Properties

Label 507.2.f.c.437.1
Level 507507
Weight 22
Character 507.437
Analytic conductor 4.0484.048
Analytic rank 00
Dimension 44
CM discriminant -3
Inner twists 44

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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] = [507,2,Mod(239,507)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("507.239"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 507=3132 507 = 3 \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 507.f (of order 44, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.048415382484.04841538248
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(i)\Q(i)
Coefficient field: Q(ζ12)\Q(\zeta_{12})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x4x2+1 x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: U(1)[D4]\mathrm{U}(1)[D_{4}]

Embedding invariants

Embedding label 437.1
Root 0.866025+0.500000i-0.866025 + 0.500000i of defining polynomial
Character χ\chi == 507.437
Dual form 507.2.f.c.239.1

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) == q1.73205q3+2.00000iq4+(2.09808+2.09808i)q7+3.00000q93.46410iq124.00000q16+(5.732055.73205i)q19+(3.633973.63397i)q21+5.00000iq255.19615q27+(4.196154.19615i)q28+(7.830137.83013i)q31+6.00000iq36+(1.53590+1.53590i)q37+1.73205iq43+6.92820q481.80385iq49+(9.92820+9.92820i)q578.66025q61+(6.29423+6.29423i)q638.00000iq64+(0.562178+0.562178i)q67+(9.36603+9.36603i)q738.66025iq75+(11.464111.4641i)q76+12.1244q79+9.00000q81+(7.26795+7.26795i)q84+(13.5622+13.5622i)q93+(12.0263+12.0263i)q97+O(q100)q-1.73205 q^{3} +2.00000i q^{4} +(-2.09808 + 2.09808i) q^{7} +3.00000 q^{9} -3.46410i q^{12} -4.00000 q^{16} +(-5.73205 - 5.73205i) q^{19} +(3.63397 - 3.63397i) q^{21} +5.00000i q^{25} -5.19615 q^{27} +(-4.19615 - 4.19615i) q^{28} +(-7.83013 - 7.83013i) q^{31} +6.00000i q^{36} +(-1.53590 + 1.53590i) q^{37} +1.73205i q^{43} +6.92820 q^{48} -1.80385i q^{49} +(9.92820 + 9.92820i) q^{57} -8.66025 q^{61} +(-6.29423 + 6.29423i) q^{63} -8.00000i q^{64} +(0.562178 + 0.562178i) q^{67} +(-9.36603 + 9.36603i) q^{73} -8.66025i q^{75} +(11.4641 - 11.4641i) q^{76} +12.1244 q^{79} +9.00000 q^{81} +(7.26795 + 7.26795i) q^{84} +(13.5622 + 13.5622i) q^{93} +(12.0263 + 12.0263i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+2q7+12q916q1616q19+18q21+4q2814q3120q37+12q57+6q6322q6734q73+32q76+36q81+36q84+30q93+10q97+O(q100) 4 q + 2 q^{7} + 12 q^{9} - 16 q^{16} - 16 q^{19} + 18 q^{21} + 4 q^{28} - 14 q^{31} - 20 q^{37} + 12 q^{57} + 6 q^{63} - 22 q^{67} - 34 q^{73} + 32 q^{76} + 36 q^{81} + 36 q^{84} + 30 q^{93} + 10 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/507Z)×\left(\mathbb{Z}/507\mathbb{Z}\right)^\times.

nn 170170 340340
χ(n)\chi(n) 1-1 e(14)e\left(\frac{1}{4}\right)

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 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
33 −1.73205 −1.00000
44 2.00000i 1.00000i
55 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
66 0 0
77 −2.09808 + 2.09808i −0.792998 + 0.792998i −0.981981 0.188982i 0.939481π-0.939481\pi
0.188982 + 0.981981i 0.439481π0.439481\pi
88 0 0
99 3.00000 1.00000
1010 0 0
1111 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
1212 3.46410i 1.00000i
1313 0 0
1414 0 0
1515 0 0
1616 −4.00000 −1.00000
1717 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1818 0 0
1919 −5.73205 5.73205i −1.31502 1.31502i −0.917663 0.397360i 0.869927π-0.869927\pi
−0.397360 0.917663i 0.630073π-0.630073\pi
2020 0 0
2121 3.63397 3.63397i 0.792998 0.792998i
2222 0 0
2323 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2424 0 0
2525 5.00000i 1.00000i
2626 0 0
2727 −5.19615 −1.00000
2828 −4.19615 4.19615i −0.792998 0.792998i
2929 0 0 1.00000 00
−1.00000 π\pi
3030 0 0
3131 −7.83013 7.83013i −1.40633 1.40633i −0.777714 0.628619i 0.783621π-0.783621\pi
−0.628619 0.777714i 0.716379π-0.716379\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 6.00000i 1.00000i
