Properties

Label 7800.2.a.bq.1.2
Level 78007800
Weight 22
Character 7800.1
Self dual yes
Analytic conductor 62.28362.283
Analytic rank 00
Dimension 33
CM no
Inner twists 11

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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] = [7800,2,Mod(1,7800)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7800, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) 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("7800.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 7800=2335213 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7800.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,0,3,0,0,0,0,0,3,0,0,0,3,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 62.283313576662.2833135766
Analytic rank: 00
Dimension: 33
Coefficient field: 3.3.2700.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x315x20 x^{3} - 15x - 20 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.61323-1.61323 of defining polynomial
Character χ\chi == 7800.1

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+1.00000q3+1.61323q7+1.00000q9+1.61323q11+1.00000q13+6.17103q17+5.17103q19+1.61323q21+8.34206q23+1.00000q27+1.00000q29+1.61323q31+1.61323q331.17103q37+1.00000q393.17103q412.00000q431.55780q474.39749q49+6.17103q517.34206q53+5.17103q574.72883q59+10.5131q61+1.61323q63+4.78426q67+8.34206q691.17103q710.773540q73+2.60251q772.39749q79+1.00000q818.72883q83+1.00000q876.34206q89+1.61323q91+1.61323q934.34206q97+1.61323q99+O(q100)q+1.00000 q^{3} +1.61323 q^{7} +1.00000 q^{9} +1.61323 q^{11} +1.00000 q^{13} +6.17103 q^{17} +5.17103 q^{19} +1.61323 q^{21} +8.34206 q^{23} +1.00000 q^{27} +1.00000 q^{29} +1.61323 q^{31} +1.61323 q^{33} -1.17103 q^{37} +1.00000 q^{39} -3.17103 q^{41} -2.00000 q^{43} -1.55780 q^{47} -4.39749 q^{49} +6.17103 q^{51} -7.34206 q^{53} +5.17103 q^{57} -4.72883 q^{59} +10.5131 q^{61} +1.61323 q^{63} +4.78426 q^{67} +8.34206 q^{69} -1.17103 q^{71} -0.773540 q^{73} +2.60251 q^{77} -2.39749 q^{79} +1.00000 q^{81} -8.72883 q^{83} +1.00000 q^{87} -6.34206 q^{89} +1.61323 q^{91} +1.61323 q^{93} -4.34206 q^{97} +1.61323 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+3q3+3q9+3q13+6q17+3q19+3q27+3q29+9q37+3q39+3q416q43+3q47+9q49+6q51+3q53+3q57+6q596q613q67++12q97+O(q100) 3 q + 3 q^{3} + 3 q^{9} + 3 q^{13} + 6 q^{17} + 3 q^{19} + 3 q^{27} + 3 q^{29} + 9 q^{37} + 3 q^{39} + 3 q^{41} - 6 q^{43} + 3 q^{47} + 9 q^{49} + 6 q^{51} + 3 q^{53} + 3 q^{57} + 6 q^{59} - 6 q^{61} - 3 q^{67}+ \cdots + 12 q^{97}+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 1.00000 0.577350
44 0 0
55 0 0
66 0 0
77 1.61323 0.609744 0.304872 0.952393i 0.401386π-0.401386\pi
0.304872 + 0.952393i 0.401386π0.401386\pi
88 0 0
99 1.00000 0.333333
1010 0 0
1111 1.61323 0.486407 0.243204 0.969975i 0.421802π-0.421802\pi
0.243204 + 0.969975i 0.421802π0.421802\pi
1212 0 0
1313 1.00000 0.277350
1414 0 0
1515 0 0
1616 0 0
1717 6.17103 1.49669 0.748347 0.663307i 0.230848π-0.230848\pi
0.748347 + 0.663307i 0.230848π0.230848\pi
1818 0 0
1919 5.17103 1.18632 0.593158 0.805086i 0.297881π-0.297881\pi
0.593158 + 0.805086i 0.297881π0.297881\pi
2020 0 0
2121 1.61323 0.352036
2222 0 0
2323 8.34206 1.73944 0.869720 0.493546i 0.164299π-0.164299\pi
0.869720 + 0.493546i 0.164299π0.164299\pi
2424 0 0
2525 0 0
2626 0 0
2727 1.00000 0.192450
2828 0 0
2929 1.00000 0.185695 0.0928477 0.995680i 0.470403π-0.470403\pi
0.0928477 + 0.995680i 0.470403π0.470403\pi
3030 0 0
3131 1.61323 0.289745 0.144872 0.989450i 0.453723π-0.453723\pi
0.144872 + 0.989450i 0.453723π0.453723\pi
3232 0 0
3333 1.61323 0.280827
3434 0 0
3535 0 0
3636 0 0
3737 −1.17103 −0.192516 −0.0962581 0.995356i 0.530687π-0.530687\pi
−0.0962581 + 0.995356i 0.530687π0.530687\pi
3838 0 0
3939 1.00000 0.160128
4040 0 0
4141 −3.17103 −0.495232 −0.247616 0.968858i 0.579647π-0.579647\pi
−0.247616 + 0.968858i 0.579647π0.579647\pi
4242 0 0
4343 −2.00000 −0.304997 −0.152499 0.988304i 0.548732π-0.548732\pi
−0.152499 + 0.988304i 0.548732π0.548732\pi
4444 0 0
4545 0 0
4646 0 0
4747 −1.55780 −0.227228 −0.113614 0.993525i 0.536243π-0.536243\pi
−0.113614 + 0.993525i 0.536243π0.536243\pi
4848 0 0
