Properties

Label 6336.2.a.cp.1.2
Level 63366336
Weight 22
Character 6336.1
Self dual yes
Analytic conductor 50.59350.593
Analytic rank 11
Dimension 22
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6336,2,Mod(1,6336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6336, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("6336.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 6336=263211 6336 = 2^{6} \cdot 3^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 6336.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: 50.593214720750.5932147207
Analytic rank: 11
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: 2 2
Twist minimal: no (minimal twist has level 792)
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 == 6336.1

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+2.82843q5+0.828427q7+1.00000q114.82843q132.00000q17+2.00000q192.82843q23+3.00000q253.65685q299.65685q31+2.34315q357.65685q370.343146q41+0.343146q4312.4853q476.31371q49+6.82843q53+2.82843q551.65685q593.17157q6113.6569q65+11.3137q67+4.48528q7113.3137q73+0.828427q774.82843q79+9.65685q835.65685q8516.0000q894.00000q91+5.65685q95+5.31371q97+O(q100)q+2.82843 q^{5} +0.828427 q^{7} +1.00000 q^{11} -4.82843 q^{13} -2.00000 q^{17} +2.00000 q^{19} -2.82843 q^{23} +3.00000 q^{25} -3.65685 q^{29} -9.65685 q^{31} +2.34315 q^{35} -7.65685 q^{37} -0.343146 q^{41} +0.343146 q^{43} -12.4853 q^{47} -6.31371 q^{49} +6.82843 q^{53} +2.82843 q^{55} -1.65685 q^{59} -3.17157 q^{61} -13.6569 q^{65} +11.3137 q^{67} +4.48528 q^{71} -13.3137 q^{73} +0.828427 q^{77} -4.82843 q^{79} +9.65685 q^{83} -5.65685 q^{85} -16.0000 q^{89} -4.00000 q^{91} +5.65685 q^{95} +5.31371 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q4q7+2q114q134q17+4q19+6q25+4q298q31+16q354q3712q41+12q438q47+10q49+8q53+8q5912q6116q65+12q97+O(q100) 2 q - 4 q^{7} + 2 q^{11} - 4 q^{13} - 4 q^{17} + 4 q^{19} + 6 q^{25} + 4 q^{29} - 8 q^{31} + 16 q^{35} - 4 q^{37} - 12 q^{41} + 12 q^{43} - 8 q^{47} + 10 q^{49} + 8 q^{53} + 8 q^{59} - 12 q^{61} - 16 q^{65}+ \cdots - 12 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 2.82843 1.26491 0.632456 0.774597i 0.282047π-0.282047\pi
0.632456 + 0.774597i 0.282047π0.282047\pi
66 0 0
77 0.828427 0.313116 0.156558 0.987669i 0.449960π-0.449960\pi
0.156558 + 0.987669i 0.449960π0.449960\pi
88 0 0
99 0 0
1010 0 0
1111 1.00000 0.301511
1212 0 0
1313 −4.82843 −1.33916 −0.669582 0.742738i 0.733527π-0.733527\pi
−0.669582 + 0.742738i 0.733527π0.733527\pi
1414 0 0
1515 0 0
1616 0 0
1717 −2.00000 −0.485071 −0.242536 0.970143i 0.577979π-0.577979\pi
−0.242536 + 0.970143i 0.577979π0.577979\pi
1818 0 0
1919 2.00000 0.458831 0.229416 0.973329i 0.426318π-0.426318\pi
0.229416 + 0.973329i 0.426318π0.426318\pi
2020 0 0
2121 0 0
2222 0 0
2323 −2.82843 −0.589768 −0.294884 0.955533i 0.595281π-0.595281\pi
−0.294884 + 0.955533i 0.595281π0.595281\pi
2424 0 0
2525 3.00000 0.600000
2626 0 0
2727 0 0
2828 0 0
2929 −3.65685 −0.679061 −0.339530 0.940595i 0.610268π-0.610268\pi
−0.339530 + 0.940595i 0.610268π0.610268\pi
3030 0 0
3131 −9.65685 −1.73442 −0.867211 0.497941i 0.834090π-0.834090\pi
−0.867211 + 0.497941i 0.834090π0.834090\pi
3232 0 0
3333 0 0
3434 0 0
3535 2.34315 0.396064
3636 0 0
3737 −7.65685 −1.25878 −0.629390 0.777090i 0.716695π-0.716695\pi
−0.629390 + 0.777090i 0.716695π0.716695\pi
3838 0 0
3939 0 0
4040 0 0
4141 −0.343146 −0.0535904 −0.0267952 0.999641i 0.508530π-0.508530\pi
−0.0267952 + 0.999641i 0.508530π0.508530\pi
4242 0 0
4343 0.343146 0.0523292 0.0261646 0.999658i 0.491671π-0.491671\pi
0.0261646 + 0.999658i 0.491671π0.491671\pi
4444 0 0
4545 0 0
4646 0 0
4747 −12.4853 −1.82117 −0.910583 0.413327i 0.864367π-0.864367\pi
−0.910583 + 0.413327i 0.864367π0.864367\pi
4848 0 0
4949 −6.31371 −0.901958
5050 0 0
5151 0 0
5252 0 0
5353 6.82843 0.937957 0.468978 0.883210i 0.344622π-0.344622\pi
0.468978 + 0.883210i 0.344622π0.344622\pi
5454 0 0
5555 2.82843 0.381385
5656 0 0
5757 0 0
5858 0 0
5959 −1.65685 −0.215704 −0.107852 0.994167i 0.534397π-0.534397\pi