3737 −1.53590 + 1.53590i −0.252500 + 0.252500i −0.821995 0.569495i 0.807139π-0.807139\pi
0.569495 + 0.821995i 0.307139π0.307139\pi
3838 0 0
3939 0 0
4040 0 0
4141 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
4242 0 0
4343 1.73205i 0.264135i 0.991241 + 0.132068i 0.0421616π0.0421616\pi
−0.991241 + 0.132068i 0.957838π0.957838\pi
4444 0 0
4545 0 0
4646 0 0
4747 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
4848 6.92820 1.00000
4949 1.80385i 0.257693i
5050 0 0
5151 0 0
5252 0 0
5353 0 0 1.00000 00
−1.00000 π\pi
5454 0 0
5555 0 0
5656 0 0
5757 9.92820 + 9.92820i 1.31502 + 1.31502i
5858 0 0
5959 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
6060 0 0
6161 −8.66025 −1.10883 −0.554416 0.832240i 0.687058π-0.687058\pi
−0.554416 + 0.832240i 0.687058π0.687058\pi
6262 0 0
6363 −6.29423 + 6.29423i −0.792998 + 0.792998i
6464 8.00000i 1.00000i
6565 0 0
6666 0 0
6767 0.562178 + 0.562178i 0.0686810 + 0.0686810i 0.740613 0.671932i 0.234535π-0.234535\pi
−0.671932 + 0.740613i 0.734535π0.734535\pi
6868 0 0
6969 0 0
7070 0 0
7171 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
7272 0 0
7373 −9.36603 + 9.36603i −1.09621 + 1.09621i −0.101361 + 0.994850i 0.532320π0.532320\pi
−0.994850 + 0.101361i 0.967680π0.967680\pi
7474 0 0
7575 8.66025i 1.00000i
7676 11.4641 11.4641i 1.31502 1.31502i
7777 0 0
7878 0 0
7979 12.1244 1.36410 0.682048 0.731307i 0.261089π-0.261089\pi
0.682048 + 0.731307i 0.261089π0.261089\pi
8080 0 0
8181 9.00000 1.00000
8282 0 0
8383 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
8484 7.26795 + 7.26795i 0.792998 + 0.792998i
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
9090 0 0
9191 0 0
9292 0 0
9393 13.5622 + 13.5622i 1.40633 + 1.40633i
9494 0 0
9595 0 0
9696 0 0
9797 12.0263 + 12.0263i 1.22108 + 1.22108i 0.967247 + 0.253837i 0.0816925π0.0816925\pi
0.253837 + 0.967247i 0.418307π0.418307\pi
9898 0 0
9999 0 0
100100 −10.0000 −1.00000
101101 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
102102 0 0
103103 15.5885i 1.53598i 0.640464 + 0.767988i 0.278742π0.278742\pi
−0.640464 + 0.767988i 0.721258π0.721258\pi
104104 0 0
105105 0 0
106106 0 0
107107 0 0 1.00000 00
−1.00000 π\pi
108108 10.3923i 1.00000i
109109 5.16987 + 5.16987i 0.495184 + 0.495184i 0.909935 0.414751i 0.136131π-0.136131\pi
−0.414751 + 0.909935i 0.636131π0.636131\pi
110110 0 0
111111 2.66025 2.66025i 0.252500 0.252500i
112112 8.39230 8.39230i 0.792998 0.792998i
113113 0 0 1.00000 00
−1.00000 π\pi
114114 0 0
115115 0 0
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 11.0000i 1.00000i
122122 0 0
123123 0 0
124124 15.6603 15.6603i 1.40633 1.40633i
125125 0 0
126126 0 0
127127 1.00000i 0.0887357i −0.999015 0.0443678i 0.985873π-0.985873\pi
0.999015 0.0443678i 0.0141274π-0.0141274\pi
128128 0 0
129129 3.00000i 0.264135i
130130 0 0
131131 0 0 1.00000 00
−1.00000 π\pi
132132 0 0
133133 24.0526 2.08562
134134 0 0
135135 0 0
136136 0 0
137137 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
138138 0 0
139139 −7.00000 −0.593732 −0.296866 0.954919i 0.595942π-0.595942\pi
−0.296866 + 0.954919i 0.595942π0.595942\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 −12.0000 −1.00000
145145 0 0
146146 0 0
147147 3.12436i 0.257693i
148148 −3.07180 3.07180i −0.252500 0.252500i
149149 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
150150 0 0
151151 −14.1244 + 14.1244i −1.14942 + 1.14942i −0.162758 + 0.986666i 0.552039π0.552039\pi
−0.986666 + 0.162758i 0.947961π0.947961\pi
152152 0 0
153153 0 0
154154 0 0
155155 0 0
156156 0 0
157157 −11.0000 −0.877896 −0.438948 0.898513i 0.644649π-0.644649\pi
−0.438948 + 0.898513i 0.644649π0.644649\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 0 0
163163 −15.0981 + 15.0981i −1.18257 + 1.18257i −0.203497 + 0.979076i 0.565231π0.565231\pi
−0.979076 + 0.203497i 0.934769π0.934769\pi
164164 0 0
165165 0 0
166166 0 0
167167 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
168168 0 0
169169 0 0
170170 0 0
171171 −17.1962 17.1962i −1.31502 1.31502i
