Properties

Label 1584.2.b.e.593.1
Level 15841584
Weight 22
Character 1584.593
Analytic conductor 12.64812.648
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] = [1584,2,Mod(593,1584)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1584, 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("1584.593");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1584=243211 1584 = 2^{4} \cdot 3^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1584.b (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: 12.648303680212.6483036802
Analytic rank: 00
Dimension: 44
Coefficient field: Q(2,3)\Q(\sqrt{-2}, \sqrt{3})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+4x2+1 x^{4} + 4x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 593.1
Root 1.93185i-1.93185i of defining polynomial
Character χ\chi == 1584.593
Dual form 1584.2.b.e.593.4

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q1.41421iq52.44949iq7+(1.73205+2.82843i)q11+4.89898iq13+7.34847iq192.82843iq23+3.00000q25+6.92820q29+4.00000q313.46410q35+8.00000q376.92820q412.44949iq432.82843iq47+1.00000q499.89949iq53+(4.000002.44949i)q5511.3137iq594.89898iq61+6.92820q65+4.00000q672.82843iq71+(6.928204.24264i)q77+12.2474iq79+13.8564q83+7.07107iq89+12.0000q91+10.3923q9510.0000q97+O(q100)q-1.41421i q^{5} -2.44949i q^{7} +(1.73205 + 2.82843i) q^{11} +4.89898i q^{13} +7.34847i q^{19} -2.82843i q^{23} +3.00000 q^{25} +6.92820 q^{29} +4.00000 q^{31} -3.46410 q^{35} +8.00000 q^{37} -6.92820 q^{41} -2.44949i q^{43} -2.82843i q^{47} +1.00000 q^{49} -9.89949i q^{53} +(4.00000 - 2.44949i) q^{55} -11.3137i q^{59} -4.89898i q^{61} +6.92820 q^{65} +4.00000 q^{67} -2.82843i q^{71} +(6.92820 - 4.24264i) q^{77} +12.2474i q^{79} +13.8564 q^{83} +7.07107i q^{89} +12.0000 q^{91} +10.3923 q^{95} -10.0000 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+12q25+16q31+32q37+4q49+16q55+16q67+48q9140q97+O(q100) 4 q + 12 q^{25} + 16 q^{31} + 32 q^{37} + 4 q^{49} + 16 q^{55} + 16 q^{67} + 48 q^{91} - 40 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1584Z)×\left(\mathbb{Z}/1584\mathbb{Z}\right)^\times.

nn 145145 353353 991991 11891189
χ(n)\chi(n) 1-1 1-1 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 1.41421i 0.632456i −0.948683 0.316228i 0.897584π-0.897584\pi
0.948683 0.316228i 0.102416π-0.102416\pi
66 0 0
77 2.44949i 0.925820i −0.886405 0.462910i 0.846805π-0.846805\pi
0.886405 0.462910i 0.153195π-0.153195\pi
88 0 0
99 0 0
1010 0 0
1111 1.73205 + 2.82843i 0.522233 + 0.852803i
1212 0 0
1313 4.89898i 1.35873i 0.733799 + 0.679366i 0.237745π0.237745\pi
−0.733799 + 0.679366i 0.762255π0.762255\pi
1414 0 0
1515 0 0
1616 0 0
1717 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1818 0 0
1919 7.34847i 1.68585i 0.538028 + 0.842927i 0.319170π0.319170\pi
−0.538028 + 0.842927i 0.680830π0.680830\pi
2020 0 0
2121 0 0
2222 0 0
2323 2.82843i 0.589768i −0.955533 0.294884i 0.904719π-0.904719\pi
0.955533 0.294884i 0.0952810π-0.0952810\pi
2424 0 0
2525 3.00000 0.600000
2626 0 0
2727 0 0
2828 0 0
2929 6.92820 1.28654 0.643268 0.765641i 0.277578π-0.277578\pi
0.643268 + 0.765641i 0.277578π0.277578\pi
3030 0 0
3131 4.00000 0.718421 0.359211 0.933257i 0.383046π-0.383046\pi
0.359211 + 0.933257i 0.383046π0.383046\pi
3232 0 0
3333 0 0
3434 0 0
3535 −3.46410 −0.585540
3636 0 0
3737 8.00000 1.31519 0.657596 0.753371i 0.271573π-0.271573\pi
0.657596 + 0.753371i 0.271573π0.271573\pi
3838 0 0
3939 0 0
4040 0 0
4141 −6.92820 −1.08200 −0.541002 0.841021i 0.681955π-0.681955\pi
−0.541002 + 0.841021i 0.681955π0.681955\pi
4242 0 0
4343 2.44949i 0.373544i −0.982403 0.186772i 0.940197π-0.940197\pi
0.982403 0.186772i 0.0598025π-0.0598025\pi
4444 0 0
4545 0 0
4646 0 0
4747 2.82843i 0.412568i −0.978492 0.206284i 0.933863π-0.933863\pi
0.978492 0.206284i 0.0661372π-0.0661372\pi
4848 0 0
4949 1.00000 0.142857
5050 0 0
5151 0 0
5252 0 0
5353 9.89949i 1.35980i −0.733305 0.679900i 0.762023π-0.762023\pi
0.733305 0.679900i 0.237977π-0.237977\pi
5454 0 0
5555 4.00000 2.44949i 0.539360 0.330289i
5656 0 0
5757 0 0
5858 0 0
5959 11.3137i 1.47292i −0.676481 0.736460i 0.736496π-0.736496\pi
0.676481 0.736460i 0.263504π-0.263504\pi
6060 0 0
6161 4.89898i 0.627250i −0.949547 0.313625i 0.898457π-0.898457\pi
0.949547 0.313625i 0.101543π-0.101543\pi
6262 0 0
6363 0 0
