Properties

Label 8400.2.a.ct.1.1
Level 84008400
Weight 22
Character 8400.1
Self dual yes
Analytic conductor 67.07467.074
Analytic rank 00
Dimension 11
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8400,2,Mod(1,8400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8400, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8400.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 8400=243527 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 8400.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 67.074337697967.0743376979
Analytic rank: 00
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 84)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 8400.1

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+1.00000q3+1.00000q7+1.00000q9+6.00000q112.00000q13+4.00000q19+1.00000q216.00000q23+1.00000q27+6.00000q298.00000q31+6.00000q332.00000q372.00000q39+12.0000q414.00000q43+12.0000q47+1.00000q49+6.00000q53+4.00000q5710.0000q61+1.00000q63+8.00000q676.00000q696.00000q71+10.0000q73+6.00000q77+4.00000q79+1.00000q8112.0000q83+6.00000q87+12.0000q892.00000q918.00000q93+10.0000q97+6.00000q99+O(q100)q+1.00000 q^{3} +1.00000 q^{7} +1.00000 q^{9} +6.00000 q^{11} -2.00000 q^{13} +4.00000 q^{19} +1.00000 q^{21} -6.00000 q^{23} +1.00000 q^{27} +6.00000 q^{29} -8.00000 q^{31} +6.00000 q^{33} -2.00000 q^{37} -2.00000 q^{39} +12.0000 q^{41} -4.00000 q^{43} +12.0000 q^{47} +1.00000 q^{49} +6.00000 q^{53} +4.00000 q^{57} -10.0000 q^{61} +1.00000 q^{63} +8.00000 q^{67} -6.00000 q^{69} -6.00000 q^{71} +10.0000 q^{73} +6.00000 q^{77} +4.00000 q^{79} +1.00000 q^{81} -12.0000 q^{83} +6.00000 q^{87} +12.0000 q^{89} -2.00000 q^{91} -8.00000 q^{93} +10.0000 q^{97} +6.00000 q^{99} +O(q^{100})

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 1.00000 0.577350
44 0 0
55 0 0
66 0 0
77 1.00000 0.377964
88 0 0
99 1.00000 0.333333
1010 0 0
1111 6.00000 1.80907 0.904534 0.426401i 0.140219π-0.140219\pi
0.904534 + 0.426401i 0.140219π0.140219\pi
1212 0 0
1313 −2.00000 −0.554700 −0.277350 0.960769i 0.589456π-0.589456\pi
−0.277350 + 0.960769i 0.589456π0.589456\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 4.00000 0.917663 0.458831 0.888523i 0.348268π-0.348268\pi
0.458831 + 0.888523i 0.348268π0.348268\pi
2020 0 0
2121 1.00000 0.218218
2222 0 0
2323 −6.00000 −1.25109 −0.625543 0.780189i 0.715123π-0.715123\pi
−0.625543 + 0.780189i 0.715123π0.715123\pi
2424 0 0
2525 0 0
2626 0 0
2727 1.00000 0.192450
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 −8.00000 −1.43684 −0.718421 0.695608i 0.755135π-0.755135\pi
−0.718421 + 0.695608i 0.755135π0.755135\pi
3232 0 0
3333 6.00000 1.04447
3434 0 0
3535 0 0
3636 0 0
3737 −2.00000 −0.328798 −0.164399 0.986394i 0.552568π-0.552568\pi
−0.164399 + 0.986394i 0.552568π0.552568\pi
3838 0 0
3939 −2.00000 −0.320256
4040 0 0
4141 12.0000 1.87409 0.937043 0.349215i 0.113552π-0.113552\pi
0.937043 + 0.349215i 0.113552π0.113552\pi
4242 0 0
4343 −4.00000 −0.609994 −0.304997 0.952353i 0.598656π-0.598656\pi
−0.304997 + 0.952353i 0.598656π0.598656\pi
4444 0 0
4545 0 0
4646 0 0
4747 12.0000 1.75038 0.875190 0.483779i 0.160736π-0.160736\pi
0.875190 + 0.483779i 0.160736π0.160736\pi
4848 0 0
4949 1.00000 0.142857
5050 0 0
5151 0 0
5252 0 0
5353 6.00000 0.824163 0.412082 0.911147i 0.364802π-0.364802\pi
0.412082 + 0.911147i 0.364802π0.364802\pi
5454 0 0
5555 0 0
5656 0 0
5757 4.00000 0.529813
5858 0 0
5959 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
6060 0 0
6161 −10.0000 −1.28037 −0.640184 0.768221i 0.721142π-0.721142\pi
−0.640184 + 0.768221i 0.721142π0.721142\pi
6262 0 0
6363 1.00000 0.125988
6464 0 0
6565 0 0
6666 0 0
6767 8.00000 0.977356 0.488678 0.872464i 0.337479π-0.337479\pi
0.488678 + 0.872464i 0.337479π0.337479\pi
6868 0 0
6969 −6.00000 −0.722315
7070 0 0
7171 −6.00000 −0.712069 −0.356034 0.934473i 0.615871π-0.615871\pi
−0.356034 + 0.934473i 0.615871π0.615871\pi
7272 0 0
7373 10.0000 1.17041 0.585206 0.810885i 0.301014π-0.301014\pi
0.585206 + 0.810885i 0.301014π0.301014\pi
7474 0 0
7575 0 0
7676 0 0
7777 6.00000 0.683763
7878 0 0
7979 4.00000 0.450035 0.225018 0.974355i 0.427756π-0.427756\pi
