Properties

Label 5408.2.a.w.1.1
Level 54085408
Weight 22
Character 5408.1
Self dual yes
Analytic conductor 43.18343.183
Analytic rank 11
Dimension 22
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [5408,2,Mod(1,5408)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5408, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5408.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 5408=25132 5408 = 2^{5} \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 5408.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,0,0,0,0,0,0,16,0,0,0,0,0,0,0,-6,0,0,0,-22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(21)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 43.183097413143.1830974131
Analytic rank: 11
Dimension: 22
Coefficient field: Q(11)\Q(\sqrt{11})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x211 x^{2} - 11 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 416)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 3.31662-3.31662 of defining polynomial
Character χ\chi == 5408.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q3.31662q3+3.31662q7+8.00000q9+3.31662q113.00000q17+3.31662q1911.0000q21+3.31662q235.00000q2516.5831q275.00000q2911.0000q339.00000q37+3.00000q419.94987q436.63325q47+4.00000q49+9.94987q518.00000q5311.0000q57+3.31662q599.00000q61+26.5330q63+9.94987q6711.0000q69+9.94987q71+4.00000q73+16.5831q75+11.0000q776.63325q79+31.0000q8113.2665q83+16.5831q87+1.00000q897.00000q97+26.5330q99+O(q100)q-3.31662 q^{3} +3.31662 q^{7} +8.00000 q^{9} +3.31662 q^{11} -3.00000 q^{17} +3.31662 q^{19} -11.0000 q^{21} +3.31662 q^{23} -5.00000 q^{25} -16.5831 q^{27} -5.00000 q^{29} -11.0000 q^{33} -9.00000 q^{37} +3.00000 q^{41} -9.94987 q^{43} -6.63325 q^{47} +4.00000 q^{49} +9.94987 q^{51} -8.00000 q^{53} -11.0000 q^{57} +3.31662 q^{59} -9.00000 q^{61} +26.5330 q^{63} +9.94987 q^{67} -11.0000 q^{69} +9.94987 q^{71} +4.00000 q^{73} +16.5831 q^{75} +11.0000 q^{77} -6.63325 q^{79} +31.0000 q^{81} -13.2665 q^{83} +16.5831 q^{87} +1.00000 q^{89} -7.00000 q^{97} +26.5330 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+16q96q1722q2110q2510q2922q3318q37+6q41+8q4916q5322q5718q6122q69+8q73+22q77+62q81+2q89+14q97+O(q100) 2 q + 16 q^{9} - 6 q^{17} - 22 q^{21} - 10 q^{25} - 10 q^{29} - 22 q^{33} - 18 q^{37} + 6 q^{41} + 8 q^{49} - 16 q^{53} - 22 q^{57} - 18 q^{61} - 22 q^{69} + 8 q^{73} + 22 q^{77} + 62 q^{81} + 2 q^{89}+ \cdots - 14 q^{97}+O(q^{100}) Copy content Toggle raw display

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
33 −3.31662 −1.91485 −0.957427 0.288675i 0.906785π-0.906785\pi
−0.957427 + 0.288675i 0.906785π0.906785\pi
44 0 0
55 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
66 0 0
77 3.31662 1.25357 0.626783 0.779194i 0.284371π-0.284371\pi
0.626783 + 0.779194i 0.284371π0.284371\pi
88 0 0
99 8.00000 2.66667
1010 0 0
1111 3.31662 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
1212 0 0
1313 0 0
1414 0 0
1515 0 0
1616 0 0
1717 −3.00000 −0.727607 −0.363803 0.931476i 0.618522π-0.618522\pi
−0.363803 + 0.931476i 0.618522π0.618522\pi
1818 0 0
1919 3.31662 0.760886 0.380443 0.924804i 0.375772π-0.375772\pi
0.380443 + 0.924804i 0.375772π0.375772\pi
2020 0 0
2121 −11.0000 −2.40040
2222 0 0
2323 3.31662 0.691564 0.345782 0.938315i 0.387614π-0.387614\pi
0.345782 + 0.938315i 0.387614π0.387614\pi
2424 0 0
2525 −5.00000 −1.00000
2626 0 0
2727 −16.5831 −3.19142
2828 0 0
2929 −5.00000 −0.928477 −0.464238 0.885710i 0.653672π-0.653672\pi
−0.464238 + 0.885710i 0.653672π0.653672\pi
3030 0 0
3131 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
3232 0 0
3333 −11.0000 −1.91485
3434 0 0
3535 0 0
3636 0 0
3737 −9.00000 −1.47959 −0.739795 0.672832i 0.765078π-0.765078\pi
−0.739795 + 0.672832i 0.765078π0.765078\pi
3838 0 0
3939 0 0
4040 0 0
4141 3.00000 0.468521 0.234261 0.972174i 0.424733π-0.424733\pi
0.234261 + 0.972174i 0.424733π0.424733\pi
4242 0 0
4343 −9.94987 −1.51734 −0.758671 0.651474i 0.774151π-0.774151\pi
−0.758671 + 0.651474i 0.774151π0.774151\pi
4444 0 0
4545 0 0
4646 0 0
4747 −6.63325 −0.967559 −0.483779 0.875190i 0.660736π-0.660736\pi
−0.483779 + 0.875190i 0.660736π0.660736\pi
