Properties

Label 4400.2.b.s.4049.3
Level 44004400
Weight 22
Character 4400.4049
Analytic conductor 35.13435.134
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] = [4400,2,Mod(4049,4400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4400, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4400.4049");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 4400=245211 4400 = 2^{4} \cdot 5^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4400.b (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: 35.134176889435.1341768894
Analytic rank: 00
Dimension: 44
Coefficient field: Q(i,21)\Q(i, \sqrt{21})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+11x2+25 x^{4} + 11x^{2} + 25 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 1100)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 4049.3
Root 1.79129i1.79129i of defining polynomial
Character χ\chi == 4400.4049
Dual form 4400.2.b.s.4049.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+1.79129iq3+4.79129iq70.208712q9+1.00000q11+1.00000iq133.79129iq172.58258q198.58258q21+0.791288iq23+5.00000iq272.20871q290.582576q31+1.79129iq33+6.58258iq371.79129q3910.5826q4110.0000iq43+10.5826iq4715.9564q49+6.79129q51+2.37386iq534.62614iq571.41742q59+8.79129q611.00000iq63+4.00000iq671.41742q6916.7477q71+3.20871iq73+4.79129iq77+16.5390q799.58258q81+12.9564iq833.95644iq873.79129q894.79129q911.04356iq9310.7913iq970.208712q99+O(q100)q+1.79129i q^{3} +4.79129i q^{7} -0.208712 q^{9} +1.00000 q^{11} +1.00000i q^{13} -3.79129i q^{17} -2.58258 q^{19} -8.58258 q^{21} +0.791288i q^{23} +5.00000i q^{27} -2.20871 q^{29} -0.582576 q^{31} +1.79129i q^{33} +6.58258i q^{37} -1.79129 q^{39} -10.5826 q^{41} -10.0000i q^{43} +10.5826i q^{47} -15.9564 q^{49} +6.79129 q^{51} +2.37386i q^{53} -4.62614i q^{57} -1.41742 q^{59} +8.79129 q^{61} -1.00000i q^{63} +4.00000i q^{67} -1.41742 q^{69} -16.7477 q^{71} +3.20871i q^{73} +4.79129i q^{77} +16.5390 q^{79} -9.58258 q^{81} +12.9564i q^{83} -3.95644i q^{87} -3.79129 q^{89} -4.79129 q^{91} -1.04356i q^{93} -10.7913i q^{97} -0.208712 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q10q9+4q11+8q1916q2118q29+16q31+2q3924q4118q49+18q5124q59+26q6124q6912q71+2q7920q816q89+10q99+O(q100) 4 q - 10 q^{9} + 4 q^{11} + 8 q^{19} - 16 q^{21} - 18 q^{29} + 16 q^{31} + 2 q^{39} - 24 q^{41} - 18 q^{49} + 18 q^{51} - 24 q^{59} + 26 q^{61} - 24 q^{69} - 12 q^{71} + 2 q^{79} - 20 q^{81} - 6 q^{89}+ \cdots - 10 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/4400Z)×\left(\mathbb{Z}/4400\mathbb{Z}\right)^\times.

nn 177177 12011201 27512751 33013301
χ(n)\chi(n) 1-1 11 11 11

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 1.79129i 1.03420i 0.855925 + 0.517100i 0.172989π0.172989\pi
−0.855925 + 0.517100i 0.827011π0.827011\pi
44 0 0
55 0 0
66 0 0
77 4.79129i 1.81094i 0.424414 + 0.905468i 0.360480π0.360480\pi
−0.424414 + 0.905468i 0.639520π0.639520\pi
88 0 0
99 −0.208712 −0.0695707
1010 0 0
1111 1.00000 0.301511
1212 0 0
1313 1.00000i 0.277350i 0.990338 + 0.138675i 0.0442844π0.0442844\pi
−0.990338 + 0.138675i 0.955716π0.955716\pi
1414 0 0
1515 0 0
1616 0 0
1717 − 3.79129i − 0.919522i −0.888043 0.459761i 0.847935π-0.847935\pi
0.888043 0.459761i 0.152065π-0.152065\pi
1818 0 0
1919 −2.58258 −0.592483 −0.296242 0.955113i 0.595733π-0.595733\pi
−0.296242 + 0.955113i 0.595733π0.595733\pi
2020 0 0
2121 −8.58258 −1.87287
2222 0 0
2323 0.791288i 0.164995i 0.996591 + 0.0824975i 0.0262896π0.0262896\pi
−0.996591 + 0.0824975i 0.973710π0.973710\pi
2424 0 0
2525 0 0
2626 0 0
2727 5.00000i 0.962250i
2828 0 0
2929 −2.20871 −0.410148 −0.205074 0.978747i 0.565743π-0.565743\pi
−0.205074 + 0.978747i 0.565743π0.565743\pi
3030 0 0
3131 −0.582576 −0.104634 −0.0523168 0.998631i 0.516661π-0.516661\pi
−0.0523168 + 0.998631i 0.516661π0.516661\pi
3232 0 0
3333 1.79129i 0.311823i
3434 0 0
3535 0 0
3636 0 0
3737 6.58258i 1.08217i 0.840968 + 0.541084i 0.181986π0.181986\pi
−0.840968 + 0.541084i 0.818014π0.818014\pi
3838 0 0
3939 −1.79129 −0.286836
4040 0 0
4141 −10.5826 −1.65272 −0.826360 0.563142i 0.809593π-0.809593\pi
−0.826360 + 0.563142i 0.809593π0.809593\pi
4242 0 0
4343 − 10.0000i − 1.52499i −0.646997 0.762493i 0.723975π-0.723975\pi
0.646997 0.762493i 0.276025π-0.276025\pi
4444 0 0
4545 0 0
4646 0 0
4747 10.5826i 1.54363i 0.635849 + 0.771814i 0.280650π0.280650\pi
