Properties

Label 2496.2.c.i.961.2
Level 24962496
Weight 22
Character 2496.961
Analytic conductor 19.93119.931
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [2496,2,Mod(961,2496)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2496, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) 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("2496.961"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 2496=26313 2496 = 2^{6} \cdot 3 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2496.c (of order 22, degree 11, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,2,0,0,0,0,0,2,0,0,0,-6,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 19.930660344519.9306603445
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x2+1 x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 156)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 961.2
Root 1.00000i1.00000i of defining polynomial
Character χ\chi == 2496.961
Dual form 2496.2.c.i.961.1

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+1.00000q3+2.00000iq5+4.00000iq7+1.00000q9+6.00000iq11+(3.000002.00000i)q13+2.00000iq152.00000q17+4.00000iq21+8.00000q23+1.00000q25+1.00000q272.00000q298.00000iq31+6.00000iq338.00000q35+8.00000iq37+(3.000002.00000i)q39+2.00000iq418.00000q43+2.00000iq456.00000iq479.00000q492.00000q516.00000q5312.0000q55+2.00000iq592.00000q61+4.00000iq63+(4.000006.00000i)q654.00000iq67+8.00000q69+6.00000iq71+4.00000iq73+1.00000q7524.0000q77+1.00000q8114.0000iq834.00000iq852.00000q876.00000iq89+(8.0000012.0000i)q918.00000iq93+12.0000iq97+6.00000iq99+O(q100)q+1.00000 q^{3} +2.00000i q^{5} +4.00000i q^{7} +1.00000 q^{9} +6.00000i q^{11} +(-3.00000 - 2.00000i) q^{13} +2.00000i q^{15} -2.00000 q^{17} +4.00000i q^{21} +8.00000 q^{23} +1.00000 q^{25} +1.00000 q^{27} -2.00000 q^{29} -8.00000i q^{31} +6.00000i q^{33} -8.00000 q^{35} +8.00000i q^{37} +(-3.00000 - 2.00000i) q^{39} +2.00000i q^{41} -8.00000 q^{43} +2.00000i q^{45} -6.00000i q^{47} -9.00000 q^{49} -2.00000 q^{51} -6.00000 q^{53} -12.0000 q^{55} +2.00000i q^{59} -2.00000 q^{61} +4.00000i q^{63} +(4.00000 - 6.00000i) q^{65} -4.00000i q^{67} +8.00000 q^{69} +6.00000i q^{71} +4.00000i q^{73} +1.00000 q^{75} -24.0000 q^{77} +1.00000 q^{81} -14.0000i q^{83} -4.00000i q^{85} -2.00000 q^{87} -6.00000i q^{89} +(8.00000 - 12.0000i) q^{91} -8.00000i q^{93} +12.0000i q^{97} +6.00000i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+2q3+2q96q134q17+16q23+2q25+2q274q2916q356q3916q4318q494q5112q5324q554q61+8q65+16q69++16q91+O(q100) 2 q + 2 q^{3} + 2 q^{9} - 6 q^{13} - 4 q^{17} + 16 q^{23} + 2 q^{25} + 2 q^{27} - 4 q^{29} - 16 q^{35} - 6 q^{39} - 16 q^{43} - 18 q^{49} - 4 q^{51} - 12 q^{53} - 24 q^{55} - 4 q^{61} + 8 q^{65} + 16 q^{69}+ \cdots + 16 q^{91}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2496Z)×\left(\mathbb{Z}/2496\mathbb{Z}\right)^\times.

nn 703703 769769 833833 10931093
χ(n)\chi(n) 11 1-1 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 1.00000 0.577350
44 0 0
55 2.00000i 0.894427i 0.894427 + 0.447214i 0.147584π0.147584\pi
−0.894427 + 0.447214i 0.852416π0.852416\pi
66 0 0
77 4.00000i 1.51186i 0.654654 + 0.755929i 0.272814π0.272814\pi
−0.654654 + 0.755929i 0.727186π0.727186\pi
88 0 0
99 1.00000 0.333333
1010 0 0
1111 6.00000i 1.80907i 0.426401 + 0.904534i 0.359781π0.359781\pi
−0.426401 + 0.904534i 0.640219π0.640219\pi
1212 0 0
1313 −3.00000 2.00000i −0.832050 0.554700i
1414 0 0
1515 2.00000i 0.516398i
1616 0 0
1717 −2.00000 −0.485071 −0.242536 0.970143i 0.577979π-0.577979\pi
−0.242536 + 0.970143i 0.577979π0.577979\pi
1818 0 0
1919 0 0 1.00000 00
−1.00000 π\pi
2020 0 0
2121 4.00000i 0.872872i
2222 0 0
2323 8.00000 1.66812 0.834058 0.551677i 0.186012π-0.186012\pi
0.834058 + 0.551677i 0.186012π0.186012\pi
2424 0 0
2525 1.00000 0.200000
2626 0 0
2727 1.00000 0.192450
2828 0 0
2929 −2.00000 −0.371391 −0.185695 0.982607i 0.559454π-0.559454\pi
−0.185695 + 0.982607i 0.559454π0.559454\pi
3030 0 0
3131 8.00000i 1.43684i −0.695608 0.718421i 0.744865π-0.744865\pi
0.695608 0.718421i 0.255135π-0.255135\pi
3232 0 0
3333 6.00000i 1.04447i
3434 0 0
3535 −8.00000 −1.35225
3636 0 0
3737 8.00000i 1.31519i 0.753371 + 0.657596i 0.228427π0.228427\pi
−0.753371 + 0.657596i 0.771573π0.771573\pi
3838 0 0
3939 −3.00000 2.00000i −0.480384 0.320256i
4040 0 0
4141 2.00000i 0.312348i 0.987730 + 0.156174i 0.0499160π0.0499160\pi
−0.987730 + 0.156174i 0.950084π0.950084\pi
4242 0 0
4343 −8.00000 −1.21999 −0.609994 0.792406i 0.708828π-0.708828\pi
−0.609994 + 0.792406i 0.708828π0.708828\pi
4444 0 0
4545 2.00000i 0.298142i
4646 0 0
4747 6.00000i 0.875190i −0.899172 0.437595i 0.855830π-0.855830\pi