0.225018 + 0.974355i 0.427756π0.427756\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 −12.0000 −1.31717 −0.658586 0.752506i 0.728845π-0.728845\pi
−0.658586 + 0.752506i 0.728845π0.728845\pi
8484 0 0
8585 0 0
8686 0 0
8787 6.00000 0.643268
8888 0 0
8989 12.0000 1.27200 0.635999 0.771690i 0.280588π-0.280588\pi
0.635999 + 0.771690i 0.280588π0.280588\pi
9090 0 0
9191 −2.00000 −0.209657
9292 0 0
9393 −8.00000 −0.829561
9494 0 0
9595 0 0
9696 0 0
9797 10.0000 1.01535 0.507673 0.861550i 0.330506π-0.330506\pi
0.507673 + 0.861550i 0.330506π0.330506\pi
9898 0 0
9999 6.00000 0.603023
100100 0 0
101101 −12.0000 −1.19404 −0.597022 0.802225i 0.703650π-0.703650\pi
−0.597022 + 0.802225i 0.703650π0.703650\pi
102102 0 0
103103 8.00000 0.788263 0.394132 0.919054i 0.371045π-0.371045\pi
0.394132 + 0.919054i 0.371045π0.371045\pi
104104 0 0
105105 0 0
106106 0 0
107107 −6.00000 −0.580042 −0.290021 0.957020i 0.593662π-0.593662\pi
−0.290021 + 0.957020i 0.593662π0.593662\pi
108108 0 0
109109 14.0000 1.34096 0.670478 0.741929i 0.266089π-0.266089\pi
0.670478 + 0.741929i 0.266089π0.266089\pi
110110 0 0
111111 −2.00000 −0.189832
112112 0 0
113113 6.00000 0.564433 0.282216 0.959351i 0.408930π-0.408930\pi
0.282216 + 0.959351i 0.408930π0.408930\pi
114114 0 0
115115 0 0
116116 0 0
117117 −2.00000 −0.184900
118118 0 0
119119 0 0
120120 0 0
121121 25.0000 2.27273
122122 0 0
123123 12.0000 1.08200
124124 0 0
125125 0 0
126126 0 0
127127 −4.00000 −0.354943 −0.177471 0.984126i 0.556792π-0.556792\pi
−0.177471 + 0.984126i 0.556792π0.556792\pi
128128 0 0
129129 −4.00000 −0.352180
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 4.00000 0.346844
134134 0 0
135135 0 0
136136 0 0
137137 −6.00000 −0.512615 −0.256307 0.966595i 0.582506π-0.582506\pi
−0.256307 + 0.966595i 0.582506π0.582506\pi
138138 0 0
139139 4.00000 0.339276 0.169638 0.985506i 0.445740π-0.445740\pi
0.169638 + 0.985506i 0.445740π0.445740\pi
140140 0 0
141141 12.0000 1.01058
142142 0 0
143143 −12.0000 −1.00349
144144 0 0
145145 0 0
146146 0 0
147147 1.00000 0.0824786
148148 0 0
149149 −6.00000 −0.491539 −0.245770 0.969328i 0.579041π-0.579041\pi
−0.245770 + 0.969328i 0.579041π0.579041\pi
150150 0 0
151151 −8.00000 −0.651031 −0.325515 0.945537i 0.605538π-0.605538\pi
−0.325515 + 0.945537i 0.605538π0.605538\pi
152152 0 0
153153 0 0
154154 0 0
155155 0 0
156156 0 0
157157 −14.0000 −1.11732 −0.558661 0.829396i 0.688685π-0.688685\pi
−0.558661 + 0.829396i 0.688685π0.688685\pi
158158 0 0
159159 6.00000 0.475831
160160 0 0
161161 −6.00000 −0.472866
162162 0 0
163163 −16.0000 −1.25322 −0.626608 0.779334i 0.715557π-0.715557\pi
−0.626608 + 0.779334i 0.715557π0.715557\pi
164164 0 0
165165 0 0
166166 0 0
167167 −12.0000 −0.928588 −0.464294 0.885681i 0.653692π-0.653692\pi
−0.464294 + 0.885681i 0.653692π0.653692\pi
168168 0 0
169169 −9.00000 −0.692308
170170 0 0
171171 4.00000 0.305888
172172 0 0
173173 12.0000 0.912343 0.456172 0.889892i 0.349220π-0.349220\pi
0.456172 + 0.889892i 0.349220π0.349220\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 0 0
179179 −6.00000 −0.448461 −0.224231 0.974536i 0.571987π-0.571987\pi
−0.224231 + 0.974536i 0.571987π0.571987\pi
180180 0 0
181181 2.00000 0.148659 0.0743294 0.997234i 0.476318π-0.476318\pi
0.0743294 + 0.997234i 0.476318π0.476318\pi
182182 0 0
183183 −10.0000 −0.739221
184184 0 0
185185 0 0
186186 0 0
187187 0 0
188188 0 0
189189 1.00000 0.0727393
190190 0 0
191191 −6.00000 −0.434145 −0.217072 0.976156i 0.569651π-0.569651\pi
−0.217072 + 0.976156i 0.569651π0.569651\pi
192192 0 0
193193 10.0000 0.719816 0.359908 0.932988i 0.382808π-0.382808\pi
0.359908 + 0.932988i 0.382808π0.382808\pi
194194 0 0
195195 0 0
196196 0 0
197197 6.00000 0.427482 0.213741 0.976890i 0.431435π-0.431435\pi
0.213741 + 0.976890i 0.431435π0.431435\pi
198198 0 0
199199 16.0000 1.13421 0.567105 0.823646i 0.308063π-0.308063\pi
0.567105 + 0.823646i 0.308063π0.308063\pi
200200 0 0
201201 8.00000 0.564276
202202 0 0
203203 6.00000 0.421117
204204 0 0
205205 0 0
206206 0 0
207207 −6.00000 −0.417029
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 −6.00000 −0.411113
214214 0 0
215215 0 0
216216 0 0
217217 −8.00000 −0.543075
218218 0 0
219219 10.0000 0.675737
220220 0 0
221221 0 0
