Properties

Label 272.2.a.d.1.1
Level 272272
Weight 22
Character 272.1
Self dual yes
Analytic conductor 2.1722.172
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] = [272,2,Mod(1,272)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(272, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("272.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 272=2417 272 = 2^{4} \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 272.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: 2.171930934982.17193093498
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 34)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 272.1

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+2.00000q3+4.00000q7+1.00000q96.00000q11+2.00000q131.00000q17+4.00000q19+8.00000q215.00000q254.00000q27+4.00000q3112.0000q334.00000q37+4.00000q39+6.00000q418.00000q43+9.00000q492.00000q516.00000q53+8.00000q574.00000q61+4.00000q638.00000q67+2.00000q7310.0000q7524.0000q778.00000q7911.0000q816.00000q89+8.00000q91+8.00000q93+14.0000q976.00000q99+O(q100)q+2.00000 q^{3} +4.00000 q^{7} +1.00000 q^{9} -6.00000 q^{11} +2.00000 q^{13} -1.00000 q^{17} +4.00000 q^{19} +8.00000 q^{21} -5.00000 q^{25} -4.00000 q^{27} +4.00000 q^{31} -12.0000 q^{33} -4.00000 q^{37} +4.00000 q^{39} +6.00000 q^{41} -8.00000 q^{43} +9.00000 q^{49} -2.00000 q^{51} -6.00000 q^{53} +8.00000 q^{57} -4.00000 q^{61} +4.00000 q^{63} -8.00000 q^{67} +2.00000 q^{73} -10.0000 q^{75} -24.0000 q^{77} -8.00000 q^{79} -11.0000 q^{81} -6.00000 q^{89} +8.00000 q^{91} +8.00000 q^{93} +14.0000 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 2.00000 1.15470 0.577350 0.816497i 0.304087π-0.304087\pi
0.577350 + 0.816497i 0.304087π0.304087\pi
44 0 0
55 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
66 0 0
77 4.00000 1.51186 0.755929 0.654654i 0.227186π-0.227186\pi
0.755929 + 0.654654i 0.227186π0.227186\pi
88 0 0
99 1.00000 0.333333
1010 0 0
1111 −6.00000 −1.80907 −0.904534 0.426401i 0.859781π-0.859781\pi
−0.904534 + 0.426401i 0.859781π0.859781\pi
1212 0 0
1313 2.00000 0.554700 0.277350 0.960769i 0.410544π-0.410544\pi
0.277350 + 0.960769i 0.410544π0.410544\pi
1414 0 0
1515 0 0
1616 0 0
1717 −1.00000 −0.242536
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 8.00000 1.74574
2222 0 0
2323 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2424 0 0
2525 −5.00000 −1.00000
2626 0 0
2727 −4.00000 −0.769800
2828 0 0
2929 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\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 −12.0000 −2.08893
3434 0 0
3535 0 0
3636 0 0
3737 −4.00000 −0.657596 −0.328798 0.944400i 0.606644π-0.606644\pi
−0.328798 + 0.944400i 0.606644π0.606644\pi
3838 0 0
3939 4.00000 0.640513
4040 0 0
4141 6.00000 0.937043 0.468521 0.883452i 0.344787π-0.344787\pi
0.468521 + 0.883452i 0.344787π0.344787\pi
4242 0 0
4343 −8.00000 −1.21999 −0.609994 0.792406i 0.708828π-0.708828\pi
−0.609994 + 0.792406i 0.708828π0.708828\pi
4444 0 0
4545 0 0
4646 0 0
4747 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4848 0 0
4949 9.00000 1.28571
5050 0 0
5151 −2.00000 −0.280056
5252 0 0
5353 −6.00000 −0.824163 −0.412082 0.911147i 0.635198π-0.635198\pi
−0.412082 + 0.911147i 0.635198π0.635198\pi
5454 0 0
5555 0 0
5656 0 0
5757 8.00000 1.05963
5858 0 0
5959 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
6060 0 0
6161 −4.00000 −0.512148 −0.256074 0.966657i 0.582429π-0.582429\pi
−0.256074 + 0.966657i 0.582429π0.582429\pi
6262 0 0
6363 4.00000 0.503953
6464 0 0
6565 0 0
6666 0 0
6767 −8.00000 −0.977356 −0.488678 0.872464i 0.662521π-0.662521\pi
−0.488678 + 0.872464i 0.662521π0.662521\pi
6868 0 0
6969 0 0
7070 0 0
7171 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7272 0 0
7373 2.00000 0.234082 0.117041 0.993127i 0.462659π-0.462659\pi
0.117041 + 0.993127i 0.462659π0.462659\pi
7474 0 0
7575 −10.0000 −1.15470
7676 0 0
7777 −24.0000 −2.73505
7878 0 0
7979 −8.00000 −0.900070 −0.450035 0.893011i 0.648589π-0.648589\pi
