Properties

Label 9360.2.a.cc.1.2
Level 93609360
Weight 22
Character 9360.1
Self dual yes
Analytic conductor 74.74074.740
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] = [9360,2,Mod(1,9360)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9360, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 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("9360.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 9360=2432513 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 9360.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,0,0,-2,0,-4,0,0,0,-4,0,-2,0,0,0,-4,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 74.739976291974.7399762919
Analytic rank: 00
Dimension: 22
Coefficient field: Q(6)\Q(\sqrt{6})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x26 x^{2} - 6 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 520)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 2.449492.44949 of defining polynomial
Character χ\chi == 9360.1

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) == q1.00000q52.00000q7+0.449490q111.00000q13+2.89898q17+4.44949q19+1.55051q23+1.00000q254.00000q290.449490q31+2.00000q354.89898q371.10102q41+3.34847q432.00000q473.00000q4910.8990q530.449490q555.34847q59+13.7980q61+1.00000q65+14.8990q678.44949q71+14.6969q730.898979q77+4.89898q79+2.00000q832.89898q856.00000q89+2.00000q914.44949q9511.7980q97+O(q100)q-1.00000 q^{5} -2.00000 q^{7} +0.449490 q^{11} -1.00000 q^{13} +2.89898 q^{17} +4.44949 q^{19} +1.55051 q^{23} +1.00000 q^{25} -4.00000 q^{29} -0.449490 q^{31} +2.00000 q^{35} -4.89898 q^{37} -1.10102 q^{41} +3.34847 q^{43} -2.00000 q^{47} -3.00000 q^{49} -10.8990 q^{53} -0.449490 q^{55} -5.34847 q^{59} +13.7980 q^{61} +1.00000 q^{65} +14.8990 q^{67} -8.44949 q^{71} +14.6969 q^{73} -0.898979 q^{77} +4.89898 q^{79} +2.00000 q^{83} -2.89898 q^{85} -6.00000 q^{89} +2.00000 q^{91} -4.44949 q^{95} -11.7980 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q54q74q112q134q17+4q19+8q23+2q258q29+4q31+4q3512q418q434q476q4912q53+4q55+4q59+4q97+O(q100) 2 q - 2 q^{5} - 4 q^{7} - 4 q^{11} - 2 q^{13} - 4 q^{17} + 4 q^{19} + 8 q^{23} + 2 q^{25} - 8 q^{29} + 4 q^{31} + 4 q^{35} - 12 q^{41} - 8 q^{43} - 4 q^{47} - 6 q^{49} - 12 q^{53} + 4 q^{55} + 4 q^{59}+ \cdots - 4 q^{97}+O(q^{100}) Copy content Toggle raw display

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0 0
44 0 0
55 −1.00000 −0.447214
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 0 0
1010 0 0
1111 0.449490 0.135526 0.0677631 0.997701i 0.478414π-0.478414\pi
0.0677631 + 0.997701i 0.478414π0.478414\pi
1212 0 0
1313 −1.00000 −0.277350
1414 0 0
1515 0 0
1616 0 0
1717 2.89898 0.703106 0.351553 0.936168i 0.385654π-0.385654\pi
0.351553 + 0.936168i 0.385654π0.385654\pi
1818 0 0
1919 4.44949 1.02078 0.510391 0.859942i 0.329501π-0.329501\pi
0.510391 + 0.859942i 0.329501π0.329501\pi
2020 0 0
2121 0 0
2222 0 0
2323 1.55051 0.323304 0.161652 0.986848i 0.448318π-0.448318\pi
0.161652 + 0.986848i 0.448318π0.448318\pi
2424 0 0
2525 1.00000 0.200000
2626 0 0
2727 0 0
2828 0 0
2929 −4.00000 −0.742781 −0.371391 0.928477i 0.621119π-0.621119\pi
−0.371391 + 0.928477i 0.621119π0.621119\pi
3030 0 0
3131 −0.449490 −0.0807307 −0.0403654 0.999185i 0.512852π-0.512852\pi
−0.0403654 + 0.999185i 0.512852π0.512852\pi
3232 0 0
3333 0 0
3434 0 0
3535 2.00000 0.338062
3636 0 0
3737 −4.89898 −0.805387 −0.402694 0.915335i 0.631926π-0.631926\pi
−0.402694 + 0.915335i 0.631926π0.631926\pi
3838 0 0
3939 0 0
4040 0 0
4141 −1.10102 −0.171951 −0.0859753 0.996297i 0.527401π-0.527401\pi
−0.0859753 + 0.996297i 0.527401π0.527401\pi
4242 0 0
4343 3.34847 0.510637 0.255318 0.966857i 0.417820π-0.417820\pi
0.255318 + 0.966857i 0.417820π0.417820\pi
4444 0 0
4545 0 0
4646 0 0
4747 −2.00000 −0.291730 −0.145865 0.989305i 0.546597π-0.546597\pi
−0.145865 + 0.989305i 0.546597π0.546597\pi
4848 0 0
4949 −3.00000 −0.428571
5050 0 0
5151 0 0
5252 0 0
5353 −10.8990 −1.49709 −0.748545 0.663084i 0.769247π-0.769247\pi
−0.748545 + 0.663084i 0.769247π0.769247\pi
5454 0 0
5555 −0.449490 −0.0606092
