Properties

Label 4655.2.a.br.1.8
Level 46554655
Weight 22
Character 4655.1
Self dual yes
Analytic conductor 37.17037.170
Analytic rank 00
Dimension 2626
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4655,2,Mod(1,4655)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4655, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4655.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 4655=57219 4655 = 5 \cdot 7^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4655.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 37.170362140937.1703621409
Analytic rank: 00
Dimension: 2626
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.8
Character χ\chi == 4655.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q1.21870q22.59660q30.514774q41.00000q5+3.16448q6+3.06475q8+3.74235q9+1.21870q10+1.34660q11+1.33666q124.31575q13+2.59660q152.70546q166.29921q174.56080q18+1.00000q19+0.514774q201.64110q22+8.99673q237.95795q24+1.00000q25+5.25960q261.92760q27+6.18505q293.16448q30+3.48591q312.83236q323.49659q33+7.67684q341.92647q362.65974q371.21870q38+11.2063q393.06475q407.39767q414.40794q430.693194q443.74235q4510.9643q46+9.10868q47+7.02501q481.21870q50+16.3566q51+2.22163q524.06456q53+2.34917q541.34660q552.59660q577.53772q580.439715q591.33666q60+11.4698q614.24827q62+8.86272q64+4.31575q65+4.26129q6610.1027q67+3.24267q6823.3609q69+7.65157q71+11.4694q7211.0854q73+3.24142q742.59660q750.514774q7613.6571q7817.5813q79+2.70546q806.22185q81+9.01553q82+3.61540q83+6.29921q85+5.37195q8616.0601q87+4.12699q882.45819q89+4.56080q904.63128q929.05153q9311.1007q941.00000q95+7.35452q96+7.31121q97+5.03946q99+O(q100)q-1.21870 q^{2} -2.59660 q^{3} -0.514774 q^{4} -1.00000 q^{5} +3.16448 q^{6} +3.06475 q^{8} +3.74235 q^{9} +1.21870 q^{10} +1.34660 q^{11} +1.33666 q^{12} -4.31575 q^{13} +2.59660 q^{15} -2.70546 q^{16} -6.29921 q^{17} -4.56080 q^{18} +1.00000 q^{19} +0.514774 q^{20} -1.64110 q^{22} +8.99673 q^{23} -7.95795 q^{24} +1.00000 q^{25} +5.25960 q^{26} -1.92760 q^{27} +6.18505 q^{29} -3.16448 q^{30} +3.48591 q^{31} -2.83236 q^{32} -3.49659 q^{33} +7.67684 q^{34} -1.92647 q^{36} -2.65974 q^{37} -1.21870 q^{38} +11.2063 q^{39} -3.06475 q^{40} -7.39767 q^{41} -4.40794 q^{43} -0.693194 q^{44} -3.74235 q^{45} -10.9643 q^{46} +9.10868 q^{47} +7.02501 q^{48} -1.21870 q^{50} +16.3566 q^{51} +2.22163 q^{52} -4.06456 q^{53} +2.34917 q^{54} -1.34660 q^{55} -2.59660 q^{57} -7.53772 q^{58} -0.439715 q^{59} -1.33666 q^{60} +11.4698 q^{61} -4.24827 q^{62} +8.86272 q^{64} +4.31575 q^{65} +4.26129 q^{66} -10.1027 q^{67} +3.24267 q^{68} -23.3609 q^{69} +7.65157 q^{71} +11.4694 q^{72} -11.0854 q^{73} +3.24142 q^{74} -2.59660 q^{75} -0.514774 q^{76} -13.6571 q^{78} -17.5813 q^{79} +2.70546 q^{80} -6.22185 q^{81} +9.01553 q^{82} +3.61540 q^{83} +6.29921 q^{85} +5.37195 q^{86} -16.0601 q^{87} +4.12699 q^{88} -2.45819 q^{89} +4.56080 q^{90} -4.63128 q^{92} -9.05153 q^{93} -11.1007 q^{94} -1.00000 q^{95} +7.35452 q^{96} +7.31121 q^{97} +5.03946 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 26q+4q26q3+36q426q5+4q6+12q8+44q94q10+14q1120q1214q13+6q15+64q1618q17+8q18+26q1936q20+36q22++24q99+O(q100) 26 q + 4 q^{2} - 6 q^{3} + 36 q^{4} - 26 q^{5} + 4 q^{6} + 12 q^{8} + 44 q^{9} - 4 q^{10} + 14 q^{11} - 20 q^{12} - 14 q^{13} + 6 q^{15} + 64 q^{16} - 18 q^{17} + 8 q^{18} + 26 q^{19} - 36 q^{20} + 36 q^{22}+ \cdots + 24 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 −1.21870 −0.861750 −0.430875 0.902412i 0.641795π-0.641795\pi
−0.430875 + 0.902412i 0.641795π0.641795\pi
33 −2.59660 −1.49915 −0.749575 0.661919i 0.769742π-0.769742\pi
−0.749575 + 0.661919i 0.769742π0.769742\pi
44 −0.514774 −0.257387
55 −1.00000 −0.447214
66 3.16448 1.29189
77 0 0
88 3.06475 1.08355
99 3.74235 1.24745
1010 1.21870 0.385386
1111 1.34660 0.406015 0.203008 0.979177i 0.434928π-0.434928\pi
0.203008 + 0.979177i 0.434928π0.434928\pi
1212 1.33666 0.385861
1313 −4.31575 −1.19697 −0.598487 0.801133i 0.704231π-0.704231\pi
−0.598487 + 0.801133i 0.704231π0.704231\pi
1414 0 0
1515 2.59660 0.670440
1616 −2.70546 −0.676365
1717 −6.29921 −1.52778 −0.763891 0.645345i 0.776714π-0.776714\pi
−0.763891 + 0.645345i 0.776714π0.776714\pi
1818 −4.56080 −1.07499
1919 1.00000 0.229416
2020 0.514774 0.115107
2121 0 0
2222 −1.64110 −0.349884
2323 8.99673 1.87595 0.937974 0.346706i 0.112700π-0.112700\pi
0.937974 + 0.346706i 0.112700π0.112700\pi
2424 −7.95795 −1.62441
2525 1.00000 0.200000
2626 5.25960 1.03149
2727 −1.92760 −0.370967
2828 0 0
2929 6.18505 1.14854 0.574268 0.818668i 0.305287π-0.305287\pi
0.574268 + 0.818668i 0.305287π0.305287\pi
3030 −3.16448 −0.577752
3131 3.48591 0.626088 0.313044 0.949739i 0.398651π-0.398651\pi
0.313044 + 0.949739i 0.398651π0.398651\pi
3232 −2.83236 −0.500695
3333 −3.49659 −0.608678
3434 7.67684 1.31657
3535 0 0
3636 −1.92647 −0.321078
3737 −2.65974 −0.437259 −0.218629 0.975808i 0.570159π-0.570159\pi
−0.218629 + 0.975808i 0.570159π0.570159\pi
3838 −1.21870 −0.197699
3939 11.2063 1.79444
4040 −3.06475 −0.484580
4141 −7.39767 −1.15532 −0.577661 0.816277i 0.696034π-0.696034\pi
