Properties

Label 7056.2.a.cx.1.1
Level 70567056
Weight 22
Character 7056.1
Self dual yes
Analytic conductor 56.34256.342
Analytic rank 00
Dimension 22
CM no
Inner twists 11

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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] = [7056,2,Mod(1,7056)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7056, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 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("7056.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 7056=243272 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7056.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,0,0,4,0,0,0,0,0,4,0,0,0,0,0,-4,0,8,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(23)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 56.342443666256.3424436662
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ8)+\Q(\zeta_{8})^+
Copy content comment:defining polynomial
 
Copy content 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 1176)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 1.41421-1.41421 of defining polynomial
Character χ\chi == 7056.1

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) == q+0.585786q50.828427q11+1.41421q13+2.24264q17+6.82843q19+4.82843q234.65685q258.48528q29+5.17157q31+1.65685q370.585786q41+8.00000q436.82843q47+13.3137q530.485281q555.17157q5913.8995q61+0.828427q65+8.00000q670.828427q71+11.0711q73+2.34315q7915.3137q83+1.31371q8510.7279q89+4.00000q95+7.75736q97+O(q100)q+0.585786 q^{5} -0.828427 q^{11} +1.41421 q^{13} +2.24264 q^{17} +6.82843 q^{19} +4.82843 q^{23} -4.65685 q^{25} -8.48528 q^{29} +5.17157 q^{31} +1.65685 q^{37} -0.585786 q^{41} +8.00000 q^{43} -6.82843 q^{47} +13.3137 q^{53} -0.485281 q^{55} -5.17157 q^{59} -13.8995 q^{61} +0.828427 q^{65} +8.00000 q^{67} -0.828427 q^{71} +11.0711 q^{73} +2.34315 q^{79} -15.3137 q^{83} +1.31371 q^{85} -10.7279 q^{89} +4.00000 q^{95} +7.75736 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+4q5+4q114q17+8q19+4q23+2q25+16q318q374q41+16q438q47+4q53+16q5516q598q614q65+16q67+4q71++24q97+O(q100) 2 q + 4 q^{5} + 4 q^{11} - 4 q^{17} + 8 q^{19} + 4 q^{23} + 2 q^{25} + 16 q^{31} - 8 q^{37} - 4 q^{41} + 16 q^{43} - 8 q^{47} + 4 q^{53} + 16 q^{55} - 16 q^{59} - 8 q^{61} - 4 q^{65} + 16 q^{67} + 4 q^{71}+ \cdots + 24 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 0.585786 0.261972 0.130986 0.991384i 0.458186π-0.458186\pi
0.130986 + 0.991384i 0.458186π0.458186\pi
66 0 0
77 0 0
88 0 0
99 0 0
1010 0 0
1111 −0.828427 −0.249780 −0.124890 0.992171i 0.539858π-0.539858\pi
−0.124890 + 0.992171i 0.539858π0.539858\pi
1212 0 0
1313 1.41421 0.392232 0.196116 0.980581i 0.437167π-0.437167\pi
0.196116 + 0.980581i 0.437167π0.437167\pi
1414 0 0
1515 0 0
1616 0 0
1717 2.24264 0.543920 0.271960 0.962309i 0.412328π-0.412328\pi
0.271960 + 0.962309i 0.412328π0.412328\pi
1818 0 0
1919 6.82843 1.56655 0.783274 0.621676i 0.213548π-0.213548\pi
0.783274 + 0.621676i 0.213548π0.213548\pi
2020 0 0
2121 0 0
2222 0 0
2323 4.82843 1.00680 0.503398 0.864054i 0.332083π-0.332083\pi
0.503398 + 0.864054i 0.332083π0.332083\pi
2424 0 0
2525 −4.65685 −0.931371
2626 0 0
2727 0 0
2828 0 0
2929 −8.48528 −1.57568 −0.787839 0.615882i 0.788800π-0.788800\pi
−0.787839 + 0.615882i 0.788800π0.788800\pi
3030 0 0
3131 5.17157 0.928842 0.464421 0.885615i 0.346262π-0.346262\pi
0.464421 + 0.885615i 0.346262π0.346262\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 0 0
3737 1.65685 0.272385 0.136193 0.990682i 0.456513π-0.456513\pi
0.136193 + 0.990682i 0.456513π0.456513\pi
3838 0 0
3939 0 0
4040 0 0
4141 −0.585786 −0.0914845 −0.0457422 0.998953i 0.514565π-0.514565\pi
−0.0457422 + 0.998953i 0.514565π0.514565\pi
4242 0 0
4343 8.00000 1.21999 0.609994 0.792406i 0.291172π-0.291172\pi
0.609994 + 0.792406i 0.291172π0.291172\pi
4444 0 0
4545 0 0
4646 0 0
4747 −6.82843 −0.996028 −0.498014 0.867169i 0.665937π-0.665937\pi
−0.498014 + 0.867169i 0.665937π0.665937\pi
4848 0 0
4949 0 0
5050 0 0
5151 0 0
5252 0 0
5353 13.3137 1.82878 0.914389 0.404836i 0.132671π-0.132671\pi
0.914389 + 0.404836i 0.132671π0.132671\pi
