Properties

Label 5120.2.a.t.1.5
Level 51205120
Weight 22
Character 5120.1
Self dual yes
Analytic conductor 40.88340.883
Analytic rank 11
Dimension 88
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [5120,2,Mod(1,5120)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5120, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5120.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 5120=2105 5120 = 2^{10} \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 5120.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,0,-4,0,8,0,-4,0,8,0,-8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 40.883405834940.8834058349
Analytic rank: 11
Dimension: 88
Coefficient field: Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x812x68x5+21x4+12x310x24x+1 x^{8} - 12x^{6} - 8x^{5} + 21x^{4} + 12x^{3} - 10x^{2} - 4x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 24 2^{4}
Twist minimal: no (minimal twist has level 80)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.5
Root 0.7313970.731397 of defining polynomial
Character χ\chi == 5120.1

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+0.169718q3+1.00000q5+2.66881q72.97120q9+4.94571q114.15881q13+0.169718q151.85116q174.87701q19+0.452946q21+0.707288q23+1.00000q251.01342q274.94847q296.84272q31+0.839377q33+2.66881q35+0.137894q370.705826q3910.2052q416.27690q432.97120q451.89428q47+0.122561q490.314175q5110.5203q53+4.94571q550.827717q57+1.35704q59+9.18991q617.92956q634.15881q654.94538q67+0.120040q69+7.86777q71+15.6564q73+0.169718q75+13.1992q776.70212q79+8.74159q815.47763q831.85116q850.839845q8710.5055q8911.0991q911.16133q934.87701q95+4.79937q9714.6947q99+O(q100)q+0.169718 q^{3} +1.00000 q^{5} +2.66881 q^{7} -2.97120 q^{9} +4.94571 q^{11} -4.15881 q^{13} +0.169718 q^{15} -1.85116 q^{17} -4.87701 q^{19} +0.452946 q^{21} +0.707288 q^{23} +1.00000 q^{25} -1.01342 q^{27} -4.94847 q^{29} -6.84272 q^{31} +0.839377 q^{33} +2.66881 q^{35} +0.137894 q^{37} -0.705826 q^{39} -10.2052 q^{41} -6.27690 q^{43} -2.97120 q^{45} -1.89428 q^{47} +0.122561 q^{49} -0.314175 q^{51} -10.5203 q^{53} +4.94571 q^{55} -0.827717 q^{57} +1.35704 q^{59} +9.18991 q^{61} -7.92956 q^{63} -4.15881 q^{65} -4.94538 q^{67} +0.120040 q^{69} +7.86777 q^{71} +15.6564 q^{73} +0.169718 q^{75} +13.1992 q^{77} -6.70212 q^{79} +8.74159 q^{81} -5.47763 q^{83} -1.85116 q^{85} -0.839845 q^{87} -10.5055 q^{89} -11.0991 q^{91} -1.16133 q^{93} -4.87701 q^{95} +4.79937 q^{97} -14.6947 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q4q3+8q54q7+8q98q114q1516q1912q23+8q2516q274q3528q43+8q4520q47+8q4924q518q5516q59+40q99+O(q100) 8 q - 4 q^{3} + 8 q^{5} - 4 q^{7} + 8 q^{9} - 8 q^{11} - 4 q^{15} - 16 q^{19} - 12 q^{23} + 8 q^{25} - 16 q^{27} - 4 q^{35} - 28 q^{43} + 8 q^{45} - 20 q^{47} + 8 q^{49} - 24 q^{51} - 8 q^{55} - 16 q^{59}+ \cdots - 40 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 0.169718 0.0979869 0.0489934 0.998799i 0.484399π-0.484399\pi
0.0489934 + 0.998799i 0.484399π0.484399\pi
44 0 0
55 1.00000 0.447214
66 0 0
77 2.66881 1.00872 0.504358 0.863495i 0.331729π-0.331729\pi
0.504358 + 0.863495i 0.331729π0.331729\pi
88 0 0
99 −2.97120 −0.990399
1010 0 0
1111 4.94571 1.49119 0.745594 0.666401i 0.232166π-0.232166\pi
0.745594 + 0.666401i 0.232166π0.232166\pi
1212 0 0
1313 −4.15881 −1.15345 −0.576723 0.816939i 0.695669π-0.695669\pi
−0.576723 + 0.816939i 0.695669π0.695669\pi
1414 0 0
1515 0.169718 0.0438211
1616 0 0
1717 −1.85116 −0.448971 −0.224486 0.974477i 0.572070π-0.572070\pi
−0.224486 + 0.974477i 0.572070π0.572070\pi
1818 0 0
1919 −4.87701 −1.11886 −0.559431 0.828877i 0.688980π-0.688980\pi
−0.559431 + 0.828877i 0.688980π0.688980\pi
2020 0 0
2121 0.452946 0.0988409
2222 0 0
2323 0.707288 0.147480 0.0737399 0.997278i 0.476507π-0.476507\pi
0.0737399 + 0.997278i 0.476507π0.476507\pi
2424 0 0
2525 1.00000 0.200000
2626 0 0
2727 −1.01342 −0.195033
2828 0 0
2929 −4.94847 −0.918907 −0.459454 0.888202i 0.651955π-0.651955\pi
−0.459454 + 0.888202i 0.651955π0.651955\pi
3030 0 0
3131 −6.84272 −1.22899 −0.614494 0.788921i 0.710640π-0.710640\pi
−0.614494 + 0.788921i 0.710640π0.710640\pi
3232 0 0
3333 0.839377 0.146117
3434 0 0
3535 2.66881 0.451112
3636 0 0
3737 0.137894 0.0226697 0.0113348 0.999936i 0.496392π-0.496392\pi
0.0113348 + 0.999936i 0.496392π0.496392\pi
3838 0 0
3939 −0.705826 −0.113023
4040 0 0
4141 −10.2052 −1.59379 −0.796896 0.604117i 0.793526π-0.793526\pi
−0.796896 + 0.604117i 0.793526π0.793526\pi
4242 0 0
4343 −6.27690 −0.957218 −0.478609 0.878028i 0.658859π-0.658859\pi
−0.478609 + 0.878028i 0.658859π0.658859\pi
4444 0 0
4545 −2.97120 −0.442920
4646 0 0
