Properties

Label 8100.2.d.h.649.1
Level 81008100
Weight 22
Character 8100.649
Analytic conductor 64.67964.679
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8100,2,Mod(649,8100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8100, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8100.649");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 8100=223452 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 8100.d (of order 22, degree 11, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 64.678825637264.6788256372
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2+1 x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 649.1
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 8100.649
Dual form 8100.2.d.h.649.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q1.00000iq7+3.00000q11+1.00000iq13+6.00000iq17+4.00000q19+3.00000iq233.00000q29+5.00000q31+2.00000iq37+3.00000q41+1.00000iq439.00000iq47+6.00000q49+6.00000iq53+3.00000q5913.0000q617.00000iq6712.0000q71+10.0000iq733.00000iq7711.0000q79+9.00000iq836.00000q89+1.00000q91+11.0000iq97+O(q100)q-1.00000i q^{7} +3.00000 q^{11} +1.00000i q^{13} +6.00000i q^{17} +4.00000 q^{19} +3.00000i q^{23} -3.00000 q^{29} +5.00000 q^{31} +2.00000i q^{37} +3.00000 q^{41} +1.00000i q^{43} -9.00000i q^{47} +6.00000 q^{49} +6.00000i q^{53} +3.00000 q^{59} -13.0000 q^{61} -7.00000i q^{67} -12.0000 q^{71} +10.0000i q^{73} -3.00000i q^{77} -11.0000 q^{79} +9.00000i q^{83} -6.00000 q^{89} +1.00000 q^{91} +11.0000i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+6q11+8q196q29+10q31+6q41+12q49+6q5926q6124q7122q7912q89+2q91+O(q100) 2 q + 6 q^{11} + 8 q^{19} - 6 q^{29} + 10 q^{31} + 6 q^{41} + 12 q^{49} + 6 q^{59} - 26 q^{61} - 24 q^{71} - 22 q^{79} - 12 q^{89} + 2 q^{91}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/8100Z)×\left(\mathbb{Z}/8100\mathbb{Z}\right)^\times.

nn 40514051 64016401 77777777
χ(n)\chi(n) 11 11 1-1

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0 0
44 0 0
55 0 0
66 0 0
77 − 1.00000i − 0.377964i −0.981981 0.188982i 0.939481π-0.939481\pi
0.981981 0.188982i 0.0605189π-0.0605189\pi
88 0 0
99 0 0
1010 0 0
1111 3.00000 0.904534 0.452267 0.891883i 0.350615π-0.350615\pi
0.452267 + 0.891883i 0.350615π0.350615\pi
1212 0 0
1313 1.00000i 0.277350i 0.990338 + 0.138675i 0.0442844π0.0442844\pi
−0.990338 + 0.138675i 0.955716π0.955716\pi
1414 0 0
1515 0 0
1616 0 0
1717 6.00000i 1.45521i 0.685994 + 0.727607i 0.259367π0.259367\pi
−0.685994 + 0.727607i 0.740633π0.740633\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 0 0
2222 0 0
2323 3.00000i 0.625543i 0.949828 + 0.312772i 0.101257π0.101257\pi
−0.949828 + 0.312772i 0.898743π0.898743\pi
2424 0 0
2525 0 0
2626 0 0
2727 0 0
2828 0 0
2929 −3.00000 −0.557086 −0.278543 0.960424i 0.589851π-0.589851\pi
−0.278543 + 0.960424i 0.589851π0.589851\pi
3030 0 0
3131 5.00000 0.898027 0.449013 0.893525i 0.351776π-0.351776\pi
0.449013 + 0.893525i 0.351776π0.351776\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 0 0
3737 2.00000i 0.328798i 0.986394 + 0.164399i 0.0525685π0.0525685\pi
−0.986394 + 0.164399i 0.947432π0.947432\pi
3838 0 0
3939 0 0
4040 0 0
4141 3.00000 0.468521 0.234261 0.972174i 0.424733π-0.424733\pi
0.234261 + 0.972174i 0.424733π0.424733\pi
4242 0 0
4343 1.00000i 0.152499i 0.997089 + 0.0762493i 0.0242945π0.0242945\pi
−0.997089 + 0.0762493i 0.975706π0.975706\pi
4444 0 0
4545 0 0
4646 0 0
4747 − 9.00000i − 1.31278i −0.754420 0.656392i 0.772082π-0.772082\pi
0.754420 0.656392i 0.227918π-0.227918\pi
4848 0 0
4949 6.00000 0.857143
5050 0 0
5151 0 0
5252 0 0
5353 6.00000i 0.824163i 0.911147 + 0.412082i 0.135198π0.135198\pi
−0.911147 + 0.412082i 0.864802π0.864802\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 0 0
5959 3.00000 0.390567 0.195283 0.980747i 0.437437π-0.437437\pi
0.195283 + 0.980747i 0.437437π0.437437\pi
6060 0 0
6161 −13.0000 −1.66448 −0.832240 0.554416i 0.812942π-0.812942\pi
−0.832240 + 0.554416i 0.812942π0.812942\pi
6262 0 0
6363 0 0
6464 0 0
6565 0 0
6666 0 0
6767 − 7.00000i − 0.855186i −0.903971 0.427593i 0.859362π-0.859362\pi
0.903971 0.427593i 0.140638π-0.140638\pi
6868 0 0
6969 0 0
7070 0 0
7171 −12.0000 −1.42414 −0.712069 0.702109i 0.752242π-0.752242\pi
−0.712069 + 0.702109i 0.752242π0.752242\pi
7272 0 0