5454 0 0
5555 −0.485281 −0.0654353
5656 0 0
5757 0 0
5858 0 0
5959 −5.17157 −0.673281 −0.336641 0.941633i 0.609291π-0.609291\pi
−0.336641 + 0.941633i 0.609291π0.609291\pi
6060 0 0
6161 −13.8995 −1.77965 −0.889824 0.456304i 0.849173π-0.849173\pi
−0.889824 + 0.456304i 0.849173π0.849173\pi
6262 0 0
6363 0 0
6464 0 0
6565 0.828427 0.102754
6666 0 0
6767 8.00000 0.977356 0.488678 0.872464i 0.337479π-0.337479\pi
0.488678 + 0.872464i 0.337479π0.337479\pi
6868 0 0
6969 0 0
7070 0 0
7171 −0.828427 −0.0983162 −0.0491581 0.998791i 0.515654π-0.515654\pi
−0.0491581 + 0.998791i 0.515654π0.515654\pi
7272 0 0
7373 11.0711 1.29577 0.647885 0.761738i 0.275654π-0.275654\pi
0.647885 + 0.761738i 0.275654π0.275654\pi
7474 0 0
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 2.34315 0.263624 0.131812 0.991275i 0.457920π-0.457920\pi
0.131812 + 0.991275i 0.457920π0.457920\pi
8080 0 0
8181 0 0
8282 0 0
8383 −15.3137 −1.68090 −0.840449 0.541891i 0.817709π-0.817709\pi
−0.840449 + 0.541891i 0.817709π0.817709\pi
8484 0 0
8585 1.31371 0.142492
8686 0 0
8787 0 0
8888 0 0
8989 −10.7279 −1.13716 −0.568579 0.822629i 0.692507π-0.692507\pi
−0.568579 + 0.822629i 0.692507π0.692507\pi
9090 0 0
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 4.00000 0.410391
9696 0 0
9797 7.75736 0.787641 0.393820 0.919187i 0.371153π-0.371153\pi
0.393820 + 0.919187i 0.371153π0.371153\pi
9898 0 0
9999 0 0
100100 0 0
101101 3.41421 0.339727 0.169863 0.985468i 0.445667π-0.445667\pi
0.169863 + 0.985468i 0.445667π0.445667\pi
102102 0 0
103103 10.8284 1.06696 0.533478 0.845814i 0.320885π-0.320885\pi
0.533478 + 0.845814i 0.320885π0.320885\pi
104104 0 0
105105 0 0
106106 0 0
107107 14.4853 1.40035 0.700173 0.713974i 0.253106π-0.253106\pi
0.700173 + 0.713974i 0.253106π0.253106\pi
108108 0 0
109109 −11.3137 −1.08366 −0.541828 0.840489i 0.682268π-0.682268\pi
−0.541828 + 0.840489i 0.682268π0.682268\pi
110110 0 0
111111 0 0
112112 0 0
113113 −6.00000 −0.564433 −0.282216 0.959351i 0.591070π-0.591070\pi
−0.282216 + 0.959351i 0.591070π0.591070\pi
114114 0 0
115115 2.82843 0.263752
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 −10.3137 −0.937610
122122 0 0
123123 0 0
124124 0 0
125125 −5.65685 −0.505964
126126 0 0
127127 15.3137 1.35887 0.679436 0.733735i 0.262225π-0.262225\pi
0.679436 + 0.733735i 0.262225π0.262225\pi
128128 0 0
129129 0 0
130130 0 0
131131 7.31371 0.639002 0.319501 0.947586i 0.396485π-0.396485\pi
0.319501 + 0.947586i 0.396485π0.396485\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 0 0
137137 −4.48528 −0.383203 −0.191602 0.981473i 0.561368π-0.561368\pi
−0.191602 + 0.981473i 0.561368π0.561368\pi
138138 0 0
139139 −1.65685 −0.140533 −0.0702663 0.997528i 0.522385π-0.522385\pi
−0.0702663 + 0.997528i 0.522385π0.522385\pi
140140 0 0
141141 0 0
142142 0 0
143143 −1.17157 −0.0979718
144144 0 0
145145 −4.97056 −0.412783
146146 0 0
147147 0 0
148148 0 0
149149 10.0000 0.819232 0.409616 0.912258i 0.365663π-0.365663\pi
0.409616 + 0.912258i 0.365663π0.365663\pi
150150 0 0
151151 −9.65685 −0.785864 −0.392932 0.919568i 0.628539π-0.628539\pi
−0.392932 + 0.919568i 0.628539π0.628539\pi
152152 0 0
153153 0 0
154154 0 0
155155 3.02944 0.243330
156156 0 0
157157 13.8995 1.10930 0.554650 0.832084i 0.312852π-0.312852\pi
0.554650 + 0.832084i 0.312852π0.312852\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 0 0
163163 13.6569 1.06969 0.534844 0.844951i 0.320370π-0.320370\pi
0.534844 + 0.844951i 0.320370π0.320370\pi
164164 0 0
165165 0 0
166166 0 0
167167 −1.17157 −0.0906590 −0.0453295 0.998972i 0.514434π-0.514434\pi
−0.0453295 + 0.998972i 0.514434π0.514434\pi
168168 0 0
169169 −11.0000 −0.846154
170170 0 0
171171 0 0
172172 0 0
173173 −3.41421 −0.259578 −0.129789 0.991542i 0.541430π-0.541430\pi
−0.129789 + 0.991542i 0.541430π0.541430\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 0 0
179179 17.7990 1.33036 0.665179 0.746684i 0.268355π-0.268355\pi
0.665179 + 0.746684i 0.268355π0.268355\pi
180180 0 0
181181 9.89949 0.735824 0.367912 0.929861i 0.380073π-0.380073\pi
0.367912 + 0.929861i 0.380073π0.380073\pi
