Properties

Label 880.2.a.o.1.2
Level 880880
Weight 22
Character 880.1
Self dual yes
Analytic conductor 7.0277.027
Analytic rank 00
Dimension 22
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [880,2,Mod(1,880)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(880, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("880.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 880=24511 880 = 2^{4} \cdot 5 \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 880.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 7.026835377877.02683537787
Analytic rank: 00
Dimension: 22
Coefficient field: Q(17)\Q(\sqrt{17})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x4 x^{2} - x - 4 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 440)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 2.561552.56155 of defining polynomial
Character χ\chi == 880.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+2.56155q3+1.00000q5+2.56155q7+3.56155q91.00000q11+2.00000q13+2.56155q150.561553q172.56155q19+6.56155q215.12311q23+1.00000q25+1.43845q27+9.68466q296.56155q312.56155q33+2.56155q355.68466q37+5.12311q39+2.00000q4110.2462q43+3.56155q45+13.1231q470.438447q491.43845q51+4.56155q531.00000q556.56155q571.12311q59+2.31534q61+9.12311q63+2.00000q656.24621q6713.1231q693.68466q712.00000q73+2.56155q752.56155q77+15.3693q797.00000q815.12311q830.561553q85+24.8078q8712.5616q89+5.12311q9116.8078q932.56155q95+7.12311q973.56155q99+O(q100)q+2.56155 q^{3} +1.00000 q^{5} +2.56155 q^{7} +3.56155 q^{9} -1.00000 q^{11} +2.00000 q^{13} +2.56155 q^{15} -0.561553 q^{17} -2.56155 q^{19} +6.56155 q^{21} -5.12311 q^{23} +1.00000 q^{25} +1.43845 q^{27} +9.68466 q^{29} -6.56155 q^{31} -2.56155 q^{33} +2.56155 q^{35} -5.68466 q^{37} +5.12311 q^{39} +2.00000 q^{41} -10.2462 q^{43} +3.56155 q^{45} +13.1231 q^{47} -0.438447 q^{49} -1.43845 q^{51} +4.56155 q^{53} -1.00000 q^{55} -6.56155 q^{57} -1.12311 q^{59} +2.31534 q^{61} +9.12311 q^{63} +2.00000 q^{65} -6.24621 q^{67} -13.1231 q^{69} -3.68466 q^{71} -2.00000 q^{73} +2.56155 q^{75} -2.56155 q^{77} +15.3693 q^{79} -7.00000 q^{81} -5.12311 q^{83} -0.561553 q^{85} +24.8078 q^{87} -12.5616 q^{89} +5.12311 q^{91} -16.8078 q^{93} -2.56155 q^{95} +7.12311 q^{97} -3.56155 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+q3+2q5+q7+3q92q11+4q13+q15+3q17q19+9q212q23+2q25+7q27+7q299q31q33+q35+q37+2q39+3q99+O(q100) 2 q + q^{3} + 2 q^{5} + q^{7} + 3 q^{9} - 2 q^{11} + 4 q^{13} + q^{15} + 3 q^{17} - q^{19} + 9 q^{21} - 2 q^{23} + 2 q^{25} + 7 q^{27} + 7 q^{29} - 9 q^{31} - q^{33} + q^{35} + q^{37} + 2 q^{39}+ \cdots - 3 q^{99}+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 0 0
33 2.56155 1.47891 0.739457 0.673204i 0.235083π-0.235083\pi
0.739457 + 0.673204i 0.235083π0.235083\pi
44 0 0
55 1.00000 0.447214
66 0 0
77 2.56155 0.968176 0.484088 0.875019i 0.339151π-0.339151\pi
0.484088 + 0.875019i 0.339151π0.339151\pi
88 0 0
99 3.56155 1.18718
1010 0 0
1111 −1.00000 −0.301511
1212 0 0
1313 2.00000 0.554700 0.277350 0.960769i 0.410544π-0.410544\pi
0.277350 + 0.960769i 0.410544π0.410544\pi
1414 0 0
1515 2.56155 0.661390
1616 0 0
1717 −0.561553 −0.136197 −0.0680983 0.997679i 0.521693π-0.521693\pi
−0.0680983 + 0.997679i 0.521693π0.521693\pi
1818 0 0
1919 −2.56155 −0.587661 −0.293830 0.955858i 0.594930π-0.594930\pi
−0.293830 + 0.955858i 0.594930π0.594930\pi
2020 0 0
2121 6.56155 1.43185
2222 0 0
2323 −5.12311 −1.06824 −0.534121 0.845408i 0.679357π-0.679357\pi
−0.534121 + 0.845408i 0.679357π0.679357\pi
2424 0 0
2525 1.00000 0.200000
2626 0 0
2727 1.43845 0.276829
2828 0 0
2929 9.68466 1.79840 0.899198 0.437542i 0.144151π-0.144151\pi
0.899198 + 0.437542i 0.144151π0.144151\pi
3030 0 0
3131 −6.56155 −1.17849 −0.589245 0.807955i 0.700575π-0.700575\pi
−0.589245 + 0.807955i 0.700575π0.700575\pi
3232 0 0
3333 −2.56155 −0.445909
3434 0 0
3535 2.56155 0.432981
3636 0 0
3737 −5.68466 −0.934552 −0.467276 0.884111i 0.654765π-0.654765\pi
−0.467276 + 0.884111i 0.654765π0.654765\pi
3838 0 0
3939 5.12311 0.820353
4040 0 0
4141 2.00000 0.312348 0.156174 0.987730i 0.450084π-0.450084\pi
0.156174 + 0.987730i 0.450084π0.450084\pi
4242 0 0
4343 −10.2462 −1.56253 −0.781266 0.624198i 0.785426π-0.785426\pi
−0.781266 + 0.624198i 0.785426π0.785426\pi
4444 0 0
4545 3.56155 0.530925
4646 0 0
4747 13.1231 1.91420 0.957101 0.289755i 0.0935738π-0.0935738\pi
0.957101 + 0.289755i 0.0935738π0.0935738\pi
4848 0 0
4949 −0.438447 −0.0626353
5050 0 0
