Properties

Label 3900.2.j.h.649.4
Level 39003900
Weight 22
Character 3900.649
Analytic conductor 31.14231.142
Analytic rank 00
Dimension 44
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3900,2,Mod(649,3900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3900, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3900.649");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 3900=2235213 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3900.j (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: 31.141656788331.1416567883
Analytic rank: 00
Dimension: 44
Coefficient field: Q(ζ12)\Q(\zeta_{12})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x2+1 x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 24 2^{4}
Twist minimal: no (minimal twist has level 156)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 649.4
Root 0.8660250.500000i0.866025 - 0.500000i of defining polynomial
Character χ\chi == 3900.649
Dual form 3900.2.j.h.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+1.00000iq31.00000q9+3.46410iq11+(3.46410+1.00000i)q13+6.00000iq17+6.92820iq191.00000iq27+6.00000q296.92820iq313.46410q33+(1.00000+3.46410i)q393.46410iq418.00000iq433.46410q477.00000q496.00000q516.00000iq536.92820q57+3.46410iq59+10.0000q6113.8564q67+10.3923iq716.92820q73+8.00000q79+1.00000q813.46410q83+6.00000iq87+17.3205iq89+6.92820q936.92820q973.46410iq99+O(q100)q+1.00000i q^{3} -1.00000 q^{9} +3.46410i q^{11} +(3.46410 + 1.00000i) q^{13} +6.00000i q^{17} +6.92820i q^{19} -1.00000i q^{27} +6.00000 q^{29} -6.92820i q^{31} -3.46410 q^{33} +(-1.00000 + 3.46410i) q^{39} -3.46410i q^{41} -8.00000i q^{43} -3.46410 q^{47} -7.00000 q^{49} -6.00000 q^{51} -6.00000i q^{53} -6.92820 q^{57} +3.46410i q^{59} +10.0000 q^{61} -13.8564 q^{67} +10.3923i q^{71} -6.92820 q^{73} +8.00000 q^{79} +1.00000 q^{81} -3.46410 q^{83} +6.00000i q^{87} +17.3205i q^{89} +6.92820 q^{93} -6.92820 q^{97} -3.46410i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q4q9+24q294q3928q4924q51+40q61+32q79+4q81+O(q100) 4 q - 4 q^{9} + 24 q^{29} - 4 q^{39} - 28 q^{49} - 24 q^{51} + 40 q^{61} + 32 q^{79} + 4 q^{81}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3900Z)×\left(\mathbb{Z}/3900\mathbb{Z}\right)^\times.

nn 301301 13011301 19511951 32773277
χ(n)\chi(n) 1-1 11 11 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 1.00000i 0.577350i
44 0 0
55 0 0
66 0 0
77 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
88 0 0
99 −1.00000 −0.333333
1010 0 0
1111 3.46410i 1.04447i 0.852803 + 0.522233i 0.174901π0.174901\pi
−0.852803 + 0.522233i 0.825099π0.825099\pi
1212 0 0
1313 3.46410 + 1.00000i 0.960769 + 0.277350i
1414 0 0
1515 0 0
1616 0 0
1717 6.00000i 1.45521i 0.685994 + 0.727607i 0.259367π0.259367\pi
−0.685994 + 0.727607i 0.740633π0.740633\pi
1818 0 0
1919 6.92820i 1.58944i 0.606977 + 0.794719i 0.292382π0.292382\pi
−0.606977 + 0.794719i 0.707618π0.707618\pi
2020 0 0
2121 0 0
2222 0 0
2323 0 0 1.00000 00
−1.00000 π\pi
2424 0 0
2525 0 0
2626 0 0
2727 1.00000i 0.192450i
2828 0 0
2929 6.00000 1.11417 0.557086 0.830455i 0.311919π-0.311919\pi
0.557086 + 0.830455i 0.311919π0.311919\pi
3030 0 0
3131 6.92820i 1.24434i −0.782881 0.622171i 0.786251π-0.786251\pi
0.782881 0.622171i 0.213749π-0.213749\pi
3232 0 0
3333 −3.46410 −0.603023
3434 0 0
3535 0 0
3636 0 0
3737 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
3838 0 0
3939 −1.00000 + 3.46410i −0.160128 + 0.554700i
4040 0 0
4141 3.46410i 0.541002i −0.962720 0.270501i 0.912811π-0.912811\pi
0.962720 0.270501i 0.0871893π-0.0871893\pi
4242 0 0
4343 8.00000i 1.21999i −0.792406 0.609994i 0.791172π-0.791172\pi
0.792406 0.609994i 0.208828π-0.208828\pi
4444 0 0
4545 0 0
4646 0 0
4747 −3.46410 −0.505291 −0.252646 0.967559i 0.581301π-0.581301\pi
−0.252646 + 0.967559i 0.581301π0.581301\pi
4848 0 0
4949 −7.00000 −1.00000
5050 0 0
5151 −6.00000 −0.840168
5252 0 0
5353 6.00000i 0.824163i −0.911147 0.412082i 0.864802π-0.864802\pi
0.911147 0.412082i 0.135198π-0.135198\pi
5454 0 0
5555 0 0
5656 0 0
5757 −6.92820 −0.917663
5858 0 0
5959 3.46410i 0.450988i 0.974245 + 0.225494i 0.0723995π0.0723995\pi
−0.974245 + 0.225494i 0.927600π0.927600\pi
6060 0 0
6161 10.0000 1.28037 0.640184 0.768221i 0.278858π-0.278858\pi
