Properties

Label 720.2.u.a.179.20
Level 720720
Weight 22
Character 720.179
Analytic conductor 5.7495.749
Analytic rank 00
Dimension 9696
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [720,2,Mod(179,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("720.179");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 720=24325 720 = 2^{4} \cdot 3^{2} \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 720.u (of order 44, degree 22, minimal)

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: no
Analytic conductor: 5.749228945535.74922894553
Analytic rank: 00
Dimension: 9696
Relative dimension: 4848 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 179.20
Character χ\chi == 720.179
Dual form 720.2.u.a.539.20

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.581659+1.28906i)q2+(1.323351.49958i)q4+(0.0342493+2.23581i)q54.97879iq7+(2.702790.833625i)q8+(2.902011.25633i)q10+(0.2996290.299629i)q11+(3.41391+3.41391i)q13+(6.41795+2.89596i)q14+(0.497509+3.96894i)q165.22586q17+(3.58000+3.58000i)q19+(3.307463.01011i)q20+(0.211957+0.560520i)q226.15703q23+(4.99765+0.153150i)q25+(2.415006.38646i)q26+(7.46612+6.58866i)q28+(3.26048+3.26048i)q297.77031iq31+(4.826822.94989i)q32+(3.039666.73644i)q34+(11.13160.170520i)q35+(2.27648+2.27648i)q37+(2.532496.69716i)q38+(1.95639+6.01436i)q40+7.32246q41+(1.765941.76594i)q43+(0.8458310.0528060i)q44+(3.581297.93678i)q46+1.69344iq4717.7884q49+(2.709516.53135i)q50+(9.63723+0.601662i)q52+(2.951552.95155i)q53+(0.680173+0.659649i)q55+(4.1504513.4566i)q56+(2.306466.09944i)q58+(4.14389+4.14389i)q59+(9.382409.38240i)q61+(10.0164+4.51967i)q62+(6.610144.50623i)q64+(7.749767.51592i)q65+(0.04096480.0409648i)q67+(6.91562+7.83661i)q68+(6.25499+14.4485i)q70+4.96779iq71+3.87421q73+(4.25865+1.61038i)q74+(10.1061+0.630932i)q76+(1.491791.49179i)q770.521248iq79+(8.890820.976399i)q80+(4.25917+9.43908i)q82+(9.49013+9.49013i)q83+(0.17898211.6840i)q85+(1.24923+3.30358i)q86+(0.5600551.05961i)q88+3.52625q89+(16.9971+16.9971i)q91+(8.14788+9.23299i)q92+(2.182940.985002i)q94+(8.126797.88156i)q953.30729iq97+(10.346722.9302i)q98+O(q100)q+(-0.581659 + 1.28906i) q^{2} +(-1.32335 - 1.49958i) q^{4} +(0.0342493 + 2.23581i) q^{5} -4.97879i q^{7} +(2.70279 - 0.833625i) q^{8} +(-2.90201 - 1.25633i) q^{10} +(0.299629 - 0.299629i) q^{11} +(-3.41391 + 3.41391i) q^{13} +(6.41795 + 2.89596i) q^{14} +(-0.497509 + 3.96894i) q^{16} -5.22586 q^{17} +(-3.58000 + 3.58000i) q^{19} +(3.30746 - 3.01011i) q^{20} +(0.211957 + 0.560520i) q^{22} -6.15703 q^{23} +(-4.99765 + 0.153150i) q^{25} +(-2.41500 - 6.38646i) q^{26} +(-7.46612 + 6.58866i) q^{28} +(-3.26048 + 3.26048i) q^{29} -7.77031i q^{31} +(-4.82682 - 2.94989i) q^{32} +(3.03966 - 6.73644i) q^{34} +(11.1316 - 0.170520i) q^{35} +(2.27648 + 2.27648i) q^{37} +(-2.53249 - 6.69716i) q^{38} +(1.95639 + 6.01436i) q^{40} +7.32246 q^{41} +(1.76594 - 1.76594i) q^{43} +(-0.845831 - 0.0528060i) q^{44} +(3.58129 - 7.93678i) q^{46} +1.69344i q^{47} -17.7884 q^{49} +(2.70951 - 6.53135i) q^{50} +(9.63723 + 0.601662i) q^{52} +(2.95155 - 2.95155i) q^{53} +(0.680173 + 0.659649i) q^{55} +(-4.15045 - 13.4566i) q^{56} +(-2.30646 - 6.09944i) q^{58} +(-4.14389 + 4.14389i) q^{59} +(-9.38240 - 9.38240i) q^{61} +(10.0164 + 4.51967i) q^{62} +(6.61014 - 4.50623i) q^{64} +(-7.74976 - 7.51592i) q^{65} +(-0.0409648 - 0.0409648i) q^{67} +(6.91562 + 7.83661i) q^{68} +(-6.25499 + 14.4485i) q^{70} +4.96779i q^{71} +3.87421 q^{73} +(-4.25865 + 1.61038i) q^{74} +(10.1061 + 0.630932i) q^{76} +(-1.49179 - 1.49179i) q^{77} -0.521248i q^{79} +(-8.89082 - 0.976399i) q^{80} +(-4.25917 + 9.43908i) q^{82} +(-9.49013 + 9.49013i) q^{83} +(-0.178982 - 11.6840i) q^{85} +(1.24923 + 3.30358i) q^{86} +(0.560055 - 1.05961i) q^{88} +3.52625 q^{89} +(16.9971 + 16.9971i) q^{91} +(8.14788 + 9.23299i) q^{92} +(-2.18294 - 0.985002i) q^{94} +(-8.12679 - 7.88156i) q^{95} -3.30729i q^{97} +(10.3467 - 22.9302i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 96q8q1616q19+72q34+8q40+8q4696q49+64q5532q61+48q64+24q70+40q7688q94+O(q100) 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/720Z)×\left(\mathbb{Z}/720\mathbb{Z}\right)^\times.

nn 181181 271271 577577 641641
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) 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 −0.581659 + 1.28906i −0.411295 + 0.911502i
33 0 0
44 −1.32335 1.49958i −0.661673 0.749792i
55 0.0342493 + 2.23581i 0.0153168 + 0.999883i
66 0 0
77 4.97879i 1.88181i −0.338676 0.940903i 0.609979π-0.609979\pi
0.338676 0.940903i 0.390021π-0.390021\pi
88 2.70279 0.833625i 0.955580 0.294731i
99 0 0
1010 −2.90201 1.25633i −0.917695 0.397285i
1111 0.299629 0.299629i 0.0903414 0.0903414i −0.660492 0.750833i 0.729652π-0.729652\pi
0.750833 + 0.660492i 0.229652π0.229652\pi
1212 0 0
1313 −3.41391 + 3.41391i −0.946848 + 0.946848i −0.998657 0.0518087i 0.983501π-0.983501\pi
0.0518087 + 0.998657i 0.483501π0.483501\pi
1414 6.41795 + 2.89596i 1.71527 + 0.773977i
1515 0 0
1616 −0.497509 + 3.96894i −0.124377 + 0.992235i
1717 −5.22586 −1.26746 −0.633728 0.773556i 0.718476π-0.718476\pi
−0.633728 + 0.773556i 0.718476π0.718476\pi
1818 0 0
1919 −3.58000 + 3.58000i −0.821307 + 0.821307i −0.986296 0.164988i 0.947241π-0.947241\pi
0.164988 + 0.986296i 0.447241π0.447241\pi
2020 3.30746 3.01011i 0.739570 0.673080i
2121 0 0
2222 0.211957 + 0.560520i 0.0451895 + 0.119503i
2323 −6.15703 −1.28383 −0.641915 0.766776i 0.721860π-0.721860\pi
−0.641915 + 0.766776i 0.721860π0.721860\pi
2424 0 0
2525 −4.99765 + 0.153150i −0.999531 + 0.0306300i
2626 −2.41500 6.38646i −0.473621 1.25249i
2727 0 0
2828 −7.46612 + 6.58866i −1.41096 + 1.24514i
2929 −3.26048 + 3.26048i −0.605456 + 0.605456i −0.941755 0.336299i 0.890825π-0.890825\pi
0.336299 + 0.941755i 0.390825π0.390825\pi
3030 0 0
3131 7.77031i 1.39559i −0.716298 0.697795i 0.754165π-0.754165\pi
0.716298 0.697795i 0.245835π-0.245835\pi
3232 −4.82682 2.94989i −0.853269 0.521471i
3333 0 0
3434 3.03966 6.73644i 0.521298 1.15529i
3535 11.1316 0.170520i 1.88159 0.0288232i
3636 0 0
3737 2.27648 + 2.27648i 0.374251 + 0.374251i 0.869023 0.494772i 0.164748π-0.164748\pi
−0.494772 + 0.869023i 0.664748π0.664748\pi
3838 −2.53249 6.69716i −0.410824 1.08642i
3939 0 0
4040 1.95639 + 6.01436i 0.309333 + 0.950954i
4141 7.32246 1.14358 0.571788 0.820401i 0.306250π-0.306250\pi
0.571788 + 0.820401i 0.306250π0.306250\pi
4242 0 0
4343 1.76594 1.76594i 0.269304 0.269304i −0.559516 0.828820i 0.689013π-0.689013\pi