6464 0 0
6565 6.92820 0.859338
6666 0 0
6767 4.00000 0.488678 0.244339 0.969690i 0.421429π-0.421429\pi
0.244339 + 0.969690i 0.421429π0.421429\pi
6868 0 0
6969 0 0
7070 0 0
7171 2.82843i 0.335673i −0.985815 0.167836i 0.946322π-0.946322\pi
0.985815 0.167836i 0.0536780π-0.0536780\pi
7272 0 0
7373 0 0 1.00000 00
−1.00000 π\pi
7474 0 0
7575 0 0
7676 0 0
7777 6.92820 4.24264i 0.789542 0.483494i
7878 0 0
7979 12.2474i 1.37795i 0.724787 + 0.688973i 0.241938π0.241938\pi
−0.724787 + 0.688973i 0.758062π0.758062\pi
8080 0 0
8181 0 0
8282 0 0
8383 13.8564 1.52094 0.760469 0.649374i 0.224969π-0.224969\pi
0.760469 + 0.649374i 0.224969π0.224969\pi
8484 0 0
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 7.07107i 0.749532i 0.927119 + 0.374766i 0.122277π0.122277\pi
−0.927119 + 0.374766i 0.877723π0.877723\pi
9090 0 0
9191 12.0000 1.25794
9292 0 0
9393 0 0
9494 0 0
9595 10.3923 1.06623
9696 0 0
9797 −10.0000 −1.01535 −0.507673 0.861550i 0.669494π-0.669494\pi
−0.507673 + 0.861550i 0.669494π0.669494\pi
9898 0 0
9999 0 0
100100 0 0
101101 −13.8564 −1.37876 −0.689382 0.724398i 0.742118π-0.742118\pi
−0.689382 + 0.724398i 0.742118π0.742118\pi
102102 0 0
103103 4.00000 0.394132 0.197066 0.980390i 0.436859π-0.436859\pi
0.197066 + 0.980390i 0.436859π0.436859\pi
104104 0 0
105105 0 0
106106 0 0
107107 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
108108 0 0
109109 14.6969i 1.40771i 0.710343 + 0.703856i 0.248540π0.248540\pi
−0.710343 + 0.703856i 0.751460π0.751460\pi
110110 0 0
111111 0 0
112112 0 0
113113 1.41421i 0.133038i −0.997785 0.0665190i 0.978811π-0.978811\pi
0.997785 0.0665190i 0.0211893π-0.0211893\pi
114114 0 0
115115 −4.00000 −0.373002
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 −5.00000 + 9.79796i −0.454545 + 0.890724i
122122 0 0
123123 0 0
124124 0 0
125125 11.3137i 1.01193i
126126 0 0
127127 7.34847i 0.652071i 0.945357 + 0.326036i 0.105713π0.105713\pi
−0.945357 + 0.326036i 0.894287π0.894287\pi
128128 0 0
129129 0 0
130130 0 0
131131 −3.46410 −0.302660 −0.151330 0.988483i 0.548356π-0.548356\pi
−0.151330 + 0.988483i 0.548356π0.548356\pi
132132 0 0
133133 18.0000 1.56080
134134 0 0
135135 0 0
136136 0 0
137137 15.5563i 1.32907i 0.747258 + 0.664534i 0.231370π0.231370\pi
−0.747258 + 0.664534i 0.768630π0.768630\pi
138138 0 0
139139 2.44949i 0.207763i 0.994590 + 0.103882i 0.0331263π0.0331263\pi
−0.994590 + 0.103882i 0.966874π0.966874\pi
140140 0 0
141141 0 0
142142 0 0
143143 −13.8564 + 8.48528i −1.15873 + 0.709575i
144144 0 0
145145 9.79796i 0.813676i
146146 0 0
147147 0 0
148148 0 0
149149 13.8564 1.13516 0.567581 0.823318i 0.307880π-0.307880\pi
0.567581 + 0.823318i 0.307880π0.307880\pi
150150 0 0
151151 2.44949i 0.199337i −0.995021 0.0996683i 0.968222π-0.968222\pi
0.995021 0.0996683i 0.0317782π-0.0317782\pi
152152 0 0
153153 0 0
154154 0 0
155155 5.65685i 0.454369i
156156 0 0
157157 14.0000 1.11732 0.558661 0.829396i 0.311315π-0.311315\pi
0.558661 + 0.829396i 0.311315π0.311315\pi
158158 0 0
159159 0 0
160160 0 0
161161 −6.92820 −0.546019
162162 0 0
163163 −8.00000 −0.626608 −0.313304 0.949653i 0.601436π-0.601436\pi
−0.313304 + 0.949653i 0.601436π0.601436\pi
164164 0 0
165165 0 0
166166 0 0
167167 −3.46410 −0.268060 −0.134030 0.990977i 0.542792π-0.542792\pi
−0.134030 + 0.990977i 0.542792π0.542792\pi
168168 0 0
169169 −11.0000 −0.846154
170170 0 0
171171 0 0
172172 0 0
173173 6.92820 0.526742 0.263371 0.964695i 0.415166π-0.415166\pi
0.263371 + 0.964695i 0.415166π0.415166\pi
174174 0 0
175175 7.34847i 0.555492i
176176 0 0
177177 0 0
178178 0 0
179179 22.6274i 1.69125i 0.533775 + 0.845626i 0.320773π0.320773\pi
−0.533775 + 0.845626i 0.679227π0.679227\pi
180180 0 0
181181 8.00000 0.594635 0.297318 0.954779i 0.403908π-0.403908\pi
0.297318 + 0.954779i 0.403908π0.403908\pi
182182 0 0
183183 0 0
184184 0 0
185185 11.3137i 0.831800i
186186 0 0
187187 0 0
188188 0 0
189189 0 0
190190 0 0
191191 2.82843i 0.204658i −0.994751 0.102329i 0.967371π-0.967371\pi
0.994751 0.102329i 0.0326294π-0.0326294\pi
192192 0 0
193193 9.79796i 0.705273i −0.935760 0.352636i 0.885285π-0.885285\pi
0.935760 0.352636i 0.114715π-0.114715\pi
194194 0 0
195195 0 0
196196 0 0
197197 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
198198 0 0
199199 −8.00000 −0.567105 −0.283552 0.958957i 0.591513π-0.591513\pi
