Properties

Label 4900.2.a.be.1.3
Level 49004900
Weight 22
Character 4900.1
Self dual yes
Analytic conductor 39.12739.127
Analytic rank 11
Dimension 44
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [4900,2,Mod(1,4900)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4900.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4900, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 4900=225272 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4900.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,0,0,0,0,0,0,0,-6,0,0,0,0,0,0,0,-2,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(23)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 39.126696990439.1266969904
Analytic rank: 11
Dimension: 44
Coefficient field: Q(3,19)\Q(\sqrt{3}, \sqrt{19})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x411x2+16 x^{4} - 11x^{2} + 16 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 140)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 3.045473.04547 of defining polynomial
Character χ\chi == 4900.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+1.73205q35.27492q11+2.62685q13+0.418627q17+3.27492q197.82300q235.19615q27+4.27492q29+3.27492q319.13642q339.97368q37+4.54983q393.72508q412.15068q43+6.50958q47+0.725083q515.67232q53+5.67232q573.27492q5913.5498q61+3.52165q6713.5498q694.54983q71+6.50958q73+7.27492q799.00000q817.40437q83+7.40437q877.00000q89+5.67232q936.92820q97+O(q100)q+1.73205 q^{3} -5.27492 q^{11} +2.62685 q^{13} +0.418627 q^{17} +3.27492 q^{19} -7.82300 q^{23} -5.19615 q^{27} +4.27492 q^{29} +3.27492 q^{31} -9.13642 q^{33} -9.97368 q^{37} +4.54983 q^{39} -3.72508 q^{41} -2.15068 q^{43} +6.50958 q^{47} +0.725083 q^{51} -5.67232 q^{53} +5.67232 q^{57} -3.27492 q^{59} -13.5498 q^{61} +3.52165 q^{67} -13.5498 q^{69} -4.54983 q^{71} +6.50958 q^{73} +7.27492 q^{79} -9.00000 q^{81} -7.40437 q^{83} +7.40437 q^{87} -7.00000 q^{89} +5.67232 q^{93} -6.92820 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q6q112q19+2q292q3112q3930q41+18q51+2q5924q6124q69+12q71+14q7936q8128q89+O(q100) 4 q - 6 q^{11} - 2 q^{19} + 2 q^{29} - 2 q^{31} - 12 q^{39} - 30 q^{41} + 18 q^{51} + 2 q^{59} - 24 q^{61} - 24 q^{69} + 12 q^{71} + 14 q^{79} - 36 q^{81} - 28 q^{89}+O(q^{100}) Copy content Toggle raw display

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 1.73205 1.00000 0.500000 0.866025i 0.333333π-0.333333\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
44 0 0
55 0 0
66 0 0
77 0 0
88 0 0
99 0 0
1010 0 0
1111 −5.27492 −1.59045 −0.795224 0.606316i 0.792647π-0.792647\pi
−0.795224 + 0.606316i 0.792647π0.792647\pi
1212 0 0
1313 2.62685 0.728557 0.364278 0.931290i 0.381316π-0.381316\pi
0.364278 + 0.931290i 0.381316π0.381316\pi
1414 0 0
1515 0 0
1616 0 0
1717 0.418627 0.101532 0.0507659 0.998711i 0.483834π-0.483834\pi
0.0507659 + 0.998711i 0.483834π0.483834\pi
1818 0 0
1919 3.27492 0.751318 0.375659 0.926758i 0.377416π-0.377416\pi
0.375659 + 0.926758i 0.377416π0.377416\pi
2020 0 0
2121 0 0
2222 0 0
2323 −7.82300 −1.63121 −0.815604 0.578610i 0.803595π-0.803595\pi
−0.815604 + 0.578610i 0.803595π0.803595\pi
2424 0 0
2525 0 0
2626 0 0
2727 −5.19615 −1.00000
2828 0 0
2929 4.27492 0.793832 0.396916 0.917855i 0.370080π-0.370080\pi
0.396916 + 0.917855i 0.370080π0.370080\pi
3030 0 0
3131 3.27492 0.588192 0.294096 0.955776i 0.404981π-0.404981\pi
0.294096 + 0.955776i 0.404981π0.404981\pi
3232 0 0
3333 −9.13642 −1.59045
3434 0 0
3535 0 0
3636 0 0
3737 −9.97368 −1.63966 −0.819831 0.572605i 0.805933π-0.805933\pi
−0.819831 + 0.572605i 0.805933π0.805933\pi
3838 0 0
3939 4.54983 0.728557
4040 0 0
4141 −3.72508 −0.581760 −0.290880 0.956760i 0.593948π-0.593948\pi
−0.290880 + 0.956760i 0.593948π0.593948\pi
4242 0 0
4343 −2.15068 −0.327975 −0.163988 0.986462i 0.552436π-0.552436\pi
−0.163988 + 0.986462i 0.552436π0.552436\pi
4444 0 0
4545 0 0
4646 0 0
4747 6.50958 0.949519 0.474760 0.880115i 0.342535π-0.342535\pi
0.474760 + 0.880115i 0.342535π0.342535\pi
4848 0 0
4949 0 0
5050 0 0
5151 0.725083 0.101532
5252 0 0
5353 −5.67232 −0.779153 −0.389577 0.920994i 0.627379π-0.627379\pi
−0.389577 + 0.920994i 0.627379π0.627379\pi
5454 0 0
5555 0 0
5656 0 0
5757 5.67232 0.751318