0.828820 + 0.559516i 0.189013π0.189013\pi
4444 −0.845831 0.0528060i −0.127514 0.00796081i
4545 0 0
4646 3.58129 7.93678i 0.528032 1.17021i
4747 1.69344i 0.247013i 0.992344 + 0.123507i 0.0394140π0.0394140\pi
−0.992344 + 0.123507i 0.960586π0.960586\pi
4848 0 0
4949 −17.7884 −2.54119
5050 2.70951 6.53135i 0.383183 0.923673i
5151 0 0
5252 9.63723 + 0.601662i 1.33644 + 0.0834355i
5353 2.95155 2.95155i 0.405427 0.405427i −0.474714 0.880140i 0.657448π-0.657448\pi
0.880140 + 0.474714i 0.157448π0.157448\pi
5454 0 0
5555 0.680173 + 0.659649i 0.0917145 + 0.0889471i
5656 −4.15045 13.4566i −0.554627 1.79822i
5757 0 0
5858 −2.30646 6.09944i −0.302854 0.800895i
5959 −4.14389 + 4.14389i −0.539489 + 0.539489i −0.923379 0.383890i 0.874584π-0.874584\pi
0.383890 + 0.923379i 0.374584π0.374584\pi
6060 0 0
6161 −9.38240 9.38240i −1.20129 1.20129i −0.973773 0.227520i 0.926938π-0.926938\pi
−0.227520 0.973773i 0.573062π-0.573062\pi
6262 10.0164 + 4.51967i 1.27208 + 0.573999i
6363 0 0
6464 6.61014 4.50623i 0.826267 0.563278i
6565 −7.74976 7.51592i −0.961240 0.932235i
6666 0 0
6767 −0.0409648 0.0409648i −0.00500465 0.00500465i 0.704600 0.709605i 0.251126π-0.251126\pi
−0.709605 + 0.704600i 0.751126π0.751126\pi
6868 6.91562 + 7.83661i 0.838642 + 0.950329i
6969 0 0
7070 −6.25499 + 14.4485i −0.747614 + 1.72692i
7171 4.96779i 0.589568i 0.955564 + 0.294784i 0.0952477π0.0952477\pi
−0.955564 + 0.294784i 0.904752π0.904752\pi
7272 0 0
7373 3.87421 0.453442 0.226721 0.973960i 0.427199π-0.427199\pi
0.226721 + 0.973960i 0.427199π0.427199\pi
7474 −4.25865 + 1.61038i −0.495058 + 0.187203i
7575 0 0
7676 10.1061 + 0.630932i 1.15925 + 0.0723729i
7777 −1.49179 1.49179i −0.170005 0.170005i
7878 0 0
7979 0.521248i 0.0586450i −0.999570 0.0293225i 0.990665π-0.990665\pi
0.999570 0.0293225i 0.00933498π-0.00933498\pi
8080 −8.89082 0.976399i −0.994024 0.109165i
8181 0 0
8282 −4.25917 + 9.43908i −0.470347 + 1.04237i
8383 −9.49013 + 9.49013i −1.04168 + 1.04168i −0.0425846 + 0.999093i 0.513559π0.513559\pi
−0.999093 + 0.0425846i 0.986441π0.986441\pi
8484 0 0
8585 −0.178982 11.6840i −0.0194133 1.26731i
8686 1.24923 + 3.30358i 0.134708 + 0.356234i
8787 0 0
8888 0.560055 1.05961i 0.0597020 0.112955i
8989 3.52625 0.373782 0.186891 0.982381i 0.440159π-0.440159\pi
0.186891 + 0.982381i 0.440159π0.440159\pi
9090 0 0
9191 16.9971 + 16.9971i 1.78178 + 1.78178i
9292 8.14788 + 9.23299i 0.849476 + 0.962606i
9393 0 0
9494 −2.18294 0.985002i −0.225153 0.101595i
9595 −8.12679 7.88156i −0.833791 0.808631i
9696 0 0
9797 3.30729i 0.335805i −0.985804 0.167902i 0.946301π-0.946301\pi
0.985804 0.167902i 0.0536993π-0.0536993\pi
9898 10.3467 22.9302i 1.04518 2.31630i
9999 0 0
100100 6.84329 + 7.29174i 0.684329 + 0.729174i
101101 −7.55836 7.55836i −0.752085 0.752085i 0.222783 0.974868i 0.428486π-0.428486\pi
−0.974868 + 0.222783i 0.928486π0.928486\pi
102102 0 0
103103 13.0592i 1.28676i −0.765546 0.643381i 0.777531π-0.777531\pi
0.765546 0.643381i 0.222469π-0.222469\pi
104104 −6.38116 + 12.0730i −0.625724 + 1.18386i
105105 0 0
106106 2.08793 + 5.52152i 0.202797 + 0.536297i
107107 7.46283 + 7.46283i 0.721459 + 0.721459i 0.968902 0.247443i 0.0795904π-0.0795904\pi
−0.247443 + 0.968902i 0.579590π0.579590\pi
108108 0 0
109109 3.43459 + 3.43459i 0.328974 + 0.328974i 0.852196 0.523222i 0.175270π-0.175270\pi
−0.523222 + 0.852196i 0.675270π0.675270\pi
110110 −1.24596 + 0.493093i −0.118797 + 0.0470146i
111111 0 0
112112 19.7605 + 2.47699i 1.86719 + 0.234054i
113113 −5.42433 −0.510278 −0.255139 0.966904i 0.582121π-0.582121\pi
−0.255139 + 0.966904i 0.582121π0.582121\pi
114114 0 0
115115 −0.210874 13.7659i −0.0196641 1.28368i
116116 9.20411 + 0.574621i 0.854580 + 0.0533523i
117117 0 0
118118 −2.93139 7.75205i −0.269856 0.713634i
119119 26.0184i 2.38511i
120120 0 0
121121 10.8204i 0.983677i
122122 17.5518 6.63712i 1.58907 0.600896i
123123 0 0
124124 −11.6522 + 10.2828i −1.04640 + 0.923424i
125125 −0.513580 11.1685i −0.0459359 0.998944i
126126 0 0
127127 9.57690 0.849813 0.424906 0.905237i 0.360307π-0.360307\pi
0.424906 + 0.905237i 0.360307π0.360307\pi
128128 1.96395 + 11.1419i 0.173590 + 0.984818i
129129 0 0
130130 14.1962 5.61821i 1.24509 0.492749i
131131 −12.5044 12.5044i −1.09252 1.09252i −0.995259 0.0972558i 0.968994π-0.968994\pi
−0.0972558 0.995259i 0.531006π-0.531006\pi
132132 0 0
133133 17.8241 + 17.8241i 1.54554 + 1.54554i
134134 0.0766335 0.0289785i 0.00662013 0.00250336i
135135 0 0
136136 −14.1244 + 4.35640i −1.21116 + 0.373559i
137137 3.21459i 0.274641i 0.990527 + 0.137320i 0.0438490π0.0438490\pi
−0.990527 + 0.137320i 0.956151π0.956151\pi
138138 0 0
139139 −0.728605 0.728605i −0.0617994 0.0617994i 0.675532 0.737331i 0.263914π-0.263914\pi
−0.737331 + 0.675532i 0.763914π0.763914\pi
140140 −14.9867 16.4671i −1.26661 1.39173i
141141 0 0
142142 −6.40377 2.88956i −0.537392 0.242486i
143143 2.04581i 0.171079i
144144 0 0
145145 −7.40147 7.17813i −0.614658 0.596111i
146146 −2.25347 + 4.99409i −0.186498 + 0.413314i
147147 0 0
148148 0.401203 6.42634i 0.0329787 0.528242i
149149 −3.90021 3.90021i −0.319518 0.319518i 0.529064 0.848582i 0.322543π-0.322543\pi
−0.848582 + 0.529064i 0.822543π0.822543\pi
150150 0 0
151151 2.48795 0.202467 0.101233 0.994863i 0.467721π-0.467721\pi
0.101233 + 0.994863i 0.467721π0.467721\pi
152152 −6.69160 + 12.6603i −0.542760 + 1.02689i
153153 0 0
154154 2.79071 1.05529i 0.224882 0.0850378i
155155 17.3729 0.266128i 1.39543 0.0213759i
156156 0 0
157157 6.88372 6.88372i 0.549380 0.549380i −0.376881 0.926262i 0.623003π-0.623003\pi
0.926262 + 0.376881i 0.123003π0.123003\pi
158158 0.671920 + 0.303189i 0.0534551 + 0.0241204i
159159 0 0
160160 6.43006 10.8929i 0.508341 0.861156i
161161 30.6546i 2.41592i
162162 0 0
163163 −0.954196 0.954196i −0.0747384 0.0747384i 0.668749 0.743488i 0.266830π-0.266830\pi
−0.743488 + 0.668749i 0.766830π0.766830\pi
164164 −9.69015 10.9806i −0.756674 0.857445i
165165 0 0
166166 −6.71332 17.7534i −0.521055 1.37793i
167167 9.73397 0.753237 0.376619 0.926368i 0.377087π-0.377087\pi
0.376619 + 0.926368i 0.377087π0.377087\pi
168168 0 0
169169 10.3096i 0.793044i
170170 15.1655 + 6.56538i 1.16314 + 0.503542i
171171 0 0
172172 −4.98514 0.311227i −0.380113 0.0237308i
173173 −7.85395 7.85395i −0.597125 0.597125i 0.342421 0.939546i 0.388753π-0.388753\pi
−0.939546 + 0.342421i 0.888753π0.888753\pi
174174 0 0
175175 0.762501 + 24.8823i 0.0576396 + 1.88092i
176176 1.04014 + 1.33828i 0.0784035 + 0.100876i