182182 0 0
183183 0 0
184184 0 0
185185 0.970563 0.0713572
186186 0 0
187187 −1.85786 −0.135860
188188 0 0
189189 0 0
190190 0 0
191191 15.1716 1.09778 0.548888 0.835896i 0.315051π-0.315051\pi
0.548888 + 0.835896i 0.315051π0.315051\pi
192192 0 0
193193 24.6274 1.77272 0.886360 0.462996i 0.153226π-0.153226\pi
0.886360 + 0.462996i 0.153226π0.153226\pi
194194 0 0
195195 0 0
196196 0 0
197197 −2.00000 −0.142494 −0.0712470 0.997459i 0.522698π-0.522698\pi
−0.0712470 + 0.997459i 0.522698π0.522698\pi
198198 0 0
199199 5.65685 0.401004 0.200502 0.979693i 0.435743π-0.435743\pi
0.200502 + 0.979693i 0.435743π0.435743\pi
200200 0 0
201201 0 0
202202 0 0
203203 0 0
204204 0 0
205205 −0.343146 −0.0239663
206206 0 0
207207 0 0
208208 0 0
209209 −5.65685 −0.391293
210210 0 0
211211 14.3431 0.987423 0.493711 0.869626i 0.335640π-0.335640\pi
0.493711 + 0.869626i 0.335640π0.335640\pi
212212 0 0
213213 0 0
214214 0 0
215215 4.68629 0.319602
216216 0 0
217217 0 0
218218 0 0
219219 0 0
220220 0 0
221221 3.17157 0.213343
222222 0 0
223223 −13.6569 −0.914531 −0.457265 0.889330i 0.651171π-0.651171\pi
−0.457265 + 0.889330i 0.651171π0.651171\pi
224224 0 0
225225 0 0
226226 0 0
227227 19.7990 1.31411 0.657053 0.753845i 0.271803π-0.271803\pi
0.657053 + 0.753845i 0.271803π0.271803\pi
228228 0 0
229229 −15.0711 −0.995924 −0.497962 0.867199i 0.665918π-0.665918\pi
−0.497962 + 0.867199i 0.665918π0.665918\pi
230230 0 0
231231 0 0
232232 0 0
233233 28.4853 1.86613 0.933066 0.359704i 0.117122π-0.117122\pi
0.933066 + 0.359704i 0.117122π0.117122\pi
234234 0 0
235235 −4.00000 −0.260931
236236 0 0
237237 0 0
238238 0 0
239239 −3.17157 −0.205152 −0.102576 0.994725i 0.532708π-0.532708\pi
−0.102576 + 0.994725i 0.532708π0.532708\pi
240240 0 0
241241 21.8995 1.41067 0.705335 0.708874i 0.250796π-0.250796\pi
0.705335 + 0.708874i 0.250796π0.250796\pi
242242 0 0
243243 0 0
244244 0 0
245245 0 0
246246 0 0
247247 9.65685 0.614451
248248 0 0
249249 0 0
250250 0 0
251251 −8.48528 −0.535586 −0.267793 0.963476i 0.586294π-0.586294\pi
−0.267793 + 0.963476i 0.586294π0.586294\pi
252252 0 0
253253 −4.00000 −0.251478
254254 0 0
255255 0 0
256256 0 0
257257 −30.2426 −1.88648 −0.943242 0.332106i 0.892241π-0.892241\pi
−0.943242 + 0.332106i 0.892241π0.892241\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 0 0
263263 24.8284 1.53099 0.765493 0.643444i 0.222495π-0.222495\pi
0.765493 + 0.643444i 0.222495π0.222495\pi
264264 0 0
265265 7.79899 0.479088
266266 0 0
267267 0 0
268268 0 0
269269 30.0416 1.83167 0.915835 0.401554i 0.131530π-0.131530\pi
0.915835 + 0.401554i 0.131530π0.131530\pi
270270 0 0
271271 −13.1716 −0.800116 −0.400058 0.916490i 0.631010π-0.631010\pi
−0.400058 + 0.916490i 0.631010π0.631010\pi
272272 0 0
273273 0 0
274274 0 0
275275 3.85786 0.232638
276276 0 0
277277 −6.00000 −0.360505 −0.180253 0.983620i 0.557691π-0.557691\pi
−0.180253 + 0.983620i 0.557691π0.557691\pi
278278 0 0
279279 0 0
280280 0 0
281281 12.4853 0.744809 0.372405 0.928070i 0.378533π-0.378533\pi
0.372405 + 0.928070i 0.378533π0.378533\pi
282282 0 0
283283 −14.8284 −0.881458 −0.440729 0.897640i 0.645280π-0.645280\pi
−0.440729 + 0.897640i 0.645280π0.645280\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 −11.9706 −0.704151
290290 0 0
291291 0 0
292292 0 0
293293 1.07107 0.0625724 0.0312862 0.999510i 0.490040π-0.490040\pi
0.0312862 + 0.999510i 0.490040π0.490040\pi
294294 0 0
295295 −3.02944 −0.176381
296296 0 0
297297 0 0
298298 0 0
299299 6.82843 0.394898
300300 0 0
301301 0 0
302302 0 0
303303 0 0
304304 0 0
305305 −8.14214 −0.466217
306306 0 0
307307 −11.5147 −0.657180 −0.328590 0.944473i 0.606573π-0.606573\pi
−0.328590 + 0.944473i 0.606573π0.606573\pi
308308 0 0
309309 0 0
310310 0 0
311311 26.1421 1.48238 0.741192 0.671293i 0.234261π-0.234261\pi
0.741192 + 0.671293i 0.234261π0.234261\pi
312312 0 0
313313 17.4142 0.984310 0.492155 0.870508i 0.336209π-0.336209\pi
0.492155 + 0.870508i 0.336209π0.336209\pi
314314 0 0
315315 0 0
316316 0 0
317317 −21.3137 −1.19710 −0.598549 0.801087i 0.704256π-0.704256\pi
−0.598549 + 0.801087i 0.704256π0.704256\pi
