Properties

Label 81.2.g.a.22.8
Level 8181
Weight 22
Character 81.22
Analytic conductor 0.6470.647
Analytic rank 00
Dimension 144144
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [81,2,Mod(4,81)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(81, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("81.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 81=34 81 = 3^{4}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 81.g (of order 2727, degree 1818, 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: 0.6467882563720.646788256372
Analytic rank: 00
Dimension: 144144
Relative dimension: 88 over Q(ζ27)\Q(\zeta_{27})
Twist minimal: yes
Sato-Tate group: SU(2)[C27]\mathrm{SU}(2)[C_{27}]

Embedding invariants

Embedding label 22.8
Character χ\chi == 81.22
Dual form 81.2.g.a.70.8

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+(1.71221+1.81484i)q2+(1.104191.33445i)q3+(0.245679+4.21814i)q4+(1.398040.163408i)q5+(0.5312054.28879i)q6+(2.850831.43174i)q7+(4.25325+3.56890i)q8+(0.561524+2.94698i)q9+(2.69030+2.25743i)q10+(1.876244.34961i)q11+(5.900184.32979i)q12+(2.07522+0.491837i)q13+(2.282847.62523i)q14+(1.761771.68519i)q15+(5.365970.627192i)q16+(0.5202492.95048i)q17+(6.30973+4.02677i)q18+(1.23380+6.99724i)q19+(0.345808+5.93730i)q20+(1.23727+5.38521i)q21+(4.6813110.8525i)q22+(2.70239+1.35719i)q23+(9.45892+1.73501i)q24+(2.93740+0.696176i)q25+(2.66061+4.60832i)q26+(4.552632.50470i)q27+(6.7396811.6735i)q28+(0.631591+2.10966i)q29+(0.04182606.08272i)q30+(3.14652+2.06950i)q31+(1.418301.90511i)q32+(3.73262+7.30654i)q33+(6.245414.10767i)q34+(4.219551.53579i)q35+(12.29283.09260i)q36+(6.31317+2.29781i)q37+(10.5863+14.2199i)q38+(1.635113.31237i)q39+(5.36304+5.68449i)q40+(2.906283.08048i)q41+(7.65481+11.4661i)q42+(0.4740970.636822i)q43+(18.80826.84563i)q44+(0.303475+4.21177i)q45+(7.090152.58060i)q46+(4.833703.17917i)q47+(5.08810+7.85317i)q48+(1.89725+2.54844i)q49+(6.292894.13890i)q50+(4.51172+2.56364i)q51+(2.58448+8.63275i)q52+(4.832548.37020i)q53+(12.3407+3.97371i)q54+(3.333825.77435i)q55+(17.23504.08478i)q56+(7.975129.37273i)q57+(4.91010+2.46595i)q58+(0.636054+1.47454i)q59+(7.541207.01737i)q60+(0.0674875+1.15872i)q61+(1.63170+9.25383i)q62+(5.820127.59739i)q63+(0.847235+4.80491i)q64+(2.98162+0.348502i)q65+(19.6512+5.73625i)q66+(1.71558+5.73045i)q67+(12.3177+2.91935i)q68+(4.79507+2.10761i)q69+(4.4375410.2874i)q70+(2.74773+2.30562i)q71+(8.1291714.5383i)q72+(8.559527.18229i)q73+(14.97967.52304i)q74+(4.17246+3.15111i)q75+(29.8185+3.48528i)q76+(0.878675+15.0863i)q77+(3.211758.63892i)q78+(3.217303.41014i)q797.60435q80+(8.369383.30960i)q81+10.5667q82+(10.265910.8812i)q83+(23.0196+3.89596i)q84+(0.2451994.20991i)q85+(1.967480.229966i)q86+(3.512641.48664i)q87+(23.5034+11.8038i)q88+(3.174492.66371i)q89+(8.16328+6.66067i)q90+(5.211934.37333i)q91+(5.0609111.7325i)q92+(0.7127136.48400i)q93+(14.0460+3.32896i)q94+(2.86831+9.58083i)q95+(0.976202+3.99627i)q96+(12.50271.46135i)q97+(1.37652+7.80666i)q98+(13.87183.08682i)q99+O(q100)q+(1.71221 + 1.81484i) q^{2} +(-1.10419 - 1.33445i) q^{3} +(-0.245679 + 4.21814i) q^{4} +(1.39804 - 0.163408i) q^{5} +(0.531205 - 4.28879i) q^{6} +(-2.85083 - 1.43174i) q^{7} +(-4.25325 + 3.56890i) q^{8} +(-0.561524 + 2.94698i) q^{9} +(2.69030 + 2.25743i) q^{10} +(-1.87624 - 4.34961i) q^{11} +(5.90018 - 4.32979i) q^{12} +(2.07522 + 0.491837i) q^{13} +(-2.28284 - 7.62523i) q^{14} +(-1.76177 - 1.68519i) q^{15} +(-5.36597 - 0.627192i) q^{16} +(0.520249 - 2.95048i) q^{17} +(-6.30973 + 4.02677i) q^{18} +(1.23380 + 6.99724i) q^{19} +(0.345808 + 5.93730i) q^{20} +(1.23727 + 5.38521i) q^{21} +(4.68131 - 10.8525i) q^{22} +(-2.70239 + 1.35719i) q^{23} +(9.45892 + 1.73501i) q^{24} +(-2.93740 + 0.696176i) q^{25} +(2.66061 + 4.60832i) q^{26} +(4.55263 - 2.50470i) q^{27} +(6.73968 - 11.6735i) q^{28} +(-0.631591 + 2.10966i) q^{29} +(0.0418260 - 6.08272i) q^{30} +(3.14652 + 2.06950i) q^{31} +(-1.41830 - 1.90511i) q^{32} +(-3.73262 + 7.30654i) q^{33} +(6.24541 - 4.10767i) q^{34} +(-4.21955 - 1.53579i) q^{35} +(-12.2928 - 3.09260i) q^{36} +(-6.31317 + 2.29781i) q^{37} +(-10.5863 + 14.2199i) q^{38} +(-1.63511 - 3.31237i) q^{39} +(-5.36304 + 5.68449i) q^{40} +(2.90628 - 3.08048i) q^{41} +(-7.65481 + 11.4661i) q^{42} +(0.474097 - 0.636822i) q^{43} +(18.8082 - 6.84563i) q^{44} +(-0.303475 + 4.21177i) q^{45} +(-7.09015 - 2.58060i) q^{46} +(4.83370 - 3.17917i) q^{47} +(5.08810 + 7.85317i) q^{48} +(1.89725 + 2.54844i) q^{49} +(-6.29289 - 4.13890i) q^{50} +(-4.51172 + 2.56364i) q^{51} +(-2.58448 + 8.63275i) q^{52} +(4.83254 - 8.37020i) q^{53} +(12.3407 + 3.97371i) q^{54} +(-3.33382 - 5.77435i) q^{55} +(17.2350 - 4.08478i) q^{56} +(7.97512 - 9.37273i) q^{57} +(-4.91010 + 2.46595i) q^{58} +(-0.636054 + 1.47454i) q^{59} +(7.54120 - 7.01737i) q^{60} +(0.0674875 + 1.15872i) q^{61} +(1.63170 + 9.25383i) q^{62} +(5.82012 - 7.59739i) q^{63} +(-0.847235 + 4.80491i) q^{64} +(2.98162 + 0.348502i) q^{65} +(-19.6512 + 5.73625i) q^{66} +(1.71558 + 5.73045i) q^{67} +(12.3177 + 2.91935i) q^{68} +(4.79507 + 2.10761i) q^{69} +(-4.43754 - 10.2874i) q^{70} +(2.74773 + 2.30562i) q^{71} +(-8.12917 - 14.5383i) q^{72} +(8.55952 - 7.18229i) q^{73} +(-14.9796 - 7.52304i) q^{74} +(4.17246 + 3.15111i) q^{75} +(-29.8185 + 3.48528i) q^{76} +(-0.878675 + 