Properties

Label 9600.2.a.e.1.1
Level 96009600
Weight 22
Character 9600.1
Self dual yes
Analytic conductor 76.65676.656
Analytic rank 00
Dimension 11
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] = [9600,2,Mod(1,9600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9600, 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("9600.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 9600=27352 9600 = 2^{7} \cdot 3 \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 9600.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: 76.656385940476.6563859404
Analytic rank: 00
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 384)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 9600.1

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) == q1.00000q32.00000q7+1.00000q94.00000q11+2.00000q13+2.00000q178.00000q19+2.00000q214.00000q231.00000q276.00000q31+4.00000q332.00000q372.00000q39+6.00000q414.00000q473.00000q492.00000q51+8.00000q57+4.00000q5914.0000q612.00000q63+4.00000q67+4.00000q69+12.0000q71+10.0000q73+8.00000q77+10.0000q79+1.00000q8112.0000q8314.0000q894.00000q91+6.00000q9310.0000q974.00000q99+O(q100)q-1.00000 q^{3} -2.00000 q^{7} +1.00000 q^{9} -4.00000 q^{11} +2.00000 q^{13} +2.00000 q^{17} -8.00000 q^{19} +2.00000 q^{21} -4.00000 q^{23} -1.00000 q^{27} -6.00000 q^{31} +4.00000 q^{33} -2.00000 q^{37} -2.00000 q^{39} +6.00000 q^{41} -4.00000 q^{47} -3.00000 q^{49} -2.00000 q^{51} +8.00000 q^{57} +4.00000 q^{59} -14.0000 q^{61} -2.00000 q^{63} +4.00000 q^{67} +4.00000 q^{69} +12.0000 q^{71} +10.0000 q^{73} +8.00000 q^{77} +10.0000 q^{79} +1.00000 q^{81} -12.0000 q^{83} -14.0000 q^{89} -4.00000 q^{91} +6.00000 q^{93} -10.0000 q^{97} -4.00000 q^{99} +O(q^{100})

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 −1.00000 −0.577350
44 0 0
55 0 0
66 0 0
77 −2.00000 −0.755929 −0.377964 0.925820i 0.623376π-0.623376\pi
−0.377964 + 0.925820i 0.623376π0.623376\pi
88 0 0
99 1.00000 0.333333
1010 0 0
1111 −4.00000 −1.20605 −0.603023 0.797724i 0.706037π-0.706037\pi
−0.603023 + 0.797724i 0.706037π0.706037\pi
1212 0 0
1313 2.00000 0.554700 0.277350 0.960769i 0.410544π-0.410544\pi
0.277350 + 0.960769i 0.410544π0.410544\pi
1414 0 0
1515 0 0
1616 0 0
1717 2.00000 0.485071 0.242536 0.970143i 0.422021π-0.422021\pi
0.242536 + 0.970143i 0.422021π0.422021\pi
1818 0 0
1919 −8.00000 −1.83533 −0.917663 0.397360i 0.869927π-0.869927\pi
−0.917663 + 0.397360i 0.869927π0.869927\pi
2020 0 0
2121 2.00000 0.436436
2222 0 0
2323 −4.00000 −0.834058 −0.417029 0.908893i 0.636929π-0.636929\pi
−0.417029 + 0.908893i 0.636929π0.636929\pi
2424 0 0
2525 0 0
2626 0 0
2727 −1.00000 −0.192450
2828 0 0
2929 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
3030 0 0
3131 −6.00000 −1.07763 −0.538816 0.842424i 0.681128π-0.681128\pi
−0.538816 + 0.842424i 0.681128π0.681128\pi
3232 0 0
3333 4.00000 0.696311
3434 0 0
3535 0 0
3636 0 0
3737 −2.00000 −0.328798 −0.164399 0.986394i 0.552568π-0.552568\pi
−0.164399 + 0.986394i 0.552568π0.552568\pi
3838 0 0
3939 −2.00000 −0.320256
4040 0 0
4141 6.00000 0.937043 0.468521 0.883452i 0.344787π-0.344787\pi
0.468521 + 0.883452i 0.344787π0.344787\pi
4242 0 0
4343 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4444 0 0
4545 0 0
4646 0 0
4747 −4.00000 −0.583460 −0.291730 0.956501i 0.594231π-0.594231\pi
−0.291730 + 0.956501i 0.594231π0.594231\pi
4848 0 0
4949 −3.00000 −0.428571
5050 0 0
5151 −2.00000 −0.280056
5252 0 0
5353 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
5454 0 0
5555 0 0
5656 0 0
5757 8.00000 1.05963
5858 0 0
5959 4.00000 0.520756 0.260378 0.965507i 0.416153π-0.416153\pi
0.260378 + 0.965507i 0.416153π0.416153\pi
6060 0 0
6161 −14.0000 −1.79252 −0.896258 0.443533i 0.853725π-0.853725\pi
−0.896258 + 0.443533i 0.853725π0.853725\pi
6262 0 0
6363 −2.00000 −0.251976
6464 0 0
6565 0 0
6666 0 0
6767 4.00000 0.488678 0.244339 0.969690i 0.421429π-0.421429\pi
0.244339 + 0.969690i 0.421429π0.421429\pi
6868 0 0
6969 4.00000 0.481543
7070 0 0
7171 12.0000 1.42414 0.712069 0.702109i 0.247758π-0.247758\pi