−0.635849 + 0.771814i 0.719350π0.719350\pi
4848 0 0
4949 −15.9564 −2.27949
5050 0 0
5151 6.79129 0.950971
5252 0 0
5353 2.37386i 0.326075i 0.986620 + 0.163038i 0.0521292π0.0521292\pi
−0.986620 + 0.163038i 0.947871π0.947871\pi
5454 0 0
5555 0 0
5656 0 0
5757 − 4.62614i − 0.612747i
5858 0 0
5959 −1.41742 −0.184533 −0.0922665 0.995734i 0.529411π-0.529411\pi
−0.0922665 + 0.995734i 0.529411π0.529411\pi
6060 0 0
6161 8.79129 1.12561 0.562805 0.826590i 0.309722π-0.309722\pi
0.562805 + 0.826590i 0.309722π0.309722\pi
6262 0 0
6363 − 1.00000i − 0.125988i
6464 0 0
6565 0 0
6666 0 0
6767 4.00000i 0.488678i 0.969690 + 0.244339i 0.0785709π0.0785709\pi
−0.969690 + 0.244339i 0.921429π0.921429\pi
6868 0 0
6969 −1.41742 −0.170638
7070 0 0
7171 −16.7477 −1.98759 −0.993795 0.111229i 0.964521π-0.964521\pi
−0.993795 + 0.111229i 0.964521π0.964521\pi
7272 0 0
7373 3.20871i 0.375551i 0.982212 + 0.187776i 0.0601278π0.0601278\pi
−0.982212 + 0.187776i 0.939872π0.939872\pi
7474 0 0
7575 0 0
7676 0 0
7777 4.79129i 0.546018i
7878 0 0
7979 16.5390 1.86078 0.930392 0.366565i 0.119466π-0.119466\pi
0.930392 + 0.366565i 0.119466π0.119466\pi
8080 0 0
8181 −9.58258 −1.06473
8282 0 0
8383 12.9564i 1.42215i 0.703114 + 0.711077i 0.251792π0.251792\pi
−0.703114 + 0.711077i 0.748208π0.748208\pi
8484 0 0
8585 0 0
8686 0 0
8787 − 3.95644i − 0.424175i
8888 0 0
8989 −3.79129 −0.401876 −0.200938 0.979604i 0.564399π-0.564399\pi
−0.200938 + 0.979604i 0.564399π0.564399\pi
9090 0 0
9191 −4.79129 −0.502263
9292 0 0
9393 − 1.04356i − 0.108212i
9494 0 0
9595 0 0
9696 0 0
9797 − 10.7913i − 1.09569i −0.836580 0.547845i 0.815448π-0.815448\pi
0.836580 0.547845i 0.184552π-0.184552\pi
9898 0 0
9999 −0.208712 −0.0209764
100100 0 0
101101 −3.62614 −0.360814 −0.180407 0.983592i 0.557741π-0.557741\pi
−0.180407 + 0.983592i 0.557741π0.557741\pi
102102 0 0
103103 − 16.9564i − 1.67077i −0.549667 0.835384i 0.685245π-0.685245\pi
0.549667 0.835384i 0.314755π-0.314755\pi
104104 0 0
105105 0 0
106106 0 0
107107 7.74773i 0.749001i 0.927227 + 0.374501i 0.122186π0.122186\pi
−0.927227 + 0.374501i 0.877814π0.877814\pi
108108 0 0
109109 0.208712 0.0199910 0.00999550 0.999950i 0.496818π-0.496818\pi
0.00999550 + 0.999950i 0.496818π0.496818\pi
110110 0 0
111111 −11.7913 −1.11918
112112 0 0
113113 − 10.5826i − 0.995525i −0.867313 0.497762i 0.834155π-0.834155\pi
0.867313 0.497762i 0.165845π-0.165845\pi
114114 0 0
115115 0 0
116116 0 0
117117 − 0.208712i − 0.0192954i
118118 0 0
119119 18.1652 1.66520
120120 0 0
121121 1.00000 0.0909091
122122 0 0
123123 − 18.9564i − 1.70924i
124124 0 0
125125 0 0
126126 0 0
127127 − 2.62614i − 0.233032i −0.993189 0.116516i 0.962827π-0.962827\pi
0.993189 0.116516i 0.0371726π-0.0371726\pi
128128 0 0
129129 17.9129 1.57714
130130 0 0
131131 14.3739 1.25585 0.627925 0.778274i 0.283904π-0.283904\pi
0.627925 + 0.778274i 0.283904π0.283904\pi
132132 0 0
133133 − 12.3739i − 1.07295i
134134 0 0
135135 0 0
136136 0 0
137137 20.5390i 1.75477i 0.479790 + 0.877383i 0.340713π0.340713\pi
−0.479790 + 0.877383i 0.659287π0.659287\pi
138138 0 0
139139 −17.7477 −1.50534 −0.752671 0.658396i 0.771235π-0.771235\pi
−0.752671 + 0.658396i 0.771235π0.771235\pi
140140 0 0
141141 −18.9564 −1.59642
142142 0 0
143143 1.00000i 0.0836242i
144144 0 0
145145 0 0
146146 0 0
147147 − 28.5826i − 2.35745i
148148 0 0
149149 15.1652 1.24238 0.621189 0.783661i 0.286650π-0.286650\pi
0.621189 + 0.783661i 0.286650π0.286650\pi
150150 0 0
151151 −5.00000 −0.406894 −0.203447 0.979086i 0.565214π-0.565214\pi
−0.203447 + 0.979086i 0.565214π0.565214\pi
152152 0 0
153153 0.791288i 0.0639718i
154154 0 0
155155 0 0
156156 0 0
157157 − 1.16515i − 0.0929892i −0.998919 0.0464946i 0.985195π-0.985195\pi
0.998919 0.0464946i 0.0148050π-0.0148050\pi
158158 0 0
159159 −4.25227 −0.337227
160160 0 0
161161 −3.79129 −0.298795
162162 0 0
163163 − 7.62614i − 0.597325i −0.954359 0.298663i 0.903459π-0.903459\pi
0.954359 0.298663i 0.0965405π-0.0965405\pi
164164 0 0
165165 0 0
166166 0 0
167167 7.41742i 0.573978i 0.957934 + 0.286989i 0.0926542π0.0926542\pi
−0.957934 + 0.286989i 0.907346π0.907346\pi
168168 0 0
169169 12.0000 0.923077
170170 0 0
171171 0.539015 0.0412195
172172 0 0
173173 − 13.7477i − 1.04522i −0.852572 0.522610i 0.824958π-0.824958\pi
0.852572 0.522610i 0.175042π-0.175042\pi
174174 0 0
175175 0 0
176176 0 0
177177 − 2.53901i − 0.190844i
178178 0 0