4848 0 0
4949 4.00000 0.571429
5050 0 0
5151 9.94987 1.39326
5252 0 0
5353 −8.00000 −1.09888 −0.549442 0.835532i 0.685160π-0.685160\pi
−0.549442 + 0.835532i 0.685160π0.685160\pi
5454 0 0
5555 0 0
5656 0 0
5757 −11.0000 −1.45699
5858 0 0
5959 3.31662 0.431788 0.215894 0.976417i 0.430733π-0.430733\pi
0.215894 + 0.976417i 0.430733π0.430733\pi
6060 0 0
6161 −9.00000 −1.15233 −0.576166 0.817333i 0.695452π-0.695452\pi
−0.576166 + 0.817333i 0.695452π0.695452\pi
6262 0 0
6363 26.5330 3.34284
6464 0 0
6565 0 0
6666 0 0
6767 9.94987 1.21557 0.607785 0.794101i 0.292058π-0.292058\pi
0.607785 + 0.794101i 0.292058π0.292058\pi
6868 0 0
6969 −11.0000 −1.32424
7070 0 0
7171 9.94987 1.18083 0.590416 0.807099i 0.298964π-0.298964\pi
0.590416 + 0.807099i 0.298964π0.298964\pi
7272 0 0
7373 4.00000 0.468165 0.234082 0.972217i 0.424791π-0.424791\pi
0.234082 + 0.972217i 0.424791π0.424791\pi
7474 0 0
7575 16.5831 1.91485
7676 0 0
7777 11.0000 1.25357
7878 0 0
7979 −6.63325 −0.746299 −0.373149 0.927771i 0.621722π-0.621722\pi
−0.373149 + 0.927771i 0.621722π0.621722\pi
8080 0 0
8181 31.0000 3.44444
8282 0 0
8383 −13.2665 −1.45619 −0.728094 0.685478i 0.759593π-0.759593\pi
−0.728094 + 0.685478i 0.759593π0.759593\pi
8484 0 0
8585 0 0
8686 0 0
8787 16.5831 1.77790
8888 0 0
8989 1.00000 0.106000 0.0529999 0.998595i 0.483122π-0.483122\pi
0.0529999 + 0.998595i 0.483122π0.483122\pi
9090 0 0
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 0 0
9797 −7.00000 −0.710742 −0.355371 0.934725i 0.615646π-0.615646\pi
−0.355371 + 0.934725i 0.615646π0.615646\pi
9898 0 0
9999 26.5330 2.66667
100100 0 0
101101 −15.0000 −1.49256 −0.746278 0.665635i 0.768161π-0.768161\pi
−0.746278 + 0.665635i 0.768161π0.768161\pi
102102 0 0
103103 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
104104 0 0
105105 0 0
106106 0 0
107107 −3.31662 −0.320630 −0.160315 0.987066i 0.551251π-0.551251\pi
−0.160315 + 0.987066i 0.551251π0.551251\pi
108108 0 0
109109 16.0000 1.53252 0.766261 0.642529i 0.222115π-0.222115\pi
0.766261 + 0.642529i 0.222115π0.222115\pi
110110 0 0
111111 29.8496 2.83320
112112 0 0
113113 −11.0000 −1.03479 −0.517396 0.855746i 0.673099π-0.673099\pi
−0.517396 + 0.855746i 0.673099π0.673099\pi
114114 0 0
115115 0 0
116116 0 0
117117 0 0
118118 0 0
119119 −9.94987 −0.912103
120120 0 0
121121 0 0
122122 0 0
123123 −9.94987 −0.897150
124124 0 0
125125 0 0
126126 0 0
127127 9.94987 0.882909 0.441454 0.897284i 0.354463π-0.354463\pi
0.441454 + 0.897284i 0.354463π0.354463\pi
128128 0 0
129129 33.0000 2.90549
130130 0 0
131131 −13.2665 −1.15910 −0.579550 0.814937i 0.696772π-0.696772\pi
−0.579550 + 0.814937i 0.696772π0.696772\pi
132132 0 0
133133 11.0000 0.953821
134134 0 0
135135 0 0
136136 0 0
137137 9.00000 0.768922 0.384461 0.923141i 0.374387π-0.374387\pi
0.384461 + 0.923141i 0.374387π0.374387\pi
138138 0 0
139139 −3.31662 −0.281312 −0.140656 0.990058i 0.544921π-0.544921\pi
−0.140656 + 0.990058i 0.544921π0.544921\pi
140140 0 0
141141 22.0000 1.85273
142142 0 0
143143 0 0
144144 0 0
145145 0 0
146146 0 0
147147 −13.2665 −1.09420
148148 0 0
149149 1.00000 0.0819232 0.0409616 0.999161i 0.486958π-0.486958\pi
0.0409616 + 0.999161i 0.486958π0.486958\pi
150150 0 0
151151 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
152152 0 0
153153 −24.0000 −1.94029
154154 0 0
155155 0 0
156156 0 0
157157 −8.00000 −0.638470 −0.319235 0.947676i 0.603426π-0.603426\pi
−0.319235 + 0.947676i 0.603426π0.603426\pi
158158 0 0
159159 26.5330 2.10420
160160 0 0
161161 11.0000 0.866921
162162 0 0
163163 −16.5831 −1.29889 −0.649445 0.760408i 0.724999π-0.724999\pi
−0.649445 + 0.760408i 0.724999π0.724999\pi
164164 0 0
165165 0 0
166166 0 0
167167 −3.31662 −0.256648 −0.128324 0.991732i 0.540960π-0.540960\pi
−0.128324 + 0.991732i 0.540960π0.540960\pi
168168 0 0
169169 0 0
170170 0 0
171171 26.5330 2.02903
172172 0 0
173173 7.00000 0.532200 0.266100 0.963945i 0.414265π-0.414265\pi
0.266100 + 0.963945i 0.414265π0.414265\pi
174174 0 0
175175 −16.5831 −1.25357
176176 0 0
177177 −11.0000 −0.826811
178178 0 0
179179 −3.31662 −0.247896 −0.123948 0.992289i 0.539556π-0.539556\pi
−0.123948 + 0.992289i 0.539556π0.539556\pi