7373 10.0000i 1.17041i 0.810885 + 0.585206i 0.198986π0.198986\pi
−0.810885 + 0.585206i 0.801014π0.801014\pi
7474 0 0
7575 0 0
7676 0 0
7777 − 3.00000i − 0.341882i
7878 0 0
7979 −11.0000 −1.23760 −0.618798 0.785550i 0.712380π-0.712380\pi
−0.618798 + 0.785550i 0.712380π0.712380\pi
8080 0 0
8181 0 0
8282 0 0
8383 9.00000i 0.987878i 0.869496 + 0.493939i 0.164443π0.164443\pi
−0.869496 + 0.493939i 0.835557π0.835557\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 1.00000 0.104828
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 0 0
9797 11.0000i 1.11688i 0.829545 + 0.558440i 0.188600π0.188600\pi
−0.829545 + 0.558440i 0.811400π0.811400\pi
9898 0 0
9999 0 0
100100 0 0
101101 15.0000 1.49256 0.746278 0.665635i 0.231839π-0.231839\pi
0.746278 + 0.665635i 0.231839π0.231839\pi
102102 0 0
103103 7.00000i 0.689730i 0.938652 + 0.344865i 0.112075π0.112075\pi
−0.938652 + 0.344865i 0.887925π0.887925\pi
104104 0 0
105105 0 0
106106 0 0
107107 12.0000i 1.16008i 0.814587 + 0.580042i 0.196964π0.196964\pi
−0.814587 + 0.580042i 0.803036π0.803036\pi
108108 0 0
109109 −2.00000 −0.191565 −0.0957826 0.995402i 0.530535π-0.530535\pi
−0.0957826 + 0.995402i 0.530535π0.530535\pi
110110 0 0
111111 0 0
112112 0 0
113113 9.00000i 0.846649i 0.905978 + 0.423324i 0.139137π0.139137\pi
−0.905978 + 0.423324i 0.860863π0.860863\pi
114114 0 0
115115 0 0
116116 0 0
117117 0 0
118118 0 0
119119 6.00000 0.550019
120120 0 0
121121 −2.00000 −0.181818
122122 0 0
123123 0 0
124124 0 0
125125 0 0
126126 0 0
127127 − 16.0000i − 1.41977i −0.704317 0.709885i 0.748747π-0.748747\pi
0.704317 0.709885i 0.251253π-0.251253\pi
128128 0 0
129129 0 0
130130 0 0
131131 21.0000 1.83478 0.917389 0.397991i 0.130293π-0.130293\pi
0.917389 + 0.397991i 0.130293π0.130293\pi
132132 0 0
133133 − 4.00000i − 0.346844i
134134 0 0
135135 0 0
136136 0 0
137137 3.00000i 0.256307i 0.991754 + 0.128154i 0.0409051π0.0409051\pi
−0.991754 + 0.128154i 0.959095π0.959095\pi
138138 0 0
139139 −5.00000 −0.424094 −0.212047 0.977259i 0.568013π-0.568013\pi
−0.212047 + 0.977259i 0.568013π0.568013\pi
140140 0 0
141141 0 0
142142 0 0
143143 3.00000i 0.250873i
144144 0 0
145145 0 0
146146 0 0
147147 0 0
148148 0 0
149149 −15.0000 −1.22885 −0.614424 0.788976i 0.710612π-0.710612\pi
−0.614424 + 0.788976i 0.710612π0.710612\pi
150150 0 0
151151 −13.0000 −1.05792 −0.528962 0.848645i 0.677419π-0.677419\pi
−0.528962 + 0.848645i 0.677419π0.677419\pi
152152 0 0
153153 0 0
154154 0 0
155155 0 0
156156 0 0
157157 − 13.0000i − 1.03751i −0.854922 0.518756i 0.826395π-0.826395\pi
0.854922 0.518756i 0.173605π-0.173605\pi
158158 0 0
159159 0 0
160160 0 0
161161 3.00000 0.236433
162162 0 0
163163 − 20.0000i − 1.56652i −0.621694 0.783260i 0.713555π-0.713555\pi
0.621694 0.783260i 0.286445π-0.286445\pi
164164 0 0
165165 0 0
166166 0 0
167167 9.00000i 0.696441i 0.937413 + 0.348220i 0.113214π0.113214\pi
−0.937413 + 0.348220i 0.886786π0.886786\pi
168168 0 0
169169 12.0000 0.923077
170170 0 0
171171 0 0
172172 0 0
173173 9.00000i 0.684257i 0.939653 + 0.342129i 0.111148π0.111148\pi
−0.939653 + 0.342129i 0.888852π0.888852\pi
174174 0 0
175175 0 0
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 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 0 0
184184 0 0
185185 0 0
186186 0 0
187187 18.0000i 1.31629i
188188 0 0
189189 0 0
190190 0 0
191191 15.0000 1.08536 0.542681 0.839939i 0.317409π-0.317409\pi
0.542681 + 0.839939i 0.317409π0.317409\pi
192192 0 0
193193 − 11.0000i − 0.791797i −0.918294 0.395899i 0.870433π-0.870433\pi
0.918294 0.395899i 0.129567π-0.129567\pi
194194 0 0
195195 0 0
196196 0 0
197197 6.00000i 0.427482i 0.976890 + 0.213741i 0.0685649π0.0685649\pi
−0.976890 + 0.213741i 0.931435π0.931435\pi
198198 0 0
199199 4.00000 0.283552 0.141776 0.989899i 0.454719π-0.454719\pi
0.141776 + 0.989899i 0.454719π0.454719\pi
200200 0 0
201201 0 0
202202 0 0
203203 3.00000i 0.210559i
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 12.0000 0.830057
210210 0 0
211211 17.0000 1.17033 0.585164 0.810915i 0.301030π-0.301030\pi
0.585164 + 0.810915i 0.301030π0.301030\pi
212212 0 0
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 − 5.00000i − 0.339422i
218218 0 0
219219 0 0
220220 0 0
221221 −6.00000 −0.403604
222222 0 0