318318 0 0
319319 7.02944 0.393573
320320 0 0
321321 0 0
322322 0 0
323323 15.3137 0.852078
324324 0 0
325325 −6.58579 −0.365314
326326 0 0
327327 0 0
328328 0 0
329329 0 0
330330 0 0
331331 8.68629 0.477442 0.238721 0.971088i 0.423272π-0.423272\pi
0.238721 + 0.971088i 0.423272π0.423272\pi
332332 0 0
333333 0 0
334334 0 0
335335 4.68629 0.256039
336336 0 0
337337 −16.9706 −0.924445 −0.462223 0.886764i 0.652948π-0.652948\pi
−0.462223 + 0.886764i 0.652948π0.652948\pi
338338 0 0
339339 0 0
340340 0 0
341341 −4.28427 −0.232006
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 0 0
347347 −4.14214 −0.222361 −0.111181 0.993800i 0.535463π-0.535463\pi
−0.111181 + 0.993800i 0.535463π0.535463\pi
348348 0 0
349349 −30.3848 −1.62646 −0.813230 0.581943i 0.802293π-0.802293\pi
−0.813230 + 0.581943i 0.802293π0.802293\pi
350350 0 0
351351 0 0
352352 0 0
353353 −15.8995 −0.846245 −0.423122 0.906073i 0.639066π-0.639066\pi
−0.423122 + 0.906073i 0.639066π0.639066\pi
354354 0 0
355355 −0.485281 −0.0257561
356356 0 0
357357 0 0
358358 0 0
359359 −35.4558 −1.87129 −0.935644 0.352945i 0.885180π-0.885180\pi
−0.935644 + 0.352945i 0.885180π0.885180\pi
360360 0 0
361361 27.6274 1.45407
362362 0 0
363363 0 0
364364 0 0
365365 6.48528 0.339455
366366 0 0
367367 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
368368 0 0
369369 0 0
370370 0 0
371371 0 0
372372 0 0
373373 14.6863 0.760427 0.380214 0.924899i 0.375850π-0.375850\pi
0.380214 + 0.924899i 0.375850π0.375850\pi
374374 0 0
375375 0 0
376376 0 0
377377 −12.0000 −0.618031
378378 0 0
379379 0.686292 0.0352524 0.0176262 0.999845i 0.494389π-0.494389\pi
0.0176262 + 0.999845i 0.494389π0.494389\pi
380380 0 0
381381 0 0
382382 0 0
383383 −24.9706 −1.27594 −0.637968 0.770063i 0.720225π-0.720225\pi
−0.637968 + 0.770063i 0.720225π0.720225\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 14.1421 0.717035 0.358517 0.933523i 0.383282π-0.383282\pi
0.358517 + 0.933523i 0.383282π0.383282\pi
390390 0 0
391391 10.8284 0.547617
392392 0 0
393393 0 0
394394 0 0
395395 1.37258 0.0690621
396396 0 0
397397 −7.27208 −0.364975 −0.182488 0.983208i 0.558415π-0.558415\pi
−0.182488 + 0.983208i 0.558415π0.558415\pi
398398 0 0
399399 0 0
400400 0 0
401401 12.4853 0.623485 0.311743 0.950167i 0.399087π-0.399087\pi
0.311743 + 0.950167i 0.399087π0.399087\pi
402402 0 0
403403 7.31371 0.364322
404404 0 0
405405 0 0
406406 0 0
407407 −1.37258 −0.0680364
408408 0 0
409409 −16.2426 −0.803147 −0.401573 0.915827i 0.631537π-0.631537\pi
−0.401573 + 0.915827i 0.631537π0.631537\pi
410410 0 0
411411 0 0
412412 0 0
413413 0 0
414414 0 0
415415 −8.97056 −0.440348
416416 0 0
417417 0 0
418418 0 0
419419 −10.8284 −0.529003 −0.264502 0.964385i 0.585207π-0.585207\pi
−0.264502 + 0.964385i 0.585207π0.585207\pi
420420 0 0
421421 6.68629 0.325870 0.162935 0.986637i 0.447904π-0.447904\pi
0.162935 + 0.986637i 0.447904π0.447904\pi
422422 0 0
423423 0 0
424424 0 0
425425 −10.4437 −0.506591
426426 0 0
427427 0 0
428428 0 0
429429 0 0
430430 0 0
431431 −30.4853 −1.46842 −0.734212 0.678920i 0.762448π-0.762448\pi
−0.734212 + 0.678920i 0.762448π0.762448\pi
432432 0 0
433433 −26.3848 −1.26797 −0.633986 0.773345i 0.718582π-0.718582\pi
−0.633986 + 0.773345i 0.718582π0.718582\pi
434434 0 0
435435 0 0
436436 0 0
437437 32.9706 1.57720
438438 0 0
439439 −3.31371 −0.158155 −0.0790773 0.996868i 0.525197π-0.525197\pi
−0.0790773 + 0.996868i 0.525197π0.525197\pi
440440 0 0
441441 0 0
442442 0 0
443443 38.4853 1.82849 0.914245 0.405161i 0.132784π-0.132784\pi
0.914245 + 0.405161i 0.132784π0.132784\pi
444444 0 0
445445 −6.28427 −0.297903
446446 0 0
447447 0 0
448448 0 0
449449 10.0000 0.471929 0.235965 0.971762i 0.424175π-0.424175\pi
0.235965 + 0.971762i 0.424175π0.424175\pi
450450 0 0
451451 0.485281 0.0228510
452452 0 0
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 20.6274 0.964910 0.482455 0.875921i 0.339745π-0.339745\pi
0.482455 + 0.875921i 0.339745π0.339745\pi
458458 0 0
459459 0 0
460460 0 0
461461 18.2426 0.849644 0.424822 0.905277i 0.360337π-0.360337\pi
0.424822 + 0.905277i 0.360337π0.360337\pi
462462 0 0
