Properties

Label 220.2.g.a.219.6
Level 220220
Weight 22
Character 220.219
Analytic conductor 1.7571.757
Analytic rank 00
Dimension 88
CM discriminant -55
Inner twists 88

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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] = [220,2,Mod(219,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.219"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 220=22511 220 = 2^{2} \cdot 5 \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 220.g (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.756708844471.75670884447
Analytic rank: 00
Dimension: 88
Coefficient field: 8.0.2342560000.5
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x8+3x4+16 x^{8} + 3x^{4} + 16 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 25 2^{5}
Twist minimal: yes
Sato-Tate group: U(1)[D2]\mathrm{U}(1)[D_{2}]

Embedding invariants

Embedding label 219.6
Root 0.664066+1.24861i0.664066 + 1.24861i of defining polynomial
Character χ\chi == 220.219
Dual form 220.2.g.a.219.5

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+(0.664066+1.24861i)q2+(1.11803+1.65831i)q42.23607q5+3.08672iq7+(2.813030.294756i)q83.00000q9+(1.484902.79197i)q10+3.31662iq11+6.95418q13+(3.85410+2.04979i)q14+(1.500003.70810i)q16+1.64166q17+(1.992203.74582i)q18+(2.500003.70810i)q20+(4.14116+2.20246i)q22+5.00000q25+(4.61803+8.68304i)q26+(5.118753.45106i)q286.63325iq31+(3.633864.33533i)q32+(1.09017+2.04979i)q346.90212iq35+(3.354104.97494i)q36+(6.29012+0.659094i)q40+13.0756iq43+(5.500003.70810i)q44+6.70820q452.52786q49+(3.32033+6.24303i)q50+(7.77501+11.5322i)q527.41620iq55+(0.9098308.68304i)q56+14.8324iq59+(8.282324.40491i)q629.26017iq63+(7.82624+1.65831i)q6415.5500q65+(1.83543+2.72239i)q68+(8.618034.58346i)q7014.8324iq71+(8.43908+0.884268i)q72+12.2667q7310.2375q77+(3.35410+8.29156i)q80+9.00000q81+0.728677iq833.67086q85+(16.3262+8.68304i)q86+(0.9775959.32975i)q8813.4164q89+(4.45469+8.37590i)q90+21.4656iq91+(1.678673.15631i)q989.94987iq99+O(q100)q+(0.664066 + 1.24861i) q^{2} +(-1.11803 + 1.65831i) q^{4} -2.23607 q^{5} +3.08672i q^{7} +(-2.81303 - 0.294756i) q^{8} -3.00000 q^{9} +(-1.48490 - 2.79197i) q^{10} +3.31662i q^{11} +6.95418 q^{13} +(-3.85410 + 2.04979i) q^{14} +(-1.50000 - 3.70810i) q^{16} +1.64166 q^{17} +(-1.99220 - 3.74582i) q^{18} +(2.50000 - 3.70810i) q^{20} +(-4.14116 + 2.20246i) q^{22} +5.00000 q^{25} +(4.61803 + 8.68304i) q^{26} +(-5.11875 - 3.45106i) q^{28} -6.63325i q^{31} +(3.63386 - 4.33533i) q^{32} +(1.09017 + 2.04979i) q^{34} -6.90212i q^{35} +(3.35410 - 4.97494i) q^{36} +(6.29012 + 0.659094i) q^{40} +13.0756i q^{43} +(-5.50000 - 3.70810i) q^{44} +6.70820 q^{45} -2.52786 q^{49} +(3.32033 + 6.24303i) q^{50} +(-7.77501 + 11.5322i) q^{52} -7.41620i q^{55} +(0.909830 - 8.68304i) q^{56} +14.8324i q^{59} +(8.28232 - 4.40491i) q^{62} -9.26017i q^{63} +(7.82624 + 1.65831i) q^{64} -15.5500 q^{65} +(-1.83543 + 2.72239i) q^{68} +(8.61803 - 4.58346i) q^{70} -14.8324i q^{71} +(8.43908 + 0.884268i) q^{72} +12.2667 q^{73} -10.2375 q^{77} +(3.35410 + 8.29156i) q^{80} +9.00000 q^{81} +0.728677i q^{83} -3.67086 q^{85} +(-16.3262 + 8.68304i) q^{86} +(0.977595 - 9.32975i) q^{88} -13.4164 q^{89} +(4.45469 + 8.37590i) q^{90} +21.4656i q^{91} +(-1.67867 - 3.15631i) q^{98} -9.94987i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q24q94q1412q16+20q20+40q25+28q2636q3444q4456q49+52q56+60q70+72q8168q86+O(q100) 8 q - 24 q^{9} - 4 q^{14} - 12 q^{16} + 20 q^{20} + 40 q^{25} + 28 q^{26} - 36 q^{34} - 44 q^{44} - 56 q^{49} + 52 q^{56} + 60 q^{70} + 72 q^{81} - 68 q^{86}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/220Z)×\left(\mathbb{Z}/220\mathbb{Z}\right)^\times.

