Properties

Label 7650.2.a.do.1.2
Level 76507650
Weight 22
Character 7650.1
Self dual yes
Analytic conductor 61.08661.086
Analytic rank 11
Dimension 33
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [7650,2,Mod(1,7650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7650, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7650.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 7650=2325217 7650 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7650.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,3,0,3,0,0,0,3,0,0,-6,0,-1,0,0,3,3,0,1,0,0,-6,-12,0,0,-1,0, 0,-17] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(29)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 61.085557546361.0855575463
Analytic rank: 11
Dimension: 33
Coefficient field: 3.3.568.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x3x26x2 x^{3} - x^{2} - 6x - 2 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 170)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.76156-1.76156 of defining polynomial
Character χ\chi == 7650.1

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+1.00000q40.864641q7+1.00000q82.00000q11+2.62620q130.864641q14+1.00000q16+1.00000q170.896916q192.00000q223.13536q23+2.62620q260.864641q289.49084q29+9.01395q31+1.00000q32+1.00000q3410.1816q370.896916q389.52311q417.25240q432.00000q443.13536q4610.4200q476.25240q49+2.62620q52+11.4017q530.864641q569.49084q58+4.14931q59+3.28467q61+9.01395q62+1.00000q641.25240q67+1.00000q68+12.5371q71+2.62620q7310.1816q740.896916q76+1.72928q777.91087q799.52311q824.20617q837.25240q862.00000q884.14931q892.27072q913.13536q9210.4200q94+6.14931q976.25240q98+O(q100)q+1.00000 q^{2} +1.00000 q^{4} -0.864641 q^{7} +1.00000 q^{8} -2.00000 q^{11} +2.62620 q^{13} -0.864641 q^{14} +1.00000 q^{16} +1.00000 q^{17} -0.896916 q^{19} -2.00000 q^{22} -3.13536 q^{23} +2.62620 q^{26} -0.864641 q^{28} -9.49084 q^{29} +9.01395 q^{31} +1.00000 q^{32} +1.00000 q^{34} -10.1816 q^{37} -0.896916 q^{38} -9.52311 q^{41} -7.25240 q^{43} -2.00000 q^{44} -3.13536 q^{46} -10.4200 q^{47} -6.25240 q^{49} +2.62620 q^{52} +11.4017 q^{53} -0.864641 q^{56} -9.49084 q^{58} +4.14931 q^{59} +3.28467 q^{61} +9.01395 q^{62} +1.00000 q^{64} -1.25240 q^{67} +1.00000 q^{68} +12.5371 q^{71} +2.62620 q^{73} -10.1816 q^{74} -0.896916 q^{76} +1.72928 q^{77} -7.91087 q^{79} -9.52311 q^{82} -4.20617 q^{83} -7.25240 q^{86} -2.00000 q^{88} -4.14931 q^{89} -2.27072 q^{91} -3.13536 q^{92} -10.4200 q^{94} +6.14931 q^{97} -6.25240 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+3q2+3q4+3q86q11q13+3q16+3q17+q196q2212q23q2617q29+3q31+3q32+3q348q37+q3816q414q43+q98+O(q100) 3 q + 3 q^{2} + 3 q^{4} + 3 q^{8} - 6 q^{11} - q^{13} + 3 q^{16} + 3 q^{17} + q^{19} - 6 q^{22} - 12 q^{23} - q^{26} - 17 q^{29} + 3 q^{31} + 3 q^{32} + 3 q^{34} - 8 q^{37} + q^{38} - 16 q^{41} - 4 q^{43}+ \cdots - q^{98}+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 0 0
66 0 0
77 −0.864641 −0.326804 −0.163402 0.986560i 0.552247π-0.552247\pi
−0.163402 + 0.986560i 0.552247π0.552247\pi
88 1.00000 0.353553
99 0 0
1010 0 0
1111 −2.00000 −0.603023 −0.301511 0.953463i 0.597491π-0.597491\pi
−0.301511 + 0.953463i 0.597491π0.597491\pi
1212 0 0
1313 2.62620 0.728376 0.364188 0.931325i 0.381347π-0.381347\pi
0.364188 + 0.931325i 0.381347π0.381347\pi
1414 −0.864641 −0.231085
1515 0 0
1616 1.00000 0.250000
1717 1.00000 0.242536
1818 0 0
1919 −0.896916 −0.205767 −0.102883 0.994693i 0.532807π-0.532807\pi
−0.102883 + 0.994693i 0.532807π0.532807\pi
2020 0 0
2121 0 0
2222 −2.00000 −0.426401
2323 −3.13536 −0.653768 −0.326884 0.945065i 0.605999π-0.605999\pi
−0.326884 + 0.945065i 0.605999π0.605999\pi
2424 0 0
2525 0 0
2626 2.62620 0.515040
2727 0 0
2828 −0.864641 −0.163402
2929 −9.49084 −1.76240 −0.881202 0.472739i 0.843265π-0.843265\pi
−0.881202 + 0.472739i 0.843265π0.843265\pi
3030 0 0
3131 9.01395 1.61895 0.809477 0.587152i 0.199751π-0.199751\pi
0.809477 + 0.587152i 0.199751π0.199751\pi
3232 1.00000 0.176777
3333 0 0
3434 1.00000 0.171499
3535 0 0
3636 0 0
3737 −10.1816 −1.67384 −0.836921 0.547323i 0.815647π-0.815647\pi
−0.836921 + 0.547323i 0.815647π0.815647\pi
3838 −0.896916 −0.145499
3939 0 0
4040 0 0
4141 −9.52311 −1.48726 −0.743630 0.668591i 0.766898π-0.766898\pi
−0.743630 + 0.668591i 0.766898π0.766898\pi
4242 0 0
4343 −7.25240 −1.10598 −0.552990 0.833188i 0.686513π-0.686513\pi
−0.552990 + 0.833188i 0.686513π0.686513\pi
4444 −2.00000 −0.301511
4545 0 0
4646 −3.13536 −0.462283
4747 −10.4200 −1.51992 −0.759959 0.649971i 0.774781π-0.774781\pi