0.712069 + 0.702109i 0.247758π0.247758\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 8.00000 0.911685
7878 0 0
7979 10.0000 1.12509 0.562544 0.826767i 0.309823π-0.309823\pi
0.562544 + 0.826767i 0.309823π0.309823\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 −12.0000 −1.31717 −0.658586 0.752506i 0.728845π-0.728845\pi
−0.658586 + 0.752506i 0.728845π0.728845\pi
8484 0 0
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 −14.0000 −1.48400 −0.741999 0.670402i 0.766122π-0.766122\pi
−0.741999 + 0.670402i 0.766122π0.766122\pi
9090 0 0
9191 −4.00000 −0.419314
9292 0 0
9393 6.00000 0.622171
9494 0 0
9595 0 0
9696 0 0
9797 −10.0000 −1.01535 −0.507673 0.861550i 0.669494π-0.669494\pi
−0.507673 + 0.861550i 0.669494π0.669494\pi
9898 0 0
9999 −4.00000 −0.402015
100100 0 0
101101 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
102102 0 0
103103 10.0000 0.985329 0.492665 0.870219i 0.336023π-0.336023\pi
0.492665 + 0.870219i 0.336023π0.336023\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 6.00000 0.574696 0.287348 0.957826i 0.407226π-0.407226\pi
0.287348 + 0.957826i 0.407226π0.407226\pi
110110 0 0
111111 2.00000 0.189832
112112 0 0
113113 −2.00000 −0.188144 −0.0940721 0.995565i 0.529988π-0.529988\pi
−0.0940721 + 0.995565i 0.529988π0.529988\pi
114114 0 0
115115 0 0
116116 0 0
117117 2.00000 0.184900
118118 0 0
119119 −4.00000 −0.366679
120120 0 0
121121 5.00000 0.454545
122122 0 0
123123 −6.00000 −0.541002
124124 0 0
125125 0 0
126126 0 0
127127 2.00000 0.177471 0.0887357 0.996055i 0.471717π-0.471717\pi
0.0887357 + 0.996055i 0.471717π0.471717\pi
128128 0 0
129129 0 0
130130 0 0
131131 −12.0000 −1.04844 −0.524222 0.851581i 0.675644π-0.675644\pi
−0.524222 + 0.851581i 0.675644π0.675644\pi
132132 0 0
133133 16.0000 1.38738
134134 0 0
135135 0 0
136136 0 0
137137 2.00000 0.170872 0.0854358 0.996344i 0.472772π-0.472772\pi
0.0854358 + 0.996344i 0.472772π0.472772\pi
138138 0 0
139139 4.00000 0.339276 0.169638 0.985506i 0.445740π-0.445740\pi
0.169638 + 0.985506i 0.445740π0.445740\pi
140140 0 0
141141 4.00000 0.336861
142142 0 0
143143 −8.00000 −0.668994
144144 0 0
145145 0 0
146146 0 0
147147 3.00000 0.247436
148148 0 0
149149 −12.0000 −0.983078 −0.491539 0.870855i 0.663566π-0.663566\pi
−0.491539 + 0.870855i 0.663566π0.663566\pi
150150 0 0
151151 10.0000 0.813788 0.406894 0.913475i 0.366612π-0.366612\pi
0.406894 + 0.913475i 0.366612π0.366612\pi
152152 0 0
153153 2.00000 0.161690
154154 0 0
155155 0 0
156156 0 0
157157 −18.0000 −1.43656 −0.718278 0.695756i 0.755069π-0.755069\pi
−0.718278 + 0.695756i 0.755069π0.755069\pi
158158 0 0
159159 0 0
160160 0 0
161161 8.00000 0.630488
162162 0 0
163163 8.00000 0.626608 0.313304 0.949653i 0.398564π-0.398564\pi
0.313304 + 0.949653i 0.398564π0.398564\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 −9.00000 −0.692308
170170 0 0
171171 −8.00000 −0.611775
172172 0 0
173173 12.0000 0.912343 0.456172 0.889892i 0.349220π-0.349220\pi
0.456172 + 0.889892i 0.349220π0.349220\pi
174174 0 0
175175 0 0
176176 0 0
177177 −4.00000 −0.300658
178178 0 0
179179 12.0000 0.896922 0.448461 0.893802i 0.351972π-0.351972\pi
0.448461 + 0.893802i 0.351972π0.351972\pi
180180 0 0
181181 22.0000 1.63525 0.817624 0.575753i 0.195291π-0.195291\pi
0.817624 + 0.575753i 0.195291π0.195291\pi
182182 0 0
183183 14.0000 1.03491
184184 0 0
185185 0 0
186186 0 0
187187 −8.00000 −0.585018
188188 0 0
189189 2.00000 0.145479
190190 0 0
191191 8.00000 0.578860 0.289430 0.957199i 0.406534π-0.406534\pi
0.289430 + 0.957199i 0.406534π0.406534\pi
192192 0 0
193193 2.00000 0.143963 0.0719816 0.997406i 0.477068π-0.477068\pi
0.0719816 + 0.997406i 0.477068π0.477068\pi
194194 0 0
195195 0 0
196196 0 0
197197 −8.00000 −0.569976 −0.284988 0.958531i 0.591990π-0.591990\pi
−0.284988 + 0.958531i 0.591990π0.591990\pi
198198 0 0
199199 14.0000 0.992434 0.496217 0.868199i 0.334722π-0.334722\pi
0.496217 + 0.868199i 0.334722π0.334722\pi
200200 0 0
201201 −4.00000 −0.282138
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 −4.00000 −0.278019