−0.107852 + 0.994167i 0.534397π0.534397\pi
6060 0 0
6161 −3.17157 −0.406078 −0.203039 0.979171i 0.565082π-0.565082\pi
−0.203039 + 0.979171i 0.565082π0.565082\pi
6262 0 0
6363 0 0
6464 0 0
6565 −13.6569 −1.69392
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 4.48528 0.532305 0.266152 0.963931i 0.414248π-0.414248\pi
0.266152 + 0.963931i 0.414248π0.414248\pi
7272 0 0
7373 −13.3137 −1.55825 −0.779126 0.626868i 0.784337π-0.784337\pi
−0.779126 + 0.626868i 0.784337π0.784337\pi
7474 0 0
7575 0 0
7676 0 0
7777 0.828427 0.0944080
7878 0 0
7979 −4.82843 −0.543240 −0.271620 0.962405i 0.587559π-0.587559\pi
−0.271620 + 0.962405i 0.587559π0.587559\pi
8080 0 0
8181 0 0
8282 0 0
8383 9.65685 1.05998 0.529989 0.848005i 0.322196π-0.322196\pi
0.529989 + 0.848005i 0.322196π0.322196\pi
8484 0 0
8585 −5.65685 −0.613572
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 −4.00000 −0.419314
9292 0 0
9393 0 0
9494 0 0
9595 5.65685 0.580381
9696 0 0
9797 5.31371 0.539525 0.269763 0.962927i 0.413055π-0.413055\pi
0.269763 + 0.962927i 0.413055π0.413055\pi
9898 0 0
9999 0 0
100100 0 0
101101 −14.0000 −1.39305 −0.696526 0.717532i 0.745272π-0.745272\pi
−0.696526 + 0.717532i 0.745272π0.745272\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 4.00000 0.386695 0.193347 0.981130i 0.438066π-0.438066\pi
0.193347 + 0.981130i 0.438066π0.438066\pi
108108 0 0
109109 11.1716 1.07004 0.535021 0.844839i 0.320304π-0.320304\pi
0.535021 + 0.844839i 0.320304π0.320304\pi
110110 0 0
111111 0 0
112112 0 0
113113 −7.31371 −0.688016 −0.344008 0.938967i 0.611785π-0.611785\pi
−0.344008 + 0.938967i 0.611785π0.611785\pi
114114 0 0
115115 −8.00000 −0.746004
116116 0 0
117117 0 0
118118 0 0
119119 −1.65685 −0.151884
120120 0 0
121121 1.00000 0.0909091
122122 0 0
123123 0 0
124124 0 0
125125 −5.65685 −0.505964
126126 0 0
127127 11.1716 0.991317 0.495658 0.868518i 0.334927π-0.334927\pi
0.495658 + 0.868518i 0.334927π0.334927\pi
128128 0 0
129129 0 0
130130 0 0
131131 12.9706 1.13324 0.566622 0.823978i 0.308250π-0.308250\pi
0.566622 + 0.823978i 0.308250π0.308250\pi
132132 0 0
133133 1.65685 0.143667
134134 0 0
135135 0 0
136136 0 0
137137 −6.34315 −0.541932 −0.270966 0.962589i 0.587343π-0.587343\pi
−0.270966 + 0.962589i 0.587343π0.587343\pi
138138 0 0
139139 −9.31371 −0.789978 −0.394989 0.918686i 0.629252π-0.629252\pi
−0.394989 + 0.918686i 0.629252π0.629252\pi
140140 0 0
141141 0 0
142142 0 0
143143 −4.82843 −0.403773
144144 0 0
145145 −10.3431 −0.858952
146146 0 0
147147 0 0
148148 0 0
149149 −15.6569 −1.28266 −0.641330 0.767265i 0.721617π-0.721617\pi
−0.641330 + 0.767265i 0.721617π0.721617\pi
150150 0 0
151151 14.4853 1.17880 0.589398 0.807843i 0.299365π-0.299365\pi
0.589398 + 0.807843i 0.299365π0.299365\pi
152152 0 0
153153 0 0
154154 0 0
155155 −27.3137 −2.19389
156156 0 0
157157 7.65685 0.611083 0.305542 0.952179i 0.401162π-0.401162\pi
0.305542 + 0.952179i 0.401162π0.401162\pi
158158 0 0
159159 0 0
160160 0 0
161161 −2.34315 −0.184666
162162 0 0
163163 −4.00000 −0.313304 −0.156652 0.987654i 0.550070π-0.550070\pi
−0.156652 + 0.987654i 0.550070π0.550070\pi
164164 0 0
165165 0 0
166166 0 0
167167 −16.0000 −1.23812 −0.619059 0.785345i 0.712486π-0.712486\pi
−0.619059 + 0.785345i 0.712486π0.712486\pi
168168 0 0
169169 10.3137 0.793362
170170 0 0
171171 0 0
172172 0 0
173173 −19.6569 −1.49448 −0.747241 0.664553i 0.768622π-0.768622\pi
−0.747241 + 0.664553i 0.768622π0.768622\pi
174174 0 0
175175 2.48528 0.187870
176176 0 0
177177 0 0
178178 0 0
179179 21.6569 1.61871 0.809355 0.587320i 0.199817π-0.199817\pi
0.809355 + 0.587320i 0.199817π0.199817\pi
180180 0 0
181181 6.00000 0.445976 0.222988 0.974821i 0.428419π-0.428419\pi
0.222988 + 0.974821i 0.428419π0.428419\pi
182182 0 0
183183 0 0
184184 0 0
185185 −21.6569 −1.59224
186186 0 0
187187 −2.00000 −0.146254
188188 0 0
189189 0 0
190190 0 0
191191 6.82843 0.494088 0.247044 0.969004i 0.420541π-0.420541\pi
0.247044 + 0.969004i 0.420541π0.420541\pi
192192 0 0