−0.577661 + 0.816277i 0.696034π0.696034\pi
4242 0 0
4343 −4.40794 −0.672205 −0.336102 0.941825i 0.609109π-0.609109\pi
−0.336102 + 0.941825i 0.609109π0.609109\pi
4444 −0.693194 −0.104503
4545 −3.74235 −0.557877
4646 −10.9643 −1.61660
4747 9.10868 1.32864 0.664319 0.747449i 0.268722π-0.268722\pi
0.664319 + 0.747449i 0.268722π0.268722\pi
4848 7.02501 1.01397
4949 0 0
5050 −1.21870 −0.172350
5151 16.3566 2.29038
5252 2.22163 0.308085
5353 −4.06456 −0.558310 −0.279155 0.960246i 0.590054π-0.590054\pi
−0.279155 + 0.960246i 0.590054π0.590054\pi
5454 2.34917 0.319681
5555 −1.34660 −0.181576
5656 0 0
5757 −2.59660 −0.343929
5858 −7.53772 −0.989751
5959 −0.439715 −0.0572460 −0.0286230 0.999590i 0.509112π-0.509112\pi
−0.0286230 + 0.999590i 0.509112π0.509112\pi
6060 −1.33666 −0.172562
6161 11.4698 1.46855 0.734277 0.678850i 0.237521π-0.237521\pi
0.734277 + 0.678850i 0.237521π0.237521\pi
6262 −4.24827 −0.539531
6363 0 0
6464 8.86272 1.10784
6565 4.31575 0.535303
6666 4.26129 0.524528
6767 −10.1027 −1.23424 −0.617122 0.786868i 0.711701π-0.711701\pi
−0.617122 + 0.786868i 0.711701π0.711701\pi
6868 3.24267 0.393231
6969 −23.3609 −2.81233
7070 0 0
7171 7.65157 0.908075 0.454037 0.890983i 0.349983π-0.349983\pi
0.454037 + 0.890983i 0.349983π0.349983\pi
7272 11.4694 1.35168
7373 −11.0854 −1.29745 −0.648725 0.761023i 0.724697π-0.724697\pi
−0.648725 + 0.761023i 0.724697π0.724697\pi
7474 3.24142 0.376808
7575 −2.59660 −0.299830
7676 −0.514774 −0.0590486
7777 0 0
7878 −13.6571 −1.54636
7979 −17.5813 −1.97805 −0.989025 0.147747i 0.952798π-0.952798\pi
−0.989025 + 0.147747i 0.952798π0.952798\pi
8080 2.70546 0.302480
8181 −6.22185 −0.691316
8282 9.01553 0.995599
8383 3.61540 0.396842 0.198421 0.980117i 0.436419π-0.436419\pi
0.198421 + 0.980117i 0.436419π0.436419\pi
8484 0 0
8585 6.29921 0.683245
8686 5.37195 0.579272
8787 −16.0601 −1.72183
8888 4.12699 0.439939
8989 −2.45819 −0.260568 −0.130284 0.991477i 0.541589π-0.541589\pi
−0.130284 + 0.991477i 0.541589π0.541589\pi
9090 4.56080 0.480751
9191 0 0
9292 −4.63128 −0.482844
9393 −9.05153 −0.938600
9494 −11.1007 −1.14495
9595 −1.00000 −0.102598
9696 7.35452 0.750618
9797 7.31121 0.742341 0.371171 0.928565i 0.378956π-0.378956\pi
0.371171 + 0.928565i 0.378956π0.378956\pi
9898 0 0
9999 5.03946 0.506484
100100 −0.514774 −0.0514774
101101 −7.95595 −0.791647 −0.395824 0.918327i 0.629541π-0.629541\pi
−0.395824 + 0.918327i 0.629541π0.629541\pi
102102 −19.9337 −1.97373
103103 −0.476109 −0.0469124 −0.0234562 0.999725i 0.507467π-0.507467\pi
−0.0234562 + 0.999725i 0.507467π0.507467\pi
104104 −13.2267 −1.29698
105105 0 0
106106 4.95347 0.481124
107107 −5.19385 −0.502108 −0.251054 0.967973i 0.580777π-0.580777\pi
−0.251054 + 0.967973i 0.580777π0.580777\pi
108108 0.992278 0.0954820
109109 19.8446 1.90077 0.950386 0.311074i 0.100689π-0.100689\pi
0.950386 + 0.311074i 0.100689π0.100689\pi
110110 1.64110 0.156473
111111 6.90630 0.655517
112112 0 0
113113 −3.33367 −0.313606 −0.156803 0.987630i 0.550119π-0.550119\pi
−0.156803 + 0.987630i 0.550119π0.550119\pi
114114 3.16448 0.296381
115115 −8.99673 −0.838949
116116 −3.18390 −0.295618
117117 −16.1511 −1.49317
118118 0.535880 0.0493317
119119 0 0
120120 7.95795 0.726458
121121 −9.18667 −0.835152
122122 −13.9782 −1.26553
123123 19.2088 1.73200
124124 −1.79445 −0.161147
125125 −1.00000 −0.0894427
126126 0 0
127127 −1.70529 −0.151320 −0.0756599 0.997134i 0.524106π-0.524106\pi
−0.0756599 + 0.997134i 0.524106π0.524106\pi
128128 −5.13626 −0.453985
129129 11.4457 1.00774
130130 −5.25960 −0.461297
131131 −11.7277 −1.02466 −0.512329 0.858789i 0.671217π-0.671217\pi
−0.512329 + 0.858789i 0.671217π0.671217\pi
132132 1.79995 0.156666
133133 0 0
134134 12.3122 1.06361
135135 1.92760 0.165902
136136 −19.3055 −1.65543
137137 −7.43129 −0.634898 −0.317449 0.948275i 0.602826π-0.602826\pi
−0.317449 + 0.948275i 0.602826π0.602826\pi
138138 28.4700 2.42352
139139 6.05613 0.513674 0.256837 0.966455i 0.417320π-0.417320\pi
0.256837 + 0.966455i 0.417320π0.417320\pi
140140 0 0
141141 −23.6516 −1.99183
142142 −9.32496 −0.782533
143143 −5.81159 −0.485989
144144 −10.1248 −0.843733
145145 −6.18505 −0.513641
146146 13.5098 1.11808
147147 0 0
148148 1.36916 0.112545
149149 −3.91575 −0.320790 −0.160395 0.987053i 0.551277π-0.551277\pi
−0.160395 + 0.987053i 0.551277π0.551277\pi
150150 3.16448 0.258379
151151 −16.1392 −1.31339 −0.656693 0.754158i 0.728045π-0.728045\pi
−0.656693 + 0.754158i 0.728045π0.728045\pi
152152 3.06475 0.248584
153153 −23.5739 −1.90583
154154 0 0
155155 −3.48591 −0.279995
156156 −5.76870 −0.461866
157157 −15.5675 −1.24242 −0.621211 0.783644i 0.713359π-0.713359\pi
−0.621211 + 0.783644i 0.713359π0.713359\pi
158158 21.4263 1.70459
159159 10.5540 0.836990
160160 2.83236 0.223918
161161 0 0
162162 7.58255 0.595742
163163 −10.7167 −0.839398 −0.419699 0.907663i 0.637864π-0.637864\pi
−0.419699 + 0.907663i 0.637864π0.637864\pi
164164 3.80812 0.297365
165165 3.49659 0.272209
166166 −4.40609 −0.341979
167167 −15.8611 −1.22737 −0.613684 0.789552i 0.710313π-0.710313\pi
−0.613684 + 0.789552i 0.710313π0.710313\pi
168168 0 0
