Properties

Label 9216.2.a.v.1.2
Level 92169216
Weight 22
Character 9216.1
Self dual yes
Analytic conductor 73.59073.590
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9216,2,Mod(1,9216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9216, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9216.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 9216=21032 9216 = 2^{10} \cdot 3^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 9216.a (trivial)

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: yes
Analytic conductor: 73.590130502873.5901305028
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ8)+\Q(\zeta_{8})^+
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x22 x^{2} - 2 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 4608)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.414211.41421 of defining polynomial
Character χ\chi == 9216.1

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+1.41421q5+4.00000q7+5.65685q114.24264q13+6.00000q17+5.65685q198.00000q233.00000q254.24264q29+4.00000q31+5.65685q351.41421q37+2.00000q415.65685q43+8.00000q47+9.00000q49+9.89949q53+8.00000q554.24264q616.00000q65+11.3137q67+10.0000q73+22.6274q77+12.0000q79+5.65685q83+8.48528q8516.0000q8916.9706q91+8.00000q95+8.00000q97+O(q100)q+1.41421 q^{5} +4.00000 q^{7} +5.65685 q^{11} -4.24264 q^{13} +6.00000 q^{17} +5.65685 q^{19} -8.00000 q^{23} -3.00000 q^{25} -4.24264 q^{29} +4.00000 q^{31} +5.65685 q^{35} -1.41421 q^{37} +2.00000 q^{41} -5.65685 q^{43} +8.00000 q^{47} +9.00000 q^{49} +9.89949 q^{53} +8.00000 q^{55} -4.24264 q^{61} -6.00000 q^{65} +11.3137 q^{67} +10.0000 q^{73} +22.6274 q^{77} +12.0000 q^{79} +5.65685 q^{83} +8.48528 q^{85} -16.0000 q^{89} -16.9706 q^{91} +8.00000 q^{95} +8.00000 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+8q7+12q1716q236q25+8q31+4q41+16q47+18q49+16q5512q65+20q73+24q7932q89+16q95+16q97+O(q100) 2 q + 8 q^{7} + 12 q^{17} - 16 q^{23} - 6 q^{25} + 8 q^{31} + 4 q^{41} + 16 q^{47} + 18 q^{49} + 16 q^{55} - 12 q^{65} + 20 q^{73} + 24 q^{79} - 32 q^{89} + 16 q^{95} + 16 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 0 0
44 0 0
55 1.41421 0.632456 0.316228 0.948683i 0.397584π-0.397584\pi
0.316228 + 0.948683i 0.397584π0.397584\pi
66 0 0
77 4.00000 1.51186 0.755929 0.654654i 0.227186π-0.227186\pi
0.755929 + 0.654654i 0.227186π0.227186\pi
88 0 0
99 0 0
1010 0 0
1111 5.65685 1.70561 0.852803 0.522233i 0.174901π-0.174901\pi
0.852803 + 0.522233i 0.174901π0.174901\pi
1212 0 0
1313 −4.24264 −1.17670 −0.588348 0.808608i 0.700222π-0.700222\pi
−0.588348 + 0.808608i 0.700222π0.700222\pi
1414 0 0
1515 0 0
1616 0 0
1717 6.00000 1.45521 0.727607 0.685994i 0.240633π-0.240633\pi
0.727607 + 0.685994i 0.240633π0.240633\pi
1818 0 0
1919 5.65685 1.29777 0.648886 0.760886i 0.275235π-0.275235\pi
0.648886 + 0.760886i 0.275235π0.275235\pi
2020 0 0
2121 0 0
2222 0 0
2323 −8.00000 −1.66812 −0.834058 0.551677i 0.813988π-0.813988\pi
−0.834058 + 0.551677i 0.813988π0.813988\pi
2424 0 0
2525 −3.00000 −0.600000
2626 0 0
2727 0 0
2828 0 0
2929 −4.24264 −0.787839 −0.393919 0.919145i 0.628881π-0.628881\pi
−0.393919 + 0.919145i 0.628881π0.628881\pi
3030 0 0
3131 4.00000 0.718421 0.359211 0.933257i 0.383046π-0.383046\pi
0.359211 + 0.933257i 0.383046π0.383046\pi
3232 0 0
3333 0 0
3434 0 0
3535 5.65685 0.956183
3636 0 0
3737 −1.41421 −0.232495 −0.116248 0.993220i 0.537087π-0.537087\pi
−0.116248 + 0.993220i 0.537087π0.537087\pi
3838 0 0
3939 0 0
4040 0 0
4141 2.00000 0.312348 0.156174 0.987730i 0.450084π-0.450084\pi
0.156174 + 0.987730i 0.450084π0.450084\pi
4242 0 0
4343 −5.65685 −0.862662 −0.431331 0.902194i 0.641956π-0.641956\pi
−0.431331 + 0.902194i 0.641956π0.641956\pi
4444 0 0
4545 0 0
4646 0 0
4747 8.00000 1.16692 0.583460 0.812142i 0.301699π-0.301699\pi
0.583460 + 0.812142i 0.301699π0.301699\pi
4848 0 0
4949 9.00000 1.28571
5050 0 0
5151 0 0
5252 0 0
5353 9.89949 1.35980 0.679900 0.733305i 0.262023π-0.262023\pi
0.679900 + 0.733305i 0.262023π0.262023\pi
5454 0 0
5555 8.00000 1.07872
5656 0 0
5757 0 0
5858 0 0