4747 −1.89428 −0.276310 −0.138155 0.990411i 0.544117π-0.544117\pi
−0.138155 + 0.990411i 0.544117π0.544117\pi
4848 0 0
4949 0.122561 0.0175087
5050 0 0
5151 −0.314175 −0.0439933
5252 0 0
5353 −10.5203 −1.44507 −0.722537 0.691332i 0.757024π-0.757024\pi
−0.722537 + 0.691332i 0.757024π0.757024\pi
5454 0 0
5555 4.94571 0.666879
5656 0 0
5757 −0.827717 −0.109634
5858 0 0
5959 1.35704 0.176672 0.0883359 0.996091i 0.471845π-0.471845\pi
0.0883359 + 0.996091i 0.471845π0.471845\pi
6060 0 0
6161 9.18991 1.17665 0.588324 0.808625i 0.299788π-0.299788\pi
0.588324 + 0.808625i 0.299788π0.299788\pi
6262 0 0
6363 −7.92956 −0.999031
6464 0 0
6565 −4.15881 −0.515837
6666 0 0
6767 −4.94538 −0.604174 −0.302087 0.953280i 0.597683π-0.597683\pi
−0.302087 + 0.953280i 0.597683π0.597683\pi
6868 0 0
6969 0.120040 0.0144511
7070 0 0
7171 7.86777 0.933733 0.466866 0.884328i 0.345383π-0.345383\pi
0.466866 + 0.884328i 0.345383π0.345383\pi
7272 0 0
7373 15.6564 1.83244 0.916220 0.400675i 0.131224π-0.131224\pi
0.916220 + 0.400675i 0.131224π0.131224\pi
7474 0 0
7575 0.169718 0.0195974
7676 0 0
7777 13.1992 1.50418
7878 0 0
7979 −6.70212 −0.754047 −0.377024 0.926204i 0.623052π-0.623052\pi
−0.377024 + 0.926204i 0.623052π0.623052\pi
8080 0 0
8181 8.74159 0.971288
8282 0 0
8383 −5.47763 −0.601248 −0.300624 0.953743i 0.597195π-0.597195\pi
−0.300624 + 0.953743i 0.597195π0.597195\pi
8484 0 0
8585 −1.85116 −0.200786
8686 0 0
8787 −0.839845 −0.0900408
8888 0 0
8989 −10.5055 −1.11358 −0.556790 0.830653i 0.687967π-0.687967\pi
−0.556790 + 0.830653i 0.687967π0.687967\pi
9090 0 0
9191 −11.0991 −1.16350
9292 0 0
9393 −1.16133 −0.120425
9494 0 0
9595 −4.87701 −0.500370
9696 0 0
9797 4.79937 0.487303 0.243651 0.969863i 0.421655π-0.421655\pi
0.243651 + 0.969863i 0.421655π0.421655\pi
9898 0 0
9999 −14.6947 −1.47687
100100 0 0
101101 −0.527472 −0.0524855 −0.0262427 0.999656i 0.508354π-0.508354\pi
−0.0262427 + 0.999656i 0.508354π0.508354\pi
102102 0 0
103103 −10.3013 −1.01502 −0.507508 0.861647i 0.669433π-0.669433\pi
−0.507508 + 0.861647i 0.669433π0.669433\pi
104104 0 0
105105 0.452946 0.0442030
106106 0 0
107107 −20.5159 −1.98335 −0.991674 0.128770i 0.958897π-0.958897\pi
−0.991674 + 0.128770i 0.958897π0.958897\pi
108108 0 0
109109 −1.12612 −0.107862 −0.0539311 0.998545i 0.517175π-0.517175\pi
−0.0539311 + 0.998545i 0.517175π0.517175\pi
110110 0 0
111111 0.0234032 0.00222133
112112 0 0
113113 −0.842524 −0.0792580 −0.0396290 0.999214i 0.512618π-0.512618\pi
−0.0396290 + 0.999214i 0.512618π0.512618\pi
114114 0 0
115115 0.707288 0.0659550
116116 0 0
117117 12.3566 1.14237
118118 0 0
119119 −4.94039 −0.452885
120120 0 0
121121 13.4600 1.22364
122122 0 0
123123 −1.73202 −0.156171
124124 0 0
125125 1.00000 0.0894427
126126 0 0
127127 21.1693 1.87847 0.939234 0.343277i 0.111537π-0.111537\pi
0.939234 + 0.343277i 0.111537π0.111537\pi
128128 0 0
129129 −1.06530 −0.0937947
130130 0 0
131131 −6.60789 −0.577334 −0.288667 0.957430i 0.593212π-0.593212\pi
−0.288667 + 0.957430i 0.593212π0.593212\pi
132132 0 0
133133 −13.0158 −1.12861
134134 0 0
135135 −1.01342 −0.0872214
136136 0 0
137137 10.2840 0.878623 0.439312 0.898335i 0.355222π-0.355222\pi
0.439312 + 0.898335i 0.355222π0.355222\pi
138138 0 0
139139 −7.05110 −0.598066 −0.299033 0.954243i 0.596664π-0.596664\pi
−0.299033 + 0.954243i 0.596664π0.596664\pi
140140 0 0
141141 −0.321495 −0.0270747
142142 0 0
143143 −20.5683 −1.72001
144144 0 0
145145 −4.94847 −0.410948
146146 0 0
147147 0.0208008 0.00171563
148148 0 0
149149 12.4379 1.01895 0.509477 0.860484i 0.329839π-0.329839\pi
0.509477 + 0.860484i 0.329839π0.329839\pi
150150 0 0
151151 22.1838 1.80529 0.902645 0.430385i 0.141622π-0.141622\pi
0.902645 + 0.430385i 0.141622π0.141622\pi
152152 0 0
153153 5.50015 0.444661
154154 0 0
155155 −6.84272 −0.549620
156156 0 0
157157 −5.26352 −0.420075 −0.210037 0.977693i 0.567359π-0.567359\pi
−0.210037 + 0.977693i 0.567359π0.567359\pi
158158 0 0
159159 −1.78549 −0.141598
160160 0 0
161161 1.88762 0.148765
162162 0 0
163163 −2.99290 −0.234422 −0.117211 0.993107i 0.537395π-0.537395\pi
−0.117211 + 0.993107i 0.537395π0.537395\pi
164164 0 0
165165 0.839377 0.0653454
166166 0 0
167167 18.1604 1.40530 0.702648 0.711538i 0.252001π-0.252001\pi
0.702648 + 0.711538i 0.252001π0.252001\pi
168168 0 0
169169 4.29572 0.330440
170170 0 0
171171 14.4905 1.10812
172172 0 0
173173 12.0709 0.917734 0.458867 0.888505i 0.348255π-0.348255\pi
0.458867 + 0.888505i 0.348255π0.348255\pi
174174 0 0
175175 2.66881 0.201743
176176 0 0
177177 0.230315 0.0173115
178178 0 0
179179 −3.42945 −0.256329 −0.128165 0.991753i 0.540909π-0.540909\pi
−0.128165 + 0.991753i 0.540909π0.540909\pi
