Properties

Label 1323.2.a.bd.1.2
Level 13231323
Weight 22
Character 1323.1
Self dual yes
Analytic conductor 10.56410.564
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1323,2,Mod(1,1323)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1323, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("1323.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1323=3372 1323 = 3^{3} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1323.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,4,0,0,0,0,0,12,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 10.564208187410.5642081874
Analytic rank: 00
Dimension: 44
Coefficient field: 4.4.7168.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x46x2+7 x^{4} - 6x^{2} + 7 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
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 1.25928-1.25928 of defining polynomial
Character χ\chi == 1323.1

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) == q1.25928q20.414214q41.25928q5+3.04017q8+1.58579q104.82106q11+1.17157q133.00000q164.29945q17+1.58579q19+0.521611q20+6.07107q22+6.60195q233.41421q251.47534q265.03712q29+10.6569q312.30250q32+5.41421q345.24264q371.99695q383.82843q400.521611q41+7.07107q43+1.99695q448.31371q4611.4230q47+4.29945q500.485281q521.04322q53+6.07107q55+6.34315q58+1.78089q59+10.4853q6113.4200q62+8.89949q641.47534q65+5.65685q67+1.78089q68+8.81496q71+8.58579q73+6.60195q740.656854q7613.8995q79+3.77784q80+0.656854q82+14.6792q83+5.41421q858.90446q8614.6569q88+17.7194q892.73462q92+14.3848q941.99695q95+9.65685q97+O(q100)q-1.25928 q^{2} -0.414214 q^{4} -1.25928 q^{5} +3.04017 q^{8} +1.58579 q^{10} -4.82106 q^{11} +1.17157 q^{13} -3.00000 q^{16} -4.29945 q^{17} +1.58579 q^{19} +0.521611 q^{20} +6.07107 q^{22} +6.60195 q^{23} -3.41421 q^{25} -1.47534 q^{26} -5.03712 q^{29} +10.6569 q^{31} -2.30250 q^{32} +5.41421 q^{34} -5.24264 q^{37} -1.99695 q^{38} -3.82843 q^{40} -0.521611 q^{41} +7.07107 q^{43} +1.99695 q^{44} -8.31371 q^{46} -11.4230 q^{47} +4.29945 q^{50} -0.485281 q^{52} -1.04322 q^{53} +6.07107 q^{55} +6.34315 q^{58} +1.78089 q^{59} +10.4853 q^{61} -13.4200 q^{62} +8.89949 q^{64} -1.47534 q^{65} +5.65685 q^{67} +1.78089 q^{68} +8.81496 q^{71} +8.58579 q^{73} +6.60195 q^{74} -0.656854 q^{76} -13.8995 q^{79} +3.77784 q^{80} +0.656854 q^{82} +14.6792 q^{83} +5.41421 q^{85} -8.90446 q^{86} -14.6569 q^{88} +17.7194 q^{89} -2.73462 q^{92} +14.3848 q^{94} -1.99695 q^{95} +9.65685 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+4q4+12q10+16q1312q16+12q194q228q25+20q31+16q344q374q40+12q46+32q524q55+48q58+8q614q64+40q73++16q97+O(q100) 4 q + 4 q^{4} + 12 q^{10} + 16 q^{13} - 12 q^{16} + 12 q^{19} - 4 q^{22} - 8 q^{25} + 20 q^{31} + 16 q^{34} - 4 q^{37} - 4 q^{40} + 12 q^{46} + 32 q^{52} - 4 q^{55} + 48 q^{58} + 8 q^{61} - 4 q^{64} + 40 q^{73}+ \cdots + 16 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 −1.25928 −0.890446 −0.445223 0.895420i 0.646876π-0.646876\pi
−0.445223 + 0.895420i 0.646876π0.646876\pi
33 0 0
44 −0.414214 −0.207107
55 −1.25928 −0.563167 −0.281584 0.959537i 0.590860π-0.590860\pi
−0.281584 + 0.959537i 0.590860π0.590860\pi
66 0 0
77 0 0
88 3.04017 1.07486
99 0 0
1010 1.58579 0.501470
1111 −4.82106 −1.45360 −0.726802 0.686847i 0.758994π-0.758994\pi
−0.726802 + 0.686847i 0.758994π0.758994\pi
1212 0 0
1313 1.17157 0.324936 0.162468 0.986714i 0.448055π-0.448055\pi
0.162468 + 0.986714i 0.448055π0.448055\pi
1414 0 0
1515 0 0
1616 −3.00000 −0.750000
1717 −4.29945 −1.04277 −0.521385 0.853322i 0.674584π-0.674584\pi
−0.521385 + 0.853322i 0.674584π0.674584\pi
1818 0 0
1919 1.58579 0.363804 0.181902 0.983317i 0.441775π-0.441775\pi
0.181902 + 0.983317i 0.441775π0.441775\pi
2020 0.521611 0.116636
2121 0 0
2222 6.07107 1.29436
2323 6.60195 1.37660 0.688301 0.725425i 0.258357π-0.258357\pi
0.688301 + 0.725425i 0.258357π0.258357\pi
2424 0 0
2525 −3.41421 −0.682843
2626 −1.47534 −0.289338
2727 0 0
2828 0 0
2929 −5.03712 −0.935370 −0.467685 0.883895i 0.654912π-0.654912\pi
−0.467685 + 0.883895i 0.654912π0.654912\pi
3030 0 0
3131 10.6569 1.91403 0.957014 0.290043i 0.0936695π-0.0936695\pi
0.957014 + 0.290043i 0.0936695π0.0936695\pi
3232 −2.30250 −0.407029
3333 0 0
3434 5.41421 0.928530
3535 0 0
3636 0 0
3737 −5.24264 −0.861885 −0.430942 0.902379i 0.641819π-0.641819\pi
−0.430942 + 0.902379i 0.641819π0.641819\pi
3838 −1.99695 −0.323948
3939 0 0
4040 −3.82843 −0.605327
4141 −0.521611 −0.0814619 −0.0407310 0.999170i 0.512969π-0.512969\pi
−0.0407310 + 0.999170i 0.512969π0.512969\pi
4242 0 0