nn 101101 111111 177177
χ(n)\chi(n) 1-1 1-1 1-1

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 0.664066 + 1.24861i 0.469565 + 0.882898i
33 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
44 −1.11803 + 1.65831i −0.559017 + 0.829156i
55 −2.23607 −1.00000
66 0 0
77 3.08672i 1.16667i 0.812231 + 0.583336i 0.198253π0.198253\pi
−0.812231 + 0.583336i 0.801747π0.801747\pi
88 −2.81303 0.294756i −0.994555 0.104212i
99 −3.00000 −1.00000
1010 −1.48490 2.79197i −0.469565 0.882898i
1111 3.31662i 1.00000i
1212 0 0
1313 6.95418 1.92874 0.964372 0.264550i 0.0852236π-0.0852236\pi
0.964372 + 0.264550i 0.0852236π0.0852236\pi
1414 −3.85410 + 2.04979i −1.03005 + 0.547829i
1515 0 0
1616 −1.50000 3.70810i −0.375000 0.927025i
1717 1.64166 0.398161 0.199081 0.979983i 0.436204π-0.436204\pi
0.199081 + 0.979983i 0.436204π0.436204\pi
1818 −1.99220 3.74582i −0.469565 0.882898i
1919 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2020 2.50000 3.70810i 0.559017 0.829156i
2121 0 0
2222 −4.14116 + 2.20246i −0.882898 + 0.469565i
2323 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
2424 0 0
2525 5.00000 1.00000
2626 4.61803 + 8.68304i 0.905671 + 1.70288i
2727 0 0
2828 −5.11875 3.45106i −0.967353 0.652189i
2929 0 0 1.00000 00
−1.00000 π\pi
3030 0 0
3131 6.63325i 1.19137i −0.803219 0.595683i 0.796881π-0.796881\pi
0.803219 0.595683i 0.203119π-0.203119\pi
3232 3.63386 4.33533i 0.642381 0.766385i
3333 0 0
3434 1.09017 + 2.04979i 0.186963 + 0.351536i
3535 6.90212i 1.16667i
3636 3.35410 4.97494i 0.559017 0.829156i
3737 0 0 1.00000 00
−1.00000 π\pi
3838 0 0
3939 0 0
4040 6.29012 + 0.659094i 0.994555 + 0.104212i
4141 0 0 1.00000 00
−1.00000 π\pi
4242 0 0
4343 13.0756i 1.99401i 0.0773627 + 0.997003i 0.475350π0.475350\pi
−0.0773627 + 0.997003i 0.524650π0.524650\pi
4444 −5.50000 3.70810i −0.829156 0.559017i
4545 6.70820 1.00000
4646 0 0
4747 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4848 0 0
4949 −2.52786 −0.361123
5050 3.32033 + 6.24303i 0.469565 + 0.882898i
5151 0 0
5252 −7.77501 + 11.5322i −1.07820 + 1.59923i
5353 0 0 1.00000 00
−1.00000 π\pi
5454 0 0
5555 7.41620i 1.00000i
5656 0.909830 8.68304i 0.121581 1.16032i
5757 0 0
5858 0 0
5959 14.8324i 1.93101i 0.260378 + 0.965507i 0.416153π0.416153\pi
−0.260378 + 0.965507i 0.583847π0.583847\pi
6060 0 0
6161 0 0 1.00000 00
−1.00000 π\pi
6262 8.28232 4.40491i 1.05186 0.559424i
6363 9.26017i 1.16667i
6464 7.82624 + 1.65831i 0.978280 + 0.207289i
6565 −15.5500 −1.92874
6666 0 0
6767 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
6868 −1.83543 + 2.72239i −0.222579 + 0.330138i
6969 0 0
7070 8.61803 4.58346i 1.03005 0.547829i
7171 14.8324i 1.76028i −0.474713 0.880141i 0.657448π-0.657448\pi
0.474713 0.880141i 0.342552π-0.342552\pi
7272 8.43908 + 0.884268i 0.994555 + 0.104212i
7373 12.2667 1.43571 0.717855 0.696193i 0.245124π-0.245124\pi
0.717855 + 0.696193i 0.245124π0.245124\pi
7474 0 0
7575 0 0
7676 0 0
7777 −10.2375 −1.16667
7878 0 0
7979 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
8080 3.35410 + 8.29156i 0.375000 + 0.927025i
8181 9.00000 1.00000
8282 0 0
8383 0.728677i 0.0799827i 0.999200 + 0.0399913i 0.0127330π0.0127330\pi
−0.999200 + 0.0399913i 0.987267π0.987267\pi
8484 0 0
8585 −3.67086 −0.398161
8686 −16.3262 + 8.68304i −1.76050 + 0.936316i
8787 0 0
8888 0.977595 9.32975i 0.104212 0.994555i
8989 −13.4164 −1.42214 −0.711068 0.703123i 0.751788π-0.751788\pi
−0.711068 + 0.703123i 0.751788π0.751788\pi
9090 4.45469 + 8.37590i 0.469565 + 0.882898i
9191 21.4656i 2.25021i
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 0 0
9797 0 0 1.00000 00
−1.00000 π\pi
9898 −1.67867 3.15631i −0.169571 0.318835i
9999 9.94987i 1.00000i
100100 −5.59017 + 8.29156i −0.559017 + 0.829156i
101101 0 0 1.00000 00
−1.00000 π\pi
102102 0 0
103103 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
104104 −19.5623 2.04979i −1.91824 0.200998i
105105 0 0
106106 0 0
107107 19.2490i 1.86087i −0.366453 0.930436i 0.619428π-0.619428\pi
0.366453 0.930436i 0.380572π-0.380572\pi
108108 0 0
109109 0 0 1.00000 00
−1.00000 π\pi
110110 9.25991 4.92484i 0.882898 0.469565i
111111 0 0
112112 11.4459 4.63009i 1.08153 0.437502i
113113 0 0 1.00000 00
−1.00000 π\pi
114114 0 0
115115 0 0
116116 0 0
117117 −20.8626 −1.92874
118118 −18.5198 + 9.84968i −1.70489 + 0.906737i
119119 5.06735i 0.464523i
120120 0 0
121121 −11.0000 −1.00000
122122 0 0
123123 0 0
124124 11.0000 + 7.41620i 0.987829 + 0.665994i
125125 −11.1803 −1.00000
126126 11.5623 6.14936i 1.03005 0.547829i
127127 16.8910i 1.49883i −0.662100 0.749416i 0.730334π-0.730334\pi