5858 0 0
5959 −3.27492 −0.426358 −0.213179 0.977013i 0.568382π-0.568382\pi
−0.213179 + 0.977013i 0.568382π0.568382\pi
6060 0 0
6161 −13.5498 −1.73488 −0.867439 0.497543i 0.834236π-0.834236\pi
−0.867439 + 0.497543i 0.834236π0.834236\pi
6262 0 0
6363 0 0
6464 0 0
6565 0 0
6666 0 0
6767 3.52165 0.430237 0.215119 0.976588i 0.430986π-0.430986\pi
0.215119 + 0.976588i 0.430986π0.430986\pi
6868 0 0
6969 −13.5498 −1.63121
7070 0 0
7171 −4.54983 −0.539966 −0.269983 0.962865i 0.587018π-0.587018\pi
−0.269983 + 0.962865i 0.587018π0.587018\pi
7272 0 0
7373 6.50958 0.761888 0.380944 0.924598i 0.375599π-0.375599\pi
0.380944 + 0.924598i 0.375599π0.375599\pi
7474 0 0
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 7.27492 0.818492 0.409246 0.912424i 0.365792π-0.365792\pi
0.409246 + 0.912424i 0.365792π0.365792\pi
8080 0 0
8181 −9.00000 −1.00000
8282 0 0
8383 −7.40437 −0.812736 −0.406368 0.913710i 0.633205π-0.633205\pi
−0.406368 + 0.913710i 0.633205π0.633205\pi
8484 0 0
8585 0 0
8686 0 0
8787 7.40437 0.793832
8888 0 0
8989 −7.00000 −0.741999 −0.370999 0.928633i 0.620985π-0.620985\pi
−0.370999 + 0.928633i 0.620985π0.620985\pi
9090 0 0
9191 0 0
9292 0 0
9393 5.67232 0.588192
9494 0 0
9595 0 0
9696 0 0
9797 −6.92820 −0.703452 −0.351726 0.936103i 0.614405π-0.614405\pi
−0.351726 + 0.936103i 0.614405π0.614405\pi
9898 0 0
9999 0 0
100100 0 0
101101 −13.5498 −1.34826 −0.674129 0.738613i 0.735481π-0.735481\pi
−0.674129 + 0.738613i 0.735481π0.735481\pi
102102 0 0
103103 11.2871 1.11215 0.556076 0.831132i 0.312306π-0.312306\pi
0.556076 + 0.831132i 0.312306π0.312306\pi
104104 0 0
105105 0 0
106106 0 0
107107 3.52165 0.340450 0.170225 0.985405i 0.445550π-0.445550\pi
0.170225 + 0.985405i 0.445550π0.445550\pi
108108 0 0
109109 −11.5498 −1.10627 −0.553137 0.833090i 0.686569π-0.686569\pi
−0.553137 + 0.833090i 0.686569π0.686569\pi
110110 0 0
111111 −17.2749 −1.63966
112112 0 0
113113 4.30136 0.404637 0.202319 0.979320i 0.435152π-0.435152\pi
0.202319 + 0.979320i 0.435152π0.435152\pi
114114 0 0
115115 0 0
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 16.8248 1.52952
122122 0 0
123123 −6.45203 −0.581760
124124 0 0
125125 0 0
126126 0 0
127127 −15.6460 −1.38836 −0.694179 0.719802i 0.744232π-0.744232\pi
−0.694179 + 0.719802i 0.744232π0.744232\pi
128128 0 0
129129 −3.72508 −0.327975
130130 0 0
131131 −10.7251 −0.937055 −0.468527 0.883449i 0.655215π-0.655215\pi
−0.468527 + 0.883449i 0.655215π0.655215\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 0 0
137137 −21.3183 −1.82135 −0.910674 0.413126i 0.864437π-0.864437\pi
−0.910674 + 0.413126i 0.864437π0.864437\pi
138138 0 0
139139 13.0997 1.11110 0.555550 0.831483i 0.312508π-0.312508\pi
0.555550 + 0.831483i 0.312508π0.312508\pi
140140 0 0
141141 11.2749 0.949519
142142 0 0
143143 −13.8564 −1.15873
144144 0 0
145145 0 0
146146 0 0
147147 0 0
148148 0 0
149149 −7.54983 −0.618507 −0.309253 0.950980i 0.600079π-0.600079\pi
−0.309253 + 0.950980i 0.600079π0.600079\pi
150150 0 0
151151 −12.7251 −1.03555 −0.517776 0.855516i 0.673240π-0.673240\pi
−0.517776 + 0.855516i 0.673240π0.673240\pi
152152 0 0
153153 0 0
154154 0 0
155155 0 0
156156 0 0
157157 −2.20822 −0.176235 −0.0881176 0.996110i 0.528085π-0.528085\pi
−0.0881176 + 0.996110i 0.528085π0.528085\pi
158158 0 0
159159 −9.82475 −0.779153
160160 0 0
161161 0 0
162162 0 0
163163 5.67232 0.444291 0.222145 0.975014i 0.428694π-0.428694\pi
0.222145 + 0.975014i 0.428694π0.428694\pi
164164 0 0
165165 0 0
166166 0 0
167167 −0.476171 −0.0368472 −0.0184236 0.999830i 0.505865π-0.505865\pi
−0.0184236 + 0.999830i 0.505865π0.505865\pi
168168 0 0
169169 −6.09967 −0.469205
170170 0 0
171171 0 0
172172 0 0
173173 20.4811 1.55715 0.778573 0.627553i 0.215944π-0.215944\pi
0.778573 + 0.627553i 0.215944π0.215944\pi
174174 0 0
175175 0 0
176176 0 0
177177 −5.67232 −0.426358
178178 0 0
179179 −7.27492 −0.543753 −0.271876 0.962332i 0.587644π-0.587644\pi
−0.271876 + 0.962332i 0.587644π0.587644\pi
180180 0 0
181181 −24.2749 −1.80434 −0.902170 0.431380i 0.858027π-0.858027\pi
−0.902170 + 0.431380i 0.858027π0.858027\pi
182182 0 0
183183 −23.4690 −1.73488
184184 0 0
185185 0 0
186186 0 0
187187 −2.20822 −0.161481