223223 1.00000i 0.0669650i 0.999439 + 0.0334825i 0.0106598π0.0106598\pi
−0.999439 + 0.0334825i 0.989340π0.989340\pi
224224 0 0
225225 0 0
226226 0 0
227227 27.0000i 1.79205i 0.444001 + 0.896026i 0.353559π0.353559\pi
−0.444001 + 0.896026i 0.646441π0.646441\pi
228228 0 0
229229 13.0000 0.859064 0.429532 0.903052i 0.358679π-0.358679\pi
0.429532 + 0.903052i 0.358679π0.358679\pi
230230 0 0
231231 0 0
232232 0 0
233233 6.00000i 0.393073i 0.980497 + 0.196537i 0.0629694π0.0629694\pi
−0.980497 + 0.196537i 0.937031π0.937031\pi
234234 0 0
235235 0 0
236236 0 0
237237 0 0
238238 0 0
239239 27.0000 1.74648 0.873242 0.487286i 0.162013π-0.162013\pi
0.873242 + 0.487286i 0.162013π0.162013\pi
240240 0 0
241241 −1.00000 −0.0644157 −0.0322078 0.999481i 0.510254π-0.510254\pi
−0.0322078 + 0.999481i 0.510254π0.510254\pi
242242 0 0
243243 0 0
244244 0 0
245245 0 0
246246 0 0
247247 4.00000i 0.254514i
248248 0 0
249249 0 0
250250 0 0
251251 12.0000 0.757433 0.378717 0.925513i 0.376365π-0.376365\pi
0.378717 + 0.925513i 0.376365π0.376365\pi
252252 0 0
253253 9.00000i 0.565825i
254254 0 0
255255 0 0
256256 0 0
257257 − 9.00000i − 0.561405i −0.959795 0.280702i 0.909433π-0.909433\pi
0.959795 0.280702i 0.0905674π-0.0905674\pi
258258 0 0
259259 2.00000 0.124274
260260 0 0
261261 0 0
262262 0 0
263263 21.0000i 1.29492i 0.762101 + 0.647458i 0.224168π0.224168\pi
−0.762101 + 0.647458i 0.775832π0.775832\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 0 0
269269 6.00000 0.365826 0.182913 0.983129i 0.441447π-0.441447\pi
0.182913 + 0.983129i 0.441447π0.441447\pi
270270 0 0
271271 8.00000 0.485965 0.242983 0.970031i 0.421874π-0.421874\pi
0.242983 + 0.970031i 0.421874π0.421874\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 0 0
277277 − 1.00000i − 0.0600842i −0.999549 0.0300421i 0.990436π-0.990436\pi
0.999549 0.0300421i 0.00956413π-0.00956413\pi
278278 0 0
279279 0 0
280280 0 0
281281 3.00000 0.178965 0.0894825 0.995988i 0.471479π-0.471479\pi
0.0894825 + 0.995988i 0.471479π0.471479\pi
282282 0 0
283283 − 5.00000i − 0.297219i −0.988896 0.148610i 0.952520π-0.952520\pi
0.988896 0.148610i 0.0474798π-0.0474798\pi
284284 0 0
285285 0 0
286286 0 0
287287 − 3.00000i − 0.177084i
288288 0 0
289289 −19.0000 −1.11765
290290 0 0
291291 0 0
292292 0 0
293293 21.0000i 1.22683i 0.789760 + 0.613417i 0.210205π0.210205\pi
−0.789760 + 0.613417i 0.789795π0.789795\pi
294294 0 0
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 −3.00000 −0.173494
300300 0 0
301301 1.00000 0.0576390
302302 0 0
303303 0 0
304304 0 0
305305 0 0
306306 0 0
307307 20.0000i 1.14146i 0.821138 + 0.570730i 0.193340π0.193340\pi
−0.821138 + 0.570730i 0.806660π0.806660\pi
308308 0 0
309309 0 0
310310 0 0
311311 21.0000 1.19080 0.595400 0.803429i 0.296993π-0.296993\pi
0.595400 + 0.803429i 0.296993π0.296993\pi
312312 0 0
313313 1.00000i 0.0565233i 0.999601 + 0.0282617i 0.00899717π0.00899717\pi
−0.999601 + 0.0282617i 0.991003π0.991003\pi
314314 0 0
315315 0 0
316316 0 0
317317 − 21.0000i − 1.17948i −0.807594 0.589739i 0.799231π-0.799231\pi
0.807594 0.589739i 0.200769π-0.200769\pi
318318 0 0
319319 −9.00000 −0.503903
320320 0 0
321321 0 0
322322 0 0
323323 24.0000i 1.33540i
324324 0 0
325325 0 0
326326 0 0
327327 0 0
328328 0 0
329329 −9.00000 −0.496186
330330 0 0
331331 11.0000 0.604615 0.302307 0.953211i 0.402243π-0.402243\pi
0.302307 + 0.953211i 0.402243π0.402243\pi
332332 0 0
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 23.0000i 1.25289i 0.779466 + 0.626445i 0.215491π0.215491\pi
−0.779466 + 0.626445i 0.784509π0.784509\pi
338338 0 0
339339 0 0
340340 0 0
341341 15.0000 0.812296
342342 0 0
343343 − 13.0000i − 0.701934i
344344 0 0
345345 0 0
346346 0 0
347347 9.00000i 0.483145i 0.970383 + 0.241573i 0.0776632π0.0776632\pi
−0.970383 + 0.241573i 0.922337π0.922337\pi
348348 0 0
349349 1.00000 0.0535288 0.0267644 0.999642i 0.491480π-0.491480\pi
0.0267644 + 0.999642i 0.491480π0.491480\pi
350350 0 0
351351 0 0
352352 0 0
353353 − 3.00000i − 0.159674i −0.996808 0.0798369i 0.974560π-0.974560\pi
0.996808 0.0798369i 0.0254400π-0.0254400\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
360360 0 0
361361 −3.00000 −0.157895
362362 0 0
363363 0 0
364364 0 0
365365 0 0
366366 0 0
367367 − 13.0000i − 0.678594i −0.940679 0.339297i 0.889811π-0.889811\pi