−0.759959 + 0.649971i 0.774781π0.774781\pi
4848 0 0
4949 −6.25240 −0.893199
5050 0 0
5151 0 0
5252 2.62620 0.364188
5353 11.4017 1.56615 0.783073 0.621930i 0.213651π-0.213651\pi
0.783073 + 0.621930i 0.213651π0.213651\pi
5454 0 0
5555 0 0
5656 −0.864641 −0.115542
5757 0 0
5858 −9.49084 −1.24621
5959 4.14931 0.540194 0.270097 0.962833i 0.412944π-0.412944\pi
0.270097 + 0.962833i 0.412944π0.412944\pi
6060 0 0
6161 3.28467 0.420559 0.210280 0.977641i 0.432563π-0.432563\pi
0.210280 + 0.977641i 0.432563π0.432563\pi
6262 9.01395 1.14477
6363 0 0
6464 1.00000 0.125000
6565 0 0
6666 0 0
6767 −1.25240 −0.153005 −0.0765023 0.997069i 0.524375π-0.524375\pi
−0.0765023 + 0.997069i 0.524375π0.524375\pi
6868 1.00000 0.121268
6969 0 0
7070 0 0
7171 12.5371 1.48788 0.743938 0.668249i 0.232956π-0.232956\pi
0.743938 + 0.668249i 0.232956π0.232956\pi
7272 0 0
7373 2.62620 0.307373 0.153687 0.988120i 0.450885π-0.450885\pi
0.153687 + 0.988120i 0.450885π0.450885\pi
7474 −10.1816 −1.18359
7575 0 0
7676 −0.896916 −0.102883
7777 1.72928 0.197070
7878 0 0
7979 −7.91087 −0.890042 −0.445021 0.895520i 0.646804π-0.646804\pi
−0.445021 + 0.895520i 0.646804π0.646804\pi
8080 0 0
8181 0 0
8282 −9.52311 −1.05165
8383 −4.20617 −0.461687 −0.230843 0.972991i 0.574149π-0.574149\pi
−0.230843 + 0.972991i 0.574149π0.574149\pi
8484 0 0
8585 0 0
8686 −7.25240 −0.782046
8787 0 0
8888 −2.00000 −0.213201
8989 −4.14931 −0.439826 −0.219913 0.975519i 0.570577π-0.570577\pi
−0.219913 + 0.975519i 0.570577π0.570577\pi
9090 0 0
9191 −2.27072 −0.238036
9292 −3.13536 −0.326884
9393 0 0
9494 −10.4200 −1.07474
9595 0 0
9696 0 0
9797 6.14931 0.624368 0.312184 0.950022i 0.398939π-0.398939\pi
0.312184 + 0.950022i 0.398939π0.398939\pi
9898 −6.25240 −0.631587
9999 0 0
100100 0 0
101101 −0.206167 −0.0205144 −0.0102572 0.999947i 0.503265π-0.503265\pi
−0.0102572 + 0.999947i 0.503265π0.503265\pi
102102 0 0
103103 −4.77551 −0.470545 −0.235273 0.971929i 0.575598π-0.575598\pi
−0.235273 + 0.971929i 0.575598π0.575598\pi
104104 2.62620 0.257520
105105 0 0
106106 11.4017 1.10743
107107 6.29862 0.608911 0.304456 0.952527i 0.401526π-0.401526\pi
0.304456 + 0.952527i 0.401526π0.401526\pi
108108 0 0
109109 5.55539 0.532110 0.266055 0.963958i 0.414280π-0.414280\pi
0.266055 + 0.963958i 0.414280π0.414280\pi
110110 0 0
111111 0 0
112112 −0.864641 −0.0817009
113113 10.6262 0.999629 0.499814 0.866133i 0.333402π-0.333402\pi
0.499814 + 0.866133i 0.333402π0.333402\pi
114114 0 0
115115 0 0
116116 −9.49084 −0.881202
117117 0 0
118118 4.14931 0.381975
119119 −0.864641 −0.0792615
120120 0 0
121121 −7.00000 −0.636364
122122 3.28467 0.297380
123123 0 0
124124 9.01395 0.809477
125125 0 0
126126 0 0
127127 14.3555 1.27384 0.636921 0.770929i 0.280208π-0.280208\pi
0.636921 + 0.770929i 0.280208π0.280208\pi
128128 1.00000 0.0883883
129129 0 0
130130 0 0
131131 −17.0462 −1.48934 −0.744668 0.667435i 0.767392π-0.767392\pi
−0.744668 + 0.667435i 0.767392π0.767392\pi
132132 0 0
133133 0.775511 0.0672453
134134 −1.25240 −0.108191
135135 0 0
136136 1.00000 0.0857493
137137 14.5048 1.23923 0.619614 0.784907i 0.287289π-0.287289\pi
0.619614 + 0.784907i 0.287289π0.287289\pi
138138 0 0
139139 −14.7110 −1.24777 −0.623884 0.781517i 0.714446π-0.714446\pi
−0.623884 + 0.781517i 0.714446π0.714446\pi
140140 0 0
141141 0 0
142142 12.5371 1.05209
143143 −5.25240 −0.439227
144144 0 0
145145 0 0
146146 2.62620 0.217346
147147 0 0
148148 −10.1816 −0.836921
149149 −10.0000 −0.819232 −0.409616 0.912258i 0.634337π-0.634337\pi
−0.409616 + 0.912258i 0.634337π0.634337\pi
150150 0 0
151151 −5.18785 −0.422181 −0.211090 0.977467i 0.567701π-0.567701\pi
−0.211090 + 0.977467i 0.567701π0.567701\pi
152152 −0.896916 −0.0727495
153153 0 0
154154 1.72928 0.139349
155155 0 0
156156 0 0
157157 −10.2341 −0.816768 −0.408384 0.912810i 0.633908π-0.633908\pi
−0.408384 + 0.912810i 0.633908π0.633908\pi
158158 −7.91087 −0.629355
159159 0 0
160160 0 0
161161 2.71096 0.213654
162162 0 0
163163 −6.47689 −0.507309 −0.253654 0.967295i 0.581633π-0.581633\pi
−0.253654 + 0.967295i 0.581633π0.581633\pi
164164 −9.52311 −0.743630
165165 0 0
166166 −4.20617 −0.326462
167167 −3.84632 −0.297637 −0.148819 0.988865i 0.547547π-0.547547\pi
−0.148819 + 0.988865i 0.547547π0.547547\pi
168168 0 0
169169 −6.10308 −0.469468
170170 0 0
171171 0 0
172172 −7.25240 −0.552990
173173 −23.9109 −1.81791 −0.908955 0.416895i 0.863118π-0.863118\pi
−0.908955 + 0.416895i 0.863118π0.863118\pi
174174 0 0
175175 0 0
176176 −2.00000 −0.150756
177177 0 0
