Properties

Label 1800.4.f.d.649.2
Level 18001800
Weight 44
Character 1800.649
Analytic conductor 106.203106.203
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1800,4,Mod(649,1800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1800.649");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 1800=233252 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 1800.f (of order 22, degree 11, not minimal)

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: no
Analytic conductor: 106.203438010106.203438010
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2+1 x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 40)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 649.2
Root 1.00000i1.00000i of defining polynomial
Character χ\chi == 1800.649
Dual form 1800.4.f.d.649.1

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+16.0000iq736.0000q11+42.0000iq13+110.000iq17+116.000q19+16.0000iq23+198.000q29+240.000q31258.000iq37442.000q41+292.000iq43392.000iq47+87.0000q49+142.000iq53348.000q59570.000q61+692.000iq67168.000q71+134.000iq73576.000iq77784.000q79+564.000iq83+1034.00q89672.000q91382.000iq97+O(q100)q+16.0000i q^{7} -36.0000 q^{11} +42.0000i q^{13} +110.000i q^{17} +116.000 q^{19} +16.0000i q^{23} +198.000 q^{29} +240.000 q^{31} -258.000i q^{37} -442.000 q^{41} +292.000i q^{43} -392.000i q^{47} +87.0000 q^{49} +142.000i q^{53} -348.000 q^{59} -570.000 q^{61} +692.000i q^{67} -168.000 q^{71} +134.000i q^{73} -576.000i q^{77} -784.000 q^{79} +564.000i q^{83} +1034.00 q^{89} -672.000 q^{91} -382.000i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q72q11+232q19+396q29+480q31884q41+174q49696q591140q61336q711568q79+2068q891344q91+O(q100) 2 q - 72 q^{11} + 232 q^{19} + 396 q^{29} + 480 q^{31} - 884 q^{41} + 174 q^{49} - 696 q^{59} - 1140 q^{61} - 336 q^{71} - 1568 q^{79} + 2068 q^{89} - 1344 q^{91}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1800Z)×\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times.

nn 577577 901901 10011001 13511351
χ(n)\chi(n) 1-1 11 11 11

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 0
66 0 0
77 16.0000i 0.863919i 0.901893 + 0.431959i 0.142178π0.142178\pi
−0.901893 + 0.431959i 0.857822π0.857822\pi
88 0 0
99 0 0
1010 0 0
1111 −36.0000 −0.986764 −0.493382 0.869813i 0.664240π-0.664240\pi
−0.493382 + 0.869813i 0.664240π0.664240\pi
1212 0 0
1313 42.0000i 0.896054i 0.894020 + 0.448027i 0.147873π0.147873\pi
−0.894020 + 0.448027i 0.852127π0.852127\pi
1414 0 0
1515 0 0
1616 0 0
1717 110.000i 1.56935i 0.619909 + 0.784674i 0.287170π0.287170\pi
−0.619909 + 0.784674i 0.712830π0.712830\pi
1818 0 0
1919 116.000 1.40064 0.700322 0.713827i 0.253040π-0.253040\pi
0.700322 + 0.713827i 0.253040π0.253040\pi
2020 0 0
2121 0 0
2222 0 0
2323 16.0000i 0.145054i 0.997366 + 0.0725268i 0.0231063π0.0231063\pi
−0.997366 + 0.0725268i 0.976894π0.976894\pi
2424 0 0
2525 0 0
2626 0 0
2727 0 0
2828 0 0
2929 198.000 1.26785 0.633925 0.773394i 0.281443π-0.281443\pi
0.633925 + 0.773394i 0.281443π0.281443\pi
3030 0 0
3131 240.000 1.39049 0.695246 0.718772i 0.255295π-0.255295\pi
0.695246 + 0.718772i 0.255295π0.255295\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 0 0
3737 − 258.000i − 1.14635i −0.819433 0.573175i 0.805712π-0.805712\pi
0.819433 0.573175i 0.194288π-0.194288\pi
3838 0 0
3939 0 0
4040 0 0
4141 −442.000 −1.68363 −0.841815 0.539767i 0.818512π-0.818512\pi
−0.841815 + 0.539767i 0.818512π0.818512\pi
4242 0 0
4343 292.000i 1.03557i 0.855510 + 0.517786i 0.173244π0.173244\pi
−0.855510 + 0.517786i 0.826756π0.826756\pi
4444 0 0
4545 0 0
4646 0 0
4747 − 392.000i − 1.21658i −0.793716 0.608288i 0.791857π-0.791857\pi
0.793716 0.608288i 0.208143π-0.208143\pi
4848 0 0
4949 87.0000 0.253644
5050 0 0
5151 0 0
5252 0 0
5353 142.000i 0.368023i 0.982924 + 0.184011i 0.0589083π0.0589083\pi
−0.982924 + 0.184011i 0.941092π0.941092\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 0 0
5959 −348.000 −0.767894 −0.383947 0.923355i 0.625435π-0.625435\pi
−0.383947 + 0.923355i 0.625435π0.625435\pi
6060 0 0