177177 0 0
178178 −2.05107 + 4.54554i −0.153734 + 0.340703i
179179 9.13459 + 9.13459i 0.682751 + 0.682751i 0.960619 0.277868i 0.0896278π-0.0896278\pi
−0.277868 + 0.960619i 0.589628π0.589628\pi
180180 0 0
181181 −15.9005 + 15.9005i −1.18188 + 1.18188i −0.202621 + 0.979257i 0.564946π0.564946\pi
−0.979257 + 0.202621i 0.935054π0.935054\pi
182182 −31.7969 + 12.0238i −2.35694 + 0.891262i
183183 0 0
184184 −16.6412 + 5.13266i −1.22680 + 0.378384i
185185 −5.01180 + 5.16773i −0.368475 + 0.379939i
186186 0 0
187187 −1.56582 + 1.56582i −0.114504 + 0.114504i
188188 2.53945 2.24100i 0.185209 0.163442i
189189 0 0
190190 14.8868 5.89153i 1.08000 0.427417i
191191 2.16753 0.156837 0.0784183 0.996921i 0.475013π-0.475013\pi
0.0784183 + 0.996921i 0.475013π0.475013\pi
192192 0 0
193193 23.0521i 1.65932i 0.558265 + 0.829662i 0.311467π0.311467\pi
−0.558265 + 0.829662i 0.688533π0.688533\pi
194194 4.26329 + 1.92371i 0.306087 + 0.138115i
195195 0 0
196196 23.5402 + 26.6751i 1.68144 + 1.90537i
197197 1.52767 1.52767i 0.108842 0.108842i −0.650588 0.759431i 0.725478π-0.725478\pi
0.759431 + 0.650588i 0.225478π0.225478\pi
198198 0 0
199199 −3.12757 −0.221708 −0.110854 0.993837i 0.535359π-0.535359\pi
−0.110854 + 0.993837i 0.535359π0.535359\pi
200200 −13.3799 + 4.58010i −0.946104 + 0.323862i
201201 0 0
202202 14.1396 5.34678i 0.994855 0.376198i
203203 16.2332 + 16.2332i 1.13935 + 1.13935i
204204 0 0
205205 0.250789 + 16.3716i 0.0175159 + 1.14344i
206206 16.8341 + 7.59600i 1.17289 + 0.529239i
207207 0 0
208208 −11.8512 15.2481i −0.821730 1.05726i
209209 2.14534i 0.148396i
210210 0 0
211211 2.66344 2.66344i 0.183359 0.183359i −0.609459 0.792818i 0.708613π-0.708613\pi
0.792818 + 0.609459i 0.208613π0.208613\pi
212212 −8.33202 0.520176i −0.572246 0.0357259i
213213 0 0
214214 −13.9608 + 5.27921i −0.954344 + 0.360879i
215215 4.00879 + 3.88782i 0.273397 + 0.265147i
216216 0 0
217217 −38.6868 −2.62623
218218 −6.42515 + 2.42963i −0.435166 + 0.164555i
219219 0 0
220220 0.0890949 1.89292i 0.00600677 0.127621i
221221 17.8406 17.8406i 1.20009 1.20009i
222222 0 0
223223 22.8494 1.53011 0.765053 0.643967i 0.222713π-0.222713\pi
0.765053 + 0.643967i 0.222713π0.222713\pi
224224 −14.6869 + 24.0317i −0.981307 + 1.60569i
225225 0 0
226226 3.15511 6.99228i 0.209875 0.465119i
227227 2.89777 2.89777i 0.192332 0.192332i −0.604371 0.796703i 0.706576π-0.706576\pi
0.796703 + 0.604371i 0.206576π0.206576\pi
228228 0 0
229229 13.7901 13.7901i 0.911276 0.911276i −0.0850965 0.996373i 0.527120π-0.527120\pi
0.996373 + 0.0850965i 0.0271199π0.0271199\pi
230230 17.8677 + 7.73524i 1.17816 + 0.510047i
231231 0 0
232232 −6.09437 + 11.5304i −0.400115 + 0.757008i
233233 27.8531i 1.82472i 0.409388 + 0.912360i 0.365742π0.365742\pi
−0.409388 + 0.912360i 0.634258π0.634258\pi
234234 0 0
235235 −3.78619 + 0.0579991i −0.246984 + 0.00378344i
236236 11.6979 + 0.730312i 0.761470 + 0.0475393i
237237 0 0
238238 −33.5393 15.1339i −2.17403 0.980982i
239239 −22.7939 −1.47441 −0.737207 0.675667i 0.763856π-0.763856\pi
−0.737207 + 0.675667i 0.763856π0.763856\pi
240240 0 0
241241 4.33189 0.279042 0.139521 0.990219i 0.455444π-0.455444\pi
0.139521 + 0.990219i 0.455444π0.455444\pi
242242 −13.9482 6.29381i −0.896624 0.404581i
243243 0 0
244244 −1.65354 + 26.4859i −0.105857 + 1.69558i
245245 −0.609240 39.7713i −0.0389229 2.54090i
246246 0 0
247247 24.4436i 1.55531i
248248 −6.47753 21.0015i −0.411324 1.33360i
249249 0 0
250250 14.6956 + 5.83424i 0.929433 + 0.368990i
251251 4.97266 4.97266i 0.313872 0.313872i −0.532536 0.846407i 0.678761π-0.678761\pi
0.846407 + 0.532536i 0.178761π0.178761\pi
252252 0 0
253253 −1.84482 + 1.84482i −0.115983 + 0.115983i
254254 −5.57049 + 12.3452i −0.349524 + 0.774606i
255255 0 0
256256 −15.5050 3.94916i −0.969061 0.246823i
257257 −8.06975 −0.503377 −0.251689 0.967808i 0.580986π-0.580986\pi
−0.251689 + 0.967808i 0.580986π0.580986\pi
258258 0 0
259259 11.3341 11.3341i 0.704267 0.704267i
260260 −1.01513 + 21.5676i −0.0629557 + 1.33757i
261261 0 0
262262 23.3922 8.84562i 1.44518 0.546484i
263263 −17.5377 −1.08142 −0.540710 0.841209i 0.681845π-0.681845\pi
−0.540710 + 0.841209i 0.681845π0.681845\pi
264264 0 0
265265 6.70018 + 6.49800i 0.411589 + 0.399169i
266266 −33.3438 + 12.6087i −2.04444 + 0.773091i
267267 0 0
268268 −0.00721956 + 0.115641i −0.000441005 + 0.00706388i
269269 −1.87139 + 1.87139i −0.114101 + 0.114101i −0.761852 0.647751i 0.775710π-0.775710\pi
0.647751 + 0.761852i 0.275710π0.275710\pi
270270 0 0
271271 22.9224i 1.39244i −0.717831 0.696218i 0.754865π-0.754865\pi
0.717831 0.696218i 0.245135π-0.245135\pi
272272 2.59991 20.7411i 0.157643 1.25761i
273273 0 0
274274 −4.14379 1.86979i −0.250336 0.112958i
275275 −1.45155 + 1.54333i −0.0875319 + 0.0930662i
276276 0 0
277277 13.2521 + 13.2521i 0.796239 + 0.796239i 0.982500 0.186261i 0.0596372π-0.0596372\pi
−0.186261 + 0.982500i 0.559637π0.559637\pi
278278 1.36301 0.515415i 0.0817481 0.0309126i
279279 0 0
280280 29.9442 9.74047i 1.78951 0.582104i
281281 12.2485 0.730684 0.365342 0.930873i 0.380952π-0.380952\pi
0.365342 + 0.930873i 0.380952π0.380952\pi
282282 0 0
283283 −2.62423 + 2.62423i −0.155994 + 0.155994i −0.780789 0.624795i 0.785183π-0.785183\pi
0.624795 + 0.780789i 0.285183π0.285183\pi
284284 7.44962 6.57410i 0.442053 0.390101i
285285 0 0
286286 −2.63717 1.18996i −0.155939 0.0703640i
287287 36.4570i 2.15199i
288288 0 0
289289 10.3096 0.606445
290290 13.5582 5.36571i 0.796163 0.315085i
291291 0 0
292292 −5.12693 5.80971i −0.300031 0.339988i
293293 3.96865 3.96865i 0.231851 0.231851i −0.581614 0.813465i 0.697578π-0.697578\pi
0.813465 + 0.581614i 0.197578π0.197578\pi
294294 0 0
295295 −9.40686 9.12301i −0.547689 0.531162i
296296 8.05057 + 4.25511i 0.467930 + 0.247323i
297297 0 0
298298 7.29619 2.75901i 0.422657 0.159825i
299299 21.0196 21.0196i 1.21559 1.21559i
300300 0 0
301301 −8.79226 8.79226i −0.506778 0.506778i
302302 −1.44714 + 3.20712i −0.0832734 + 0.184549i
303303 0 0
304304 −12.4277 15.9899i −0.712778 0.917082i
305305 20.6559 21.2986i 1.18275 1.21955i
306306 0 0
307307 5.66311 + 5.66311i 0.323211 + 0.323211i 0.849997 0.526787i 0.176603π-0.176603\pi
−0.526787 + 0.849997i 0.676603π0.676603\pi
308308 −0.262910 + 4.21121i −0.0149807 + 0.239956i
309309 0 0
310310 −9.76205 + 22.5495i −0.554447 + 1.28073i
311311 29.5732i 1.67694i −0.544947 0.838470i 0.683450π-0.683450\pi
0.544947 0.838470i 0.316550π-0.316550\pi
312312 0 0