4949 −4.39749 −0.628213
5050 0 0
5151 6.17103 0.864117
5252 0 0
5353 −7.34206 −1.00851 −0.504255 0.863555i 0.668233π-0.668233\pi
−0.504255 + 0.863555i 0.668233π0.668233\pi
5454 0 0
5555 0 0
5656 0 0
5757 5.17103 0.684920
5858 0 0
5959 −4.72883 −0.615641 −0.307821 0.951444i 0.599600π-0.599600\pi
−0.307821 + 0.951444i 0.599600π0.599600\pi
6060 0 0
6161 10.5131 1.34606 0.673032 0.739614i 0.264992π-0.264992\pi
0.673032 + 0.739614i 0.264992π0.264992\pi
6262 0 0
6363 1.61323 0.203248
6464 0 0
6565 0 0
6666 0 0
6767 4.78426 0.584490 0.292245 0.956343i 0.405598π-0.405598\pi
0.292245 + 0.956343i 0.405598π0.405598\pi
6868 0 0
6969 8.34206 1.00427
7070 0 0
7171 −1.17103 −0.138976 −0.0694878 0.997583i 0.522137π-0.522137\pi
−0.0694878 + 0.997583i 0.522137π0.522137\pi
7272 0 0
7373 −0.773540 −0.0905360 −0.0452680 0.998975i 0.514414π-0.514414\pi
−0.0452680 + 0.998975i 0.514414π0.514414\pi
7474 0 0
7575 0 0
7676 0 0
7777 2.60251 0.296584
7878 0 0
7979 −2.39749 −0.269739 −0.134869 0.990863i 0.543061π-0.543061\pi
−0.134869 + 0.990863i 0.543061π0.543061\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 −8.72883 −0.958114 −0.479057 0.877784i 0.659021π-0.659021\pi
−0.479057 + 0.877784i 0.659021π0.659021\pi
8484 0 0
8585 0 0
8686 0 0
8787 1.00000 0.107211
8888 0 0
8989 −6.34206 −0.672257 −0.336128 0.941816i 0.609118π-0.609118\pi
−0.336128 + 0.941816i 0.609118π0.609118\pi
9090 0 0
9191 1.61323 0.169112
9292 0 0
9393 1.61323 0.167284
9494 0 0
9595 0 0
9696 0 0
9797 −4.34206 −0.440869 −0.220435 0.975402i 0.570748π-0.570748\pi
−0.220435 + 0.975402i 0.570748π0.570748\pi
9898 0 0
9999 1.61323 0.162136
100100 0 0
101101 −11.7395 −1.16813 −0.584064 0.811707i 0.698538π-0.698538\pi
−0.584064 + 0.811707i 0.698538π0.698538\pi
102102 0 0
103103 −15.5685 −1.53401 −0.767006 0.641640i 0.778254π-0.778254\pi
−0.767006 + 0.641640i 0.778254π0.778254\pi
104104 0 0
105105 0 0
106106 0 0
107107 −5.17103 −0.499902 −0.249951 0.968258i 0.580415π-0.580415\pi
−0.249951 + 0.968258i 0.580415π0.580415\pi
108108 0 0
109109 0.718110 0.0687825 0.0343913 0.999408i 0.489051π-0.489051\pi
0.0343913 + 0.999408i 0.489051π0.489051\pi
110110 0 0
111111 −1.17103 −0.111149
112112 0 0
113113 −6.00000 −0.564433 −0.282216 0.959351i 0.591070π-0.591070\pi
−0.282216 + 0.959351i 0.591070π0.591070\pi
114114 0 0
115115 0 0
116116 0 0
117117 1.00000 0.0924500
118118 0 0
119119 9.95529 0.912600
120120 0 0
121121 −8.39749 −0.763408
122122 0 0
123123 −3.17103 −0.285922
124124 0 0
125125 0 0
126126 0 0
127127 0.0554299 0.00491861 0.00245930 0.999997i 0.499217π-0.499217\pi
0.00245930 + 0.999997i 0.499217π0.499217\pi
128128 0 0
129129 −2.00000 −0.176090
130130 0 0
131131 11.1710 0.976017 0.488009 0.872839i 0.337723π-0.337723\pi
0.488009 + 0.872839i 0.337723π0.337723\pi
132132 0 0
133133 8.34206 0.723348
134134 0 0
135135 0 0
136136 0 0
137137 20.2866 1.73320 0.866602 0.499000i 0.166299π-0.166299\pi
0.866602 + 0.499000i 0.166299π0.166299\pi
138138 0 0
139139 7.22646 0.612940 0.306470 0.951880i 0.400852π-0.400852\pi
0.306470 + 0.951880i 0.400852π0.400852\pi
140140 0 0
141141 −1.55780 −0.131190
142142 0 0
143143 1.61323 0.134905
144144 0 0
145145 0 0
146146 0 0
147147 −4.39749 −0.362699
148148 0 0
149149 14.7950 1.21205 0.606026 0.795445i 0.292763π-0.292763\pi
0.606026 + 0.795445i 0.292763π0.292763\pi
150150 0 0
151151 −10.2973 −0.837986 −0.418993 0.907989i 0.637617π-0.637617\pi
−0.418993 + 0.907989i 0.637617π0.637617\pi
152152 0 0
153153 6.17103 0.498898
154154 0 0
155155 0 0
156156 0 0
157157 16.5131 1.31789 0.658944 0.752192i 0.271003π-0.271003\pi
0.658944 + 0.752192i 0.271003π0.271003\pi
158158 0 0
159159 −7.34206 −0.582263
160160 0 0
161161 13.4577 1.06061
162162 0 0
163163 −11.2265 −0.879324 −0.439662 0.898163i 0.644902π-0.644902\pi
−0.439662 + 0.898163i 0.644902π0.644902\pi
164164 0 0
165165 0 0
166166 0 0
167167 15.5131 1.20044 0.600219 0.799835i 0.295080π-0.295080\pi
0.600219 + 0.799835i 0.295080π0.295080\pi
168168 0 0
169169 1.00000 0.0769231
170170 0 0
171171 5.17103 0.395439
172172 0 0
173173 11.2312 0.853892 0.426946 0.904277i 0.359589π-0.359589\pi
0.426946 + 0.904277i 0.359589π0.359589\pi
174174 0 0
175175 0 0