193193 4.34315 0.312626 0.156313 0.987708i 0.450039π-0.450039\pi
0.156313 + 0.987708i 0.450039π0.450039\pi
194194 0 0
195195 0 0
196196 0 0
197197 13.3137 0.948562 0.474281 0.880373i 0.342708π-0.342708\pi
0.474281 + 0.880373i 0.342708π0.342708\pi
198198 0 0
199199 25.6569 1.81877 0.909383 0.415960i 0.136554π-0.136554\pi
0.909383 + 0.415960i 0.136554π0.136554\pi
200200 0 0
201201 0 0
202202 0 0
203203 −3.02944 −0.212625
204204 0 0
205205 −0.970563 −0.0677870
206206 0 0
207207 0 0
208208 0 0
209209 2.00000 0.138343
210210 0 0
211211 15.6569 1.07786 0.538931 0.842350i 0.318828π-0.318828\pi
0.538931 + 0.842350i 0.318828π0.318828\pi
212212 0 0
213213 0 0
214214 0 0
215215 0.970563 0.0661918
216216 0 0
217217 −8.00000 −0.543075
218218 0 0
219219 0 0
220220 0 0
221221 9.65685 0.649590
222222 0 0
223223 −11.3137 −0.757622 −0.378811 0.925474i 0.623667π-0.623667\pi
−0.378811 + 0.925474i 0.623667π0.623667\pi
224224 0 0
225225 0 0
226226 0 0
227227 −26.6274 −1.76732 −0.883662 0.468126i 0.844929π-0.844929\pi
−0.883662 + 0.468126i 0.844929π0.844929\pi
228228 0 0
229229 18.9706 1.25361 0.626805 0.779176i 0.284362π-0.284362\pi
0.626805 + 0.779176i 0.284362π0.284362\pi
230230 0 0
231231 0 0
232232 0 0
233233 26.9706 1.76690 0.883450 0.468525i 0.155214π-0.155214\pi
0.883450 + 0.468525i 0.155214π0.155214\pi
234234 0 0
235235 −35.3137 −2.30361
236236 0 0
237237 0 0
238238 0 0
239239 22.6274 1.46365 0.731823 0.681495i 0.238670π-0.238670\pi
0.731823 + 0.681495i 0.238670π0.238670\pi
240240 0 0
241241 3.65685 0.235559 0.117779 0.993040i 0.462422π-0.462422\pi
0.117779 + 0.993040i 0.462422π0.462422\pi
242242 0 0
243243 0 0
244244 0 0
245245 −17.8579 −1.14090
246246 0 0
247247 −9.65685 −0.614451
248248 0 0
249249 0 0
250250 0 0
251251 −10.3431 −0.652854 −0.326427 0.945222i 0.605845π-0.605845\pi
−0.326427 + 0.945222i 0.605845π0.605845\pi
252252 0 0
253253 −2.82843 −0.177822
254254 0 0
255255 0 0
256256 0 0
257257 3.31371 0.206703 0.103352 0.994645i 0.467043π-0.467043\pi
0.103352 + 0.994645i 0.467043π0.467043\pi
258258 0 0
259259 −6.34315 −0.394144
260260 0 0
261261 0 0
262262 0 0
263263 29.6569 1.82872 0.914360 0.404902i 0.132694π-0.132694\pi
0.914360 + 0.404902i 0.132694π0.132694\pi
264264 0 0
265265 19.3137 1.18643
266266 0 0
267267 0 0
268268 0 0
269269 −4.48528 −0.273472 −0.136736 0.990607i 0.543661π-0.543661\pi
−0.136736 + 0.990607i 0.543661π0.543661\pi
270270 0 0
271271 −25.7990 −1.56718 −0.783589 0.621280i 0.786613π-0.786613\pi
−0.783589 + 0.621280i 0.786613π0.786613\pi
272272 0 0
273273 0 0
274274 0 0
275275 3.00000 0.180907
276276 0 0
277277 31.4558 1.89000 0.944999 0.327072i 0.106062π-0.106062\pi
0.944999 + 0.327072i 0.106062π0.106062\pi
278278 0 0
279279 0 0
280280 0 0
281281 −1.31371 −0.0783693 −0.0391846 0.999232i 0.512476π-0.512476\pi
−0.0391846 + 0.999232i 0.512476π0.512476\pi
282282 0 0
283283 30.9706 1.84101 0.920504 0.390732i 0.127778π-0.127778\pi
0.920504 + 0.390732i 0.127778π0.127778\pi
284284 0 0
285285 0 0
286286 0 0
287287 −0.284271 −0.0167800
288288 0 0
289289 −13.0000 −0.764706
290290 0 0
291291 0 0
292292 0 0
293293 −18.0000 −1.05157 −0.525786 0.850617i 0.676229π-0.676229\pi
−0.525786 + 0.850617i 0.676229π0.676229\pi
294294 0 0
295295 −4.68629 −0.272846
296296 0 0
297297 0 0
298298 0 0
299299 13.6569 0.789796
300300 0 0
301301 0.284271 0.0163851
302302 0 0
303303 0 0
304304 0 0
305305 −8.97056 −0.513653
306306 0 0
307307 13.3137 0.759853 0.379927 0.925017i 0.375949π-0.375949\pi
0.379927 + 0.925017i 0.375949π0.375949\pi
308308 0 0
309309 0 0
310310 0 0
311311 −26.8284 −1.52130 −0.760650 0.649162i 0.775120π-0.775120\pi
−0.760650 + 0.649162i 0.775120π0.775120\pi
312312 0 0
313313 25.3137 1.43082 0.715408 0.698707i 0.246241π-0.246241\pi
0.715408 + 0.698707i 0.246241π0.246241\pi
314314 0 0
315315 0 0
316316 0 0
317317 −10.8284 −0.608185 −0.304093 0.952643i 0.598353π-0.598353\pi
−0.304093 + 0.952643i 0.598353π0.598353\pi
318318 0 0
319319 −3.65685 −0.204745
320320 0 0
321321 0 0
322322 0 0
323323 −4.00000 −0.222566