180180 0 0
181181 −8.00000 −0.594635 −0.297318 0.954779i 0.596092π-0.596092\pi
−0.297318 + 0.954779i 0.596092π0.596092\pi
182182 0 0
183183 29.8496 2.20655
184184 0 0
185185 0 0
186186 0 0
187187 −9.94987 −0.727607
188188 0 0
189189 −55.0000 −4.00066
190190 0 0
191191 23.2164 1.67988 0.839939 0.542681i 0.182591π-0.182591\pi
0.839939 + 0.542681i 0.182591π0.182591\pi
192192 0 0
193193 −13.0000 −0.935760 −0.467880 0.883792i 0.654982π-0.654982\pi
−0.467880 + 0.883792i 0.654982π0.654982\pi
194194 0 0
195195 0 0
196196 0 0
197197 13.0000 0.926212 0.463106 0.886303i 0.346735π-0.346735\pi
0.463106 + 0.886303i 0.346735π0.346735\pi
198198 0 0
199199 −9.94987 −0.705328 −0.352664 0.935750i 0.614724π-0.614724\pi
−0.352664 + 0.935750i 0.614724π0.614724\pi
200200 0 0
201201 −33.0000 −2.32764
202202 0 0
203203 −16.5831 −1.16391
204204 0 0
205205 0 0
206206 0 0
207207 26.5330 1.84417
208208 0 0
209209 11.0000 0.760886
210210 0 0
211211 −3.31662 −0.228326 −0.114163 0.993462i 0.536419π-0.536419\pi
−0.114163 + 0.993462i 0.536419π0.536419\pi
212212 0 0
213213 −33.0000 −2.26112
214214 0 0
215215 0 0
216216 0 0
217217 0 0
218218 0 0
219219 −13.2665 −0.896467
220220 0 0
221221 0 0
222222 0 0
223223 −3.31662 −0.222098 −0.111049 0.993815i 0.535421π-0.535421\pi
−0.111049 + 0.993815i 0.535421π0.535421\pi
224224 0 0
225225 −40.0000 −2.66667
226226 0 0
227227 3.31662 0.220132 0.110066 0.993924i 0.464894π-0.464894\pi
0.110066 + 0.993924i 0.464894π0.464894\pi
228228 0 0
229229 −8.00000 −0.528655 −0.264327 0.964433i 0.585150π-0.585150\pi
−0.264327 + 0.964433i 0.585150π0.585150\pi
230230 0 0
231231 −36.4829 −2.40040
232232 0 0
233233 4.00000 0.262049 0.131024 0.991379i 0.458173π-0.458173\pi
0.131024 + 0.991379i 0.458173π0.458173\pi
234234 0 0
235235 0 0
236236 0 0
237237 22.0000 1.42905
238238 0 0
239239 26.5330 1.71628 0.858138 0.513418i 0.171621π-0.171621\pi
0.858138 + 0.513418i 0.171621π0.171621\pi
240240 0 0
241241 −13.0000 −0.837404 −0.418702 0.908124i 0.637515π-0.637515\pi
−0.418702 + 0.908124i 0.637515π0.637515\pi
242242 0 0
243243 −53.0660 −3.40419
244244 0 0
245245 0 0
246246 0 0
247247 0 0
248248 0 0
249249 44.0000 2.78839
250250 0 0
251251 16.5831 1.04672 0.523359 0.852112i 0.324679π-0.324679\pi
0.523359 + 0.852112i 0.324679π0.324679\pi
252252 0 0
253253 11.0000 0.691564
254254 0 0
255255 0 0
256256 0 0
257257 13.0000 0.810918 0.405459 0.914113i 0.367112π-0.367112\pi
0.405459 + 0.914113i 0.367112π0.367112\pi
258258 0 0
259259 −29.8496 −1.85477
260260 0 0
261261 −40.0000 −2.47594
262262 0 0
263263 −23.2164 −1.43158 −0.715791 0.698314i 0.753934π-0.753934\pi
−0.715791 + 0.698314i 0.753934π0.753934\pi
264264 0 0
265265 0 0
266266 0 0
267267 −3.31662 −0.202974
268268 0 0
269269 29.0000 1.76816 0.884081 0.467334i 0.154786π-0.154786\pi
0.884081 + 0.467334i 0.154786π0.154786\pi
270270 0 0
271271 −29.8496 −1.81324 −0.906618 0.421953i 0.861345π-0.861345\pi
−0.906618 + 0.421953i 0.861345π0.861345\pi
272272 0 0
273273 0 0
274274 0 0
275275 −16.5831 −1.00000
276276 0 0
277277 5.00000 0.300421 0.150210 0.988654i 0.452005π-0.452005\pi
0.150210 + 0.988654i 0.452005π0.452005\pi
278278 0 0
279279 0 0
280280 0 0
281281 −20.0000 −1.19310 −0.596550 0.802576i 0.703462π-0.703462\pi
−0.596550 + 0.802576i 0.703462π0.703462\pi
282282 0 0
283283 23.2164 1.38007 0.690035 0.723776i 0.257595π-0.257595\pi
0.690035 + 0.723776i 0.257595π0.257595\pi
284284 0 0
285285 0 0
286286 0 0
287287 9.94987 0.587323
288288 0 0
289289 −8.00000 −0.470588
290290 0 0
291291 23.2164 1.36097
292292 0 0
293293 −7.00000 −0.408944 −0.204472 0.978872i 0.565548π-0.565548\pi
−0.204472 + 0.978872i 0.565548π0.565548\pi
294294 0 0
295295 0 0
296296 0 0
297297 −55.0000 −3.19142
298298 0 0
299299 0 0
300300 0 0
301301 −33.0000 −1.90209
302302 0 0
303303 49.7494 2.85803
304304 0 0
305305 0 0
306306 0 0
307307 13.2665 0.757159 0.378580 0.925569i 0.376413π-0.376413\pi
0.378580 + 0.925569i 0.376413π0.376413\pi
308308 0 0
309309 0 0
310310 0 0
311311 −26.5330 −1.50455 −0.752274 0.658850i 0.771043π-0.771043\pi
−0.752274 + 0.658850i 0.771043π0.771043\pi
312312 0 0