172172 −3.46410 −0.264135
173173 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
174174 0 0
175175 −10.4904 10.4904i −0.792998 0.792998i
176176 0 0
177177 0 0
178178 0 0
179179 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
180180 0 0
181181 6.92820i 0.514969i −0.966282 0.257485i 0.917106π-0.917106\pi
0.966282 0.257485i 0.0828937π-0.0828937\pi
182182 0 0
183183 15.0000 1.10883
184184 0 0
185185 0 0
186186 0 0
187187 0 0
188188 0 0
189189 10.9019 10.9019i 0.792998 0.792998i
190190 0 0
191191 0 0 1.00000 00
−1.00000 π\pi
192192 13.8564i 1.00000i
193193 −19.2942 + 19.2942i −1.38883 + 1.38883i −0.561041 + 0.827788i 0.689599π0.689599\pi
−0.827788 + 0.561041i 0.810401π0.810401\pi
194194 0 0
195195 0 0
196196 3.60770 0.257693
197197 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
198198 0 0
199199 17.0000i 1.20510i 0.798082 + 0.602549i 0.205848π0.205848\pi
−0.798082 + 0.602549i 0.794152π0.794152\pi
200200 0 0
201201 −0.973721 0.973721i −0.0686810 0.0686810i
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 0 0
210210 0 0
211211 −25.9808 −1.78859 −0.894295 0.447478i 0.852322π-0.852322\pi
−0.894295 + 0.447478i 0.852322π0.852322\pi
212212 0 0
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 32.8564 2.23044
218218 0 0
219219 16.2224 16.2224i 1.09621 1.09621i
220220 0 0
221221 0 0
222222 0 0
223223 8.80385 + 8.80385i 0.589549 + 0.589549i 0.937509 0.347960i 0.113126π-0.113126\pi
−0.347960 + 0.937509i 0.613126π0.613126\pi
224224 0 0
225225 15.0000i 1.00000i
226226 0 0
227227 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
228228 −19.8564 + 19.8564i −1.31502 + 1.31502i
229229 21.3923 21.3923i 1.41364 1.41364i 0.686743 0.726900i 0.259040π-0.259040\pi
0.726900 0.686743i 0.240960π-0.240960\pi
230230 0 0
231231 0 0
232232 0 0
233233 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
234234 0 0
235235 0 0
236236 0 0
237237 −21.0000 −1.36410
238238 0 0
239239 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
240240 0 0
241241 −6.85641 + 6.85641i −0.441660 + 0.441660i −0.892570 0.450910i 0.851100π-0.851100\pi
0.450910 + 0.892570i 0.351100π0.351100\pi
242242 0 0
243243 −15.5885 −1.00000
244244 17.3205i 1.10883i
245245 0 0
246246 0 0
247247 0 0
248248 0 0
249249 0 0
250250 0 0
251251 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
252252 −12.5885 12.5885i −0.792998 0.792998i
253253 0 0
254254 0 0
255255 0 0
256256 16.0000 1.00000
257257 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
258258 0 0
259259 6.44486i 0.400464i
260260 0 0
261261 0 0
262262 0 0
263263 0 0 1.00000 00
−1.00000 π\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 −1.12436 + 1.12436i −0.0686810 + 0.0686810i
269269 0 0 1.00000 00
−1.00000 π\pi
270270 0 0
271271 6.70577 6.70577i 0.407347 0.407347i −0.473466 0.880812i 0.656997π-0.656997\pi
0.880812 + 0.473466i 0.156997π0.156997\pi
272272 0 0
273273 0 0
274274 0 0
275275 0 0
276276 0 0
277277 20.7846i 1.24883i −0.781094 0.624413i 0.785338π-0.785338\pi
0.781094 0.624413i 0.214662π-0.214662\pi
278278 0 0
279279 −23.4904 23.4904i −1.40633 1.40633i
280280 0 0
281281 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
282282 0 0
283283 25.0000i 1.48610i 0.669238 + 0.743048i 0.266621π0.266621\pi
−0.669238 + 0.743048i 0.733379π0.733379\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 −17.0000 −1.00000
290290 0 0
291291 −20.8301 20.8301i −1.22108 1.22108i
292292 −18.7321 18.7321i −1.09621 1.09621i
293293 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
294294 0 0
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 17.3205 1.00000
301301 −3.63397 3.63397i −0.209459 0.209459i
302302 0 0
303303 0 0
304304 22.9282 + 22.9282i 1.31502 + 1.31502i
305305 0 0
306306 0 0
307307 16.6340 16.6340i 0.949351 0.949351i −0.0494267 0.998778i 0.515739π-0.515739\pi
0.998778 + 0.0494267i 0.0157394π0.0157394\pi
308308 0 0
309309 27.0000i 1.53598i
310310 0 0
311311 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
312312 0 0