5151 −1.43845 −0.201423
5252 0 0
5353 4.56155 0.626577 0.313289 0.949658i 0.398569π-0.398569\pi
0.313289 + 0.949658i 0.398569π0.398569\pi
5454 0 0
5555 −1.00000 −0.134840
5656 0 0
5757 −6.56155 −0.869099
5858 0 0
5959 −1.12311 −0.146216 −0.0731079 0.997324i 0.523292π-0.523292\pi
−0.0731079 + 0.997324i 0.523292π0.523292\pi
6060 0 0
6161 2.31534 0.296449 0.148225 0.988954i 0.452644π-0.452644\pi
0.148225 + 0.988954i 0.452644π0.452644\pi
6262 0 0
6363 9.12311 1.14940
6464 0 0
6565 2.00000 0.248069
6666 0 0
6767 −6.24621 −0.763096 −0.381548 0.924349i 0.624609π-0.624609\pi
−0.381548 + 0.924349i 0.624609π0.624609\pi
6868 0 0
6969 −13.1231 −1.57984
7070 0 0
7171 −3.68466 −0.437289 −0.218644 0.975805i 0.570163π-0.570163\pi
−0.218644 + 0.975805i 0.570163π0.570163\pi
7272 0 0
7373 −2.00000 −0.234082 −0.117041 0.993127i 0.537341π-0.537341\pi
−0.117041 + 0.993127i 0.537341π0.537341\pi
7474 0 0
7575 2.56155 0.295783
7676 0 0
7777 −2.56155 −0.291916
7878 0 0
7979 15.3693 1.72918 0.864592 0.502475i 0.167577π-0.167577\pi
0.864592 + 0.502475i 0.167577π0.167577\pi
8080 0 0
8181 −7.00000 −0.777778
8282 0 0
8383 −5.12311 −0.562334 −0.281167 0.959659i 0.590721π-0.590721\pi
−0.281167 + 0.959659i 0.590721π0.590721\pi
8484 0 0
8585 −0.561553 −0.0609090
8686 0 0
8787 24.8078 2.65967
8888 0 0
8989 −12.5616 −1.33152 −0.665761 0.746165i 0.731893π-0.731893\pi
−0.665761 + 0.746165i 0.731893π0.731893\pi
9090 0 0
9191 5.12311 0.537047
9292 0 0
9393 −16.8078 −1.74288
9494 0 0
9595 −2.56155 −0.262810
9696 0 0
9797 7.12311 0.723242 0.361621 0.932325i 0.382223π-0.382223\pi
0.361621 + 0.932325i 0.382223π0.382223\pi
9898 0 0
9999 −3.56155 −0.357950
100100 0 0
101101 −4.24621 −0.422514 −0.211257 0.977431i 0.567756π-0.567756\pi
−0.211257 + 0.977431i 0.567756π0.567756\pi
102102 0 0
103103 −10.2462 −1.00959 −0.504795 0.863239i 0.668432π-0.668432\pi
−0.504795 + 0.863239i 0.668432π0.668432\pi
104104 0 0
105105 6.56155 0.640342
106106 0 0
107107 16.0000 1.54678 0.773389 0.633932i 0.218560π-0.218560\pi
0.773389 + 0.633932i 0.218560π0.218560\pi
108108 0 0
109109 18.4924 1.77125 0.885626 0.464398i 0.153729π-0.153729\pi
0.885626 + 0.464398i 0.153729π0.153729\pi
110110 0 0
111111 −14.5616 −1.38212
112112 0 0
113113 −19.1231 −1.79895 −0.899475 0.436972i 0.856051π-0.856051\pi
−0.899475 + 0.436972i 0.856051π0.856051\pi
114114 0 0
115115 −5.12311 −0.477732
116116 0 0
117117 7.12311 0.658531
118118 0 0
119119 −1.43845 −0.131862
120120 0 0
121121 1.00000 0.0909091
122122 0 0
123123 5.12311 0.461935
124124 0 0
125125 1.00000 0.0894427
126126 0 0
127127 −14.2462 −1.26415 −0.632073 0.774909i 0.717796π-0.717796\pi
−0.632073 + 0.774909i 0.717796π0.717796\pi
128128 0 0
129129 −26.2462 −2.31085
130130 0 0
131131 7.68466 0.671412 0.335706 0.941967i 0.391025π-0.391025\pi
0.335706 + 0.941967i 0.391025π0.391025\pi
132132 0 0
133133 −6.56155 −0.568959
134134 0 0
135135 1.43845 0.123802
136136 0 0
137137 19.6155 1.67587 0.837934 0.545772i 0.183763π-0.183763\pi
0.837934 + 0.545772i 0.183763π0.183763\pi
138138 0 0
139139 −12.0000 −1.01783 −0.508913 0.860818i 0.669953π-0.669953\pi
−0.508913 + 0.860818i 0.669953π0.669953\pi
140140 0 0
141141 33.6155 2.83094
142142 0 0
143143 −2.00000 −0.167248
144144 0 0
145145 9.68466 0.804267
146146 0 0
147147 −1.12311 −0.0926322
148148 0 0
149149 2.31534 0.189680 0.0948401 0.995493i 0.469766π-0.469766\pi
0.0948401 + 0.995493i 0.469766π0.469766\pi
150150 0 0
151151 −13.1231 −1.06794 −0.533972 0.845502i 0.679301π-0.679301\pi
−0.533972 + 0.845502i 0.679301π0.679301\pi
152152 0 0
153153 −2.00000 −0.161690
154154 0 0
155155 −6.56155 −0.527037
156156 0 0
157157 14.8078 1.18179 0.590894 0.806749i 0.298775π-0.298775\pi
0.590894 + 0.806749i 0.298775π0.298775\pi
158158 0 0
159159 11.6847 0.926654
160160 0 0
161161 −13.1231 −1.03425
162162 0 0
163163 −3.19224 −0.250035 −0.125018 0.992155i 0.539899π-0.539899\pi
−0.125018 + 0.992155i 0.539899π0.539899\pi
164164 0 0
165165 −2.56155 −0.199417
166166 0 0
167167 10.5616 0.817277 0.408639 0.912696i 0.366004π-0.366004\pi
0.408639 + 0.912696i 0.366004π0.366004\pi
168168 0 0
169169 −9.00000 −0.692308
170170 0 0
171171 −9.12311 −0.697661
172172 0 0
173173 4.24621 0.322833 0.161417 0.986886i 0.448394π-0.448394\pi
0.161417 + 0.986886i 0.448394π0.448394\pi
174174 0 0
175175 2.56155 0.193635
176176 0 0
177177 −2.87689 −0.216241
178178 0 0
179179 6.24621 0.466864 0.233432 0.972373i 0.425004π-0.425004\pi