176176 0 0
177177 −4.72883 −0.355441
178178 0 0
179179 11.5685 0.864672 0.432336 0.901713i 0.357689π-0.357689\pi
0.432336 + 0.901713i 0.357689π0.357689\pi
180180 0 0
181181 −0.281890 −0.0209527 −0.0104763 0.999945i 0.503335π-0.503335\pi
−0.0104763 + 0.999945i 0.503335π0.503335\pi
182182 0 0
183183 10.5131 0.777150
184184 0 0
185185 0 0
186186 0 0
187187 9.95529 0.728003
188188 0 0
189189 1.61323 0.117345
190190 0 0
191191 17.5685 1.27121 0.635607 0.772013i 0.280750π-0.280750\pi
0.635607 + 0.772013i 0.280750π0.280750\pi
192192 0 0
193193 −13.1156 −0.944082 −0.472041 0.881577i 0.656482π-0.656482\pi
−0.472041 + 0.881577i 0.656482π0.656482\pi
194194 0 0
195195 0 0
196196 0 0
197197 0.431481 0.0307417 0.0153709 0.999882i 0.495107π-0.495107\pi
0.0153709 + 0.999882i 0.495107π0.495107\pi
198198 0 0
199199 17.0602 1.20936 0.604682 0.796467i 0.293300π-0.293300\pi
0.604682 + 0.796467i 0.293300π0.293300\pi
200200 0 0
201201 4.78426 0.337456
202202 0 0
203203 1.61323 0.113227
204204 0 0
205205 0 0
206206 0 0
207207 8.34206 0.579813
208208 0 0
209209 8.34206 0.577032
210210 0 0
211211 12.3421 0.849662 0.424831 0.905273i 0.360333π-0.360333\pi
0.424831 + 0.905273i 0.360333π0.360333\pi
212212 0 0
213213 −1.17103 −0.0802376
214214 0 0
215215 0 0
216216 0 0
217217 2.60251 0.176670
218218 0 0
219219 −0.773540 −0.0522710
220220 0 0
221221 6.17103 0.415108
222222 0 0
223223 −8.88440 −0.594943 −0.297472 0.954731i 0.596143π-0.596143\pi
−0.297472 + 0.954731i 0.596143π0.596143\pi
224224 0 0
225225 0 0
226226 0 0
227227 −6.49763 −0.431263 −0.215631 0.976475i 0.569181π-0.569181\pi
−0.215631 + 0.976475i 0.569181π0.569181\pi
228228 0 0
229229 −15.0816 −0.996621 −0.498310 0.866999i 0.666046π-0.666046\pi
−0.498310 + 0.866999i 0.666046π0.666046\pi
230230 0 0
231231 2.60251 0.171233
232232 0 0
233233 −18.7950 −1.23130 −0.615650 0.788020i 0.711106π-0.711106\pi
−0.615650 + 0.788020i 0.711106π0.711106\pi
234234 0 0
235235 0 0
236236 0 0
237237 −2.39749 −0.155734
238238 0 0
239239 −16.4082 −1.06136 −0.530679 0.847573i 0.678063π-0.678063\pi
−0.530679 + 0.847573i 0.678063π0.678063\pi
240240 0 0
241241 −25.7997 −1.66191 −0.830953 0.556343i 0.812204π-0.812204\pi
−0.830953 + 0.556343i 0.812204π0.812204\pi
242242 0 0
243243 1.00000 0.0641500
244244 0 0
245245 0 0
246246 0 0
247247 5.17103 0.329025
248248 0 0
249249 −8.72883 −0.553167
250250 0 0
251251 19.0602 1.20307 0.601534 0.798847i 0.294557π-0.294557\pi
0.601534 + 0.798847i 0.294557π0.294557\pi
252252 0 0
253253 13.4577 0.846076
254254 0 0
255255 0 0
256256 0 0
257257 1.48691 0.0927509 0.0463755 0.998924i 0.485233π-0.485233\pi
0.0463755 + 0.998924i 0.485233π0.485233\pi
258258 0 0
259259 −1.88914 −0.117385
260260 0 0
261261 1.00000 0.0618984
262262 0 0
263263 −13.9106 −0.857763 −0.428882 0.903361i 0.641092π-0.641092\pi
−0.428882 + 0.903361i 0.641092π0.641092\pi
264264 0 0
265265 0 0
266266 0 0
267267 −6.34206 −0.388128
268268 0 0
269269 15.4529 0.942181 0.471091 0.882085i 0.343860π-0.343860\pi
0.471091 + 0.882085i 0.343860π0.343860\pi
270270 0 0
271271 10.3868 0.630951 0.315476 0.948934i 0.397836π-0.397836\pi
0.315476 + 0.948934i 0.397836π0.397836\pi
272272 0 0
273273 1.61323 0.0976371
274274 0 0
275275 0 0
276276 0 0
277277 16.4529 0.988560 0.494280 0.869303i 0.335432π-0.335432\pi
0.494280 + 0.869303i 0.335432π0.335432\pi
278278 0 0
279279 1.61323 0.0965815
280280 0 0
281281 18.3975 1.09750 0.548751 0.835986i 0.315103π-0.315103\pi
0.548751 + 0.835986i 0.315103π0.315103\pi
282282 0 0
283283 −17.6794 −1.05093 −0.525465 0.850815i 0.676109π-0.676109\pi
−0.525465 + 0.850815i 0.676109π0.676109\pi
284284 0 0
285285 0 0
286286 0 0
287287 −5.11560 −0.301964
288288 0 0
289289 21.0816 1.24009
290290 0 0
291291 −4.34206 −0.254536
292292 0 0
293293 14.7950 0.864332 0.432166 0.901794i 0.357749π-0.357749\pi
0.432166 + 0.901794i 0.357749π0.357749\pi
294294 0 0
295295 0 0
296296 0 0
297297 1.61323 0.0936091
298298 0 0
299299 8.34206 0.482434
300300 0 0
301301 −3.22646 −0.185970
302302 0 0
303303 −11.7395 −0.674419
304304 0 0
305305 0 0
306306 0 0
307307 −32.3081 −1.84392 −0.921959 0.387286i 0.873412π-0.873412\pi
−0.921959 + 0.387286i 0.873412π0.873412\pi