6161 −570.000 −1.19641 −0.598205 0.801343i 0.704119π-0.704119\pi
−0.598205 + 0.801343i 0.704119π0.704119\pi
6262 0 0
6363 0 0
6464 0 0
6565 0 0
6666 0 0
6767 692.000i 1.26181i 0.775860 + 0.630905i 0.217316π0.217316\pi
−0.775860 + 0.630905i 0.782684π0.782684\pi
6868 0 0
6969 0 0
7070 0 0
7171 −168.000 −0.280816 −0.140408 0.990094i 0.544841π-0.544841\pi
−0.140408 + 0.990094i 0.544841π0.544841\pi
7272 0 0
7373 134.000i 0.214843i 0.994214 + 0.107421i 0.0342594π0.0342594\pi
−0.994214 + 0.107421i 0.965741π0.965741\pi
7474 0 0
7575 0 0
7676 0 0
7777 − 576.000i − 0.852484i
7878 0 0
7979 −784.000 −1.11654 −0.558271 0.829658i 0.688535π-0.688535\pi
−0.558271 + 0.829658i 0.688535π0.688535\pi
8080 0 0
8181 0 0
8282 0 0
8383 564.000i 0.745868i 0.927858 + 0.372934i 0.121648π0.121648\pi
−0.927858 + 0.372934i 0.878352π0.878352\pi
8484 0 0
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 1034.00 1.23150 0.615752 0.787940i 0.288852π-0.288852\pi
0.615752 + 0.787940i 0.288852π0.288852\pi
9090 0 0
9191 −672.000 −0.774118
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 0 0
9797 − 382.000i − 0.399858i −0.979810 0.199929i 0.935929π-0.935929\pi
0.979810 0.199929i 0.0640711π-0.0640711\pi
9898 0 0
9999 0 0
100100 0 0
101101 674.000 0.664015 0.332007 0.943277i 0.392274π-0.392274\pi
0.332007 + 0.943277i 0.392274π0.392274\pi
102102 0 0
103103 992.000i 0.948977i 0.880262 + 0.474489i 0.157367π0.157367\pi
−0.880262 + 0.474489i 0.842633π0.842633\pi
104104 0 0
105105 0 0
106106 0 0
107107 500.000i 0.451746i 0.974157 + 0.225873i 0.0725234π0.0725234\pi
−0.974157 + 0.225873i 0.927477π0.927477\pi
108108 0 0
109109 −1046.00 −0.919162 −0.459581 0.888136i 0.652000π-0.652000\pi
−0.459581 + 0.888136i 0.652000π0.652000\pi
110110 0 0
111111 0 0
112112 0 0
113113 − 558.000i − 0.464533i −0.972652 0.232266i 0.925386π-0.925386\pi
0.972652 0.232266i 0.0746141π-0.0746141\pi
114114 0 0
115115 0 0
116116 0 0
117117 0 0
118118 0 0
119119 −1760.00 −1.35579
120120 0 0
121121 −35.0000 −0.0262960
122122 0 0
123123 0 0
124124 0 0
125125 0 0
126126 0 0
127127 − 328.000i − 0.229176i −0.993413 0.114588i 0.963445π-0.963445\pi
0.993413 0.114588i 0.0365547π-0.0365547\pi
128128 0 0
129129 0 0
130130 0 0
131131 212.000 0.141393 0.0706967 0.997498i 0.477478π-0.477478\pi
0.0706967 + 0.997498i 0.477478π0.477478\pi
132132 0 0
133133 1856.00i 1.21004i
134134 0 0
135135 0 0
136136 0 0
137137 − 1434.00i − 0.894269i −0.894467 0.447135i 0.852444π-0.852444\pi
0.894467 0.447135i 0.147556π-0.147556\pi
138138 0 0
139139 −2196.00 −1.34002 −0.670008 0.742354i 0.733709π-0.733709\pi
−0.670008 + 0.742354i 0.733709π0.733709\pi
140140 0 0
141141 0 0
142142 0 0
143143 − 1512.00i − 0.884194i
144144 0 0
145145 0 0
146146 0 0
147147 0 0
148148 0 0
149149 −2418.00 −1.32946 −0.664732 0.747081i 0.731454π-0.731454\pi
−0.664732 + 0.747081i 0.731454π0.731454\pi
150150 0 0
151151 3672.00 1.97896 0.989481 0.144666i 0.0462108π-0.0462108\pi
0.989481 + 0.144666i 0.0462108π0.0462108\pi
152152 0 0
153153 0 0
154154 0 0
155155 0 0
156156 0 0
157157 358.000i 0.181984i 0.995852 + 0.0909921i 0.0290038π0.0290038\pi
−0.995852 + 0.0909921i 0.970996π0.970996\pi
158158 0 0
159159 0 0
160160 0 0
161161 −256.000 −0.125314
162162 0 0
163163 − 2564.00i − 1.23207i −0.787717 0.616037i 0.788737π-0.788737\pi
0.787717 0.616037i 0.211263π-0.211263\pi
164164 0 0
165165 0 0
166166 0 0
167167 3056.00i 1.41605i 0.706187 + 0.708025i 0.250414π0.250414\pi
−0.706187 + 0.708025i 0.749586π0.749586\pi
168168 0 0
169169 433.000 0.197087
170170 0 0
171171 0 0
172172 0 0
173173 − 234.000i − 0.102836i −0.998677 0.0514182i 0.983626π-0.983626\pi
0.998677 0.0514182i 0.0163741π-0.0163741\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 0 0
179179 524.000 0.218802 0.109401 0.993998i 0.465107π-0.465107\pi
0.109401 + 0.993998i 0.465107π0.465107\pi
180180 0 0
181181 −1138.00 −0.467331 −0.233665 0.972317i 0.575072π-0.575072\pi
−0.233665 + 0.972317i 0.575072π0.575072\pi
182182 0 0
183183 0 0
184184 0 0
185185 0 0
186186 0 0
187187 − 3960.00i − 1.54858i
188188 0 0
189189 0 0
190190 0 0