0.233432 + 0.972373i 0.425004π0.425004\pi
180180 0 0
181181 −4.24621 −0.315618 −0.157809 0.987470i 0.550443π-0.550443\pi
−0.157809 + 0.987470i 0.550443π0.550443\pi
182182 0 0
183183 5.93087 0.438423
184184 0 0
185185 −5.68466 −0.417944
186186 0 0
187187 0.561553 0.0410648
188188 0 0
189189 3.68466 0.268019
190190 0 0
191191 −10.2462 −0.741390 −0.370695 0.928755i 0.620880π-0.620880\pi
−0.370695 + 0.928755i 0.620880π0.620880\pi
192192 0 0
193193 5.19224 0.373745 0.186873 0.982384i 0.440165π-0.440165\pi
0.186873 + 0.982384i 0.440165π0.440165\pi
194194 0 0
195195 5.12311 0.366873
196196 0 0
197197 −5.36932 −0.382548 −0.191274 0.981537i 0.561262π-0.561262\pi
−0.191274 + 0.981537i 0.561262π0.561262\pi
198198 0 0
199199 0.807764 0.0572609 0.0286304 0.999590i 0.490885π-0.490885\pi
0.0286304 + 0.999590i 0.490885π0.490885\pi
200200 0 0
201201 −16.0000 −1.12855
202202 0 0
203203 24.8078 1.74116
204204 0 0
205205 2.00000 0.139686
206206 0 0
207207 −18.2462 −1.26820
208208 0 0
209209 2.56155 0.177186
210210 0 0
211211 −8.31534 −0.572452 −0.286226 0.958162i 0.592401π-0.592401\pi
−0.286226 + 0.958162i 0.592401π0.592401\pi
212212 0 0
213213 −9.43845 −0.646712
214214 0 0
215215 −10.2462 −0.698786
216216 0 0
217217 −16.8078 −1.14099
218218 0 0
219219 −5.12311 −0.346187
220220 0 0
221221 −1.12311 −0.0755483
222222 0 0
223223 −13.1231 −0.878788 −0.439394 0.898294i 0.644807π-0.644807\pi
−0.439394 + 0.898294i 0.644807π0.644807\pi
224224 0 0
225225 3.56155 0.237437
226226 0 0
227227 −2.87689 −0.190946 −0.0954731 0.995432i 0.530436π-0.530436\pi
−0.0954731 + 0.995432i 0.530436π0.530436\pi
228228 0 0
229229 −24.7386 −1.63477 −0.817387 0.576088i 0.804578π-0.804578\pi
−0.817387 + 0.576088i 0.804578π0.804578\pi
230230 0 0
231231 −6.56155 −0.431718
232232 0 0
233233 19.9309 1.30571 0.652857 0.757481i 0.273570π-0.273570\pi
0.652857 + 0.757481i 0.273570π0.273570\pi
234234 0 0
235235 13.1231 0.856057
236236 0 0
237237 39.3693 2.55731
238238 0 0
239239 −25.6155 −1.65693 −0.828465 0.560040i 0.810786π-0.810786\pi
−0.828465 + 0.560040i 0.810786π0.810786\pi
240240 0 0
241241 −16.2462 −1.04651 −0.523255 0.852176i 0.675283π-0.675283\pi
−0.523255 + 0.852176i 0.675283π0.675283\pi
242242 0 0
243243 −22.2462 −1.42710
244244 0 0
245245 −0.438447 −0.0280114
246246 0 0
247247 −5.12311 −0.325975
248248 0 0
249249 −13.1231 −0.831643
250250 0 0
251251 29.6155 1.86932 0.934658 0.355549i 0.115706π-0.115706\pi
0.934658 + 0.355549i 0.115706π0.115706\pi
252252 0 0
253253 5.12311 0.322087
254254 0 0
255255 −1.43845 −0.0900791
256256 0 0
257257 −28.7386 −1.79267 −0.896333 0.443381i 0.853779π-0.853779\pi
−0.896333 + 0.443381i 0.853779π0.853779\pi
258258 0 0
259259 −14.5616 −0.904811
260260 0 0
261261 34.4924 2.13503
262262 0 0
263263 −4.80776 −0.296459 −0.148230 0.988953i 0.547357π-0.547357\pi
−0.148230 + 0.988953i 0.547357π0.547357\pi
264264 0 0
265265 4.56155 0.280214
266266 0 0
267267 −32.1771 −1.96921
268268 0 0
269269 −19.6155 −1.19598 −0.597990 0.801504i 0.704034π-0.704034\pi
−0.597990 + 0.801504i 0.704034π0.704034\pi
270270 0 0
271271 −28.4924 −1.73079 −0.865396 0.501089i 0.832933π-0.832933\pi
−0.865396 + 0.501089i 0.832933π0.832933\pi
272272 0 0
273273 13.1231 0.794246
274274 0 0
275275 −1.00000 −0.0603023
276276 0 0
277277 7.12311 0.427986 0.213993 0.976835i 0.431353π-0.431353\pi
0.213993 + 0.976835i 0.431353π0.431353\pi
278278 0 0
279279 −23.3693 −1.39908
280280 0 0
281281 −8.24621 −0.491928 −0.245964 0.969279i 0.579104π-0.579104\pi
−0.245964 + 0.969279i 0.579104π0.579104\pi
282282 0 0
283283 23.3693 1.38916 0.694581 0.719415i 0.255590π-0.255590\pi
0.694581 + 0.719415i 0.255590π0.255590\pi
284284 0 0
285285 −6.56155 −0.388673
286286 0 0
287287 5.12311 0.302407
288288 0 0
289289 −16.6847 −0.981450
290290 0 0
291291 18.2462 1.06961
292292 0 0
293293 14.4924 0.846656 0.423328 0.905976i 0.360862π-0.360862\pi
0.423328 + 0.905976i 0.360862π0.360862\pi
294294 0 0
295295 −1.12311 −0.0653897
296296 0 0
297297 −1.43845 −0.0834672
298298 0 0
299299 −10.2462 −0.592554
300300 0 0
301301 −26.2462 −1.51281
302302 0 0
303303 −10.8769 −0.624861
304304 0 0
305305 2.31534 0.132576
306306 0 0
307307 25.6155 1.46196 0.730978 0.682401i 0.239064π-0.239064\pi
0.730978 + 0.682401i 0.239064π0.239064\pi
308308 0 0
309309 −26.2462 −1.49309
310310 0 0
311311 25.4384 1.44248 0.721241 0.692684i 0.243572π-0.243572\pi
0.721241 + 0.692684i 0.243572π0.243572\pi
312312 0 0
313313 30.4924 1.72353 0.861767 0.507305i 0.169358π-0.169358\pi
