Properties

Label 3168.2.a.bc.1.2
Level 31683168
Weight 22
Character 3168.1
Self dual yes
Analytic conductor 25.29725.297
Analytic rank 11
Dimension 22
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3168,2,Mod(1,3168)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3168, 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("3168.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 3168=253211 3168 = 2^{5} \cdot 3^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3168.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: 25.296607360325.2966073603
Analytic rank: 11
Dimension: 22
Coefficient field: Q(17)\Q(\sqrt{17})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x4 x^{2} - x - 4 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 352)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.56155-1.56155 of defining polynomial
Character χ\chi == 3168.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+0.561553q51.00000q11+2.00000q137.12311q171.12311q19+7.68466q234.68466q257.12311q295.43845q315.68466q37+8.24621q411.12311q43+4.00000q477.00000q498.24621q530.561553q55+0.315342q59+9.36932q61+1.12311q65+7.68466q6715.6847q716.00000q7313.1231q79+11.3693q834.00000q850.561553q890.630683q95+5.68466q97+O(q100)q+0.561553 q^{5} -1.00000 q^{11} +2.00000 q^{13} -7.12311 q^{17} -1.12311 q^{19} +7.68466 q^{23} -4.68466 q^{25} -7.12311 q^{29} -5.43845 q^{31} -5.68466 q^{37} +8.24621 q^{41} -1.12311 q^{43} +4.00000 q^{47} -7.00000 q^{49} -8.24621 q^{53} -0.561553 q^{55} +0.315342 q^{59} +9.36932 q^{61} +1.12311 q^{65} +7.68466 q^{67} -15.6847 q^{71} -6.00000 q^{73} -13.1231 q^{79} +11.3693 q^{83} -4.00000 q^{85} -0.561553 q^{89} -0.630683 q^{95} +5.68466 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q3q52q11+4q136q17+6q19+3q23+3q256q2915q31+q37+6q43+8q4714q49+3q55+13q596q616q65+3q67+q97+O(q100) 2 q - 3 q^{5} - 2 q^{11} + 4 q^{13} - 6 q^{17} + 6 q^{19} + 3 q^{23} + 3 q^{25} - 6 q^{29} - 15 q^{31} + q^{37} + 6 q^{43} + 8 q^{47} - 14 q^{49} + 3 q^{55} + 13 q^{59} - 6 q^{61} - 6 q^{65} + 3 q^{67}+ \cdots - 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 0.561553 0.251134 0.125567 0.992085i 0.459925π-0.459925\pi
0.125567 + 0.992085i 0.459925π0.459925\pi
66 0 0
77 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
88 0 0
99 0 0
1010 0 0
1111 −1.00000 −0.301511
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 −7.12311 −1.72761 −0.863803 0.503829i 0.831924π-0.831924\pi
−0.863803 + 0.503829i 0.831924π0.831924\pi
1818 0 0
1919 −1.12311 −0.257658 −0.128829 0.991667i 0.541122π-0.541122\pi
−0.128829 + 0.991667i 0.541122π0.541122\pi
2020 0 0
2121 0 0
2222 0 0
2323 7.68466 1.60236 0.801181 0.598422i 0.204205π-0.204205\pi
0.801181 + 0.598422i 0.204205π0.204205\pi
2424 0 0
2525 −4.68466 −0.936932
2626 0 0
2727 0 0
2828 0 0
2929 −7.12311 −1.32273 −0.661364 0.750065i 0.730022π-0.730022\pi
−0.661364 + 0.750065i 0.730022π0.730022\pi
3030 0 0
3131 −5.43845 −0.976774 −0.488387 0.872627i 0.662415π-0.662415\pi
−0.488387 + 0.872627i 0.662415π0.662415\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 0 0
3737 −5.68466 −0.934552 −0.467276 0.884111i 0.654765π-0.654765\pi
−0.467276 + 0.884111i 0.654765π0.654765\pi
3838 0 0
3939 0 0
4040 0 0
4141 8.24621 1.28784 0.643921 0.765092i 0.277307π-0.277307\pi
0.643921 + 0.765092i 0.277307π0.277307\pi
4242 0 0
4343 −1.12311 −0.171272 −0.0856360 0.996326i 0.527292π-0.527292\pi
−0.0856360 + 0.996326i 0.527292π0.527292\pi
4444 0 0
4545 0 0
4646 0 0
4747 4.00000 0.583460 0.291730 0.956501i 0.405769π-0.405769\pi
0.291730 + 0.956501i 0.405769π0.405769\pi
4848 0 0
4949 −7.00000 −1.00000
5050 0 0
5151 0 0
5252 0 0
5353 −8.24621 −1.13270 −0.566352 0.824163i 0.691646π-0.691646\pi
−0.566352 + 0.824163i 0.691646π0.691646\pi
5454 0 0
5555 −0.561553 −0.0757198
5656 0 0
5757 0 0
5858 0 0
5959 0.315342 0.0410540 0.0205270 0.999789i 0.493466π-0.493466\pi
0.0205270 + 0.999789i 0.493466π0.493466\pi
6060 0 0
6161 9.36932 1.19962 0.599809 0.800143i 0.295243π-0.295243\pi