188188 0 0
189189 0 0
190190 0 0
191191 0.175248 0.0126805 0.00634026 0.999980i 0.497982π-0.497982\pi
0.00634026 + 0.999980i 0.497982π0.497982\pi
192192 0 0
193193 21.3183 1.53453 0.767263 0.641332i 0.221618π-0.221618\pi
0.767263 + 0.641332i 0.221618π0.221618\pi
194194 0 0
195195 0 0
196196 0 0
197197 8.60271 0.612918 0.306459 0.951884i 0.400856π-0.400856\pi
0.306459 + 0.951884i 0.400856π0.400856\pi
198198 0 0
199199 17.2749 1.22459 0.612293 0.790631i 0.290247π-0.290247\pi
0.612293 + 0.790631i 0.290247π0.290247\pi
200200 0 0
201201 6.09967 0.430237
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 −17.2749 −1.19493
210210 0 0
211211 25.6495 1.76578 0.882892 0.469576i 0.155593π-0.155593\pi
0.882892 + 0.469576i 0.155593π0.155593\pi
212212 0 0
213213 −7.88054 −0.539966
214214 0 0
215215 0 0
216216 0 0
217217 0 0
218218 0 0
219219 11.2749 0.761888
220220 0 0
221221 1.09967 0.0739717
222222 0 0
223223 −8.71780 −0.583787 −0.291893 0.956451i 0.594285π-0.594285\pi
−0.291893 + 0.956451i 0.594285π0.594285\pi
224224 0 0
225225 0 0
226226 0 0
227227 −19.5287 −1.29617 −0.648084 0.761569i 0.724429π-0.724429\pi
−0.648084 + 0.761569i 0.724429π0.724429\pi
228228 0 0
229229 3.27492 0.216413 0.108206 0.994128i 0.465489π-0.465489\pi
0.108206 + 0.994128i 0.465489π0.465489\pi
230230 0 0
231231 0 0
232232 0 0
233233 14.2750 0.935189 0.467594 0.883943i 0.345121π-0.345121\pi
0.467594 + 0.883943i 0.345121π0.345121\pi
234234 0 0
235235 0 0
236236 0 0
237237 12.6005 0.818492
238238 0 0
239239 0.549834 0.0355658 0.0177829 0.999842i 0.494339π-0.494339\pi
0.0177829 + 0.999842i 0.494339π0.494339\pi
240240 0 0
241241 9.82475 0.632868 0.316434 0.948615i 0.397514π-0.397514\pi
0.316434 + 0.948615i 0.397514π0.397514\pi
242242 0 0
243243 0 0
244244 0 0
245245 0 0
246246 0 0
247247 8.60271 0.547377
248248 0 0
249249 −12.8248 −0.812736
250250 0 0
251251 −20.5498 −1.29709 −0.648547 0.761175i 0.724623π-0.724623\pi
−0.648547 + 0.761175i 0.724623π0.724623\pi
252252 0 0
253253 41.2657 2.59435
254254 0 0
255255 0 0
256256 0 0
257257 −11.6482 −0.726594 −0.363297 0.931673i 0.618349π-0.618349\pi
−0.363297 + 0.931673i 0.618349π0.618349\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 0 0
263263 0.779710 0.0480790 0.0240395 0.999711i 0.492347π-0.492347\pi
0.0240395 + 0.999711i 0.492347π0.492347\pi
264264 0 0
265265 0 0
266266 0 0
267267 −12.1244 −0.741999
268268 0 0
269269 −14.4502 −0.881042 −0.440521 0.897742i 0.645206π-0.645206\pi
−0.440521 + 0.897742i 0.645206π0.645206\pi
270270 0 0
271271 9.82475 0.596811 0.298406 0.954439i 0.403545π-0.403545\pi
0.298406 + 0.954439i 0.403545π0.403545\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 0 0
277277 14.2750 0.857704 0.428852 0.903375i 0.358918π-0.358918\pi
0.428852 + 0.903375i 0.358918π0.358918\pi
278278 0 0
279279 0 0
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 10.9260 0.649484 0.324742 0.945803i 0.394722π-0.394722\pi
0.324742 + 0.945803i 0.394722π0.394722\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 −16.8248 −0.989691
290290 0 0
291291 −12.0000 −0.703452
292292 0 0
293293 6.92820 0.404750 0.202375 0.979308i 0.435134π-0.435134\pi
0.202375 + 0.979308i 0.435134π0.435134\pi
294294 0 0
295295 0 0
296296 0 0
297297 27.4093 1.59045
298298 0 0
299299 −20.5498 −1.18843
300300 0 0
301301 0 0
302302 0 0
303303 −23.4690 −1.34826
304304 0 0
305305 0 0
306306 0 0
307307 26.5145 1.51326 0.756631 0.653843i 0.226844π-0.226844\pi
0.756631 + 0.653843i 0.226844π0.226844\pi
308308 0 0
309309 19.5498 1.11215
310310 0 0
311311 −9.82475 −0.557111 −0.278555 0.960420i 0.589856π-0.589856\pi
−0.278555 + 0.960420i 0.589856π0.589856\pi
312312 0 0
313313 −33.5002 −1.89354 −0.946772 0.321904i 0.895677π-0.895677\pi
−0.946772 + 0.321904i 0.895677π0.895677\pi
314314 0 0
315315 0 0
316316 0 0
317317 25.6197 1.43894 0.719472 0.694521i 0.244384π-0.244384\pi
0.719472 + 0.694521i 0.244384π0.244384\pi
318318 0 0
319319 −22.5498 −1.26255
320320 0 0
321321 6.09967 0.340450
322322 0 0
323323 1.37097 0.0762827
324324 0 0
325325 0 0
326326 0 0
327327 −20.0049 −1.10627
328328 0 0
329329 0 0
330330 0 0
331331 17.8248 0.979737 0.489868 0.871796i 0.337045π-0.337045\pi