5656 0 0
5757 0 0
5858 0 0
5959 −5.34847 −0.696311 −0.348156 0.937437i 0.613192π-0.613192\pi
−0.348156 + 0.937437i 0.613192π0.613192\pi
6060 0 0
6161 13.7980 1.76665 0.883324 0.468763i 0.155300π-0.155300\pi
0.883324 + 0.468763i 0.155300π0.155300\pi
6262 0 0
6363 0 0
6464 0 0
6565 1.00000 0.124035
6666 0 0
6767 14.8990 1.82020 0.910100 0.414389i 0.136005π-0.136005\pi
0.910100 + 0.414389i 0.136005π0.136005\pi
6868 0 0
6969 0 0
7070 0 0
7171 −8.44949 −1.00277 −0.501385 0.865224i 0.667176π-0.667176\pi
−0.501385 + 0.865224i 0.667176π0.667176\pi
7272 0 0
7373 14.6969 1.72015 0.860073 0.510171i 0.170418π-0.170418\pi
0.860073 + 0.510171i 0.170418π0.170418\pi
7474 0 0
7575 0 0
7676 0 0
7777 −0.898979 −0.102448
7878 0 0
7979 4.89898 0.551178 0.275589 0.961276i 0.411127π-0.411127\pi
0.275589 + 0.961276i 0.411127π0.411127\pi
8080 0 0
8181 0 0
8282 0 0
8383 2.00000 0.219529 0.109764 0.993958i 0.464990π-0.464990\pi
0.109764 + 0.993958i 0.464990π0.464990\pi
8484 0 0
8585 −2.89898 −0.314438
8686 0 0
8787 0 0
8888 0 0
8989 −6.00000 −0.635999 −0.317999 0.948091i 0.603011π-0.603011\pi
−0.317999 + 0.948091i 0.603011π0.603011\pi
9090 0 0
9191 2.00000 0.209657
9292 0 0
9393 0 0
9494 0 0
9595 −4.44949 −0.456508
9696 0 0
9797 −11.7980 −1.19790 −0.598951 0.800786i 0.704415π-0.704415\pi
−0.598951 + 0.800786i 0.704415π0.704415\pi
9898 0 0
9999 0 0
100100 0 0
101101 −3.79796 −0.377911 −0.188956 0.981986i 0.560510π-0.560510\pi
−0.188956 + 0.981986i 0.560510π0.560510\pi
102102 0 0
103103 3.34847 0.329934 0.164967 0.986299i 0.447248π-0.447248\pi
0.164967 + 0.986299i 0.447248π0.447248\pi
104104 0 0
105105 0 0
106106 0 0
107107 12.2474 1.18401 0.592003 0.805936i 0.298337π-0.298337\pi
0.592003 + 0.805936i 0.298337π0.298337\pi
108108 0 0
109109 −10.0000 −0.957826 −0.478913 0.877862i 0.658969π-0.658969\pi
−0.478913 + 0.877862i 0.658969π0.658969\pi
110110 0 0
111111 0 0
112112 0 0
113113 −10.8990 −1.02529 −0.512645 0.858601i 0.671334π-0.671334\pi
−0.512645 + 0.858601i 0.671334π0.671334\pi
114114 0 0
115115 −1.55051 −0.144586
116116 0 0
117117 0 0
118118 0 0
119119 −5.79796 −0.531498
120120 0 0
121121 −10.7980 −0.981633
122122 0 0
123123 0 0
124124 0 0
125125 −1.00000 −0.0894427
126126 0 0
127127 −19.3485 −1.71690 −0.858450 0.512898i 0.828572π-0.828572\pi
−0.858450 + 0.512898i 0.828572π0.828572\pi
128128 0 0
129129 0 0
130130 0 0
131131 −19.5959 −1.71210 −0.856052 0.516890i 0.827090π-0.827090\pi
−0.856052 + 0.516890i 0.827090π0.827090\pi
132132 0 0
133133 −8.89898 −0.771639
134134 0 0
135135 0 0
136136 0 0
137137 14.0000 1.19610 0.598050 0.801459i 0.295942π-0.295942\pi
0.598050 + 0.801459i 0.295942π0.295942\pi
138138 0 0
139139 7.10102 0.602301 0.301150 0.953577i 0.402629π-0.402629\pi
0.301150 + 0.953577i 0.402629π0.402629\pi
140140 0 0
141141 0 0
142142 0 0
143143 −0.449490 −0.0375882
144144 0 0
145145 4.00000 0.332182
146146 0 0
147147 0 0
148148 0 0
149149 7.79796 0.638834 0.319417 0.947614i 0.396513π-0.396513\pi
0.319417 + 0.947614i 0.396513π0.396513\pi
150150 0 0
151151 17.3485 1.41180 0.705899 0.708312i 0.250543π-0.250543\pi
0.705899 + 0.708312i 0.250543π0.250543\pi
152152 0 0
153153 0 0
154154 0 0
155155 0.449490 0.0361039
156156 0 0
157157 10.0000 0.798087 0.399043 0.916932i 0.369342π-0.369342\pi
0.399043 + 0.916932i 0.369342π0.369342\pi
158158 0 0
159159 0 0
160160 0 0
161161 −3.10102 −0.244395
162162 0 0
163163 18.8990 1.48028 0.740141 0.672452i 0.234759π-0.234759\pi
0.740141 + 0.672452i 0.234759π0.234759\pi
164164 0 0
165165 0 0
166166 0 0
167167 18.0000 1.39288 0.696441 0.717614i 0.254766π-0.254766\pi
0.696441 + 0.717614i 0.254766π0.254766\pi
168168 0 0
169169 1.00000 0.0769231
170170 0 0
171171 0 0
172172 0 0
173173 2.89898 0.220405 0.110203 0.993909i 0.464850π-0.464850\pi
0.110203 + 0.993909i 0.464850π0.464850\pi
174174 0 0
175175 −2.00000 −0.151186
176176 0 0
177177 0 0
178178 0 0
179179 8.00000 0.597948 0.298974 0.954261i 0.403356π-0.403356\pi
0.298974 + 0.954261i 0.403356π0.403356\pi
180180 0 0
181181 −13.7980 −1.02559 −0.512797 0.858510i 0.671391π-0.671391\pi