0.899172 0.437595i 0.144170π-0.144170\pi
4848 0 0
4949 −9.00000 −1.28571
5050 0 0
5151 −2.00000 −0.280056
5252 0 0
5353 −6.00000 −0.824163 −0.412082 0.911147i 0.635198π-0.635198\pi
−0.412082 + 0.911147i 0.635198π0.635198\pi
5454 0 0
5555 −12.0000 −1.61808
5656 0 0
5757 0 0
5858 0 0
5959 2.00000i 0.260378i 0.991489 + 0.130189i 0.0415584π0.0415584\pi
−0.991489 + 0.130189i 0.958442π0.958442\pi
6060 0 0
6161 −2.00000 −0.256074 −0.128037 0.991769i 0.540868π-0.540868\pi
−0.128037 + 0.991769i 0.540868π0.540868\pi
6262 0 0
6363 4.00000i 0.503953i
6464 0 0
6565 4.00000 6.00000i 0.496139 0.744208i
6666 0 0
6767 4.00000i 0.488678i −0.969690 0.244339i 0.921429π-0.921429\pi
0.969690 0.244339i 0.0785709π-0.0785709\pi
6868 0 0
6969 8.00000 0.963087
7070 0 0
7171 6.00000i 0.712069i 0.934473 + 0.356034i 0.115871π0.115871\pi
−0.934473 + 0.356034i 0.884129π0.884129\pi
7272 0 0
7373 4.00000i 0.468165i 0.972217 + 0.234082i 0.0752085π0.0752085\pi
−0.972217 + 0.234082i 0.924791π0.924791\pi
7474 0 0
7575 1.00000 0.115470
7676 0 0
7777 −24.0000 −2.73505
7878 0 0
7979 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 14.0000i 1.53670i −0.640030 0.768350i 0.721078π-0.721078\pi
0.640030 0.768350i 0.278922π-0.278922\pi
8484 0 0
8585 4.00000i 0.433861i
8686 0 0
8787 −2.00000 −0.214423
8888 0 0
8989 6.00000i 0.635999i −0.948091 0.317999i 0.896989π-0.896989\pi
0.948091 0.317999i 0.103011π-0.103011\pi
9090 0 0
9191 8.00000 12.0000i 0.838628 1.25794i
9292 0 0
9393 8.00000i 0.829561i
9494 0 0
9595 0 0
9696 0 0
9797 12.0000i 1.21842i 0.793011 + 0.609208i 0.208512π0.208512\pi
−0.793011 + 0.609208i 0.791488π0.791488\pi
9898 0 0
9999 6.00000i 0.603023i
100100 0 0
101101 10.0000 0.995037 0.497519 0.867453i 0.334245π-0.334245\pi
0.497519 + 0.867453i 0.334245π0.334245\pi
102102 0 0
103103 4.00000 0.394132 0.197066 0.980390i 0.436859π-0.436859\pi
0.197066 + 0.980390i 0.436859π0.436859\pi
104104 0 0
105105 −8.00000 −0.780720
106106 0 0
107107 20.0000 1.93347 0.966736 0.255774i 0.0823304π-0.0823304\pi
0.966736 + 0.255774i 0.0823304π0.0823304\pi
108108 0 0
109109 4.00000i 0.383131i 0.981480 + 0.191565i 0.0613564π0.0613564\pi
−0.981480 + 0.191565i 0.938644π0.938644\pi
110110 0 0
111111 8.00000i 0.759326i
112112 0 0
113113 −10.0000 −0.940721 −0.470360 0.882474i 0.655876π-0.655876\pi
−0.470360 + 0.882474i 0.655876π0.655876\pi
114114 0 0
115115 16.0000i 1.49201i
116116 0 0
117117 −3.00000 2.00000i −0.277350 0.184900i
118118 0 0
119119 8.00000i 0.733359i
120120 0 0
121121 −25.0000 −2.27273
122122 0 0
123123 2.00000i 0.180334i
124124 0 0
125125 12.0000i 1.07331i
126126 0 0
127127 −8.00000 −0.709885 −0.354943 0.934888i 0.615500π-0.615500\pi
−0.354943 + 0.934888i 0.615500π0.615500\pi
128128 0 0
129129 −8.00000 −0.704361
130130 0 0
131131 4.00000 0.349482 0.174741 0.984614i 0.444091π-0.444091\pi
0.174741 + 0.984614i 0.444091π0.444091\pi
132132 0 0
133133 0 0
134134 0 0
135135 2.00000i 0.172133i
136136 0 0
137137 10.0000i 0.854358i −0.904167 0.427179i 0.859507π-0.859507\pi
0.904167 0.427179i 0.140493π-0.140493\pi
138138 0 0
139139 −8.00000 −0.678551 −0.339276 0.940687i 0.610182π-0.610182\pi
−0.339276 + 0.940687i 0.610182π0.610182\pi
140140 0 0
141141 6.00000i 0.505291i
142142 0 0
143143 12.0000 18.0000i 1.00349 1.50524i
144144 0 0
145145 4.00000i 0.332182i
146146 0 0
147147 −9.00000 −0.742307
148148 0 0
149149 10.0000i 0.819232i −0.912258 0.409616i 0.865663π-0.865663\pi
0.912258 0.409616i 0.134337π-0.134337\pi
150150 0 0
151151 16.0000i 1.30206i 0.759051 + 0.651031i 0.225663π0.225663\pi
−0.759051 + 0.651031i 0.774337π0.774337\pi
152152 0 0
153153 −2.00000 −0.161690
154154 0 0
155155 16.0000 1.28515
156156 0 0
157157 14.0000 1.11732 0.558661 0.829396i 0.311315π-0.311315\pi
0.558661 + 0.829396i 0.311315π0.311315\pi
158158 0 0
159159 −6.00000 −0.475831
160160 0 0
161161 32.0000i 2.52195i
162162 0 0
163163 8.00000i 0.626608i 0.949653 + 0.313304i 0.101436π0.101436\pi
−0.949653 + 0.313304i 0.898564π0.898564\pi
164164 0 0
165165 −12.0000 −0.934199
166166 0 0
167167 18.0000i 1.39288i 0.717614 + 0.696441i 0.245234π0.245234\pi
−0.717614 + 0.696441i 0.754766π0.754766\pi
168168 0 0
169169 5.00000 + 12.0000i 0.384615 + 0.923077i
170170 0 0
171171 0 0
172172 0 0
173173 −6.00000 −0.456172 −0.228086 0.973641i 0.573247π-0.573247\pi
−0.228086 + 0.973641i 0.573247π0.573247\pi
174174 0 0
175175 4.00000i 0.302372i
176176 0 0
177177 2.00000i 0.150329i
178178 0 0
179179 −12.0000 −0.896922 −0.448461 0.893802i 0.648028π-0.648028\pi
−0.448461 + 0.893802i 0.648028π0.648028\pi
180180 0 0
181181 −10.0000 −0.743294 −0.371647 0.928374i 0.621207π-0.621207\pi
−0.371647 + 0.928374i 0.621207π0.621207\pi
