Properties

Label 588.2.e.a.491.2
Level 588588
Weight 22
Character 588.491
Analytic conductor 4.6954.695
Analytic rank 00
Dimension 44
CM discriminant -84
Inner twists 88

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [588,2,Mod(491,588)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(588, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("588.491");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 588=22372 588 = 2^{2} \cdot 3 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 588.e (of order 22, degree 11, 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: 4.695203638854.69520363885
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+2x2+4 x^{4} + 2x^{2} + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 22 2^{2}
Twist minimal: yes
Sato-Tate group: U(1)[D2]\mathrm{U}(1)[D_{2}]

Embedding invariants

Embedding label 491.2
Root 0.7071071.22474i0.707107 - 1.22474i of defining polynomial
Character χ\chi == 588.491
Dual form 588.2.e.a.491.1

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) == q1.41421q2+1.73205iq3+2.00000q42.44949iq52.44949iq62.82843q83.00000q9+3.46410iq101.41421q11+3.46410iq12+4.24264q15+4.00000q16+7.34847iq17+4.24264q18+6.92820iq194.89898iq20+2.00000q22+7.07107q234.89898iq241.00000q255.19615iq276.00000q30+3.46410iq315.65685q322.44949iq3310.3923iq346.00000q36+8.00000q379.79796iq38+6.92820iq40+12.2474iq412.82843q44+7.34847iq4510.0000q46+6.92820iq48+1.41421q5012.7279q51+7.34847iq54+3.46410iq5512.0000q57+8.48528q604.89898iq62+8.00000q64+3.46410iq66+14.6969iq68+12.2474iq6915.5563q71+8.48528q7211.3137q741.73205iq75+13.8564iq769.79796iq80+9.00000q8117.3205iq82+18.0000q85+4.00000q882.44949iq8910.3923iq90+14.1421q926.00000q93+16.9706q959.79796iq96+4.24264q99+O(q100)q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{5} -2.44949i q^{6} -2.82843 q^{8} -3.00000 q^{9} +3.46410i q^{10} -1.41421 q^{11} +3.46410i q^{12} +4.24264 q^{15} +4.00000 q^{16} +7.34847i q^{17} +4.24264 q^{18} +6.92820i q^{19} -4.89898i q^{20} +2.00000 q^{22} +7.07107 q^{23} -4.89898i q^{24} -1.00000 q^{25} -5.19615i q^{27} -6.00000 q^{30} +3.46410i q^{31} -5.65685 q^{32} -2.44949i q^{33} -10.3923i q^{34} -6.00000 q^{36} +8.00000 q^{37} -9.79796i q^{38} +6.92820i q^{40} +12.2474i q^{41} -2.82843 q^{44} +7.34847i q^{45} -10.0000 q^{46} +6.92820i q^{48} +1.41421 q^{50} -12.7279 q^{51} +7.34847i q^{54} +3.46410i q^{55} -12.0000 q^{57} +8.48528 q^{60} -4.89898i q^{62} +8.00000 q^{64} +3.46410i q^{66} +14.6969i q^{68} +12.2474i q^{69} -15.5563 q^{71} +8.48528 q^{72} -11.3137 q^{74} -1.73205i q^{75} +13.8564i q^{76} -9.79796i q^{80} +9.00000 q^{81} -17.3205i q^{82} +18.0000 q^{85} +4.00000 q^{88} -2.44949i q^{89} -10.3923i q^{90} +14.1421 q^{92} -6.00000 q^{93} +16.9706 q^{95} -9.79796i q^{96} +4.24264 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+8q412q9+16q16+8q224q2524q3024q36+32q3740q4648q57+32q64+36q81+72q85+16q8824q93+O(q100) 4 q + 8 q^{4} - 12 q^{9} + 16 q^{16} + 8 q^{22} - 4 q^{25} - 24 q^{30} - 24 q^{36} + 32 q^{37} - 40 q^{46} - 48 q^{57} + 32 q^{64} + 36 q^{81} + 72 q^{85} + 16 q^{88} - 24 q^{93}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/588Z)×\left(\mathbb{Z}/588\mathbb{Z}\right)^\times.