5959 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
6060 0 0
6161 −4.24264 −0.543214 −0.271607 0.962408i 0.587555π-0.587555\pi
−0.271607 + 0.962408i 0.587555π0.587555\pi
6262 0 0
6363 0 0
6464 0 0
6565 −6.00000 −0.744208
6666 0 0
6767 11.3137 1.38219 0.691095 0.722764i 0.257129π-0.257129\pi
0.691095 + 0.722764i 0.257129π0.257129\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 10.0000 1.17041 0.585206 0.810885i 0.301014π-0.301014\pi
0.585206 + 0.810885i 0.301014π0.301014\pi
7474 0 0
7575 0 0
7676 0 0
7777 22.6274 2.57863
7878 0 0
7979 12.0000 1.35011 0.675053 0.737769i 0.264121π-0.264121\pi
0.675053 + 0.737769i 0.264121π0.264121\pi
8080 0 0
8181 0 0
8282 0 0
8383 5.65685 0.620920 0.310460 0.950586i 0.399517π-0.399517\pi
0.310460 + 0.950586i 0.399517π0.399517\pi
8484 0 0
8585 8.48528 0.920358
8686 0 0
8787 0 0
8888 0 0
8989 −16.0000 −1.69600 −0.847998 0.529999i 0.822192π-0.822192\pi
−0.847998 + 0.529999i 0.822192π0.822192\pi
9090 0 0
9191 −16.9706 −1.77900
9292 0 0
9393 0 0
9494 0 0
9595 8.00000 0.820783
9696 0 0
9797 8.00000 0.812277 0.406138 0.913812i 0.366875π-0.366875\pi
0.406138 + 0.913812i 0.366875π0.366875\pi
9898 0 0
9999 0 0
100100 0 0
101101 −9.89949 −0.985037 −0.492518 0.870302i 0.663924π-0.663924\pi
−0.492518 + 0.870302i 0.663924π0.663924\pi
102102 0 0
103103 −4.00000 −0.394132 −0.197066 0.980390i 0.563141π-0.563141\pi
−0.197066 + 0.980390i 0.563141π0.563141\pi
104104 0 0
105105 0 0
106106 0 0
107107 −11.3137 −1.09374 −0.546869 0.837218i 0.684180π-0.684180\pi
−0.546869 + 0.837218i 0.684180π0.684180\pi
108108 0 0
109109 −7.07107 −0.677285 −0.338643 0.940915i 0.609968π-0.609968\pi
−0.338643 + 0.940915i 0.609968π0.609968\pi
110110 0 0
111111 0 0
112112 0 0
113113 16.0000 1.50515 0.752577 0.658505i 0.228811π-0.228811\pi
0.752577 + 0.658505i 0.228811π0.228811\pi
114114 0 0
115115 −11.3137 −1.05501
116116 0 0
117117 0 0
118118 0 0
119119 24.0000 2.20008
120120 0 0
121121 21.0000 1.90909
122122 0 0
123123 0 0
124124 0 0
125125 −11.3137 −1.01193
126126 0 0
127127 4.00000 0.354943 0.177471 0.984126i 0.443208π-0.443208\pi
0.177471 + 0.984126i 0.443208π0.443208\pi
128128 0 0
129129 0 0
130130 0 0
131131 −11.3137 −0.988483 −0.494242 0.869325i 0.664554π-0.664554\pi
−0.494242 + 0.869325i 0.664554π0.664554\pi
132132 0 0
133133 22.6274 1.96205
134134 0 0
135135 0 0
136136 0 0
137137 −2.00000 −0.170872 −0.0854358 0.996344i 0.527228π-0.527228\pi
−0.0854358 + 0.996344i 0.527228π0.527228\pi
138138 0 0
139139 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
140140 0 0
141141 0 0
142142 0 0
143143 −24.0000 −2.00698
144144 0 0
145145 −6.00000 −0.498273
146146 0 0
147147 0 0
148148 0 0
149149 −1.41421 −0.115857 −0.0579284 0.998321i 0.518450π-0.518450\pi
−0.0579284 + 0.998321i 0.518450π0.518450\pi
150150 0 0
151151 −4.00000 −0.325515 −0.162758 0.986666i 0.552039π-0.552039\pi
−0.162758 + 0.986666i 0.552039π0.552039\pi
152152 0 0
153153 0 0
154154 0 0
155155 5.65685 0.454369
156156 0 0
157157 −4.24264 −0.338600 −0.169300 0.985565i 0.554151π-0.554151\pi
−0.169300 + 0.985565i 0.554151π0.554151\pi
158158 0 0
159159 0 0
160160 0 0
161161 −32.0000 −2.52195
162162 0 0
163163 −16.9706 −1.32924 −0.664619 0.747183i 0.731406π-0.731406\pi
−0.664619 + 0.747183i 0.731406π0.731406\pi
164164 0 0
165165 0 0
166166 0 0
167167 −8.00000 −0.619059 −0.309529 0.950890i 0.600171π-0.600171\pi
−0.309529 + 0.950890i 0.600171π0.600171\pi
168168 0 0
169169 5.00000 0.384615
170170 0 0
171171 0 0
172172 0 0
173173 15.5563 1.18273 0.591364 0.806405i 0.298590π-0.298590\pi
0.591364 + 0.806405i 0.298590π0.298590\pi
174174 0 0
175175 −12.0000 −0.907115
176176 0 0
177177 0 0
178178 0 0
179179 −11.3137 −0.845626 −0.422813 0.906217i 0.638957π-0.638957\pi
−0.422813 + 0.906217i 0.638957π0.638957\pi
180180 0 0
181181 12.7279 0.946059 0.473029 0.881047i 0.343160π-0.343160\pi
0.473029 + 0.881047i 0.343160π0.343160\pi
182182 0 0
183183 0 0
184184 0 0
185185 −2.00000 −0.147043
186186 0 0
187187 33.9411 2.48202
188188 0 0
189189 0 0
190190 0 0
191191 −24.0000 −1.73658 −0.868290 0.496058i 0.834780π-0.834780\pi