15.0863i) q^{77} +(3.21175 - 8.63892i) q^{78} +(-3.21730 - 3.41014i) q^{79} -7.60435 q^{80} +(-8.36938 - 3.30960i) q^{81} +10.5667 q^{82} +(-10.2659 - 10.8812i) q^{83} +(-23.0196 + 3.89596i) q^{84} +(0.245199 - 4.20991i) q^{85} +(1.96748 - 0.229966i) q^{86} +(3.51264 - 1.48664i) q^{87} +(23.5034 + 11.8038i) q^{88} +(3.17449 - 2.66371i) q^{89} +(-8.16328 + 6.66067i) q^{90} +(-5.21193 - 4.37333i) q^{91} +(-5.06091 - 11.7325i) q^{92} +(-0.712713 - 6.48400i) q^{93} +(14.0460 + 3.32896i) q^{94} +(2.86831 + 9.58083i) q^{95} +(-0.976202 + 3.99627i) q^{96} +(-12.5027 - 1.46135i) q^{97} +(-1.37652 + 7.80666i) q^{98} +(13.8718 - 3.08682i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 144q18q218q318q418q518q618q718q818q918q1018q1118q1218q1318q1418q1518q1618q179q1818q19++54q99+O(q100) 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/81Z)×\left(\mathbb{Z}/81\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(727)e\left(\frac{7}{27}\right)

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 1.71221 + 1.81484i 1.21071 + 1.28328i 0.947949 + 0.318423i 0.103153π0.103153\pi
0.262766 + 0.964860i 0.415365π0.415365\pi
33 −1.10419 1.33445i −0.637505 0.770446i
44 −0.245679 + 4.21814i −0.122839 + 2.10907i
55 1.39804 0.163408i 0.625224 0.0730783i 0.202419 0.979299i 0.435120π-0.435120\pi
0.422805 + 0.906221i 0.361046π0.361046\pi
66 0.531205 4.28879i 0.216863 1.75089i
77 −2.85083 1.43174i −1.07751 0.541147i −0.180691 0.983540i 0.557834π-0.557834\pi
−0.896822 + 0.442393i 0.854130π0.854130\pi
88 −4.25325 + 3.56890i −1.50375 + 1.26180i
99 −0.561524 + 2.94698i −0.187175 + 0.982327i
1010 2.69030 + 2.25743i 0.850749 + 0.713863i
1111 −1.87624 4.34961i −0.565707 1.31146i −0.925615 0.378468i 0.876451π-0.876451\pi
0.359908 0.932988i 0.382808π-0.382808\pi
1212 5.90018 4.32979i 1.70324 1.24990i
1313 2.07522 + 0.491837i 0.575563 + 0.136411i 0.508081 0.861309i 0.330355π-0.330355\pi
0.0674826 + 0.997720i 0.478503π0.478503\pi
1414 −2.28284 7.62523i −0.610116 2.03793i
1515 −1.76177 1.68519i −0.454887 0.435114i
1616 −5.36597 0.627192i −1.34149 0.156798i
1717 0.520249 2.95048i 0.126179 0.715596i −0.854422 0.519580i 0.826088π-0.826088\pi
0.980601 0.196016i 0.0628004π-0.0628004\pi
1818 −6.30973 + 4.02677i −1.48722 + 0.949120i
1919 1.23380 + 6.99724i 0.283053 + 1.60528i 0.712157 + 0.702020i 0.247718π0.247718\pi
−0.429103 + 0.903255i 0.641170π0.641170\pi
2020 0.345808 + 5.93730i 0.0773250 + 1.32762i
2121 1.23727 + 5.38521i 0.269995 + 1.17515i
2222 4.68131 10.8525i 0.998059 2.31376i
2323 −2.70239 + 1.35719i −0.563488 + 0.282994i −0.707654 0.706559i 0.750246π-0.750246\pi
0.144166 + 0.989554i 0.453950π0.453950\pi