nn 197197 295295 493493
χ(n)\chi(n) 1-1 1-1 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 −1.41421 −1.00000
33 1.73205i 1.00000i
44 2.00000 1.00000
55 − 2.44949i − 1.09545i −0.836660 0.547723i 0.815495π-0.815495\pi
0.836660 0.547723i 0.184505π-0.184505\pi
66 − 2.44949i − 1.00000i
77 0 0
88 −2.82843 −1.00000
99 −3.00000 −1.00000
1010 3.46410i 1.09545i
1111 −1.41421 −0.426401 −0.213201 0.977008i 0.568389π-0.568389\pi
−0.213201 + 0.977008i 0.568389π0.568389\pi
1212 3.46410i 1.00000i
1313 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1414 0 0
1515 4.24264 1.09545
1616 4.00000 1.00000
1717 7.34847i 1.78227i 0.453743 + 0.891133i 0.350089π0.350089\pi
−0.453743 + 0.891133i 0.649911π0.649911\pi
1818 4.24264 1.00000
1919 6.92820i 1.58944i 0.606977 + 0.794719i 0.292382π0.292382\pi
−0.606977 + 0.794719i 0.707618π0.707618\pi
2020 − 4.89898i − 1.09545i
2121 0 0
2222 2.00000 0.426401
2323 7.07107 1.47442 0.737210 0.675664i 0.236143π-0.236143\pi
0.737210 + 0.675664i 0.236143π0.236143\pi
2424 − 4.89898i − 1.00000i
2525 −1.00000 −0.200000
2626 0 0
2727 − 5.19615i − 1.00000i
2828 0 0
2929 0 0 1.00000 00
−1.00000 π\pi
3030 −6.00000 −1.09545
3131 3.46410i 0.622171i 0.950382 + 0.311086i 0.100693π0.100693\pi
−0.950382 + 0.311086i 0.899307π0.899307\pi
3232 −5.65685 −1.00000
3333 − 2.44949i − 0.426401i
3434 − 10.3923i − 1.78227i
3535 0 0
3636 −6.00000 −1.00000
3737 8.00000 1.31519 0.657596 0.753371i 0.271573π-0.271573\pi
0.657596 + 0.753371i 0.271573π0.271573\pi
3838 − 9.79796i − 1.58944i
3939 0 0
4040 6.92820i 1.09545i
4141 12.2474i 1.91273i 0.292174 + 0.956365i 0.405621π0.405621\pi
−0.292174 + 0.956365i 0.594379π0.594379\pi
4242 0 0
4343 0 0 1.00000 00
−1.00000 π\pi
4444 −2.82843 −0.426401
4545 7.34847i 1.09545i
4646 −10.0000 −1.47442
4747 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4848 6.92820i 1.00000i
4949 0 0
5050 1.41421 0.200000
5151 −12.7279 −1.78227
5252 0 0
5353 0 0 1.00000 00
−1.00000 π\pi
5454 7.34847i 1.00000i
5555 3.46410i 0.467099i
5656 0 0
5757 −12.0000 −1.58944
5858 0 0
5959 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
6060 8.48528 1.09545
6161 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
6262 − 4.89898i − 0.622171i
6363 0 0
6464 8.00000 1.00000
6565 0 0
6666 3.46410i 0.426401i
6767 0 0 1.00000 00
−1.00000 π\pi
6868 14.6969i 1.78227i
6969 12.2474i 1.47442i
7070 0 0
7171 −15.5563 −1.84620 −0.923099 0.384561i 0.874353π-0.874353\pi
−0.923099 + 0.384561i 0.874353π0.874353\pi
7272 8.48528 1.00000
7373 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7474 −11.3137 −1.31519
7575 − 1.73205i − 0.200000i
7676 13.8564i 1.58944i
7777 0 0
7878 0 0
7979 0 0 1.00000 00
−1.00000 π\pi
8080 − 9.79796i − 1.09545i
8181 9.00000 1.00000
8282 − 17.3205i − 1.91273i
8383 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
8484 0 0
8585 18.0000 1.95237
8686 0 0
8787 0 0
8888 4.00000 0.426401
8989 − 2.44949i − 0.259645i −0.991537 0.129823i 0.958559π-0.958559\pi
0.991537 0.129823i 0.0414408π-0.0414408\pi
9090 − 10.3923i − 1.09545i
9191 0 0
9292 14.1421 1.47442
9393 −6.00000 −0.622171
9494 0 0
9595 16.9706 1.74114
9696 − 9.79796i − 1.00000i
9797 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
9898 0 0
9999 4.24264 0.426401
100100 −2.00000 −0.200000
101101 7.34847i 0.731200i 0.930772 + 0.365600i 0.119136π0.119136\pi
−0.930772 + 0.365600i 0.880864π0.880864\pi
102102 18.0000 1.78227
103103 − 17.3205i − 1.70664i −0.521387 0.853320i 0.674585π-0.674585\pi
0.521387 0.853320i 0.325415π-0.325415\pi
104104 0 0
105105 0 0
106106 0 0
107107 7.07107 0.683586 0.341793 0.939775i 0.388966π-0.388966\pi
0.341793 + 0.939775i 0.388966π0.388966\pi
108108 − 10.3923i − 1.00000i
109109 −10.0000 −0.957826 −0.478913 0.877862i 0.658969π-0.658969\pi
−0.478913 + 0.877862i 0.658969π0.658969\pi
110110 − 4.89898i − 0.467099i
111111 13.8564i 1.31519i
112112 0 0
113113 0 0 1.00000 00
−1.00000 π\pi
114114 16.9706 1.58944
115115 − 17.3205i − 1.61515i
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 −12.0000 −1.09545
121121 −9.00000 −0.818182
122122 0 0
123123 −21.2132 −1.91273
124124 6.92820i 0.622171i
125125 − 9.79796i − 0.876356i
126126 0 0
127127 0 0 1.00000 00
−1.00000 π\pi
128128 −11.3137 −1.00000