178178 −4.14931 −0.311004
179179 14.7110 1.09955 0.549774 0.835313i 0.314714π-0.314714\pi
0.549774 + 0.835313i 0.314714π0.314714\pi
180180 0 0
181181 −23.4340 −1.74183 −0.870917 0.491430i 0.836474π-0.836474\pi
−0.870917 + 0.491430i 0.836474π0.836474\pi
182182 −2.27072 −0.168317
183183 0 0
184184 −3.13536 −0.231142
185185 0 0
186186 0 0
187187 −2.00000 −0.146254
188188 −10.4200 −0.759959
189189 0 0
190190 0 0
191191 −18.5048 −1.33896 −0.669480 0.742830i 0.733483π-0.733483\pi
−0.669480 + 0.742830i 0.733483π0.733483\pi
192192 0 0
193193 −5.45856 −0.392916 −0.196458 0.980512i 0.562944π-0.562944\pi
−0.196458 + 0.980512i 0.562944π0.562944\pi
194194 6.14931 0.441495
195195 0 0
196196 −6.25240 −0.446600
197197 −13.9388 −0.993097 −0.496548 0.868009i 0.665399π-0.665399\pi
−0.496548 + 0.868009i 0.665399π0.665399\pi
198198 0 0
199199 −11.2847 −0.799949 −0.399975 0.916526i 0.630981π-0.630981\pi
−0.399975 + 0.916526i 0.630981π0.630981\pi
200200 0 0
201201 0 0
202202 −0.206167 −0.0145059
203203 8.20617 0.575960
204204 0 0
205205 0 0
206206 −4.77551 −0.332726
207207 0 0
208208 2.62620 0.182094
209209 1.79383 0.124082
210210 0 0
211211 −14.8401 −1.02163 −0.510816 0.859690i 0.670657π-0.670657\pi
−0.510816 + 0.859690i 0.670657π0.670657\pi
212212 11.4017 0.783073
213213 0 0
214214 6.29862 0.430565
215215 0 0
216216 0 0
217217 −7.79383 −0.529080
218218 5.55539 0.376258
219219 0 0
220220 0 0
221221 2.62620 0.176657
222222 0 0
223223 3.30925 0.221604 0.110802 0.993843i 0.464658π-0.464658\pi
0.110802 + 0.993843i 0.464658π0.464658\pi
224224 −0.864641 −0.0577712
225225 0 0
226226 10.6262 0.706844
227227 24.7187 1.64063 0.820317 0.571909i 0.193797π-0.193797\pi
0.820317 + 0.571909i 0.193797π0.193797\pi
228228 0 0
229229 4.27072 0.282217 0.141109 0.989994i 0.454933π-0.454933\pi
0.141109 + 0.989994i 0.454933π0.454933\pi
230230 0 0
231231 0 0
232232 −9.49084 −0.623104
233233 −0.832365 −0.0545301 −0.0272650 0.999628i 0.508680π-0.508680\pi
−0.0272650 + 0.999628i 0.508680π0.508680\pi
234234 0 0
235235 0 0
236236 4.14931 0.270097
237237 0 0
238238 −0.864641 −0.0560463
239239 4.71096 0.304727 0.152363 0.988325i 0.451312π-0.451312\pi
0.152363 + 0.988325i 0.451312π0.451312\pi
240240 0 0
241241 −23.4865 −1.51290 −0.756448 0.654054i 0.773067π-0.773067\pi
−0.756448 + 0.654054i 0.773067π0.773067\pi
242242 −7.00000 −0.449977
243243 0 0
244244 3.28467 0.210280
245245 0 0
246246 0 0
247247 −2.35548 −0.149876
248248 9.01395 0.572387
249249 0 0
250250 0 0
251251 6.29862 0.397566 0.198783 0.980044i 0.436301π-0.436301\pi
0.198783 + 0.980044i 0.436301π0.436301\pi
252252 0 0
253253 6.27072 0.394237
254254 14.3555 0.900743
255255 0 0
256256 1.00000 0.0625000
257257 1.49521 0.0932685 0.0466342 0.998912i 0.485150π-0.485150\pi
0.0466342 + 0.998912i 0.485150π0.485150\pi
258258 0 0
259259 8.80342 0.547018
260260 0 0
261261 0 0
262262 −17.0462 −1.05312
263263 9.94315 0.613121 0.306560 0.951851i 0.400822π-0.400822\pi
0.306560 + 0.951851i 0.400822π0.400822\pi
264264 0 0
265265 0 0
266266 0.775511 0.0475496
267267 0 0
268268 −1.25240 −0.0765023
269269 −1.96772 −0.119974 −0.0599871 0.998199i 0.519106π-0.519106\pi
−0.0599871 + 0.998199i 0.519106π0.519106\pi
270270 0 0
271271 8.84006 0.536995 0.268498 0.963280i 0.413473π-0.413473\pi
0.268498 + 0.963280i 0.413473π0.413473\pi
272272 1.00000 0.0606339
273273 0 0
274274 14.5048 0.876267
275275 0 0
276276 0 0
277277 −19.8463 −1.19245 −0.596225 0.802817i 0.703333π-0.703333\pi
−0.596225 + 0.802817i 0.703333π0.703333\pi
278278 −14.7110 −0.882305
279279 0 0
280280 0 0
281281 11.9065 0.710282 0.355141 0.934813i 0.384433π-0.384433\pi
0.355141 + 0.934813i 0.384433π0.384433\pi
282282 0 0
283283 13.7370 0.816579 0.408289 0.912853i 0.366125π-0.366125\pi
0.408289 + 0.912853i 0.366125π0.366125\pi
284284 12.5371 0.743938
285285 0 0
286286 −5.25240 −0.310581
287287 8.23407 0.486042
288288 0 0
289289 1.00000 0.0588235
290290 0 0
291291 0 0
292292 2.62620 0.153687
293293 12.1772 0.711401 0.355700 0.934600i 0.384242π-0.384242\pi
0.355700 + 0.934600i 0.384242π0.384242\pi
294294 0 0
295295 0 0
296296 −10.1816 −0.591793
297297 0 0
298298 −10.0000 −0.579284
299299 −8.23407 −0.476189
300300 0 0
301301 6.27072 0.361438
302302 −5.18785 −0.298527
303303 0 0
304304 −0.896916 −0.0514417
305305 0 0
306306 0 0
307307 23.7938 1.35799 0.678993 0.734145i 0.262417π-0.262417\pi
0.678993 + 0.734145i 0.262417π0.262417\pi
308308 1.72928 0.0985350
309309 0 0
310310 0 0
311311 −32.9205 −1.86675 −0.933374 0.358906i 0.883150π-0.883150\pi
