Properties

Label 432.7.e.j.161.1
Level 432432
Weight 77
Character 432.161
Analytic conductor 99.38399.383
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [432,7,Mod(161,432)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(432, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("432.161");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: N N == 432=2433 432 = 2^{4} \cdot 3^{3}
Weight: k k == 7 7
Character orbit: [χ][\chi] == 432.e (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: 99.383364123899.3833641238
Analytic rank: 00
Dimension: 44
Coefficient field: Q(i,41)\Q(i, \sqrt{41})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+21x2+100 x^{4} + 21x^{2} + 100 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 2438 2^{4}\cdot 3^{8}
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 161.1
Root 3.70156i-3.70156i of defining polynomial
Character χ\chi == 432.161
Dual form 432.7.e.j.161.4

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) == q137.419iq5+514.769q71218.26iq11170.463q131574.10iq17+11289.1q1910572.6iq233258.91q258665.42iq29+26209.1q3170738.9iq35+21866.9q37+38166.6iq4123895.1q43+26698.7iq47+147338.q49+213997.iq53167412.q55+163689.iq59+111078.q61+23424.8iq65+381035.q67675048.iq71762939.q73627123.iq77515708.q79+903773.iq83216311.q85644278.iq8987748.8q911.55133e6iq95616470.q97+O(q100)q-137.419i q^{5} +514.769 q^{7} -1218.26i q^{11} -170.463 q^{13} -1574.10i q^{17} +11289.1 q^{19} -10572.6i q^{23} -3258.91 q^{25} -8665.42i q^{29} +26209.1 q^{31} -70738.9i q^{35} +21866.9 q^{37} +38166.6i q^{41} -23895.1 q^{43} +26698.7i q^{47} +147338. q^{49} +213997. i q^{53} -167412. q^{55} +163689. i q^{59} +111078. q^{61} +23424.8i q^{65} +381035. q^{67} -675048. i q^{71} -762939. q^{73} -627123. i q^{77} -515708. q^{79} +903773. i q^{83} -216311. q^{85} -644278. i q^{89} -87748.8 q^{91} -1.55133e6i q^{95} -616470. q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+676q73448q13+3664q19+17392q25+153244q31+128960q37126008q43+121872q4954180q55+167696q618q671881676q731188728q79176472q85++975212q97+O(q100) 4 q + 676 q^{7} - 3448 q^{13} + 3664 q^{19} + 17392 q^{25} + 153244 q^{31} + 128960 q^{37} - 126008 q^{43} + 121872 q^{49} - 54180 q^{55} + 167696 q^{61} - 8 q^{67} - 1881676 q^{73} - 1188728 q^{79} - 176472 q^{85}+ \cdots + 975212 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/432Z)×\left(\mathbb{Z}/432\mathbb{Z}\right)^\times.

nn 271271 325325 353353
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 − 137.419i − 1.09935i −0.835379 0.549675i 0.814752π-0.814752\pi
0.835379 0.549675i 0.185248π-0.185248\pi
66 0 0
77 514.769 1.50078 0.750392 0.660993i 0.229865π-0.229865\pi
0.750392 + 0.660993i 0.229865π0.229865\pi
88 0 0
99 0 0
1010 0 0
1111 − 1218.26i − 0.915298i −0.889133 0.457649i 0.848692π-0.848692\pi
0.889133 0.457649i 0.151308π-0.151308\pi
1212 0 0
1313 −170.463 −0.0775888 −0.0387944 0.999247i 0.512352π-0.512352\pi
−0.0387944 + 0.999247i 0.512352π0.512352\pi
1414 0 0
1515 0 0
1616 0 0
1717 − 1574.10i − 0.320395i −0.987085 0.160197i 0.948787π-0.948787\pi
0.987085 0.160197i 0.0512131π-0.0512131\pi
1818 0 0
1919 11289.1 1.64588 0.822938 0.568131i 0.192333π-0.192333\pi
0.822938 + 0.568131i 0.192333π0.192333\pi
2020 0 0
2121 0 0
2222 0 0
2323 − 10572.6i − 0.868960i −0.900681 0.434480i 0.856932π-0.856932\pi
0.900681 0.434480i 0.143068π-0.143068\pi
2424 0 0
2525 −3258.91 −0.208570
2626 0 0
2727 0 0
2828 0 0
2929 − 8665.42i − 0.355300i −0.984094 0.177650i 0.943150π-0.943150\pi
0.984094 0.177650i 0.0568496π-0.0568496\pi
3030 0 0
3131 26209.1 0.879766 0.439883 0.898055i 0.355020π-0.355020\pi
0.439883 + 0.898055i 0.355020π0.355020\pi
3232 0 0
3333 0 0
3434 0 0
3535 − 70738.9i − 1.64989i
3636 0 0
3737 21866.9 0.431701 0.215850 0.976426i 0.430748π-0.430748\pi
0.215850 + 0.976426i 0.430748π0.430748\pi
3838 0 0
3939 0 0
4040 0 0
4141 38166.6i 0.553774i 0.960903 + 0.276887i 0.0893027π0.0893027\pi
−0.960903 + 0.276887i 0.910697π0.910697\pi
4242 0 0
4343 −23895.1 −0.300541 −0.150270 0.988645i 0.548014π-0.548014\pi
−0.150270 + 0.988645i 0.548014π0.548014\pi
4444 0 0
4545 0 0
4646 0 0
4747 26698.7i 0.257156i 0.991699 + 0.128578i 0.0410413π0.0410413\pi
−0.991699 + 0.128578i 0.958959π0.958959\pi