169169 5.62569 0.432745
170170 −7.67684 −0.588786
171171 3.74235 0.286185
172172 2.26909 0.173017
173173 1.46256 0.111196 0.0555981 0.998453i 0.482293π-0.482293\pi
0.0555981 + 0.998453i 0.482293π0.482293\pi
174174 19.5725 1.48378
175175 0 0
176176 −3.64317 −0.274615
177177 1.14176 0.0858203
178178 2.99580 0.224544
179179 9.52438 0.711886 0.355943 0.934508i 0.384160π-0.384160\pi
0.355943 + 0.934508i 0.384160π0.384160\pi
180180 1.92647 0.143590
181181 −23.9915 −1.78327 −0.891635 0.452754i 0.850441π-0.850441\pi
−0.891635 + 0.452754i 0.850441π0.850441\pi
182182 0 0
183183 −29.7825 −2.20158
184184 27.5727 2.03269
185185 2.65974 0.195548
186186 11.0311 0.808839
187187 −8.48251 −0.620303
188188 −4.68891 −0.341974
189189 0 0
190190 1.21870 0.0884137
191191 8.43884 0.610613 0.305306 0.952254i 0.401241π-0.401241\pi
0.305306 + 0.952254i 0.401241π0.401241\pi
192192 −23.0130 −1.66082
193193 24.4605 1.76071 0.880354 0.474318i 0.157305π-0.157305\pi
0.880354 + 0.474318i 0.157305π0.157305\pi
194194 −8.91017 −0.639713
195195 −11.2063 −0.802499
196196 0 0
197197 −22.5738 −1.60832 −0.804158 0.594416i 0.797383π-0.797383\pi
−0.804158 + 0.594416i 0.797383π0.797383\pi
198198 −6.14158 −0.436463
199199 8.25872 0.585445 0.292723 0.956197i 0.405439π-0.405439\pi
0.292723 + 0.956197i 0.405439π0.405439\pi
200200 3.06475 0.216711
201201 26.2328 1.85032
202202 9.69591 0.682202
203203 0 0
204204 −8.41992 −0.589512
205205 7.39767 0.516676
206206 0.580233 0.0404268
207207 33.6689 2.34015
208208 11.6761 0.809591
209209 1.34660 0.0931463
210210 0 0
211211 8.12000 0.559004 0.279502 0.960145i 0.409831π-0.409831\pi
0.279502 + 0.960145i 0.409831π0.409831\pi
212212 2.09233 0.143702
213213 −19.8681 −1.36134
214214 6.32974 0.432692
215215 4.40794 0.300619
216216 −5.90762 −0.401963
217217 0 0
218218 −24.1846 −1.63799
219219 28.7844 1.94507
220220 0.693194 0.0467351
221221 27.1858 1.82871
222222 −8.41669 −0.564891
223223 22.6800 1.51876 0.759381 0.650646i 0.225502π-0.225502\pi
0.759381 + 0.650646i 0.225502π0.225502\pi
224224 0 0
225225 3.74235 0.249490
226226 4.06274 0.270250
227227 −1.82891 −0.121389 −0.0606944 0.998156i 0.519332π-0.519332\pi
−0.0606944 + 0.998156i 0.519332π0.519332\pi
228228 1.33666 0.0885227
229229 −0.187466 −0.0123881 −0.00619405 0.999981i 0.501972π-0.501972\pi
−0.00619405 + 0.999981i 0.501972π0.501972\pi
230230 10.9643 0.722965
231231 0 0
232232 18.9556 1.24450
233233 −0.267637 −0.0175335 −0.00876675 0.999962i 0.502791π-0.502791\pi
−0.00876675 + 0.999962i 0.502791π0.502791\pi
234234 19.6833 1.28674
235235 −9.10868 −0.594185
236236 0.226353 0.0147344
237237 45.6517 2.96539
238238 0 0
239239 19.1664 1.23977 0.619887 0.784691i 0.287178π-0.287178\pi
0.619887 + 0.784691i 0.287178π0.287178\pi
240240 −7.02501 −0.453463
241241 5.42779 0.349635 0.174817 0.984601i 0.444066π-0.444066\pi
0.174817 + 0.984601i 0.444066π0.444066\pi
242242 11.1958 0.719692
243243 21.9385 1.40735
244244 −5.90434 −0.377986
245245 0 0
246246 −23.4098 −1.49255
247247 −4.31575 −0.274605
248248 10.6834 0.678400
249249 −9.38777 −0.594926
250250 1.21870 0.0770773
251251 13.5886 0.857703 0.428851 0.903375i 0.358918π-0.358918\pi
0.428851 + 0.903375i 0.358918π0.358918\pi
252252 0 0
253253 12.1150 0.761663
254254 2.07823 0.130400
255255 −16.3566 −1.02429
256256 −11.4659 −0.716617
257257 −15.2880 −0.953638 −0.476819 0.879001i 0.658210π-0.658210\pi
−0.476819 + 0.879001i 0.658210π0.658210\pi
258258 −13.9488 −0.868416
259259 0 0
260260 −2.22163 −0.137780
261261 23.1467 1.43274
262262 14.2926 0.882999
263263 14.4321 0.889921 0.444960 0.895550i 0.353218π-0.353218\pi
0.444960 + 0.895550i 0.353218π0.353218\pi
264264 −10.7162 −0.659535
265265 4.06456 0.249684
266266 0 0
267267 6.38296 0.390631
268268 5.20061 0.317678
269269 8.70066 0.530488 0.265244 0.964181i 0.414547π-0.414547\pi
0.265244 + 0.964181i 0.414547π0.414547\pi
270270 −2.34917 −0.142966
271271 22.1555 1.34585 0.672924 0.739712i 0.265038π-0.265038\pi
0.672924 + 0.739712i 0.265038π0.265038\pi
272272 17.0423 1.03334
273273 0 0
274274 9.05650 0.547123
275275 1.34660 0.0812031
276276 12.0256 0.723856
277277 22.6124 1.35864 0.679322 0.733840i 0.262274π-0.262274\pi
0.679322 + 0.733840i 0.262274π0.262274\pi
278278 −7.38060 −0.442659
279279 13.0455 0.781014
280280 0 0
281281 30.6197 1.82662 0.913308 0.407269i 0.133519π-0.133519\pi
0.913308 + 0.407269i 0.133519π0.133519\pi
282282 28.8242 1.71646
283283 14.3623 0.853751 0.426876 0.904310i 0.359614π-0.359614\pi
0.426876 + 0.904310i 0.359614π0.359614\pi
284284 −3.93883 −0.233726
285285 2.59660 0.153810
286286 7.08258 0.418801
287287 0 0
288288 −10.5997 −0.624593
289289 22.6800 1.33412
290290 7.53772 0.442630
291291 −18.9843 −1.11288
292292 5.70648 0.333946
293293 14.0391 0.820171 0.410086 0.912047i 0.365499π-0.365499\pi
0.410086 + 0.912047i 0.365499π0.365499\pi
294294 0 0
295295 0.439715 0.0256012
296296 −8.15144 −0.473793
297297 −2.59571 −0.150618
298298 4.77212 0.276441
299299 −38.8276 −2.24546
300300 1.33666 0.0771723
301301 0 0
302302 19.6688 1.13181
303303 20.6585 1.18680
304304 −2.70546 −0.155169