180180 0 0
181181 6.31578 0.469448 0.234724 0.972062i 0.424581π-0.424581\pi
0.234724 + 0.972062i 0.424581π0.424581\pi
182182 0 0
183183 1.55970 0.115296
184184 0 0
185185 0.137894 0.0101382
186186 0 0
187187 −9.15528 −0.669500
188188 0 0
189189 −2.70463 −0.196733
190190 0 0
191191 −7.75030 −0.560792 −0.280396 0.959884i 0.590466π-0.590466\pi
−0.280396 + 0.959884i 0.590466π0.590466\pi
192192 0 0
193193 −11.3388 −0.816181 −0.408091 0.912941i 0.633805π-0.633805\pi
−0.408091 + 0.912941i 0.633805π0.633805\pi
194194 0 0
195195 −0.705826 −0.0505453
196196 0 0
197197 −1.55565 −0.110836 −0.0554178 0.998463i 0.517649π-0.517649\pi
−0.0554178 + 0.998463i 0.517649π0.517649\pi
198198 0 0
199199 14.2722 1.01173 0.505864 0.862614i 0.331174π-0.331174\pi
0.505864 + 0.862614i 0.331174π0.331174\pi
200200 0 0
201201 −0.839321 −0.0592012
202202 0 0
203203 −13.2065 −0.926917
204204 0 0
205205 −10.2052 −0.712765
206206 0 0
207207 −2.10149 −0.146064
208208 0 0
209209 −24.1203 −1.66843
210210 0 0
211211 −17.6374 −1.21421 −0.607106 0.794621i 0.707670π-0.707670\pi
−0.607106 + 0.794621i 0.707670π0.707670\pi
212212 0 0
213213 1.33530 0.0914935
214214 0 0
215215 −6.27690 −0.428081
216216 0 0
217217 −18.2619 −1.23970
218218 0 0
219219 2.65717 0.179555
220220 0 0
221221 7.69861 0.517865
222222 0 0
223223 −3.08673 −0.206703 −0.103351 0.994645i 0.532957π-0.532957\pi
−0.103351 + 0.994645i 0.532957π0.532957\pi
224224 0 0
225225 −2.97120 −0.198080
226226 0 0
227227 −11.7617 −0.780651 −0.390326 0.920677i 0.627638π-0.627638\pi
−0.390326 + 0.920677i 0.627638π0.627638\pi
228228 0 0
229229 14.1267 0.933520 0.466760 0.884384i 0.345421π-0.345421\pi
0.466760 + 0.884384i 0.345421π0.345421\pi
230230 0 0
231231 2.24014 0.147390
232232 0 0
233233 −13.9015 −0.910718 −0.455359 0.890308i 0.650489π-0.650489\pi
−0.455359 + 0.890308i 0.650489π0.650489\pi
234234 0 0
235235 −1.89428 −0.123570
236236 0 0
237237 −1.13747 −0.0738867
238238 0 0
239239 −10.7687 −0.696569 −0.348284 0.937389i 0.613236π-0.613236\pi
−0.348284 + 0.937389i 0.613236π0.613236\pi
240240 0 0
241241 12.4707 0.803305 0.401653 0.915792i 0.368436π-0.368436\pi
0.401653 + 0.915792i 0.368436π0.368436\pi
242242 0 0
243243 4.52387 0.290206
244244 0 0
245245 0.122561 0.00783014
246246 0 0
247247 20.2826 1.29055
248248 0 0
249249 −0.929654 −0.0589144
250250 0 0
251251 5.21976 0.329468 0.164734 0.986338i 0.447323π-0.447323\pi
0.164734 + 0.986338i 0.447323π0.447323\pi
252252 0 0
253253 3.49804 0.219920
254254 0 0
255255 −0.314175 −0.0196744
256256 0 0
257257 3.11011 0.194003 0.0970016 0.995284i 0.469075π-0.469075\pi
0.0970016 + 0.995284i 0.469075π0.469075\pi
258258 0 0
259259 0.368014 0.0228673
260260 0 0
261261 14.7029 0.910084
262262 0 0
263263 17.9512 1.10692 0.553458 0.832877i 0.313308π-0.313308\pi
0.553458 + 0.832877i 0.313308π0.313308\pi
264264 0 0
265265 −10.5203 −0.646257
266266 0 0
267267 −1.78297 −0.109116
268268 0 0
269269 −2.29720 −0.140063 −0.0700313 0.997545i 0.522310π-0.522310\pi
−0.0700313 + 0.997545i 0.522310π0.522310\pi
270270 0 0
271271 18.1808 1.10440 0.552201 0.833711i 0.313788π-0.313788\pi
0.552201 + 0.833711i 0.313788π0.313788\pi
272272 0 0
273273 −1.88372 −0.114008
274274 0 0
275275 4.94571 0.298237
276276 0 0
277277 −19.6116 −1.17835 −0.589174 0.808006i 0.700547π-0.700547\pi
−0.589174 + 0.808006i 0.700547π0.700547\pi
278278 0 0
279279 20.3310 1.21719
280280 0 0
281281 −10.7377 −0.640556 −0.320278 0.947324i 0.603776π-0.603776\pi
−0.320278 + 0.947324i 0.603776π0.603776\pi
282282 0 0
283283 −23.1477 −1.37599 −0.687994 0.725716i 0.741509π-0.741509\pi
−0.687994 + 0.725716i 0.741509π0.741509\pi
284284 0 0
285285 −0.827717 −0.0490297
286286 0 0
287287 −27.2359 −1.60768
288288 0 0
289289 −13.5732 −0.798425
290290 0 0
291291 0.814541 0.0477493
292292 0 0
293293 5.96872 0.348696 0.174348 0.984684i 0.444218π-0.444218\pi
0.174348 + 0.984684i 0.444218π0.444218\pi
294294 0 0
295295 1.35704 0.0790101
296296 0 0
297297 −5.01208 −0.290831
298298 0 0
299299 −2.94148 −0.170110
300300 0 0
301301 −16.7519 −0.965561
302302 0 0
303303 −0.0895217 −0.00514289
304304 0 0
305305 9.18991 0.526213
306306 0 0
307307 −17.8704 −1.01992 −0.509958 0.860199i 0.670339π-0.670339\pi
−0.509958 + 0.860199i 0.670339π0.670339\pi
308308 0 0
309309 −1.74832 −0.0994582
310310 0 0
311311 8.56815 0.485855 0.242928 0.970044i 0.421892π-0.421892\pi
0.242928 + 0.970044i 0.421892π0.421892\pi
312312 0 0
313313 19.1825 1.08426 0.542129 0.840295i 0.317618π-0.317618\pi
0.542129 + 0.840295i 0.317618π0.317618\pi
314314 0 0
315315 −7.92956 −0.446780
316316 0 0
317317 −13.3185 −0.748044 −0.374022 0.927420i 0.622022π-0.622022\pi