−0.868290 + 0.496058i 0.834780π0.834780\pi
192192 0 0
193193 8.00000 0.575853 0.287926 0.957653i 0.407034π-0.407034\pi
0.287926 + 0.957653i 0.407034π0.407034\pi
194194 0 0
195195 0 0
196196 0 0
197197 −1.41421 −0.100759 −0.0503793 0.998730i 0.516043π-0.516043\pi
−0.0503793 + 0.998730i 0.516043π0.516043\pi
198198 0 0
199199 4.00000 0.283552 0.141776 0.989899i 0.454719π-0.454719\pi
0.141776 + 0.989899i 0.454719π0.454719\pi
200200 0 0
201201 0 0
202202 0 0
203203 −16.9706 −1.19110
204204 0 0
205205 2.82843 0.197546
206206 0 0
207207 0 0
208208 0 0
209209 32.0000 2.21349
210210 0 0
211211 22.6274 1.55774 0.778868 0.627188i 0.215794π-0.215794\pi
0.778868 + 0.627188i 0.215794π0.215794\pi
212212 0 0
213213 0 0
214214 0 0
215215 −8.00000 −0.545595
216216 0 0
217217 16.0000 1.08615
218218 0 0
219219 0 0
220220 0 0
221221 −25.4558 −1.71235
222222 0 0
223223 −12.0000 −0.803579 −0.401790 0.915732i 0.631612π-0.631612\pi
−0.401790 + 0.915732i 0.631612π0.631612\pi
224224 0 0
225225 0 0
226226 0 0
227227 −16.9706 −1.12638 −0.563188 0.826329i 0.690425π-0.690425\pi
−0.563188 + 0.826329i 0.690425π0.690425\pi
228228 0 0
229229 9.89949 0.654177 0.327089 0.944994i 0.393932π-0.393932\pi
0.327089 + 0.944994i 0.393932π0.393932\pi
230230 0 0
231231 0 0
232232 0 0
233233 16.0000 1.04819 0.524097 0.851658i 0.324403π-0.324403\pi
0.524097 + 0.851658i 0.324403π0.324403\pi
234234 0 0
235235 11.3137 0.738025
236236 0 0
237237 0 0
238238 0 0
239239 8.00000 0.517477 0.258738 0.965947i 0.416693π-0.416693\pi
0.258738 + 0.965947i 0.416693π0.416693\pi
240240 0 0
241241 24.0000 1.54598 0.772988 0.634421i 0.218761π-0.218761\pi
0.772988 + 0.634421i 0.218761π0.218761\pi
242242 0 0
243243 0 0
244244 0 0
245245 12.7279 0.813157
246246 0 0
247247 −24.0000 −1.52708
248248 0 0
249249 0 0
250250 0 0
251251 −5.65685 −0.357057 −0.178529 0.983935i 0.557134π-0.557134\pi
−0.178529 + 0.983935i 0.557134π0.557134\pi
252252 0 0
253253 −45.2548 −2.84515
254254 0 0
255255 0 0
256256 0 0
257257 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
258258 0 0
259259 −5.65685 −0.351500
260260 0 0
261261 0 0
262262 0 0
263263 16.0000 0.986602 0.493301 0.869859i 0.335790π-0.335790\pi
0.493301 + 0.869859i 0.335790π0.335790\pi
264264 0 0
265265 14.0000 0.860013
266266 0 0
267267 0 0
268268 0 0
269269 4.24264 0.258678 0.129339 0.991600i 0.458714π-0.458714\pi
0.129339 + 0.991600i 0.458714π0.458714\pi
270270 0 0
271271 −28.0000 −1.70088 −0.850439 0.526073i 0.823664π-0.823664\pi
−0.850439 + 0.526073i 0.823664π0.823664\pi
272272 0 0
273273 0 0
274274 0 0
275275 −16.9706 −1.02336
276276 0 0
277277 21.2132 1.27458 0.637289 0.770625i 0.280056π-0.280056\pi
0.637289 + 0.770625i 0.280056π0.280056\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 −11.3137 −0.672530 −0.336265 0.941767i 0.609164π-0.609164\pi
−0.336265 + 0.941767i 0.609164π0.609164\pi
284284 0 0
285285 0 0
286286 0 0
287287 8.00000 0.472225
288288 0 0
289289 19.0000 1.11765
290290 0 0
291291 0 0
292292 0 0
293293 −1.41421 −0.0826192 −0.0413096 0.999146i 0.513153π-0.513153\pi
−0.0413096 + 0.999146i 0.513153π0.513153\pi
294294 0 0
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 33.9411 1.96287
300300 0 0
301301 −22.6274 −1.30422
302302 0 0
303303 0 0
304304 0 0
305305 −6.00000 −0.343559
306306 0 0
307307 −33.9411 −1.93712 −0.968561 0.248776i 0.919972π-0.919972\pi
−0.968561 + 0.248776i 0.919972π0.919972\pi
308308 0 0
309309 0 0
310310 0 0
311311 −16.0000 −0.907277 −0.453638 0.891186i 0.649874π-0.649874\pi
−0.453638 + 0.891186i 0.649874π0.649874\pi
312312 0 0
313313 8.00000 0.452187 0.226093 0.974106i 0.427405π-0.427405\pi
0.226093 + 0.974106i 0.427405π0.427405\pi
314314 0 0
315315 0 0
316316 0 0
317317 −26.8701 −1.50917 −0.754586 0.656201i 0.772162π-0.772162\pi
−0.754586 + 0.656201i 0.772162π0.772162\pi
318318 0 0
319319 −24.0000 −1.34374
320320 0 0
321321 0 0
322322 0 0
323323 33.9411 1.88853
324324 0 0
325325 12.7279 0.706018
326326 0 0
327327 0 0
328328 0 0
329329 32.0000 1.76422
330330 0 0
331331 22.6274 1.24372 0.621858 0.783130i 0.286378π-0.286378\pi