305305 −11.4698 −0.656757
306306 28.7294 1.64235
307307 −30.7563 −1.75536 −0.877678 0.479251i 0.840908π-0.840908\pi
−0.877678 + 0.479251i 0.840908π0.840908\pi
308308 0 0
309309 1.23627 0.0703288
310310 4.24827 0.241286
311311 16.5154 0.936500 0.468250 0.883596i 0.344885π-0.344885\pi
0.468250 + 0.883596i 0.344885π0.344885\pi
312312 34.3445 1.94437
313313 −11.0388 −0.623950 −0.311975 0.950090i 0.600991π-0.600991\pi
−0.311975 + 0.950090i 0.600991π0.600991\pi
314314 18.9721 1.07066
315315 0 0
316316 9.05039 0.509124
317317 −23.5720 −1.32394 −0.661968 0.749532i 0.730279π-0.730279\pi
−0.661968 + 0.749532i 0.730279π0.730279\pi
318318 −12.8622 −0.721277
319319 8.32879 0.466323
320320 −8.86272 −0.495441
321321 13.4864 0.752736
322322 0 0
323323 −6.29921 −0.350497
324324 3.20284 0.177936
325325 −4.31575 −0.239395
326326 13.0605 0.723352
327327 −51.5287 −2.84954
328328 −22.6720 −1.25185
329329 0 0
330330 −4.26129 −0.234576
331331 −8.88565 −0.488400 −0.244200 0.969725i 0.578525π-0.578525\pi
−0.244200 + 0.969725i 0.578525π0.578525\pi
332332 −1.86111 −0.102142
333333 −9.95369 −0.545459
334334 19.3299 1.05768
335335 10.1027 0.551971
336336 0 0
337337 4.27124 0.232669 0.116335 0.993210i 0.462886π-0.462886\pi
0.116335 + 0.993210i 0.462886π0.462886\pi
338338 −6.85602 −0.372918
339339 8.65623 0.470142
340340 −3.24267 −0.175858
341341 4.69413 0.254201
342342 −4.56080 −0.246620
343343 0 0
344344 −13.5092 −0.728370
345345 23.3609 1.25771
346346 −1.78242 −0.0958233
347347 −33.7353 −1.81101 −0.905504 0.424339i 0.860507π-0.860507\pi
−0.905504 + 0.424339i 0.860507π0.860507\pi
348348 8.26733 0.443176
349349 35.8204 1.91742 0.958710 0.284386i 0.0917898π-0.0917898\pi
0.958710 + 0.284386i 0.0917898π0.0917898\pi
350350 0 0
351351 8.31904 0.444038
352352 −3.81406 −0.203290
353353 4.81697 0.256382 0.128191 0.991750i 0.459083π-0.459083\pi
0.128191 + 0.991750i 0.459083π0.459083\pi
354354 −1.39147 −0.0739557
355355 −7.65157 −0.406103
356356 1.26541 0.0670668
357357 0 0
358358 −11.6074 −0.613468
359359 31.0854 1.64062 0.820312 0.571917i 0.193800π-0.193800\pi
0.820312 + 0.571917i 0.193800π0.193800\pi
360360 −11.4694 −0.604490
361361 1.00000 0.0526316
362362 29.2383 1.53673
363363 23.8541 1.25202
364364 0 0
365365 11.0854 0.580237
366366 36.2959 1.89721
367367 4.65599 0.243041 0.121520 0.992589i 0.461223π-0.461223\pi
0.121520 + 0.992589i 0.461223π0.461223\pi
368368 −24.3403 −1.26883
369369 −27.6847 −1.44121
370370 −3.24142 −0.168514
371371 0 0
372372 4.65949 0.241583
373373 −3.63513 −0.188220 −0.0941099 0.995562i 0.530001π-0.530001\pi
−0.0941099 + 0.995562i 0.530001π0.530001\pi
374374 10.3376 0.534546
375375 2.59660 0.134088
376376 27.9158 1.43965
377377 −26.6931 −1.37477
378378 0 0
379379 −13.9090 −0.714458 −0.357229 0.934017i 0.616279π-0.616279\pi
−0.357229 + 0.934017i 0.616279π0.616279\pi
380380 0.514774 0.0264073
381381 4.42796 0.226851
382382 −10.2844 −0.526196
383383 14.0305 0.716927 0.358464 0.933544i 0.383301π-0.383301\pi
0.358464 + 0.933544i 0.383301π0.383301\pi
384384 13.3368 0.680592
385385 0 0
386386 −29.8100 −1.51729
387387 −16.4961 −0.838543
388388 −3.76362 −0.191069
389389 36.4415 1.84766 0.923829 0.382806i 0.125042π-0.125042\pi
0.923829 + 0.382806i 0.125042π0.125042\pi
390390 13.6571 0.691554
391391 −56.6723 −2.86604
392392 0 0
393393 30.4523 1.53612
394394 27.5106 1.38597
395395 17.5813 0.884611
396396 −2.59418 −0.130362
397397 31.2870 1.57025 0.785125 0.619337i 0.212599π-0.212599\pi
0.785125 + 0.619337i 0.212599π0.212599\pi
398398 −10.0649 −0.504508
399399 0 0
400400 −2.70546 −0.135273
401401 −26.8571 −1.34118 −0.670589 0.741829i 0.733959π-0.733959\pi
−0.670589 + 0.741829i 0.733959π0.733959\pi
402402 −31.9698 −1.59451
403403 −15.0443 −0.749411
404404 4.09551 0.203759
405405 6.22185 0.309166
406406 0 0
407407 −3.58161 −0.177534
408408 50.1288 2.48174
409409 −9.94796 −0.491895 −0.245947 0.969283i 0.579099π-0.579099\pi
−0.245947 + 0.969283i 0.579099π0.579099\pi
410410 −9.01553 −0.445245
411411 19.2961 0.951807
412412 0.245088 0.0120746
413413 0 0
414414 −41.0323 −2.01663
415415 −3.61540 −0.177473
416416 12.2238 0.599319
417417 −15.7254 −0.770075
418418 −1.64110 −0.0802688
419419 −13.6597 −0.667319 −0.333659 0.942694i 0.608284π-0.608284\pi
−0.333659 + 0.942694i 0.608284π0.608284\pi
420420 0 0
421421 −10.0275 −0.488711 −0.244356 0.969686i 0.578576π-0.578576\pi
−0.244356 + 0.969686i 0.578576π0.578576\pi
422422 −9.89583 −0.481721
423423 34.0879 1.65741
424424 −12.4569 −0.604958
425425 −6.29921 −0.305556
426426 24.2132 1.17314
427427 0 0
428428 2.67366 0.129236
429429 15.0904 0.728571
430430 −5.37195 −0.259059
431431 −20.7275 −0.998410 −0.499205 0.866484i 0.666375π-0.666375\pi
−0.499205 + 0.866484i 0.666375π0.666375\pi
432432 5.21505 0.250909
433433 25.2058 1.21131 0.605657 0.795726i 0.292910π-0.292910\pi
0.605657 + 0.795726i 0.292910π0.292910\pi
434434 0 0
435435 16.0601 0.770025
436436 −10.2155 −0.489233
437437 8.99673 0.430372
438438 −35.0795 −1.67617
439439 0.410047 0.0195705 0.00978525 0.999952i 0.496885π-0.496885\pi
0.00978525 + 0.999952i 0.496885π0.496885\pi