−0.512797 + 0.858510i 0.671391π0.671391\pi
182182 0 0
183183 0 0
184184 0 0
185185 4.89898 0.360180
186186 0 0
187187 1.30306 0.0952893
188188 0 0
189189 0 0
190190 0 0
191191 17.7980 1.28782 0.643908 0.765103i 0.277312π-0.277312\pi
0.643908 + 0.765103i 0.277312π0.277312\pi
192192 0 0
193193 19.7980 1.42509 0.712544 0.701627i 0.247543π-0.247543\pi
0.712544 + 0.701627i 0.247543π0.247543\pi
194194 0 0
195195 0 0
196196 0 0
197197 4.20204 0.299383 0.149692 0.988733i 0.452172π-0.452172\pi
0.149692 + 0.988733i 0.452172π0.452172\pi
198198 0 0
199199 13.7980 0.978111 0.489056 0.872253i 0.337341π-0.337341\pi
0.489056 + 0.872253i 0.337341π0.337341\pi
200200 0 0
201201 0 0
202202 0 0
203203 8.00000 0.561490
204204 0 0
205205 1.10102 0.0768986
206206 0 0
207207 0 0
208208 0 0
209209 2.00000 0.138343
210210 0 0
211211 6.20204 0.426966 0.213483 0.976947i 0.431519π-0.431519\pi
0.213483 + 0.976947i 0.431519π0.431519\pi
212212 0 0
213213 0 0
214214 0 0
215215 −3.34847 −0.228364
216216 0 0
217217 0.898979 0.0610267
218218 0 0
219219 0 0
220220 0 0
221221 −2.89898 −0.195006
222222 0 0
223223 −21.5959 −1.44617 −0.723085 0.690759i 0.757276π-0.757276\pi
−0.723085 + 0.690759i 0.757276π0.757276\pi
224224 0 0
225225 0 0
226226 0 0
227227 13.1010 0.869545 0.434773 0.900540i 0.356829π-0.356829\pi
0.434773 + 0.900540i 0.356829π0.356829\pi
228228 0 0
229229 −9.10102 −0.601412 −0.300706 0.953717i 0.597222π-0.597222\pi
−0.300706 + 0.953717i 0.597222π0.597222\pi
230230 0 0
231231 0 0
232232 0 0
233233 −13.5959 −0.890698 −0.445349 0.895357i 0.646920π-0.646920\pi
−0.445349 + 0.895357i 0.646920π0.646920\pi
234234 0 0
235235 2.00000 0.130466
236236 0 0
237237 0 0
238238 0 0
239239 23.1464 1.49722 0.748609 0.663012i 0.230722π-0.230722\pi
0.748609 + 0.663012i 0.230722π0.230722\pi
240240 0 0
241241 28.6969 1.84853 0.924266 0.381749i 0.124678π-0.124678\pi
0.924266 + 0.381749i 0.124678π0.124678\pi
242242 0 0
243243 0 0
244244 0 0
245245 3.00000 0.191663
246246 0 0
247247 −4.44949 −0.283114
248248 0 0
249249 0 0
250250 0 0
251251 14.6969 0.927663 0.463831 0.885924i 0.346474π-0.346474\pi
0.463831 + 0.885924i 0.346474π0.346474\pi
252252 0 0
253253 0.696938 0.0438161
254254 0 0
255255 0 0
256256 0 0
257257 −15.7980 −0.985450 −0.492725 0.870185i 0.663999π-0.663999\pi
−0.492725 + 0.870185i 0.663999π0.663999\pi
258258 0 0
259259 9.79796 0.608816
260260 0 0
261261 0 0
262262 0 0
263263 21.5505 1.32886 0.664431 0.747350i 0.268674π-0.268674\pi
0.664431 + 0.747350i 0.268674π0.268674\pi
264264 0 0
265265 10.8990 0.669519
266266 0 0
267267 0 0
268268 0 0
269269 −26.0000 −1.58525 −0.792624 0.609711i 0.791286π-0.791286\pi
−0.792624 + 0.609711i 0.791286π0.791286\pi
270270 0 0
271271 −8.44949 −0.513270 −0.256635 0.966508i 0.582614π-0.582614\pi
−0.256635 + 0.966508i 0.582614π0.582614\pi
272272 0 0
273273 0 0
274274 0 0
275275 0.449490 0.0271053
276276 0 0
277277 26.4949 1.59192 0.795962 0.605347i 0.206965π-0.206965\pi
0.795962 + 0.605347i 0.206965π0.206965\pi
278278 0 0
279279 0 0
280280 0 0
281281 −2.89898 −0.172939 −0.0864693 0.996255i 0.527558π-0.527558\pi
−0.0864693 + 0.996255i 0.527558π0.527558\pi
282282 0 0
283283 1.55051 0.0921683 0.0460841 0.998938i 0.485326π-0.485326\pi
0.0460841 + 0.998938i 0.485326π0.485326\pi
284284 0 0
285285 0 0
286286 0 0
287287 2.20204 0.129982
288288 0 0
289289 −8.59592 −0.505642
290290 0 0
291291 0 0
292292 0 0
293293 20.4949 1.19732 0.598662 0.801001i 0.295699π-0.295699\pi
0.598662 + 0.801001i 0.295699π0.295699\pi
294294 0 0
295295 5.34847 0.311400
296296 0 0
297297 0 0
298298 0 0
299299 −1.55051 −0.0896683
300300 0 0
301301 −6.69694 −0.386005
302302 0 0
303303 0 0
304304 0 0
305305 −13.7980 −0.790069
306306 0 0
307307 11.7980 0.673345 0.336673 0.941622i 0.390698π-0.390698\pi
0.336673 + 0.941622i 0.390698π0.390698\pi
308308 0 0
309309 0 0
310310 0 0
311311 12.8990 0.731434 0.365717 0.930726i 0.380824π-0.380824\pi
0.365717 + 0.930726i 0.380824π0.380824\pi
312312 0 0
313313 26.4949 1.49758 0.748790 0.662807i 0.230635π-0.230635\pi
0.748790 + 0.662807i 0.230635π0.230635\pi