0.599809 + 0.800143i 0.295243π0.295243\pi
6262 0 0
6363 0 0
6464 0 0
6565 1.12311 0.139304
6666 0 0
6767 7.68466 0.938830 0.469415 0.882978i 0.344465π-0.344465\pi
0.469415 + 0.882978i 0.344465π0.344465\pi
6868 0 0
6969 0 0
7070 0 0
7171 −15.6847 −1.86143 −0.930713 0.365750i 0.880813π-0.880813\pi
−0.930713 + 0.365750i 0.880813π0.880813\pi
7272 0 0
7373 −6.00000 −0.702247 −0.351123 0.936329i 0.614200π-0.614200\pi
−0.351123 + 0.936329i 0.614200π0.614200\pi
7474 0 0
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 −13.1231 −1.47646 −0.738232 0.674546i 0.764339π-0.764339\pi
−0.738232 + 0.674546i 0.764339π0.764339\pi
8080 0 0
8181 0 0
8282 0 0
8383 11.3693 1.24794 0.623972 0.781446i 0.285518π-0.285518\pi
0.623972 + 0.781446i 0.285518π0.285518\pi
8484 0 0
8585 −4.00000 −0.433861
8686 0 0
8787 0 0
8888 0 0
8989 −0.561553 −0.0595245 −0.0297622 0.999557i 0.509475π-0.509475\pi
−0.0297622 + 0.999557i 0.509475π0.509475\pi
9090 0 0
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 −0.630683 −0.0647067
9696 0 0
9797 5.68466 0.577190 0.288595 0.957451i 0.406812π-0.406812\pi
0.288595 + 0.957451i 0.406812π0.406812\pi
9898 0 0
9999 0 0
100100 0 0
101101 −4.87689 −0.485269 −0.242635 0.970118i 0.578012π-0.578012\pi
−0.242635 + 0.970118i 0.578012π0.578012\pi
102102 0 0
103103 −14.2462 −1.40372 −0.701860 0.712314i 0.747647π-0.747647\pi
−0.701860 + 0.712314i 0.747647π0.747647\pi
104104 0 0
105105 0 0
106106 0 0
107107 12.0000 1.16008 0.580042 0.814587i 0.303036π-0.303036\pi
0.580042 + 0.814587i 0.303036π0.303036\pi
108108 0 0
109109 −14.0000 −1.34096 −0.670478 0.741929i 0.733911π-0.733911\pi
−0.670478 + 0.741929i 0.733911π0.733911\pi
110110 0 0
111111 0 0
112112 0 0
113113 −11.4384 −1.07604 −0.538019 0.842933i 0.680827π-0.680827\pi
−0.538019 + 0.842933i 0.680827π0.680827\pi
114114 0 0
115115 4.31534 0.402408
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 1.00000 0.0909091
122122 0 0
123123 0 0
124124 0 0
125125 −5.43845 −0.486430
126126 0 0
127127 15.3693 1.36381 0.681903 0.731442i 0.261153π-0.261153\pi
0.681903 + 0.731442i 0.261153π0.261153\pi
128128 0 0
129129 0 0
130130 0 0
131131 −4.00000 −0.349482 −0.174741 0.984614i 0.555909π-0.555909\pi
−0.174741 + 0.984614i 0.555909π0.555909\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 0 0
137137 −13.6847 −1.16916 −0.584580 0.811336i 0.698741π-0.698741\pi
−0.584580 + 0.811336i 0.698741π0.698741\pi
138138 0 0
139139 12.0000 1.01783 0.508913 0.860818i 0.330047π-0.330047\pi
0.508913 + 0.860818i 0.330047π0.330047\pi
140140 0 0
141141 0 0
142142 0 0
143143 −2.00000 −0.167248
144144 0 0
145145 −4.00000 −0.332182
146146 0 0
147147 0 0
148148 0 0
149149 −4.87689 −0.399531 −0.199765 0.979844i 0.564018π-0.564018\pi
−0.199765 + 0.979844i 0.564018π0.564018\pi
150150 0 0
151151 15.3693 1.25074 0.625369 0.780329i 0.284949π-0.284949\pi
0.625369 + 0.780329i 0.284949π0.284949\pi
152152 0 0
153153 0 0
154154 0 0
155155 −3.05398 −0.245301
156156 0 0
157157 1.68466 0.134450 0.0672252 0.997738i 0.478585π-0.478585\pi
0.0672252 + 0.997738i 0.478585π0.478585\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 0 0
163163 −12.0000 −0.939913 −0.469956 0.882690i 0.655730π-0.655730\pi
−0.469956 + 0.882690i 0.655730π0.655730\pi
164164 0 0
165165 0 0
166166 0 0
167167 −7.36932 −0.570255 −0.285127 0.958490i 0.592036π-0.592036\pi
−0.285127 + 0.958490i 0.592036π0.592036\pi
168168 0 0
169169 −9.00000 −0.692308
170170 0 0
171171 0 0
172172 0 0
173173 −18.0000 −1.36851 −0.684257 0.729241i 0.739873π-0.739873\pi
−0.684257 + 0.729241i 0.739873π0.739873\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 0 0
179179 −7.68466 −0.574378 −0.287189 0.957874i 0.592721π-0.592721\pi
−0.287189 + 0.957874i 0.592721π0.592721\pi
180180 0 0
181181 25.0540 1.86225 0.931124 0.364704i 0.118830π-0.118830\pi
0.931124 + 0.364704i 0.118830π0.118830\pi
182182 0 0
183183 0 0
184184 0 0
185185 −3.19224 −0.234698
186186 0 0
187187 7.12311 0.520893
188188 0 0
189189 0 0
190190 0 0