463463 −20.9706 −0.974585 −0.487292 0.873239i 0.662015π-0.662015\pi
−0.487292 + 0.873239i 0.662015π0.662015\pi
464464 0 0
465465 0 0
466466 0 0
467467 10.8284 0.501080 0.250540 0.968106i 0.419392π-0.419392\pi
0.250540 + 0.968106i 0.419392π0.419392\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 0 0
473473 −6.62742 −0.304729
474474 0 0
475475 −31.7990 −1.45904
476476 0 0
477477 0 0
478478 0 0
479479 43.1127 1.96987 0.984935 0.172926i 0.0553223π-0.0553223\pi
0.984935 + 0.172926i 0.0553223π0.0553223\pi
480480 0 0
481481 2.34315 0.106838
482482 0 0
483483 0 0
484484 0 0
485485 4.54416 0.206339
486486 0 0
487487 20.9706 0.950267 0.475133 0.879914i 0.342400π-0.342400\pi
0.475133 + 0.879914i 0.342400π0.342400\pi
488488 0 0
489489 0 0
490490 0 0
491491 24.1421 1.08952 0.544760 0.838592i 0.316621π-0.316621\pi
0.544760 + 0.838592i 0.316621π0.316621\pi
492492 0 0
493493 −19.0294 −0.857043
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 28.2843 1.26618 0.633089 0.774079i 0.281787π-0.281787\pi
0.633089 + 0.774079i 0.281787π0.281787\pi
500500 0 0
501501 0 0
502502 0 0
503503 14.6274 0.652204 0.326102 0.945335i 0.394265π-0.394265\pi
0.326102 + 0.945335i 0.394265π0.394265\pi
504504 0 0
505505 2.00000 0.0889988
506506 0 0
507507 0 0
508508 0 0
509509 37.0711 1.64315 0.821573 0.570103i 0.193097π-0.193097\pi
0.821573 + 0.570103i 0.193097π0.193097\pi
510510 0 0
511511 0 0
512512 0 0
513513 0 0
514514 0 0
515515 6.34315 0.279512
516516 0 0
517517 5.65685 0.248788
518518 0 0
519519 0 0
520520 0 0
521521 30.7279 1.34621 0.673107 0.739545i 0.264959π-0.264959\pi
0.673107 + 0.739545i 0.264959π0.264959\pi
522522 0 0
523523 9.65685 0.422265 0.211132 0.977457i 0.432285π-0.432285\pi
0.211132 + 0.977457i 0.432285π0.432285\pi
524524 0 0
525525 0 0
526526 0 0
527527 11.5980 0.505216
528528 0 0
529529 0.313708 0.0136395
530530 0 0
531531 0 0
532532 0 0
533533 −0.828427 −0.0358832
534534 0 0
535535 8.48528 0.366851
536536 0 0
537537 0 0
538538 0 0
539539 0 0
540540 0 0
541541 36.6274 1.57474 0.787368 0.616483i 0.211443π-0.211443\pi
0.787368 + 0.616483i 0.211443π0.211443\pi
542542 0 0
543543 0 0
544544 0 0
545545 −6.62742 −0.283887
546546 0 0
547547 −28.9706 −1.23869 −0.619346 0.785118i 0.712602π-0.712602\pi
−0.619346 + 0.785118i 0.712602π0.712602\pi
548548 0 0
549549 0 0
550550 0 0
551551 −57.9411 −2.46837
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 0 0
557557 23.9411 1.01442 0.507209 0.861823i 0.330677π-0.330677\pi
0.507209 + 0.861823i 0.330677π0.330677\pi
558558 0 0
559559 11.3137 0.478519
560560 0 0
561561 0 0
562562 0 0
563563 −21.1716 −0.892275 −0.446138 0.894964i 0.647201π-0.647201\pi
−0.446138 + 0.894964i 0.647201π0.647201\pi
564564 0 0
565565 −3.51472 −0.147865
566566 0 0
567567 0 0
568568 0 0
569569 −1.17157 −0.0491149 −0.0245574 0.999698i 0.507818π-0.507818\pi
−0.0245574 + 0.999698i 0.507818π0.507818\pi
570570 0 0
571571 16.2843 0.681476 0.340738 0.940158i 0.389323π-0.389323\pi
0.340738 + 0.940158i 0.389323π0.389323\pi
572572 0 0
573573 0 0
574574 0 0
575575 −22.4853 −0.937701
576576 0 0
577577 6.58579 0.274170 0.137085 0.990559i 0.456227π-0.456227\pi
0.137085 + 0.990559i 0.456227π0.456227\pi
578578 0 0
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 −11.0294 −0.456793
584584 0 0
585585 0 0
586586 0 0
587587 21.1716 0.873844 0.436922 0.899499i 0.356069π-0.356069\pi
0.436922 + 0.899499i 0.356069π0.356069\pi
588588 0 0
589589 35.3137 1.45508
590590 0 0
591591 0 0
592592 0 0
593593 14.9289 0.613058 0.306529 0.951861i 0.400832π-0.400832\pi
0.306529 + 0.951861i 0.400832π0.400832\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 −12.1421 −0.496114 −0.248057 0.968745i 0.579792π-0.579792\pi
−0.248057 + 0.968745i 0.579792π0.579792\pi
600600 0 0
601601 3.75736 0.153266 0.0766329 0.997059i 0.475583π-0.475583\pi
0.0766329 + 0.997059i 0.475583π0.475583\pi
602602 0 0
603603 0 0
604604 0 0
605605 −6.04163 −0.245627
606606 0 0
607607 −47.5980 −1.93194 −0.965971 0.258650i 0.916722π-0.916722\pi
−0.965971 + 0.258650i 0.916722π0.916722\pi
608608 0 0
609609 0 0
610610 0 0
611611 −9.65685 −0.390675