0.640184 + 0.768221i 0.278858π0.278858\pi
6262 0 0
6363 0 0
6464 0 0
6565 0 0
6666 0 0
6767 −13.8564 −1.69283 −0.846415 0.532524i 0.821244π-0.821244\pi
−0.846415 + 0.532524i 0.821244π0.821244\pi
6868 0 0
6969 0 0
7070 0 0
7171 10.3923i 1.23334i 0.787222 + 0.616670i 0.211519π0.211519\pi
−0.787222 + 0.616670i 0.788481π0.788481\pi
7272 0 0
7373 −6.92820 −0.810885 −0.405442 0.914121i 0.632883π-0.632883\pi
−0.405442 + 0.914121i 0.632883π0.632883\pi
7474 0 0
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 8.00000 0.900070 0.450035 0.893011i 0.351411π-0.351411\pi
0.450035 + 0.893011i 0.351411π0.351411\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 −3.46410 −0.380235 −0.190117 0.981761i 0.560887π-0.560887\pi
−0.190117 + 0.981761i 0.560887π0.560887\pi
8484 0 0
8585 0 0
8686 0 0
8787 6.00000i 0.643268i
8888 0 0
8989 17.3205i 1.83597i 0.396615 + 0.917985i 0.370185π0.370185\pi
−0.396615 + 0.917985i 0.629815π0.629815\pi
9090 0 0
9191 0 0
9292 0 0
9393 6.92820 0.718421
9494 0 0
9595 0 0
9696 0 0
9797 −6.92820 −0.703452 −0.351726 0.936103i 0.614405π-0.614405\pi
−0.351726 + 0.936103i 0.614405π0.614405\pi
9898 0 0
9999 3.46410i 0.348155i
100100 0 0
101101 6.00000 0.597022 0.298511 0.954406i 0.403510π-0.403510\pi
0.298511 + 0.954406i 0.403510π0.403510\pi
102102 0 0
103103 4.00000i 0.394132i 0.980390 + 0.197066i 0.0631413π0.0631413\pi
−0.980390 + 0.197066i 0.936859π0.936859\pi
104104 0 0
105105 0 0
106106 0 0
107107 12.0000i 1.16008i −0.814587 0.580042i 0.803036π-0.803036\pi
0.814587 0.580042i 0.196964π-0.196964\pi
108108 0 0
109109 6.92820i 0.663602i 0.943349 + 0.331801i 0.107656π0.107656\pi
−0.943349 + 0.331801i 0.892344π0.892344\pi
110110 0 0
111111 0 0
112112 0 0
113113 18.0000i 1.69330i 0.532152 + 0.846649i 0.321383π0.321383\pi
−0.532152 + 0.846649i 0.678617π0.678617\pi
114114 0 0
115115 0 0
116116 0 0
117117 −3.46410 1.00000i −0.320256 0.0924500i
118118 0 0
119119 0 0
120120 0 0
121121 −1.00000 −0.0909091
122122 0 0
123123 3.46410 0.312348
124124 0 0
125125 0 0
126126 0 0
127127 16.0000i 1.41977i 0.704317 + 0.709885i 0.251253π0.251253\pi
−0.704317 + 0.709885i 0.748747π0.748747\pi
128128 0 0
129129 8.00000 0.704361
130130 0 0
131131 −12.0000 −1.04844 −0.524222 0.851581i 0.675644π-0.675644\pi
−0.524222 + 0.851581i 0.675644π0.675644\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 0 0
137137 10.3923 0.887875 0.443937 0.896058i 0.353581π-0.353581\pi
0.443937 + 0.896058i 0.353581π0.353581\pi
138138 0 0
139139 −8.00000 −0.678551 −0.339276 0.940687i 0.610182π-0.610182\pi
−0.339276 + 0.940687i 0.610182π0.610182\pi
140140 0 0
141141 3.46410i 0.291730i
142142 0 0
143143 −3.46410 + 12.0000i −0.289683 + 1.00349i
144144 0 0
145145 0 0
146146 0 0
147147 7.00000i 0.577350i
148148 0 0
149149 17.3205i 1.41895i 0.704730 + 0.709476i 0.251068π0.251068\pi
−0.704730 + 0.709476i 0.748932π0.748932\pi
150150 0 0
151151 6.92820i 0.563809i 0.959442 + 0.281905i 0.0909662π0.0909662\pi
−0.959442 + 0.281905i 0.909034π0.909034\pi
152152 0 0
153153 6.00000i 0.485071i
154154 0 0
155155 0 0
156156 0 0
157157 2.00000i 0.159617i 0.996810 + 0.0798087i 0.0254309π0.0254309\pi
−0.996810 + 0.0798087i 0.974569π0.974569\pi
158158 0 0
159159 6.00000 0.475831
160160 0 0
161161 0 0
162162 0 0
163163 −20.7846 −1.62798 −0.813988 0.580881i 0.802708π-0.802708\pi
−0.813988 + 0.580881i 0.802708π0.802708\pi
164164 0 0
165165 0 0
166166 0 0
167167 −17.3205 −1.34030 −0.670151 0.742225i 0.733770π-0.733770\pi
−0.670151 + 0.742225i 0.733770π0.733770\pi
168168 0 0
169169 11.0000 + 6.92820i 0.846154 + 0.532939i
170170 0 0
171171 6.92820i 0.529813i
172172 0 0
173173 6.00000i 0.456172i −0.973641 0.228086i 0.926753π-0.926753\pi
0.973641 0.228086i 0.0732467π-0.0732467\pi
174174 0 0
175175 0 0
176176 0 0
177177 −3.46410 −0.260378
178178 0 0
179179 12.0000 0.896922 0.448461 0.893802i 0.351972π-0.351972\pi
0.448461 + 0.893802i 0.351972π0.351972\pi
180180 0 0
181181 −22.0000 −1.63525 −0.817624 0.575753i 0.804709π-0.804709\pi
−0.817624 + 0.575753i 0.804709π0.804709\pi
182182 0 0
183183 10.0000i 0.739221i
184184 0 0
185185 0 0
186186 0 0
187187 −20.7846 −1.51992
188188 0 0
189189 0 0
190190 0 0
191191 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
192192 0 0
