Properties

Label 5408.2.a.bd.1.2
Level 54085408
Weight 22
Character 5408.1
Self dual yes
Analytic conductor 43.18343.183
Analytic rank 11
Dimension 22
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [5408,2,Mod(1,5408)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5408.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5408, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 5408=25132 5408 = 2^{5} \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 5408.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,1,0,3,0,-3,0,3,0,-4,0,0,0,-7,0,3,0,-12,0,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(21)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 43.183097413143.1830974131
Analytic rank: 11
Dimension: 22
Coefficient field: Q(17)\Q(\sqrt{17})
Copy content comment:defining polynomial
 
Copy content 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 416)
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 == 5408.1

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+2.56155q30.561553q5+0.561553q7+3.56155q92.00000q111.43845q150.561553q176.00000q19+1.43845q214.68466q25+1.43845q278.24621q297.12311q315.12311q330.315342q35+9.68466q377.12311q418.80776q432.00000q451.68466q476.68466q491.43845q514.87689q53+1.12311q5515.3693q57+6.00000q59+13.3693q61+2.00000q636.00000q67+1.68466q7110.0000q7312.0000q751.12311q77+12.0000q797.00000q81+17.3693q83+0.315342q8521.1231q87+8.24621q8918.2462q93+3.36932q95+6.00000q977.12311q99+O(q100)q+2.56155 q^{3} -0.561553 q^{5} +0.561553 q^{7} +3.56155 q^{9} -2.00000 q^{11} -1.43845 q^{15} -0.561553 q^{17} -6.00000 q^{19} +1.43845 q^{21} -4.68466 q^{25} +1.43845 q^{27} -8.24621 q^{29} -7.12311 q^{31} -5.12311 q^{33} -0.315342 q^{35} +9.68466 q^{37} -7.12311 q^{41} -8.80776 q^{43} -2.00000 q^{45} -1.68466 q^{47} -6.68466 q^{49} -1.43845 q^{51} -4.87689 q^{53} +1.12311 q^{55} -15.3693 q^{57} +6.00000 q^{59} +13.3693 q^{61} +2.00000 q^{63} -6.00000 q^{67} +1.68466 q^{71} -10.0000 q^{73} -12.0000 q^{75} -1.12311 q^{77} +12.0000 q^{79} -7.00000 q^{81} +17.3693 q^{83} +0.315342 q^{85} -21.1231 q^{87} +8.24621 q^{89} -18.2462 q^{93} +3.36932 q^{95} +6.00000 q^{97} -7.12311 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+q3+3q53q7+3q94q117q15+3q1712q19+7q21+3q25+7q276q312q3313q35+7q376q41+3q434q45+9q47+6q99+O(q100) 2 q + q^{3} + 3 q^{5} - 3 q^{7} + 3 q^{9} - 4 q^{11} - 7 q^{15} + 3 q^{17} - 12 q^{19} + 7 q^{21} + 3 q^{25} + 7 q^{27} - 6 q^{31} - 2 q^{33} - 13 q^{35} + 7 q^{37} - 6 q^{41} + 3 q^{43} - 4 q^{45} + 9 q^{47}+ \cdots - 6 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 −0.561553 −0.251134 −0.125567 0.992085i 0.540075π-0.540075\pi
−0.125567 + 0.992085i 0.540075π0.540075\pi
66 0 0
77 0.561553 0.212247 0.106124 0.994353i 0.466156π-0.466156\pi
0.106124 + 0.994353i 0.466156π0.466156\pi
88 0 0
99 3.56155 1.18718
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 0 0
1414 0 0
1515 −1.43845 −0.371405
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 −6.00000 −1.37649 −0.688247 0.725476i 0.741620π-0.741620\pi
−0.688247 + 0.725476i 0.741620π0.741620\pi
2020 0 0
2121 1.43845 0.313895
2222 0 0
2323 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2424 0 0
2525 −4.68466 −0.936932
2626 0 0
2727 1.43845 0.276829
2828 0 0
2929 −8.24621 −1.53128 −0.765641 0.643268i 0.777578π-0.777578\pi
−0.765641 + 0.643268i 0.777578π0.777578\pi
3030 0 0
3131 −7.12311 −1.27935 −0.639674 0.768647i 0.720931π-0.720931\pi
−0.639674 + 0.768647i 0.720931π0.720931\pi
3232 0 0
3333 −5.12311 −0.891818
3434 0 0
3535 −0.315342 −0.0533025
3636 0 0
3737 9.68466 1.59215 0.796074 0.605199i 0.206907π-0.206907\pi
0.796074 + 0.605199i 0.206907π0.206907\pi
3838 0 0
3939 0 0
4040 0 0
4141 −7.12311 −1.11244 −0.556221 0.831034i 0.687749π-0.687749\pi
−0.556221 + 0.831034i 0.687749π0.687749\pi
4242 0 0
4343 −8.80776 −1.34317 −0.671586 0.740927i 0.734386π-0.734386\pi
−0.671586 + 0.740927i 0.734386π0.734386\pi
4444 0 0
4545 −2.00000 −0.298142
4646 0 0
4747 −1.68466 −0.245733 −0.122866 0.992423i 0.539209π-0.539209\pi
−0.122866 + 0.992423i 0.539209π0.539209\pi
4848 0 0
4949 −6.68466 −0.954951
5050 0 0
5151 −1.43845 −0.201423
5252 0 0
5353 −4.87689 −0.669893 −0.334946 0.942237i 0.608718π-0.608718\pi
−0.334946 + 0.942237i 0.608718π0.608718\pi
5454 0 0