314314 0 0
315315 0 0
316316 0 0
317317 2.69694 0.151475 0.0757376 0.997128i 0.475869π-0.475869\pi
0.0757376 + 0.997128i 0.475869π0.475869\pi
318318 0 0
319319 −1.79796 −0.100666
320320 0 0
321321 0 0
322322 0 0
323323 12.8990 0.717718
324324 0 0
325325 −1.00000 −0.0554700
326326 0 0
327327 0 0
328328 0 0
329329 4.00000 0.220527
330330 0 0
331331 8.44949 0.464426 0.232213 0.972665i 0.425403π-0.425403\pi
0.232213 + 0.972665i 0.425403π0.425403\pi
332332 0 0
333333 0 0
334334 0 0
335335 −14.8990 −0.814018
336336 0 0
337337 12.6969 0.691646 0.345823 0.938300i 0.387600π-0.387600\pi
0.345823 + 0.938300i 0.387600π0.387600\pi
338338 0 0
339339 0 0
340340 0 0
341341 −0.202041 −0.0109411
342342 0 0
343343 20.0000 1.07990
344344 0 0
345345 0 0
346346 0 0
347347 −4.24745 −0.228015 −0.114007 0.993480i 0.536369π-0.536369\pi
−0.114007 + 0.993480i 0.536369π0.536369\pi
348348 0 0
349349 −8.69694 −0.465536 −0.232768 0.972532i 0.574778π-0.574778\pi
−0.232768 + 0.972532i 0.574778π0.574778\pi
350350 0 0
351351 0 0
352352 0 0
353353 −20.4949 −1.09083 −0.545417 0.838165i 0.683629π-0.683629\pi
−0.545417 + 0.838165i 0.683629π0.683629\pi
354354 0 0
355355 8.44949 0.448452
356356 0 0
357357 0 0
358358 0 0
359359 −30.2474 −1.59640 −0.798200 0.602393i 0.794214π-0.794214\pi
−0.798200 + 0.602393i 0.794214π0.794214\pi
360360 0 0
361361 0.797959 0.0419978
362362 0 0
363363 0 0
364364 0 0
365365 −14.6969 −0.769273
366366 0 0
367367 18.9444 0.988889 0.494444 0.869209i 0.335372π-0.335372\pi
0.494444 + 0.869209i 0.335372π0.335372\pi
368368 0 0
369369 0 0
370370 0 0
371371 21.7980 1.13169
372372 0 0
373373 −9.59592 −0.496858 −0.248429 0.968650i 0.579914π-0.579914\pi
−0.248429 + 0.968650i 0.579914π0.579914\pi
374374 0 0
375375 0 0
376376 0 0
377377 4.00000 0.206010
378378 0 0
379379 11.5505 0.593310 0.296655 0.954985i 0.404129π-0.404129\pi
0.296655 + 0.954985i 0.404129π0.404129\pi
380380 0 0
381381 0 0
382382 0 0
383383 13.5959 0.694719 0.347359 0.937732i 0.387078π-0.387078\pi
0.347359 + 0.937732i 0.387078π0.387078\pi
384384 0 0
385385 0.898979 0.0458162
386386 0 0
387387 0 0
388388 0 0
389389 37.5959 1.90619 0.953094 0.302673i 0.0978791π-0.0978791\pi
0.953094 + 0.302673i 0.0978791π0.0978791\pi
390390 0 0
391391 4.49490 0.227317
392392 0 0
393393 0 0
394394 0 0
395395 −4.89898 −0.246494
396396 0 0
397397 1.30306 0.0653988 0.0326994 0.999465i 0.489590π-0.489590\pi
0.0326994 + 0.999465i 0.489590π0.489590\pi
398398 0 0
399399 0 0
400400 0 0
401401 −6.00000 −0.299626 −0.149813 0.988714i 0.547867π-0.547867\pi
−0.149813 + 0.988714i 0.547867π0.547867\pi
402402 0 0
403403 0.449490 0.0223907
404404 0 0
405405 0 0
406406 0 0
407407 −2.20204 −0.109151
408408 0 0
409409 2.89898 0.143345 0.0716727 0.997428i 0.477166π-0.477166\pi
0.0716727 + 0.997428i 0.477166π0.477166\pi
410410 0 0
411411 0 0
412412 0 0
413413 10.6969 0.526362
414414 0 0
415415 −2.00000 −0.0981761
416416 0 0
417417 0 0
418418 0 0
419419 9.30306 0.454484 0.227242 0.973838i 0.427029π-0.427029\pi
0.227242 + 0.973838i 0.427029π0.427029\pi
420420 0 0
421421 15.7980 0.769945 0.384973 0.922928i 0.374211π-0.374211\pi
0.384973 + 0.922928i 0.374211π0.374211\pi
422422 0 0
423423 0 0
424424 0 0
425425 2.89898 0.140621
426426 0 0
427427 −27.5959 −1.33546
428428 0 0
429429 0 0
430430 0 0
431431 12.0454 0.580207 0.290103 0.956995i 0.406310π-0.406310\pi
0.290103 + 0.956995i 0.406310π0.406310\pi
432432 0 0
433433 −7.79796 −0.374746 −0.187373 0.982289i 0.559997π-0.559997\pi
−0.187373 + 0.982289i 0.559997π0.559997\pi
434434 0 0
435435 0 0
436436 0 0
437437 6.89898 0.330023
438438 0 0
439439 −1.79796 −0.0858119 −0.0429059 0.999079i 0.513662π-0.513662\pi
−0.0429059 + 0.999079i 0.513662π0.513662\pi
440440 0 0
441441 0 0
442442 0 0
443443 22.0454 1.04741 0.523704 0.851900i 0.324550π-0.324550\pi
0.523704 + 0.851900i 0.324550π0.324550\pi
444444 0 0
445445 6.00000 0.284427
446446 0 0
447447 0 0
448448 0 0
449449 −8.69694 −0.410434 −0.205217 0.978717i 0.565790π-0.565790\pi
−0.205217 + 0.978717i 0.565790π0.565790\pi
450450 0 0