182182 0 0
183183 −2.00000 −0.147844
184184 0 0
185185 −16.0000 −1.17634
186186 0 0
187187 12.0000i 0.877527i
188188 0 0
189189 4.00000i 0.290957i
190190 0 0
191191 24.0000 1.73658 0.868290 0.496058i 0.165220π-0.165220\pi
0.868290 + 0.496058i 0.165220π0.165220\pi
192192 0 0
193193 8.00000i 0.575853i 0.957653 + 0.287926i 0.0929658π0.0929658\pi
−0.957653 + 0.287926i 0.907034π0.907034\pi
194194 0 0
195195 4.00000 6.00000i 0.286446 0.429669i
196196 0 0
197197 26.0000i 1.85242i 0.377004 + 0.926212i 0.376954π0.376954\pi
−0.377004 + 0.926212i 0.623046π0.623046\pi
198198 0 0
199199 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
200200 0 0
201201 4.00000i 0.282138i
202202 0 0
203203 8.00000i 0.561490i
204204 0 0
205205 −4.00000 −0.279372
206206 0 0
207207 8.00000 0.556038
208208 0 0
209209 0 0
210210 0 0
211211 12.0000 0.826114 0.413057 0.910705i 0.364461π-0.364461\pi
0.413057 + 0.910705i 0.364461π0.364461\pi
212212 0 0
213213 6.00000i 0.411113i
214214 0 0
215215 16.0000i 1.09119i
216216 0 0
217217 32.0000 2.17230
218218 0 0
219219 4.00000i 0.270295i
220220 0 0
221221 6.00000 + 4.00000i 0.403604 + 0.269069i
222222 0 0
223223 8.00000i 0.535720i −0.963458 0.267860i 0.913684π-0.913684\pi
0.963458 0.267860i 0.0863164π-0.0863164\pi
224224 0 0
225225 1.00000 0.0666667
226226 0 0
227227 2.00000i 0.132745i −0.997795 0.0663723i 0.978857π-0.978857\pi
0.997795 0.0663723i 0.0211425π-0.0211425\pi
228228 0 0
229229 20.0000i 1.32164i −0.750546 0.660819i 0.770209π-0.770209\pi
0.750546 0.660819i 0.229791π-0.229791\pi
230230 0 0
231231 −24.0000 −1.57908
232232 0 0
233233 18.0000 1.17922 0.589610 0.807688i 0.299282π-0.299282\pi
0.589610 + 0.807688i 0.299282π0.299282\pi
234234 0 0
235235 12.0000 0.782794
236236 0 0
237237 0 0
238238 0 0
239239 10.0000i 0.646846i −0.946254 0.323423i 0.895166π-0.895166\pi
0.946254 0.323423i 0.104834π-0.104834\pi
240240 0 0
241241 20.0000i 1.28831i −0.764894 0.644157i 0.777208π-0.777208\pi
0.764894 0.644157i 0.222792π-0.222792\pi
242242 0 0
243243 1.00000 0.0641500
244244 0 0
245245 18.0000i 1.14998i
246246 0 0
247247 0 0
248248 0 0
249249 14.0000i 0.887214i
250250 0 0
251251 20.0000 1.26239 0.631194 0.775625i 0.282565π-0.282565\pi
0.631194 + 0.775625i 0.282565π0.282565\pi
252252 0 0
253253 48.0000i 3.01773i
254254 0 0
255255 4.00000i 0.250490i
256256 0 0
257257 −6.00000 −0.374270 −0.187135 0.982334i 0.559920π-0.559920\pi
−0.187135 + 0.982334i 0.559920π0.559920\pi
258258 0 0
259259 −32.0000 −1.98838
260260 0 0
261261 −2.00000 −0.123797
262262 0 0
263263 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
264264 0 0
265265 12.0000i 0.737154i
266266 0 0
267267 6.00000i 0.367194i
268268 0 0
269269 22.0000 1.34136 0.670682 0.741745i 0.266002π-0.266002\pi
0.670682 + 0.741745i 0.266002π0.266002\pi
270270 0 0
271271 20.0000i 1.21491i 0.794353 + 0.607457i 0.207810π0.207810\pi
−0.794353 + 0.607457i 0.792190π0.792190\pi
272272 0 0
273273 8.00000 12.0000i 0.484182 0.726273i
274274 0 0
275275 6.00000i 0.361814i
276276 0 0
277277 −22.0000 −1.32185 −0.660926 0.750451i 0.729836π-0.729836\pi
−0.660926 + 0.750451i 0.729836π0.729836\pi
278278 0 0
279279 8.00000i 0.478947i
280280 0 0
281281 22.0000i 1.31241i 0.754583 + 0.656205i 0.227839π0.227839\pi
−0.754583 + 0.656205i 0.772161π0.772161\pi
282282 0 0
283283 4.00000 0.237775 0.118888 0.992908i 0.462067π-0.462067\pi
0.118888 + 0.992908i 0.462067π0.462067\pi
284284 0 0
285285 0 0
286286 0 0
287287 −8.00000 −0.472225
288288 0 0
289289 −13.0000 −0.764706
290290 0 0
291291 12.0000i 0.703452i
292292 0 0
293293 14.0000i 0.817889i −0.912559 0.408944i 0.865897π-0.865897\pi
0.912559 0.408944i 0.134103π-0.134103\pi
294294 0 0
295295 −4.00000 −0.232889
296296 0 0
297297 6.00000i 0.348155i
298298 0 0
299299 −24.0000 16.0000i −1.38796 0.925304i
300300 0 0
301301 32.0000i 1.84445i
302302 0 0
303303 10.0000 0.574485
304304 0 0
305305 4.00000i 0.229039i
306306 0 0
307307 20.0000i 1.14146i 0.821138 + 0.570730i 0.193340π0.193340\pi
−0.821138 + 0.570730i 0.806660π0.806660\pi
308308 0 0
309309 4.00000 0.227552
310310 0 0
311311 16.0000 0.907277 0.453638 0.891186i 0.350126π-0.350126\pi
0.453638 + 0.891186i 0.350126π0.350126\pi
312312 0 0
313313 −14.0000 −0.791327 −0.395663 0.918396i 0.629485π-0.629485\pi
−0.395663 + 0.918396i 0.629485π0.629485\pi
314314 0 0
315315 −8.00000 −0.450749
316316 0 0
317317 18.0000i 1.01098i 0.862832 + 0.505490i 0.168688π0.168688\pi
−0.862832 + 0.505490i 0.831312π0.831312\pi
318318 0 0
319319 12.0000i 0.671871i
320320 0 0
321321 20.0000 1.11629
322322 0 0
323323 0 0
324324 0 0
325325 −3.00000 2.00000i −0.166410 0.110940i
326326 0 0
327327 4.00000i 0.221201i
328328 0 0