−0.450035 + 0.893011i 0.648589π0.648589\pi
8080 0 0
8181 −11.0000 −1.22222
8282 0 0
8383 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
8484 0 0
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 −6.00000 −0.635999 −0.317999 0.948091i 0.603011π-0.603011\pi
−0.317999 + 0.948091i 0.603011π0.603011\pi
9090 0 0
9191 8.00000 0.838628
9292 0 0
9393 8.00000 0.829561
9494 0 0
9595 0 0
9696 0 0
9797 14.0000 1.42148 0.710742 0.703452i 0.248359π-0.248359\pi
0.710742 + 0.703452i 0.248359π0.248359\pi
9898 0 0
9999 −6.00000 −0.603023
100100 0 0
101101 18.0000 1.79107 0.895533 0.444994i 0.146794π-0.146794\pi
0.895533 + 0.444994i 0.146794π0.146794\pi
102102 0 0
103103 16.0000 1.57653 0.788263 0.615338i 0.210980π-0.210980\pi
0.788263 + 0.615338i 0.210980π0.210980\pi
104104 0 0
105105 0 0
106106 0 0
107107 6.00000 0.580042 0.290021 0.957020i 0.406338π-0.406338\pi
0.290021 + 0.957020i 0.406338π0.406338\pi
108108 0 0
109109 −16.0000 −1.53252 −0.766261 0.642529i 0.777885π-0.777885\pi
−0.766261 + 0.642529i 0.777885π0.777885\pi
110110 0 0
111111 −8.00000 −0.759326
112112 0 0
113113 −6.00000 −0.564433 −0.282216 0.959351i 0.591070π-0.591070\pi
−0.282216 + 0.959351i 0.591070π0.591070\pi
114114 0 0
115115 0 0
116116 0 0
117117 2.00000 0.184900
118118 0 0
119119 −4.00000 −0.366679
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 16.0000 1.41977 0.709885 0.704317i 0.248747π-0.248747\pi
0.709885 + 0.704317i 0.248747π0.248747\pi
128128 0 0
129129 −16.0000 −1.40872
130130 0 0
131131 6.00000 0.524222 0.262111 0.965038i 0.415581π-0.415581\pi
0.262111 + 0.965038i 0.415581π0.415581\pi
132132 0 0
133133 16.0000 1.38738
134134 0 0
135135 0 0
136136 0 0
137137 6.00000 0.512615 0.256307 0.966595i 0.417494π-0.417494\pi
0.256307 + 0.966595i 0.417494π0.417494\pi
138138 0 0
139139 −2.00000 −0.169638 −0.0848189 0.996396i 0.527031π-0.527031\pi
−0.0848189 + 0.996396i 0.527031π0.527031\pi
140140 0 0
141141 0 0
142142 0 0
143143 −12.0000 −1.00349
144144 0 0
145145 0 0
146146 0 0
147147 18.0000 1.48461
148148 0 0
149149 6.00000 0.491539 0.245770 0.969328i 0.420959π-0.420959\pi
0.245770 + 0.969328i 0.420959π0.420959\pi
150150 0 0
151151 16.0000 1.30206 0.651031 0.759051i 0.274337π-0.274337\pi
0.651031 + 0.759051i 0.274337π0.274337\pi
152152 0 0
153153 −1.00000 −0.0808452
154154 0 0
155155 0 0
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 −12.0000 −0.951662
160160 0 0
161161 0 0
162162 0 0
163163 −2.00000 −0.156652 −0.0783260 0.996928i 0.524958π-0.524958\pi
−0.0783260 + 0.996928i 0.524958π0.524958\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 24.0000 1.82469 0.912343 0.409426i 0.134271π-0.134271\pi
0.912343 + 0.409426i 0.134271π0.134271\pi
174174 0 0
175175 −20.0000 −1.51186
176176 0 0
177177 0 0
178178 0 0
179179 −12.0000 −0.896922 −0.448461 0.893802i 0.648028π-0.648028\pi
−0.448461 + 0.893802i 0.648028π0.648028\pi
180180 0 0
181181 −4.00000 −0.297318 −0.148659 0.988889i 0.547496π-0.547496\pi
−0.148659 + 0.988889i 0.547496π0.547496\pi
182182 0 0
183183 −8.00000 −0.591377
184184 0 0
185185 0 0
186186 0 0
187187 6.00000 0.438763
188188 0 0
189189 −16.0000 −1.16383
190190 0 0
191191 24.0000 1.73658 0.868290 0.496058i 0.165220π-0.165220\pi
0.868290 + 0.496058i 0.165220π0.165220\pi
192192 0 0
193193 −10.0000 −0.719816 −0.359908 0.932988i 0.617192π-0.617192\pi
−0.359908 + 0.932988i 0.617192π0.617192\pi
194194 0 0
195195 0 0
196196 0 0
197197 −12.0000 −0.854965 −0.427482 0.904024i 0.640599π-0.640599\pi
−0.427482 + 0.904024i 0.640599π0.640599\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 −16.0000 −1.12855
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 −24.0000 −1.66011
210210 0 0
211211 10.0000 0.688428 0.344214 0.938891i 0.388145π-0.388145\pi
0.344214 + 0.938891i 0.388145π0.388145\pi
212212 0 0
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 16.0000 1.08615
218218 0 0
219219 4.00000 0.270295
220220 0 0
221221 −2.00000 −0.134535