313313 −32.9090 −1.86012 −0.930062 0.367402i 0.880247π-0.880247\pi
−0.930062 + 0.367402i 0.880247π0.880247\pi
314314 0 0
315315 0 0
316316 24.2487i 1.36410i
317317 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
318318 0 0
319319 0 0
320320 0 0
321321 0 0
322322 0 0
323323 0 0
324324 18.0000i 1.00000i
325325 0 0
326326 0 0
327327 −8.95448 8.95448i −0.495184 0.495184i
328328 0 0
329329 0 0
330330 0 0
331331 25.0263 + 25.0263i 1.37557 + 1.37557i 0.851957 + 0.523612i 0.175416π0.175416\pi
0.523612 + 0.851957i 0.324584π0.324584\pi
332332 0 0
333333 −4.60770 + 4.60770i −0.252500 + 0.252500i
334334 0 0
335335 0 0
336336 −14.5359 + 14.5359i −0.792998 + 0.792998i
337337 29.0000i 1.57973i −0.613280 0.789865i 0.710150π-0.710150\pi
0.613280 0.789865i 0.289850π-0.289850\pi
338338 0 0
339339 0 0
340340 0 0
341341 0 0
342342 0 0
343343 −10.9019 10.9019i −0.588649 0.588649i
344344 0 0
345345 0 0
346346 0 0
347347 0 0 1.00000 00
−1.00000 π\pi
348348 0 0
349349 3.22243 3.22243i 0.172493 0.172493i −0.615581 0.788074i 0.711079π-0.711079\pi
0.788074 + 0.615581i 0.211079π0.211079\pi
350350 0 0
351351 0 0
352352 0 0
353353 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
360360 0 0
361361 46.7128i 2.45857i
362362 0 0
363363 19.0526i 1.00000i
364364 0 0
365365 0 0
366366 0 0
367367 31.0000 1.61819 0.809093 0.587680i 0.199959π-0.199959\pi
0.809093 + 0.587680i 0.199959π0.199959\pi
368368 0 0
369369 0 0
370370 0 0
371371 0 0
372372 −27.1244 + 27.1244i −1.40633 + 1.40633i
373373 36.3731 1.88333 0.941663 0.336557i 0.109263π-0.109263\pi
0.941663 + 0.336557i 0.109263π0.109263\pi
374374 0 0
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 −12.4378 12.4378i −0.638888 0.638888i 0.311393 0.950281i 0.399204π-0.399204\pi
−0.950281 + 0.311393i 0.899204π0.899204\pi
380380 0 0
381381 1.73205i 0.0887357i
382382 0 0
383383 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
384384 0 0
385385 0 0
386386 0 0
387387 5.19615i 0.264135i
388388 −24.0526 + 24.0526i −1.22108 + 1.22108i
389389 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
390390 0 0
391391 0 0
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 20.4186 20.4186i 1.02478 1.02478i 0.0250943 0.999685i 0.492011π-0.492011\pi
0.999685 0.0250943i 0.00798860π-0.00798860\pi
398398 0 0
399399 −41.6603 −2.08562
400400 20.0000i 1.00000i
401401 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
402402 0 0
403403 0 0
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 2.50962 + 2.50962i 0.124093 + 0.124093i 0.766426 0.642333i 0.222033π-0.222033\pi
−0.642333 + 0.766426i 0.722033π0.722033\pi
410410 0 0
411411 0 0
412412 −31.1769 −1.53598
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 12.1244 0.593732
418418 0 0
419419 0 0 1.00000 00
−1.00000 π\pi
420420 0 0
421421 27.6865 + 27.6865i 1.34936 + 1.34936i 0.886357 + 0.463002i 0.153228π0.153228\pi
0.463002 + 0.886357i 0.346772π0.346772\pi
422422 0 0
423423 0 0
424424 0 0
425425 0 0
426426 0 0
427427 18.1699 18.1699i 0.879302 0.879302i
428428 0 0
429429 0 0
430430 0 0
431431 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
432432 20.7846 1.00000
433433 35.0000i 1.68199i −0.541041 0.840996i 0.681970π-0.681970\pi
0.541041 0.840996i 0.318030π-0.318030\pi
434434 0 0
435435 0 0
436436 −10.3397 + 10.3397i −0.495184 + 0.495184i
437437 0 0
438438 0 0
439439 39.8372i 1.90132i −0.310228 0.950662i 0.600405π-0.600405\pi
0.310228 0.950662i 0.399595π-0.399595\pi
440440 0 0
441441 5.41154i 0.257693i
442442 0 0
443443 0 0 1.00000 00
−1.00000 π\pi
444444 5.32051 + 5.32051i 0.252500 + 0.252500i
445445 0 0
446446 0 0
447447 0 0
448448 16.7846 + 16.7846i 0.792998 + 0.792998i
449449 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
450450 0 0
451451 0 0
452452 0 0
453453 24.4641 24.4641i 1.14942 1.14942i
454454 0 0
455455 0 0
456456 0 0
457457 26.5622 + 26.5622i 1.24253 + 1.24253i 0.958950 + 0.283577i 0.0915211π0.0915211\pi
0.283577 + 0.958950i 0.408479π0.408479\pi
458458 0 0
459459 0 0
460460 0 0