179179 −19.1216 −1.42921 −0.714607 0.699526i 0.753395π-0.753395\pi
−0.714607 + 0.699526i 0.753395π0.753395\pi
180180 0 0
181181 10.3739 0.771083 0.385542 0.922690i 0.374015π-0.374015\pi
0.385542 + 0.922690i 0.374015π0.374015\pi
182182 0 0
183183 15.7477i 1.16411i
184184 0 0
185185 0 0
186186 0 0
187187 − 3.79129i − 0.277246i
188188 0 0
189189 −23.9564 −1.74257
190190 0 0
191191 −21.7913 −1.57676 −0.788381 0.615187i 0.789080π-0.789080\pi
−0.788381 + 0.615187i 0.789080π0.789080\pi
192192 0 0
193193 − 11.1652i − 0.803685i −0.915709 0.401843i 0.868370π-0.868370\pi
0.915709 0.401843i 0.131630π-0.131630\pi
194194 0 0
195195 0 0
196196 0 0
197197 − 5.53901i − 0.394638i −0.980339 0.197319i 0.936776π-0.936776\pi
0.980339 0.197319i 0.0632235π-0.0632235\pi
198198 0 0
199199 −15.3739 −1.08982 −0.544912 0.838493i 0.683437π-0.683437\pi
−0.544912 + 0.838493i 0.683437π0.683437\pi
200200 0 0
201201 −7.16515 −0.505391
202202 0 0
203203 − 10.5826i − 0.742751i
204204 0 0
205205 0 0
206206 0 0
207207 − 0.165151i − 0.0114788i
208208 0 0
209209 −2.58258 −0.178640
210210 0 0
211211 −5.00000 −0.344214 −0.172107 0.985078i 0.555058π-0.555058\pi
−0.172107 + 0.985078i 0.555058π0.555058\pi
212212 0 0
213213 − 30.0000i − 2.05557i
214214 0 0
215215 0 0
216216 0 0
217217 − 2.79129i − 0.189485i
218218 0 0
219219 −5.74773 −0.388395
220220 0 0
221221 3.79129 0.255030
222222 0 0
223223 − 11.4174i − 0.764567i −0.924045 0.382284i 0.875138π-0.875138\pi
0.924045 0.382284i 0.124862π-0.124862\pi
224224 0 0
225225 0 0
226226 0 0
227227 20.5390i 1.36322i 0.731715 + 0.681611i 0.238720π0.238720\pi
−0.731715 + 0.681611i 0.761280π0.761280\pi
228228 0 0
229229 21.3739 1.41242 0.706212 0.708000i 0.250402π-0.250402\pi
0.706212 + 0.708000i 0.250402π0.250402\pi
230230 0 0
231231 −8.58258 −0.564692
232232 0 0
233233 − 11.2087i − 0.734307i −0.930160 0.367154i 0.880332π-0.880332\pi
0.930160 0.367154i 0.119668π-0.119668\pi
234234 0 0
235235 0 0
236236 0 0
237237 29.6261i 1.92442i
238238 0 0
239239 −6.79129 −0.439292 −0.219646 0.975580i 0.570490π-0.570490\pi
−0.219646 + 0.975580i 0.570490π0.570490\pi
240240 0 0
241241 18.1216 1.16731 0.583657 0.812000i 0.301621π-0.301621\pi
0.583657 + 0.812000i 0.301621π0.301621\pi
242242 0 0
243243 − 2.16515i − 0.138895i
244244 0 0
245245 0 0
246246 0 0
247247 − 2.58258i − 0.164325i
248248 0 0
249249 −23.2087 −1.47079
250250 0 0
251251 −20.5390 −1.29641 −0.648206 0.761465i 0.724480π-0.724480\pi
−0.648206 + 0.761465i 0.724480π0.724480\pi
252252 0 0
253253 0.791288i 0.0497478i
254254 0 0
255255 0 0
256256 0 0
257257 18.0000i 1.12281i 0.827541 + 0.561405i 0.189739π0.189739\pi
−0.827541 + 0.561405i 0.810261π0.810261\pi
258258 0 0
259259 −31.5390 −1.95974
260260 0 0
261261 0.460985 0.0285343
262262 0 0
263263 5.83485i 0.359792i 0.983686 + 0.179896i 0.0575762π0.0575762\pi
−0.983686 + 0.179896i 0.942424π0.942424\pi
264264 0 0
265265 0 0
266266 0 0
267267 − 6.79129i − 0.415620i
268268 0 0
269269 −29.7042 −1.81109 −0.905547 0.424245i 0.860540π-0.860540\pi
−0.905547 + 0.424245i 0.860540π0.860540\pi
270270 0 0
271271 11.7477 0.713624 0.356812 0.934176i 0.383864π-0.383864\pi
0.356812 + 0.934176i 0.383864π0.383864\pi
272272 0 0
273273 − 8.58258i − 0.519441i
274274 0 0
275275 0 0
276276 0 0
277277 0.582576i 0.0350036i 0.999847 + 0.0175018i 0.00557128π0.00557128\pi
−0.999847 + 0.0175018i 0.994429π0.994429\pi
278278 0 0
279279 0.121591 0.00727944
280280 0 0
281281 13.7477 0.820121 0.410060 0.912058i 0.365508π-0.365508\pi
0.410060 + 0.912058i 0.365508π0.365508\pi
282282 0 0
283283 19.7042i 1.17129i 0.810567 + 0.585646i 0.199159π0.199159\pi
−0.810567 + 0.585646i 0.800841π0.800841\pi
284284 0 0
285285 0 0
286286 0 0
287287 − 50.7042i − 2.99297i
288288 0 0
289289 2.62614 0.154479
290290 0 0
291291 19.3303 1.13316
292292 0 0
293293 21.1652i 1.23648i 0.785989 + 0.618241i 0.212154π0.212154\pi
−0.785989 + 0.618241i 0.787846π0.787846\pi
294294 0 0
295295 0 0
296296 0 0
297297 5.00000i 0.290129i
298298 0 0
299299 −0.791288 −0.0457614
300300 0 0
301301 47.9129 2.76165
302302 0 0
303303 − 6.49545i − 0.373154i
304304 0 0
305305 0 0
306306 0 0
307307 31.7913i 1.81442i 0.420673 + 0.907212i 0.361794π0.361794\pi
−0.420673 + 0.907212i 0.638206π0.638206\pi
308308 0 0
309309 30.3739 1.72791
310310 0 0
311311 24.1652 1.37028 0.685140 0.728411i 0.259741π-0.259741\pi