4848 0 0
4949 147338. 1.25235
5050 0 0
5151 0 0
5252 0 0
5353 213997.i 1.43741i 0.695315 + 0.718705i 0.255265π0.255265\pi
−0.695315 + 0.718705i 0.744735π0.744735\pi
5454 0 0
5555 −167412. −1.00623
5656 0 0
5757 0 0
5858 0 0
5959 163689.i 0.797010i 0.917166 + 0.398505i 0.130471π0.130471\pi
−0.917166 + 0.398505i 0.869529π0.869529\pi
6060 0 0
6161 111078. 0.489370 0.244685 0.969603i 0.421315π-0.421315\pi
0.244685 + 0.969603i 0.421315π0.421315\pi
6262 0 0
6363 0 0
6464 0 0
6565 23424.8i 0.0852972i
6666 0 0
6767 381035. 1.26689 0.633447 0.773786i 0.281639π-0.281639\pi
0.633447 + 0.773786i 0.281639π0.281639\pi
6868 0 0
6969 0 0
7070 0 0
7171 − 675048.i − 1.88608i −0.332682 0.943039i 0.607953π-0.607953\pi
0.332682 0.943039i 0.392047π-0.392047\pi
7272 0 0
7373 −762939. −1.96120 −0.980599 0.196025i 0.937197π-0.937197\pi
−0.980599 + 0.196025i 0.937197π0.937197\pi
7474 0 0
7575 0 0
7676 0 0
7777 − 627123.i − 1.37366i
7878 0 0
7979 −515708. −1.04598 −0.522989 0.852340i 0.675183π-0.675183\pi
−0.522989 + 0.852340i 0.675183π0.675183\pi
8080 0 0
8181 0 0
8282 0 0
8383 903773.i 1.58061i 0.612713 + 0.790306i 0.290078π0.290078\pi
−0.612713 + 0.790306i 0.709922π0.709922\pi
8484 0 0
8585 −216311. −0.352226
8686 0 0
8787 0 0
8888 0 0
8989 − 644278.i − 0.913910i −0.889490 0.456955i 0.848940π-0.848940\pi
0.889490 0.456955i 0.151060π-0.151060\pi
9090 0 0
9191 −87748.8 −0.116444
9292 0 0
9393 0 0
9494 0 0
9595 − 1.55133e6i − 1.80939i
9696 0 0
9797 −616470. −0.675455 −0.337728 0.941244i 0.609658π-0.609658\pi
−0.337728 + 0.941244i 0.609658π0.609658\pi
9898 0 0
9999 0 0
100100 0 0
101101 − 623027.i − 0.604704i −0.953196 0.302352i 0.902228π-0.902228\pi
0.953196 0.302352i 0.0977718π-0.0977718\pi
102102 0 0
103103 750695. 0.686992 0.343496 0.939154i 0.388389π-0.388389\pi
0.343496 + 0.939154i 0.388389π0.388389\pi
104104 0 0
105105 0 0
106106 0 0
107107 345428.i 0.281973i 0.990012 + 0.140986i 0.0450273π0.0450273\pi
−0.990012 + 0.140986i 0.954973π0.954973\pi
108108 0 0
109109 1.17208e6 0.905061 0.452530 0.891749i 0.350521π-0.350521\pi
0.452530 + 0.891749i 0.350521π0.350521\pi
110110 0 0
111111 0 0
112112 0 0
113113 − 2.45331e6i − 1.70026i −0.526569 0.850132i 0.676522π-0.676522\pi
0.526569 0.850132i 0.323478π-0.323478\pi
114114 0 0
115115 −1.45288e6 −0.955291
116116 0 0
117117 0 0
118118 0 0
119119 − 810297.i − 0.480843i
120120 0 0
121121 287398. 0.162229
122122 0 0
123123 0 0
124124 0 0
125125 − 1.69933e6i − 0.870058i
126126 0 0
127127 1.53816e6 0.750913 0.375456 0.926840i 0.377486π-0.377486\pi
0.375456 + 0.926840i 0.377486π0.377486\pi
128128 0 0
129129 0 0
130130 0 0
131131 − 1.12723e6i − 0.501416i −0.968063 0.250708i 0.919337π-0.919337\pi
0.968063 0.250708i 0.0806635π-0.0806635\pi
132132 0 0
133133 5.81126e6 2.47010
134134 0 0
135135 0 0
136136 0 0
137137 3.20599e6i 1.24681i 0.781899 + 0.623406i 0.214251π0.214251\pi
−0.781899 + 0.623406i 0.785749π0.785749\pi
138138 0 0
139139 66685.5 0.0248306 0.0124153 0.999923i 0.496048π-0.496048\pi
0.0124153 + 0.999923i 0.496048π0.496048\pi
140140 0 0
141141 0 0
142142 0 0
143143 207668.i 0.0710169i
144144 0 0
145145 −1.19079e6 −0.390600
146146 0 0
147147 0 0
148148 0 0
149149 1.62846e6i 0.492288i 0.969233 + 0.246144i 0.0791635π0.0791635\pi
−0.969233 + 0.246144i 0.920836π0.920836\pi
150150 0 0
151151 365620. 0.106194 0.0530968 0.998589i 0.483091π-0.483091\pi
0.0530968 + 0.998589i 0.483091π0.483091\pi
152152 0 0
153153 0 0
154154 0 0
155155 − 3.60162e6i − 0.967170i
156156 0 0
157157 −5.18926e6 −1.34093 −0.670465 0.741941i 0.733905π-0.733905\pi
−0.670465 + 0.741941i 0.733905π0.733905\pi
158158 0 0
159159 0 0
160160 0 0
161161 − 5.44246e6i − 1.30412i
162162 0 0
163163 3.00726e6 0.694397 0.347199 0.937792i 0.387133π-0.387133\pi
0.347199 + 0.937792i 0.387133π0.387133\pi
164164 0 0
165165 0 0
166166 0 0
167167 − 4.78381e6i − 1.02713i −0.858051 0.513564i 0.828325π-0.828325\pi
0.858051 0.513564i 0.171675π-0.171675\pi
168168 0 0
169169 −4.79775e6 −0.993980
170170 0 0
171171 0 0
172172 0 0
173173 − 3.53596e6i − 0.682918i −0.939897 0.341459i 0.889079π-0.889079\pi
0.939897 0.341459i 0.110921π-0.110921\pi
174174 0 0
175175 −1.67759e6 −0.313019
176176 0 0
177177 0 0
178178 0 0