0.662100 0.749416i 0.269666π-0.269666\pi
128128 3.12656 + 10.8731i 0.276351 + 0.961057i
129129 0 0
130130 −10.3262 19.4159i −0.905671 1.70288i
131131 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 −4.61803 0.483889i −0.395993 0.0414931i
137137 0 0 1.00000 00
−1.00000 π\pi
138138 0 0
139139 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
140140 11.4459 + 7.71681i 0.967353 + 0.652189i
141141 0 0
142142 18.5198 9.84968i 1.55415 0.826567i
143143 23.0644i 1.92874i
144144 4.50000 + 11.1243i 0.375000 + 0.927025i
145145 0 0
146146 8.14590 + 15.3163i 0.674159 + 1.26758i
147147 0 0
148148 0 0
149149 0 0 1.00000 00
−1.00000 π\pi
150150 0 0
151151 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
152152 0 0
153153 −4.92498 −0.398161
154154 −6.79837 12.7826i −0.547829 1.03005i
155155 14.8324i 1.19137i
156156 0 0
157157 0 0 1.00000 00
−1.00000 π\pi
158158 0 0
159159 0 0
160160 −8.12555 + 9.69409i −0.642381 + 0.766385i
161161 0 0
162162 5.97659 + 11.2375i 0.469565 + 0.882898i
163163 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
164164 0 0
165165 0 0
166166 −0.909830 + 0.483889i −0.0706165 + 0.0375571i
167167 10.7175i 0.829347i 0.909970 + 0.414673i 0.136104π0.136104\pi
−0.909970 + 0.414673i 0.863896π0.863896\pi
168168 0 0
169169 35.3607 2.72005
170170 −2.43769 4.58346i −0.186963 0.351536i
171171 0 0
172172 −21.6834 14.6189i −1.65334 1.11468i
173173 24.1459 1.83578 0.917888 0.396839i 0.129893π-0.129893\pi
0.917888 + 0.396839i 0.129893π0.129893\pi
174174 0 0
175175 15.4336i 1.16667i
176176 12.2984 4.97494i 0.927025 0.375000i
177177 0 0
178178 −8.90937 16.7518i −0.667786 1.25560i
179179 19.8997i 1.48738i −0.668526 0.743689i 0.733075π-0.733075\pi
0.668526 0.743689i 0.266925π-0.266925\pi
180180 −7.50000 + 11.1243i −0.559017 + 0.829156i
181181 −4.47214 −0.332411 −0.166206 0.986091i 0.553152π-0.553152\pi
−0.166206 + 0.986091i 0.553152π0.553152\pi
182182 −26.8021 + 14.2546i −1.98671 + 1.05662i
183183 0 0
184184 0 0
185185 0 0
186186 0 0
187187 5.44477i 0.398161i
188188 0 0
189189 0 0
190190 0 0
191191 6.63325i 0.479965i −0.970777 0.239983i 0.922858π-0.922858\pi
0.970777 0.239983i 0.0771417π-0.0771417\pi
192192 0 0
193193 18.8333 1.35565 0.677827 0.735221i 0.262922π-0.262922\pi
0.677827 + 0.735221i 0.262922π0.262922\pi
194194 0 0
195195 0 0
196196 2.82624 4.19199i 0.201874 0.299428i
197197 17.5792 1.25247 0.626234 0.779635i 0.284595π-0.284595\pi
0.626234 + 0.779635i 0.284595π0.284595\pi
198198 12.4235 6.60737i 0.882898 0.469565i
199199 14.8324i 1.05144i −0.850657 0.525720i 0.823796π-0.823796\pi
0.850657 0.525720i 0.176204π-0.176204\pi
200200 −14.0651 1.47378i −0.994555 0.104212i
201201 0 0
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 −10.4313 25.7868i −0.723279 1.78799i
209209 0 0
210210 0 0
211211 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
212212 0 0
213213 0 0
214214 24.0344 12.7826i 1.64296 0.873801i
215215 29.2379i 1.99401i
216216 0 0
217217 20.4750 1.38993
218218 0 0
219219 0 0
220220 12.2984 + 8.29156i 0.829156 + 0.559017i
221221 11.4164 0.767951
222222 0 0
223223 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
224224 13.3820 + 11.2167i 0.894120 + 0.749448i
225225 −15.0000 −1.00000
226226 0 0
227227 25.4225i 1.68735i 0.536855 + 0.843674i 0.319612π0.319612\pi
−0.536855 + 0.843674i 0.680388π0.680388\pi
228228 0 0
229229 6.00000 0.396491 0.198246 0.980152i 0.436476π-0.436476\pi
0.198246 + 0.980152i 0.436476π0.436476\pi
230230 0 0
231231 0 0
232232 0 0
233233 −26.1751 −1.71479 −0.857393 0.514662i 0.827917π-0.827917\pi
−0.857393 + 0.514662i 0.827917π0.827917\pi
234234 −13.8541 26.0491i −0.905671 1.70288i
235235 0 0
236236 −24.5967 16.5831i −1.60111 1.07947i
237237 0 0
238238 −6.32713 + 3.36505i −0.410127 + 0.218124i
239239 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
240240 0 0
241241 0 0 1.00000 00
−1.00000 π\pi
242242 −7.30472 13.7347i −0.469565 0.882898i
243243 0 0
244244 0 0
245245 5.65248 0.361123
246246 0 0
247247 0 0
248248 −1.95519 + 18.6595i −0.124155 + 1.18488i
249249 0 0
250250 −7.42448 13.9598i −0.469565 0.882898i
251251 14.8324i 0.936213i 0.883672 + 0.468106i 0.155064π0.155064\pi
−0.883672 + 0.468106i 0.844936π0.844936\pi
252252 15.3563 + 10.3532i 0.967353 + 0.652189i
253253 0 0
254254 21.0902 11.2167i 1.32331 0.703799i
255255 0 0
256256 −11.5000 + 11.1243i −0.718750 + 0.695269i
257257 0 0 1.00000 00
−1.00000 π\pi
258258 0 0
259259 0 0
260260 17.3855 25.7868i 1.07820 1.59923i
261261 0 0
262262 0 0
263263 4.54408i 0.280200i −0.990137 0.140100i 0.955258π-0.955258\pi
