Properties

Label 2646.2.a.bo.1.2
Level 26462646
Weight 22
Character 2646.1
Self dual yes
Analytic conductor 21.12821.128
Analytic rank 00
Dimension 22
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [2646,2,Mod(1,2646)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2646, 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("2646.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 2646=23372 2646 = 2 \cdot 3^{3} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2646.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,2,0,2,2,0,0,2,0,2,2,0,4] 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: 21.128416374821.1284163748
Analytic rank: 00
Dimension: 22
Coefficient field: Q(7)\Q(\sqrt{7})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x27 x^{2} - 7 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 378)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 2.645752.64575 of defining polynomial
Character χ\chi == 2646.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+1.00000q2+1.00000q4+3.64575q5+1.00000q8+3.64575q10+3.64575q11+4.64575q13+1.00000q163.64575q172.00000q19+3.64575q20+3.64575q221.29150q23+8.29150q25+4.64575q26+2.35425q29+4.64575q31+1.00000q323.64575q3411.9373q372.00000q38+3.64575q4010.9373q41+5.00000q43+3.64575q441.29150q464.93725q47+8.29150q50+4.64575q52+6.00000q53+13.2915q55+2.35425q588.35425q597.35425q61+4.64575q62+1.00000q64+16.9373q652.29150q673.64575q68+15.6458q7110.5830q7311.9373q742.00000q76+11.2288q79+3.64575q8010.9373q82+13.2915q8313.2915q85+5.00000q86+3.64575q884.93725q891.29150q924.93725q947.29150q9513.5830q97+O(q100)q+1.00000 q^{2} +1.00000 q^{4} +3.64575 q^{5} +1.00000 q^{8} +3.64575 q^{10} +3.64575 q^{11} +4.64575 q^{13} +1.00000 q^{16} -3.64575 q^{17} -2.00000 q^{19} +3.64575 q^{20} +3.64575 q^{22} -1.29150 q^{23} +8.29150 q^{25} +4.64575 q^{26} +2.35425 q^{29} +4.64575 q^{31} +1.00000 q^{32} -3.64575 q^{34} -11.9373 q^{37} -2.00000 q^{38} +3.64575 q^{40} -10.9373 q^{41} +5.00000 q^{43} +3.64575 q^{44} -1.29150 q^{46} -4.93725 q^{47} +8.29150 q^{50} +4.64575 q^{52} +6.00000 q^{53} +13.2915 q^{55} +2.35425 q^{58} -8.35425 q^{59} -7.35425 q^{61} +4.64575 q^{62} +1.00000 q^{64} +16.9373 q^{65} -2.29150 q^{67} -3.64575 q^{68} +15.6458 q^{71} -10.5830 q^{73} -11.9373 q^{74} -2.00000 q^{76} +11.2288 q^{79} +3.64575 q^{80} -10.9373 q^{82} +13.2915 q^{83} -13.2915 q^{85} +5.00000 q^{86} +3.64575 q^{88} -4.93725 q^{89} -1.29150 q^{92} -4.93725 q^{94} -7.29150 q^{95} -13.5830 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+2q2+2q4+2q5+2q8+2q10+2q11+4q13+2q162q174q19+2q20+2q22+8q23+6q25+4q26+10q29+4q31+2q322q34+6q97+O(q100) 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 2 q^{8} + 2 q^{10} + 2 q^{11} + 4 q^{13} + 2 q^{16} - 2 q^{17} - 4 q^{19} + 2 q^{20} + 2 q^{22} + 8 q^{23} + 6 q^{25} + 4 q^{26} + 10 q^{29} + 4 q^{31} + 2 q^{32} - 2 q^{34}+ \cdots - 6 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 1.00000 0.707107
33 0 0
44 1.00000 0.500000
55 3.64575 1.63043 0.815215 0.579159i 0.196619π-0.196619\pi
0.815215 + 0.579159i 0.196619π0.196619\pi
66 0 0
77 0 0
88 1.00000 0.353553
99 0 0
1010 3.64575 1.15289
1111 3.64575 1.09924 0.549618 0.835416i 0.314773π-0.314773\pi
0.549618 + 0.835416i 0.314773π0.314773\pi
1212 0 0
1313 4.64575 1.28850 0.644250 0.764815i 0.277170π-0.277170\pi
0.644250 + 0.764815i 0.277170π0.277170\pi
1414 0 0
1515 0 0
1616 1.00000 0.250000
1717 −3.64575 −0.884225 −0.442112 0.896960i 0.645771π-0.645771\pi
−0.442112 + 0.896960i 0.645771π0.645771\pi
1818 0 0
1919 −2.00000 −0.458831 −0.229416 0.973329i 0.573682π-0.573682\pi
−0.229416 + 0.973329i 0.573682π0.573682\pi
2020 3.64575 0.815215
2121 0 0
2222 3.64575 0.777277
2323 −1.29150 −0.269297 −0.134648 0.990893i 0.542991π-0.542991\pi
−0.134648 + 0.990893i 0.542991π0.542991\pi
2424 0 0
2525 8.29150 1.65830
2626 4.64575 0.911107
2727 0 0
2828 0 0
2929 2.35425 0.437173 0.218587 0.975818i 0.429855π-0.429855\pi
0.218587 + 0.975818i 0.429855π0.429855\pi
3030 0 0
3131 4.64575 0.834402 0.417201 0.908814i 0.363011π-0.363011\pi
0.417201 + 0.908814i 0.363011π0.363011\pi
3232 1.00000 0.176777
3333 0 0
3434 −3.64575 −0.625241
3535 0 0
3636 0 0
3737 −11.9373 −1.96247 −0.981236 0.192809i 0.938240π-0.938240\pi
−0.981236 + 0.192809i 0.938240π0.938240\pi
3838 −2.00000 −0.324443
3939 0 0
4040 3.64575 0.576444
4141 −10.9373 −1.70811 −0.854056 0.520181i 0.825864π-0.825864\pi
−0.854056 + 0.520181i 0.825864π0.825864\pi
4242 0 0
4343 5.00000 0.762493 0.381246 0.924473i 0.375495π-0.375495\pi
0.381246 + 0.924473i 0.375495π0.375495\pi
4444 3.64575 0.549618
4545 0 0
4646 −1.29150 −0.190422