222222 0 0
223223 8.00000 0.535720 0.267860 0.963458i 0.413684π-0.413684\pi
0.267860 + 0.963458i 0.413684π0.413684\pi
224224 0 0
225225 0 0
226226 0 0
227227 24.0000 1.59294 0.796468 0.604681i 0.206699π-0.206699\pi
0.796468 + 0.604681i 0.206699π0.206699\pi
228228 0 0
229229 2.00000 0.132164 0.0660819 0.997814i 0.478950π-0.478950\pi
0.0660819 + 0.997814i 0.478950π0.478950\pi
230230 0 0
231231 6.00000 0.394771
232232 0 0
233233 −6.00000 −0.393073 −0.196537 0.980497i 0.562969π-0.562969\pi
−0.196537 + 0.980497i 0.562969π0.562969\pi
234234 0 0
235235 0 0
236236 0 0
237237 4.00000 0.259828
238238 0 0
239239 −18.0000 −1.16432 −0.582162 0.813073i 0.697793π-0.697793\pi
−0.582162 + 0.813073i 0.697793π0.697793\pi
240240 0 0
241241 −10.0000 −0.644157 −0.322078 0.946713i 0.604381π-0.604381\pi
−0.322078 + 0.946713i 0.604381π0.604381\pi
242242 0 0
243243 1.00000 0.0641500
244244 0 0
245245 0 0
246246 0 0
247247 −8.00000 −0.509028
248248 0 0
249249 −12.0000 −0.760469
250250 0 0
251251 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
252252 0 0
253253 −36.0000 −2.26330
254254 0 0
255255 0 0
256256 0 0
257257 12.0000 0.748539 0.374270 0.927320i 0.377893π-0.377893\pi
0.374270 + 0.927320i 0.377893π0.377893\pi
258258 0 0
259259 −2.00000 −0.124274
260260 0 0
261261 6.00000 0.371391
262262 0 0
263263 −6.00000 −0.369976 −0.184988 0.982741i 0.559225π-0.559225\pi
−0.184988 + 0.982741i 0.559225π0.559225\pi
264264 0 0
265265 0 0
266266 0 0
267267 12.0000 0.734388
268268 0 0
269269 24.0000 1.46331 0.731653 0.681677i 0.238749π-0.238749\pi
0.731653 + 0.681677i 0.238749π0.238749\pi
270270 0 0
271271 16.0000 0.971931 0.485965 0.873978i 0.338468π-0.338468\pi
0.485965 + 0.873978i 0.338468π0.338468\pi
272272 0 0
273273 −2.00000 −0.121046
274274 0 0
275275 0 0
276276 0 0
277277 22.0000 1.32185 0.660926 0.750451i 0.270164π-0.270164\pi
0.660926 + 0.750451i 0.270164π0.270164\pi
278278 0 0
279279 −8.00000 −0.478947
280280 0 0
281281 −18.0000 −1.07379 −0.536895 0.843649i 0.680403π-0.680403\pi
−0.536895 + 0.843649i 0.680403π0.680403\pi
282282 0 0
283283 20.0000 1.18888 0.594438 0.804141i 0.297374π-0.297374\pi
0.594438 + 0.804141i 0.297374π0.297374\pi
284284 0 0
285285 0 0
286286 0 0
287287 12.0000 0.708338
288288 0 0
289289 −17.0000 −1.00000
290290 0 0
291291 10.0000 0.586210
292292 0 0
293293 12.0000 0.701047 0.350524 0.936554i 0.386004π-0.386004\pi
0.350524 + 0.936554i 0.386004π0.386004\pi
294294 0 0
295295 0 0
296296 0 0
297297 6.00000 0.348155
298298 0 0
299299 12.0000 0.693978
300300 0 0
301301 −4.00000 −0.230556
302302 0 0
303303 −12.0000 −0.689382
304304 0 0
305305 0 0
306306 0 0
307307 20.0000 1.14146 0.570730 0.821138i 0.306660π-0.306660\pi
0.570730 + 0.821138i 0.306660π0.306660\pi
308308 0 0
309309 8.00000 0.455104
310310 0 0
311311 12.0000 0.680458 0.340229 0.940343i 0.389495π-0.389495\pi
0.340229 + 0.940343i 0.389495π0.389495\pi
312312 0 0
313313 −26.0000 −1.46961 −0.734803 0.678280i 0.762726π-0.762726\pi
−0.734803 + 0.678280i 0.762726π0.762726\pi
314314 0 0
315315 0 0
316316 0 0
317317 30.0000 1.68497 0.842484 0.538721i 0.181092π-0.181092\pi
0.842484 + 0.538721i 0.181092π0.181092\pi
318318 0 0
319319 36.0000 2.01561
320320 0 0
321321 −6.00000 −0.334887
322322 0 0
323323 0 0
324324 0 0
325325 0 0
326326 0 0
327327 14.0000 0.774202
328328 0 0
329329 12.0000 0.661581
330330 0 0
331331 −20.0000 −1.09930 −0.549650 0.835395i 0.685239π-0.685239\pi
−0.549650 + 0.835395i 0.685239π0.685239\pi
332332 0 0
333333 −2.00000 −0.109599
334334 0 0
335335 0 0
336336 0 0
337337 22.0000 1.19842 0.599208 0.800593i 0.295482π-0.295482\pi
0.599208 + 0.800593i 0.295482π0.295482\pi
338338 0 0
339339 6.00000 0.325875
340340 0 0
341341 −48.0000 −2.59935
342342 0 0
343343 1.00000 0.0539949
344344 0 0
345345 0 0
346346 0 0
347347 −18.0000 −0.966291 −0.483145 0.875540i 0.660506π-0.660506\pi
−0.483145 + 0.875540i 0.660506π0.660506\pi
348348 0 0
349349 −10.0000 −0.535288 −0.267644 0.963518i 0.586245π-0.586245\pi
−0.267644 + 0.963518i 0.586245π0.586245\pi
350350 0 0
351351 −2.00000 −0.106752
352352 0 0
353353 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 −6.00000 −0.316668 −0.158334 0.987386i 0.550612π-0.550612\pi