0.940679 0.339297i 0.110189π-0.110189\pi
368368 0 0
369369 0 0
370370 0 0
371371 6.00000 0.311504
372372 0 0
373373 1.00000i 0.0517780i 0.999665 + 0.0258890i 0.00824165π0.00824165\pi
−0.999665 + 0.0258890i 0.991758π0.991758\pi
374374 0 0
375375 0 0
376376 0 0
377377 − 3.00000i − 0.154508i
378378 0 0
379379 16.0000 0.821865 0.410932 0.911666i 0.365203π-0.365203\pi
0.410932 + 0.911666i 0.365203π0.365203\pi
380380 0 0
381381 0 0
382382 0 0
383383 15.0000i 0.766464i 0.923652 + 0.383232i 0.125189π0.125189\pi
−0.923652 + 0.383232i 0.874811π0.874811\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 −15.0000 −0.760530 −0.380265 0.924878i 0.624167π-0.624167\pi
−0.380265 + 0.924878i 0.624167π0.624167\pi
390390 0 0
391391 −18.0000 −0.910299
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 2.00000i 0.100377i 0.998740 + 0.0501886i 0.0159822π0.0159822\pi
−0.998740 + 0.0501886i 0.984018π0.984018\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 5.00000i 0.249068i
404404 0 0
405405 0 0
406406 0 0
407407 6.00000i 0.297409i
408408 0 0
409409 −23.0000 −1.13728 −0.568638 0.822588i 0.692530π-0.692530\pi
−0.568638 + 0.822588i 0.692530π0.692530\pi
410410 0 0
411411 0 0
412412 0 0
413413 − 3.00000i − 0.147620i
414414 0 0
415415 0 0
416416 0 0
417417 0 0
418418 0 0
419419 −9.00000 −0.439679 −0.219839 0.975536i 0.570553π-0.570553\pi
−0.219839 + 0.975536i 0.570553π0.570553\pi
420420 0 0
421421 35.0000 1.70580 0.852898 0.522078i 0.174843π-0.174843\pi
0.852898 + 0.522078i 0.174843π0.174843\pi
422422 0 0
423423 0 0
424424 0 0
425425 0 0
426426 0 0
427427 13.0000i 0.629114i
428428 0 0
429429 0 0
430430 0 0
431431 24.0000 1.15604 0.578020 0.816023i 0.303826π-0.303826\pi
0.578020 + 0.816023i 0.303826π0.303826\pi
432432 0 0
433433 34.0000i 1.63394i 0.576683 + 0.816968i 0.304347π0.304347\pi
−0.576683 + 0.816968i 0.695653π0.695653\pi
434434 0 0
435435 0 0
436436 0 0
437437 12.0000i 0.574038i
438438 0 0
439439 −35.0000 −1.67046 −0.835229 0.549902i 0.814665π-0.814665\pi
−0.835229 + 0.549902i 0.814665π0.814665\pi
440440 0 0
441441 0 0
442442 0 0
443443 9.00000i 0.427603i 0.976877 + 0.213801i 0.0685846π0.0685846\pi
−0.976877 + 0.213801i 0.931415π0.931415\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 18.0000 0.849473 0.424736 0.905317i 0.360367π-0.360367\pi
0.424736 + 0.905317i 0.360367π0.360367\pi
450450 0 0
451451 9.00000 0.423793
452452 0 0
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 − 37.0000i − 1.73079i −0.501093 0.865393i 0.667069π-0.667069\pi
0.501093 0.865393i 0.332931π-0.332931\pi
458458 0 0
459459 0 0
460460 0 0
461461 3.00000 0.139724 0.0698620 0.997557i 0.477744π-0.477744\pi
0.0698620 + 0.997557i 0.477744π0.477744\pi
462462 0 0
463463 19.0000i 0.883005i 0.897260 + 0.441502i 0.145554π0.145554\pi
−0.897260 + 0.441502i 0.854446π0.854446\pi
464464 0 0
465465 0 0
466466 0 0
467467 12.0000i 0.555294i 0.960683 + 0.277647i 0.0895545π0.0895545\pi
−0.960683 + 0.277647i 0.910445π0.910445\pi
468468 0 0
469469 −7.00000 −0.323230
470470 0 0
471471 0 0
472472 0 0
473473 3.00000i 0.137940i
474474 0 0
475475 0 0
476476 0 0
477477 0 0
478478 0 0
479479 −27.0000 −1.23366 −0.616831 0.787096i 0.711584π-0.711584\pi
−0.616831 + 0.787096i 0.711584π0.711584\pi
480480 0 0
481481 −2.00000 −0.0911922
482482 0 0
483483 0 0
484484 0 0
485485 0 0
486486 0 0
487487 32.0000i 1.45006i 0.688718 + 0.725029i 0.258174π0.258174\pi
−0.688718 + 0.725029i 0.741826π0.741826\pi
488488 0 0
489489 0 0
490490 0 0
491491 −3.00000 −0.135388 −0.0676941 0.997706i 0.521564π-0.521564\pi
−0.0676941 + 0.997706i 0.521564π0.521564\pi
492492 0 0
493493 − 18.0000i − 0.810679i
494494 0 0
495495 0 0
496496 0 0
497497 12.0000i 0.538274i
498498 0 0
499499 −5.00000 −0.223831 −0.111915 0.993718i 0.535699π-0.535699\pi
−0.111915 + 0.993718i 0.535699π0.535699\pi
500500 0 0
501501 0 0
502502 0 0
503503 36.0000i 1.60516i 0.596544 + 0.802580i 0.296540π0.296540\pi
−0.596544 + 0.802580i 0.703460π0.703460\pi
504504 0 0
505505 0 0
506506 0 0
507507 0 0
508508 0 0
509509 −39.0000 −1.72864 −0.864322 0.502938i 0.832252π-0.832252\pi
−0.864322 + 0.502938i 0.832252π0.832252\pi
510510 0 0
511511 10.0000 0.442374
512512 0 0
513513 0 0
514514 0 0
515515 0 0
516516 0 0
517517 − 27.0000i − 1.18746i
518518 0 0
519519 0 0
520520 0 0