4747 −4.93725 −0.720173 −0.360086 0.932919i 0.617253π-0.617253\pi
−0.360086 + 0.932919i 0.617253π0.617253\pi
4848 0 0
4949 0 0
5050 8.29150 1.17260
5151 0 0
5252 4.64575 0.644250
5353 6.00000 0.824163 0.412082 0.911147i 0.364802π-0.364802\pi
0.412082 + 0.911147i 0.364802π0.364802\pi
5454 0 0
5555 13.2915 1.79223
5656 0 0
5757 0 0
5858 2.35425 0.309128
5959 −8.35425 −1.08763 −0.543815 0.839205i 0.683021π-0.683021\pi
−0.543815 + 0.839205i 0.683021π0.683021\pi
6060 0 0
6161 −7.35425 −0.941615 −0.470808 0.882236i 0.656037π-0.656037\pi
−0.470808 + 0.882236i 0.656037π0.656037\pi
6262 4.64575 0.590011
6363 0 0
6464 1.00000 0.125000
6565 16.9373 2.10081
6666 0 0
6767 −2.29150 −0.279952 −0.139976 0.990155i 0.544702π-0.544702\pi
−0.139976 + 0.990155i 0.544702π0.544702\pi
6868 −3.64575 −0.442112
6969 0 0
7070 0 0
7171 15.6458 1.85681 0.928405 0.371571i 0.121181π-0.121181\pi
0.928405 + 0.371571i 0.121181π0.121181\pi
7272 0 0
7373 −10.5830 −1.23865 −0.619324 0.785136i 0.712593π-0.712593\pi
−0.619324 + 0.785136i 0.712593π0.712593\pi
7474 −11.9373 −1.38768
7575 0 0
7676 −2.00000 −0.229416
7777 0 0
7878 0 0
7979 11.2288 1.26333 0.631667 0.775240i 0.282371π-0.282371\pi
0.631667 + 0.775240i 0.282371π0.282371\pi
8080 3.64575 0.407607
8181 0 0
8282 −10.9373 −1.20782
8383 13.2915 1.45893 0.729466 0.684017i 0.239769π-0.239769\pi
0.729466 + 0.684017i 0.239769π0.239769\pi
8484 0 0
8585 −13.2915 −1.44167
8686 5.00000 0.539164
8787 0 0
8888 3.64575 0.388638
8989 −4.93725 −0.523348 −0.261674 0.965156i 0.584275π-0.584275\pi
−0.261674 + 0.965156i 0.584275π0.584275\pi
9090 0 0
9191 0 0
9292 −1.29150 −0.134648
9393 0 0
9494 −4.93725 −0.509239
9595 −7.29150 −0.748092
9696 0 0
9797 −13.5830 −1.37915 −0.689573 0.724217i 0.742202π-0.742202\pi
−0.689573 + 0.724217i 0.742202π0.742202\pi
9898 0 0
9999 0 0
100100 8.29150 0.829150
101101 −8.35425 −0.831279 −0.415639 0.909529i 0.636442π-0.636442\pi
−0.415639 + 0.909529i 0.636442π0.636442\pi
102102 0 0
103103 −3.93725 −0.387949 −0.193975 0.981007i 0.562138π-0.562138\pi
−0.193975 + 0.981007i 0.562138π0.562138\pi
104104 4.64575 0.455553
105105 0 0
106106 6.00000 0.582772
107107 −6.00000 −0.580042 −0.290021 0.957020i 0.593662π-0.593662\pi
−0.290021 + 0.957020i 0.593662π0.593662\pi
108108 0 0
109109 −3.35425 −0.321279 −0.160639 0.987013i 0.551356π-0.551356\pi
−0.160639 + 0.987013i 0.551356π0.551356\pi
110110 13.2915 1.26730
111111 0 0
112112 0 0
113113 2.35425 0.221469 0.110735 0.993850i 0.464680π-0.464680\pi
0.110735 + 0.993850i 0.464680π0.464680\pi
114114 0 0
115115 −4.70850 −0.439070
116116 2.35425 0.218587
117117 0 0
118118 −8.35425 −0.769071
119119 0 0
120120 0 0
121121 2.29150 0.208318
122122 −7.35425 −0.665822
123123 0 0
124124 4.64575 0.417201
125125 12.0000 1.07331
126126 0 0
127127 1.35425 0.120170 0.0600851 0.998193i 0.480863π-0.480863\pi
0.0600851 + 0.998193i 0.480863π0.480863\pi
128128 1.00000 0.0883883
129129 0 0
130130 16.9373 1.48550
131131 14.5830 1.27412 0.637062 0.770813i 0.280150π-0.280150\pi
0.637062 + 0.770813i 0.280150π0.280150\pi
132132 0 0
133133 0 0
134134 −2.29150 −0.197956
135135 0 0
136136 −3.64575 −0.312621
137137 1.29150 0.110341 0.0551703 0.998477i 0.482430π-0.482430\pi
0.0551703 + 0.998477i 0.482430π0.482430\pi
138138 0 0
139139 −1.58301 −0.134269 −0.0671344 0.997744i 0.521386π-0.521386\pi
−0.0671344 + 0.997744i 0.521386π0.521386\pi
140140 0 0
141141 0 0
142142 15.6458 1.31296
143143 16.9373 1.41636
144144 0 0
145145 8.58301 0.712780
146146 −10.5830 −0.875856
147147 0 0
148148 −11.9373 −0.981236
149149 22.9373 1.87909 0.939547 0.342421i 0.111247π-0.111247\pi
0.939547 + 0.342421i 0.111247π0.111247\pi
150150 0 0
151151 −19.2288 −1.56481 −0.782407 0.622767i 0.786008π-0.786008\pi
−0.782407 + 0.622767i 0.786008π0.786008\pi
152152 −2.00000 −0.162221
153153 0 0
154154 0 0
155155 16.9373 1.36043
156156 0 0
157157 4.00000 0.319235 0.159617 0.987179i 0.448974π-0.448974\pi
0.159617 + 0.987179i 0.448974π0.448974\pi
158158 11.2288 0.893312
159159 0 0
160160 3.64575 0.288222
161161 0 0
162162 0 0
163163 −1.00000 −0.0783260 −0.0391630 0.999233i 0.512469π-0.512469\pi
−0.0391630 + 0.999233i 0.512469π0.512469\pi
164164 −10.9373 −0.854056
165165 0 0
166166 13.2915 1.03162
167167 8.58301 0.664173 0.332086 0.943249i 0.392247π-0.392247\pi
0.332086 + 0.943249i 0.392247π0.392247\pi
168168 0 0
169169 8.58301 0.660231
170170 −13.2915 −1.01941
171171 0 0
172172 5.00000 0.381246
173173 14.5830 1.10873 0.554363 0.832275i 0.312962π-0.312962\pi
0.554363 + 0.832275i 0.312962π0.312962\pi
174174 0 0
175175 0 0
176176 3.64575 0.274809
177177 0 0
178178 −4.93725 −0.370063