179179 − 8.57291e6i − 1.49475i −0.664401 0.747376i 0.731313π-0.731313\pi
0.664401 0.747376i 0.268687π-0.268687\pi
180180 0 0
181181 1.79208e6 0.302219 0.151110 0.988517i 0.451715π-0.451715\pi
0.151110 + 0.988517i 0.451715π0.451715\pi
182182 0 0
183183 0 0
184184 0 0
185185 − 3.00493e6i − 0.474590i
186186 0 0
187187 −1.91767e6 −0.293257
188188 0 0
189189 0 0
190190 0 0
191191 − 1.01076e7i − 1.45061i −0.688429 0.725304i 0.741699π-0.741699\pi
0.688429 0.725304i 0.258301π-0.258301\pi
192192 0 0
193193 −7.64657e6 −1.06364 −0.531820 0.846857i 0.678492π-0.678492\pi
−0.531820 + 0.846857i 0.678492π0.678492\pi
194194 0 0
195195 0 0
196196 0 0
197197 − 4.94403e6i − 0.646669i −0.946285 0.323335i 0.895196π-0.895196\pi
0.946285 0.323335i 0.104804π-0.104804\pi
198198 0 0
199199 1.96814e6 0.249745 0.124872 0.992173i 0.460148π-0.460148\pi
0.124872 + 0.992173i 0.460148π0.460148\pi
200200 0 0
201201 0 0
202202 0 0
203203 − 4.46069e6i − 0.533229i
204204 0 0
205205 5.24481e6 0.608791
206206 0 0
207207 0 0
208208 0 0
209209 − 1.37530e7i − 1.50647i
210210 0 0
211211 −8.29966e6 −0.883513 −0.441756 0.897135i 0.645644π-0.645644\pi
−0.441756 + 0.897135i 0.645644π0.645644\pi
212212 0 0
213213 0 0
214214 0 0
215215 3.28363e6i 0.330399i
216216 0 0
217217 1.34916e7 1.32034
218218 0 0
219219 0 0
220220 0 0
221221 268325.i 0.0248590i
222222 0 0
223223 −9.37779e6 −0.845641 −0.422821 0.906213i 0.638960π-0.638960\pi
−0.422821 + 0.906213i 0.638960π0.638960\pi
224224 0 0
225225 0 0
226226 0 0
227227 − 3.66419e6i − 0.313257i −0.987658 0.156628i 0.949938π-0.949938\pi
0.987658 0.156628i 0.0500625π-0.0500625\pi
228228 0 0
229229 4.98904e6 0.415442 0.207721 0.978188i 0.433395π-0.433395\pi
0.207721 + 0.978188i 0.433395π0.433395\pi
230230 0 0
231231 0 0
232232 0 0
233233 5.00370e6i 0.395570i 0.980245 + 0.197785i 0.0633749π0.0633749\pi
−0.980245 + 0.197785i 0.936625π0.936625\pi
234234 0 0
235235 3.66890e6 0.282705
236236 0 0
237237 0 0
238238 0 0
239239 1.89151e7i 1.38553i 0.721163 + 0.692765i 0.243608π0.243608\pi
−0.721163 + 0.692765i 0.756392π0.756392\pi
240240 0 0
241241 −1.52515e7 −1.08958 −0.544791 0.838572i 0.683391π-0.683391\pi
−0.544791 + 0.838572i 0.683391π0.683391\pi
242242 0 0
243243 0 0
244244 0 0
245245 − 2.02470e7i − 1.37677i
246246 0 0
247247 −1.92436e6 −0.127702
248248 0 0
249249 0 0
250250 0 0
251251 − 1.44796e7i − 0.915661i −0.889040 0.457830i 0.848627π-0.848627\pi
0.889040 0.457830i 0.151373π-0.151373\pi
252252 0 0
253253 −1.28802e7 −0.795358
254254 0 0
255255 0 0
256256 0 0
257257 − 1.19468e7i − 0.703807i −0.936036 0.351904i 0.885534π-0.885534\pi
0.936036 0.351904i 0.114466π-0.114466\pi
258258 0 0
259259 1.12564e7 0.647889
260260 0 0
261261 0 0
262262 0 0
263263 1.51400e7i 0.832258i 0.909306 + 0.416129i 0.136614π0.136614\pi
−0.909306 + 0.416129i 0.863386π0.863386\pi
264264 0 0
265265 2.94073e7 1.58022
266266 0 0
267267 0 0
268268 0 0
269269 3.37864e7i 1.73574i 0.496789 + 0.867871i 0.334512π0.334512\pi
−0.496789 + 0.867871i 0.665488π0.665488\pi
270270 0 0
271271 292052. 0.0146741 0.00733707 0.999973i 0.497665π-0.497665\pi
0.00733707 + 0.999973i 0.497665π0.497665\pi
272272 0 0
273273 0 0
274274 0 0
275275 3.97021e6i 0.190904i
276276 0 0
277277 −1.18466e7 −0.557384 −0.278692 0.960381i 0.589901π-0.589901\pi
−0.278692 + 0.960381i 0.589901π0.589901\pi
278278 0 0
279279 0 0
280280 0 0
281281 − 2.67693e6i − 0.120648i −0.998179 0.0603238i 0.980787π-0.980787\pi
0.998179 0.0603238i 0.0192133π-0.0192133\pi
282282 0 0
283283 3.11101e7 1.37260 0.686298 0.727321i 0.259235π-0.259235\pi
0.686298 + 0.727321i 0.259235π0.259235\pi
284284 0 0
285285 0 0
286286 0 0
287287 1.96470e7i 0.831094i
288288 0 0
289289 2.16598e7 0.897347
290290 0 0
291291 0 0
292292 0 0
293293 − 2.35392e6i − 0.0935813i −0.998905 0.0467906i 0.985101π-0.985101\pi
0.998905 0.0467906i 0.0148994π-0.0148994\pi
294294 0 0
295295 2.24939e7 0.876193
296296 0 0
297297 0 0
298298 0 0
299299 1.80224e6i 0.0674216i
300300 0 0
301301 −1.23004e7 −0.451046
302302 0 0
303303 0 0
304304 0 0
305305 − 1.52642e7i − 0.537989i
306306 0 0
307307 −3.99249e6 −0.137984 −0.0689920 0.997617i 0.521978π-0.521978\pi
−0.0689920 + 0.997617i 0.521978π0.521978\pi
308308 0 0
309309 0 0
310310 0 0
311311 − 3.01385e7i − 1.00194i −0.865465 0.500969i 0.832977π-0.832977\pi