208208 0 0
209209 32.0000 2.21349
210210 0 0
211211 −20.0000 −1.37686 −0.688428 0.725304i 0.741699π-0.741699\pi
−0.688428 + 0.725304i 0.741699π0.741699\pi
212212 0 0
213213 −12.0000 −0.822226
214214 0 0
215215 0 0
216216 0 0
217217 12.0000 0.814613
218218 0 0
219219 −10.0000 −0.675737
220220 0 0
221221 4.00000 0.269069
222222 0 0
223223 18.0000 1.20537 0.602685 0.797980i 0.294098π-0.294098\pi
0.602685 + 0.797980i 0.294098π0.294098\pi
224224 0 0
225225 0 0
226226 0 0
227227 −12.0000 −0.796468 −0.398234 0.917284i 0.630377π-0.630377\pi
−0.398234 + 0.917284i 0.630377π0.630377\pi
228228 0 0
229229 14.0000 0.925146 0.462573 0.886581i 0.346926π-0.346926\pi
0.462573 + 0.886581i 0.346926π0.346926\pi
230230 0 0
231231 −8.00000 −0.526361
232232 0 0
233233 6.00000 0.393073 0.196537 0.980497i 0.437031π-0.437031\pi
0.196537 + 0.980497i 0.437031π0.437031\pi
234234 0 0
235235 0 0
236236 0 0
237237 −10.0000 −0.649570
238238 0 0
239239 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
240240 0 0
241241 −2.00000 −0.128831 −0.0644157 0.997923i 0.520518π-0.520518\pi
−0.0644157 + 0.997923i 0.520518π0.520518\pi
242242 0 0
243243 −1.00000 −0.0641500
244244 0 0
245245 0 0
246246 0 0
247247 −16.0000 −1.01806
248248 0 0
249249 12.0000 0.760469
250250 0 0
251251 12.0000 0.757433 0.378717 0.925513i 0.376365π-0.376365\pi
0.378717 + 0.925513i 0.376365π0.376365\pi
252252 0 0
253253 16.0000 1.00591
254254 0 0
255255 0 0
256256 0 0
257257 −18.0000 −1.12281 −0.561405 0.827541i 0.689739π-0.689739\pi
−0.561405 + 0.827541i 0.689739π0.689739\pi
258258 0 0
259259 4.00000 0.248548
260260 0 0
261261 0 0
262262 0 0
263263 24.0000 1.47990 0.739952 0.672660i 0.234848π-0.234848\pi
0.739952 + 0.672660i 0.234848π0.234848\pi
264264 0 0
265265 0 0
266266 0 0
267267 14.0000 0.856786
268268 0 0
269269 −16.0000 −0.975537 −0.487769 0.872973i 0.662189π-0.662189\pi
−0.487769 + 0.872973i 0.662189π0.662189\pi
270270 0 0
271271 14.0000 0.850439 0.425220 0.905090i 0.360197π-0.360197\pi
0.425220 + 0.905090i 0.360197π0.360197\pi
272272 0 0
273273 4.00000 0.242091
274274 0 0
275275 0 0
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 −6.00000 −0.359211
280280 0 0
281281 18.0000 1.07379 0.536895 0.843649i 0.319597π-0.319597\pi
0.536895 + 0.843649i 0.319597π0.319597\pi
282282 0 0
283283 −12.0000 −0.713326 −0.356663 0.934233i 0.616086π-0.616086\pi
−0.356663 + 0.934233i 0.616086π0.616086\pi
284284 0 0
285285 0 0
286286 0 0
287287 −12.0000 −0.708338
288288 0 0
289289 −13.0000 −0.764706
290290 0 0
291291 10.0000 0.586210
292292 0 0
293293 16.0000 0.934730 0.467365 0.884064i 0.345203π-0.345203\pi
0.467365 + 0.884064i 0.345203π0.345203\pi
294294 0 0
295295 0 0
296296 0 0
297297 4.00000 0.232104
298298 0 0
299299 −8.00000 −0.462652
300300 0 0
301301 0 0
302302 0 0
303303 0 0
304304 0 0
305305 0 0
306306 0 0
307307 −12.0000 −0.684876 −0.342438 0.939540i 0.611253π-0.611253\pi
−0.342438 + 0.939540i 0.611253π0.611253\pi
308308 0 0
309309 −10.0000 −0.568880
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 26.0000 1.46961 0.734803 0.678280i 0.237274π-0.237274\pi
0.734803 + 0.678280i 0.237274π0.237274\pi
314314 0 0
315315 0 0
316316 0 0
317317 −24.0000 −1.34797 −0.673987 0.738743i 0.735420π-0.735420\pi
−0.673987 + 0.738743i 0.735420π0.735420\pi
318318 0 0
319319 0 0
320320 0 0
321321 −4.00000 −0.223258
322322 0 0
323323 −16.0000 −0.890264
324324 0 0
325325 0 0
326326 0 0
327327 −6.00000 −0.331801
328328 0 0
329329 8.00000 0.441054
330330 0 0
331331 −20.0000 −1.09930 −0.549650 0.835395i 0.685239π-0.685239\pi
−0.549650 + 0.835395i 0.685239π0.685239\pi
332332 0 0
333333 −2.00000 −0.109599
334334 0 0
335335 0 0
336336 0 0
337337 2.00000 0.108947 0.0544735 0.998515i 0.482652π-0.482652\pi
0.0544735 + 0.998515i 0.482652π0.482652\pi
338338 0 0
339339 2.00000 0.108625
340340 0 0
341341 24.0000 1.29967
342342 0 0
343343 20.0000 1.07990
344344 0 0
345345 0 0
346346 0 0
347347 12.0000 0.644194 0.322097 0.946707i 0.395612π-0.395612\pi
0.322097 + 0.946707i 0.395612π0.395612\pi