4343 7.07107 1.07833 0.539164 0.842201i 0.318740π-0.318740\pi
0.539164 + 0.842201i 0.318740π0.318740\pi
4444 1.99695 0.301051
4545 0 0
4646 −8.31371 −1.22579
4747 −11.4230 −1.66622 −0.833109 0.553109i 0.813441π-0.813441\pi
−0.833109 + 0.553109i 0.813441π0.813441\pi
4848 0 0
4949 0 0
5050 4.29945 0.608034
5151 0 0
5252 −0.485281 −0.0672964
5353 −1.04322 −0.143298 −0.0716488 0.997430i 0.522826π-0.522826\pi
−0.0716488 + 0.997430i 0.522826π0.522826\pi
5454 0 0
5555 6.07107 0.818623
5656 0 0
5757 0 0
5858 6.34315 0.832896
5959 1.78089 0.231852 0.115926 0.993258i 0.463016π-0.463016\pi
0.115926 + 0.993258i 0.463016π0.463016\pi
6060 0 0
6161 10.4853 1.34250 0.671251 0.741230i 0.265757π-0.265757\pi
0.671251 + 0.741230i 0.265757π0.265757\pi
6262 −13.4200 −1.70434
6363 0 0
6464 8.89949 1.11244
6565 −1.47534 −0.182993
6666 0 0
6767 5.65685 0.691095 0.345547 0.938401i 0.387693π-0.387693\pi
0.345547 + 0.938401i 0.387693π0.387693\pi
6868 1.78089 0.215965
6969 0 0
7070 0 0
7171 8.81496 1.04614 0.523072 0.852289i 0.324786π-0.324786\pi
0.523072 + 0.852289i 0.324786π0.324786\pi
7272 0 0
7373 8.58579 1.00489 0.502445 0.864609i 0.332434π-0.332434\pi
0.502445 + 0.864609i 0.332434π0.332434\pi
7474 6.60195 0.767461
7575 0 0
7676 −0.656854 −0.0753463
7777 0 0
7878 0 0
7979 −13.8995 −1.56382 −0.781908 0.623394i 0.785753π-0.785753\pi
−0.781908 + 0.623394i 0.785753π0.785753\pi
8080 3.77784 0.422375
8181 0 0
8282 0.656854 0.0725374
8383 14.6792 1.61126 0.805628 0.592421i 0.201828π-0.201828\pi
0.805628 + 0.592421i 0.201828π0.201828\pi
8484 0 0
8585 5.41421 0.587254
8686 −8.90446 −0.960192
8787 0 0
8888 −14.6569 −1.56243
8989 17.7194 1.87825 0.939127 0.343570i 0.111636π-0.111636\pi
0.939127 + 0.343570i 0.111636π0.111636\pi
9090 0 0
9191 0 0
9292 −2.73462 −0.285104
9393 0 0
9494 14.3848 1.48368
9595 −1.99695 −0.204883
9696 0 0
9797 9.65685 0.980505 0.490252 0.871580i 0.336905π-0.336905\pi
0.490252 + 0.871580i 0.336905π0.336905\pi
9898 0 0
9999 0 0
100100 1.41421 0.141421
101101 16.4601 1.63784 0.818922 0.573904i 0.194572π-0.194572\pi
0.818922 + 0.573904i 0.194572π0.194572\pi
102102 0 0
103103 −3.48528 −0.343415 −0.171707 0.985148i 0.554928π-0.554928\pi
−0.171707 + 0.985148i 0.554928π0.554928\pi
104104 3.56178 0.349261
105105 0 0
106106 1.31371 0.127599
107107 6.81801 0.659122 0.329561 0.944134i 0.393099π-0.393099\pi
0.329561 + 0.944134i 0.393099π0.393099\pi
108108 0 0
109109 2.65685 0.254480 0.127240 0.991872i 0.459388π-0.459388\pi
0.127240 + 0.991872i 0.459388π0.459388\pi
110110 −7.64518 −0.728939
111111 0 0
112112 0 0
113113 −11.4230 −1.07459 −0.537293 0.843395i 0.680553π-0.680553\pi
−0.537293 + 0.843395i 0.680553π0.680553\pi
114114 0 0
115115 −8.31371 −0.775257
116116 2.08644 0.193721
117117 0 0
118118 −2.24264 −0.206452
119119 0 0
120120 0 0
121121 12.2426 1.11297
122122 −13.2039 −1.19543
123123 0 0
124124 −4.41421 −0.396408
125125 10.5959 0.947722
126126 0 0
127127 −4.82843 −0.428454 −0.214227 0.976784i 0.568723π-0.568723\pi
−0.214227 + 0.976784i 0.568723π0.568723\pi
128128 −6.60195 −0.583536
129129 0 0
130130 1.85786 0.162945
131131 15.4169 1.34698 0.673491 0.739195i 0.264794π-0.264794\pi
0.673491 + 0.739195i 0.264794π0.264794\pi
132132 0 0
133133 0 0
134134 −7.12356 −0.615382
135135 0 0
136136 −13.0711 −1.12083
137137 4.60500 0.393432 0.196716 0.980461i 0.436972π-0.436972\pi
0.196716 + 0.980461i 0.436972π0.436972\pi
138138 0 0
139139 −8.82843 −0.748817 −0.374409 0.927264i 0.622154π-0.622154\pi
−0.374409 + 0.927264i 0.622154π0.622154\pi
140140 0 0
141141 0 0
142142 −11.1005 −0.931534
143143 −5.64823 −0.472328
144144 0 0
145145 6.34315 0.526770
146146 −10.8119 −0.894800
147147 0 0
148148 2.17157 0.178502
149149 −6.81801 −0.558553 −0.279277 0.960211i 0.590095π-0.590095\pi
−0.279277 + 0.960211i 0.590095π0.590095\pi
150150 0 0
151151 4.24264 0.345261 0.172631 0.984987i 0.444773π-0.444773\pi
0.172631 + 0.984987i 0.444773π0.444773\pi
152152 4.82106 0.391040
153153 0 0
154154 0 0
155155 −13.4200 −1.07792
156156 0 0
157157 18.4853 1.47529 0.737643 0.675191i 0.235939π-0.235939\pi
0.737643 + 0.675191i 0.235939π0.235939\pi
158158 17.5034 1.39249
159159 0 0
160160 2.89949 0.229225
161161 0 0
162162 0 0
163163 −11.6569 −0.913035 −0.456518 0.889714i 0.650903π-0.650903\pi
−0.456518 + 0.889714i 0.650903π0.650903\pi
164164 0.216058 0.0168713
165165 0 0
166166 −18.4853 −1.43474
167167 −11.4230 −0.883939 −0.441970 0.897030i 0.645720π-0.645720\pi
−0.441970 + 0.897030i 0.645720π0.645720\pi
168168 0 0
169169 −11.6274 −0.894417
170170 −6.81801 −0.522918
171171 0 0