0.685140 + 0.728411i 0.259741π0.259741\pi
312312 0 0
313313 20.7477i 1.17273i 0.810047 + 0.586365i 0.199442π0.199442\pi
−0.810047 + 0.586365i 0.800558π0.800558\pi
314314 0 0
315315 0 0
316316 0 0
317317 5.37386i 0.301826i 0.988547 + 0.150913i 0.0482214π0.0482214\pi
−0.988547 + 0.150913i 0.951779π0.951779\pi
318318 0 0
319319 −2.20871 −0.123664
320320 0 0
321321 −13.8784 −0.774617
322322 0 0
323323 9.79129i 0.544802i
324324 0 0
325325 0 0
326326 0 0
327327 0.373864i 0.0206747i
328328 0 0
329329 −50.7042 −2.79541
330330 0 0
331331 19.3303 1.06249 0.531245 0.847218i 0.321724π-0.321724\pi
0.531245 + 0.847218i 0.321724π0.321724\pi
332332 0 0
333333 − 1.37386i − 0.0752873i
334334 0 0
335335 0 0
336336 0 0
337337 − 22.0000i − 1.19842i −0.800593 0.599208i 0.795482π-0.795482\pi
0.800593 0.599208i 0.204518π-0.204518\pi
338338 0 0
339339 18.9564 1.02957
340340 0 0
341341 −0.582576 −0.0315482
342342 0 0
343343 − 42.9129i − 2.31708i
344344 0 0
345345 0 0
346346 0 0
347347 − 26.3739i − 1.41582i −0.706301 0.707912i 0.749638π-0.749638\pi
0.706301 0.707912i 0.250362π-0.250362\pi
348348 0 0
349349 5.41742 0.289988 0.144994 0.989433i 0.453684π-0.453684\pi
0.144994 + 0.989433i 0.453684π0.453684\pi
350350 0 0
351351 −5.00000 −0.266880
352352 0 0
353353 0.165151i 0.00879012i 0.999990 + 0.00439506i 0.00139900π0.00139900\pi
−0.999990 + 0.00439506i 0.998601π0.998601\pi
354354 0 0
355355 0 0
356356 0 0
357357 32.5390i 1.72215i
358358 0 0
359359 −6.00000 −0.316668 −0.158334 0.987386i 0.550612π-0.550612\pi
−0.158334 + 0.987386i 0.550612π0.550612\pi
360360 0 0
361361 −12.3303 −0.648963
362362 0 0
363363 1.79129i 0.0940182i
364364 0 0
365365 0 0
366366 0 0
367367 − 22.3739i − 1.16791i −0.811787 0.583953i 0.801505π-0.801505\pi
0.811787 0.583953i 0.198495π-0.198495\pi
368368 0 0
369369 2.20871 0.114981
370370 0 0
371371 −11.3739 −0.590502
372372 0 0
373373 − 17.3303i − 0.897329i −0.893700 0.448665i 0.851900π-0.851900\pi
0.893700 0.448665i 0.148100π-0.148100\pi
374374 0 0
375375 0 0
376376 0 0
377377 − 2.20871i − 0.113754i
378378 0 0
379379 −31.0000 −1.59236 −0.796182 0.605058i 0.793150π-0.793150\pi
−0.796182 + 0.605058i 0.793150π0.793150\pi
380380 0 0
381381 4.70417 0.241002
382382 0 0
383383 − 18.0000i − 0.919757i −0.887982 0.459879i 0.847893π-0.847893\pi
0.887982 0.459879i 0.152107π-0.152107\pi
384384 0 0
385385 0 0
386386 0 0
387387 2.08712i 0.106094i
388388 0 0
389389 12.0000 0.608424 0.304212 0.952604i 0.401607π-0.401607\pi
0.304212 + 0.952604i 0.401607π0.401607\pi
390390 0 0
391391 3.00000 0.151717
392392 0 0
393393 25.7477i 1.29880i
394394 0 0
395395 0 0
396396 0 0
397397 11.7913i 0.591788i 0.955221 + 0.295894i 0.0956175π0.0956175\pi
−0.955221 + 0.295894i 0.904383π0.904383\pi
398398 0 0
399399 22.1652 1.10965
400400 0 0
401401 −33.1652 −1.65619 −0.828094 0.560589i 0.810575π-0.810575\pi
−0.828094 + 0.560589i 0.810575π0.810575\pi
402402 0 0
403403 − 0.582576i − 0.0290202i
404404 0 0
405405 0 0
406406 0 0
407407 6.58258i 0.326286i
408408 0 0
409409 −17.0000 −0.840596 −0.420298 0.907386i 0.638074π-0.638074\pi
−0.420298 + 0.907386i 0.638074π0.638074\pi
410410 0 0
411411 −36.7913 −1.81478
412412 0 0
413413 − 6.79129i − 0.334177i
414414 0 0
415415 0 0
416416 0 0
417417 − 31.7913i − 1.55683i
418418 0 0
419419 27.0000 1.31904 0.659518 0.751689i 0.270760π-0.270760\pi
0.659518 + 0.751689i 0.270760π0.270760\pi
420420 0 0
421421 11.6261 0.566623 0.283312 0.959028i 0.408567π-0.408567\pi
0.283312 + 0.959028i 0.408567π0.408567\pi
422422 0 0
423423 − 2.20871i − 0.107391i
424424 0 0
425425 0 0
426426 0 0
427427 42.1216i 2.03841i
428428 0 0
429429 −1.79129 −0.0864842
430430 0 0
431431 34.9129 1.68169 0.840847 0.541273i 0.182057π-0.182057\pi
0.840847 + 0.541273i 0.182057π0.182057\pi
432432 0 0
433433 − 23.3303i − 1.12118i −0.828093 0.560591i 0.810574π-0.810574\pi
0.828093 0.560591i 0.189426π-0.189426\pi
434434 0 0
435435 0 0
436436 0 0
437437 − 2.04356i − 0.0977568i
438438 0 0
439439 −10.9564 −0.522922 −0.261461 0.965214i 0.584204π-0.584204\pi
−0.261461 + 0.965214i 0.584204π0.584204\pi
440440 0 0
441441 3.33030 0.158586
442442 0 0
443443 31.5826i 1.50053i 0.661135 + 0.750267i 0.270075π0.270075\pi
−0.661135 + 0.750267i 0.729925π0.729925\pi
444444 0 0
445445 0 0
446446 0 0
447447 27.1652i 1.28487i
448448 0 0
449449 −30.7913 −1.45313 −0.726565 0.687097i 0.758885π-0.758885\pi