222222 0 0
223223 −8.00000 −0.535720 −0.267860 0.963458i 0.586316π-0.586316\pi
−0.267860 + 0.963458i 0.586316π0.586316\pi
224224 0 0
225225 −5.00000 −0.333333
226226 0 0
227227 6.00000 0.398234 0.199117 0.979976i 0.436193π-0.436193\pi
0.199117 + 0.979976i 0.436193π0.436193\pi
228228 0 0
229229 14.0000 0.925146 0.462573 0.886581i 0.346926π-0.346926\pi
0.462573 + 0.886581i 0.346926π0.346926\pi
230230 0 0
231231 −48.0000 −3.15817
232232 0 0
233233 18.0000 1.17922 0.589610 0.807688i 0.299282π-0.299282\pi
0.589610 + 0.807688i 0.299282π0.299282\pi
234234 0 0
235235 0 0
236236 0 0
237237 −16.0000 −1.03931
238238 0 0
239239 −24.0000 −1.55243 −0.776215 0.630468i 0.782863π-0.782863\pi
−0.776215 + 0.630468i 0.782863π0.782863\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 −10.0000 −0.641500
244244 0 0
245245 0 0
246246 0 0
247247 8.00000 0.509028
248248 0 0
249249 0 0
250250 0 0
251251 24.0000 1.51487 0.757433 0.652913i 0.226453π-0.226453\pi
0.757433 + 0.652913i 0.226453π0.226453\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 0 0
257257 6.00000 0.374270 0.187135 0.982334i 0.440080π-0.440080\pi
0.187135 + 0.982334i 0.440080π0.440080\pi
258258 0 0
259259 −16.0000 −0.994192
260260 0 0
261261 0 0
262262 0 0
263263 −24.0000 −1.47990 −0.739952 0.672660i 0.765152π-0.765152\pi
−0.739952 + 0.672660i 0.765152π0.765152\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 0.761251π-0.761251\pi
−0.731653 + 0.681677i 0.761251π0.761251\pi
270270 0 0
271271 −8.00000 −0.485965 −0.242983 0.970031i 0.578126π-0.578126\pi
−0.242983 + 0.970031i 0.578126π0.578126\pi
272272 0 0
273273 16.0000 0.968364
274274 0 0
275275 30.0000 1.80907
276276 0 0
277277 8.00000 0.480673 0.240337 0.970690i 0.422742π-0.422742\pi
0.240337 + 0.970690i 0.422742π0.422742\pi
278278 0 0
279279 4.00000 0.239474
280280 0 0
281281 6.00000 0.357930 0.178965 0.983855i 0.442725π-0.442725\pi
0.178965 + 0.983855i 0.442725π0.442725\pi
282282 0 0
283283 −14.0000 −0.832214 −0.416107 0.909316i 0.636606π-0.636606\pi
−0.416107 + 0.909316i 0.636606π0.636606\pi
284284 0 0
285285 0 0
286286 0 0
287287 24.0000 1.41668
288288 0 0
289289 1.00000 0.0588235
290290 0 0
291291 28.0000 1.64139
292292 0 0
293293 6.00000 0.350524 0.175262 0.984522i 0.443923π-0.443923\pi
0.175262 + 0.984522i 0.443923π0.443923\pi
294294 0 0
295295 0 0
296296 0 0
297297 24.0000 1.39262
298298 0 0
299299 0 0
300300 0 0
301301 −32.0000 −1.84445
302302 0 0
303303 36.0000 2.06815
304304 0 0
305305 0 0
306306 0 0
307307 −20.0000 −1.14146 −0.570730 0.821138i 0.693340π-0.693340\pi
−0.570730 + 0.821138i 0.693340π0.693340\pi
308308 0 0
309309 32.0000 1.82042
310310 0 0
311311 −12.0000 −0.680458 −0.340229 0.940343i 0.610505π-0.610505\pi
−0.340229 + 0.940343i 0.610505π0.610505\pi
312312 0 0
313313 −34.0000 −1.92179 −0.960897 0.276907i 0.910691π-0.910691\pi
−0.960897 + 0.276907i 0.910691π0.910691\pi
314314 0 0
315315 0 0
316316 0 0
317317 −12.0000 −0.673987 −0.336994 0.941507i 0.609410π-0.609410\pi
−0.336994 + 0.941507i 0.609410π0.609410\pi
318318 0 0
319319 0 0
320320 0 0
321321 12.0000 0.669775
322322 0 0
323323 −4.00000 −0.222566
324324 0 0
325325 −10.0000 −0.554700
326326 0 0
327327 −32.0000 −1.76960
328328 0 0
329329 0 0
330330 0 0
331331 16.0000 0.879440 0.439720 0.898135i 0.355078π-0.355078\pi
0.439720 + 0.898135i 0.355078π0.355078\pi
332332 0 0
333333 −4.00000 −0.219199
334334 0 0
335335 0 0
336336 0 0
337337 −22.0000 −1.19842 −0.599208 0.800593i 0.704518π-0.704518\pi
−0.599208 + 0.800593i 0.704518π0.704518\pi
338338 0 0
339339 −12.0000 −0.651751
340340 0 0
341341 −24.0000 −1.29967
342342 0 0
343343 8.00000 0.431959
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 26.0000 1.39175 0.695874 0.718164i 0.255017π-0.255017\pi
0.695874 + 0.718164i 0.255017π0.255017\pi
350350 0 0
351351 −8.00000 −0.427008
352352 0 0
353353 6.00000 0.319348 0.159674 0.987170i 0.448956π-0.448956\pi
0.159674 + 0.987170i 0.448956π0.448956\pi
354354 0 0
355355 0 0