172172 −2.92893 −0.223329
173173 13.1144 0.997070 0.498535 0.866869i 0.333871π-0.333871\pi
0.498535 + 0.866869i 0.333871π0.333871\pi
174174 0 0
175175 0 0
176176 14.4632 1.09020
177177 0 0
178178 −22.3137 −1.67248
179179 17.9355 1.34056 0.670280 0.742108i 0.266174π-0.266174\pi
0.670280 + 0.742108i 0.266174π0.266174\pi
180180 0 0
181181 4.10051 0.304788 0.152394 0.988320i 0.451302π-0.451302\pi
0.152394 + 0.988320i 0.451302π0.451302\pi
182182 0 0
183183 0 0
184184 20.0711 1.47966
185185 6.60195 0.485385
186186 0 0
187187 20.7279 1.51578
188188 4.73157 0.345085
189189 0 0
190190 2.51472 0.182437
191191 −9.12051 −0.659937 −0.329969 0.943992i 0.607038π-0.607038\pi
−0.329969 + 0.943992i 0.607038π0.607038\pi
192192 0 0
193193 23.6569 1.70286 0.851429 0.524470i 0.175737π-0.175737\pi
0.851429 + 0.524470i 0.175737π0.175737\pi
194194 −12.1607 −0.873086
195195 0 0
196196 0 0
197197 3.25623 0.231997 0.115998 0.993249i 0.462993π-0.462993\pi
0.115998 + 0.993249i 0.462993π0.462993\pi
198198 0 0
199199 −3.92893 −0.278515 −0.139257 0.990256i 0.544472π-0.544472\pi
−0.139257 + 0.990256i 0.544472π0.544472\pi
200200 −10.3798 −0.733962
201201 0 0
202202 −20.7279 −1.45841
203203 0 0
204204 0 0
205205 0.656854 0.0458767
206206 4.38895 0.305792
207207 0 0
208208 −3.51472 −0.243702
209209 −7.64518 −0.528828
210210 0 0
211211 −8.24264 −0.567447 −0.283723 0.958906i 0.591570π-0.591570\pi
−0.283723 + 0.958906i 0.591570π0.591570\pi
212212 0.432117 0.0296779
213213 0 0
214214 −8.58579 −0.586912
215215 −8.90446 −0.607279
216216 0 0
217217 0 0
218218 −3.34572 −0.226601
219219 0 0
220220 −2.51472 −0.169542
221221 −5.03712 −0.338833
222222 0 0
223223 −13.7279 −0.919290 −0.459645 0.888103i 0.652023π-0.652023\pi
−0.459645 + 0.888103i 0.652023π0.652023\pi
224224 0 0
225225 0 0
226226 14.3848 0.956861
227227 −7.86123 −0.521768 −0.260884 0.965370i 0.584014π-0.584014\pi
−0.260884 + 0.965370i 0.584014π0.584014\pi
228228 0 0
229229 1.51472 0.100095 0.0500477 0.998747i 0.484063π-0.484063\pi
0.0500477 + 0.998747i 0.484063π0.484063\pi
230230 10.4693 0.690324
231231 0 0
232232 −15.3137 −1.00539
233233 20.0219 1.31168 0.655840 0.754900i 0.272315π-0.272315\pi
0.655840 + 0.754900i 0.272315π0.272315\pi
234234 0 0
235235 14.3848 0.938359
236236 −0.737669 −0.0480182
237237 0 0
238238 0 0
239239 1.78089 0.115196 0.0575981 0.998340i 0.481656π-0.481656\pi
0.0575981 + 0.998340i 0.481656π0.481656\pi
240240 0 0
241241 −24.7279 −1.59287 −0.796433 0.604727i 0.793282π-0.793282\pi
−0.796433 + 0.604727i 0.793282π0.793282\pi
242242 −15.4169 −0.991037
243243 0 0
244244 −4.34315 −0.278041
245245 0 0
246246 0 0
247247 1.85786 0.118213
248248 32.3987 2.05732
249249 0 0
250250 −13.3431 −0.843895
251251 11.7286 0.740301 0.370150 0.928972i 0.379306π-0.379306\pi
0.370150 + 0.928972i 0.379306π0.379306\pi
252252 0 0
253253 −31.8284 −2.00104
254254 6.08034 0.381515
255255 0 0
256256 −9.48528 −0.592830
257257 −10.2903 −0.641891 −0.320946 0.947098i 0.604001π-0.604001\pi
−0.320946 + 0.947098i 0.604001π0.604001\pi
258258 0 0
259259 0 0
260260 0.611105 0.0378991
261261 0 0
262262 −19.4142 −1.19941
263263 −6.16984 −0.380448 −0.190224 0.981741i 0.560921π-0.560921\pi
−0.190224 + 0.981741i 0.560921π0.560921\pi
264264 0 0
265265 1.31371 0.0807005
266266 0 0
267267 0 0
268268 −2.34315 −0.143130
269269 0.521611 0.0318032 0.0159016 0.999874i 0.494938π-0.494938\pi
0.0159016 + 0.999874i 0.494938π0.494938\pi
270270 0 0
271271 −16.8284 −1.02225 −0.511127 0.859505i 0.670772π-0.670772\pi
−0.511127 + 0.859505i 0.670772π0.670772\pi
272272 12.8984 0.782078
273273 0 0
274274 −5.79899 −0.350330
275275 16.4601 0.992584
276276 0 0
277277 8.55635 0.514101 0.257051 0.966398i 0.417249π-0.417249\pi
0.257051 + 0.966398i 0.417249π0.417249\pi
278278 11.1175 0.666781
279279 0 0
280280 0 0
281281 22.5405 1.34465 0.672326 0.740255i 0.265295π-0.265295\pi
0.672326 + 0.740255i 0.265295π0.265295\pi
282282 0 0
283283 8.48528 0.504398 0.252199 0.967675i 0.418846π-0.418846\pi
0.252199 + 0.967675i 0.418846π0.418846\pi
284284 −3.65128 −0.216663
285285 0 0
286286 7.11270 0.420583
287287 0 0
288288 0 0
289289 1.48528 0.0873695
290290 −7.98780 −0.469060
291291 0 0
292292 −3.55635 −0.208120
293293 −9.94768 −0.581149 −0.290575 0.956852i 0.593846π-0.593846\pi
−0.290575 + 0.956852i 0.593846π0.593846\pi
294294 0 0
295295 −2.24264 −0.130572
296296 −15.9385 −0.926408
297297 0 0
298298 8.58579 0.497361
299299 7.73467 0.447307
300300 0 0
301301 0 0
302302 −5.34267 −0.307436
303303 0 0
304304 −4.75736 −0.272853
305305 −13.2039 −0.756053