179179 16.9373 1.26595 0.632975 0.774172i 0.281834π-0.281834\pi
0.632975 + 0.774172i 0.281834π0.281834\pi
180180 0 0
181181 2.70850 0.201321 0.100661 0.994921i 0.467904π-0.467904\pi
0.100661 + 0.994921i 0.467904π0.467904\pi
182182 0 0
183183 0 0
184184 −1.29150 −0.0952108
185185 −43.5203 −3.19967
186186 0 0
187187 −13.2915 −0.971971
188188 −4.93725 −0.360086
189189 0 0
190190 −7.29150 −0.528981
191191 −20.8118 −1.50589 −0.752943 0.658086i 0.771366π-0.771366\pi
−0.752943 + 0.658086i 0.771366π0.771366\pi
192192 0 0
193193 −7.00000 −0.503871 −0.251936 0.967744i 0.581067π-0.581067\pi
−0.251936 + 0.967744i 0.581067π0.581067\pi
194194 −13.5830 −0.975203
195195 0 0
196196 0 0
197197 4.70850 0.335467 0.167733 0.985832i 0.446355π-0.446355\pi
0.167733 + 0.985832i 0.446355π0.446355\pi
198198 0 0
199199 −6.06275 −0.429777 −0.214888 0.976639i 0.568939π-0.568939\pi
−0.214888 + 0.976639i 0.568939π0.568939\pi
200200 8.29150 0.586298
201201 0 0
202202 −8.35425 −0.587803
203203 0 0
204204 0 0
205205 −39.8745 −2.78496
206206 −3.93725 −0.274321
207207 0 0
208208 4.64575 0.322125
209209 −7.29150 −0.504364
210210 0 0
211211 14.8745 1.02400 0.512002 0.858984i 0.328904π-0.328904\pi
0.512002 + 0.858984i 0.328904π0.328904\pi
212212 6.00000 0.412082
213213 0 0
214214 −6.00000 −0.410152
215215 18.2288 1.24319
216216 0 0
217217 0 0
218218 −3.35425 −0.227178
219219 0 0
220220 13.2915 0.896113
221221 −16.9373 −1.13932
222222 0 0
223223 13.8745 0.929106 0.464553 0.885545i 0.346215π-0.346215\pi
0.464553 + 0.885545i 0.346215π0.346215\pi
224224 0 0
225225 0 0
226226 2.35425 0.156602
227227 −6.00000 −0.398234 −0.199117 0.979976i 0.563807π-0.563807\pi
−0.199117 + 0.979976i 0.563807π0.563807\pi
228228 0 0
229229 9.35425 0.618146 0.309073 0.951038i 0.399981π-0.399981\pi
0.309073 + 0.951038i 0.399981π0.399981\pi
230230 −4.70850 −0.310469
231231 0 0
232232 2.35425 0.154564
233233 −19.2915 −1.26383 −0.631914 0.775038i 0.717730π-0.717730\pi
−0.631914 + 0.775038i 0.717730π0.717730\pi
234234 0 0
235235 −18.0000 −1.17419
236236 −8.35425 −0.543815
237237 0 0
238238 0 0
239239 −10.9373 −0.707472 −0.353736 0.935345i 0.615089π-0.615089\pi
−0.353736 + 0.935345i 0.615089π0.615089\pi
240240 0 0
241241 −5.00000 −0.322078 −0.161039 0.986948i 0.551485π-0.551485\pi
−0.161039 + 0.986948i 0.551485π0.551485\pi
242242 2.29150 0.147303
243243 0 0
244244 −7.35425 −0.470808
245245 0 0
246246 0 0
247247 −9.29150 −0.591204
248248 4.64575 0.295006
249249 0 0
250250 12.0000 0.758947
251251 18.0000 1.13615 0.568075 0.822977i 0.307688π-0.307688\pi
0.568075 + 0.822977i 0.307688π0.307688\pi
252252 0 0
253253 −4.70850 −0.296021
254254 1.35425 0.0849731
255255 0 0
256256 1.00000 0.0625000
257257 −15.8745 −0.990225 −0.495112 0.868829i 0.664873π-0.664873\pi
−0.495112 + 0.868829i 0.664873π0.664873\pi
258258 0 0
259259 0 0
260260 16.9373 1.05040
261261 0 0
262262 14.5830 0.900941
263263 −4.93725 −0.304444 −0.152222 0.988346i 0.548643π-0.548643\pi
−0.152222 + 0.988346i 0.548643π0.548643\pi
264264 0 0
265265 21.8745 1.34374
266266 0 0
267267 0 0
268268 −2.29150 −0.139976
269269 16.7085 1.01874 0.509368 0.860549i 0.329879π-0.329879\pi
0.509368 + 0.860549i 0.329879π0.329879\pi
270270 0 0
271271 −5.22876 −0.317624 −0.158812 0.987309i 0.550766π-0.550766\pi
−0.158812 + 0.987309i 0.550766π0.550766\pi
272272 −3.64575 −0.221056
273273 0 0
274274 1.29150 0.0780225
275275 30.2288 1.82286
276276 0 0
277277 −2.06275 −0.123938 −0.0619692 0.998078i 0.519738π-0.519738\pi
−0.0619692 + 0.998078i 0.519738π0.519738\pi
278278 −1.58301 −0.0949423
279279 0 0
280280 0 0
281281 19.5203 1.16448 0.582241 0.813017i 0.302176π-0.302176\pi
0.582241 + 0.813017i 0.302176π0.302176\pi
282282 0 0
283283 2.29150 0.136216 0.0681078 0.997678i 0.478304π-0.478304\pi
0.0681078 + 0.997678i 0.478304π0.478304\pi
284284 15.6458 0.928405
285285 0 0
286286 16.9373 1.00152
287287 0 0
288288 0 0
289289 −3.70850 −0.218147
290290 8.58301 0.504011
291291 0 0
292292 −10.5830 −0.619324
293293 −7.06275 −0.412610 −0.206305 0.978488i 0.566144π-0.566144\pi
−0.206305 + 0.978488i 0.566144π0.566144\pi
294294 0 0
295295 −30.4575 −1.77330
296296 −11.9373 −0.693839
297297 0 0
298298 22.9373 1.32872
299299 −6.00000 −0.346989
300300 0 0
301301 0 0
302302 −19.2288 −1.10649
303303 0 0
304304 −2.00000 −0.114708
305305 −26.8118 −1.53524
306306 0 0
307307 −7.58301 −0.432785 −0.216392 0.976306i 0.569429π-0.569429\pi
−0.216392 + 0.976306i 0.569429π0.569429\pi
308308 0 0
309309 0 0
310310 16.9373 0.961971
311311 13.5203 0.766664 0.383332 0.923611i 0.374777π-0.374777\pi
0.383332 + 0.923611i 0.374777π0.374777\pi
312312 0 0