313313 12.2408 0.691891 0.345945 0.938255i 0.387558π-0.387558\pi
0.345945 + 0.938255i 0.387558π0.387558\pi
314314 4.86954 + 12.8775i 0.274804 + 0.726719i
315315 0 0
316316 −0.781656 + 0.689792i −0.0439716 + 0.0388038i
317317 12.0077 + 12.0077i 0.674419 + 0.674419i 0.958732 0.284312i 0.0917653π-0.0917653\pi
−0.284312 + 0.958732i 0.591765π0.591765\pi
318318 0 0
319319 1.95387i 0.109395i
320320 10.3014 + 14.6246i 0.575868 + 0.817543i
321321 0 0
322322 −39.5155 17.8305i −2.20212 0.993655i
323323 18.7085 18.7085i 1.04097 1.04097i
324324 0 0
325325 16.5387 17.5844i 0.917402 0.975406i
326326 1.78503 0.674998i 0.0988637 0.0373847i
327327 0 0
328328 19.7911 6.10419i 1.09278 0.337047i
329329 8.43126 0.464831
330330 0 0
331331 6.22467 + 6.22467i 0.342139 + 0.342139i 0.857171 0.515032i 0.172220π-0.172220\pi
−0.515032 + 0.857171i 0.672220π0.672220\pi
332332 26.7900 + 1.67253i 1.47029 + 0.0917917i
333333 0 0
334334 −5.66185 + 12.5477i −0.309803 + 0.686578i
335335 0.0901863 0.0929923i 0.00492740 0.00508071i
336336 0 0
337337 2.44733i 0.133315i −0.997776 0.0666574i 0.978767π-0.978767\pi
0.997776 0.0666574i 0.0212335π-0.0212335\pi
338338 13.2896 + 5.99665i 0.722861 + 0.326175i
339339 0 0
340340 −17.2843 + 15.7304i −0.937372 + 0.853099i
341341 −2.32821 2.32821i −0.126080 0.126080i
342342 0 0
343343 53.7130i 2.90023i
344344 3.30084 6.24511i 0.177969 0.336714i
345345 0 0
346346 14.6925 5.55589i 0.789875 0.298687i
347347 −7.80648 7.80648i −0.419074 0.419074i 0.465811 0.884884i 0.345763π-0.345763\pi
−0.884884 + 0.465811i 0.845763π0.845763\pi
348348 0 0
349349 −18.4011 18.4011i −0.984990 0.984990i 0.0148993 0.999889i 0.495257π-0.495257\pi
−0.999889 + 0.0148993i 0.995257π0.995257\pi
350350 −32.5182 13.4901i −1.73817 0.721075i
351351 0 0
352352 −2.33012 + 0.562382i −0.124196 + 0.0299751i
353353 −23.6781 −1.26026 −0.630128 0.776491i 0.716998π-0.716998\pi
−0.630128 + 0.776491i 0.716998π0.716998\pi
354354 0 0
355355 −11.1070 + 0.170143i −0.589499 + 0.00903028i
356356 −4.66645 5.28791i −0.247321 0.280259i
357357 0 0
358358 −17.0882 + 6.46181i −0.903141 + 0.341517i
359359 0.461358i 0.0243495i 0.999926 + 0.0121748i 0.00387544π0.00387544\pi
−0.999926 + 0.0121748i 0.996125π0.996125\pi
360360 0 0
361361 6.63274i 0.349092i
362362 −11.2481 29.7454i −0.591185 1.56339i
363363 0 0
364364 2.99555 47.9818i 0.157009 2.51493i
365365 0.132689 + 8.66199i 0.00694528 + 0.453389i
366366 0 0
367367 −20.2030 −1.05459 −0.527294 0.849683i 0.676793π-0.676793\pi
−0.527294 + 0.849683i 0.676793π0.676793\pi
368368 3.06318 24.4369i 0.159679 1.27386i
369369 0 0
370370 −3.74636 9.46636i −0.194764 0.492133i
371371 −14.6952 14.6952i −0.762934 0.762934i
372372 0 0
373373 −5.66776 5.66776i −0.293465 0.293465i 0.544982 0.838448i 0.316536π-0.316536\pi
−0.838448 + 0.544982i 0.816536π0.816536\pi
374374 −1.10766 2.92920i −0.0572757 0.151465i
375375 0 0
376376 1.41169 + 4.57700i 0.0728024 + 0.236041i
377377 22.2620i 1.14655i
378378 0 0
379379 6.20237 + 6.20237i 0.318594 + 0.318594i 0.848227 0.529633i 0.177670π-0.177670\pi
−0.529633 + 0.848227i 0.677670π0.677670\pi
380380 −1.06452 + 22.6168i −0.0546085 + 1.16022i
381381 0 0
382382 −1.26076 + 2.79407i −0.0645061 + 0.142957i
383383 4.89671i 0.250210i 0.992143 + 0.125105i 0.0399268π0.0399268\pi
−0.992143 + 0.125105i 0.960073π0.960073\pi
384384 0 0
385385 3.28425 3.38644i 0.167381 0.172589i
386386 −29.7155 13.4084i −1.51248 0.682472i
387387 0 0
388388 −4.95956 + 4.37669i −0.251784 + 0.222193i
389389 −13.7639 13.7639i −0.697860 0.697860i 0.266089 0.963949i 0.414269π-0.414269\pi
−0.963949 + 0.266089i 0.914269π0.914269\pi
390390 0 0
391391 32.1758 1.62720
392392 −48.0782 + 14.8288i −2.42831 + 0.748969i
393393 0 0
394394 1.08068 + 2.85784i 0.0544437 + 0.143976i
395395 1.16541 0.0178524i 0.0586381 0.000898253i
396396 0 0
397397 −16.2544 + 16.2544i −0.815787 + 0.815787i −0.985495 0.169707i 0.945718π-0.945718\pi
0.169707 + 0.985495i 0.445718π0.445718\pi
398398 1.81918 4.03162i 0.0911872 0.202087i
399399 0 0
400400 1.87853 19.9116i 0.0939267 0.995579i
401401 10.0348i 0.501116i 0.968102 + 0.250558i 0.0806140π0.0806140\pi
−0.968102 + 0.250558i 0.919386π0.919386\pi
402402 0 0
403403 26.5272 + 26.5272i 1.32141 + 1.32141i
404404 −1.33207 + 21.3367i −0.0662731 + 1.06154i
405405 0 0
406406 −30.3678 + 11.4834i −1.50713 + 0.569912i
407407 1.36420 0.0676207
408408 0 0
409409 33.3911i 1.65108i 0.564341 + 0.825542i 0.309130π0.309130\pi
−0.564341 + 0.825542i 0.690870π0.690870\pi
410410 −21.2498 9.19940i −1.04945 0.454326i
411411 0 0
412412 −19.5834 + 17.2819i −0.964804 + 0.851416i
413413 20.6316 + 20.6316i 1.01521 + 1.01521i
414414 0 0
415415 −21.5431 20.8931i −1.05751 1.02560i
416416 26.5490 6.40768i 1.30167 0.314162i
417417 0 0
418418 −2.76547 1.24785i −0.135263 0.0610346i
419419 12.9105 + 12.9105i 0.630718 + 0.630718i 0.948248 0.317530i 0.102853π-0.102853\pi
−0.317530 + 0.948248i 0.602853π0.602853\pi
420420 0 0
421421 0.923750 0.923750i 0.0450208 0.0450208i −0.684238 0.729259i 0.739865π-0.739865\pi
0.729259 + 0.684238i 0.239865π0.239865\pi
422422 1.88412 + 4.98255i 0.0917175 + 0.242547i
423423 0 0
424424 5.51693 10.4379i 0.267926 0.506910i
425425 26.1170 0.800339i 1.26686 0.0388221i
426426 0 0
427427 −46.7130 + 46.7130i −2.26060 + 2.26060i
428428 1.31524 21.0671i 0.0635743 1.01831i
429429 0 0
430430 −7.34338 + 2.90618i −0.354129 + 0.140148i
431431 −23.5531 −1.13451 −0.567255 0.823542i 0.691995π-0.691995\pi
−0.567255 + 0.823542i 0.691995π0.691995\pi
432432 0 0
433433 38.5735i 1.85373i −0.375400 0.926863i 0.622495π-0.622495\pi
0.375400 0.926863i 0.377505π-0.377505\pi
434434 22.5025 49.8695i 1.08015 2.39381i
435435 0 0
436436 0.605306 9.69561i 0.0289889 0.464336i
437437 22.0421 22.0421i 1.05442 1.05442i
438438 0 0
439439 −30.3538 −1.44871 −0.724355 0.689427i 0.757862π-0.757862\pi
−0.724355 + 0.689427i 0.757862π0.757862\pi
440440 2.38827 + 1.21588i 0.113856 + 0.0579649i
441441 0 0
442442 12.6204 + 33.3747i 0.600294 + 1.58747i
443443 4.74763 + 4.74763i 0.225567 + 0.225567i 0.810838 0.585271i 0.199012π-0.199012\pi
−0.585271 + 0.810838i 0.699012π0.699012\pi
444444 0 0
445445 0.120772 + 7.88401i 0.00572513 + 0.373738i
446446 −13.2905 + 29.4542i −0.629325 + 1.39470i
447447 0 0
448448 −22.4356 32.9105i −1.05998 1.55487i
449449 10.1268i 0.477914i −0.971030 0.238957i 0.923194π-0.923194\pi
0.971030 0.238957i 0.0768055π-0.0768055\pi
450450 0 0
451451 2.19402 2.19402i 0.103312 0.103312i
452452 7.17826 + 8.13424i 0.337637 + 0.382602i