191191 −1520.00 −0.575829 −0.287915 0.957656i 0.592962π-0.592962\pi
−0.287915 + 0.957656i 0.592962π0.592962\pi
192192 0 0
193193 2142.00i 0.798884i 0.916759 + 0.399442i 0.130796π0.130796\pi
−0.916759 + 0.399442i 0.869204π0.869204\pi
194194 0 0
195195 0 0
196196 0 0
197197 2306.00i 0.833988i 0.908909 + 0.416994i 0.136916π0.136916\pi
−0.908909 + 0.416994i 0.863084π0.863084\pi
198198 0 0
199199 −3288.00 −1.17126 −0.585628 0.810580i 0.699152π-0.699152\pi
−0.585628 + 0.810580i 0.699152π0.699152\pi
200200 0 0
201201 0 0
202202 0 0
203203 3168.00i 1.09532i
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 −4176.00 −1.38211
210210 0 0
211211 −3876.00 −1.26462 −0.632310 0.774715i 0.717893π-0.717893\pi
−0.632310 + 0.774715i 0.717893π0.717893\pi
212212 0 0
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 3840.00i 1.20127i
218218 0 0
219219 0 0
220220 0 0
221221 −4620.00 −1.40622
222222 0 0
223223 5688.00i 1.70806i 0.520226 + 0.854028i 0.325848π0.325848\pi
−0.520226 + 0.854028i 0.674152π0.674152\pi
224224 0 0
225225 0 0
226226 0 0
227227 2796.00i 0.817520i 0.912642 + 0.408760i 0.134039π0.134039\pi
−0.912642 + 0.408760i 0.865961π0.865961\pi
228228 0 0
229229 −4446.00 −1.28297 −0.641485 0.767136i 0.721681π-0.721681\pi
−0.641485 + 0.767136i 0.721681π0.721681\pi
230230 0 0
231231 0 0
232232 0 0
233233 2522.00i 0.709106i 0.935036 + 0.354553i 0.115367π0.115367\pi
−0.935036 + 0.354553i 0.884633π0.884633\pi
234234 0 0
235235 0 0
236236 0 0
237237 0 0
238238 0 0
239239 816.000 0.220848 0.110424 0.993885i 0.464779π-0.464779\pi
0.110424 + 0.993885i 0.464779π0.464779\pi
240240 0 0
241241 −5422.00 −1.44922 −0.724609 0.689160i 0.757980π-0.757980\pi
−0.724609 + 0.689160i 0.757980π0.757980\pi
242242 0 0
243243 0 0
244244 0 0
245245 0 0
246246 0 0
247247 4872.00i 1.25505i
248248 0 0
249249 0 0
250250 0 0
251251 5900.00 1.48368 0.741842 0.670575i 0.233952π-0.233952\pi
0.741842 + 0.670575i 0.233952π0.233952\pi
252252 0 0
253253 − 576.000i − 0.143134i
254254 0 0
255255 0 0
256256 0 0
257257 − 5250.00i − 1.27426i −0.770754 0.637132i 0.780120π-0.780120\pi
0.770754 0.637132i 0.219880π-0.219880\pi
258258 0 0
259259 4128.00 0.990353
260260 0 0
261261 0 0
262262 0 0
263263 6240.00i 1.46302i 0.681829 + 0.731511i 0.261185π0.261185\pi
−0.681829 + 0.731511i 0.738815π0.738815\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 0 0
269269 −714.000 −0.161834 −0.0809170 0.996721i 0.525785π-0.525785\pi
−0.0809170 + 0.996721i 0.525785π0.525785\pi
270270 0 0
271271 2144.00 0.480586 0.240293 0.970700i 0.422757π-0.422757\pi
0.240293 + 0.970700i 0.422757π0.422757\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 0 0
277277 − 4466.00i − 0.968722i −0.874868 0.484361i 0.839052π-0.839052\pi
0.874868 0.484361i 0.160948π-0.160948\pi
278278 0 0
279279 0 0
280280 0 0
281281 5302.00 1.12559 0.562795 0.826596i 0.309726π-0.309726\pi
0.562795 + 0.826596i 0.309726π0.309726\pi
282282 0 0
283283 6932.00i 1.45606i 0.685546 + 0.728029i 0.259564π0.259564\pi
−0.685546 + 0.728029i 0.740436π0.740436\pi
284284 0 0
285285 0 0
286286 0 0
287287 − 7072.00i − 1.45452i
288288 0 0
289289 −7187.00 −1.46285
290290 0 0
291291 0 0
292292 0 0
293293 − 4034.00i − 0.804330i −0.915567 0.402165i 0.868258π-0.868258\pi
0.915567 0.402165i 0.131742π-0.131742\pi
294294 0 0
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 −672.000 −0.129976
300300 0 0
301301 −4672.00 −0.894650
302302 0 0
303303 0 0
304304 0 0
305305 0 0
306306 0 0
307307 − 3836.00i − 0.713134i −0.934270 0.356567i 0.883947π-0.883947\pi
0.934270 0.356567i 0.116053π-0.116053\pi
308308 0 0
309309 0 0
310310 0 0
311311 −664.000 −0.121067 −0.0605337 0.998166i 0.519280π-0.519280\pi
−0.0605337 + 0.998166i 0.519280π0.519280\pi
312312 0 0
313313 − 2986.00i − 0.539229i −0.962968 0.269615i 0.913104π-0.913104\pi
0.962968 0.269615i 0.0868963π-0.0868963\pi
314314 0 0
315315 0 0
316316 0 0
317317 − 2726.00i − 0.482989i −0.970402 0.241494i 0.922362π-0.922362\pi
0.970402 0.241494i 0.0776375π-0.0776375\pi
318318 0 0
319319 −7128.00 −1.25107
320320 0 0
321321 0 0
322322 0 0