0.865465 0.500969i 0.167023π-0.167023\pi
312312 0 0
313313 −3.78911e7 −1.23568 −0.617838 0.786305i 0.711991π-0.711991\pi
−0.617838 + 0.786305i 0.711991π0.711991\pi
314314 0 0
315315 0 0
316316 0 0
317317 3.47444e7i 1.09070i 0.838207 + 0.545352i 0.183604π0.183604\pi
−0.838207 + 0.545352i 0.816396π0.816396\pi
318318 0 0
319319 −1.05568e7 −0.325206
320320 0 0
321321 0 0
322322 0 0
323323 − 1.77701e7i − 0.527330i
324324 0 0
325325 555522. 0.0161827
326326 0 0
327327 0 0
328328 0 0
329329 1.37437e7i 0.385936i
330330 0 0
331331 −3.66213e7 −1.00983 −0.504917 0.863168i 0.668477π-0.668477\pi
−0.504917 + 0.863168i 0.668477π0.668477\pi
332332 0 0
333333 0 0
334334 0 0
335335 − 5.23614e7i − 1.39276i
336336 0 0
337337 4.53144e7 1.18398 0.591992 0.805944i 0.298342π-0.298342\pi
0.591992 + 0.805944i 0.298342π0.298342\pi
338338 0 0
339339 0 0
340340 0 0
341341 − 3.19296e7i − 0.805248i
342342 0 0
343343 1.52829e7 0.378724
344344 0 0
345345 0 0
346346 0 0
347347 2.92265e7i 0.699502i 0.936843 + 0.349751i 0.113734π0.113734\pi
−0.936843 + 0.349751i 0.886266π0.886266\pi
348348 0 0
349349 −9.61270e6 −0.226136 −0.113068 0.993587i 0.536068π-0.536068\pi
−0.113068 + 0.993587i 0.536068π0.536068\pi
350350 0 0
351351 0 0
352352 0 0
353353 3.01291e7i 0.684955i 0.939526 + 0.342478i 0.111266π0.111266\pi
−0.939526 + 0.342478i 0.888734π0.888734\pi
354354 0 0
355355 −9.27643e7 −2.07346
356356 0 0
357357 0 0
358358 0 0
359359 3.63910e7i 0.786521i 0.919427 + 0.393260i 0.128653π0.128653\pi
−0.919427 + 0.393260i 0.871347π0.871347\pi
360360 0 0
361361 8.03970e7 1.70891
362362 0 0
363363 0 0
364364 0 0
365365 1.04842e8i 2.15604i
366366 0 0
367367 −5.05958e7 −1.02357 −0.511784 0.859114i 0.671015π-0.671015\pi
−0.511784 + 0.859114i 0.671015π0.671015\pi
368368 0 0
369369 0 0
370370 0 0
371371 1.10159e8i 2.15724i
372372 0 0
373373 −9.44996e7 −1.82097 −0.910487 0.413538i 0.864293π-0.864293\pi
−0.910487 + 0.413538i 0.864293π0.864293\pi
374374 0 0
375375 0 0
376376 0 0
377377 1.47713e6i 0.0275673i
378378 0 0
379379 5.62274e7 1.03283 0.516417 0.856337i 0.327266π-0.327266\pi
0.516417 + 0.856337i 0.327266π0.327266\pi
380380 0 0
381381 0 0
382382 0 0
383383 − 2.12413e7i − 0.378080i −0.981969 0.189040i 0.939462π-0.939462\pi
0.981969 0.189040i 0.0605376π-0.0605376\pi
384384 0 0
385385 −8.61785e7 −1.51014
386386 0 0
387387 0 0
388388 0 0
389389 9.62174e7i 1.63458i 0.576230 + 0.817288i 0.304523π0.304523\pi
−0.576230 + 0.817288i 0.695477π0.695477\pi
390390 0 0
391391 −1.66424e7 −0.278410
392392 0 0
393393 0 0
394394 0 0
395395 7.08679e7i 1.14990i
396396 0 0
397397 2.71686e7 0.434206 0.217103 0.976149i 0.430339π-0.430339\pi
0.217103 + 0.976149i 0.430339π0.430339\pi
398398 0 0
399399 0 0
400400 0 0
401401 − 1.53926e7i − 0.238715i −0.992851 0.119357i 0.961917π-0.961917\pi
0.992851 0.119357i 0.0380834π-0.0380834\pi
402402 0 0
403403 −4.46767e6 −0.0682599
404404 0 0
405405 0 0
406406 0 0
407407 − 2.66397e7i − 0.395135i
408408 0 0
409409 −3.26408e7 −0.477080 −0.238540 0.971133i 0.576669π-0.576669\pi
−0.238540 + 0.971133i 0.576669π0.576669\pi
410410 0 0
411411 0 0
412412 0 0
413413 8.42620e7i 1.19614i
414414 0 0
415415 1.24195e8 1.73765
416416 0 0
417417 0 0
418418 0 0
419419 8.86249e7i 1.20480i 0.798196 + 0.602398i 0.205788π0.205788\pi
−0.798196 + 0.602398i 0.794212π0.794212\pi
420420 0 0
421421 9.51173e7 1.27472 0.637358 0.770568i 0.280027π-0.280027\pi
0.637358 + 0.770568i 0.280027π0.280027\pi
422422 0 0
423423 0 0
424424 0 0
425425 5.12985e6i 0.0668249i
426426 0 0
427427 5.71793e7 0.734439
428428 0 0
429429 0 0
430430 0 0
431431 8.05617e7i 1.00623i 0.864220 + 0.503115i 0.167813π0.167813\pi
−0.864220 + 0.503115i 0.832187π0.832187\pi
432432 0 0
433433 3.50511e7 0.431755 0.215878 0.976420i 0.430739π-0.430739\pi
0.215878 + 0.976420i 0.430739π0.430739\pi
434434 0 0
435435 0 0
436436 0 0
437437 − 1.19355e8i − 1.43020i
438438 0 0
439439 4.63062e7 0.547325 0.273663 0.961826i 0.411765π-0.411765\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
440440 0 0
441441 0 0
442442 0 0
443443 1.19041e8i 1.36926i 0.728893 + 0.684628i 0.240035π0.240035\pi
−0.728893 + 0.684628i 0.759965π0.759965\pi
444444 0 0
445445 −8.85359e7 −1.00471
446446 0 0
447447 0 0
448448 0 0