0.489868 + 0.871796i 0.337045π0.337045\pi
332332 0 0
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 −4.30136 −0.234310 −0.117155 0.993114i 0.537377π-0.537377\pi
−0.117155 + 0.993114i 0.537377π0.537377\pi
338338 0 0
339339 7.45017 0.404637
340340 0 0
341341 −17.2749 −0.935489
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 0 0
347347 12.1244 0.650870 0.325435 0.945564i 0.394489π-0.394489\pi
0.325435 + 0.945564i 0.394489π0.394489\pi
348348 0 0
349349 −3.72508 −0.199399 −0.0996996 0.995018i 0.531788π-0.531788\pi
−0.0996996 + 0.995018i 0.531788π0.531788\pi
350350 0 0
351351 −13.6495 −0.728557
352352 0 0
353353 8.18408 0.435595 0.217797 0.975994i 0.430113π-0.430113\pi
0.217797 + 0.975994i 0.430113π0.430113\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 36.3746 1.91978 0.959889 0.280382i 0.0904610π-0.0904610\pi
0.959889 + 0.280382i 0.0904610π0.0904610\pi
360360 0 0
361361 −8.27492 −0.435522
362362 0 0
363363 29.1413 1.52952
364364 0 0
365365 0 0
366366 0 0
367367 −6.03341 −0.314941 −0.157471 0.987524i 0.550334π-0.550334\pi
−0.157471 + 0.987524i 0.550334π0.550334\pi
368368 0 0
369369 0 0
370370 0 0
371371 0 0
372372 0 0
373373 9.97368 0.516417 0.258209 0.966089i 0.416868π-0.416868\pi
0.258209 + 0.966089i 0.416868π0.416868\pi
374374 0 0
375375 0 0
376376 0 0
377377 11.2296 0.578352
378378 0 0
379379 −21.6495 −1.11206 −0.556030 0.831162i 0.687676π-0.687676\pi
−0.556030 + 0.831162i 0.687676π0.687676\pi
380380 0 0
381381 −27.0997 −1.38836
382382 0 0
383383 −6.14849 −0.314173 −0.157087 0.987585i 0.550210π-0.550210\pi
−0.157087 + 0.987585i 0.550210π0.550210\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 32.3746 1.64146 0.820728 0.571319i 0.193568π-0.193568\pi
0.820728 + 0.571319i 0.193568π0.193568\pi
390390 0 0
391391 −3.27492 −0.165620
392392 0 0
393393 −18.5764 −0.937055
394394 0 0
395395 0 0
396396 0 0
397397 10.8109 0.542585 0.271293 0.962497i 0.412549π-0.412549\pi
0.271293 + 0.962497i 0.412549π0.412549\pi
398398 0 0
399399 0 0
400400 0 0
401401 3.00000 0.149813 0.0749064 0.997191i 0.476134π-0.476134\pi
0.0749064 + 0.997191i 0.476134π0.476134\pi
402402 0 0
403403 8.60271 0.428532
404404 0 0
405405 0 0
406406 0 0
407407 52.6103 2.60780
408408 0 0
409409 −20.0997 −0.993865 −0.496932 0.867789i 0.665540π-0.665540\pi
−0.496932 + 0.867789i 0.665540π0.665540\pi
410410 0 0
411411 −36.9244 −1.82135
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 22.6893 1.11110
418418 0 0
419419 −13.0997 −0.639961 −0.319980 0.947424i 0.603676π-0.603676\pi
−0.319980 + 0.947424i 0.603676π0.603676\pi
420420 0 0
421421 −4.27492 −0.208347 −0.104173 0.994559i 0.533220π-0.533220\pi
−0.104173 + 0.994559i 0.533220π0.533220\pi
422422 0 0
423423 0 0
424424 0 0
425425 0 0
426426 0 0
427427 0 0
428428 0 0
429429 −24.0000 −1.15873
430430 0 0
431431 −18.3746 −0.885073 −0.442536 0.896751i 0.645921π-0.645921\pi
−0.442536 + 0.896751i 0.645921π0.645921\pi
432432 0 0
433433 −18.1578 −0.872606 −0.436303 0.899800i 0.643712π-0.643712\pi
−0.436303 + 0.899800i 0.643712π0.643712\pi
434434 0 0
435435 0 0
436436 0 0
437437 −25.6197 −1.22556
438438 0 0
439439 23.8248 1.13709 0.568547 0.822651i 0.307506π-0.307506\pi
0.568547 + 0.822651i 0.307506π0.307506\pi
440440 0 0
441441 0 0
442442 0 0
443443 −12.1244 −0.576046 −0.288023 0.957624i 0.592998π-0.592998\pi
−0.288023 + 0.957624i 0.592998π0.592998\pi
444444 0 0
445445 0 0
446446 0 0
447447 −13.0767 −0.618507
448448 0 0
449449 −3.17525 −0.149849 −0.0749246 0.997189i 0.523872π-0.523872\pi
−0.0749246 + 0.997189i 0.523872π0.523872\pi
450450 0 0
451451 19.6495 0.925259
452452 0 0
453453 −22.0405 −1.03555
454454 0 0
455455 0 0
456456 0 0
457457 −1.37097 −0.0641312 −0.0320656 0.999486i 0.510209π-0.510209\pi
−0.0320656 + 0.999486i 0.510209π0.510209\pi
458458 0 0
459459 −2.17525 −0.101532
460460 0 0
461461 −14.0000 −0.652045 −0.326023 0.945362i 0.605709π-0.605709\pi
−0.326023 + 0.945362i 0.605709π0.605709\pi
462462 0 0
463463 2.15068 0.0999505 0.0499752 0.998750i 0.484086π-0.484086\pi
0.0499752 + 0.998750i 0.484086π0.484086\pi
464464 0 0
465465 0 0
466466 0 0
467467 15.7035 0.726673 0.363337 0.931658i 0.381637π-0.381637\pi
0.363337 + 0.931658i 0.381637π0.381637\pi