0.990137 0.140100i 0.0447424π-0.0447424\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 0 0
269269 14.0000 0.853595 0.426798 0.904347i 0.359642π-0.359642\pi
0.426798 + 0.904347i 0.359642π0.359642\pi
270270 0 0
271271 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
272272 −2.46249 6.08744i −0.149310 0.369105i
273273 0 0
274274 0 0
275275 16.5831i 1.00000i
276276 0 0
277277 13.5208 0.812388 0.406194 0.913787i 0.366856π-0.366856\pi
0.406194 + 0.913787i 0.366856π0.366856\pi
278278 0 0
279279 19.8997i 1.19137i
280280 −2.03444 + 19.4159i −0.121581 + 1.16032i
281281 0 0 1.00000 00
−1.00000 π\pi
282282 0 0
283283 26.8798i 1.59784i −0.601438 0.798920i 0.705405π-0.705405\pi
0.601438 0.798920i 0.294595π-0.294595\pi
284284 24.5967 + 16.5831i 1.45955 + 0.984027i
285285 0 0
286286 −28.7984 + 15.3163i −1.70288 + 0.905671i
287287 0 0
288288 −10.9016 + 13.0060i −0.642381 + 0.766385i
289289 −14.3050 −0.841468
290290 0 0
291291 0 0
292292 −13.7146 + 20.3420i −0.802586 + 1.19043i
293293 0.387543 0.0226405 0.0113203 0.999936i 0.496397π-0.496397\pi
0.0113203 + 0.999936i 0.496397π0.496397\pi
294294 0 0
295295 33.1662i 1.93101i
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 0 0
301301 −40.3607 −2.32635
302302 0 0
303303 0 0
304304 0 0
305305 0 0
306306 −3.27051 6.14936i −0.186963 0.351536i
307307 33.0533i 1.88645i 0.332155 + 0.943225i 0.392224π0.392224\pi
−0.332155 + 0.943225i 0.607776π0.607776\pi
308308 11.4459 16.9770i 0.652189 0.967353i
309309 0 0
310310 −18.5198 + 9.84968i −1.05186 + 0.559424i
311311 14.8324i 0.841068i −0.907277 0.420534i 0.861843π-0.861843\pi
0.907277 0.420534i 0.138157π-0.138157\pi
312312 0 0
313313 0 0 1.00000 00
−1.00000 π\pi
314314 0 0
315315 20.7064i 1.16667i
316316 0 0
317317 0 0 1.00000 00
−1.00000 π\pi
318318 0 0
319319 0 0
320320 −17.5000 3.70810i −0.978280 0.207289i
321321 0 0
322322 0 0
323323 0 0
324324 −10.0623 + 14.9248i −0.559017 + 0.829156i
325325 34.7709 1.92874
326326 0 0
327327 0 0
328328 0 0
329329 0 0
330330 0 0
331331 6.63325i 0.364596i 0.983243 + 0.182298i 0.0583536π0.0583536\pi
−0.983243 + 0.182298i 0.941646π0.941646\pi
332332 −1.20837 0.814685i −0.0663181 0.0447117i
333333 0 0
334334 −13.3820 + 7.11714i −0.732229 + 0.389432i
335335 0 0
336336 0 0
337337 −32.7417 −1.78356 −0.891778 0.452474i 0.850541π-0.850541\pi
−0.891778 + 0.452474i 0.850541π0.850541\pi
338338 23.4818 + 44.1516i 1.27724 + 2.40153i
339339 0 0
340340 4.10415 6.08744i 0.222579 0.330138i
341341 22.0000 1.19137
342342 0 0
343343 13.8042i 0.745359i
344344 3.85410 36.7819i 0.207799 1.98315i
345345 0 0
346346 16.0344 + 30.1487i 0.862017 + 1.62080i
347347 11.6182i 0.623699i −0.950132 0.311849i 0.899052π-0.899052\pi
0.950132 0.311849i 0.100948π-0.100948\pi
348348 0 0
349349 0 0 1.00000 00
−1.00000 π\pi
350350 −19.2705 + 10.2489i −1.03005 + 0.547829i
351351 0 0
352352 14.3787 + 12.0521i 0.766385 + 0.642381i
353353 0 0 1.00000 00
−1.00000 π\pi
354354 0 0
355355 33.1662i 1.76028i
356356 15.0000 22.2486i 0.794998 1.17917i
357357 0 0
358358 24.8469 13.2147i 1.31320 0.698421i
359359 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
360360 −18.8704 1.97728i −0.994555 0.104212i
361361 −19.0000 −1.00000
362362 −2.96979 5.58394i −0.156089 0.293485i
363363 0 0
364364 −35.5967 23.9993i −1.86578 1.25791i
365365 −27.4292 −1.43571
366366 0 0
367367 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
368368 0 0
369369 0 0
370370 0 0
371371 0 0
372372 0 0
373373 −38.0542 −1.97037 −0.985187 0.171484i 0.945144π-0.945144\pi
−0.985187 + 0.171484i 0.945144π0.945144\pi
374374 −6.79837 + 3.61568i −0.351536 + 0.186963i
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 14.8324i 0.761889i 0.924598 + 0.380945i 0.124401π0.124401\pi
−0.924598 + 0.380945i 0.875599π0.875599\pi
380380 0 0
381381 0 0
382382 8.28232 4.40491i 0.423760 0.225375i
383383 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
384384 0 0
385385 22.8918 1.16667
386386 12.5066 + 23.5154i 0.636568 + 1.19690i
387387 39.2267i 1.99401i
388388 0 0
389389 −26.0000 −1.31825 −0.659126 0.752032i 0.729074π-0.729074\pi
−0.659126 + 0.752032i 0.729074π0.729074\pi
390390 0 0
391391 0 0
392392 7.11095 + 0.745103i 0.359157 + 0.0376334i
393393 0 0
394394 11.6738 + 21.9495i 0.588116 + 1.10580i
395395 0 0
396396 16.5000 + 11.1243i 0.829156 + 0.559017i
397397 0 0 1.00000 00
−1.00000 π\pi
398398 18.5198 9.84968i 0.928315 0.493720i
399399 0 0
400400 −7.50000 18.5405i −0.375000 0.927025i
401401 4.47214 0.223328 0.111664 0.993746i 0.464382π-0.464382\pi
0.111664 + 0.993746i 0.464382π0.464382\pi
402402 0 0
403403 46.1288i 2.29784i
404404 0 0
405405 −20.1246 −1.00000