313313 4.00000 0.226093 0.113047 0.993590i 0.463939π-0.463939\pi
0.113047 + 0.993590i 0.463939π0.463939\pi
314314 0 0
315315 0 0
316316 0 0
317317 −18.0000 −1.01098 −0.505490 0.862832i 0.668688π-0.668688\pi
−0.505490 + 0.862832i 0.668688π0.668688\pi
318318 0 0
319319 −16.5831 −0.928477
320320 0 0
321321 11.0000 0.613960
322322 0 0
323323 −9.94987 −0.553626
324324 0 0
325325 0 0
326326 0 0
327327 −53.0660 −2.93456
328328 0 0
329329 −22.0000 −1.21290
330330 0 0
331331 9.94987 0.546895 0.273447 0.961887i 0.411836π-0.411836\pi
0.273447 + 0.961887i 0.411836π0.411836\pi
332332 0 0
333333 −72.0000 −3.94558
334334 0 0
335335 0 0
336336 0 0
337337 −12.0000 −0.653682 −0.326841 0.945079i 0.605984π-0.605984\pi
−0.326841 + 0.945079i 0.605984π0.605984\pi
338338 0 0
339339 36.4829 1.98148
340340 0 0
341341 0 0
342342 0 0
343343 −9.94987 −0.537243
344344 0 0
345345 0 0
346346 0 0
347347 16.5831 0.890229 0.445114 0.895474i 0.353163π-0.353163\pi
0.445114 + 0.895474i 0.353163π0.353163\pi
348348 0 0
349349 −1.00000 −0.0535288 −0.0267644 0.999642i 0.508520π-0.508520\pi
−0.0267644 + 0.999642i 0.508520π0.508520\pi
350350 0 0
351351 0 0
352352 0 0
353353 −31.0000 −1.64996 −0.824982 0.565159i 0.808815π-0.808815\pi
−0.824982 + 0.565159i 0.808815π0.808815\pi
354354 0 0
355355 0 0
356356 0 0
357357 33.0000 1.74655
358358 0 0
359359 −26.5330 −1.40036 −0.700179 0.713967i 0.746897π-0.746897\pi
−0.700179 + 0.713967i 0.746897π0.746897\pi
360360 0 0
361361 −8.00000 −0.421053
362362 0 0
363363 0 0
364364 0 0
365365 0 0
366366 0 0
367367 −23.2164 −1.21188 −0.605942 0.795509i 0.707204π-0.707204\pi
−0.605942 + 0.795509i 0.707204π0.707204\pi
368368 0 0
369369 24.0000 1.24939
370370 0 0
371371 −26.5330 −1.37752
372372 0 0
373373 13.0000 0.673114 0.336557 0.941663i 0.390737π-0.390737\pi
0.336557 + 0.941663i 0.390737π0.390737\pi
374374 0 0
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 29.8496 1.53327 0.766636 0.642082i 0.221929π-0.221929\pi
0.766636 + 0.642082i 0.221929π0.221929\pi
380380 0 0
381381 −33.0000 −1.69064
382382 0 0
383383 3.31662 0.169472 0.0847358 0.996403i 0.472995π-0.472995\pi
0.0847358 + 0.996403i 0.472995π0.472995\pi
384384 0 0
385385 0 0
386386 0 0
387387 −79.5990 −4.04624
388388 0 0
389389 −10.0000 −0.507020 −0.253510 0.967333i 0.581585π-0.581585\pi
−0.253510 + 0.967333i 0.581585π0.581585\pi
390390 0 0
391391 −9.94987 −0.503187
392392 0 0
393393 44.0000 2.21951
394394 0 0
395395 0 0
396396 0 0
397397 −5.00000 −0.250943 −0.125471 0.992097i 0.540044π-0.540044\pi
−0.125471 + 0.992097i 0.540044π0.540044\pi
398398 0 0
399399 −36.4829 −1.82643
400400 0 0
401401 11.0000 0.549314 0.274657 0.961542i 0.411436π-0.411436\pi
0.274657 + 0.961542i 0.411436π0.411436\pi
402402 0 0
403403 0 0
404404 0 0
405405 0 0
406406 0 0
407407 −29.8496 −1.47959
408408 0 0
409409 −13.0000 −0.642809 −0.321404 0.946942i 0.604155π-0.604155\pi
−0.321404 + 0.946942i 0.604155π0.604155\pi
410410 0 0
411411 −29.8496 −1.47237
412412 0 0
413413 11.0000 0.541275
414414 0 0
415415 0 0
416416 0 0
417417 11.0000 0.538672
418418 0 0
419419 16.5831 0.810139 0.405069 0.914286i 0.367247π-0.367247\pi
0.405069 + 0.914286i 0.367247π0.367247\pi
420420 0 0
421421 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
422422 0 0
423423 −53.0660 −2.58016
424424 0 0
425425 15.0000 0.727607
426426 0 0
427427 −29.8496 −1.44452
428428 0 0
429429 0 0
430430 0 0
431431 16.5831 0.798781 0.399390 0.916781i 0.369222π-0.369222\pi
0.399390 + 0.916781i 0.369222π0.369222\pi
432432 0 0
433433 21.0000 1.00920 0.504598 0.863355i 0.331641π-0.331641\pi
0.504598 + 0.863355i 0.331641π0.331641\pi
434434 0 0
435435 0 0
436436 0 0
437437 11.0000 0.526201
438438 0 0
439439 −16.5831 −0.791469 −0.395735 0.918365i 0.629510π-0.629510\pi
−0.395735 + 0.918365i 0.629510π0.629510\pi
440440 0 0
441441 32.0000 1.52381
442442 0 0
443443 13.2665 0.630310 0.315155 0.949040i 0.397943π-0.397943\pi
0.315155 + 0.949040i 0.397943π0.397943\pi
444444 0 0
445445 0 0
446446 0 0
447447 −3.31662 −0.156871
448448 0 0
449449 3.00000 0.141579 0.0707894 0.997491i 0.477448π-0.477448\pi
0.0707894 + 0.997491i 0.477448π0.477448\pi
450450 0 0
451451 9.94987 0.468521
452452 0 0