356356 0 0
357357 −8.00000 −0.423405
358358 0 0
359359 −24.0000 −1.26667 −0.633336 0.773877i 0.718315π-0.718315\pi
−0.633336 + 0.773877i 0.718315π0.718315\pi
360360 0 0
361361 −3.00000 −0.157895
362362 0 0
363363 50.0000 2.62432
364364 0 0
365365 0 0
366366 0 0
367367 16.0000 0.835193 0.417597 0.908633i 0.362873π-0.362873\pi
0.417597 + 0.908633i 0.362873π0.362873\pi
368368 0 0
369369 6.00000 0.312348
370370 0 0
371371 −24.0000 −1.24602
372372 0 0
373373 −22.0000 −1.13912 −0.569558 0.821951i 0.692886π-0.692886\pi
−0.569558 + 0.821951i 0.692886π0.692886\pi
374374 0 0
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 −14.0000 −0.719132 −0.359566 0.933120i 0.617075π-0.617075\pi
−0.359566 + 0.933120i 0.617075π0.617075\pi
380380 0 0
381381 32.0000 1.63941
382382 0 0
383383 24.0000 1.22634 0.613171 0.789950i 0.289894π-0.289894\pi
0.613171 + 0.789950i 0.289894π0.289894\pi
384384 0 0
385385 0 0
386386 0 0
387387 −8.00000 −0.406663
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 20.0000 1.00377 0.501886 0.864934i 0.332640π-0.332640\pi
0.501886 + 0.864934i 0.332640π0.332640\pi
398398 0 0
399399 32.0000 1.60200
400400 0 0
401401 30.0000 1.49813 0.749064 0.662497i 0.230503π-0.230503\pi
0.749064 + 0.662497i 0.230503π0.230503\pi
402402 0 0
403403 8.00000 0.398508
404404 0 0
405405 0 0
406406 0 0
407407 24.0000 1.18964
408408 0 0
409409 −10.0000 −0.494468 −0.247234 0.968956i 0.579522π-0.579522\pi
−0.247234 + 0.968956i 0.579522π0.579522\pi
410410 0 0
411411 12.0000 0.591916
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 −4.00000 −0.195881
418418 0 0
419419 30.0000 1.46560 0.732798 0.680446i 0.238214π-0.238214\pi
0.732798 + 0.680446i 0.238214π0.238214\pi
420420 0 0
421421 2.00000 0.0974740 0.0487370 0.998812i 0.484480π-0.484480\pi
0.0487370 + 0.998812i 0.484480π0.484480\pi
422422 0 0
423423 0 0
424424 0 0
425425 5.00000 0.242536
426426 0 0
427427 −16.0000 −0.774294
428428 0 0
429429 −24.0000 −1.15873
430430 0 0
431431 −24.0000 −1.15604 −0.578020 0.816023i 0.696174π-0.696174\pi
−0.578020 + 0.816023i 0.696174π0.696174\pi
432432 0 0
433433 2.00000 0.0961139 0.0480569 0.998845i 0.484697π-0.484697\pi
0.0480569 + 0.998845i 0.484697π0.484697\pi
434434 0 0
435435 0 0
436436 0 0
437437 0 0
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 9.00000 0.428571
442442 0 0
443443 24.0000 1.14027 0.570137 0.821549i 0.306890π-0.306890\pi
0.570137 + 0.821549i 0.306890π0.306890\pi
444444 0 0
445445 0 0
446446 0 0
447447 12.0000 0.567581
448448 0 0
449449 −18.0000 −0.849473 −0.424736 0.905317i 0.639633π-0.639633\pi
−0.424736 + 0.905317i 0.639633π0.639633\pi
450450 0 0
451451 −36.0000 −1.69517
452452 0 0
453453 32.0000 1.50349
454454 0 0
455455 0 0
456456 0 0
457457 26.0000 1.21623 0.608114 0.793849i 0.291926π-0.291926\pi
0.608114 + 0.793849i 0.291926π0.291926\pi
458458 0 0
459459 4.00000 0.186704
460460 0 0
461461 −6.00000 −0.279448 −0.139724 0.990190i 0.544622π-0.544622\pi
−0.139724 + 0.990190i 0.544622π0.544622\pi
462462 0 0
463463 16.0000 0.743583 0.371792 0.928316i 0.378744π-0.378744\pi
0.371792 + 0.928316i 0.378744π0.378744\pi
464464 0 0
465465 0 0
466466 0 0
467467 −12.0000 −0.555294 −0.277647 0.960683i 0.589555π-0.589555\pi
−0.277647 + 0.960683i 0.589555π0.589555\pi
468468 0 0
469469 −32.0000 −1.47762
470470 0 0
471471 28.0000 1.29017
472472 0 0
473473 48.0000 2.20704
474474 0 0
475475 −20.0000 −0.917663
476476 0 0
477477 −6.00000 −0.274721
478478 0 0
479479 −24.0000 −1.09659 −0.548294 0.836286i 0.684723π-0.684723\pi
−0.548294 + 0.836286i 0.684723π0.684723\pi
480480 0 0
481481 −8.00000 −0.364769
482482 0 0
483483 0 0
484484 0 0
485485 0 0
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 −4.00000 −0.180886
490490 0 0
491491 12.0000 0.541552 0.270776 0.962642i 0.412720π-0.412720\pi
0.270776 + 0.962642i 0.412720π0.412720\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 −14.0000 −0.626726 −0.313363 0.949633i 0.601456π-0.601456\pi