612612 0 0
613613 −13.6569 −0.551595 −0.275798 0.961216i 0.588942π-0.588942\pi
−0.275798 + 0.961216i 0.588942π0.588942\pi
614614 0 0
615615 0 0
616616 0 0
617617 29.4558 1.18585 0.592924 0.805259i 0.297974π-0.297974\pi
0.592924 + 0.805259i 0.297974π0.297974\pi
618618 0 0
619619 16.2843 0.654520 0.327260 0.944934i 0.393875π-0.393875\pi
0.327260 + 0.944934i 0.393875π0.393875\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 19.9706 0.798823
626626 0 0
627627 0 0
628628 0 0
629629 3.71573 0.148156
630630 0 0
631631 −48.2843 −1.92217 −0.961083 0.276259i 0.910905π-0.910905\pi
−0.961083 + 0.276259i 0.910905π0.910905\pi
632632 0 0
633633 0 0
634634 0 0
635635 8.97056 0.355986
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 0 0
641641 −30.8284 −1.21765 −0.608825 0.793305i 0.708359π-0.708359\pi
−0.608825 + 0.793305i 0.708359π0.708359\pi
642642 0 0
643643 36.4853 1.43884 0.719420 0.694576i 0.244408π-0.244408\pi
0.719420 + 0.694576i 0.244408π0.244408\pi
644644 0 0
645645 0 0
646646 0 0
647647 −9.17157 −0.360572 −0.180286 0.983614i 0.557702π-0.557702\pi
−0.180286 + 0.983614i 0.557702π0.557702\pi
648648 0 0
649649 4.28427 0.168172
650650 0 0
651651 0 0
652652 0 0
653653 2.82843 0.110685 0.0553425 0.998467i 0.482375π-0.482375\pi
0.0553425 + 0.998467i 0.482375π0.482375\pi
654654 0 0
655655 4.28427 0.167400
656656 0 0
657657 0 0
658658 0 0
659659 42.4853 1.65499 0.827496 0.561472i 0.189765π-0.189765\pi
0.827496 + 0.561472i 0.189765π0.189765\pi
660660 0 0
661661 −47.3553 −1.84191 −0.920955 0.389670i 0.872589π-0.872589\pi
−0.920955 + 0.389670i 0.872589π0.872589\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 −40.9706 −1.58639
668668 0 0
669669 0 0
670670 0 0
671671 11.5147 0.444521
672672 0 0
673673 −7.31371 −0.281923 −0.140961 0.990015i 0.545019π-0.545019\pi
−0.140961 + 0.990015i 0.545019π0.545019\pi
674674 0 0
675675 0 0
676676 0 0
677677 29.5563 1.13594 0.567971 0.823048i 0.307728π-0.307728\pi
0.567971 + 0.823048i 0.307728π0.307728\pi
678678 0 0
679679 0 0
680680 0 0
681681 0 0
682682 0 0
683683 −16.1421 −0.617662 −0.308831 0.951117i 0.599938π-0.599938\pi
−0.308831 + 0.951117i 0.599938π0.599938\pi
684684 0 0
685685 −2.62742 −0.100388
686686 0 0
687687 0 0
688688 0 0
689689 18.8284 0.717306
690690 0 0
691691 28.0000 1.06517 0.532585 0.846376i 0.321221π-0.321221\pi
0.532585 + 0.846376i 0.321221π0.321221\pi
692692 0 0
693693 0 0
694694 0 0
695695 −0.970563 −0.0368155
696696 0 0
697697 −1.31371 −0.0497603
698698 0 0
699699 0 0
700700 0 0
701701 5.17157 0.195328 0.0976638 0.995219i 0.468863π-0.468863\pi
0.0976638 + 0.995219i 0.468863π0.468863\pi
702702 0 0
703703 11.3137 0.426705
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 −8.00000 −0.300446 −0.150223 0.988652i 0.547999π-0.547999\pi
−0.150223 + 0.988652i 0.547999π0.547999\pi
710710 0 0
711711 0 0
712712 0 0
713713 24.9706 0.935155
714714 0 0
715715 −0.686292 −0.0256658
716716 0 0
717717 0 0
718718 0 0
719719 4.68629 0.174769 0.0873846 0.996175i 0.472149π-0.472149\pi
0.0873846 + 0.996175i 0.472149π0.472149\pi
720720 0 0
721721 0 0
722722 0 0
723723 0 0
724724 0 0
725725 39.5147 1.46754
726726 0 0
727727 25.4558 0.944105 0.472052 0.881570i 0.343513π-0.343513\pi
0.472052 + 0.881570i 0.343513π0.343513\pi
728728 0 0
729729 0 0
730730 0 0
731731 17.9411 0.663576
732732 0 0
733733 −11.7574 −0.434268 −0.217134 0.976142i 0.569671π-0.569671\pi
−0.217134 + 0.976142i 0.569671π0.569671\pi
734734 0 0
735735 0 0
736736 0 0
737737 −6.62742 −0.244124
738738 0 0
739739 −20.2843 −0.746169 −0.373084 0.927797i 0.621700π-0.621700\pi
−0.373084 + 0.927797i 0.621700π0.621700\pi
740740 0 0
741741 0 0
742742 0 0
743743 −11.1716 −0.409845 −0.204923 0.978778i 0.565694π-0.565694\pi
−0.204923 + 0.978778i 0.565694π0.565694\pi
744744 0 0
745745 5.85786 0.214616
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 −29.6569 −1.08219 −0.541097 0.840960i 0.681991π-0.681991\pi
−0.541097 + 0.840960i 0.681991π0.681991\pi
752752 0 0
753753 0 0
754754 0 0
755755 −5.65685 −0.205874
756756 0 0
757757 −11.3137 −0.411204 −0.205602 0.978636i 0.565915π-0.565915\pi