193193 13.8564 0.997406 0.498703 0.866773i 0.333810π-0.333810\pi
0.498703 + 0.866773i 0.333810π0.333810\pi
194194 0 0
195195 0 0
196196 0 0
197197 −17.3205 −1.23404 −0.617018 0.786949i 0.711659π-0.711659\pi
−0.617018 + 0.786949i 0.711659π0.711659\pi
198198 0 0
199199 8.00000 0.567105 0.283552 0.958957i 0.408487π-0.408487\pi
0.283552 + 0.958957i 0.408487π0.408487\pi
200200 0 0
201201 13.8564i 0.977356i
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 −24.0000 −1.66011
210210 0 0
211211 4.00000 0.275371 0.137686 0.990476i 0.456034π-0.456034\pi
0.137686 + 0.990476i 0.456034π0.456034\pi
212212 0 0
213213 −10.3923 −0.712069
214214 0 0
215215 0 0
216216 0 0
217217 0 0
218218 0 0
219219 6.92820i 0.468165i
220220 0 0
221221 −6.00000 + 20.7846i −0.403604 + 1.39812i
222222 0 0
223223 −6.92820 −0.463947 −0.231973 0.972722i 0.574518π-0.574518\pi
−0.231973 + 0.972722i 0.574518π0.574518\pi
224224 0 0
225225 0 0
226226 0 0
227227 10.3923 0.689761 0.344881 0.938647i 0.387919π-0.387919\pi
0.344881 + 0.938647i 0.387919π0.387919\pi
228228 0 0
229229 6.92820i 0.457829i −0.973447 0.228914i 0.926482π-0.926482\pi
0.973447 0.228914i 0.0735176π-0.0735176\pi
230230 0 0
231231 0 0
232232 0 0
233233 18.0000i 1.17922i −0.807688 0.589610i 0.799282π-0.799282\pi
0.807688 0.589610i 0.200718π-0.200718\pi
234234 0 0
235235 0 0
236236 0 0
237237 8.00000i 0.519656i
238238 0 0
239239 10.3923i 0.672222i −0.941822 0.336111i 0.890888π-0.890888\pi
0.941822 0.336111i 0.109112π-0.109112\pi
240240 0 0
241241 20.7846i 1.33885i −0.742878 0.669427i 0.766540π-0.766540\pi
0.742878 0.669427i 0.233460π-0.233460\pi
242242 0 0
243243 1.00000i 0.0641500i
244244 0 0
245245 0 0
246246 0 0
247247 −6.92820 + 24.0000i −0.440831 + 1.52708i
248248 0 0
249249 3.46410i 0.219529i
250250 0 0
251251 12.0000 0.757433 0.378717 0.925513i 0.376365π-0.376365\pi
0.378717 + 0.925513i 0.376365π0.376365\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 0 0
257257 6.00000i 0.374270i −0.982334 0.187135i 0.940080π-0.940080\pi
0.982334 0.187135i 0.0599201π-0.0599201\pi
258258 0 0
259259 0 0
260260 0 0
261261 −6.00000 −0.371391
262262 0 0
263263 0 0 1.00000 00
−1.00000 π\pi
264264 0 0
265265 0 0
266266 0 0
267267 −17.3205 −1.06000
268268 0 0
269269 30.0000 1.82913 0.914566 0.404436i 0.132532π-0.132532\pi
0.914566 + 0.404436i 0.132532π0.132532\pi
270270 0 0
271271 27.7128i 1.68343i −0.539919 0.841717i 0.681545π-0.681545\pi
0.539919 0.841717i 0.318455π-0.318455\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 0 0
277277 10.0000i 0.600842i −0.953807 0.300421i 0.902873π-0.902873\pi
0.953807 0.300421i 0.0971271π-0.0971271\pi
278278 0 0
279279 6.92820i 0.414781i
280280 0 0
281281 17.3205i 1.03325i 0.856210 + 0.516627i 0.172813π0.172813\pi
−0.856210 + 0.516627i 0.827187π0.827187\pi
282282 0 0
283283 20.0000i 1.18888i 0.804141 + 0.594438i 0.202626π0.202626\pi
−0.804141 + 0.594438i 0.797374π0.797374\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 −19.0000 −1.11765
290290 0 0
291291 6.92820i 0.406138i
292292 0 0
293293 3.46410 0.202375 0.101187 0.994867i 0.467736π-0.467736\pi
0.101187 + 0.994867i 0.467736π0.467736\pi
294294 0 0
295295 0 0
296296 0 0
297297 3.46410 0.201008
298298 0 0
299299 0 0
300300 0 0
301301 0 0
302302 0 0
303303 6.00000i 0.344691i
304304 0 0
305305 0 0
306306 0 0
307307 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
308308 0 0
309309 −4.00000 −0.227552
310310 0 0
311311 24.0000 1.36092 0.680458 0.732787i 0.261781π-0.261781\pi
0.680458 + 0.732787i 0.261781π0.261781\pi
312312 0 0
313313 10.0000i 0.565233i −0.959233 0.282617i 0.908798π-0.908798\pi
0.959233 0.282617i 0.0912024π-0.0912024\pi
314314 0 0
315315 0 0
316316 0 0
317317 24.2487 1.36194 0.680972 0.732310i 0.261558π-0.261558\pi
0.680972 + 0.732310i 0.261558π0.261558\pi
318318 0 0
319319 20.7846i 1.16371i
320320 0 0
321321 12.0000 0.669775
322322 0 0
323323 −41.5692 −2.31297
324324 0 0
325325 0 0
326326 0 0
327327 −6.92820 −0.383131
328328 0 0
329329 0 0
330330 0 0
331331 13.8564i 0.761617i 0.924654 + 0.380808i 0.124354π0.124354\pi
−0.924654 + 0.380808i 0.875646π0.875646\pi
332332 0 0
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 10.0000i 0.544735i 0.962193 + 0.272367i 0.0878066π0.0878066\pi
−0.962193 + 0.272367i 0.912193π0.912193\pi