191191 −7.68466 −0.556042 −0.278021 0.960575i 0.589679π-0.589679\pi
−0.278021 + 0.960575i 0.589679π0.589679\pi
192192 0 0
193193 −13.3693 −0.962344 −0.481172 0.876626i 0.659789π-0.659789\pi
−0.481172 + 0.876626i 0.659789π0.659789\pi
194194 0 0
195195 0 0
196196 0 0
197197 8.24621 0.587518 0.293759 0.955879i 0.405094π-0.405094\pi
0.293759 + 0.955879i 0.405094π0.405094\pi
198198 0 0
199199 −14.2462 −1.00989 −0.504944 0.863152i 0.668487π-0.668487\pi
−0.504944 + 0.863152i 0.668487π0.668487\pi
200200 0 0
201201 0 0
202202 0 0
203203 0 0
204204 0 0
205205 4.63068 0.323421
206206 0 0
207207 0 0
208208 0 0
209209 1.12311 0.0776868
210210 0 0
211211 16.4924 1.13539 0.567693 0.823241i 0.307836π-0.307836\pi
0.567693 + 0.823241i 0.307836π0.307836\pi
212212 0 0
213213 0 0
214214 0 0
215215 −0.630683 −0.0430122
216216 0 0
217217 0 0
218218 0 0
219219 0 0
220220 0 0
221221 −14.2462 −0.958304
222222 0 0
223223 −7.68466 −0.514603 −0.257301 0.966331i 0.582833π-0.582833\pi
−0.257301 + 0.966331i 0.582833π0.582833\pi
224224 0 0
225225 0 0
226226 0 0
227227 −20.0000 −1.32745 −0.663723 0.747978i 0.731025π-0.731025\pi
−0.663723 + 0.747978i 0.731025π0.731025\pi
228228 0 0
229229 −21.6847 −1.43296 −0.716481 0.697606i 0.754248π-0.754248\pi
−0.716481 + 0.697606i 0.754248π0.754248\pi
230230 0 0
231231 0 0
232232 0 0
233233 −7.12311 −0.466650 −0.233325 0.972399i 0.574961π-0.574961\pi
−0.233325 + 0.972399i 0.574961π0.574961\pi
234234 0 0
235235 2.24621 0.146527
236236 0 0
237237 0 0
238238 0 0
239239 0.630683 0.0407955 0.0203977 0.999792i 0.493507π-0.493507\pi
0.0203977 + 0.999792i 0.493507π0.493507\pi
240240 0 0
241241 2.63068 0.169457 0.0847286 0.996404i 0.472998π-0.472998\pi
0.0847286 + 0.996404i 0.472998π0.472998\pi
242242 0 0
243243 0 0
244244 0 0
245245 −3.93087 −0.251134
246246 0 0
247247 −2.24621 −0.142923
248248 0 0
249249 0 0
250250 0 0
251251 23.0540 1.45515 0.727577 0.686026i 0.240646π-0.240646\pi
0.727577 + 0.686026i 0.240646π0.240646\pi
252252 0 0
253253 −7.68466 −0.483130
254254 0 0
255255 0 0
256256 0 0
257257 8.24621 0.514385 0.257192 0.966360i 0.417203π-0.417203\pi
0.257192 + 0.966360i 0.417203π0.417203\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 0 0
263263 −8.00000 −0.493301 −0.246651 0.969104i 0.579330π-0.579330\pi
−0.246651 + 0.969104i 0.579330π0.579330\pi
264264 0 0
265265 −4.63068 −0.284461
266266 0 0
267267 0 0
268268 0 0
269269 −10.4924 −0.639734 −0.319867 0.947462i 0.603638π-0.603638\pi
−0.319867 + 0.947462i 0.603638π0.603638\pi
270270 0 0
271271 −13.1231 −0.797172 −0.398586 0.917131i 0.630499π-0.630499\pi
−0.398586 + 0.917131i 0.630499π0.630499\pi
272272 0 0
273273 0 0
274274 0 0
275275 4.68466 0.282496
276276 0 0
277277 2.00000 0.120168 0.0600842 0.998193i 0.480863π-0.480863\pi
0.0600842 + 0.998193i 0.480863π0.480863\pi
278278 0 0
279279 0 0
280280 0 0
281281 6.00000 0.357930 0.178965 0.983855i 0.442725π-0.442725\pi
0.178965 + 0.983855i 0.442725π0.442725\pi
282282 0 0
283283 9.75379 0.579803 0.289901 0.957057i 0.406378π-0.406378\pi
0.289901 + 0.957057i 0.406378π0.406378\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 33.7386 1.98463
290290 0 0
291291 0 0
292292 0 0
293293 10.4924 0.612974 0.306487 0.951875i 0.400846π-0.400846\pi
0.306487 + 0.951875i 0.400846π0.400846\pi
294294 0 0
295295 0.177081 0.0103101
296296 0 0
297297 0 0
298298 0 0
299299 15.3693 0.888831
300300 0 0
301301 0 0
302302 0 0
303303 0 0
304304 0 0
305305 5.26137 0.301265
306306 0 0
307307 27.3693 1.56205 0.781025 0.624500i 0.214697π-0.214697\pi
0.781025 + 0.624500i 0.214697π0.214697\pi
308308 0 0
309309 0 0
310310 0 0
311311 −18.7386 −1.06257 −0.531285 0.847193i 0.678291π-0.678291\pi
−0.531285 + 0.847193i 0.678291π0.678291\pi
312312 0 0
313313 6.31534 0.356964 0.178482 0.983943i 0.442881π-0.442881\pi
0.178482 + 0.983943i 0.442881π0.442881\pi
314314 0 0
315315 0 0
316316 0 0
317317 29.0540 1.63183 0.815917 0.578169i 0.196233π-0.196233\pi
0.815917 + 0.578169i 0.196233π0.196233\pi
318318 0 0