306306 0 0
307307 −9.92893 −0.566674 −0.283337 0.959020i 0.591442π-0.591442\pi
−0.283337 + 0.959020i 0.591442π0.591442\pi
308308 0 0
309309 0 0
310310 16.8995 0.959827
311311 −22.2349 −1.26083 −0.630413 0.776260i 0.717115π-0.717115\pi
−0.630413 + 0.776260i 0.717115π0.717115\pi
312312 0 0
313313 24.8284 1.40339 0.701693 0.712480i 0.252428π-0.252428\pi
0.701693 + 0.712480i 0.252428π0.252428\pi
314314 −23.2781 −1.31366
315315 0 0
316316 5.75736 0.323877
317317 19.4108 1.09022 0.545110 0.838365i 0.316488π-0.316488\pi
0.545110 + 0.838365i 0.316488π0.316488\pi
318318 0 0
319319 24.2843 1.35966
320320 −11.2070 −0.626488
321321 0 0
322322 0 0
323323 −6.81801 −0.379364
324324 0 0
325325 −4.00000 −0.221880
326326 14.6792 0.813008
327327 0 0
328328 −1.58579 −0.0875604
329329 0 0
330330 0 0
331331 −2.97056 −0.163277 −0.0816384 0.996662i 0.526015π-0.526015\pi
−0.0816384 + 0.996662i 0.526015π0.526015\pi
332332 −6.08034 −0.333702
333333 0 0
334334 14.3848 0.787100
335335 −7.12356 −0.389202
336336 0 0
337337 −28.7990 −1.56878 −0.784390 0.620267i 0.787024π-0.787024\pi
−0.784390 + 0.620267i 0.787024π0.787024\pi
338338 14.6422 0.796429
339339 0 0
340340 −2.24264 −0.121624
341341 −51.3774 −2.78224
342342 0 0
343343 0 0
344344 21.4973 1.15905
345345 0 0
346346 −16.5147 −0.887837
347347 −11.6391 −0.624818 −0.312409 0.949948i 0.601136π-0.601136\pi
−0.312409 + 0.949948i 0.601136π0.601136\pi
348348 0 0
349349 −1.07107 −0.0573329 −0.0286665 0.999589i 0.509126π-0.509126\pi
−0.0286665 + 0.999589i 0.509126π0.509126\pi
350350 0 0
351351 0 0
352352 11.1005 0.591659
353353 −28.4048 −1.51183 −0.755916 0.654668i 0.772808π-0.772808\pi
−0.755916 + 0.654668i 0.772808π0.772808\pi
354354 0 0
355355 −11.1005 −0.589154
356356 −7.33962 −0.388999
357357 0 0
358358 −22.5858 −1.19370
359359 −26.5344 −1.40043 −0.700215 0.713932i 0.746913π-0.746913\pi
−0.700215 + 0.713932i 0.746913π0.746913\pi
360360 0 0
361361 −16.4853 −0.867646
362362 −5.16368 −0.271397
363363 0 0
364364 0 0
365365 −10.8119 −0.565921
366366 0 0
367367 −7.38478 −0.385482 −0.192741 0.981250i 0.561738π-0.561738\pi
−0.192741 + 0.981250i 0.561738π0.561738\pi
368368 −19.8059 −1.03245
369369 0 0
370370 −8.31371 −0.432209
371371 0 0
372372 0 0
373373 13.1421 0.680474 0.340237 0.940340i 0.389493π-0.389493\pi
0.340237 + 0.940340i 0.389493π0.389493\pi
374374 −26.1023 −1.34972
375375 0 0
376376 −34.7279 −1.79096
377377 −5.90135 −0.303935
378378 0 0
379379 −1.89949 −0.0975705 −0.0487853 0.998809i 0.515535π-0.515535\pi
−0.0487853 + 0.998809i 0.515535π0.515535\pi
380380 0.827164 0.0424326
381381 0 0
382382 11.4853 0.587638
383383 6.81801 0.348384 0.174192 0.984712i 0.444269π-0.444269\pi
0.174192 + 0.984712i 0.444269π0.444269\pi
384384 0 0
385385 0 0
386386 −29.7906 −1.51630
387387 0 0
388388 −4.00000 −0.203069
389389 −11.1175 −0.563678 −0.281839 0.959462i 0.590944π-0.590944\pi
−0.281839 + 0.959462i 0.590944π0.590944\pi
390390 0 0
391391 −28.3848 −1.43548
392392 0 0
393393 0 0
394394 −4.10051 −0.206580
395395 17.5034 0.880690
396396 0 0
397397 8.92893 0.448130 0.224065 0.974574i 0.428067π-0.428067\pi
0.224065 + 0.974574i 0.428067π0.428067\pi
398398 4.94763 0.248002
399399 0 0
400400 10.2426 0.512132
401401 −21.8028 −1.08878 −0.544390 0.838832i 0.683239π-0.683239\pi
−0.544390 + 0.838832i 0.683239π0.683239\pi
402402 0 0
403403 12.4853 0.621936
404404 −6.81801 −0.339209
405405 0 0
406406 0 0
407407 25.2751 1.25284
408408 0 0
409409 −9.07107 −0.448535 −0.224268 0.974528i 0.571999π-0.571999\pi
−0.224268 + 0.974528i 0.571999π0.571999\pi
410410 −0.827164 −0.0408507
411411 0 0
412412 1.44365 0.0711236
413413 0 0
414414 0 0
415415 −18.4853 −0.907407
416416 −2.69755 −0.132258
417417 0 0
418418 9.62742 0.470892
419419 17.5034 0.855095 0.427547 0.903993i 0.359378π-0.359378\pi
0.427547 + 0.903993i 0.359378π0.359378\pi
420420 0 0
421421 22.0711 1.07568 0.537839 0.843048i 0.319241π-0.319241\pi
0.537839 + 0.843048i 0.319241π0.319241\pi
422422 10.3798 0.505280
423423 0 0
424424 −3.17157 −0.154025
425425 14.6792 0.712048
426426 0 0
427427 0 0
428428 −2.82411 −0.136509
429429 0 0
430430 11.2132 0.540749
431431 17.7194 0.853514 0.426757 0.904366i 0.359656π-0.359656\pi
0.426757 + 0.904366i 0.359656π0.359656\pi
432432 0 0
433433 24.9706 1.20001 0.600004 0.799997i 0.295166π-0.295166\pi
0.600004 + 0.799997i 0.295166π0.295166\pi
434434 0 0
435435 0 0
436436 −1.10051 −0.0527046
437437 10.4693 0.500814
438438 0 0
439439 19.7990 0.944954 0.472477 0.881343i 0.343360π-0.343360\pi
0.472477 + 0.881343i 0.343360π0.343360\pi