338338 0 0
339339 −18.0000 −0.977626
340340 0 0
341341 24.0000 1.29967
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 0 0
347347 12.0000i 0.644194i −0.946707 0.322097i 0.895612π-0.895612\pi
0.946707 0.322097i 0.104388π-0.104388\pi
348348 0 0
349349 0 0 1.00000 00
−1.00000 π\pi
350350 0 0
351351 1.00000 3.46410i 0.0533761 0.184900i
352352 0 0
353353 10.3923 0.553127 0.276563 0.960996i 0.410804π-0.410804\pi
0.276563 + 0.960996i 0.410804π0.410804\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 24.2487i 1.27980i 0.768459 + 0.639899i 0.221024π0.221024\pi
−0.768459 + 0.639899i 0.778976π0.778976\pi
360360 0 0
361361 −29.0000 −1.52632
362362 0 0
363363 1.00000i 0.0524864i
364364 0 0
365365 0 0
366366 0 0
367367 28.0000i 1.46159i −0.682598 0.730794i 0.739150π-0.739150\pi
0.682598 0.730794i 0.260850π-0.260850\pi
368368 0 0
369369 3.46410i 0.180334i
370370 0 0
371371 0 0
372372 0 0
373373 2.00000i 0.103556i 0.998659 + 0.0517780i 0.0164888π0.0164888\pi
−0.998659 + 0.0517780i 0.983511π0.983511\pi
374374 0 0
375375 0 0
376376 0 0
377377 20.7846 + 6.00000i 1.07046 + 0.309016i
378378 0 0
379379 20.7846i 1.06763i −0.845600 0.533817i 0.820757π-0.820757\pi
0.845600 0.533817i 0.179243π-0.179243\pi
380380 0 0
381381 −16.0000 −0.819705
382382 0 0
383383 −24.2487 −1.23905 −0.619526 0.784976i 0.712675π-0.712675\pi
−0.619526 + 0.784976i 0.712675π0.712675\pi
384384 0 0
385385 0 0
386386 0 0
387387 8.00000i 0.406663i
388388 0 0
389389 6.00000 0.304212 0.152106 0.988364i 0.451394π-0.451394\pi
0.152106 + 0.988364i 0.451394π0.451394\pi
390390 0 0
391391 0 0
392392 0 0
393393 12.0000i 0.605320i
394394 0 0
395395 0 0
396396 0 0
397397 −13.8564 −0.695433 −0.347717 0.937600i 0.613043π-0.613043\pi
−0.347717 + 0.937600i 0.613043π0.613043\pi
398398 0 0
399399 0 0
400400 0 0
401401 10.3923i 0.518967i 0.965748 + 0.259483i 0.0835523π0.0835523\pi
−0.965748 + 0.259483i 0.916448π0.916448\pi
402402 0 0
403403 6.92820 24.0000i 0.345118 1.19553i
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 20.7846i 1.02773i −0.857870 0.513866i 0.828213π-0.828213\pi
0.857870 0.513866i 0.171787π-0.171787\pi
410410 0 0
411411 10.3923i 0.512615i
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 8.00000i 0.391762i
418418 0 0
419419 −12.0000 −0.586238 −0.293119 0.956076i 0.594693π-0.594693\pi
−0.293119 + 0.956076i 0.594693π0.594693\pi
420420 0 0
421421 20.7846i 1.01298i −0.862246 0.506490i 0.830943π-0.830943\pi
0.862246 0.506490i 0.169057π-0.169057\pi
422422 0 0
423423 3.46410 0.168430
424424 0 0
425425 0 0
426426 0 0
427427 0 0
428428 0 0
429429 −12.0000 3.46410i −0.579365 0.167248i
430430 0 0
431431 31.1769i 1.50174i 0.660451 + 0.750870i 0.270365π0.270365\pi
−0.660451 + 0.750870i 0.729635π0.729635\pi
432432 0 0
433433 2.00000i 0.0961139i 0.998845 + 0.0480569i 0.0153029π0.0153029\pi
−0.998845 + 0.0480569i 0.984697π0.984697\pi
434434 0 0
435435 0 0
436436 0 0
437437 0 0
438438 0 0
439439 −20.0000 −0.954548 −0.477274 0.878755i 0.658375π-0.658375\pi
−0.477274 + 0.878755i 0.658375π0.658375\pi
440440 0 0
441441 7.00000 0.333333
442442 0 0
443443 12.0000i 0.570137i 0.958507 + 0.285069i 0.0920164π0.0920164\pi
−0.958507 + 0.285069i 0.907984π0.907984\pi
444444 0 0
445445 0 0
446446 0 0
447447 −17.3205 −0.819232
448448 0 0
449449 3.46410i 0.163481i 0.996654 + 0.0817405i 0.0260479π0.0260479\pi
−0.996654 + 0.0817405i 0.973952π0.973952\pi
450450 0 0
451451 12.0000 0.565058
452452 0 0
453453 −6.92820 −0.325515
454454 0 0
455455 0 0
456456 0 0
457457 −6.92820 −0.324088 −0.162044 0.986784i 0.551809π-0.551809\pi
−0.162044 + 0.986784i 0.551809π0.551809\pi
458458 0 0
459459 6.00000 0.280056
460460 0 0
461461 10.3923i 0.484018i −0.970274 0.242009i 0.922194π-0.922194\pi
0.970274 0.242009i 0.0778063π-0.0778063\pi
462462 0 0
463463 13.8564 0.643962 0.321981 0.946746i 0.395651π-0.395651\pi
0.321981 + 0.946746i 0.395651π0.395651\pi
464464 0 0
465465 0 0
466466 0 0
467467 36.0000i 1.66588i 0.553362 + 0.832941i 0.313345π0.313345\pi
−0.553362 + 0.832941i 0.686655π0.686655\pi
468468 0 0
469469 0 0
470470 0 0
471471 −2.00000 −0.0921551
472472 0 0
473473 27.7128 1.27424
474474 0 0
475475 0 0
476476 0 0
477477 6.00000i 0.274721i
478478 0 0
479479 3.46410i 0.158279i 0.996864 + 0.0791394i 0.0252172π0.0252172\pi