5555 1.12311 0.151440
5656 0 0
5757 −15.3693 −2.03572
5858 0 0
5959 6.00000 0.781133 0.390567 0.920575i 0.372279π-0.372279\pi
0.390567 + 0.920575i 0.372279π0.372279\pi
6060 0 0
6161 13.3693 1.71177 0.855883 0.517170i 0.173014π-0.173014\pi
0.855883 + 0.517170i 0.173014π0.173014\pi
6262 0 0
6363 2.00000 0.251976
6464 0 0
6565 0 0
6666 0 0
6767 −6.00000 −0.733017 −0.366508 0.930415i 0.619447π-0.619447\pi
−0.366508 + 0.930415i 0.619447π0.619447\pi
6868 0 0
6969 0 0
7070 0 0
7171 1.68466 0.199932 0.0999661 0.994991i 0.468127π-0.468127\pi
0.0999661 + 0.994991i 0.468127π0.468127\pi
7272 0 0
7373 −10.0000 −1.17041 −0.585206 0.810885i 0.698986π-0.698986\pi
−0.585206 + 0.810885i 0.698986π0.698986\pi
7474 0 0
7575 −12.0000 −1.38564
7676 0 0
7777 −1.12311 −0.127990
7878 0 0
7979 12.0000 1.35011 0.675053 0.737769i 0.264121π-0.264121\pi
0.675053 + 0.737769i 0.264121π0.264121\pi
8080 0 0
8181 −7.00000 −0.777778
8282 0 0
8383 17.3693 1.90653 0.953265 0.302135i 0.0976994π-0.0976994\pi
0.953265 + 0.302135i 0.0976994π0.0976994\pi
8484 0 0
8585 0.315342 0.0342036
8686 0 0
8787 −21.1231 −2.26463
8888 0 0
8989 8.24621 0.874097 0.437048 0.899438i 0.356024π-0.356024\pi
0.437048 + 0.899438i 0.356024π0.356024\pi
9090 0 0
9191 0 0
9292 0 0
9393 −18.2462 −1.89204
9494 0 0
9595 3.36932 0.345685
9696 0 0
9797 6.00000 0.609208 0.304604 0.952479i 0.401476π-0.401476\pi
0.304604 + 0.952479i 0.401476π0.401476\pi
9898 0 0
9999 −7.12311 −0.715899
100100 0 0
101101 −7.12311 −0.708776 −0.354388 0.935099i 0.615311π-0.615311\pi
−0.354388 + 0.935099i 0.615311π0.615311\pi
102102 0 0
103103 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
104104 0 0
105105 −0.807764 −0.0788297
106106 0 0
107107 −12.0000 −1.16008 −0.580042 0.814587i 0.696964π-0.696964\pi
−0.580042 + 0.814587i 0.696964π0.696964\pi
108108 0 0
109109 1.68466 0.161361 0.0806805 0.996740i 0.474291π-0.474291\pi
0.0806805 + 0.996740i 0.474291π0.474291\pi
110110 0 0
111111 24.8078 2.35465
112112 0 0
113113 8.24621 0.775738 0.387869 0.921714i 0.373211π-0.373211\pi
0.387869 + 0.921714i 0.373211π0.373211\pi
114114 0 0
115115 0 0
116116 0 0
117117 0 0
118118 0 0
119119 −0.315342 −0.0289073
120120 0 0
121121 −7.00000 −0.636364
122122 0 0
123123 −18.2462 −1.64521
124124 0 0
125125 5.43845 0.486430
126126 0 0
127127 2.24621 0.199319 0.0996595 0.995022i 0.468225π-0.468225\pi
0.0996595 + 0.995022i 0.468225π0.468225\pi
128128 0 0
129129 −22.5616 −1.98643
130130 0 0
131131 15.6847 1.37037 0.685187 0.728367i 0.259720π-0.259720\pi
0.685187 + 0.728367i 0.259720π0.259720\pi
132132 0 0
133133 −3.36932 −0.292157
134134 0 0
135135 −0.807764 −0.0695213
136136 0 0
137137 −4.87689 −0.416661 −0.208331 0.978058i 0.566803π-0.566803\pi
−0.208331 + 0.978058i 0.566803π0.566803\pi
138138 0 0
139139 7.68466 0.651804 0.325902 0.945404i 0.394332π-0.394332\pi
0.325902 + 0.945404i 0.394332π0.394332\pi
140140 0 0
141141 −4.31534 −0.363417
142142 0 0
143143 0 0
144144 0 0
145145 4.63068 0.384557
146146 0 0
147147 −17.1231 −1.41229
148148 0 0
149149 8.24621 0.675556 0.337778 0.941226i 0.390325π-0.390325\pi
0.337778 + 0.941226i 0.390325π0.390325\pi
150150 0 0
151151 −10.3153 −0.839451 −0.419725 0.907651i 0.637874π-0.637874\pi
−0.419725 + 0.907651i 0.637874π0.637874\pi
152152 0 0
153153 −2.00000 −0.161690
154154 0 0
155155 4.00000 0.321288
156156 0 0
157157 2.00000 0.159617 0.0798087 0.996810i 0.474569π-0.474569\pi
0.0798087 + 0.996810i 0.474569π0.474569\pi
158158 0 0
159159 −12.4924 −0.990714
160160 0 0
161161 0 0
162162 0 0
163163 −9.36932 −0.733862 −0.366931 0.930248i 0.619591π-0.619591\pi
−0.366931 + 0.930248i 0.619591π0.619591\pi
164164 0 0
165165 2.87689 0.223966
166166 0 0
167167 9.36932 0.725020 0.362510 0.931980i 0.381920π-0.381920\pi
0.362510 + 0.931980i 0.381920π0.381920\pi
168168 0 0
169169 0 0
170170 0 0
171171 −21.3693 −1.63415
172172 0 0
173173 21.3693 1.62468 0.812340 0.583185i 0.198194π-0.198194\pi
0.812340 + 0.583185i 0.198194π0.198194\pi
174174 0 0
175175 −2.63068 −0.198861
176176 0 0
177177 15.3693 1.15523
178178 0 0
179179 −19.0540 −1.42416 −0.712080 0.702098i 0.752247π-0.752247\pi
−0.712080 + 0.702098i 0.752247π0.752247\pi
180180 0 0
181181 17.3693 1.29105 0.645526 0.763739i 0.276638π-0.276638\pi
0.645526 + 0.763739i 0.276638π0.276638\pi
182182 0 0
183183 34.2462 2.53155