440440 18.4571 0.879907
441441 0 0
442442 6.34315 0.301713
443443 14.4632 0.687167 0.343583 0.939122i 0.388359π-0.388359\pi
0.343583 + 0.939122i 0.388359π0.388359\pi
444444 0 0
445445 −22.3137 −1.05777
446446 17.2873 0.818577
447447 0 0
448448 0 0
449449 9.94768 0.469460 0.234730 0.972061i 0.424579π-0.424579\pi
0.234730 + 0.972061i 0.424579π0.424579\pi
450450 0 0
451451 2.51472 0.118413
452452 4.73157 0.222554
453453 0 0
454454 9.89949 0.464606
455455 0 0
456456 0 0
457457 19.9706 0.934184 0.467092 0.884209i 0.345302π-0.345302\pi
0.467092 + 0.884209i 0.345302π0.345302\pi
458458 −1.90746 −0.0891295
459459 0 0
460460 3.44365 0.160561
461461 −30.3122 −1.41178 −0.705890 0.708321i 0.749453π-0.749453\pi
−0.705890 + 0.708321i 0.749453π0.749453\pi
462462 0 0
463463 11.8995 0.553016 0.276508 0.961012i 0.410823π-0.410823\pi
0.276508 + 0.961012i 0.410823π0.410823\pi
464464 15.1114 0.701527
465465 0 0
466466 −25.2132 −1.16798
467467 −2.82411 −0.130684 −0.0653422 0.997863i 0.520814π-0.520814\pi
−0.0653422 + 0.997863i 0.520814π0.520814\pi
468468 0 0
469469 0 0
470470 −18.1145 −0.835558
471471 0 0
472472 5.41421 0.249209
473473 −34.0901 −1.56746
474474 0 0
475475 −5.41421 −0.248421
476476 0 0
477477 0 0
478478 −2.24264 −0.102576
479479 26.4078 1.20660 0.603302 0.797513i 0.293851π-0.293851\pi
0.603302 + 0.797513i 0.293851π0.293851\pi
480480 0 0
481481 −6.14214 −0.280057
482482 31.1394 1.41836
483483 0 0
484484 −5.07107 −0.230503
485485 −12.1607 −0.552188
486486 0 0
487487 32.5858 1.47660 0.738301 0.674471i 0.235628π-0.235628\pi
0.738301 + 0.674471i 0.235628π0.235628\pi
488488 31.8771 1.44301
489489 0 0
490490 0 0
491491 11.2070 0.505763 0.252881 0.967497i 0.418622π-0.418622\pi
0.252881 + 0.967497i 0.418622π0.418622\pi
492492 0 0
493493 21.6569 0.975376
494494 −2.33957 −0.105262
495495 0 0
496496 −31.9706 −1.43552
497497 0 0
498498 0 0
499499 −41.5563 −1.86032 −0.930159 0.367157i 0.880331π-0.880331\pi
−0.930159 + 0.367157i 0.880331π0.880331\pi
500500 −4.38895 −0.196280
501501 0 0
502502 −14.7696 −0.659197
503503 18.2410 0.813327 0.406664 0.913578i 0.366692π-0.366692\pi
0.406664 + 0.913578i 0.366692π0.366692\pi
504504 0 0
505505 −20.7279 −0.922380
506506 40.0809 1.78181
507507 0 0
508508 2.00000 0.0887357
509509 −8.90446 −0.394683 −0.197342 0.980335i 0.563231π-0.563231\pi
−0.197342 + 0.980335i 0.563231π0.563231\pi
510510 0 0
511511 0 0
512512 25.1485 1.11142
513513 0 0
514514 12.9584 0.571569
515515 4.38895 0.193400
516516 0 0
517517 55.0711 2.42202
518518 0 0
519519 0 0
520520 −4.48528 −0.196693
521521 −10.4693 −0.458668 −0.229334 0.973348i 0.573655π-0.573655\pi
−0.229334 + 0.973348i 0.573655π0.573655\pi
522522 0 0
523523 −29.7696 −1.30173 −0.650866 0.759193i 0.725594π-0.725594\pi
−0.650866 + 0.759193i 0.725594π0.725594\pi
524524 −6.38589 −0.278969
525525 0 0
526526 7.76955 0.338769
527527 −45.8186 −1.99589
528528 0 0
529529 20.5858 0.895034
530530 −1.65433 −0.0718594
531531 0 0
532532 0 0
533533 −0.611105 −0.0264699
534534 0 0
535535 −8.58579 −0.371196
536536 17.1978 0.742832
537537 0 0
538538 −0.656854 −0.0283190
539539 0 0
540540 0 0
541541 15.3848 0.661443 0.330722 0.943728i 0.392708π-0.392708\pi
0.330722 + 0.943728i 0.392708π0.392708\pi
542542 21.1917 0.910262
543543 0 0
544544 9.89949 0.424437
545545 −3.34572 −0.143315
546546 0 0
547547 24.4853 1.04692 0.523458 0.852052i 0.324642π-0.324642\pi
0.523458 + 0.852052i 0.324642π0.324642\pi
548548 −1.90746 −0.0814824
549549 0 0
550550 −20.7279 −0.883842
551551 −7.98780 −0.340292
552552 0 0
553553 0 0
554554 −10.7748 −0.457779
555555 0 0
556556 3.65685 0.155085
557557 39.7383 1.68377 0.841883 0.539661i 0.181448π-0.181448\pi
0.841883 + 0.539661i 0.181448π0.181448\pi
558558 0 0
559559 8.28427 0.350387
560560 0 0
561561 0 0
562562 −28.3848 −1.19734
563563 40.4760 1.70586 0.852929 0.522027i 0.174824π-0.174824\pi
0.852929 + 0.522027i 0.174824π0.174824\pi
564564 0 0
565565 14.3848 0.605172
566566 −10.6853 −0.449139
567567 0 0
568568 26.7990 1.12446
569569 −24.6269 −1.03241 −0.516207 0.856464i 0.672657π-0.672657\pi
−0.516207 + 0.856464i 0.672657π0.672657\pi
570570 0 0
571571 −32.0416 −1.34090 −0.670450 0.741954i 0.733899π-0.733899\pi
−0.670450 + 0.741954i 0.733899π0.733899\pi
572572 2.33957 0.0978224
573573 0 0
574574 0 0
575575 −22.5405 −0.940003
576576 0 0
577577 41.3553 1.72165 0.860823 0.508905i 0.169950π-0.169950\pi
0.860823 + 0.508905i 0.169950π0.169950\pi
578578 −1.87039 −0.0777978
579579 0 0
580580 −2.62742 −0.109098
581581 0 0
582582 0 0
583583 5.02944 0.208298