313313 −12.7085 −0.718327 −0.359163 0.933275i 0.616938π-0.616938\pi
−0.359163 + 0.933275i 0.616938π0.616938\pi
314314 4.00000 0.225733
315315 0 0
316316 11.2288 0.631667
317317 26.8118 1.50590 0.752949 0.658079i 0.228631π-0.228631\pi
0.752949 + 0.658079i 0.228631π0.228631\pi
318318 0 0
319319 8.58301 0.480556
320320 3.64575 0.203804
321321 0 0
322322 0 0
323323 7.29150 0.405710
324324 0 0
325325 38.5203 2.13672
326326 −1.00000 −0.0553849
327327 0 0
328328 −10.9373 −0.603909
329329 0 0
330330 0 0
331331 −31.8745 −1.75198 −0.875991 0.482328i 0.839791π-0.839791\pi
−0.875991 + 0.482328i 0.839791π0.839791\pi
332332 13.2915 0.729466
333333 0 0
334334 8.58301 0.469641
335335 −8.35425 −0.456441
336336 0 0
337337 −30.5830 −1.66596 −0.832981 0.553301i 0.813368π-0.813368\pi
−0.832981 + 0.553301i 0.813368π0.813368\pi
338338 8.58301 0.466854
339339 0 0
340340 −13.2915 −0.720833
341341 16.9373 0.917204
342342 0 0
343343 0 0
344344 5.00000 0.269582
345345 0 0
346346 14.5830 0.783987
347347 −12.0000 −0.644194 −0.322097 0.946707i 0.604388π-0.604388\pi
−0.322097 + 0.946707i 0.604388π0.604388\pi
348348 0 0
349349 1.22876 0.0657738 0.0328869 0.999459i 0.489530π-0.489530\pi
0.0328869 + 0.999459i 0.489530π0.489530\pi
350350 0 0
351351 0 0
352352 3.64575 0.194319
353353 12.0000 0.638696 0.319348 0.947638i 0.396536π-0.396536\pi
0.319348 + 0.947638i 0.396536π0.396536\pi
354354 0 0
355355 57.0405 3.02740
356356 −4.93725 −0.261674
357357 0 0
358358 16.9373 0.895162
359359 11.1660 0.589319 0.294660 0.955602i 0.404794π-0.404794\pi
0.294660 + 0.955602i 0.404794π0.404794\pi
360360 0 0
361361 −15.0000 −0.789474
362362 2.70850 0.142355
363363 0 0
364364 0 0
365365 −38.5830 −2.01953
366366 0 0
367367 −29.8745 −1.55944 −0.779718 0.626130i 0.784638π-0.784638\pi
−0.779718 + 0.626130i 0.784638π0.784638\pi
368368 −1.29150 −0.0673242
369369 0 0
370370 −43.5203 −2.26251
371371 0 0
372372 0 0
373373 4.58301 0.237299 0.118650 0.992936i 0.462144π-0.462144\pi
0.118650 + 0.992936i 0.462144π0.462144\pi
374374 −13.2915 −0.687287
375375 0 0
376376 −4.93725 −0.254619
377377 10.9373 0.563297
378378 0 0
379379 25.5830 1.31411 0.657055 0.753842i 0.271802π-0.271802\pi
0.657055 + 0.753842i 0.271802π0.271802\pi
380380 −7.29150 −0.374046
381381 0 0
382382 −20.8118 −1.06482
383383 −20.5830 −1.05174 −0.525871 0.850564i 0.676261π-0.676261\pi
−0.525871 + 0.850564i 0.676261π0.676261\pi
384384 0 0
385385 0 0
386386 −7.00000 −0.356291
387387 0 0
388388 −13.5830 −0.689573
389389 19.2915 0.978118 0.489059 0.872251i 0.337340π-0.337340\pi
0.489059 + 0.872251i 0.337340π0.337340\pi
390390 0 0
391391 4.70850 0.238119
392392 0 0
393393 0 0
394394 4.70850 0.237211
395395 40.9373 2.05978
396396 0 0
397397 16.6458 0.835426 0.417713 0.908579i 0.362832π-0.362832\pi
0.417713 + 0.908579i 0.362832π0.362832\pi
398398 −6.06275 −0.303898
399399 0 0
400400 8.29150 0.414575
401401 −20.8118 −1.03929 −0.519645 0.854382i 0.673936π-0.673936\pi
−0.519645 + 0.854382i 0.673936π0.673936\pi
402402 0 0
403403 21.5830 1.07513
404404 −8.35425 −0.415639
405405 0 0
406406 0 0
407407 −43.5203 −2.15722
408408 0 0
409409 −14.8745 −0.735497 −0.367749 0.929925i 0.619871π-0.619871\pi
−0.367749 + 0.929925i 0.619871π0.619871\pi
410410 −39.8745 −1.96926
411411 0 0
412412 −3.93725 −0.193975
413413 0 0
414414 0 0
415415 48.4575 2.37869
416416 4.64575 0.227777
417417 0 0
418418 −7.29150 −0.356639
419419 −28.9373 −1.41368 −0.706839 0.707375i 0.749879π-0.749879\pi
−0.706839 + 0.707375i 0.749879π0.749879\pi
420420 0 0
421421 −14.7085 −0.716848 −0.358424 0.933559i 0.616686π-0.616686\pi
−0.358424 + 0.933559i 0.616686π0.616686\pi
422422 14.8745 0.724080
423423 0 0
424424 6.00000 0.291386
425425 −30.2288 −1.46631
426426 0 0
427427 0 0
428428 −6.00000 −0.290021
429429 0 0
430430 18.2288 0.879069
431431 38.8118 1.86950 0.934748 0.355310i 0.115625π-0.115625\pi
0.934748 + 0.355310i 0.115625π0.115625\pi
432432 0 0
433433 19.0000 0.913082 0.456541 0.889702i 0.349088π-0.349088\pi
0.456541 + 0.889702i 0.349088π0.349088\pi
434434 0 0
435435 0 0
436436 −3.35425 −0.160639
437437 2.58301 0.123562
438438 0 0
439439 −25.1660 −1.20111 −0.600554 0.799584i 0.705053π-0.705053\pi
−0.600554 + 0.799584i 0.705053π0.705053\pi
440440 13.2915 0.633648
441441 0 0
442442 −16.9373 −0.805623
443443 −19.2915 −0.916567 −0.458283 0.888806i 0.651536π-0.651536\pi
−0.458283 + 0.888806i 0.651536π0.651536\pi
444444 0 0
445445 −18.0000 −0.853282
446446 13.8745 0.656977
447447 0 0
448448 0 0
449449 2.35425 0.111104 0.0555519 0.998456i 0.482308π-0.482308\pi
0.0555519 + 0.998456i 0.482308π0.482308\pi
450450 0 0
451451 −39.8745 −1.87762