−0.283552 + 0.958957i 0.591513π0.591513\pi
200200 0 0
201201 0 0
202202 0 0
203203 16.9706i 1.19110i
204204 0 0
205205 9.79796i 0.684319i
206206 0 0
207207 0 0
208208 0 0
209209 −20.7846 + 12.7279i −1.43770 + 0.880409i
210210 0 0
211211 12.2474i 0.843149i −0.906794 0.421575i 0.861478π-0.861478\pi
0.906794 0.421575i 0.138522π-0.138522\pi
212212 0 0
213213 0 0
214214 0 0
215215 −3.46410 −0.236250
216216 0 0
217217 9.79796i 0.665129i
218218 0 0
219219 0 0
220220 0 0
221221 0 0
222222 0 0
223223 16.0000 1.07144 0.535720 0.844396i 0.320040π-0.320040\pi
0.535720 + 0.844396i 0.320040π0.320040\pi
224224 0 0
225225 0 0
226226 0 0
227227 −27.7128 −1.83936 −0.919682 0.392664i 0.871554π-0.871554\pi
−0.919682 + 0.392664i 0.871554π0.871554\pi
228228 0 0
229229 −10.0000 −0.660819 −0.330409 0.943838i 0.607187π-0.607187\pi
−0.330409 + 0.943838i 0.607187π0.607187\pi
230230 0 0
231231 0 0
232232 0 0
233233 20.7846 1.36165 0.680823 0.732448i 0.261622π-0.261622\pi
0.680823 + 0.732448i 0.261622π0.261622\pi
234234 0 0
235235 −4.00000 −0.260931
236236 0 0
237237 0 0
238238 0 0
239239 17.3205 1.12037 0.560185 0.828367i 0.310730π-0.310730\pi
0.560185 + 0.828367i 0.310730π0.310730\pi
240240 0 0
241241 19.5959i 1.26228i −0.775667 0.631142i 0.782587π-0.782587\pi
0.775667 0.631142i 0.217413π-0.217413\pi
242242 0 0
243243 0 0
244244 0 0
245245 1.41421i 0.0903508i
246246 0 0
247247 −36.0000 −2.29063
248248 0 0
249249 0 0
250250 0 0
251251 5.65685i 0.357057i 0.983935 + 0.178529i 0.0571337π0.0571337\pi
−0.983935 + 0.178529i 0.942866π0.942866\pi
252252 0 0
253253 8.00000 4.89898i 0.502956 0.307996i
254254 0 0
255255 0 0
256256 0 0
257257 9.89949i 0.617514i −0.951141 0.308757i 0.900087π-0.900087\pi
0.951141 0.308757i 0.0999129π-0.0999129\pi
258258 0 0
259259 19.5959i 1.21763i
260260 0 0
261261 0 0
262262 0 0
263263 3.46410 0.213606 0.106803 0.994280i 0.465939π-0.465939\pi
0.106803 + 0.994280i 0.465939π0.465939\pi
264264 0 0
265265 −14.0000 −0.860013
266266 0 0
267267 0 0
268268 0 0
269269 15.5563i 0.948487i 0.880394 + 0.474244i 0.157278π0.157278\pi
−0.880394 + 0.474244i 0.842722π0.842722\pi
270270 0 0
271271 7.34847i 0.446388i −0.974774 0.223194i 0.928352π-0.928352\pi
0.974774 0.223194i 0.0716483π-0.0716483\pi
272272 0 0
273273 0 0
274274 0 0
275275 5.19615 + 8.48528i 0.313340 + 0.511682i
276276 0 0
277277 24.4949i 1.47176i 0.677114 + 0.735878i 0.263230π0.263230\pi
−0.677114 + 0.735878i 0.736770π0.736770\pi
278278 0 0
279279 0 0
280280 0 0
281281 −13.8564 −0.826604 −0.413302 0.910594i 0.635625π-0.635625\pi
−0.413302 + 0.910594i 0.635625π0.635625\pi
282282 0 0
283283 2.44949i 0.145607i 0.997346 + 0.0728035i 0.0231946π0.0231946\pi
−0.997346 + 0.0728035i 0.976805π0.976805\pi
284284 0 0
285285 0 0
286286 0 0
287287 16.9706i 1.00174i
288288 0 0
289289 −17.0000 −1.00000
290290 0 0
291291 0 0
292292 0 0
293293 −6.92820 −0.404750 −0.202375 0.979308i 0.564866π-0.564866\pi
−0.202375 + 0.979308i 0.564866π0.564866\pi
294294 0 0
295295 −16.0000 −0.931556
296296 0 0
297297 0 0
298298 0 0
299299 13.8564 0.801337
300300 0 0
301301 −6.00000 −0.345834
302302 0 0
303303 0 0
304304 0 0
305305 −6.92820 −0.396708
306306 0 0
307307 7.34847i 0.419399i 0.977766 + 0.209700i 0.0672486π0.0672486\pi
−0.977766 + 0.209700i 0.932751π0.932751\pi
308308 0 0
309309 0 0
310310 0 0
311311 14.1421i 0.801927i 0.916094 + 0.400963i 0.131325π0.131325\pi
−0.916094 + 0.400963i 0.868675π0.868675\pi
312312 0 0
313313 −16.0000 −0.904373 −0.452187 0.891923i 0.649356π-0.649356\pi
−0.452187 + 0.891923i 0.649356π0.649356\pi
314314 0 0
315315 0 0
316316 0 0
317317 18.3848i 1.03259i −0.856410 0.516296i 0.827310π-0.827310\pi
0.856410 0.516296i 0.172690π-0.172690\pi
318318 0 0
319319 12.0000 + 19.5959i 0.671871 + 1.09716i
320320 0 0
321321 0 0
322322 0 0
323323 0 0
324324 0 0
325325 14.6969i 0.815239i
326326 0 0
327327 0 0
328328 0 0
329329 −6.92820 −0.381964
330330 0 0
331331 −8.00000 −0.439720 −0.219860 0.975531i 0.570560π-0.570560\pi
−0.219860 + 0.975531i 0.570560π0.570560\pi
332332 0 0
333333 0 0
334334 0 0
335335 5.65685i 0.309067i
336336 0 0
337337 9.79796i 0.533729i −0.963734 0.266864i 0.914012π-0.914012\pi
0.963734 0.266864i 0.0859876π-0.0859876\pi
338338 0 0
339339 0 0
340340 0 0
341341 6.92820 + 11.3137i 0.375183 + 0.612672i