−0.374022 + 0.927420i 0.622022π0.622022\pi
318318 0 0
319319 −24.4737 −1.37026
320320 0 0
321321 −3.48193 −0.194342
322322 0 0
323323 9.02810 0.502337
324324 0 0
325325 −4.15881 −0.230689
326326 0 0
327327 −0.191122 −0.0105691
328328 0 0
329329 −5.05549 −0.278718
330330 0 0
331331 −18.1838 −0.999471 −0.499736 0.866178i 0.666569π-0.666569\pi
−0.499736 + 0.866178i 0.666569π0.666569\pi
332332 0 0
333333 −0.409711 −0.0224520
334334 0 0
335335 −4.94538 −0.270195
336336 0 0
337337 −3.31961 −0.180831 −0.0904153 0.995904i 0.528819π-0.528819\pi
−0.0904153 + 0.995904i 0.528819π0.528819\pi
338338 0 0
339339 −0.142992 −0.00776624
340340 0 0
341341 −33.8421 −1.83265
342342 0 0
343343 −18.3546 −0.991055
344344 0 0
345345 0.120040 0.00646272
346346 0 0
347347 25.2946 1.35789 0.678943 0.734191i 0.262438π-0.262438\pi
0.678943 + 0.734191i 0.262438π0.262438\pi
348348 0 0
349349 −5.21557 −0.279183 −0.139591 0.990209i 0.544579π-0.544579\pi
−0.139591 + 0.990209i 0.544579π0.544579\pi
350350 0 0
351351 4.21463 0.224960
352352 0 0
353353 33.0951 1.76148 0.880738 0.473604i 0.157047π-0.157047\pi
0.880738 + 0.473604i 0.157047π0.157047\pi
354354 0 0
355355 7.86777 0.417578
356356 0 0
357357 −0.838474 −0.0443767
358358 0 0
359359 −6.52522 −0.344388 −0.172194 0.985063i 0.555086π-0.555086\pi
−0.172194 + 0.985063i 0.555086π0.555086\pi
360360 0 0
361361 4.78519 0.251852
362362 0 0
363363 2.28441 0.119901
364364 0 0
365365 15.6564 0.819492
366366 0 0
367367 −11.0338 −0.575959 −0.287980 0.957636i 0.592984π-0.592984\pi
−0.287980 + 0.957636i 0.592984π0.592984\pi
368368 0 0
369369 30.3218 1.57849
370370 0 0
371371 −28.0767 −1.45767
372372 0 0
373373 9.67984 0.501203 0.250602 0.968090i 0.419372π-0.419372\pi
0.250602 + 0.968090i 0.419372π0.419372\pi
374374 0 0
375375 0.169718 0.00876421
376376 0 0
377377 20.5797 1.05991
378378 0 0
379379 −14.2937 −0.734219 −0.367109 0.930178i 0.619653π-0.619653\pi
−0.367109 + 0.930178i 0.619653π0.619653\pi
380380 0 0
381381 3.59281 0.184065
382382 0 0
383383 −29.5283 −1.50883 −0.754413 0.656400i 0.772078π-0.772078\pi
−0.754413 + 0.656400i 0.772078π0.772078\pi
384384 0 0
385385 13.1992 0.672692
386386 0 0
387387 18.6499 0.948027
388388 0 0
389389 −1.40141 −0.0710545 −0.0355272 0.999369i 0.511311π-0.511311\pi
−0.0355272 + 0.999369i 0.511311π0.511311\pi
390390 0 0
391391 −1.30930 −0.0662142
392392 0 0
393393 −1.12148 −0.0565711
394394 0 0
395395 −6.70212 −0.337220
396396 0 0
397397 −24.0450 −1.20678 −0.603392 0.797444i 0.706185π-0.706185\pi
−0.603392 + 0.797444i 0.706185π0.706185\pi
398398 0 0
399399 −2.20902 −0.110589
400400 0 0
401401 −26.7791 −1.33728 −0.668642 0.743585i 0.733124π-0.733124\pi
−0.668642 + 0.743585i 0.733124π0.733124\pi
402402 0 0
403403 28.4576 1.41757
404404 0 0
405405 8.74159 0.434373
406406 0 0
407407 0.681985 0.0338048
408408 0 0
409409 13.1970 0.652550 0.326275 0.945275i 0.394206π-0.394206\pi
0.326275 + 0.945275i 0.394206π0.394206\pi
410410 0 0
411411 1.74539 0.0860935
412412 0 0
413413 3.62169 0.178212
414414 0 0
415415 −5.47763 −0.268886
416416 0 0
417417 −1.19670 −0.0586026
418418 0 0
419419 14.0356 0.685684 0.342842 0.939393i 0.388610π-0.388610\pi
0.342842 + 0.939393i 0.388610π0.388610\pi
420420 0 0
421421 −22.3346 −1.08852 −0.544261 0.838916i 0.683190π-0.683190\pi
−0.544261 + 0.838916i 0.683190π0.683190\pi
422422 0 0
423423 5.62829 0.273657
424424 0 0
425425 −1.85116 −0.0897943
426426 0 0
427427 24.5262 1.18690
428428 0 0
429429 −3.49081 −0.168538
430430 0 0
431431 −0.285215 −0.0137383 −0.00686917 0.999976i 0.502187π-0.502187\pi
−0.00686917 + 0.999976i 0.502187π0.502187\pi
432432 0 0
433433 18.1101 0.870318 0.435159 0.900354i 0.356692π-0.356692\pi
0.435159 + 0.900354i 0.356692π0.356692\pi
434434 0 0
435435 −0.839845 −0.0402675
436436 0 0
437437 −3.44945 −0.165010
438438 0 0
439439 −11.5931 −0.553308 −0.276654 0.960970i 0.589226π-0.589226\pi
−0.276654 + 0.960970i 0.589226π0.589226\pi
440440 0 0
441441 −0.364153 −0.0173406
442442 0 0
443443 −32.0821 −1.52427 −0.762133 0.647420i 0.775848π-0.775848\pi
−0.762133 + 0.647420i 0.775848π0.775848\pi
444444 0 0
445445 −10.5055 −0.498008
446446 0 0
447447 2.11094 0.0998440
448448 0 0
449449 12.1999 0.575747 0.287873 0.957669i 0.407052π-0.407052\pi
0.287873 + 0.957669i 0.407052π0.407052\pi
450450 0 0
451451 −50.4722 −2.37664
452452 0 0
453453 3.76499 0.176895
454454 0 0
455455 −11.0991 −0.520333
456456 0 0
457457 −1.70660 −0.0798314 −0.0399157 0.999203i 0.512709π-0.512709\pi
−0.0399157 + 0.999203i 0.512709π0.512709\pi
458458 0 0
459459 1.87600 0.0875642
460460 0 0
461461 6.71341 0.312675 0.156337 0.987704i 0.450031π-0.450031\pi