0.861767 + 0.507305i 0.169358π0.169358\pi
314314 0 0
315315 9.12311 0.514029
316316 0 0
317317 13.1922 0.740950 0.370475 0.928842i 0.379195π-0.379195\pi
0.370475 + 0.928842i 0.379195π0.379195\pi
318318 0 0
319319 −9.68466 −0.542237
320320 0 0
321321 40.9848 2.28755
322322 0 0
323323 1.43845 0.0800373
324324 0 0
325325 2.00000 0.110940
326326 0 0
327327 47.3693 2.61953
328328 0 0
329329 33.6155 1.85328
330330 0 0
331331 8.49242 0.466786 0.233393 0.972383i 0.425017π-0.425017\pi
0.233393 + 0.972383i 0.425017π0.425017\pi
332332 0 0
333333 −20.2462 −1.10949
334334 0 0
335335 −6.24621 −0.341267
336336 0 0
337337 2.31534 0.126125 0.0630623 0.998010i 0.479913π-0.479913\pi
0.0630623 + 0.998010i 0.479913π0.479913\pi
338338 0 0
339339 −48.9848 −2.66049
340340 0 0
341341 6.56155 0.355328
342342 0 0
343343 −19.0540 −1.02882
344344 0 0
345345 −13.1231 −0.706524
346346 0 0
347347 18.8769 1.01336 0.506682 0.862133i 0.330872π-0.330872\pi
0.506682 + 0.862133i 0.330872π0.330872\pi
348348 0 0
349349 10.4924 0.561646 0.280823 0.959760i 0.409393π-0.409393\pi
0.280823 + 0.959760i 0.409393π0.409393\pi
350350 0 0
351351 2.87689 0.153557
352352 0 0
353353 −34.4924 −1.83585 −0.917923 0.396758i 0.870135π-0.870135\pi
−0.917923 + 0.396758i 0.870135π0.870135\pi
354354 0 0
355355 −3.68466 −0.195561
356356 0 0
357357 −3.68466 −0.195013
358358 0 0
359359 −26.2462 −1.38522 −0.692611 0.721311i 0.743540π-0.743540\pi
−0.692611 + 0.721311i 0.743540π0.743540\pi
360360 0 0
361361 −12.4384 −0.654655
362362 0 0
363363 2.56155 0.134447
364364 0 0
365365 −2.00000 −0.104685
366366 0 0
367367 14.7386 0.769350 0.384675 0.923052i 0.374313π-0.374313\pi
0.384675 + 0.923052i 0.374313π0.374313\pi
368368 0 0
369369 7.12311 0.370814
370370 0 0
371371 11.6847 0.606637
372372 0 0
373373 2.00000 0.103556 0.0517780 0.998659i 0.483511π-0.483511\pi
0.0517780 + 0.998659i 0.483511π0.483511\pi
374374 0 0
375375 2.56155 0.132278
376376 0 0
377377 19.3693 0.997571
378378 0 0
379379 25.1231 1.29049 0.645244 0.763977i 0.276756π-0.276756\pi
0.645244 + 0.763977i 0.276756π0.276756\pi
380380 0 0
381381 −36.4924 −1.86956
382382 0 0
383383 31.3693 1.60290 0.801449 0.598064i 0.204063π-0.204063\pi
0.801449 + 0.598064i 0.204063π0.204063\pi
384384 0 0
385385 −2.56155 −0.130549
386386 0 0
387387 −36.4924 −1.85501
388388 0 0
389389 32.2462 1.63495 0.817474 0.575966i 0.195374π-0.195374\pi
0.817474 + 0.575966i 0.195374π0.195374\pi
390390 0 0
391391 2.87689 0.145491
392392 0 0
393393 19.6847 0.992960
394394 0 0
395395 15.3693 0.773314
396396 0 0
397397 −18.0000 −0.903394 −0.451697 0.892171i 0.649181π-0.649181\pi
−0.451697 + 0.892171i 0.649181π0.649181\pi
398398 0 0
399399 −16.8078 −0.841441
400400 0 0
401401 −7.43845 −0.371458 −0.185729 0.982601i 0.559465π-0.559465\pi
−0.185729 + 0.982601i 0.559465π0.559465\pi
402402 0 0
403403 −13.1231 −0.653708
404404 0 0
405405 −7.00000 −0.347833
406406 0 0
407407 5.68466 0.281778
408408 0 0
409409 7.12311 0.352215 0.176107 0.984371i 0.443649π-0.443649\pi
0.176107 + 0.984371i 0.443649π0.443649\pi
410410 0 0
411411 50.2462 2.47846
412412 0 0
413413 −2.87689 −0.141563
414414 0 0
415415 −5.12311 −0.251483
416416 0 0
417417 −30.7386 −1.50528
418418 0 0
419419 26.7386 1.30627 0.653134 0.757242i 0.273454π-0.273454\pi
0.653134 + 0.757242i 0.273454π0.273454\pi
420420 0 0
421421 7.61553 0.371158 0.185579 0.982629i 0.440584π-0.440584\pi
0.185579 + 0.982629i 0.440584π0.440584\pi
422422 0 0
423423 46.7386 2.27251
424424 0 0
425425 −0.561553 −0.0272393
426426 0 0
427427 5.93087 0.287015
428428 0 0
429429 −5.12311 −0.247346
430430 0 0
431431 16.0000 0.770693 0.385346 0.922772i 0.374082π-0.374082\pi
0.385346 + 0.922772i 0.374082π0.374082\pi
432432 0 0
433433 33.3693 1.60363 0.801814 0.597574i 0.203869π-0.203869\pi
0.801814 + 0.597574i 0.203869π0.203869\pi
434434 0 0
435435 24.8078 1.18944
436436 0 0
437437 13.1231 0.627763
438438 0 0
439439 34.2462 1.63448 0.817241 0.576296i 0.195502π-0.195502\pi
0.817241 + 0.576296i 0.195502π0.195502\pi
440440 0 0
441441 −1.56155 −0.0743597
442442 0 0
443443 4.00000 0.190046 0.0950229 0.995475i 0.469708π-0.469708\pi
0.0950229 + 0.995475i 0.469708π0.469708\pi
444444 0 0
445445 −12.5616 −0.595475
446446 0 0
447447 5.93087 0.280521
448448 0 0
449449 18.0000 0.849473 0.424736 0.905317i 0.360367π-0.360367\pi
0.424736 + 0.905317i 0.360367π0.360367\pi
450450 0 0
451451 −2.00000 −0.0941763
452452 0 0
453453 −33.6155 −1.57940