0.621858 + 0.783130i 0.286378π0.286378\pi
332332 0 0
333333 0 0
334334 0 0
335335 16.0000 0.874173
336336 0 0
337337 30.0000 1.63420 0.817102 0.576493i 0.195579π-0.195579\pi
0.817102 + 0.576493i 0.195579π0.195579\pi
338338 0 0
339339 0 0
340340 0 0
341341 22.6274 1.22534
342342 0 0
343343 8.00000 0.431959
344344 0 0
345345 0 0
346346 0 0
347347 −28.2843 −1.51838 −0.759190 0.650870i 0.774404π-0.774404\pi
−0.759190 + 0.650870i 0.774404π0.774404\pi
348348 0 0
349349 15.5563 0.832712 0.416356 0.909202i 0.363307π-0.363307\pi
0.416356 + 0.909202i 0.363307π0.363307\pi
350350 0 0
351351 0 0
352352 0 0
353353 −16.0000 −0.851594 −0.425797 0.904819i 0.640006π-0.640006\pi
−0.425797 + 0.904819i 0.640006π0.640006\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 16.0000 0.844448 0.422224 0.906492i 0.361250π-0.361250\pi
0.422224 + 0.906492i 0.361250π0.361250\pi
360360 0 0
361361 13.0000 0.684211
362362 0 0
363363 0 0
364364 0 0
365365 14.1421 0.740233
366366 0 0
367367 20.0000 1.04399 0.521996 0.852948i 0.325188π-0.325188\pi
0.521996 + 0.852948i 0.325188π0.325188\pi
368368 0 0
369369 0 0
370370 0 0
371371 39.5980 2.05582
372372 0 0
373373 −21.2132 −1.09838 −0.549189 0.835698i 0.685063π-0.685063\pi
−0.549189 + 0.835698i 0.685063π0.685063\pi
374374 0 0
375375 0 0
376376 0 0
377377 18.0000 0.927047
378378 0 0
379379 16.9706 0.871719 0.435860 0.900015i 0.356444π-0.356444\pi
0.435860 + 0.900015i 0.356444π0.356444\pi
380380 0 0
381381 0 0
382382 0 0
383383 24.0000 1.22634 0.613171 0.789950i 0.289894π-0.289894\pi
0.613171 + 0.789950i 0.289894π0.289894\pi
384384 0 0
385385 32.0000 1.63087
386386 0 0
387387 0 0
388388 0 0
389389 −35.3553 −1.79259 −0.896293 0.443461i 0.853750π-0.853750\pi
−0.896293 + 0.443461i 0.853750π0.853750\pi
390390 0 0
391391 −48.0000 −2.42746
392392 0 0
393393 0 0
394394 0 0
395395 16.9706 0.853882
396396 0 0
397397 −38.1838 −1.91639 −0.958194 0.286119i 0.907635π-0.907635\pi
−0.958194 + 0.286119i 0.907635π0.907635\pi
398398 0 0
399399 0 0
400400 0 0
401401 −6.00000 −0.299626 −0.149813 0.988714i 0.547867π-0.547867\pi
−0.149813 + 0.988714i 0.547867π0.547867\pi
402402 0 0
403403 −16.9706 −0.845364
404404 0 0
405405 0 0
406406 0 0
407407 −8.00000 −0.396545
408408 0 0
409409 8.00000 0.395575 0.197787 0.980245i 0.436624π-0.436624\pi
0.197787 + 0.980245i 0.436624π0.436624\pi
410410 0 0
411411 0 0
412412 0 0
413413 0 0
414414 0 0
415415 8.00000 0.392705
416416 0 0
417417 0 0
418418 0 0
419419 16.9706 0.829066 0.414533 0.910034i 0.363945π-0.363945\pi
0.414533 + 0.910034i 0.363945π0.363945\pi
420420 0 0
421421 −12.7279 −0.620321 −0.310160 0.950684i 0.600383π-0.600383\pi
−0.310160 + 0.950684i 0.600383π0.600383\pi
422422 0 0
423423 0 0
424424 0 0
425425 −18.0000 −0.873128
426426 0 0
427427 −16.9706 −0.821263
428428 0 0
429429 0 0
430430 0 0
431431 8.00000 0.385346 0.192673 0.981263i 0.438284π-0.438284\pi
0.192673 + 0.981263i 0.438284π0.438284\pi
432432 0 0
433433 −8.00000 −0.384455 −0.192228 0.981350i 0.561571π-0.561571\pi
−0.192228 + 0.981350i 0.561571π0.561571\pi
434434 0 0
435435 0 0
436436 0 0
437437 −45.2548 −2.16483
438438 0 0
439439 20.0000 0.954548 0.477274 0.878755i 0.341625π-0.341625\pi
0.477274 + 0.878755i 0.341625π0.341625\pi
440440 0 0
441441 0 0
442442 0 0
443443 16.9706 0.806296 0.403148 0.915135i 0.367916π-0.367916\pi
0.403148 + 0.915135i 0.367916π0.367916\pi
444444 0 0
445445 −22.6274 −1.07264
446446 0 0
447447 0 0
448448 0 0
449449 −10.0000 −0.471929 −0.235965 0.971762i 0.575825π-0.575825\pi
−0.235965 + 0.971762i 0.575825π0.575825\pi
450450 0 0
451451 11.3137 0.532742
452452 0 0
453453 0 0
454454 0 0
455455 −24.0000 −1.12514
456456 0 0
457457 8.00000 0.374224 0.187112 0.982339i 0.440087π-0.440087\pi
0.187112 + 0.982339i 0.440087π0.440087\pi
458458 0 0
459459 0 0
460460 0 0
461461 −26.8701 −1.25146 −0.625732 0.780038i 0.715200π-0.715200\pi
−0.625732 + 0.780038i 0.715200π0.715200\pi
462462 0 0
463463 4.00000 0.185896 0.0929479 0.995671i 0.470371π-0.470371\pi
0.0929479 + 0.995671i 0.470371π0.470371\pi
464464 0 0
465465 0 0
466466 0 0