348348 0 0
349349 2.00000 0.107058 0.0535288 0.998566i 0.482953π-0.482953\pi
0.0535288 + 0.998566i 0.482953π0.482953\pi
350350 0 0
351351 −2.00000 −0.106752
352352 0 0
353353 30.0000 1.59674 0.798369 0.602168i 0.205696π-0.205696\pi
0.798369 + 0.602168i 0.205696π0.205696\pi
354354 0 0
355355 0 0
356356 0 0
357357 4.00000 0.211702
358358 0 0
359359 −4.00000 −0.211112 −0.105556 0.994413i 0.533662π-0.533662\pi
−0.105556 + 0.994413i 0.533662π0.533662\pi
360360 0 0
361361 45.0000 2.36842
362362 0 0
363363 −5.00000 −0.262432
364364 0 0
365365 0 0
366366 0 0
367367 38.0000 1.98358 0.991792 0.127862i 0.0408116π-0.0408116\pi
0.991792 + 0.127862i 0.0408116π0.0408116\pi
368368 0 0
369369 6.00000 0.312348
370370 0 0
371371 0 0
372372 0 0
373373 −2.00000 −0.103556 −0.0517780 0.998659i 0.516489π-0.516489\pi
−0.0517780 + 0.998659i 0.516489π0.516489\pi
374374 0 0
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 32.0000 1.64373 0.821865 0.569683i 0.192934π-0.192934\pi
0.821865 + 0.569683i 0.192934π0.192934\pi
380380 0 0
381381 −2.00000 −0.102463
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 0 0
386386 0 0
387387 0 0
388388 0 0
389389 20.0000 1.01404 0.507020 0.861934i 0.330747π-0.330747\pi
0.507020 + 0.861934i 0.330747π0.330747\pi
390390 0 0
391391 −8.00000 −0.404577
392392 0 0
393393 12.0000 0.605320
394394 0 0
395395 0 0
396396 0 0
397397 6.00000 0.301131 0.150566 0.988600i 0.451890π-0.451890\pi
0.150566 + 0.988600i 0.451890π0.451890\pi
398398 0 0
399399 −16.0000 −0.801002
400400 0 0
401401 6.00000 0.299626 0.149813 0.988714i 0.452133π-0.452133\pi
0.149813 + 0.988714i 0.452133π0.452133\pi
402402 0 0
403403 −12.0000 −0.597763
404404 0 0
405405 0 0
406406 0 0
407407 8.00000 0.396545
408408 0 0
409409 −14.0000 −0.692255 −0.346128 0.938187i 0.612504π-0.612504\pi
−0.346128 + 0.938187i 0.612504π0.612504\pi
410410 0 0
411411 −2.00000 −0.0986527
412412 0 0
413413 −8.00000 −0.393654
414414 0 0
415415 0 0
416416 0 0
417417 −4.00000 −0.195881
418418 0 0
419419 −20.0000 −0.977064 −0.488532 0.872546i 0.662467π-0.662467\pi
−0.488532 + 0.872546i 0.662467π0.662467\pi
420420 0 0
421421 38.0000 1.85201 0.926003 0.377515i 0.123221π-0.123221\pi
0.926003 + 0.377515i 0.123221π0.123221\pi
422422 0 0
423423 −4.00000 −0.194487
424424 0 0
425425 0 0
426426 0 0
427427 28.0000 1.35501
428428 0 0
429429 8.00000 0.386244
430430 0 0
431431 28.0000 1.34871 0.674356 0.738406i 0.264421π-0.264421\pi
0.674356 + 0.738406i 0.264421π0.264421\pi
432432 0 0
433433 −18.0000 −0.865025 −0.432512 0.901628i 0.642373π-0.642373\pi
−0.432512 + 0.901628i 0.642373π0.642373\pi
434434 0 0
435435 0 0
436436 0 0
437437 32.0000 1.53077
438438 0 0
439439 6.00000 0.286364 0.143182 0.989696i 0.454267π-0.454267\pi
0.143182 + 0.989696i 0.454267π0.454267\pi
440440 0 0
441441 −3.00000 −0.142857
442442 0 0
443443 −36.0000 −1.71041 −0.855206 0.518289i 0.826569π-0.826569\pi
−0.855206 + 0.518289i 0.826569π0.826569\pi
444444 0 0
445445 0 0
446446 0 0
447447 12.0000 0.567581
448448 0 0
449449 14.0000 0.660701 0.330350 0.943858i 0.392833π-0.392833\pi
0.330350 + 0.943858i 0.392833π0.392833\pi
450450 0 0
451451 −24.0000 −1.13012
452452 0 0
453453 −10.0000 −0.469841
454454 0 0
455455 0 0
456456 0 0
457457 −18.0000 −0.842004 −0.421002 0.907060i 0.638322π-0.638322\pi
−0.421002 + 0.907060i 0.638322π0.638322\pi
458458 0 0
459459 −2.00000 −0.0933520
460460 0 0
461461 −28.0000 −1.30409 −0.652045 0.758180i 0.726089π-0.726089\pi
−0.652045 + 0.758180i 0.726089π0.726089\pi
462462 0 0
463463 26.0000 1.20832 0.604161 0.796862i 0.293508π-0.293508\pi
0.604161 + 0.796862i 0.293508π0.293508\pi
464464 0 0
465465 0 0
466466 0 0
467467 4.00000 0.185098 0.0925490 0.995708i 0.470499π-0.470499\pi
0.0925490 + 0.995708i 0.470499π0.470499\pi
468468 0 0
469469 −8.00000 −0.369406
470470 0 0
471471 18.0000 0.829396
472472 0 0
473473 0 0
474474 0 0
475475 0 0
476476 0 0
477477 0 0
478478 0 0
479479 36.0000 1.64488 0.822441 0.568850i 0.192612π-0.192612\pi
0.822441 + 0.568850i 0.192612π0.192612\pi