451451 −0.494897 −0.0233038
452452 0 0
453453 0 0
454454 0 0
455455 −2.00000 −0.0937614
456456 0 0
457457 22.0000 1.02912 0.514558 0.857455i 0.327956π-0.327956\pi
0.514558 + 0.857455i 0.327956π0.327956\pi
458458 0 0
459459 0 0
460460 0 0
461461 3.30306 0.153839 0.0769195 0.997037i 0.475492π-0.475492\pi
0.0769195 + 0.997037i 0.475492π0.475492\pi
462462 0 0
463463 13.1010 0.608856 0.304428 0.952535i 0.401535π-0.401535\pi
0.304428 + 0.952535i 0.401535π0.401535\pi
464464 0 0
465465 0 0
466466 0 0
467467 −30.9444 −1.43194 −0.715968 0.698133i 0.754014π-0.754014\pi
−0.715968 + 0.698133i 0.754014π0.754014\pi
468468 0 0
469469 −29.7980 −1.37594
470470 0 0
471471 0 0
472472 0 0
473473 1.50510 0.0692047
474474 0 0
475475 4.44949 0.204157
476476 0 0
477477 0 0
478478 0 0
479479 5.34847 0.244378 0.122189 0.992507i 0.461009π-0.461009\pi
0.122189 + 0.992507i 0.461009π0.461009\pi
480480 0 0
481481 4.89898 0.223374
482482 0 0
483483 0 0
484484 0 0
485485 11.7980 0.535718
486486 0 0
487487 −2.89898 −0.131365 −0.0656826 0.997841i 0.520922π-0.520922\pi
−0.0656826 + 0.997841i 0.520922π0.520922\pi
488488 0 0
489489 0 0
490490 0 0
491491 34.2929 1.54761 0.773807 0.633421i 0.218350π-0.218350\pi
0.773807 + 0.633421i 0.218350π0.218350\pi
492492 0 0
493493 −11.5959 −0.522254
494494 0 0
495495 0 0
496496 0 0
497497 16.8990 0.758023
498498 0 0
499499 −21.3485 −0.955689 −0.477844 0.878445i 0.658582π-0.658582\pi
−0.477844 + 0.878445i 0.658582π0.658582\pi
500500 0 0
501501 0 0
502502 0 0
503503 −26.9444 −1.20139 −0.600695 0.799478i 0.705110π-0.705110\pi
−0.600695 + 0.799478i 0.705110π0.705110\pi
504504 0 0
505505 3.79796 0.169007
506506 0 0
507507 0 0
508508 0 0
509509 −26.8990 −1.19228 −0.596138 0.802882i 0.703299π-0.703299\pi
−0.596138 + 0.802882i 0.703299π0.703299\pi
510510 0 0
511511 −29.3939 −1.30031
512512 0 0
513513 0 0
514514 0 0
515515 −3.34847 −0.147551
516516 0 0
517517 −0.898979 −0.0395371
518518 0 0
519519 0 0
520520 0 0
521521 −6.20204 −0.271716 −0.135858 0.990728i 0.543379π-0.543379\pi
−0.135858 + 0.990728i 0.543379π0.543379\pi
522522 0 0
523523 39.3485 1.72059 0.860294 0.509798i 0.170280π-0.170280\pi
0.860294 + 0.509798i 0.170280π0.170280\pi
524524 0 0
525525 0 0
526526 0 0
527527 −1.30306 −0.0567623
528528 0 0
529529 −20.5959 −0.895475
530530 0 0
531531 0 0
532532 0 0
533533 1.10102 0.0476905
534534 0 0
535535 −12.2474 −0.529503
536536 0 0
537537 0 0
538538 0 0
539539 −1.34847 −0.0580827
540540 0 0
541541 5.10102 0.219310 0.109655 0.993970i 0.465025π-0.465025\pi
0.109655 + 0.993970i 0.465025π0.465025\pi
542542 0 0
543543 0 0
544544 0 0
545545 10.0000 0.428353
546546 0 0
547547 −0.651531 −0.0278574 −0.0139287 0.999903i 0.504434π-0.504434\pi
−0.0139287 + 0.999903i 0.504434π0.504434\pi
548548 0 0
549549 0 0
550550 0 0
551551 −17.7980 −0.758219
552552 0 0
553553 −9.79796 −0.416652
554554 0 0
555555 0 0
556556 0 0
557557 1.30306 0.0552125 0.0276062 0.999619i 0.491212π-0.491212\pi
0.0276062 + 0.999619i 0.491212π0.491212\pi
558558 0 0
559559 −3.34847 −0.141625
560560 0 0
561561 0 0
562562 0 0
563563 −7.75255 −0.326731 −0.163366 0.986566i 0.552235π-0.552235\pi
−0.163366 + 0.986566i 0.552235π0.552235\pi
564564 0 0
565565 10.8990 0.458524
566566 0 0
567567 0 0
568568 0 0
569569 −10.2020 −0.427692 −0.213846 0.976867i 0.568599π-0.568599\pi
−0.213846 + 0.976867i 0.568599π0.568599\pi
570570 0 0
571571 −28.4949 −1.19247 −0.596237 0.802808i 0.703338π-0.703338\pi
−0.596237 + 0.802808i 0.703338π0.703338\pi
572572 0 0
573573 0 0
574574 0 0
575575 1.55051 0.0646607
576576 0 0
577577 27.1010 1.12823 0.564115 0.825696i 0.309217π-0.309217\pi
0.564115 + 0.825696i 0.309217π0.309217\pi
578578 0 0
579579 0 0
580580 0 0
581581 −4.00000 −0.165948
582582 0 0
583583 −4.89898 −0.202895
584584 0 0
585585 0 0
586586 0 0
587587 −10.8990 −0.449849 −0.224925 0.974376i 0.572214π-0.572214\pi
−0.224925 + 0.974376i 0.572214π0.572214\pi
588588 0 0
589589 −2.00000 −0.0824086
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 5.79796 0.237693
596596 0 0
597597 0 0
598598 0 0