467467 5.65685 0.261768 0.130884 0.991398i 0.458218π-0.458218\pi
0.130884 + 0.991398i 0.458218π0.458218\pi
468468 0 0
469469 45.2548 2.08967
470470 0 0
471471 0 0
472472 0 0
473473 −32.0000 −1.47136
474474 0 0
475475 −16.9706 −0.778663
476476 0 0
477477 0 0
478478 0 0
479479 −16.0000 −0.731059 −0.365529 0.930800i 0.619112π-0.619112\pi
−0.365529 + 0.930800i 0.619112π0.619112\pi
480480 0 0
481481 6.00000 0.273576
482482 0 0
483483 0 0
484484 0 0
485485 11.3137 0.513729
486486 0 0
487487 12.0000 0.543772 0.271886 0.962329i 0.412353π-0.412353\pi
0.271886 + 0.962329i 0.412353π0.412353\pi
488488 0 0
489489 0 0
490490 0 0
491491 −11.3137 −0.510581 −0.255290 0.966864i 0.582171π-0.582171\pi
−0.255290 + 0.966864i 0.582171π0.582171\pi
492492 0 0
493493 −25.4558 −1.14647
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 11.3137 0.506471 0.253236 0.967405i 0.418505π-0.418505\pi
0.253236 + 0.967405i 0.418505π0.418505\pi
500500 0 0
501501 0 0
502502 0 0
503503 −16.0000 −0.713405 −0.356702 0.934218i 0.616099π-0.616099\pi
−0.356702 + 0.934218i 0.616099π0.616099\pi
504504 0 0
505505 −14.0000 −0.622992
506506 0 0
507507 0 0
508508 0 0
509509 15.5563 0.689523 0.344762 0.938690i 0.387960π-0.387960\pi
0.344762 + 0.938690i 0.387960π0.387960\pi
510510 0 0
511511 40.0000 1.76950
512512 0 0
513513 0 0
514514 0 0
515515 −5.65685 −0.249271
516516 0 0
517517 45.2548 1.99031
518518 0 0
519519 0 0
520520 0 0
521521 −30.0000 −1.31432 −0.657162 0.753749i 0.728243π-0.728243\pi
−0.657162 + 0.753749i 0.728243π0.728243\pi
522522 0 0
523523 −16.9706 −0.742071 −0.371035 0.928619i 0.620997π-0.620997\pi
−0.371035 + 0.928619i 0.620997π0.620997\pi
524524 0 0
525525 0 0
526526 0 0
527527 24.0000 1.04546
528528 0 0
529529 41.0000 1.78261
530530 0 0
531531 0 0
532532 0 0
533533 −8.48528 −0.367538
534534 0 0
535535 −16.0000 −0.691740
536536 0 0
537537 0 0
538538 0 0
539539 50.9117 2.19292
540540 0 0
541541 4.24264 0.182405 0.0912027 0.995832i 0.470929π-0.470929\pi
0.0912027 + 0.995832i 0.470929π0.470929\pi
542542 0 0
543543 0 0
544544 0 0
545545 −10.0000 −0.428353
546546 0 0
547547 −16.9706 −0.725609 −0.362804 0.931865i 0.618181π-0.618181\pi
−0.362804 + 0.931865i 0.618181π0.618181\pi
548548 0 0
549549 0 0
550550 0 0
551551 −24.0000 −1.02243
552552 0 0
553553 48.0000 2.04117
554554 0 0
555555 0 0
556556 0 0
557557 15.5563 0.659144 0.329572 0.944131i 0.393096π-0.393096\pi
0.329572 + 0.944131i 0.393096π0.393096\pi
558558 0 0
559559 24.0000 1.01509
560560 0 0
561561 0 0
562562 0 0
563563 −28.2843 −1.19204 −0.596020 0.802970i 0.703252π-0.703252\pi
−0.596020 + 0.802970i 0.703252π0.703252\pi
564564 0 0
565565 22.6274 0.951943
566566 0 0
567567 0 0
568568 0 0
569569 18.0000 0.754599 0.377300 0.926091i 0.376853π-0.376853\pi
0.377300 + 0.926091i 0.376853π0.376853\pi
570570 0 0
571571 −33.9411 −1.42039 −0.710196 0.704004i 0.751394π-0.751394\pi
−0.710196 + 0.704004i 0.751394π0.751394\pi
572572 0 0
573573 0 0
574574 0 0
575575 24.0000 1.00087
576576 0 0
577577 −18.0000 −0.749350 −0.374675 0.927156i 0.622246π-0.622246\pi
−0.374675 + 0.927156i 0.622246π0.622246\pi
578578 0 0
579579 0 0
580580 0 0
581581 22.6274 0.938743
582582 0 0
583583 56.0000 2.31928
584584 0 0
585585 0 0
586586 0 0
587587 −22.6274 −0.933933 −0.466967 0.884275i 0.654653π-0.654653\pi
−0.466967 + 0.884275i 0.654653π0.654653\pi
588588 0 0
589589 22.6274 0.932346
590590 0 0
591591 0 0
592592 0 0
593593 −16.0000 −0.657041 −0.328521 0.944497i 0.606550π-0.606550\pi
−0.328521 + 0.944497i 0.606550π0.606550\pi
594594 0 0
595595 33.9411 1.39145
596596 0 0
597597 0 0
598598 0 0
599599 40.0000 1.63436 0.817178 0.576386i 0.195537π-0.195537\pi
0.817178 + 0.576386i 0.195537π0.195537\pi
600600 0 0
601601 38.0000 1.55005 0.775026 0.631929i 0.217737π-0.217737\pi
0.775026 + 0.631929i 0.217737π0.217737\pi
602602 0 0
603603 0 0
604604 0 0
605605 29.6985 1.20742
606606 0 0
607607 −12.0000 −0.487065 −0.243532 0.969893i 0.578306π-0.578306\pi
−0.243532 + 0.969893i 0.578306π0.578306\pi
608608 0 0
609609 0 0
610610 0 0
611611 −33.9411 −1.37311
612612 0 0