−0.933374 + 0.358906i 0.883150π0.883150\pi
312312 0 0
313313 −29.0462 −1.64179 −0.820895 0.571079i 0.806525π-0.806525\pi
−0.820895 + 0.571079i 0.806525π0.806525\pi
314314 −10.2341 −0.577542
315315 0 0
316316 −7.91087 −0.445021
317317 −20.6864 −1.16186 −0.580931 0.813953i 0.697312π-0.697312\pi
−0.580931 + 0.813953i 0.697312π0.697312\pi
318318 0 0
319319 18.9817 1.06277
320320 0 0
321321 0 0
322322 2.71096 0.151076
323323 −0.896916 −0.0499058
324324 0 0
325325 0 0
326326 −6.47689 −0.358722
327327 0 0
328328 −9.52311 −0.525826
329329 9.00958 0.496714
330330 0 0
331331 4.02021 0.220971 0.110485 0.993878i 0.464759π-0.464759\pi
0.110485 + 0.993878i 0.464759π0.464759\pi
332332 −4.20617 −0.230843
333333 0 0
334334 −3.84632 −0.210461
335335 0 0
336336 0 0
337337 2.21386 0.120597 0.0602984 0.998180i 0.480795π-0.480795\pi
0.0602984 + 0.998180i 0.480795π0.480795\pi
338338 −6.10308 −0.331964
339339 0 0
340340 0 0
341341 −18.0279 −0.976266
342342 0 0
343343 11.4586 0.618704
344344 −7.25240 −0.391023
345345 0 0
346346 −23.9109 −1.28546
347347 1.37380 0.0737496 0.0368748 0.999320i 0.488260π-0.488260\pi
0.0368748 + 0.999320i 0.488260π0.488260\pi
348348 0 0
349349 −20.8680 −1.11704 −0.558518 0.829492i 0.688630π-0.688630\pi
−0.558518 + 0.829492i 0.688630π0.688630\pi
350350 0 0
351351 0 0
352352 −2.00000 −0.106600
353353 13.7572 0.732221 0.366111 0.930571i 0.380689π-0.380689\pi
0.366111 + 0.930571i 0.380689π0.380689\pi
354354 0 0
355355 0 0
356356 −4.14931 −0.219913
357357 0 0
358358 14.7110 0.777498
359359 −9.31695 −0.491730 −0.245865 0.969304i 0.579072π-0.579072\pi
−0.245865 + 0.969304i 0.579072π0.579072\pi
360360 0 0
361361 −18.1955 −0.957660
362362 −23.4340 −1.23166
363363 0 0
364364 −2.27072 −0.119018
365365 0 0
366366 0 0
367367 12.3878 0.646636 0.323318 0.946290i 0.395202π-0.395202\pi
0.323318 + 0.946290i 0.395202π0.395202\pi
368368 −3.13536 −0.163442
369369 0 0
370370 0 0
371371 −9.85838 −0.511822
372372 0 0
373373 −23.3169 −1.20731 −0.603653 0.797247i 0.706289π-0.706289\pi
−0.603653 + 0.797247i 0.706289π0.706289\pi
374374 −2.00000 −0.103418
375375 0 0
376376 −10.4200 −0.537372
377377 −24.9248 −1.28369
378378 0 0
379379 28.9817 1.48869 0.744344 0.667796i 0.232762π-0.232762\pi
0.744344 + 0.667796i 0.232762π0.232762\pi
380380 0 0
381381 0 0
382382 −18.5048 −0.946788
383383 −14.9527 −0.764049 −0.382024 0.924152i 0.624773π-0.624773\pi
−0.382024 + 0.924152i 0.624773π0.624773\pi
384384 0 0
385385 0 0
386386 −5.45856 −0.277834
387387 0 0
388388 6.14931 0.312184
389389 19.3169 0.979408 0.489704 0.871889i 0.337105π-0.337105\pi
0.489704 + 0.871889i 0.337105π0.337105\pi
390390 0 0
391391 −3.13536 −0.158562
392392 −6.25240 −0.315794
393393 0 0
394394 −13.9388 −0.702225
395395 0 0
396396 0 0
397397 9.57560 0.480586 0.240293 0.970700i 0.422757π-0.422757\pi
0.240293 + 0.970700i 0.422757π0.422757\pi
398398 −11.2847 −0.565649
399399 0 0
400400 0 0
401401 −11.3169 −0.565141 −0.282571 0.959246i 0.591187π-0.591187\pi
−0.282571 + 0.959246i 0.591187π0.591187\pi
402402 0 0
403403 23.6724 1.17921
404404 −0.206167 −0.0102572
405405 0 0
406406 8.20617 0.407265
407407 20.3632 1.00937
408408 0 0
409409 −9.10308 −0.450119 −0.225059 0.974345i 0.572258π-0.572258\pi
−0.225059 + 0.974345i 0.572258π0.572258\pi
410410 0 0
411411 0 0
412412 −4.77551 −0.235273
413413 −3.58767 −0.176537
414414 0 0
415415 0 0
416416 2.62620 0.128760
417417 0 0
418418 1.79383 0.0877392
419419 4.02791 0.196776 0.0983881 0.995148i 0.468631π-0.468631\pi
0.0983881 + 0.995148i 0.468631π0.468631\pi
420420 0 0
421421 15.2524 0.743356 0.371678 0.928362i 0.378782π-0.378782\pi
0.371678 + 0.928362i 0.378782π0.378782\pi
422422 −14.8401 −0.722403
423423 0 0
424424 11.4017 0.553716
425425 0 0
426426 0 0
427427 −2.84006 −0.137440
428428 6.29862 0.304456
429429 0 0
430430 0 0
431431 4.45231 0.214460 0.107230 0.994234i 0.465802π-0.465802\pi
0.107230 + 0.994234i 0.465802π0.465802\pi
432432 0 0
433433 10.7110 0.514736 0.257368 0.966313i 0.417145π-0.417145\pi
0.257368 + 0.966313i 0.417145π0.417145\pi
434434 −7.79383 −0.374116
435435 0 0
436436 5.55539 0.266055
437437 2.81215 0.134524
438438 0 0
439439 5.09871 0.243348 0.121674 0.992570i 0.461174π-0.461174\pi
0.121674 + 0.992570i 0.461174π0.461174\pi
440440 0 0
441441 0 0
442442 2.62620 0.124916
443443 −10.8034 −0.513286 −0.256643 0.966506i 0.582616π-0.582616\pi
−0.256643 + 0.966506i 0.582616π0.582616\pi
444444 0 0
445445 0 0
446446 3.30925 0.156698
447447 0 0
448448 −0.864641 −0.0408504