440440 −4.12699 −0.196747
441441 0 0
442442 −33.1313 −1.57590
443443 −15.5041 −0.736622 −0.368311 0.929703i 0.620064π-0.620064\pi
−0.368311 + 0.929703i 0.620064π0.620064\pi
444444 −3.55518 −0.168721
445445 2.45819 0.116530
446446 −27.6400 −1.30879
447447 10.1676 0.480913
448448 0 0
449449 13.9261 0.657212 0.328606 0.944467i 0.393421π-0.393421\pi
0.328606 + 0.944467i 0.393421π0.393421\pi
450450 −4.56080 −0.214998
451451 −9.96170 −0.469078
452452 1.71609 0.0807179
453453 41.9070 1.96896
454454 2.22889 0.104607
455455 0 0
456456 −7.95795 −0.372665
457457 32.8812 1.53812 0.769058 0.639179i 0.220726π-0.220726\pi
0.769058 + 0.639179i 0.220726π0.220726\pi
458458 0.228464 0.0106754
459459 12.1424 0.566757
460460 4.63128 0.215934
461461 21.2325 0.988896 0.494448 0.869207i 0.335370π-0.335370\pi
0.494448 + 0.869207i 0.335370π0.335370\pi
462462 0 0
463463 −5.41515 −0.251663 −0.125832 0.992052i 0.540160π-0.540160\pi
−0.125832 + 0.992052i 0.540160π0.540160\pi
464464 −16.7334 −0.776830
465465 9.05153 0.419755
466466 0.326169 0.0151095
467467 −26.5030 −1.22641 −0.613206 0.789923i 0.710120π-0.710120\pi
−0.613206 + 0.789923i 0.710120π0.710120\pi
468468 8.31414 0.384321
469469 0 0
470470 11.1007 0.512039
471471 40.4226 1.86258
472472 −1.34762 −0.0620291
473473 −5.93573 −0.272925
474474 −55.6356 −2.55543
475475 1.00000 0.0458831
476476 0 0
477477 −15.2110 −0.696465
478478 −23.3581 −1.06838
479479 14.9268 0.682021 0.341011 0.940059i 0.389231π-0.389231\pi
0.341011 + 0.940059i 0.389231π0.389231\pi
480480 −7.35452 −0.335686
481481 11.4788 0.523387
482482 −6.61484 −0.301298
483483 0 0
484484 4.72905 0.214957
485485 −7.31121 −0.331985
486486 −26.7364 −1.21279
487487 11.1025 0.503101 0.251550 0.967844i 0.419060π-0.419060\pi
0.251550 + 0.967844i 0.419060π0.419060\pi
488488 35.1520 1.59126
489489 27.8271 1.25838
490490 0 0
491491 −20.3610 −0.918880 −0.459440 0.888209i 0.651950π-0.651950\pi
−0.459440 + 0.888209i 0.651950π0.651950\pi
492492 −9.88819 −0.445794
493493 −38.9609 −1.75471
494494 5.25960 0.236640
495495 −5.03946 −0.226507
496496 −9.43099 −0.423464
497497 0 0
498498 11.4409 0.512677
499499 −19.3442 −0.865967 −0.432984 0.901402i 0.642539π-0.642539\pi
−0.432984 + 0.901402i 0.642539π0.642539\pi
500500 0.514774 0.0230214
501501 41.1850 1.84001
502502 −16.5604 −0.739125
503503 −25.7994 −1.15034 −0.575170 0.818034i 0.695064π-0.695064\pi
−0.575170 + 0.818034i 0.695064π0.695064\pi
504504 0 0
505505 7.95595 0.354035
506506 −14.7645 −0.656363
507507 −14.6077 −0.648750
508508 0.877837 0.0389477
509509 −19.0053 −0.842396 −0.421198 0.906969i 0.638390π-0.638390\pi
−0.421198 + 0.906969i 0.638390π0.638390\pi
510510 19.9337 0.882679
511511 0 0
512512 24.2460 1.07153
513513 −1.92760 −0.0851057
514514 18.6314 0.821798
515515 0.476109 0.0209799
516516 −5.89193 −0.259378
517517 12.2658 0.539447
518518 0 0
519519 −3.79768 −0.166700
520520 13.2267 0.580029
521521 −27.7992 −1.21791 −0.608953 0.793206i 0.708410π-0.708410\pi
−0.608953 + 0.793206i 0.708410π0.708410\pi
522522 −28.2088 −1.23467
523523 2.83110 0.123796 0.0618978 0.998082i 0.480285π-0.480285\pi
0.0618978 + 0.998082i 0.480285π0.480285\pi
524524 6.03713 0.263733
525525 0 0
526526 −17.5884 −0.766889
527527 −21.9585 −0.956526
528528 9.45988 0.411689
529529 57.9411 2.51918
530530 −4.95347 −0.215165
531531 −1.64557 −0.0714116
532532 0 0
533533 31.9265 1.38289
534534 −7.77890 −0.336626
535535 5.19385 0.224550
536536 −30.9623 −1.33737
537537 −24.7311 −1.06722
538538 −10.6035 −0.457149
539539 0 0
540540 −0.992278 −0.0427009
541541 14.5758 0.626663 0.313331 0.949644i 0.398555π-0.398555\pi
0.313331 + 0.949644i 0.398555π0.398555\pi
542542 −27.0008 −1.15978
543543 62.2963 2.67339
544544 17.8416 0.764953
545545 −19.8446 −0.850051
546546 0 0
547547 −1.26617 −0.0541377 −0.0270688 0.999634i 0.508617π-0.508617\pi
−0.0270688 + 0.999634i 0.508617π0.508617\pi
548548 3.82543 0.163414
549549 42.9240 1.83195
550550 −1.64110 −0.0699767
551551 6.18505 0.263492
552552 −71.5955 −3.04731
553553 0 0
554554 −27.5577 −1.17081
555555 −6.90630 −0.293156
556556 −3.11753 −0.132213
557557 −28.0971 −1.19051 −0.595255 0.803537i 0.702949π-0.702949\pi
−0.595255 + 0.803537i 0.702949π0.702949\pi
558558 −15.8985 −0.673039
559559 19.0236 0.804611
560560 0 0
561561 22.0257 0.929927
562562 −37.3162 −1.57409
563563 21.3119 0.898191 0.449096 0.893484i 0.351746π-0.351746\pi
0.449096 + 0.893484i 0.351746π0.351746\pi
564564 12.1752 0.512670
565565 3.33367 0.140249
566566 −17.5033 −0.735720
567567 0 0
568568 23.4502 0.983947
569569 −31.8597 −1.33563 −0.667815 0.744327i 0.732770π-0.732770\pi
−0.667815 + 0.744327i 0.732770π0.732770\pi
570570 −3.16448 −0.132545
571571 22.6689 0.948666 0.474333 0.880346i 0.342689π-0.342689\pi
0.474333 + 0.880346i 0.342689π0.342689\pi
572572 2.99165 0.125087
573573 −21.9123 −0.915401
574574 0 0
575575 8.99673 0.375189
576576 33.1674 1.38198
577577 23.6964 0.986492 0.493246 0.869890i 0.335810π-0.335810\pi
0.493246 + 0.869890i 0.335810π0.335810\pi
578578 −27.6401 −1.14968
579579 −63.5143 −2.63956
580580 3.18390 0.132204