324324 0 0
325325 −14.4853 −0.803499
326326 0 0
327327 0 0
328328 0 0
329329 −10.3431 −0.570236
330330 0 0
331331 −18.6274 −1.02386 −0.511928 0.859029i 0.671068π-0.671068\pi
−0.511928 + 0.859029i 0.671068π0.671068\pi
332332 0 0
333333 0 0
334334 0 0
335335 32.0000 1.74835
336336 0 0
337337 14.0000 0.762629 0.381314 0.924445i 0.375472π-0.375472\pi
0.381314 + 0.924445i 0.375472π0.375472\pi
338338 0 0
339339 0 0
340340 0 0
341341 −9.65685 −0.522948
342342 0 0
343343 −11.0294 −0.595534
344344 0 0
345345 0 0
346346 0 0
347347 12.9706 0.696296 0.348148 0.937440i 0.386811π-0.386811\pi
0.348148 + 0.937440i 0.386811π0.386811\pi
348348 0 0
349349 13.7990 0.738643 0.369321 0.929302i 0.379590π-0.379590\pi
0.369321 + 0.929302i 0.379590π0.379590\pi
350350 0 0
351351 0 0
352352 0 0
353353 −8.00000 −0.425797 −0.212899 0.977074i 0.568290π-0.568290\pi
−0.212899 + 0.977074i 0.568290π0.568290\pi
354354 0 0
355355 12.6863 0.673318
356356 0 0
357357 0 0
358358 0 0
359359 −28.2843 −1.49279 −0.746393 0.665505i 0.768216π-0.768216\pi
−0.746393 + 0.665505i 0.768216π0.768216\pi
360360 0 0
361361 −15.0000 −0.789474
362362 0 0
363363 0 0
364364 0 0
365365 −37.6569 −1.97105
366366 0 0
367367 −3.31371 −0.172974 −0.0864871 0.996253i 0.527564π-0.527564\pi
−0.0864871 + 0.996253i 0.527564π0.527564\pi
368368 0 0
369369 0 0
370370 0 0
371371 5.65685 0.293689
372372 0 0
373373 −20.1421 −1.04292 −0.521460 0.853276i 0.674612π-0.674612\pi
−0.521460 + 0.853276i 0.674612π0.674612\pi
374374 0 0
375375 0 0
376376 0 0
377377 17.6569 0.909374
378378 0 0
379379 −0.686292 −0.0352524 −0.0176262 0.999845i 0.505611π-0.505611\pi
−0.0176262 + 0.999845i 0.505611π0.505611\pi
380380 0 0
381381 0 0
382382 0 0
383383 32.4853 1.65992 0.829960 0.557823i 0.188363π-0.188363\pi
0.829960 + 0.557823i 0.188363π0.188363\pi
384384 0 0
385385 2.34315 0.119418
386386 0 0
387387 0 0
388388 0 0
389389 −21.1716 −1.07344 −0.536721 0.843760i 0.680337π-0.680337\pi
−0.536721 + 0.843760i 0.680337π0.680337\pi
390390 0 0
391391 5.65685 0.286079
392392 0 0
393393 0 0
394394 0 0
395395 −13.6569 −0.687151
396396 0 0
397397 −6.68629 −0.335575 −0.167788 0.985823i 0.553662π-0.553662\pi
−0.167788 + 0.985823i 0.553662π0.553662\pi
398398 0 0
399399 0 0
400400 0 0
401401 −25.6569 −1.28124 −0.640621 0.767857i 0.721323π-0.721323\pi
−0.640621 + 0.767857i 0.721323π0.721323\pi
402402 0 0
403403 46.6274 2.32268
404404 0 0
405405 0 0
406406 0 0
407407 −7.65685 −0.379536
408408 0 0
409409 −12.3431 −0.610329 −0.305165 0.952300i 0.598711π-0.598711\pi
−0.305165 + 0.952300i 0.598711π0.598711\pi
410410 0 0
411411 0 0
412412 0 0
413413 −1.37258 −0.0675404
414414 0 0
415415 27.3137 1.34078
416416 0 0
417417 0 0
418418 0 0
419419 −36.2843 −1.77260 −0.886301 0.463109i 0.846734π-0.846734\pi
−0.886301 + 0.463109i 0.846734π0.846734\pi
420420 0 0
421421 −15.6569 −0.763068 −0.381534 0.924355i 0.624604π-0.624604\pi
−0.381534 + 0.924355i 0.624604π0.624604\pi
422422 0 0
423423 0 0
424424 0 0
425425 −6.00000 −0.291043
426426 0 0
427427 −2.62742 −0.127150
428428 0 0
429429 0 0
430430 0 0
431431 −10.3431 −0.498212 −0.249106 0.968476i 0.580137π-0.580137\pi
−0.249106 + 0.968476i 0.580137π0.580137\pi
432432 0 0
433433 30.0000 1.44171 0.720854 0.693087i 0.243750π-0.243750\pi
0.720854 + 0.693087i 0.243750π0.243750\pi
434434 0 0
435435 0 0
436436 0 0
437437 −5.65685 −0.270604
438438 0 0
439439 −20.1421 −0.961332 −0.480666 0.876904i 0.659605π-0.659605\pi
−0.480666 + 0.876904i 0.659605π0.659605\pi
440440 0 0
441441 0 0
442442 0 0
443443 −20.9706 −0.996342 −0.498171 0.867079i 0.665995π-0.665995\pi
−0.498171 + 0.867079i 0.665995π0.665995\pi
444444 0 0
445445 −45.2548 −2.14528
446446 0 0
447447 0 0
448448 0 0
449449 −18.3431 −0.865667 −0.432833 0.901474i 0.642486π-0.642486\pi
−0.432833 + 0.901474i 0.642486π0.642486\pi
450450 0 0
451451 −0.343146 −0.0161581
452452 0 0
453453 0 0
454454 0 0
455455 −11.3137 −0.530395
456456 0 0
457457 27.6569 1.29373 0.646867 0.762603i 0.276079π-0.276079\pi
0.646867 + 0.762603i 0.276079π0.276079\pi