480480 0 0
481481 −4.00000 −0.182384
482482 0 0
483483 −8.00000 −0.364013
484484 0 0
485485 0 0
486486 0 0
487487 14.0000 0.634401 0.317200 0.948359i 0.397257π-0.397257\pi
0.317200 + 0.948359i 0.397257π0.397257\pi
488488 0 0
489489 −8.00000 −0.361773
490490 0 0
491491 4.00000 0.180517 0.0902587 0.995918i 0.471231π-0.471231\pi
0.0902587 + 0.995918i 0.471231π0.471231\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 −24.0000 −1.07655
498498 0 0
499499 4.00000 0.179065 0.0895323 0.995984i 0.471463π-0.471463\pi
0.0895323 + 0.995984i 0.471463π0.471463\pi
500500 0 0
501501 16.0000 0.714827
502502 0 0
503503 −44.0000 −1.96186 −0.980932 0.194354i 0.937739π-0.937739\pi
−0.980932 + 0.194354i 0.937739π0.937739\pi
504504 0 0
505505 0 0
506506 0 0
507507 9.00000 0.399704
508508 0 0
509509 8.00000 0.354594 0.177297 0.984157i 0.443265π-0.443265\pi
0.177297 + 0.984157i 0.443265π0.443265\pi
510510 0 0
511511 −20.0000 −0.884748
512512 0 0
513513 8.00000 0.353209
514514 0 0
515515 0 0
516516 0 0
517517 16.0000 0.703679
518518 0 0
519519 −12.0000 −0.526742
520520 0 0
521521 14.0000 0.613351 0.306676 0.951814i 0.400783π-0.400783\pi
0.306676 + 0.951814i 0.400783π0.400783\pi
522522 0 0
523523 −16.0000 −0.699631 −0.349816 0.936819i 0.613756π-0.613756\pi
−0.349816 + 0.936819i 0.613756π0.613756\pi
524524 0 0
525525 0 0
526526 0 0
527527 −12.0000 −0.522728
528528 0 0
529529 −7.00000 −0.304348
530530 0 0
531531 4.00000 0.173585
532532 0 0
533533 12.0000 0.519778
534534 0 0
535535 0 0
536536 0 0
537537 −12.0000 −0.517838
538538 0 0
539539 12.0000 0.516877
540540 0 0
541541 14.0000 0.601907 0.300954 0.953639i 0.402695π-0.402695\pi
0.300954 + 0.953639i 0.402695π0.402695\pi
542542 0 0
543543 −22.0000 −0.944110
544544 0 0
545545 0 0
546546 0 0
547547 16.0000 0.684111 0.342055 0.939680i 0.388877π-0.388877\pi
0.342055 + 0.939680i 0.388877π0.388877\pi
548548 0 0
549549 −14.0000 −0.597505
550550 0 0
551551 0 0
552552 0 0
553553 −20.0000 −0.850487
554554 0 0
555555 0 0
556556 0 0
557557 −28.0000 −1.18640 −0.593199 0.805056i 0.702135π-0.702135\pi
−0.593199 + 0.805056i 0.702135π0.702135\pi
558558 0 0
559559 0 0
560560 0 0
561561 8.00000 0.337760
562562 0 0
563563 −36.0000 −1.51722 −0.758610 0.651546i 0.774121π-0.774121\pi
−0.758610 + 0.651546i 0.774121π0.774121\pi
564564 0 0
565565 0 0
566566 0 0
567567 −2.00000 −0.0839921
568568 0 0
569569 38.0000 1.59304 0.796521 0.604610i 0.206671π-0.206671\pi
0.796521 + 0.604610i 0.206671π0.206671\pi
570570 0 0
571571 4.00000 0.167395 0.0836974 0.996491i 0.473327π-0.473327\pi
0.0836974 + 0.996491i 0.473327π0.473327\pi
572572 0 0
573573 −8.00000 −0.334205
574574 0 0
575575 0 0
576576 0 0
577577 −38.0000 −1.58196 −0.790980 0.611842i 0.790429π-0.790429\pi
−0.790980 + 0.611842i 0.790429π0.790429\pi
578578 0 0
579579 −2.00000 −0.0831172
580580 0 0
581581 24.0000 0.995688
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 −4.00000 −0.165098 −0.0825488 0.996587i 0.526306π-0.526306\pi
−0.0825488 + 0.996587i 0.526306π0.526306\pi
588588 0 0
589589 48.0000 1.97781
590590 0 0
591591 8.00000 0.329076
592592 0 0
593593 30.0000 1.23195 0.615976 0.787765i 0.288762π-0.288762\pi
0.615976 + 0.787765i 0.288762π0.288762\pi
594594 0 0
595595 0 0
596596 0 0
597597 −14.0000 −0.572982
598598 0 0
599599 −36.0000 −1.47092 −0.735460 0.677568i 0.763034π-0.763034\pi
−0.735460 + 0.677568i 0.763034π0.763034\pi
600600 0 0
601601 30.0000 1.22373 0.611863 0.790964i 0.290420π-0.290420\pi
0.611863 + 0.790964i 0.290420π0.290420\pi
602602 0 0
603603 4.00000 0.162893
604604 0 0
605605 0 0
606606 0 0
607607 −14.0000 −0.568242 −0.284121 0.958788i 0.591702π-0.591702\pi
−0.284121 + 0.958788i 0.591702π0.591702\pi
608608 0 0
609609 0 0
610610 0 0
611611 −8.00000 −0.323645
612612 0 0
613613 46.0000 1.85792 0.928961 0.370177i 0.120703π-0.120703\pi
0.928961 + 0.370177i 0.120703π0.120703\pi
614614 0 0
615615 0 0
616616 0 0
617617 14.0000 0.563619 0.281809 0.959470i 0.409065π-0.409065\pi
0.281809 + 0.959470i 0.409065π0.409065\pi
618618 0 0