−0.726565 + 0.687097i 0.758885π0.758885\pi
450450 0 0
451451 −10.5826 −0.498314
452452 0 0
453453 − 8.95644i − 0.420810i
454454 0 0
455455 0 0
456456 0 0
457457 − 0.373864i − 0.0174886i −0.999962 0.00874430i 0.997217π-0.997217\pi
0.999962 0.00874430i 0.00278343π-0.00278343\pi
458458 0 0
459459 18.9564 0.884811
460460 0 0
461461 30.4955 1.42031 0.710157 0.704043i 0.248624π-0.248624\pi
0.710157 + 0.704043i 0.248624π0.248624\pi
462462 0 0
463463 − 29.7477i − 1.38249i −0.722619 0.691247i 0.757062π-0.757062\pi
0.722619 0.691247i 0.242938π-0.242938\pi
464464 0 0
465465 0 0
466466 0 0
467467 − 1.41742i − 0.0655906i −0.999462 0.0327953i 0.989559π-0.989559\pi
0.999462 0.0327953i 0.0104409π-0.0104409\pi
468468 0 0
469469 −19.1652 −0.884964
470470 0 0
471471 2.08712 0.0961695
472472 0 0
473473 − 10.0000i − 0.459800i
474474 0 0
475475 0 0
476476 0 0
477477 − 0.495454i − 0.0226853i
478478 0 0
479479 −18.1652 −0.829987 −0.414993 0.909824i 0.636216π-0.636216\pi
−0.414993 + 0.909824i 0.636216π0.636216\pi
480480 0 0
481481 −6.58258 −0.300140
482482 0 0
483483 − 6.79129i − 0.309014i
484484 0 0
485485 0 0
486486 0 0
487487 2.25227i 0.102060i 0.998697 + 0.0510301i 0.0162504π0.0162504\pi
−0.998697 + 0.0510301i 0.983750π0.983750\pi
488488 0 0
489489 13.6606 0.617754
490490 0 0
491491 16.5826 0.748361 0.374181 0.927356i 0.377924π-0.377924\pi
0.374181 + 0.927356i 0.377924π0.377924\pi
492492 0 0
493493 8.37386i 0.377140i
494494 0 0
495495 0 0
496496 0 0
497497 − 80.2432i − 3.59940i
498498 0 0
499499 −7.95644 −0.356179 −0.178090 0.984014i 0.556992π-0.556992\pi
−0.178090 + 0.984014i 0.556992π0.556992\pi
500500 0 0
501501 −13.2867 −0.593608
502502 0 0
503503 25.5826i 1.14067i 0.821412 + 0.570335i 0.193187π0.193187\pi
−0.821412 + 0.570335i 0.806813π0.806813\pi
504504 0 0
505505 0 0
506506 0 0
507507 21.4955i 0.954647i
508508 0 0
509509 31.1216 1.37944 0.689720 0.724076i 0.257734π-0.257734\pi
0.689720 + 0.724076i 0.257734π0.257734\pi
510510 0 0
511511 −15.3739 −0.680100
512512 0 0
513513 − 12.9129i − 0.570118i
514514 0 0
515515 0 0
516516 0 0
517517 10.5826i 0.465421i
518518 0 0
519519 24.6261 1.08097
520520 0 0
521521 −7.58258 −0.332199 −0.166099 0.986109i 0.553117π-0.553117\pi
−0.166099 + 0.986109i 0.553117π0.553117\pi
522522 0 0
523523 − 6.83485i − 0.298867i −0.988772 0.149434i 0.952255π-0.952255\pi
0.988772 0.149434i 0.0477450π-0.0477450\pi
524524 0 0
525525 0 0
526526 0 0
527527 2.20871i 0.0962130i
528528 0 0
529529 22.3739 0.972777
530530 0 0
531531 0.295834 0.0128381
532532 0 0
533533 − 10.5826i − 0.458382i
534534 0 0
535535 0 0
536536 0 0
537537 − 34.2523i − 1.47809i
538538 0 0
539539 −15.9564 −0.687292
540540 0 0
541541 −24.3739 −1.04791 −0.523957 0.851745i 0.675545π-0.675545\pi
−0.523957 + 0.851745i 0.675545π0.675545\pi
542542 0 0
543543 18.5826i 0.797455i
544544 0 0
545545 0 0
546546 0 0
547547 6.37386i 0.272527i 0.990673 + 0.136263i 0.0435093π0.0435093\pi
−0.990673 + 0.136263i 0.956491π0.956491\pi
548548 0 0
549549 −1.83485 −0.0783094
550550 0 0
551551 5.70417 0.243006
552552 0 0
553553 79.2432i 3.36976i
554554 0 0
555555 0 0
556556 0 0
557557 27.6606i 1.17202i 0.810305 + 0.586009i 0.199302π0.199302\pi
−0.810305 + 0.586009i 0.800698π0.800698\pi
558558 0 0
559559 10.0000 0.422955
560560 0 0
561561 6.79129 0.286728
562562 0 0
563563 1.12159i 0.0472694i 0.999721 + 0.0236347i 0.00752386π0.00752386\pi
−0.999721 + 0.0236347i 0.992476π0.992476\pi
564564 0 0
565565 0 0
566566 0 0
567567 − 45.9129i − 1.92816i
568568 0 0
569569 3.95644 0.165863 0.0829313 0.996555i 0.473572π-0.473572\pi
0.0829313 + 0.996555i 0.473572π0.473572\pi
570570 0 0
571571 32.2867 1.35116 0.675579 0.737288i 0.263894π-0.263894\pi
0.675579 + 0.737288i 0.263894π0.263894\pi
572572 0 0
573573 − 39.0345i − 1.63069i
574574 0 0
575575 0 0
576576 0 0
577577 − 10.9564i − 0.456123i −0.973647 0.228061i 0.926761π-0.926761\pi
0.973647 0.228061i 0.0732387π-0.0732387\pi
578578 0 0
579579 20.0000 0.831172
580580 0 0
581581 −62.0780 −2.57543
582582 0 0
583583 2.37386i 0.0983154i
584584 0 0
585585 0 0
586586 0 0
587587 6.95644i 0.287123i 0.989641 + 0.143561i 0.0458555π0.0458555\pi
−0.989641 + 0.143561i 0.954145π0.954145\pi
588588 0 0
589589 1.50455 0.0619937
590590 0 0
591591 9.92197 0.408135
592592 0 0
593593 13.4174i 0.550988i 0.961303 + 0.275494i 0.0888413π0.0888413\pi
−0.961303 + 0.275494i 0.911159π0.911159\pi