329329 24.0000 1.32316
330330 0 0
331331 28.0000i 1.53902i 0.638635 + 0.769510i 0.279499π0.279499\pi
−0.638635 + 0.769510i 0.720501π0.720501\pi
332332 0 0
333333 8.00000i 0.438397i
334334 0 0
335335 8.00000 0.437087
336336 0 0
337337 −14.0000 −0.762629 −0.381314 0.924445i 0.624528π-0.624528\pi
−0.381314 + 0.924445i 0.624528π0.624528\pi
338338 0 0
339339 −10.0000 −0.543125
340340 0 0
341341 48.0000 2.59935
342342 0 0
343343 8.00000i 0.431959i
344344 0 0
345345 16.0000i 0.861411i
346346 0 0
347347 12.0000 0.644194 0.322097 0.946707i 0.395612π-0.395612\pi
0.322097 + 0.946707i 0.395612π0.395612\pi
348348 0 0
349349 8.00000i 0.428230i 0.976808 + 0.214115i 0.0686868π0.0686868\pi
−0.976808 + 0.214115i 0.931313π0.931313\pi
350350 0 0
351351 −3.00000 2.00000i −0.160128 0.106752i
352352 0 0
353353 10.0000i 0.532246i 0.963939 + 0.266123i 0.0857428π0.0857428\pi
−0.963939 + 0.266123i 0.914257π0.914257\pi
354354 0 0
355355 −12.0000 −0.636894
356356 0 0
357357 8.00000i 0.423405i
358358 0 0
359359 10.0000i 0.527780i 0.964553 + 0.263890i 0.0850056π0.0850056\pi
−0.964553 + 0.263890i 0.914994π0.914994\pi
360360 0 0
361361 19.0000 1.00000
362362 0 0
363363 −25.0000 −1.31216
364364 0 0
365365 −8.00000 −0.418739
366366 0 0
367367 28.0000 1.46159 0.730794 0.682598i 0.239150π-0.239150\pi
0.730794 + 0.682598i 0.239150π0.239150\pi
368368 0 0
369369 2.00000i 0.104116i
370370 0 0
371371 24.0000i 1.24602i
372372 0 0
373373 −6.00000 −0.310668 −0.155334 0.987862i 0.549645π-0.549645\pi
−0.155334 + 0.987862i 0.549645π0.549645\pi
374374 0 0
375375 12.0000i 0.619677i
376376 0 0
377377 6.00000 + 4.00000i 0.309016 + 0.206010i
378378 0 0
379379 16.0000i 0.821865i −0.911666 0.410932i 0.865203π-0.865203\pi
0.911666 0.410932i 0.134797π-0.134797\pi
380380 0 0
381381 −8.00000 −0.409852
382382 0 0
383383 22.0000i 1.12415i −0.827087 0.562074i 0.810004π-0.810004\pi
0.827087 0.562074i 0.189996π-0.189996\pi
384384 0 0
385385 48.0000i 2.44631i
386386 0 0
387387 −8.00000 −0.406663
388388 0 0
389389 −18.0000 −0.912636 −0.456318 0.889817i 0.650832π-0.650832\pi
−0.456318 + 0.889817i 0.650832π0.650832\pi
390390 0 0
391391 −16.0000 −0.809155
392392 0 0
393393 4.00000 0.201773
394394 0 0
395395 0 0
396396 0 0
397397 16.0000i 0.803017i −0.915855 0.401508i 0.868486π-0.868486\pi
0.915855 0.401508i 0.131514π-0.131514\pi
398398 0 0
399399 0 0
400400 0 0
401401 6.00000i 0.299626i −0.988714 0.149813i 0.952133π-0.952133\pi
0.988714 0.149813i 0.0478671π-0.0478671\pi
402402 0 0
403403 −16.0000 + 24.0000i −0.797017 + 1.19553i
404404 0 0
405405 2.00000i 0.0993808i
406406 0 0
407407 −48.0000 −2.37927
408408 0 0
409409 20.0000i 0.988936i 0.869196 + 0.494468i 0.164637π0.164637\pi
−0.869196 + 0.494468i 0.835363π0.835363\pi
410410 0 0
411411 10.0000i 0.493264i
412412 0 0
413413 −8.00000 −0.393654
414414 0 0
415415 28.0000 1.37447
416416 0 0
417417 −8.00000 −0.391762
418418 0 0
419419 28.0000 1.36789 0.683945 0.729534i 0.260263π-0.260263\pi
0.683945 + 0.729534i 0.260263π0.260263\pi
420420 0 0
421421 4.00000i 0.194948i −0.995238 0.0974740i 0.968924π-0.968924\pi
0.995238 0.0974740i 0.0310763π-0.0310763\pi
422422 0 0
423423 6.00000i 0.291730i
424424 0 0
425425 −2.00000 −0.0970143
426426 0 0
427427 8.00000i 0.387147i
428428 0 0
429429 12.0000 18.0000i 0.579365 0.869048i
430430 0 0
431431 10.0000i 0.481683i 0.970564 + 0.240842i 0.0774234π0.0774234\pi
−0.970564 + 0.240842i 0.922577π0.922577\pi
432432 0 0
433433 22.0000 1.05725 0.528626 0.848855i 0.322707π-0.322707\pi
0.528626 + 0.848855i 0.322707π0.322707\pi
434434 0 0
435435 4.00000i 0.191785i
436436 0 0
437437 0 0
438438 0 0
439439 −36.0000 −1.71819 −0.859093 0.511819i 0.828972π-0.828972\pi
−0.859093 + 0.511819i 0.828972π0.828972\pi
440440 0 0
441441 −9.00000 −0.428571
442442 0 0
443443 20.0000 0.950229 0.475114 0.879924i 0.342407π-0.342407\pi
0.475114 + 0.879924i 0.342407π0.342407\pi
444444 0 0
445445 12.0000 0.568855
446446 0 0
447447 10.0000i 0.472984i
448448 0 0
449449 30.0000i 1.41579i −0.706319 0.707894i 0.749646π-0.749646\pi
0.706319 0.707894i 0.250354π-0.250354\pi
450450 0 0
451451 −12.0000 −0.565058
452452 0 0
453453 16.0000i 0.751746i
454454 0 0
455455 24.0000 + 16.0000i 1.12514 + 0.750092i
456456 0 0
457457 4.00000i 0.187112i −0.995614 0.0935561i 0.970177π-0.970177\pi
0.995614 0.0935561i 0.0298234π-0.0298234\pi
458458 0 0
459459 −2.00000 −0.0933520
460460 0 0
461461 6.00000i 0.279448i −0.990190 0.139724i 0.955378π-0.955378\pi
0.990190 0.139724i 0.0446215π-0.0446215\pi
462462 0 0
463463 12.0000i 0.557687i 0.960337 + 0.278844i 0.0899511π0.0899511\pi
−0.960337 + 0.278844i 0.910049π0.910049\pi
464464 0 0
465465 16.0000 0.741982
466466 0 0