452452 2.35425 0.110735
453453 0 0
454454 −6.00000 −0.281594
455455 0 0
456456 0 0
457457 −8.29150 −0.387860 −0.193930 0.981015i 0.562123π-0.562123\pi
−0.193930 + 0.981015i 0.562123π0.562123\pi
458458 9.35425 0.437095
459459 0 0
460460 −4.70850 −0.219535
461461 −24.2288 −1.12845 −0.564223 0.825623i 0.690824π-0.690824\pi
−0.564223 + 0.825623i 0.690824π0.690824\pi
462462 0 0
463463 18.7085 0.869458 0.434729 0.900561i 0.356844π-0.356844\pi
0.434729 + 0.900561i 0.356844π0.356844\pi
464464 2.35425 0.109293
465465 0 0
466466 −19.2915 −0.893662
467467 −0.228757 −0.0105856 −0.00529280 0.999986i 0.501685π-0.501685\pi
−0.00529280 + 0.999986i 0.501685π0.501685\pi
468468 0 0
469469 0 0
470470 −18.0000 −0.830278
471471 0 0
472472 −8.35425 −0.384535
473473 18.2288 0.838159
474474 0 0
475475 −16.5830 −0.760880
476476 0 0
477477 0 0
478478 −10.9373 −0.500258
479479 −3.64575 −0.166579 −0.0832893 0.996525i 0.526543π-0.526543\pi
−0.0832893 + 0.996525i 0.526543π0.526543\pi
480480 0 0
481481 −55.4575 −2.52864
482482 −5.00000 −0.227744
483483 0 0
484484 2.29150 0.104159
485485 −49.5203 −2.24860
486486 0 0
487487 23.8745 1.08186 0.540929 0.841069i 0.318073π-0.318073\pi
0.540929 + 0.841069i 0.318073π0.318073\pi
488488 −7.35425 −0.332911
489489 0 0
490490 0 0
491491 25.7490 1.16204 0.581018 0.813890i 0.302654π-0.302654\pi
0.581018 + 0.813890i 0.302654π0.302654\pi
492492 0 0
493493 −8.58301 −0.386559
494494 −9.29150 −0.418044
495495 0 0
496496 4.64575 0.208600
497497 0 0
498498 0 0
499499 −6.16601 −0.276029 −0.138014 0.990430i 0.544072π-0.544072\pi
−0.138014 + 0.990430i 0.544072π0.544072\pi
500500 12.0000 0.536656
501501 0 0
502502 18.0000 0.803379
503503 −3.87451 −0.172756 −0.0863779 0.996262i 0.527529π-0.527529\pi
−0.0863779 + 0.996262i 0.527529π0.527529\pi
504504 0 0
505505 −30.4575 −1.35534
506506 −4.70850 −0.209318
507507 0 0
508508 1.35425 0.0600851
509509 −8.12549 −0.360156 −0.180078 0.983652i 0.557635π-0.557635\pi
−0.180078 + 0.983652i 0.557635π0.557635\pi
510510 0 0
511511 0 0
512512 1.00000 0.0441942
513513 0 0
514514 −15.8745 −0.700195
515515 −14.3542 −0.632524
516516 0 0
517517 −18.0000 −0.791639
518518 0 0
519519 0 0
520520 16.9373 0.742748
521521 8.12549 0.355984 0.177992 0.984032i 0.443040π-0.443040\pi
0.177992 + 0.984032i 0.443040π0.443040\pi
522522 0 0
523523 1.00000 0.0437269 0.0218635 0.999761i 0.493040π-0.493040\pi
0.0218635 + 0.999761i 0.493040π0.493040\pi
524524 14.5830 0.637062
525525 0 0
526526 −4.93725 −0.215275
527527 −16.9373 −0.737798
528528 0 0
529529 −21.3320 −0.927479
530530 21.8745 0.950168
531531 0 0
532532 0 0
533533 −50.8118 −2.20090
534534 0 0
535535 −21.8745 −0.945717
536536 −2.29150 −0.0989778
537537 0 0
538538 16.7085 0.720354
539539 0 0
540540 0 0
541541 1.16601 0.0501307 0.0250654 0.999686i 0.492021π-0.492021\pi
0.0250654 + 0.999686i 0.492021π0.492021\pi
542542 −5.22876 −0.224594
543543 0 0
544544 −3.64575 −0.156310
545545 −12.2288 −0.523822
546546 0 0
547547 18.2915 0.782088 0.391044 0.920372i 0.372114π-0.372114\pi
0.391044 + 0.920372i 0.372114π0.372114\pi
548548 1.29150 0.0551703
549549 0 0
550550 30.2288 1.28896
551551 −4.70850 −0.200589
552552 0 0
553553 0 0
554554 −2.06275 −0.0876377
555555 0 0
556556 −1.58301 −0.0671344
557557 −5.77124 −0.244535 −0.122268 0.992497i 0.539017π-0.539017\pi
−0.122268 + 0.992497i 0.539017π0.539017\pi
558558 0 0
559559 23.2288 0.982472
560560 0 0
561561 0 0
562562 19.5203 0.823412
563563 −18.4575 −0.777891 −0.388946 0.921261i 0.627161π-0.627161\pi
−0.388946 + 0.921261i 0.627161π0.627161\pi
564564 0 0
565565 8.58301 0.361090
566566 2.29150 0.0963190
567567 0 0
568568 15.6458 0.656481
569569 −16.9373 −0.710047 −0.355023 0.934857i 0.615527π-0.615527\pi
−0.355023 + 0.934857i 0.615527π0.615527\pi
570570 0 0
571571 9.29150 0.388837 0.194419 0.980919i 0.437718π-0.437718\pi
0.194419 + 0.980919i 0.437718π0.437718\pi
572572 16.9373 0.708182
573573 0 0
574574 0 0
575575 −10.7085 −0.446575
576576 0 0
577577 32.2915 1.34431 0.672156 0.740409i 0.265368π-0.265368\pi
0.672156 + 0.740409i 0.265368π0.265368\pi
578578 −3.70850 −0.154253
579579 0 0
580580 8.58301 0.356390
581581 0 0
582582 0 0
583583 21.8745 0.905950
584584 −10.5830 −0.437928
585585 0 0
586586 −7.06275 −0.291759
587587 −11.7712 −0.485851 −0.242926 0.970045i 0.578107π-0.578107\pi
−0.242926 + 0.970045i 0.578107π0.578107\pi
588588 0 0
589589 −9.29150 −0.382850
590590 −30.4575 −1.25392
591591 0 0
592592 −11.9373 −0.490618
593593 −40.9373 −1.68109 −0.840546 0.541741i 0.817766π-0.817766\pi
−0.840546 + 0.541741i 0.817766π0.817766\pi
594594 0 0
595595 0 0
596596 22.9373 0.939547
597597 0 0