599599 −28.8990 −1.18078 −0.590390 0.807118i 0.701026π-0.701026\pi
−0.590390 + 0.807118i 0.701026π0.701026\pi
600600 0 0
601601 −33.5959 −1.37041 −0.685203 0.728352i 0.740287π-0.740287\pi
−0.685203 + 0.728352i 0.740287π0.740287\pi
602602 0 0
603603 0 0
604604 0 0
605605 10.7980 0.438999
606606 0 0
607607 −21.5505 −0.874708 −0.437354 0.899289i 0.644084π-0.644084\pi
−0.437354 + 0.899289i 0.644084π0.644084\pi
608608 0 0
609609 0 0
610610 0 0
611611 2.00000 0.0809113
612612 0 0
613613 45.1918 1.82528 0.912641 0.408763i 0.134040π-0.134040\pi
0.912641 + 0.408763i 0.134040π0.134040\pi
614614 0 0
615615 0 0
616616 0 0
617617 35.3939 1.42490 0.712452 0.701721i 0.247585π-0.247585\pi
0.712452 + 0.701721i 0.247585π0.247585\pi
618618 0 0
619619 5.34847 0.214973 0.107487 0.994207i 0.465720π-0.465720\pi
0.107487 + 0.994207i 0.465720π0.465720\pi
620620 0 0
621621 0 0
622622 0 0
623623 12.0000 0.480770
624624 0 0
625625 1.00000 0.0400000
626626 0 0
627627 0 0
628628 0 0
629629 −14.2020 −0.566272
630630 0 0
631631 16.4495 0.654844 0.327422 0.944878i 0.393820π-0.393820\pi
0.327422 + 0.944878i 0.393820π0.393820\pi
632632 0 0
633633 0 0
634634 0 0
635635 19.3485 0.767821
636636 0 0
637637 3.00000 0.118864
638638 0 0
639639 0 0
640640 0 0
641641 35.3939 1.39797 0.698987 0.715134i 0.253634π-0.253634\pi
0.698987 + 0.715134i 0.253634π0.253634\pi
642642 0 0
643643 30.0000 1.18308 0.591542 0.806274i 0.298519π-0.298519\pi
0.591542 + 0.806274i 0.298519π0.298519\pi
644644 0 0
645645 0 0
646646 0 0
647647 14.9444 0.587524 0.293762 0.955879i 0.405093π-0.405093\pi
0.293762 + 0.955879i 0.405093π0.405093\pi
648648 0 0
649649 −2.40408 −0.0943685
650650 0 0
651651 0 0
652652 0 0
653653 43.7980 1.71395 0.856973 0.515361i 0.172342π-0.172342\pi
0.856973 + 0.515361i 0.172342π0.172342\pi
654654 0 0
655655 19.5959 0.765676
656656 0 0
657657 0 0
658658 0 0
659659 14.6969 0.572511 0.286256 0.958153i 0.407589π-0.407589\pi
0.286256 + 0.958153i 0.407589π0.407589\pi
660660 0 0
661661 39.7980 1.54796 0.773981 0.633209i 0.218263π-0.218263\pi
0.773981 + 0.633209i 0.218263π0.218263\pi
662662 0 0
663663 0 0
664664 0 0
665665 8.89898 0.345088
666666 0 0
667667 −6.20204 −0.240144
668668 0 0
669669 0 0
670670 0 0
671671 6.20204 0.239427
672672 0 0
673673 −1.10102 −0.0424412 −0.0212206 0.999775i 0.506755π-0.506755\pi
−0.0212206 + 0.999775i 0.506755π0.506755\pi
674674 0 0
675675 0 0
676676 0 0
677677 40.6969 1.56411 0.782055 0.623209i 0.214171π-0.214171\pi
0.782055 + 0.623209i 0.214171π0.214171\pi
678678 0 0
679679 23.5959 0.905528
680680 0 0
681681 0 0
682682 0 0
683683 −42.4949 −1.62602 −0.813011 0.582248i 0.802173π-0.802173\pi
−0.813011 + 0.582248i 0.802173π0.802173\pi
684684 0 0
685685 −14.0000 −0.534913
686686 0 0
687687 0 0
688688 0 0
689689 10.8990 0.415218
690690 0 0
691691 14.6515 0.557370 0.278685 0.960382i 0.410101π-0.410101\pi
0.278685 + 0.960382i 0.410101π0.410101\pi
692692 0 0
693693 0 0
694694 0 0
695695 −7.10102 −0.269357
696696 0 0
697697 −3.19184 −0.120899
698698 0 0
699699 0 0
700700 0 0
701701 37.1918 1.40472 0.702358 0.711824i 0.252131π-0.252131\pi
0.702358 + 0.711824i 0.252131π0.252131\pi
702702 0 0
703703 −21.7980 −0.822126
704704 0 0
705705 0 0
706706 0 0
707707 7.59592 0.285674
708708 0 0
709709 −32.2929 −1.21278 −0.606392 0.795166i 0.707384π-0.707384\pi
−0.606392 + 0.795166i 0.707384π0.707384\pi
710710 0 0
711711 0 0
712712 0 0
713713 −0.696938 −0.0261006
714714 0 0
715715 0.449490 0.0168100
716716 0 0
717717 0 0
718718 0 0
719719 −20.0000 −0.745874 −0.372937 0.927857i 0.621649π-0.621649\pi
−0.372937 + 0.927857i 0.621649π0.621649\pi
720720 0 0
721721 −6.69694 −0.249407
722722 0 0
723723 0 0
724724 0 0
725725 −4.00000 −0.148556
726726 0 0
727727 −18.0454 −0.669267 −0.334634 0.942348i 0.608613π-0.608613\pi
−0.334634 + 0.942348i 0.608613π0.608613\pi
728728 0 0
729729 0 0
730730 0 0
731731 9.70714 0.359032
732732 0 0
733733 −6.00000 −0.221615 −0.110808 0.993842i 0.535344π-0.535344\pi
−0.110808 + 0.993842i 0.535344π0.535344\pi
734734 0 0
735735 0 0
736736 0 0
737737 6.69694 0.246685
738738 0 0