129129 0 0
130130 0 0
131131 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
132132 − 4.89898i − 0.426401i
133133 0 0
134134 0 0
135135 −12.7279 −1.09545
136136 − 20.7846i − 1.78227i
137137 0 0 1.00000 00
−1.00000 π\pi
138138 − 17.3205i − 1.47442i
139139 − 10.3923i − 0.881464i −0.897639 0.440732i 0.854719π-0.854719\pi
0.897639 0.440732i 0.145281π-0.145281\pi
140140 0 0
141141 0 0
142142 22.0000 1.84620
143143 0 0
144144 −12.0000 −1.00000
145145 0 0
146146 0 0
147147 0 0
148148 16.0000 1.31519
149149 0 0 1.00000 00
−1.00000 π\pi
150150 2.44949i 0.200000i
151151 0 0 1.00000 00
−1.00000 π\pi
152152 − 19.5959i − 1.58944i
153153 − 22.0454i − 1.78227i
154154 0 0
155155 8.48528 0.681554
156156 0 0
157157 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
158158 0 0
159159 0 0
160160 13.8564i 1.09545i
161161 0 0
162162 −12.7279 −1.00000
163163 0 0 1.00000 00
−1.00000 π\pi
164164 24.4949i 1.91273i
165165 −6.00000 −0.467099
166166 0 0
167167 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
168168 0 0
169169 −13.0000 −1.00000
170170 −25.4558 −1.95237
171171 − 20.7846i − 1.58944i
172172 0 0
173173 − 2.44949i − 0.186231i −0.995655 0.0931156i 0.970317π-0.970317\pi
0.995655 0.0931156i 0.0296826π-0.0296826\pi
174174 0 0
175175 0 0
176176 −5.65685 −0.426401
177177 0 0
178178 3.46410i 0.259645i
179179 18.3848 1.37414 0.687071 0.726590i 0.258896π-0.258896\pi
0.687071 + 0.726590i 0.258896π0.258896\pi
180180 14.6969i 1.09545i
181181 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
182182 0 0
183183 0 0
184184 −20.0000 −1.47442
185185 − 19.5959i − 1.44072i
186186 8.48528 0.622171
187187 − 10.3923i − 0.759961i
188188 0 0
189189 0 0
190190 −24.0000 −1.74114
191191 26.8701 1.94425 0.972125 0.234465i 0.0753338π-0.0753338\pi
0.972125 + 0.234465i 0.0753338π0.0753338\pi
192192 13.8564i 1.00000i
193193 4.00000 0.287926 0.143963 0.989583i 0.454015π-0.454015\pi
0.143963 + 0.989583i 0.454015π0.454015\pi
194194 0 0
195195 0 0
196196 0 0
197197 0 0 1.00000 00
−1.00000 π\pi
198198 −6.00000 −0.426401
199199 27.7128i 1.96451i 0.187552 + 0.982255i 0.439945π0.439945\pi
−0.187552 + 0.982255i 0.560055π0.560055\pi
200200 2.82843 0.200000
201201 0 0
202202 − 10.3923i − 0.731200i
203203 0 0
204204 −25.4558 −1.78227
205205 30.0000 2.09529
206206 24.4949i 1.70664i
207207 −21.2132 −1.47442
208208 0 0
209209 − 9.79796i − 0.677739i
210210 0 0
211211 0 0 1.00000 00
−1.00000 π\pi
212212 0 0
213213 − 26.9444i − 1.84620i
214214 −10.0000 −0.683586
215215 0 0
216216 14.6969i 1.00000i
217217 0 0
218218 14.1421 0.957826
219219 0 0
220220 6.92820i 0.467099i
221221 0 0
222222 − 19.5959i − 1.31519i
223223 13.8564i 0.927894i 0.885863 + 0.463947i 0.153567π0.153567\pi
−0.885863 + 0.463947i 0.846433π0.846433\pi
224224 0 0
225225 3.00000 0.200000
226226 0 0
227227 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
228228 −24.0000 −1.58944
229229 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
230230 24.4949i 1.61515i
231231 0 0
232232 0 0
233233 0 0 1.00000 00
−1.00000 π\pi
234234 0 0
235235 0 0
236236 0 0
237237 0 0
238238 0 0
239239 24.0416 1.55512 0.777562 0.628806i 0.216456π-0.216456\pi
0.777562 + 0.628806i 0.216456π0.216456\pi
240240 16.9706 1.09545
241241 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
242242 12.7279 0.818182
243243 15.5885i 1.00000i
244244 0 0
245245 0 0
246246 30.0000 1.91273
247247 0 0
248248 − 9.79796i − 0.622171i
249249 0 0
250250 13.8564i 0.876356i
251251 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
252252 0 0
253253 −10.0000 −0.628695
254254 0 0
255255 31.1769i 1.95237i
256256 16.0000 1.00000
257257 31.8434i 1.98633i 0.116699 + 0.993167i 0.462769π0.462769\pi
−0.116699 + 0.993167i 0.537231π0.537231\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 0 0
263263 −1.41421 −0.0872041 −0.0436021 0.999049i 0.513883π-0.513883\pi
−0.0436021 + 0.999049i 0.513883π0.513883\pi
264264 6.92820i 0.426401i
265265 0 0
266266 0 0
267267 4.24264 0.259645
268268 0 0
269269 − 26.9444i − 1.64283i −0.570332 0.821414i 0.693186π-0.693186\pi
0.570332 0.821414i 0.306814π-0.306814\pi
270270 18.0000 1.09545
271271 31.1769i 1.89386i 0.321436 + 0.946931i 0.395835π0.395835\pi
−0.321436 + 0.946931i 0.604165π0.604165\pi