308308 0 0
309309 −15.5685 −0.885662
310310 0 0
311311 25.5685 1.44986 0.724929 0.688824i 0.241873π-0.241873\pi
0.724929 + 0.688824i 0.241873π0.241873\pi
312312 0 0
313313 −15.0000 −0.847850 −0.423925 0.905697i 0.639348π-0.639348\pi
−0.423925 + 0.905697i 0.639348π0.639348\pi
314314 0 0
315315 0 0
316316 0 0
317317 13.6794 0.768310 0.384155 0.923269i 0.374493π-0.374493\pi
0.384155 + 0.923269i 0.374493π0.374493\pi
318318 0 0
319319 1.61323 0.0903235
320320 0 0
321321 −5.17103 −0.288619
322322 0 0
323323 31.9106 1.77555
324324 0 0
325325 0 0
326326 0 0
327327 0.718110 0.0397116
328328 0 0
329329 −2.51309 −0.138551
330330 0 0
331331 0.773540 0.0425176 0.0212588 0.999774i 0.493233π-0.493233\pi
0.0212588 + 0.999774i 0.493233π0.493233\pi
332332 0 0
333333 −1.17103 −0.0641720
334334 0 0
335335 0 0
336336 0 0
337337 36.0816 1.96549 0.982745 0.184964i 0.0592170π-0.0592170\pi
0.982745 + 0.184964i 0.0592170π0.0592170\pi
338338 0 0
339339 −6.00000 −0.325875
340340 0 0
341341 2.60251 0.140934
342342 0 0
343343 −18.3868 −0.992792
344344 0 0
345345 0 0
346346 0 0
347347 −25.9660 −1.39393 −0.696964 0.717106i 0.745466π-0.745466\pi
−0.696964 + 0.717106i 0.745466π0.745466\pi
348348 0 0
349349 13.5685 0.726306 0.363153 0.931729i 0.381700π-0.381700\pi
0.363153 + 0.931729i 0.381700π0.381700\pi
350350 0 0
351351 1.00000 0.0533761
352352 0 0
353353 −25.6239 −1.36383 −0.681913 0.731434i 0.738852π-0.738852\pi
−0.681913 + 0.731434i 0.738852π0.738852\pi
354354 0 0
355355 0 0
356356 0 0
357357 9.95529 0.526890
358358 0 0
359359 −0.895119 −0.0472426 −0.0236213 0.999721i 0.507520π-0.507520\pi
−0.0236213 + 0.999721i 0.507520π0.507520\pi
360360 0 0
361361 7.73955 0.407345
362362 0 0
363363 −8.39749 −0.440754
364364 0 0
365365 0 0
366366 0 0
367367 −16.2866 −0.850155 −0.425078 0.905157i 0.639753π-0.639753\pi
−0.425078 + 0.905157i 0.639753π0.639753\pi
368368 0 0
369369 −3.17103 −0.165077
370370 0 0
371371 −11.8444 −0.614932
372372 0 0
373373 −36.8551 −1.90829 −0.954144 0.299349i 0.903230π-0.903230\pi
−0.954144 + 0.299349i 0.903230π0.903230\pi
374374 0 0
375375 0 0
376376 0 0
377377 1.00000 0.0515026
378378 0 0
379379 11.7241 0.602226 0.301113 0.953588i 0.402642π-0.402642\pi
0.301113 + 0.953588i 0.402642π0.402642\pi
380380 0 0
381381 0.0554299 0.00283976
382382 0 0
383383 17.9660 0.918020 0.459010 0.888431i 0.348204π-0.348204\pi
0.459010 + 0.888431i 0.348204π0.348204\pi
384384 0 0
385385 0 0
386386 0 0
387387 −2.00000 −0.101666
388388 0 0
389389 −11.8337 −0.599993 −0.299996 0.953940i 0.596986π-0.596986\pi
−0.299996 + 0.953940i 0.596986π0.596986\pi
390390 0 0
391391 51.4791 2.60341
392392 0 0
393393 11.1710 0.563504
394394 0 0
395395 0 0
396396 0 0
397397 7.94457 0.398727 0.199363 0.979926i 0.436113π-0.436113\pi
0.199363 + 0.979926i 0.436113π0.436113\pi
398398 0 0
399399 8.34206 0.417625
400400 0 0
401401 17.5685 0.877330 0.438665 0.898651i 0.355451π-0.355451\pi
0.438665 + 0.898651i 0.355451π0.355451\pi
402402 0 0
403403 1.61323 0.0803607
404404 0 0
405405 0 0
406406 0 0
407407 −1.88914 −0.0936412
408408 0 0
409409 14.8844 0.735986 0.367993 0.929829i 0.380045π-0.380045\pi
0.367993 + 0.929829i 0.380045π0.380045\pi
410410 0 0
411411 20.2866 1.00067
412412 0 0
413413 −7.62869 −0.375383
414414 0 0
415415 0 0
416416 0 0
417417 7.22646 0.353881
418418 0 0
419419 −17.6239 −0.860986 −0.430493 0.902594i 0.641660π-0.641660\pi
−0.430493 + 0.902594i 0.641660π0.641660\pi
420420 0 0
421421 −22.3421 −1.08889 −0.544443 0.838798i 0.683259π-0.683259\pi
−0.544443 + 0.838798i 0.683259π0.683259\pi
422422 0 0
423423 −1.55780 −0.0757428
424424 0 0
425425 0 0
426426 0 0
427427 16.9600 0.820753
428428 0 0
429429 1.61323 0.0778875
430430 0 0
431431 −20.1972 −0.972865 −0.486433 0.873718i 0.661702π-0.661702\pi
−0.486433 + 0.873718i 0.661702π0.661702\pi
432432 0 0
433433 −35.1925 −1.69124 −0.845621 0.533784i 0.820770π-0.820770\pi
−0.845621 + 0.533784i 0.820770π0.820770\pi
434434 0 0
435435 0 0
436436 0 0
437437 43.1370 2.06352
438438 0 0
439439 −12.7395 −0.608026 −0.304013 0.952668i 0.598327π-0.598327\pi
−0.304013 + 0.952668i 0.598327π0.598327\pi
440440 0 0
441441 −4.39749 −0.209404
442442 0 0