619619 −4.00000 −0.160774 −0.0803868 0.996764i 0.525616π-0.525616\pi
−0.0803868 + 0.996764i 0.525616π0.525616\pi
620620 0 0
621621 4.00000 0.160514
622622 0 0
623623 28.0000 1.12180
624624 0 0
625625 0 0
626626 0 0
627627 −32.0000 −1.27796
628628 0 0
629629 −4.00000 −0.159490
630630 0 0
631631 34.0000 1.35352 0.676759 0.736204i 0.263384π-0.263384\pi
0.676759 + 0.736204i 0.263384π0.263384\pi
632632 0 0
633633 20.0000 0.794929
634634 0 0
635635 0 0
636636 0 0
637637 −6.00000 −0.237729
638638 0 0
639639 12.0000 0.474713
640640 0 0
641641 −42.0000 −1.65890 −0.829450 0.558581i 0.811346π-0.811346\pi
−0.829450 + 0.558581i 0.811346π0.811346\pi
642642 0 0
643643 48.0000 1.89294 0.946468 0.322799i 0.104624π-0.104624\pi
0.946468 + 0.322799i 0.104624π0.104624\pi
644644 0 0
645645 0 0
646646 0 0
647647 12.0000 0.471769 0.235884 0.971781i 0.424201π-0.424201\pi
0.235884 + 0.971781i 0.424201π0.424201\pi
648648 0 0
649649 −16.0000 −0.628055
650650 0 0
651651 −12.0000 −0.470317
652652 0 0
653653 −12.0000 −0.469596 −0.234798 0.972044i 0.575443π-0.575443\pi
−0.234798 + 0.972044i 0.575443π0.575443\pi
654654 0 0
655655 0 0
656656 0 0
657657 10.0000 0.390137
658658 0 0
659659 −36.0000 −1.40236 −0.701180 0.712984i 0.747343π-0.747343\pi
−0.701180 + 0.712984i 0.747343π0.747343\pi
660660 0 0
661661 −22.0000 −0.855701 −0.427850 0.903850i 0.640729π-0.640729\pi
−0.427850 + 0.903850i 0.640729π0.640729\pi
662662 0 0
663663 −4.00000 −0.155347
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 −18.0000 −0.695920
670670 0 0
671671 56.0000 2.16186
672672 0 0
673673 −34.0000 −1.31060 −0.655302 0.755367i 0.727459π-0.727459\pi
−0.655302 + 0.755367i 0.727459π0.727459\pi
674674 0 0
675675 0 0
676676 0 0
677677 20.0000 0.768662 0.384331 0.923195i 0.374432π-0.374432\pi
0.384331 + 0.923195i 0.374432π0.374432\pi
678678 0 0
679679 20.0000 0.767530
680680 0 0
681681 12.0000 0.459841
682682 0 0
683683 12.0000 0.459167 0.229584 0.973289i 0.426264π-0.426264\pi
0.229584 + 0.973289i 0.426264π0.426264\pi
684684 0 0
685685 0 0
686686 0 0
687687 −14.0000 −0.534133
688688 0 0
689689 0 0
690690 0 0
691691 24.0000 0.913003 0.456502 0.889723i 0.349102π-0.349102\pi
0.456502 + 0.889723i 0.349102π0.349102\pi
692692 0 0
693693 8.00000 0.303895
694694 0 0
695695 0 0
696696 0 0
697697 12.0000 0.454532
698698 0 0
699699 −6.00000 −0.226941
700700 0 0
701701 40.0000 1.51078 0.755390 0.655276i 0.227448π-0.227448\pi
0.755390 + 0.655276i 0.227448π0.227448\pi
702702 0 0
703703 16.0000 0.603451
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 −2.00000 −0.0751116 −0.0375558 0.999295i 0.511957π-0.511957\pi
−0.0375558 + 0.999295i 0.511957π0.511957\pi
710710 0 0
711711 10.0000 0.375029
712712 0 0
713713 24.0000 0.898807
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 −36.0000 −1.34257 −0.671287 0.741198i 0.734258π-0.734258\pi
−0.671287 + 0.741198i 0.734258π0.734258\pi
720720 0 0
721721 −20.0000 −0.744839
722722 0 0
723723 2.00000 0.0743808
724724 0 0
725725 0 0
726726 0 0
727727 −42.0000 −1.55769 −0.778847 0.627214i 0.784195π-0.784195\pi
−0.778847 + 0.627214i 0.784195π0.784195\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 0 0
732732 0 0
733733 42.0000 1.55131 0.775653 0.631160i 0.217421π-0.217421\pi
0.775653 + 0.631160i 0.217421π0.217421\pi
734734 0 0
735735 0 0
736736 0 0
737737 −16.0000 −0.589368
738738 0 0
739739 12.0000 0.441427 0.220714 0.975339i 0.429161π-0.429161\pi
0.220714 + 0.975339i 0.429161π0.429161\pi
740740 0 0
741741 16.0000 0.587775
742742 0 0
743743 40.0000 1.46746 0.733729 0.679442i 0.237778π-0.237778\pi
0.733729 + 0.679442i 0.237778π0.237778\pi
744744 0 0
745745 0 0
746746 0 0
747747 −12.0000 −0.439057
748748 0 0
749749 −8.00000 −0.292314
750750 0 0
751751 −22.0000 −0.802791 −0.401396 0.915905i 0.631475π-0.631475\pi
−0.401396 + 0.915905i 0.631475π0.631475\pi
752752 0 0
753753 −12.0000 −0.437304
754754 0 0
755755 0 0
756756 0 0
757757 2.00000 0.0726912 0.0363456 0.999339i 0.488428π-0.488428\pi
0.0363456 + 0.999339i 0.488428π0.488428\pi
758758 0 0
759759 −16.0000 −0.580763