−0.158334 + 0.987386i 0.550612π0.550612\pi
360360 0 0
361361 −3.00000 −0.157895
362362 0 0
363363 25.0000 1.31216
364364 0 0
365365 0 0
366366 0 0
367367 32.0000 1.67039 0.835193 0.549957i 0.185356π-0.185356\pi
0.835193 + 0.549957i 0.185356π0.185356\pi
368368 0 0
369369 12.0000 0.624695
370370 0 0
371371 6.00000 0.311504
372372 0 0
373373 10.0000 0.517780 0.258890 0.965907i 0.416643π-0.416643\pi
0.258890 + 0.965907i 0.416643π0.416643\pi
374374 0 0
375375 0 0
376376 0 0
377377 −12.0000 −0.618031
378378 0 0
379379 −20.0000 −1.02733 −0.513665 0.857991i 0.671713π-0.671713\pi
−0.513665 + 0.857991i 0.671713π0.671713\pi
380380 0 0
381381 −4.00000 −0.204926
382382 0 0
383383 −24.0000 −1.22634 −0.613171 0.789950i 0.710106π-0.710106\pi
−0.613171 + 0.789950i 0.710106π0.710106\pi
384384 0 0
385385 0 0
386386 0 0
387387 −4.00000 −0.203331
388388 0 0
389389 30.0000 1.52106 0.760530 0.649303i 0.224939π-0.224939\pi
0.760530 + 0.649303i 0.224939π0.224939\pi
390390 0 0
391391 0 0
392392 0 0
393393 −12.0000 −0.605320
394394 0 0
395395 0 0
396396 0 0
397397 −14.0000 −0.702640 −0.351320 0.936255i 0.614267π-0.614267\pi
−0.351320 + 0.936255i 0.614267π0.614267\pi
398398 0 0
399399 4.00000 0.200250
400400 0 0
401401 6.00000 0.299626 0.149813 0.988714i 0.452133π-0.452133\pi
0.149813 + 0.988714i 0.452133π0.452133\pi
402402 0 0
403403 16.0000 0.797017
404404 0 0
405405 0 0
406406 0 0
407407 −12.0000 −0.594818
408408 0 0
409409 14.0000 0.692255 0.346128 0.938187i 0.387496π-0.387496\pi
0.346128 + 0.938187i 0.387496π0.387496\pi
410410 0 0
411411 −6.00000 −0.295958
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 4.00000 0.195881
418418 0 0
419419 24.0000 1.17248 0.586238 0.810139i 0.300608π-0.300608\pi
0.586238 + 0.810139i 0.300608π0.300608\pi
420420 0 0
421421 26.0000 1.26716 0.633581 0.773676i 0.281584π-0.281584\pi
0.633581 + 0.773676i 0.281584π0.281584\pi
422422 0 0
423423 12.0000 0.583460
424424 0 0
425425 0 0
426426 0 0
427427 −10.0000 −0.483934
428428 0 0
429429 −12.0000 −0.579365
430430 0 0
431431 −6.00000 −0.289010 −0.144505 0.989504i 0.546159π-0.546159\pi
−0.144505 + 0.989504i 0.546159π0.546159\pi
432432 0 0
433433 −26.0000 −1.24948 −0.624740 0.780833i 0.714795π-0.714795\pi
−0.624740 + 0.780833i 0.714795π0.714795\pi
434434 0 0
435435 0 0
436436 0 0
437437 −24.0000 −1.14808
438438 0 0
439439 −8.00000 −0.381819 −0.190910 0.981608i 0.561144π-0.561144\pi
−0.190910 + 0.981608i 0.561144π0.561144\pi
440440 0 0
441441 1.00000 0.0476190
442442 0 0
443443 30.0000 1.42534 0.712672 0.701498i 0.247485π-0.247485\pi
0.712672 + 0.701498i 0.247485π0.247485\pi
444444 0 0
445445 0 0
446446 0 0
447447 −6.00000 −0.283790
448448 0 0
449449 −30.0000 −1.41579 −0.707894 0.706319i 0.750354π-0.750354\pi
−0.707894 + 0.706319i 0.750354π0.750354\pi
450450 0 0
451451 72.0000 3.39035
452452 0 0
453453 −8.00000 −0.375873
454454 0 0
455455 0 0
456456 0 0
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 0 0
460460 0 0
461461 12.0000 0.558896 0.279448 0.960161i 0.409849π-0.409849\pi
0.279448 + 0.960161i 0.409849π0.409849\pi
462462 0 0
463463 −28.0000 −1.30127 −0.650635 0.759390i 0.725497π-0.725497\pi
−0.650635 + 0.759390i 0.725497π0.725497\pi
464464 0 0
465465 0 0
466466 0 0
467467 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
468468 0 0
469469 8.00000 0.369406
470470 0 0
471471 −14.0000 −0.645086
472472 0 0
473473 −24.0000 −1.10352
474474 0 0
475475 0 0
476476 0 0
477477 6.00000 0.274721
478478 0 0
479479 12.0000 0.548294 0.274147 0.961688i 0.411605π-0.411605\pi
0.274147 + 0.961688i 0.411605π0.411605\pi
480480 0 0
481481 4.00000 0.182384
482482 0 0
483483 −6.00000 −0.273009
484484 0 0
485485 0 0
486486 0 0
487487 32.0000 1.45006 0.725029 0.688718i 0.241826π-0.241826\pi
0.725029 + 0.688718i 0.241826π0.241826\pi
488488 0 0
489489 −16.0000 −0.723545
490490 0 0
491491 18.0000 0.812329 0.406164 0.913800i 0.366866π-0.366866\pi
0.406164 + 0.913800i 0.366866π0.366866\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 −6.00000 −0.269137
498498 0 0
499499 4.00000 0.179065 0.0895323 0.995984i 0.471463π-0.471463\pi
0.0895323 + 0.995984i 0.471463π0.471463\pi
500500 0 0
501501 −12.0000 −0.536120
502502 0 0