443443 −11.8337 −0.562237 −0.281118 0.959673i 0.590705π-0.590705\pi
−0.281118 + 0.959673i 0.590705π0.590705\pi
444444 0 0
445445 0 0
446446 0 0
447447 14.7950 0.699778
448448 0 0
449449 20.2866 0.957385 0.478693 0.877983i 0.341111π-0.341111\pi
0.478693 + 0.877983i 0.341111π0.341111\pi
450450 0 0
451451 −5.11560 −0.240884
452452 0 0
453453 −10.2973 −0.483812
454454 0 0
455455 0 0
456456 0 0
457457 −4.43148 −0.207296 −0.103648 0.994614i 0.533052π-0.533052\pi
−0.103648 + 0.994614i 0.533052π0.533052\pi
458458 0 0
459459 6.17103 0.288039
460460 0 0
461461 33.2479 1.54851 0.774255 0.632874i 0.218125π-0.218125\pi
0.774255 + 0.632874i 0.218125π0.218125\pi
462462 0 0
463463 −16.0447 −0.745661 −0.372830 0.927899i 0.621613π-0.621613\pi
−0.372830 + 0.927899i 0.621613π0.621613\pi
464464 0 0
465465 0 0
466466 0 0
467467 −14.0554 −0.650408 −0.325204 0.945644i 0.605433π-0.605433\pi
−0.325204 + 0.945644i 0.605433π0.605433\pi
468468 0 0
469469 7.71811 0.356389
470470 0 0
471471 16.5131 0.760883
472472 0 0
473473 −3.22646 −0.148353
474474 0 0
475475 0 0
476476 0 0
477477 −7.34206 −0.336170
478478 0 0
479479 −24.7843 −1.13242 −0.566211 0.824260i 0.691591π-0.691591\pi
−0.566211 + 0.824260i 0.691591π0.691591\pi
480480 0 0
481481 −1.17103 −0.0533944
482482 0 0
483483 13.4577 0.612345
484484 0 0
485485 0 0
486486 0 0
487487 −34.4082 −1.55918 −0.779592 0.626287i 0.784574π-0.784574\pi
−0.779592 + 0.626287i 0.784574π0.784574\pi
488488 0 0
489489 −11.2265 −0.507678
490490 0 0
491491 −5.45766 −0.246301 −0.123150 0.992388i 0.539300π-0.539300\pi
−0.123150 + 0.992388i 0.539300π0.539300\pi
492492 0 0
493493 6.17103 0.277929
494494 0 0
495495 0 0
496496 0 0
497497 −1.88914 −0.0847395
498498 0 0
499499 −11.3480 −0.508008 −0.254004 0.967203i 0.581748π-0.581748\pi
−0.254004 + 0.967203i 0.581748π0.581748\pi
500500 0 0
501501 15.5131 0.693074
502502 0 0
503503 10.0214 0.446834 0.223417 0.974723i 0.428279π-0.428279\pi
0.223417 + 0.974723i 0.428279π0.428279\pi
504504 0 0
505505 0 0
506506 0 0
507507 1.00000 0.0444116
508508 0 0
509509 6.66268 0.295318 0.147659 0.989038i 0.452826π-0.452826\pi
0.147659 + 0.989038i 0.452826π0.452826\pi
510510 0 0
511511 −1.24790 −0.0552038
512512 0 0
513513 5.17103 0.228307
514514 0 0
515515 0 0
516516 0 0
517517 −2.51309 −0.110526
518518 0 0
519519 11.2312 0.492995
520520 0 0
521521 −15.4791 −0.678152 −0.339076 0.940759i 0.610114π-0.610114\pi
−0.339076 + 0.940759i 0.610114π0.610114\pi
522522 0 0
523523 9.56852 0.418402 0.209201 0.977873i 0.432914π-0.432914\pi
0.209201 + 0.977873i 0.432914π0.432914\pi
524524 0 0
525525 0 0
526526 0 0
527527 9.95529 0.433659
528528 0 0
529529 46.5900 2.02565
530530 0 0
531531 −4.72883 −0.205214
532532 0 0
533533 −3.17103 −0.137353
534534 0 0
535535 0 0
536536 0 0
537537 11.5685 0.499218
538538 0 0
539539 −7.09416 −0.305567
540540 0 0
541541 30.4744 1.31019 0.655097 0.755544i 0.272628π-0.272628\pi
0.655097 + 0.755544i 0.272628π0.272628\pi
542542 0 0
543543 −0.281890 −0.0120970
544544 0 0
545545 0 0
546546 0 0
547547 −6.77354 −0.289616 −0.144808 0.989460i 0.546256π-0.546256\pi
−0.144808 + 0.989460i 0.546256π0.546256\pi
548548 0 0
549549 10.5131 0.448688
550550 0 0
551551 5.17103 0.220293
552552 0 0
553553 −3.86770 −0.164471
554554 0 0
555555 0 0
556556 0 0
557557 −9.91058 −0.419925 −0.209962 0.977709i 0.567334π-0.567334\pi
−0.209962 + 0.977709i 0.567334π0.567334\pi
558558 0 0
559559 −2.00000 −0.0845910
560560 0 0
561561 9.95529 0.420313
562562 0 0
563563 26.9707 1.13668 0.568341 0.822793i 0.307586π-0.307586\pi
0.568341 + 0.822793i 0.307586π0.307586\pi
564564 0 0
565565 0 0
566566 0 0
567567 1.61323 0.0677493
568568 0 0
569569 9.60725 0.402757 0.201378 0.979514i 0.435458π-0.435458\pi
0.201378 + 0.979514i 0.435458π0.435458\pi
570570 0 0
571571 −17.0262 −0.712523 −0.356262 0.934386i 0.615949π-0.615949\pi
−0.356262 + 0.934386i 0.615949π0.615949\pi
572572 0 0
573573 17.5685 0.733935
574574 0 0
575575 0 0
576576 0 0
577577 −37.0262 −1.54142 −0.770710 0.637186i 0.780098π-0.780098\pi
−0.770710 + 0.637186i 0.780098π0.780098\pi
578578 0 0
579579 −13.1156 −0.545066
580580 0 0
581581 −14.0816 −0.584204
582582 0 0
583583 −11.8444 −0.490546
584584 0 0