323323 12760.0i 2.19810i
324324 0 0
325325 0 0
326326 0 0
327327 0 0
328328 0 0
329329 6272.00 1.05102
330330 0 0
331331 −9212.00 −1.52972 −0.764860 0.644197i 0.777192π-0.777192\pi
−0.764860 + 0.644197i 0.777192π0.777192\pi
332332 0 0
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 − 3278.00i − 0.529864i −0.964267 0.264932i 0.914651π-0.914651\pi
0.964267 0.264932i 0.0853494π-0.0853494\pi
338338 0 0
339339 0 0
340340 0 0
341341 −8640.00 −1.37209
342342 0 0
343343 6880.00i 1.08305i
344344 0 0
345345 0 0
346346 0 0
347347 − 4956.00i − 0.766721i −0.923599 0.383360i 0.874767π-0.874767\pi
0.923599 0.383360i 0.125233π-0.125233\pi
348348 0 0
349349 −4678.00 −0.717500 −0.358750 0.933434i 0.616797π-0.616797\pi
−0.358750 + 0.933434i 0.616797π0.616797\pi
350350 0 0
351351 0 0
352352 0 0
353353 1890.00i 0.284970i 0.989797 + 0.142485i 0.0455093π0.0455093\pi
−0.989797 + 0.142485i 0.954491π0.954491\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 −6472.00 −0.951474 −0.475737 0.879588i 0.657819π-0.657819\pi
−0.475737 + 0.879588i 0.657819π0.657819\pi
360360 0 0
361361 6597.00 0.961802
362362 0 0
363363 0 0
364364 0 0
365365 0 0
366366 0 0
367367 1960.00i 0.278777i 0.990238 + 0.139389i 0.0445137π0.0445137\pi
−0.990238 + 0.139389i 0.955486π0.955486\pi
368368 0 0
369369 0 0
370370 0 0
371371 −2272.00 −0.317942
372372 0 0
373373 − 8750.00i − 1.21463i −0.794460 0.607316i 0.792246π-0.792246\pi
0.794460 0.607316i 0.207754π-0.207754\pi
374374 0 0
375375 0 0
376376 0 0
377377 8316.00i 1.13606i
378378 0 0
379379 380.000 0.0515021 0.0257510 0.999668i 0.491802π-0.491802\pi
0.0257510 + 0.999668i 0.491802π0.491802\pi
380380 0 0
381381 0 0
382382 0 0
383383 − 9688.00i − 1.29252i −0.763119 0.646258i 0.776333π-0.776333\pi
0.763119 0.646258i 0.223667π-0.223667\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 3870.00 0.504413 0.252207 0.967673i 0.418844π-0.418844\pi
0.252207 + 0.967673i 0.418844π0.418844\pi
390390 0 0
391391 −1760.00 −0.227639
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 1622.00i 0.205053i 0.994730 + 0.102526i 0.0326926π0.0326926\pi
−0.994730 + 0.102526i 0.967307π0.967307\pi
398398 0 0
399399 0 0
400400 0 0
401401 −9906.00 −1.23362 −0.616811 0.787112i 0.711576π-0.711576\pi
−0.616811 + 0.787112i 0.711576π0.711576\pi
402402 0 0
403403 10080.0i 1.24596i
404404 0 0
405405 0 0
406406 0 0
407407 9288.00i 1.13118i
408408 0 0
409409 4214.00 0.509459 0.254730 0.967012i 0.418014π-0.418014\pi
0.254730 + 0.967012i 0.418014π0.418014\pi
410410 0 0
411411 0 0
412412 0 0
413413 − 5568.00i − 0.663398i
414414 0 0
415415 0 0
416416 0 0
417417 0 0
418418 0 0
419419 −7012.00 −0.817562 −0.408781 0.912632i 0.634046π-0.634046\pi
−0.408781 + 0.912632i 0.634046π0.634046\pi
420420 0 0
421421 −1602.00 −0.185455 −0.0927277 0.995692i 0.529559π-0.529559\pi
−0.0927277 + 0.995692i 0.529559π0.529559\pi
422422 0 0
423423 0 0
424424 0 0
425425 0 0
426426 0 0
427427 − 9120.00i − 1.03360i
428428 0 0
429429 0 0
430430 0 0
431431 3584.00 0.400546 0.200273 0.979740i 0.435817π-0.435817\pi
0.200273 + 0.979740i 0.435817π0.435817\pi
432432 0 0
433433 3470.00i 0.385121i 0.981285 + 0.192561i 0.0616792π0.0616792\pi
−0.981285 + 0.192561i 0.938321π0.938321\pi
434434 0 0
435435 0 0
436436 0 0
437437 1856.00i 0.203168i
438438 0 0
439439 3416.00 0.371382 0.185691 0.982608i 0.440548π-0.440548\pi
0.185691 + 0.982608i 0.440548π0.440548\pi
440440 0 0
441441 0 0
442442 0 0
443443 9708.00i 1.04118i 0.853808 + 0.520588i 0.174287π0.174287\pi
−0.853808 + 0.520588i 0.825713π0.825713\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 −10366.0 −1.08954 −0.544768 0.838587i 0.683382π-0.683382\pi
−0.544768 + 0.838587i 0.683382π0.683382\pi
450450 0 0
451451 15912.0 1.66135
452452 0 0
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 − 16742.0i − 1.71369i −0.515572 0.856847i 0.672420π-0.672420\pi
0.515572 0.856847i 0.327580π-0.327580\pi
458458 0 0
459459 0 0
460460 0 0
461461 1258.00 0.127095 0.0635476 0.997979i 0.479759π-0.479759\pi
0.0635476 + 0.997979i 0.479759π0.479759\pi
462462 0 0