272272 29.3939i 1.78227i
273273 0 0
274274 0 0
275275 1.41421 0.0852803
276276 24.4949i 1.47442i
277277 32.0000 1.92269 0.961347 0.275340i 0.0887905π-0.0887905\pi
0.961347 + 0.275340i 0.0887905π0.0887905\pi
278278 14.6969i 0.881464i
279279 − 10.3923i − 0.622171i
280280 0 0
281281 0 0 1.00000 00
−1.00000 π\pi
282282 0 0
283283 − 20.7846i − 1.23552i −0.786368 0.617758i 0.788041π-0.788041\pi
0.786368 0.617758i 0.211959π-0.211959\pi
284284 −31.1127 −1.84620
285285 29.3939i 1.74114i
286286 0 0
287287 0 0
288288 16.9706 1.00000
289289 −37.0000 −2.17647
290290 0 0
291291 0 0
292292 0 0
293293 − 22.0454i − 1.28791i −0.765065 0.643953i 0.777293π-0.777293\pi
0.765065 0.643953i 0.222707π-0.222707\pi
294294 0 0
295295 0 0
296296 −22.6274 −1.31519
297297 7.34847i 0.426401i
298298 0 0
299299 0 0
300300 − 3.46410i − 0.200000i
301301 0 0
302302 0 0
303303 −12.7279 −0.731200
304304 27.7128i 1.58944i
305305 0 0
306306 31.1769i 1.78227i
307307 − 34.6410i − 1.97707i −0.151001 0.988534i 0.548250π-0.548250\pi
0.151001 0.988534i 0.451750π-0.451750\pi
308308 0 0
309309 30.0000 1.70664
310310 −12.0000 −0.681554
311311 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
312312 0 0
313313 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
314314 0 0
315315 0 0
316316 0 0
317317 0 0 1.00000 00
−1.00000 π\pi
318318 0 0
319319 0 0
320320 − 19.5959i − 1.09545i
321321 12.2474i 0.683586i
322322 0 0
323323 −50.9117 −2.83280
324324 18.0000 1.00000
325325 0 0
326326 0 0
327327 − 17.3205i − 0.957826i
328328 − 34.6410i − 1.91273i
329329 0 0
330330 8.48528 0.467099
331331 0 0 1.00000 00
−1.00000 π\pi
332332 0 0
333333 −24.0000 −1.31519
334334 0 0
335335 0 0
336336 0 0
337337 2.00000 0.108947 0.0544735 0.998515i 0.482652π-0.482652\pi
0.0544735 + 0.998515i 0.482652π0.482652\pi
338338 18.3848 1.00000
339339 0 0
340340 36.0000 1.95237
341341 − 4.89898i − 0.265295i
342342 29.3939i 1.58944i
343343 0 0
344344 0 0
345345 30.0000 1.61515
346346 3.46410i 0.186231i
347347 18.3848 0.986947 0.493473 0.869761i 0.335727π-0.335727\pi
0.493473 + 0.869761i 0.335727π0.335727\pi
348348 0 0
349349 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
350350 0 0
351351 0 0
352352 8.00000 0.426401
353353 − 26.9444i − 1.43411i −0.697019 0.717053i 0.745491π-0.745491\pi
0.697019 0.717053i 0.254509π-0.254509\pi
354354 0 0
355355 38.1051i 2.02241i
356356 − 4.89898i − 0.259645i
357357 0 0
358358 −26.0000 −1.37414
359359 −32.5269 −1.71670 −0.858352 0.513061i 0.828512π-0.828512\pi
−0.858352 + 0.513061i 0.828512π0.828512\pi
360360 − 20.7846i − 1.09545i
361361 −29.0000 −1.52632
362362 0 0
363363 − 15.5885i − 0.818182i
364364 0 0
365365 0 0
366366 0 0
367367 27.7128i 1.44660i 0.690535 + 0.723299i 0.257375π0.257375\pi
−0.690535 + 0.723299i 0.742625π0.742625\pi
368368 28.2843 1.47442
369369 − 36.7423i − 1.91273i
370370 27.7128i 1.44072i
371371 0 0
372372 −12.0000 −0.622171
373373 −34.0000 −1.76045 −0.880227 0.474554i 0.842610π-0.842610\pi
−0.880227 + 0.474554i 0.842610π0.842610\pi
374374 14.6969i 0.759961i
375375 16.9706 0.876356
376376 0 0
377377 0 0
378378 0 0
379379 0 0 1.00000 00
−1.00000 π\pi
380380 33.9411 1.74114
381381 0 0
382382 −38.0000 −1.94425
383383 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
384384 − 19.5959i − 1.00000i
385385 0 0
386386 −5.65685 −0.287926
387387 0 0
388388 0 0
389389 0 0 1.00000 00
−1.00000 π\pi
390390 0 0
391391 51.9615i 2.62781i
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 8.48528 0.426401
397397 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
398398 − 39.1918i − 1.96451i
399399 0 0
400400 −4.00000 −0.200000
401401 0 0 1.00000 00
−1.00000 π\pi
402402 0 0
403403 0 0
404404 14.6969i 0.731200i
405405 − 22.0454i − 1.09545i
406406 0 0
407407 −11.3137 −0.560800
408408 36.0000 1.78227
409409 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
410410 −42.4264 −2.09529
411411 0 0
412412 − 34.6410i − 1.70664i
413413 0 0
414414 30.0000 1.47442
415415 0 0
416416 0 0
417417 18.0000 0.881464
418418 13.8564i 0.677739i
419419 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
420420 0 0
421421 −40.0000 −1.94948 −0.974740 0.223341i 0.928304π-0.928304\pi
−0.974740 + 0.223341i 0.928304π0.928304\pi