468468 0 0
469469 0 0
470470 0 0
471471 −3.82475 −0.176235
472472 0 0
473473 11.3446 0.521627
474474 0 0
475475 0 0
476476 0 0
477477 0 0
478478 0 0
479479 9.82475 0.448904 0.224452 0.974485i 0.427941π-0.427941\pi
0.224452 + 0.974485i 0.427941π0.427941\pi
480480 0 0
481481 −26.1993 −1.19459
482482 0 0
483483 0 0
484484 0 0
485485 0 0
486486 0 0
487487 2.93039 0.132789 0.0663943 0.997793i 0.478850π-0.478850\pi
0.0663943 + 0.997793i 0.478850π0.478850\pi
488488 0 0
489489 9.82475 0.444291
490490 0 0
491491 −28.5498 −1.28844 −0.644218 0.764842i 0.722817π-0.722817\pi
−0.644218 + 0.764842i 0.722817π0.722817\pi
492492 0 0
493493 1.78959 0.0805993
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 1.62541 0.0727635 0.0363818 0.999338i 0.488417π-0.488417\pi
0.0363818 + 0.999338i 0.488417π0.488417\pi
500500 0 0
501501 −0.824752 −0.0368472
502502 0 0
503503 31.7682 1.41647 0.708236 0.705975i 0.249491π-0.249491\pi
0.708236 + 0.705975i 0.249491π0.249491\pi
504504 0 0
505505 0 0
506506 0 0
507507 −10.5649 −0.469205
508508 0 0
509509 −14.4502 −0.640492 −0.320246 0.947334i 0.603766π-0.603766\pi
−0.320246 + 0.947334i 0.603766π0.603766\pi
510510 0 0
511511 0 0
512512 0 0
513513 −17.0170 −0.751318
514514 0 0
515515 0 0
516516 0 0
517517 −34.3375 −1.51016
518518 0 0
519519 35.4743 1.55715
520520 0 0
521521 9.82475 0.430430 0.215215 0.976567i 0.430955π-0.430955\pi
0.215215 + 0.976567i 0.430955π0.430955\pi
522522 0 0
523523 7.34683 0.321254 0.160627 0.987015i 0.448648π-0.448648\pi
0.160627 + 0.987015i 0.448648π0.448648\pi
524524 0 0
525525 0 0
526526 0 0
527527 1.37097 0.0597203
528528 0 0
529529 38.1993 1.66084
530530 0 0
531531 0 0
532532 0 0
533533 −9.78523 −0.423845
534534 0 0
535535 0 0
536536 0 0
537537 −12.6005 −0.543753
538538 0 0
539539 0 0
540540 0 0
541541 −17.5498 −0.754526 −0.377263 0.926106i 0.623135π-0.623135\pi
−0.377263 + 0.926106i 0.623135π0.623135\pi
542542 0 0
543543 −42.0454 −1.80434
544544 0 0
545545 0 0
546546 0 0
547547 −20.5386 −0.878168 −0.439084 0.898446i 0.644697π-0.644697\pi
−0.439084 + 0.898446i 0.644697π0.644697\pi
548548 0 0
549549 0 0
550550 0 0
551551 14.0000 0.596420
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 0 0
557557 9.97368 0.422598 0.211299 0.977421i 0.432231π-0.432231\pi
0.211299 + 0.977421i 0.432231π0.432231\pi
558558 0 0
559559 −5.64950 −0.238949
560560 0 0
561561 −3.82475 −0.161481
562562 0 0
563563 −22.6317 −0.953814 −0.476907 0.878954i 0.658242π-0.658242\pi
−0.476907 + 0.878954i 0.658242π0.658242\pi
564564 0 0
565565 0 0
566566 0 0
567567 0 0
568568 0 0
569569 8.37459 0.351081 0.175540 0.984472i 0.443833π-0.443833\pi
0.175540 + 0.984472i 0.443833π0.443833\pi
570570 0 0
571571 7.27492 0.304446 0.152223 0.988346i 0.451357π-0.451357\pi
0.152223 + 0.988346i 0.451357π0.451357\pi
572572 0 0
573573 0.303539 0.0126805
574574 0 0
575575 0 0
576576 0 0
577577 −3.88273 −0.161640 −0.0808200 0.996729i 0.525754π-0.525754\pi
−0.0808200 + 0.996729i 0.525754π0.525754\pi
578578 0 0
579579 36.9244 1.53453
580580 0 0
581581 0 0
582582 0 0
583583 29.9210 1.23920
584584 0 0
585585 0 0
586586 0 0
587587 20.8997 0.862623 0.431311 0.902203i 0.358051π-0.358051\pi
0.431311 + 0.902203i 0.358051π0.358051\pi
588588 0 0
589589 10.7251 0.441919
590590 0 0
591591 14.9003 0.612918
592592 0 0
593593 33.3851 1.37096 0.685482 0.728090i 0.259592π-0.259592\pi
0.685482 + 0.728090i 0.259592π0.259592\pi
594594 0 0
595595 0 0
596596 0 0
597597 29.9210 1.22459
598598 0 0
599599 5.27492 0.215527 0.107764 0.994177i 0.465631π-0.465631\pi
0.107764 + 0.994177i 0.465631π0.465631\pi
600600 0 0
601601 14.0000 0.571072 0.285536 0.958368i 0.407828π-0.407828\pi
0.285536 + 0.958368i 0.407828π0.407828\pi
602602 0 0
603603 0 0
604604 0 0
605605 0 0
606606 0 0
607607 11.4022 0.462801 0.231400 0.972859i 0.425669π-0.425669\pi
0.231400 + 0.972859i 0.425669π0.425669\pi
608608 0 0
609609 0 0
610610 0 0
611611 17.0997 0.691779
612612 0 0
613613 −28.3616 −1.14551 −0.572757 0.819725i 0.694126π-0.694126\pi
−0.572757 + 0.819725i 0.694126π0.694126\pi
614614 0 0
615615 0 0
616616 0 0
617617 −31.2920 −1.25977 −0.629884 0.776689i 0.716898π-0.716898\pi