−0.996864 + 0.0791394i 0.974783π0.974783\pi
480480 0 0
481481 0 0
482482 0 0
483483 0 0
484484 0 0
485485 0 0
486486 0 0
487487 −6.92820 −0.313947 −0.156973 0.987603i 0.550174π-0.550174\pi
−0.156973 + 0.987603i 0.550174π0.550174\pi
488488 0 0
489489 20.7846i 0.939913i
490490 0 0
491491 −36.0000 −1.62466 −0.812329 0.583200i 0.801800π-0.801800\pi
−0.812329 + 0.583200i 0.801800π0.801800\pi
492492 0 0
493493 36.0000i 1.62136i
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 0 0 1.00000 00
−1.00000 π\pi
500500 0 0
501501 17.3205i 0.773823i
502502 0 0
503503 24.0000i 1.07011i −0.844818 0.535054i 0.820291π-0.820291\pi
0.844818 0.535054i 0.179709π-0.179709\pi
504504 0 0
505505 0 0
506506 0 0
507507 −6.92820 + 11.0000i −0.307692 + 0.488527i
508508 0 0
509509 24.2487i 1.07481i 0.843326 + 0.537403i 0.180594π0.180594\pi
−0.843326 + 0.537403i 0.819406π0.819406\pi
510510 0 0
511511 0 0
512512 0 0
513513 6.92820 0.305888
514514 0 0
515515 0 0
516516 0 0
517517 12.0000i 0.527759i
518518 0 0
519519 6.00000 0.263371
520520 0 0
521521 6.00000 0.262865 0.131432 0.991325i 0.458042π-0.458042\pi
0.131432 + 0.991325i 0.458042π0.458042\pi
522522 0 0
523523 8.00000i 0.349816i −0.984585 0.174908i 0.944037π-0.944037\pi
0.984585 0.174908i 0.0559627π-0.0559627\pi
524524 0 0
525525 0 0
526526 0 0
527527 41.5692 1.81078
528528 0 0
529529 23.0000 1.00000
530530 0 0
531531 3.46410i 0.150329i
532532 0 0
533533 3.46410 12.0000i 0.150047 0.519778i
534534 0 0
535535 0 0
536536 0 0
537537 12.0000i 0.517838i
538538 0 0
539539 24.2487i 1.04447i
540540 0 0
541541 20.7846i 0.893600i −0.894634 0.446800i 0.852564π-0.852564\pi
0.894634 0.446800i 0.147436π-0.147436\pi
542542 0 0
543543 22.0000i 0.944110i
544544 0 0
545545 0 0
546546 0 0
547547 8.00000i 0.342055i 0.985266 + 0.171028i 0.0547087π0.0547087\pi
−0.985266 + 0.171028i 0.945291π0.945291\pi
548548 0 0
549549 −10.0000 −0.426790
550550 0 0
551551 41.5692i 1.77091i
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 0 0
557557 24.2487 1.02745 0.513725 0.857955i 0.328265π-0.328265\pi
0.513725 + 0.857955i 0.328265π0.328265\pi
558558 0 0
559559 8.00000 27.7128i 0.338364 1.17213i
560560 0 0
561561 20.7846i 0.877527i
562562 0 0
563563 36.0000i 1.51722i 0.651546 + 0.758610i 0.274121π0.274121\pi
−0.651546 + 0.758610i 0.725879π0.725879\pi
564564 0 0
565565 0 0
566566 0 0
567567 0 0
568568 0 0
569569 −18.0000 −0.754599 −0.377300 0.926091i 0.623147π-0.623147\pi
−0.377300 + 0.926091i 0.623147π0.623147\pi
570570 0 0
571571 28.0000 1.17176 0.585882 0.810397i 0.300748π-0.300748\pi
0.585882 + 0.810397i 0.300748π0.300748\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 0 0
577577 13.8564 0.576850 0.288425 0.957503i 0.406868π-0.406868\pi
0.288425 + 0.957503i 0.406868π0.406868\pi
578578 0 0
579579 13.8564i 0.575853i
580580 0 0
581581 0 0
582582 0 0
583583 20.7846 0.860811
584584 0 0
585585 0 0
586586 0 0
587587 31.1769 1.28681 0.643404 0.765526i 0.277521π-0.277521\pi
0.643404 + 0.765526i 0.277521π0.277521\pi
588588 0 0
589589 48.0000 1.97781
590590 0 0
591591 17.3205i 0.712470i
592592 0 0
593593 24.2487 0.995775 0.497888 0.867242i 0.334109π-0.334109\pi
0.497888 + 0.867242i 0.334109π0.334109\pi
594594 0 0
595595 0 0
596596 0 0
597597 8.00000i 0.327418i
598598 0 0
599599 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
600600 0 0
601601 10.0000 0.407909 0.203954 0.978980i 0.434621π-0.434621\pi
0.203954 + 0.978980i 0.434621π0.434621\pi
602602 0 0
603603 13.8564 0.564276
604604 0 0
605605 0 0
606606 0 0
607607 28.0000i 1.13648i −0.822861 0.568242i 0.807624π-0.807624\pi
0.822861 0.568242i 0.192376π-0.192376\pi
608608 0 0
609609 0 0
610610 0 0
611611 −12.0000 3.46410i −0.485468 0.140143i
612612 0 0
613613 13.8564 0.559655 0.279827 0.960050i 0.409723π-0.409723\pi
0.279827 + 0.960050i 0.409723π0.409723\pi
614614 0 0
615615 0 0
616616 0 0
617617 31.1769 1.25514 0.627568 0.778562i 0.284051π-0.284051\pi
0.627568 + 0.778562i 0.284051π0.284051\pi
618618 0 0
619619 27.7128i 1.11387i 0.830555 + 0.556936i 0.188023π0.188023\pi
−0.830555 + 0.556936i 0.811977π0.811977\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 0 0
626626 0 0
627627 24.0000i 0.958468i
628628 0 0
629629 0 0
630630 0 0