467467 12.0000 0.555294 0.277647 0.960683i 0.410445π-0.410445\pi
0.277647 + 0.960683i 0.410445π0.410445\pi
468468 0 0
469469 16.0000 0.738811
470470 0 0
471471 14.0000 0.645086
472472 0 0
473473 48.0000i 2.20704i
474474 0 0
475475 0 0
476476 0 0
477477 −6.00000 −0.274721
478478 0 0
479479 18.0000i 0.822441i −0.911536 0.411220i 0.865103π-0.865103\pi
0.911536 0.411220i 0.134897π-0.134897\pi
480480 0 0
481481 16.0000 24.0000i 0.729537 1.09431i
482482 0 0
483483 32.0000i 1.45605i
484484 0 0
485485 −24.0000 −1.08978
486486 0 0
487487 0 0 1.00000 00
−1.00000 π\pi
488488 0 0
489489 8.00000i 0.361773i
490490 0 0
491491 20.0000 0.902587 0.451294 0.892375i 0.350963π-0.350963\pi
0.451294 + 0.892375i 0.350963π0.350963\pi
492492 0 0
493493 4.00000 0.180151
494494 0 0
495495 −12.0000 −0.539360
496496 0 0
497497 −24.0000 −1.07655
498498 0 0
499499 4.00000i 0.179065i 0.995984 + 0.0895323i 0.0285372π0.0285372\pi
−0.995984 + 0.0895323i 0.971463π0.971463\pi
500500 0 0
501501 18.0000i 0.804181i
502502 0 0
503503 −24.0000 −1.07011 −0.535054 0.844818i 0.679709π-0.679709\pi
−0.535054 + 0.844818i 0.679709π0.679709\pi
504504 0 0
505505 20.0000i 0.889988i
506506 0 0
507507 5.00000 + 12.0000i 0.222058 + 0.532939i
508508 0 0
509509 30.0000i 1.32973i −0.746965 0.664863i 0.768490π-0.768490\pi
0.746965 0.664863i 0.231510π-0.231510\pi
510510 0 0
511511 −16.0000 −0.707798
512512 0 0
513513 0 0
514514 0 0
515515 8.00000i 0.352522i
516516 0 0
517517 36.0000 1.58328
518518 0 0
519519 −6.00000 −0.263371
520520 0 0
521521 −18.0000 −0.788594 −0.394297 0.918983i 0.629012π-0.629012\pi
−0.394297 + 0.918983i 0.629012π0.629012\pi
522522 0 0
523523 −8.00000 −0.349816 −0.174908 0.984585i 0.555963π-0.555963\pi
−0.174908 + 0.984585i 0.555963π0.555963\pi
524524 0 0
525525 4.00000i 0.174574i
526526 0 0
527527 16.0000i 0.696971i
528528 0 0
529529 41.0000 1.78261
530530 0 0
531531 2.00000i 0.0867926i
532532 0 0
533533 4.00000 6.00000i 0.173259 0.259889i
534534 0 0
535535 40.0000i 1.72935i
536536 0 0
537537 −12.0000 −0.517838
538538 0 0
539539 54.0000i 2.32594i
540540 0 0
541541 20.0000i 0.859867i −0.902861 0.429934i 0.858537π-0.858537\pi
0.902861 0.429934i 0.141463π-0.141463\pi
542542 0 0
543543 −10.0000 −0.429141
544544 0 0
545545 −8.00000 −0.342682
546546 0 0
547547 −8.00000 −0.342055 −0.171028 0.985266i 0.554709π-0.554709\pi
−0.171028 + 0.985266i 0.554709π0.554709\pi
548548 0 0
549549 −2.00000 −0.0853579
550550 0 0
551551 0 0
552552 0 0
553553 0 0
554554 0 0
555555 −16.0000 −0.679162
556556 0 0
557557 30.0000i 1.27114i −0.772043 0.635570i 0.780765π-0.780765\pi
0.772043 0.635570i 0.219235π-0.219235\pi
558558 0 0
559559 24.0000 + 16.0000i 1.01509 + 0.676728i
560560 0 0
561561 12.0000i 0.506640i
562562 0 0
563563 −4.00000 −0.168580 −0.0842900 0.996441i 0.526862π-0.526862\pi
−0.0842900 + 0.996441i 0.526862π0.526862\pi
564564 0 0
565565 20.0000i 0.841406i
566566 0 0
567567 4.00000i 0.167984i
568568 0 0
569569 34.0000 1.42535 0.712677 0.701492i 0.247483π-0.247483\pi
0.712677 + 0.701492i 0.247483π0.247483\pi
570570 0 0
571571 20.0000 0.836974 0.418487 0.908223i 0.362561π-0.362561\pi
0.418487 + 0.908223i 0.362561π0.362561\pi
572572 0 0
573573 24.0000 1.00261
574574 0 0
575575 8.00000 0.333623
576576 0 0
577577 40.0000i 1.66522i 0.553858 + 0.832611i 0.313155π0.313155\pi
−0.553858 + 0.832611i 0.686845π0.686845\pi
578578 0 0
579579 8.00000i 0.332469i
580580 0 0
581581 56.0000 2.32327
582582 0 0
583583 36.0000i 1.49097i
584584 0 0
585585 4.00000 6.00000i 0.165380 0.248069i
586586 0 0
587587 2.00000i 0.0825488i 0.999148 + 0.0412744i 0.0131418π0.0131418\pi
−0.999148 + 0.0412744i 0.986858π0.986858\pi
588588 0 0
589589 0 0
590590 0 0
591591 26.0000i 1.06950i
592592 0 0
593593 34.0000i 1.39621i 0.715994 + 0.698106i 0.245974π0.245974\pi
−0.715994 + 0.698106i 0.754026π0.754026\pi
594594 0 0
595595 16.0000 0.655936
596596 0 0
597597 0 0
598598 0 0
599599 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
600600 0 0
601601 −14.0000 −0.571072 −0.285536 0.958368i 0.592172π-0.592172\pi
−0.285536 + 0.958368i 0.592172π0.592172\pi
602602 0 0
603603 4.00000i 0.162893i
604604 0 0
605605 50.0000i 2.03279i
606606 0 0
607607 −4.00000 −0.162355 −0.0811775 0.996700i 0.525868π-0.525868\pi
−0.0811775 + 0.996700i 0.525868π0.525868\pi
608608 0 0
609609 8.00000i 0.324176i
610610 0 0
611611 −12.0000 + 18.0000i −0.485468 + 0.728202i
612612 0 0
613613 16.0000i 0.646234i 0.946359 + 0.323117i 0.104731π0.104731\pi
−0.946359 + 0.323117i 0.895269π0.895269\pi
614614 0 0
615615 −4.00000 −0.161296
616616 0 0
617617 14.0000i 0.563619i −0.959470 0.281809i 0.909065π-0.909065\pi
0.959470 0.281809i 0.0909346π-0.0909346\pi