184184 0 0
185185 −5.43845 −0.399843
186186 0 0
187187 1.12311 0.0821296
188188 0 0
189189 0.807764 0.0587562
190190 0 0
191191 −19.3693 −1.40151 −0.700757 0.713400i 0.747154π-0.747154\pi
−0.700757 + 0.713400i 0.747154π0.747154\pi
192192 0 0
193193 −1.36932 −0.0985656 −0.0492828 0.998785i 0.515694π-0.515694\pi
−0.0492828 + 0.998785i 0.515694π0.515694\pi
194194 0 0
195195 0 0
196196 0 0
197197 −13.6847 −0.974992 −0.487496 0.873125i 0.662090π-0.662090\pi
−0.487496 + 0.873125i 0.662090π0.662090\pi
198198 0 0
199199 15.3693 1.08950 0.544751 0.838598i 0.316624π-0.316624\pi
0.544751 + 0.838598i 0.316624π0.316624\pi
200200 0 0
201201 −15.3693 −1.08407
202202 0 0
203203 −4.63068 −0.325010
204204 0 0
205205 4.00000 0.279372
206206 0 0
207207 0 0
208208 0 0
209209 12.0000 0.830057
210210 0 0
211211 3.19224 0.219763 0.109881 0.993945i 0.464953π-0.464953\pi
0.109881 + 0.993945i 0.464953π0.464953\pi
212212 0 0
213213 4.31534 0.295682
214214 0 0
215215 4.94602 0.337316
216216 0 0
217217 −4.00000 −0.271538
218218 0 0
219219 −25.6155 −1.73094
220220 0 0
221221 0 0
222222 0 0
223223 −26.8078 −1.79518 −0.897590 0.440831i 0.854684π-0.854684\pi
−0.897590 + 0.440831i 0.854684π0.854684\pi
224224 0 0
225225 −16.6847 −1.11231
226226 0 0
227227 −21.3693 −1.41833 −0.709166 0.705042i 0.750928π-0.750928\pi
−0.709166 + 0.705042i 0.750928π0.750928\pi
228228 0 0
229229 −13.6847 −0.904308 −0.452154 0.891940i 0.649344π-0.649344\pi
−0.452154 + 0.891940i 0.649344π0.649344\pi
230230 0 0
231231 −2.87689 −0.189286
232232 0 0
233233 13.6847 0.896512 0.448256 0.893905i 0.352045π-0.352045\pi
0.448256 + 0.893905i 0.352045π0.352045\pi
234234 0 0
235235 0.946025 0.0617118
236236 0 0
237237 30.7386 1.99669
238238 0 0
239239 −21.6847 −1.40266 −0.701332 0.712835i 0.747411π-0.747411\pi
−0.701332 + 0.712835i 0.747411π0.747411\pi
240240 0 0
241241 −2.00000 −0.128831 −0.0644157 0.997923i 0.520518π-0.520518\pi
−0.0644157 + 0.997923i 0.520518π0.520518\pi
242242 0 0
243243 −22.2462 −1.42710
244244 0 0
245245 3.75379 0.239821
246246 0 0
247247 0 0
248248 0 0
249249 44.4924 2.81959
250250 0 0
251251 −16.0000 −1.00991 −0.504956 0.863145i 0.668491π-0.668491\pi
−0.504956 + 0.863145i 0.668491π0.668491\pi
252252 0 0
253253 0 0
254254 0 0
255255 0.807764 0.0505841
256256 0 0
257257 15.9309 0.993740 0.496870 0.867825i 0.334483π-0.334483\pi
0.496870 + 0.867825i 0.334483π0.334483\pi
258258 0 0
259259 5.43845 0.337929
260260 0 0
261261 −29.3693 −1.81792
262262 0 0
263263 26.7386 1.64877 0.824387 0.566026i 0.191520π-0.191520\pi
0.824387 + 0.566026i 0.191520π0.191520\pi
264264 0 0
265265 2.73863 0.168233
266266 0 0
267267 21.1231 1.29271
268268 0 0
269269 −21.3693 −1.30291 −0.651455 0.758687i 0.725841π-0.725841\pi
−0.651455 + 0.758687i 0.725841π0.725841\pi
270270 0 0
271271 −1.68466 −0.102336 −0.0511679 0.998690i 0.516294π-0.516294\pi
−0.0511679 + 0.998690i 0.516294π0.516294\pi
272272 0 0
273273 0 0
274274 0 0
275275 9.36932 0.564991
276276 0 0
277277 −1.36932 −0.0822743 −0.0411371 0.999154i 0.513098π-0.513098\pi
−0.0411371 + 0.999154i 0.513098π0.513098\pi
278278 0 0
279279 −25.3693 −1.51882
280280 0 0
281281 −20.2462 −1.20779 −0.603894 0.797065i 0.706385π-0.706385\pi
−0.603894 + 0.797065i 0.706385π0.706385\pi
282282 0 0
283283 2.24621 0.133523 0.0667617 0.997769i 0.478733π-0.478733\pi
0.0667617 + 0.997769i 0.478733π0.478733\pi
284284 0 0
285285 8.63068 0.511238
286286 0 0
287287 −4.00000 −0.236113
288288 0 0
289289 −16.6847 −0.981450
290290 0 0
291291 15.3693 0.900965
292292 0 0
293293 23.4384 1.36929 0.684644 0.728877i 0.259958π-0.259958\pi
0.684644 + 0.728877i 0.259958π0.259958\pi
294294 0 0
295295 −3.36932 −0.196169
296296 0 0
297297 −2.87689 −0.166934
298298 0 0
299299 0 0
300300 0 0
301301 −4.94602 −0.285084
302302 0 0
303303 −18.2462 −1.04822
304304 0 0
305305 −7.50758 −0.429883
306306 0 0
307307 6.00000 0.342438 0.171219 0.985233i 0.445229π-0.445229\pi
0.171219 + 0.985233i 0.445229π0.445229\pi
308308 0 0
309309 0 0
310310 0 0
311311 −15.3693 −0.871514 −0.435757 0.900064i 0.643519π-0.643519\pi
−0.435757 + 0.900064i 0.643519π0.643519\pi
312312 0 0
313313 17.0540 0.963948 0.481974 0.876186i 0.339920π-0.339920\pi
0.481974 + 0.876186i 0.339920π0.339920\pi
314314 0 0
315315 −1.12311 −0.0632798
316316 0 0
317317 32.2462 1.81113 0.905564 0.424210i 0.139448π-0.139448\pi