585585 0 0
586586 0 0
587587 −14.3868 −0.593806 −0.296903 0.954908i 0.595954π-0.595954\pi
−0.296903 + 0.954908i 0.595954π0.595954\pi
588588 0 0
589589 8.34206 0.343729
590590 0 0
591591 0.431481 0.0177487
592592 0 0
593593 31.7657 1.30446 0.652231 0.758020i 0.273833π-0.273833\pi
0.652231 + 0.758020i 0.273833π0.273833\pi
594594 0 0
595595 0 0
596596 0 0
597597 17.0602 0.698226
598598 0 0
599599 −34.0214 −1.39008 −0.695039 0.718972i 0.744613π-0.744613\pi
−0.695039 + 0.718972i 0.744613π0.744613\pi
600600 0 0
601601 −6.65794 −0.271583 −0.135792 0.990737i 0.543358π-0.543358\pi
−0.135792 + 0.990737i 0.543358π0.543358\pi
602602 0 0
603603 4.78426 0.194830
604604 0 0
605605 0 0
606606 0 0
607607 −0.486911 −0.0197631 −0.00988155 0.999951i 0.503145π-0.503145\pi
−0.00988155 + 0.999951i 0.503145π0.503145\pi
608608 0 0
609609 1.61323 0.0653714
610610 0 0
611611 −1.55780 −0.0630218
612612 0 0
613613 −7.54708 −0.304824 −0.152412 0.988317i 0.548704π-0.548704\pi
−0.152412 + 0.988317i 0.548704π0.548704\pi
614614 0 0
615615 0 0
616616 0 0
617617 23.8337 0.959509 0.479755 0.877403i 0.340726π-0.340726\pi
0.479755 + 0.877403i 0.340726π0.340726\pi
618618 0 0
619619 26.3635 1.05964 0.529819 0.848111i 0.322260π-0.322260\pi
0.529819 + 0.848111i 0.322260π0.322260\pi
620620 0 0
621621 8.34206 0.334755
622622 0 0
623623 −10.2312 −0.409904
624624 0 0
625625 0 0
626626 0 0
627627 8.34206 0.333150
628628 0 0
629629 −7.22646 −0.288138
630630 0 0
631631 45.2788 1.80252 0.901261 0.433277i 0.142643π-0.142643\pi
0.901261 + 0.433277i 0.142643π0.142643\pi
632632 0 0
633633 12.3421 0.490553
634634 0 0
635635 0 0
636636 0 0
637637 −4.39749 −0.174235
638638 0 0
639639 −1.17103 −0.0463252
640640 0 0
641641 37.7610 1.49147 0.745735 0.666243i 0.232099π-0.232099\pi
0.745735 + 0.666243i 0.232099π0.232099\pi
642642 0 0
643643 −27.2914 −1.07627 −0.538133 0.842860i 0.680870π-0.680870\pi
−0.538133 + 0.842860i 0.680870π0.680870\pi
644644 0 0
645645 0 0
646646 0 0
647647 29.3682 1.15458 0.577292 0.816538i 0.304109π-0.304109\pi
0.577292 + 0.816538i 0.304109π0.304109\pi
648648 0 0
649649 −7.62869 −0.299452
650650 0 0
651651 2.60251 0.102000
652652 0 0
653653 28.9446 1.13269 0.566344 0.824169i 0.308357π-0.308357\pi
0.566344 + 0.824169i 0.308357π0.308357\pi
654654 0 0
655655 0 0
656656 0 0
657657 −0.773540 −0.0301787
658658 0 0
659659 −10.2866 −0.400710 −0.200355 0.979723i 0.564210π-0.564210\pi
−0.200355 + 0.979723i 0.564210π0.564210\pi
660660 0 0
661661 9.62395 0.374328 0.187164 0.982329i 0.440070π-0.440070\pi
0.187164 + 0.982329i 0.440070π0.440070\pi
662662 0 0
663663 6.17103 0.239663
664664 0 0
665665 0 0
666666 0 0
667667 8.34206 0.323006
668668 0 0
669669 −8.88440 −0.343491
670670 0 0
671671 16.9600 0.654735
672672 0 0
673673 1.45292 0.0560059 0.0280030 0.999608i 0.491085π-0.491085\pi
0.0280030 + 0.999608i 0.491085π0.491085\pi
674674 0 0
675675 0 0
676676 0 0
677677 −0.231200 −0.00888573 −0.00444286 0.999990i 0.501414π-0.501414\pi
−0.00444286 + 0.999990i 0.501414π0.501414\pi
678678 0 0
679679 −7.00474 −0.268817
680680 0 0
681681 −6.49763 −0.248990
682682 0 0
683683 −7.84443 −0.300159 −0.150079 0.988674i 0.547953π-0.547953\pi
−0.150079 + 0.988674i 0.547953π0.547953\pi
684684 0 0
685685 0 0
686686 0 0
687687 −15.0816 −0.575399
688688 0 0
689689 −7.34206 −0.279710
690690 0 0
691691 1.44694 0.0550442 0.0275221 0.999621i 0.491238π-0.491238\pi
0.0275221 + 0.999621i 0.491238π0.491238\pi
692692 0 0
693693 2.60251 0.0988612
694694 0 0
695695 0 0
696696 0 0
697697 −19.5685 −0.741211
698698 0 0
699699 −18.7950 −0.710891
700700 0 0
701701 18.4917 0.698420 0.349210 0.937044i 0.386450π-0.386450\pi
0.349210 + 0.937044i 0.386450π0.386450\pi
702702 0 0
703703 −6.05543 −0.228385
704704 0 0
705705 0 0
706706 0 0
707707 −18.9386 −0.712259
708708 0 0
709709 −16.3635 −0.614544 −0.307272 0.951622i 0.599416π-0.599416\pi
−0.307272 + 0.951622i 0.599416π0.599416\pi
710710 0 0
711711 −2.39749 −0.0899129
712712 0 0
713713 13.4577 0.503993
714714 0 0
715715 0 0
716716 0 0
717717 −16.4082 −0.612776
718718 0 0
719719 −32.4744 −1.21109 −0.605545 0.795811i 0.707045π-0.707045\pi
−0.605545 + 0.795811i 0.707045π0.707045\pi