581581 0 0
582582 23.1362 0.959025
583583 −5.47333 −0.226682
584584 −33.9740 −1.40586
585585 16.1511 0.667764
586586 −17.1094 −0.706783
587587 −2.44246 −0.100811 −0.0504055 0.998729i 0.516051π-0.516051\pi
−0.0504055 + 0.998729i 0.516051π0.516051\pi
588588 0 0
589589 3.48591 0.143634
590590 −0.535880 −0.0220618
591591 58.6152 2.41111
592592 7.19583 0.295747
593593 −8.05391 −0.330734 −0.165367 0.986232i 0.552881π-0.552881\pi
−0.165367 + 0.986232i 0.552881π0.552881\pi
594594 3.16339 0.129795
595595 0 0
596596 2.01572 0.0825672
597597 −21.4446 −0.877671
598598 47.3192 1.93502
599599 −14.0509 −0.574106 −0.287053 0.957915i 0.592676π-0.592676\pi
−0.287053 + 0.957915i 0.592676π0.592676\pi
600600 −7.95795 −0.324882
601601 12.3953 0.505615 0.252807 0.967517i 0.418646π-0.418646\pi
0.252807 + 0.967517i 0.418646π0.418646\pi
602602 0 0
603603 −37.8080 −1.53966
604604 8.30801 0.338048
605605 9.18667 0.373491
606606 −25.1764 −1.02272
607607 −9.54948 −0.387602 −0.193801 0.981041i 0.562082π-0.562082\pi
−0.193801 + 0.981041i 0.562082π0.562082\pi
608608 −2.83236 −0.114867
609609 0 0
610610 13.9782 0.565961
611611 −39.3108 −1.59034
612612 12.1352 0.490537
613613 10.0870 0.407409 0.203705 0.979032i 0.434702π-0.434702\pi
0.203705 + 0.979032i 0.434702π0.434702\pi
614614 37.4827 1.51268
615615 −19.2088 −0.774574
616616 0 0
617617 44.2405 1.78106 0.890529 0.454927i 0.150335π-0.150335\pi
0.890529 + 0.454927i 0.150335π0.150335\pi
618618 −1.50664 −0.0606058
619619 −28.3095 −1.13786 −0.568928 0.822388i 0.692642π-0.692642\pi
−0.568928 + 0.822388i 0.692642π0.692642\pi
620620 1.79445 0.0720670
621621 −17.3421 −0.695915
622622 −20.1273 −0.807029
623623 0 0
624624 −30.3182 −1.21370
625625 1.00000 0.0400000
626626 13.4530 0.537689
627627 −3.49659 −0.139640
628628 8.01374 0.319783
629629 16.7543 0.668036
630630 0 0
631631 20.8647 0.830610 0.415305 0.909682i 0.363675π-0.363675\pi
0.415305 + 0.909682i 0.363675π0.363675\pi
632632 −53.8823 −2.14332
633633 −21.0844 −0.838031
634634 28.7272 1.14090
635635 1.70529 0.0676723
636636 −5.43294 −0.215430
637637 0 0
638638 −10.1503 −0.401854
639639 28.6349 1.13278
640640 5.13626 0.203028
641641 −4.61134 −0.182137 −0.0910686 0.995845i 0.529028π-0.529028\pi
−0.0910686 + 0.995845i 0.529028π0.529028\pi
642642 −16.4358 −0.648670
643643 9.85158 0.388508 0.194254 0.980951i 0.437771π-0.437771\pi
0.194254 + 0.980951i 0.437771π0.437771\pi
644644 0 0
645645 −11.4457 −0.450673
646646 7.67684 0.302041
647647 −12.3295 −0.484723 −0.242362 0.970186i 0.577922π-0.577922\pi
−0.242362 + 0.970186i 0.577922π0.577922\pi
648648 −19.0684 −0.749078
649649 −0.592120 −0.0232427
650650 5.25960 0.206298
651651 0 0
652652 5.51668 0.216050
653653 24.9967 0.978197 0.489098 0.872229i 0.337326π-0.337326\pi
0.489098 + 0.872229i 0.337326π0.337326\pi
654654 62.7979 2.45559
655655 11.7277 0.458241
656656 20.0141 0.781420
657657 −41.4855 −1.61851
658658 0 0
659659 −10.3506 −0.403201 −0.201600 0.979468i 0.564614π-0.564614\pi
−0.201600 + 0.979468i 0.564614π0.564614\pi
660660 −1.79995 −0.0700630
661661 12.2629 0.476973 0.238486 0.971146i 0.423349π-0.423349\pi
0.238486 + 0.971146i 0.423349π0.423349\pi
662662 10.8289 0.420878
663663 −70.5908 −2.74152
664664 11.0803 0.429999
665665 0 0
666666 12.1306 0.470049
667667 55.6452 2.15459
668668 8.16487 0.315908
669669 −58.8909 −2.27685
670670 −12.3122 −0.475661
671671 15.4452 0.596255
672672 0 0
673673 18.7370 0.722258 0.361129 0.932516i 0.382391π-0.382391\pi
0.361129 + 0.932516i 0.382391π0.382391\pi
674674 −5.20535 −0.200503
675675 −1.92760 −0.0741934
676676 −2.89596 −0.111383
677677 −38.3777 −1.47498 −0.737488 0.675360i 0.763988π-0.763988\pi
−0.737488 + 0.675360i 0.763988π0.763988\pi
678678 −10.5493 −0.405145
679679 0 0
680680 19.3055 0.740332
681681 4.74895 0.181980
682682 −5.72073 −0.219058
683683 −7.86791 −0.301057 −0.150529 0.988606i 0.548098π-0.548098\pi
−0.150529 + 0.988606i 0.548098π0.548098\pi
684684 −1.92647 −0.0736602
685685 7.43129 0.283935
686686 0 0
687687 0.486775 0.0185716
688688 11.9255 0.454656
689689 17.5416 0.668282
690690 −28.4700 −1.08383
691691 −41.4312 −1.57612 −0.788059 0.615600i 0.788914π-0.788914\pi
−0.788059 + 0.615600i 0.788914π0.788914\pi
692692 −0.752886 −0.0286204
693693 0 0
694694 41.1132 1.56064
695695 −6.05613 −0.229722
696696 −49.2203 −1.86569
697697 46.5995 1.76508
698698 −43.6542 −1.65234
699699 0.694948 0.0262853
700700 0 0
701701 18.4630 0.697337 0.348668 0.937246i 0.386634π-0.386634\pi
0.348668 + 0.937246i 0.386634π0.386634\pi
702702 −10.1384 −0.382650
703703 −2.65974 −0.100314
704704 11.9345 0.449800
705705 23.6516 0.890772
706706 −5.87044 −0.220937
707707 0 0
708708 −0.587750 −0.0220890
709709 −9.71093 −0.364701 −0.182351 0.983234i 0.558371π-0.558371\pi
−0.182351 + 0.983234i 0.558371π0.558371\pi
710710 9.32496 0.349960
711711 −65.7954 −2.46752
712712 −7.53375 −0.282339
713713 31.3618 1.17451
714714 0 0
715715 5.81159 0.217341
716716 −4.90290 −0.183230
717717 −49.7677 −1.85861
718718 −37.8837 −1.41381
719719 3.88966 0.145060 0.0725299 0.997366i 0.476893π-0.476893\pi