618618 0 0
619619 20.0000i 0.803868i 0.915669 + 0.401934i 0.131662π0.131662\pi
−0.915669 + 0.401934i 0.868338π0.868338\pi
620620 0 0
621621 8.00000 0.321029
622622 0 0
623623 24.0000 0.961540
624624 0 0
625625 −19.0000 −0.760000
626626 0 0
627627 0 0
628628 0 0
629629 16.0000i 0.637962i
630630 0 0
631631 8.00000i 0.318475i −0.987240 0.159237i 0.949096π-0.949096\pi
0.987240 0.159237i 0.0509036π-0.0509036\pi
632632 0 0
633633 12.0000 0.476957
634634 0 0
635635 16.0000i 0.634941i
636636 0 0
637637 27.0000 + 18.0000i 1.06978 + 0.713186i
638638 0 0
639639 6.00000i 0.237356i
640640 0 0
641641 −42.0000 −1.65890 −0.829450 0.558581i 0.811346π-0.811346\pi
−0.829450 + 0.558581i 0.811346π0.811346\pi
642642 0 0
643643 36.0000i 1.41970i −0.704352 0.709851i 0.748762π-0.748762\pi
0.704352 0.709851i 0.251238π-0.251238\pi
644644 0 0
645645 16.0000i 0.629999i
646646 0 0
647647 32.0000 1.25805 0.629025 0.777385i 0.283454π-0.283454\pi
0.629025 + 0.777385i 0.283454π0.283454\pi
648648 0 0
649649 −12.0000 −0.471041
650650 0 0
651651 32.0000 1.25418
652652 0 0
653653 14.0000 0.547862 0.273931 0.961749i 0.411676π-0.411676\pi
0.273931 + 0.961749i 0.411676π0.411676\pi
654654 0 0
655655 8.00000i 0.312586i
656656 0 0
657657 4.00000i 0.156055i
658658 0 0
659659 20.0000 0.779089 0.389545 0.921008i 0.372632π-0.372632\pi
0.389545 + 0.921008i 0.372632π0.372632\pi
660660 0 0
661661 32.0000i 1.24466i 0.782757 + 0.622328i 0.213813π0.213813\pi
−0.782757 + 0.622328i 0.786187π0.786187\pi
662662 0 0
663663 6.00000 + 4.00000i 0.233021 + 0.155347i
664664 0 0
665665 0 0
666666 0 0
667667 −16.0000 −0.619522
668668 0 0
669669 8.00000i 0.309298i
670670 0 0
671671 12.0000i 0.463255i
672672 0 0
673673 30.0000 1.15642 0.578208 0.815890i 0.303752π-0.303752\pi
0.578208 + 0.815890i 0.303752π0.303752\pi
674674 0 0
675675 1.00000 0.0384900
676676 0 0
677677 18.0000 0.691796 0.345898 0.938272i 0.387574π-0.387574\pi
0.345898 + 0.938272i 0.387574π0.387574\pi
678678 0 0
679679 −48.0000 −1.84207
680680 0 0
681681 2.00000i 0.0766402i
682682 0 0
683683 6.00000i 0.229584i 0.993390 + 0.114792i 0.0366201π0.0366201\pi
−0.993390 + 0.114792i 0.963380π0.963380\pi
684684 0 0
685685 20.0000 0.764161
686686 0 0
687687 20.0000i 0.763048i
688688 0 0
689689 18.0000 + 12.0000i 0.685745 + 0.457164i
690690 0 0
691691 4.00000i 0.152167i 0.997101 + 0.0760836i 0.0242416π0.0242416\pi
−0.997101 + 0.0760836i 0.975758π0.975758\pi
692692 0 0
693693 −24.0000 −0.911685
694694 0 0
695695 16.0000i 0.606915i
696696 0 0
697697 4.00000i 0.151511i
698698 0 0
699699 18.0000 0.680823
700700 0 0
701701 −10.0000 −0.377695 −0.188847 0.982006i 0.560475π-0.560475\pi
−0.188847 + 0.982006i 0.560475π0.560475\pi
702702 0 0
703703 0 0
704704 0 0
705705 12.0000 0.451946
706706 0 0
707707 40.0000i 1.50435i
708708 0 0
709709 36.0000i 1.35201i 0.736898 + 0.676004i 0.236290π0.236290\pi
−0.736898 + 0.676004i 0.763710π0.763710\pi
710710 0 0
711711 0 0
712712 0 0
713713 64.0000i 2.39682i
714714 0 0
715715 36.0000 + 24.0000i 1.34632 + 0.897549i
716716 0 0
717717 10.0000i 0.373457i
718718 0 0
719719 16.0000 0.596699 0.298350 0.954457i 0.403564π-0.403564\pi
0.298350 + 0.954457i 0.403564π0.403564\pi
720720 0 0
721721 16.0000i 0.595871i
722722 0 0
723723 20.0000i 0.743808i
724724 0 0
725725 −2.00000 −0.0742781
726726 0 0
727727 −8.00000 −0.296704 −0.148352 0.988935i 0.547397π-0.547397\pi
−0.148352 + 0.988935i 0.547397π0.547397\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 16.0000 0.591781
732732 0 0
733733 20.0000i 0.738717i −0.929287 0.369358i 0.879577π-0.879577\pi
0.929287 0.369358i 0.120423π-0.120423\pi
734734 0 0
735735 18.0000i 0.663940i
736736 0 0
737737 24.0000 0.884051
738738 0 0
739739 28.0000i 1.03000i −0.857191 0.514998i 0.827793π-0.827793\pi
0.857191 0.514998i 0.172207π-0.172207\pi
740740 0 0
741741 0 0
742742 0 0
743743 22.0000i 0.807102i 0.914957 + 0.403551i 0.132224π0.132224\pi
−0.914957 + 0.403551i 0.867776π0.867776\pi
744744 0 0
745745 20.0000 0.732743
746746 0 0
747747 14.0000i 0.512233i
748748 0 0
749749 80.0000i 2.92314i
750750 0 0
751751 −20.0000 −0.729810 −0.364905 0.931045i 0.618899π-0.618899\pi
−0.364905 + 0.931045i 0.618899π0.618899\pi
752752 0 0
753753 20.0000 0.728841
754754 0 0
755755 −32.0000 −1.16460
756756 0 0
757757 −2.00000 −0.0726912 −0.0363456 0.999339i 0.511572π-0.511572\pi
−0.0363456 + 0.999339i 0.511572π0.511572\pi
758758 0 0
759759 48.0000i 1.74229i
760760 0 0
761761 30.0000i 1.08750i 0.839248 + 0.543750i 0.182996π0.182996\pi
−0.839248 + 0.543750i 0.817004π0.817004\pi
762762 0 0
763763 −16.0000 −0.579239
764764 0 0
765765 4.00000i 0.144620i
766766 0 0
767767 4.00000 6.00000i 0.144432 0.216647i