406406 0 0
407407 0 0
408408 0 0
409409 0 0 1.00000 00
−1.00000 π\pi
410410 0 0
411411 0 0
412412 0 0
413413 −45.7835 −2.25286
414414 0 0
415415 1.62937i 0.0799827i
416416 25.2705 30.1487i 1.23899 1.47816i
417417 0 0
418418 0 0
419419 19.8997i 0.972166i −0.873913 0.486083i 0.838425π-0.838425\pi
0.873913 0.486083i 0.161575π-0.161575\pi
420420 0 0
421421 31.3050 1.52571 0.762855 0.646570i 0.223797π-0.223797\pi
0.762855 + 0.646570i 0.223797π0.223797\pi
422422 0 0
423423 0 0
424424 0 0
425425 8.20830 0.398161
426426 0 0
427427 0 0
428428 31.9209 + 21.5211i 1.54295 + 1.04026i
429429 0 0
430430 36.5066 19.4159i 1.76050 0.936316i
431431 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
432432 0 0
433433 0 0 1.00000 00
−1.00000 π\pi
434434 13.5967 + 25.5652i 0.652665 + 1.22717i
435435 0 0
436436 0 0
437437 0 0
438438 0 0
439439 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
440440 −2.18597 + 20.8620i −0.104212 + 0.994555i
441441 7.58359 0.361123
442442 7.58124 + 14.2546i 0.360603 + 0.678022i
443443 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
444444 0 0
445445 30.0000 1.42214
446446 0 0
447447 0 0
448448 −5.11875 + 24.1574i −0.241838 + 1.14133i
449449 40.2492 1.89948 0.949739 0.313042i 0.101348π-0.101348\pi
0.949739 + 0.313042i 0.101348π0.101348\pi
450450 −9.96098 18.7291i −0.469565 0.882898i
451451 0 0
452452 0 0
453453 0 0
454454 −31.7426 + 16.8822i −1.48976 + 0.792320i
455455 47.9986i 2.25021i
456456 0 0
457457 −22.1167 −1.03457 −0.517287 0.855812i 0.673058π-0.673058\pi
−0.517287 + 0.855812i 0.673058π0.673058\pi
458458 3.98439 + 7.49164i 0.186178 + 0.350061i
459459 0 0
460460 0 0
461461 0 0 1.00000 00
−1.00000 π\pi
462462 0 0
463463 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
464464 0 0
465465 0 0
466466 −17.3820 32.6824i −0.805204 1.51398i
467467 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
468468 23.3250 34.5966i 1.07820 1.59923i
469469 0 0
470470 0 0
471471 0 0
472472 4.37194 41.7239i 0.201235 1.92050i
473473 −43.3668 −1.99401
474474 0 0
475475 0 0
476476 −8.40325 5.66547i −0.385162 0.259676i
477477 0 0
478478 0 0
479479 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
480480 0 0
481481 0 0
482482 0 0
483483 0 0
484484 12.2984 18.2414i 0.559017 0.829156i
485485 0 0
486486 0 0
487487 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
488488 0 0
489489 0 0
490490 3.75361 + 7.05772i 0.169571 + 0.318835i
491491 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
492492 0 0
493493 0 0
494494 0 0
495495 22.2486i 1.00000i
496496 −24.5967 + 9.94987i −1.10443 + 0.446763i
497497 45.7835 2.05367
498498 0 0
499499 44.4972i 1.99197i −0.0895323 0.995984i 0.528537π-0.528537\pi
0.0895323 0.995984i 0.471463π-0.471463\pi
500500 12.5000 18.5405i 0.559017 0.829156i
501501 0 0
502502 −18.5198 + 9.84968i −0.826580 + 0.439613i
503503 36.8687i 1.64389i −0.569565 0.821946i 0.692888π-0.692888\pi
0.569565 0.821946i 0.307112π-0.307112\pi
504504 −2.72949 + 26.0491i −0.121581 + 1.16032i
505505 0 0
506506 0 0
507507 0 0
508508 28.0105 + 18.8847i 1.24277 + 0.837872i
509509 −34.0000 −1.50702 −0.753512 0.657434i 0.771642π-0.771642\pi
−0.753512 + 0.657434i 0.771642π0.771642\pi
510510 0 0
511511 37.8639i 1.67500i
512512 −21.5266 6.97171i −0.951351 0.308109i
513513 0 0
514514 0 0
515515 0 0
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 43.7426 + 4.58346i 1.91824 + 0.200998i
521521 22.3607 0.979639 0.489820 0.871824i 0.337063π-0.337063\pi
0.489820 + 0.871824i 0.337063π0.337063\pi
522522 0 0
523523 45.4002i 1.98521i 0.121387 + 0.992605i 0.461266π0.461266\pi
−0.121387 + 0.992605i 0.538734π0.538734\pi
524524 0 0
525525 0 0
526526 5.67376 3.01756i 0.247388 0.131572i
527527 10.8895i 0.474356i
528528 0 0
529529 −23.0000 −1.00000
530530 0 0
531531 44.4972i 1.93101i
532532 0 0
533533 0 0
534534 0 0
535535 43.0421i 1.86087i
536536 0 0
537537 0 0
538538 9.29692 + 17.4805i 0.400819 + 0.753637i
539539 8.38398i 0.361123i
540540 0 0
541541 0 0 1.00000 00
−1.00000 π\pi
542542 0 0
543543 0 0
544544 5.96556 7.11714i 0.255771 0.305145i
545545 0 0
546546 0 0
547547 8.35948i 0.357425i 0.983901 + 0.178713i 0.0571933π0.0571933\pi
−0.983901 + 0.178713i 0.942807π0.942807\pi
548548 0 0
549549 0 0
550550 −20.7058 + 11.0123i −0.882898 + 0.469565i
551551 0 0
552552 0 0
553553 0 0
554554 8.97871 + 16.8822i 0.381469 + 0.717255i
555555 0 0
556556 0 0
557557 41.3376 1.75153 0.875764 0.482739i 0.160358π-0.160358\pi
0.875764 + 0.482739i 0.160358π0.160358\pi
558558 −24.8469 + 13.2147i −1.05186 + 0.559424i
559559 90.9299i 3.84593i