449449 5.82174 0.274745 0.137372 0.990519i 0.456134π-0.456134\pi
0.137372 + 0.990519i 0.456134π0.456134\pi
450450 0 0
451451 19.0462 0.896852
452452 10.6262 0.499814
453453 0 0
454454 24.7187 1.16010
455455 0 0
456456 0 0
457457 13.7014 0.640923 0.320462 0.947261i 0.396162π-0.396162\pi
0.320462 + 0.947261i 0.396162π0.396162\pi
458458 4.27072 0.199558
459459 0 0
460460 0 0
461461 27.0741 1.26097 0.630484 0.776202i 0.282856π-0.282856\pi
0.630484 + 0.776202i 0.282856π0.282856\pi
462462 0 0
463463 37.3372 1.73520 0.867602 0.497258i 0.165660π-0.165660\pi
0.867602 + 0.497258i 0.165660π0.165660\pi
464464 −9.49084 −0.440601
465465 0 0
466466 −0.832365 −0.0385586
467467 −35.3449 −1.63556 −0.817782 0.575528i 0.804797π-0.804797\pi
−0.817782 + 0.575528i 0.804797π0.804797\pi
468468 0 0
469469 1.08287 0.0500024
470470 0 0
471471 0 0
472472 4.14931 0.190988
473473 14.5048 0.666931
474474 0 0
475475 0 0
476476 −0.864641 −0.0396308
477477 0 0
478478 4.71096 0.215474
479479 −31.0419 −1.41834 −0.709169 0.705038i 0.750930π-0.750930\pi
−0.709169 + 0.705038i 0.750930π0.750930\pi
480480 0 0
481481 −26.7389 −1.21919
482482 −23.4865 −1.06978
483483 0 0
484484 −7.00000 −0.318182
485485 0 0
486486 0 0
487487 13.1633 0.596485 0.298242 0.954490i 0.403600π-0.403600\pi
0.298242 + 0.954490i 0.403600π0.403600\pi
488488 3.28467 0.148690
489489 0 0
490490 0 0
491491 −24.3555 −1.09915 −0.549574 0.835445i 0.685210π-0.685210\pi
−0.549574 + 0.835445i 0.685210π0.685210\pi
492492 0 0
493493 −9.49084 −0.427446
494494 −2.35548 −0.105978
495495 0 0
496496 9.01395 0.404738
497497 −10.8401 −0.486243
498498 0 0
499499 36.2620 1.62331 0.811655 0.584138i 0.198567π-0.198567\pi
0.811655 + 0.584138i 0.198567π0.198567\pi
500500 0 0
501501 0 0
502502 6.29862 0.281121
503503 42.3511 1.88834 0.944171 0.329455i 0.106865π-0.106865\pi
0.944171 + 0.329455i 0.106865π0.106865\pi
504504 0 0
505505 0 0
506506 6.27072 0.278767
507507 0 0
508508 14.3555 0.636921
509509 1.70138 0.0754121 0.0377061 0.999289i 0.487995π-0.487995\pi
0.0377061 + 0.999289i 0.487995π0.487995\pi
510510 0 0
511511 −2.27072 −0.100451
512512 1.00000 0.0441942
513513 0 0
514514 1.49521 0.0659508
515515 0 0
516516 0 0
517517 20.8401 0.916545
518518 8.80342 0.386800
519519 0 0
520520 0 0
521521 −3.01832 −0.132235 −0.0661175 0.997812i 0.521061π-0.521061\pi
−0.0661175 + 0.997812i 0.521061π0.521061\pi
522522 0 0
523523 −5.79383 −0.253347 −0.126673 0.991944i 0.540430π-0.540430\pi
−0.126673 + 0.991944i 0.540430π0.540430\pi
524524 −17.0462 −0.744668
525525 0 0
526526 9.94315 0.433542
527527 9.01395 0.392654
528528 0 0
529529 −13.1695 −0.572588
530530 0 0
531531 0 0
532532 0.775511 0.0336226
533533 −25.0096 −1.08329
534534 0 0
535535 0 0
536536 −1.25240 −0.0540953
537537 0 0
538538 −1.96772 −0.0848346
539539 12.5048 0.538620
540540 0 0
541541 0.258654 0.0111204 0.00556019 0.999985i 0.498230π-0.498230\pi
0.00556019 + 0.999985i 0.498230π0.498230\pi
542542 8.84006 0.379713
543543 0 0
544544 1.00000 0.0428746
545545 0 0
546546 0 0
547547 32.4113 1.38581 0.692903 0.721030i 0.256331π-0.256331\pi
0.692903 + 0.721030i 0.256331π0.256331\pi
548548 14.5048 0.619614
549549 0 0
550550 0 0
551551 8.51249 0.362644
552552 0 0
553553 6.84006 0.290869
554554 −19.8463 −0.843189
555555 0 0
556556 −14.7110 −0.623884
557557 22.9248 0.971356 0.485678 0.874138i 0.338573π-0.338573\pi
0.485678 + 0.874138i 0.338573π0.338573\pi
558558 0 0
559559 −19.0462 −0.805570
560560 0 0
561561 0 0
562562 11.9065 0.502245
563563 −17.8863 −0.753817 −0.376909 0.926250i 0.623013π-0.623013\pi
−0.376909 + 0.926250i 0.623013π0.623013\pi
564564 0 0
565565 0 0
566566 13.7370 0.577408
567567 0 0
568568 12.5371 0.526044
569569 −12.3555 −0.517969 −0.258984 0.965882i 0.583388π-0.583388\pi
−0.258984 + 0.965882i 0.583388π0.583388\pi
570570 0 0
571571 −27.3169 −1.14318 −0.571589 0.820540i 0.693673π-0.693673\pi
−0.571589 + 0.820540i 0.693673π0.693673\pi
572572 −5.25240 −0.219614
573573 0 0
574574 8.23407 0.343684
575575 0 0
576576 0 0
577577 10.6339 0.442695 0.221347 0.975195i 0.428955π-0.428955\pi
0.221347 + 0.975195i 0.428955π0.428955\pi
578578 1.00000 0.0415945
579579 0 0
580580 0 0
581581 3.63682 0.150881
582582 0 0
583583 −22.8034 −0.944421
584584 2.62620 0.108673
585585 0 0
586586 12.1772 0.503036
587587 22.3757 0.923544 0.461772 0.886999i 0.347214π-0.347214\pi
0.461772 + 0.886999i 0.347214π0.347214\pi
588588 0 0
589589 −8.08476 −0.333127
590590 0 0
591591 0 0
592592 −10.1816 −0.418461
593593 −12.1695 −0.499742 −0.249871 0.968279i 0.580388π-0.580388\pi