463463 − 13528.0i − 1.35788i −0.734193 0.678941i 0.762439π-0.762439\pi
0.734193 0.678941i 0.237561π-0.237561\pi
464464 0 0
465465 0 0
466466 0 0
467467 − 6916.00i − 0.685298i −0.939463 0.342649i 0.888676π-0.888676\pi
0.939463 0.342649i 0.111324π-0.111324\pi
468468 0 0
469469 −11072.0 −1.09010
470470 0 0
471471 0 0
472472 0 0
473473 − 10512.0i − 1.02187i
474474 0 0
475475 0 0
476476 0 0
477477 0 0
478478 0 0
479479 1728.00 0.164832 0.0824158 0.996598i 0.473736π-0.473736\pi
0.0824158 + 0.996598i 0.473736π0.473736\pi
480480 0 0
481481 10836.0 1.02719
482482 0 0
483483 0 0
484484 0 0
485485 0 0
486486 0 0
487487 16656.0i 1.54981i 0.632080 + 0.774903i 0.282201π0.282201\pi
−0.632080 + 0.774903i 0.717799π0.717799\pi
488488 0 0
489489 0 0
490490 0 0
491491 1084.00 0.0996339 0.0498169 0.998758i 0.484136π-0.484136\pi
0.0498169 + 0.998758i 0.484136π0.484136\pi
492492 0 0
493493 21780.0i 1.98970i
494494 0 0
495495 0 0
496496 0 0
497497 − 2688.00i − 0.242602i
498498 0 0
499499 −5804.00 −0.520687 −0.260343 0.965516i 0.583836π-0.583836\pi
−0.260343 + 0.965516i 0.583836π0.583836\pi
500500 0 0
501501 0 0
502502 0 0
503503 10512.0i 0.931823i 0.884831 + 0.465911i 0.154273π0.154273\pi
−0.884831 + 0.465911i 0.845727π0.845727\pi
504504 0 0
505505 0 0
506506 0 0
507507 0 0
508508 0 0
509509 −4314.00 −0.375667 −0.187834 0.982201i 0.560147π-0.560147\pi
−0.187834 + 0.982201i 0.560147π0.560147\pi
510510 0 0
511511 −2144.00 −0.185607
512512 0 0
513513 0 0
514514 0 0
515515 0 0
516516 0 0
517517 14112.0i 1.20047i
518518 0 0
519519 0 0
520520 0 0
521521 1190.00 0.100067 0.0500334 0.998748i 0.484067π-0.484067\pi
0.0500334 + 0.998748i 0.484067π0.484067\pi
522522 0 0
523523 3780.00i 0.316038i 0.987436 + 0.158019i 0.0505107π0.0505107\pi
−0.987436 + 0.158019i 0.949489π0.949489\pi
524524 0 0
525525 0 0
526526 0 0
527527 26400.0i 2.18217i
528528 0 0
529529 11911.0 0.978959
530530 0 0
531531 0 0
532532 0 0
533533 − 18564.0i − 1.50862i
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 0 0
539539 −3132.00 −0.250287
540540 0 0
541541 −11002.0 −0.874331 −0.437165 0.899381i 0.644018π-0.644018\pi
−0.437165 + 0.899381i 0.644018π0.644018\pi
542542 0 0
543543 0 0
544544 0 0
545545 0 0
546546 0 0
547547 5908.00i 0.461806i 0.972977 + 0.230903i 0.0741680π0.0741680\pi
−0.972977 + 0.230903i 0.925832π0.925832\pi
548548 0 0
549549 0 0
550550 0 0
551551 22968.0 1.77581
552552 0 0
553553 − 12544.0i − 0.964602i
554554 0 0
555555 0 0
556556 0 0
557557 − 14806.0i − 1.12630i −0.826354 0.563151i 0.809589π-0.809589\pi
0.826354 0.563151i 0.190411π-0.190411\pi
558558 0 0
559559 −12264.0 −0.927928
560560 0 0
561561 0 0
562562 0 0
563563 − 684.000i − 0.0512028i −0.999672 0.0256014i 0.991850π-0.991850\pi
0.999672 0.0256014i 0.00815007π-0.00815007\pi
564564 0 0
565565 0 0
566566 0 0
567567 0 0
568568 0 0
569569 −2582.00 −0.190234 −0.0951169 0.995466i 0.530323π-0.530323\pi
−0.0951169 + 0.995466i 0.530323π0.530323\pi
570570 0 0
571571 −2540.00 −0.186157 −0.0930785 0.995659i 0.529671π-0.529671\pi
−0.0930785 + 0.995659i 0.529671π0.529671\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 0 0
577577 22786.0i 1.64401i 0.569480 + 0.822005i 0.307144π0.307144\pi
−0.569480 + 0.822005i 0.692856π0.692856\pi
578578 0 0
579579 0 0
580580 0 0
581581 −9024.00 −0.644369
582582 0 0
583583 − 5112.00i − 0.363152i
584584 0 0
585585 0 0
586586 0 0
587587 − 7884.00i − 0.554357i −0.960818 0.277178i 0.910601π-0.910601\pi
0.960818 0.277178i 0.0893993π-0.0893993\pi
588588 0 0
589589 27840.0 1.94758
590590 0 0
591591 0 0
592592 0 0
593593 − 21902.0i − 1.51671i −0.651843 0.758354i 0.726004π-0.726004\pi
0.651843 0.758354i 0.273996π-0.273996\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 15080.0 1.02863 0.514317 0.857600i 0.328045π-0.328045\pi
0.514317 + 0.857600i 0.328045π0.328045\pi
600600 0 0
601601 −19702.0 −1.33721 −0.668603 0.743619i 0.733108π-0.733108\pi
−0.668603 + 0.743619i 0.733108π0.733108\pi
602602 0 0
603603 0 0
604604 0 0
605605 0 0
606606 0 0
607607 7320.00i 0.489472i 0.969590 + 0.244736i 0.0787013π0.0787013\pi