560560 −25.5938 + 10.3532i −1.08153 + 0.437502i
561561 0 0
562562 0 0
563563 17.7917i 0.749829i 0.927059 + 0.374915i 0.122328π0.122328\pi
−0.927059 + 0.374915i 0.877672π0.877672\pi
564564 0 0
565565 0 0
566566 33.5623 17.8500i 1.41073 0.750290i
567567 27.7805i 1.16667i
568568 −4.37194 + 41.7239i −0.183442 + 1.75070i
569569 0 0 1.00000 00
−1.00000 π\pi
570570 0 0
571571 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
572572 −38.2480 25.7868i −1.59923 1.07820i
573573 0 0
574574 0 0
575575 0 0
576576 −23.4787 4.97494i −0.978280 0.207289i
577577 0 0 1.00000 00
−1.00000 π\pi
578578 −9.49943 17.8612i −0.395124 0.742930i
579579 0 0
580580 0 0
581581 −2.24922 −0.0933135
582582 0 0
583583 0 0
584584 −34.5066 3.61568i −1.42789 0.149618i
585585 46.6501 1.92874
586586 0.257354 + 0.483889i 0.0106312 + 0.0199893i
587587 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
588588 0 0
589589 0 0
590590 41.4116 22.0246i 1.70489 0.906737i
591591 0 0
592592 0 0
593593 36.0250 1.47937 0.739686 0.672953i 0.234974π-0.234974\pi
0.739686 + 0.672953i 0.234974π0.234974\pi
594594 0 0
595595 11.3309i 0.464523i
596596 0 0
597597 0 0
598598 0 0
599599 19.8997i 0.813082i 0.913633 + 0.406541i 0.133265π0.133265\pi
−0.913633 + 0.406541i 0.866735π0.866735\pi
600600 0 0
601601 0 0 1.00000 00
−1.00000 π\pi
602602 −26.8021 50.3946i −1.09237 2.05393i
603603 0 0
604604 0 0
605605 24.5967 1.00000
606606 0 0
607607 24.5218i 0.995308i −0.867376 0.497654i 0.834195π-0.834195\pi
0.867376 0.497654i 0.165805π-0.165805\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 5.50630 8.16716i 0.222579 0.330138i
613613 −16.8041 −0.678713 −0.339357 0.940658i 0.610209π-0.610209\pi
−0.339357 + 0.940658i 0.610209π0.610209\pi
614614 −41.2705 + 21.9495i −1.66554 + 0.885811i
615615 0 0
616616 28.7984 + 3.01756i 1.16032 + 0.121581i
617617 0 0 1.00000 00
−1.00000 π\pi
618618 0 0
619619 46.4327i 1.86629i −0.359501 0.933145i 0.617053π-0.617053\pi
0.359501 0.933145i 0.382947π-0.382947\pi
620620 −24.5967 16.5831i −0.987829 0.665994i
621621 0 0
622622 18.5198 9.84968i 0.742577 0.394936i
623623 41.4127i 1.65917i
624624 0 0
625625 25.0000 1.00000
626626 0 0
627627 0 0
628628 0 0
629629 0 0
630630 −25.8541 + 13.7504i −1.03005 + 0.547829i
631631 14.8324i 0.590468i −0.955425 0.295234i 0.904602π-0.904602\pi
0.955425 0.295234i 0.0953977π-0.0953977\pi
632632 0 0
633633 0 0
634634 0 0
635635 37.7694i 1.49883i
636636 0 0
637637 −17.5792 −0.696515
638638 0 0
639639 44.4972i 1.76028i
640640 −6.99119 24.3130i −0.276351 0.961057i
641641 −31.3050 −1.23647 −0.618236 0.785993i 0.712152π-0.712152\pi
−0.618236 + 0.785993i 0.712152π0.712152\pi
642642 0 0
643643 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
648648 −25.3172 2.65280i −0.994555 0.104212i
649649 −49.1935 −1.93101
650650 23.0902 + 43.4152i 0.905671 + 1.70288i
651651 0 0
652652 0 0
653653 0 0 1.00000 00
−1.00000 π\pi
654654 0 0
655655 0 0
656656 0 0
657657 −36.8001 −1.43571
658658 0 0
659659 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
660660 0 0
661661 −42.0000 −1.63361 −0.816805 0.576913i 0.804257π-0.804257\pi
−0.816805 + 0.576913i 0.804257π0.804257\pi
662662 −8.28232 + 4.40491i −0.321901 + 0.171202i
663663 0 0
664664 0.214782 2.04979i 0.00833515 0.0795472i
665665 0 0
666666 0 0
667667 0 0
668668 −17.7730 11.9826i −0.687658 0.463619i
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 −19.6084 −0.755850 −0.377925 0.925836i 0.623362π-0.623362\pi
−0.377925 + 0.925836i 0.623362π0.623362\pi
674674 −21.7426 40.8815i −0.837495 1.57470i
675675 0 0
676676 −39.5344 + 58.6391i −1.52056 + 2.25535i
677677 51.9626 1.99709 0.998543 0.0539677i 0.0171868π-0.0171868\pi
0.998543 + 0.0539677i 0.0171868π0.0171868\pi
678678 0 0
679679 0 0
680680 10.3262 + 1.08201i 0.395993 + 0.0414931i
681681 0 0
682682 14.6094 + 27.4693i 0.559424 + 1.05186i
683683 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
684684 0 0
685685 0 0
686686 −17.2361 + 9.16693i −0.658076 + 0.349995i
687687 0 0
688688 48.4855 19.6134i 1.84849 0.747752i
689689 0 0
690690 0 0
691691 44.4972i 1.69275i −0.532585 0.846376i 0.678779π-0.678779\pi
0.532585 0.846376i 0.321221π-0.321221\pi
692692 −26.9959 + 40.0414i −1.02623 + 1.52215i
693693 30.7125 1.16667
694694 14.5066 7.71526i 0.550662 0.292867i
695695 0 0
696696 0 0
697697 0 0
698698 0 0
699699 0 0
700700 −25.5938 17.2553i −0.967353 0.652189i
701701 0 0 1.00000 00
−1.00000 π\pi
702702 0 0
703703 0 0
704704 −5.50000 + 25.9567i −0.207289 + 0.978280i
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 −4.47214 −0.167955 −0.0839773 0.996468i 0.526762π-0.526762\pi