594594 0 0
595595 0 0
596596 0 0
597597 − 27.5390i − 1.12710i
598598 0 0
599599 −5.70417 −0.233066 −0.116533 0.993187i 0.537178π-0.537178\pi
−0.116533 + 0.993187i 0.537178π0.537178\pi
600600 0 0
601601 −3.53901 −0.144359 −0.0721797 0.997392i 0.522996π-0.522996\pi
−0.0721797 + 0.997392i 0.522996π0.522996\pi
602602 0 0
603603 − 0.834849i − 0.0339977i
604604 0 0
605605 0 0
606606 0 0
607607 34.0000i 1.38002i 0.723801 + 0.690009i 0.242393π0.242393\pi
−0.723801 + 0.690009i 0.757607π0.757607\pi
608608 0 0
609609 18.9564 0.768154
610610 0 0
611611 −10.5826 −0.428125
612612 0 0
613613 44.4519i 1.79540i 0.440612 + 0.897698i 0.354761π0.354761\pi
−0.440612 + 0.897698i 0.645239π0.645239\pi
614614 0 0
615615 0 0
616616 0 0
617617 − 1.25227i − 0.0504146i −0.999682 0.0252073i 0.991975π-0.991975\pi
0.999682 0.0252073i 0.00802458π-0.00802458\pi
618618 0 0
619619 33.7477 1.35644 0.678218 0.734861i 0.262753π-0.262753\pi
0.678218 + 0.734861i 0.262753π0.262753\pi
620620 0 0
621621 −3.95644 −0.158766
622622 0 0
623623 − 18.1652i − 0.727771i
624624 0 0
625625 0 0
626626 0 0
627627 − 4.62614i − 0.184750i
628628 0 0
629629 24.9564 0.995078
630630 0 0
631631 23.1216 0.920456 0.460228 0.887801i 0.347768π-0.347768\pi
0.460228 + 0.887801i 0.347768π0.347768\pi
632632 0 0
633633 − 8.95644i − 0.355987i
634634 0 0
635635 0 0
636636 0 0
637637 − 15.9564i − 0.632217i
638638 0 0
639639 3.49545 0.138278
640640 0 0
641641 −42.1652 −1.66542 −0.832712 0.553707i 0.813213π-0.813213\pi
−0.832712 + 0.553707i 0.813213π0.813213\pi
642642 0 0
643643 11.4955i 0.453336i 0.973972 + 0.226668i 0.0727833π0.0727833\pi
−0.973972 + 0.226668i 0.927217π0.927217\pi
644644 0 0
645645 0 0
646646 0 0
647647 15.3303i 0.602696i 0.953514 + 0.301348i 0.0974366π0.0974366\pi
−0.953514 + 0.301348i 0.902563π0.902563\pi
648648 0 0
649649 −1.41742 −0.0556388
650650 0 0
651651 5.00000 0.195965
652652 0 0
653653 23.7042i 0.927616i 0.885936 + 0.463808i 0.153517π0.153517\pi
−0.885936 + 0.463808i 0.846483π0.846483\pi
654654 0 0
655655 0 0
656656 0 0
657657 − 0.669697i − 0.0261274i
658658 0 0
659659 32.5390 1.26754 0.633770 0.773522i 0.281507π-0.281507\pi
0.633770 + 0.773522i 0.281507π0.281507\pi
660660 0 0
661661 21.4174 0.833041 0.416521 0.909126i 0.363249π-0.363249\pi
0.416521 + 0.909126i 0.363249π0.363249\pi
662662 0 0
663663 6.79129i 0.263752i
664664 0 0
665665 0 0
666666 0 0
667667 − 1.74773i − 0.0676723i
668668 0 0
669669 20.4519 0.790716
670670 0 0
671671 8.79129 0.339384
672672 0 0
673673 − 6.91288i − 0.266472i −0.991084 0.133236i 0.957463π-0.957463\pi
0.991084 0.133236i 0.0425368π-0.0425368\pi
674674 0 0
675675 0 0
676676 0 0
677677 7.58258i 0.291422i 0.989327 + 0.145711i 0.0465470π0.0465470\pi
−0.989327 + 0.145711i 0.953453π0.953453\pi
678678 0 0
679679 51.7042 1.98422
680680 0 0
681681 −36.7913 −1.40985
682682 0 0
683683 − 10.9129i − 0.417570i −0.977962 0.208785i 0.933049π-0.933049\pi
0.977962 0.208785i 0.0669508π-0.0669508\pi
684684 0 0
685685 0 0
686686 0 0
687687 38.2867i 1.46073i
688688 0 0
689689 −2.37386 −0.0904370
690690 0 0
691691 −9.12159 −0.347002 −0.173501 0.984834i 0.555508π-0.555508\pi
−0.173501 + 0.984834i 0.555508π0.555508\pi
692692 0 0
693693 − 1.00000i − 0.0379869i
694694 0 0
695695 0 0
696696 0 0
697697 40.1216i 1.51971i
698698 0 0
699699 20.0780 0.759421
700700 0 0
701701 39.1652 1.47925 0.739624 0.673021i 0.235004π-0.235004\pi
0.739624 + 0.673021i 0.235004π0.235004\pi
702702 0 0
703703 − 17.0000i − 0.641167i
704704 0 0
705705 0 0
706706 0 0
707707 − 17.3739i − 0.653411i
708708 0 0
709709 25.4955 0.957502 0.478751 0.877951i 0.341090π-0.341090\pi
0.478751 + 0.877951i 0.341090π0.341090\pi
710710 0 0
711711 −3.45189 −0.129456
712712 0 0
713713 − 0.460985i − 0.0172640i
714714 0 0
715715 0 0
716716 0 0
717717 − 12.1652i − 0.454316i
718718 0 0
719719 −48.4955 −1.80858 −0.904288 0.426924i 0.859597π-0.859597\pi
−0.904288 + 0.426924i 0.859597π0.859597\pi
720720 0 0
721721 81.2432 3.02565
722722 0 0
723723 32.4610i 1.20724i
724724 0 0
725725 0 0
726726 0 0
727727 − 18.1216i − 0.672093i −0.941845 0.336046i 0.890910π-0.890910\pi
0.941845 0.336046i 0.109090π-0.109090\pi
728728 0 0
729729 −24.8693 −0.921086
730730 0 0
731731 −37.9129 −1.40226
732732 0 0
733733 51.2432i 1.89271i 0.323129 + 0.946355i 0.395265π0.395265\pi
−0.323129 + 0.946355i 0.604735π0.604735\pi