613613 −9.89949 −0.399837 −0.199918 0.979813i 0.564068π-0.564068\pi
−0.199918 + 0.979813i 0.564068π0.564068\pi
614614 0 0
615615 0 0
616616 0 0
617617 32.0000 1.28827 0.644136 0.764911i 0.277217π-0.277217\pi
0.644136 + 0.764911i 0.277217π0.277217\pi
618618 0 0
619619 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
620620 0 0
621621 0 0
622622 0 0
623623 −64.0000 −2.56411
624624 0 0
625625 −1.00000 −0.0400000
626626 0 0
627627 0 0
628628 0 0
629629 −8.48528 −0.338330
630630 0 0
631631 −20.0000 −0.796187 −0.398094 0.917345i 0.630328π-0.630328\pi
−0.398094 + 0.917345i 0.630328π0.630328\pi
632632 0 0
633633 0 0
634634 0 0
635635 5.65685 0.224485
636636 0 0
637637 −38.1838 −1.51290
638638 0 0
639639 0 0
640640 0 0
641641 22.0000 0.868948 0.434474 0.900684i 0.356934π-0.356934\pi
0.434474 + 0.900684i 0.356934π0.356934\pi
642642 0 0
643643 16.9706 0.669254 0.334627 0.942351i 0.391390π-0.391390\pi
0.334627 + 0.942351i 0.391390π0.391390\pi
644644 0 0
645645 0 0
646646 0 0
647647 −24.0000 −0.943537 −0.471769 0.881722i 0.656384π-0.656384\pi
−0.471769 + 0.881722i 0.656384π0.656384\pi
648648 0 0
649649 0 0
650650 0 0
651651 0 0
652652 0 0
653653 −26.8701 −1.05151 −0.525753 0.850637i 0.676216π-0.676216\pi
−0.525753 + 0.850637i 0.676216π0.676216\pi
654654 0 0
655655 −16.0000 −0.625172
656656 0 0
657657 0 0
658658 0 0
659659 11.3137 0.440720 0.220360 0.975419i 0.429277π-0.429277\pi
0.220360 + 0.975419i 0.429277π0.429277\pi
660660 0 0
661661 9.89949 0.385046 0.192523 0.981292i 0.438333π-0.438333\pi
0.192523 + 0.981292i 0.438333π0.438333\pi
662662 0 0
663663 0 0
664664 0 0
665665 32.0000 1.24091
666666 0 0
667667 33.9411 1.31421
668668 0 0
669669 0 0
670670 0 0
671671 −24.0000 −0.926510
672672 0 0
673673 −8.00000 −0.308377 −0.154189 0.988041i 0.549276π-0.549276\pi
−0.154189 + 0.988041i 0.549276π0.549276\pi
674674 0 0
675675 0 0
676676 0 0
677677 −12.7279 −0.489174 −0.244587 0.969627i 0.578652π-0.578652\pi
−0.244587 + 0.969627i 0.578652π0.578652\pi
678678 0 0
679679 32.0000 1.22805
680680 0 0
681681 0 0
682682 0 0
683683 −16.9706 −0.649361 −0.324680 0.945824i 0.605257π-0.605257\pi
−0.324680 + 0.945824i 0.605257π0.605257\pi
684684 0 0
685685 −2.82843 −0.108069
686686 0 0
687687 0 0
688688 0 0
689689 −42.0000 −1.60007
690690 0 0
691691 50.9117 1.93677 0.968386 0.249457i 0.0802520π-0.0802520\pi
0.968386 + 0.249457i 0.0802520π0.0802520\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 12.0000 0.454532
698698 0 0
699699 0 0
700700 0 0
701701 15.5563 0.587555 0.293778 0.955874i 0.405087π-0.405087\pi
0.293778 + 0.955874i 0.405087π0.405087\pi
702702 0 0
703703 −8.00000 −0.301726
704704 0 0
705705 0 0
706706 0 0
707707 −39.5980 −1.48924
708708 0 0
709709 46.6690 1.75269 0.876346 0.481681i 0.159974π-0.159974\pi
0.876346 + 0.481681i 0.159974π0.159974\pi
710710 0 0
711711 0 0
712712 0 0
713713 −32.0000 −1.19841
714714 0 0
715715 −33.9411 −1.26933
716716 0 0
717717 0 0
718718 0 0
719719 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
720720 0 0
721721 −16.0000 −0.595871
722722 0 0
723723 0 0
724724 0 0
725725 12.7279 0.472703
726726 0 0
727727 52.0000 1.92857 0.964287 0.264861i 0.0853260π-0.0853260\pi
0.964287 + 0.264861i 0.0853260π0.0853260\pi
728728 0 0
729729 0 0
730730 0 0
731731 −33.9411 −1.25536
732732 0 0
733733 52.3259 1.93270 0.966351 0.257228i 0.0828093π-0.0828093\pi
0.966351 + 0.257228i 0.0828093π0.0828093\pi
734734 0 0
735735 0 0
736736 0 0
737737 64.0000 2.35747
738738 0 0
739739 33.9411 1.24854 0.624272 0.781207i 0.285396π-0.285396\pi
0.624272 + 0.781207i 0.285396π0.285396\pi
740740 0 0
741741 0 0
742742 0 0
743743 24.0000 0.880475 0.440237 0.897881i 0.354894π-0.354894\pi
0.440237 + 0.897881i 0.354894π0.354894\pi
744744 0 0
745745 −2.00000 −0.0732743
746746 0 0
747747 0 0
748748 0 0
749749 −45.2548 −1.65358
750750 0 0
751751 −28.0000 −1.02173 −0.510867 0.859660i 0.670676π-0.670676\pi
−0.510867 + 0.859660i 0.670676π0.670676\pi
752752 0 0
753753 0 0
754754 0 0
755755 −5.65685 −0.205874
756756 0 0
757757 −9.89949 −0.359803 −0.179902 0.983685i 0.557578π-0.557578\pi