453453 0 0
454454 2.04988 + 5.42091i 0.0962058 + 0.254416i
455455 −37.4202 + 38.5845i −1.75428 + 1.80887i
456456 0 0
457457 1.44447 0.0675695 0.0337847 0.999429i 0.489244π-0.489244\pi
0.0337847 + 0.999429i 0.489244π0.489244\pi
458458 9.75513 + 25.7974i 0.455827 + 1.20543i
459459 0 0
460460 −20.3641 + 18.5333i −0.949482 + 0.864120i
461461 −26.8623 + 26.8623i −1.25110 + 1.25110i −0.295878 + 0.955226i 0.595612π0.595612\pi
−0.955226 + 0.295878i 0.904388π0.904388\pi
462462 0 0
463463 20.2597 0.941547 0.470774 0.882254i 0.343975π-0.343975\pi
0.470774 + 0.882254i 0.343975π0.343975\pi
464464 −11.3185 14.5628i −0.525450 0.676059i
465465 0 0
466466 −35.9044 16.2010i −1.66324 0.750498i
467467 −9.09888 + 9.09888i −0.421046 + 0.421046i −0.885564 0.464518i 0.846228π-0.846228\pi
0.464518 + 0.885564i 0.346228π0.346228\pi
468468 0 0
469469 −0.203955 + 0.203955i −0.00941777 + 0.00941777i
470470 2.12751 4.91436i 0.0981346 0.226683i
471471 0 0
472472 −7.74561 + 14.6545i −0.356521 + 0.674529i
473473 1.05825i 0.0486586i
474474 0 0
475475 17.3433 18.4399i 0.795765 0.846079i
476476 39.0169 34.4314i 1.78833 1.57816i
477477 0 0
478478 13.2583 29.3827i 0.606419 1.34393i
479479 4.60465 0.210392 0.105196 0.994452i 0.466453π-0.466453\pi
0.105196 + 0.994452i 0.466453π0.466453\pi
480480 0 0
481481 −15.5434 −0.708718
482482 −2.51968 + 5.58406i −0.114768 + 0.254347i
483483 0 0
484484 16.2262 14.3192i 0.737553 0.650873i
485485 7.39446 0.113273i 0.335765 0.00514344i
486486 0 0
487487 32.2084i 1.45950i −0.683713 0.729751i 0.739636π-0.739636\pi
0.683713 0.729751i 0.260364π-0.260364\pi
488488 −33.1801 17.5372i −1.50199 0.793874i
489489 0 0
490490 51.6219 + 22.3480i 2.33204 + 1.00958i
491491 17.4179 17.4179i 0.786059 0.786059i −0.194786 0.980846i 0.562401π-0.562401\pi
0.980846 + 0.194786i 0.0624014π0.0624014\pi
492492 0 0
493493 17.0388 17.0388i 0.767389 0.767389i
494494 31.5092 + 14.2178i 1.41767 + 0.639690i
495495 0 0
496496 30.8399 + 3.86580i 1.38475 + 0.173579i
497497 24.7336 1.10945
498498 0 0
499499 −15.6000 + 15.6000i −0.698354 + 0.698354i −0.964055 0.265701i 0.914396π-0.914396\pi
0.265701 + 0.964055i 0.414396π0.414396\pi
500500 −16.0685 + 15.5500i −0.718606 + 0.695417i
501501 0 0
502502 3.51766 + 9.30245i 0.157001 + 0.415189i
503503 2.39149 0.106631 0.0533157 0.998578i 0.483021π-0.483021\pi
0.0533157 + 0.998578i 0.483021π0.483021\pi
504504 0 0
505505 16.6401 17.1579i 0.740477 0.763516i
506506 −1.30503 3.45114i −0.0580156 0.153422i
507507 0 0
508508 −12.6736 14.3614i −0.562298 0.637183i
509509 1.78164 1.78164i 0.0789700 0.0789700i −0.666518 0.745489i 0.732216π-0.732216\pi
0.745489 + 0.666518i 0.232216π0.232216\pi
510510 0 0
511511 19.2889i 0.853291i
512512 14.1093 17.6898i 0.623549 0.781784i
513513 0 0
514514 4.69384 10.4024i 0.207036 0.458829i
515515 29.1979 0.447269i 1.28661 0.0197090i
516516 0 0
517517 0.507402 + 0.507402i 0.0223155 + 0.0223155i
518518 8.01776 + 21.2029i 0.352280 + 0.931603i
519519 0 0
520520 −27.2114 13.8535i −1.19330 0.607518i
521521 6.52761 0.285980 0.142990 0.989724i 0.454328π-0.454328\pi
0.142990 + 0.989724i 0.454328π0.454328\pi
522522 0 0
523523 −8.63265 + 8.63265i −0.377479 + 0.377479i −0.870192 0.492713i 0.836005π-0.836005\pi
0.492713 + 0.870192i 0.336005π0.336005\pi
524524 −2.20376 + 35.2991i −0.0962715 + 1.54205i
525525 0 0
526526 10.2010 22.6071i 0.444783 0.985718i
527527 40.6065i 1.76885i
528528 0 0
529529 14.9090 0.648219
530530 −12.2735 + 4.85731i −0.533128 + 0.210988i
531531 0 0
532532 3.14128 50.3161i 0.136192 2.18148i
533533 −24.9982 + 24.9982i −1.08279 + 1.08279i
534534 0 0
535535 −16.4298 + 16.9410i −0.710324 + 0.732425i
536536 −0.144868 0.0765699i −0.00625736 0.00330732i
537537 0 0
538538 −1.32382 3.50085i −0.0570741 0.150932i
539539 −5.32990 + 5.32990i −0.229575 + 0.229575i
540540 0 0
541541 28.4777 + 28.4777i 1.22435 + 1.22435i 0.966070 + 0.258280i 0.0831557π0.0831557\pi
0.258280 + 0.966070i 0.416844π0.416844\pi
542542 29.5483 + 13.3330i 1.26921 + 0.572701i
543543 0 0
544544 25.2243 + 15.4157i 1.08148 + 0.660942i
545545 −7.56144 + 7.79671i −0.323897 + 0.333974i
546546 0 0
547547 7.40756 + 7.40756i 0.316724 + 0.316724i 0.847508 0.530783i 0.178102π-0.178102\pi
−0.530783 + 0.847508i 0.678102π0.678102\pi
548548 4.82055 4.25401i 0.205924 0.181722i
549549 0 0
550550 −1.14513 2.76883i −0.0488286 0.118063i
551551 23.3450i 0.994531i
552552 0 0
553553 −2.59519 −0.110359
554554 −24.7909 + 9.37451i −1.05326 + 0.398285i
555555 0 0
556556 −0.128408 + 2.05680i −0.00544571 + 0.0872278i
557557 1.55719 + 1.55719i 0.0659803 + 0.0659803i 0.739327 0.673347i 0.235144π-0.235144\pi
−0.673347 + 0.739327i 0.735144π0.735144\pi
558558 0 0
559559 12.0575i 0.509980i
560560 −4.86129 + 44.2655i −0.205427 + 1.87056i
561561 0 0
562562 −7.12444 + 15.7890i −0.300526 + 0.666020i
563563 −14.0768 + 14.0768i −0.593265 + 0.593265i −0.938512 0.345247i 0.887795π-0.887795\pi
0.345247 + 0.938512i 0.387795π0.387795\pi
564564 0 0
565565 −0.185780 12.1277i −0.00781581 0.510218i
566566 −1.85638 4.90920i −0.0780296 0.206349i
567567 0 0
568568 4.14127 + 13.4269i 0.173764 + 0.563379i
569569 −19.8358 −0.831559 −0.415779 0.909466i 0.636491π-0.636491\pi
−0.415779 + 0.909466i 0.636491π0.636491\pi
570570 0 0
571571 −14.2584 14.2584i −0.596696 0.596696i 0.342736 0.939432i 0.388646π-0.388646\pi
−0.939432 + 0.342736i 0.888646π0.888646\pi
572572 3.06787 2.70732i 0.128274 0.113199i
573573 0 0
574574 46.9952 + 21.2055i 1.96154 + 0.885101i
575575 30.7707 0.942948i 1.28323 0.0393236i
576576 0 0
577577 16.0197i 0.666908i −0.942766 0.333454i 0.891786π-0.891786\pi
0.942766 0.333454i 0.108214π-0.108214\pi
578578 −5.99665 + 13.2896i −0.249428 + 0.552776i
579579 0 0
580580 −0.969507 + 20.5983i −0.0402566 + 0.855297i
581581 47.2494 + 47.2494i 1.96023 + 1.96023i
582582 0 0
583583 1.76874i 0.0732536i
584584 10.4712 3.22964i 0.433301 0.133644i
585585 0 0
586586 2.80743 + 7.42423i 0.115974 + 0.306692i
587587 −6.80793 6.80793i −0.280993 0.280993i 0.552512 0.833505i 0.313669π-0.313669\pi
−0.833505 + 0.552512i 0.813669π0.813669\pi
588588 0 0
589589 27.8177 + 27.8177i 1.14621 + 1.14621i
590590 17.2317 6.81952i 0.709417 0.280755i
591591 0 0
592592 −10.1678 + 7.90264i −0.417893 + 0.324797i
593593 −27.4172 −1.12589 −0.562944 0.826495i 0.690331π-0.690331\pi
−0.562944 + 0.826495i 0.690331π0.690331\pi
594594 0 0
595595 −58.1722 + 0.891115i −2.38483 + 0.0365321i
596596 −0.687367 + 11.0100i −0.0281556 + 0.450988i