0.0725299 + 0.997366i 0.476893π0.476893\pi
720720 10.1248 0.377329
721721 0 0
722722 −1.21870 −0.0453553
723723 −14.0938 −0.524155
724724 12.3502 0.458990
725725 6.18505 0.229707
726726 −29.0710 −1.07893
727727 43.9305 1.62929 0.814646 0.579958i 0.196931π-0.196931\pi
0.814646 + 0.579958i 0.196931π0.196931\pi
728728 0 0
729729 −38.3000 −1.41852
730730 −13.5098 −0.500019
731731 27.7665 1.02698
732732 15.3312 0.566658
733733 30.0305 1.10920 0.554601 0.832116i 0.312871π-0.312871\pi
0.554601 + 0.832116i 0.312871π0.312871\pi
734734 −5.67425 −0.209441
735735 0 0
736736 −25.4820 −0.939278
737737 −13.6043 −0.501122
738738 33.7393 1.24196
739739 −26.1955 −0.963617 −0.481808 0.876277i 0.660020π-0.660020\pi
−0.481808 + 0.876277i 0.660020π0.660020\pi
740740 −1.36916 −0.0503315
741741 11.2063 0.411673
742742 0 0
743743 −7.24377 −0.265748 −0.132874 0.991133i 0.542421π-0.542421\pi
−0.132874 + 0.991133i 0.542421π0.542421\pi
744744 −27.7407 −1.01702
745745 3.91575 0.143462
746746 4.43013 0.162198
747747 13.5301 0.495041
748748 4.36657 0.159658
749749 0 0
750750 −3.16448 −0.115550
751751 33.7313 1.23087 0.615436 0.788187i 0.288980π-0.288980\pi
0.615436 + 0.788187i 0.288980π0.288980\pi
752752 −24.6432 −0.898644
753753 −35.2841 −1.28582
754754 32.5309 1.18471
755755 16.1392 0.587364
756756 0 0
757757 40.4892 1.47160 0.735802 0.677196i 0.236805π-0.236805\pi
0.735802 + 0.677196i 0.236805π0.236805\pi
758758 16.9509 0.615685
759759 −31.4579 −1.14185
760760 −3.06475 −0.111170
761761 12.1473 0.440341 0.220170 0.975461i 0.429339π-0.429339\pi
0.220170 + 0.975461i 0.429339π0.429339\pi
762762 −5.39635 −0.195489
763763 0 0
764764 −4.34409 −0.157164
765765 23.5739 0.852315
766766 −17.0990 −0.617812
767767 1.89770 0.0685219
768768 29.7724 1.07432
769769 26.4500 0.953811 0.476906 0.878954i 0.341758π-0.341758\pi
0.476906 + 0.878954i 0.341758π0.341758\pi
770770 0 0
771771 39.6969 1.42965
772772 −12.5916 −0.453183
773773 −22.4933 −0.809028 −0.404514 0.914532i 0.632559π-0.632559\pi
−0.404514 + 0.914532i 0.632559π0.632559\pi
774774 20.1037 0.722614
775775 3.48591 0.125218
776776 22.4071 0.804366
777777 0 0
778778 −44.4112 −1.59222
779779 −7.39767 −0.265049
780780 5.76870 0.206553
781781 10.3036 0.368692
782782 69.0664 2.46981
783783 −11.9223 −0.426069
784784 0 0
785785 15.5675 0.555628
786786 −37.1122 −1.32375
787787 −11.1505 −0.397472 −0.198736 0.980053i 0.563684π-0.563684\pi
−0.198736 + 0.980053i 0.563684π0.563684\pi
788788 11.6204 0.413959
789789 −37.4744 −1.33412
790790 −21.4263 −0.762314
791791 0 0
792792 15.4447 0.548803
793793 −49.5007 −1.75782
794794 −38.1295 −1.35316
795795 −10.5540 −0.374313
796796 −4.25137 −0.150686
797797 −2.00143 −0.0708944 −0.0354472 0.999372i 0.511286π-0.511286\pi
−0.0354472 + 0.999372i 0.511286π0.511286\pi
798798 0 0
799799 −57.3775 −2.02987
800800 −2.83236 −0.100139
801801 −9.19943 −0.325046
802802 32.7307 1.15576
803803 −14.9276 −0.526784
804804 −13.5039 −0.476247
805805 0 0
806806 18.3345 0.645805
807807 −22.5922 −0.795282
808808 −24.3830 −0.857792
809809 27.3887 0.962934 0.481467 0.876464i 0.340104π-0.340104\pi
0.481467 + 0.876464i 0.340104π0.340104\pi
810810 −7.58255 −0.266424
811811 −49.9883 −1.75533 −0.877664 0.479277i 0.840899π-0.840899\pi
−0.877664 + 0.479277i 0.840899π0.840899\pi
812812 0 0
813813 −57.5289 −2.01763
814814 4.36490 0.152990
815815 10.7167 0.375390
816816 −44.2520 −1.54913
817817 −4.40794 −0.154214
818818 12.1236 0.423890
819819 0 0
820820 −3.80812 −0.132985
821821 −33.4012 −1.16571 −0.582855 0.812576i 0.698064π-0.698064\pi
−0.582855 + 0.812576i 0.698064π0.698064\pi
822822 −23.5161 −0.820220
823823 4.64616 0.161955 0.0809775 0.996716i 0.474196π-0.474196\pi
0.0809775 + 0.996716i 0.474196π0.474196\pi
824824 −1.45916 −0.0508321
825825 −3.49659 −0.121736
826826 0 0
827827 5.64229 0.196201 0.0981007 0.995176i 0.468723π-0.468723\pi
0.0981007 + 0.995176i 0.468723π0.468723\pi
828828 −17.3319 −0.602325
829829 39.9143 1.38628 0.693141 0.720802i 0.256226π-0.256226\pi
0.693141 + 0.720802i 0.256226π0.256226\pi
830830 4.40609 0.152937
831831 −58.7154 −2.03681
832832 −38.2493 −1.32605
833833 0 0
834834 19.1645 0.663612
835835 15.8611 0.548896
836836 −0.693194 −0.0239746
837837 −6.71945 −0.232258
838838 16.6470 0.575062
839839 23.4423 0.809317 0.404659 0.914468i 0.367390π-0.367390\pi
0.404659 + 0.914468i 0.367390π0.367390\pi
840840 0 0
841841 9.25488 0.319134
842842 12.2205 0.421147
843843 −79.5072 −2.73837
844844 −4.17996 −0.143880
845845 −5.62569 −0.193530
846846 −41.5429 −1.42827
847847 0 0
848848 10.9965 0.377621
849849 −37.2933 −1.27990
850850 7.67684 0.263313
851851 −23.9290 −0.820274
852852 10.2276 0.350391
853853 −23.1897 −0.793999 −0.396999 0.917819i 0.629949π-0.629949\pi
−0.396999 + 0.917819i 0.629949π0.629949\pi
854854 0 0
855855 −3.74235 −0.127986
856856 −15.9179 −0.544061
857857 −14.1698 −0.484033 −0.242016 0.970272i 0.577809π-0.577809\pi
−0.242016 + 0.970272i 0.577809π0.577809\pi
858858 −18.3906 −0.627846
859859 28.2375 0.963451 0.481726 0.876322i 0.340010π-0.340010\pi
0.481726 + 0.876322i 0.340010π0.340010\pi