−0.629884 + 0.776689i 0.716898π0.716898\pi
618618 0 0
619619 −8.92442 −0.358703 −0.179351 0.983785i 0.557400π-0.557400\pi
−0.179351 + 0.983785i 0.557400π0.557400\pi
620620 0 0
621621 40.6495 1.63121
622622 0 0
623623 0 0
624624 0 0
625625 0 0
626626 0 0
627627 −29.9210 −1.19493
628628 0 0
629629 −4.17525 −0.166478
630630 0 0
631631 33.0997 1.31768 0.658839 0.752284i 0.271048π-0.271048\pi
0.658839 + 0.752284i 0.271048π0.271048\pi
632632 0 0
633633 44.4262 1.76578
634634 0 0
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 0 0
641641 −2.09967 −0.0829319 −0.0414660 0.999140i 0.513203π-0.513203\pi
−0.0414660 + 0.999140i 0.513203π0.513203\pi
642642 0 0
643643 −31.4071 −1.23857 −0.619287 0.785164i 0.712578π-0.712578\pi
−0.619287 + 0.785164i 0.712578π0.712578\pi
644644 0 0
645645 0 0
646646 0 0
647647 26.9331 1.05885 0.529425 0.848357i 0.322408π-0.322408\pi
0.529425 + 0.848357i 0.322408π0.322408\pi
648648 0 0
649649 17.2749 0.678100
650650 0 0
651651 0 0
652652 0 0
653653 28.3616 1.10988 0.554938 0.831892i 0.312742π-0.312742\pi
0.554938 + 0.831892i 0.312742π0.312742\pi
654654 0 0
655655 0 0
656656 0 0
657657 0 0
658658 0 0
659659 −40.5498 −1.57960 −0.789799 0.613366i 0.789815π-0.789815\pi
−0.789799 + 0.613366i 0.789815π0.789815\pi
660660 0 0
661661 −0.450166 −0.0175094 −0.00875471 0.999962i 0.502787π-0.502787\pi
−0.00875471 + 0.999962i 0.502787π0.502787\pi
662662 0 0
663663 1.90468 0.0739717
664664 0 0
665665 0 0
666666 0 0
667667 −33.4427 −1.29491
668668 0 0
669669 −15.0997 −0.583787
670670 0 0
671671 71.4743 2.75923
672672 0 0
673673 −31.2920 −1.20622 −0.603109 0.797659i 0.706072π-0.706072\pi
−0.603109 + 0.797659i 0.706072π0.706072\pi
674674 0 0
675675 0 0
676676 0 0
677677 46.4043 1.78346 0.891731 0.452566i 0.149491π-0.149491\pi
0.891731 + 0.452566i 0.149491π0.149491\pi
678678 0 0
679679 0 0
680680 0 0
681681 −33.8248 −1.29617
682682 0 0
683683 19.1676 0.733430 0.366715 0.930333i 0.380482π-0.380482\pi
0.366715 + 0.930333i 0.380482π0.380482\pi
684684 0 0
685685 0 0
686686 0 0
687687 5.67232 0.216413
688688 0 0
689689 −14.9003 −0.567657
690690 0 0
691691 30.3746 1.15550 0.577752 0.816212i 0.303930π-0.303930\pi
0.577752 + 0.816212i 0.303930π0.303930\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 −1.55942 −0.0590672
698698 0 0
699699 24.7251 0.935189
700700 0 0
701701 8.82475 0.333306 0.166653 0.986016i 0.446704π-0.446704\pi
0.166653 + 0.986016i 0.446704π0.446704\pi
702702 0 0
703703 −32.6630 −1.23191
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 −10.4502 −0.392464 −0.196232 0.980557i 0.562871π-0.562871\pi
−0.196232 + 0.980557i 0.562871π0.562871\pi
710710 0 0
711711 0 0
712712 0 0
713713 −25.6197 −0.959465
714714 0 0
715715 0 0
716716 0 0
717717 0.952341 0.0355658
718718 0 0
719719 −30.3746 −1.13278 −0.566390 0.824137i 0.691661π-0.691661\pi
−0.566390 + 0.824137i 0.691661π0.691661\pi
720720 0 0
721721 0 0
722722 0 0
723723 17.0170 0.632868
724724 0 0
725725 0 0
726726 0 0
727727 3.10302 0.115085 0.0575423 0.998343i 0.481674π-0.481674\pi
0.0575423 + 0.998343i 0.481674π0.481674\pi
728728 0 0
729729 27.0000 1.00000
730730 0 0
731731 −0.900331 −0.0332999
732732 0 0
733733 37.6865 1.39198 0.695991 0.718050i 0.254965π-0.254965\pi
0.695991 + 0.718050i 0.254965π0.254965\pi
734734 0 0
735735 0 0
736736 0 0
737737 −18.5764 −0.684270
738738 0 0
739739 −20.9244 −0.769717 −0.384859 0.922976i 0.625750π-0.625750\pi
−0.384859 + 0.922976i 0.625750π0.625750\pi
740740 0 0
741741 14.9003 0.547377
742742 0 0
743743 −6.45203 −0.236702 −0.118351 0.992972i 0.537761π-0.537761\pi
−0.118351 + 0.992972i 0.537761π0.537761\pi
744744 0 0
745745 0 0
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 −14.7251 −0.537326 −0.268663 0.963234i 0.586582π-0.586582\pi
−0.268663 + 0.963234i 0.586582π0.586582\pi
752752 0 0
753753 −35.5934 −1.29709
754754 0 0
755755 0 0
756756 0 0
757757 35.5934 1.29366 0.646831 0.762633i 0.276094π-0.276094\pi
0.646831 + 0.762633i 0.276094π0.276094\pi
758758 0 0
759759 71.4743 2.59435
760760 0 0
761761 22.9244 0.831010 0.415505 0.909591i 0.363605π-0.363605\pi
0.415505 + 0.909591i 0.363605π0.363605\pi
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 0 0
