 1.00000i
429429 0 0
430430 0 0
431431 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
432432 0 0
433433 2.00000i 2.00000i 1.00000i 0.5π0.5\pi
1.00000i 0.5π0.5\pi
434434 0 0
435435 0 0
436436 0 0
437437 0 0
438438 2.00000 2.00000
439439 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
440440 0 0
441441 1.00000 1.00000
442442 0 0
443443 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
450450 1.00000i 1.00000i
451451 2.00000i 2.00000i
452452 1.00000 + 1.00000i 1.00000 + 1.00000i
453453 0 0
454454 1.00000 1.00000i 1.00000 1.00000i
455455 0 0
456456 2.00000 2.00000i 2.00000 2.00000i
457457 2.00000i 2.00000i 1.00000i 0.5π-0.5\pi
1.00000i 0.5π-0.5\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 0 0 1.00000 00
−1.00000 π\pi
464464 0 0
465465 0 0
466466 1.00000 + 1.00000i 1.00000 + 1.00000i
467467 2.00000i 2.00000i 1.00000i 0.5π0.5\pi
1.00000i 0.5π0.5\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 0 0
473473 0 0
474474 0 0
475475 −2.00000 −2.00000
476476 0 0
477477 0 0
478478 0 0
479479 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
480480 0 0
481481 0 0
482482 1.00000 + 1.00000i 1.00000 + 1.00000i
483483 0 0
484484 1.00000i 1.00000i
485485 0 0
486486 −1.00000 1.00000i −1.00000 1.00000i
487487 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
488488 0 0
489489 −2.00000 −2.00000
490490 0 0
491491 2.00000i 2.00000i 1.00000i 0.5π-0.5\pi
1.00000i 0.5π-0.5\pi
492492 −2.00000 −2.00000
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
500500 0 0
501501 0 0
502502 0 0
503503 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
504504 0 0
505505 0 0
506506 0 0
507507 −1.00000 + 1.00000i −1.00000 + 1.00000i
508508 0 0
509509 0 0 1.00000 00
−1.00000 π\pi
510510 0 0
511511 0 0
512512 1.00000i 1.00000i
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 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
522522 0 0
523523 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
524524 1.00000 1.00000i 1.00000 1.00000i
525525 0 0
526526 0 0
527527 0 0
528528 −2.00000 −2.00000
529529 1.00000i 1.00000i
530530 0 0
531531 0 0
532532 0 0
533533 0 0
534534 0 0
535535 0 0
536536 0 0
537537 −2.00000 2.00000i −2.00000 2.00000i
538538 0 0
539539 −1.00000 + 1.00000i −1.00000 + 1.00000i
540540 0 0
541541 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
542542 0 0
543543 0 0
544544 −1.00000 −1.00000
545545 0 0
546546 0 0
547547 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
548548 2.00000 2.00000
549549 0 0
550550 1.00000 + 1.00000i 1.00000 + 1.00000i
551551 0 0
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 1.00000 1.00000i 1.00000 1.00000i
557557 0 0 1.00000 00
−1.00000 π\pi
558558 0 0
559559 0 0
560560 0 0
561561 2.00000i 2.00000i
562562 −2.00000 −2.00000
563563 0 0 1.00000 00
−1.00000 π\pi
564564 0 0
565565 0 0
566566 −1.00000 + 1.00000i −1.00000 + 1.00000i
567567 0 0
568568 0 0
569569 0 0 1.00000 00
−1.00000 π\pi
570570 0 0
571571 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 1.00000i 1.00000i
577577 2.00000 2.00000 1.00000 00
1.00000 00
578578 1.00000i 1.00000i
579579 2.00000 2.00000
580580 0 0
581581 0 0
582582 −2.00000 −2.00000
583583 0 0
584584 1.00000 + 1.00000i 1.00000 + 1.00000i
585585 0 0
586586 0 0
587587 2.00000i 2.00000i 1.00000i 0.5π-0.5\pi
1.00000i 0.5π-0.5\pi
588588 1.00000 + 1.00000i 1.00000 + 1.00000i
589589 0 0
590590 0 0
591591 0 0
592592 0 0
593593 0 0 1.00000 00
−1.00000 π\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 0 0 1.00000 00
−1.00000 π\pi
600600 1.00000 1.00000i 1.00000 1.00000i
601601 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
602602 0 0
603603 0 0
604604 0 0
605605 0 0
606606 0 0
607607 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
608608 2.00000 2.00000
609609 0 0
610610 0 0
611611 0 0
612612 −1.00000 −1.00000