454454 0 0
455455 5.12311 0.240175
456456 0 0
457457 28.5616 1.33605 0.668027 0.744137i 0.267139π-0.267139\pi
0.668027 + 0.744137i 0.267139π0.267139\pi
458458 0 0
459459 −0.807764 −0.0377032
460460 0 0
461461 20.5616 0.957647 0.478823 0.877911i 0.341063π-0.341063\pi
0.478823 + 0.877911i 0.341063π0.341063\pi
462462 0 0
463463 7.36932 0.342481 0.171241 0.985229i 0.445222π-0.445222\pi
0.171241 + 0.985229i 0.445222π0.445222\pi
464464 0 0
465465 −16.8078 −0.779441
466466 0 0
467467 −9.93087 −0.459546 −0.229773 0.973244i 0.573798π-0.573798\pi
−0.229773 + 0.973244i 0.573798π0.573798\pi
468468 0 0
469469 −16.0000 −0.738811
470470 0 0
471471 37.9309 1.74776
472472 0 0
473473 10.2462 0.471121
474474 0 0
475475 −2.56155 −0.117532
476476 0 0
477477 16.2462 0.743863
478478 0 0
479479 32.9848 1.50712 0.753558 0.657381i 0.228336π-0.228336\pi
0.753558 + 0.657381i 0.228336π0.228336\pi
480480 0 0
481481 −11.3693 −0.518396
482482 0 0
483483 −33.6155 −1.52956
484484 0 0
485485 7.12311 0.323444
486486 0 0
487487 2.24621 0.101786 0.0508928 0.998704i 0.483793π-0.483793\pi
0.0508928 + 0.998704i 0.483793π0.483793\pi
488488 0 0
489489 −8.17708 −0.369780
490490 0 0
491491 −7.05398 −0.318341 −0.159171 0.987251i 0.550882π-0.550882\pi
−0.159171 + 0.987251i 0.550882π0.550882\pi
492492 0 0
493493 −5.43845 −0.244935
494494 0 0
495495 −3.56155 −0.160080
496496 0 0
497497 −9.43845 −0.423372
498498 0 0
499499 −16.4924 −0.738302 −0.369151 0.929369i 0.620352π-0.620352\pi
−0.369151 + 0.929369i 0.620352π0.620352\pi
500500 0 0
501501 27.0540 1.20868
502502 0 0
503503 14.2462 0.635207 0.317604 0.948224i 0.397122π-0.397122\pi
0.317604 + 0.948224i 0.397122π0.397122\pi
504504 0 0
505505 −4.24621 −0.188954
506506 0 0
507507 −23.0540 −1.02386
508508 0 0
509509 21.3693 0.947178 0.473589 0.880746i 0.342958π-0.342958\pi
0.473589 + 0.880746i 0.342958π0.342958\pi
510510 0 0
511511 −5.12311 −0.226633
512512 0 0
513513 −3.68466 −0.162682
514514 0 0
515515 −10.2462 −0.451502
516516 0 0
517517 −13.1231 −0.577154
518518 0 0
519519 10.8769 0.477443
520520 0 0
521521 8.73863 0.382846 0.191423 0.981508i 0.438690π-0.438690\pi
0.191423 + 0.981508i 0.438690π0.438690\pi
522522 0 0
523523 3.50758 0.153376 0.0766878 0.997055i 0.475566π-0.475566\pi
0.0766878 + 0.997055i 0.475566π0.475566\pi
524524 0 0
525525 6.56155 0.286370
526526 0 0
527527 3.68466 0.160506
528528 0 0
529529 3.24621 0.141140
530530 0 0
531531 −4.00000 −0.173585
532532 0 0
533533 4.00000 0.173259
534534 0 0
535535 16.0000 0.691740
536536 0 0
537537 16.0000 0.690451
538538 0 0
539539 0.438447 0.0188853
540540 0 0
541541 −33.5464 −1.44227 −0.721136 0.692793i 0.756380π-0.756380\pi
−0.721136 + 0.692793i 0.756380π0.756380\pi
542542 0 0
543543 −10.8769 −0.466772
544544 0 0
545545 18.4924 0.792128
546546 0 0
547547 16.0000 0.684111 0.342055 0.939680i 0.388877π-0.388877\pi
0.342055 + 0.939680i 0.388877π0.388877\pi
548548 0 0
549549 8.24621 0.351940
550550 0 0
551551 −24.8078 −1.05685
552552 0 0
553553 39.3693 1.67415
554554 0 0
555555 −14.5616 −0.618103
556556 0 0
557557 46.4924 1.96995 0.984974 0.172705i 0.0552508π-0.0552508\pi
0.984974 + 0.172705i 0.0552508π0.0552508\pi
558558 0 0
559559 −20.4924 −0.866737
560560 0 0
561561 1.43845 0.0607313
562562 0 0
563563 2.87689 0.121247 0.0606233 0.998161i 0.480691π-0.480691\pi
0.0606233 + 0.998161i 0.480691π0.480691\pi
564564 0 0
565565 −19.1231 −0.804515
566566 0 0
567567 −17.9309 −0.753026
568568 0 0
569569 −28.1080 −1.17835 −0.589173 0.808007i 0.700546π-0.700546\pi
−0.589173 + 0.808007i 0.700546π0.700546\pi
570570 0 0
571571 −30.4233 −1.27318 −0.636588 0.771204i 0.719655π-0.719655\pi
−0.636588 + 0.771204i 0.719655π0.719655\pi
572572 0 0
573573 −26.2462 −1.09645
574574 0 0
575575 −5.12311 −0.213648
576576 0 0
577577 24.7386 1.02988 0.514941 0.857225i 0.327814π-0.327814\pi
0.514941 + 0.857225i 0.327814π0.327814\pi
578578 0 0
579579 13.3002 0.552737
580580 0 0
581581 −13.1231 −0.544438
582582 0 0
583583 −4.56155 −0.188920
584584 0 0
585585 7.12311 0.294504
586586 0 0
587587 −32.3153 −1.33380 −0.666898 0.745149i 0.732379π-0.732379\pi
−0.666898 + 0.745149i 0.732379π0.732379\pi
588588 0 0
589589 16.8078 0.692552
590590 0 0
591591 −13.7538 −0.565755
592592 0 0
593593 1.50758 0.0619088 0.0309544 0.999521i 0.490145π-0.490145\pi
0.0309544 + 0.999521i 0.490145π0.490145\pi
594594 0 0
595595 −1.43845 −0.0589706
596596 0 0
597597 2.06913 0.0846839
598598 0 0