458458 0 0
459459 0 0
460460 0 0
461461 −5.31371 −0.247484 −0.123742 0.992314i 0.539490π-0.539490\pi
−0.123742 + 0.992314i 0.539490π0.539490\pi
462462 0 0
463463 −8.00000 −0.371792 −0.185896 0.982569i 0.559519π-0.559519\pi
−0.185896 + 0.982569i 0.559519π0.559519\pi
464464 0 0
465465 0 0
466466 0 0
467467 0.686292 0.0317578 0.0158789 0.999874i 0.494945π-0.494945\pi
0.0158789 + 0.999874i 0.494945π0.494945\pi
468468 0 0
469469 9.37258 0.432786
470470 0 0
471471 0 0
472472 0 0
473473 0.343146 0.0157779
474474 0 0
475475 6.00000 0.275299
476476 0 0
477477 0 0
478478 0 0
479479 24.9706 1.14093 0.570467 0.821320i 0.306762π-0.306762\pi
0.570467 + 0.821320i 0.306762π0.306762\pi
480480 0 0
481481 36.9706 1.68571
482482 0 0
483483 0 0
484484 0 0
485485 15.0294 0.682452
486486 0 0
487487 9.65685 0.437594 0.218797 0.975770i 0.429787π-0.429787\pi
0.218797 + 0.975770i 0.429787π0.429787\pi
488488 0 0
489489 0 0
490490 0 0
491491 −26.6274 −1.20168 −0.600839 0.799370i 0.705167π-0.705167\pi
−0.600839 + 0.799370i 0.705167π0.705167\pi
492492 0 0
493493 7.31371 0.329393
494494 0 0
495495 0 0
496496 0 0
497497 3.71573 0.166673
498498 0 0
499499 −43.3137 −1.93899 −0.969494 0.245115i 0.921174π-0.921174\pi
−0.969494 + 0.245115i 0.921174π0.921174\pi
500500 0 0
501501 0 0
502502 0 0
503503 −19.3137 −0.861156 −0.430578 0.902553i 0.641690π-0.641690\pi
−0.430578 + 0.902553i 0.641690π0.641690\pi
504504 0 0
505505 −39.5980 −1.76209
506506 0 0
507507 0 0
508508 0 0
509509 −39.7990 −1.76406 −0.882030 0.471194i 0.843823π-0.843823\pi
−0.882030 + 0.471194i 0.843823π0.843823\pi
510510 0 0
511511 −11.0294 −0.487914
512512 0 0
513513 0 0
514514 0 0
515515 0 0
516516 0 0
517517 −12.4853 −0.549102
518518 0 0
519519 0 0
520520 0 0
521521 −28.9706 −1.26922 −0.634612 0.772831i 0.718840π-0.718840\pi
−0.634612 + 0.772831i 0.718840π0.718840\pi
522522 0 0
523523 −10.9706 −0.479709 −0.239855 0.970809i 0.577100π-0.577100\pi
−0.239855 + 0.970809i 0.577100π0.577100\pi
524524 0 0
525525 0 0
526526 0 0
527527 19.3137 0.841318
528528 0 0
529529 −15.0000 −0.652174
530530 0 0
531531 0 0
532532 0 0
533533 1.65685 0.0717663
534534 0 0
535535 11.3137 0.489134
536536 0 0
537537 0 0
538538 0 0
539539 −6.31371 −0.271951
540540 0 0
541541 19.1716 0.824250 0.412125 0.911127i 0.364787π-0.364787\pi
0.412125 + 0.911127i 0.364787π0.364787\pi
542542 0 0
543543 0 0
544544 0 0
545545 31.5980 1.35351
546546 0 0
547547 2.68629 0.114858 0.0574288 0.998350i 0.481710π-0.481710\pi
0.0574288 + 0.998350i 0.481710π0.481710\pi
548548 0 0
549549 0 0
550550 0 0
551551 −7.31371 −0.311574
552552 0 0
553553 −4.00000 −0.170097
554554 0 0
555555 0 0
556556 0 0
557557 17.3137 0.733605 0.366803 0.930299i 0.380452π-0.380452\pi
0.366803 + 0.930299i 0.380452π0.380452\pi
558558 0 0
559559 −1.65685 −0.0700775
560560 0 0
561561 0 0
562562 0 0
563563 39.3137 1.65688 0.828438 0.560081i 0.189230π-0.189230\pi
0.828438 + 0.560081i 0.189230π0.189230\pi
564564 0 0
565565 −20.6863 −0.870279
566566 0 0
567567 0 0
568568 0 0
569569 9.31371 0.390451 0.195225 0.980758i 0.437456π-0.437456\pi
0.195225 + 0.980758i 0.437456π0.437456\pi
570570 0 0
571571 28.6274 1.19802 0.599010 0.800742i 0.295561π-0.295561\pi
0.599010 + 0.800742i 0.295561π0.295561\pi
572572 0 0
573573 0 0
574574 0 0
575575 −8.48528 −0.353861
576576 0 0
577577 −28.6274 −1.19177 −0.595887 0.803068i 0.703200π-0.703200\pi
−0.595887 + 0.803068i 0.703200π0.703200\pi
578578 0 0
579579 0 0
580580 0 0
581581 8.00000 0.331896
582582 0 0
583583 6.82843 0.282805
584584 0 0
585585 0 0
586586 0 0
587587 1.65685 0.0683857 0.0341928 0.999415i 0.489114π-0.489114\pi
0.0341928 + 0.999415i 0.489114π0.489114\pi
588588 0 0
589589 −19.3137 −0.795807
590590 0 0
591591 0 0
592592 0 0
593593 −6.00000 −0.246390 −0.123195 0.992382i 0.539314π-0.539314\pi
−0.123195 + 0.992382i 0.539314π0.539314\pi
594594 0 0
595595 −4.68629 −0.192119
596596 0 0
597597 0 0
598598 0 0
599599 −7.51472 −0.307043 −0.153522 0.988145i 0.549061π-0.549061\pi