319319 7.12311 0.398817
320320 0 0
321321 0 0
322322 0 0
323323 8.00000 0.445132
324324 0 0
325325 −9.36932 −0.519716
326326 0 0
327327 0 0
328328 0 0
329329 0 0
330330 0 0
331331 16.3153 0.896772 0.448386 0.893840i 0.351999π-0.351999\pi
0.448386 + 0.893840i 0.351999π0.351999\pi
332332 0 0
333333 0 0
334334 0 0
335335 4.31534 0.235772
336336 0 0
337337 −6.63068 −0.361196 −0.180598 0.983557i 0.557803π-0.557803\pi
−0.180598 + 0.983557i 0.557803π0.557803\pi
338338 0 0
339339 0 0
340340 0 0
341341 5.43845 0.294508
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 0 0
347347 −27.3693 −1.46926 −0.734631 0.678467i 0.762645π-0.762645\pi
−0.734631 + 0.678467i 0.762645π0.762645\pi
348348 0 0
349349 −13.3693 −0.715643 −0.357822 0.933790i 0.616480π-0.616480\pi
−0.357822 + 0.933790i 0.616480π0.616480\pi
350350 0 0
351351 0 0
352352 0 0
353353 −24.5616 −1.30728 −0.653640 0.756806i 0.726759π-0.726759\pi
−0.653640 + 0.756806i 0.726759π0.726759\pi
354354 0 0
355355 −8.80776 −0.467468
356356 0 0
357357 0 0
358358 0 0
359359 −15.3693 −0.811162 −0.405581 0.914059i 0.632931π-0.632931\pi
−0.405581 + 0.914059i 0.632931π0.632931\pi
360360 0 0
361361 −17.7386 −0.933612
362362 0 0
363363 0 0
364364 0 0
365365 −3.36932 −0.176358
366366 0 0
367367 −0.946025 −0.0493821 −0.0246910 0.999695i 0.507860π-0.507860\pi
−0.0246910 + 0.999695i 0.507860π0.507860\pi
368368 0 0
369369 0 0
370370 0 0
371371 0 0
372372 0 0
373373 −21.3693 −1.10646 −0.553231 0.833028i 0.686605π-0.686605\pi
−0.553231 + 0.833028i 0.686605π0.686605\pi
374374 0 0
375375 0 0
376376 0 0
377377 −14.2462 −0.733717
378378 0 0
379379 18.5616 0.953443 0.476721 0.879054i 0.341825π-0.341825\pi
0.476721 + 0.879054i 0.341825π0.341825\pi
380380 0 0
381381 0 0
382382 0 0
383383 −8.31534 −0.424894 −0.212447 0.977173i 0.568143π-0.568143\pi
−0.212447 + 0.977173i 0.568143π0.568143\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 26.8078 1.35921 0.679604 0.733579i 0.262152π-0.262152\pi
0.679604 + 0.733579i 0.262152π0.262152\pi
390390 0 0
391391 −54.7386 −2.76825
392392 0 0
393393 0 0
394394 0 0
395395 −7.36932 −0.370791
396396 0 0
397397 14.0000 0.702640 0.351320 0.936255i 0.385733π-0.385733\pi
0.351320 + 0.936255i 0.385733π0.385733\pi
398398 0 0
399399 0 0
400400 0 0
401401 −22.4924 −1.12322 −0.561609 0.827403i 0.689817π-0.689817\pi
−0.561609 + 0.827403i 0.689817π0.689817\pi
402402 0 0
403403 −10.8769 −0.541817
404404 0 0
405405 0 0
406406 0 0
407407 5.68466 0.281778
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 0 0
412412 0 0
413413 0 0
414414 0 0
415415 6.38447 0.313401
416416 0 0
417417 0 0
418418 0 0
419419 18.7386 0.915442 0.457721 0.889096i 0.348666π-0.348666\pi
0.457721 + 0.889096i 0.348666π0.348666\pi
420420 0 0
421421 −10.0000 −0.487370 −0.243685 0.969854i 0.578356π-0.578356\pi
−0.243685 + 0.969854i 0.578356π0.578356\pi
422422 0 0
423423 0 0
424424 0 0
425425 33.3693 1.61865
426426 0 0
427427 0 0
428428 0 0
429429 0 0
430430 0 0
431431 38.7386 1.86597 0.932987 0.359910i 0.117192π-0.117192\pi
0.932987 + 0.359910i 0.117192π0.117192\pi
432432 0 0
433433 5.68466 0.273187 0.136594 0.990627i 0.456385π-0.456385\pi
0.136594 + 0.990627i 0.456385π0.456385\pi
434434 0 0
435435 0 0
436436 0 0
437437 −8.63068 −0.412862
438438 0 0
439439 −26.2462 −1.25266 −0.626332 0.779557i 0.715444π-0.715444\pi
−0.626332 + 0.779557i 0.715444π0.715444\pi
440440 0 0
441441 0 0
442442 0 0
443443 8.31534 0.395074 0.197537 0.980295i 0.436706π-0.436706\pi
0.197537 + 0.980295i 0.436706π0.436706\pi
444444 0 0
445445 −0.315342 −0.0149486
446446 0 0
447447 0 0
448448 0 0
449449 −2.80776 −0.132507 −0.0662533 0.997803i 0.521105π-0.521105\pi
−0.0662533 + 0.997803i 0.521105π0.521105\pi
450450 0 0
451451 −8.24621 −0.388299
452452 0 0
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 41.3693 1.93518 0.967588 0.252536i 0.0812646π-0.0812646\pi
0.967588 + 0.252536i 0.0812646π0.0812646\pi
458458 0 0
459459 0 0
460460 0 0
461461 19.1231 0.890652 0.445326 0.895369i 0.353088π-0.353088\pi