760760 0 0
761761 22.0000 0.797499 0.398750 0.917060i 0.369444π-0.369444\pi
0.398750 + 0.917060i 0.369444π0.369444\pi
762762 0 0
763763 −12.0000 −0.434429
764764 0 0
765765 0 0
766766 0 0
767767 8.00000 0.288863
768768 0 0
769769 14.0000 0.504853 0.252426 0.967616i 0.418771π-0.418771\pi
0.252426 + 0.967616i 0.418771π0.418771\pi
770770 0 0
771771 18.0000 0.648254
772772 0 0
773773 24.0000 0.863220 0.431610 0.902060i 0.357946π-0.357946\pi
0.431610 + 0.902060i 0.357946π0.357946\pi
774774 0 0
775775 0 0
776776 0 0
777777 −4.00000 −0.143499
778778 0 0
779779 −48.0000 −1.71978
780780 0 0
781781 −48.0000 −1.71758
782782 0 0
783783 0 0
784784 0 0
785785 0 0
786786 0 0
787787 32.0000 1.14068 0.570338 0.821410i 0.306812π-0.306812\pi
0.570338 + 0.821410i 0.306812π0.306812\pi
788788 0 0
789789 −24.0000 −0.854423
790790 0 0
791791 4.00000 0.142224
792792 0 0
793793 −28.0000 −0.994309
794794 0 0
795795 0 0
796796 0 0
797797 −12.0000 −0.425062 −0.212531 0.977154i 0.568171π-0.568171\pi
−0.212531 + 0.977154i 0.568171π0.568171\pi
798798 0 0
799799 −8.00000 −0.283020
800800 0 0
801801 −14.0000 −0.494666
802802 0 0
803803 −40.0000 −1.41157
804804 0 0
805805 0 0
806806 0 0
807807 16.0000 0.563227
808808 0 0
809809 −18.0000 −0.632846 −0.316423 0.948618i 0.602482π-0.602482\pi
−0.316423 + 0.948618i 0.602482π0.602482\pi
810810 0 0
811811 −24.0000 −0.842754 −0.421377 0.906886i 0.638453π-0.638453\pi
−0.421377 + 0.906886i 0.638453π0.638453\pi
812812 0 0
813813 −14.0000 −0.491001
814814 0 0
815815 0 0
816816 0 0
817817 0 0
818818 0 0
819819 −4.00000 −0.139771
820820 0 0
821821 8.00000 0.279202 0.139601 0.990208i 0.455418π-0.455418\pi
0.139601 + 0.990208i 0.455418π0.455418\pi
822822 0 0
823823 22.0000 0.766872 0.383436 0.923567i 0.374741π-0.374741\pi
0.383436 + 0.923567i 0.374741π0.374741\pi
824824 0 0
825825 0 0
826826 0 0
827827 −44.0000 −1.53003 −0.765015 0.644013i 0.777268π-0.777268\pi
−0.765015 + 0.644013i 0.777268π0.777268\pi
828828 0 0
829829 38.0000 1.31979 0.659897 0.751356i 0.270600π-0.270600\pi
0.659897 + 0.751356i 0.270600π0.270600\pi
830830 0 0
831831 6.00000 0.208138
832832 0 0
833833 −6.00000 −0.207888
834834 0 0
835835 0 0
836836 0 0
837837 6.00000 0.207390
838838 0 0
839839 36.0000 1.24286 0.621429 0.783470i 0.286552π-0.286552\pi
0.621429 + 0.783470i 0.286552π0.286552\pi
840840 0 0
841841 −29.0000 −1.00000
842842 0 0
843843 −18.0000 −0.619953
844844 0 0
845845 0 0
846846 0 0
847847 −10.0000 −0.343604
848848 0 0
849849 12.0000 0.411839
850850 0 0
851851 8.00000 0.274236
852852 0 0
853853 38.0000 1.30110 0.650548 0.759465i 0.274539π-0.274539\pi
0.650548 + 0.759465i 0.274539π0.274539\pi
854854 0 0
855855 0 0
856856 0 0
857857 42.0000 1.43469 0.717346 0.696717i 0.245357π-0.245357\pi
0.717346 + 0.696717i 0.245357π0.245357\pi
858858 0 0
859859 8.00000 0.272956 0.136478 0.990643i 0.456422π-0.456422\pi
0.136478 + 0.990643i 0.456422π0.456422\pi
860860 0 0
861861 12.0000 0.408959
862862 0 0
863863 8.00000 0.272323 0.136162 0.990687i 0.456523π-0.456523\pi
0.136162 + 0.990687i 0.456523π0.456523\pi
864864 0 0
865865 0 0
866866 0 0
867867 13.0000 0.441503
868868 0 0
869869 −40.0000 −1.35691
870870 0 0
871871 8.00000 0.271070
872872 0 0
873873 −10.0000 −0.338449
874874 0 0
875875 0 0
876876 0 0
877877 −34.0000 −1.14810 −0.574049 0.818821i 0.694628π-0.694628\pi
−0.574049 + 0.818821i 0.694628π0.694628\pi
878878 0 0
879879 −16.0000 −0.539667
880880 0 0
881881 −46.0000 −1.54978 −0.774890 0.632096i 0.782195π-0.782195\pi
−0.774890 + 0.632096i 0.782195π0.782195\pi
882882 0 0
883883 40.0000 1.34611 0.673054 0.739594i 0.264982π-0.264982\pi
0.673054 + 0.739594i 0.264982π0.264982\pi
884884 0 0
885885 0 0
886886 0 0
887887 24.0000 0.805841 0.402921 0.915235i 0.367995π-0.367995\pi
0.402921 + 0.915235i 0.367995π0.367995\pi
888888 0 0
889889 −4.00000 −0.134156
890890 0 0
891891 −4.00000 −0.134005
892892 0 0
893893 32.0000 1.07084
894894 0 0
895895 0 0
896896 0 0
897897 8.00000 0.267112
898898 0 0
899899 0 0
900900 0 0
901901 0 0
902902 0 0
903903 0 0