461461 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
462462 0 0
463463 −22.3660 + 22.3660i −1.03944 + 1.03944i −0.0402476 + 0.999190i 0.512815π0.512815\pi
−0.999190 + 0.0402476i 0.987185π0.987185\pi
464464 0 0
465465 0 0
466466 0 0
467467 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
468468 0 0
469469 −2.35898 −0.108928
470470 0 0
471471 19.0526 0.877896
472472 0 0
473473 0 0
474474 0 0
475475 28.6603 28.6603i 1.31502 1.31502i
476476 0 0
477477 0 0
478478 0 0
479479 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
480480 0 0
481481 0 0
482482 0 0
483483 0 0
484484 22.0000 1.00000
485485 0 0
486486 0 0
487487 20.2679 + 20.2679i 0.918428 + 0.918428i 0.996915 0.0784867i 0.0250088π-0.0250088\pi
−0.0784867 + 0.996915i 0.525009π0.525009\pi
488488 0 0
489489 26.1506 26.1506i 1.18257 1.18257i
490490 0 0
491491 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 31.3205 + 31.3205i 1.40633 + 1.40633i
497497 0 0
498498 0 0
499499 0.411543 + 0.411543i 0.0184232 + 0.0184232i 0.716258 0.697835i 0.245853π-0.245853\pi
−0.697835 + 0.716258i 0.745853π0.745853\pi
500500 0 0
501501 0 0
502502 0 0
503503 0 0 1.00000 00
−1.00000 π\pi
504504 0 0
505505 0 0
506506 0 0
507507 0 0
508508 2.00000 0.0887357
509509 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
510510 0 0
511511 39.3013i 1.73859i
512512 0 0
513513 29.7846 + 29.7846i 1.31502 + 1.31502i
514514 0 0
515515 0 0
516516 6.00000 0.264135
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 0 0 1.00000 00
−1.00000 π\pi
522522 0 0
523523 −8.00000 −0.349816 −0.174908 0.984585i 0.555963π-0.555963\pi
−0.174908 + 0.984585i 0.555963π0.555963\pi
524524 0 0
525525 18.1699 + 18.1699i 0.792998 + 0.792998i
526526 0 0
527527 0 0
528528 0 0
529529 −23.0000 −1.00000
530530 0 0
531531 0 0
532532 48.1051i 2.08562i
533533 0 0
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 0 0
539539 0 0
540540 0 0
541541 13.1506 13.1506i 0.565390 0.565390i −0.365444 0.930834i 0.619083π-0.619083\pi
0.930834 + 0.365444i 0.119083π0.119083\pi
542542 0 0
543543 12.0000i 0.514969i
544544 0 0
545545 0 0
546546 0 0
547547 41.0000 1.75303 0.876517 0.481371i 0.159861π-0.159861\pi
0.876517 + 0.481371i 0.159861π0.159861\pi
548548 0 0
549549 −25.9808 −1.10883
550550 0 0
551551 0 0
552552 0 0
553553 −25.4378 + 25.4378i −1.08173 + 1.08173i
554554 0 0
555555 0 0
556556 14.0000i 0.593732i
557557 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 0 0
563563 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
564564 0 0
565565 0 0
566566 0 0
567567 −18.8827 + 18.8827i −0.792998 + 0.792998i
568568 0 0
569569 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
570570 0 0
571571 16.0000i 0.669579i −0.942293 0.334790i 0.891335π-0.891335\pi
0.942293 0.334790i 0.108665π-0.108665\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 24.0000i 1.00000i
577577 −16.0718 16.0718i −0.669078 0.669078i 0.288425 0.957503i 0.406868π-0.406868\pi
−0.957503 + 0.288425i 0.906868π0.906868\pi
578578 0 0
579579 33.4186 33.4186i 1.38883 1.38883i
580580 0 0
581581 0 0
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
588588 −6.24871 −0.257693
589589 89.7654i 3.69872i
590590 0 0
591591 0 0
592592 6.14359 6.14359i 0.252500 0.252500i
593593 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
594594 0 0
595595 0 0
596596 0 0
597597 29.4449i 1.20510i
598598 0 0
599599 0 0 1.00000 00
−1.00000 π\pi
600600 0 0
601601 41.5692 1.69564 0.847822 0.530281i 0.177914π-0.177914\pi
0.847822 + 0.530281i 0.177914π0.177914\pi
602602 0 0
603603 1.68653 + 1.68653i 0.0686810 + 0.0686810i
604604 −28.2487 28.2487i −1.14942 1.14942i
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 −34.9545 34.9545i −1.41180 1.41180i −0.747208 0.664590i 0.768606π-0.768606\pi
−0.664590 0.747208i 0.731394π-0.731394\pi
614614 0 0
615615 0 0
616616 0 0
617617 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
618618 0 0
619619 −31.8827 + 31.8827i −1.28147 + 1.28147i −0.341644 + 0.939829i 0.610984π0.610984\pi