613613 0 0 1.00000 00
−1.00000 π\pi
614614 2.00000i 2.00000i
615615 0 0
616616 0 0
617617 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
618618 0 0
619619 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 −1.00000 −1.00000
626626 −1.00000 + 1.00000i −1.00000 + 1.00000i
627627 4.00000i 4.00000i
628628 0 0
629629 0 0
630630 0 0
631631 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
632632 0 0
633633 2.00000 2.00000
634634 0 0
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 0 0
641641 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
642642 −2.00000 −2.00000
643643 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
644644 0 0
645645 0 0
646646 2.00000i 2.00000i
647647 0 0 1.00000 00
−1.00000 π\pi
648648 1.00000i 1.00000i
649649 0 0
650650 0 0
651651 0 0
652652 −1.00000 1.00000i −1.00000 1.00000i
653653 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
654654 0 0
655655 0 0
656656 −1.00000 1.00000i −1.00000 1.00000i
657657 1.00000 + 1.00000i 1.00000 + 1.00000i
658658 0 0
659659 −2.00000 −2.00000 −1.00000 π\pi
−1.00000 π\pi
660660 0 0
661661 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\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 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
674674 −1.00000 1.00000i −1.00000 1.00000i
675675 0 0
676676 −1.00000 −1.00000
677677 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
678678 2.00000i 2.00000i
679679 0 0
680680 0 0
681681 2.00000 2.00000
682682 0 0
683683 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
684684 2.00000 2.00000
685685 0 0
686686 0 0
687687 0 0
688688 0 0
689689 0 0
690690 0 0
691691 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
692692 0 0
693693 0 0
694694 1.00000 1.00000i 1.00000 1.00000i
695695 0 0
696696 0 0
697697 1.00000 1.00000i 1.00000 1.00000i
698698 0 0
699699 2.00000i 2.00000i
700700 0 0
701701 0 0 1.00000 00
−1.00000 π\pi
702702 0 0
703703 0 0
704704 −1.00000 1.00000i −1.00000 1.00000i
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
710710 0 0
711711 0 0
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 2.00000i 2.00000i
717717 0 0
718718 0 0
719719 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
720720 0 0
721721 0 0
722722 3.00000i 3.00000i
723723 2.00000i 2.00000i
724724 0 0
725725 0 0
726726 1.00000 1.00000i 1.00000 1.00000i
727727 0 0 1.00000 00
−1.00000 π\pi
728728 0 0
729729 1.00000i 1.00000i
730730 0 0
731731 0 0
732732 0 0
733733 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 −1.00000 1.00000i −1.00000 1.00000i
739739 2.00000i 2.00000i 1.00000i 0.5π-0.5\pi
1.00000i 0.5π-0.5\pi
740740 0 0
741741 0 0
742742 0 0
743743 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
744744 0 0
745745 0 0
746746 0 0
747747 0 0
748748 1.00000 1.00000i 1.00000 1.00000i
749749 0 0
750750 0 0
751751 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
758758 −1.00000 1.00000i −1.00000 1.00000i
759759 0 0
760760 0 0
761761 2.00000 2.00000 1.00000 00
1.00000 00
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 −1.00000 + 1.00000i −1.00000 + 1.00000i
769769 2.00000 2.00000 1.00000 00
1.00000 00
770770 0 0
771771 0 0
772772 1.00000 + 1.00000i 1.00000 + 1.00000i
773773 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
774774 0 0
775775 0 0
776776 −1.00000 1.00000i −1.00000 1.00000i
777777 0 0
778778 0 0
779779 −2.00000 + 2.00000i −2.00000 + 2.00000i
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 1.00000i 1.00000i
785785 0 0
786786 2.00000 2.00000
787787 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 −1.00000 1.00000i −1.00000 1.00000i
793793 0 0
794794 0 0
795795 0 0
796796 0 0
797797 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
798798 0 0
799799 0 0
800800 1.00000 1.00000
801801 0 0
802802 −1.00000 + 1.00000i −1.00000 + 1.00000i