0.156337 + 0.987704i 0.450031π0.450031\pi
462462 0 0
463463 −11.1761 −0.519398 −0.259699 0.965690i 0.583623π-0.583623\pi
−0.259699 + 0.965690i 0.583623π0.583623\pi
464464 0 0
465465 −1.16133 −0.0538556
466466 0 0
467467 2.91995 0.135119 0.0675595 0.997715i 0.478479π-0.478479\pi
0.0675595 + 0.997715i 0.478479π0.478479\pi
468468 0 0
469469 −13.1983 −0.609441
470470 0 0
471471 −0.893315 −0.0411618
472472 0 0
473473 −31.0437 −1.42739
474474 0 0
475475 −4.87701 −0.223772
476476 0 0
477477 31.2579 1.43120
478478 0 0
479479 41.6214 1.90173 0.950864 0.309608i 0.100198π-0.100198\pi
0.950864 + 0.309608i 0.100198π0.100198\pi
480480 0 0
481481 −0.573477 −0.0261483
482482 0 0
483483 0.320364 0.0145770
484484 0 0
485485 4.79937 0.217928
486486 0 0
487487 8.25627 0.374127 0.187064 0.982348i 0.440103π-0.440103\pi
0.187064 + 0.982348i 0.440103π0.440103\pi
488488 0 0
489489 −0.507950 −0.0229703
490490 0 0
491491 −6.06007 −0.273487 −0.136744 0.990606i 0.543664π-0.543664\pi
−0.136744 + 0.990606i 0.543664π0.543664\pi
492492 0 0
493493 9.16038 0.412563
494494 0 0
495495 −14.6947 −0.660476
496496 0 0
497497 20.9976 0.941871
498498 0 0
499499 −21.3952 −0.957780 −0.478890 0.877875i 0.658961π-0.658961\pi
−0.478890 + 0.877875i 0.658961π0.658961\pi
500500 0 0
501501 3.08215 0.137700
502502 0 0
503503 −18.6439 −0.831291 −0.415646 0.909527i 0.636444π-0.636444\pi
−0.415646 + 0.909527i 0.636444π0.636444\pi
504504 0 0
505505 −0.527472 −0.0234722
506506 0 0
507507 0.729062 0.0323788
508508 0 0
509509 16.4393 0.728658 0.364329 0.931270i 0.381298π-0.381298\pi
0.364329 + 0.931270i 0.381298π0.381298\pi
510510 0 0
511511 41.7839 1.84841
512512 0 0
513513 4.94246 0.218215
514514 0 0
515515 −10.3013 −0.453929
516516 0 0
517517 −9.36858 −0.412030
518518 0 0
519519 2.04865 0.0899259
520520 0 0
521521 36.9052 1.61684 0.808422 0.588603i 0.200322π-0.200322\pi
0.808422 + 0.588603i 0.200322π0.200322\pi
522522 0 0
523523 −8.54409 −0.373607 −0.186803 0.982397i 0.559813π-0.559813\pi
−0.186803 + 0.982397i 0.559813π0.559813\pi
524524 0 0
525525 0.452946 0.0197682
526526 0 0
527527 12.6669 0.551780
528528 0 0
529529 −22.4997 −0.978250
530530 0 0
531531 −4.03204 −0.174976
532532 0 0
533533 42.4417 1.83835
534534 0 0
535535 −20.5159 −0.886981
536536 0 0
537537 −0.582041 −0.0251169
538538 0 0
539539 0.606151 0.0261088
540540 0 0
541541 −40.1951 −1.72812 −0.864061 0.503387i 0.832087π-0.832087\pi
−0.864061 + 0.503387i 0.832087π0.832087\pi
542542 0 0
543543 1.07190 0.0459997
544544 0 0
545545 −1.12612 −0.0482375
546546 0 0
547547 −33.0307 −1.41229 −0.706145 0.708067i 0.749567π-0.749567\pi
−0.706145 + 0.708067i 0.749567π0.749567\pi
548548 0 0
549549 −27.3050 −1.16535
550550 0 0
551551 24.1337 1.02813
552552 0 0
553553 −17.8867 −0.760620
554554 0 0
555555 0.0234032 0.000993410 0
556556 0 0
557557 6.92285 0.293331 0.146665 0.989186i 0.453146π-0.453146\pi
0.146665 + 0.989186i 0.453146π0.453146\pi
558558 0 0
559559 26.1044 1.10410
560560 0 0
561561 −1.55382 −0.0656022
562562 0 0
563563 1.81887 0.0766561 0.0383280 0.999265i 0.487797π-0.487797\pi
0.0383280 + 0.999265i 0.487797π0.487797\pi
564564 0 0
565565 −0.842524 −0.0354453
566566 0 0
567567 23.3297 0.979754
568568 0 0
569569 11.4799 0.481261 0.240631 0.970617i 0.422646π-0.422646\pi
0.240631 + 0.970617i 0.422646π0.422646\pi
570570 0 0
571571 40.5976 1.69896 0.849479 0.527623i 0.176917π-0.176917\pi
0.849479 + 0.527623i 0.176917π0.176917\pi
572572 0 0
573573 −1.31537 −0.0549503
574574 0 0
575575 0.707288 0.0294960
576576 0 0
577577 −20.3419 −0.846842 −0.423421 0.905933i 0.639171π-0.639171\pi
−0.423421 + 0.905933i 0.639171π0.639171\pi
578578 0 0
579579 −1.92439 −0.0799751
580580 0 0
581581 −14.6188 −0.606489
582582 0 0
583583 −52.0303 −2.15488
584584 0 0
585585 12.3566 0.510884
586586 0 0
587587 36.5059 1.50676 0.753379 0.657586i 0.228422π-0.228422\pi
0.753379 + 0.657586i 0.228422π0.228422\pi
588588 0 0
589589 33.3720 1.37507
590590 0 0
591591 −0.264022 −0.0108604
592592 0 0
593593 −4.02945 −0.165470 −0.0827349 0.996572i 0.526365π-0.526365\pi
−0.0827349 + 0.996572i 0.526365π0.526365\pi
594594 0 0
595595 −4.94039 −0.202536
596596 0 0
597597 2.42225 0.0991360
598598 0 0
599599 31.6701 1.29400 0.647002 0.762489i 0.276023π-0.276023\pi
0.647002 + 0.762489i 0.276023π0.276023\pi
600600 0 0
601601 −19.4667 −0.794065 −0.397032 0.917805i 0.629960π-0.629960\pi
−0.397032 + 0.917805i 0.629960π0.629960\pi
602602 0 0
603603 14.6937 0.598373
604604 0 0
605605 13.4600 0.547228
606606 0 0
607607 −13.6128 −0.552528 −0.276264 0.961082i 0.589096π-0.589096\pi
−0.276264 + 0.961082i 0.589096π0.589096\pi
608608 0 0
609609 −2.24139 −0.0908257