−0.179902 + 0.983685i 0.557578π0.557578\pi
758758 0 0
759759 0 0
760760 0 0
761761 −18.0000 −0.652499 −0.326250 0.945284i 0.605785π-0.605785\pi
−0.326250 + 0.945284i 0.605785π0.605785\pi
762762 0 0
763763 −28.2843 −1.02396
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 0 0
769769 40.0000 1.44244 0.721218 0.692708i 0.243582π-0.243582\pi
0.721218 + 0.692708i 0.243582π0.243582\pi
770770 0 0
771771 0 0
772772 0 0
773773 12.7279 0.457792 0.228896 0.973451i 0.426489π-0.426489\pi
0.228896 + 0.973451i 0.426489π0.426489\pi
774774 0 0
775775 −12.0000 −0.431053
776776 0 0
777777 0 0
778778 0 0
779779 11.3137 0.405356
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 0 0
785785 −6.00000 −0.214149
786786 0 0
787787 −16.9706 −0.604935 −0.302468 0.953160i 0.597810π-0.597810\pi
−0.302468 + 0.953160i 0.597810π0.597810\pi
788788 0 0
789789 0 0
790790 0 0
791791 64.0000 2.27558
792792 0 0
793793 18.0000 0.639199
794794 0 0
795795 0 0
796796 0 0
797797 7.07107 0.250470 0.125235 0.992127i 0.460032π-0.460032\pi
0.125235 + 0.992127i 0.460032π0.460032\pi
798798 0 0
799799 48.0000 1.69812
800800 0 0
801801 0 0
802802 0 0
803803 56.5685 1.99626
804804 0 0
805805 −45.2548 −1.59502
806806 0 0
807807 0 0
808808 0 0
809809 −2.00000 −0.0703163 −0.0351581 0.999382i 0.511193π-0.511193\pi
−0.0351581 + 0.999382i 0.511193π0.511193\pi
810810 0 0
811811 5.65685 0.198639 0.0993195 0.995056i 0.468333π-0.468333\pi
0.0993195 + 0.995056i 0.468333π0.468333\pi
812812 0 0
813813 0 0
814814 0 0
815815 −24.0000 −0.840683
816816 0 0
817817 −32.0000 −1.11954
818818 0 0
819819 0 0
820820 0 0
821821 55.1543 1.92490 0.962450 0.271460i 0.0875065π-0.0875065\pi
0.962450 + 0.271460i 0.0875065π0.0875065\pi
822822 0 0
823823 44.0000 1.53374 0.766872 0.641800i 0.221812π-0.221812\pi
0.766872 + 0.641800i 0.221812π0.221812\pi
824824 0 0
825825 0 0
826826 0 0
827827 −45.2548 −1.57366 −0.786832 0.617167i 0.788280π-0.788280\pi
−0.786832 + 0.617167i 0.788280π0.788280\pi
828828 0 0
829829 −41.0122 −1.42441 −0.712206 0.701970i 0.752304π-0.752304\pi
−0.712206 + 0.701970i 0.752304π0.752304\pi
830830 0 0
831831 0 0
832832 0 0
833833 54.0000 1.87099
834834 0 0
835835 −11.3137 −0.391527
836836 0 0
837837 0 0
838838 0 0
839839 48.0000 1.65714 0.828572 0.559883i 0.189154π-0.189154\pi
0.828572 + 0.559883i 0.189154π0.189154\pi
840840 0 0
841841 −11.0000 −0.379310
842842 0 0
843843 0 0
844844 0 0
845845 7.07107 0.243252
846846 0 0
847847 84.0000 2.88627
848848 0 0
849849 0 0
850850 0 0
851851 11.3137 0.387829
852852 0 0
853853 1.41421 0.0484218 0.0242109 0.999707i 0.492293π-0.492293\pi
0.0242109 + 0.999707i 0.492293π0.492293\pi
854854 0 0
855855 0 0
856856 0 0
857857 18.0000 0.614868 0.307434 0.951569i 0.400530π-0.400530\pi
0.307434 + 0.951569i 0.400530π0.400530\pi
858858 0 0
859859 16.9706 0.579028 0.289514 0.957174i 0.406506π-0.406506\pi
0.289514 + 0.957174i 0.406506π0.406506\pi
860860 0 0
861861 0 0
862862 0 0
863863 −24.0000 −0.816970 −0.408485 0.912765i 0.633943π-0.633943\pi
−0.408485 + 0.912765i 0.633943π0.633943\pi
864864 0 0
865865 22.0000 0.748022
866866 0 0
867867 0 0
868868 0 0
869869 67.8823 2.30275
870870 0 0
871871 −48.0000 −1.62642
872872 0 0
873873 0 0
874874 0 0
875875 −45.2548 −1.52989
876876 0 0
877877 7.07107 0.238773 0.119386 0.992848i 0.461907π-0.461907\pi
0.119386 + 0.992848i 0.461907π0.461907\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 −5.65685 −0.190368 −0.0951842 0.995460i 0.530344π-0.530344\pi
−0.0951842 + 0.995460i 0.530344π0.530344\pi
884884 0 0
885885 0 0
886886 0 0
887887 −48.0000 −1.61168 −0.805841 0.592132i 0.798286π-0.798286\pi
−0.805841 + 0.592132i 0.798286π0.798286\pi
888888 0 0
889889 16.0000 0.536623
890890 0 0
891891 0 0
892892 0 0
893893 45.2548 1.51440
894894 0 0
895895 −16.0000 −0.534821
896896 0 0
897897 0 0
898898 0 0
899899 −16.9706 −0.566000
900900 0 0
901901 59.3970 1.97880
902902 0 0
903903 0 0
904904 0 0
905905 18.0000 0.598340
906906 0 0
907907 39.5980 1.31483 0.657415 0.753529i 0.271650π-0.271650\pi
0.657415 + 0.753529i 0.271650π0.271650\pi
908908 0 0
909909 0 0
910910 0 0