−0.249871 + 0.968279i 0.580388π0.580388\pi
594594 0 0
595595 0 0
596596 −10.0000 −0.409616
597597 0 0
598598 −8.23407 −0.336716
599599 25.1387 1.02714 0.513569 0.858048i 0.328323π-0.328323\pi
0.513569 + 0.858048i 0.328323π0.328323\pi
600600 0 0
601601 −4.50479 −0.183754 −0.0918772 0.995770i 0.529287π-0.529287\pi
−0.0918772 + 0.995770i 0.529287π0.529287\pi
602602 6.27072 0.255575
603603 0 0
604604 −5.18785 −0.211090
605605 0 0
606606 0 0
607607 7.00626 0.284375 0.142188 0.989840i 0.454586π-0.454586\pi
0.142188 + 0.989840i 0.454586π0.454586\pi
608608 −0.896916 −0.0363748
609609 0 0
610610 0 0
611611 −27.3651 −1.10707
612612 0 0
613613 −7.46626 −0.301559 −0.150780 0.988567i 0.548178π-0.548178\pi
−0.150780 + 0.988567i 0.548178π0.548178\pi
614614 23.7938 0.960241
615615 0 0
616616 1.72928 0.0696747
617617 36.1772 1.45644 0.728220 0.685343i 0.240348π-0.240348\pi
0.728220 + 0.685343i 0.240348π0.240348\pi
618618 0 0
619619 −4.27072 −0.171655 −0.0858273 0.996310i 0.527353π-0.527353\pi
−0.0858273 + 0.996310i 0.527353π0.527353\pi
620620 0 0
621621 0 0
622622 −32.9205 −1.31999
623623 3.58767 0.143737
624624 0 0
625625 0 0
626626 −29.0462 −1.16092
627627 0 0
628628 −10.2341 −0.408384
629629 −10.1816 −0.405966
630630 0 0
631631 26.0279 1.03615 0.518077 0.855334i 0.326648π-0.326648\pi
0.518077 + 0.855334i 0.326648π0.326648\pi
632632 −7.91087 −0.314677
633633 0 0
634634 −20.6864 −0.821561
635635 0 0
636636 0 0
637637 −16.4200 −0.650585
638638 18.9817 0.751492
639639 0 0
640640 0 0
641641 −12.6831 −0.500950 −0.250475 0.968123i 0.580587π-0.580587\pi
−0.250475 + 0.968123i 0.580587π0.580587\pi
642642 0 0
643643 −25.1108 −0.990272 −0.495136 0.868815i 0.664882π-0.664882\pi
−0.495136 + 0.868815i 0.664882π0.664882\pi
644644 2.71096 0.106827
645645 0 0
646646 −0.896916 −0.0352887
647647 38.0635 1.49643 0.748215 0.663456i 0.230911π-0.230911\pi
0.748215 + 0.663456i 0.230911π0.230911\pi
648648 0 0
649649 −8.29862 −0.325750
650650 0 0
651651 0 0
652652 −6.47689 −0.253654
653653 45.2682 1.77148 0.885742 0.464179i 0.153650π-0.153650\pi
0.885742 + 0.464179i 0.153650π0.153650\pi
654654 0 0
655655 0 0
656656 −9.52311 −0.371815
657657 0 0
658658 9.00958 0.351230
659659 −40.7466 −1.58726 −0.793630 0.608400i 0.791812π-0.791812\pi
−0.793630 + 0.608400i 0.791812π0.791812\pi
660660 0 0
661661 2.53270 0.0985106 0.0492553 0.998786i 0.484315π-0.484315\pi
0.0492553 + 0.998786i 0.484315π0.484315\pi
662662 4.02021 0.156250
663663 0 0
664664 −4.20617 −0.163231
665665 0 0
666666 0 0
667667 29.7572 1.15220
668668 −3.84632 −0.148819
669669 0 0
670670 0 0
671671 −6.56934 −0.253607
672672 0 0
673673 37.0818 1.42940 0.714700 0.699431i 0.246563π-0.246563\pi
0.714700 + 0.699431i 0.246563π0.246563\pi
674674 2.21386 0.0852748
675675 0 0
676676 −6.10308 −0.234734
677677 −44.3790 −1.70562 −0.852812 0.522218i 0.825105π-0.825105\pi
−0.852812 + 0.522218i 0.825105π0.825105\pi
678678 0 0
679679 −5.31695 −0.204046
680680 0 0
681681 0 0
682682 −18.0279 −0.690324
683683 7.46626 0.285688 0.142844 0.989745i 0.454375π-0.454375\pi
0.142844 + 0.989745i 0.454375π0.454375\pi
684684 0 0
685685 0 0
686686 11.4586 0.437490
687687 0 0
688688 −7.25240 −0.276495
689689 29.9431 1.14074
690690 0 0
691691 26.8959 1.02317 0.511584 0.859233i 0.329059π-0.329059\pi
0.511584 + 0.859233i 0.329059π0.329059\pi
692692 −23.9109 −0.908955
693693 0 0
694694 1.37380 0.0521488
695695 0 0
696696 0 0
697697 −9.52311 −0.360714
698698 −20.8680 −0.789864
699699 0 0
700700 0 0
701701 −23.7938 −0.898681 −0.449340 0.893361i 0.648341π-0.648341\pi
−0.449340 + 0.893361i 0.648341π0.648341\pi
702702 0 0
703703 9.13203 0.344421
704704 −2.00000 −0.0753778
705705 0 0
706706 13.7572 0.517759
707707 0.178261 0.00670419
708708 0 0
709709 −17.0140 −0.638972 −0.319486 0.947591i 0.603510π-0.603510\pi
−0.319486 + 0.947591i 0.603510π0.603510\pi
710710 0 0
711711 0 0
712712 −4.14931 −0.155502
713713 −28.2620 −1.05842
714714 0 0
715715 0 0
716716 14.7110 0.549774
717717 0 0
718718 −9.31695 −0.347705
719719 23.8665 0.890071 0.445036 0.895513i 0.353191π-0.353191\pi
0.445036 + 0.895513i 0.353191π0.353191\pi
720720 0 0
721721 4.12910 0.153776
722722 −18.1955 −0.677168
723723 0 0
724724 −23.4340 −0.870917
725725 0 0
726726 0 0
727727 28.3834 1.05268 0.526341 0.850274i 0.323564π-0.323564\pi
0.526341 + 0.850274i 0.323564π0.323564\pi
728728 −2.27072 −0.0841584
729729 0 0
730730 0 0
731731 −7.25240 −0.268240
732732 0 0
733733 28.2216 1.04239 0.521194 0.853439i 0.325487π-0.325487\pi
0.521194 + 0.853439i 0.325487π0.325487\pi