−0.939829 + 0.341644i 0.889016π0.889016\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 −25.0000 −1.00000
626626 0 0
627627 0 0
628628 22.0000i 0.877896i
629629 0 0
630630 0 0
631631 −24.6147 + 24.6147i −0.979897 + 0.979897i −0.999802 0.0199047i 0.993664π-0.993664\pi
0.0199047 + 0.999802i 0.493664π0.493664\pi
632632 0 0
633633 45.0000 1.78859
634634 0 0
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 0 0
641641 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
642642 0 0
643643 −13.9737 13.9737i −0.551070 0.551070i 0.375680 0.926750i 0.377409π-0.377409\pi
−0.926750 + 0.375680i 0.877409π0.877409\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
648648 0 0
649649 0 0
650650 0 0
651651 −56.9090 −2.23044
652652 −30.1962 30.1962i −1.18257 1.18257i
653653 0 0 1.00000 00
−1.00000 π\pi
654654 0 0
655655 0 0
656656 0 0
657657 −28.0981 + 28.0981i −1.09621 + 1.09621i
658658 0 0
659659 0 0 1.00000 00
−1.00000 π\pi
660660 0 0
661661 −32.2942 + 32.2942i −1.25610 + 1.25610i −0.303160 + 0.952940i 0.598042π0.598042\pi
−0.952940 + 0.303160i 0.901958π0.901958\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 −15.2487 15.2487i −0.589549 0.589549i
670670 0 0
671671 0 0
672672 0 0
673673 50.2295i 1.93620i 0.250557 + 0.968102i 0.419386π0.419386\pi
−0.250557 + 0.968102i 0.580614π0.580614\pi
674674 0 0
675675 25.9808i 1.00000i
676676 0 0
677677 0 0 1.00000 00
−1.00000 π\pi
678678 0 0
679679 −50.4641 −1.93663
680680 0 0
681681 0 0
682682 0 0
683683 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
684684 34.3923 34.3923i 1.31502 1.31502i
685685 0 0
686686 0 0
687687 −37.0526 + 37.0526i −1.41364 + 1.41364i
688688 6.92820i 0.264135i
689689 0 0
690690 0 0
691691 4.04552 + 4.04552i 0.153899 + 0.153899i 0.779857 0.625958i 0.215292π-0.215292\pi
−0.625958 + 0.779857i 0.715292π0.715292\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 0 0
698698 0 0
699699 0 0
700700 20.9808 20.9808i 0.792998 0.792998i
701701 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
702702 0 0
703703 17.6077 0.664087
704704 0 0
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 23.9019 23.9019i 0.897656 0.897656i −0.0975728 0.995228i 0.531108π-0.531108\pi
0.995228 + 0.0975728i 0.0311079π0.0311079\pi
710710 0 0
711711 36.3731 1.36410
712712 0 0
713713 0 0
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 −32.7058 32.7058i −1.21803 1.21803i
722722 0 0
723723 11.8756 11.8756i 0.441660 0.441660i
724724 13.8564 0.514969
725725 0 0
726726 0 0
727727 49.0000i 1.81731i 0.417548 + 0.908655i 0.362889π0.362889\pi
−0.417548 + 0.908655i 0.637111π0.637111\pi
728728 0 0
729729 27.0000 1.00000
730730 0 0
731731 0 0
732732 30.0000i 1.10883i
733733 −30.3468 30.3468i −1.12088 1.12088i −0.991609 0.129275i 0.958735π-0.958735\pi
−0.129275 0.991609i 0.541265π-0.541265\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 33.9808 33.9808i 1.25000 1.25000i 0.294285 0.955718i 0.404919π-0.404919\pi
0.955718 0.294285i 0.0950814π-0.0950814\pi
740740 0 0
741741 0 0
742742 0 0
743743 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
744744 0 0
745745 0 0
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 17.3205i 0.632034i −0.948753 0.316017i 0.897654π-0.897654\pi
0.948753 0.316017i 0.102346π-0.102346\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 21.8038 + 21.8038i 0.792998 + 0.792998i
757757 −48.4974 −1.76267 −0.881334 0.472493i 0.843354π-0.843354\pi
−0.881334 + 0.472493i 0.843354π0.843354\pi
758758 0 0
759759 0 0
760760 0 0
761761 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
762762 0 0
763763 −21.6936 −0.785360
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 −27.7128 −1.00000
769769 −26.7128 26.7128i −0.963289 0.963289i 0.0360609 0.999350i 0.488519π-0.488519\pi
−0.999350 + 0.0360609i 0.988519π0.988519\pi
770770 0 0
771771 0 0
772772 −38.5885 38.5885i −1.38883 1.38883i
773773 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
774774 0 0