0.905564 + 0.424210i 0.139448π0.139448\pi
318318 0 0
319319 16.4924 0.923398
320320 0 0
321321 −30.7386 −1.71566
322322 0 0
323323 3.36932 0.187474
324324 0 0
325325 0 0
326326 0 0
327327 4.31534 0.238639
328328 0 0
329329 −0.946025 −0.0521560
330330 0 0
331331 −21.3693 −1.17456 −0.587282 0.809382i 0.699802π-0.699802\pi
−0.587282 + 0.809382i 0.699802π0.699802\pi
332332 0 0
333333 34.4924 1.89017
334334 0 0
335335 3.36932 0.184085
336336 0 0
337337 1.05398 0.0574137 0.0287068 0.999588i 0.490861π-0.490861\pi
0.0287068 + 0.999588i 0.490861π0.490861\pi
338338 0 0
339339 21.1231 1.14725
340340 0 0
341341 14.2462 0.771476
342342 0 0
343343 −7.68466 −0.414933
344344 0 0
345345 0 0
346346 0 0
347347 −16.3153 −0.875853 −0.437927 0.899011i 0.644287π-0.644287\pi
−0.437927 + 0.899011i 0.644287π0.644287\pi
348348 0 0
349349 −29.0540 −1.55522 −0.777612 0.628745i 0.783569π-0.783569\pi
−0.777612 + 0.628745i 0.783569π0.783569\pi
350350 0 0
351351 0 0
352352 0 0
353353 25.8617 1.37648 0.688241 0.725482i 0.258383π-0.258383\pi
0.688241 + 0.725482i 0.258383π0.258383\pi
354354 0 0
355355 −0.946025 −0.0502098
356356 0 0
357357 −0.807764 −0.0427514
358358 0 0
359359 17.3693 0.916717 0.458359 0.888767i 0.348437π-0.348437\pi
0.458359 + 0.888767i 0.348437π0.348437\pi
360360 0 0
361361 17.0000 0.894737
362362 0 0
363363 −17.9309 −0.941127
364364 0 0
365365 5.61553 0.293930
366366 0 0
367367 −27.3693 −1.42867 −0.714333 0.699806i 0.753270π-0.753270\pi
−0.714333 + 0.699806i 0.753270π0.753270\pi
368368 0 0
369369 −25.3693 −1.32067
370370 0 0
371371 −2.73863 −0.142183
372372 0 0
373373 −13.3693 −0.692237 −0.346118 0.938191i 0.612500π-0.612500\pi
−0.346118 + 0.938191i 0.612500π0.612500\pi
374374 0 0
375375 13.9309 0.719387
376376 0 0
377377 0 0
378378 0 0
379379 −16.8769 −0.866908 −0.433454 0.901176i 0.642705π-0.642705\pi
−0.433454 + 0.901176i 0.642705π0.642705\pi
380380 0 0
381381 5.75379 0.294776
382382 0 0
383383 1.68466 0.0860820 0.0430410 0.999073i 0.486295π-0.486295\pi
0.0430410 + 0.999073i 0.486295π0.486295\pi
384384 0 0
385385 0.630683 0.0321426
386386 0 0
387387 −31.3693 −1.59459
388388 0 0
389389 20.2462 1.02652 0.513262 0.858232i 0.328437π-0.328437\pi
0.513262 + 0.858232i 0.328437π0.328437\pi
390390 0 0
391391 0 0
392392 0 0
393393 40.1771 2.02667
394394 0 0
395395 −6.73863 −0.339057
396396 0 0
397397 6.00000 0.301131 0.150566 0.988600i 0.451890π-0.451890\pi
0.150566 + 0.988600i 0.451890π0.451890\pi
398398 0 0
399399 −8.63068 −0.432075
400400 0 0
401401 −31.1231 −1.55421 −0.777107 0.629369i 0.783314π-0.783314\pi
−0.777107 + 0.629369i 0.783314π0.783314\pi
402402 0 0
403403 0 0
404404 0 0
405405 3.93087 0.195326
406406 0 0
407407 −19.3693 −0.960101
408408 0 0
409409 6.63068 0.327866 0.163933 0.986471i 0.447582π-0.447582\pi
0.163933 + 0.986471i 0.447582π0.447582\pi
410410 0 0
411411 −12.4924 −0.616206
412412 0 0
413413 3.36932 0.165793
414414 0 0
415415 −9.75379 −0.478795
416416 0 0
417417 19.6847 0.963962
418418 0 0
419419 15.0540 0.735435 0.367717 0.929938i 0.380139π-0.380139\pi
0.367717 + 0.929938i 0.380139π0.380139\pi
420420 0 0
421421 33.6847 1.64169 0.820845 0.571151i 0.193503π-0.193503\pi
0.820845 + 0.571151i 0.193503π0.193503\pi
422422 0 0
423423 −6.00000 −0.291730
424424 0 0
425425 2.63068 0.127607
426426 0 0
427427 7.50758 0.363317
428428 0 0
429429 0 0
430430 0 0
431431 −5.68466 −0.273820 −0.136910 0.990583i 0.543717π-0.543717\pi
−0.136910 + 0.990583i 0.543717π0.543717\pi
432432 0 0
433433 14.3153 0.687951 0.343976 0.938979i 0.388226π-0.388226\pi
0.343976 + 0.938979i 0.388226π0.388226\pi
434434 0 0
435435 11.8617 0.568727
436436 0 0
437437 0 0
438438 0 0
439439 −41.6155 −1.98620 −0.993100 0.117267i 0.962587π-0.962587\pi
−0.993100 + 0.117267i 0.962587π0.962587\pi
440440 0 0
441441 −23.8078 −1.13370
442442 0 0
443443 −7.68466 −0.365109 −0.182555 0.983196i 0.558437π-0.558437\pi
−0.182555 + 0.983196i 0.558437π0.558437\pi
444444 0 0
445445 −4.63068 −0.219515
446446 0 0
447447 21.1231 0.999089
448448 0 0
449449 −18.0000 −0.849473 −0.424736 0.905317i 0.639633π-0.639633\pi
−0.424736 + 0.905317i 0.639633π0.639633\pi
450450 0 0
451451 14.2462 0.670828
452452 0 0
453453 −26.4233 −1.24147
454454 0 0
455455 0 0
456456 0 0
457457 14.0000 0.654892 0.327446 0.944870i 0.393812π-0.393812\pi