734734 12.3878 0.457240
735735 0 0
736736 −3.13536 −0.115571
737737 2.50479 0.0922652
738738 0 0
739739 0.226378 0.00832746 0.00416373 0.999991i 0.498675π-0.498675\pi
0.00416373 + 0.999991i 0.498675π0.498675\pi
740740 0 0
741741 0 0
742742 −9.85838 −0.361913
743743 −47.6035 −1.74640 −0.873202 0.487359i 0.837960π-0.837960\pi
−0.873202 + 0.487359i 0.837960π0.837960\pi
744744 0 0
745745 0 0
746746 −23.3169 −0.853694
747747 0 0
748748 −2.00000 −0.0731272
749749 −5.44605 −0.198994
750750 0 0
751751 0.124733 0.00455157 0.00227578 0.999997i 0.499276π-0.499276\pi
0.00227578 + 0.999997i 0.499276π0.499276\pi
752752 −10.4200 −0.379979
753753 0 0
754754 −24.9248 −0.907709
755755 0 0
756756 0 0
757757 33.7774 1.22766 0.613830 0.789438i 0.289628π-0.289628\pi
0.613830 + 0.789438i 0.289628π0.289628\pi
758758 28.9817 1.05266
759759 0 0
760760 0 0
761761 −11.4219 −0.414044 −0.207022 0.978336i 0.566377π-0.566377\pi
−0.207022 + 0.978336i 0.566377π0.566377\pi
762762 0 0
763763 −4.80342 −0.173895
764764 −18.5048 −0.669480
765765 0 0
766766 −14.9527 −0.540264
767767 10.8969 0.393465
768768 0 0
769769 12.1127 0.436794 0.218397 0.975860i 0.429917π-0.429917\pi
0.218397 + 0.975860i 0.429917π0.429917\pi
770770 0 0
771771 0 0
772772 −5.45856 −0.196458
773773 −37.4586 −1.34729 −0.673645 0.739055i 0.735272π-0.735272\pi
−0.673645 + 0.739055i 0.735272π0.735272\pi
774774 0 0
775775 0 0
776776 6.14931 0.220747
777777 0 0
778778 19.3169 0.692546
779779 8.54144 0.306029
780780 0 0
781781 −25.0741 −0.897223
782782 −3.13536 −0.112120
783783 0 0
784784 −6.25240 −0.223300
785785 0 0
786786 0 0
787787 −25.0664 −0.893522 −0.446761 0.894653i 0.647423π-0.647423\pi
−0.446761 + 0.894653i 0.647423π0.647423\pi
788788 −13.9388 −0.496548
789789 0 0
790790 0 0
791791 −9.18785 −0.326682
792792 0 0
793793 8.62620 0.306325
794794 9.57560 0.339825
795795 0 0
796796 −11.2847 −0.399975
797797 19.5510 0.692533 0.346266 0.938136i 0.387449π-0.387449\pi
0.346266 + 0.938136i 0.387449π0.387449\pi
798798 0 0
799799 −10.4200 −0.368634
800800 0 0
801801 0 0
802802 −11.3169 −0.399615
803803 −5.25240 −0.185353
804804 0 0
805805 0 0
806806 23.6724 0.833826
807807 0 0
808808 −0.206167 −0.00725294
809809 −20.1974 −0.710104 −0.355052 0.934847i 0.615537π-0.615537\pi
−0.355052 + 0.934847i 0.615537π0.615537\pi
810810 0 0
811811 28.1570 0.988726 0.494363 0.869255i 0.335401π-0.335401\pi
0.494363 + 0.869255i 0.335401π0.335401\pi
812812 8.20617 0.287980
813813 0 0
814814 20.3632 0.713729
815815 0 0
816816 0 0
817817 6.50479 0.227574
818818 −9.10308 −0.318282
819819 0 0
820820 0 0
821821 51.2759 1.78954 0.894771 0.446525i 0.147339π-0.147339\pi
0.894771 + 0.446525i 0.147339π0.147339\pi
822822 0 0
823823 52.9850 1.84694 0.923471 0.383669i 0.125340π-0.125340\pi
0.923471 + 0.383669i 0.125340π0.125340\pi
824824 −4.77551 −0.166363
825825 0 0
826826 −3.58767 −0.124831
827827 −39.7205 −1.38122 −0.690609 0.723228i 0.742658π-0.742658\pi
−0.690609 + 0.723228i 0.742658π0.742658\pi
828828 0 0
829829 23.0096 0.799156 0.399578 0.916699i 0.369157π-0.369157\pi
0.399578 + 0.916699i 0.369157π0.369157\pi
830830 0 0
831831 0 0
832832 2.62620 0.0910470
833833 −6.25240 −0.216633
834834 0 0
835835 0 0
836836 1.79383 0.0620410
837837 0 0
838838 4.02791 0.139142
839839 −2.39545 −0.0827002 −0.0413501 0.999145i 0.513166π-0.513166\pi
−0.0413501 + 0.999145i 0.513166π0.513166\pi
840840 0 0
841841 61.0760 2.10607
842842 15.2524 0.525632
843843 0 0
844844 −14.8401 −0.510816
845845 0 0
846846 0 0
847847 6.05249 0.207966
848848 11.4017 0.391536
849849 0 0
850850 0 0
851851 31.9229 1.09430
852852 0 0
853853 −2.24614 −0.0769063 −0.0384532 0.999260i 0.512243π-0.512243\pi
−0.0384532 + 0.999260i 0.512243π0.512243\pi
854854 −2.84006 −0.0971849
855855 0 0
856856 6.29862 0.215283
857857 18.3188 0.625760 0.312880 0.949793i 0.398706π-0.398706\pi
0.312880 + 0.949793i 0.398706π0.398706\pi
858858 0 0
859859 −42.1127 −1.43687 −0.718433 0.695596i 0.755140π-0.755140\pi
−0.718433 + 0.695596i 0.755140π0.755140\pi
860860 0 0
861861 0 0
862862 4.45231 0.151646
863863 −44.8313 −1.52608 −0.763038 0.646354i 0.776293π-0.776293\pi
−0.763038 + 0.646354i 0.776293π0.776293\pi
864864 0 0
865865 0 0
866866 10.7110 0.363973
867867 0 0
868868 −7.79383 −0.264540
869869 15.8217 0.536716
870870 0 0
871871 −3.28904 −0.111445
872872 5.55539 0.188129
873873 0 0
874874 2.81215 0.0951226
875875 0 0
876876 0 0
877877 2.29530 0.0775067 0.0387533 0.999249i 0.487661π-0.487661\pi
0.0387533 + 0.999249i 0.487661π0.487661\pi