449449 − 9.75546e7i − 1.07773i −0.842393 0.538864i 0.818854π-0.818854\pi
0.842393 0.538864i 0.181146π-0.181146\pi
450450 0 0
451451 4.64970e7 0.506868
452452 0 0
453453 0 0
454454 0 0
455455 1.20583e7i 0.128013i
456456 0 0
457457 −8.13740e6 −0.0852583 −0.0426292 0.999091i 0.513573π-0.513573\pi
−0.0426292 + 0.999091i 0.513573π0.513573\pi
458458 0 0
459459 0 0
460460 0 0
461461 1.55318e8i 1.58533i 0.609659 + 0.792664i 0.291306π0.291306\pi
−0.609659 + 0.792664i 0.708694π0.708694\pi
462462 0 0
463463 −7.62984e7 −0.768728 −0.384364 0.923182i 0.625579π-0.625579\pi
−0.384364 + 0.923182i 0.625579π0.625579\pi
464464 0 0
465465 0 0
466466 0 0
467467 − 1.85842e8i − 1.82470i −0.409408 0.912352i 0.634265π-0.634265\pi
0.409408 0.912352i 0.365735π-0.365735\pi
468468 0 0
469469 1.96145e8 1.90133
470470 0 0
471471 0 0
472472 0 0
473473 2.91105e7i 0.275084i
474474 0 0
475475 −3.67901e7 −0.343281
476476 0 0
477477 0 0
478478 0 0
479479 1.23819e8i 1.12663i 0.826243 + 0.563314i 0.190474π0.190474\pi
−0.826243 + 0.563314i 0.809526π0.809526\pi
480480 0 0
481481 −3.72749e6 −0.0334951
482482 0 0
483483 0 0
484484 0 0
485485 8.47145e7i 0.742561i
486486 0 0
487487 6.09360e7 0.527578 0.263789 0.964580i 0.415028π-0.415028\pi
0.263789 + 0.964580i 0.415028π0.415028\pi
488488 0 0
489489 0 0
490490 0 0
491491 − 6.48068e7i − 0.547490i −0.961802 0.273745i 0.911738π-0.911738\pi
0.961802 0.273745i 0.0882624π-0.0882624\pi
492492 0 0
493493 −1.36402e7 −0.113836
494494 0 0
495495 0 0
496496 0 0
497497 − 3.47494e8i − 2.83060i
498498 0 0
499499 −2.87096e7 −0.231061 −0.115530 0.993304i 0.536857π-0.536857\pi
−0.115530 + 0.993304i 0.536857π0.536857\pi
500500 0 0
501501 0 0
502502 0 0
503503 1.12463e8i 0.883702i 0.897088 + 0.441851i 0.145678π0.145678\pi
−0.897088 + 0.441851i 0.854322π0.854322\pi
504504 0 0
505505 −8.56156e7 −0.664781
506506 0 0
507507 0 0
508508 0 0
509509 5.61786e7i 0.426008i 0.977051 + 0.213004i 0.0683247π0.0683247\pi
−0.977051 + 0.213004i 0.931675π0.931675\pi
510510 0 0
511511 −3.92737e8 −2.94333
512512 0 0
513513 0 0
514514 0 0
515515 − 1.03160e8i − 0.755245i
516516 0 0
517517 3.25260e7 0.235375
518518 0 0
519519 0 0
520520 0 0
521521 1.68861e8i 1.19403i 0.802230 + 0.597015i 0.203647π0.203647\pi
−0.802230 + 0.597015i 0.796353π0.796353\pi
522522 0 0
523523 2.39748e8 1.67591 0.837955 0.545739i 0.183751π-0.183751\pi
0.837955 + 0.545739i 0.183751π0.183751\pi
524524 0 0
525525 0 0
526526 0 0
527527 − 4.12557e7i − 0.281872i
528528 0 0
529529 3.62552e7 0.244908
530530 0 0
531531 0 0
532532 0 0
533533 − 6.50598e6i − 0.0429666i
534534 0 0
535535 4.74683e7 0.309986
536536 0 0
537537 0 0
538538 0 0
539539 − 1.79496e8i − 1.14627i
540540 0 0
541541 1.85322e8 1.17040 0.585200 0.810889i 0.301016π-0.301016\pi
0.585200 + 0.810889i 0.301016π0.301016\pi
542542 0 0
543543 0 0
544544 0 0
545545 − 1.61066e8i − 0.994978i
546546 0 0
547547 −2.52846e8 −1.54488 −0.772438 0.635090i 0.780963π-0.780963\pi
−0.772438 + 0.635090i 0.780963π0.780963\pi
548548 0 0
549549 0 0
550550 0 0
551551 − 9.78245e7i − 0.584780i
552552 0 0
553553 −2.65470e8 −1.56979
554554 0 0
555555 0 0
556556 0 0
557557 1.01472e8i 0.587194i 0.955929 + 0.293597i 0.0948524π0.0948524\pi
−0.955929 + 0.293597i 0.905148π0.905148\pi
558558 0 0
559559 4.07322e6 0.0233186
560560 0 0
561561 0 0
562562 0 0
563563 1.15852e8i 0.649202i 0.945851 + 0.324601i 0.105230π0.105230\pi
−0.945851 + 0.324601i 0.894770π0.894770\pi
564564 0 0
565565 −3.37130e8 −1.86919
566566 0 0
567567 0 0
568568 0 0
569569 7.30159e7i 0.396352i 0.980166 + 0.198176i 0.0635017π0.0635017\pi
−0.980166 + 0.198176i 0.936498π0.936498\pi
570570 0 0
571571 9.75143e7 0.523793 0.261897 0.965096i 0.415652π-0.415652\pi
0.261897 + 0.965096i 0.415652π0.415652\pi
572572 0 0
573573 0 0
574574 0 0
575575 3.44553e7i 0.181239i
576576 0 0
577577 8.90080e7 0.463342 0.231671 0.972794i 0.425581π-0.425581\pi
0.231671 + 0.972794i 0.425581π0.425581\pi
578578 0 0
579579 0 0
580580 0 0
581581 4.65234e8i 2.37216i
582582 0 0
583583 2.60705e8 1.31566
584584 0 0
585585 0 0
586586 0 0
587587 − 1.26314e8i − 0.624509i −0.949998 0.312255i 0.898916π-0.898916\pi
0.949998 0.312255i 0.101084π-0.101084\pi
588588 0 0
589589 2.95876e8 1.44798
590590 0 0
591591 0 0
592592 0 0