584584 26.1023 1.08012
585585 0 0
586586 12.5269 0.517482
587587 −35.1333 −1.45011 −0.725053 0.688693i 0.758185π-0.758185\pi
−0.725053 + 0.688693i 0.758185π0.758185\pi
588588 0 0
589589 16.8995 0.696332
590590 2.82411 0.116267
591591 0 0
592592 15.7279 0.646414
593593 −1.87039 −0.0768075 −0.0384038 0.999262i 0.512227π-0.512227\pi
−0.0384038 + 0.999262i 0.512227π0.512227\pi
594594 0 0
595595 0 0
596596 2.82411 0.115680
597597 0 0
598598 −9.74012 −0.398303
599599 44.5593 1.82065 0.910323 0.413899i 0.135833π-0.135833\pi
0.910323 + 0.413899i 0.135833π0.135833\pi
600600 0 0
601601 −18.6274 −0.759828 −0.379914 0.925022i 0.624046π-0.624046\pi
−0.379914 + 0.925022i 0.624046π0.624046\pi
602602 0 0
603603 0 0
604604 −1.75736 −0.0715059
605605 −15.4169 −0.626787
606606 0 0
607607 29.3137 1.18981 0.594903 0.803797i 0.297190π-0.297190\pi
0.594903 + 0.803797i 0.297190π0.297190\pi
608608 −3.65128 −0.148079
609609 0 0
610610 16.6274 0.673224
611611 −13.3829 −0.541414
612612 0 0
613613 −39.6274 −1.60054 −0.800268 0.599642i 0.795310π-0.795310\pi
−0.800268 + 0.599642i 0.795310π0.795310\pi
614614 12.5033 0.504592
615615 0 0
616616 0 0
617617 −11.8551 −0.477270 −0.238635 0.971109i 0.576700π-0.576700\pi
−0.238635 + 0.971109i 0.576700π0.576700\pi
618618 0 0
619619 16.4558 0.661416 0.330708 0.943733i 0.392712π-0.392712\pi
0.330708 + 0.943733i 0.392712π0.392712\pi
620620 5.55873 0.223244
621621 0 0
622622 28.0000 1.12270
623623 0 0
624624 0 0
625625 3.72792 0.149117
626626 −31.2659 −1.24964
627627 0 0
628628 −7.65685 −0.305542
629629 22.5405 0.898748
630630 0 0
631631 29.3553 1.16862 0.584309 0.811531i 0.301366π-0.301366\pi
0.584309 + 0.811531i 0.301366π0.301366\pi
632632 −42.2568 −1.68089
633633 0 0
634634 −24.4437 −0.970781
635635 6.08034 0.241291
636636 0 0
637637 0 0
638638 −30.5807 −1.21070
639639 0 0
640640 8.31371 0.328628
641641 45.3865 1.79266 0.896330 0.443388i 0.146224π-0.146224\pi
0.896330 + 0.443388i 0.146224π0.146224\pi
642642 0 0
643643 −2.75736 −0.108740 −0.0543698 0.998521i 0.517315π-0.517315\pi
−0.0543698 + 0.998521i 0.517315π0.517315\pi
644644 0 0
645645 0 0
646646 8.58579 0.337803
647647 −6.81801 −0.268044 −0.134022 0.990978i 0.542789π-0.542789\pi
−0.134022 + 0.990978i 0.542789π0.542789\pi
648648 0 0
649649 −8.58579 −0.337022
650650 5.03712 0.197572
651651 0 0
652652 4.82843 0.189096
653653 37.6518 1.47343 0.736715 0.676203i 0.236376π-0.236376\pi
0.736715 + 0.676203i 0.236376π0.236376\pi
654654 0 0
655655 −19.4142 −0.758576
656656 1.56483 0.0610965
657657 0 0
658658 0 0
659659 −13.8521 −0.539600 −0.269800 0.962916i 0.586958π-0.586958\pi
−0.269800 + 0.962916i 0.586958π0.586958\pi
660660 0 0
661661 1.85786 0.0722625 0.0361313 0.999347i 0.488497π-0.488497\pi
0.0361313 + 0.999347i 0.488497π0.488497\pi
662662 3.74077 0.145389
663663 0 0
664664 44.6274 1.73188
665665 0 0
666666 0 0
667667 −33.2548 −1.28763
668668 4.73157 0.183070
669669 0 0
670670 8.97056 0.346563
671671 −50.5502 −1.95147
672672 0 0
673673 15.1716 0.584821 0.292411 0.956293i 0.405543π-0.405543\pi
0.292411 + 0.956293i 0.405543π0.405543\pi
674674 36.2660 1.39691
675675 0 0
676676 4.81623 0.185240
677677 23.4942 0.902956 0.451478 0.892282i 0.350897π-0.350897\pi
0.451478 + 0.892282i 0.350897π0.350897\pi
678678 0 0
679679 0 0
680680 16.4601 0.631217
681681 0 0
682682 64.6985 2.47743
683683 −13.8521 −0.530035 −0.265018 0.964244i 0.585378π-0.585378\pi
−0.265018 + 0.964244i 0.585378π0.585378\pi
684684 0 0
685685 −5.79899 −0.221568
686686 0 0
687687 0 0
688688 −21.2132 −0.808746
689689 −1.22221 −0.0465625
690690 0 0
691691 −44.8284 −1.70535 −0.852677 0.522439i 0.825022π-0.825022\pi
−0.852677 + 0.522439i 0.825022π0.825022\pi
692692 −5.43217 −0.206500
693693 0 0
694694 14.6569 0.556367
695695 11.1175 0.421709
696696 0 0
697697 2.24264 0.0849461
698698 1.34877 0.0510519
699699 0 0
700700 0 0
701701 −2.51856 −0.0951247 −0.0475624 0.998868i 0.515145π-0.515145\pi
−0.0475624 + 0.998868i 0.515145π0.515145\pi
702702 0 0
703703 −8.31371 −0.313557
704704 −42.9050 −1.61704
705705 0 0
706706 35.7696 1.34620
707707 0 0
708708 0 0
709709 31.3431 1.17712 0.588558 0.808455i 0.299696π-0.299696\pi
0.588558 + 0.808455i 0.299696π0.299696\pi
710710 13.9786 0.524609
711711 0 0
712712 53.8701 2.01887
713713 70.3561 2.63485
714714 0 0
715715 7.11270 0.266000
716716 −7.42912 −0.277639
717717 0 0
718718 33.4142 1.24701
719719 29.0529 1.08349 0.541746 0.840542i 0.317764π-0.317764\pi
0.541746 + 0.840542i 0.317764π0.317764\pi
720720 0 0
721721 0 0
722722 20.7596 0.772592
723723 0 0