631631 20.7846i 0.827422i 0.910408 + 0.413711i 0.135768π0.135768\pi
−0.910408 + 0.413711i 0.864232π0.864232\pi
632632 0 0
633633 4.00000i 0.158986i
634634 0 0
635635 0 0
636636 0 0
637637 −24.2487 7.00000i −0.960769 0.277350i
638638 0 0
639639 10.3923i 0.411113i
640640 0 0
641641 30.0000 1.18493 0.592464 0.805597i 0.298155π-0.298155\pi
0.592464 + 0.805597i 0.298155π0.298155\pi
642642 0 0
643643 −41.5692 −1.63933 −0.819665 0.572843i 0.805840π-0.805840\pi
−0.819665 + 0.572843i 0.805840π0.805840\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 1.00000 00
−1.00000 π\pi
648648 0 0
649649 −12.0000 −0.471041
650650 0 0
651651 0 0
652652 0 0
653653 6.00000i 0.234798i 0.993085 + 0.117399i 0.0374557π0.0374557\pi
−0.993085 + 0.117399i 0.962544π0.962544\pi
654654 0 0
655655 0 0
656656 0 0
657657 6.92820 0.270295
658658 0 0
659659 −12.0000 −0.467454 −0.233727 0.972302i 0.575092π-0.575092\pi
−0.233727 + 0.972302i 0.575092π0.575092\pi
660660 0 0
661661 13.8564i 0.538952i −0.963007 0.269476i 0.913150π-0.913150\pi
0.963007 0.269476i 0.0868504π-0.0868504\pi
662662 0 0
663663 −20.7846 6.00000i −0.807207 0.233021i
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 6.92820i 0.267860i
670670 0 0
671671 34.6410i 1.33730i
672672 0 0
673673 14.0000i 0.539660i −0.962908 0.269830i 0.913032π-0.913032\pi
0.962908 0.269830i 0.0869676π-0.0869676\pi
674674 0 0
675675 0 0
676676 0 0
677677 18.0000i 0.691796i −0.938272 0.345898i 0.887574π-0.887574\pi
0.938272 0.345898i 0.112426π-0.112426\pi
678678 0 0
679679 0 0
680680 0 0
681681 10.3923i 0.398234i
682682 0 0
683683 3.46410 0.132550 0.0662751 0.997801i 0.478889π-0.478889\pi
0.0662751 + 0.997801i 0.478889π0.478889\pi
684684 0 0
685685 0 0
686686 0 0
687687 6.92820 0.264327
688688 0 0
689689 6.00000 20.7846i 0.228582 0.791831i
690690 0 0
691691 27.7128i 1.05425i 0.849789 + 0.527123i 0.176729π0.176729\pi
−0.849789 + 0.527123i 0.823271π0.823271\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 20.7846 0.787273
698698 0 0
699699 18.0000 0.680823
700700 0 0
701701 −30.0000 −1.13308 −0.566542 0.824033i 0.691719π-0.691719\pi
−0.566542 + 0.824033i 0.691719π0.691719\pi
702702 0 0
703703 0 0
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 6.92820i 0.260194i 0.991501 + 0.130097i 0.0415289π0.0415289\pi
−0.991501 + 0.130097i 0.958471π0.958471\pi
710710 0 0
711711 −8.00000 −0.300023
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 10.3923 0.388108
718718 0 0
719719 −24.0000 −0.895049 −0.447524 0.894272i 0.647694π-0.647694\pi
−0.447524 + 0.894272i 0.647694π0.647694\pi
720720 0 0
721721 0 0
722722 0 0
723723 20.7846 0.772988
724724 0 0
725725 0 0
726726 0 0
727727 16.0000i 0.593407i 0.954970 + 0.296704i 0.0958873π0.0958873\pi
−0.954970 + 0.296704i 0.904113π0.904113\pi
728728 0 0
729729 −1.00000 −0.0370370
730730 0 0
731731 48.0000 1.77534
732732 0 0
733733 6.92820 0.255899 0.127950 0.991781i 0.459160π-0.459160\pi
0.127950 + 0.991781i 0.459160π0.459160\pi
734734 0 0
735735 0 0
736736 0 0
737737 48.0000i 1.76810i
738738 0 0
739739 27.7128i 1.01943i −0.860343 0.509716i 0.829750π-0.829750\pi
0.860343 0.509716i 0.170250π-0.170250\pi
740740 0 0
741741 −24.0000 6.92820i −0.881662 0.254514i
742742 0 0
743743 10.3923 0.381257 0.190628 0.981662i 0.438947π-0.438947\pi
0.190628 + 0.981662i 0.438947π0.438947\pi
744744 0 0
745745 0 0
746746 0 0
747747 3.46410 0.126745
748748 0 0
749749 0 0
750750 0 0
751751 −28.0000 −1.02173 −0.510867 0.859660i 0.670676π-0.670676\pi
−0.510867 + 0.859660i 0.670676π0.670676\pi
752752 0 0
753753 12.0000i 0.437304i
754754 0 0
755755 0 0
756756 0 0
757757 38.0000i 1.38113i −0.723269 0.690567i 0.757361π-0.757361\pi
0.723269 0.690567i 0.242639π-0.242639\pi
758758 0 0
759759 0 0
760760 0 0
761761 31.1769i 1.13016i 0.825035 + 0.565081i 0.191155π0.191155\pi
−0.825035 + 0.565081i 0.808845π0.808845\pi
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 0 0
767767 −3.46410 + 12.0000i −0.125081 + 0.433295i
768768 0 0
769769 27.7128i 0.999350i −0.866213 0.499675i 0.833453π-0.833453\pi
0.866213 0.499675i 0.166547π-0.166547\pi
770770 0 0
771771 6.00000 0.216085
772772 0 0
773773 51.9615 1.86893 0.934463 0.356060i 0.115880π-0.115880\pi
0.934463 + 0.356060i 0.115880π0.115880\pi
774774 0 0
775775 0 0