503503 −24.0000 −1.07011 −0.535054 0.844818i 0.679709π-0.679709\pi
−0.535054 + 0.844818i 0.679709π0.679709\pi
504504 0 0
505505 0 0
506506 0 0
507507 −9.00000 −0.399704
508508 0 0
509509 24.0000 1.06378 0.531891 0.846813i 0.321482π-0.321482\pi
0.531891 + 0.846813i 0.321482π0.321482\pi
510510 0 0
511511 10.0000 0.442374
512512 0 0
513513 4.00000 0.176604
514514 0 0
515515 0 0
516516 0 0
517517 72.0000 3.16656
518518 0 0
519519 12.0000 0.526742
520520 0 0
521521 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
522522 0 0
523523 −4.00000 −0.174908 −0.0874539 0.996169i 0.527873π-0.527873\pi
−0.0874539 + 0.996169i 0.527873π0.527873\pi
524524 0 0
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 13.0000 0.565217
530530 0 0
531531 0 0
532532 0 0
533533 −24.0000 −1.03956
534534 0 0
535535 0 0
536536 0 0
537537 −6.00000 −0.258919
538538 0 0
539539 6.00000 0.258438
540540 0 0
541541 2.00000 0.0859867 0.0429934 0.999075i 0.486311π-0.486311\pi
0.0429934 + 0.999075i 0.486311π0.486311\pi
542542 0 0
543543 2.00000 0.0858282
544544 0 0
545545 0 0
546546 0 0
547547 8.00000 0.342055 0.171028 0.985266i 0.445291π-0.445291\pi
0.171028 + 0.985266i 0.445291π0.445291\pi
548548 0 0
549549 −10.0000 −0.426790
550550 0 0
551551 24.0000 1.02243
552552 0 0
553553 4.00000 0.170097
554554 0 0
555555 0 0
556556 0 0
557557 −42.0000 −1.77960 −0.889799 0.456354i 0.849155π-0.849155\pi
−0.889799 + 0.456354i 0.849155π0.849155\pi
558558 0 0
559559 8.00000 0.338364
560560 0 0
561561 0 0
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 0 0
567567 1.00000 0.0419961
568568 0 0
569569 6.00000 0.251533 0.125767 0.992060i 0.459861π-0.459861\pi
0.125767 + 0.992060i 0.459861π0.459861\pi
570570 0 0
571571 40.0000 1.67395 0.836974 0.547243i 0.184323π-0.184323\pi
0.836974 + 0.547243i 0.184323π0.184323\pi
572572 0 0
573573 −6.00000 −0.250654
574574 0 0
575575 0 0
576576 0 0
577577 22.0000 0.915872 0.457936 0.888985i 0.348589π-0.348589\pi
0.457936 + 0.888985i 0.348589π0.348589\pi
578578 0 0
579579 10.0000 0.415586
580580 0 0
581581 −12.0000 −0.497844
582582 0 0
583583 36.0000 1.49097
584584 0 0
585585 0 0
586586 0 0
587587 −24.0000 −0.990586 −0.495293 0.868726i 0.664939π-0.664939\pi
−0.495293 + 0.868726i 0.664939π0.664939\pi
588588 0 0
589589 −32.0000 −1.31854
590590 0 0
591591 6.00000 0.246807
592592 0 0
593593 −48.0000 −1.97112 −0.985562 0.169316i 0.945844π-0.945844\pi
−0.985562 + 0.169316i 0.945844π0.945844\pi
594594 0 0
595595 0 0
596596 0 0
597597 16.0000 0.654836
598598 0 0
599599 −30.0000 −1.22577 −0.612883 0.790173i 0.709990π-0.709990\pi
−0.612883 + 0.790173i 0.709990π0.709990\pi
600600 0 0
601601 2.00000 0.0815817 0.0407909 0.999168i 0.487012π-0.487012\pi
0.0407909 + 0.999168i 0.487012π0.487012\pi
602602 0 0
603603 8.00000 0.325785
604604 0 0
605605 0 0
606606 0 0
607607 32.0000 1.29884 0.649420 0.760430i 0.275012π-0.275012\pi
0.649420 + 0.760430i 0.275012π0.275012\pi
608608 0 0
609609 6.00000 0.243132
610610 0 0
611611 −24.0000 −0.970936
612612 0 0
613613 −38.0000 −1.53481 −0.767403 0.641165i 0.778451π-0.778451\pi
−0.767403 + 0.641165i 0.778451π0.778451\pi
614614 0 0
615615 0 0
616616 0 0
617617 18.0000 0.724653 0.362326 0.932051i 0.381983π-0.381983\pi
0.362326 + 0.932051i 0.381983π0.381983\pi
618618 0 0
619619 −20.0000 −0.803868 −0.401934 0.915669i 0.631662π-0.631662\pi
−0.401934 + 0.915669i 0.631662π0.631662\pi
620620 0 0
621621 −6.00000 −0.240772
622622 0 0
623623 12.0000 0.480770
624624 0 0
625625 0 0
626626 0 0
627627 24.0000 0.958468
628628 0 0
629629 0 0
630630 0 0
631631 −20.0000 −0.796187 −0.398094 0.917345i 0.630328π-0.630328\pi
−0.398094 + 0.917345i 0.630328π0.630328\pi
632632 0 0
633633 4.00000 0.158986
634634 0 0
635635 0 0
636636 0 0
637637 −2.00000 −0.0792429
638638 0 0
639639 −6.00000 −0.237356
640640 0 0
641641 −18.0000 −0.710957 −0.355479 0.934684i 0.615682π-0.615682\pi
−0.355479 + 0.934684i 0.615682π0.615682\pi
642642 0 0
643643 −4.00000 −0.157745 −0.0788723 0.996885i 0.525132π-0.525132\pi
−0.0788723 + 0.996885i 0.525132π0.525132\pi
644644 0 0
645645 0 0
646646 0 0
647647 −36.0000 −1.41531 −0.707653 0.706560i 0.750246π-0.750246\pi
−0.707653 + 0.706560i 0.750246π0.750246\pi