422422 0 0
423423 0 0
424424 0 0
425425 − 7.34847i − 0.356453i
426426 38.1051i 1.84620i
427427 0 0
428428 14.1421 0.683586
429429 0 0
430430 0 0
431431 −41.0122 −1.97549 −0.987744 0.156083i 0.950113π-0.950113\pi
−0.987744 + 0.156083i 0.950113π0.950113\pi
432432 − 20.7846i − 1.00000i
433433 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
434434 0 0
435435 0 0
436436 −20.0000 −0.957826
437437 48.9898i 2.34350i
438438 0 0
439439 − 41.5692i − 1.98399i −0.126275 0.991995i 0.540302π-0.540302\pi
0.126275 0.991995i 0.459698π-0.459698\pi
440440 − 9.79796i − 0.467099i
441441 0 0
442442 0 0
443443 26.8701 1.27663 0.638317 0.769773i 0.279631π-0.279631\pi
0.638317 + 0.769773i 0.279631π0.279631\pi
444444 27.7128i 1.31519i
445445 −6.00000 −0.284427
446446 − 19.5959i − 0.927894i
447447 0 0
448448 0 0
449449 0 0 1.00000 00
−1.00000 π\pi
450450 −4.24264 −0.200000
451451 − 17.3205i − 0.815591i
452452 0 0
453453 0 0
454454 0 0
455455 0 0
456456 33.9411 1.58944
457457 22.0000 1.02912 0.514558 0.857455i 0.327956π-0.327956\pi
0.514558 + 0.857455i 0.327956π0.327956\pi
458458 0 0
459459 38.1838 1.78227
460460 − 34.6410i − 1.61515i
461461 12.2474i 0.570421i 0.958465 + 0.285210i 0.0920634π0.0920634\pi
−0.958465 + 0.285210i 0.907937π0.907937\pi
462462 0 0
463463 0 0 1.00000 00
−1.00000 π\pi
464464 0 0
465465 14.6969i 0.681554i
466466 0 0
467467 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 0 0
473473 0 0
474474 0 0
475475 − 6.92820i − 0.317888i
476476 0 0
477477 0 0
478478 −34.0000 −1.55512
479479 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
480480 −24.0000 −1.09545
481481 0 0
482482 0 0
483483 0 0
484484 −18.0000 −0.818182
485485 0 0
486486 − 22.0454i − 1.00000i
487487 0 0 1.00000 00
−1.00000 π\pi
488488 0 0
489489 0 0
490490 0 0
491491 43.8406 1.97850 0.989250 0.146236i 0.0467158π-0.0467158\pi
0.989250 + 0.146236i 0.0467158π0.0467158\pi
492492 −42.4264 −1.91273
493493 0 0
494494 0 0
495495 − 10.3923i − 0.467099i
496496 13.8564i 0.622171i
497497 0 0
498498 0 0
499499 0 0 1.00000 00
−1.00000 π\pi
500500 − 19.5959i − 0.876356i
501501 0 0
502502 0 0
503503 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
504504 0 0
505505 18.0000 0.800989
506506 14.1421 0.628695
507507 − 22.5167i − 1.00000i
508508 0 0
509509 − 36.7423i − 1.62858i −0.580461 0.814288i 0.697128π-0.697128\pi
0.580461 0.814288i 0.302872π-0.302872\pi
510510 − 44.0908i − 1.95237i
511511 0 0
512512 −22.6274 −1.00000
513513 36.0000 1.58944
514514 − 45.0333i − 1.98633i
515515 −42.4264 −1.86953
516516 0 0
517517 0 0
518518 0 0
519519 4.24264 0.186231
520520 0 0
521521 41.6413i 1.82434i 0.409812 + 0.912170i 0.365594π0.365594\pi
−0.409812 + 0.912170i 0.634406π0.634406\pi
522522 0 0
523523 − 17.3205i − 0.757373i −0.925525 0.378686i 0.876376π-0.876376\pi
0.925525 0.378686i 0.123624π-0.123624\pi
524524 0 0
525525 0 0
526526 2.00000 0.0872041
527527 −25.4558 −1.10887
528528 − 9.79796i − 0.426401i
529529 27.0000 1.17391
530530 0 0
531531 0 0
532532 0 0
533533 0 0
534534 −6.00000 −0.259645
535535 − 17.3205i − 0.748831i
536536 0 0
537537 31.8434i 1.37414i
538538 38.1051i 1.64283i
539539 0 0
540540 −25.4558 −1.09545
541541 8.00000 0.343947 0.171973 0.985102i 0.444986π-0.444986\pi
0.171973 + 0.985102i 0.444986π0.444986\pi
542542 − 44.0908i − 1.89386i
543543 0 0
544544 − 41.5692i − 1.78227i
545545 24.4949i 1.04925i
546546 0 0
547547 0 0 1.00000 00
−1.00000 π\pi
548548 0 0
549549 0 0
550550 −2.00000 −0.0852803
551551 0 0
552552 − 34.6410i − 1.47442i
553553 0 0
554554 −45.2548 −1.92269
555555 33.9411 1.44072
556556 − 20.7846i − 0.881464i
557557 0 0 1.00000 00
−1.00000 π\pi
558558 14.6969i 0.622171i
559559 0 0
560560 0 0
561561 18.0000 0.759961
562562 0 0
563563 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
564564 0 0
565565 0 0
566566 29.3939i 1.23552i
567567 0 0
568568 44.0000 1.84620
569569 0 0 1.00000 00
−1.00000 π\pi
570570 − 41.5692i − 1.74114i
571571 0 0 1.00000 00
−1.00000 π\pi
572572 0 0
573573 46.5403i 1.94425i
574574 0 0
575575 −7.07107 −0.294884
576576 −24.0000 −1.00000
577577 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
578578 52.3259 2.17647
579579 6.92820i 0.287926i
580580 0 0
581581 0 0