342342 0 0
343343 19.5959i 1.05808i
344344 0 0
345345 0 0
346346 0 0
347347 −13.8564 −0.743851 −0.371925 0.928263i 0.621302π-0.621302\pi
−0.371925 + 0.928263i 0.621302π0.621302\pi
348348 0 0
349349 4.89898i 0.262236i −0.991367 0.131118i 0.958143π-0.958143\pi
0.991367 0.131118i 0.0418567π-0.0418567\pi
350350 0 0
351351 0 0
352352 0 0
353353 32.5269i 1.73123i 0.500708 + 0.865616i 0.333073π0.333073\pi
−0.500708 + 0.865616i 0.666927π0.666927\pi
354354 0 0
355355 −4.00000 −0.212298
356356 0 0
357357 0 0
358358 0 0
359359 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
360360 0 0
361361 −35.0000 −1.84211
362362 0 0
363363 0 0
364364 0 0
365365 0 0
366366 0 0
367367 −8.00000 −0.417597 −0.208798 0.977959i 0.566955π-0.566955\pi
−0.208798 + 0.977959i 0.566955π0.566955\pi
368368 0 0
369369 0 0
370370 0 0
371371 −24.2487 −1.25893
372372 0 0
373373 24.4949i 1.26830i −0.773211 0.634149i 0.781351π-0.781351\pi
0.773211 0.634149i 0.218649π-0.218649\pi
374374 0 0
375375 0 0
376376 0 0
377377 33.9411i 1.74806i
378378 0 0
379379 16.0000 0.821865 0.410932 0.911666i 0.365203π-0.365203\pi
0.410932 + 0.911666i 0.365203π0.365203\pi
380380 0 0
381381 0 0
382382 0 0
383383 36.7696i 1.87884i −0.342773 0.939418i 0.611366π-0.611366\pi
0.342773 0.939418i 0.388634π-0.388634\pi
384384 0 0
385385 −6.00000 9.79796i −0.305788 0.499350i
386386 0 0
387387 0 0
388388 0 0
389389 9.89949i 0.501924i −0.967997 0.250962i 0.919253π-0.919253\pi
0.967997 0.250962i 0.0807470π-0.0807470\pi
390390 0 0
391391 0 0
392392 0 0
393393 0 0
394394 0 0
395395 17.3205 0.871489
396396 0 0
397397 8.00000 0.401508 0.200754 0.979642i 0.435661π-0.435661\pi
0.200754 + 0.979642i 0.435661π0.435661\pi
398398 0 0
399399 0 0
400400 0 0
401401 1.41421i 0.0706225i −0.999376 0.0353112i 0.988758π-0.988758\pi
0.999376 0.0353112i 0.0112422π-0.0112422\pi
402402 0 0
403403 19.5959i 0.976142i
404404 0 0
405405 0 0
406406 0 0
407407 13.8564 + 22.6274i 0.686837 + 1.12160i
408408 0 0
409409 39.1918i 1.93791i −0.247234 0.968956i 0.579522π-0.579522\pi
0.247234 0.968956i 0.420478π-0.420478\pi
410410 0 0
411411 0 0
412412 0 0
413413 −27.7128 −1.36366
414414 0 0
415415 19.5959i 0.961926i
416416 0 0
417417 0 0
418418 0 0
419419 11.3137i 0.552711i −0.961056 0.276355i 0.910873π-0.910873\pi
0.961056 0.276355i 0.0891267π-0.0891267\pi
420420 0 0
421421 8.00000 0.389896 0.194948 0.980814i 0.437546π-0.437546\pi
0.194948 + 0.980814i 0.437546π0.437546\pi
422422 0 0
423423 0 0
424424 0 0
425425 0 0
426426 0 0
427427 −12.0000 −0.580721
428428 0 0
429429 0 0
430430 0 0
431431 −10.3923 −0.500580 −0.250290 0.968171i 0.580526π-0.580526\pi
−0.250290 + 0.968171i 0.580526π0.580526\pi
432432 0 0
433433 −16.0000 −0.768911 −0.384455 0.923144i 0.625611π-0.625611\pi
−0.384455 + 0.923144i 0.625611π0.625611\pi
434434 0 0
435435 0 0
436436 0 0
437437 20.7846 0.994263
438438 0 0
439439 2.44949i 0.116908i −0.998290 0.0584539i 0.981383π-0.981383\pi
0.998290 0.0584539i 0.0186171π-0.0186171\pi
440440 0 0
441441 0 0
442442 0 0
443443 22.6274i 1.07506i 0.843244 + 0.537531i 0.180643π0.180643\pi
−0.843244 + 0.537531i 0.819357π0.819357\pi
444444 0 0
445445 10.0000 0.474045
446446 0 0
447447 0 0
448448 0 0
449449 9.89949i 0.467186i −0.972334 0.233593i 0.924952π-0.924952\pi
0.972334 0.233593i 0.0750483π-0.0750483\pi
450450 0 0
451451 −12.0000 19.5959i −0.565058 0.922736i
452452 0 0
453453 0 0
454454 0 0
455455 16.9706i 0.795592i
456456 0 0
457457 9.79796i 0.458329i 0.973388 + 0.229165i 0.0735994π0.0735994\pi
−0.973388 + 0.229165i 0.926401π0.926401\pi
458458 0 0
459459 0 0
460460 0 0
461461 6.92820 0.322679 0.161339 0.986899i 0.448419π-0.448419\pi
0.161339 + 0.986899i 0.448419π0.448419\pi
462462 0 0
463463 28.0000 1.30127 0.650635 0.759390i 0.274503π-0.274503\pi
0.650635 + 0.759390i 0.274503π0.274503\pi
464464 0 0
465465 0 0
466466 0 0
467467 22.6274i 1.04707i 0.852004 + 0.523536i 0.175387π0.175387\pi
−0.852004 + 0.523536i 0.824613π0.824613\pi
468468 0 0
469469 9.79796i 0.452428i
470470 0 0
471471 0 0
472472 0 0
473473 6.92820 4.24264i 0.318559 0.195077i
474474 0 0
475475 22.0454i 1.01151i
476476 0 0
477477 0 0
478478 0 0
479479 −38.1051 −1.74107 −0.870534 0.492109i 0.836226π-0.836226\pi
−0.870534 + 0.492109i 0.836226π0.836226\pi
480480 0 0
481481 39.1918i 1.78699i