−0.153522 + 0.988145i 0.549061π0.549061\pi
600600 0 0
601601 −17.3137 −0.706241 −0.353120 0.935578i 0.614879π-0.614879\pi
−0.353120 + 0.935578i 0.614879π0.614879\pi
602602 0 0
603603 0 0
604604 0 0
605605 2.82843 0.114992
606606 0 0
607607 −36.8284 −1.49482 −0.747410 0.664363i 0.768703π-0.768703\pi
−0.747410 + 0.664363i 0.768703π0.768703\pi
608608 0 0
609609 0 0
610610 0 0
611611 60.2843 2.43884
612612 0 0
613613 4.82843 0.195018 0.0975092 0.995235i 0.468912π-0.468912\pi
0.0975092 + 0.995235i 0.468912π0.468912\pi
614614 0 0
615615 0 0
616616 0 0
617617 −31.3137 −1.26064 −0.630321 0.776334i 0.717077π-0.717077\pi
−0.630321 + 0.776334i 0.717077π0.717077\pi
618618 0 0
619619 −0.686292 −0.0275844 −0.0137922 0.999905i 0.504390π-0.504390\pi
−0.0137922 + 0.999905i 0.504390π0.504390\pi
620620 0 0
621621 0 0
622622 0 0
623623 −13.2548 −0.531044
624624 0 0
625625 −31.0000 −1.24000
626626 0 0
627627 0 0
628628 0 0
629629 15.3137 0.610598
630630 0 0
631631 11.0294 0.439075 0.219537 0.975604i 0.429545π-0.429545\pi
0.219537 + 0.975604i 0.429545π0.429545\pi
632632 0 0
633633 0 0
634634 0 0
635635 31.5980 1.25393
636636 0 0
637637 30.4853 1.20787
638638 0 0
639639 0 0
640640 0 0
641641 28.2843 1.11716 0.558581 0.829450i 0.311346π-0.311346\pi
0.558581 + 0.829450i 0.311346π0.311346\pi
642642 0 0
643643 −34.6274 −1.36557 −0.682786 0.730618i 0.739232π-0.739232\pi
−0.682786 + 0.730618i 0.739232π0.739232\pi
644644 0 0
645645 0 0
646646 0 0
647647 11.7990 0.463866 0.231933 0.972732i 0.425495π-0.425495\pi
0.231933 + 0.972732i 0.425495π0.425495\pi
648648 0 0
649649 −1.65685 −0.0650372
650650 0 0
651651 0 0
652652 0 0
653653 27.1127 1.06100 0.530501 0.847684i 0.322004π-0.322004\pi
0.530501 + 0.847684i 0.322004π0.322004\pi
654654 0 0
655655 36.6863 1.43345
656656 0 0
657657 0 0
658658 0 0
659659 −0.686292 −0.0267341 −0.0133671 0.999911i 0.504255π-0.504255\pi
−0.0133671 + 0.999911i 0.504255π0.504255\pi
660660 0 0
661661 −11.6569 −0.453399 −0.226700 0.973965i 0.572794π-0.572794\pi
−0.226700 + 0.973965i 0.572794π0.572794\pi
662662 0 0
663663 0 0
664664 0 0
665665 4.68629 0.181727
666666 0 0
667667 10.3431 0.400488
668668 0 0
669669 0 0
670670 0 0
671671 −3.17157 −0.122437
672672 0 0
673673 −8.34315 −0.321605 −0.160802 0.986987i 0.551408π-0.551408\pi
−0.160802 + 0.986987i 0.551408π0.551408\pi
674674 0 0
675675 0 0
676676 0 0
677677 −23.9411 −0.920132 −0.460066 0.887885i 0.652174π-0.652174\pi
−0.460066 + 0.887885i 0.652174π0.652174\pi
678678 0 0
679679 4.40202 0.168934
680680 0 0
681681 0 0
682682 0 0
683683 −40.9706 −1.56770 −0.783848 0.620953i 0.786746π-0.786746\pi
−0.783848 + 0.620953i 0.786746π0.786746\pi
684684 0 0
685685 −17.9411 −0.685495
686686 0 0
687687 0 0
688688 0 0
689689 −32.9706 −1.25608
690690 0 0
691691 45.9411 1.74768 0.873841 0.486211i 0.161621π-0.161621\pi
0.873841 + 0.486211i 0.161621π0.161621\pi
692692 0 0
693693 0 0
694694 0 0
695695 −26.3431 −0.999252
696696 0 0
697697 0.686292 0.0259951
698698 0 0
699699 0 0
700700 0 0
701701 44.6274 1.68555 0.842777 0.538263i 0.180919π-0.180919\pi
0.842777 + 0.538263i 0.180919π0.180919\pi
702702 0 0
703703 −15.3137 −0.577567
704704 0 0
705705 0 0
706706 0 0
707707 −11.5980 −0.436187
708708 0 0
709709 39.6569 1.48934 0.744672 0.667430i 0.232606π-0.232606\pi
0.744672 + 0.667430i 0.232606π0.232606\pi
710710 0 0
711711 0 0
712712 0 0
713713 27.3137 1.02291
714714 0 0
715715 −13.6569 −0.510737
716716 0 0
717717 0 0
718718 0 0
719719 −3.51472 −0.131077 −0.0655384 0.997850i 0.520876π-0.520876\pi
−0.0655384 + 0.997850i 0.520876π0.520876\pi
720720 0 0
721721 0 0
722722 0 0
723723 0 0
724724 0 0
725725 −10.9706 −0.407436
726726 0 0
727727 20.9706 0.777755 0.388878 0.921289i 0.372863π-0.372863\pi
0.388878 + 0.921289i 0.372863π0.372863\pi
728728 0 0
729729 0 0
730730 0 0
731731 −0.686292 −0.0253834
732732 0 0
733733 25.7990 0.952907 0.476454 0.879200i 0.341922π-0.341922\pi
0.476454 + 0.879200i 0.341922π0.341922\pi
734734 0 0
735735 0 0
736736 0 0
737737 11.3137 0.416746
738738 0 0