−0.969590 + 0.244736i 0.921299π0.921299\pi
608608 0 0
609609 0 0
610610 0 0
611611 16464.0 1.09012
612612 0 0
613613 − 24350.0i − 1.60438i −0.597066 0.802192i 0.703667π-0.703667\pi
0.597066 0.802192i 0.296333π-0.296333\pi
614614 0 0
615615 0 0
616616 0 0
617617 − 19546.0i − 1.27535i −0.770305 0.637676i 0.779896π-0.779896\pi
0.770305 0.637676i 0.220104π-0.220104\pi
618618 0 0
619619 −3476.00 −0.225706 −0.112853 0.993612i 0.535999π-0.535999\pi
−0.112853 + 0.993612i 0.535999π0.535999\pi
620620 0 0
621621 0 0
622622 0 0
623623 16544.0i 1.06392i
624624 0 0
625625 0 0
626626 0 0
627627 0 0
628628 0 0
629629 28380.0 1.79902
630630 0 0
631631 21880.0 1.38039 0.690197 0.723621i 0.257524π-0.257524\pi
0.690197 + 0.723621i 0.257524π0.257524\pi
632632 0 0
633633 0 0
634634 0 0
635635 0 0
636636 0 0
637637 3654.00i 0.227279i
638638 0 0
639639 0 0
640640 0 0
641641 −20994.0 −1.29362 −0.646812 0.762649i 0.723898π-0.723898\pi
−0.646812 + 0.762649i 0.723898π0.723898\pi
642642 0 0
643643 18204.0i 1.11648i 0.829680 + 0.558239i 0.188523π0.188523\pi
−0.829680 + 0.558239i 0.811477π0.811477\pi
644644 0 0
645645 0 0
646646 0 0
647647 2064.00i 0.125416i 0.998032 + 0.0627080i 0.0199737π0.0199737\pi
−0.998032 + 0.0627080i 0.980026π0.980026\pi
648648 0 0
649649 12528.0 0.757730
650650 0 0
651651 0 0
652652 0 0
653653 9942.00i 0.595805i 0.954596 + 0.297902i 0.0962870π0.0962870\pi
−0.954596 + 0.297902i 0.903713π0.903713\pi
654654 0 0
655655 0 0
656656 0 0
657657 0 0
658658 0 0
659659 24236.0 1.43263 0.716313 0.697779i 0.245828π-0.245828\pi
0.716313 + 0.697779i 0.245828π0.245828\pi
660660 0 0
661661 17614.0 1.03647 0.518234 0.855239i 0.326590π-0.326590\pi
0.518234 + 0.855239i 0.326590π0.326590\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 3168.00i 0.183906i
668668 0 0
669669 0 0
670670 0 0
671671 20520.0 1.18057
672672 0 0
673673 − 13058.0i − 0.747918i −0.927445 0.373959i 0.878000π-0.878000\pi
0.927445 0.373959i 0.122000π-0.122000\pi
674674 0 0
675675 0 0
676676 0 0
677677 33186.0i 1.88396i 0.335668 + 0.941980i 0.391038π0.391038\pi
−0.335668 + 0.941980i 0.608962π0.608962\pi
678678 0 0
679679 6112.00 0.345445
680680 0 0
681681 0 0
682682 0 0
683683 − 31716.0i − 1.77684i −0.459035 0.888418i 0.651805π-0.651805\pi
0.459035 0.888418i 0.348195π-0.348195\pi
684684 0 0
685685 0 0
686686 0 0
687687 0 0
688688 0 0
689689 −5964.00 −0.329768
690690 0 0
691691 −2084.00 −0.114731 −0.0573655 0.998353i 0.518270π-0.518270\pi
−0.0573655 + 0.998353i 0.518270π0.518270\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 − 48620.0i − 2.64220i
698698 0 0
699699 0 0
700700 0 0
701701 7418.00 0.399678 0.199839 0.979829i 0.435958π-0.435958\pi
0.199839 + 0.979829i 0.435958π0.435958\pi
702702 0 0
703703 − 29928.0i − 1.60563i
704704 0 0
705705 0 0
706706 0 0
707707 10784.0i 0.573655i
708708 0 0
709709 18242.0 0.966280 0.483140 0.875543i 0.339496π-0.339496\pi
0.483140 + 0.875543i 0.339496π0.339496\pi
710710 0 0
711711 0 0
712712 0 0
713713 3840.00i 0.201696i
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 3024.00 0.156851 0.0784257 0.996920i 0.475011π-0.475011\pi
0.0784257 + 0.996920i 0.475011π0.475011\pi
720720 0 0
721721 −15872.0 −0.819839
722722 0 0
723723 0 0
724724 0 0
725725 0 0
726726 0 0
727727 − 26176.0i − 1.33537i −0.744444 0.667685i 0.767285π-0.767285\pi
0.744444 0.667685i 0.232715π-0.232715\pi
728728 0 0
729729 0 0
730730 0 0
731731 −32120.0 −1.62517
732732 0 0
733733 17818.0i 0.897848i 0.893570 + 0.448924i 0.148193π0.148193\pi
−0.893570 + 0.448924i 0.851807π0.851807\pi
734734 0 0
735735 0 0
736736 0 0
737737 − 24912.0i − 1.24511i
738738 0 0
739739 22052.0 1.09769 0.548847 0.835923i 0.315067π-0.315067\pi
0.548847 + 0.835923i 0.315067π0.315067\pi
740740 0 0
741741 0 0
742742 0 0
743743 15840.0i 0.782117i 0.920366 + 0.391059i 0.127891π0.127891\pi
−0.920366 + 0.391059i 0.872109π0.872109\pi
744744 0 0
745745 0 0
746746 0 0
747747 0 0
748748 0 0
749749 −8000.00 −0.390272
750750 0 0
751751 21024.0 1.02154 0.510770 0.859717i 0.329360π-0.329360\pi