482482 0 0
483483 0 0
484484 0 0
485485 14.1421i 0.642161i
486486 0 0
487487 −8.00000 −0.362515 −0.181257 0.983436i 0.558017π-0.558017\pi
−0.181257 + 0.983436i 0.558017π0.558017\pi
488488 0 0
489489 0 0
490490 0 0
491491 27.7128 1.25066 0.625331 0.780360i 0.284964π-0.284964\pi
0.625331 + 0.780360i 0.284964π0.284964\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 −6.92820 −0.310772
498498 0 0
499499 −32.0000 −1.43252 −0.716258 0.697835i 0.754147π-0.754147\pi
−0.716258 + 0.697835i 0.754147π0.754147\pi
500500 0 0
501501 0 0
502502 0 0
503503 −31.1769 −1.39011 −0.695055 0.718957i 0.744620π-0.744620\pi
−0.695055 + 0.718957i 0.744620π0.744620\pi
504504 0 0
505505 19.5959i 0.872007i
506506 0 0
507507 0 0
508508 0 0
509509 15.5563i 0.689523i 0.938690 + 0.344762i 0.112040π0.112040\pi
−0.938690 + 0.344762i 0.887960π0.887960\pi
510510 0 0
511511 0 0
512512 0 0
513513 0 0
514514 0 0
515515 5.65685i 0.249271i
516516 0 0
517517 8.00000 4.89898i 0.351840 0.215457i
518518 0 0
519519 0 0
520520 0 0
521521 15.5563i 0.681536i 0.940147 + 0.340768i 0.110687π0.110687\pi
−0.940147 + 0.340768i 0.889313π0.889313\pi
522522 0 0
523523 22.0454i 0.963978i 0.876177 + 0.481989i 0.160086π0.160086\pi
−0.876177 + 0.481989i 0.839914π0.839914\pi
524524 0 0
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 15.0000 0.652174
530530 0 0
531531 0 0
532532 0 0
533533 33.9411i 1.47015i
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 0 0
539539 1.73205 + 2.82843i 0.0746047 + 0.121829i
540540 0 0
541541 14.6969i 0.631871i −0.948781 0.315935i 0.897682π-0.897682\pi
0.948781 0.315935i 0.102318π-0.102318\pi
542542 0 0
543543 0 0
544544 0 0
545545 20.7846 0.890315
546546 0 0
547547 31.8434i 1.36152i −0.732505 0.680762i 0.761649π-0.761649\pi
0.732505 0.680762i 0.238351π-0.238351\pi
548548 0 0
549549 0 0
550550 0 0
551551 50.9117i 2.16891i
552552 0 0
553553 30.0000 1.27573
554554 0 0
555555 0 0
556556 0 0
557557 −20.7846 −0.880672 −0.440336 0.897833i 0.645141π-0.645141\pi
−0.440336 + 0.897833i 0.645141π0.645141\pi
558558 0 0
559559 12.0000 0.507546
560560 0 0
561561 0 0
562562 0 0
563563 17.3205 0.729972 0.364986 0.931013i 0.381074π-0.381074\pi
0.364986 + 0.931013i 0.381074π0.381074\pi
564564 0 0
565565 −2.00000 −0.0841406
566566 0 0
567567 0 0
568568 0 0
569569 −13.8564 −0.580891 −0.290445 0.956892i 0.593803π-0.593803\pi
−0.290445 + 0.956892i 0.593803π0.593803\pi
570570 0 0
571571 2.44949i 0.102508i 0.998686 + 0.0512540i 0.0163218π0.0163218\pi
−0.998686 + 0.0512540i 0.983678π0.983678\pi
572572 0 0
573573 0 0
574574 0 0
575575 8.48528i 0.353861i
576576 0 0
577577 −10.0000 −0.416305 −0.208153 0.978096i 0.566745π-0.566745\pi
−0.208153 + 0.978096i 0.566745π0.566745\pi
578578 0 0
579579 0 0
580580 0 0
581581 33.9411i 1.40812i
582582 0 0
583583 28.0000 17.1464i 1.15964 0.710132i
584584 0 0
585585 0 0
586586 0 0
587587 28.2843i 1.16742i −0.811963 0.583708i 0.801601π-0.801601\pi
0.811963 0.583708i 0.198399π-0.198399\pi
588588 0 0
589589 29.3939i 1.21115i
590590 0 0
591591 0 0
592592 0 0
593593 −41.5692 −1.70704 −0.853522 0.521057i 0.825538π-0.825538\pi
−0.853522 + 0.521057i 0.825538π0.825538\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 2.82843i 0.115566i −0.998329 0.0577832i 0.981597π-0.981597\pi
0.998329 0.0577832i 0.0184032π-0.0184032\pi
600600 0 0
601601 19.5959i 0.799334i −0.916660 0.399667i 0.869126π-0.869126\pi
0.916660 0.399667i 0.130874π-0.130874\pi
602602 0 0
603603 0 0
604604 0 0
605605 13.8564 + 7.07107i 0.563343 + 0.287480i
606606 0 0
607607 12.2474i 0.497109i −0.968618 0.248554i 0.920045π-0.920045\pi
0.968618 0.248554i 0.0799554π-0.0799554\pi
608608 0 0
609609 0 0
610610 0 0
611611 13.8564 0.560570
612612 0 0
613613 14.6969i 0.593604i 0.954939 + 0.296802i 0.0959201π0.0959201\pi
−0.954939 + 0.296802i 0.904080π0.904080\pi
614614 0 0
615615 0 0
616616 0 0
617617 26.8701i 1.08175i −0.841104 0.540874i 0.818094π-0.818094\pi
0.841104 0.540874i 0.181906π-0.181906\pi
618618 0 0
619619 28.0000 1.12542 0.562708 0.826656i 0.309760π-0.309760\pi
0.562708 + 0.826656i 0.309760π0.309760\pi
620620 0 0
621621 0 0
622622 0 0
623623 17.3205 0.693932
624624 0 0
625625 −1.00000 −0.0400000
626626 0 0
627627 0 0
628628 0 0
629629 0 0
630630 0 0
631631 −44.0000 −1.75161 −0.875806 0.482663i 0.839670π-0.839670\pi