−0.313363 + 0.949633i 0.601456π0.601456\pi
500500 0 0
501501 −24.0000 −1.07224
502502 0 0
503503 24.0000 1.07011 0.535054 0.844818i 0.320291π-0.320291\pi
0.535054 + 0.844818i 0.320291π0.320291\pi
504504 0 0
505505 0 0
506506 0 0
507507 −18.0000 −0.799408
508508 0 0
509509 30.0000 1.32973 0.664863 0.746965i 0.268490π-0.268490\pi
0.664863 + 0.746965i 0.268490π0.268490\pi
510510 0 0
511511 8.00000 0.353899
512512 0 0
513513 −16.0000 −0.706417
514514 0 0
515515 0 0
516516 0 0
517517 0 0
518518 0 0
519519 48.0000 2.10697
520520 0 0
521521 −18.0000 −0.788594 −0.394297 0.918983i 0.629012π-0.629012\pi
−0.394297 + 0.918983i 0.629012π0.629012\pi
522522 0 0
523523 16.0000 0.699631 0.349816 0.936819i 0.386244π-0.386244\pi
0.349816 + 0.936819i 0.386244π0.386244\pi
524524 0 0
525525 −40.0000 −1.74574
526526 0 0
527527 −4.00000 −0.174243
528528 0 0
529529 −23.0000 −1.00000
530530 0 0
531531 0 0
532532 0 0
533533 12.0000 0.519778
534534 0 0
535535 0 0
536536 0 0
537537 −24.0000 −1.03568
538538 0 0
539539 −54.0000 −2.32594
540540 0 0
541541 20.0000 0.859867 0.429934 0.902861i 0.358537π-0.358537\pi
0.429934 + 0.902861i 0.358537π0.358537\pi
542542 0 0
543543 −8.00000 −0.343313
544544 0 0
545545 0 0
546546 0 0
547547 −2.00000 −0.0855138 −0.0427569 0.999086i 0.513614π-0.513614\pi
−0.0427569 + 0.999086i 0.513614π0.513614\pi
548548 0 0
549549 −4.00000 −0.170716
550550 0 0
551551 0 0
552552 0 0
553553 −32.0000 −1.36078
554554 0 0
555555 0 0
556556 0 0
557557 −30.0000 −1.27114 −0.635570 0.772043i 0.719235π-0.719235\pi
−0.635570 + 0.772043i 0.719235π0.719235\pi
558558 0 0
559559 −16.0000 −0.676728
560560 0 0
561561 12.0000 0.506640
562562 0 0
563563 24.0000 1.01148 0.505740 0.862686i 0.331220π-0.331220\pi
0.505740 + 0.862686i 0.331220π0.331220\pi
564564 0 0
565565 0 0
566566 0 0
567567 −44.0000 −1.84783
568568 0 0
569569 −30.0000 −1.25767 −0.628833 0.777541i 0.716467π-0.716467\pi
−0.628833 + 0.777541i 0.716467π0.716467\pi
570570 0 0
571571 −26.0000 −1.08807 −0.544033 0.839064i 0.683103π-0.683103\pi
−0.544033 + 0.839064i 0.683103π0.683103\pi
572572 0 0
573573 48.0000 2.00523
574574 0 0
575575 0 0
576576 0 0
577577 14.0000 0.582828 0.291414 0.956597i 0.405874π-0.405874\pi
0.291414 + 0.956597i 0.405874π0.405874\pi
578578 0 0
579579 −20.0000 −0.831172
580580 0 0
581581 0 0
582582 0 0
583583 36.0000 1.49097
584584 0 0
585585 0 0
586586 0 0
587587 −12.0000 −0.495293 −0.247647 0.968850i 0.579657π-0.579657\pi
−0.247647 + 0.968850i 0.579657π0.579657\pi
588588 0 0
589589 16.0000 0.659269
590590 0 0
591591 −24.0000 −0.987228
592592 0 0
593593 −30.0000 −1.23195 −0.615976 0.787765i 0.711238π-0.711238\pi
−0.615976 + 0.787765i 0.711238π0.711238\pi
594594 0 0
595595 0 0
596596 0 0
597597 32.0000 1.30967
598598 0 0
599599 24.0000 0.980613 0.490307 0.871550i 0.336885π-0.336885\pi
0.490307 + 0.871550i 0.336885π0.336885\pi
600600 0 0
601601 −46.0000 −1.87638 −0.938190 0.346122i 0.887498π-0.887498\pi
−0.938190 + 0.346122i 0.887498π0.887498\pi
602602 0 0
603603 −8.00000 −0.325785
604604 0 0
605605 0 0
606606 0 0
607607 −20.0000 −0.811775 −0.405887 0.913923i 0.633038π-0.633038\pi
−0.405887 + 0.913923i 0.633038π0.633038\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 0 0
613613 14.0000 0.565455 0.282727 0.959200i 0.408761π-0.408761\pi
0.282727 + 0.959200i 0.408761π0.408761\pi
614614 0 0
615615 0 0
616616 0 0
617617 −30.0000 −1.20775 −0.603877 0.797077i 0.706378π-0.706378\pi
−0.603877 + 0.797077i 0.706378π0.706378\pi
618618 0 0
619619 −26.0000 −1.04503 −0.522514 0.852631i 0.675006π-0.675006\pi
−0.522514 + 0.852631i 0.675006π0.675006\pi
620620 0 0
621621 0 0
622622 0 0
623623 −24.0000 −0.961540
624624 0 0
625625 25.0000 1.00000
626626 0 0
627627 −48.0000 −1.91694
628628 0 0
629629 4.00000 0.159490
630630 0 0
631631 −8.00000 −0.318475 −0.159237 0.987240i 0.550904π-0.550904\pi
−0.159237 + 0.987240i 0.550904π0.550904\pi
632632 0 0
633633 20.0000 0.794929
634634 0 0
635635 0 0
636636 0 0
637637 18.0000 0.713186