−0.205602 + 0.978636i 0.565915π0.565915\pi
758758 0 0
759759 0 0
760760 0 0
761761 −9.75736 −0.353704 −0.176852 0.984237i 0.556591π-0.556591\pi
−0.176852 + 0.984237i 0.556591π0.556591\pi
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 0 0
767767 −7.31371 −0.264083
768768 0 0
769769 −15.0711 −0.543477 −0.271738 0.962371i 0.587599π-0.587599\pi
−0.271738 + 0.962371i 0.587599π0.587599\pi
770770 0 0
771771 0 0
772772 0 0
773773 −3.41421 −0.122801 −0.0614004 0.998113i 0.519557π-0.519557\pi
−0.0614004 + 0.998113i 0.519557π0.519557\pi
774774 0 0
775775 −24.0833 −0.865096
776776 0 0
777777 0 0
778778 0 0
779779 −4.00000 −0.143315
780780 0 0
781781 0.686292 0.0245574
782782 0 0
783783 0 0
784784 0 0
785785 8.14214 0.290605
786786 0 0
787787 −10.6274 −0.378827 −0.189413 0.981897i 0.560659π-0.560659\pi
−0.189413 + 0.981897i 0.560659π0.560659\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 −19.6569 −0.698035
794794 0 0
795795 0 0
796796 0 0
797797 −43.2132 −1.53069 −0.765345 0.643620i 0.777432π-0.777432\pi
−0.765345 + 0.643620i 0.777432π0.777432\pi
798798 0 0
799799 −15.3137 −0.541760
800800 0 0
801801 0 0
802802 0 0
803803 −9.17157 −0.323658
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 30.0000 1.05474 0.527372 0.849635i 0.323177π-0.323177\pi
0.527372 + 0.849635i 0.323177π0.323177\pi
810810 0 0
811811 −20.9706 −0.736376 −0.368188 0.929751i 0.620022π-0.620022\pi
−0.368188 + 0.929751i 0.620022π0.620022\pi
812812 0 0
813813 0 0
814814 0 0
815815 8.00000 0.280228
816816 0 0
817817 54.6274 1.91117
818818 0 0
819819 0 0
820820 0 0
821821 −10.0000 −0.349002 −0.174501 0.984657i 0.555831π-0.555831\pi
−0.174501 + 0.984657i 0.555831π0.555831\pi
822822 0 0
823823 2.34315 0.0816769 0.0408385 0.999166i 0.486997π-0.486997\pi
0.0408385 + 0.999166i 0.486997π0.486997\pi
824824 0 0
825825 0 0
826826 0 0
827827 −19.4558 −0.676546 −0.338273 0.941048i 0.609843π-0.609843\pi
−0.338273 + 0.941048i 0.609843π0.609843\pi
828828 0 0
829829 −3.27208 −0.113644 −0.0568220 0.998384i 0.518097π-0.518097\pi
−0.0568220 + 0.998384i 0.518097π0.518097\pi
830830 0 0
831831 0 0
832832 0 0
833833 0 0
834834 0 0
835835 −0.686292 −0.0237501
836836 0 0
837837 0 0
838838 0 0
839839 −49.1716 −1.69759 −0.848796 0.528721i 0.822672π-0.822672\pi
−0.848796 + 0.528721i 0.822672π0.822672\pi
840840 0 0
841841 43.0000 1.48276
842842 0 0
843843 0 0
844844 0 0
845845 −6.44365 −0.221668
846846 0 0
847847 0 0
848848 0 0
849849 0 0
850850 0 0
851851 8.00000 0.274236
852852 0 0
853853 −36.0416 −1.23404 −0.617021 0.786947i 0.711661π-0.711661\pi
−0.617021 + 0.786947i 0.711661π0.711661\pi
854854 0 0
855855 0 0
856856 0 0
857857 −43.6985 −1.49271 −0.746356 0.665547i 0.768198π-0.768198\pi
−0.746356 + 0.665547i 0.768198π0.768198\pi
858858 0 0
859859 −38.8284 −1.32481 −0.662404 0.749146i 0.730464π-0.730464\pi
−0.662404 + 0.749146i 0.730464π0.730464\pi
860860 0 0
861861 0 0
862862 0 0
863863 −29.5147 −1.00469 −0.502346 0.864666i 0.667530π-0.667530\pi
−0.502346 + 0.864666i 0.667530π0.667530\pi
864864 0 0
865865 −2.00000 −0.0680020
866866 0 0
867867 0 0
868868 0 0
869869 −1.94113 −0.0658482
870870 0 0
871871 11.3137 0.383350
872872 0 0
873873 0 0
874874 0 0
875875 0 0
876876 0 0
877877 20.2843 0.684951 0.342476 0.939527i 0.388735π-0.388735\pi
0.342476 + 0.939527i 0.388735π0.388735\pi
878878 0 0
879879 0 0
880880 0 0
881881 −25.0711 −0.844666 −0.422333 0.906441i 0.638789π-0.638789\pi
−0.422333 + 0.906441i 0.638789π0.638789\pi
882882 0 0
883883 −18.3431 −0.617296 −0.308648 0.951176i 0.599877π-0.599877\pi
−0.308648 + 0.951176i 0.599877π0.599877\pi
884884 0 0
885885 0 0
886886 0 0
887887 −21.4558 −0.720417 −0.360208 0.932872i 0.617294π-0.617294\pi
−0.360208 + 0.932872i 0.617294π0.617294\pi
888888 0 0
889889 0 0
890890 0 0
891891 0 0
892892 0 0
893893 −46.6274 −1.56033
894894 0 0
895895 10.4264 0.348516
896896 0 0
897897 0 0
898898 0 0
899899 −43.8823 −1.46356
900900 0 0
901901 29.8579 0.994710
902902 0 0
903903 0 0
904904 0 0
905905 5.79899 0.192765
906906 0 0
907907 7.02944 0.233409 0.116704 0.993167i 0.462767π-0.462767\pi