904904 0 0
905905 0 0
906906 0 0
907907 8.00000 0.265636 0.132818 0.991140i 0.457597π-0.457597\pi
0.132818 + 0.991140i 0.457597π0.457597\pi
908908 0 0
909909 0 0
910910 0 0
911911 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
912912 0 0
913913 48.0000 1.58857
914914 0 0
915915 0 0
916916 0 0
917917 24.0000 0.792550
918918 0 0
919919 −6.00000 −0.197922 −0.0989609 0.995091i 0.531552π-0.531552\pi
−0.0989609 + 0.995091i 0.531552π0.531552\pi
920920 0 0
921921 12.0000 0.395413
922922 0 0
923923 24.0000 0.789970
924924 0 0
925925 0 0
926926 0 0
927927 10.0000 0.328443
928928 0 0
929929 −42.0000 −1.37798 −0.688988 0.724773i 0.741945π-0.741945\pi
−0.688988 + 0.724773i 0.741945π0.741945\pi
930930 0 0
931931 24.0000 0.786568
932932 0 0
933933 16.0000 0.523816
934934 0 0
935935 0 0
936936 0 0
937937 38.0000 1.24141 0.620703 0.784046i 0.286847π-0.286847\pi
0.620703 + 0.784046i 0.286847π0.286847\pi
938938 0 0
939939 −26.0000 −0.848478
940940 0 0
941941 −28.0000 −0.912774 −0.456387 0.889781i 0.650857π-0.650857\pi
−0.456387 + 0.889781i 0.650857π0.650857\pi
942942 0 0
943943 −24.0000 −0.781548
944944 0 0
945945 0 0
946946 0 0
947947 52.0000 1.68977 0.844886 0.534946i 0.179668π-0.179668\pi
0.844886 + 0.534946i 0.179668π0.179668\pi
948948 0 0
949949 20.0000 0.649227
950950 0 0
951951 24.0000 0.778253
952952 0 0
953953 2.00000 0.0647864 0.0323932 0.999475i 0.489687π-0.489687\pi
0.0323932 + 0.999475i 0.489687π0.489687\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 −4.00000 −0.129167
960960 0 0
961961 5.00000 0.161290
962962 0 0
963963 4.00000 0.128898
964964 0 0
965965 0 0
966966 0 0
967967 2.00000 0.0643157 0.0321578 0.999483i 0.489762π-0.489762\pi
0.0321578 + 0.999483i 0.489762π0.489762\pi
968968 0 0
969969 16.0000 0.513994
970970 0 0
971971 4.00000 0.128366 0.0641831 0.997938i 0.479556π-0.479556\pi
0.0641831 + 0.997938i 0.479556π0.479556\pi
972972 0 0
973973 −8.00000 −0.256468
974974 0 0
975975 0 0
976976 0 0
977977 −6.00000 −0.191957 −0.0959785 0.995383i 0.530598π-0.530598\pi
−0.0959785 + 0.995383i 0.530598π0.530598\pi
978978 0 0
979979 56.0000 1.78977
980980 0 0
981981 6.00000 0.191565
982982 0 0
983983 −56.0000 −1.78612 −0.893061 0.449935i 0.851447π-0.851447\pi
−0.893061 + 0.449935i 0.851447π0.851447\pi
984984 0 0
985985 0 0
986986 0 0
987987 −8.00000 −0.254643
988988 0 0
989989 0 0
990990 0 0
991991 10.0000 0.317660 0.158830 0.987306i 0.449228π-0.449228\pi
0.158830 + 0.987306i 0.449228π0.449228\pi
992992 0 0
993993 20.0000 0.634681
994994 0 0
995995 0 0
996996 0 0
997997 54.0000 1.71020 0.855099 0.518465i 0.173497π-0.173497\pi
0.855099 + 0.518465i 0.173497π0.173497\pi
998998 0 0
999999 2.00000 0.0632772
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 9600.2.a.e.1.1 1
4.3 odd 2 9600.2.a.bz.1.1 1
5.4 even 2 384.2.a.h.1.1 yes 1
8.3 odd 2 9600.2.a.t.1.1 1
8.5 even 2 9600.2.a.bk.1.1 1
15.14 odd 2 1152.2.a.b.1.1 1
20.19 odd 2 384.2.a.d.1.1 yes 1
40.19 odd 2 384.2.a.e.1.1 yes 1
40.29 even 2 384.2.a.a.1.1 1
60.59 even 2 1152.2.a.a.1.1 1
80.19 odd 4 768.2.d.f.385.1 2
80.29 even 4 768.2.d.c.385.2 2
80.59 odd 4 768.2.d.f.385.2 2
80.69 even 4 768.2.d.c.385.1 2
120.29 odd 2 1152.2.a.t.1.1 1
120.59 even 2 1152.2.a.s.1.1 1
240.29 odd 4 2304.2.d.f.1153.2 2
240.59 even 4 2304.2.d.o.1153.1 2
240.149 odd 4 2304.2.d.f.1153.1 2
240.179 even 4 2304.2.d.o.1153.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
384.2.a.a.1.1 1 40.29 even 2
384.2.a.d.1.1 yes 1 20.19 odd 2
384.2.a.e.1.1 yes 1 40.19 odd 2
384.2.a.h.1.1 yes 1 5.4 even 2
768.2.d.c.385.1 2 80.69 even 4
768.2.d.c.385.2 2 80.29 even 4
768.2.d.f.385.1 2 80.19 odd 4
768.2.d.f.385.2 2 80.59 odd 4
1152.2.a.a.1.1 1 60.59 even 2
1152.2.a.b.1.1 1 15.14 odd 2
1152.2.a.s.1.1 1 120.59 even 2
1152.2.a.t.1.1 1 120.29 odd 2
2304.2.d.f.1153.1 2 240.149 odd 4
2304.2.d.f.1153.2 2 240.29 odd 4
2304.2.d.o.1153.1 2 240.59 even 4
2304.2.d.o.1153.2 2 240.179 even 4
9600.2.a.e.1.1 1 1.1 even 1 trivial
9600.2.a.t.1.1 1 8.3 odd 2
9600.2.a.bk.1.1 1 8.5 even 2
9600.2.a.bz.1.1 1 4.3 odd 2