720720 0 0
721721 −25.1156 −0.935354
722722 0 0
723723 −25.7997 −0.959502
724724 0 0
725725 0 0
726726 0 0
727727 −32.0309 −1.18796 −0.593981 0.804479i 0.702444π-0.702444\pi
−0.593981 + 0.804479i 0.702444π0.702444\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 −12.3421 −0.456488
732732 0 0
733733 20.0649 0.741114 0.370557 0.928810i 0.379167π-0.379167\pi
0.370557 + 0.928810i 0.379167π0.379167\pi
734734 0 0
735735 0 0
736736 0 0
737737 7.71811 0.284300
738738 0 0
739739 −7.10488 −0.261357 −0.130679 0.991425i 0.541716π-0.541716\pi
−0.130679 + 0.991425i 0.541716π0.541716\pi
740740 0 0
741741 5.17103 0.189963
742742 0 0
743743 −51.0583 −1.87315 −0.936574 0.350469i 0.886022π-0.886022\pi
−0.936574 + 0.350469i 0.886022π0.886022\pi
744744 0 0
745745 0 0
746746 0 0
747747 −8.72883 −0.319371
748748 0 0
749749 −8.34206 −0.304812
750750 0 0
751751 38.1758 1.39305 0.696527 0.717531i 0.254728π-0.254728\pi
0.696527 + 0.717531i 0.254728π0.254728\pi
752752 0 0
753753 19.0602 0.694591
754754 0 0
755755 0 0
756756 0 0
757757 29.0863 1.05716 0.528581 0.848883i 0.322724π-0.322724\pi
0.528581 + 0.848883i 0.322724π0.322724\pi
758758 0 0
759759 13.4577 0.488482
760760 0 0
761761 9.17103 0.332450 0.166225 0.986088i 0.446842π-0.446842\pi
0.166225 + 0.986088i 0.446842π0.446842\pi
762762 0 0
763763 1.15848 0.0419397
764764 0 0
765765 0 0
766766 0 0
767767 −4.72883 −0.170748
768768 0 0
769769 35.3588 1.27507 0.637535 0.770422i 0.279954π-0.279954\pi
0.637535 + 0.770422i 0.279954π0.279954\pi
770770 0 0
771771 1.48691 0.0535498
772772 0 0
773773 23.0167 0.827853 0.413927 0.910310i 0.364157π-0.364157\pi
0.413927 + 0.910310i 0.364157π0.364157\pi
774774 0 0
775775 0 0
776776 0 0
777777 −1.88914 −0.0677725
778778 0 0
779779 −16.3975 −0.587501
780780 0 0
781781 −1.88914 −0.0675988
782782 0 0
783783 1.00000 0.0357371
784784 0 0
785785 0 0
786786 0 0
787787 −50.7717 −1.80982 −0.904908 0.425607i 0.860060π-0.860060\pi
−0.904908 + 0.425607i 0.860060π0.860060\pi
788788 0 0
789789 −13.9106 −0.495230
790790 0 0
791791 −9.67938 −0.344159
792792 0 0
793793 10.5131 0.373331
794794 0 0
795795 0 0
796796 0 0
797797 29.2866 1.03739 0.518693 0.854961i 0.326419π-0.326419\pi
0.518693 + 0.854961i 0.326419π0.326419\pi
798798 0 0
799799 −9.61323 −0.340092
800800 0 0
801801 −6.34206 −0.224086
802802 0 0
803803 −1.24790 −0.0440374
804804 0 0
805805 0 0
806806 0 0
807807 15.4529 0.543969
808808 0 0
809809 −25.3588 −0.891566 −0.445783 0.895141i 0.647075π-0.647075\pi
−0.445783 + 0.895141i 0.647075π0.647075\pi
810810 0 0
811811 −36.9600 −1.29784 −0.648921 0.760856i 0.724779π-0.724779\pi
−0.648921 + 0.760856i 0.724779π0.724779\pi
812812 0 0
813813 10.3868 0.364280
814814 0 0
815815 0 0
816816 0 0
817817 −10.3421 −0.361823
818818 0 0
819819 1.61323 0.0563708
820820 0 0
821821 −3.33732 −0.116473 −0.0582366 0.998303i 0.518548π-0.518548\pi
−0.0582366 + 0.998303i 0.518548π0.518548\pi
822822 0 0
823823 −29.9446 −1.04380 −0.521901 0.853006i 0.674777π-0.674777\pi
−0.521901 + 0.853006i 0.674777π0.674777\pi
824824 0 0
825825 0 0
826826 0 0
827827 39.7550 1.38242 0.691209 0.722655i 0.257079π-0.257079\pi
0.691209 + 0.722655i 0.257079π0.257079\pi
828828 0 0
829829 6.06017 0.210478 0.105239 0.994447i 0.466439π-0.466439\pi
0.105239 + 0.994447i 0.466439π0.466439\pi
830830 0 0
831831 16.4529 0.570745
832832 0 0
833833 −27.1370 −0.940243
834834 0 0
835835 0 0
836836 0 0
837837 1.61323 0.0557614
838838 0 0
839839 8.13230 0.280758 0.140379 0.990098i 0.455168π-0.455168\pi
0.140379 + 0.990098i 0.455168π0.455168\pi
840840 0 0
841841 −28.0000 −0.965517
842842 0 0
843843 18.3975 0.633643
844844 0 0
845845 0 0
846846 0 0
847847 −13.5471 −0.465483
848848 0 0
849849 −17.6794 −0.606755
850850 0 0
851851 −9.76880 −0.334870
852852 0 0
853853 −24.9707 −0.854982 −0.427491 0.904020i 0.640602π-0.640602\pi
−0.427491 + 0.904020i 0.640602π0.640602\pi
854854 0 0
855855 0 0
856856 0 0
857857 −23.5900 −0.805818 −0.402909 0.915240i 0.632001π-0.632001\pi
−0.402909 + 0.915240i 0.632001π0.632001\pi
858858 0 0
859859 32.9153 1.12306 0.561528 0.827458i 0.310214π-0.310214\pi
0.561528 + 0.827458i 0.310214π0.310214\pi
860860 0 0
861861 −5.11560 −0.174339