2424 9.45892 + 1.73501i 1.93079 + 0.354157i
2525 −2.93740 + 0.696176i −0.587480 + 0.139235i
2626 2.66061 + 4.60832i 0.521789 + 0.903765i
2727 4.55263 2.50470i 0.876155 0.482030i
2828 6.73968 11.6735i 1.27368 2.20608i
2929 −0.631591 + 2.10966i −0.117284 + 0.391754i −0.996392 0.0848670i 0.972953π-0.972953\pi
0.879109 + 0.476621i 0.158139π0.158139\pi
3030 0.0418260 6.08272i 0.00763634 1.11055i
3131 3.14652 + 2.06950i 0.565132 + 0.371693i 0.799694 0.600408i 0.204995π-0.204995\pi
−0.234562 + 0.972101i 0.575366π0.575366\pi
3232 −1.41830 1.90511i −0.250723 0.336779i
3333 −3.73262 + 7.30654i −0.649765 + 1.27191i
3434 6.24541 4.10767i 1.07108 0.704459i
3535 −4.21955 1.53579i −0.713233 0.259596i
3636 −12.2928 3.09260i −2.04880 0.515433i
3737 −6.31317 + 2.29781i −1.03788 + 0.377757i −0.804076 0.594527i 0.797339π-0.797339\pi
−0.233803 + 0.972284i 0.575117π0.575117\pi
3838 −10.5863 + 14.2199i −1.71733 + 2.30677i
3939 −1.63511 3.31237i −0.261827 0.530403i
4040 −5.36304 + 5.68449i −0.847971 + 0.898797i
4141 2.90628 3.08048i 0.453884 0.481089i −0.459506 0.888175i 0.651973π-0.651973\pi
0.913390 + 0.407085i 0.133455π0.133455\pi
4242 −7.65481 + 11.4661i −1.18116 + 1.76925i
4343 0.474097 0.636822i 0.0722991 0.0971145i −0.764503 0.644621i 0.777015π-0.777015\pi
0.836802 + 0.547506i 0.184423π0.184423\pi
4444 18.8082 6.84563i 2.83544 1.03202i
4545 −0.303475 + 4.21177i −0.0452394 + 0.627853i
4646 −7.09015 2.58060i −1.04538 0.380489i
4747 4.83370 3.17917i 0.705067 0.463730i −0.145662 0.989334i 0.546531π-0.546531\pi
0.850729 + 0.525605i 0.176161π0.176161\pi
4848 5.08810 + 7.85317i 0.734404 + 1.13351i
4949 1.89725 + 2.54844i 0.271035 + 0.364063i
5050 −6.29289 4.13890i −0.889949 0.585328i
5151 −4.51172 + 2.56364i −0.631768 + 0.358982i
5252 −2.58448 + 8.63275i −0.358402 + 1.19715i
5353 4.83254 8.37020i 0.663800 1.14973i −0.315809 0.948823i 0.602276π-0.602276\pi
0.979609 0.200912i 0.0643906π-0.0643906\pi
5454 12.3407 + 3.97371i 1.67935 + 0.540753i
5555 −3.33382 5.77435i −0.449532 0.778613i
5656 17.2350 4.08478i 2.30313 0.545851i
5757 7.97512 9.37273i 1.05633 1.24145i
5858 −4.91010 + 2.46595i −0.644728 + 0.323795i
5959 −0.636054 + 1.47454i −0.0828072 + 0.191969i −0.954589 0.297926i 0.903705π-0.903705\pi
0.871782 + 0.489894i 0.162965π0.162965\pi
6060 7.54120 7.01737i 0.973564 0.905939i
6161 0.0674875 + 1.15872i 0.00864089 + 0.148358i 0.999869 + 0.0161951i 0.00515528π0.00515528\pi
−0.991228 + 0.132163i 0.957808π0.957808\pi
6262 1.63170 + 9.25383i 0.207226 + 1.17524i
6363 5.82012 7.59739i 0.733266 0.957181i
6464 −0.847235 + 4.80491i −0.105904 + 0.600613i
6565 2.98162 + 0.348502i 0.369825 + 0.0432263i