648648 0 0
649649 0 0
650650 0 0
651651 −8.00000 −0.313545
652652 0 0
653653 18.0000 0.704394 0.352197 0.935926i 0.385435π-0.385435\pi
0.352197 + 0.935926i 0.385435π0.385435\pi
654654 0 0
655655 0 0
656656 0 0
657657 10.0000 0.390137
658658 0 0
659659 6.00000 0.233727 0.116863 0.993148i 0.462716π-0.462716\pi
0.116863 + 0.993148i 0.462716π0.462716\pi
660660 0 0
661661 38.0000 1.47803 0.739014 0.673690i 0.235292π-0.235292\pi
0.739014 + 0.673690i 0.235292π0.235292\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 −36.0000 −1.39393
668668 0 0
669669 8.00000 0.309298
670670 0 0
671671 −60.0000 −2.31627
672672 0 0
673673 34.0000 1.31060 0.655302 0.755367i 0.272541π-0.272541\pi
0.655302 + 0.755367i 0.272541π0.272541\pi
674674 0 0
675675 0 0
676676 0 0
677677 −12.0000 −0.461197 −0.230599 0.973049i 0.574068π-0.574068\pi
−0.230599 + 0.973049i 0.574068π0.574068\pi
678678 0 0
679679 10.0000 0.383765
680680 0 0
681681 24.0000 0.919682
682682 0 0
683683 −42.0000 −1.60709 −0.803543 0.595247i 0.797054π-0.797054\pi
−0.803543 + 0.595247i 0.797054π0.797054\pi
684684 0 0
685685 0 0
686686 0 0
687687 2.00000 0.0763048
688688 0 0
689689 −12.0000 −0.457164
690690 0 0
691691 4.00000 0.152167 0.0760836 0.997101i 0.475758π-0.475758\pi
0.0760836 + 0.997101i 0.475758π0.475758\pi
692692 0 0
693693 6.00000 0.227921
694694 0 0
695695 0 0
696696 0 0
697697 0 0
698698 0 0
699699 −6.00000 −0.226941
700700 0 0
701701 6.00000 0.226617 0.113308 0.993560i 0.463855π-0.463855\pi
0.113308 + 0.993560i 0.463855π0.463855\pi
702702 0 0
703703 −8.00000 −0.301726
704704 0 0
705705 0 0
706706 0 0
707707 −12.0000 −0.451306
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 4.00000 0.150012
712712 0 0
713713 48.0000 1.79761
714714 0 0
715715 0 0
716716 0 0
717717 −18.0000 −0.672222
718718 0 0
719719 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
720720 0 0
721721 8.00000 0.297936
722722 0 0
723723 −10.0000 −0.371904
724724 0 0
725725 0 0
726726 0 0
727727 8.00000 0.296704 0.148352 0.988935i 0.452603π-0.452603\pi
0.148352 + 0.988935i 0.452603π0.452603\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 0 0
732732 0 0
733733 46.0000 1.69905 0.849524 0.527549i 0.176889π-0.176889\pi
0.849524 + 0.527549i 0.176889π0.176889\pi
734734 0 0
735735 0 0
736736 0 0
737737 48.0000 1.76810
738738 0 0
739739 −32.0000 −1.17714 −0.588570 0.808447i 0.700309π-0.700309\pi
−0.588570 + 0.808447i 0.700309π0.700309\pi
740740 0 0
741741 −8.00000 −0.293887
742742 0 0
743743 6.00000 0.220119 0.110059 0.993925i 0.464896π-0.464896\pi
0.110059 + 0.993925i 0.464896π0.464896\pi
744744 0 0
745745 0 0
746746 0 0
747747 −12.0000 −0.439057
748748 0 0
749749 −6.00000 −0.219235
750750 0 0
751751 −32.0000 −1.16770 −0.583848 0.811863i 0.698454π-0.698454\pi
−0.583848 + 0.811863i 0.698454π0.698454\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 −38.0000 −1.38113 −0.690567 0.723269i 0.742639π-0.742639\pi
−0.690567 + 0.723269i 0.742639π0.742639\pi
758758 0 0
759759 −36.0000 −1.30672
760760 0 0
761761 −36.0000 −1.30500 −0.652499 0.757789i 0.726280π-0.726280\pi
−0.652499 + 0.757789i 0.726280π0.726280\pi
762762 0 0
763763 14.0000 0.506834
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 0 0
769769 26.0000 0.937584 0.468792 0.883309i 0.344689π-0.344689\pi
0.468792 + 0.883309i 0.344689π0.344689\pi
770770 0 0
771771 12.0000 0.432169
772772 0 0
773773 −12.0000 −0.431610 −0.215805 0.976436i 0.569238π-0.569238\pi
−0.215805 + 0.976436i 0.569238π0.569238\pi
774774 0 0
775775 0 0
776776 0 0
777777 −2.00000 −0.0717496
778778 0 0
779779 48.0000 1.71978
780780 0 0
781781 −36.0000 −1.28818
782782 0 0
783783 6.00000 0.214423
784784 0 0
785785 0 0
786786 0 0
787787 −4.00000 −0.142585 −0.0712923 0.997455i 0.522712π-0.522712\pi
−0.0712923 + 0.997455i 0.522712π0.522712\pi
788788 0 0
789789 −6.00000 −0.213606
790790 0 0
791791 6.00000 0.213335
792792 0 0
793793 20.0000 0.710221
794794 0 0
795795 0 0
796796 0 0
797797 −36.0000 −1.27519 −0.637593 0.770374i 0.720070π-0.720070\pi
−0.637593 + 0.770374i 0.720070π0.720070\pi
798798 0 0
799799 0 0
800800 0 0
801801 12.0000 0.423999
802802 0 0
803803 60.0000 2.11735
804804 0 0
805805 0 0
806806 0 0