734734 0 0
735735 0 0
736736 0 0
737737 4.00000i 0.147342i
738738 0 0
739739 0.878409 0.0323128 0.0161564 0.999869i 0.494857π-0.494857\pi
0.0161564 + 0.999869i 0.494857π0.494857\pi
740740 0 0
741741 4.62614 0.169945
742742 0 0
743743 35.2087i 1.29168i 0.763472 + 0.645841i 0.223493π0.223493\pi
−0.763472 + 0.645841i 0.776507π0.776507\pi
744744 0 0
745745 0 0
746746 0 0
747747 − 2.70417i − 0.0989403i
748748 0 0
749749 −37.1216 −1.35639
750750 0 0
751751 −17.7913 −0.649213 −0.324607 0.945849i 0.605232π-0.605232\pi
−0.324607 + 0.945849i 0.605232π0.605232\pi
752752 0 0
753753 − 36.7913i − 1.34075i
754754 0 0
755755 0 0
756756 0 0
757757 29.3303i 1.06603i 0.846106 + 0.533014i 0.178941π0.178941\pi
−0.846106 + 0.533014i 0.821059π0.821059\pi
758758 0 0
759759 −1.41742 −0.0514492
760760 0 0
761761 −6.33030 −0.229473 −0.114737 0.993396i 0.536602π-0.536602\pi
−0.114737 + 0.993396i 0.536602π0.536602\pi
762762 0 0
763763 1.00000i 0.0362024i
764764 0 0
765765 0 0
766766 0 0
767767 − 1.41742i − 0.0511802i
768768 0 0
769769 14.2523 0.513950 0.256975 0.966418i 0.417274π-0.417274\pi
0.256975 + 0.966418i 0.417274π0.417274\pi
770770 0 0
771771 −32.2432 −1.16121
772772 0 0
773773 − 30.7913i − 1.10749i −0.832688 0.553743i 0.813199π-0.813199\pi
0.832688 0.553743i 0.186801π-0.186801\pi
774774 0 0
775775 0 0
776776 0 0
777777 − 56.4955i − 2.02676i
778778 0 0
779779 27.3303 0.979210
780780 0 0
781781 −16.7477 −0.599281
782782 0 0
783783 − 11.0436i − 0.394665i
784784 0 0
785785 0 0
786786 0 0
787787 − 9.74773i − 0.347469i −0.984793 0.173734i 0.944417π-0.944417\pi
0.984793 0.173734i 0.0555834π-0.0555834\pi
788788 0 0
789789 −10.4519 −0.372097
790790 0 0
791791 50.7042 1.80283
792792 0 0
793793 8.79129i 0.312188i
794794 0 0
795795 0 0
796796 0 0
797797 − 25.2867i − 0.895702i −0.894108 0.447851i 0.852189π-0.852189\pi
0.894108 0.447851i 0.147811π-0.147811\pi
798798 0 0
799799 40.1216 1.41940
800800 0 0
801801 0.791288 0.0279588
802802 0 0
803803 3.20871i 0.113233i
804804 0 0
805805 0 0
806806 0 0
807807 − 53.2087i − 1.87304i
808808 0 0
809809 −9.49545 −0.333842 −0.166921 0.985970i 0.553383π-0.553383\pi
−0.166921 + 0.985970i 0.553383π0.553383\pi
810810 0 0
811811 −17.6606 −0.620148 −0.310074 0.950712i 0.600354π-0.600354\pi
−0.310074 + 0.950712i 0.600354π0.600354\pi
812812 0 0
813813 21.0436i 0.738030i
814814 0 0
815815 0 0
816816 0 0
817817 25.8258i 0.903529i
818818 0 0
819819 1.00000 0.0349428
820820 0 0
821821 −24.6606 −0.860661 −0.430331 0.902671i 0.641603π-0.641603\pi
−0.430331 + 0.902671i 0.641603π0.641603\pi
822822 0 0
823823 8.00000i 0.278862i 0.990232 + 0.139431i 0.0445274π0.0445274\pi
−0.990232 + 0.139431i 0.955473π0.955473\pi
824824 0 0
825825 0 0
826826 0 0
827827 19.5826i 0.680953i 0.940253 + 0.340476i 0.110588π0.110588\pi
−0.940253 + 0.340476i 0.889412π0.889412\pi
828828 0 0
829829 15.0436 0.522484 0.261242 0.965273i 0.415868π-0.415868\pi
0.261242 + 0.965273i 0.415868π0.415868\pi
830830 0 0
831831 −1.04356 −0.0362007
832832 0 0
833833 60.4955i 2.09604i
834834 0 0
835835 0 0
836836 0 0
837837 − 2.91288i − 0.100684i
838838 0 0
839839 26.7042 0.921930 0.460965 0.887418i 0.347503π-0.347503\pi
0.460965 + 0.887418i 0.347503π0.347503\pi
840840 0 0
841841 −24.1216 −0.831779
842842 0 0
843843 24.6261i 0.848169i
844844 0 0
845845 0 0
846846 0 0
847847 4.79129i 0.164631i
848848 0 0
849849 −35.2958 −1.21135
850850 0 0
851851 −5.20871 −0.178552
852852 0 0
853853 38.1216i 1.30526i 0.757677 + 0.652629i 0.226334π0.226334\pi
−0.757677 + 0.652629i 0.773666π0.773666\pi
854854 0 0
855855 0 0
856856 0 0
857857 24.4955i 0.836749i 0.908275 + 0.418374i 0.137400π0.137400\pi
−0.908275 + 0.418374i 0.862600π0.862600\pi
858858 0 0
859859 −47.9129 −1.63477 −0.817383 0.576094i 0.804576π-0.804576\pi
−0.817383 + 0.576094i 0.804576π0.804576\pi
860860 0 0
861861 90.8258 3.09533
862862 0 0
863863 9.33030i 0.317607i 0.987310 + 0.158804i 0.0507637π0.0507637\pi
−0.987310 + 0.158804i 0.949236π0.949236\pi
864864 0 0
865865 0 0
866866 0 0
867867 4.70417i 0.159762i
868868 0 0
869869 16.5390 0.561048
870870 0 0
871871 −4.00000 −0.135535
872872 0 0
873873 2.25227i 0.0762279i
874874 0 0
875875 0 0
876876 0 0
877877 56.6606i 1.91329i 0.291252 + 0.956646i 0.405928π0.405928\pi
−0.291252 + 0.956646i 0.594072π0.594072\pi
878878 0 0
879879 −37.9129 −1.27877
880880 0 0