593593 − 1.59275e8i − 0.763805i −0.924203 0.381902i 0.875269π-0.875269\pi
0.924203 0.381902i 0.124731π-0.124731\pi
594594 0 0
595595 −1.11350e8 −0.528615
596596 0 0
597597 0 0
598598 0 0
599599 1.42561e8i 0.663315i 0.943400 + 0.331658i 0.107608π0.107608\pi
−0.943400 + 0.331658i 0.892392π0.892392\pi
600600 0 0
601601 −1.18489e8 −0.545828 −0.272914 0.962038i 0.587987π-0.587987\pi
−0.272914 + 0.962038i 0.587987π0.587987\pi
602602 0 0
603603 0 0
604604 0 0
605605 − 3.94939e7i − 0.178346i
606606 0 0
607607 8.06041e7 0.360405 0.180203 0.983630i 0.442325π-0.442325\pi
0.180203 + 0.983630i 0.442325π0.442325\pi
608608 0 0
609609 0 0
610610 0 0
611611 − 4.55113e6i − 0.0199524i
612612 0 0
613613 −2.49459e8 −1.08297 −0.541486 0.840710i 0.682138π-0.682138\pi
−0.541486 + 0.840710i 0.682138π0.682138\pi
614614 0 0
615615 0 0
616616 0 0
617617 − 3.44285e8i − 1.46576i −0.680358 0.732880i 0.738176π-0.738176\pi
0.680358 0.732880i 0.261824π-0.261824\pi
618618 0 0
619619 −4.59439e7 −0.193712 −0.0968558 0.995298i 0.530879π-0.530879\pi
−0.0968558 + 0.995298i 0.530879π0.530879\pi
620620 0 0
621621 0 0
622622 0 0
623623 − 3.31654e8i − 1.37158i
624624 0 0
625625 −2.84441e8 −1.16507
626626 0 0
627627 0 0
628628 0 0
629629 − 3.44207e7i − 0.138315i
630630 0 0
631631 2.71320e8 1.07993 0.539963 0.841689i 0.318438π-0.318438\pi
0.539963 + 0.841689i 0.318438π0.318438\pi
632632 0 0
633633 0 0
634634 0 0
635635 − 2.11372e8i − 0.825516i
636636 0 0
637637 −2.51156e7 −0.0971684
638638 0 0
639639 0 0
640640 0 0
641641 − 3.13515e8i − 1.19037i −0.803587 0.595187i 0.797078π-0.797078\pi
0.803587 0.595187i 0.202922π-0.202922\pi
642642 0 0
643643 −5.94578e7 −0.223654 −0.111827 0.993728i 0.535670π-0.535670\pi
−0.111827 + 0.993728i 0.535670π0.535670\pi
644644 0 0
645645 0 0
646646 0 0
647647 − 2.04779e8i − 0.756089i −0.925787 0.378045i 0.876597π-0.876597\pi
0.925787 0.378045i 0.123403π-0.123403\pi
648648 0 0
649649 1.99416e8 0.729502
650650 0 0
651651 0 0
652652 0 0
653653 − 3.40035e7i − 0.122119i −0.998134 0.0610596i 0.980552π-0.980552\pi
0.998134 0.0610596i 0.0194480π-0.0194480\pi
654654 0 0
655655 −1.54902e8 −0.551232
656656 0 0
657657 0 0
658658 0 0
659659 − 2.43145e8i − 0.849590i −0.905290 0.424795i 0.860346π-0.860346\pi
0.905290 0.424795i 0.139654π-0.139654\pi
660660 0 0
661661 4.51973e8 1.56498 0.782488 0.622665i 0.213950π-0.213950\pi
0.782488 + 0.622665i 0.213950π0.213950\pi
662662 0 0
663663 0 0
664664 0 0
665665 − 7.98575e8i − 2.71551i
666666 0 0
667667 −9.16164e7 −0.308742
668668 0 0
669669 0 0
670670 0 0
671671 − 1.35322e8i − 0.447920i
672672 0 0
673673 3.17560e8 1.04179 0.520896 0.853620i 0.325598π-0.325598\pi
0.520896 + 0.853620i 0.325598π0.325598\pi
674674 0 0
675675 0 0
676676 0 0
677677 − 6.70541e7i − 0.216102i −0.994145 0.108051i 0.965539π-0.965539\pi
0.994145 0.108051i 0.0344610π-0.0344610\pi
678678 0 0
679679 −3.17339e8 −1.01371
680680 0 0
681681 0 0
682682 0 0
683683 1.51437e8i 0.475303i 0.971350 + 0.237652i 0.0763777π0.0763777\pi
−0.971350 + 0.237652i 0.923622π0.923622\pi
684684 0 0
685685 4.40563e8 1.37068
686686 0 0
687687 0 0
688688 0 0
689689 − 3.64786e7i − 0.111527i
690690 0 0
691691 −9.46804e7 −0.286963 −0.143482 0.989653i 0.545830π-0.545830\pi
−0.143482 + 0.989653i 0.545830π0.545830\pi
692692 0 0
693693 0 0
694694 0 0
695695 − 9.16384e6i − 0.0272975i
696696 0 0
697697 6.00781e7 0.177426
698698 0 0
699699 0 0
700700 0 0
701701 7.92713e6i 0.0230124i 0.999934 + 0.0115062i 0.00366262π0.00366262\pi
−0.999934 + 0.0115062i 0.996337π0.996337\pi
702702 0 0
703703 2.46857e8 0.710526
704704 0 0
705705 0 0
706706 0 0
707707 − 3.20715e8i − 0.907530i
708708 0 0
709709 −6.65474e8 −1.86721 −0.933603 0.358310i 0.883353π-0.883353\pi
−0.933603 + 0.358310i 0.883353π0.883353\pi
710710 0 0
711711 0 0
712712 0 0
713713 − 2.77099e8i − 0.764481i
714714 0 0
715715 2.85375e7 0.0780724
716716 0 0
717717 0 0
718718 0 0
719719 4.90198e8i 1.31882i 0.751784 + 0.659409i 0.229194π0.229194\pi
−0.751784 + 0.659409i 0.770806π0.770806\pi
720720 0 0
721721 3.86434e8 1.03103
722722 0 0
723723 0 0
724724 0 0
725725 2.82398e7i 0.0741051i
726726 0 0
727727 2.09307e8 0.544730 0.272365 0.962194i 0.412194π-0.412194\pi
0.272365 + 0.962194i 0.412194π0.412194\pi
728728 0 0