803803 −2.00000 −2.00000
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
810810 0 0
811811 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 −1.00000 1.00000i −1.00000 1.00000i
817817 0 0
818818 0 0
819819 0 0
820820 0 0
821821 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
822822 2.00000 + 2.00000i 2.00000 + 2.00000i
823823 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
824824 0 0
825825 2.00000i 2.00000i
826826 0 0
827827 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
828828 0 0
829829 0 0 1.00000 00
−1.00000 π\pi
830830 0 0
831831 0 0
832832 0 0
833833 −1.00000 −1.00000
834834 2.00000 2.00000
835835 0 0
836836 −2.00000 + 2.00000i −2.00000 + 2.00000i
837837 0 0
838838 1.00000 1.00000i 1.00000 1.00000i
839839 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
840840 0 0
841841 1.00000i 1.00000i
842842 0 0
843843 −2.00000 2.00000i −2.00000 2.00000i
844844 1.00000 + 1.00000i 1.00000 + 1.00000i
845845 0 0
846846 0 0
847847 0 0
848848 0 0
849849 −2.00000 −2.00000
850850 1.00000i 1.00000i
851851 0 0
852852 0 0
853853 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
854854 0 0
855855 0 0
856856 −1.00000 1.00000i −1.00000 1.00000i
857857 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
858858 0 0
859859 0 0 1.00000 00
−1.00000 π\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 1.00000 00
−1.00000 π\pi
864864 0 0
865865 0 0
866866 −2.00000 −2.00000
867867 1.00000 1.00000i 1.00000 1.00000i
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0 0
873873 −1.00000 1.00000i −1.00000 1.00000i
874874 0 0
875875 0 0
876876 2.00000i 2.00000i
877877 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
878878 0 0
879879 0 0
880880 0 0
881881 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
882882 1.00000i 1.00000i
883883 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
884884 0 0
885885 0 0
886886 0 0
887887 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
888888 0 0
889889 0 0
890890 0 0
891891 1.00000 + 1.00000i 1.00000 + 1.00000i
892892 0 0
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 −1.00000 + 1.00000i −1.00000 + 1.00000i
899899 0 0
900900 1.00000 1.00000
901901 0 0
902902 2.00000 2.00000
903903 0 0
904904 −1.00000 + 1.00000i −1.00000 + 1.00000i
905905 0 0
906906 0 0
907907 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
908908 1.00000 + 1.00000i 1.00000 + 1.00000i
909909 0 0
910910 0 0
911911 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
912912 2.00000 + 2.00000i 2.00000 + 2.00000i
913913 0 0
914914 2.00000 2.00000
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 0 0 1.00000 00
−1.00000 π\pi
920920 0 0
921921 −2.00000 + 2.00000i −2.00000 + 2.00000i
922922 0 0
923923 0 0
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 0 0
929929 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
930930 0 0
931931 2.00000 2.00000
932932 −1.00000 + 1.00000i −1.00000 + 1.00000i
933933 0 0
934934 −2.00000 −2.00000
935935 0 0
936936 0 0
937937 2.00000i 2.00000i 1.00000i 0.5π0.5\pi
1.00000i 0.5π0.5\pi
938938 0 0
939939 −2.00000 −2.00000
940940 0 0
941941 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
948948 0 0
949949 0 0
950950 2.00000i 2.00000i
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 1.00000i 1.00000i
962962 0 0
963963 −1.00000 1.00000i −1.00000 1.00000i
964964 −1.00000 + 1.00000i −1.00000 + 1.00000i
965965 0 0
966966 0 0
967967 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
968968 1.00000 1.00000
969969 −2.00000 + 2.00000i −2.00000 + 2.00000i
970970 0 0
971971 0 0 1.00000 00
−1.00000 π\pi
972972 1.00000 1.00000i 1.00000 1.00000i
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 0 0 1.00000 00
−1.00000 π\pi
978978 2.00000i 2.00000i
979979 0 0
980980 0 0
981981 0 0
982982 2.00000 2.00000