739739 −34.9706 −1.28641 −0.643206 0.765693i 0.722396π-0.722396\pi
−0.643206 + 0.765693i 0.722396π0.722396\pi
740740 0 0
741741 0 0
742742 0 0
743743 8.97056 0.329098 0.164549 0.986369i 0.447383π-0.447383\pi
0.164549 + 0.986369i 0.447383π0.447383\pi
744744 0 0
745745 −44.2843 −1.62245
746746 0 0
747747 0 0
748748 0 0
749749 3.31371 0.121080
750750 0 0
751751 43.5980 1.59091 0.795456 0.606011i 0.207231π-0.207231\pi
0.795456 + 0.606011i 0.207231π0.207231\pi
752752 0 0
753753 0 0
754754 0 0
755755 40.9706 1.49107
756756 0 0
757757 0.343146 0.0124718 0.00623592 0.999981i 0.498015π-0.498015\pi
0.00623592 + 0.999981i 0.498015π0.498015\pi
758758 0 0
759759 0 0
760760 0 0
761761 −32.6274 −1.18274 −0.591371 0.806399i 0.701413π-0.701413\pi
−0.591371 + 0.806399i 0.701413π0.701413\pi
762762 0 0
763763 9.25483 0.335047
764764 0 0
765765 0 0
766766 0 0
767767 8.00000 0.288863
768768 0 0
769769 −27.6569 −0.997332 −0.498666 0.866794i 0.666177π-0.666177\pi
−0.498666 + 0.866794i 0.666177π0.666177\pi
770770 0 0
771771 0 0
772772 0 0
773773 19.5147 0.701896 0.350948 0.936395i 0.385859π-0.385859\pi
0.350948 + 0.936395i 0.385859π0.385859\pi
774774 0 0
775775 −28.9706 −1.04065
776776 0 0
777777 0 0
778778 0 0
779779 −0.686292 −0.0245889
780780 0 0
781781 4.48528 0.160496
782782 0 0
783783 0 0
784784 0 0
785785 21.6569 0.772966
786786 0 0
787787 −31.6569 −1.12844 −0.564222 0.825623i 0.690824π-0.690824\pi
−0.564222 + 0.825623i 0.690824π0.690824\pi
788788 0 0
789789 0 0
790790 0 0
791791 −6.05887 −0.215429
792792 0 0
793793 15.3137 0.543806
794794 0 0
795795 0 0
796796 0 0
797797 30.1421 1.06769 0.533845 0.845583i 0.320747π-0.320747\pi
0.533845 + 0.845583i 0.320747π0.320747\pi
798798 0 0
799799 24.9706 0.883395
800800 0 0
801801 0 0
802802 0 0
803803 −13.3137 −0.469831
804804 0 0
805805 −6.62742 −0.233586
806806 0 0
807807 0 0
808808 0 0
809809 −41.5980 −1.46251 −0.731254 0.682106i 0.761064π-0.761064\pi
−0.731254 + 0.682106i 0.761064π0.761064\pi
810810 0 0
811811 12.3431 0.433426 0.216713 0.976235i 0.430466π-0.430466\pi
0.216713 + 0.976235i 0.430466π0.430466\pi
812812 0 0
813813 0 0
814814 0 0
815815 −11.3137 −0.396302
816816 0 0
817817 0.686292 0.0240103
818818 0 0
819819 0 0
820820 0 0
821821 48.6274 1.69711 0.848554 0.529108i 0.177473π-0.177473\pi
0.848554 + 0.529108i 0.177473π0.177473\pi
822822 0 0
823823 −35.3137 −1.23096 −0.615479 0.788153i 0.711038π-0.711038\pi
−0.615479 + 0.788153i 0.711038π0.711038\pi
824824 0 0
825825 0 0
826826 0 0
827827 −12.9706 −0.451031 −0.225515 0.974240i 0.572407π-0.572407\pi
−0.225515 + 0.974240i 0.572407π0.572407\pi
828828 0 0
829829 −20.6274 −0.716420 −0.358210 0.933641i 0.616613π-0.616613\pi
−0.358210 + 0.933641i 0.616613π0.616613\pi
830830 0 0
831831 0 0
832832 0 0
833833 12.6274 0.437514
834834 0 0
835835 −45.2548 −1.56611
836836 0 0
837837 0 0
838838 0 0
839839 −5.17157 −0.178543 −0.0892713 0.996007i 0.528454π-0.528454\pi
−0.0892713 + 0.996007i 0.528454π0.528454\pi
840840 0 0
841841 −15.6274 −0.538876
842842 0 0
843843 0 0
844844 0 0
845845 29.1716 1.00353
846846 0 0
847847 0.828427 0.0284651
848848 0 0
849849 0 0
850850 0 0
851851 21.6569 0.742387
852852 0 0
853853 −15.8579 −0.542963 −0.271481 0.962444i 0.587514π-0.587514\pi
−0.271481 + 0.962444i 0.587514π0.587514\pi
854854 0 0
855855 0 0
856856 0 0
857857 14.9706 0.511385 0.255692 0.966758i 0.417697π-0.417697\pi
0.255692 + 0.966758i 0.417697π0.417697\pi
858858 0 0
859859 13.9411 0.475665 0.237833 0.971306i 0.423563π-0.423563\pi
0.237833 + 0.971306i 0.423563π0.423563\pi
860860 0 0
861861 0 0
862862 0 0
863863 28.7696 0.979327 0.489663 0.871912i 0.337120π-0.337120\pi
0.489663 + 0.871912i 0.337120π0.337120\pi
864864 0 0
865865 −55.5980 −1.89039
866866 0 0
867867 0 0
868868 0 0
869869 −4.82843 −0.163793
870870 0 0
871871 −54.6274 −1.85098
872872 0 0
873873 0 0
874874 0 0
875875 −4.68629 −0.158426
876876 0 0
877877 −23.4558 −0.792048 −0.396024 0.918240i 0.629610π-0.629610\pi
−0.396024 + 0.918240i 0.629610π0.629610\pi
878878 0 0