729729 0 0
730730 0 0
731731 3.76133e7i 0.0962917i
732732 0 0
733733 −3.66672e8 −0.931034 −0.465517 0.885039i 0.654132π-0.654132\pi
−0.465517 + 0.885039i 0.654132π0.654132\pi
734734 0 0
735735 0 0
736736 0 0
737737 − 4.64201e8i − 1.15959i
738738 0 0
739739 6.11387e8 1.51490 0.757449 0.652895i 0.226446π-0.226446\pi
0.757449 + 0.652895i 0.226446π0.226446\pi
740740 0 0
741741 0 0
742742 0 0
743743 − 2.10111e8i − 0.512252i −0.966643 0.256126i 0.917554π-0.917554\pi
0.966643 0.256126i 0.0824461π-0.0824461\pi
744744 0 0
745745 2.23781e8 0.541196
746746 0 0
747747 0 0
748748 0 0
749749 1.77816e8i 0.423180i
750750 0 0
751751 −5.05697e8 −1.19391 −0.596953 0.802276i 0.703622π-0.703622\pi
−0.596953 + 0.802276i 0.703622π0.703622\pi
752752 0 0
753753 0 0
754754 0 0
755755 − 5.02430e7i − 0.116744i
756756 0 0
757757 4.19839e8 0.967822 0.483911 0.875117i 0.339216π-0.339216\pi
0.483911 + 0.875117i 0.339216π0.339216\pi
758758 0 0
759759 0 0
760760 0 0
761761 − 7.32156e8i − 1.66131i −0.556791 0.830653i 0.687968π-0.687968\pi
0.556791 0.830653i 0.312032π-0.312032\pi
762762 0 0
763763 6.03350e8 1.35830
764764 0 0
765765 0 0
766766 0 0
767767 − 2.79029e7i − 0.0618390i
768768 0 0
769769 −2.53294e8 −0.556988 −0.278494 0.960438i 0.589835π-0.589835\pi
−0.278494 + 0.960438i 0.589835π0.589835\pi
770770 0 0
771771 0 0
772772 0 0
773773 7.82197e8i 1.69347i 0.532014 + 0.846735i 0.321435π0.321435\pi
−0.532014 + 0.846735i 0.678565π0.678565\pi
774774 0 0
775775 −8.54131e7 −0.183493
776776 0 0
777777 0 0
778778 0 0
779779 4.30865e8i 0.911443i
780780 0 0
781781 −8.22386e8 −1.72632
782782 0 0
783783 0 0
784784 0 0
785785 7.13101e8i 1.47415i
786786 0 0
787787 −6.81837e8 −1.39880 −0.699401 0.714730i 0.746550π-0.746550\pi
−0.699401 + 0.714730i 0.746550π0.746550\pi
788788 0 0
789789 0 0
790790 0 0
791791 − 1.26289e9i − 2.55173i
792792 0 0
793793 −1.89346e7 −0.0379696
794794 0 0
795795 0 0
796796 0 0
797797 5.08452e7i 0.100433i 0.998738 + 0.0502163i 0.0159911π0.0159911\pi
−0.998738 + 0.0502163i 0.984009π0.984009\pi
798798 0 0
799799 4.20264e7 0.0823915
800800 0 0
801801 0 0
802802 0 0
803803 9.29460e8i 1.79508i
804804 0 0
805805 −7.47896e8 −1.43369
806806 0 0
807807 0 0
808808 0 0
809809 1.02851e7i 0.0194251i 0.999953 + 0.00971257i 0.00309166π0.00309166\pi
−0.999953 + 0.00971257i 0.996908π0.996908\pi
810810 0 0
811811 −4.84952e8 −0.909152 −0.454576 0.890708i 0.650209π-0.650209\pi
−0.454576 + 0.890708i 0.650209π0.650209\pi
812812 0 0
813813 0 0
814814 0 0
815815 − 4.13254e8i − 0.763385i
816816 0 0
817817 −2.69753e8 −0.494653
818818 0 0
819819 0 0
820820 0 0
821821 4.96161e8i 0.896588i 0.893886 + 0.448294i 0.147968π0.147968\pi
−0.893886 + 0.448294i 0.852032π0.852032\pi
822822 0 0
823823 3.21483e8 0.576711 0.288356 0.957523i 0.406891π-0.406891\pi
0.288356 + 0.957523i 0.406891π0.406891\pi
824824 0 0
825825 0 0
826826 0 0
827827 7.54902e8i 1.33467i 0.744757 + 0.667336i 0.232565π0.232565\pi
−0.744757 + 0.667336i 0.767435π0.767435\pi
828828 0 0
829829 −5.82262e8 −1.02201 −0.511004 0.859578i 0.670726π-0.670726\pi
−0.511004 + 0.859578i 0.670726π0.670726\pi
830830 0 0
831831 0 0
832832 0 0
833833 − 2.31924e8i − 0.401247i
834834 0 0
835835 −6.57385e8 −1.12917
836836 0 0
837837 0 0
838838 0 0
839839 6.64141e8i 1.12454i 0.826954 + 0.562270i 0.190072π0.190072\pi
−0.826954 + 0.562270i 0.809928π0.809928\pi
840840 0 0
841841 5.19734e8 0.873762
842842 0 0
843843 0 0
844844 0 0
845845 6.59301e8i 1.09273i
846846 0 0
847847 1.47943e8 0.243470
848848 0 0
849849 0 0
850850 0 0
851851 − 2.31191e8i − 0.375131i
852852 0 0
853853 7.87779e8 1.26928 0.634640 0.772808i 0.281148π-0.281148\pi
0.634640 + 0.772808i 0.281148π0.281148\pi
854854 0 0
855855 0 0
856856 0 0
857857 − 9.65175e8i − 1.53343i −0.641988 0.766715i 0.721890π-0.721890\pi
0.641988 0.766715i 0.278110π-0.278110\pi
858858 0 0
859859 5.95457e8 0.939444 0.469722 0.882814i 0.344354π-0.344354\pi
0.469722 + 0.882814i 0.344354π0.344354\pi
860860 0 0
861861 0 0
862862 0 0
863863 − 9.85551e8i − 1.53337i −0.642024 0.766684i 0.721905π-0.721905\pi
0.642024 0.766684i 0.278095π-0.278095\pi
864864 0 0
865865 −4.85907e8 −0.750766
866866 0 0
867867 0 0
868868 0 0
869869 6.28267e8i 0.957382i
870870 0 0
871871 −6.49522e7 −0.0982969