0.327446 + 0.944870i 0.393812π0.393812\pi
458458 0 0
459459 −0.807764 −0.0377032
460460 0 0
461461 21.1922 0.987021 0.493510 0.869740i 0.335713π-0.335713\pi
0.493510 + 0.869740i 0.335713π0.335713\pi
462462 0 0
463463 −23.6155 −1.09751 −0.548753 0.835984i 0.684897π-0.684897\pi
−0.548753 + 0.835984i 0.684897π0.684897\pi
464464 0 0
465465 10.2462 0.475157
466466 0 0
467467 14.7386 0.682023 0.341011 0.940059i 0.389231π-0.389231\pi
0.341011 + 0.940059i 0.389231π0.389231\pi
468468 0 0
469469 −3.36932 −0.155581
470470 0 0
471471 5.12311 0.236060
472472 0 0
473473 17.6155 0.809963
474474 0 0
475475 28.1080 1.28968
476476 0 0
477477 −17.3693 −0.795286
478478 0 0
479479 −33.6847 −1.53909 −0.769546 0.638592i 0.779517π-0.779517\pi
−0.769546 + 0.638592i 0.779517π0.779517\pi
480480 0 0
481481 0 0
482482 0 0
483483 0 0
484484 0 0
485485 −3.36932 −0.152993
486486 0 0
487487 19.1231 0.866551 0.433275 0.901262i 0.357358π-0.357358\pi
0.433275 + 0.901262i 0.357358π0.357358\pi
488488 0 0
489489 −24.0000 −1.08532
490490 0 0
491491 35.6847 1.61043 0.805213 0.592986i 0.202051π-0.202051\pi
0.805213 + 0.592986i 0.202051π0.202051\pi
492492 0 0
493493 4.63068 0.208555
494494 0 0
495495 4.00000 0.179787
496496 0 0
497497 0.946025 0.0424350
498498 0 0
499499 −16.8769 −0.755514 −0.377757 0.925905i 0.623304π-0.623304\pi
−0.377757 + 0.925905i 0.623304π0.623304\pi
500500 0 0
501501 24.0000 1.07224
502502 0 0
503503 −4.63068 −0.206472 −0.103236 0.994657i 0.532920π-0.532920\pi
−0.103236 + 0.994657i 0.532920π0.532920\pi
504504 0 0
505505 4.00000 0.177998
506506 0 0
507507 0 0
508508 0 0
509509 10.4924 0.465068 0.232534 0.972588i 0.425298π-0.425298\pi
0.232534 + 0.972588i 0.425298π0.425298\pi
510510 0 0
511511 −5.61553 −0.248416
512512 0 0
513513 −8.63068 −0.381054
514514 0 0
515515 0 0
516516 0 0
517517 3.36932 0.148182
518518 0 0
519519 54.7386 2.40276
520520 0 0
521521 12.5616 0.550332 0.275166 0.961397i 0.411267π-0.411267\pi
0.275166 + 0.961397i 0.411267π0.411267\pi
522522 0 0
523523 −40.4924 −1.77061 −0.885305 0.465011i 0.846050π-0.846050\pi
−0.885305 + 0.465011i 0.846050π0.846050\pi
524524 0 0
525525 −6.73863 −0.294098
526526 0 0
527527 4.00000 0.174243
528528 0 0
529529 −23.0000 −1.00000
530530 0 0
531531 21.3693 0.927349
532532 0 0
533533 0 0
534534 0 0
535535 6.73863 0.291337
536536 0 0
537537 −48.8078 −2.10621
538538 0 0
539539 13.3693 0.575857
540540 0 0
541541 18.3153 0.787438 0.393719 0.919231i 0.371188π-0.371188\pi
0.393719 + 0.919231i 0.371188π0.371188\pi
542542 0 0
543543 44.4924 1.90935
544544 0 0
545545 −0.946025 −0.0405232
546546 0 0
547547 23.0540 0.985717 0.492858 0.870110i 0.335952π-0.335952\pi
0.492858 + 0.870110i 0.335952π0.335952\pi
548548 0 0
549549 47.6155 2.03218
550550 0 0
551551 49.4773 2.10780
552552 0 0
553553 6.73863 0.286556
554554 0 0
555555 −13.9309 −0.591332
556556 0 0
557557 43.3002 1.83469 0.917344 0.398096i 0.130329π-0.130329\pi
0.917344 + 0.398096i 0.130329π0.130329\pi
558558 0 0
559559 0 0
560560 0 0
561561 2.87689 0.121463
562562 0 0
563563 43.6847 1.84109 0.920544 0.390638i 0.127746π-0.127746\pi
0.920544 + 0.390638i 0.127746π0.127746\pi
564564 0 0
565565 −4.63068 −0.194814
566566 0 0
567567 −3.93087 −0.165081
568568 0 0
569569 −25.6847 −1.07676 −0.538378 0.842703i 0.680963π-0.680963\pi
−0.538378 + 0.842703i 0.680963π0.680963\pi
570570 0 0
571571 −17.4384 −0.729776 −0.364888 0.931051i 0.618893π-0.618893\pi
−0.364888 + 0.931051i 0.618893π0.618893\pi
572572 0 0
573573 −49.6155 −2.07272
574574 0 0
575575 0 0
576576 0 0
577577 4.73863 0.197272 0.0986360 0.995124i 0.468552π-0.468552\pi
0.0986360 + 0.995124i 0.468552π0.468552\pi
578578 0 0
579579 −3.50758 −0.145770
580580 0 0
581581 9.75379 0.404655
582582 0 0
583583 9.75379 0.403961
584584 0 0
585585 0 0
586586 0 0
587587 9.36932 0.386713 0.193357 0.981129i 0.438063π-0.438063\pi
0.193357 + 0.981129i 0.438063π0.438063\pi
588588 0 0
589589 42.7386 1.76101
590590 0 0
591591 −35.0540 −1.44193
592592 0 0
593593 −20.2462 −0.831412 −0.415706 0.909499i 0.636466π-0.636466\pi
−0.415706 + 0.909499i 0.636466π0.636466\pi
594594 0 0
595595 0.177081 0.00725961
596596 0 0
597597 39.3693 1.61128
598598 0 0
599599 35.3693 1.44515 0.722576 0.691292i 0.242958π-0.242958\pi
0.722576 + 0.691292i 0.242958π0.242958\pi
600600 0 0