775775 39.1506 39.1506i 1.40633 1.40633i
776776 0 0
777777 11.1628i 0.400464i
778778 0 0
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 7.21539i 0.257693i
785785 0 0
786786 0 0
787787 −37.6147 + 37.6147i −1.34082 + 1.34082i −0.445577 + 0.895244i 0.647001π0.647001\pi
−0.895244 + 0.445577i 0.852999π0.852999\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 0 0
794794 0 0
795795 0 0
796796 −34.0000 −1.20510
797797 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
798798 0 0
799799 0 0
800800 0 0
801801 0 0
802802 0 0
803803 0 0
804804 1.94744 1.94744i 0.0686810 0.0686810i
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 0 0 1.00000 00
−1.00000 π\pi
810810 0 0
811811 −17.3468 17.3468i −0.609128 0.609128i 0.333590 0.942718i 0.391740π-0.391740\pi
−0.942718 + 0.333590i 0.891740π0.891740\pi
812812 0 0
813813 −11.6147 + 11.6147i −0.407347 + 0.407347i
814814 0 0
815815 0 0
816816 0 0
817817 9.92820 9.92820i 0.347344 0.347344i
818818 0 0
819819 0 0
820820 0 0
821821 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
822822 0 0
823823 24.2487i 0.845257i 0.906303 + 0.422628i 0.138892π0.138892\pi
−0.906303 + 0.422628i 0.861108π0.861108\pi
824824 0 0
825825 0 0
826826 0 0
827827 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
828828 0 0
829829 53.0000i 1.84077i −0.391018 0.920383i 0.627877π-0.627877\pi
0.391018 0.920383i 0.372123π-0.372123\pi
830830 0 0
831831 36.0000i 1.24883i
832832 0 0
833833 0 0
834834 0 0
835835 0 0
836836 0 0
837837 40.6865 + 40.6865i 1.40633 + 1.40633i
838838 0 0
839839 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
840840 0 0
841841 29.0000 1.00000
842842 0 0
843843 0 0
844844 51.9615i 1.78859i
845845 0 0
846846 0 0
847847 23.0788 + 23.0788i 0.792998 + 0.792998i
848848 0 0
849849 43.3013i 1.48610i
850850 0 0
851851 0 0
852852 0 0
853853 −5.88269 + 5.88269i −0.201419 + 0.201419i −0.800608 0.599189i 0.795490π-0.795490\pi
0.599189 + 0.800608i 0.295490π0.295490\pi
854854 0 0
855855 0 0
856856 0 0
857857 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
858858 0 0
859859 57.1577 1.95019 0.975097 0.221777i 0.0711857π-0.0711857\pi
0.975097 + 0.221777i 0.0711857π0.0711857\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
864864 0 0
865865 0 0
866866 0 0
867867 29.4449 1.00000
868868 65.7128i 2.23044i
869869 0 0
870870 0 0
871871 0 0
872872 0 0
873873 36.0788 + 36.0788i 1.22108 + 1.22108i
874874 0 0
875875 0 0
876876 32.4449 + 32.4449i 1.09621 + 1.09621i
877877 −41.2487 41.2487i −1.39287 1.39287i −0.818821 0.574049i 0.805372π-0.805372\pi
−0.574049 0.818821i 0.694628π-0.694628\pi
878878 0 0
879879 0 0
880880 0 0
881881 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
882882 0 0
883883 55.0000i 1.85090i −0.378873 0.925449i 0.623688π-0.623688\pi
0.378873 0.925449i 0.376312π-0.376312\pi
884884 0 0
885885 0 0
886886 0 0
887887 0 0 1.00000 00
−1.00000 π\pi
888888 0 0
889889 2.09808 + 2.09808i 0.0703672 + 0.0703672i
890890 0 0
891891 0 0
892892 −17.6077 + 17.6077i −0.589549 + 0.589549i
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 −30.0000 −1.00000
901901 0 0
902902 0 0
903903 6.29423 + 6.29423i 0.209459 + 0.209459i
904904 0 0
905905 0 0
906906 0 0
907907 40.0000i 1.32818i −0.747653 0.664089i 0.768820π-0.768820\pi
0.747653 0.664089i 0.231180π-0.231180\pi
908908 0 0
909909 0 0
910910 0 0
911911 0 0 1.00000 00
−1.00000 π\pi
912912 −39.7128 39.7128i −1.31502 1.31502i
913913 0 0
914914 0 0
915915 0 0
916916 42.7846 + 42.7846i 1.41364 + 1.41364i
917917 0 0
918918 0 0
919919 −31.1769 −1.02843 −0.514216 0.857661i 0.671917π-0.671917\pi
−0.514216 + 0.857661i 0.671917π0.671917\pi
920920 0 0
921921 −28.8109 + 28.8109i −0.949351 + 0.949351i
922922 0 0
923923 0 0
924924 0 0
925925 −7.67949 7.67949i −0.252500 0.252500i
926926 0 0
927927 46.7654i 1.53598i
928928 0 0
929929 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
930930 0 0
931931 −10.3397 + 10.3397i −0.338871 + 0.338871i
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 −55.4256 −1.81068 −0.905338 0.424691i 0.860383π-0.860383\pi