878878 5.09871 0.172073
879879 0 0
880880 0 0
881881 20.9171 0.704716 0.352358 0.935865i 0.385380π-0.385380\pi
0.352358 + 0.935865i 0.385380π0.385380\pi
882882 0 0
883883 −26.6743 −0.897662 −0.448831 0.893617i 0.648160π-0.648160\pi
−0.448831 + 0.893617i 0.648160π0.648160\pi
884884 2.62620 0.0883286
885885 0 0
886886 −10.8034 −0.362948
887887 29.1633 0.979207 0.489603 0.871945i 0.337142π-0.337142\pi
0.489603 + 0.871945i 0.337142π0.337142\pi
888888 0 0
889889 −12.4123 −0.416296
890890 0 0
891891 0 0
892892 3.30925 0.110802
893893 9.34590 0.312748
894894 0 0
895895 0 0
896896 −0.864641 −0.0288856
897897 0 0
898898 5.82174 0.194274
899899 −85.5500 −2.85325
900900 0 0
901901 11.4017 0.379846
902902 19.0462 0.634170
903903 0 0
904904 10.6262 0.353422
905905 0 0
906906 0 0
907907 23.2322 0.771412 0.385706 0.922622i 0.373958π-0.373958\pi
0.385706 + 0.922622i 0.373958π0.373958\pi
908908 24.7187 0.820317
909909 0 0
910910 0 0
911911 20.8646 0.691276 0.345638 0.938368i 0.387662π-0.387662\pi
0.345638 + 0.938368i 0.387662π0.387662\pi
912912 0 0
913913 8.41233 0.278408
914914 13.7014 0.453201
915915 0 0
916916 4.27072 0.141109
917917 14.7389 0.486720
918918 0 0
919919 18.2062 0.600566 0.300283 0.953850i 0.402919π-0.402919\pi
0.300283 + 0.953850i 0.402919π0.402919\pi
920920 0 0
921921 0 0
922922 27.0741 0.891639
923923 32.9248 1.08373
924924 0 0
925925 0 0
926926 37.3372 1.22698
927927 0 0
928928 −9.49084 −0.311552
929929 −17.2803 −0.566948 −0.283474 0.958980i 0.591487π-0.591487\pi
−0.283474 + 0.958980i 0.591487π0.591487\pi
930930 0 0
931931 5.60788 0.183791
932932 −0.832365 −0.0272650
933933 0 0
934934 −35.3449 −1.15652
935935 0 0
936936 0 0
937937 50.2986 1.64318 0.821592 0.570076i 0.193086π-0.193086\pi
0.821592 + 0.570076i 0.193086π0.193086\pi
938938 1.08287 0.0353571
939939 0 0
940940 0 0
941941 −20.7153 −0.675300 −0.337650 0.941272i 0.609632π-0.609632\pi
−0.337650 + 0.941272i 0.609632π0.609632\pi
942942 0 0
943943 29.8584 0.972323
944944 4.14931 0.135049
945945 0 0
946946 14.5048 0.471591
947947 8.89692 0.289111 0.144555 0.989497i 0.453825π-0.453825\pi
0.144555 + 0.989497i 0.453825π0.453825\pi
948948 0 0
949949 6.89692 0.223883
950950 0 0
951951 0 0
952952 −0.864641 −0.0280232
953953 −17.2158 −0.557673 −0.278836 0.960339i 0.589949π-0.589949\pi
−0.278836 + 0.960339i 0.589949π0.589949\pi
954954 0 0
955955 0 0
956956 4.71096 0.152363
957957 0 0
958958 −31.0419 −1.00292
959959 −12.5414 −0.404984
960960 0 0
961961 50.2514 1.62101
962962 −26.7389 −0.862096
963963 0 0
964964 −23.4865 −0.756448
965965 0 0
966966 0 0
967967 1.90754 0.0613424 0.0306712 0.999530i 0.490236π-0.490236\pi
0.0306712 + 0.999530i 0.490236π0.490236\pi
968968 −7.00000 −0.224989
969969 0 0
970970 0 0
971971 4.97398 0.159623 0.0798113 0.996810i 0.474568π-0.474568\pi
0.0798113 + 0.996810i 0.474568π0.474568\pi
972972 0 0
973973 12.7197 0.407775
974974 13.1633 0.421778
975975 0 0
976976 3.28467 0.105140
977977 −51.2716 −1.64032 −0.820161 0.572132i 0.806116π-0.806116\pi
−0.820161 + 0.572132i 0.806116π0.806116\pi
978978 0 0
979979 8.29862 0.265225
980980 0 0
981981 0 0
982982 −24.3555 −0.777215
983983 −9.88296 −0.315218 −0.157609 0.987502i 0.550378π-0.550378\pi
−0.157609 + 0.987502i 0.550378π0.550378\pi
984984 0 0
985985 0 0
986986 −9.49084 −0.302250
987987 0 0
988988 −2.35548 −0.0749378
989989 22.7389 0.723054
990990 0 0
991991 −37.7807 −1.20014 −0.600072 0.799946i 0.704861π-0.704861\pi
−0.600072 + 0.799946i 0.704861π0.704861\pi
992992 9.01395 0.286193
993993 0 0
994994 −10.8401 −0.343826
995995 0 0
996996 0 0
997997 −8.14494 −0.257953 −0.128976 0.991648i 0.541169π-0.541169\pi
−0.128976 + 0.991648i 0.541169π0.541169\pi
998998 36.2620 1.14785
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 7650.2.a.do.1.2 3
3.2 odd 2 850.2.a.p.1.3 3
5.2 odd 4 1530.2.d.g.919.6 6
5.3 odd 4 1530.2.d.g.919.3 6
5.4 even 2 7650.2.a.dj.1.2 3
12.11 even 2 6800.2.a.bp.1.1 3
15.2 even 4 170.2.c.b.69.1 6
15.8 even 4 170.2.c.b.69.6 yes 6
15.14 odd 2 850.2.a.q.1.1 3
60.23 odd 4 1360.2.e.c.1089.2 6
60.47 odd 4 1360.2.e.c.1089.5 6
60.59 even 2 6800.2.a.bk.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.c.b.69.1 6 15.2 even 4
170.2.c.b.69.6 yes 6 15.8 even 4
850.2.a.p.1.3 3 3.2 odd 2
850.2.a.q.1.1 3 15.14 odd 2
1360.2.e.c.1089.2 6 60.23 odd 4
1360.2.e.c.1089.5 6 60.47 odd 4
1530.2.d.g.919.3 6 5.3 odd 4
1530.2.d.g.919.6 6 5.2 odd 4
6800.2.a.bk.1.3 3 60.59 even 2
6800.2.a.bp.1.1 3 12.11 even 2
7650.2.a.dj.1.2 3 5.4 even 2
7650.2.a.do.1.2 3 1.1 even 1 trivial