807807 24.0000 0.844840
808808 0 0
809809 −54.0000 −1.89854 −0.949269 0.314464i 0.898175π-0.898175\pi
−0.949269 + 0.314464i 0.898175π0.898175\pi
810810 0 0
811811 −20.0000 −0.702295 −0.351147 0.936320i 0.614208π-0.614208\pi
−0.351147 + 0.936320i 0.614208π0.614208\pi
812812 0 0
813813 16.0000 0.561144
814814 0 0
815815 0 0
816816 0 0
817817 −16.0000 −0.559769
818818 0 0
819819 −2.00000 −0.0698857
820820 0 0
821821 18.0000 0.628204 0.314102 0.949389i 0.398297π-0.398297\pi
0.314102 + 0.949389i 0.398297π0.398297\pi
822822 0 0
823823 −4.00000 −0.139431 −0.0697156 0.997567i 0.522209π-0.522209\pi
−0.0697156 + 0.997567i 0.522209π0.522209\pi
824824 0 0
825825 0 0
826826 0 0
827827 −6.00000 −0.208640 −0.104320 0.994544i 0.533267π-0.533267\pi
−0.104320 + 0.994544i 0.533267π0.533267\pi
828828 0 0
829829 −22.0000 −0.764092 −0.382046 0.924143i 0.624780π-0.624780\pi
−0.382046 + 0.924143i 0.624780π0.624780\pi
830830 0 0
831831 22.0000 0.763172
832832 0 0
833833 0 0
834834 0 0
835835 0 0
836836 0 0
837837 −8.00000 −0.276520
838838 0 0
839839 −12.0000 −0.414286 −0.207143 0.978311i 0.566417π-0.566417\pi
−0.207143 + 0.978311i 0.566417π0.566417\pi
840840 0 0
841841 7.00000 0.241379
842842 0 0
843843 −18.0000 −0.619953
844844 0 0
845845 0 0
846846 0 0
847847 25.0000 0.859010
848848 0 0
849849 20.0000 0.686398
850850 0 0
851851 12.0000 0.411355
852852 0 0
853853 −14.0000 −0.479351 −0.239675 0.970853i 0.577041π-0.577041\pi
−0.239675 + 0.970853i 0.577041π0.577041\pi
854854 0 0
855855 0 0
856856 0 0
857857 −12.0000 −0.409912 −0.204956 0.978771i 0.565705π-0.565705\pi
−0.204956 + 0.978771i 0.565705π0.565705\pi
858858 0 0
859859 4.00000 0.136478 0.0682391 0.997669i 0.478262π-0.478262\pi
0.0682391 + 0.997669i 0.478262π0.478262\pi
860860 0 0
861861 12.0000 0.408959
862862 0 0
863863 −6.00000 −0.204242 −0.102121 0.994772i 0.532563π-0.532563\pi
−0.102121 + 0.994772i 0.532563π0.532563\pi
864864 0 0
865865 0 0
866866 0 0
867867 −17.0000 −0.577350
868868 0 0
869869 24.0000 0.814144
870870 0 0
871871 −16.0000 −0.542139
872872 0 0
873873 10.0000 0.338449
874874 0 0
875875 0 0
876876 0 0
877877 −14.0000 −0.472746 −0.236373 0.971662i 0.575959π-0.575959\pi
−0.236373 + 0.971662i 0.575959π0.575959\pi
878878 0 0
879879 12.0000 0.404750
880880 0 0
881881 24.0000 0.808581 0.404290 0.914631i 0.367519π-0.367519\pi
0.404290 + 0.914631i 0.367519π0.367519\pi
882882 0 0
883883 −4.00000 −0.134611 −0.0673054 0.997732i 0.521440π-0.521440\pi
−0.0673054 + 0.997732i 0.521440π0.521440\pi
884884 0 0
885885 0 0
886886 0 0
887887 36.0000 1.20876 0.604381 0.796696i 0.293421π-0.293421\pi
0.604381 + 0.796696i 0.293421π0.293421\pi
888888 0 0
889889 −4.00000 −0.134156
890890 0 0
891891 6.00000 0.201008
892892 0 0
893893 48.0000 1.60626
894894 0 0
895895 0 0
896896 0 0
897897 12.0000 0.400668
898898 0 0
899899 −48.0000 −1.60089
900900 0 0
901901 0 0
902902 0 0
903903 −4.00000 −0.133112
904904 0 0
905905 0 0
906906 0 0
907907 −4.00000 −0.132818 −0.0664089 0.997792i 0.521154π-0.521154\pi
−0.0664089 + 0.997792i 0.521154π0.521154\pi
908908 0 0
909909 −12.0000 −0.398015
910910 0 0
911911 −54.0000 −1.78910 −0.894550 0.446968i 0.852504π-0.852504\pi
−0.894550 + 0.446968i 0.852504π0.852504\pi
912912 0 0
913913 −72.0000 −2.38285
914914 0 0
915915 0 0
916916 0 0
917917 −12.0000 −0.396275
918918 0 0
919919 16.0000 0.527791 0.263896 0.964551i 0.414993π-0.414993\pi
0.263896 + 0.964551i 0.414993π0.414993\pi
920920 0 0
921921 20.0000 0.659022
922922 0 0
923923 12.0000 0.394985
924924 0 0
925925 0 0
926926 0 0
927927 8.00000 0.262754
928928 0 0
929929 12.0000 0.393707 0.196854 0.980433i 0.436928π-0.436928\pi
0.196854 + 0.980433i 0.436928π0.436928\pi
930930 0 0
931931 4.00000 0.131095
932932 0 0
933933 12.0000 0.392862
934934 0 0
935935 0 0
936936 0 0
937937 −2.00000 −0.0653372 −0.0326686 0.999466i 0.510401π-0.510401\pi
−0.0326686 + 0.999466i 0.510401π0.510401\pi
938938 0 0
939939 −26.0000 −0.848478
940940 0 0
941941 −24.0000 −0.782378 −0.391189 0.920310i 0.627936π-0.627936\pi
−0.391189 + 0.920310i 0.627936π0.627936\pi
942942 0 0
943943 −72.0000 −2.34464
944944 0 0
945945 0 0
946946 0 0
947947 −30.0000 −0.974869 −0.487435 0.873160i 0.662067π-0.662067\pi