638638 0 0
639639 0 0
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 −14.0000 −0.552106 −0.276053 0.961142i 0.589027π-0.589027\pi
−0.276053 + 0.961142i 0.589027π0.589027\pi
644644 0 0
645645 0 0
646646 0 0
647647 48.0000 1.88707 0.943537 0.331266i 0.107476π-0.107476\pi
0.943537 + 0.331266i 0.107476π0.107476\pi
648648 0 0
649649 0 0
650650 0 0
651651 32.0000 1.25418
652652 0 0
653653 24.0000 0.939193 0.469596 0.882881i 0.344399π-0.344399\pi
0.469596 + 0.882881i 0.344399π0.344399\pi
654654 0 0
655655 0 0
656656 0 0
657657 2.00000 0.0780274
658658 0 0
659659 12.0000 0.467454 0.233727 0.972302i 0.424908π-0.424908\pi
0.233727 + 0.972302i 0.424908π0.424908\pi
660660 0 0
661661 −46.0000 −1.78919 −0.894596 0.446875i 0.852537π-0.852537\pi
−0.894596 + 0.446875i 0.852537π0.852537\pi
662662 0 0
663663 −4.00000 −0.155347
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 −16.0000 −0.618596
670670 0 0
671671 24.0000 0.926510
672672 0 0
673673 38.0000 1.46479 0.732396 0.680879i 0.238402π-0.238402\pi
0.732396 + 0.680879i 0.238402π0.238402\pi
674674 0 0
675675 20.0000 0.769800
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 56.0000 2.14908
680680 0 0
681681 12.0000 0.459841
682682 0 0
683683 −30.0000 −1.14792 −0.573959 0.818884i 0.694593π-0.694593\pi
−0.573959 + 0.818884i 0.694593π0.694593\pi
684684 0 0
685685 0 0
686686 0 0
687687 28.0000 1.06827
688688 0 0
689689 −12.0000 −0.457164
690690 0 0
691691 10.0000 0.380418 0.190209 0.981744i 0.439083π-0.439083\pi
0.190209 + 0.981744i 0.439083π0.439083\pi
692692 0 0
693693 −24.0000 −0.911685
694694 0 0
695695 0 0
696696 0 0
697697 −6.00000 −0.227266
698698 0 0
699699 36.0000 1.36165
700700 0 0
701701 18.0000 0.679851 0.339925 0.940452i 0.389598π-0.389598\pi
0.339925 + 0.940452i 0.389598π0.389598\pi
702702 0 0
703703 −16.0000 −0.603451
704704 0 0
705705 0 0
706706 0 0
707707 72.0000 2.70784
708708 0 0
709709 −16.0000 −0.600893 −0.300446 0.953799i 0.597136π-0.597136\pi
−0.300446 + 0.953799i 0.597136π0.597136\pi
710710 0 0
711711 −8.00000 −0.300023
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 −48.0000 −1.79259
718718 0 0
719719 −48.0000 −1.79010 −0.895049 0.445968i 0.852860π-0.852860\pi
−0.895049 + 0.445968i 0.852860π0.852860\pi
720720 0 0
721721 64.0000 2.38348
722722 0 0
723723 −20.0000 −0.743808
724724 0 0
725725 0 0
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 13.0000 0.481481
730730 0 0
731731 8.00000 0.295891
732732 0 0
733733 −22.0000 −0.812589 −0.406294 0.913742i 0.633179π-0.633179\pi
−0.406294 + 0.913742i 0.633179π0.633179\pi
734734 0 0
735735 0 0
736736 0 0
737737 48.0000 1.76810
738738 0 0
739739 −20.0000 −0.735712 −0.367856 0.929883i 0.619908π-0.619908\pi
−0.367856 + 0.929883i 0.619908π0.619908\pi
740740 0 0
741741 16.0000 0.587775
742742 0 0
743743 36.0000 1.32071 0.660356 0.750953i 0.270405π-0.270405\pi
0.660356 + 0.750953i 0.270405π0.270405\pi
744744 0 0
745745 0 0
746746 0 0
747747 0 0
748748 0 0
749749 24.0000 0.876941
750750 0 0
751751 −8.00000 −0.291924 −0.145962 0.989290i 0.546628π-0.546628\pi
−0.145962 + 0.989290i 0.546628π0.546628\pi
752752 0 0
753753 48.0000 1.74922
754754 0 0
755755 0 0
756756 0 0
757757 −10.0000 −0.363456 −0.181728 0.983349i 0.558169π-0.558169\pi
−0.181728 + 0.983349i 0.558169π0.558169\pi
758758 0 0
759759 0 0
760760 0 0
761761 6.00000 0.217500 0.108750 0.994069i 0.465315π-0.465315\pi
0.108750 + 0.994069i 0.465315π0.465315\pi
762762 0 0
763763 −64.0000 −2.31696
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 0 0
769769 14.0000 0.504853 0.252426 0.967616i 0.418771π-0.418771\pi
0.252426 + 0.967616i 0.418771π0.418771\pi
770770 0 0
771771 12.0000 0.432169
772772 0 0
773773 −42.0000 −1.51064 −0.755318 0.655359i 0.772517π-0.772517\pi
−0.755318 + 0.655359i 0.772517π0.772517\pi
774774 0 0
775775 −20.0000 −0.718421
776776 0 0
777777 −32.0000 −1.14799
778778 0 0
779779 24.0000 0.859889
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 0 0