0.510770 + 0.859717i 0.329360π0.329360\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 − 38034.0i − 1.82612i −0.407831 0.913058i 0.633715π-0.633715\pi
0.407831 0.913058i 0.366285π-0.366285\pi
758758 0 0
759759 0 0
760760 0 0
761761 −37802.0 −1.80069 −0.900343 0.435182i 0.856684π-0.856684\pi
−0.900343 + 0.435182i 0.856684π0.856684\pi
762762 0 0
763763 − 16736.0i − 0.794081i
764764 0 0
765765 0 0
766766 0 0
767767 − 14616.0i − 0.688075i
768768 0 0
769769 −15042.0 −0.705369 −0.352684 0.935742i 0.614731π-0.614731\pi
−0.352684 + 0.935742i 0.614731π0.614731\pi
770770 0 0
771771 0 0
772772 0 0
773773 5950.00i 0.276852i 0.990373 + 0.138426i 0.0442043π0.0442043\pi
−0.990373 + 0.138426i 0.955796π0.955796\pi
774774 0 0
775775 0 0
776776 0 0
777777 0 0
778778 0 0
779779 −51272.0 −2.35816
780780 0 0
781781 6048.00 0.277099
782782 0 0
783783 0 0
784784 0 0
785785 0 0
786786 0 0
787787 23364.0i 1.05824i 0.848546 + 0.529121i 0.177478π0.177478\pi
−0.848546 + 0.529121i 0.822522π0.822522\pi
788788 0 0
789789 0 0
790790 0 0
791791 8928.00 0.401319
792792 0 0
793793 − 23940.0i − 1.07205i
794794 0 0
795795 0 0
796796 0 0
797797 − 19846.0i − 0.882034i −0.897499 0.441017i 0.854618π-0.854618\pi
0.897499 0.441017i 0.145382π-0.145382\pi
798798 0 0
799799 43120.0 1.90923
800800 0 0
801801 0 0
802802 0 0
803803 − 4824.00i − 0.211999i
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 24762.0 1.07613 0.538063 0.842905i 0.319156π-0.319156\pi
0.538063 + 0.842905i 0.319156π0.319156\pi
810810 0 0
811811 16644.0 0.720653 0.360327 0.932826i 0.382665π-0.382665\pi
0.360327 + 0.932826i 0.382665π0.382665\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 0 0
817817 33872.0i 1.45047i
818818 0 0
819819 0 0
820820 0 0
821821 −3182.00 −0.135265 −0.0676325 0.997710i 0.521545π-0.521545\pi
−0.0676325 + 0.997710i 0.521545π0.521545\pi
822822 0 0
823823 7504.00i 0.317829i 0.987292 + 0.158914i 0.0507994π0.0507994\pi
−0.987292 + 0.158914i 0.949201π0.949201\pi
824824 0 0
825825 0 0
826826 0 0
827827 − 12604.0i − 0.529969i −0.964253 0.264984i 0.914633π-0.914633\pi
0.964253 0.264984i 0.0853668π-0.0853668\pi
828828 0 0
829829 −12230.0 −0.512383 −0.256191 0.966626i 0.582468π-0.582468\pi
−0.256191 + 0.966626i 0.582468π0.582468\pi
830830 0 0
831831 0 0
832832 0 0
833833 9570.00i 0.398056i
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0 0
839839 9656.00 0.397333 0.198666 0.980067i 0.436339π-0.436339\pi
0.198666 + 0.980067i 0.436339π0.436339\pi
840840 0 0
841841 14815.0 0.607446
842842 0 0
843843 0 0
844844 0 0
845845 0 0
846846 0 0
847847 − 560.000i − 0.0227176i
848848 0 0
849849 0 0
850850 0 0
851851 4128.00 0.166282
852852 0 0
853853 − 5806.00i − 0.233052i −0.993188 0.116526i 0.962824π-0.962824\pi
0.993188 0.116526i 0.0371759π-0.0371759\pi
854854 0 0
855855 0 0
856856 0 0
857857 39094.0i 1.55826i 0.626865 + 0.779128i 0.284338π0.284338\pi
−0.626865 + 0.779128i 0.715662π0.715662\pi
858858 0 0
859859 18876.0 0.749756 0.374878 0.927074i 0.377685π-0.377685\pi
0.374878 + 0.927074i 0.377685π0.377685\pi
860860 0 0
861861 0 0
862862 0 0
863863 32296.0i 1.27389i 0.770909 + 0.636946i 0.219803π0.219803\pi
−0.770909 + 0.636946i 0.780197π0.780197\pi
864864 0 0
865865 0 0
866866 0 0
867867 0 0
868868 0 0
869869 28224.0 1.10176
870870 0 0
871871 −29064.0 −1.13065
872872 0 0
873873 0 0
874874 0 0
875875 0 0
876876 0 0
877877 − 9578.00i − 0.368787i −0.982853 0.184393i 0.940968π-0.940968\pi
0.982853 0.184393i 0.0590321π-0.0590321\pi
878878 0 0
879879 0 0
880880 0 0
881881 41710.0 1.59506 0.797529 0.603281i 0.206140π-0.206140\pi
0.797529 + 0.603281i 0.206140π0.206140\pi
882882 0 0
883883 − 2260.00i − 0.0861326i −0.999072 0.0430663i 0.986287π-0.986287\pi
0.999072 0.0430663i 0.0137127π-0.0137127\pi
884884 0 0
885885 0 0
886886 0 0
887887 33696.0i 1.27554i 0.770228 + 0.637768i 0.220142π0.220142\pi
−0.770228 + 0.637768i 0.779858π0.779858\pi
888888 0 0
889889 5248.00 0.197989
890890 0 0
891891 0 0
892892 0 0
893893 − 45472.0i − 1.70399i
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 47520.0 1.76294
900900 0 0
901901 −15620.0 −0.577556