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 1.00000 0.0467780 0.0233890 0.999726i 0.492554π-0.492554\pi
0.0233890 + 0.999726i 0.492554π0.492554\pi
458458 0 0
459459 49.7494 2.32210
460460 0 0
461461 3.00000 0.139724 0.0698620 0.997557i 0.477744π-0.477744\pi
0.0698620 + 0.997557i 0.477744π0.477744\pi
462462 0 0
463463 −26.5330 −1.23309 −0.616547 0.787318i 0.711469π-0.711469\pi
−0.616547 + 0.787318i 0.711469π0.711469\pi
464464 0 0
465465 0 0
466466 0 0
467467 −19.8997 −0.920851 −0.460425 0.887698i 0.652303π-0.652303\pi
−0.460425 + 0.887698i 0.652303π0.652303\pi
468468 0 0
469469 33.0000 1.52380
470470 0 0
471471 26.5330 1.22258
472472 0 0
473473 −33.0000 −1.51734
474474 0 0
475475 −16.5831 −0.760886
476476 0 0
477477 −64.0000 −2.93036
478478 0 0
479479 −9.94987 −0.454621 −0.227311 0.973822i 0.572993π-0.572993\pi
−0.227311 + 0.973822i 0.572993π0.572993\pi
480480 0 0
481481 0 0
482482 0 0
483483 −36.4829 −1.66003
484484 0 0
485485 0 0
486486 0 0
487487 9.94987 0.450872 0.225436 0.974258i 0.427619π-0.427619\pi
0.225436 + 0.974258i 0.427619π0.427619\pi
488488 0 0
489489 55.0000 2.48719
490490 0 0
491491 16.5831 0.748386 0.374193 0.927351i 0.377920π-0.377920\pi
0.374193 + 0.927351i 0.377920π0.377920\pi
492492 0 0
493493 15.0000 0.675566
494494 0 0
495495 0 0
496496 0 0
497497 33.0000 1.48025
498498 0 0
499499 −13.2665 −0.593890 −0.296945 0.954895i 0.595968π-0.595968\pi
−0.296945 + 0.954895i 0.595968π0.595968\pi
500500 0 0
501501 11.0000 0.491444
502502 0 0
503503 −3.31662 −0.147881 −0.0739405 0.997263i 0.523557π-0.523557\pi
−0.0739405 + 0.997263i 0.523557π0.523557\pi
504504 0 0
505505 0 0
506506 0 0
507507 0 0
508508 0 0
509509 39.0000 1.72864 0.864322 0.502938i 0.167748π-0.167748\pi
0.864322 + 0.502938i 0.167748π0.167748\pi
510510 0 0
511511 13.2665 0.586875
512512 0 0
513513 −55.0000 −2.42831
514514 0 0
515515 0 0
516516 0 0
517517 −22.0000 −0.967559
518518 0 0
519519 −23.2164 −1.01909
520520 0 0
521521 −12.0000 −0.525730 −0.262865 0.964833i 0.584667π-0.584667\pi
−0.262865 + 0.964833i 0.584667π0.584667\pi
522522 0 0
523523 16.5831 0.725129 0.362565 0.931959i 0.381901π-0.381901\pi
0.362565 + 0.931959i 0.381901π0.381901\pi
524524 0 0
525525 55.0000 2.40040
526526 0 0
527527 0 0
528528 0 0
529529 −12.0000 −0.521739
530530 0 0
531531 26.5330 1.15143
532532 0 0
533533 0 0
534534 0 0
535535 0 0
536536 0 0
537537 11.0000 0.474685
538538 0 0
539539 13.2665 0.571429
540540 0 0
541541 18.0000 0.773880 0.386940 0.922105i 0.373532π-0.373532\pi
0.386940 + 0.922105i 0.373532π0.373532\pi
542542 0 0
543543 26.5330 1.13864
544544 0 0
545545 0 0
546546 0 0
547547 13.2665 0.567235 0.283617 0.958938i 0.408465π-0.408465\pi
0.283617 + 0.958938i 0.408465π0.408465\pi
548548 0 0
549549 −72.0000 −3.07289
550550 0 0
551551 −16.5831 −0.706465
552552 0 0
553553 −22.0000 −0.935535
554554 0 0
555555 0 0
556556 0 0
557557 37.0000 1.56774 0.783870 0.620925i 0.213243π-0.213243\pi
0.783870 + 0.620925i 0.213243π0.213243\pi
558558 0 0
559559 0 0
560560 0 0
561561 33.0000 1.39326
562562 0 0
563563 −3.31662 −0.139779 −0.0698895 0.997555i 0.522265π-0.522265\pi
−0.0698895 + 0.997555i 0.522265π0.522265\pi
564564 0 0
565565 0 0
566566 0 0
567567 102.815 4.31784
568568 0 0
569569 15.0000 0.628833 0.314416 0.949285i 0.398191π-0.398191\pi
0.314416 + 0.949285i 0.398191π0.398191\pi
570570 0 0
571571 −13.2665 −0.555186 −0.277593 0.960699i 0.589537π-0.589537\pi
−0.277593 + 0.960699i 0.589537π0.589537\pi
572572 0 0
573573 −77.0000 −3.21672
574574 0 0
575575 −16.5831 −0.691564
576576 0 0
577577 −20.0000 −0.832611 −0.416305 0.909225i 0.636675π-0.636675\pi
−0.416305 + 0.909225i 0.636675π0.636675\pi
578578 0 0
579579 43.1161 1.79184
580580 0 0
581581 −44.0000 −1.82543
582582 0 0
583583 −26.5330 −1.09888
584584 0 0
585585 0 0
586586 0 0
587587 −43.1161 −1.77959 −0.889796 0.456358i 0.849154π-0.849154\pi
−0.889796 + 0.456358i 0.849154π0.849154\pi
588588 0 0
589589 0 0
590590 0 0
591591 −43.1161 −1.77356
592592 0 0
593593 36.0000 1.47834 0.739171 0.673517i 0.235217π-0.235217\pi
0.739171 + 0.673517i 0.235217π0.235217\pi
594594 0 0
595595 0 0
596596 0 0
597597 33.0000 1.35060