785785 0 0
786786 0 0
787787 46.0000 1.63972 0.819861 0.572562i 0.194050π-0.194050\pi
0.819861 + 0.572562i 0.194050π0.194050\pi
788788 0 0
789789 −48.0000 −1.70885
790790 0 0
791791 −24.0000 −0.853342
792792 0 0
793793 −8.00000 −0.284088
794794 0 0
795795 0 0
796796 0 0
797797 42.0000 1.48772 0.743858 0.668338i 0.232994π-0.232994\pi
0.743858 + 0.668338i 0.232994π0.232994\pi
798798 0 0
799799 0 0
800800 0 0
801801 −6.00000 −0.212000
802802 0 0
803803 −12.0000 −0.423471
804804 0 0
805805 0 0
806806 0 0
807807 −48.0000 −1.68968
808808 0 0
809809 30.0000 1.05474 0.527372 0.849635i 0.323177π-0.323177\pi
0.527372 + 0.849635i 0.323177π0.323177\pi
810810 0 0
811811 −38.0000 −1.33436 −0.667180 0.744896i 0.732499π-0.732499\pi
−0.667180 + 0.744896i 0.732499π0.732499\pi
812812 0 0
813813 −16.0000 −0.561144
814814 0 0
815815 0 0
816816 0 0
817817 −32.0000 −1.11954
818818 0 0
819819 8.00000 0.279543
820820 0 0
821821 36.0000 1.25641 0.628204 0.778048i 0.283790π-0.283790\pi
0.628204 + 0.778048i 0.283790π0.283790\pi
822822 0 0
823823 16.0000 0.557725 0.278862 0.960331i 0.410043π-0.410043\pi
0.278862 + 0.960331i 0.410043π0.410043\pi
824824 0 0
825825 60.0000 2.08893
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 −10.0000 −0.347314 −0.173657 0.984806i 0.555558π-0.555558\pi
−0.173657 + 0.984806i 0.555558π0.555558\pi
830830 0 0
831831 16.0000 0.555034
832832 0 0
833833 −9.00000 −0.311832
834834 0 0
835835 0 0
836836 0 0
837837 −16.0000 −0.553041
838838 0 0
839839 36.0000 1.24286 0.621429 0.783470i 0.286552π-0.286552\pi
0.621429 + 0.783470i 0.286552π0.286552\pi
840840 0 0
841841 −29.0000 −1.00000
842842 0 0
843843 12.0000 0.413302
844844 0 0
845845 0 0
846846 0 0
847847 100.000 3.43604
848848 0 0
849849 −28.0000 −0.960958
850850 0 0
851851 0 0
852852 0 0
853853 −40.0000 −1.36957 −0.684787 0.728743i 0.740105π-0.740105\pi
−0.684787 + 0.728743i 0.740105π0.740105\pi
854854 0 0
855855 0 0
856856 0 0
857857 −18.0000 −0.614868 −0.307434 0.951569i 0.599470π-0.599470\pi
−0.307434 + 0.951569i 0.599470π0.599470\pi
858858 0 0
859859 16.0000 0.545913 0.272956 0.962026i 0.411998π-0.411998\pi
0.272956 + 0.962026i 0.411998π0.411998\pi
860860 0 0
861861 48.0000 1.63584
862862 0 0
863863 −48.0000 −1.63394 −0.816970 0.576681i 0.804348π-0.804348\pi
−0.816970 + 0.576681i 0.804348π0.804348\pi
864864 0 0
865865 0 0
866866 0 0
867867 2.00000 0.0679236
868868 0 0
869869 48.0000 1.62829
870870 0 0
871871 −16.0000 −0.542139
872872 0 0
873873 14.0000 0.473828
874874 0 0
875875 0 0
876876 0 0
877877 32.0000 1.08056 0.540282 0.841484i 0.318318π-0.318318\pi
0.540282 + 0.841484i 0.318318π0.318318\pi
878878 0 0
879879 12.0000 0.404750
880880 0 0
881881 18.0000 0.606435 0.303218 0.952921i 0.401939π-0.401939\pi
0.303218 + 0.952921i 0.401939π0.401939\pi
882882 0 0
883883 16.0000 0.538443 0.269221 0.963078i 0.413234π-0.413234\pi
0.269221 + 0.963078i 0.413234π0.413234\pi
884884 0 0
885885 0 0
886886 0 0
887887 −24.0000 −0.805841 −0.402921 0.915235i 0.632005π-0.632005\pi
−0.402921 + 0.915235i 0.632005π0.632005\pi
888888 0 0
889889 64.0000 2.14649
890890 0 0
891891 66.0000 2.21108
892892 0 0
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 0 0
901901 6.00000 0.199889
902902 0 0
903903 −64.0000 −2.12979
904904 0 0
905905 0 0
906906 0 0
907907 58.0000 1.92586 0.962929 0.269754i 0.0869425π-0.0869425\pi
0.962929 + 0.269754i 0.0869425π0.0869425\pi
908908 0 0
909909 18.0000 0.597022
910910 0 0
911911 −12.0000 −0.397578 −0.198789 0.980042i 0.563701π-0.563701\pi
−0.198789 + 0.980042i 0.563701π0.563701\pi
912912 0 0
913913 0 0
914914 0 0
915915 0 0
916916 0 0
917917 24.0000 0.792550
918918 0 0
919919 −56.0000 −1.84727 −0.923635 0.383274i 0.874797π-0.874797\pi
−0.923635 + 0.383274i 0.874797π0.874797\pi
920920 0 0
921921 −40.0000 −1.31804
922922 0 0
923923 0 0
924924 0 0
925925 20.0000 0.657596
926926 0 0
927927 16.0000 0.525509
928928 0 0
929929 −18.0000 −0.590561 −0.295280 0.955411i 0.595413π-0.595413\pi