6666 −19.6512 + 5.73625i −2.41890 + 0.706083i
6767 1.71558 + 5.73045i 0.209592 + 0.700085i 0.996544 + 0.0830710i 0.0264728π0.0264728\pi
−0.786952 + 0.617014i 0.788342π0.788342\pi
6868 12.3177 + 2.91935i 1.49374 + 0.354024i
6969 4.79507 + 2.10761i 0.577258 + 0.253727i
7070 −4.43754 10.2874i −0.530388 1.22958i
7171 2.74773 + 2.30562i 0.326095 + 0.273626i 0.791107 0.611678i 0.209505π-0.209505\pi
−0.465011 + 0.885305i 0.653950π0.653950\pi
7272 −8.12917 14.5383i −0.958032 1.71335i
7373 8.55952 7.18229i 1.00182 0.840623i 0.0145810 0.999894i 0.495359π-0.495359\pi
0.987235 + 0.159270i 0.0509141π0.0509141\pi
7474 −14.9796 7.52304i −1.74134 0.874536i
7575 4.17246 + 3.15111i 0.481795 + 0.363858i
7676 −29.8185 + 3.48528i −3.42041 + 0.399789i
7777 −0.878675 + 15.0863i −0.100134 + 1.71924i
7878 3.21175 8.63892i 0.363659 0.978165i
7979 −3.21730 3.41014i −0.361975 0.383671i 0.520633 0.853780i 0.325696π-0.325696\pi
−0.882608 + 0.470110i 0.844214π0.844214\pi
8080 −7.60435 −0.850192
8181 −8.36938 3.30960i −0.929931 0.367733i
8282 10.5667 1.16690
8383 −10.2659 10.8812i −1.12683 1.19437i −0.978677 0.205406i 0.934148π-0.934148\pi
−0.148154 0.988964i 0.547333π-0.547333\pi
8484 −23.0196 + 3.89596i −2.51164 + 0.425084i
8585 0.245199 4.20991i 0.0265956 0.456629i
8686 1.96748 0.229966i 0.212159 0.0247978i
8787 3.51264 1.48664i 0.376594 0.159385i
8888 23.5034 + 11.8038i 2.50547 + 1.25829i
8989 3.17449 2.66371i 0.336495 0.282353i −0.458845 0.888516i 0.651737π-0.651737\pi
0.795340 + 0.606164i 0.207292π0.207292\pi
9090 −8.16328 + 6.66067i −0.860485 + 0.702096i
9191 −5.21193 4.37333i −0.546358 0.458449i
9292 −5.06091 11.7325i −0.527637 1.22320i
9393 −0.712713 6.48400i −0.0739049 0.672360i
9494 14.0460 + 3.32896i 1.44873 + 0.343356i
9595 2.86831 + 9.58083i 0.294283 + 0.982973i
9696 −0.976202 + 3.99627i −0.0996332 + 0.407867i
9797 −12.5027 1.46135i −1.26946 0.148378i −0.545433 0.838154i 0.683635π-0.683635\pi
−0.724023 + 0.689776i 0.757709π0.757709\pi
9898 −1.37652 + 7.80666i −0.139050 + 0.788591i
9999 13.8718 3.08682i 1.39416 0.310238i
100100 −2.21491 12.5614i −0.221491 1.25614i
101101 0.261942 + 4.49737i 0.0260642 + 0.447505i 0.985942 + 0.167087i 0.0534361π0.0534361\pi
−0.959878 + 0.280418i 0.909527π0.909527\pi
102102 −12.3776 3.79854i −1.22557 0.376112i
103103 5.52933 12.8184i 0.544821 1.26304i −0.394152 0.919045i 0.628962π-0.628962\pi
0.938973 0.343992i 0.111779π-0.111779\pi
104104 −10.5817 + 5.31435i −1.03763 + 0.521115i
105105 2.60975 + 7.32659i 0.254685 + 0.715002i
106106 23.4648 5.56127i 2.27911 0.540158i
107107 −2.27719 3.94420i −0.220144 0.381301i 0.734708 0.678384i 0.237319π-0.237319\pi