598598 0 0
599599 33.1662 1.35514 0.677568 0.735460i 0.263034π-0.263034\pi
0.677568 + 0.735460i 0.263034π0.263034\pi
600600 0 0
601601 29.0000 1.18293 0.591467 0.806329i 0.298549π-0.298549\pi
0.591467 + 0.806329i 0.298549π0.298549\pi
602602 0 0
603603 79.5990 3.24152
604604 0 0
605605 0 0
606606 0 0
607607 −9.94987 −0.403853 −0.201926 0.979401i 0.564720π-0.564720\pi
−0.201926 + 0.979401i 0.564720π0.564720\pi
608608 0 0
609609 55.0000 2.22871
610610 0 0
611611 0 0
612612 0 0
613613 7.00000 0.282727 0.141364 0.989958i 0.454851π-0.454851\pi
0.141364 + 0.989958i 0.454851π0.454851\pi
614614 0 0
615615 0 0
616616 0 0
617617 17.0000 0.684394 0.342197 0.939628i 0.388829π-0.388829\pi
0.342197 + 0.939628i 0.388829π0.388829\pi
618618 0 0
619619 −39.7995 −1.59968 −0.799838 0.600215i 0.795082π-0.795082\pi
−0.799838 + 0.600215i 0.795082π0.795082\pi
620620 0 0
621621 −55.0000 −2.20707
622622 0 0
623623 3.31662 0.132878
624624 0 0
625625 25.0000 1.00000
626626 0 0
627627 −36.4829 −1.45699
628628 0 0
629629 27.0000 1.07656
630630 0 0
631631 9.94987 0.396098 0.198049 0.980192i 0.436539π-0.436539\pi
0.198049 + 0.980192i 0.436539π0.436539\pi
632632 0 0
633633 11.0000 0.437211
634634 0 0
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 79.5990 3.14889
640640 0 0
641641 21.0000 0.829450 0.414725 0.909947i 0.363878π-0.363878\pi
0.414725 + 0.909947i 0.363878π0.363878\pi
642642 0 0
643643 36.4829 1.43874 0.719372 0.694625i 0.244430π-0.244430\pi
0.719372 + 0.694625i 0.244430π0.244430\pi
644644 0 0
645645 0 0
646646 0 0
647647 9.94987 0.391170 0.195585 0.980687i 0.437339π-0.437339\pi
0.195585 + 0.980687i 0.437339π0.437339\pi
648648 0 0
649649 11.0000 0.431788
650650 0 0
651651 0 0
652652 0 0
653653 −15.0000 −0.586995 −0.293498 0.955960i 0.594819π-0.594819\pi
−0.293498 + 0.955960i 0.594819π0.594819\pi
654654 0 0
655655 0 0
656656 0 0
657657 32.0000 1.24844
658658 0 0
659659 43.1161 1.67957 0.839783 0.542922i 0.182682π-0.182682\pi
0.839783 + 0.542922i 0.182682π0.182682\pi
660660 0 0
661661 −17.0000 −0.661223 −0.330612 0.943767i 0.607255π-0.607255\pi
−0.330612 + 0.943767i 0.607255π0.607255\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 −16.5831 −0.642101
668668 0 0
669669 11.0000 0.425285
670670 0 0
671671 −29.8496 −1.15233
672672 0 0
673673 −49.0000 −1.88881 −0.944406 0.328783i 0.893362π-0.893362\pi
−0.944406 + 0.328783i 0.893362π0.893362\pi
674674 0 0
675675 82.9156 3.19142
676676 0 0
677677 −24.0000 −0.922395 −0.461197 0.887298i 0.652580π-0.652580\pi
−0.461197 + 0.887298i 0.652580π0.652580\pi
678678 0 0
679679 −23.2164 −0.890963
680680 0 0
681681 −11.0000 −0.421521
682682 0 0
683683 29.8496 1.14216 0.571082 0.820893i 0.306524π-0.306524\pi
0.571082 + 0.820893i 0.306524π0.306524\pi
684684 0 0
685685 0 0
686686 0 0
687687 26.5330 1.01230
688688 0 0
689689 0 0
690690 0 0
691691 −23.2164 −0.883192 −0.441596 0.897214i 0.645588π-0.645588\pi
−0.441596 + 0.897214i 0.645588π0.645588\pi
692692 0 0
693693 88.0000 3.34284
694694 0 0
695695 0 0
696696 0 0
697697 −9.00000 −0.340899
698698 0 0
699699 −13.2665 −0.501785
700700 0 0
701701 −32.0000 −1.20862 −0.604312 0.796748i 0.706552π-0.706552\pi
−0.604312 + 0.796748i 0.706552π0.706552\pi
702702 0 0
703703 −29.8496 −1.12580
704704 0 0
705705 0 0
706706 0 0
707707 −49.7494 −1.87102
708708 0 0
709709 −29.0000 −1.08912 −0.544559 0.838723i 0.683303π-0.683303\pi
−0.544559 + 0.838723i 0.683303π0.683303\pi
710710 0 0
711711 −53.0660 −1.99013
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 −88.0000 −3.28642
718718 0 0
719719 −29.8496 −1.11320 −0.556602 0.830780i 0.687895π-0.687895\pi
−0.556602 + 0.830780i 0.687895π0.687895\pi
720720 0 0
721721 0 0
722722 0 0
723723 43.1161 1.60351
724724 0 0
725725 25.0000 0.928477
726726 0 0
727727 26.5330 0.984054 0.492027 0.870580i 0.336256π-0.336256\pi
0.492027 + 0.870580i 0.336256π0.336256\pi
728728 0 0
729729 83.0000 3.07407
730730 0 0
731731 29.8496 1.10403
732732 0 0
733733 −18.0000 −0.664845 −0.332423 0.943131i 0.607866π-0.607866\pi
−0.332423 + 0.943131i 0.607866π0.607866\pi
734734 0 0
735735 0 0
736736 0 0
737737 33.0000 1.21557
738738 0 0