610610 0 0
611611 7.87797 0.318709
612612 0 0
613613 15.7657 0.636771 0.318386 0.947961i 0.396859π-0.396859\pi
0.318386 + 0.947961i 0.396859π0.396859\pi
614614 0 0
615615 −1.73202 −0.0698416
616616 0 0
617617 1.96695 0.0791863 0.0395932 0.999216i 0.487394π-0.487394\pi
0.0395932 + 0.999216i 0.487394π0.487394\pi
618618 0 0
619619 −11.0895 −0.445723 −0.222862 0.974850i 0.571540π-0.571540\pi
−0.222862 + 0.974850i 0.571540π0.571540\pi
620620 0 0
621621 −0.716781 −0.0287634
622622 0 0
623623 −28.0372 −1.12329
624624 0 0
625625 1.00000 0.0400000
626626 0 0
627627 −4.09365 −0.163484
628628 0 0
629629 −0.255264 −0.0101780
630630 0 0
631631 −0.220729 −0.00878708 −0.00439354 0.999990i 0.501399π-0.501399\pi
−0.00439354 + 0.999990i 0.501399π0.501399\pi
632632 0 0
633633 −2.99339 −0.118977
634634 0 0
635635 21.1693 0.840077
636636 0 0
637637 −0.509709 −0.0201954
638638 0 0
639639 −23.3767 −0.924767
640640 0 0
641641 −19.2037 −0.758502 −0.379251 0.925294i 0.623818π-0.623818\pi
−0.379251 + 0.925294i 0.623818π0.623818\pi
642642 0 0
643643 10.1415 0.399940 0.199970 0.979802i 0.435915π-0.435915\pi
0.199970 + 0.979802i 0.435915π0.435915\pi
644644 0 0
645645 −1.06530 −0.0419463
646646 0 0
647647 −26.4735 −1.04078 −0.520391 0.853928i 0.674214π-0.674214\pi
−0.520391 + 0.853928i 0.674214π0.674214\pi
648648 0 0
649649 6.71153 0.263451
650650 0 0
651651 −3.09938 −0.121474
652652 0 0
653653 −14.9547 −0.585222 −0.292611 0.956232i 0.594524π-0.594524\pi
−0.292611 + 0.956232i 0.594524π0.594524\pi
654654 0 0
655655 −6.60789 −0.258192
656656 0 0
657657 −46.5182 −1.81485
658658 0 0
659659 34.1237 1.32927 0.664636 0.747167i 0.268587π-0.268587\pi
0.664636 + 0.747167i 0.268587π0.268587\pi
660660 0 0
661661 33.1342 1.28877 0.644386 0.764701i 0.277113π-0.277113\pi
0.644386 + 0.764701i 0.277113π0.277113\pi
662662 0 0
663663 1.30659 0.0507439
664664 0 0
665665 −13.0158 −0.504732
666666 0 0
667667 −3.49999 −0.135520
668668 0 0
669669 −0.523874 −0.0202541
670670 0 0
671671 45.4506 1.75460
672672 0 0
673673 −41.8069 −1.61154 −0.805769 0.592230i 0.798248π-0.798248\pi
−0.805769 + 0.592230i 0.798248π0.798248\pi
674674 0 0
675675 −1.01342 −0.0390066
676676 0 0
677677 32.1521 1.23571 0.617853 0.786294i 0.288003π-0.288003\pi
0.617853 + 0.786294i 0.288003π0.288003\pi
678678 0 0
679679 12.8086 0.491550
680680 0 0
681681 −1.99617 −0.0764936
682682 0 0
683683 −48.7058 −1.86367 −0.931837 0.362877i 0.881794π-0.881794\pi
−0.931837 + 0.362877i 0.881794π0.881794\pi
684684 0 0
685685 10.2840 0.392932
686686 0 0
687687 2.39756 0.0914727
688688 0 0
689689 43.7519 1.66682
690690 0 0
691691 22.7675 0.866117 0.433059 0.901366i 0.357434π-0.357434\pi
0.433059 + 0.901366i 0.357434π0.357434\pi
692692 0 0
693693 −39.2173 −1.48974
694694 0 0
695695 −7.05110 −0.267463
696696 0 0
697697 18.8915 0.715567
698698 0 0
699699 −2.35934 −0.0892384
700700 0 0
701701 −42.4981 −1.60513 −0.802566 0.596563i 0.796533π-0.796533\pi
−0.802566 + 0.596563i 0.796533π0.796533\pi
702702 0 0
703703 −0.672512 −0.0253643
704704 0 0
705705 −0.321495 −0.0121082
706706 0 0
707707 −1.40773 −0.0529430
708708 0 0
709709 18.2700 0.686143 0.343071 0.939309i 0.388533π-0.388533\pi
0.343071 + 0.939309i 0.388533π0.388533\pi
710710 0 0
711711 19.9133 0.746807
712712 0 0
713713 −4.83977 −0.181251
714714 0 0
715715 −20.5683 −0.769210
716716 0 0
717717 −1.82764 −0.0682546
718718 0 0
719719 17.0356 0.635319 0.317659 0.948205i 0.397103π-0.397103\pi
0.317659 + 0.948205i 0.397103π0.397103\pi
720720 0 0
721721 −27.4922 −1.02386
722722 0 0
723723 2.11650 0.0787134
724724 0 0
725725 −4.94847 −0.183781
726726 0 0
727727 −31.7051 −1.17588 −0.587939 0.808905i 0.700061π-0.700061\pi
−0.587939 + 0.808905i 0.700061π0.700061\pi
728728 0 0
729729 −25.4570 −0.942852
730730 0 0
731731 11.6195 0.429763
732732 0 0
733733 5.48230 0.202493 0.101247 0.994861i 0.467717π-0.467717\pi
0.101247 + 0.994861i 0.467717π0.467717\pi
734734 0 0
735735 0.0208008 0.000767251 0
736736 0 0
737737 −24.4584 −0.900937
738738 0 0
739739 −15.9840 −0.587983 −0.293991 0.955808i 0.594984π-0.594984\pi
−0.293991 + 0.955808i 0.594984π0.594984\pi
740740 0 0
741741 3.44232 0.126457
742742 0 0
743743 −30.7210 −1.12704 −0.563521 0.826102i 0.690554π-0.690554\pi
−0.563521 + 0.826102i 0.690554π0.690554\pi
744744 0 0
745745 12.4379 0.455690
746746 0 0
747747 16.2751 0.595475
748748 0 0
749749 −54.7531 −2.00064
750750 0 0
751751 16.4695 0.600981 0.300491 0.953785i 0.402850π-0.402850\pi
0.300491 + 0.953785i 0.402850π0.402850\pi
752752 0 0
753753 0.885888 0.0322836
754754 0 0
755755 22.1838 0.807350
756756 0 0
757757 31.0756 1.12946 0.564730 0.825276i 0.308980π-0.308980\pi