902902 0 0
903903 0 0
904904 0 0
905905 0 0
906906 0 0
907907 7756.00i 0.283940i 0.989871 + 0.141970i 0.0453437π0.0453437\pi
−0.989871 + 0.141970i 0.954656π0.954656\pi
908908 0 0
909909 0 0
910910 0 0
911911 5312.00 0.193188 0.0965941 0.995324i 0.469205π-0.469205\pi
0.0965941 + 0.995324i 0.469205π0.469205\pi
912912 0 0
913913 − 20304.0i − 0.735996i
914914 0 0
915915 0 0
916916 0 0
917917 3392.00i 0.122152i
918918 0 0
919919 23576.0 0.846246 0.423123 0.906072i 0.360934π-0.360934\pi
0.423123 + 0.906072i 0.360934π0.360934\pi
920920 0 0
921921 0 0
922922 0 0
923923 − 7056.00i − 0.251626i
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 0 0
929929 −19038.0 −0.672354 −0.336177 0.941799i 0.609134π-0.609134\pi
−0.336177 + 0.941799i 0.609134π0.609134\pi
930930 0 0
931931 10092.0 0.355265
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 20570.0i 0.717175i 0.933496 + 0.358587i 0.116741π0.116741\pi
−0.933496 + 0.358587i 0.883259π0.883259\pi
938938 0 0
939939 0 0
940940 0 0
941941 21386.0 0.740875 0.370438 0.928857i 0.379208π-0.379208\pi
0.370438 + 0.928857i 0.379208π0.379208\pi
942942 0 0
943943 − 7072.00i − 0.244216i
944944 0 0
945945 0 0
946946 0 0
947947 − 38020.0i − 1.30463i −0.757948 0.652315i 0.773798π-0.773798\pi
0.757948 0.652315i 0.226202π-0.226202\pi
948948 0 0
949949 −5628.00 −0.192511
950950 0 0
951951 0 0
952952 0 0
953953 20202.0i 0.686681i 0.939211 + 0.343340i 0.111558π0.111558\pi
−0.939211 + 0.343340i 0.888442π0.888442\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 22944.0 0.772576
960960 0 0
961961 27809.0 0.933470
962962 0 0
963963 0 0
964964 0 0
965965 0 0
966966 0 0
967967 29840.0i 0.992337i 0.868226 + 0.496168i 0.165260π0.165260\pi
−0.868226 + 0.496168i 0.834740π0.834740\pi
968968 0 0
969969 0 0
970970 0 0
971971 12476.0 0.412332 0.206166 0.978517i 0.433901π-0.433901\pi
0.206166 + 0.978517i 0.433901π0.433901\pi
972972 0 0
973973 − 35136.0i − 1.15767i
974974 0 0
975975 0 0
976976 0 0
977977 36974.0i 1.21075i 0.795940 + 0.605375i 0.206977π0.206977\pi
−0.795940 + 0.605375i 0.793023π0.793023\pi
978978 0 0
979979 −37224.0 −1.21520
980980 0 0
981981 0 0
982982 0 0
983983 − 16368.0i − 0.531087i −0.964099 0.265543i 0.914449π-0.914449\pi
0.964099 0.265543i 0.0855513π-0.0855513\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 −4672.00 −0.150213
990990 0 0
991991 −49552.0 −1.58837 −0.794183 0.607678i 0.792101π-0.792101\pi
−0.794183 + 0.607678i 0.792101π0.792101\pi
992992 0 0
993993 0 0
994994 0 0
995995 0 0
996996 0 0
997997 24414.0i 0.775526i 0.921759 + 0.387763i 0.126752π0.126752\pi
−0.921759 + 0.387763i 0.873248π0.873248\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 1800.4.f.d.649.2 2
3.2 odd 2 200.4.c.f.49.1 2
5.2 odd 4 1800.4.a.h.1.1 1
5.3 odd 4 360.4.a.f.1.1 1
5.4 even 2 inner 1800.4.f.d.649.1 2
12.11 even 2 400.4.c.h.49.2 2
15.2 even 4 200.4.a.d.1.1 1
15.8 even 4 40.4.a.b.1.1 1
15.14 odd 2 200.4.c.f.49.2 2
20.3 even 4 720.4.a.d.1.1 1
60.23 odd 4 80.4.a.b.1.1 1
60.47 odd 4 400.4.a.p.1.1 1
60.59 even 2 400.4.c.h.49.1 2
105.83 odd 4 1960.4.a.e.1.1 1
120.53 even 4 320.4.a.e.1.1 1
120.77 even 4 1600.4.a.bk.1.1 1
120.83 odd 4 320.4.a.j.1.1 1
120.107 odd 4 1600.4.a.q.1.1 1
240.53 even 4 1280.4.d.d.641.1 2
240.83 odd 4 1280.4.d.m.641.1 2
240.173 even 4 1280.4.d.d.641.2 2
240.203 odd 4 1280.4.d.m.641.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.4.a.b.1.1 1 15.8 even 4
80.4.a.b.1.1 1 60.23 odd 4
200.4.a.d.1.1 1 15.2 even 4
200.4.c.f.49.1 2 3.2 odd 2
200.4.c.f.49.2 2 15.14 odd 2
320.4.a.e.1.1 1 120.53 even 4
320.4.a.j.1.1 1 120.83 odd 4
360.4.a.f.1.1 1 5.3 odd 4
400.4.a.p.1.1 1 60.47 odd 4
400.4.c.h.49.1 2 60.59 even 2
400.4.c.h.49.2 2 12.11 even 2
720.4.a.d.1.1 1 20.3 even 4
1280.4.d.d.641.1 2 240.53 even 4
1280.4.d.d.641.2 2 240.173 even 4
1280.4.d.m.641.1 2 240.83 odd 4
1280.4.d.m.641.2 2 240.203 odd 4
1600.4.a.q.1.1 1 120.107 odd 4
1600.4.a.bk.1.1 1 120.77 even 4
1800.4.a.h.1.1 1 5.2 odd 4
1800.4.f.d.649.1 2 5.4 even 2 inner
1800.4.f.d.649.2 2 1.1 even 1 trivial
1960.4.a.e.1.1 1 105.83 odd 4