860860 −2.26909 −0.0773754
861861 0 0
862862 25.2606 0.860380
863863 43.0648 1.46594 0.732972 0.680259i 0.238133π-0.238133\pi
0.732972 + 0.680259i 0.238133π0.238133\pi
864864 5.45966 0.185741
865865 −1.46256 −0.0497284
866866 −30.7183 −1.04385
867867 −58.8910 −2.00004
868868 0 0
869869 −23.6750 −0.803119
870870 −19.5725 −0.663569
871871 43.6008 1.47736
872872 60.8189 2.05959
873873 27.3612 0.926035
874874 −10.9643 −0.370873
875875 0 0
876876 −14.8175 −0.500636
877877 −40.9748 −1.38362 −0.691810 0.722080i 0.743186π-0.743186\pi
−0.691810 + 0.722080i 0.743186π0.743186\pi
878878 −0.499724 −0.0168649
879879 −36.4539 −1.22956
880880 3.64317 0.122811
881881 8.65739 0.291675 0.145837 0.989309i 0.453412π-0.453412\pi
0.145837 + 0.989309i 0.453412π0.453412\pi
882882 0 0
883883 43.8087 1.47428 0.737140 0.675740i 0.236176π-0.236176\pi
0.737140 + 0.675740i 0.236176π0.236176\pi
884884 −13.9945 −0.470687
885885 −1.14176 −0.0383800
886886 18.8948 0.634784
887887 30.6402 1.02880 0.514398 0.857552i 0.328015π-0.328015\pi
0.514398 + 0.857552i 0.328015π0.328015\pi
888888 21.1661 0.710287
889889 0 0
890890 −2.99580 −0.100419
891891 −8.37834 −0.280685
892892 −11.6750 −0.390909
893893 9.10868 0.304810
894894 −12.3913 −0.414427
895895 −9.52438 −0.318365
896896 0 0
897897 100.820 3.36628
898898 −16.9717 −0.566353
899899 21.5605 0.719084
900900 −1.92647 −0.0642155
901901 25.6035 0.852976
902902 12.1403 0.404228
903903 0 0
904904 −10.2169 −0.339808
905905 23.9915 0.797503
906906 −51.0720 −1.69675
907907 −18.7440 −0.622386 −0.311193 0.950347i 0.600729π-0.600729\pi
−0.311193 + 0.950347i 0.600729π0.600729\pi
908908 0.941473 0.0312439
909909 −29.7740 −0.987541
910910 0 0
911911 41.6954 1.38143 0.690715 0.723127i 0.257296π-0.257296\pi
0.690715 + 0.723127i 0.257296π0.257296\pi
912912 7.02501 0.232621
913913 4.86850 0.161124
914914 −40.0722 −1.32547
915915 29.7825 0.984578
916916 0.0965025 0.00318853
917917 0 0
918918 −14.7979 −0.488403
919919 48.1289 1.58763 0.793813 0.608162i 0.208093π-0.208093\pi
0.793813 + 0.608162i 0.208093π0.208093\pi
920920 −27.5727 −0.909046
921921 79.8620 2.63154
922922 −25.8760 −0.852181
923923 −33.0223 −1.08694
924924 0 0
925925 −2.65974 −0.0874518
926926 6.59944 0.216871
927927 −1.78177 −0.0585210
928928 −17.5183 −0.575066
929929 −14.5530 −0.477470 −0.238735 0.971085i 0.576733π-0.576733\pi
−0.238735 + 0.971085i 0.576733π0.576733\pi
930930 −11.0311 −0.361724
931931 0 0
932932 0.137773 0.00451289
933933 −42.8839 −1.40395
934934 32.2992 1.05686
935935 8.48251 0.277408
936936 −49.4990 −1.61793
937937 −30.5187 −0.997002 −0.498501 0.866889i 0.666116π-0.666116\pi
−0.498501 + 0.866889i 0.666116π0.666116\pi
938938 0 0
939939 28.6634 0.935395
940940 4.68891 0.152935
941941 47.1839 1.53815 0.769076 0.639157i 0.220717π-0.220717\pi
0.769076 + 0.639157i 0.220717π0.220717\pi
942942 −49.2630 −1.60508
943943 −66.5548 −2.16732
944944 1.18963 0.0387192
945945 0 0
946946 7.23387 0.235193
947947 29.9827 0.974308 0.487154 0.873316i 0.338035π-0.338035\pi
0.487154 + 0.873316i 0.338035π0.338035\pi
948948 −23.5003 −0.763253
949949 47.8419 1.55301
950950 −1.21870 −0.0395398
951951 61.2072 1.98478
952952 0 0
953953 −29.4974 −0.955515 −0.477757 0.878492i 0.658550π-0.658550\pi
−0.477757 + 0.878492i 0.658550π0.658550\pi
954954 18.5376 0.600178
955955 −8.43884 −0.273074
956956 −9.86638 −0.319101
957957 −21.6266 −0.699088
958958 −18.1912 −0.587732
959959 0 0
960960 23.0130 0.742740
961961 −18.8484 −0.608014
962962 −13.9892 −0.451029
963963 −19.4372 −0.626356
964964 −2.79408 −0.0899914
965965 −24.4605 −0.787412
966966 0 0
967967 49.4422 1.58996 0.794978 0.606639i 0.207483π-0.207483\pi
0.794978 + 0.606639i 0.207483π0.207483\pi
968968 −28.1549 −0.904931
969969 16.3566 0.525448
970970 8.91017 0.286088
971971 21.0324 0.674961 0.337481 0.941333i 0.390425π-0.390425\pi
0.337481 + 0.941333i 0.390425π0.390425\pi
972972 −11.2933 −0.362234
973973 0 0
974974 −13.5306 −0.433547
975975 11.2063 0.358889
976976 −31.0310 −0.993279
977977 −7.12218 −0.227859 −0.113929 0.993489i 0.536344π-0.536344\pi
−0.113929 + 0.993489i 0.536344π0.536344\pi
978978 −33.9128 −1.08441
979979 −3.31020 −0.105795
980980 0 0
981981 74.2657 2.37112
982982 24.8140 0.791845
983983 35.4689 1.13128 0.565641 0.824652i 0.308629π-0.308629\pi
0.565641 + 0.824652i 0.308629π0.308629\pi
984984 58.8703 1.87672
985985 22.5738 0.719260
986986 47.4816 1.51212
987987 0 0
988988 2.22163 0.0706796
989989 −39.6570 −1.26102
990990 6.14158 0.195192
991991 −35.0928 −1.11476 −0.557380 0.830258i 0.688193π-0.688193\pi
−0.557380 + 0.830258i 0.688193π0.688193\pi
992992 −9.87335 −0.313479
993993 23.0725 0.732184
994994 0 0
995995 −8.25872 −0.261819
996996 4.83258 0.153126
997997 51.0328 1.61622 0.808112 0.589029i 0.200490π-0.200490\pi
0.808112 + 0.589029i 0.200490π0.200490\pi
998998 23.5748 0.746247
999999 5.12692 0.162209
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 4655.2.a.br.1.8 26
7.6 odd 2 4655.2.a.bs.1.8 yes 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4655.2.a.br.1.8 26 1.1 even 1 trivial
4655.2.a.bs.1.8 yes 26 7.6 odd 2