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 31.1769i 1.28791i
587587 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
588588 0 0
589589 −24.0000 −0.988903
590590 0 0
591591 0 0
592592 32.0000 1.31519
593593 − 2.44949i − 0.100588i −0.998734 0.0502942i 0.983984π-0.983984\pi
0.998734 0.0502942i 0.0160159π-0.0160159\pi
594594 − 10.3923i − 0.426401i
595595 0 0
596596 0 0
597597 −48.0000 −1.96451
598598 0 0
599599 18.3848 0.751182 0.375591 0.926786i 0.377440π-0.377440\pi
0.375591 + 0.926786i 0.377440π0.377440\pi
600600 4.89898i 0.200000i
601601 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
602602 0 0
603603 0 0
604604 0 0
605605 22.0454i 0.896273i
606606 18.0000 0.731200
607607 − 41.5692i − 1.68724i −0.536939 0.843621i 0.680419π-0.680419\pi
0.536939 0.843621i 0.319581π-0.319581\pi
608608 − 39.1918i − 1.58944i
609609 0 0
610610 0 0
611611 0 0
612612 − 44.0908i − 1.78227i
613613 46.0000 1.85792 0.928961 0.370177i 0.120703π-0.120703\pi
0.928961 + 0.370177i 0.120703π0.120703\pi
614614 48.9898i 1.97707i
615615 51.9615i 2.09529i
616616 0 0
617617 0 0 1.00000 00
−1.00000 π\pi
618618 −42.4264 −1.70664
619619 − 45.0333i − 1.81004i −0.425367 0.905021i 0.639855π-0.639855\pi
0.425367 0.905021i 0.360145π-0.360145\pi
620620 16.9706 0.681554
621621 − 36.7423i − 1.47442i
622622 0 0
623623 0 0
624624 0 0
625625 −29.0000 −1.16000
626626 0 0
627627 16.9706 0.677739
628628 0 0
629629 58.7878i 2.34402i
630630 0 0
631631 0 0 1.00000 00
−1.00000 π\pi
632632 0 0
633633 0 0
634634 0 0
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 46.6690 1.84620
640640 27.7128i 1.09545i
641641 0 0 1.00000 00
−1.00000 π\pi
642642 − 17.3205i − 0.683586i
643643 − 34.6410i − 1.36611i −0.730368 0.683054i 0.760651π-0.760651\pi
0.730368 0.683054i 0.239349π-0.239349\pi
644644 0 0
645645 0 0
646646 72.0000 2.83280
647647 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
648648 −25.4558 −1.00000
649649 0 0
650650 0 0
651651 0 0
652652 0 0
653653 0 0 1.00000 00
−1.00000 π\pi
654654 24.4949i 0.957826i
655655 0 0
656656 48.9898i 1.91273i
657657 0 0
658658 0 0
659659 24.0416 0.936529 0.468264 0.883588i 0.344879π-0.344879\pi
0.468264 + 0.883588i 0.344879π0.344879\pi
660660 −12.0000 −0.467099
661661 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 33.9411 1.31519
667667 0 0
668668 0 0
669669 −24.0000 −0.927894
670670 0 0
671671 0 0
672672 0 0
673673 44.0000 1.69608 0.848038 0.529936i 0.177784π-0.177784\pi
0.848038 + 0.529936i 0.177784π0.177784\pi
674674 −2.82843 −0.108947
675675 5.19615i 0.200000i
676676 −26.0000 −1.00000
677677 31.8434i 1.22384i 0.790920 + 0.611920i 0.209603π0.209603\pi
−0.790920 + 0.611920i 0.790397π0.790397\pi
678678 0 0
679679 0 0
680680 −50.9117 −1.95237
681681 0 0
682682 6.92820i 0.265295i
683683 −41.0122 −1.56929 −0.784644 0.619947i 0.787154π-0.787154\pi
−0.784644 + 0.619947i 0.787154π0.787154\pi
684684 − 41.5692i − 1.58944i
685685 0 0
686686 0 0
687687 0 0
688688 0 0
689689 0 0
690690 −42.4264 −1.61515
691691 31.1769i 1.18603i 0.805193 + 0.593013i 0.202062π0.202062\pi
−0.805193 + 0.593013i 0.797938π0.797938\pi
692692 − 4.89898i − 0.186231i
693693 0 0
694694 −26.0000 −0.986947
695695 −25.4558 −0.965595
696696 0 0
697697 −90.0000 −3.40899
698698 0 0
699699 0 0
700700 0 0
701701 0 0 1.00000 00
−1.00000 π\pi
702702 0 0
703703 55.4256i 2.09042i
704704 −11.3137 −0.426401
705705 0 0
706706 38.1051i 1.43411i
707707 0 0
708708 0 0
709709 50.0000 1.87779 0.938895 0.344204i 0.111851π-0.111851\pi
0.938895 + 0.344204i 0.111851π0.111851\pi
710710 − 53.8888i − 2.02241i
711711 0 0
712712 6.92820i 0.259645i
713713 24.4949i 0.917341i
714714 0 0
715715 0 0
716716 36.7696 1.37414
717717 41.6413i 1.55512i
718718 46.0000 1.71670
719719 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
720720 29.3939i 1.09545i
721721 0 0
722722 41.0122 1.52632
723723 0 0
724724 0 0
725725 0 0
726726 22.0454i 0.818182i
727727 − 10.3923i − 0.385429i −0.981255 0.192715i 0.938271π-0.938271\pi
0.981255 0.192715i 0.0617292π-0.0617292\pi
728728 0 0
729729 −27.0000 −1.00000
730730 0 0
731731 0 0
732732 0 0
733733 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
734734 − 39.1918i − 1.44660i
735735 0 0
736736 −40.0000 −1.47442
737737 0 0