739739 6.24745 0.229816 0.114908 0.993376i 0.463343π-0.463343\pi
0.114908 + 0.993376i 0.463343π0.463343\pi
740740 0 0
741741 0 0
742742 0 0
743743 −35.3939 −1.29848 −0.649238 0.760586i 0.724912π-0.724912\pi
−0.649238 + 0.760586i 0.724912π0.724912\pi
744744 0 0
745745 −7.79796 −0.285695
746746 0 0
747747 0 0
748748 0 0
749749 −24.4949 −0.895024
750750 0 0
751751 −31.1010 −1.13489 −0.567446 0.823410i 0.692069π-0.692069\pi
−0.567446 + 0.823410i 0.692069π0.692069\pi
752752 0 0
753753 0 0
754754 0 0
755755 −17.3485 −0.631375
756756 0 0
757757 26.4949 0.962973 0.481487 0.876453i 0.340097π-0.340097\pi
0.481487 + 0.876453i 0.340097π0.340097\pi
758758 0 0
759759 0 0
760760 0 0
761761 10.4041 0.377148 0.188574 0.982059i 0.439614π-0.439614\pi
0.188574 + 0.982059i 0.439614π0.439614\pi
762762 0 0
763763 20.0000 0.724049
764764 0 0
765765 0 0
766766 0 0
767767 5.34847 0.193122
768768 0 0
769769 39.3939 1.42058 0.710290 0.703909i 0.248564π-0.248564\pi
0.710290 + 0.703909i 0.248564π0.248564\pi
770770 0 0
771771 0 0
772772 0 0
773773 −44.0908 −1.58584 −0.792918 0.609328i 0.791439π-0.791439\pi
−0.792918 + 0.609328i 0.791439π0.791439\pi
774774 0 0
775775 −0.449490 −0.0161461
776776 0 0
777777 0 0
778778 0 0
779779 −4.89898 −0.175524
780780 0 0
781781 −3.79796 −0.135902
782782 0 0
783783 0 0
784784 0 0
785785 −10.0000 −0.356915
786786 0 0
787787 −38.0000 −1.35455 −0.677277 0.735728i 0.736840π-0.736840\pi
−0.677277 + 0.735728i 0.736840π0.736840\pi
788788 0 0
789789 0 0
790790 0 0
791791 21.7980 0.775046
792792 0 0
793793 −13.7980 −0.489980
794794 0 0
795795 0 0
796796 0 0
797797 −27.7980 −0.984654 −0.492327 0.870410i 0.663854π-0.663854\pi
−0.492327 + 0.870410i 0.663854π0.663854\pi
798798 0 0
799799 −5.79796 −0.205117
800800 0 0
801801 0 0
802802 0 0
803803 6.60612 0.233125
804804 0 0
805805 3.10102 0.109297
806806 0 0
807807 0 0
808808 0 0
809809 −12.0000 −0.421898 −0.210949 0.977497i 0.567655π-0.567655\pi
−0.210949 + 0.977497i 0.567655π0.567655\pi
810810 0 0
811811 53.8434 1.89070 0.945348 0.326063i 0.105722π-0.105722\pi
0.945348 + 0.326063i 0.105722π0.105722\pi
812812 0 0
813813 0 0
814814 0 0
815815 −18.8990 −0.662002
816816 0 0
817817 14.8990 0.521249
818818 0 0
819819 0 0
820820 0 0
821821 53.1918 1.85641 0.928204 0.372072i 0.121352π-0.121352\pi
0.928204 + 0.372072i 0.121352π0.121352\pi
822822 0 0
823823 −30.4495 −1.06140 −0.530701 0.847559i 0.678071π-0.678071\pi
−0.530701 + 0.847559i 0.678071π0.678071\pi
824824 0 0
825825 0 0
826826 0 0
827827 57.1918 1.98875 0.994377 0.105893i 0.0337702π-0.0337702\pi
0.994377 + 0.105893i 0.0337702π0.0337702\pi
828828 0 0
829829 −20.0000 −0.694629 −0.347314 0.937749i 0.612906π-0.612906\pi
−0.347314 + 0.937749i 0.612906π0.612906\pi
830830 0 0
831831 0 0
832832 0 0
833833 −8.69694 −0.301331
834834 0 0
835835 −18.0000 −0.622916
836836 0 0
837837 0 0
838838 0 0
839839 −19.5505 −0.674959 −0.337479 0.941333i 0.609574π-0.609574\pi
−0.337479 + 0.941333i 0.609574π0.609574\pi
840840 0 0
841841 −13.0000 −0.448276
842842 0 0
843843 0 0
844844 0 0
845845 −1.00000 −0.0344010
846846 0 0
847847 21.5959 0.742045
848848 0 0
849849 0 0
850850 0 0
851851 −7.59592 −0.260385
852852 0 0
853853 −18.6969 −0.640171 −0.320085 0.947389i 0.603712π-0.603712\pi
−0.320085 + 0.947389i 0.603712π0.603712\pi
854854 0 0
855855 0 0
856856 0 0
857857 −35.3939 −1.20903 −0.604516 0.796593i 0.706633π-0.706633\pi
−0.604516 + 0.796593i 0.706633π0.706633\pi
858858 0 0
859859 30.6969 1.04737 0.523683 0.851913i 0.324558π-0.324558\pi
0.523683 + 0.851913i 0.324558π0.324558\pi
860860 0 0
861861 0 0
862862 0 0
863863 23.3939 0.796337 0.398168 0.917312i 0.369646π-0.369646\pi
0.398168 + 0.917312i 0.369646π0.369646\pi
864864 0 0
865865 −2.89898 −0.0985683
866866 0 0
867867 0 0
868868 0 0
869869 2.20204 0.0746991
870870 0 0
871871 −14.8990 −0.504833
872872 0 0
873873 0 0
874874 0 0
875875 2.00000 0.0676123
876876 0 0
877877 17.5959 0.594172 0.297086 0.954851i 0.403985π-0.403985\pi
0.297086 + 0.954851i 0.403985π0.403985\pi
878878 0 0
879879 0 0
880880 0 0