−0.954852 + 0.297083i 0.903986π0.903986\pi
108108 9.44671 + 19.8190i 0.909010 + 1.90708i
109109 −3.56879 + 6.18132i −0.341828 + 0.592063i −0.984772 0.173850i 0.944379π-0.944379\pi
0.642944 + 0.765913i 0.277713π0.277713\pi
110110 4.77129 15.9372i 0.454925 1.51956i
111111 10.0373 + 5.88741i 0.952695 + 0.558808i
112112 14.3995 + 9.47070i 1.36062 + 0.894897i
113113 4.67557 + 6.28038i 0.439840 + 0.590808i 0.965667 0.259784i 0.0836513π-0.0836513\pi
−0.525826 + 0.850592i 0.676244π0.676244\pi
114114 30.6651 1.57455i 2.87205 0.147470i
115115 −3.55629 + 2.33901i −0.331626 + 0.218114i
116116 −8.74368 3.18244i −0.811830 0.295482i
117117 −2.61472 + 5.83946i −0.241731 + 0.539859i
118118 −3.76510 + 1.37039i −0.346606 + 0.126154i
119119 −5.70746 + 7.66645i −0.523202 + 0.702782i
120120 13.5075 + 0.879955i 1.23306 + 0.0803285i
121121 −7.85014 + 8.32067i −0.713649 + 0.756424i
122122 −1.98733 + 2.10644i −0.179924 + 0.190708i
123123 −7.31983 0.476855i −0.660007 0.0429966i
124124 −9.50247 + 12.7640i −0.853347 + 1.14624i
125125 −10.6062 + 3.86035i −0.948650 + 0.345280i
126126 23.7533 2.44575i 2.11611 0.217885i
127127 9.61531 + 3.49969i 0.853220 + 0.310547i 0.731353 0.681999i 0.238889π-0.238889\pi
0.121868 + 0.992546i 0.461112π0.461112\pi
128128 −14.1395 + 9.29968i −1.24976 + 0.821983i
129129 −1.37330 + 0.0705144i −0.120913 + 0.00620845i
130130 4.47269 + 6.00787i 0.392281 + 0.526925i
131131 −7.19028 4.72912i −0.628218 0.413185i 0.195086 0.980786i 0.437501π-0.437501\pi
−0.823304 + 0.567601i 0.807872π0.807872\pi
132132 −29.9030 17.5398i −2.60272 1.52664i
133133 6.50087 21.7144i 0.563697 1.88288i
134134 −7.46238 + 12.9252i −0.644652 + 1.11657i
135135 5.95549 4.24562i 0.512567 0.365405i
136136 8.31720 + 14.4058i 0.713194 + 1.23529i
137137 1.03986 0.246452i 0.0888413 0.0210558i −0.185955 0.982558i 0.559538π-0.559538\pi
0.274796 + 0.961503i 0.411390π0.411390\pi
138138 4.38519 + 12.3109i 0.373292 + 1.04798i
139139 −6.65577 + 3.34265i −0.564535 + 0.283520i −0.708090 0.706122i 0.750443π-0.750443\pi
0.143555 + 0.989642i 0.454147π0.454147\pi
140140 7.51483 17.4213i 0.635119 1.47237i
141141 −9.57978 2.93992i −0.806763 0.247586i
142142 0.520368 + 8.93437i 0.0436683 + 0.749756i
143143 −1.75431 9.94920i −0.146703 0.831994i
144144 4.86144 15.4612i 0.405120 1.28844i
145145 −0.538257 + 3.05261i −0.0446998 + 0.253505i
146146 27.6904 + 3.23654i 2.29167 + 0.267858i
147147 1.30585 5.34575i 0.107705 0.440910i
148148 −8.14146 27.1944i −0.669224 2.23536i
149149 −2.37562 0.563032i −0.194618 0.0461254i 0.132151 0.991230i 0.457812π-0.457812\pi
−0.326769 + 0.945104i 0.605960π0.605960\pi