597597 0 0
598598 14.8692 + 39.3216i 0.608048 + 1.60798i
599599 39.5624i 1.61647i −0.588857 0.808237i 0.700422π-0.700422\pi
0.588857 0.808237i 0.299578π-0.299578\pi
600600 0 0
601601 20.5453i 0.838061i 0.907972 + 0.419030i 0.137630π0.137630\pi
−0.907972 + 0.419030i 0.862370π0.862370\pi
602602 16.4478 6.21965i 0.670364 0.253494i
603603 0 0
604604 −3.29242 3.73089i −0.133967 0.151808i
605605 −24.1924 + 0.370593i −0.983561 + 0.0150668i
606606 0 0
607607 −19.1918 −0.778971 −0.389485 0.921033i 0.627347π-0.627347\pi
−0.389485 + 0.921033i 0.627347π0.627347\pi
608608 27.8406 6.71941i 1.12908 0.272508i
609609 0 0
610610 15.4404 + 39.0152i 0.625165 + 1.57968i
611611 −5.78124 5.78124i −0.233884 0.233884i
612612 0 0
613613 3.14030 + 3.14030i 0.126836 + 0.126836i 0.767675 0.640839i 0.221414π-0.221414\pi
−0.640839 + 0.767675i 0.721414π0.721414\pi
614614 −10.5941 + 4.00608i −0.427542 + 0.161672i
615615 0 0
616616 −5.27558 2.78840i −0.212559 0.112348i
617617 26.9611i 1.08541i −0.839922 0.542707i 0.817399π-0.817399\pi
0.839922 0.542707i 0.182601π-0.182601\pi
618618 0 0
619619 −10.1272 10.1272i −0.407046 0.407046i 0.473661 0.880707i 0.342932π-0.342932\pi
−0.880707 + 0.473661i 0.842932π0.842932\pi
620620 −23.3895 25.7000i −0.939343 1.03214i
621621 0 0
622622 38.1216 + 17.2015i 1.52854 + 0.689717i
623623 17.5565i 0.703385i
624624 0 0
625625 24.9531 1.53078i 0.998124 0.0612312i
626626 −7.11997 + 15.7791i −0.284571 + 0.630660i
627627 0 0
628628 −19.4323 1.21317i −0.775432 0.0484109i
629629 −11.8966 11.8966i −0.474347 0.474347i
630630 0 0
631631 −24.9414 −0.992900 −0.496450 0.868065i 0.665363π-0.665363\pi
−0.496450 + 0.868065i 0.665363π0.665363\pi
632632 −0.434526 1.40882i −0.0172845 0.0560400i
633633 0 0
634634 −22.4630 + 8.49425i −0.892120 + 0.337350i
635635 0.328003 + 21.4121i 0.0130164 + 0.849713i
636636 0 0
637637 60.7278 60.7278i 2.40612 2.40612i
638638 −2.51865 1.13648i −0.0997142 0.0449938i
639639 0 0
640640 −24.8440 + 4.77261i −0.982044 + 0.188654i
641641 20.1001i 0.793908i 0.917839 + 0.396954i 0.129933π0.129933\pi
−0.917839 + 0.396954i 0.870067π0.870067\pi
642642 0 0
643643 −6.20809 6.20809i −0.244823 0.244823i 0.574019 0.818842i 0.305384π-0.305384\pi
−0.818842 + 0.574019i 0.805384π0.805384\pi
644644 45.9691 40.5666i 1.81144 1.59855i
645645 0 0
646646 13.2344 + 34.9984i 0.520702 + 1.37699i
647647 3.57164 0.140416 0.0702078 0.997532i 0.477634π-0.477634\pi
0.0702078 + 0.997532i 0.477634π0.477634\pi
648648 0 0
649649 2.48326i 0.0974763i
650650 13.0474 + 31.5475i 0.511762 + 1.23739i
651651 0 0
652652 −0.168166 + 2.69363i −0.00658588 + 0.105491i
653653 −27.2873 27.2873i −1.06783 1.06783i −0.997525 0.0703096i 0.977601π-0.977601\pi
−0.0703096 0.997525i 0.522399π-0.522399\pi
654654 0 0
655655 27.5292 28.3857i 1.07565 1.10912i
656656 −3.64299 + 29.0624i −0.142235 + 1.13470i
657657 0 0
658658 −4.90412 + 10.8684i −0.191182 + 0.423694i
659659 −32.0510 32.0510i −1.24853 1.24853i −0.956370 0.292159i 0.905626π-0.905626\pi
−0.292159 0.956370i 0.594374π-0.594374\pi
660660 0 0
661661 11.8765 11.8765i 0.461942 0.461942i −0.437350 0.899291i 0.644083π-0.644083\pi
0.899291 + 0.437350i 0.144083π0.144083\pi
662662 −11.6446 + 4.40334i −0.452580 + 0.171140i
663663 0 0
664664 −17.7386 + 33.5610i −0.688392 + 1.30242i
665665 −39.2407 + 40.4616i −1.52169 + 1.56903i
666666 0 0
667667 20.0749 20.0749i 0.777302 0.777302i
668668 −12.8814 14.5969i −0.498397 0.564772i
669669 0 0
670670 0.0674150 + 0.170345i 0.00260447 + 0.00658101i
671671 −5.62247 −0.217053
672672 0 0
673673 4.29764i 0.165662i 0.996564 + 0.0828309i 0.0263961π0.0263961\pi
−0.996564 + 0.0828309i 0.973604π0.973604\pi
674674 3.15476 + 1.42351i 0.121517 + 0.0548317i
675675 0 0
676676 −15.4601 + 13.6431i −0.594618 + 0.524736i
677677 −22.4731 + 22.4731i −0.863711 + 0.863711i −0.991767 0.128056i 0.959126π-0.959126\pi
0.128056 + 0.991767i 0.459126π0.459126\pi
678678 0 0
679679 −16.4663 −0.631919
680680 −10.2238 31.4302i −0.392066 1.20529i
681681 0 0
682682 4.35542 1.64698i 0.166778 0.0630659i
683683 −6.83685 6.83685i −0.261605 0.261605i 0.564101 0.825706i 0.309223π-0.309223\pi
−0.825706 + 0.564101i 0.809223π0.809223\pi
684684 0 0
685685 −7.18720 + 0.110098i −0.274609 + 0.00420661i
686686 −69.2392 31.2426i −2.64356 1.19285i
687687 0 0
688688 6.13035 + 7.88750i 0.233717 + 0.300708i
689689 20.1527i 0.767755i
690690 0 0
691691 8.12866 8.12866i 0.309229 0.309229i −0.535381 0.844610i 0.679832π-0.679832\pi
0.844610 + 0.535381i 0.179832π0.179832\pi
692692 −1.38417 + 22.1712i −0.0526182 + 0.842821i
693693 0 0
694694 14.6037 5.52231i 0.554349 0.209624i
695695 1.60406 1.65397i 0.0608456 0.0627388i
696696 0 0
697697 −38.2661 −1.44943
698698 34.4233 13.0170i 1.30294 0.492699i
699699 0 0
700700 36.3040 34.0713i 1.37216 1.28777i
701701 −32.3973 + 32.3973i −1.22363 + 1.22363i −0.257298 + 0.966332i 0.582832π0.582832\pi
−0.966332 + 0.257298i 0.917168π0.917168\pi
702702 0 0
703703 −16.2996 −0.614750
704704 0.630392 3.33078i 0.0237588 0.125533i
705705 0 0
706706 13.7726 30.5224i 0.518337 1.14873i
707707 −37.6315 + 37.6315i −1.41528 + 1.41528i
708708 0 0
709709 11.9419 11.9419i 0.448488 0.448488i −0.446364 0.894852i 0.647281π-0.647281\pi
0.894852 + 0.446364i 0.147281π0.147281\pi
710710 6.24116 14.4166i 0.234227 0.541044i
711711 0 0
712712 9.53071 2.93957i 0.357178 0.110165i
713713 47.8421i 1.79170i
714714 0 0
715715 −4.57403 + 0.0700677i −0.171059 + 0.00262038i
716716 1.60986 25.7863i 0.0601634 0.963680i
717717 0 0
718718 −0.594717 0.268353i −0.0221947 0.0100148i
719719 50.1912 1.87182 0.935908 0.352243i 0.114581π-0.114581\pi
0.935908 + 0.352243i 0.114581π0.114581\pi
720720 0 0
721721 −65.0191 −2.42144
722722 8.55000 + 3.85799i 0.318198 + 0.143580i
723723 0 0
724724 44.8862 + 2.80229i 1.66818 + 0.104146i
725725 15.7954 16.7941i 0.586627 0.623717i
726726 0 0
727727 8.79380i 0.326144i −0.986614 0.163072i 0.947860π-0.947860\pi
0.986614 0.163072i 0.0521403π-0.0521403\pi
728728 60.1089 + 31.7704i 2.22779 + 1.17749i
729729 0 0
730730 −11.2430 4.86728i −0.416122 0.180146i
731731 −9.22857 + 9.22857i −0.341331 + 0.341331i
732732 0 0
733733 −23.9818 + 23.9818i −0.885787 + 0.885787i −0.994115 0.108328i 0.965450π-0.965450\pi
0.108328 + 0.994115i 0.465450π0.465450\pi
734734 11.7513 26.0429i 0.433747 0.961260i
735735 0 0
736736 29.7189 + 18.1625i 1.09545 + 0.669480i
737737 −0.0245484 −0.000904253
738738 0 0
739739 −4.55372 + 4.55372i −0.167511 + 0.167511i −0.785884 0.618373i 0.787792π-0.787792\pi