−0.487435 + 0.873160i 0.662067π0.662067\pi
948948 0 0
949949 −20.0000 −0.649227
950950 0 0
951951 30.0000 0.972817
952952 0 0
953953 −42.0000 −1.36051 −0.680257 0.732974i 0.738132π-0.738132\pi
−0.680257 + 0.732974i 0.738132π0.738132\pi
954954 0 0
955955 0 0
956956 0 0
957957 36.0000 1.16371
958958 0 0
959959 −6.00000 −0.193750
960960 0 0
961961 33.0000 1.06452
962962 0 0
963963 −6.00000 −0.193347
964964 0 0
965965 0 0
966966 0 0
967967 −28.0000 −0.900419 −0.450210 0.892923i 0.648651π-0.648651\pi
−0.450210 + 0.892923i 0.648651π0.648651\pi
968968 0 0
969969 0 0
970970 0 0
971971 −12.0000 −0.385098 −0.192549 0.981287i 0.561675π-0.561675\pi
−0.192549 + 0.981287i 0.561675π0.561675\pi
972972 0 0
973973 4.00000 0.128234
974974 0 0
975975 0 0
976976 0 0
977977 −6.00000 −0.191957 −0.0959785 0.995383i 0.530598π-0.530598\pi
−0.0959785 + 0.995383i 0.530598π0.530598\pi
978978 0 0
979979 72.0000 2.30113
980980 0 0
981981 14.0000 0.446986
982982 0 0
983983 −48.0000 −1.53096 −0.765481 0.643458i 0.777499π-0.777499\pi
−0.765481 + 0.643458i 0.777499π0.777499\pi
984984 0 0
985985 0 0
986986 0 0
987987 12.0000 0.381964
988988 0 0
989989 24.0000 0.763156
990990 0 0
991991 40.0000 1.27064 0.635321 0.772248i 0.280868π-0.280868\pi
0.635321 + 0.772248i 0.280868π0.280868\pi
992992 0 0
993993 −20.0000 −0.634681
994994 0 0
995995 0 0
996996 0 0
997997 10.0000 0.316703 0.158352 0.987383i 0.449382π-0.449382\pi
0.158352 + 0.987383i 0.449382π0.449382\pi
998998 0 0
999999 −2.00000 −0.0632772
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 8400.2.a.ct.1.1 1
4.3 odd 2 2100.2.a.a.1.1 1
5.4 even 2 336.2.a.b.1.1 1
12.11 even 2 6300.2.a.p.1.1 1
15.14 odd 2 1008.2.a.g.1.1 1
20.3 even 4 2100.2.k.a.1849.1 2
20.7 even 4 2100.2.k.a.1849.2 2
20.19 odd 2 84.2.a.b.1.1 1
35.4 even 6 2352.2.q.s.961.1 2
35.9 even 6 2352.2.q.s.1537.1 2
35.19 odd 6 2352.2.q.g.1537.1 2
35.24 odd 6 2352.2.q.g.961.1 2
35.34 odd 2 2352.2.a.s.1.1 1
40.19 odd 2 1344.2.a.f.1.1 1
40.29 even 2 1344.2.a.o.1.1 1
60.23 odd 4 6300.2.k.r.6049.2 2
60.47 odd 4 6300.2.k.r.6049.1 2
60.59 even 2 252.2.a.b.1.1 1
80.19 odd 4 5376.2.c.i.2689.2 2
80.29 even 4 5376.2.c.x.2689.1 2
80.59 odd 4 5376.2.c.i.2689.1 2
80.69 even 4 5376.2.c.x.2689.2 2
105.104 even 2 7056.2.a.x.1.1 1
120.29 odd 2 4032.2.a.t.1.1 1
120.59 even 2 4032.2.a.u.1.1 1
140.19 even 6 588.2.i.f.361.1 2
140.39 odd 6 588.2.i.c.373.1 2
140.59 even 6 588.2.i.f.373.1 2
140.79 odd 6 588.2.i.c.361.1 2
140.139 even 2 588.2.a.c.1.1 1
180.59 even 6 2268.2.j.f.1513.1 2
180.79 odd 6 2268.2.j.i.757.1 2
180.119 even 6 2268.2.j.f.757.1 2
180.139 odd 6 2268.2.j.i.1513.1 2
280.69 odd 2 9408.2.a.r.1.1 1
280.139 even 2 9408.2.a.co.1.1 1
420.59 odd 6 1764.2.k.d.1549.1 2
420.179 even 6 1764.2.k.e.1549.1 2
420.299 odd 6 1764.2.k.d.361.1 2
420.359 even 6 1764.2.k.e.361.1 2
420.419 odd 2 1764.2.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.2.a.b.1.1 1 20.19 odd 2
252.2.a.b.1.1 1 60.59 even 2
336.2.a.b.1.1 1 5.4 even 2
588.2.a.c.1.1 1 140.139 even 2
588.2.i.c.361.1 2 140.79 odd 6
588.2.i.c.373.1 2 140.39 odd 6
588.2.i.f.361.1 2 140.19 even 6
588.2.i.f.373.1 2 140.59 even 6
1008.2.a.g.1.1 1 15.14 odd 2
1344.2.a.f.1.1 1 40.19 odd 2
1344.2.a.o.1.1 1 40.29 even 2
1764.2.a.g.1.1 1 420.419 odd 2
1764.2.k.d.361.1 2 420.299 odd 6
1764.2.k.d.1549.1 2 420.59 odd 6
1764.2.k.e.361.1 2 420.359 even 6
1764.2.k.e.1549.1 2 420.179 even 6
2100.2.a.a.1.1 1 4.3 odd 2
2100.2.k.a.1849.1 2 20.3 even 4
2100.2.k.a.1849.2 2 20.7 even 4
2268.2.j.f.757.1 2 180.119 even 6
2268.2.j.f.1513.1 2 180.59 even 6
2268.2.j.i.757.1 2 180.79 odd 6
2268.2.j.i.1513.1 2 180.139 odd 6
2352.2.a.s.1.1 1 35.34 odd 2
2352.2.q.g.961.1 2 35.24 odd 6
2352.2.q.g.1537.1 2 35.19 odd 6
2352.2.q.s.961.1 2 35.4 even 6
2352.2.q.s.1537.1 2 35.9 even 6
4032.2.a.t.1.1 1 120.29 odd 2
4032.2.a.u.1.1 1 120.59 even 2
5376.2.c.i.2689.1 2 80.59 odd 4
5376.2.c.i.2689.2 2 80.19 odd 4
5376.2.c.x.2689.1 2 80.29 even 4
5376.2.c.x.2689.2 2 80.69 even 4
6300.2.a.p.1.1 1 12.11 even 2
6300.2.k.r.6049.1 2 60.47 odd 4
6300.2.k.r.6049.2 2 60.23 odd 4
7056.2.a.x.1.1 1 105.104 even 2
8400.2.a.ct.1.1 1 1.1 even 1 trivial
9408.2.a.r.1.1 1 280.69 odd 2
9408.2.a.co.1.1 1 280.139 even 2