601601 −21.0540 −0.858810 −0.429405 0.903112i 0.641277π-0.641277\pi
−0.429405 + 0.903112i 0.641277π0.641277\pi
602602 0 0
603603 −21.3693 −0.870226
604604 0 0
605605 3.93087 0.159813
606606 0 0
607607 31.8617 1.29323 0.646614 0.762817i 0.276184π-0.276184\pi
0.646614 + 0.762817i 0.276184π0.276184\pi
608608 0 0
609609 −11.8617 −0.480662
610610 0 0
611611 0 0
612612 0 0
613613 −10.0000 −0.403896 −0.201948 0.979396i 0.564727π-0.564727\pi
−0.201948 + 0.979396i 0.564727π0.564727\pi
614614 0 0
615615 10.2462 0.413167
616616 0 0
617617 23.6155 0.950725 0.475363 0.879790i 0.342317π-0.342317\pi
0.475363 + 0.879790i 0.342317π0.342317\pi
618618 0 0
619619 −9.36932 −0.376585 −0.188292 0.982113i 0.560295π-0.560295\pi
−0.188292 + 0.982113i 0.560295π0.560295\pi
620620 0 0
621621 0 0
622622 0 0
623623 4.63068 0.185524
624624 0 0
625625 20.3693 0.814773
626626 0 0
627627 30.7386 1.22758
628628 0 0
629629 −5.43845 −0.216845
630630 0 0
631631 −41.0540 −1.63433 −0.817166 0.576402i 0.804456π-0.804456\pi
−0.817166 + 0.576402i 0.804456π0.804456\pi
632632 0 0
633633 8.17708 0.325010
634634 0 0
635635 −1.26137 −0.0500558
636636 0 0
637637 0 0
638638 0 0
639639 6.00000 0.237356
640640 0 0
641641 10.4924 0.414426 0.207213 0.978296i 0.433561π-0.433561\pi
0.207213 + 0.978296i 0.433561π0.433561\pi
642642 0 0
643643 18.0000 0.709851 0.354925 0.934895i 0.384506π-0.384506\pi
0.354925 + 0.934895i 0.384506π0.384506\pi
644644 0 0
645645 12.6695 0.498861
646646 0 0
647647 −30.1080 −1.18367 −0.591833 0.806061i 0.701595π-0.701595\pi
−0.591833 + 0.806061i 0.701595π0.701595\pi
648648 0 0
649649 −12.0000 −0.471041
650650 0 0
651651 −10.2462 −0.401581
652652 0 0
653653 −47.6155 −1.86334 −0.931670 0.363306i 0.881648π-0.881648\pi
−0.931670 + 0.363306i 0.881648π0.881648\pi
654654 0 0
655655 −8.80776 −0.344148
656656 0 0
657657 −35.6155 −1.38949
658658 0 0
659659 12.0000 0.467454 0.233727 0.972302i 0.424908π-0.424908\pi
0.233727 + 0.972302i 0.424908π0.424908\pi
660660 0 0
661661 20.7386 0.806639 0.403320 0.915059i 0.367856π-0.367856\pi
0.403320 + 0.915059i 0.367856π0.367856\pi
662662 0 0
663663 0 0
664664 0 0
665665 1.89205 0.0733705
666666 0 0
667667 0 0
668668 0 0
669669 −68.6695 −2.65492
670670 0 0
671671 −26.7386 −1.03223
672672 0 0
673673 −21.0540 −0.811571 −0.405786 0.913968i 0.633002π-0.633002\pi
−0.405786 + 0.913968i 0.633002π0.633002\pi
674674 0 0
675675 −6.73863 −0.259370
676676 0 0
677677 21.3693 0.821290 0.410645 0.911795i 0.365304π-0.365304\pi
0.410645 + 0.911795i 0.365304π0.365304\pi
678678 0 0
679679 3.36932 0.129303
680680 0 0
681681 −54.7386 −2.09759
682682 0 0
683683 5.36932 0.205451 0.102726 0.994710i 0.467244π-0.467244\pi
0.102726 + 0.994710i 0.467244π0.467244\pi
684684 0 0
685685 2.73863 0.104638
686686 0 0
687687 −35.0540 −1.33739
688688 0 0
689689 0 0
690690 0 0
691691 4.87689 0.185526 0.0927629 0.995688i 0.470430π-0.470430\pi
0.0927629 + 0.995688i 0.470430π0.470430\pi
692692 0 0
693693 −4.00000 −0.151947
694694 0 0
695695 −4.31534 −0.163690
696696 0 0
697697 4.00000 0.151511
698698 0 0
699699 35.0540 1.32586
700700 0 0
701701 9.36932 0.353874 0.176937 0.984222i 0.443381π-0.443381\pi
0.176937 + 0.984222i 0.443381π0.443381\pi
702702 0 0
703703 −58.1080 −2.19158
704704 0 0
705705 2.42329 0.0912665
706706 0 0
707707 −4.00000 −0.150435
708708 0 0
709709 −16.7386 −0.628633 −0.314316 0.949318i 0.601775π-0.601775\pi
−0.314316 + 0.949318i 0.601775π0.601775\pi
710710 0 0
711711 42.7386 1.60282
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 −55.5464 −2.07442
718718 0 0
719719 −15.3693 −0.573179 −0.286589 0.958054i 0.592522π-0.592522\pi
−0.286589 + 0.958054i 0.592522π0.592522\pi
720720 0 0
721721 0 0
722722 0 0
723723 −5.12311 −0.190530
724724 0 0
725725 38.6307 1.43471
726726 0 0
727727 −41.6155 −1.54343 −0.771717 0.635966i 0.780602π-0.780602\pi
−0.771717 + 0.635966i 0.780602π0.780602\pi
728728 0 0
729729 −35.9848 −1.33277
730730 0 0
731731 4.94602 0.182935
732732 0 0
733733 25.0540 0.925390 0.462695 0.886518i 0.346883π-0.346883\pi
0.462695 + 0.886518i 0.346883π0.346883\pi
734734 0 0
735735 9.61553 0.354674
736736 0 0
737737 12.0000 0.442026
738738 0 0
739739 52.1080 1.91682 0.958411 0.285392i 0.0921237π-0.0921237\pi
0.958411 + 0.285392i 0.0921237π0.0921237\pi
740740 0 0
741741 0 0
742742 0 0