−0.875806 + 0.482663i 0.839670π0.839670\pi
632632 0 0
633633 0 0
634634 0 0
635635 10.3923 0.412406
636636 0 0
637637 4.89898i 0.194105i
638638 0 0
639639 0 0
640640 0 0
641641 32.5269i 1.28474i 0.766396 + 0.642368i 0.222048π0.222048\pi
−0.766396 + 0.642368i 0.777952π0.777952\pi
642642 0 0
643643 28.0000 1.10421 0.552106 0.833774i 0.313824π-0.313824\pi
0.552106 + 0.833774i 0.313824π0.313824\pi
644644 0 0
645645 0 0
646646 0 0
647647 19.7990i 0.778379i −0.921158 0.389189i 0.872755π-0.872755\pi
0.921158 0.389189i 0.127245π-0.127245\pi
648648 0 0
649649 32.0000 19.5959i 1.25611 0.769207i
650650 0 0
651651 0 0
652652 0 0
653653 26.8701i 1.05151i −0.850637 0.525753i 0.823784π-0.823784\pi
0.850637 0.525753i 0.176216π-0.176216\pi
654654 0 0
655655 4.89898i 0.191419i
656656 0 0
657657 0 0
658658 0 0
659659 −38.1051 −1.48436 −0.742182 0.670198i 0.766209π-0.766209\pi
−0.742182 + 0.670198i 0.766209π0.766209\pi
660660 0 0
661661 −22.0000 −0.855701 −0.427850 0.903850i 0.640729π-0.640729\pi
−0.427850 + 0.903850i 0.640729π0.640729\pi
662662 0 0
663663 0 0
664664 0 0
665665 25.4558i 0.987135i
666666 0 0
667667 19.5959i 0.758757i
668668 0 0
669669 0 0
670670 0 0
671671 13.8564 8.48528i 0.534921 0.327571i
672672 0 0
673673 39.1918i 1.51073i 0.655302 + 0.755367i 0.272541π0.272541\pi
−0.655302 + 0.755367i 0.727459π0.727459\pi
674674 0 0
675675 0 0
676676 0 0
677677 27.7128 1.06509 0.532545 0.846402i 0.321236π-0.321236\pi
0.532545 + 0.846402i 0.321236π0.321236\pi
678678 0 0
679679 24.4949i 0.940028i
680680 0 0
681681 0 0
682682 0 0
683683 28.2843i 1.08227i −0.840937 0.541134i 0.817995π-0.817995\pi
0.840937 0.541134i 0.182005π-0.182005\pi
684684 0 0
685685 22.0000 0.840577
686686 0 0
687687 0 0
688688 0 0
689689 48.4974 1.84760
690690 0 0
691691 −44.0000 −1.67384 −0.836919 0.547326i 0.815646π-0.815646\pi
−0.836919 + 0.547326i 0.815646π0.815646\pi
692692 0 0
693693 0 0
694694 0 0
695695 3.46410 0.131401
696696 0 0
697697 0 0
698698 0 0
699699 0 0
700700 0 0
701701 20.7846 0.785024 0.392512 0.919747i 0.371606π-0.371606\pi
0.392512 + 0.919747i 0.371606π0.371606\pi
702702 0 0
703703 58.7878i 2.21722i
704704 0 0
705705 0 0
706706 0 0
707707 33.9411i 1.27649i
708708 0 0
709709 −10.0000 −0.375558 −0.187779 0.982211i 0.560129π-0.560129\pi
−0.187779 + 0.982211i 0.560129π0.560129\pi
710710 0 0
711711 0 0
712712 0 0
713713 11.3137i 0.423702i
714714 0 0
715715 12.0000 + 19.5959i 0.448775 + 0.732846i
716716 0 0
717717 0 0
718718 0 0
719719 2.82843i 0.105483i −0.998608 0.0527413i 0.983204π-0.983204\pi
0.998608 0.0527413i 0.0167959π-0.0167959\pi
720720 0 0
721721 9.79796i 0.364895i
722722 0 0
723723 0 0
724724 0 0
725725 20.7846 0.771921
726726 0 0
727727 −8.00000 −0.296704 −0.148352 0.988935i 0.547397π-0.547397\pi
−0.148352 + 0.988935i 0.547397π0.547397\pi
728728 0 0
729729 0 0
730730 0 0
731731 0 0
732732 0 0
733733 34.2929i 1.26664i 0.773892 + 0.633318i 0.218307π0.218307\pi
−0.773892 + 0.633318i 0.781693π0.781693\pi
734734 0 0
735735 0 0
736736 0 0
737737 6.92820 + 11.3137i 0.255204 + 0.416746i
738738 0 0
739739 7.34847i 0.270318i −0.990824 0.135159i 0.956846π-0.956846\pi
0.990824 0.135159i 0.0431545π-0.0431545\pi
740740 0 0
741741 0 0
742742 0 0
743743 27.7128 1.01668 0.508342 0.861155i 0.330258π-0.330258\pi
0.508342 + 0.861155i 0.330258π0.330258\pi
744744 0 0
745745 19.5959i 0.717939i
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 4.00000 0.145962 0.0729810 0.997333i 0.476749π-0.476749\pi
0.0729810 + 0.997333i 0.476749π0.476749\pi
752752 0 0
753753 0 0
754754 0 0
755755 −3.46410 −0.126072
756756 0 0
757757 8.00000 0.290765 0.145382 0.989376i 0.453559π-0.453559\pi
0.145382 + 0.989376i 0.453559π0.453559\pi
758758 0 0
759759 0 0
760760 0 0
761761 13.8564 0.502294 0.251147 0.967949i 0.419192π-0.419192\pi
0.251147 + 0.967949i 0.419192π0.419192\pi
762762 0 0
763763 36.0000 1.30329
764764 0 0
765765 0 0
766766 0 0
767767 55.4256 2.00130
768768 0 0
769769 19.5959i 0.706647i 0.935501 + 0.353323i 0.114948π0.114948\pi
−0.935501 + 0.353323i 0.885052π0.885052\pi
770770 0 0
771771 0 0
772772 0 0
773773 32.5269i 1.16991i 0.811065 + 0.584956i 0.198888π0.198888\pi
−0.811065 + 0.584956i 0.801112π0.801112\pi
774774 0 0
775775 12.0000 0.431053
776776 0 0
777777 0 0
778778 0 0
779779 50.9117i 1.82410i