0.445326 + 0.895369i 0.353088π0.353088\pi
462462 0 0
463463 33.9309 1.57690 0.788451 0.615098i 0.210884π-0.210884\pi
0.788451 + 0.615098i 0.210884π0.210884\pi
464464 0 0
465465 0 0
466466 0 0
467467 8.31534 0.384788 0.192394 0.981318i 0.438375π-0.438375\pi
0.192394 + 0.981318i 0.438375π0.438375\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 0 0
473473 1.12311 0.0516405
474474 0 0
475475 5.26137 0.241408
476476 0 0
477477 0 0
478478 0 0
479479 −0.630683 −0.0288166 −0.0144083 0.999896i 0.504586π-0.504586\pi
−0.0144083 + 0.999896i 0.504586π0.504586\pi
480480 0 0
481481 −11.3693 −0.518396
482482 0 0
483483 0 0
484484 0 0
485485 3.19224 0.144952
486486 0 0
487487 −31.6847 −1.43577 −0.717884 0.696162i 0.754889π-0.754889\pi
−0.717884 + 0.696162i 0.754889π0.754889\pi
488488 0 0
489489 0 0
490490 0 0
491491 26.7386 1.20670 0.603349 0.797477i 0.293833π-0.293833\pi
0.603349 + 0.797477i 0.293833π0.293833\pi
492492 0 0
493493 50.7386 2.28515
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 −40.4924 −1.81269 −0.906345 0.422539i 0.861139π-0.861139\pi
−0.906345 + 0.422539i 0.861139π0.861139\pi
500500 0 0
501501 0 0
502502 0 0
503503 −15.3693 −0.685284 −0.342642 0.939466i 0.611322π-0.611322\pi
−0.342642 + 0.939466i 0.611322π0.611322\pi
504504 0 0
505505 −2.73863 −0.121868
506506 0 0
507507 0 0
508508 0 0
509509 13.6847 0.606562 0.303281 0.952901i 0.401918π-0.401918\pi
0.303281 + 0.952901i 0.401918π0.401918\pi
510510 0 0
511511 0 0
512512 0 0
513513 0 0
514514 0 0
515515 −8.00000 −0.352522
516516 0 0
517517 −4.00000 −0.175920
518518 0 0
519519 0 0
520520 0 0
521521 17.0540 0.747148 0.373574 0.927600i 0.378132π-0.378132\pi
0.373574 + 0.927600i 0.378132π0.378132\pi
522522 0 0
523523 34.1080 1.49144 0.745718 0.666261i 0.232106π-0.232106\pi
0.745718 + 0.666261i 0.232106π0.232106\pi
524524 0 0
525525 0 0
526526 0 0
527527 38.7386 1.68748
528528 0 0
529529 36.0540 1.56756
530530 0 0
531531 0 0
532532 0 0
533533 16.4924 0.714366
534534 0 0
535535 6.73863 0.291337
536536 0 0
537537 0 0
538538 0 0
539539 7.00000 0.301511
540540 0 0
541541 18.0000 0.773880 0.386940 0.922105i 0.373532π-0.373532\pi
0.386940 + 0.922105i 0.373532π0.373532\pi
542542 0 0
543543 0 0
544544 0 0
545545 −7.86174 −0.336760
546546 0 0
547547 12.0000 0.513083 0.256541 0.966533i 0.417417π-0.417417\pi
0.256541 + 0.966533i 0.417417π0.417417\pi
548548 0 0
549549 0 0
550550 0 0
551551 8.00000 0.340811
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 0 0
557557 −33.3693 −1.41390 −0.706952 0.707262i 0.749930π-0.749930\pi
−0.706952 + 0.707262i 0.749930π0.749930\pi
558558 0 0
559559 −2.24621 −0.0950046
560560 0 0
561561 0 0
562562 0 0
563563 −18.7386 −0.789739 −0.394870 0.918737i 0.629210π-0.629210\pi
−0.394870 + 0.918737i 0.629210π0.629210\pi
564564 0 0
565565 −6.42329 −0.270230
566566 0 0
567567 0 0
568568 0 0
569569 21.3693 0.895848 0.447924 0.894072i 0.352163π-0.352163\pi
0.447924 + 0.894072i 0.352163π0.352163\pi
570570 0 0
571571 12.0000 0.502184 0.251092 0.967963i 0.419210π-0.419210\pi
0.251092 + 0.967963i 0.419210π0.419210\pi
572572 0 0
573573 0 0
574574 0 0
575575 −36.0000 −1.50130
576576 0 0
577577 5.68466 0.236655 0.118328 0.992975i 0.462247π-0.462247\pi
0.118328 + 0.992975i 0.462247π0.462247\pi
578578 0 0
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 8.24621 0.341523
584584 0 0
585585 0 0
586586 0 0
587587 −28.0000 −1.15568 −0.577842 0.816149i 0.696105π-0.696105\pi
−0.577842 + 0.816149i 0.696105π0.696105\pi
588588 0 0
589589 6.10795 0.251674
590590 0 0
591591 0 0
592592 0 0
593593 25.8617 1.06201 0.531007 0.847367i 0.321814π-0.321814\pi
0.531007 + 0.847367i 0.321814π0.321814\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 34.7386 1.41938 0.709691 0.704513i 0.248835π-0.248835\pi
0.709691 + 0.704513i 0.248835π0.248835\pi
600600 0 0
601601 32.1080 1.30971 0.654855 0.755754i 0.272730π-0.272730\pi
0.654855 + 0.755754i 0.272730π0.272730\pi
602602 0 0
603603 0 0
604604 0 0
605605 0.561553 0.0228304