−0.0839773 + 0.996468i 0.526762π0.526762\pi
710710 −41.4116 + 22.0246i −1.55415 + 0.826567i
711711 0 0
712712 37.7407 + 3.95457i 1.41439 + 0.148204i
713713 0 0
714714 0 0
715715 51.5736i 1.92874i
716716 33.0000 + 22.2486i 1.23327 + 0.831469i
717717 0 0
718718 0 0
719719 46.4327i 1.73165i 0.500348 + 0.865825i 0.333206π0.333206\pi
−0.500348 + 0.865825i 0.666794π0.666794\pi
720720 −10.0623 24.8747i −0.375000 0.927025i
721721 0 0
722722 −12.6172 23.7235i −0.469565 0.882898i
723723 0 0
724724 5.00000 7.41620i 0.185824 0.275621i
725725 0 0
726726 0 0
727727 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
728728 6.32713 60.3834i 0.234499 2.23796i
729729 −27.0000 −1.00000
730730 −18.2148 34.2483i −0.674159 1.26758i
731731 21.4656i 0.793936i
732732 0 0
733733 45.3960 1.67674 0.838369 0.545103i 0.183509π-0.183509\pi
0.838369 + 0.545103i 0.183509π0.183509\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
740740 0 0
741741 0 0
742742 0 0
743743 18.3483i 0.673135i 0.941659 + 0.336567i 0.109266π0.109266\pi
−0.941659 + 0.336567i 0.890734π0.890734\pi
744744 0 0
745745 0 0
746746 −25.2705 47.5148i −0.925219 1.73964i
747747 2.18603i 0.0799827i
748748 −9.02913 6.08744i −0.330138 0.222579i
749749 59.4164 2.17103
750750 0 0
751751 44.4972i 1.62373i 0.583848 + 0.811863i 0.301546π0.301546\pi
−0.583848 + 0.811863i 0.698454π0.698454\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 0 0 1.00000 00
−1.00000 π\pi
758758 −18.5198 + 9.84968i −0.672670 + 0.357757i
759759 0 0
760760 0 0
761761 0 0 1.00000 00
−1.00000 π\pi
762762 0 0
763763 0 0
764764 11.0000 + 7.41620i 0.397966 + 0.268309i
765765 11.0126 0.398161
766766 0 0
767767 103.147i 3.72443i
768768 0 0
769769 0 0 1.00000 00
−1.00000 π\pi
770770 15.2016 + 28.5828i 0.547829 + 1.03005i
771771 0 0
772772 −21.0563 + 31.2316i −0.757834 + 1.12405i
773773 0 0 1.00000 00
−1.00000 π\pi
774774 48.9787 26.0491i 1.76050 0.936316i
775775 33.1662i 1.19137i
776776 0 0
777777 0 0
778778 −17.2657 32.4638i −0.619005 1.16388i
779779 0 0
780780 0 0
781781 49.1935 1.76028
782782 0 0
783783 0 0
784784 3.79180 + 9.37357i 0.135421 + 0.334770i
785785 0 0
786786 0 0
787787 46.8575i 1.67029i −0.550030 0.835145i 0.685384π-0.685384\pi
0.550030 0.835145i 0.314616π-0.314616\pi
788788 −19.6542 + 29.1519i −0.700151 + 1.03849i
789789 0 0
790790 0 0
791791 0 0
792792 −2.93278 + 27.9893i −0.104212 + 0.994555i
793793 0 0
794794 0 0
795795 0 0
796796 24.5967 + 16.5831i 0.871809 + 0.587773i
797797 0 0 1.00000 00
−1.00000 π\pi
798798 0 0
799799 0 0
800800 18.1693 21.6766i 0.642381 0.766385i
801801 40.2492 1.42214
802802 2.96979 + 5.58394i 0.104867 + 0.197176i
803803 40.6841i 1.43571i
804804 0 0
805805 0 0
806806 57.5967 30.6326i 2.02876 1.07899i
807807 0 0
808808 0 0
809809 0 0 1.00000 00
−1.00000 π\pi
810810 −13.3641 25.1277i −0.469565 0.882898i
811811 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 0 0
817817 0 0
818818 0 0
819819 64.3969i 2.25021i
820820 0 0
821821 0 0 1.00000 00
−1.00000 π\pi
822822 0 0
823823 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
824824 0 0
825825 0 0
826826 −30.4033 57.1656i −1.05786 1.98904i
827827 53.0310i 1.84407i 0.387110 + 0.922034i 0.373473π0.373473\pi
−0.387110 + 0.922034i 0.626527π0.626527\pi
828828 0 0
829829 −22.3607 −0.776619 −0.388309 0.921529i 0.626941π-0.626941\pi
−0.388309 + 0.921529i 0.626941π0.626941\pi
830830 2.03444 1.08201i 0.0706165 0.0375571i
831831 0 0
832832 54.4251 + 11.5322i 1.88685 + 0.399807i
833833 −4.14989 −0.143785
834834 0 0
835835 23.9651i 0.829347i
836836 0 0
837837 0 0
838838 24.8469 13.2147i 0.858324 0.456496i
839839 14.8324i 0.512071i −0.966667 0.256036i 0.917584π-0.917584\pi
0.966667 0.256036i 0.0824164π-0.0824164\pi
840840 0 0
841841 29.0000 1.00000
842842 20.7885 + 39.0876i 0.716420 + 1.34705i
843843 0 0
844844 0 0
845845 −79.0689 −2.72005
846846 0 0
847847 33.9540i 1.16667i
848848 0 0
849849 0 0
850850 5.45085 + 10.2489i 0.186963 + 0.351536i
851851 0 0
852852 0 0
853853 −55.2459 −1.89158 −0.945792 0.324772i 0.894712π-0.894712\pi
−0.945792 + 0.324772i 0.894712π0.894712\pi
854854 0 0
855855 0 0
856856 −5.67376 + 54.1480i −0.193925 + 1.85074i
857857 25.4000 0.867647 0.433824 0.900998i 0.357164π-0.357164\pi
0.433824 + 0.900998i 0.357164π0.357164\pi
858858 0 0
859859 46.4327i 1.58426i −0.610349 0.792132i 0.708971π-0.708971\pi
0.610349 0.792132i 0.291029π-0.291029\pi
860860 48.4855 + 32.6889i 1.65334 + 1.11468i
861861 0 0
862862 0 0
863863 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
864864 0 0
865865 −53.9918 −1.83578
866866 0 0
867867 0 0