768768 0 0
769769 0 0 1.00000 00
−1.00000 π\pi
770770 0 0
771771 −6.00000 −0.216085
772772 0 0
773773 18.0000i 0.647415i −0.946157 0.323708i 0.895071π-0.895071\pi
0.946157 0.323708i 0.104929π-0.104929\pi
774774 0 0
775775 8.00000i 0.287368i
776776 0 0
777777 −32.0000 −1.14799
778778 0 0
779779 0 0
780780 0 0
781781 −36.0000 −1.28818
782782 0 0
783783 −2.00000 −0.0714742
784784 0 0
785785 28.0000i 0.999363i
786786 0 0
787787 44.0000i 1.56843i −0.620489 0.784215i 0.713066π-0.713066\pi
0.620489 0.784215i 0.286934π-0.286934\pi
788788 0 0
789789 0 0
790790 0 0
791791 40.0000i 1.42224i
792792 0 0
793793 6.00000 + 4.00000i 0.213066 + 0.142044i
794794 0 0
795795 12.0000i 0.425596i
796796 0 0
797797 −10.0000 −0.354218 −0.177109 0.984191i 0.556675π-0.556675\pi
−0.177109 + 0.984191i 0.556675π0.556675\pi
798798 0 0
799799 12.0000i 0.424529i
800800 0 0
801801 6.00000i 0.212000i
802802 0 0
803803 −24.0000 −0.846942
804804 0 0
805805 −64.0000 −2.25570
806806 0 0
807807 22.0000 0.774437
808808 0 0
809809 22.0000 0.773479 0.386739 0.922189i 0.373601π-0.373601\pi
0.386739 + 0.922189i 0.373601π0.373601\pi
810810 0 0
811811 40.0000i 1.40459i −0.711886 0.702295i 0.752159π-0.752159\pi
0.711886 0.702295i 0.247841π-0.247841\pi
812812 0 0
813813 20.0000i 0.701431i
814814 0 0
815815 −16.0000 −0.560456
816816 0 0
817817 0 0
818818 0 0
819819 8.00000 12.0000i 0.279543 0.419314i
820820 0 0
821821 30.0000i 1.04701i 0.852023 + 0.523504i 0.175375π0.175375\pi
−0.852023 + 0.523504i 0.824625π0.824625\pi
822822 0 0
823823 36.0000 1.25488 0.627441 0.778664i 0.284103π-0.284103\pi
0.627441 + 0.778664i 0.284103π0.284103\pi
824824 0 0
825825 6.00000i 0.208893i
826826 0 0
827827 18.0000i 0.625921i −0.949766 0.312961i 0.898679π-0.898679\pi
0.949766 0.312961i 0.101321π-0.101321\pi
828828 0 0
829829 54.0000 1.87550 0.937749 0.347314i 0.112906π-0.112906\pi
0.937749 + 0.347314i 0.112906π0.112906\pi
830830 0 0
831831 −22.0000 −0.763172
832832 0 0
833833 18.0000 0.623663
834834 0 0
835835 −36.0000 −1.24583
836836 0 0
837837 8.00000i 0.276520i
838838 0 0
839839 10.0000i 0.345238i −0.984989 0.172619i 0.944777π-0.944777\pi
0.984989 0.172619i 0.0552230π-0.0552230\pi
840840 0 0
841841 −25.0000 −0.862069
842842 0 0
843843 22.0000i 0.757720i
844844 0 0
845845 −24.0000 + 10.0000i −0.825625 + 0.344010i
846846 0 0
847847 100.000i 3.43604i
848848 0 0
849849 4.00000 0.137280
850850 0 0
851851 64.0000i 2.19389i
852852 0 0
853853 16.0000i 0.547830i −0.961754 0.273915i 0.911681π-0.911681\pi
0.961754 0.273915i 0.0883186π-0.0883186\pi
854854 0 0
855855 0 0
856856 0 0
857857 −22.0000 −0.751506 −0.375753 0.926720i 0.622616π-0.622616\pi
−0.375753 + 0.926720i 0.622616π0.622616\pi
858858 0 0
859859 52.0000 1.77422 0.887109 0.461561i 0.152710π-0.152710\pi
0.887109 + 0.461561i 0.152710π0.152710\pi
860860 0 0
861861 −8.00000 −0.272639
862862 0 0
863863 34.0000i 1.15737i 0.815550 + 0.578687i 0.196435π0.196435\pi
−0.815550 + 0.578687i 0.803565π0.803565\pi
864864 0 0
865865 12.0000i 0.408012i
866866 0 0
867867 −13.0000 −0.441503
868868 0 0
869869 0 0
870870 0 0
871871 −8.00000 + 12.0000i −0.271070 + 0.406604i
872872 0 0
873873 12.0000i 0.406138i
874874 0 0
875875 −48.0000 −1.62270
876876 0 0
877877 16.0000i 0.540282i −0.962821 0.270141i 0.912930π-0.912930\pi
0.962821 0.270141i 0.0870703π-0.0870703\pi
878878 0 0
879879 14.0000i 0.472208i
880880 0 0
881881 42.0000 1.41502 0.707508 0.706705i 0.249819π-0.249819\pi
0.707508 + 0.706705i 0.249819π0.249819\pi
882882 0 0
883883 −12.0000 −0.403832 −0.201916 0.979403i 0.564717π-0.564717\pi
−0.201916 + 0.979403i 0.564717π0.564717\pi
884884 0 0
885885 −4.00000 −0.134459
886886 0 0
887887 −24.0000 −0.805841 −0.402921 0.915235i 0.632005π-0.632005\pi
−0.402921 + 0.915235i 0.632005π0.632005\pi
888888 0 0
889889 32.0000i 1.07325i
890890 0 0
891891 6.00000i 0.201008i
892892 0 0
893893 0 0
894894 0 0
895895 24.0000i 0.802232i
896896 0 0
897897 −24.0000 16.0000i −0.801337 0.534224i
898898 0 0
899899 16.0000i 0.533630i
900900 0 0
901901 12.0000 0.399778
902902 0 0
903903 32.0000i 1.06489i
904904 0 0
905905 20.0000i 0.664822i
906906 0 0
907907 −44.0000 −1.46100 −0.730498 0.682915i 0.760712π-0.760712\pi
−0.730498 + 0.682915i 0.760712π0.760712\pi
908908 0 0
909909 10.0000 0.331679
910910 0 0
911911 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
912912 0 0
913913 84.0000 2.77999
914914 0 0
915915 4.00000i 0.132236i
916916 0 0
917917 16.0000i 0.528367i
918918 0 0
919919 24.0000 0.791687 0.395843 0.918318i 0.370452π-0.370452\pi
0.395843 + 0.918318i 0.370452π0.370452\pi
920920 0 0
921921 20.0000i 0.659022i
922922 0 0
923923 12.0000 18.0000i 0.394985 0.592477i