521521 42.0000 1.84005 0.920027 0.391856i 0.128167π-0.128167\pi
0.920027 + 0.391856i 0.128167π0.128167\pi
522522 0 0
523523 − 8.00000i − 0.349816i −0.984585 0.174908i 0.944037π-0.944037\pi
0.984585 0.174908i 0.0559627π-0.0559627\pi
524524 0 0
525525 0 0
526526 0 0
527527 30.0000i 1.30682i
528528 0 0
529529 14.0000 0.608696
530530 0 0
531531 0 0
532532 0 0
533533 3.00000i 0.129944i
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 0 0
539539 18.0000 0.775315
540540 0 0
541541 −34.0000 −1.46177 −0.730887 0.682498i 0.760893π-0.760893\pi
−0.730887 + 0.682498i 0.760893π0.760893\pi
542542 0 0
543543 0 0
544544 0 0
545545 0 0
546546 0 0
547547 − 13.0000i − 0.555840i −0.960604 0.277920i 0.910355π-0.910355\pi
0.960604 0.277920i 0.0896450π-0.0896450\pi
548548 0 0
549549 0 0
550550 0 0
551551 −12.0000 −0.511217
552552 0 0
553553 11.0000i 0.467768i
554554 0 0
555555 0 0
556556 0 0
557557 − 30.0000i − 1.27114i −0.772043 0.635570i 0.780765π-0.780765\pi
0.772043 0.635570i 0.219235π-0.219235\pi
558558 0 0
559559 −1.00000 −0.0422955
560560 0 0
561561 0 0
562562 0 0
563563 − 9.00000i − 0.379305i −0.981851 0.189652i 0.939264π-0.939264\pi
0.981851 0.189652i 0.0607361π-0.0607361\pi
564564 0 0
565565 0 0
566566 0 0
567567 0 0
568568 0 0
569569 −15.0000 −0.628833 −0.314416 0.949285i 0.601809π-0.601809\pi
−0.314416 + 0.949285i 0.601809π0.601809\pi
570570 0 0
571571 −31.0000 −1.29731 −0.648655 0.761083i 0.724668π-0.724668\pi
−0.648655 + 0.761083i 0.724668π0.724668\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 0 0
577577 − 10.0000i − 0.416305i −0.978096 0.208153i 0.933255π-0.933255\pi
0.978096 0.208153i 0.0667451π-0.0667451\pi
578578 0 0
579579 0 0
580580 0 0
581581 9.00000 0.373383
582582 0 0
583583 18.0000i 0.745484i
584584 0 0
585585 0 0
586586 0 0
587587 15.0000i 0.619116i 0.950881 + 0.309558i 0.100181π0.100181\pi
−0.950881 + 0.309558i 0.899819π0.899819\pi
588588 0 0
589589 20.0000 0.824086
590590 0 0
591591 0 0
592592 0 0
593593 − 6.00000i − 0.246390i −0.992382 0.123195i 0.960686π-0.960686\pi
0.992382 0.123195i 0.0393141π-0.0393141\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 39.0000 1.59350 0.796748 0.604311i 0.206552π-0.206552\pi
0.796748 + 0.604311i 0.206552π0.206552\pi
600600 0 0
601601 35.0000 1.42768 0.713840 0.700309i 0.246954π-0.246954\pi
0.713840 + 0.700309i 0.246954π0.246954\pi
602602 0 0
603603 0 0
604604 0 0
605605 0 0
606606 0 0
607607 41.0000i 1.66414i 0.554672 + 0.832069i 0.312844π0.312844\pi
−0.554672 + 0.832069i 0.687156π0.687156\pi
608608 0 0
609609 0 0
610610 0 0
611611 9.00000 0.364101
612612 0 0
613613 − 26.0000i − 1.05013i −0.851062 0.525065i 0.824041π-0.824041\pi
0.851062 0.525065i 0.175959π-0.175959\pi
614614 0 0
615615 0 0
616616 0 0
617617 3.00000i 0.120775i 0.998175 + 0.0603877i 0.0192337π0.0192337\pi
−0.998175 + 0.0603877i 0.980766π0.980766\pi
618618 0 0
619619 13.0000 0.522514 0.261257 0.965269i 0.415863π-0.415863\pi
0.261257 + 0.965269i 0.415863π0.415863\pi
620620 0 0
621621 0 0
622622 0 0
623623 6.00000i 0.240385i
624624 0 0
625625 0 0
626626 0 0
627627 0 0
628628 0 0
629629 −12.0000 −0.478471
630630 0 0
631631 −16.0000 −0.636950 −0.318475 0.947931i 0.603171π-0.603171\pi
−0.318475 + 0.947931i 0.603171π0.603171\pi
632632 0 0
633633 0 0
634634 0 0
635635 0 0
636636 0 0
637637 6.00000i 0.237729i
638638 0 0
639639 0 0
640640 0 0
641641 −33.0000 −1.30342 −0.651711 0.758468i 0.725948π-0.725948\pi
−0.651711 + 0.758468i 0.725948π0.725948\pi
642642 0 0
643643 − 41.0000i − 1.61688i −0.588577 0.808441i 0.700312π-0.700312\pi
0.588577 0.808441i 0.299688π-0.299688\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 1.00000 00
−1.00000 π\pi
648648 0 0
649649 9.00000 0.353281
650650 0 0
651651 0 0
652652 0 0
653653 21.0000i 0.821794i 0.911682 + 0.410897i 0.134784π0.134784\pi
−0.911682 + 0.410897i 0.865216π0.865216\pi
654654 0 0
655655 0 0
656656 0 0
657657 0 0
658658 0 0
659659 21.0000 0.818044 0.409022 0.912525i 0.365870π-0.365870\pi
0.409022 + 0.912525i 0.365870π0.365870\pi
660660 0 0
661661 11.0000 0.427850 0.213925 0.976850i 0.431375π-0.431375\pi
0.213925 + 0.976850i 0.431375π0.431375\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 − 9.00000i − 0.348481i
668668 0 0
669669 0 0
670670 0 0
671671 −39.0000 −1.50558
672672 0 0