743743 −13.6847 −0.502041 −0.251021 0.967982i 0.580766π-0.580766\pi
−0.251021 + 0.967982i 0.580766π0.580766\pi
744744 0 0
745745 −4.63068 −0.169655
746746 0 0
747747 61.8617 2.26340
748748 0 0
749749 −6.73863 −0.246224
750750 0 0
751751 −26.2462 −0.957738 −0.478869 0.877886i 0.658953π-0.658953\pi
−0.478869 + 0.877886i 0.658953π0.658953\pi
752752 0 0
753753 −40.9848 −1.49357
754754 0 0
755755 5.79261 0.210815
756756 0 0
757757 −9.36932 −0.340534 −0.170267 0.985398i 0.554463π-0.554463\pi
−0.170267 + 0.985398i 0.554463π0.554463\pi
758758 0 0
759759 0 0
760760 0 0
761761 30.0000 1.08750 0.543750 0.839248i 0.317004π-0.317004\pi
0.543750 + 0.839248i 0.317004π0.317004\pi
762762 0 0
763763 0.946025 0.0342484
764764 0 0
765765 1.12311 0.0406060
766766 0 0
767767 0 0
768768 0 0
769769 −9.36932 −0.337866 −0.168933 0.985628i 0.554032π-0.554032\pi
−0.168933 + 0.985628i 0.554032π0.554032\pi
770770 0 0
771771 40.8078 1.46966
772772 0 0
773773 25.6847 0.923813 0.461906 0.886929i 0.347166π-0.347166\pi
0.461906 + 0.886929i 0.347166π0.347166\pi
774774 0 0
775775 33.3693 1.19866
776776 0 0
777777 13.9309 0.499767
778778 0 0
779779 42.7386 1.53127
780780 0 0
781781 −3.36932 −0.120564
782782 0 0
783783 −11.8617 −0.423904
784784 0 0
785785 −1.12311 −0.0400854
786786 0 0
787787 −35.6155 −1.26956 −0.634778 0.772694i 0.718909π-0.718909\pi
−0.634778 + 0.772694i 0.718909π0.718909\pi
788788 0 0
789789 68.4924 2.43839
790790 0 0
791791 4.63068 0.164648
792792 0 0
793793 0 0
794794 0 0
795795 7.01515 0.248802
796796 0 0
797797 −12.7386 −0.451226 −0.225613 0.974217i 0.572438π-0.572438\pi
−0.225613 + 0.974217i 0.572438π0.572438\pi
798798 0 0
799799 0.946025 0.0334679
800800 0 0
801801 29.3693 1.03771
802802 0 0
803803 20.0000 0.705785
804804 0 0
805805 0 0
806806 0 0
807807 −54.7386 −1.92689
808808 0 0
809809 −39.9309 −1.40389 −0.701947 0.712229i 0.747686π-0.747686\pi
−0.701947 + 0.712229i 0.747686π0.747686\pi
810810 0 0
811811 −25.8617 −0.908128 −0.454064 0.890969i 0.650026π-0.650026\pi
−0.454064 + 0.890969i 0.650026π0.650026\pi
812812 0 0
813813 −4.31534 −0.151346
814814 0 0
815815 5.26137 0.184298
816816 0 0
817817 52.8466 1.84887
818818 0 0
819819 0 0
820820 0 0
821821 −5.05398 −0.176385 −0.0881925 0.996103i 0.528109π-0.528109\pi
−0.0881925 + 0.996103i 0.528109π0.528109\pi
822822 0 0
823823 −39.3693 −1.37233 −0.686164 0.727447i 0.740707π-0.740707\pi
−0.686164 + 0.727447i 0.740707π0.740707\pi
824824 0 0
825825 24.0000 0.835573
826826 0 0
827827 36.7386 1.27753 0.638764 0.769403i 0.279446π-0.279446\pi
0.638764 + 0.769403i 0.279446π0.279446\pi
828828 0 0
829829 −32.7386 −1.13706 −0.568530 0.822663i 0.692488π-0.692488\pi
−0.568530 + 0.822663i 0.692488π0.692488\pi
830830 0 0
831831 −3.50758 −0.121677
832832 0 0
833833 3.75379 0.130061
834834 0 0
835835 −5.26137 −0.182077
836836 0 0
837837 −10.2462 −0.354161
838838 0 0
839839 −36.1080 −1.24658 −0.623292 0.781989i 0.714205π-0.714205\pi
−0.623292 + 0.781989i 0.714205π0.714205\pi
840840 0 0
841841 39.0000 1.34483
842842 0 0
843843 −51.8617 −1.78621
844844 0 0
845845 0 0
846846 0 0
847847 −3.93087 −0.135066
848848 0 0
849849 5.75379 0.197470
850850 0 0
851851 0 0
852852 0 0
853853 −21.6847 −0.742469 −0.371234 0.928539i 0.621065π-0.621065\pi
−0.371234 + 0.928539i 0.621065π0.621065\pi
854854 0 0
855855 12.0000 0.410391
856856 0 0
857857 −32.2462 −1.10151 −0.550755 0.834667i 0.685660π-0.685660\pi
−0.550755 + 0.834667i 0.685660π0.685660\pi
858858 0 0
859859 −36.0000 −1.22830 −0.614152 0.789188i 0.710502π-0.710502\pi
−0.614152 + 0.789188i 0.710502π0.710502\pi
860860 0 0
861861 −10.2462 −0.349190
862862 0 0
863863 25.0540 0.852847 0.426424 0.904524i 0.359773π-0.359773\pi
0.426424 + 0.904524i 0.359773π0.359773\pi
864864 0 0
865865 −12.0000 −0.408012
866866 0 0
867867 −42.7386 −1.45148
868868 0 0
869869 −24.0000 −0.814144
870870 0 0
871871 0 0
872872 0 0
873873 21.3693 0.723242
874874 0 0
875875 3.05398 0.103243
876876 0 0
877877 31.7926 1.07356 0.536780 0.843722i 0.319640π-0.319640\pi
0.536780 + 0.843722i 0.319640π0.319640\pi
878878 0 0
879879 60.0388 2.02506
880880 0 0
881881 −19.3002 −0.650240 −0.325120 0.945673i 0.605405π-0.605405\pi
−0.325120 + 0.945673i 0.605405π0.605405\pi
882882 0 0
883883 −17.4384 −0.586850 −0.293425 0.955982i 0.594795π-0.594795\pi