776776 0 0
777777 0 0
778778 0 0
779779 24.0000 0.859889
780780 0 0
781781 −36.0000 −1.28818
782782 0 0
783783 6.00000i 0.214423i
784784 0 0
785785 0 0
786786 0 0
787787 27.7128 0.987855 0.493928 0.869503i 0.335561π-0.335561\pi
0.493928 + 0.869503i 0.335561π0.335561\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 34.6410 + 10.0000i 1.23014 + 0.355110i
794794 0 0
795795 0 0
796796 0 0
797797 30.0000i 1.06265i −0.847167 0.531327i 0.821693π-0.821693\pi
0.847167 0.531327i 0.178307π-0.178307\pi
798798 0 0
799799 20.7846i 0.735307i
800800 0 0
801801 17.3205i 0.611990i
802802 0 0
803803 24.0000i 0.846942i
804804 0 0
805805 0 0
806806 0 0
807807 30.0000i 1.05605i
808808 0 0
809809 18.0000 0.632846 0.316423 0.948618i 0.397518π-0.397518\pi
0.316423 + 0.948618i 0.397518π0.397518\pi
810810 0 0
811811 6.92820i 0.243282i 0.992574 + 0.121641i 0.0388157π0.0388157\pi
−0.992574 + 0.121641i 0.961184π0.961184\pi
812812 0 0
813813 27.7128 0.971931
814814 0 0
815815 0 0
816816 0 0
817817 55.4256 1.93910
818818 0 0
819819 0 0
820820 0 0
821821 3.46410i 0.120898i −0.998171 0.0604490i 0.980747π-0.980747\pi
0.998171 0.0604490i 0.0192532π-0.0192532\pi
822822 0 0
823823 4.00000i 0.139431i 0.997567 + 0.0697156i 0.0222092π0.0222092\pi
−0.997567 + 0.0697156i 0.977791π0.977791\pi
824824 0 0
825825 0 0
826826 0 0
827827 −17.3205 −0.602293 −0.301147 0.953578i 0.597369π-0.597369\pi
−0.301147 + 0.953578i 0.597369π0.597369\pi
828828 0 0
829829 −34.0000 −1.18087 −0.590434 0.807086i 0.701044π-0.701044\pi
−0.590434 + 0.807086i 0.701044π0.701044\pi
830830 0 0
831831 10.0000 0.346896
832832 0 0
833833 42.0000i 1.45521i
834834 0 0
835835 0 0
836836 0 0
837837 −6.92820 −0.239474
838838 0 0
839839 10.3923i 0.358782i −0.983778 0.179391i 0.942587π-0.942587\pi
0.983778 0.179391i 0.0574128π-0.0574128\pi
840840 0 0
841841 7.00000 0.241379
842842 0 0
843843 −17.3205 −0.596550
844844 0 0
845845 0 0
846846 0 0
847847 0 0
848848 0 0
849849 −20.0000 −0.686398
850850 0 0
851851 0 0
852852 0 0
853853 13.8564 0.474434 0.237217 0.971457i 0.423765π-0.423765\pi
0.237217 + 0.971457i 0.423765π0.423765\pi
854854 0 0
855855 0 0
856856 0 0
857857 6.00000i 0.204956i −0.994735 0.102478i 0.967323π-0.967323\pi
0.994735 0.102478i 0.0326771π-0.0326771\pi
858858 0 0
859859 −28.0000 −0.955348 −0.477674 0.878537i 0.658520π-0.658520\pi
−0.477674 + 0.878537i 0.658520π0.658520\pi
860860 0 0
861861 0 0
862862 0 0
863863 −38.1051 −1.29711 −0.648557 0.761166i 0.724627π-0.724627\pi
−0.648557 + 0.761166i 0.724627π0.724627\pi
864864 0 0
865865 0 0
866866 0 0
867867 19.0000i 0.645274i
868868 0 0
869869 27.7128i 0.940093i
870870 0 0
871871 −48.0000 13.8564i −1.62642 0.469506i
872872 0 0
873873 6.92820 0.234484
874874 0 0
875875 0 0
876876 0 0
877877 −41.5692 −1.40369 −0.701846 0.712328i 0.747641π-0.747641\pi
−0.701846 + 0.712328i 0.747641π0.747641\pi
878878 0 0
879879 3.46410i 0.116841i
880880 0 0
881881 −6.00000 −0.202145 −0.101073 0.994879i 0.532227π-0.532227\pi
−0.101073 + 0.994879i 0.532227π0.532227\pi
882882 0 0
883883 20.0000i 0.673054i 0.941674 + 0.336527i 0.109252π0.109252\pi
−0.941674 + 0.336527i 0.890748π0.890748\pi
884884 0 0
885885 0 0
886886 0 0
887887 48.0000i 1.61168i −0.592132 0.805841i 0.701714π-0.701714\pi
0.592132 0.805841i 0.298286π-0.298286\pi
888888 0 0
889889 0 0
890890 0 0
891891 3.46410i 0.116052i
892892 0 0
893893 24.0000i 0.803129i
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 41.5692i 1.38641i
900900 0 0
901901 36.0000 1.19933
902902 0 0
903903 0 0
904904 0 0
905905 0 0
906906 0 0
907907 28.0000i 0.929725i 0.885383 + 0.464862i 0.153896π0.153896\pi
−0.885383 + 0.464862i 0.846104π0.846104\pi
908908 0 0
909909 −6.00000 −0.199007
910910 0 0
911911 −24.0000 −0.795155 −0.397578 0.917568i 0.630149π-0.630149\pi
−0.397578 + 0.917568i 0.630149π0.630149\pi
912912 0 0
913913 12.0000i 0.397142i
914914 0 0
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 32.0000 1.05558 0.527791 0.849374i 0.323020π-0.323020\pi
0.527791 + 0.849374i 0.323020π0.323020\pi
920920 0 0
921921 0 0
922922 0 0
923923 −10.3923 + 36.0000i −0.342067 + 1.18495i
924924 0 0
925925 0 0
926926 0 0
927927 4.00000i 0.131377i
928928 0 0
929929 31.1769i 1.02288i 0.859319 + 0.511441i 0.170888π0.170888\pi