0.618373 + 0.785884i 0.287792π0.287792\pi
740740 14.3818 + 0.676913i 0.528685 + 0.0248838i
741741 0 0
742742 27.4905 10.3954i 1.00921 0.381626i
743743 −5.94900 −0.218248 −0.109124 0.994028i 0.534805π-0.534805\pi
−0.109124 + 0.994028i 0.534805π0.534805\pi
744744 0 0
745745 8.58653 8.85369i 0.314586 0.324374i
746746 10.6028 4.00937i 0.388195 0.146794i
747747 0 0
748748 4.42019 + 0.275957i 0.161618 + 0.0100900i
749749 37.1559 37.1559i 1.35765 1.35765i
750750 0 0
751751 40.6618i 1.48377i 0.670528 + 0.741884i 0.266068π0.266068\pi
−0.670528 + 0.741884i 0.733932π0.733932\pi
752752 −6.72115 0.842499i −0.245095 0.0307228i
753753 0 0
754754 28.6970 + 12.9489i 1.04508 + 0.471570i
755755 0.0852107 + 5.56257i 0.00310113 + 0.202443i
756756 0 0
757757 13.2358 + 13.2358i 0.481064 + 0.481064i 0.905471 0.424407i 0.139518π-0.139518\pi
−0.424407 + 0.905471i 0.639518π0.639518\pi
758758 −11.6029 + 4.38756i −0.421436 + 0.159363i
759759 0 0
760760 −28.5353 14.5275i −1.03508 0.526968i
761761 3.22651 0.116961 0.0584805 0.998289i 0.481374π-0.481374\pi
0.0584805 + 0.998289i 0.481374π0.481374\pi
762762 0 0
763763 17.1001 17.1001i 0.619065 0.619065i
764764 −2.86839 3.25039i −0.103775 0.117595i
765765 0 0
766766 −6.31215 2.84821i −0.228067 0.102910i
767767 28.2937i 1.02163i
768768 0 0
769769 33.3777 1.20363 0.601815 0.798635i 0.294444π-0.294444\pi
0.601815 + 0.798635i 0.294444π0.294444\pi
770770 2.45501 + 6.20335i 0.0884723 + 0.223553i
771771 0 0
772772 34.5685 30.5059i 1.24415 1.09793i
773773 22.5192 22.5192i 0.809958 0.809958i −0.174669 0.984627i 0.555886π-0.555886\pi
0.984627 + 0.174669i 0.0558857π0.0558857\pi
774774 0 0
775775 1.19002 + 38.8333i 0.0427468 + 1.39493i
776776 −2.75704 8.93891i −0.0989720 0.320888i
777777 0 0
778778 25.7485 9.73662i 0.923127 0.349075i
779779 −26.2144 + 26.2144i −0.939227 + 0.939227i
780780 0 0
781781 1.48849 + 1.48849i 0.0532624 + 0.0532624i
782782 −18.7153 + 41.4764i −0.669258 + 1.48319i
783783 0 0
784784 8.84986 70.6009i 0.316066 2.52146i
785785 15.6264 + 15.1549i 0.557731 + 0.540901i
786786 0 0
787787 23.0883 + 23.0883i 0.823007 + 0.823007i 0.986538 0.163531i 0.0522883π-0.0522883\pi
−0.163531 + 0.986538i 0.552288π0.552288\pi
788788 −4.31251 0.269234i −0.153627 0.00959108i
789789 0 0
790790 −0.654858 + 1.51267i −0.0232988 + 0.0538183i
791791 27.0066i 0.960244i
792792 0 0
793793 64.0614 2.27489
794794 −11.4984 30.4075i −0.408063 1.07912i
795795 0 0
796796 4.13886 + 4.69006i 0.146698 + 0.166235i
797797 14.3550 + 14.3550i 0.508481 + 0.508481i 0.914060 0.405579i 0.132930π-0.132930\pi
−0.405579 + 0.914060i 0.632930π0.632930\pi
798798 0 0
799799 8.84965i 0.313078i
800800 24.5745 + 14.0033i 0.868841 + 0.495091i
801801 0 0
802802 −12.9355 5.83685i −0.456768 0.206106i
803803 1.16083 1.16083i 0.0409646 0.0409646i
804804 0 0
805805 −68.5377 + 1.04990i −2.41563 + 0.0370041i
806806 −49.6248 + 18.7653i −1.74796 + 0.660980i
807807 0 0
808808 −26.7295 14.1278i −0.940340 0.497014i
809809 −26.4918 −0.931404 −0.465702 0.884942i 0.654198π-0.654198\pi
−0.465702 + 0.884942i 0.654198π0.654198\pi
810810 0 0
811811 −15.3655 15.3655i −0.539554 0.539554i 0.383844 0.923398i 0.374600π-0.374600\pi
−0.923398 + 0.383844i 0.874600π0.874600\pi
812812 2.86092 45.8253i 0.100399 1.60815i
813813 0 0
814814 −0.793497 + 1.75853i −0.0278120 + 0.0616364i
815815 2.10072 2.16608i 0.0735849 0.0758744i
816816 0 0
817817 12.6441i 0.442362i
818818 −43.0431 19.4222i −1.50497 0.679082i
819819 0 0
820820 24.2187 22.0414i 0.845754 0.769718i
821821 38.5448 + 38.5448i 1.34522 + 1.34522i 0.890772 + 0.454450i 0.150164π0.150164\pi
0.454450 + 0.890772i 0.349836π0.349836\pi
822822 0 0
823823 15.7862i 0.550272i 0.961405 + 0.275136i 0.0887229π0.0887229\pi
−0.961405 + 0.275136i 0.911277π0.911277\pi
824824 −10.8865 35.2963i −0.379249 1.22960i
825825 0 0
826826 −38.5958 + 14.5948i −1.34292 + 0.507817i
827827 −38.2660 38.2660i −1.33064 1.33064i −0.904799 0.425840i 0.859979π-0.859979\pi
−0.425840 0.904799i 0.640021π-0.640021\pi
828828 0 0
829829 17.1402 + 17.1402i 0.595303 + 0.595303i 0.939059 0.343756i 0.111699π-0.111699\pi
−0.343756 + 0.939059i 0.611699π0.611699\pi
830830 39.4631 15.6177i 1.36979 0.542099i
831831 0 0
832832 −7.18257 + 37.9503i −0.249011 + 1.31569i
833833 92.9594 3.22085
834834 0 0
835835 0.333382 + 21.7633i 0.0115372 + 0.753149i
836836 3.21712 2.83903i 0.111266 0.0981897i
837837 0 0
838838 −24.1519 + 9.13288i −0.834312 + 0.315490i
839839 49.2982i 1.70196i 0.525197 + 0.850981i 0.323992π0.323992\pi
−0.525197 + 0.850981i 0.676008π0.676008\pi
840840 0 0
841841 7.73855i 0.266847i
842842 0.653461 + 1.72807i 0.0225197 + 0.0595534i
843843 0 0
844844 −7.51871 0.469400i −0.258805 0.0161574i
845845 23.0502 0.353096i 0.792951 0.0121469i
846846 0 0
847847 53.8727 1.85109
848848 10.2461 + 13.1829i 0.351853 + 0.452704i
849849 0 0
850850 −14.1595 + 34.1319i −0.485667 + 1.17071i
851851 −14.0164 14.0164i −0.480474 0.480474i
852852 0 0
853853 −36.9286 36.9286i −1.26441 1.26441i −0.948933 0.315477i 0.897835π-0.897835\pi
−0.315477 0.948933i 0.602165π-0.602165\pi
854854 −33.0448 87.3869i −1.13077 2.99032i
855855 0 0
856856 26.3917 + 13.9493i 0.902048 + 0.476776i
857857 2.74943i 0.0939189i −0.998897 0.0469594i 0.985047π-0.985047\pi
0.998897 0.0469594i 0.0149532π-0.0149532\pi
858858 0 0
859859 14.1089 + 14.1089i 0.481390 + 0.481390i 0.905575 0.424186i 0.139440π-0.139440\pi
−0.424186 + 0.905575i 0.639440π0.639440\pi
860860 0.525105 11.1565i 0.0179059 0.380432i
861861 0 0
862862 13.6998 30.3613i 0.466618 1.03411i
863863 3.40986i 0.116073i −0.998314 0.0580364i 0.981516π-0.981516\pi
0.998314 0.0580364i 0.0184840π-0.0184840\pi
864864 0 0
865865 17.2909 17.8289i 0.587909 0.606201i
866866 49.7236 + 22.4366i 1.68968 + 0.762428i
867867 0 0
868868 51.1960 + 58.0141i 1.73771 + 1.96913i
869869 −0.156181 0.156181i −0.00529807 0.00529807i
870870 0 0
871871 0.279700 0.00947728
872872 12.1461 + 6.41981i 0.411320 + 0.217402i
873873 0 0
874874 15.5926 + 41.2346i 0.527428 + 1.39478i
875875 −55.6058 + 2.55700i −1.87982 + 0.0864425i
876876 0 0
877877 31.8968 31.8968i 1.07708 1.07708i 0.0803069 0.996770i 0.474410π-0.474410\pi
0.996770 0.0803069i 0.0255900π-0.0255900\pi
878878 17.6556 39.1279i 0.595847 1.32050i
879879 0 0
880880 −2.95650 + 2.37139i −0.0996636 + 0.0799394i
881881 7.77943i 0.262096i 0.991376 + 0.131048i 0.0418342π0.0418342\pi
−0.991376 + 0.131048i 0.958166π0.958166\pi
882882 0 0