738738 51.9615i 1.91273i
739739 0 0 1.00000 00
−1.00000 π\pi
740740 − 39.1918i − 1.44072i
741741 0 0
742742 0 0
743743 43.8406 1.60836 0.804178 0.594388i 0.202606π-0.202606\pi
0.804178 + 0.594388i 0.202606π0.202606\pi
744744 16.9706 0.622171
745745 0 0
746746 48.0833 1.76045
747747 0 0
748748 − 20.7846i − 0.759961i
749749 0 0
750750 −24.0000 −0.876356
751751 0 0 1.00000 00
−1.00000 π\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 2.00000 0.0726912 0.0363456 0.999339i 0.488428π-0.488428\pi
0.0363456 + 0.999339i 0.488428π0.488428\pi
758758 0 0
759759 − 17.3205i − 0.628695i
760760 −48.0000 −1.74114
761761 − 36.7423i − 1.33191i −0.745992 0.665955i 0.768024π-0.768024\pi
0.745992 0.665955i 0.231976π-0.231976\pi
762762 0 0
763763 0 0
764764 53.7401 1.94425
765765 −54.0000 −1.95237
766766 0 0
767767 0 0
768768 27.7128i 1.00000i
769769 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
770770 0 0
771771 −55.1543 −1.98633
772772 8.00000 0.287926
773773 − 26.9444i − 0.969122i −0.874757 0.484561i 0.838979π-0.838979\pi
0.874757 0.484561i 0.161021π-0.161021\pi
774774 0 0
775775 − 3.46410i − 0.124434i
776776 0 0
777777 0 0
778778 0 0
779779 −84.8528 −3.04017
780780 0 0
781781 22.0000 0.787222
782782 − 73.4847i − 2.62781i
783783 0 0
784784 0 0
785785 0 0
786786 0 0
787787 51.9615i 1.85223i 0.377243 + 0.926114i 0.376872π0.376872\pi
−0.377243 + 0.926114i 0.623128π0.623128\pi
788788 0 0
789789 − 2.44949i − 0.0872041i
790790 0 0
791791 0 0
792792 −12.0000 −0.426401
793793 0 0
794794 0 0
795795 0 0
796796 55.4256i 1.96451i
797797 − 56.3383i − 1.99560i −0.0662682 0.997802i 0.521109π-0.521109\pi
0.0662682 0.997802i 0.478891π-0.478891\pi
798798 0 0
799799 0 0
800800 5.65685 0.200000
801801 7.34847i 0.259645i
802802 0 0
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 46.6690 1.64283
808808 − 20.7846i − 0.731200i
809809 0 0 1.00000 00
−1.00000 π\pi
810810 31.1769i 1.09545i
811811 38.1051i 1.33805i 0.743239 + 0.669026i 0.233288π0.233288\pi
−0.743239 + 0.669026i 0.766712π0.766712\pi
812812 0 0
813813 −54.0000 −1.89386
814814 16.0000 0.560800
815815 0 0
816816 −50.9117 −1.78227
817817 0 0
818818 0 0
819819 0 0
820820 60.0000 2.09529
821821 0 0 1.00000 00
−1.00000 π\pi
822822 0 0
823823 0 0 1.00000 00
−1.00000 π\pi
824824 48.9898i 1.70664i
825825 2.44949i 0.0852803i
826826 0 0
827827 −35.3553 −1.22943 −0.614713 0.788751i 0.710728π-0.710728\pi
−0.614713 + 0.788751i 0.710728π0.710728\pi
828828 −42.4264 −1.47442
829829 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
830830 0 0
831831 55.4256i 1.92269i
832832 0 0
833833 0 0
834834 −25.4558 −0.881464
835835 0 0
836836 − 19.5959i − 0.677739i
837837 18.0000 0.622171
838838 0 0
839839 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
840840 0 0
841841 29.0000 1.00000
842842 56.5685 1.94948
843843 0 0
844844 0 0
845845 31.8434i 1.09545i
846846 0 0
847847 0 0
848848 0 0
849849 36.0000 1.23552
850850 10.3923i 0.356453i
851851 56.5685 1.93914
852852 − 53.8888i − 1.84620i
853853 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
854854 0 0
855855 −50.9117 −1.74114
856856 −20.0000 −0.683586
857857 41.6413i 1.42244i 0.702969 + 0.711220i 0.251857π0.251857\pi
−0.702969 + 0.711220i 0.748143π0.748143\pi
858858 0 0
859859 6.92820i 0.236387i 0.992991 + 0.118194i 0.0377103π0.0377103\pi
−0.992991 + 0.118194i 0.962290π0.962290\pi
860860 0 0
861861 0 0
862862 58.0000 1.97549
863863 7.07107 0.240702 0.120351 0.992731i 0.461598π-0.461598\pi
0.120351 + 0.992731i 0.461598π0.461598\pi
864864 29.3939i 1.00000i
865865 −6.00000 −0.204006
866866 0 0
867867 − 64.0859i − 2.17647i
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 28.2843 0.957826
873873 0 0
874874 − 69.2820i − 2.34350i
875875 0 0
876876 0 0
877877 22.0000 0.742887 0.371444 0.928456i 0.378863π-0.378863\pi
0.371444 + 0.928456i 0.378863π0.378863\pi
878878 58.7878i 1.98399i
879879 38.1838 1.28791
880880 13.8564i 0.467099i
881881 − 56.3383i − 1.89808i −0.315149 0.949042i 0.602055π-0.602055\pi
0.315149 0.949042i 0.397945π-0.397945\pi
882882 0 0
883883 0 0 1.00000 00
−1.00000 π\pi
884884 0 0
885885 0 0
886886 −38.0000 −1.27663
887887 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
888888 − 39.1918i − 1.31519i