−0.293425 + 0.955982i 0.594795π0.594795\pi
884884 0 0
885885 −8.63068 −0.290117
886886 0 0
887887 12.0000 0.402921 0.201460 0.979497i 0.435431π-0.435431\pi
0.201460 + 0.979497i 0.435431π0.435431\pi
888888 0 0
889889 1.26137 0.0423049
890890 0 0
891891 14.0000 0.469018
892892 0 0
893893 10.1080 0.338250
894894 0 0
895895 10.6998 0.357655
896896 0 0
897897 0 0
898898 0 0
899899 58.7386 1.95904
900900 0 0
901901 2.73863 0.0912371
902902 0 0
903903 −12.6695 −0.421615
904904 0 0
905905 −9.75379 −0.324227
906906 0 0
907907 26.4233 0.877371 0.438686 0.898641i 0.355444π-0.355444\pi
0.438686 + 0.898641i 0.355444π0.355444\pi
908908 0 0
909909 −25.3693 −0.841447
910910 0 0
911911 −27.3693 −0.906786 −0.453393 0.891311i 0.649787π-0.649787\pi
−0.453393 + 0.891311i 0.649787π0.649787\pi
912912 0 0
913913 −34.7386 −1.14968
914914 0 0
915915 −19.2311 −0.635759
916916 0 0
917917 8.80776 0.290858
918918 0 0
919919 33.7538 1.11343 0.556717 0.830702i 0.312061π-0.312061\pi
0.556717 + 0.830702i 0.312061π0.312061\pi
920920 0 0
921921 15.3693 0.506436
922922 0 0
923923 0 0
924924 0 0
925925 −45.3693 −1.49173
926926 0 0
927927 0 0
928928 0 0
929929 −35.6155 −1.16851 −0.584254 0.811571i 0.698613π-0.698613\pi
−0.584254 + 0.811571i 0.698613π0.698613\pi
930930 0 0
931931 40.1080 1.31448
932932 0 0
933933 −39.3693 −1.28889
934934 0 0
935935 −0.630683 −0.0206255
936936 0 0
937937 40.7386 1.33087 0.665437 0.746454i 0.268245π-0.268245\pi
0.665437 + 0.746454i 0.268245π0.268245\pi
938938 0 0
939939 43.6847 1.42559
940940 0 0
941941 −37.6847 −1.22848 −0.614242 0.789117i 0.710538π-0.710538\pi
−0.614242 + 0.789117i 0.710538π0.710538\pi
942942 0 0
943943 0 0
944944 0 0
945945 −0.453602 −0.0147557
946946 0 0
947947 −2.00000 −0.0649913 −0.0324956 0.999472i 0.510346π-0.510346\pi
−0.0324956 + 0.999472i 0.510346π0.510346\pi
948948 0 0
949949 0 0
950950 0 0
951951 82.6004 2.67850
952952 0 0
953953 −21.1922 −0.686484 −0.343242 0.939247i 0.611525π-0.611525\pi
−0.343242 + 0.939247i 0.611525π0.611525\pi
954954 0 0
955955 10.8769 0.351968
956956 0 0
957957 42.2462 1.36563
958958 0 0
959959 −2.73863 −0.0884351
960960 0 0
961961 19.7386 0.636730
962962 0 0
963963 −42.7386 −1.37723
964964 0 0
965965 0.768944 0.0247532
966966 0 0
967967 8.42329 0.270875 0.135437 0.990786i 0.456756π-0.456756\pi
0.135437 + 0.990786i 0.456756π0.456756\pi
968968 0 0
969969 8.63068 0.277257
970970 0 0
971971 −15.6847 −0.503345 −0.251672 0.967813i 0.580981π-0.580981\pi
−0.251672 + 0.967813i 0.580981π0.580981\pi
972972 0 0
973973 4.31534 0.138343
974974 0 0
975975 0 0
976976 0 0
977977 −50.9848 −1.63115 −0.815575 0.578652i 0.803579π-0.803579\pi
−0.815575 + 0.578652i 0.803579π0.803579\pi
978978 0 0
979979 −16.4924 −0.527100
980980 0 0
981981 6.00000 0.191565
982982 0 0
983983 −40.4233 −1.28930 −0.644651 0.764477i 0.722997π-0.722997\pi
−0.644651 + 0.764477i 0.722997π0.722997\pi
984984 0 0
985985 7.68466 0.244854
986986 0 0
987987 −2.42329 −0.0771342
988988 0 0
989989 0 0
990990 0 0
991991 3.36932 0.107030 0.0535149 0.998567i 0.482958π-0.482958\pi
0.0535149 + 0.998567i 0.482958π0.482958\pi
992992 0 0
993993 −54.7386 −1.73708
994994 0 0
995995 −8.63068 −0.273611
996996 0 0
997997 44.7386 1.41689 0.708443 0.705768i 0.249398π-0.249398\pi
0.708443 + 0.705768i 0.249398π0.249398\pi
998998 0 0
999999 13.9309 0.440753
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 5408.2.a.bd.1.2 2
4.3 odd 2 5408.2.a.p.1.1 2
13.12 even 2 416.2.a.e.1.2 yes 2
39.38 odd 2 3744.2.a.y.1.1 2
52.51 odd 2 416.2.a.c.1.1 2
104.51 odd 2 832.2.a.o.1.2 2
104.77 even 2 832.2.a.l.1.1 2
156.155 even 2 3744.2.a.x.1.1 2
208.51 odd 4 3328.2.b.ba.1665.1 4
208.77 even 4 3328.2.b.u.1665.4 4
208.155 odd 4 3328.2.b.ba.1665.4 4
208.181 even 4 3328.2.b.u.1665.1 4
312.77 odd 2 7488.2.a.cf.1.2 2
312.155 even 2 7488.2.a.ce.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
416.2.a.c.1.1 2 52.51 odd 2
416.2.a.e.1.2 yes 2 13.12 even 2
832.2.a.l.1.1 2 104.77 even 2
832.2.a.o.1.2 2 104.51 odd 2
3328.2.b.u.1665.1 4 208.181 even 4
3328.2.b.u.1665.4 4 208.77 even 4
3328.2.b.ba.1665.1 4 208.51 odd 4
3328.2.b.ba.1665.4 4 208.155 odd 4
3744.2.a.x.1.1 2 156.155 even 2
3744.2.a.y.1.1 2 39.38 odd 2
5408.2.a.p.1.1 2 4.3 odd 2
5408.2.a.bd.1.2 2 1.1 even 1 trivial
7488.2.a.ce.1.2 2 312.155 even 2
7488.2.a.cf.1.2 2 312.77 odd 2