868868 −22.8918 + 33.9540i −0.776997 + 1.15247i
869869 0 0
870870 0 0
871871 0 0
872872 0 0
873873 0 0
874874 0 0
875875 34.5106i 1.16667i
876876 0 0
877877 −44.6209 −1.50674 −0.753370 0.657597i 0.771573π-0.771573\pi
−0.753370 + 0.657597i 0.771573π0.771573\pi
878878 0 0
879879 0 0
880880 −27.5000 + 11.1243i −0.927025 + 0.375000i
881881 2.00000 0.0673817 0.0336909 0.999432i 0.489274π-0.489274\pi
0.0336909 + 0.999432i 0.489274π0.489274\pi
882882 5.03600 + 9.46892i 0.169571 + 0.318835i
883883 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
884884 −12.7639 + 18.9320i −0.429297 + 0.636751i
885885 0 0
886886 0 0
887887 13.9763i 0.469277i −0.972083 0.234639i 0.924609π-0.924609\pi
0.972083 0.234639i 0.0753906π-0.0753906\pi
888888 0 0
889889 52.1378 1.74864
890890 19.9220 + 37.4582i 0.667786 + 1.25560i
891891 29.8496i 1.00000i
892892 0 0
893893 0 0
894894 0 0
895895 44.4972i 1.48738i
896896 −33.5623 + 9.65081i −1.12124 + 0.322411i
897897 0 0
898898 26.7281 + 50.2554i 0.891929 + 1.67705i
899899 0 0
900900 16.7705 24.8747i 0.559017 0.829156i
901901 0 0
902902 0 0
903903 0 0
904904 0 0
905905 10.0000 0.332411
906906 0 0
907907 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
908908 −42.1584 28.4232i −1.39908 0.943256i
909909 0 0
910910 59.9314 31.8742i 1.98671 1.05662i
911911 59.6992i 1.97792i −0.148168 0.988962i 0.547338π-0.547338\pi
0.148168 0.988962i 0.452662π-0.452662\pi
912912 0 0
913913 −2.41675 −0.0799827
914914 −14.6869 27.6150i −0.485800 0.913423i
915915 0 0
916916 −6.70820 + 9.94987i −0.221645 + 0.328753i
917917 0 0
918918 0 0
919919 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
920920 0 0
921921 0 0
922922 0 0
923923 103.147i 3.39513i
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 0 0
929929 −14.0000 −0.459325 −0.229663 0.973270i 0.573762π-0.573762\pi
−0.229663 + 0.973270i 0.573762π0.573762\pi
930930 0 0
931931 0 0
932932 29.2646 43.4065i 0.958595 1.42183i
933933 0 0
934934 0 0
935935 12.1749i 0.398161i
936936 58.6869 + 6.14936i 1.91824 + 0.200998i
937937 −60.5585 −1.97836 −0.989179 0.146712i 0.953131π-0.953131\pi
−0.989179 + 0.146712i 0.953131π0.953131\pi
938938 0 0
939939 0 0
940940 0 0
941941 0 0 1.00000 00
−1.00000 π\pi
942942 0 0
943943 0 0
944944 55.0000 22.2486i 1.79010 0.724130i
945945 0 0
946946 −28.7984 54.1480i −0.936316 1.76050i
947947 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
948948 0 0
949949 85.3050 2.76912
950950 0 0
951951 0 0
952952 1.49363 14.2546i 0.0484089 0.461994i
953953 33.5168 1.08572 0.542858 0.839825i 0.317342π-0.317342\pi
0.542858 + 0.839825i 0.317342π0.317342\pi
954954 0 0
955955 14.8324i 0.479965i
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 −13.0000 −0.419355
962962 0 0
963963 57.7471i 1.86087i
964964 0 0
965965 −42.1126 −1.35565
966966 0 0
967967 61.5625i 1.97972i −0.142063 0.989858i 0.545374π-0.545374\pi
0.142063 0.989858i 0.454626π-0.454626\pi
968968 30.9433 + 3.24231i 0.994555 + 0.104212i
969969 0 0
970970 0 0
971971 59.6992i 1.91584i 0.287035 + 0.957920i 0.407330π0.407330\pi
−0.287035 + 0.957920i 0.592670π0.592670\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 0 0 1.00000 00
−1.00000 π\pi
978978 0 0
979979 44.4972i 1.42214i
980980 −6.31966 + 9.37357i −0.201874 + 0.299428i
981981 0 0
982982 0 0
983983 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
984984 0 0
985985 −39.3084 −1.25247
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 −27.7797 + 14.7745i −0.882898 + 0.469565i
991991 6.63325i 0.210712i −0.994435 0.105356i 0.966402π-0.966402\pi
0.994435 0.105356i 0.0335982π-0.0335982\pi
992992 −28.7573 24.1043i −0.913046 0.765312i
993993 0 0
994994 30.4033 + 57.1656i 0.964333 + 1.81318i
995995 33.1662i 1.05144i
996996 0 0
997997 −24.9210 −0.789255 −0.394627 0.918841i 0.629126π-0.629126\pi
−0.394627 + 0.918841i 0.629126π0.629126\pi
998998 55.5595 29.5490i 1.75870 0.935359i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 220.2.g.a.219.6 yes 8
4.3 odd 2 inner 220.2.g.a.219.5 yes 8
5.4 even 2 inner 220.2.g.a.219.3 8
11.10 odd 2 inner 220.2.g.a.219.3 8
20.19 odd 2 inner 220.2.g.a.219.4 yes 8
44.43 even 2 inner 220.2.g.a.219.4 yes 8
55.54 odd 2 CM 220.2.g.a.219.6 yes 8
220.219 even 2 inner 220.2.g.a.219.5 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
220.2.g.a.219.3 8 5.4 even 2 inner
220.2.g.a.219.3 8 11.10 odd 2 inner
220.2.g.a.219.4 yes 8 20.19 odd 2 inner
220.2.g.a.219.4 yes 8 44.43 even 2 inner
220.2.g.a.219.5 yes 8 4.3 odd 2 inner
220.2.g.a.219.5 yes 8 220.219 even 2 inner
220.2.g.a.219.6 yes 8 1.1 even 1 trivial
220.2.g.a.219.6 yes 8 55.54 odd 2 CM