−0.859319 + 0.511441i 0.829112π0.829112\pi
930930 0 0
931931 48.4974i 1.58944i
932932 0 0
933933 24.0000i 0.785725i
934934 0 0
935935 0 0
936936 0 0
937937 22.0000i 0.718709i 0.933201 + 0.359354i 0.117003π0.117003\pi
−0.933201 + 0.359354i 0.882997π0.882997\pi
938938 0 0
939939 10.0000 0.326338
940940 0 0
941941 10.3923i 0.338779i 0.985549 + 0.169390i 0.0541797π0.0541797\pi
−0.985549 + 0.169390i 0.945820π0.945820\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 45.0333 1.46339 0.731693 0.681634i 0.238730π-0.238730\pi
0.731693 + 0.681634i 0.238730π0.238730\pi
948948 0 0
949949 −24.0000 6.92820i −0.779073 0.224899i
950950 0 0
951951 24.2487i 0.786318i
952952 0 0
953953 6.00000i 0.194359i 0.995267 + 0.0971795i 0.0309821π0.0309821\pi
−0.995267 + 0.0971795i 0.969018π0.969018\pi
954954 0 0
955955 0 0
956956 0 0
957957 −20.7846 −0.671871
958958 0 0
959959 0 0
960960 0 0
961961 −17.0000 −0.548387
962962 0 0
963963 12.0000i 0.386695i
964964 0 0
965965 0 0
966966 0 0
967967 34.6410 1.11398 0.556990 0.830519i 0.311956π-0.311956\pi
0.556990 + 0.830519i 0.311956π0.311956\pi
968968 0 0
969969 41.5692i 1.33540i
970970 0 0
971971 60.0000 1.92549 0.962746 0.270408i 0.0871586π-0.0871586\pi
0.962746 + 0.270408i 0.0871586π0.0871586\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 24.2487 0.775785 0.387893 0.921705i 0.373203π-0.373203\pi
0.387893 + 0.921705i 0.373203π0.373203\pi
978978 0 0
979979 −60.0000 −1.91761
980980 0 0
981981 6.92820i 0.221201i
982982 0 0
983983 −31.1769 −0.994389 −0.497195 0.867639i 0.665636π-0.665636\pi
−0.497195 + 0.867639i 0.665636π0.665636\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 20.0000 0.635321 0.317660 0.948205i 0.397103π-0.397103\pi
0.317660 + 0.948205i 0.397103π0.397103\pi
992992 0 0
993993 −13.8564 −0.439720
994994 0 0
995995 0 0
996996 0 0
997997 38.0000i 1.20347i 0.798695 + 0.601736i 0.205524π0.205524\pi
−0.798695 + 0.601736i 0.794476π0.794476\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 3900.2.j.h.649.4 4
5.2 odd 4 3900.2.c.c.3301.2 2
5.3 odd 4 156.2.b.a.25.2 yes 2
5.4 even 2 inner 3900.2.j.h.649.2 4
13.12 even 2 inner 3900.2.j.h.649.3 4
15.8 even 4 468.2.b.a.181.1 2
20.3 even 4 624.2.c.f.337.2 2
35.13 even 4 7644.2.e.g.4705.1 2
40.3 even 4 2496.2.c.e.961.1 2
40.13 odd 4 2496.2.c.l.961.1 2
60.23 odd 4 1872.2.c.c.1585.1 2
65.3 odd 12 2028.2.q.b.1837.1 2
65.8 even 4 2028.2.a.g.1.1 2
65.12 odd 4 3900.2.c.c.3301.1 2
65.18 even 4 2028.2.a.g.1.2 2
65.23 odd 12 2028.2.q.c.1837.1 2
65.28 even 12 2028.2.i.i.529.2 4
65.33 even 12 2028.2.i.i.2005.1 4
65.38 odd 4 156.2.b.a.25.1 2
65.43 odd 12 2028.2.q.b.361.1 2
65.48 odd 12 2028.2.q.c.361.1 2
65.58 even 12 2028.2.i.i.2005.2 4
65.63 even 12 2028.2.i.i.529.1 4
65.64 even 2 inner 3900.2.j.h.649.1 4
195.8 odd 4 6084.2.a.v.1.2 2
195.38 even 4 468.2.b.a.181.2 2
195.83 odd 4 6084.2.a.v.1.1 2
260.83 odd 4 8112.2.a.bs.1.2 2
260.103 even 4 624.2.c.f.337.1 2
260.203 odd 4 8112.2.a.bs.1.1 2
455.363 even 4 7644.2.e.g.4705.2 2
520.363 even 4 2496.2.c.e.961.2 2
520.493 odd 4 2496.2.c.l.961.2 2
780.623 odd 4 1872.2.c.c.1585.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
156.2.b.a.25.1 2 65.38 odd 4
156.2.b.a.25.2 yes 2 5.3 odd 4
468.2.b.a.181.1 2 15.8 even 4
468.2.b.a.181.2 2 195.38 even 4
624.2.c.f.337.1 2 260.103 even 4
624.2.c.f.337.2 2 20.3 even 4
1872.2.c.c.1585.1 2 60.23 odd 4
1872.2.c.c.1585.2 2 780.623 odd 4
2028.2.a.g.1.1 2 65.8 even 4
2028.2.a.g.1.2 2 65.18 even 4
2028.2.i.i.529.1 4 65.63 even 12
2028.2.i.i.529.2 4 65.28 even 12
2028.2.i.i.2005.1 4 65.33 even 12
2028.2.i.i.2005.2 4 65.58 even 12
2028.2.q.b.361.1 2 65.43 odd 12
2028.2.q.b.1837.1 2 65.3 odd 12
2028.2.q.c.361.1 2 65.48 odd 12
2028.2.q.c.1837.1 2 65.23 odd 12
2496.2.c.e.961.1 2 40.3 even 4
2496.2.c.e.961.2 2 520.363 even 4
2496.2.c.l.961.1 2 40.13 odd 4
2496.2.c.l.961.2 2 520.493 odd 4
3900.2.c.c.3301.1 2 65.12 odd 4
3900.2.c.c.3301.2 2 5.2 odd 4
3900.2.j.h.649.1 4 65.64 even 2 inner
3900.2.j.h.649.2 4 5.4 even 2 inner
3900.2.j.h.649.3 4 13.12 even 2 inner
3900.2.j.h.649.4 4 1.1 even 1 trivial
6084.2.a.v.1.1 2 195.83 odd 4
6084.2.a.v.1.2 2 195.8 odd 4
7644.2.e.g.4705.1 2 35.13 even 4
7644.2.e.g.4705.2 2 455.363 even 4
8112.2.a.bs.1.1 2 260.203 odd 4
8112.2.a.bs.1.2 2 260.83 odd 4