767767 −8.60271 −0.310626
768768 0 0
769769 −14.0000 −0.504853 −0.252426 0.967616i 0.581229π-0.581229\pi
−0.252426 + 0.967616i 0.581229π0.581229\pi
770770 0 0
771771 −20.1752 −0.726594
772772 0 0
773773 −40.3133 −1.44997 −0.724985 0.688765i 0.758153π-0.758153\pi
−0.724985 + 0.688765i 0.758153π0.758153\pi
774774 0 0
775775 0 0
776776 0 0
777777 0 0
778778 0 0
779779 −12.1993 −0.437087
780780 0 0
781781 24.0000 0.858788
782782 0 0
783783 −22.2131 −0.793832
784784 0 0
785785 0 0
786786 0 0
787787 −1.73205 −0.0617409 −0.0308705 0.999523i 0.509828π-0.509828\pi
−0.0308705 + 0.999523i 0.509828π0.509828\pi
788788 0 0
789789 1.35050 0.0480790
790790 0 0
791791 0 0
792792 0 0
793793 −35.5934 −1.26396
794794 0 0
795795 0 0
796796 0 0
797797 −46.8229 −1.65855 −0.829276 0.558839i 0.811247π-0.811247\pi
−0.829276 + 0.558839i 0.811247π0.811247\pi
798798 0 0
799799 2.72508 0.0964065
800800 0 0
801801 0 0
802802 0 0
803803 −34.3375 −1.21174
804804 0 0
805805 0 0
806806 0 0
807807 −25.0284 −0.881042
808808 0 0
809809 −17.1993 −0.604697 −0.302348 0.953198i 0.597771π-0.597771\pi
−0.302348 + 0.953198i 0.597771π0.597771\pi
810810 0 0
811811 7.45017 0.261611 0.130805 0.991408i 0.458244π-0.458244\pi
0.130805 + 0.991408i 0.458244π0.458244\pi
812812 0 0
813813 17.0170 0.596811
814814 0 0
815815 0 0
816816 0 0
817817 −7.04329 −0.246414
818818 0 0
819819 0 0
820820 0 0
821821 −20.3746 −0.711078 −0.355539 0.934661i 0.615703π-0.615703\pi
−0.355539 + 0.934661i 0.615703π0.615703\pi
822822 0 0
823823 46.1583 1.60898 0.804488 0.593968i 0.202440π-0.202440\pi
0.804488 + 0.593968i 0.202440π0.202440\pi
824824 0 0
825825 0 0
826826 0 0
827827 −15.0547 −0.523505 −0.261752 0.965135i 0.584300π-0.584300\pi
−0.261752 + 0.965135i 0.584300π0.584300\pi
828828 0 0
829829 −50.9244 −1.76868 −0.884339 0.466845i 0.845391π-0.845391\pi
−0.884339 + 0.466845i 0.845391π0.845391\pi
830830 0 0
831831 24.7251 0.857704
832832 0 0
833833 0 0
834834 0 0
835835 0 0
836836 0 0
837837 −17.0170 −0.588192
838838 0 0
839839 41.0997 1.41892 0.709459 0.704747i 0.248939π-0.248939\pi
0.709459 + 0.704747i 0.248939π0.248939\pi
840840 0 0
841841 −10.7251 −0.369830
842842 0 0
843843 10.3923 0.357930
844844 0 0
845845 0 0
846846 0 0
847847 0 0
848848 0 0
849849 18.9244 0.649484
850850 0 0
851851 78.0241 2.67463
852852 0 0
853853 13.1342 0.449708 0.224854 0.974392i 0.427810π-0.427810\pi
0.224854 + 0.974392i 0.427810π0.427810\pi
854854 0 0
855855 0 0
856856 0 0
857857 37.6865 1.28735 0.643673 0.765301i 0.277410π-0.277410\pi
0.643673 + 0.765301i 0.277410π0.277410\pi
858858 0 0
859859 −2.37459 −0.0810198 −0.0405099 0.999179i 0.512898π-0.512898\pi
−0.0405099 + 0.999179i 0.512898π0.512898\pi
860860 0 0
861861 0 0
862862 0 0
863863 −16.4257 −0.559138 −0.279569 0.960126i 0.590192π-0.590192\pi
−0.279569 + 0.960126i 0.590192π0.590192\pi
864864 0 0
865865 0 0
866866 0 0
867867 −29.1413 −0.989691
868868 0 0
869869 −38.3746 −1.30177
870870 0 0
871871 9.25083 0.313452
872872 0 0
873873 0 0
874874 0 0
875875 0 0
876876 0 0
877877 −22.8777 −0.772527 −0.386263 0.922389i 0.626234π-0.626234\pi
−0.386263 + 0.922389i 0.626234π0.626234\pi
878878 0 0
879879 12.0000 0.404750
880880 0 0
881881 −43.0241 −1.44952 −0.724759 0.689002i 0.758049π-0.758049\pi
−0.724759 + 0.689002i 0.758049π0.758049\pi
882882 0 0
883883 55.5407 1.86909 0.934547 0.355840i 0.115805π-0.115805\pi
0.934547 + 0.355840i 0.115805π0.115805\pi
884884 0 0
885885 0 0
886886 0 0
887887 −39.2301 −1.31722 −0.658609 0.752486i 0.728855π-0.728855\pi
−0.658609 + 0.752486i 0.728855π0.728855\pi
888888 0 0
889889 0 0
890890 0 0
891891 47.4743 1.59045
892892 0 0
893893 21.3183 0.713391
894894 0 0
895895 0 0
896896 0 0
897897 −35.5934 −1.18843
898898 0 0
899899 14.0000 0.466926
900900 0 0
901901 −2.37459 −0.0791089
902902 0 0
903903 0 0
904904 0 0
905905 0 0
906906 0 0
907907 −41.8569 −1.38984 −0.694918 0.719089i 0.744560π-0.744560\pi
−0.694918 + 0.719089i 0.744560π0.744560\pi
908908 0 0
909909 0 0
910910 0 0
911911 −25.0997 −0.831589 −0.415795 0.909459i 0.636496π-0.636496\pi
−0.415795 + 0.909459i 0.636496π0.636496\pi
912912 0 0
913913 39.0575 1.29261
914914 0 0