599599 17.4384 0.712516 0.356258 0.934388i 0.384052π-0.384052\pi
0.356258 + 0.934388i 0.384052π0.384052\pi
600600 0 0
601601 −30.0000 −1.22373 −0.611863 0.790964i 0.709580π-0.709580\pi
−0.611863 + 0.790964i 0.709580π0.709580\pi
602602 0 0
603603 −22.2462 −0.905936
604604 0 0
605605 1.00000 0.0406558
606606 0 0
607607 −20.8078 −0.844561 −0.422281 0.906465i 0.638770π-0.638770\pi
−0.422281 + 0.906465i 0.638770π0.638770\pi
608608 0 0
609609 63.5464 2.57503
610610 0 0
611611 26.2462 1.06181
612612 0 0
613613 16.7386 0.676067 0.338034 0.941134i 0.390238π-0.390238\pi
0.338034 + 0.941134i 0.390238π0.390238\pi
614614 0 0
615615 5.12311 0.206584
616616 0 0
617617 −6.63068 −0.266941 −0.133471 0.991053i 0.542612π-0.542612\pi
−0.133471 + 0.991053i 0.542612π0.542612\pi
618618 0 0
619619 8.49242 0.341339 0.170670 0.985328i 0.445407π-0.445407\pi
0.170670 + 0.985328i 0.445407π0.445407\pi
620620 0 0
621621 −7.36932 −0.295720
622622 0 0
623623 −32.1771 −1.28915
624624 0 0
625625 1.00000 0.0400000
626626 0 0
627627 6.56155 0.262043
628628 0 0
629629 3.19224 0.127283
630630 0 0
631631 16.8078 0.669107 0.334553 0.942377i 0.391415π-0.391415\pi
0.334553 + 0.942377i 0.391415π0.391415\pi
632632 0 0
633633 −21.3002 −0.846606
634634 0 0
635635 −14.2462 −0.565344
636636 0 0
637637 −0.876894 −0.0347438
638638 0 0
639639 −13.1231 −0.519142
640640 0 0
641641 −38.1771 −1.50790 −0.753952 0.656929i 0.771855π-0.771855\pi
−0.753952 + 0.656929i 0.771855π0.771855\pi
642642 0 0
643643 −23.6847 −0.934032 −0.467016 0.884249i 0.654671π-0.654671\pi
−0.467016 + 0.884249i 0.654671π0.654671\pi
644644 0 0
645645 −26.2462 −1.03344
646646 0 0
647647 13.1231 0.515923 0.257961 0.966155i 0.416949π-0.416949\pi
0.257961 + 0.966155i 0.416949π0.416949\pi
648648 0 0
649649 1.12311 0.0440858
650650 0 0
651651 −43.0540 −1.68742
652652 0 0
653653 −10.8078 −0.422940 −0.211470 0.977384i 0.567825π-0.567825\pi
−0.211470 + 0.977384i 0.567825π0.567825\pi
654654 0 0
655655 7.68466 0.300264
656656 0 0
657657 −7.12311 −0.277899
658658 0 0
659659 −19.1922 −0.747623 −0.373812 0.927505i 0.621949π-0.621949\pi
−0.373812 + 0.927505i 0.621949π0.621949\pi
660660 0 0
661661 16.2462 0.631904 0.315952 0.948775i 0.397676π-0.397676\pi
0.315952 + 0.948775i 0.397676π0.397676\pi
662662 0 0
663663 −2.87689 −0.111729
664664 0 0
665665 −6.56155 −0.254446
666666 0 0
667667 −49.6155 −1.92112
668668 0 0
669669 −33.6155 −1.29965
670670 0 0
671671 −2.31534 −0.0893828
672672 0 0
673673 −35.7926 −1.37970 −0.689852 0.723951i 0.742324π-0.742324\pi
−0.689852 + 0.723951i 0.742324π0.742324\pi
674674 0 0
675675 1.43845 0.0553659
676676 0 0
677677 27.6155 1.06135 0.530675 0.847575i 0.321938π-0.321938\pi
0.530675 + 0.847575i 0.321938π0.321938\pi
678678 0 0
679679 18.2462 0.700225
680680 0 0
681681 −7.36932 −0.282393
682682 0 0
683683 25.9309 0.992217 0.496109 0.868260i 0.334762π-0.334762\pi
0.496109 + 0.868260i 0.334762π0.334762\pi
684684 0 0
685685 19.6155 0.749471
686686 0 0
687687 −63.3693 −2.41769
688688 0 0
689689 9.12311 0.347563
690690 0 0
691691 −3.36932 −0.128175 −0.0640874 0.997944i 0.520414π-0.520414\pi
−0.0640874 + 0.997944i 0.520414π0.520414\pi
692692 0 0
693693 −9.12311 −0.346558
694694 0 0
695695 −12.0000 −0.455186
696696 0 0
697697 −1.12311 −0.0425407
698698 0 0
699699 51.0540 1.93104
700700 0 0
701701 34.3153 1.29607 0.648036 0.761609i 0.275591π-0.275591\pi
0.648036 + 0.761609i 0.275591π0.275591\pi
702702 0 0
703703 14.5616 0.549199
704704 0 0
705705 33.6155 1.26603
706706 0 0
707707 −10.8769 −0.409068
708708 0 0
709709 1.50758 0.0566183 0.0283091 0.999599i 0.490988π-0.490988\pi
0.0283091 + 0.999599i 0.490988π0.490988\pi
710710 0 0
711711 54.7386 2.05286
712712 0 0
713713 33.6155 1.25891
714714 0 0
715715 −2.00000 −0.0747958
716716 0 0
717717 −65.6155 −2.45046
718718 0 0
719719 −7.82292 −0.291746 −0.145873 0.989303i 0.546599π-0.546599\pi
−0.145873 + 0.989303i 0.546599π0.546599\pi
720720 0 0
721721 −26.2462 −0.977460
722722 0 0
723723 −41.6155 −1.54770
724724 0 0
725725 9.68466 0.359679
726726 0 0
727727 −17.6155 −0.653324 −0.326662 0.945141i 0.605924π-0.605924\pi
−0.326662 + 0.945141i 0.605924π0.605924\pi
728728 0 0
729729 −35.9848 −1.33277
730730 0 0
731731 5.75379 0.212812
732732 0 0
733733 −19.1231 −0.706328 −0.353164 0.935561i 0.614894π-0.614894\pi
−0.353164 + 0.935561i 0.614894π0.614894\pi
734734 0 0
735735 −1.12311 −0.0414264
736736 0 0
737737 6.24621 0.230082
738738 0 0
739739 42.7386 1.57217 0.786083 0.618121i 0.212106π-0.212106\pi