872872 0 0
873873 0 0
874874 0 0
875875 − 8.74763e8i − 1.30577i
876876 0 0
877877 3.68680e8 0.546577 0.273288 0.961932i 0.411889π-0.411889\pi
0.273288 + 0.961932i 0.411889π0.411889\pi
878878 0 0
879879 0 0
880880 0 0
881881 7.29792e8i 1.06726i 0.845717 + 0.533632i 0.179173π0.179173\pi
−0.845717 + 0.533632i 0.820827π0.820827\pi
882882 0 0
883883 7.12900e7 0.103549 0.0517746 0.998659i 0.483512π-0.483512\pi
0.0517746 + 0.998659i 0.483512π0.483512\pi
884884 0 0
885885 0 0
886886 0 0
887887 3.15305e8i 0.451814i 0.974149 + 0.225907i 0.0725346π0.0725346\pi
−0.974149 + 0.225907i 0.927465π0.927465\pi
888888 0 0
889889 7.91795e8 1.12696
890890 0 0
891891 0 0
892892 0 0
893893 3.01403e8i 0.423247i
894894 0 0
895895 −1.17808e9 −1.64326
896896 0 0
897897 0 0
898898 0 0
899899 − 2.27113e8i − 0.312581i
900900 0 0
901901 3.36853e8 0.460539
902902 0 0
903903 0 0
904904 0 0
905905 − 2.46266e8i − 0.332245i
906906 0 0
907907 5.70419e8 0.764491 0.382245 0.924061i 0.375151π-0.375151\pi
0.382245 + 0.924061i 0.375151π0.375151\pi
908908 0 0
909909 0 0
910910 0 0
911911 3.43557e8i 0.454406i 0.973847 + 0.227203i 0.0729581π0.0729581\pi
−0.973847 + 0.227203i 0.927042π0.927042\pi
912912 0 0
913913 1.10103e9 1.44673
914914 0 0
915915 0 0
916916 0 0
917917 − 5.80262e8i − 0.752517i
918918 0 0
919919 −7.92851e8 −1.02152 −0.510758 0.859725i 0.670635π-0.670635\pi
−0.510758 + 0.859725i 0.670635π0.670635\pi
920920 0 0
921921 0 0
922922 0 0
923923 1.15070e8i 0.146339i
924924 0 0
925925 −7.12624e7 −0.0900400
926926 0 0
927927 0 0
928928 0 0
929929 − 1.82427e8i − 0.227531i −0.993508 0.113766i 0.963709π-0.963709\pi
0.993508 0.113766i 0.0362913π-0.0362913\pi
930930 0 0
931931 1.66331e9 2.06121
932932 0 0
933933 0 0
934934 0 0
935935 2.63523e8i 0.322392i
936936 0 0
937937 −3.34488e8 −0.406594 −0.203297 0.979117i 0.565166π-0.565166\pi
−0.203297 + 0.979117i 0.565166π0.565166\pi
938938 0 0
939939 0 0
940940 0 0
941941 2.91160e8i 0.349433i 0.984619 + 0.174716i 0.0559008π0.0559008\pi
−0.984619 + 0.174716i 0.944099π0.944099\pi
942942 0 0
943943 4.03522e8 0.481207
944944 0 0
945945 0 0
946946 0 0
947947 1.69634e8i 0.199739i 0.995001 + 0.0998694i 0.0318425π0.0318425\pi
−0.995001 + 0.0998694i 0.968158π0.968158\pi
948948 0 0
949949 1.30053e8 0.152167
950950 0 0
951951 0 0
952952 0 0
953953 − 5.17958e8i − 0.598434i −0.954185 0.299217i 0.903275π-0.903275\pi
0.954185 0.299217i 0.0967254π-0.0967254\pi
954954 0 0
955955 −1.38898e9 −1.59473
956956 0 0
957957 0 0
958958 0 0
959959 1.65034e9i 1.87119i
960960 0 0
961961 −2.00587e8 −0.226013
962962 0 0
963963 0 0
964964 0 0
965965 1.05078e9i 1.16931i
966966 0 0
967967 1.37422e9 1.51976 0.759881 0.650062i 0.225257π-0.225257\pi
0.759881 + 0.650062i 0.225257π0.225257\pi
968968 0 0
969969 0 0
970970 0 0
971971 7.45510e8i 0.814321i 0.913357 + 0.407160i 0.133481π0.133481\pi
−0.913357 + 0.407160i 0.866519π0.866519\pi
972972 0 0
973973 3.43276e7 0.0372653
974974 0 0
975975 0 0
976976 0 0
977977 9.80224e8i 1.05109i 0.850764 + 0.525547i 0.176139π0.176139\pi
−0.850764 + 0.525547i 0.823861π0.823861\pi
978978 0 0
979979 −7.84900e8 −0.836501
980980 0 0
981981 0 0
982982 0 0
983983 1.01328e9i 1.06676i 0.845875 + 0.533381i 0.179079π0.179079\pi
−0.845875 + 0.533381i 0.820921π0.820921\pi
984984 0 0
985985 −6.79402e8 −0.710916
986986 0 0
987987 0 0
988988 0 0
989989 2.52634e8i 0.261158i
990990 0 0
991991 1.85231e9 1.90324 0.951620 0.307279i 0.0994183π-0.0994183\pi
0.951620 + 0.307279i 0.0994183π0.0994183\pi
992992 0 0
993993 0 0
994994 0 0
995995 − 2.70459e8i − 0.274557i
996996 0 0
997997 1.25665e9 1.26803 0.634013 0.773322i 0.281407π-0.281407\pi
0.634013 + 0.773322i 0.281407π0.281407\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 432.7.e.j.161.1 4
3.2 odd 2 inner 432.7.e.j.161.4 4
4.3 odd 2 27.7.b.c.26.4 yes 4
12.11 even 2 27.7.b.c.26.1 4
36.7 odd 6 81.7.d.e.53.4 8
36.11 even 6 81.7.d.e.53.1 8
36.23 even 6 81.7.d.e.26.4 8
36.31 odd 6 81.7.d.e.26.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.7.b.c.26.1 4 12.11 even 2
27.7.b.c.26.4 yes 4 4.3 odd 2
81.7.d.e.26.1 8 36.31 odd 6
81.7.d.e.26.4 8 36.23 even 6
81.7.d.e.53.1 8 36.11 even 6
81.7.d.e.53.4 8 36.7 odd 6
432.7.e.j.161.1 4 1.1 even 1 trivial
432.7.e.j.161.4 4 3.2 odd 2 inner