911911 40.0000 1.32526 0.662630 0.748947i 0.269440π-0.269440\pi
0.662630 + 0.748947i 0.269440π0.269440\pi
912912 0 0
913913 32.0000 1.05905
914914 0 0
915915 0 0
916916 0 0
917917 −45.2548 −1.49445
918918 0 0
919919 −20.0000 −0.659739 −0.329870 0.944027i 0.607005π-0.607005\pi
−0.329870 + 0.944027i 0.607005π0.607005\pi
920920 0 0
921921 0 0
922922 0 0
923923 0 0
924924 0 0
925925 4.24264 0.139497
926926 0 0
927927 0 0
928928 0 0
929929 42.0000 1.37798 0.688988 0.724773i 0.258055π-0.258055\pi
0.688988 + 0.724773i 0.258055π0.258055\pi
930930 0 0
931931 50.9117 1.66856
932932 0 0
933933 0 0
934934 0 0
935935 48.0000 1.56977
936936 0 0
937937 −26.0000 −0.849383 −0.424691 0.905338i 0.639617π-0.639617\pi
−0.424691 + 0.905338i 0.639617π0.639617\pi
938938 0 0
939939 0 0
940940 0 0
941941 −49.4975 −1.61357 −0.806786 0.590844i 0.798795π-0.798795\pi
−0.806786 + 0.590844i 0.798795π0.798795\pi
942942 0 0
943943 −16.0000 −0.521032
944944 0 0
945945 0 0
946946 0 0
947947 −56.5685 −1.83823 −0.919115 0.393989i 0.871095π-0.871095\pi
−0.919115 + 0.393989i 0.871095π0.871095\pi
948948 0 0
949949 −42.4264 −1.37722
950950 0 0
951951 0 0
952952 0 0
953953 18.0000 0.583077 0.291539 0.956559i 0.405833π-0.405833\pi
0.291539 + 0.956559i 0.405833π0.405833\pi
954954 0 0
955955 −33.9411 −1.09831
956956 0 0
957957 0 0
958958 0 0
959959 −8.00000 −0.258333
960960 0 0
961961 −15.0000 −0.483871
962962 0 0
963963 0 0
964964 0 0
965965 11.3137 0.364201
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 39.5980 1.27076 0.635380 0.772200i 0.280844π-0.280844\pi
0.635380 + 0.772200i 0.280844π0.280844\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 −38.0000 −1.21573 −0.607864 0.794041i 0.707973π-0.707973\pi
−0.607864 + 0.794041i 0.707973π0.707973\pi
978978 0 0
979979 −90.5097 −2.89270
980980 0 0
981981 0 0
982982 0 0
983983 −32.0000 −1.02064 −0.510321 0.859984i 0.670473π-0.670473\pi
−0.510321 + 0.859984i 0.670473π0.670473\pi
984984 0 0
985985 −2.00000 −0.0637253
986986 0 0
987987 0 0
988988 0 0
989989 45.2548 1.43902
990990 0 0
991991 −44.0000 −1.39771 −0.698853 0.715265i 0.746306π-0.746306\pi
−0.698853 + 0.715265i 0.746306π0.746306\pi
992992 0 0
993993 0 0
994994 0 0
995995 5.65685 0.179334
996996 0 0
997997 −46.6690 −1.47802 −0.739012 0.673693i 0.764707π-0.764707\pi
−0.739012 + 0.673693i 0.764707π0.764707\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 9216.2.a.v.1.2 2
3.2 odd 2 9216.2.a.t.1.1 2
4.3 odd 2 9216.2.a.c.1.2 2
8.3 odd 2 9216.2.a.c.1.1 2
8.5 even 2 inner 9216.2.a.v.1.1 2
12.11 even 2 9216.2.a.a.1.1 2
24.5 odd 2 9216.2.a.t.1.2 2
24.11 even 2 9216.2.a.a.1.2 2
32.3 odd 8 4608.2.k.e.1153.1 yes 2
32.5 even 8 4608.2.k.m.3457.1 yes 2
32.11 odd 8 4608.2.k.e.3457.1 yes 2
32.13 even 8 4608.2.k.m.1153.1 yes 2
32.19 odd 8 4608.2.k.t.1153.1 yes 2
32.21 even 8 4608.2.k.l.3457.1 yes 2
32.27 odd 8 4608.2.k.t.3457.1 yes 2
32.29 even 8 4608.2.k.l.1153.1 yes 2
96.5 odd 8 4608.2.k.k.3457.1 yes 2
96.11 even 8 4608.2.k.u.3457.1 yes 2
96.29 odd 8 4608.2.k.n.1153.1 yes 2
96.35 even 8 4608.2.k.u.1153.1 yes 2
96.53 odd 8 4608.2.k.n.3457.1 yes 2
96.59 even 8 4608.2.k.d.3457.1 yes 2
96.77 odd 8 4608.2.k.k.1153.1 yes 2
96.83 even 8 4608.2.k.d.1153.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4608.2.k.d.1153.1 2 96.83 even 8
4608.2.k.d.3457.1 yes 2 96.59 even 8
4608.2.k.e.1153.1 yes 2 32.3 odd 8
4608.2.k.e.3457.1 yes 2 32.11 odd 8
4608.2.k.k.1153.1 yes 2 96.77 odd 8
4608.2.k.k.3457.1 yes 2 96.5 odd 8
4608.2.k.l.1153.1 yes 2 32.29 even 8
4608.2.k.l.3457.1 yes 2 32.21 even 8
4608.2.k.m.1153.1 yes 2 32.13 even 8
4608.2.k.m.3457.1 yes 2 32.5 even 8
4608.2.k.n.1153.1 yes 2 96.29 odd 8
4608.2.k.n.3457.1 yes 2 96.53 odd 8
4608.2.k.t.1153.1 yes 2 32.19 odd 8
4608.2.k.t.3457.1 yes 2 32.27 odd 8
4608.2.k.u.1153.1 yes 2 96.35 even 8
4608.2.k.u.3457.1 yes 2 96.11 even 8
9216.2.a.a.1.1 2 12.11 even 2
9216.2.a.a.1.2 2 24.11 even 2
9216.2.a.c.1.1 2 8.3 odd 2
9216.2.a.c.1.2 2 4.3 odd 2
9216.2.a.t.1.1 2 3.2 odd 2
9216.2.a.t.1.2 2 24.5 odd 2
9216.2.a.v.1.1 2 8.5 even 2 inner
9216.2.a.v.1.2 2 1.1 even 1 trivial