606606 0 0
607607 37.1231 1.50678 0.753390 0.657574i 0.228417π-0.228417\pi
0.753390 + 0.657574i 0.228417π0.228417\pi
608608 0 0
609609 0 0
610610 0 0
611611 8.00000 0.323645
612612 0 0
613613 17.3693 0.701540 0.350770 0.936462i 0.385920π-0.385920\pi
0.350770 + 0.936462i 0.385920π0.385920\pi
614614 0 0
615615 0 0
616616 0 0
617617 32.2462 1.29818 0.649092 0.760710i 0.275149π-0.275149\pi
0.649092 + 0.760710i 0.275149π0.275149\pi
618618 0 0
619619 −7.68466 −0.308873 −0.154436 0.988003i 0.549356π-0.549356\pi
−0.154436 + 0.988003i 0.549356π0.549356\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 20.3693 0.814773
626626 0 0
627627 0 0
628628 0 0
629629 40.4924 1.61454
630630 0 0
631631 −38.4233 −1.52961 −0.764804 0.644264i 0.777164π-0.777164\pi
−0.764804 + 0.644264i 0.777164π0.777164\pi
632632 0 0
633633 0 0
634634 0 0
635635 8.63068 0.342498
636636 0 0
637637 −14.0000 −0.554700
638638 0 0
639639 0 0
640640 0 0
641641 27.9309 1.10320 0.551602 0.834108i 0.314017π-0.314017\pi
0.551602 + 0.834108i 0.314017π0.314017\pi
642642 0 0
643643 −42.5616 −1.67846 −0.839232 0.543774i 0.816995π-0.816995\pi
−0.839232 + 0.543774i 0.816995π0.816995\pi
644644 0 0
645645 0 0
646646 0 0
647647 −31.6847 −1.24565 −0.622826 0.782360i 0.714016π-0.714016\pi
−0.622826 + 0.782360i 0.714016π0.714016\pi
648648 0 0
649649 −0.315342 −0.0123782
650650 0 0
651651 0 0
652652 0 0
653653 13.6847 0.535522 0.267761 0.963485i 0.413716π-0.413716\pi
0.267761 + 0.963485i 0.413716π0.413716\pi
654654 0 0
655655 −2.24621 −0.0877667
656656 0 0
657657 0 0
658658 0 0
659659 12.6307 0.492022 0.246011 0.969267i 0.420880π-0.420880\pi
0.246011 + 0.969267i 0.420880π0.420880\pi
660660 0 0
661661 −21.0540 −0.818905 −0.409452 0.912331i 0.634280π-0.634280\pi
−0.409452 + 0.912331i 0.634280π0.634280\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 −54.7386 −2.11949
668668 0 0
669669 0 0
670670 0 0
671671 −9.36932 −0.361698
672672 0 0
673673 24.7386 0.953604 0.476802 0.879011i 0.341796π-0.341796\pi
0.476802 + 0.879011i 0.341796π0.341796\pi
674674 0 0
675675 0 0
676676 0 0
677677 −37.8617 −1.45514 −0.727572 0.686031i 0.759351π-0.759351\pi
−0.727572 + 0.686031i 0.759351π0.759351\pi
678678 0 0
679679 0 0
680680 0 0
681681 0 0
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 −7.68466 −0.293616
686686 0 0
687687 0 0
688688 0 0
689689 −16.4924 −0.628311
690690 0 0
691691 −25.3002 −0.962464 −0.481232 0.876593i 0.659811π-0.659811\pi
−0.481232 + 0.876593i 0.659811π0.659811\pi
692692 0 0
693693 0 0
694694 0 0
695695 6.73863 0.255611
696696 0 0
697697 −58.7386 −2.22488
698698 0 0
699699 0 0
700700 0 0
701701 47.6155 1.79841 0.899207 0.437524i 0.144144π-0.144144\pi
0.899207 + 0.437524i 0.144144π0.144144\pi
702702 0 0
703703 6.38447 0.240795
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 10.3153 0.387401 0.193700 0.981061i 0.437951π-0.437951\pi
0.193700 + 0.981061i 0.437951π0.437951\pi
710710 0 0
711711 0 0
712712 0 0
713713 −41.7926 −1.56515
714714 0 0
715715 −1.12311 −0.0420018
716716 0 0
717717 0 0
718718 0 0
719719 −16.3153 −0.608460 −0.304230 0.952599i 0.598399π-0.598399\pi
−0.304230 + 0.952599i 0.598399π0.598399\pi
720720 0 0
721721 0 0
722722 0 0
723723 0 0
724724 0 0
725725 33.3693 1.23931
726726 0 0
727727 16.3153 0.605103 0.302551 0.953133i 0.402162π-0.402162\pi
0.302551 + 0.953133i 0.402162π0.402162\pi
728728 0 0
729729 0 0
730730 0 0
731731 8.00000 0.295891
732732 0 0
733733 −36.1080 −1.33368 −0.666839 0.745202i 0.732353π-0.732353\pi
−0.666839 + 0.745202i 0.732353π0.732353\pi
734734 0 0
735735 0 0
736736 0 0
737737 −7.68466 −0.283068
738738 0 0
739739 29.6155 1.08942 0.544712 0.838623i 0.316639π-0.316639\pi
0.544712 + 0.838623i 0.316639π0.316639\pi
740740 0 0
741741 0 0
742742 0 0
743743 30.7386 1.12769 0.563846 0.825880i 0.309321π-0.309321\pi
0.563846 + 0.825880i 0.309321π0.309321\pi
744744 0 0
745745 −2.73863 −0.100336
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 12.1771 0.444348 0.222174 0.975007i 0.428685π-0.428685\pi