879879 0 0
880880 0 0
881881 10.6274 0.358047 0.179023 0.983845i 0.442706π-0.442706\pi
0.179023 + 0.983845i 0.442706π0.442706\pi
882882 0 0
883883 28.6863 0.965371 0.482685 0.875794i 0.339662π-0.339662\pi
0.482685 + 0.875794i 0.339662π0.339662\pi
884884 0 0
885885 0 0
886886 0 0
887887 −45.6569 −1.53301 −0.766504 0.642240i 0.778005π-0.778005\pi
−0.766504 + 0.642240i 0.778005π0.778005\pi
888888 0 0
889889 9.25483 0.310397
890890 0 0
891891 0 0
892892 0 0
893893 −24.9706 −0.835608
894894 0 0
895895 61.2548 2.04752
896896 0 0
897897 0 0
898898 0 0
899899 35.3137 1.17778
900900 0 0
901901 −13.6569 −0.454976
902902 0 0
903903 0 0
904904 0 0
905905 16.9706 0.564121
906906 0 0
907907 −47.3137 −1.57103 −0.785513 0.618845i 0.787601π-0.787601\pi
−0.785513 + 0.618845i 0.787601π0.787601\pi
908908 0 0
909909 0 0
910910 0 0
911911 −11.5147 −0.381500 −0.190750 0.981639i 0.561092π-0.561092\pi
−0.190750 + 0.981639i 0.561092π0.561092\pi
912912 0 0
913913 9.65685 0.319595
914914 0 0
915915 0 0
916916 0 0
917917 10.7452 0.354837
918918 0 0
919919 51.4558 1.69737 0.848686 0.528897i 0.177394π-0.177394\pi
0.848686 + 0.528897i 0.177394π0.177394\pi
920920 0 0
921921 0 0
922922 0 0
923923 −21.6569 −0.712844
924924 0 0
925925 −22.9706 −0.755267
926926 0 0
927927 0 0
928928 0 0
929929 −17.6569 −0.579303 −0.289651 0.957132i 0.593539π-0.593539\pi
−0.289651 + 0.957132i 0.593539π0.593539\pi
930930 0 0
931931 −12.6274 −0.413847
932932 0 0
933933 0 0
934934 0 0
935935 −5.65685 −0.184999
936936 0 0
937937 19.9411 0.651448 0.325724 0.945465i 0.394392π-0.394392\pi
0.325724 + 0.945465i 0.394392π0.394392\pi
938938 0 0
939939 0 0
940940 0 0
941941 40.6274 1.32442 0.662208 0.749320i 0.269620π-0.269620\pi
0.662208 + 0.749320i 0.269620π0.269620\pi
942942 0 0
943943 0.970563 0.0316059
944944 0 0
945945 0 0
946946 0 0
947947 32.0000 1.03986 0.519930 0.854209i 0.325958π-0.325958\pi
0.519930 + 0.854209i 0.325958π0.325958\pi
948948 0 0
949949 64.2843 2.08676
950950 0 0
951951 0 0
952952 0 0
953953 43.6569 1.41418 0.707092 0.707121i 0.250007π-0.250007\pi
0.707092 + 0.707121i 0.250007π0.250007\pi
954954 0 0
955955 19.3137 0.624977
956956 0 0
957957 0 0
958958 0 0
959959 −5.25483 −0.169687
960960 0 0
961961 62.2548 2.00822
962962 0 0
963963 0 0
964964 0 0
965965 12.2843 0.395445
966966 0 0
967967 −17.5147 −0.563235 −0.281618 0.959527i 0.590871π-0.590871\pi
−0.281618 + 0.959527i 0.590871π0.590871\pi
968968 0 0
969969 0 0
970970 0 0
971971 9.65685 0.309903 0.154952 0.987922i 0.450478π-0.450478\pi
0.154952 + 0.987922i 0.450478π0.450478\pi
972972 0 0
973973 −7.71573 −0.247355
974974 0 0
975975 0 0
976976 0 0
977977 6.34315 0.202935 0.101468 0.994839i 0.467646π-0.467646\pi
0.101468 + 0.994839i 0.467646π0.467646\pi
978978 0 0
979979 −16.0000 −0.511362
980980 0 0
981981 0 0
982982 0 0
983983 −38.1421 −1.21655 −0.608273 0.793728i 0.708137π-0.708137\pi
−0.608273 + 0.793728i 0.708137π0.708137\pi
984984 0 0
985985 37.6569 1.19985
986986 0 0
987987 0 0
988988 0 0
989989 −0.970563 −0.0308621
990990 0 0
991991 −16.2843 −0.517287 −0.258643 0.965973i 0.583275π-0.583275\pi
−0.258643 + 0.965973i 0.583275π0.583275\pi
992992 0 0
993993 0 0
994994 0 0
995995 72.5685 2.30058
996996 0 0
997997 7.17157 0.227126 0.113563 0.993531i 0.463774π-0.463774\pi
0.113563 + 0.993531i 0.463774π0.463774\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 6336.2.a.cp.1.2 2
3.2 odd 2 6336.2.a.co.1.1 2
4.3 odd 2 6336.2.a.cq.1.2 2
8.3 odd 2 792.2.a.j.1.1 yes 2
8.5 even 2 1584.2.a.u.1.1 2
12.11 even 2 6336.2.a.cr.1.1 2
24.5 odd 2 1584.2.a.v.1.2 2
24.11 even 2 792.2.a.i.1.2 2
88.43 even 2 8712.2.a.bi.1.1 2
264.131 odd 2 8712.2.a.bh.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
792.2.a.i.1.2 2 24.11 even 2
792.2.a.j.1.1 yes 2 8.3 odd 2
1584.2.a.u.1.1 2 8.5 even 2
1584.2.a.v.1.2 2 24.5 odd 2
6336.2.a.co.1.1 2 3.2 odd 2
6336.2.a.cp.1.2 2 1.1 even 1 trivial
6336.2.a.cq.1.2 2 4.3 odd 2
6336.2.a.cr.1.1 2 12.11 even 2
8712.2.a.bh.1.2 2 264.131 odd 2
8712.2.a.bi.1.1 2 88.43 even 2