780780 0 0
781781 8.00000 4.89898i 0.286263 0.175299i
782782 0 0
783783 0 0
784784 0 0
785785 19.7990i 0.706656i
786786 0 0
787787 12.2474i 0.436574i −0.975885 0.218287i 0.929953π-0.929953\pi
0.975885 0.218287i 0.0700470π-0.0700470\pi
788788 0 0
789789 0 0
790790 0 0
791791 −3.46410 −0.123169
792792 0 0
793793 24.0000 0.852265
794794 0 0
795795 0 0
796796 0 0
797797 26.8701i 0.951786i −0.879503 0.475893i 0.842125π-0.842125\pi
0.879503 0.475893i 0.157875π-0.157875\pi
798798 0 0
799799 0 0
800800 0 0
801801 0 0
802802 0 0
803803 0 0
804804 0 0
805805 9.79796i 0.345333i
806806 0 0
807807 0 0
808808 0 0
809809 −20.7846 −0.730748 −0.365374 0.930861i 0.619059π-0.619059\pi
−0.365374 + 0.930861i 0.619059π0.619059\pi
810810 0 0
811811 22.0454i 0.774119i 0.922055 + 0.387059i 0.126509π0.126509\pi
−0.922055 + 0.387059i 0.873491π0.873491\pi
812812 0 0
813813 0 0
814814 0 0
815815 11.3137i 0.396302i
816816 0 0
817817 18.0000 0.629740
818818 0 0
819819 0 0
820820 0 0
821821 −13.8564 −0.483592 −0.241796 0.970327i 0.577736π-0.577736\pi
−0.241796 + 0.970327i 0.577736π0.577736\pi
822822 0 0
823823 −8.00000 −0.278862 −0.139431 0.990232i 0.544527π-0.544527\pi
−0.139431 + 0.990232i 0.544527π0.544527\pi
824824 0 0
825825 0 0
826826 0 0
827827 −41.5692 −1.44550 −0.722752 0.691108i 0.757123π-0.757123\pi
−0.722752 + 0.691108i 0.757123π0.757123\pi
828828 0 0
829829 −46.0000 −1.59765 −0.798823 0.601566i 0.794544π-0.794544\pi
−0.798823 + 0.601566i 0.794544π0.794544\pi
830830 0 0
831831 0 0
832832 0 0
833833 0 0
834834 0 0
835835 4.89898i 0.169536i
836836 0 0
837837 0 0
838838 0 0
839839 19.7990i 0.683537i −0.939784 0.341769i 0.888974π-0.888974\pi
0.939784 0.341769i 0.111026π-0.111026\pi
840840 0 0
841841 19.0000 0.655172
842842 0 0
843843 0 0
844844 0 0
845845 15.5563i 0.535155i
846846 0 0
847847 24.0000 + 12.2474i 0.824650 + 0.420827i
848848 0 0
849849 0 0
850850 0 0
851851 22.6274i 0.775658i
852852 0 0
853853 34.2929i 1.17417i −0.809527 0.587083i 0.800276π-0.800276\pi
0.809527 0.587083i 0.199724π-0.199724\pi
854854 0 0
855855 0 0
856856 0 0
857857 −34.6410 −1.18331 −0.591657 0.806190i 0.701526π-0.701526\pi
−0.591657 + 0.806190i 0.701526π0.701526\pi
858858 0 0
859859 40.0000 1.36478 0.682391 0.730987i 0.260940π-0.260940\pi
0.682391 + 0.730987i 0.260940π0.260940\pi
860860 0 0
861861 0 0
862862 0 0
863863 19.7990i 0.673965i −0.941511 0.336983i 0.890594π-0.890594\pi
0.941511 0.336983i 0.109406π-0.109406\pi
864864 0 0
865865 9.79796i 0.333141i
866866 0 0
867867 0 0
868868 0 0
869869 −34.6410 + 21.2132i −1.17512 + 0.719609i
870870 0 0
871871 19.5959i 0.663982i
872872 0 0
873873 0 0
874874 0 0
875875 −27.7128 −0.936864
876876 0 0
877877 53.8888i 1.81969i −0.414943 0.909847i 0.636199π-0.636199\pi
0.414943 0.909847i 0.363801π-0.363801\pi
878878 0 0
879879 0 0
880880 0 0
881881 9.89949i 0.333522i −0.985997 0.166761i 0.946669π-0.946669\pi
0.985997 0.166761i 0.0533309π-0.0533309\pi
882882 0 0
883883 28.0000 0.942275 0.471138 0.882060i 0.343844π-0.343844\pi
0.471138 + 0.882060i 0.343844π0.343844\pi
884884 0 0
885885 0 0
886886 0 0
887887 −55.4256 −1.86101 −0.930505 0.366279i 0.880632π-0.880632\pi
−0.930505 + 0.366279i 0.880632π0.880632\pi
888888 0 0
889889 18.0000 0.603701
890890 0 0
891891 0 0
892892 0 0
893893 20.7846 0.695530
894894 0 0
895895 32.0000 1.06964
896896 0 0
897897 0 0
898898 0 0
899899 27.7128 0.924274
900900 0 0
901901 0 0
902902 0 0
903903 0 0
904904 0 0
905905 11.3137i 0.376080i
906906 0 0
907907 52.0000 1.72663 0.863316 0.504664i 0.168384π-0.168384\pi
0.863316 + 0.504664i 0.168384π0.168384\pi
908908 0 0
909909 0 0
910910 0 0
911911 53.7401i 1.78049i −0.455483 0.890245i 0.650533π-0.650533\pi
0.455483 0.890245i 0.349467π-0.349467\pi
912912 0 0
913913 24.0000 + 39.1918i 0.794284 + 1.29706i
914914 0 0
915915 0 0
916916 0 0
917917 8.48528i 0.280209i
918918 0 0
919919 36.7423i 1.21202i −0.795458 0.606009i 0.792770π-0.792770\pi
0.795458 0.606009i 0.207230π-0.207230\pi
920920 0 0
921921 0 0
922922 0 0
923923 13.8564 0.456089
924924 0 0
925925 24.0000 0.789115
926926 0 0
927927 0 0
928928 0 0
929929 9.89949i 0.324792i −0.986726 0.162396i 0.948078π-0.948078\pi
0.986726 0.162396i 0.0519222π-0.0519222\pi
930930 0 0
931931 7.34847i 0.240836i