881881 −9.79796 −0.330102 −0.165051 0.986285i 0.552779π-0.552779\pi
−0.165051 + 0.986285i 0.552779π0.552779\pi
882882 0 0
883883 11.3485 0.381906 0.190953 0.981599i 0.438842π-0.438842\pi
0.190953 + 0.981599i 0.438842π0.438842\pi
884884 0 0
885885 0 0
886886 0 0
887887 4.24745 0.142615 0.0713077 0.997454i 0.477283π-0.477283\pi
0.0713077 + 0.997454i 0.477283π0.477283\pi
888888 0 0
889889 38.6969 1.29785
890890 0 0
891891 0 0
892892 0 0
893893 −8.89898 −0.297793
894894 0 0
895895 −8.00000 −0.267411
896896 0 0
897897 0 0
898898 0 0
899899 1.79796 0.0599653
900900 0 0
901901 −31.5959 −1.05261
902902 0 0
903903 0 0
904904 0 0
905905 13.7980 0.458660
906906 0 0
907907 −43.8434 −1.45580 −0.727898 0.685686i 0.759502π-0.759502\pi
−0.727898 + 0.685686i 0.759502π0.759502\pi
908908 0 0
909909 0 0
910910 0 0
911911 −49.3939 −1.63649 −0.818246 0.574868i 0.805053π-0.805053\pi
−0.818246 + 0.574868i 0.805053π0.805053\pi
912912 0 0
913913 0.898979 0.0297519
914914 0 0
915915 0 0
916916 0 0
917917 39.1918 1.29423
918918 0 0
919919 11.1010 0.366189 0.183094 0.983095i 0.441389π-0.441389\pi
0.183094 + 0.983095i 0.441389π0.441389\pi
920920 0 0
921921 0 0
922922 0 0
923923 8.44949 0.278118
924924 0 0
925925 −4.89898 −0.161077
926926 0 0
927927 0 0
928928 0 0
929929 −24.6969 −0.810280 −0.405140 0.914255i 0.632777π-0.632777\pi
−0.405140 + 0.914255i 0.632777π0.632777\pi
930930 0 0
931931 −13.3485 −0.437478
932932 0 0
933933 0 0
934934 0 0
935935 −1.30306 −0.0426147
936936 0 0
937937 −19.3939 −0.633570 −0.316785 0.948497i 0.602603π-0.602603\pi
−0.316785 + 0.948497i 0.602603π0.602603\pi
938938 0 0
939939 0 0
940940 0 0
941941 23.3031 0.759658 0.379829 0.925057i 0.375983π-0.375983\pi
0.379829 + 0.925057i 0.375983π0.375983\pi
942942 0 0
943943 −1.70714 −0.0555922
944944 0 0
945945 0 0
946946 0 0
947947 −47.7980 −1.55322 −0.776612 0.629979i 0.783064π-0.783064\pi
−0.776612 + 0.629979i 0.783064π0.783064\pi
948948 0 0
949949 −14.6969 −0.477083
950950 0 0
951951 0 0
952952 0 0
953953 57.1918 1.85263 0.926313 0.376756i 0.122960π-0.122960\pi
0.926313 + 0.376756i 0.122960π0.122960\pi
954954 0 0
955955 −17.7980 −0.575928
956956 0 0
957957 0 0
958958 0 0
959959 −28.0000 −0.904167
960960 0 0
961961 −30.7980 −0.993483
962962 0 0
963963 0 0
964964 0 0
965965 −19.7980 −0.637319
966966 0 0
967967 −25.1010 −0.807194 −0.403597 0.914937i 0.632240π-0.632240\pi
−0.403597 + 0.914937i 0.632240π0.632240\pi
968968 0 0
969969 0 0
970970 0 0
971971 27.5959 0.885595 0.442798 0.896622i 0.353986π-0.353986\pi
0.442798 + 0.896622i 0.353986π0.353986\pi
972972 0 0
973973 −14.2020 −0.455297
974974 0 0
975975 0 0
976976 0 0
977977 1.30306 0.0416886 0.0208443 0.999783i 0.493365π-0.493365\pi
0.0208443 + 0.999783i 0.493365π0.493365\pi
978978 0 0
979979 −2.69694 −0.0861945
980980 0 0
981981 0 0
982982 0 0
983983 58.8990 1.87859 0.939293 0.343117i 0.111483π-0.111483\pi
0.939293 + 0.343117i 0.111483π0.111483\pi
984984 0 0
985985 −4.20204 −0.133888
986986 0 0
987987 0 0
988988 0 0
989989 5.19184 0.165091
990990 0 0
991991 30.2020 0.959399 0.479700 0.877433i 0.340746π-0.340746\pi
0.479700 + 0.877433i 0.340746π0.340746\pi
992992 0 0
993993 0 0
994994 0 0
995995 −13.7980 −0.437425
996996 0 0
997997 25.1010 0.794957 0.397479 0.917611i 0.369885π-0.369885\pi
0.397479 + 0.917611i 0.369885π0.369885\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 9360.2.a.cc.1.2 2
3.2 odd 2 1040.2.a.k.1.1 2
4.3 odd 2 4680.2.a.z.1.1 2
12.11 even 2 520.2.a.f.1.2 2
15.14 odd 2 5200.2.a.bv.1.2 2
24.5 odd 2 4160.2.a.ba.1.2 2
24.11 even 2 4160.2.a.bg.1.1 2
60.23 odd 4 2600.2.d.h.1249.3 4
60.47 odd 4 2600.2.d.h.1249.2 4
60.59 even 2 2600.2.a.q.1.1 2
156.155 even 2 6760.2.a.s.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
520.2.a.f.1.2 2 12.11 even 2
1040.2.a.k.1.1 2 3.2 odd 2
2600.2.a.q.1.1 2 60.59 even 2
2600.2.d.h.1249.2 4 60.47 odd 4
2600.2.d.h.1249.3 4 60.23 odd 4
4160.2.a.ba.1.2 2 24.5 odd 2
4160.2.a.bg.1.1 2 24.11 even 2
4680.2.a.z.1.1 2 4.3 odd 2
5200.2.a.bv.1.2 2 15.14 odd 2
6760.2.a.s.1.2 2 156.155 even 2
9360.2.a.cc.1.2 2 1.1 even 1 trivial