598598 −6.00000 −0.245358
599599 9.87451 0.403461 0.201731 0.979441i 0.435343π-0.435343\pi
0.201731 + 0.979441i 0.435343π0.435343\pi
600600 0 0
601601 −26.8745 −1.09623 −0.548117 0.836402i 0.684655π-0.684655\pi
−0.548117 + 0.836402i 0.684655π0.684655\pi
602602 0 0
603603 0 0
604604 −19.2288 −0.782407
605605 8.35425 0.339649
606606 0 0
607607 −5.41699 −0.219869 −0.109935 0.993939i 0.535064π-0.535064\pi
−0.109935 + 0.993939i 0.535064π0.535064\pi
608608 −2.00000 −0.0811107
609609 0 0
610610 −26.8118 −1.08558
611611 −22.9373 −0.927942
612612 0 0
613613 −42.3948 −1.71231 −0.856154 0.516720i 0.827153π-0.827153\pi
−0.856154 + 0.516720i 0.827153π0.827153\pi
614614 −7.58301 −0.306025
615615 0 0
616616 0 0
617617 1.52026 0.0612033 0.0306017 0.999532i 0.490258π-0.490258\pi
0.0306017 + 0.999532i 0.490258π0.490258\pi
618618 0 0
619619 8.29150 0.333264 0.166632 0.986019i 0.446711π-0.446711\pi
0.166632 + 0.986019i 0.446711π0.446711\pi
620620 16.9373 0.680216
621621 0 0
622622 13.5203 0.542113
623623 0 0
624624 0 0
625625 2.29150 0.0916601
626626 −12.7085 −0.507934
627627 0 0
628628 4.00000 0.159617
629629 43.5203 1.73527
630630 0 0
631631 6.06275 0.241354 0.120677 0.992692i 0.461493π-0.461493\pi
0.120677 + 0.992692i 0.461493π0.461493\pi
632632 11.2288 0.446656
633633 0 0
634634 26.8118 1.06483
635635 4.93725 0.195929
636636 0 0
637637 0 0
638638 8.58301 0.339804
639639 0 0
640640 3.64575 0.144111
641641 −18.2288 −0.719993 −0.359996 0.932954i 0.617222π-0.617222\pi
−0.359996 + 0.932954i 0.617222π0.617222\pi
642642 0 0
643643 3.12549 0.123257 0.0616287 0.998099i 0.480371π-0.480371\pi
0.0616287 + 0.998099i 0.480371π0.480371\pi
644644 0 0
645645 0 0
646646 7.29150 0.286880
647647 −9.87451 −0.388207 −0.194103 0.980981i 0.562180π-0.562180\pi
−0.194103 + 0.980981i 0.562180π0.562180\pi
648648 0 0
649649 −30.4575 −1.19556
650650 38.5203 1.51089
651651 0 0
652652 −1.00000 −0.0391630
653653 −6.00000 −0.234798 −0.117399 0.993085i 0.537456π-0.537456\pi
−0.117399 + 0.993085i 0.537456π0.537456\pi
654654 0 0
655655 53.1660 2.07737
656656 −10.9373 −0.427028
657657 0 0
658658 0 0
659659 −24.2288 −0.943818 −0.471909 0.881647i 0.656435π-0.656435\pi
−0.471909 + 0.881647i 0.656435π0.656435\pi
660660 0 0
661661 3.16601 0.123144 0.0615718 0.998103i 0.480389π-0.480389\pi
0.0615718 + 0.998103i 0.480389π0.480389\pi
662662 −31.8745 −1.23884
663663 0 0
664664 13.2915 0.515810
665665 0 0
666666 0 0
667667 −3.04052 −0.117729
668668 8.58301 0.332086
669669 0 0
670670 −8.35425 −0.322753
671671 −26.8118 −1.03506
672672 0 0
673673 15.7490 0.607080 0.303540 0.952819i 0.401831π-0.401831\pi
0.303540 + 0.952819i 0.401831π0.401831\pi
674674 −30.5830 −1.17801
675675 0 0
676676 8.58301 0.330116
677677 45.8745 1.76310 0.881550 0.472090i 0.156500π-0.156500\pi
0.881550 + 0.472090i 0.156500π0.156500\pi
678678 0 0
679679 0 0
680680 −13.2915 −0.509706
681681 0 0
682682 16.9373 0.648561
683683 −26.8118 −1.02592 −0.512962 0.858411i 0.671452π-0.671452\pi
−0.512962 + 0.858411i 0.671452π0.671452\pi
684684 0 0
685685 4.70850 0.179902
686686 0 0
687687 0 0
688688 5.00000 0.190623
689689 27.8745 1.06193
690690 0 0
691691 38.7490 1.47408 0.737041 0.675848i 0.236222π-0.236222\pi
0.737041 + 0.675848i 0.236222π0.236222\pi
692692 14.5830 0.554363
693693 0 0
694694 −12.0000 −0.455514
695695 −5.77124 −0.218916
696696 0 0
697697 39.8745 1.51035
698698 1.22876 0.0465091
699699 0 0
700700 0 0
701701 −26.5830 −1.00403 −0.502013 0.864860i 0.667407π-0.667407\pi
−0.502013 + 0.864860i 0.667407π0.667407\pi
702702 0 0
703703 23.8745 0.900444
704704 3.64575 0.137404
705705 0 0
706706 12.0000 0.451626
707707 0 0
708708 0 0
709709 37.8118 1.42005 0.710025 0.704176i 0.248683π-0.248683\pi
0.710025 + 0.704176i 0.248683π0.248683\pi
710710 57.0405 2.14069
711711 0 0
712712 −4.93725 −0.185031
713713 −6.00000 −0.224702
714714 0 0
715715 61.7490 2.30928
716716 16.9373 0.632975
717717 0 0
718718 11.1660 0.416712
719719 −22.9373 −0.855415 −0.427708 0.903917i 0.640679π-0.640679\pi
−0.427708 + 0.903917i 0.640679π0.640679\pi
720720 0 0
721721 0 0
722722 −15.0000 −0.558242
723723 0 0
724724 2.70850 0.100661
725725 19.5203 0.724964
726726 0 0
727727 1.22876 0.0455721 0.0227860 0.999740i 0.492746π-0.492746\pi
0.0227860 + 0.999740i 0.492746π0.492746\pi
728728 0 0
729729 0 0
730730 −38.5830 −1.42802
731731 −18.2288 −0.674215
732732 0 0
733733 −35.2288 −1.30120 −0.650602 0.759419i 0.725483π-0.725483\pi
−0.650602 + 0.759419i 0.725483π0.725483\pi
734734 −29.8745 −1.10269
735735 0 0
736736 −1.29150 −0.0476054
737737 −8.35425 −0.307733
738738 0 0
739739 −31.4575 −1.15718 −0.578592 0.815617i 0.696397π-0.696397\pi