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 29.3939i 0.960256i 0.877198 + 0.480128i 0.159410π0.159410\pi
−0.877198 + 0.480128i 0.840590π0.840590\pi
938938 0 0
939939 0 0
940940 0 0
941941 −27.7128 −0.903412 −0.451706 0.892167i 0.649184π-0.649184\pi
−0.451706 + 0.892167i 0.649184π0.649184\pi
942942 0 0
943943 19.5959i 0.638131i
944944 0 0
945945 0 0
946946 0 0
947947 22.6274i 0.735292i 0.929966 + 0.367646i 0.119836π0.119836\pi
−0.929966 + 0.367646i 0.880164π0.880164\pi
948948 0 0
949949 0 0
950950 0 0
951951 0 0
952952 0 0
953953 20.7846 0.673280 0.336640 0.941634i 0.390710π-0.390710\pi
0.336640 + 0.941634i 0.390710π0.390710\pi
954954 0 0
955955 −4.00000 −0.129437
956956 0 0
957957 0 0
958958 0 0
959959 38.1051 1.23048
960960 0 0
961961 −15.0000 −0.483871
962962 0 0
963963 0 0
964964 0 0
965965 −13.8564 −0.446054
966966 0 0
967967 41.6413i 1.33909i −0.742769 0.669547i 0.766488π-0.766488\pi
0.742769 0.669547i 0.233512π-0.233512\pi
968968 0 0
969969 0 0
970970 0 0
971971 56.5685i 1.81537i 0.419651 + 0.907685i 0.362152π0.362152\pi
−0.419651 + 0.907685i 0.637848π0.637848\pi
972972 0 0
973973 6.00000 0.192351
974974 0 0
975975 0 0
976976 0 0
977977 35.3553i 1.13112i −0.824708 0.565559i 0.808661π-0.808661\pi
0.824708 0.565559i 0.191339π-0.191339\pi
978978 0 0
979979 −20.0000 + 12.2474i −0.639203 + 0.391430i
980980 0 0
981981 0 0
982982 0 0
983983 48.0833i 1.53362i 0.641875 + 0.766809i 0.278157π0.278157\pi
−0.641875 + 0.766809i 0.721843π0.721843\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 −6.92820 −0.220304
990990 0 0
991991 52.0000 1.65183 0.825917 0.563791i 0.190658π-0.190658\pi
0.825917 + 0.563791i 0.190658π0.190658\pi
992992 0 0
993993 0 0
994994 0 0
995995 11.3137i 0.358669i
996996 0 0
997997 24.4949i 0.775761i 0.921710 + 0.387881i 0.126793π0.126793\pi
−0.921710 + 0.387881i 0.873207π0.873207\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 1584.2.b.e.593.1 4
3.2 odd 2 inner 1584.2.b.e.593.3 4
4.3 odd 2 99.2.d.a.98.3 yes 4
8.3 odd 2 6336.2.b.s.2177.4 4
8.5 even 2 6336.2.b.t.2177.3 4
11.10 odd 2 inner 1584.2.b.e.593.2 4
12.11 even 2 99.2.d.a.98.2 yes 4
20.3 even 4 2475.2.d.a.2474.3 8
20.7 even 4 2475.2.d.a.2474.5 8
20.19 odd 2 2475.2.f.e.2276.1 4
24.5 odd 2 6336.2.b.t.2177.1 4
24.11 even 2 6336.2.b.s.2177.2 4
33.32 even 2 inner 1584.2.b.e.593.4 4
36.7 odd 6 891.2.g.c.296.2 8
36.11 even 6 891.2.g.c.296.3 8
36.23 even 6 891.2.g.c.593.4 8
36.31 odd 6 891.2.g.c.593.1 8
44.43 even 2 99.2.d.a.98.1 4
60.23 odd 4 2475.2.d.a.2474.8 8
60.47 odd 4 2475.2.d.a.2474.2 8
60.59 even 2 2475.2.f.e.2276.3 4
88.21 odd 2 6336.2.b.t.2177.4 4
88.43 even 2 6336.2.b.s.2177.3 4
132.131 odd 2 99.2.d.a.98.4 yes 4
220.43 odd 4 2475.2.d.a.2474.6 8
220.87 odd 4 2475.2.d.a.2474.4 8
220.219 even 2 2475.2.f.e.2276.4 4
264.131 odd 2 6336.2.b.s.2177.1 4
264.197 even 2 6336.2.b.t.2177.2 4
396.43 even 6 891.2.g.c.296.4 8
396.131 odd 6 891.2.g.c.593.2 8
396.175 even 6 891.2.g.c.593.3 8
396.263 odd 6 891.2.g.c.296.1 8
660.263 even 4 2475.2.d.a.2474.1 8
660.527 even 4 2475.2.d.a.2474.7 8
660.659 odd 2 2475.2.f.e.2276.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.d.a.98.1 4 44.43 even 2
99.2.d.a.98.2 yes 4 12.11 even 2
99.2.d.a.98.3 yes 4 4.3 odd 2
99.2.d.a.98.4 yes 4 132.131 odd 2
891.2.g.c.296.1 8 396.263 odd 6
891.2.g.c.296.2 8 36.7 odd 6
891.2.g.c.296.3 8 36.11 even 6
891.2.g.c.296.4 8 396.43 even 6
891.2.g.c.593.1 8 36.31 odd 6
891.2.g.c.593.2 8 396.131 odd 6
891.2.g.c.593.3 8 396.175 even 6
891.2.g.c.593.4 8 36.23 even 6
1584.2.b.e.593.1 4 1.1 even 1 trivial
1584.2.b.e.593.2 4 11.10 odd 2 inner
1584.2.b.e.593.3 4 3.2 odd 2 inner
1584.2.b.e.593.4 4 33.32 even 2 inner
2475.2.d.a.2474.1 8 660.263 even 4
2475.2.d.a.2474.2 8 60.47 odd 4
2475.2.d.a.2474.3 8 20.3 even 4
2475.2.d.a.2474.4 8 220.87 odd 4
2475.2.d.a.2474.5 8 20.7 even 4
2475.2.d.a.2474.6 8 220.43 odd 4
2475.2.d.a.2474.7 8 660.527 even 4
2475.2.d.a.2474.8 8 60.23 odd 4
2475.2.f.e.2276.1 4 20.19 odd 2
2475.2.f.e.2276.2 4 660.659 odd 2
2475.2.f.e.2276.3 4 60.59 even 2
2475.2.f.e.2276.4 4 220.219 even 2
6336.2.b.s.2177.1 4 264.131 odd 2
6336.2.b.s.2177.2 4 24.11 even 2
6336.2.b.s.2177.3 4 88.43 even 2
6336.2.b.s.2177.4 4 8.3 odd 2
6336.2.b.t.2177.1 4 24.5 odd 2
6336.2.b.t.2177.2 4 264.197 even 2
6336.2.b.t.2177.3 4 8.5 even 2
6336.2.b.t.2177.4 4 88.21 odd 2