0.222174 + 0.975007i 0.428685π0.428685\pi
752752 0 0
753753 0 0
754754 0 0
755755 8.63068 0.314103
756756 0 0
757757 −10.0000 −0.363456 −0.181728 0.983349i 0.558169π-0.558169\pi
−0.181728 + 0.983349i 0.558169π0.558169\pi
758758 0 0
759759 0 0
760760 0 0
761761 3.75379 0.136075 0.0680374 0.997683i 0.478326π-0.478326\pi
0.0680374 + 0.997683i 0.478326π0.478326\pi
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 0 0
767767 0.630683 0.0227726
768768 0 0
769769 −38.0000 −1.37032 −0.685158 0.728395i 0.740267π-0.740267\pi
−0.685158 + 0.728395i 0.740267π0.740267\pi
770770 0 0
771771 0 0
772772 0 0
773773 −8.24621 −0.296596 −0.148298 0.988943i 0.547379π-0.547379\pi
−0.148298 + 0.988943i 0.547379π0.547379\pi
774774 0 0
775775 25.4773 0.915170
776776 0 0
777777 0 0
778778 0 0
779779 −9.26137 −0.331823
780780 0 0
781781 15.6847 0.561241
782782 0 0
783783 0 0
784784 0 0
785785 0.946025 0.0337651
786786 0 0
787787 −12.0000 −0.427754 −0.213877 0.976861i 0.568609π-0.568609\pi
−0.213877 + 0.976861i 0.568609π0.568609\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 18.7386 0.665428
794794 0 0
795795 0 0
796796 0 0
797797 24.5616 0.870015 0.435007 0.900427i 0.356746π-0.356746\pi
0.435007 + 0.900427i 0.356746π0.356746\pi
798798 0 0
799799 −28.4924 −1.00799
800800 0 0
801801 0 0
802802 0 0
803803 6.00000 0.211735
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 8.24621 0.289921 0.144961 0.989437i 0.453694π-0.453694\pi
0.144961 + 0.989437i 0.453694π0.453694\pi
810810 0 0
811811 51.3693 1.80382 0.901910 0.431923i 0.142165π-0.142165\pi
0.901910 + 0.431923i 0.142165π0.142165\pi
812812 0 0
813813 0 0
814814 0 0
815815 −6.73863 −0.236044
816816 0 0
817817 1.26137 0.0441296
818818 0 0
819819 0 0
820820 0 0
821821 −0.738634 −0.0257785 −0.0128892 0.999917i 0.504103π-0.504103\pi
−0.0128892 + 0.999917i 0.504103π0.504103\pi
822822 0 0
823823 18.5616 0.647015 0.323508 0.946226i 0.395138π-0.395138\pi
0.323508 + 0.946226i 0.395138π0.395138\pi
824824 0 0
825825 0 0
826826 0 0
827827 −3.36932 −0.117163 −0.0585813 0.998283i 0.518658π-0.518658\pi
−0.0585813 + 0.998283i 0.518658π0.518658\pi
828828 0 0
829829 17.6847 0.614214 0.307107 0.951675i 0.400639π-0.400639\pi
0.307107 + 0.951675i 0.400639π0.400639\pi
830830 0 0
831831 0 0
832832 0 0
833833 49.8617 1.72761
834834 0 0
835835 −4.13826 −0.143210
836836 0 0
837837 0 0
838838 0 0
839839 30.4233 1.05033 0.525164 0.851001i 0.324004π-0.324004\pi
0.525164 + 0.851001i 0.324004π0.324004\pi
840840 0 0
841841 21.7386 0.749608
842842 0 0
843843 0 0
844844 0 0
845845 −5.05398 −0.173862
846846 0 0
847847 0 0
848848 0 0
849849 0 0
850850 0 0
851851 −43.6847 −1.49749
852852 0 0
853853 40.7386 1.39486 0.697432 0.716651i 0.254326π-0.254326\pi
0.697432 + 0.716651i 0.254326π0.254326\pi
854854 0 0
855855 0 0
856856 0 0
857857 −4.87689 −0.166592 −0.0832958 0.996525i 0.526545π-0.526545\pi
−0.0832958 + 0.996525i 0.526545π0.526545\pi
858858 0 0
859859 57.9309 1.97658 0.988288 0.152601i 0.0487649π-0.0487649\pi
0.988288 + 0.152601i 0.0487649π0.0487649\pi
860860 0 0
861861 0 0
862862 0 0
863863 −18.7386 −0.637871 −0.318935 0.947777i 0.603325π-0.603325\pi
−0.318935 + 0.947777i 0.603325π0.603325\pi
864864 0 0
865865 −10.1080 −0.343681
866866 0 0
867867 0 0
868868 0 0
869869 13.1231 0.445171
870870 0 0
871871 15.3693 0.520769
872872 0 0
873873 0 0
874874 0 0
875875 0 0
876876 0 0
877877 −7.26137 −0.245199 −0.122599 0.992456i 0.539123π-0.539123\pi
−0.122599 + 0.992456i 0.539123π0.539123\pi
878878 0 0
879879 0 0
880880 0 0
881881 19.3002 0.650240 0.325120 0.945673i 0.394595π-0.394595\pi
0.325120 + 0.945673i 0.394595π0.394595\pi
882882 0 0
883883 −36.0000 −1.21150 −0.605748 0.795656i 0.707126π-0.707126\pi
−0.605748 + 0.795656i 0.707126π0.707126\pi
884884 0 0
885885 0 0
886886 0 0
887887 −22.1080 −0.742312 −0.371156 0.928570i 0.621039π-0.621039\pi
−0.371156 + 0.928570i 0.621039π0.621039\pi
888888 0 0
889889 0 0
890890 0 0
891891 0 0
892892 0 0
893893 −4.49242 −0.150333