673673 − 11.0000i − 0.424019i −0.977268 0.212009i 0.931999π-0.931999\pi
0.977268 0.212009i 0.0680008π-0.0680008\pi
674674 0 0
675675 0 0
676676 0 0
677677 15.0000i 0.576497i 0.957556 + 0.288248i 0.0930729π0.0930729\pi
−0.957556 + 0.288248i 0.906927π0.906927\pi
678678 0 0
679679 11.0000 0.422141
680680 0 0
681681 0 0
682682 0 0
683683 36.0000i 1.37750i 0.724998 + 0.688751i 0.241841π0.241841\pi
−0.724998 + 0.688751i 0.758159π0.758159\pi
684684 0 0
685685 0 0
686686 0 0
687687 0 0
688688 0 0
689689 −6.00000 −0.228582
690690 0 0
691691 −1.00000 −0.0380418 −0.0190209 0.999819i 0.506055π-0.506055\pi
−0.0190209 + 0.999819i 0.506055π0.506055\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 18.0000i 0.681799i
698698 0 0
699699 0 0
700700 0 0
701701 −6.00000 −0.226617 −0.113308 0.993560i 0.536145π-0.536145\pi
−0.113308 + 0.993560i 0.536145π0.536145\pi
702702 0 0
703703 8.00000i 0.301726i
704704 0 0
705705 0 0
706706 0 0
707707 − 15.0000i − 0.564133i
708708 0 0
709709 25.0000 0.938895 0.469447 0.882960i 0.344453π-0.344453\pi
0.469447 + 0.882960i 0.344453π0.344453\pi
710710 0 0
711711 0 0
712712 0 0
713713 15.0000i 0.561754i
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
720720 0 0
721721 7.00000 0.260694
722722 0 0
723723 0 0
724724 0 0
725725 0 0
726726 0 0
727727 − 37.0000i − 1.37225i −0.727482 0.686127i 0.759309π-0.759309\pi
0.727482 0.686127i 0.240691π-0.240691\pi
728728 0 0
729729 0 0
730730 0 0
731731 −6.00000 −0.221918
732732 0 0
733733 − 23.0000i − 0.849524i −0.905305 0.424762i 0.860358π-0.860358\pi
0.905305 0.424762i 0.139642π-0.139642\pi
734734 0 0
735735 0 0
736736 0 0
737737 − 21.0000i − 0.773545i
738738 0 0
739739 16.0000 0.588570 0.294285 0.955718i 0.404919π-0.404919\pi
0.294285 + 0.955718i 0.404919π0.404919\pi
740740 0 0
741741 0 0
742742 0 0
743743 − 9.00000i − 0.330178i −0.986279 0.165089i 0.947209π-0.947209\pi
0.986279 0.165089i 0.0527911π-0.0527911\pi
744744 0 0
745745 0 0
746746 0 0
747747 0 0
748748 0 0
749749 12.0000 0.438470
750750 0 0
751751 −31.0000 −1.13121 −0.565603 0.824678i 0.691357π-0.691357\pi
−0.565603 + 0.824678i 0.691357π0.691357\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 − 10.0000i − 0.363456i −0.983349 0.181728i 0.941831π-0.941831\pi
0.983349 0.181728i 0.0581691π-0.0581691\pi
758758 0 0
759759 0 0
760760 0 0
761761 27.0000 0.978749 0.489375 0.872074i 0.337225π-0.337225\pi
0.489375 + 0.872074i 0.337225π0.337225\pi
762762 0 0
763763 2.00000i 0.0724049i
764764 0 0
765765 0 0
766766 0 0
767767 3.00000i 0.108324i
768768 0 0
769769 1.00000 0.0360609 0.0180305 0.999837i 0.494260π-0.494260\pi
0.0180305 + 0.999837i 0.494260π0.494260\pi
770770 0 0
771771 0 0
772772 0 0
773773 − 18.0000i − 0.647415i −0.946157 0.323708i 0.895071π-0.895071\pi
0.946157 0.323708i 0.104929π-0.104929\pi
774774 0 0
775775 0 0
776776 0 0
777777 0 0
778778 0 0
779779 12.0000 0.429945
780780 0 0
781781 −36.0000 −1.28818
782782 0 0
783783 0 0
784784 0 0
785785 0 0
786786 0 0
787787 − 43.0000i − 1.53278i −0.642373 0.766392i 0.722050π-0.722050\pi
0.642373 0.766392i 0.277950π-0.277950\pi
788788 0 0
789789 0 0
790790 0 0
791791 9.00000 0.320003
792792 0 0
793793 − 13.0000i − 0.461644i
794794 0 0
795795 0 0
796796 0 0
797797 − 9.00000i − 0.318796i −0.987214 0.159398i 0.949045π-0.949045\pi
0.987214 0.159398i 0.0509554π-0.0509554\pi
798798 0 0
799799 54.0000 1.91038
800800 0 0
801801 0 0
802802 0 0
803803 30.0000i 1.05868i
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 −6.00000 −0.210949 −0.105474 0.994422i 0.533636π-0.533636\pi
−0.105474 + 0.994422i 0.533636π0.533636\pi
810810 0 0
811811 20.0000 0.702295 0.351147 0.936320i 0.385792π-0.385792\pi
0.351147 + 0.936320i 0.385792π0.385792\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 0 0
817817 4.00000i 0.139942i
818818 0 0
819819 0 0
820820 0 0
821821 51.0000 1.77991 0.889956 0.456046i 0.150735π-0.150735\pi
0.889956 + 0.456046i 0.150735π0.150735\pi
822822 0 0
823823 19.0000i 0.662298i 0.943578 + 0.331149i 0.107436π0.107436\pi
−0.943578 + 0.331149i 0.892564π0.892564\pi
824824 0 0
825825 0 0
826826 0 0
827827 − 12.0000i − 0.417281i −0.977992 0.208640i 0.933096π-0.933096\pi
0.977992 0.208640i 0.0669038π-0.0669038\pi
828828 0 0
829829 −50.0000 −1.73657 −0.868286 0.496064i 0.834778π-0.834778\pi