739739 9.94987 0.366012 0.183006 0.983112i 0.441417π-0.441417\pi
0.183006 + 0.983112i 0.441417π0.441417\pi
740740 0 0
741741 0 0
742742 0 0
743743 43.1161 1.58178 0.790889 0.611960i 0.209619π-0.209619\pi
0.790889 + 0.611960i 0.209619π0.209619\pi
744744 0 0
745745 0 0
746746 0 0
747747 −106.132 −3.88317
748748 0 0
749749 −11.0000 −0.401931
750750 0 0
751751 29.8496 1.08923 0.544614 0.838687i 0.316676π-0.316676\pi
0.544614 + 0.838687i 0.316676π0.316676\pi
752752 0 0
753753 −55.0000 −2.00431
754754 0 0
755755 0 0
756756 0 0
757757 −7.00000 −0.254419 −0.127210 0.991876i 0.540602π-0.540602\pi
−0.127210 + 0.991876i 0.540602π0.540602\pi
758758 0 0
759759 −36.4829 −1.32424
760760 0 0
761761 27.0000 0.978749 0.489375 0.872074i 0.337225π-0.337225\pi
0.489375 + 0.872074i 0.337225π0.337225\pi
762762 0 0
763763 53.0660 1.92112
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 0 0
769769 27.0000 0.973645 0.486822 0.873501i 0.338156π-0.338156\pi
0.486822 + 0.873501i 0.338156π0.338156\pi
770770 0 0
771771 −43.1161 −1.55279
772772 0 0
773773 −21.0000 −0.755318 −0.377659 0.925945i 0.623271π-0.623271\pi
−0.377659 + 0.925945i 0.623271π0.623271\pi
774774 0 0
775775 0 0
776776 0 0
777777 99.0000 3.55161
778778 0 0
779779 9.94987 0.356491
780780 0 0
781781 33.0000 1.18083
782782 0 0
783783 82.9156 2.96316
784784 0 0
785785 0 0
786786 0 0
787787 9.94987 0.354675 0.177337 0.984150i 0.443252π-0.443252\pi
0.177337 + 0.984150i 0.443252π0.443252\pi
788788 0 0
789789 77.0000 2.74127
790790 0 0
791791 −36.4829 −1.29718
792792 0 0
793793 0 0
794794 0 0
795795 0 0
796796 0 0
797797 −33.0000 −1.16892 −0.584460 0.811423i 0.698694π-0.698694\pi
−0.584460 + 0.811423i 0.698694π0.698694\pi
798798 0 0
799799 19.8997 0.704003
800800 0 0
801801 8.00000 0.282666
802802 0 0
803803 13.2665 0.468165
804804 0 0
805805 0 0
806806 0 0
807807 −96.1821 −3.38577
808808 0 0
809809 −19.0000 −0.668004 −0.334002 0.942572i 0.608399π-0.608399\pi
−0.334002 + 0.942572i 0.608399π0.608399\pi
810810 0 0
811811 −6.63325 −0.232925 −0.116462 0.993195i 0.537155π-0.537155\pi
−0.116462 + 0.993195i 0.537155π0.537155\pi
812812 0 0
813813 99.0000 3.47208
814814 0 0
815815 0 0
816816 0 0
817817 −33.0000 −1.15452
818818 0 0
819819 0 0
820820 0 0
821821 −27.0000 −0.942306 −0.471153 0.882051i 0.656162π-0.656162\pi
−0.471153 + 0.882051i 0.656162π0.656162\pi
822822 0 0
823823 −36.4829 −1.27171 −0.635856 0.771807i 0.719353π-0.719353\pi
−0.635856 + 0.771807i 0.719353π0.719353\pi
824824 0 0
825825 55.0000 1.91485
826826 0 0
827827 −13.2665 −0.461321 −0.230661 0.973034i 0.574089π-0.574089\pi
−0.230661 + 0.973034i 0.574089π0.574089\pi
828828 0 0
829829 11.0000 0.382046 0.191023 0.981586i 0.438820π-0.438820\pi
0.191023 + 0.981586i 0.438820π0.438820\pi
830830 0 0
831831 −16.5831 −0.575262
832832 0 0
833833 −12.0000 −0.415775
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0 0
839839 9.94987 0.343508 0.171754 0.985140i 0.445057π-0.445057\pi
0.171754 + 0.985140i 0.445057π0.445057\pi
840840 0 0
841841 −4.00000 −0.137931
842842 0 0
843843 66.3325 2.28461
844844 0 0
845845 0 0
846846 0 0
847847 0 0
848848 0 0
849849 −77.0000 −2.64263
850850 0 0
851851 −29.8496 −1.02323
852852 0 0
853853 −56.0000 −1.91740 −0.958702 0.284413i 0.908201π-0.908201\pi
−0.958702 + 0.284413i 0.908201π0.908201\pi
854854 0 0
855855 0 0
856856 0 0
857857 28.0000 0.956462 0.478231 0.878234i 0.341278π-0.341278\pi
0.478231 + 0.878234i 0.341278π0.341278\pi
858858 0 0
859859 13.2665 0.452647 0.226324 0.974052i 0.427329π-0.427329\pi
0.226324 + 0.974052i 0.427329π0.427329\pi
860860 0 0
861861 −33.0000 −1.12464
862862 0 0
863863 53.0660 1.80639 0.903194 0.429233i 0.141216π-0.141216\pi
0.903194 + 0.429233i 0.141216π0.141216\pi
864864 0 0
865865 0 0
866866 0 0
867867 26.5330 0.901108
868868 0 0
869869 −22.0000 −0.746299
870870 0 0
871871 0 0
872872 0 0
873873 −56.0000 −1.89531
874874 0 0
875875 0 0
876876 0 0
877877 −15.0000 −0.506514 −0.253257 0.967399i 0.581502π-0.581502\pi
−0.253257 + 0.967399i 0.581502π0.581502\pi
878878 0 0
879879 23.2164 0.783069
880880 0 0
881881 5.00000 0.168454 0.0842271 0.996447i 0.473158π-0.473158\pi