894894 0 0
895895 −4.31534 −0.144246
896896 0 0
897897 0 0
898898 0 0
899899 38.7386 1.29201
900900 0 0
901901 58.7386 1.95687
902902 0 0
903903 0 0
904904 0 0
905905 14.0691 0.467674
906906 0 0
907907 −16.4924 −0.547622 −0.273811 0.961784i 0.588284π-0.588284\pi
−0.273811 + 0.961784i 0.588284π0.588284\pi
908908 0 0
909909 0 0
910910 0 0
911911 −26.7386 −0.885890 −0.442945 0.896549i 0.646066π-0.646066\pi
−0.442945 + 0.896549i 0.646066π0.646066\pi
912912 0 0
913913 −11.3693 −0.376269
914914 0 0
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 17.6155 0.581083 0.290541 0.956862i 0.406165π-0.406165\pi
0.290541 + 0.956862i 0.406165π0.406165\pi
920920 0 0
921921 0 0
922922 0 0
923923 −31.3693 −1.03253
924924 0 0
925925 26.6307 0.875611
926926 0 0
927927 0 0
928928 0 0
929929 −22.4924 −0.737952 −0.368976 0.929439i 0.620292π-0.620292\pi
−0.368976 + 0.929439i 0.620292π0.620292\pi
930930 0 0
931931 7.86174 0.257658
932932 0 0
933933 0 0
934934 0 0
935935 4.00000 0.130814
936936 0 0
937937 −20.7386 −0.677502 −0.338751 0.940876i 0.610004π-0.610004\pi
−0.338751 + 0.940876i 0.610004π0.610004\pi
938938 0 0
939939 0 0
940940 0 0
941941 8.24621 0.268819 0.134409 0.990926i 0.457086π-0.457086\pi
0.134409 + 0.990926i 0.457086π0.457086\pi
942942 0 0
943943 63.3693 2.06359
944944 0 0
945945 0 0
946946 0 0
947947 −31.6847 −1.02961 −0.514807 0.857306i 0.672136π-0.672136\pi
−0.514807 + 0.857306i 0.672136π0.672136\pi
948948 0 0
949949 −12.0000 −0.389536
950950 0 0
951951 0 0
952952 0 0
953953 47.6155 1.54242 0.771209 0.636582i 0.219652π-0.219652\pi
0.771209 + 0.636582i 0.219652π0.219652\pi
954954 0 0
955955 −4.31534 −0.139641
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 −1.42329 −0.0459127
962962 0 0
963963 0 0
964964 0 0
965965 −7.50758 −0.241677
966966 0 0
967967 −30.7386 −0.988488 −0.494244 0.869323i 0.664555π-0.664555\pi
−0.494244 + 0.869323i 0.664555π0.664555\pi
968968 0 0
969969 0 0
970970 0 0
971971 −16.3153 −0.523584 −0.261792 0.965124i 0.584313π-0.584313\pi
−0.261792 + 0.965124i 0.584313π0.584313\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 50.0388 1.60088 0.800442 0.599410i 0.204598π-0.204598\pi
0.800442 + 0.599410i 0.204598π0.204598\pi
978978 0 0
979979 0.561553 0.0179473
980980 0 0
981981 0 0
982982 0 0
983983 −16.3153 −0.520379 −0.260189 0.965558i 0.583785π-0.583785\pi
−0.260189 + 0.965558i 0.583785π0.583785\pi
984984 0 0
985985 4.63068 0.147546
986986 0 0
987987 0 0
988988 0 0
989989 −8.63068 −0.274440
990990 0 0
991991 5.26137 0.167133 0.0835664 0.996502i 0.473369π-0.473369\pi
0.0835664 + 0.996502i 0.473369π0.473369\pi
992992 0 0
993993 0 0
994994 0 0
995995 −8.00000 −0.253617
996996 0 0
997997 25.3693 0.803454 0.401727 0.915759i 0.368410π-0.368410\pi
0.401727 + 0.915759i 0.368410π0.368410\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 3168.2.a.bc.1.2 2
3.2 odd 2 352.2.a.h.1.2 yes 2
4.3 odd 2 3168.2.a.bd.1.2 2
8.3 odd 2 6336.2.a.cv.1.1 2
8.5 even 2 6336.2.a.cw.1.1 2
12.11 even 2 352.2.a.g.1.1 2
15.14 odd 2 8800.2.a.bd.1.1 2
24.5 odd 2 704.2.a.n.1.1 2
24.11 even 2 704.2.a.o.1.2 2
33.32 even 2 3872.2.a.ba.1.2 2
48.5 odd 4 2816.2.c.s.1409.1 4
48.11 even 4 2816.2.c.t.1409.4 4
48.29 odd 4 2816.2.c.s.1409.4 4
48.35 even 4 2816.2.c.t.1409.1 4
60.59 even 2 8800.2.a.be.1.2 2
132.131 odd 2 3872.2.a.p.1.1 2
264.131 odd 2 7744.2.a.cm.1.2 2
264.197 even 2 7744.2.a.bw.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
352.2.a.g.1.1 2 12.11 even 2
352.2.a.h.1.2 yes 2 3.2 odd 2
704.2.a.n.1.1 2 24.5 odd 2
704.2.a.o.1.2 2 24.11 even 2
2816.2.c.s.1409.1 4 48.5 odd 4
2816.2.c.s.1409.4 4 48.29 odd 4
2816.2.c.t.1409.1 4 48.35 even 4
2816.2.c.t.1409.4 4 48.11 even 4
3168.2.a.bc.1.2 2 1.1 even 1 trivial
3168.2.a.bd.1.2 2 4.3 odd 2
3872.2.a.p.1.1 2 132.131 odd 2
3872.2.a.ba.1.2 2 33.32 even 2
6336.2.a.cv.1.1 2 8.3 odd 2
6336.2.a.cw.1.1 2 8.5 even 2
7744.2.a.bw.1.1 2 264.197 even 2
7744.2.a.cm.1.2 2 264.131 odd 2
8800.2.a.bd.1.1 2 15.14 odd 2
8800.2.a.be.1.2 2 60.59 even 2