−0.868286 + 0.496064i 0.834778π0.834778\pi
830830 0 0
831831 0 0
832832 0 0
833833 36.0000i 1.24733i
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0 0
839839 9.00000 0.310715 0.155357 0.987858i 0.450347π-0.450347\pi
0.155357 + 0.987858i 0.450347π0.450347\pi
840840 0 0
841841 −20.0000 −0.689655
842842 0 0
843843 0 0
844844 0 0
845845 0 0
846846 0 0
847847 2.00000i 0.0687208i
848848 0 0
849849 0 0
850850 0 0
851851 −6.00000 −0.205677
852852 0 0
853853 13.0000i 0.445112i 0.974920 + 0.222556i 0.0714399π0.0714399\pi
−0.974920 + 0.222556i 0.928560π0.928560\pi
854854 0 0
855855 0 0
856856 0 0
857857 27.0000i 0.922302i 0.887322 + 0.461151i 0.152563π0.152563\pi
−0.887322 + 0.461151i 0.847437π0.847437\pi
858858 0 0
859859 −41.0000 −1.39890 −0.699451 0.714681i 0.746572π-0.746572\pi
−0.699451 + 0.714681i 0.746572π0.746572\pi
860860 0 0
861861 0 0
862862 0 0
863863 − 24.0000i − 0.816970i −0.912765 0.408485i 0.866057π-0.866057\pi
0.912765 0.408485i 0.133943π-0.133943\pi
864864 0 0
865865 0 0
866866 0 0
867867 0 0
868868 0 0
869869 −33.0000 −1.11945
870870 0 0
871871 7.00000 0.237186
872872 0 0
873873 0 0
874874 0 0
875875 0 0
876876 0 0
877877 23.0000i 0.776655i 0.921521 + 0.388327i 0.126947π0.126947\pi
−0.921521 + 0.388327i 0.873053π0.873053\pi
878878 0 0
879879 0 0
880880 0 0
881881 30.0000 1.01073 0.505363 0.862907i 0.331359π-0.331359\pi
0.505363 + 0.862907i 0.331359π0.331359\pi
882882 0 0
883883 4.00000i 0.134611i 0.997732 + 0.0673054i 0.0214402π0.0214402\pi
−0.997732 + 0.0673054i 0.978560π0.978560\pi
884884 0 0
885885 0 0
886886 0 0
887887 21.0000i 0.705111i 0.935791 + 0.352555i 0.114687π0.114687\pi
−0.935791 + 0.352555i 0.885313π0.885313\pi
888888 0 0
889889 −16.0000 −0.536623
890890 0 0
891891 0 0
892892 0 0
893893 − 36.0000i − 1.20469i
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 −15.0000 −0.500278
900900 0 0
901901 −36.0000 −1.19933
902902 0 0
903903 0 0
904904 0 0
905905 0 0
906906 0 0
907907 47.0000i 1.56061i 0.625400 + 0.780305i 0.284936π0.284936\pi
−0.625400 + 0.780305i 0.715064π0.715064\pi
908908 0 0
909909 0 0
910910 0 0
911911 −45.0000 −1.49092 −0.745458 0.666552i 0.767769π-0.767769\pi
−0.745458 + 0.666552i 0.767769π0.767769\pi
912912 0 0
913913 27.0000i 0.893570i
914914 0 0
915915 0 0
916916 0 0
917917 − 21.0000i − 0.693481i
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 0 0
922922 0 0
923923 − 12.0000i − 0.394985i
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 0 0
929929 −27.0000 −0.885841 −0.442921 0.896561i 0.646058π-0.646058\pi
−0.442921 + 0.896561i 0.646058π0.646058\pi
930930 0 0
931931 24.0000 0.786568
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 − 34.0000i − 1.11073i −0.831606 0.555366i 0.812578π-0.812578\pi
0.831606 0.555366i 0.187422π-0.187422\pi
938938 0 0
939939 0 0
940940 0 0
941941 −21.0000 −0.684580 −0.342290 0.939594i 0.611203π-0.611203\pi
−0.342290 + 0.939594i 0.611203π0.611203\pi
942942 0 0
943943 9.00000i 0.293080i
944944 0 0
945945 0 0
946946 0 0
947947 27.0000i 0.877382i 0.898638 + 0.438691i 0.144558π0.144558\pi
−0.898638 + 0.438691i 0.855442π0.855442\pi
948948 0 0
949949 −10.0000 −0.324614
950950 0 0
951951 0 0
952952 0 0
953953 − 54.0000i − 1.74923i −0.484817 0.874616i 0.661114π-0.661114\pi
0.484817 0.874616i 0.338886π-0.338886\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 3.00000 0.0968751
960960 0 0
961961 −6.00000 −0.193548
962962 0 0
963963 0 0
964964 0 0
965965 0 0
966966 0 0
967967 − 43.0000i − 1.38279i −0.722478 0.691393i 0.756997π-0.756997\pi
0.722478 0.691393i 0.243003π-0.243003\pi
968968 0 0
969969 0 0
970970 0 0
971971 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
972972 0 0
973973 5.00000i 0.160293i
974974 0 0
975975 0 0
976976 0 0
977977 − 57.0000i − 1.82359i −0.410644 0.911796i 0.634696π-0.634696\pi
0.410644 0.911796i 0.365304π-0.365304\pi
978978 0 0
979979 −18.0000 −0.575282
980980 0 0
981981 0 0
982982 0 0
983983 − 51.0000i − 1.62665i −0.581811 0.813324i 0.697656π-0.697656\pi
0.581811 0.813324i 0.302344π-0.302344\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 −3.00000 −0.0953945
990990 0 0
991991 8.00000 0.254128 0.127064 0.991894i 0.459445π-0.459445\pi
0.127064 + 0.991894i 0.459445π0.459445\pi
992992 0 0
993993 0 0
994994 0 0
995995 0 0
996996 0 0