889889 0 0
890890 8.48528 0.284427
891891 −12.7279 −0.426401
892892 27.7128i 0.927894i
893893 0 0
894894 0 0
895895 − 45.0333i − 1.50530i
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 6.00000 0.200000
901901 0 0
902902 24.4949i 0.815591i
903903 0 0
904904 0 0
905905 0 0
906906 0 0
907907 0 0 1.00000 00
−1.00000 π\pi
908908 0 0
909909 − 22.0454i − 0.731200i
910910 0 0
911911 −15.5563 −0.515405 −0.257702 0.966224i 0.582965π-0.582965\pi
−0.257702 + 0.966224i 0.582965π0.582965\pi
912912 −48.0000 −1.58944
913913 0 0
914914 −31.1127 −1.02912
915915 0 0
916916 0 0
917917 0 0
918918 −54.0000 −1.78227
919919 0 0 1.00000 00
−1.00000 π\pi
920920 48.9898i 1.61515i
921921 60.0000 1.97707
922922 − 17.3205i − 0.570421i
923923 0 0
924924 0 0
925925 −8.00000 −0.263038
926926 0 0
927927 51.9615i 1.70664i
928928 0 0
929929 − 36.7423i − 1.20548i −0.797939 0.602739i 0.794076π-0.794076\pi
0.797939 0.602739i 0.205924π-0.205924\pi
930930 − 20.7846i − 0.681554i
931931 0 0
932932 0 0
933933 0 0
934934 0 0
935935 −25.4558 −0.832495
936936 0 0
937937 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
938938 0 0
939939 0 0
940940 0 0
941941 − 61.2372i − 1.99628i −0.0609873 0.998139i 0.519425π-0.519425\pi
0.0609873 0.998139i 0.480575π-0.480575\pi
942942 0 0
943943 86.6025i 2.82017i
944944 0 0
945945 0 0
946946 0 0
947947 −52.3259 −1.70036 −0.850182 0.526489i 0.823508π-0.823508\pi
−0.850182 + 0.526489i 0.823508π0.823508\pi
948948 0 0
949949 0 0
950950 9.79796i 0.317888i
951951 0 0
952952 0 0
953953 0 0 1.00000 00
−1.00000 π\pi
954954 0 0
955955 − 65.8179i − 2.12982i
956956 48.0833 1.55512
957957 0 0
958958 0 0
959959 0 0
960960 33.9411 1.09545
961961 19.0000 0.612903
962962 0 0
963963 −21.2132 −0.683586
964964 0 0
965965 − 9.79796i − 0.315407i
966966 0 0
967967 0 0 1.00000 00
−1.00000 π\pi
968968 25.4558 0.818182
969969 − 88.1816i − 2.83280i
970970 0 0
971971 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
972972 31.1769i 1.00000i
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 0 0 1.00000 00
−1.00000 π\pi
978978 0 0
979979 3.46410i 0.110713i
980980 0 0
981981 30.0000 0.957826
982982 −62.0000 −1.97850
983983 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
984984 60.0000 1.91273
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 14.6969i 0.467099i
991991 0 0 1.00000 00
−1.00000 π\pi
992992 − 19.5959i − 0.622171i
993993 0 0
994994 0 0
995995 67.8823 2.15201
996996 0 0
997997 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
998998 0 0
999999 − 41.5692i − 1.31519i
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 588.2.e.a.491.2 yes 4
3.2 odd 2 inner 588.2.e.a.491.4 yes 4
4.3 odd 2 inner 588.2.e.a.491.3 yes 4
7.2 even 3 588.2.n.a.263.2 4
7.3 odd 6 588.2.n.a.275.2 4
7.4 even 3 588.2.n.b.275.2 4
7.5 odd 6 588.2.n.b.263.2 4
7.6 odd 2 inner 588.2.e.a.491.1 4
12.11 even 2 inner 588.2.e.a.491.1 4
21.2 odd 6 588.2.n.a.263.1 4
21.5 even 6 588.2.n.b.263.1 4
21.11 odd 6 588.2.n.b.275.1 4
21.17 even 6 588.2.n.a.275.1 4
21.20 even 2 inner 588.2.e.a.491.3 yes 4
28.3 even 6 588.2.n.b.275.1 4
28.11 odd 6 588.2.n.a.275.1 4
28.19 even 6 588.2.n.a.263.1 4
28.23 odd 6 588.2.n.b.263.1 4
28.27 even 2 inner 588.2.e.a.491.4 yes 4
84.11 even 6 588.2.n.a.275.2 4
84.23 even 6 588.2.n.b.263.2 4
84.47 odd 6 588.2.n.a.263.2 4
84.59 odd 6 588.2.n.b.275.2 4
84.83 odd 2 CM 588.2.e.a.491.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
588.2.e.a.491.1 4 7.6 odd 2 inner
588.2.e.a.491.1 4 12.11 even 2 inner
588.2.e.a.491.2 yes 4 1.1 even 1 trivial
588.2.e.a.491.2 yes 4 84.83 odd 2 CM
588.2.e.a.491.3 yes 4 4.3 odd 2 inner
588.2.e.a.491.3 yes 4 21.20 even 2 inner
588.2.e.a.491.4 yes 4 3.2 odd 2 inner
588.2.e.a.491.4 yes 4 28.27 even 2 inner
588.2.n.a.263.1 4 21.2 odd 6
588.2.n.a.263.1 4 28.19 even 6
588.2.n.a.263.2 4 7.2 even 3
588.2.n.a.263.2 4 84.47 odd 6
588.2.n.a.275.1 4 21.17 even 6
588.2.n.a.275.1 4 28.11 odd 6
588.2.n.a.275.2 4 7.3 odd 6
588.2.n.a.275.2 4 84.11 even 6
588.2.n.b.263.1 4 21.5 even 6
588.2.n.b.263.1 4 28.23 odd 6
588.2.n.b.263.2 4 7.5 odd 6
588.2.n.b.263.2 4 84.23 even 6
588.2.n.b.275.1 4 21.11 odd 6
588.2.n.b.275.1 4 28.3 even 6
588.2.n.b.275.2 4 7.4 even 3
588.2.n.b.275.2 4 84.59 odd 6