−0.295280 + 0.955411i 0.595413π0.595413\pi
930930 0 0
931931 36.0000 1.17985
932932 0 0
933933 −24.0000 −0.785725
934934 0 0
935935 0 0
936936 0 0
937937 −58.0000 −1.89478 −0.947389 0.320085i 0.896288π-0.896288\pi
−0.947389 + 0.320085i 0.896288π0.896288\pi
938938 0 0
939939 −68.0000 −2.21910
940940 0 0
941941 −36.0000 −1.17357 −0.586783 0.809744i 0.699606π-0.699606\pi
−0.586783 + 0.809744i 0.699606π0.699606\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 −18.0000 −0.584921 −0.292461 0.956278i 0.594474π-0.594474\pi
−0.292461 + 0.956278i 0.594474π0.594474\pi
948948 0 0
949949 4.00000 0.129845
950950 0 0
951951 −24.0000 −0.778253
952952 0 0
953953 −30.0000 −0.971795 −0.485898 0.874016i 0.661507π-0.661507\pi
−0.485898 + 0.874016i 0.661507π0.661507\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 24.0000 0.775000
960960 0 0
961961 −15.0000 −0.483871
962962 0 0
963963 6.00000 0.193347
964964 0 0
965965 0 0
966966 0 0
967967 40.0000 1.28631 0.643157 0.765735i 0.277624π-0.277624\pi
0.643157 + 0.765735i 0.277624π0.277624\pi
968968 0 0
969969 −8.00000 −0.256997
970970 0 0
971971 24.0000 0.770197 0.385098 0.922876i 0.374168π-0.374168\pi
0.385098 + 0.922876i 0.374168π0.374168\pi
972972 0 0
973973 −8.00000 −0.256468
974974 0 0
975975 −20.0000 −0.640513
976976 0 0
977977 42.0000 1.34370 0.671850 0.740688i 0.265500π-0.265500\pi
0.671850 + 0.740688i 0.265500π0.265500\pi
978978 0 0
979979 36.0000 1.15056
980980 0 0
981981 −16.0000 −0.510841
982982 0 0
983983 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 16.0000 0.508257 0.254128 0.967170i 0.418211π-0.418211\pi
0.254128 + 0.967170i 0.418211π0.418211\pi
992992 0 0
993993 32.0000 1.01549
994994 0 0
995995 0 0
996996 0 0
997997 −28.0000 −0.886769 −0.443384 0.896332i 0.646222π-0.646222\pi
−0.443384 + 0.896332i 0.646222π0.646222\pi
998998 0 0
999999 16.0000 0.506218
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 272.2.a.d.1.1 1
3.2 odd 2 2448.2.a.k.1.1 1
4.3 odd 2 34.2.a.a.1.1 1
5.4 even 2 6800.2.a.b.1.1 1
8.3 odd 2 1088.2.a.l.1.1 1
8.5 even 2 1088.2.a.d.1.1 1
12.11 even 2 306.2.a.a.1.1 1
17.16 even 2 4624.2.a.a.1.1 1
20.3 even 4 850.2.c.b.749.1 2
20.7 even 4 850.2.c.b.749.2 2
20.19 odd 2 850.2.a.e.1.1 1
24.5 odd 2 9792.2.a.bj.1.1 1
24.11 even 2 9792.2.a.y.1.1 1
28.27 even 2 1666.2.a.m.1.1 1
44.43 even 2 4114.2.a.a.1.1 1
52.51 odd 2 5746.2.a.b.1.1 1
60.59 even 2 7650.2.a.ci.1.1 1
68.3 even 16 578.2.d.e.179.1 8
68.7 even 16 578.2.d.e.423.2 8
68.11 even 16 578.2.d.e.155.2 8
68.15 odd 8 578.2.c.e.327.2 4
68.19 odd 8 578.2.c.e.327.1 4
68.23 even 16 578.2.d.e.155.1 8
68.27 even 16 578.2.d.e.423.1 8
68.31 even 16 578.2.d.e.179.2 8
68.39 even 16 578.2.d.e.399.2 8
68.43 odd 8 578.2.c.e.251.1 4
68.47 odd 4 578.2.b.a.577.1 2
68.55 odd 4 578.2.b.a.577.2 2
68.59 odd 8 578.2.c.e.251.2 4
68.63 even 16 578.2.d.e.399.1 8
68.67 odd 2 578.2.a.a.1.1 1
204.203 even 2 5202.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
34.2.a.a.1.1 1 4.3 odd 2
272.2.a.d.1.1 1 1.1 even 1 trivial
306.2.a.a.1.1 1 12.11 even 2
578.2.a.a.1.1 1 68.67 odd 2
578.2.b.a.577.1 2 68.47 odd 4
578.2.b.a.577.2 2 68.55 odd 4
578.2.c.e.251.1 4 68.43 odd 8
578.2.c.e.251.2 4 68.59 odd 8
578.2.c.e.327.1 4 68.19 odd 8
578.2.c.e.327.2 4 68.15 odd 8
578.2.d.e.155.1 8 68.23 even 16
578.2.d.e.155.2 8 68.11 even 16
578.2.d.e.179.1 8 68.3 even 16
578.2.d.e.179.2 8 68.31 even 16
578.2.d.e.399.1 8 68.63 even 16
578.2.d.e.399.2 8 68.39 even 16
578.2.d.e.423.1 8 68.27 even 16
578.2.d.e.423.2 8 68.7 even 16
850.2.a.e.1.1 1 20.19 odd 2
850.2.c.b.749.1 2 20.3 even 4
850.2.c.b.749.2 2 20.7 even 4
1088.2.a.d.1.1 1 8.5 even 2
1088.2.a.l.1.1 1 8.3 odd 2
1666.2.a.m.1.1 1 28.27 even 2
2448.2.a.k.1.1 1 3.2 odd 2
4114.2.a.a.1.1 1 44.43 even 2
4624.2.a.a.1.1 1 17.16 even 2
5202.2.a.d.1.1 1 204.203 even 2
5746.2.a.b.1.1 1 52.51 odd 2
6800.2.a.b.1.1 1 5.4 even 2
7650.2.a.ci.1.1 1 60.59 even 2
9792.2.a.y.1.1 1 24.11 even 2
9792.2.a.bj.1.1 1 24.5 odd 2