−0.905338 + 0.424691i 0.860383π0.860383\pi
938938 0 0
939939 57.0000 1.86012
940940 0 0
941941 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
948948 42.0000i 1.36410i
949949 0 0
950950 0 0
951951 0 0
952952 0 0
953953 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 91.6218i 2.95554i
962962 0 0
963963 0 0
964964 −13.7128 13.7128i −0.441660 0.441660i
965965 0 0
966966 0 0
967967 19.4449 + 19.4449i 0.625305 + 0.625305i 0.946883 0.321578i 0.104213π-0.104213\pi
−0.321578 + 0.946883i 0.604213π0.604213\pi
968968 0 0
969969 0 0
970970 0 0
971971 0 0 1.00000 00
−1.00000 π\pi
972972 31.1769i 1.00000i
973973 14.6865 14.6865i 0.470829 0.470829i
974974 0 0
975975 0 0
976976 34.6410 1.10883
977977 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
978978 0 0
979979 0 0
980980 0 0
981981 15.5096 + 15.5096i 0.495184 + 0.495184i
982982 0 0
983983 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 44.0000 1.39771 0.698853 0.715265i 0.253694π-0.253694\pi
0.698853 + 0.715265i 0.253694π0.253694\pi
992992 0 0
993993 −43.3468 43.3468i −1.37557 1.37557i
994994 0 0
995995 0 0
996996 0 0
997997 −59.0000 −1.86855 −0.934274 0.356555i 0.883951π-0.883951\pi
−0.934274 + 0.356555i 0.883951π0.883951\pi
998998 0 0
999999 7.98076 7.98076i 0.252500 0.252500i
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 507.2.f.c.437.1 4
3.2 odd 2 CM 507.2.f.c.437.1 4
13.2 odd 12 39.2.k.a.32.1 yes 4
13.3 even 3 507.2.k.b.488.1 4
13.4 even 6 507.2.k.c.89.1 4
13.5 odd 4 inner 507.2.f.c.239.1 4
13.6 odd 12 507.2.k.b.80.1 4
13.7 odd 12 507.2.k.a.80.1 4
13.8 odd 4 507.2.f.b.239.1 4
13.9 even 3 39.2.k.a.11.1 4
13.10 even 6 507.2.k.a.488.1 4
13.11 odd 12 507.2.k.c.188.1 4
13.12 even 2 507.2.f.b.437.1 4
39.2 even 12 39.2.k.a.32.1 yes 4
39.5 even 4 inner 507.2.f.c.239.1 4
39.8 even 4 507.2.f.b.239.1 4
39.11 even 12 507.2.k.c.188.1 4
39.17 odd 6 507.2.k.c.89.1 4
39.20 even 12 507.2.k.a.80.1 4
39.23 odd 6 507.2.k.a.488.1 4
39.29 odd 6 507.2.k.b.488.1 4
39.32 even 12 507.2.k.b.80.1 4
39.35 odd 6 39.2.k.a.11.1 4
39.38 odd 2 507.2.f.b.437.1 4
52.15 even 12 624.2.cn.b.305.1 4
52.35 odd 6 624.2.cn.b.401.1 4
65.2 even 12 975.2.bp.a.149.1 4
65.9 even 6 975.2.bo.c.401.1 4
65.22 odd 12 975.2.bp.d.674.1 4
65.28 even 12 975.2.bp.d.149.1 4
65.48 odd 12 975.2.bp.a.674.1 4
65.54 odd 12 975.2.bo.c.851.1 4
156.35 even 6 624.2.cn.b.401.1 4
156.119 odd 12 624.2.cn.b.305.1 4
195.2 odd 12 975.2.bp.a.149.1 4
195.74 odd 6 975.2.bo.c.401.1 4
195.113 even 12 975.2.bp.a.674.1 4
195.119 even 12 975.2.bo.c.851.1 4
195.152 even 12 975.2.bp.d.674.1 4
195.158 odd 12 975.2.bp.d.149.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.k.a.11.1 4 13.9 even 3
39.2.k.a.11.1 4 39.35 odd 6
39.2.k.a.32.1 yes 4 13.2 odd 12
39.2.k.a.32.1 yes 4 39.2 even 12
507.2.f.b.239.1 4 13.8 odd 4
507.2.f.b.239.1 4 39.8 even 4
507.2.f.b.437.1 4 13.12 even 2
507.2.f.b.437.1 4 39.38 odd 2
507.2.f.c.239.1 4 13.5 odd 4 inner
507.2.f.c.239.1 4 39.5 even 4 inner
507.2.f.c.437.1 4 1.1 even 1 trivial
507.2.f.c.437.1 4 3.2 odd 2 CM
507.2.k.a.80.1 4 13.7 odd 12
507.2.k.a.80.1 4 39.20 even 12
507.2.k.a.488.1 4 13.10 even 6
507.2.k.a.488.1 4 39.23 odd 6
507.2.k.b.80.1 4 13.6 odd 12
507.2.k.b.80.1 4 39.32 even 12
507.2.k.b.488.1 4 13.3 even 3
507.2.k.b.488.1 4 39.29 odd 6
507.2.k.c.89.1 4 13.4 even 6
507.2.k.c.89.1 4 39.17 odd 6
507.2.k.c.188.1 4 13.11 odd 12
507.2.k.c.188.1 4 39.11 even 12
624.2.cn.b.305.1 4 52.15 even 12
624.2.cn.b.305.1 4 156.119 odd 12
624.2.cn.b.401.1 4 52.35 odd 6
624.2.cn.b.401.1 4 156.35 even 6
975.2.bo.c.401.1 4 65.9 even 6
975.2.bo.c.401.1 4 195.74 odd 6
975.2.bo.c.851.1 4 65.54 odd 12
975.2.bo.c.851.1 4 195.119 even 12
975.2.bp.a.149.1 4 65.2 even 12
975.2.bp.a.149.1 4 195.2 odd 12
975.2.bp.a.674.1 4 65.48 odd 12
975.2.bp.a.674.1 4 195.113 even 12
975.2.bp.d.149.1 4 65.28 even 12
975.2.bp.d.149.1 4 195.158 odd 12
975.2.bp.d.674.1 4 65.22 odd 12
975.2.bp.d.674.1 4 195.152 even 12