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 −46.9244 −1.54789 −0.773947 0.633250i 0.781720π-0.781720\pi
−0.773947 + 0.633250i 0.781720π0.781720\pi
920920 0 0
921921 45.9244 1.51326
922922 0 0
923923 −11.9517 −0.393396
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 0 0
929929 −48.0997 −1.57810 −0.789049 0.614330i 0.789427π-0.789427\pi
−0.789049 + 0.614330i 0.789427π0.789427\pi
930930 0 0
931931 0 0
932932 0 0
933933 −17.0170 −0.557111
934934 0 0
935935 0 0
936936 0 0
937937 24.3638 0.795931 0.397965 0.917400i 0.369716π-0.369716\pi
0.397965 + 0.917400i 0.369716π0.369716\pi
938938 0 0
939939 −58.0241 −1.89354
940940 0 0
941941 −3.27492 −0.106759 −0.0533796 0.998574i 0.516999π-0.516999\pi
−0.0533796 + 0.998574i 0.516999π0.516999\pi
942942 0 0
943943 29.1413 0.948972
944944 0 0
945945 0 0
946946 0 0
947947 −10.5649 −0.343314 −0.171657 0.985157i 0.554912π-0.554912\pi
−0.171657 + 0.985157i 0.554912π0.554912\pi
948948 0 0
949949 17.0997 0.555079
950950 0 0
951951 44.3746 1.43894
952952 0 0
953953 22.6893 0.734978 0.367489 0.930028i 0.380218π-0.380218\pi
0.367489 + 0.930028i 0.380218π0.380218\pi
954954 0 0
955955 0 0
956956 0 0
957957 −39.0575 −1.26255
958958 0 0
959959 0 0
960960 0 0
961961 −20.2749 −0.654030
962962 0 0
963963 0 0
964964 0 0
965965 0 0
966966 0 0
967967 −2.15068 −0.0691611 −0.0345806 0.999402i 0.511010π-0.511010\pi
−0.0345806 + 0.999402i 0.511010π0.511010\pi
968968 0 0
969969 2.37459 0.0762827
970970 0 0
971971 −36.9244 −1.18496 −0.592481 0.805585i 0.701851π-0.701851\pi
−0.592481 + 0.805585i 0.701851π0.701851\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 −29.9210 −0.957259 −0.478629 0.878017i 0.658866π-0.658866\pi
−0.478629 + 0.878017i 0.658866π0.658866\pi
978978 0 0
979979 36.9244 1.18011
980980 0 0
981981 0 0
982982 0 0
983983 45.9281 1.46488 0.732440 0.680832i 0.238382π-0.238382\pi
0.732440 + 0.680832i 0.238382π0.238382\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 16.8248 0.534996
990990 0 0
991991 33.4743 1.06334 0.531672 0.846950i 0.321564π-0.321564\pi
0.531672 + 0.846950i 0.321564π0.321564\pi
992992 0 0
993993 30.8734 0.979737
994994 0 0
995995 0 0
996996 0 0
997997 0.418627 0.0132580 0.00662902 0.999978i 0.497890π-0.497890\pi
0.00662902 + 0.999978i 0.497890π0.497890\pi
998998 0 0
999999 51.8248 1.63966
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 4900.2.a.be.1.3 4
5.2 odd 4 980.2.e.f.589.1 4
5.3 odd 4 980.2.e.f.589.3 4
5.4 even 2 inner 4900.2.a.be.1.1 4
7.2 even 3 700.2.i.f.501.2 8
7.4 even 3 700.2.i.f.401.2 8
7.6 odd 2 4900.2.a.bf.1.1 4
35.2 odd 12 140.2.q.b.109.2 yes 4
35.3 even 12 980.2.q.b.569.2 4
35.4 even 6 700.2.i.f.401.3 8
35.9 even 6 700.2.i.f.501.3 8
35.12 even 12 980.2.q.b.949.1 4
35.13 even 4 980.2.e.c.589.2 4
35.17 even 12 980.2.q.g.569.1 4
35.18 odd 12 140.2.q.b.9.1 yes 4
35.23 odd 12 140.2.q.a.109.2 yes 4
35.27 even 4 980.2.e.c.589.4 4
35.32 odd 12 140.2.q.a.9.2 4
35.33 even 12 980.2.q.g.949.1 4
35.34 odd 2 4900.2.a.bf.1.3 4
105.2 even 12 1260.2.bm.b.109.1 4
105.23 even 12 1260.2.bm.a.109.1 4
105.32 even 12 1260.2.bm.a.289.1 4
105.53 even 12 1260.2.bm.b.289.2 4
140.23 even 12 560.2.bw.e.529.2 4
140.67 even 12 560.2.bw.e.289.2 4
140.107 even 12 560.2.bw.a.529.2 4
140.123 even 12 560.2.bw.a.289.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.q.a.9.2 4 35.32 odd 12
140.2.q.a.109.2 yes 4 35.23 odd 12
140.2.q.b.9.1 yes 4 35.18 odd 12
140.2.q.b.109.2 yes 4 35.2 odd 12
560.2.bw.a.289.1 4 140.123 even 12
560.2.bw.a.529.2 4 140.107 even 12
560.2.bw.e.289.2 4 140.67 even 12
560.2.bw.e.529.2 4 140.23 even 12
700.2.i.f.401.2 8 7.4 even 3
700.2.i.f.401.3 8 35.4 even 6
700.2.i.f.501.2 8 7.2 even 3
700.2.i.f.501.3 8 35.9 even 6
980.2.e.c.589.2 4 35.13 even 4
980.2.e.c.589.4 4 35.27 even 4
980.2.e.f.589.1 4 5.2 odd 4
980.2.e.f.589.3 4 5.3 odd 4
980.2.q.b.569.2 4 35.3 even 12
980.2.q.b.949.1 4 35.12 even 12
980.2.q.g.569.1 4 35.17 even 12
980.2.q.g.949.1 4 35.33 even 12
1260.2.bm.a.109.1 4 105.23 even 12
1260.2.bm.a.289.1 4 105.32 even 12
1260.2.bm.b.109.1 4 105.2 even 12
1260.2.bm.b.289.2 4 105.53 even 12
4900.2.a.be.1.1 4 5.4 even 2 inner
4900.2.a.be.1.3 4 1.1 even 1 trivial
4900.2.a.bf.1.1 4 7.6 odd 2
4900.2.a.bf.1.3 4 35.34 odd 2