0.786083 + 0.618121i 0.212106π0.212106\pi
740740 0 0
741741 −13.1231 −0.482089
742742 0 0
743743 2.56155 0.0939743 0.0469871 0.998895i 0.485038π-0.485038\pi
0.0469871 + 0.998895i 0.485038π0.485038\pi
744744 0 0
745745 2.31534 0.0848276
746746 0 0
747747 −18.2462 −0.667594
748748 0 0
749749 40.9848 1.49755
750750 0 0
751751 16.1771 0.590310 0.295155 0.955449i 0.404629π-0.404629\pi
0.295155 + 0.955449i 0.404629π0.404629\pi
752752 0 0
753753 75.8617 2.76456
754754 0 0
755755 −13.1231 −0.477599
756756 0 0
757757 −26.0000 −0.944986 −0.472493 0.881334i 0.656646π-0.656646\pi
−0.472493 + 0.881334i 0.656646π0.656646\pi
758758 0 0
759759 13.1231 0.476339
760760 0 0
761761 −36.7386 −1.33177 −0.665887 0.746052i 0.731947π-0.731947\pi
−0.665887 + 0.746052i 0.731947π0.731947\pi
762762 0 0
763763 47.3693 1.71488
764764 0 0
765765 −2.00000 −0.0723102
766766 0 0
767767 −2.24621 −0.0811060
768768 0 0
769769 24.7386 0.892098 0.446049 0.895009i 0.352831π-0.352831\pi
0.446049 + 0.895009i 0.352831π0.352831\pi
770770 0 0
771771 −73.6155 −2.65120
772772 0 0
773773 −37.6847 −1.35542 −0.677711 0.735328i 0.737028π-0.737028\pi
−0.677711 + 0.735328i 0.737028π0.737028\pi
774774 0 0
775775 −6.56155 −0.235698
776776 0 0
777777 −37.3002 −1.33814
778778 0 0
779779 −5.12311 −0.183554
780780 0 0
781781 3.68466 0.131847
782782 0 0
783783 13.9309 0.497849
784784 0 0
785785 14.8078 0.528512
786786 0 0
787787 54.7386 1.95122 0.975611 0.219508i 0.0704451π-0.0704451\pi
0.975611 + 0.219508i 0.0704451π0.0704451\pi
788788 0 0
789789 −12.3153 −0.438438
790790 0 0
791791 −48.9848 −1.74170
792792 0 0
793793 4.63068 0.164440
794794 0 0
795795 11.6847 0.414412
796796 0 0
797797 −23.7538 −0.841402 −0.420701 0.907199i 0.638216π-0.638216\pi
−0.420701 + 0.907199i 0.638216π0.638216\pi
798798 0 0
799799 −7.36932 −0.260708
800800 0 0
801801 −44.7386 −1.58076
802802 0 0
803803 2.00000 0.0705785
804804 0 0
805805 −13.1231 −0.462529
806806 0 0
807807 −50.2462 −1.76875
808808 0 0
809809 6.49242 0.228261 0.114131 0.993466i 0.463592π-0.463592\pi
0.114131 + 0.993466i 0.463592π0.463592\pi
810810 0 0
811811 −27.1922 −0.954849 −0.477424 0.878673i 0.658430π-0.658430\pi
−0.477424 + 0.878673i 0.658430π0.658430\pi
812812 0 0
813813 −72.9848 −2.55969
814814 0 0
815815 −3.19224 −0.111819
816816 0 0
817817 26.2462 0.918239
818818 0 0
819819 18.2462 0.637574
820820 0 0
821821 −2.00000 −0.0698005 −0.0349002 0.999391i 0.511111π-0.511111\pi
−0.0349002 + 0.999391i 0.511111π0.511111\pi
822822 0 0
823823 52.4924 1.82977 0.914885 0.403714i 0.132281π-0.132281\pi
0.914885 + 0.403714i 0.132281π0.132281\pi
824824 0 0
825825 −2.56155 −0.0891818
826826 0 0
827827 4.49242 0.156217 0.0781084 0.996945i 0.475112π-0.475112\pi
0.0781084 + 0.996945i 0.475112π0.475112\pi
828828 0 0
829829 5.36932 0.186484 0.0932420 0.995643i 0.470277π-0.470277\pi
0.0932420 + 0.995643i 0.470277π0.470277\pi
830830 0 0
831831 18.2462 0.632954
832832 0 0
833833 0.246211 0.00853071
834834 0 0
835835 10.5616 0.365498
836836 0 0
837837 −9.43845 −0.326240
838838 0 0
839839 −11.5076 −0.397286 −0.198643 0.980072i 0.563653π-0.563653\pi
−0.198643 + 0.980072i 0.563653π0.563653\pi
840840 0 0
841841 64.7926 2.23423
842842 0 0
843843 −21.1231 −0.727518
844844 0 0
845845 −9.00000 −0.309609
846846 0 0
847847 2.56155 0.0880160
848848 0 0
849849 59.8617 2.05445
850850 0 0
851851 29.1231 0.998327
852852 0 0
853853 −3.75379 −0.128527 −0.0642636 0.997933i 0.520470π-0.520470\pi
−0.0642636 + 0.997933i 0.520470π0.520470\pi
854854 0 0
855855 −9.12311 −0.312004
856856 0 0
857857 32.4233 1.10756 0.553779 0.832664i 0.313185π-0.313185\pi
0.553779 + 0.832664i 0.313185π0.313185\pi
858858 0 0
859859 38.8769 1.32646 0.663231 0.748415i 0.269185π-0.269185\pi
0.663231 + 0.748415i 0.269185π0.269185\pi
860860 0 0
861861 13.1231 0.447234
862862 0 0
863863 −9.61553 −0.327316 −0.163658 0.986517i 0.552329π-0.552329\pi
−0.163658 + 0.986517i 0.552329π0.552329\pi
864864 0 0
865865 4.24621 0.144376
866866 0 0
867867 −42.7386 −1.45148
868868 0 0
869869 −15.3693 −0.521368
870870 0 0
871871 −12.4924 −0.423290
872872 0 0
873873 25.3693 0.858621
874874 0 0
875875 2.56155 0.0865963
876876 0 0
877877 −32.2462 −1.08888 −0.544439 0.838801i 0.683257π-0.683257\pi
−0.544439 + 0.838801i 0.683257π0.683257\pi
878878 0 0
879879 37.1231 1.25213
880880 0 0
881881 2.00000 0.0673817 0.0336909 0.999432i 0.489274π-0.489274\pi
0.0336909 + 0.999432i 0.489274π0.489274\pi