724724 −1.69848 −0.0631237
725725 17.1978 0.638710
726726 0 0
727727 −26.0000 −0.964287 −0.482143 0.876092i 0.660142π-0.660142\pi
−0.482143 + 0.876092i 0.660142π0.660142\pi
728728 0 0
729729 0 0
730730 13.6152 0.503922
731731 −30.4017 −1.12445
732732 0 0
733733 24.2426 0.895422 0.447711 0.894178i 0.352239π-0.352239\pi
0.447711 + 0.894178i 0.352239π0.352239\pi
734734 9.29950 0.343251
735735 0 0
736736 −15.2010 −0.560317
737737 −27.2720 −1.00458
738738 0 0
739739 1.55635 0.0572512 0.0286256 0.999590i 0.490887π-0.490887\pi
0.0286256 + 0.999590i 0.490887π0.490887\pi
740740 −2.73462 −0.100527
741741 0 0
742742 0 0
743743 −10.2903 −0.377514 −0.188757 0.982024i 0.560446π-0.560446\pi
−0.188757 + 0.982024i 0.560446π0.560446\pi
744744 0 0
745745 8.58579 0.314559
746746 −16.5496 −0.605925
747747 0 0
748748 −8.58579 −0.313927
749749 0 0
750750 0 0
751751 −31.8995 −1.16403 −0.582015 0.813178i 0.697735π-0.697735\pi
−0.582015 + 0.813178i 0.697735π0.697735\pi
752752 34.2690 1.24966
753753 0 0
754754 7.43146 0.270638
755755 −5.34267 −0.194440
756756 0 0
757757 1.65685 0.0602194 0.0301097 0.999547i 0.490414π-0.490414\pi
0.0301097 + 0.999547i 0.490414π0.490414\pi
758758 2.39200 0.0868812
759759 0 0
760760 −6.07107 −0.220221
761761 0.305553 0.0110763 0.00553814 0.999985i 0.498237π-0.498237\pi
0.00553814 + 0.999985i 0.498237π0.498237\pi
762762 0 0
763763 0 0
764764 3.77784 0.136677
765765 0 0
766766 −8.58579 −0.310217
767767 2.08644 0.0753371
768768 0 0
769769 22.9706 0.828340 0.414170 0.910200i 0.364072π-0.364072\pi
0.414170 + 0.910200i 0.364072π0.364072\pi
770770 0 0
771771 0 0
772772 −9.79899 −0.352673
773773 −6.72852 −0.242008 −0.121004 0.992652i 0.538611π-0.538611\pi
−0.121004 + 0.992652i 0.538611π0.538611\pi
774774 0 0
775775 −36.3848 −1.30698
776776 29.3585 1.05391
777777 0 0
778778 14.0000 0.501924
779779 −0.827164 −0.0296362
780780 0 0
781781 −42.4975 −1.52068
782782 35.7444 1.27822
783783 0 0
784784 0 0
785785 −23.2781 −0.830833
786786 0 0
787787 −17.6569 −0.629399 −0.314699 0.949191i 0.601904π-0.601904\pi
−0.314699 + 0.949191i 0.601904π0.601904\pi
788788 −1.34877 −0.0480481
789789 0 0
790790 −22.0416 −0.784206
791791 0 0
792792 0 0
793793 12.2843 0.436227
794794 −11.2440 −0.399036
795795 0 0
796796 1.62742 0.0576823
797797 −3.16674 −0.112172 −0.0560858 0.998426i 0.517862π-0.517862\pi
−0.0560858 + 0.998426i 0.517862π0.517862\pi
798798 0 0
799799 49.1127 1.73748
800800 7.86123 0.277937
801801 0 0
802802 27.4558 0.969500
803803 −41.3926 −1.46071
804804 0 0
805805 0 0
806806 −15.7225 −0.553800
807807 0 0
808808 50.0416 1.76046
809809 −29.9696 −1.05367 −0.526837 0.849966i 0.676622π-0.676622\pi
−0.526837 + 0.849966i 0.676622π0.676622\pi
810810 0 0
811811 37.6274 1.32128 0.660639 0.750704i 0.270286π-0.270286\pi
0.660639 + 0.750704i 0.270286π0.270286\pi
812812 0 0
813813 0 0
814814 −31.8284 −1.11559
815815 14.6792 0.514192
816816 0 0
817817 11.2132 0.392300
818818 11.4230 0.399396
819819 0 0
820820 −0.272078 −0.00950137
821821 −42.2568 −1.47477 −0.737387 0.675471i 0.763941π-0.763941\pi
−0.737387 + 0.675471i 0.763941π0.763941\pi
822822 0 0
823823 −50.7279 −1.76826 −0.884132 0.467237i 0.845249π-0.845249\pi
−0.884132 + 0.467237i 0.845249π0.845249\pi
824824 −10.5959 −0.369124
825825 0 0
826826 0 0
827827 18.1515 0.631191 0.315595 0.948894i 0.397796π-0.397796\pi
0.315595 + 0.948894i 0.397796π0.397796\pi
828828 0 0
829829 39.2132 1.36193 0.680965 0.732316i 0.261560π-0.261560\pi
0.680965 + 0.732316i 0.261560π0.261560\pi
830830 23.2781 0.807996
831831 0 0
832832 10.4264 0.361471
833833 0 0
834834 0 0
835835 14.3848 0.497806
836836 3.16674 0.109524
837837 0 0
838838 −22.0416 −0.761415
839839 −12.1607 −0.419833 −0.209917 0.977719i 0.567319π-0.567319\pi
−0.209917 + 0.977719i 0.567319π0.567319\pi
840840 0 0
841841 −3.62742 −0.125083
842842 −27.7937 −0.957833
843843 0 0
844844 3.41421 0.117522
845845 14.6422 0.503706
846846 0 0
847847 0 0
848848 3.12967 0.107473
849849 0 0
850850 −18.4853 −0.634040
851851 −34.6117 −1.18647
852852 0 0
853853 38.8284 1.32946 0.664730 0.747084i 0.268547π-0.268547\pi
0.664730 + 0.747084i 0.268547π0.268547\pi
854854 0 0
855855 0 0
856856 20.7279 0.708466
857857 33.0098 1.12759 0.563796 0.825914i 0.309340π-0.309340\pi
0.563796 + 0.825914i 0.309340π0.309340\pi
858858 0 0
859859 −6.27208 −0.214001 −0.107000 0.994259i 0.534125π-0.534125\pi
−0.107000 + 0.994259i 0.534125π0.534125\pi
860860 3.68835 0.125772
861861 0 0
862862 −22.3137 −0.760008
863863 40.3494 1.37351 0.686755 0.726889i 0.259035π-0.259035\pi