0.116704 + 0.993167i 0.462767π0.462767\pi
908908 0 0
909909 0 0
910910 0 0
911911 −54.4853 −1.80518 −0.902589 0.430503i 0.858336π-0.858336\pi
−0.902589 + 0.430503i 0.858336π0.858336\pi
912912 0 0
913913 12.6863 0.419855
914914 0 0
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 49.2548 1.62477 0.812384 0.583123i 0.198170π-0.198170\pi
0.812384 + 0.583123i 0.198170π0.198170\pi
920920 0 0
921921 0 0
922922 0 0
923923 −1.17157 −0.0385628
924924 0 0
925925 −7.71573 −0.253692
926926 0 0
927927 0 0
928928 0 0
929929 60.8701 1.99708 0.998541 0.0540006i 0.0171973π-0.0171973\pi
0.998541 + 0.0540006i 0.0171973π0.0171973\pi
930930 0 0
931931 0 0
932932 0 0
933933 0 0
934934 0 0
935935 −1.08831 −0.0355916
936936 0 0
937937 6.10051 0.199295 0.0996474 0.995023i 0.468229π-0.468229\pi
0.0996474 + 0.995023i 0.468229π0.468229\pi
938938 0 0
939939 0 0
940940 0 0
941941 −43.8995 −1.43108 −0.715541 0.698570i 0.753820π-0.753820\pi
−0.715541 + 0.698570i 0.753820π0.753820\pi
942942 0 0
943943 −2.82843 −0.0921063
944944 0 0
945945 0 0
946946 0 0
947947 20.1421 0.654531 0.327266 0.944932i 0.393873π-0.393873\pi
0.327266 + 0.944932i 0.393873π0.393873\pi
948948 0 0
949949 15.6569 0.508243
950950 0 0
951951 0 0
952952 0 0
953953 7.37258 0.238821 0.119411 0.992845i 0.461899π-0.461899\pi
0.119411 + 0.992845i 0.461899π0.461899\pi
954954 0 0
955955 8.88730 0.287586
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 −4.25483 −0.137253
962962 0 0
963963 0 0
964964 0 0
965965 14.4264 0.464402
966966 0 0
967967 34.6274 1.11354 0.556771 0.830666i 0.312040π-0.312040\pi
0.556771 + 0.830666i 0.312040π0.312040\pi
968968 0 0
969969 0 0
970970 0 0
971971 57.2548 1.83740 0.918698 0.394962i 0.129242π-0.129242\pi
0.918698 + 0.394962i 0.129242π0.129242\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 −21.8579 −0.699295 −0.349648 0.936881i 0.613699π-0.613699\pi
−0.349648 + 0.936881i 0.613699π0.613699\pi
978978 0 0
979979 8.88730 0.284039
980980 0 0
981981 0 0
982982 0 0
983983 14.6274 0.466542 0.233271 0.972412i 0.425057π-0.425057\pi
0.233271 + 0.972412i 0.425057π0.425057\pi
984984 0 0
985985 −1.17157 −0.0373294
986986 0 0
987987 0 0
988988 0 0
989989 38.6274 1.22828
990990 0 0
991991 −23.3137 −0.740584 −0.370292 0.928915i 0.620742π-0.620742\pi
−0.370292 + 0.928915i 0.620742π0.620742\pi
992992 0 0
993993 0 0
994994 0 0
995995 3.31371 0.105052
996996 0 0
997997 34.5858 1.09534 0.547671 0.836693i 0.315514π-0.315514\pi
0.547671 + 0.836693i 0.315514π0.315514\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 7056.2.a.cx.1.1 2
3.2 odd 2 2352.2.a.bd.1.2 2
4.3 odd 2 3528.2.a.bl.1.1 2
7.6 odd 2 7056.2.a.cg.1.2 2
12.11 even 2 1176.2.a.j.1.2 2
21.2 odd 6 2352.2.q.bc.1537.1 4
21.5 even 6 2352.2.q.be.1537.2 4
21.11 odd 6 2352.2.q.bc.961.1 4
21.17 even 6 2352.2.q.be.961.2 4
21.20 even 2 2352.2.a.bb.1.1 2
24.5 odd 2 9408.2.a.ds.1.1 2
24.11 even 2 9408.2.a.ee.1.1 2
28.3 even 6 3528.2.s.bm.3313.1 4
28.11 odd 6 3528.2.s.bd.3313.2 4
28.19 even 6 3528.2.s.bm.361.1 4
28.23 odd 6 3528.2.s.bd.361.2 4
28.27 even 2 3528.2.a.bb.1.2 2
84.11 even 6 1176.2.q.o.961.1 4
84.23 even 6 1176.2.q.o.361.1 4
84.47 odd 6 1176.2.q.k.361.2 4
84.59 odd 6 1176.2.q.k.961.2 4
84.83 odd 2 1176.2.a.o.1.1 yes 2
168.83 odd 2 9408.2.a.dg.1.2 2
168.125 even 2 9408.2.a.du.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1176.2.a.j.1.2 2 12.11 even 2
1176.2.a.o.1.1 yes 2 84.83 odd 2
1176.2.q.k.361.2 4 84.47 odd 6
1176.2.q.k.961.2 4 84.59 odd 6
1176.2.q.o.361.1 4 84.23 even 6
1176.2.q.o.961.1 4 84.11 even 6
2352.2.a.bb.1.1 2 21.20 even 2
2352.2.a.bd.1.2 2 3.2 odd 2
2352.2.q.bc.961.1 4 21.11 odd 6
2352.2.q.bc.1537.1 4 21.2 odd 6
2352.2.q.be.961.2 4 21.17 even 6
2352.2.q.be.1537.2 4 21.5 even 6
3528.2.a.bb.1.2 2 28.27 even 2
3528.2.a.bl.1.1 2 4.3 odd 2
3528.2.s.bd.361.2 4 28.23 odd 6
3528.2.s.bd.3313.2 4 28.11 odd 6
3528.2.s.bm.361.1 4 28.19 even 6
3528.2.s.bm.3313.1 4 28.3 even 6
7056.2.a.cg.1.2 2 7.6 odd 2
7056.2.a.cx.1.1 2 1.1 even 1 trivial
9408.2.a.dg.1.2 2 168.83 odd 2
9408.2.a.ds.1.1 2 24.5 odd 2
9408.2.a.du.1.2 2 168.125 even 2
9408.2.a.ee.1.1 2 24.11 even 2