−0.578592 + 0.815617i 0.696397π0.696397\pi
740740 −43.5203 −1.59984
741741 0 0
742742 0 0
743743 −28.9373 −1.06160 −0.530802 0.847496i 0.678109π-0.678109\pi
−0.530802 + 0.847496i 0.678109π0.678109\pi
744744 0 0
745745 83.6235 3.06373
746746 4.58301 0.167796
747747 0 0
748748 −13.2915 −0.485985
749749 0 0
750750 0 0
751751 −52.4575 −1.91420 −0.957101 0.289755i 0.906426π-0.906426\pi
−0.957101 + 0.289755i 0.906426π0.906426\pi
752752 −4.93725 −0.180043
753753 0 0
754754 10.9373 0.398311
755755 −70.1033 −2.55132
756756 0 0
757757 48.9778 1.78013 0.890064 0.455836i 0.150660π-0.150660\pi
0.890064 + 0.455836i 0.150660π0.150660\pi
758758 25.5830 0.929217
759759 0 0
760760 −7.29150 −0.264491
761761 −2.58301 −0.0936339 −0.0468169 0.998903i 0.514908π-0.514908\pi
−0.0468169 + 0.998903i 0.514908π0.514908\pi
762762 0 0
763763 0 0
764764 −20.8118 −0.752943
765765 0 0
766766 −20.5830 −0.743694
767767 −38.8118 −1.40141
768768 0 0
769769 −40.5830 −1.46346 −0.731730 0.681594i 0.761287π-0.761287\pi
−0.731730 + 0.681594i 0.761287π0.761287\pi
770770 0 0
771771 0 0
772772 −7.00000 −0.251936
773773 46.3320 1.66645 0.833223 0.552936i 0.186493π-0.186493\pi
0.833223 + 0.552936i 0.186493π0.186493\pi
774774 0 0
775775 38.5203 1.38369
776776 −13.5830 −0.487601
777777 0 0
778778 19.2915 0.691634
779779 21.8745 0.783736
780780 0 0
781781 57.0405 2.04107
782782 4.70850 0.168376
783783 0 0
784784 0 0
785785 14.5830 0.520490
786786 0 0
787787 11.7085 0.417363 0.208681 0.977984i 0.433083π-0.433083\pi
0.208681 + 0.977984i 0.433083π0.433083\pi
788788 4.70850 0.167733
789789 0 0
790790 40.9373 1.45648
791791 0 0
792792 0 0
793793 −34.1660 −1.21327
794794 16.6458 0.590736
795795 0 0
796796 −6.06275 −0.214888
797797 14.8118 0.524660 0.262330 0.964978i 0.415509π-0.415509\pi
0.262330 + 0.964978i 0.415509π0.415509\pi
798798 0 0
799799 18.0000 0.636794
800800 8.29150 0.293149
801801 0 0
802802 −20.8118 −0.734889
803803 −38.5830 −1.36156
804804 0 0
805805 0 0
806806 21.5830 0.760229
807807 0 0
808808 −8.35425 −0.293901
809809 15.4170 0.542033 0.271016 0.962575i 0.412640π-0.412640\pi
0.271016 + 0.962575i 0.412640π0.412640\pi
810810 0 0
811811 29.2915 1.02856 0.514282 0.857621i 0.328059π-0.328059\pi
0.514282 + 0.857621i 0.328059π0.328059\pi
812812 0 0
813813 0 0
814814 −43.5203 −1.52538
815815 −3.64575 −0.127705
816816 0 0
817817 −10.0000 −0.349856
818818 −14.8745 −0.520075
819819 0 0
820820 −39.8745 −1.39248
821821 20.5830 0.718352 0.359176 0.933270i 0.383058π-0.383058\pi
0.359176 + 0.933270i 0.383058π0.383058\pi
822822 0 0
823823 −35.1033 −1.22362 −0.611811 0.791004i 0.709559π-0.709559\pi
−0.611811 + 0.791004i 0.709559π0.709559\pi
824824 −3.93725 −0.137161
825825 0 0
826826 0 0
827827 −43.7490 −1.52130 −0.760651 0.649161i 0.775120π-0.775120\pi
−0.760651 + 0.649161i 0.775120π0.775120\pi
828828 0 0
829829 29.2915 1.01734 0.508668 0.860963i 0.330138π-0.330138\pi
0.508668 + 0.860963i 0.330138π0.330138\pi
830830 48.4575 1.68198
831831 0 0
832832 4.64575 0.161062
833833 0 0
834834 0 0
835835 31.2915 1.08289
836836 −7.29150 −0.252182
837837 0 0
838838 −28.9373 −0.999621
839839 49.2915 1.70173 0.850866 0.525383i 0.176078π-0.176078\pi
0.850866 + 0.525383i 0.176078π0.176078\pi
840840 0 0
841841 −23.4575 −0.808880
842842 −14.7085 −0.506888
843843 0 0
844844 14.8745 0.512002
845845 31.2915 1.07646
846846 0 0
847847 0 0
848848 6.00000 0.206041
849849 0 0
850850 −30.2288 −1.03684
851851 15.4170 0.528488
852852 0 0
853853 −47.8745 −1.63919 −0.819596 0.572942i 0.805802π-0.805802\pi
−0.819596 + 0.572942i 0.805802π0.805802\pi
854854 0 0
855855 0 0
856856 −6.00000 −0.205076
857857 26.8118 0.915872 0.457936 0.888985i 0.348589π-0.348589\pi
0.457936 + 0.888985i 0.348589π0.348589\pi
858858 0 0
859859 7.00000 0.238837 0.119418 0.992844i 0.461897π-0.461897\pi
0.119418 + 0.992844i 0.461897π0.461897\pi
860860 18.2288 0.621595
861861 0 0
862862 38.8118 1.32193
863863 29.1660 0.992823 0.496411 0.868087i 0.334651π-0.334651\pi
0.496411 + 0.868087i 0.334651π0.334651\pi
864864 0 0
865865 53.1660 1.80770
866866 19.0000 0.645646
867867 0 0
868868 0 0
869869 40.9373 1.38870
870870 0 0
871871 −10.6458 −0.360718
872872 −3.35425 −0.113589
873873 0 0
874874 2.58301 0.0873715
875875 0 0
876876 0 0
877877 26.6458 0.899763 0.449882 0.893088i 0.351466π-0.351466\pi
0.449882 + 0.893088i 0.351466π0.351466\pi
878878 −25.1660 −0.849312
879879 0 0
880880 13.2915 0.448056
881881 3.87451 0.130535 0.0652677 0.997868i 0.479210π-0.479210\pi
0.0652677 + 0.997868i 0.479210π0.479210\pi
882882 0 0
883883 −19.8745 −0.668830 −0.334415 0.942426i 0.608539π-0.608539\pi