983983 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
984984 2.00000i 2.00000i
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
992992 0 0
993993 0 0
994994 0 0
995995 0 0
996996 0 0
997997 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
998998 −1.00000 + 1.00000i −1.00000 + 1.00000i
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 136.1.j.a.123.1 yes 2
3.2 odd 2 1224.1.s.a.667.1 2
4.3 odd 2 544.1.n.a.463.1 2
5.2 odd 4 3400.1.bc.a.2299.1 2
5.3 odd 4 3400.1.bc.b.2299.1 2
5.4 even 2 3400.1.y.a.3251.1 2
8.3 odd 2 CM 136.1.j.a.123.1 yes 2
8.5 even 2 544.1.n.a.463.1 2
17.2 even 8 2312.1.e.a.1155.2 2
17.3 odd 16 2312.1.p.e.155.1 8
17.4 even 4 2312.1.j.b.251.1 2
17.5 odd 16 2312.1.p.e.1579.1 8
17.6 odd 16 2312.1.p.e.1555.1 8
17.7 odd 16 2312.1.p.e.179.2 8
17.8 even 8 2312.1.f.b.579.2 2
17.9 even 8 2312.1.f.b.579.1 2
17.10 odd 16 2312.1.p.e.179.1 8
17.11 odd 16 2312.1.p.e.1555.2 8
17.12 odd 16 2312.1.p.e.1579.2 8
17.13 even 4 inner 136.1.j.a.115.1 2
17.14 odd 16 2312.1.p.e.155.2 8
17.15 even 8 2312.1.e.a.1155.1 2
17.16 even 2 2312.1.j.b.1483.1 2
24.11 even 2 1224.1.s.a.667.1 2
40.3 even 4 3400.1.bc.b.2299.1 2
40.19 odd 2 3400.1.y.a.3251.1 2
40.27 even 4 3400.1.bc.a.2299.1 2
51.47 odd 4 1224.1.s.a.523.1 2
68.47 odd 4 544.1.n.a.47.1 2
85.13 odd 4 3400.1.bc.a.2699.1 2
85.47 odd 4 3400.1.bc.b.2699.1 2
85.64 even 4 3400.1.y.a.251.1 2
136.3 even 16 2312.1.p.e.155.1 8
136.11 even 16 2312.1.p.e.1555.2 8
136.13 even 4 544.1.n.a.47.1 2
136.19 odd 8 2312.1.e.a.1155.2 2
136.27 even 16 2312.1.p.e.179.1 8
136.43 odd 8 2312.1.f.b.579.1 2
136.59 odd 8 2312.1.f.b.579.2 2
136.67 odd 2 2312.1.j.b.1483.1 2
136.75 even 16 2312.1.p.e.179.2 8
136.83 odd 8 2312.1.e.a.1155.1 2
136.91 even 16 2312.1.p.e.1555.1 8
136.99 even 16 2312.1.p.e.155.2 8
136.107 even 16 2312.1.p.e.1579.1 8
136.115 odd 4 inner 136.1.j.a.115.1 2
136.123 odd 4 2312.1.j.b.251.1 2
136.131 even 16 2312.1.p.e.1579.2 8
408.251 even 4 1224.1.s.a.523.1 2
680.387 even 4 3400.1.bc.b.2699.1 2
680.523 even 4 3400.1.bc.a.2699.1 2
680.659 odd 4 3400.1.y.a.251.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
136.1.j.a.115.1 2 17.13 even 4 inner
136.1.j.a.115.1 2 136.115 odd 4 inner
136.1.j.a.123.1 yes 2 1.1 even 1 trivial
136.1.j.a.123.1 yes 2 8.3 odd 2 CM
544.1.n.a.47.1 2 68.47 odd 4
544.1.n.a.47.1 2 136.13 even 4
544.1.n.a.463.1 2 4.3 odd 2
544.1.n.a.463.1 2 8.5 even 2
1224.1.s.a.523.1 2 51.47 odd 4
1224.1.s.a.523.1 2 408.251 even 4
1224.1.s.a.667.1 2 3.2 odd 2
1224.1.s.a.667.1 2 24.11 even 2
2312.1.e.a.1155.1 2 17.15 even 8
2312.1.e.a.1155.1 2 136.83 odd 8
2312.1.e.a.1155.2 2 17.2 even 8
2312.1.e.a.1155.2 2 136.19 odd 8
2312.1.f.b.579.1 2 17.9 even 8
2312.1.f.b.579.1 2 136.43 odd 8
2312.1.f.b.579.2 2 17.8 even 8
2312.1.f.b.579.2 2 136.59 odd 8
2312.1.j.b.251.1 2 17.4 even 4
2312.1.j.b.251.1 2 136.123 odd 4
2312.1.j.b.1483.1 2 17.16 even 2
2312.1.j.b.1483.1 2 136.67 odd 2
2312.1.p.e.155.1 8 17.3 odd 16
2312.1.p.e.155.1 8 136.3 even 16
2312.1.p.e.155.2 8 17.14 odd 16
2312.1.p.e.155.2 8 136.99 even 16
2312.1.p.e.179.1 8 17.10 odd 16
2312.1.p.e.179.1 8 136.27 even 16
2312.1.p.e.179.2 8 17.7 odd 16
2312.1.p.e.179.2 8 136.75 even 16
2312.1.p.e.1555.1 8 17.6 odd 16
2312.1.p.e.1555.1 8 136.91 even 16
2312.1.p.e.1555.2 8 17.11 odd 16
2312.1.p.e.1555.2 8 136.11 even 16
2312.1.p.e.1579.1 8 17.5 odd 16
2312.1.p.e.1579.1 8 136.107 even 16
2312.1.p.e.1579.2 8 17.12 odd 16
2312.1.p.e.1579.2 8 136.131 even 16
3400.1.y.a.251.1 2 85.64 even 4
3400.1.y.a.251.1 2 680.659 odd 4
3400.1.y.a.3251.1 2 5.4 even 2
3400.1.y.a.3251.1 2 40.19 odd 2
3400.1.bc.a.2299.1 2 5.2 odd 4
3400.1.bc.a.2299.1 2 40.27 even 4
3400.1.bc.a.2699.1 2 85.13 odd 4
3400.1.bc.a.2699.1 2 680.523 even 4
3400.1.bc.b.2299.1 2 5.3 odd 4
3400.1.bc.b.2299.1 2 40.3 even 4
3400.1.bc.b.2699.1 2 85.47 odd 4
3400.1.bc.b.2699.1 2 680.387 even 4