883883 −29.0951 29.0951i −0.979129 0.979129i 0.0206577 0.999787i 0.493424π-0.493424\pi
−0.999787 + 0.0206577i 0.993424π0.993424\pi
884884 −50.3628 3.14420i −1.69388 0.105751i
885885 0 0
886886 −8.88148 + 3.35848i −0.298379 + 0.112830i
887887 20.4586 0.686933 0.343467 0.939165i 0.388399π-0.388399\pi
0.343467 + 0.939165i 0.388399π0.388399\pi
888888 0 0
889889 47.6814i 1.59918i
890890 −10.2332 4.43012i −0.343018 0.148498i
891891 0 0
892892 −30.2376 34.2646i −1.01243 1.14726i
893893 −6.06250 6.06250i −0.202874 0.202874i
894894 0 0
895895 −20.1103 + 20.7360i −0.672213 + 0.693128i
896896 55.4734 9.77808i 1.85324 0.326663i
897897 0 0
898898 13.0541 + 5.89035i 0.435620 + 0.196564i
899899 25.3349 + 25.3349i 0.844968 + 0.844968i
900900 0 0
901901 −15.4244 + 15.4244i −0.513861 + 0.513861i
902902 1.55205 + 4.10439i 0.0516776 + 0.136661i
903903 0 0
904904 −14.6608 + 4.52186i −0.487611 + 0.150395i
905905 −36.0951 35.0060i −1.19984 1.16364i
906906 0 0
907907 −24.1511 + 24.1511i −0.801925 + 0.801925i −0.983396 0.181471i 0.941914π-0.941914\pi
0.181471 + 0.983396i 0.441914π0.441914\pi
908908 −8.18021 0.510698i −0.271470 0.0169481i
909909 0 0
910910 −27.9719 70.6798i −0.927258 2.34301i
911911 −29.3578 −0.972668 −0.486334 0.873773i 0.661666π-0.661666\pi
−0.486334 + 0.873773i 0.661666π0.661666\pi
912912 0 0
913913 5.68703i 0.188213i
914914 −0.840189 + 1.86201i −0.0277910 + 0.0615897i
915915 0 0
916916 −38.9285 2.43035i −1.28623 0.0803009i
917917 −62.2568 + 62.2568i −2.05590 + 2.05590i
918918 0 0
919919 42.3082 1.39562 0.697809 0.716284i 0.254159π-0.254159\pi
0.697809 + 0.716284i 0.254159π0.254159\pi
920920 −12.0456 37.0306i −0.397131 1.22086i
921921 0 0
922922 −19.0024 50.2518i −0.625811 1.65496i
923923 −16.9596 16.9596i −0.558231 0.558231i
924924 0 0
925925 −11.7257 11.0284i −0.385539 0.362612i
926926 −11.7842 + 26.1159i −0.387253 + 0.858223i
927927 0 0
928928 25.3558 6.11970i 0.832344 0.200889i
929929 27.8428i 0.913494i −0.889597 0.456747i 0.849014π-0.849014\pi
0.889597 0.456747i 0.150986π-0.150986\pi
930930 0 0
931931 63.6822 63.6822i 2.08710 2.08710i
932932 41.7682 36.8594i 1.36816 1.20737i
933933 0 0
934934 −6.43655 17.0214i −0.210610 0.556958i
935935 −3.55449 3.44723i −0.116244 0.112737i
936936 0 0
937937 −29.0721 −0.949745 −0.474873 0.880054i 0.657506π-0.657506\pi
−0.474873 + 0.880054i 0.657506π0.657506\pi
938938 −0.144278 0.381542i −0.00471084 0.0124578i
939939 0 0
940940 5.09742 + 5.60097i 0.166260 + 0.182683i
941941 −3.40692 + 3.40692i −0.111062 + 0.111062i −0.760454 0.649392i 0.775024π-0.775024\pi
0.649392 + 0.760454i 0.275024π0.275024\pi
942942 0 0
943943 −45.0846 −1.46816
944944 −14.3852 18.5085i −0.468200 0.602400i
945945 0 0
946946 1.36415 + 0.615543i 0.0443524 + 0.0200130i
947947 9.01416 9.01416i 0.292921 0.292921i −0.545312 0.838233i 0.683589π-0.683589\pi
0.838233 + 0.545312i 0.183589π0.183589\pi
948948 0 0
949949 −13.2262 + 13.2262i −0.429341 + 0.429341i
950950 13.6822 + 33.0822i 0.443909 + 1.07333i
951951 0 0
952952 21.6896 + 70.3224i 0.702965 + 2.27916i
953953 35.7289i 1.15737i −0.815550 0.578687i 0.803565π-0.803565\pi
0.815550 0.578687i 0.196435π-0.196435\pi
954954 0 0
955955 0.0742364 + 4.84617i 0.00240223 + 0.156818i
956956 30.1642 + 34.1814i 0.975581 + 1.10550i
957957 0 0
958958 −2.67834 + 5.93567i −0.0865331 + 0.191773i
959959 16.0048 0.516821
960960 0 0
961961 −29.3778 −0.947671
962962 9.04095 20.0363i 0.291492 0.645998i
963963 0 0
964964 −5.73259 6.49604i −0.184634 0.209223i
965965 −51.5400 + 0.789519i −1.65913 + 0.0254155i
966966 0 0
967967 0.997773i 0.0320862i 0.999871 + 0.0160431i 0.00510690π0.00510690\pi
−0.999871 + 0.0160431i 0.994893π0.994893\pi
968968 9.02020 + 29.2454i 0.289920 + 0.939982i
969969 0 0
970970 −4.15504 + 9.59778i −0.133410 + 0.308166i
971971 42.0632 42.0632i 1.34987 1.34987i 0.464075 0.885796i 0.346387π-0.346387\pi
0.885796 0.464075i 0.153613π-0.153613\pi
972972 0 0
973973 −3.62757 + 3.62757i −0.116295 + 0.116295i
974974 41.5185 + 18.7343i 1.33034 + 0.600285i
975975 0 0
976976 41.9060 32.5704i 1.34138 1.04255i
977977 −16.7515 −0.535927 −0.267963 0.963429i 0.586351π-0.586351\pi
−0.267963 + 0.963429i 0.586351π0.586351\pi
978978 0 0
979979 1.05657 1.05657i 0.0337680 0.0337680i
980980 −58.8342 + 53.5448i −1.87939 + 1.71043i
981981 0 0
982982 12.3214 + 32.5840i 0.393193 + 1.03980i
983983 −40.1381 −1.28021 −0.640103 0.768289i 0.721108π-0.721108\pi
−0.640103 + 0.768289i 0.721108π0.721108\pi
984984 0 0
985985 3.46790 + 3.36326i 0.110497 + 0.107162i
986986 12.0532 + 31.8748i 0.383854 + 1.01510i
987987 0 0
988988 −36.6552 + 32.3473i −1.16616 + 1.02911i
989989 −10.8730 + 10.8730i −0.345740 + 0.345740i
990990 0 0
991991 52.3742i 1.66372i 0.554984 + 0.831861i 0.312724π0.312724\pi
−0.554984 + 0.831861i 0.687276π0.687276\pi
992992 −22.9215 + 37.5059i −0.727760 + 1.19081i
993993 0 0
994994 −14.3865 + 31.8830i −0.456312 + 1.01127i
995995 −0.107117 6.99264i −0.00339585 0.221682i
996996 0 0
997997 7.28564 + 7.28564i 0.230738 + 0.230738i 0.813001 0.582262i 0.197832π-0.197832\pi
−0.582262 + 0.813001i 0.697832π0.697832\pi
998998 −11.0355 29.1833i −0.349322 0.923781i
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 720.2.u.a.179.20 yes 96
3.2 odd 2 inner 720.2.u.a.179.29 yes 96
4.3 odd 2 2880.2.u.a.2159.25 96
5.4 even 2 inner 720.2.u.a.179.30 yes 96
12.11 even 2 2880.2.u.a.2159.24 96
15.14 odd 2 inner 720.2.u.a.179.19 96
16.5 even 4 2880.2.u.a.719.1 96
16.11 odd 4 inner 720.2.u.a.539.19 yes 96
20.19 odd 2 2880.2.u.a.2159.48 96
48.5 odd 4 2880.2.u.a.719.48 96
48.11 even 4 inner 720.2.u.a.539.30 yes 96
60.59 even 2 2880.2.u.a.2159.1 96
80.59 odd 4 inner 720.2.u.a.539.29 yes 96
80.69 even 4 2880.2.u.a.719.24 96
240.59 even 4 inner 720.2.u.a.539.20 yes 96
240.149 odd 4 2880.2.u.a.719.25 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
720.2.u.a.179.19 96 15.14 odd 2 inner
720.2.u.a.179.20 yes 96 1.1 even 1 trivial
720.2.u.a.179.29 yes 96 3.2 odd 2 inner
720.2.u.a.179.30 yes 96 5.4 even 2 inner
720.2.u.a.539.19 yes 96 16.11 odd 4 inner
720.2.u.a.539.20 yes 96 240.59 even 4 inner
720.2.u.a.539.29 yes 96 80.59 odd 4 inner
720.2.u.a.539.30 yes 96 48.11 even 4 inner
2880.2.u.a.719.1 96 16.5 even 4
2880.2.u.a.719.24 96 80.69 even 4
2880.2.u.a.719.25 96 240.149 odd 4
2880.2.u.a.719.48 96 48.5 odd 4
2880.2.u.a.2159.1 96 60.59 even 2
2880.2.u.a.2159.24 96 12.11 even 2
2880.2.u.a.2159.25 96 4.3 odd 2
2880.2.u.a.2159.48 96 20.19 odd 2