862862 0 0
863863 −8.10014 −0.275732 −0.137866 0.990451i 0.544024π-0.544024\pi
−0.137866 + 0.990451i 0.544024π0.544024\pi
864864 0 0
865865 0 0
866866 0 0
867867 21.0816 0.715969
868868 0 0
869869 −3.86770 −0.131203
870870 0 0
871871 4.78426 0.162108
872872 0 0
873873 −4.34206 −0.146956
874874 0 0
875875 0 0
876876 0 0
877877 −16.2866 −0.549960 −0.274980 0.961450i 0.588671π-0.588671\pi
−0.274980 + 0.961450i 0.588671π0.588671\pi
878878 0 0
879879 14.7950 0.499022
880880 0 0
881881 6.51309 0.219432 0.109716 0.993963i 0.465006π-0.465006\pi
0.109716 + 0.993963i 0.465006π0.465006\pi
882882 0 0
883883 48.5053 1.63233 0.816166 0.577817i 0.196095π-0.196095\pi
0.816166 + 0.577817i 0.196095π0.196095\pi
884884 0 0
885885 0 0
886886 0 0
887887 17.8891 0.600659 0.300329 0.953836i 0.402903π-0.402903\pi
0.300329 + 0.953836i 0.402903π0.402903\pi
888888 0 0
889889 0.0894212 0.00299909
890890 0 0
891891 1.61323 0.0540452
892892 0 0
893893 −8.05543 −0.269565
894894 0 0
895895 0 0
896896 0 0
897897 8.34206 0.278533
898898 0 0
899899 1.61323 0.0538042
900900 0 0
901901 −45.3081 −1.50943
902902 0 0
903903 −3.22646 −0.107370
904904 0 0
905905 0 0
906906 0 0
907907 29.4791 0.978837 0.489419 0.872049i 0.337209π-0.337209\pi
0.489419 + 0.872049i 0.337209π0.337209\pi
908908 0 0
909909 −11.7395 −0.389376
910910 0 0
911911 10.2217 0.338661 0.169330 0.985559i 0.445840π-0.445840\pi
0.169330 + 0.985559i 0.445840π0.445840\pi
912912 0 0
913913 −14.0816 −0.466033
914914 0 0
915915 0 0
916916 0 0
917917 18.0214 0.595120
918918 0 0
919919 −9.85515 −0.325091 −0.162546 0.986701i 0.551970π-0.551970\pi
−0.162546 + 0.986701i 0.551970π0.551970\pi
920920 0 0
921921 −32.3081 −1.06459
922922 0 0
923923 −1.17103 −0.0385449
924924 0 0
925925 0 0
926926 0 0
927927 −15.5685 −0.511337
928928 0 0
929929 14.5083 0.476003 0.238002 0.971265i 0.423508π-0.423508\pi
0.238002 + 0.971265i 0.423508π0.423508\pi
930930 0 0
931931 −22.7395 −0.745259
932932 0 0
933933 25.5685 0.837076
934934 0 0
935935 0 0
936936 0 0
937937 −7.61921 −0.248909 −0.124454 0.992225i 0.539718π-0.539718\pi
−0.124454 + 0.992225i 0.539718π0.539718\pi
938938 0 0
939939 −15.0000 −0.489506
940940 0 0
941941 −31.9106 −1.04026 −0.520128 0.854089i 0.674116π-0.674116\pi
−0.520128 + 0.854089i 0.674116π0.674116\pi
942942 0 0
943943 −26.4529 −0.861426
944944 0 0
945945 0 0
946946 0 0
947947 −31.8444 −1.03480 −0.517402 0.855742i 0.673101π-0.673101\pi
−0.517402 + 0.855742i 0.673101π0.673101\pi
948948 0 0
949949 −0.773540 −0.0251102
950950 0 0
951951 13.6794 0.443584
952952 0 0
953953 −33.6501 −1.09003 −0.545017 0.838425i 0.683477π-0.683477\pi
−0.545017 + 0.838425i 0.683477π0.683477\pi
954954 0 0
955955 0 0
956956 0 0
957957 1.61323 0.0521483
958958 0 0
959959 32.7270 1.05681
960960 0 0
961961 −28.3975 −0.916048
962962 0 0
963963 −5.17103 −0.166634
964964 0 0
965965 0 0
966966 0 0
967967 25.3021 0.813660 0.406830 0.913504i 0.366634π-0.366634\pi
0.406830 + 0.913504i 0.366634π0.366634\pi
968968 0 0
969969 31.9106 1.02512
970970 0 0
971971 12.9922 0.416939 0.208470 0.978029i 0.433152π-0.433152\pi
0.208470 + 0.978029i 0.433152π0.433152\pi
972972 0 0
973973 11.6579 0.373736
974974 0 0
975975 0 0
976976 0 0
977977 24.5733 0.786168 0.393084 0.919503i 0.371408π-0.371408\pi
0.393084 + 0.919503i 0.371408π0.371408\pi
978978 0 0
979979 −10.2312 −0.326991
980980 0 0
981981 0.718110 0.0229275
982982 0 0
983983 −29.3140 −0.934973 −0.467486 0.884000i 0.654840π-0.654840\pi
−0.467486 + 0.884000i 0.654840π0.654840\pi
984984 0 0
985985 0 0
986986 0 0
987987 −2.51309 −0.0799925
988988 0 0
989989 −16.6841 −0.530524
990990 0 0
991991 −51.6549 −1.64087 −0.820435 0.571739i 0.806269π-0.806269\pi
−0.820435 + 0.571739i 0.806269π0.806269\pi
992992 0 0
993993 0.773540 0.0245476
994994 0 0
995995 0 0
996996 0 0
997997 14.0602 0.445290 0.222645 0.974900i 0.428531π-0.428531\pi
0.222645 + 0.974900i 0.428531π0.428531\pi
998998 0 0
999999 −1.17103 −0.0370497
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 7800.2.a.bq.1.2 yes 3
5.4 even 2 7800.2.a.bk.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7800.2.a.bk.1.2 3 5.4 even 2
7800.2.a.bq.1.2 yes 3 1.1 even 1 trivial