0.564730 + 0.825276i 0.308980π0.308980\pi
758758 0 0
759759 0.593681 0.0215493
760760 0 0
761761 5.91749 0.214509 0.107254 0.994232i 0.465794π-0.465794\pi
0.107254 + 0.994232i 0.465794π0.465794\pi
762762 0 0
763763 −3.00539 −0.108802
764764 0 0
765765 5.50015 0.198858
766766 0 0
767767 −5.64368 −0.203782
768768 0 0
769769 10.7206 0.386596 0.193298 0.981140i 0.438082π-0.438082\pi
0.193298 + 0.981140i 0.438082π0.438082\pi
770770 0 0
771771 0.527842 0.0190098
772772 0 0
773773 23.8053 0.856219 0.428109 0.903727i 0.359180π-0.359180\pi
0.428109 + 0.903727i 0.359180π0.359180\pi
774774 0 0
775775 −6.84272 −0.245798
776776 0 0
777777 0.0624587 0.00224069
778778 0 0
779779 49.7710 1.78323
780780 0 0
781781 38.9117 1.39237
782782 0 0
783783 5.01488 0.179217
784784 0 0
785785 −5.26352 −0.187863
786786 0 0
787787 −36.0086 −1.28357 −0.641784 0.766886i 0.721805π-0.721805\pi
−0.641784 + 0.766886i 0.721805π0.721805\pi
788788 0 0
789789 3.04664 0.108463
790790 0 0
791791 −2.24854 −0.0799489
792792 0 0
793793 −38.2191 −1.35720
794794 0 0
795795 −1.78549 −0.0633247
796796 0 0
797797 10.1048 0.357931 0.178965 0.983855i 0.442725π-0.442725\pi
0.178965 + 0.983855i 0.442725π0.442725\pi
798798 0 0
799799 3.50662 0.124055
800800 0 0
801801 31.2139 1.10289
802802 0 0
803803 77.4319 2.73251
804804 0 0
805805 1.88762 0.0665299
806806 0 0
807807 −0.389876 −0.0137243
808808 0 0
809809 12.4413 0.437412 0.218706 0.975791i 0.429817π-0.429817\pi
0.218706 + 0.975791i 0.429817π0.429817\pi
810810 0 0
811811 43.3448 1.52204 0.761020 0.648728i 0.224699π-0.224699\pi
0.761020 + 0.648728i 0.224699π0.224699\pi
812812 0 0
813813 3.08561 0.108217
814814 0 0
815815 −2.99290 −0.104837
816816 0 0
817817 30.6125 1.07099
818818 0 0
819819 32.9776 1.15233
820820 0 0
821821 12.5145 0.436758 0.218379 0.975864i 0.429923π-0.429923\pi
0.218379 + 0.975864i 0.429923π0.429923\pi
822822 0 0
823823 −11.7501 −0.409583 −0.204792 0.978806i 0.565652π-0.565652\pi
−0.204792 + 0.978806i 0.565652π0.565652\pi
824824 0 0
825825 0.839377 0.0292233
826826 0 0
827827 −4.81408 −0.167402 −0.0837010 0.996491i 0.526674π-0.526674\pi
−0.0837010 + 0.996491i 0.526674π0.526674\pi
828828 0 0
829829 35.1740 1.22165 0.610823 0.791768i 0.290839π-0.290839\pi
0.610823 + 0.791768i 0.290839π0.290839\pi
830830 0 0
831831 −3.32845 −0.115463
832832 0 0
833833 −0.226880 −0.00786092
834834 0 0
835835 18.1604 0.628467
836836 0 0
837837 6.93455 0.239693
838838 0 0
839839 3.26196 0.112615 0.0563076 0.998413i 0.482067π-0.482067\pi
0.0563076 + 0.998413i 0.482067π0.482067\pi
840840 0 0
841841 −4.51268 −0.155610
842842 0 0
843843 −1.82238 −0.0627661
844844 0 0
845845 4.29572 0.147777
846846 0 0
847847 35.9223 1.23430
848848 0 0
849849 −3.92859 −0.134829
850850 0 0
851851 0.0975311 0.00334332
852852 0 0
853853 5.68904 0.194789 0.0973945 0.995246i 0.468949π-0.468949\pi
0.0973945 + 0.995246i 0.468949π0.468949\pi
854854 0 0
855855 14.4905 0.495566
856856 0 0
857857 44.6563 1.52543 0.762714 0.646736i 0.223866π-0.223866\pi
0.762714 + 0.646736i 0.223866π0.223866\pi
858858 0 0
859859 7.39442 0.252294 0.126147 0.992012i 0.459739π-0.459739\pi
0.126147 + 0.992012i 0.459739π0.459739\pi
860860 0 0
861861 −4.62243 −0.157532
862862 0 0
863863 −36.9653 −1.25831 −0.629157 0.777278i 0.716600π-0.716600\pi
−0.629157 + 0.777278i 0.716600π0.716600\pi
864864 0 0
865865 12.0709 0.410423
866866 0 0
867867 −2.30362 −0.0782351
868868 0 0
869869 −33.1467 −1.12443
870870 0 0
871871 20.5669 0.696883
872872 0 0
873873 −14.2599 −0.482624
874874 0 0
875875 2.66881 0.0902223
876876 0 0
877877 −13.2963 −0.448985 −0.224493 0.974476i 0.572072π-0.572072\pi
−0.224493 + 0.974476i 0.572072π0.572072\pi
878878 0 0
879879 1.01300 0.0341677
880880 0 0
881881 10.3069 0.347248 0.173624 0.984812i 0.444452π-0.444452\pi
0.173624 + 0.984812i 0.444452π0.444452\pi
882882 0 0
883883 48.5606 1.63419 0.817097 0.576500i 0.195582π-0.195582\pi
0.817097 + 0.576500i 0.195582π0.195582\pi
884884 0 0
885885 0.230315 0.00774195
886886 0 0
887887 −6.79523 −0.228161 −0.114081 0.993471i 0.536392π-0.536392\pi
−0.114081 + 0.993471i 0.536392π0.536392\pi
888888 0 0
889889 56.4968 1.89484
890890 0 0
891891 43.2334 1.44837
892892 0 0
893893 9.23844 0.309153
894894 0 0
895895 −3.42945 −0.114634
896896 0 0
897897 −0.499223 −0.0166686
898898 0 0
899899 33.8610 1.12933
900900 0 0
901901 19.4747 0.648797
902902 0 0
903903 −2.84310 −0.0946123
904904 0 0
905905 6.31578 0.209944
906906 0 0
907907 5.40783 0.179564 0.0897820 0.995961i 0.471383π-0.471383\pi
0.0897820 + 0.995961i 0.471383π0.471383\pi
908908 0 0
909909 1.56722 0.0519815
910910 0 0