−0.334415 + 0.942426i 0.608539π0.608539\pi
884884 −16.9373 −0.569661
885885 0 0
886886 −19.2915 −0.648111
887887 −15.8745 −0.533014 −0.266507 0.963833i 0.585870π-0.585870\pi
−0.266507 + 0.963833i 0.585870π0.585870\pi
888888 0 0
889889 0 0
890890 −18.0000 −0.603361
891891 0 0
892892 13.8745 0.464553
893893 9.87451 0.330438
894894 0 0
895895 61.7490 2.06404
896896 0 0
897897 0 0
898898 2.35425 0.0785623
899899 10.9373 0.364778
900900 0 0
901901 −21.8745 −0.728746
902902 −39.8745 −1.32768
903903 0 0
904904 2.35425 0.0783011
905905 9.87451 0.328240
906906 0 0
907907 36.2915 1.20504 0.602520 0.798104i 0.294163π-0.294163\pi
0.602520 + 0.798104i 0.294163π0.294163\pi
908908 −6.00000 −0.199117
909909 0 0
910910 0 0
911911 28.9373 0.958734 0.479367 0.877615i 0.340866π-0.340866\pi
0.479367 + 0.877615i 0.340866π0.340866\pi
912912 0 0
913913 48.4575 1.60371
914914 −8.29150 −0.274259
915915 0 0
916916 9.35425 0.309073
917917 0 0
918918 0 0
919919 28.7712 0.949076 0.474538 0.880235i 0.342615π-0.342615\pi
0.474538 + 0.880235i 0.342615π0.342615\pi
920920 −4.70850 −0.155235
921921 0 0
922922 −24.2288 −0.797932
923923 72.6863 2.39250
924924 0 0
925925 −98.9778 −3.25437
926926 18.7085 0.614799
927927 0 0
928928 2.35425 0.0772820
929929 16.9373 0.555693 0.277847 0.960625i 0.410379π-0.410379\pi
0.277847 + 0.960625i 0.410379π0.410379\pi
930930 0 0
931931 0 0
932932 −19.2915 −0.631914
933933 0 0
934934 −0.228757 −0.00748514
935935 −48.4575 −1.58473
936936 0 0
937937 44.7490 1.46189 0.730943 0.682438i 0.239080π-0.239080\pi
0.730943 + 0.682438i 0.239080π0.239080\pi
938938 0 0
939939 0 0
940940 −18.0000 −0.587095
941941 53.3948 1.74062 0.870310 0.492505i 0.163919π-0.163919\pi
0.870310 + 0.492505i 0.163919π0.163919\pi
942942 0 0
943943 14.1255 0.459989
944944 −8.35425 −0.271908
945945 0 0
946946 18.2288 0.592668
947947 10.4797 0.340546 0.170273 0.985397i 0.445535π-0.445535\pi
0.170273 + 0.985397i 0.445535π0.445535\pi
948948 0 0
949949 −49.1660 −1.59600
950950 −16.5830 −0.538024
951951 0 0
952952 0 0
953953 52.3320 1.69520 0.847600 0.530635i 0.178047π-0.178047\pi
0.847600 + 0.530635i 0.178047π0.178047\pi
954954 0 0
955955 −75.8745 −2.45524
956956 −10.9373 −0.353736
957957 0 0
958958 −3.64575 −0.117789
959959 0 0
960960 0 0
961961 −9.41699 −0.303774
962962 −55.4575 −1.78802
963963 0 0
964964 −5.00000 −0.161039
965965 −25.5203 −0.821526
966966 0 0
967967 36.0627 1.15970 0.579850 0.814723i 0.303111π-0.303111\pi
0.579850 + 0.814723i 0.303111π0.303111\pi
968968 2.29150 0.0736517
969969 0 0
970970 −49.5203 −1.59000
971971 9.87451 0.316888 0.158444 0.987368i 0.449352π-0.449352\pi
0.158444 + 0.987368i 0.449352π0.449352\pi
972972 0 0
973973 0 0
974974 23.8745 0.764989
975975 0 0
976976 −7.35425 −0.235404
977977 −51.8745 −1.65961 −0.829806 0.558052i 0.811549π-0.811549\pi
−0.829806 + 0.558052i 0.811549π0.811549\pi
978978 0 0
979979 −18.0000 −0.575282
980980 0 0
981981 0 0
982982 25.7490 0.821684
983983 −20.8118 −0.663792 −0.331896 0.943316i 0.607688π-0.607688\pi
−0.331896 + 0.943316i 0.607688π0.607688\pi
984984 0 0
985985 17.1660 0.546955
986986 −8.58301 −0.273339
987987 0 0
988988 −9.29150 −0.295602
989989 −6.45751 −0.205337
990990 0 0
991991 −26.0627 −0.827910 −0.413955 0.910297i 0.635853π-0.635853\pi
−0.413955 + 0.910297i 0.635853π0.635853\pi
992992 4.64575 0.147503
993993 0 0
994994 0 0
995995 −22.1033 −0.700721
996996 0 0
997997 −23.6863 −0.750152 −0.375076 0.926994i 0.622383π-0.622383\pi
−0.375076 + 0.926994i 0.622383π0.622383\pi
998998 −6.16601 −0.195182
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 2646.2.a.bo.1.2 2
3.2 odd 2 2646.2.a.bf.1.1 2
7.3 odd 6 378.2.g.g.163.2 yes 4
7.5 odd 6 378.2.g.g.109.2 4
7.6 odd 2 2646.2.a.bl.1.1 2
21.5 even 6 378.2.g.h.109.1 yes 4
21.17 even 6 378.2.g.h.163.1 yes 4
21.20 even 2 2646.2.a.bi.1.2 2
63.5 even 6 1134.2.e.q.865.1 4
63.31 odd 6 1134.2.h.q.541.1 4
63.38 even 6 1134.2.e.q.919.1 4
63.40 odd 6 1134.2.e.t.865.2 4
63.47 even 6 1134.2.h.t.109.2 4
63.52 odd 6 1134.2.e.t.919.2 4
63.59 even 6 1134.2.h.t.541.2 4
63.61 odd 6 1134.2.h.q.109.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.g.g.109.2 4 7.5 odd 6
378.2.g.g.163.2 yes 4 7.3 odd 6
378.2.g.h.109.1 yes 4 21.5 even 6
378.2.g.h.163.1 yes 4 21.17 even 6
1134.2.e.q.865.1 4 63.5 even 6
1134.2.e.q.919.1 4 63.38 even 6
1134.2.e.t.865.2 4 63.40 odd 6
1134.2.e.t.919.2 4 63.52 odd 6
1134.2.h.q.109.1 4 63.61 odd 6
1134.2.h.q.541.1 4 63.31 odd 6
1134.2.h.t.109.2 4 63.47 even 6
1134.2.h.t.541.2 4 63.59 even 6
2646.2.a.bf.1.1 2 3.2 odd 2
2646.2.a.bi.1.2 2 21.20 even 2
2646.2.a.bl.1.1 2 7.6 odd 2
2646.2.a.bo.1.2 2 1.1 even 1 trivial