882882 0 0
883883 −6.06913 −0.204242 −0.102121 0.994772i 0.532563π-0.532563\pi
−0.102121 + 0.994772i 0.532563π0.532563\pi
884884 0 0
885885 −2.87689 −0.0967057
886886 0 0
887887 30.2462 1.01557 0.507784 0.861484i 0.330465π-0.330465\pi
0.507784 + 0.861484i 0.330465π0.330465\pi
888888 0 0
889889 −36.4924 −1.22392
890890 0 0
891891 7.00000 0.234509
892892 0 0
893893 −33.6155 −1.12490
894894 0 0
895895 6.24621 0.208788
896896 0 0
897897 −26.2462 −0.876335
898898 0 0
899899 −63.5464 −2.11939
900900 0 0
901901 −2.56155 −0.0853377
902902 0 0
903903 −67.2311 −2.23731
904904 0 0
905905 −4.24621 −0.141149
906906 0 0
907907 −8.94602 −0.297048 −0.148524 0.988909i 0.547452π-0.547452\pi
−0.148524 + 0.988909i 0.547452π0.547452\pi
908908 0 0
909909 −15.1231 −0.501602
910910 0 0
911911 2.06913 0.0685533 0.0342767 0.999412i 0.489087π-0.489087\pi
0.0342767 + 0.999412i 0.489087π0.489087\pi
912912 0 0
913913 5.12311 0.169550
914914 0 0
915915 5.93087 0.196069
916916 0 0
917917 19.6847 0.650045
918918 0 0
919919 −8.00000 −0.263896 −0.131948 0.991257i 0.542123π-0.542123\pi
−0.131948 + 0.991257i 0.542123π0.542123\pi
920920 0 0
921921 65.6155 2.16211
922922 0 0
923923 −7.36932 −0.242564
924924 0 0
925925 −5.68466 −0.186910
926926 0 0
927927 −36.4924 −1.19857
928928 0 0
929929 45.0540 1.47817 0.739086 0.673611i 0.235257π-0.235257\pi
0.739086 + 0.673611i 0.235257π0.235257\pi
930930 0 0
931931 1.12311 0.0368083
932932 0 0
933933 65.1619 2.13331
934934 0 0
935935 0.561553 0.0183647
936936 0 0
937937 −42.0000 −1.37208 −0.686040 0.727564i 0.740653π-0.740653\pi
−0.686040 + 0.727564i 0.740653π0.740653\pi
938938 0 0
939939 78.1080 2.54896
940940 0 0
941941 −4.06913 −0.132650 −0.0663249 0.997798i 0.521127π-0.521127\pi
−0.0663249 + 0.997798i 0.521127π0.521127\pi
942942 0 0
943943 −10.2462 −0.333663
944944 0 0
945945 3.68466 0.119862
946946 0 0
947947 39.6847 1.28958 0.644789 0.764361i 0.276945π-0.276945\pi
0.644789 + 0.764361i 0.276945π0.276945\pi
948948 0 0
949949 −4.00000 −0.129845
950950 0 0
951951 33.7926 1.09580
952952 0 0
953953 −34.1771 −1.10710 −0.553552 0.832815i 0.686728π-0.686728\pi
−0.553552 + 0.832815i 0.686728π0.686728\pi
954954 0 0
955955 −10.2462 −0.331560
956956 0 0
957957 −24.8078 −0.801921
958958 0 0
959959 50.2462 1.62253
960960 0 0
961961 12.0540 0.388838
962962 0 0
963963 56.9848 1.83631
964964 0 0
965965 5.19224 0.167144
966966 0 0
967967 −11.5464 −0.371307 −0.185654 0.982615i 0.559440π-0.559440\pi
−0.185654 + 0.982615i 0.559440π0.559440\pi
968968 0 0
969969 3.68466 0.118368
970970 0 0
971971 −6.24621 −0.200450 −0.100225 0.994965i 0.531956π-0.531956\pi
−0.100225 + 0.994965i 0.531956π0.531956\pi
972972 0 0
973973 −30.7386 −0.985435
974974 0 0
975975 5.12311 0.164071
976976 0 0
977977 −24.8769 −0.795882 −0.397941 0.917411i 0.630275π-0.630275\pi
−0.397941 + 0.917411i 0.630275π0.630275\pi
978978 0 0
979979 12.5616 0.401469
980980 0 0
981981 65.8617 2.10280
982982 0 0
983983 −18.8769 −0.602079 −0.301040 0.953612i 0.597334π-0.597334\pi
−0.301040 + 0.953612i 0.597334π0.597334\pi
984984 0 0
985985 −5.36932 −0.171081
986986 0 0
987987 86.1080 2.74085
988988 0 0
989989 52.4924 1.66916
990990 0 0
991991 −32.0000 −1.01651 −0.508257 0.861206i 0.669710π-0.669710\pi
−0.508257 + 0.861206i 0.669710π0.669710\pi
992992 0 0
993993 21.7538 0.690336
994994 0 0
995995 0.807764 0.0256078
996996 0 0
997997 13.8617 0.439006 0.219503 0.975612i 0.429556π-0.429556\pi
0.219503 + 0.975612i 0.429556π0.429556\pi
998998 0 0
999999 −8.17708 −0.258711
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 880.2.a.o.1.2 2
3.2 odd 2 7920.2.a.bu.1.2 2
4.3 odd 2 440.2.a.e.1.1 2
5.2 odd 4 4400.2.b.t.4049.1 4
5.3 odd 4 4400.2.b.t.4049.4 4
5.4 even 2 4400.2.a.bj.1.1 2
8.3 odd 2 3520.2.a.bp.1.2 2
8.5 even 2 3520.2.a.bk.1.1 2
11.10 odd 2 9680.2.a.bs.1.2 2
12.11 even 2 3960.2.a.w.1.1 2
20.3 even 4 2200.2.b.i.1849.1 4
20.7 even 4 2200.2.b.i.1849.4 4
20.19 odd 2 2200.2.a.s.1.2 2
44.43 even 2 4840.2.a.j.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
440.2.a.e.1.1 2 4.3 odd 2
880.2.a.o.1.2 2 1.1 even 1 trivial
2200.2.a.s.1.2 2 20.19 odd 2
2200.2.b.i.1849.1 4 20.3 even 4
2200.2.b.i.1849.4 4 20.7 even 4
3520.2.a.bk.1.1 2 8.5 even 2
3520.2.a.bp.1.2 2 8.3 odd 2
3960.2.a.w.1.1 2 12.11 even 2
4400.2.a.bj.1.1 2 5.4 even 2
4400.2.b.t.4049.1 4 5.2 odd 4
4400.2.b.t.4049.4 4 5.3 odd 4
4840.2.a.j.1.1 2 44.43 even 2
7920.2.a.bu.1.2 2 3.2 odd 2
9680.2.a.bs.1.2 2 11.10 odd 2