0.0842271 + 0.996447i 0.473158π0.473158\pi
882882 0 0
883883 −13.2665 −0.446453 −0.223227 0.974767i 0.571659π-0.571659\pi
−0.223227 + 0.974767i 0.571659π0.571659\pi
884884 0 0
885885 0 0
886886 0 0
887887 −43.1161 −1.44770 −0.723849 0.689959i 0.757629π-0.757629\pi
−0.723849 + 0.689959i 0.757629π0.757629\pi
888888 0 0
889889 33.0000 1.10678
890890 0 0
891891 102.815 3.44444
892892 0 0
893893 −22.0000 −0.736202
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 0 0
901901 24.0000 0.799556
902902 0 0
903903 109.449 3.64222
904904 0 0
905905 0 0
906906 0 0
907907 49.7494 1.65190 0.825950 0.563743i 0.190639π-0.190639\pi
0.825950 + 0.563743i 0.190639π0.190639\pi
908908 0 0
909909 −120.000 −3.98015
910910 0 0
911911 −26.5330 −0.879077 −0.439539 0.898224i 0.644858π-0.644858\pi
−0.439539 + 0.898224i 0.644858π0.644858\pi
912912 0 0
913913 −44.0000 −1.45619
914914 0 0
915915 0 0
916916 0 0
917917 −44.0000 −1.45301
918918 0 0
919919 −3.31662 −0.109405 −0.0547027 0.998503i 0.517421π-0.517421\pi
−0.0547027 + 0.998503i 0.517421π0.517421\pi
920920 0 0
921921 −44.0000 −1.44985
922922 0 0
923923 0 0
924924 0 0
925925 45.0000 1.47959
926926 0 0
927927 0 0
928928 0 0
929929 −13.0000 −0.426516 −0.213258 0.976996i 0.568408π-0.568408\pi
−0.213258 + 0.976996i 0.568408π0.568408\pi
930930 0 0
931931 13.2665 0.434792
932932 0 0
933933 88.0000 2.88099
934934 0 0
935935 0 0
936936 0 0
937937 20.0000 0.653372 0.326686 0.945133i 0.394068π-0.394068\pi
0.326686 + 0.945133i 0.394068π0.394068\pi
938938 0 0
939939 −13.2665 −0.432936
940940 0 0
941941 −30.0000 −0.977972 −0.488986 0.872292i 0.662633π-0.662633\pi
−0.488986 + 0.872292i 0.662633π0.662633\pi
942942 0 0
943943 9.94987 0.324012
944944 0 0
945945 0 0
946946 0 0
947947 3.31662 0.107776 0.0538879 0.998547i 0.482839π-0.482839\pi
0.0538879 + 0.998547i 0.482839π0.482839\pi
948948 0 0
949949 0 0
950950 0 0
951951 59.6992 1.93588
952952 0 0
953953 15.0000 0.485898 0.242949 0.970039i 0.421885π-0.421885\pi
0.242949 + 0.970039i 0.421885π0.421885\pi
954954 0 0
955955 0 0
956956 0 0
957957 55.0000 1.77790
958958 0 0
959959 29.8496 0.963895
960960 0 0
961961 −31.0000 −1.00000
962962 0 0
963963 −26.5330 −0.855014
964964 0 0
965965 0 0
966966 0 0
967967 −26.5330 −0.853244 −0.426622 0.904430i 0.640296π-0.640296\pi
−0.426622 + 0.904430i 0.640296π0.640296\pi
968968 0 0
969969 33.0000 1.06011
970970 0 0
971971 16.5831 0.532178 0.266089 0.963948i 0.414269π-0.414269\pi
0.266089 + 0.963948i 0.414269π0.414269\pi
972972 0 0
973973 −11.0000 −0.352644
974974 0 0
975975 0 0
976976 0 0
977977 −7.00000 −0.223950 −0.111975 0.993711i 0.535718π-0.535718\pi
−0.111975 + 0.993711i 0.535718π0.535718\pi
978978 0 0
979979 3.31662 0.106000
980980 0 0
981981 128.000 4.08673
982982 0 0
983983 53.0660 1.69254 0.846271 0.532752i 0.178842π-0.178842\pi
0.846271 + 0.532752i 0.178842π0.178842\pi
984984 0 0
985985 0 0
986986 0 0
987987 72.9657 2.32253
988988 0 0
989989 −33.0000 −1.04934
990990 0 0
991991 −43.1161 −1.36963 −0.684814 0.728718i 0.740117π-0.740117\pi
−0.684814 + 0.728718i 0.740117π0.740117\pi
992992 0 0
993993 −33.0000 −1.04722
994994 0 0
995995 0 0
996996 0 0
997997 −17.0000 −0.538395 −0.269198 0.963085i 0.586759π-0.586759\pi
−0.269198 + 0.963085i 0.586759π0.586759\pi
998998 0 0
999999 149.248 4.72200
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 5408.2.a.w.1.1 2
4.3 odd 2 inner 5408.2.a.w.1.2 2
13.4 even 6 416.2.i.d.289.2 yes 4
13.10 even 6 416.2.i.d.321.2 yes 4
13.12 even 2 5408.2.a.x.1.1 2
52.23 odd 6 416.2.i.d.321.1 yes 4
52.43 odd 6 416.2.i.d.289.1 4
52.51 odd 2 5408.2.a.x.1.2 2
104.43 odd 6 832.2.i.n.705.2 4
104.69 even 6 832.2.i.n.705.1 4
104.75 odd 6 832.2.i.n.321.2 4
104.101 even 6 832.2.i.n.321.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
416.2.i.d.289.1 4 52.43 odd 6
416.2.i.d.289.2 yes 4 13.4 even 6
416.2.i.d.321.1 yes 4 52.23 odd 6
416.2.i.d.321.2 yes 4 13.10 even 6
832.2.i.n.321.1 4 104.101 even 6
832.2.i.n.321.2 4 104.75 odd 6
832.2.i.n.705.1 4 104.69 even 6
832.2.i.n.705.2 4 104.43 odd 6
5408.2.a.w.1.1 2 1.1 even 1 trivial
5408.2.a.w.1.2 2 4.3 odd 2 inner
5408.2.a.x.1.1 2 13.12 even 2
5408.2.a.x.1.2 2 52.51 odd 2