881881 43.1216 1.45280 0.726402 0.687270i 0.241191π-0.241191\pi
0.726402 + 0.687270i 0.241191π0.241191\pi
882882 0 0
883883 7.83485i 0.263664i 0.991272 + 0.131832i 0.0420859π0.0420859\pi
−0.991272 + 0.131832i 0.957914π0.957914\pi
884884 0 0
885885 0 0
886886 0 0
887887 2.66970i 0.0896397i 0.998995 + 0.0448198i 0.0142714π0.0142714\pi
−0.998995 + 0.0448198i 0.985729π0.985729\pi
888888 0 0
889889 12.5826 0.422006
890890 0 0
891891 −9.58258 −0.321028
892892 0 0
893893 − 27.3303i − 0.914574i
894894 0 0
895895 0 0
896896 0 0
897897 − 1.41742i − 0.0473264i
898898 0 0
899899 1.28674 0.0429152
900900 0 0
901901 9.00000 0.299833
902902 0 0
903903 85.8258i 2.85610i
904904 0 0
905905 0 0
906906 0 0
907907 40.6606i 1.35011i 0.737766 + 0.675057i 0.235881π0.235881\pi
−0.737766 + 0.675057i 0.764119π0.764119\pi
908908 0 0
909909 0.756819 0.0251021
910910 0 0
911911 −24.3303 −0.806099 −0.403049 0.915178i 0.632050π-0.632050\pi
−0.403049 + 0.915178i 0.632050π0.632050\pi
912912 0 0
913913 12.9564i 0.428796i
914914 0 0
915915 0 0
916916 0 0
917917 68.8693i 2.27427i
918918 0 0
919919 47.1652 1.55583 0.777917 0.628367i 0.216276π-0.216276\pi
0.777917 + 0.628367i 0.216276π0.216276\pi
920920 0 0
921921 −56.9473 −1.87648
922922 0 0
923923 − 16.7477i − 0.551258i
924924 0 0
925925 0 0
926926 0 0
927927 3.53901i 0.116237i
928928 0 0
929929 13.7477 0.451048 0.225524 0.974238i 0.427591π-0.427591\pi
0.225524 + 0.974238i 0.427591π0.427591\pi
930930 0 0
931931 41.2087 1.35056
932932 0 0
933933 43.2867i 1.41714i
934934 0 0
935935 0 0
936936 0 0
937937 16.8348i 0.549971i 0.961448 + 0.274985i 0.0886730π0.0886730\pi
−0.961448 + 0.274985i 0.911327π0.911327\pi
938938 0 0
939939 −37.1652 −1.21284
940940 0 0
941941 14.0780 0.458931 0.229465 0.973317i 0.426302π-0.426302\pi
0.229465 + 0.973317i 0.426302π0.426302\pi
942942 0 0
943943 − 8.37386i − 0.272691i
944944 0 0
945945 0 0
946946 0 0
947947 − 40.9129i − 1.32949i −0.747070 0.664745i 0.768540π-0.768540\pi
0.747070 0.664745i 0.231460π-0.231460\pi
948948 0 0
949949 −3.20871 −0.104159
950950 0 0
951951 −9.62614 −0.312149
952952 0 0
953953 42.0000i 1.36051i 0.732974 + 0.680257i 0.238132π0.238132\pi
−0.732974 + 0.680257i 0.761868π0.761868\pi
954954 0 0
955955 0 0
956956 0 0
957957 − 3.95644i − 0.127894i
958958 0 0
959959 −98.4083 −3.17777
960960 0 0
961961 −30.6606 −0.989052
962962 0 0
963963 − 1.61704i − 0.0521085i
964964 0 0
965965 0 0
966966 0 0
967967 − 11.4610i − 0.368560i −0.982874 0.184280i 0.941005π-0.941005\pi
0.982874 0.184280i 0.0589954π-0.0589954\pi
968968 0 0
969969 −17.5390 −0.563434
970970 0 0
971971 3.95644 0.126968 0.0634841 0.997983i 0.479779π-0.479779\pi
0.0634841 + 0.997983i 0.479779π0.479779\pi
972972 0 0
973973 − 85.0345i − 2.72608i
974974 0 0
975975 0 0
976976 0 0
977977 1.74773i 0.0559147i 0.999609 + 0.0279574i 0.00890027π0.00890027\pi
−0.999609 + 0.0279574i 0.991100π0.991100\pi
978978 0 0
979979 −3.79129 −0.121170
980980 0 0
981981 −0.0435608 −0.00139079
982982 0 0
983983 24.6606i 0.786551i 0.919421 + 0.393276i 0.128658π0.128658\pi
−0.919421 + 0.393276i 0.871342π0.871342\pi
984984 0 0
985985 0 0
986986 0 0
987987 − 90.8258i − 2.89102i
988988 0 0
989989 7.91288 0.251615
990990 0 0
991991 12.8693 0.408807 0.204404 0.978887i 0.434474π-0.434474\pi
0.204404 + 0.978887i 0.434474π0.434474\pi
992992 0 0
993993 34.6261i 1.09883i
994994 0 0
995995 0 0
996996 0 0
997997 26.6261i 0.843258i 0.906768 + 0.421629i 0.138542π0.138542\pi
−0.906768 + 0.421629i 0.861458π0.861458\pi
998998 0 0
999999 −32.9129 −1.04132
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 4400.2.b.s.4049.3 4
4.3 odd 2 1100.2.b.d.749.2 4
5.2 odd 4 4400.2.a.bi.1.2 2
5.3 odd 4 4400.2.a.bu.1.1 2
5.4 even 2 inner 4400.2.b.s.4049.2 4
12.11 even 2 9900.2.c.x.5149.1 4
20.3 even 4 1100.2.a.g.1.2 2
20.7 even 4 1100.2.a.h.1.1 yes 2
20.19 odd 2 1100.2.b.d.749.3 4
60.23 odd 4 9900.2.a.bh.1.1 2
60.47 odd 4 9900.2.a.bz.1.2 2
60.59 even 2 9900.2.c.x.5149.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1100.2.a.g.1.2 2 20.3 even 4
1100.2.a.h.1.1 yes 2 20.7 even 4
1100.2.b.d.749.2 4 4.3 odd 2
1100.2.b.d.749.3 4 20.19 odd 2
4400.2.a.bi.1.2 2 5.2 odd 4
4400.2.a.bu.1.1 2 5.3 odd 4
4400.2.b.s.4049.2 4 5.4 even 2 inner
4400.2.b.s.4049.3 4 1.1 even 1 trivial
9900.2.a.bh.1.1 2 60.23 odd 4
9900.2.a.bz.1.2 2 60.47 odd 4
9900.2.c.x.5149.1 4 12.11 even 2
9900.2.c.x.5149.4 4 60.59 even 2