0.686755 + 0.726889i 0.259035π0.259035\pi
864864 0 0
865865 −16.5147 −0.561517
866866 −31.4449 −1.06854
867867 0 0
868868 0 0
869869 67.0103 2.27317
870870 0 0
871871 6.62742 0.224561
872872 8.07729 0.273532
873873 0 0
874874 −13.1838 −0.445948
875875 0 0
876876 0 0
877877 −21.1716 −0.714913 −0.357457 0.933930i 0.616356π-0.616356\pi
−0.357457 + 0.933930i 0.616356π0.616356\pi
878878 −24.9325 −0.841430
879879 0 0
880880 −18.2132 −0.613967
881881 −52.1150 −1.75580 −0.877900 0.478844i 0.841056π-0.841056\pi
−0.877900 + 0.478844i 0.841056π0.841056\pi
882882 0 0
883883 0.627417 0.0211143 0.0105571 0.999944i 0.496639π-0.496639\pi
0.0105571 + 0.999944i 0.496639π0.496639\pi
884884 2.08644 0.0701747
885885 0 0
886886 −18.2132 −0.611885
887887 −36.3031 −1.21894 −0.609469 0.792810i 0.708617π-0.708617\pi
−0.609469 + 0.792810i 0.708617π0.708617\pi
888888 0 0
889889 0 0
890890 28.0992 0.941888
891891 0 0
892892 5.68629 0.190391
893893 −18.1145 −0.606177
894894 0 0
895895 −22.5858 −0.754960
896896 0 0
897897 0 0
898898 −12.5269 −0.418028
899899 −53.6799 −1.79032
900900 0 0
901901 4.48528 0.149426
902902 −3.16674 −0.105441
903903 0 0
904904 −34.7279 −1.15503
905905 −5.16368 −0.171647
906906 0 0
907907 50.7279 1.68439 0.842197 0.539171i 0.181262π-0.181262\pi
0.842197 + 0.539171i 0.181262π0.181262\pi
908908 3.25623 0.108062
909909 0 0
910910 0 0
911911 0.916658 0.0303702 0.0151851 0.999885i 0.495166π-0.495166\pi
0.0151851 + 0.999885i 0.495166π0.495166\pi
912912 0 0
913913 −70.7696 −2.34213
914914 −25.1485 −0.831840
915915 0 0
916916 −0.627417 −0.0207304
917917 0 0
918918 0 0
919919 −13.1716 −0.434490 −0.217245 0.976117i 0.569707π-0.569707\pi
−0.217245 + 0.976117i 0.569707π0.569707\pi
920920 −25.2751 −0.833295
921921 0 0
922922 38.1716 1.25711
923923 10.3274 0.339929
924924 0 0
925925 17.8995 0.588532
926926 −14.9848 −0.492431
927927 0 0
928928 11.5980 0.380722
929929 −38.6951 −1.26954 −0.634772 0.772700i 0.718906π-0.718906\pi
−0.634772 + 0.772700i 0.718906π0.718906\pi
930930 0 0
931931 0 0
932932 −8.29335 −0.271658
933933 0 0
934934 3.55635 0.116367
935935 −26.1023 −0.853635
936936 0 0
937937 −31.2548 −1.02105 −0.510525 0.859863i 0.670549π-0.670549\pi
−0.510525 + 0.859863i 0.670549π0.670549\pi
938938 0 0
939939 0 0
940940 −5.95837 −0.194341
941941 −10.2903 −0.335454 −0.167727 0.985833i 0.553643π-0.553643\pi
−0.167727 + 0.985833i 0.553643π0.553643\pi
942942 0 0
943943 −3.44365 −0.112141
944944 −5.34267 −0.173889
945945 0 0
946946 42.9289 1.39574
947947 6.16984 0.200493 0.100246 0.994963i 0.468037π-0.468037\pi
0.100246 + 0.994963i 0.468037π0.468037\pi
948948 0 0
949949 10.0589 0.326525
950950 6.81801 0.221206
951951 0 0
952952 0 0
953953 31.2659 1.01280 0.506402 0.862298i 0.330975π-0.330975\pi
0.506402 + 0.862298i 0.330975π0.330975\pi
954954 0 0
955955 11.4853 0.371655
956956 −0.737669 −0.0238579
957957 0 0
958958 −33.2548 −1.07441
959959 0 0
960960 0 0
961961 82.5685 2.66350
962962 7.73467 0.249376
963963 0 0
964964 10.2426 0.329893
965965 −29.7906 −0.958994
966966 0 0
967967 −17.8995 −0.575609 −0.287804 0.957689i 0.592925π-0.592925\pi
−0.287804 + 0.957689i 0.592925π0.592925\pi
968968 37.2197 1.19629
969969 0 0
970970 15.3137 0.491694
971971 −0.432117 −0.0138673 −0.00693364 0.999976i 0.502207π-0.502207\pi
−0.00693364 + 0.999976i 0.502207π0.502207\pi
972972 0 0
973973 0 0
974974 −41.0346 −1.31483
975975 0 0
976976 −31.4558 −1.00688
977977 18.0620 0.577856 0.288928 0.957351i 0.406701π-0.406701\pi
0.288928 + 0.957351i 0.406701π0.406701\pi
978978 0 0
979979 −85.4264 −2.73024
980980 0 0
981981 0 0
982982 −14.1127 −0.450354
983983 5.77479 0.184187 0.0920936 0.995750i 0.470644π-0.470644\pi
0.0920936 + 0.995750i 0.470644π0.470644\pi
984984 0 0
985985 −4.10051 −0.130653
986986 −27.2720 −0.868519
987987 0 0
988988 −0.769553 −0.0244827
989989 46.6829 1.48443
990990 0 0
991991 −6.97056 −0.221427 −0.110714 0.993852i 0.535314π-0.535314\pi
−0.110714 + 0.993852i 0.535314π0.535314\pi
992992 −24.5374 −0.779064
993993 0 0
994994 0 0
995995 4.94763 0.156850
996996 0 0
997997 −0.870058 −0.0275550 −0.0137775 0.999905i 0.504386π-0.504386\pi
−0.0137775 + 0.999905i 0.504386π0.504386\pi
998998 52.3311 1.65651
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 1323.2.a.bd.1.2 yes 4
3.2 odd 2 inner 1323.2.a.bd.1.3 yes 4
7.6 odd 2 1323.2.a.bc.1.2 4
21.20 even 2 1323.2.a.bc.1.3 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1323.2.a.bc.1.2 4 7.6 odd 2
1323.2.a.bc.1.3 yes 4 21.20 even 2
1323.2.a.bd.1.2 yes 4 1.1 even 1 trivial
1323.2.a.bd.1.3 yes 4 3.2 odd 2 inner