924924 0 0
925925 8.00000i 0.263038i
926926 0 0
927927 4.00000 0.131377
928928 0 0
929929 30.0000i 0.984268i −0.870519 0.492134i 0.836217π-0.836217\pi
0.870519 0.492134i 0.163783π-0.163783\pi
930930 0 0
931931 0 0
932932 0 0
933933 16.0000 0.523816
934934 0 0
935935 24.0000 0.784884
936936 0 0
937937 −50.0000 −1.63343 −0.816714 0.577042i 0.804207π-0.804207\pi
−0.816714 + 0.577042i 0.804207π0.804207\pi
938938 0 0
939939 −14.0000 −0.456873
940940 0 0
941941 38.0000i 1.23876i 0.785090 + 0.619382i 0.212617π0.212617\pi
−0.785090 + 0.619382i 0.787383π0.787383\pi
942942 0 0
943943 16.0000i 0.521032i
944944 0 0
945945 −8.00000 −0.260240
946946 0 0
947947 38.0000i 1.23483i −0.786636 0.617417i 0.788179π-0.788179\pi
0.786636 0.617417i 0.211821π-0.211821\pi
948948 0 0
949949 8.00000 12.0000i 0.259691 0.389536i
950950 0 0
951951 18.0000i 0.583690i
952952 0 0
953953 −54.0000 −1.74923 −0.874616 0.484817i 0.838886π-0.838886\pi
−0.874616 + 0.484817i 0.838886π0.838886\pi
954954 0 0
955955 48.0000i 1.55324i
956956 0 0
957957 12.0000i 0.387905i
958958 0 0
959959 40.0000 1.29167
960960 0 0
961961 −33.0000 −1.06452
962962 0 0
963963 20.0000 0.644491
964964 0 0
965965 −16.0000 −0.515058
966966 0 0
967967 8.00000i 0.257263i 0.991692 + 0.128631i 0.0410584π0.0410584\pi
−0.991692 + 0.128631i 0.958942π0.958942\pi
968968 0 0
969969 0 0
970970 0 0
971971 −12.0000 −0.385098 −0.192549 0.981287i 0.561675π-0.561675\pi
−0.192549 + 0.981287i 0.561675π0.561675\pi
972972 0 0
973973 32.0000i 1.02587i
974974 0 0
975975 −3.00000 2.00000i −0.0960769 0.0640513i
976976 0 0
977977 30.0000i 0.959785i 0.877327 + 0.479893i 0.159324π0.159324\pi
−0.877327 + 0.479893i 0.840676π0.840676\pi
978978 0 0
979979 36.0000 1.15056
980980 0 0
981981 4.00000i 0.127710i
982982 0 0
983983 18.0000i 0.574111i −0.957914 0.287055i 0.907324π-0.907324\pi
0.957914 0.287055i 0.0926764π-0.0926764\pi
984984 0 0
985985 −52.0000 −1.65686
986986 0 0
987987 24.0000 0.763928
988988 0 0
989989 −64.0000 −2.03508
990990 0 0
991991 44.0000 1.39771 0.698853 0.715265i 0.253694π-0.253694\pi
0.698853 + 0.715265i 0.253694π0.253694\pi
992992 0 0
993993 28.0000i 0.888553i
994994 0 0
995995 0 0
996996 0 0
997997 −6.00000 −0.190022 −0.0950110 0.995476i 0.530289π-0.530289\pi
−0.0950110 + 0.995476i 0.530289π0.530289\pi
998998 0 0
999999 8.00000i 0.253109i
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 2496.2.c.i.961.2 2
4.3 odd 2 2496.2.c.b.961.2 2
8.3 odd 2 156.2.b.b.25.1 2
8.5 even 2 624.2.c.d.337.1 2
13.12 even 2 inner 2496.2.c.i.961.1 2
24.5 odd 2 1872.2.c.h.1585.2 2
24.11 even 2 468.2.b.c.181.2 2
40.3 even 4 3900.2.j.b.649.2 2
40.19 odd 2 3900.2.c.a.3301.2 2
40.27 even 4 3900.2.j.e.649.1 2
52.51 odd 2 2496.2.c.b.961.1 2
56.27 even 2 7644.2.e.b.4705.2 2
104.3 odd 6 2028.2.q.e.1837.1 4
104.5 odd 4 8112.2.a.d.1.1 1
104.11 even 12 2028.2.i.d.529.1 2
104.19 even 12 2028.2.i.a.2005.1 2
104.21 odd 4 8112.2.a.l.1.1 1
104.35 odd 6 2028.2.q.e.361.1 4
104.43 odd 6 2028.2.q.e.361.2 4
104.51 odd 2 156.2.b.b.25.2 yes 2
104.59 even 12 2028.2.i.d.2005.1 2
104.67 even 12 2028.2.i.a.529.1 2
104.75 odd 6 2028.2.q.e.1837.2 4
104.77 even 2 624.2.c.d.337.2 2
104.83 even 4 2028.2.a.d.1.1 1
104.99 even 4 2028.2.a.f.1.1 1
312.77 odd 2 1872.2.c.h.1585.1 2
312.83 odd 4 6084.2.a.n.1.1 1
312.155 even 2 468.2.b.c.181.1 2
312.203 odd 4 6084.2.a.d.1.1 1
520.259 odd 2 3900.2.c.a.3301.1 2
520.363 even 4 3900.2.j.e.649.2 2
520.467 even 4 3900.2.j.b.649.1 2
728.363 even 2 7644.2.e.b.4705.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
156.2.b.b.25.1 2 8.3 odd 2
156.2.b.b.25.2 yes 2 104.51 odd 2
468.2.b.c.181.1 2 312.155 even 2
468.2.b.c.181.2 2 24.11 even 2
624.2.c.d.337.1 2 8.5 even 2
624.2.c.d.337.2 2 104.77 even 2
1872.2.c.h.1585.1 2 312.77 odd 2
1872.2.c.h.1585.2 2 24.5 odd 2
2028.2.a.d.1.1 1 104.83 even 4
2028.2.a.f.1.1 1 104.99 even 4
2028.2.i.a.529.1 2 104.67 even 12
2028.2.i.a.2005.1 2 104.19 even 12
2028.2.i.d.529.1 2 104.11 even 12
2028.2.i.d.2005.1 2 104.59 even 12
2028.2.q.e.361.1 4 104.35 odd 6
2028.2.q.e.361.2 4 104.43 odd 6
2028.2.q.e.1837.1 4 104.3 odd 6
2028.2.q.e.1837.2 4 104.75 odd 6
2496.2.c.b.961.1 2 52.51 odd 2
2496.2.c.b.961.2 2 4.3 odd 2
2496.2.c.i.961.1 2 13.12 even 2 inner
2496.2.c.i.961.2 2 1.1 even 1 trivial
3900.2.c.a.3301.1 2 520.259 odd 2
3900.2.c.a.3301.2 2 40.19 odd 2
3900.2.j.b.649.1 2 520.467 even 4
3900.2.j.b.649.2 2 40.3 even 4
3900.2.j.e.649.1 2 40.27 even 4
3900.2.j.e.649.2 2 520.363 even 4
6084.2.a.d.1.1 1 312.203 odd 4
6084.2.a.n.1.1 1 312.83 odd 4
7644.2.e.b.4705.1 2 728.363 even 2
7644.2.e.b.4705.2 2 56.27 even 2
8112.2.a.d.1.1 1 104.5 odd 4
8112.2.a.l.1.1 1 104.21 odd 4