997997 − 1.00000i − 0.0316703i −0.999875 0.0158352i 0.994959π-0.994959\pi
0.999875 0.0158352i 0.00504070π-0.00504070\pi
998998 0 0
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8100.2.d.h.649.1 2
3.2 odd 2 8100.2.d.c.649.1 2
5.2 odd 4 8100.2.a.j.1.1 1
5.3 odd 4 324.2.a.c.1.1 1
5.4 even 2 inner 8100.2.d.h.649.2 2
9.2 odd 6 2700.2.s.b.1549.1 4
9.4 even 3 900.2.s.b.349.2 4
9.5 odd 6 2700.2.s.b.2449.2 4
9.7 even 3 900.2.s.b.49.1 4
15.2 even 4 8100.2.a.g.1.1 1
15.8 even 4 324.2.a.a.1.1 1
15.14 odd 2 8100.2.d.c.649.2 2
20.3 even 4 1296.2.a.k.1.1 1
40.3 even 4 5184.2.a.f.1.1 1
40.13 odd 4 5184.2.a.e.1.1 1
45.2 even 12 2700.2.i.b.901.1 2
45.4 even 6 900.2.s.b.349.1 4
45.7 odd 12 900.2.i.b.301.1 2
45.13 odd 12 36.2.e.a.25.1 yes 2
45.14 odd 6 2700.2.s.b.2449.1 4
45.22 odd 12 900.2.i.b.601.1 2
45.23 even 12 108.2.e.a.73.1 2
45.29 odd 6 2700.2.s.b.1549.2 4
45.32 even 12 2700.2.i.b.1801.1 2
45.34 even 6 900.2.s.b.49.2 4
45.38 even 12 108.2.e.a.37.1 2
45.43 odd 12 36.2.e.a.13.1 2
60.23 odd 4 1296.2.a.b.1.1 1
120.53 even 4 5184.2.a.ba.1.1 1
120.83 odd 4 5184.2.a.bb.1.1 1
180.23 odd 12 432.2.i.c.289.1 2
180.43 even 12 144.2.i.a.49.1 2
180.83 odd 12 432.2.i.c.145.1 2
180.103 even 12 144.2.i.a.97.1 2
315.13 even 12 1764.2.j.b.1177.1 2
315.23 even 12 5292.2.i.c.2125.1 2
315.38 odd 12 5292.2.i.a.1549.1 2
315.58 odd 12 1764.2.i.a.1537.1 2
315.68 odd 12 5292.2.i.a.2125.1 2
315.83 odd 12 5292.2.j.a.1765.1 2
315.88 odd 12 1764.2.i.a.373.1 2
315.103 even 12 1764.2.i.c.1537.1 2
315.128 even 12 5292.2.l.a.361.1 2
315.158 even 12 5292.2.l.a.3313.1 2
315.173 odd 12 5292.2.l.c.361.1 2
315.178 even 12 1764.2.i.c.373.1 2
315.193 odd 12 1764.2.l.c.961.1 2
315.223 even 12 1764.2.j.b.589.1 2
315.248 odd 12 5292.2.l.c.3313.1 2
315.263 even 12 5292.2.i.c.1549.1 2
315.268 odd 12 1764.2.l.c.949.1 2
315.283 even 12 1764.2.l.a.961.1 2
315.293 odd 12 5292.2.j.a.3529.1 2
315.313 even 12 1764.2.l.a.949.1 2
360.13 odd 12 576.2.i.f.385.1 2
360.43 even 12 576.2.i.e.193.1 2
360.83 odd 12 1728.2.i.c.577.1 2
360.133 odd 12 576.2.i.f.193.1 2
360.173 even 12 1728.2.i.d.577.1 2
360.203 odd 12 1728.2.i.c.1153.1 2
360.283 even 12 576.2.i.e.385.1 2
360.293 even 12 1728.2.i.d.1153.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.2.e.a.13.1 2 45.43 odd 12
36.2.e.a.25.1 yes 2 45.13 odd 12
108.2.e.a.37.1 2 45.38 even 12
108.2.e.a.73.1 2 45.23 even 12
144.2.i.a.49.1 2 180.43 even 12
144.2.i.a.97.1 2 180.103 even 12
324.2.a.a.1.1 1 15.8 even 4
324.2.a.c.1.1 1 5.3 odd 4
432.2.i.c.145.1 2 180.83 odd 12
432.2.i.c.289.1 2 180.23 odd 12
576.2.i.e.193.1 2 360.43 even 12
576.2.i.e.385.1 2 360.283 even 12
576.2.i.f.193.1 2 360.133 odd 12
576.2.i.f.385.1 2 360.13 odd 12
900.2.i.b.301.1 2 45.7 odd 12
900.2.i.b.601.1 2 45.22 odd 12
900.2.s.b.49.1 4 9.7 even 3
900.2.s.b.49.2 4 45.34 even 6
900.2.s.b.349.1 4 45.4 even 6
900.2.s.b.349.2 4 9.4 even 3
1296.2.a.b.1.1 1 60.23 odd 4
1296.2.a.k.1.1 1 20.3 even 4
1728.2.i.c.577.1 2 360.83 odd 12
1728.2.i.c.1153.1 2 360.203 odd 12
1728.2.i.d.577.1 2 360.173 even 12
1728.2.i.d.1153.1 2 360.293 even 12
1764.2.i.a.373.1 2 315.88 odd 12
1764.2.i.a.1537.1 2 315.58 odd 12
1764.2.i.c.373.1 2 315.178 even 12
1764.2.i.c.1537.1 2 315.103 even 12
1764.2.j.b.589.1 2 315.223 even 12
1764.2.j.b.1177.1 2 315.13 even 12
1764.2.l.a.949.1 2 315.313 even 12
1764.2.l.a.961.1 2 315.283 even 12
1764.2.l.c.949.1 2 315.268 odd 12
1764.2.l.c.961.1 2 315.193 odd 12
2700.2.i.b.901.1 2 45.2 even 12
2700.2.i.b.1801.1 2 45.32 even 12
2700.2.s.b.1549.1 4 9.2 odd 6
2700.2.s.b.1549.2 4 45.29 odd 6
2700.2.s.b.2449.1 4 45.14 odd 6
2700.2.s.b.2449.2 4 9.5 odd 6
5184.2.a.e.1.1 1 40.13 odd 4
5184.2.a.f.1.1 1 40.3 even 4
5184.2.a.ba.1.1 1 120.53 even 4
5184.2.a.bb.1.1 1 120.83 odd 4
5292.2.i.a.1549.1 2 315.38 odd 12
5292.2.i.a.2125.1 2 315.68 odd 12
5292.2.i.c.1549.1 2 315.263 even 12
5292.2.i.c.2125.1 2 315.23 even 12
5292.2.j.a.1765.1 2 315.83 odd 12
5292.2.j.a.3529.1 2 315.293 odd 12
5292.2.l.a.361.1 2 315.128 even 12
5292.2.l.a.3313.1 2 315.158 even 12
5292.2.l.c.361.1 2 315.173 odd 12
5292.2.l.c.3313.1 2 315.248 odd 12
8100.2.a.g.1.1 1 15.2 even 4
8100.2.a.j.1.1 1 5.2 odd 4
8100.2.d.c.649.1 2 3.2 odd 2
8100.2.d.c.649.2 2 15.14 odd 2
8100.2.d.h.649.1 2 1.1 even 1 trivial
8100.2.d.h.649.2 2 5.4 even 2 inner