911911 −18.9169 −0.626743 −0.313372 0.949631i 0.601459π-0.601459\pi
−0.313372 + 0.949631i 0.601459π0.601459\pi
912912 0 0
913913 −27.0908 −0.896574
914914 0 0
915915 1.55970 0.0515619
916916 0 0
917917 −17.6352 −0.582366
918918 0 0
919919 −48.9075 −1.61331 −0.806655 0.591022i 0.798724π-0.798724\pi
−0.806655 + 0.591022i 0.798724π0.798724\pi
920920 0 0
921921 −3.03293 −0.0999384
922922 0 0
923923 −32.7206 −1.07701
924924 0 0
925925 0.137894 0.00453394
926926 0 0
927927 30.6071 1.00527
928928 0 0
929929 35.4660 1.16360 0.581801 0.813331i 0.302348π-0.302348\pi
0.581801 + 0.813331i 0.302348π0.302348\pi
930930 0 0
931931 −0.597731 −0.0195898
932932 0 0
933933 1.45417 0.0476074
934934 0 0
935935 −9.15528 −0.299410
936936 0 0
937937 −56.4991 −1.84575 −0.922873 0.385105i 0.874165π-0.874165\pi
−0.922873 + 0.385105i 0.874165π0.874165\pi
938938 0 0
939939 3.25562 0.106243
940940 0 0
941941 4.04514 0.131868 0.0659338 0.997824i 0.478997π-0.478997\pi
0.0659338 + 0.997824i 0.478997π0.478997\pi
942942 0 0
943943 −7.21805 −0.235052
944944 0 0
945945 −2.70463 −0.0879816
946946 0 0
947947 8.29692 0.269614 0.134807 0.990872i 0.456959π-0.456959\pi
0.134807 + 0.990872i 0.456959π0.456959\pi
948948 0 0
949949 −65.1119 −2.11362
950950 0 0
951951 −2.26040 −0.0732985
952952 0 0
953953 25.0238 0.810599 0.405299 0.914184i 0.367167π-0.367167\pi
0.405299 + 0.914184i 0.367167π0.367167\pi
954954 0 0
955955 −7.75030 −0.250794
956956 0 0
957957 −4.15363 −0.134268
958958 0 0
959959 27.4461 0.886281
960960 0 0
961961 15.8228 0.510412
962962 0 0
963963 60.9568 1.96431
964964 0 0
965965 −11.3388 −0.365007
966966 0 0
967967 −16.6523 −0.535502 −0.267751 0.963488i 0.586280π-0.586280\pi
−0.267751 + 0.963488i 0.586280π0.586280\pi
968968 0 0
969969 1.53223 0.0492224
970970 0 0
971971 43.3530 1.39126 0.695631 0.718399i 0.255125π-0.255125\pi
0.695631 + 0.718399i 0.255125π0.255125\pi
972972 0 0
973973 −18.8181 −0.603279
974974 0 0
975975 −0.705826 −0.0226045
976976 0 0
977977 13.4307 0.429687 0.214844 0.976648i 0.431076π-0.431076\pi
0.214844 + 0.976648i 0.431076π0.431076\pi
978978 0 0
979979 −51.9571 −1.66056
980980 0 0
981981 3.34591 0.106827
982982 0 0
983983 7.94549 0.253422 0.126711 0.991940i 0.459558π-0.459558\pi
0.126711 + 0.991940i 0.459558π0.459558\pi
984984 0 0
985985 −1.55565 −0.0495672
986986 0 0
987987 −0.858009 −0.0273107
988988 0 0
989989 −4.43958 −0.141170
990990 0 0
991991 25.0787 0.796652 0.398326 0.917244i 0.369591π-0.369591\pi
0.398326 + 0.917244i 0.369591π0.369591\pi
992992 0 0
993993 −3.08612 −0.0979350
994994 0 0
995995 14.2722 0.452458
996996 0 0
997997 −51.1689 −1.62054 −0.810268 0.586060i 0.800678π-0.800678\pi
−0.810268 + 0.586060i 0.800678π0.800678\pi
998998 0 0
999999 −0.139745 −0.00442134
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 5120.2.a.t.1.5 8
4.3 odd 2 5120.2.a.v.1.4 8
8.3 odd 2 5120.2.a.s.1.5 8
8.5 even 2 5120.2.a.u.1.4 8
32.3 odd 8 80.2.l.a.61.7 yes 16
32.5 even 8 640.2.l.a.481.4 16
32.11 odd 8 80.2.l.a.21.7 16
32.13 even 8 640.2.l.a.161.4 16
32.19 odd 8 640.2.l.b.161.5 16
32.21 even 8 320.2.l.a.241.5 16
32.27 odd 8 640.2.l.b.481.5 16
32.29 even 8 320.2.l.a.81.5 16
96.11 even 8 720.2.t.c.181.2 16
96.29 odd 8 2880.2.t.c.721.6 16
96.35 even 8 720.2.t.c.541.2 16
96.53 odd 8 2880.2.t.c.2161.7 16
160.3 even 8 400.2.q.g.349.3 16
160.29 even 8 1600.2.l.i.401.4 16
160.43 even 8 400.2.q.h.149.6 16
160.53 odd 8 1600.2.q.g.49.5 16
160.67 even 8 400.2.q.h.349.6 16
160.93 odd 8 1600.2.q.h.849.4 16
160.99 odd 8 400.2.l.h.301.2 16
160.107 even 8 400.2.q.g.149.3 16
160.117 odd 8 1600.2.q.h.49.4 16
160.139 odd 8 400.2.l.h.101.2 16
160.149 even 8 1600.2.l.i.1201.4 16
160.157 odd 8 1600.2.q.g.849.5 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
80.2.l.a.21.7 16 32.11 odd 8
80.2.l.a.61.7 yes 16 32.3 odd 8
320.2.l.a.81.5 16 32.29 even 8
320.2.l.a.241.5 16 32.21 even 8
400.2.l.h.101.2 16 160.139 odd 8
400.2.l.h.301.2 16 160.99 odd 8
400.2.q.g.149.3 16 160.107 even 8
400.2.q.g.349.3 16 160.3 even 8
400.2.q.h.149.6 16 160.43 even 8
400.2.q.h.349.6 16 160.67 even 8
640.2.l.a.161.4 16 32.13 even 8
640.2.l.a.481.4 16 32.5 even 8
640.2.l.b.161.5 16 32.19 odd 8
640.2.l.b.481.5 16 32.27 odd 8
720.2.t.c.181.2 16 96.11 even 8
720.2.t.c.541.2 16 96.35 even 8
1600.2.l.i.401.4 16 160.29 even 8
1600.2.l.i.1201.4 16 160.149 even 8
1600.2.q.g.49.5 16 160.53 odd 8
1600.2.q.g.849.5 16 160.157 odd 8
1600.2.q.h.49.4 16 160.117 odd 8
1600.2.q.h.849.4 16 160.93 odd 8
2880.2.t.c.721.6 16 96.29 odd 8
2880.2.t.c.2161.7 16 96.53 odd 8
5120.2.a.s.1.5 8 8.3 odd 2
5120.2.a.t.1.5 8 1.1 even 1 trivial
5120.2.a.u.1.4 8 8.5 even 2
5120.2.a.v.1.4 8 4.3 odd 2