150150 1.42539 + 12.9677i 0.116383 + 1.05881i
151151 8.46731 + 19.6294i 0.689060 + 1.59742i 0.797501 + 0.603318i 0.206155π0.206155\pi
−0.108440 + 0.994103i 0.534586π0.534586\pi
152152 −30.2201 25.3577i −2.45117 2.05678i
153153 8.40287 + 3.18993i 0.679331 + 0.257890i
154154 −28.8836 + 24.2362i −2.32751 + 1.95301i
155155 4.73715 + 2.37908i 0.380497 + 0.191093i
156156 14.3737 6.08335i 1.15082 0.487058i
157157 6.41788 0.750143i 0.512203 0.0598679i 0.143934 0.989587i 0.454025π-0.454025\pi
0.368269 + 0.929719i 0.379951π0.379951\pi
158158 0.680151 11.6777i 0.0541099 0.929031i
159159 −16.5057 + 2.79351i −1.30898 + 0.221540i
160160 −2.29416 2.43167i −0.181369 0.192240i
161161 9.64722 0.760307
162162 −8.32376 20.8558i −0.653976 1.63858i
163163 −6.49040 −0.508367 −0.254184 0.967156i 0.581807π-0.581807\pi
−0.254184 + 0.967156i 0.581807π0.581807\pi
164164 12.2799 + 13.0159i 0.958897 + 1.01637i
165165 −4.02441 + 10.8248i −0.313300 + 0.842710i
166166 2.17026 37.2619i 0.168445 2.89208i
167167 3.87721 0.453181i 0.300028 0.0350682i 0.0352527 0.999378i 0.488776π-0.488776\pi
0.264775 + 0.964310i 0.414702π0.414702\pi
168168 −24.4817 18.4889i −1.88880 1.42645i
169169 −7.55258 3.79305i −0.580967 0.291773i
170170 8.06013 6.76325i 0.618184 0.518718i
171171 −21.3135 0.293126i −1.62989 0.0224159i
172172 2.56973 + 2.15626i 0.195940 + 0.164413i
173173 6.46827 + 14.9951i 0.491774 + 1.14006i 0.965739 + 0.259516i 0.0835630π0.0835630\pi
−0.473965 + 0.880544i 0.657178π0.657178\pi
174174 8.71238 + 3.82942i 0.660484 + 0.290308i
175175 9.37077 + 2.22091i 0.708364 + 0.167885i
176176 7.33979 + 24.5166i 0.553258 + 1.84801i
177177 2.67003 0.779389i 0.200691 0.0585825i
178178 10.2696 + 1.20034i 0.769737 + 0.0899694i
179179 −3.76729 + 21.3654i −0.281581 + 1.59692i 0.435670 + 0.900107i 0.356512π0.356512\pi
−0.717250 + 0.696816i 0.754599π0.754599\pi
180180 −17.6913 2.31484i −1.31863 0.172538i
181181 −1.10326 6.25687i −0.0820043 0.465070i −0.997963 0.0637968i 0.979679π-0.979679\pi
0.915959 0.401273i 0.131432π-0.131432\pi
182182 −0.987041 16.9468i −0.0731644 1.25618i
183183 1.47173 1.36950i 0.108794 0.101237i
184184 6.65026 15.4170i 0.490264 1.13656i
185185 −8.45061 + 4.24406i −0.621301 + 0.312029i
186186 10.5471 12.3954i 0.773350 0.908877i
187187 −13.8095 + 3.27292i −1.00985 + 0.239339i
188188 12.2227 + 21.1703i 0.891429 + 1.54400i
189189 −16.5649 + 0.622293i −1.20492 + 0.0452652i
190190 −12.4765 + 21.6099i −0.905139 + 1.56775i
191191 −3.95814 + 13.2211i −0.286401 + 0.956646i 0.686830 + 0.726818i 0.259002π0.259002\pi
−0.973231 + 0.229828i 0.926184π0.926184\pi
192192 7.34743 4.17494i 0.530255 0.301301i
193193 −3.15541 2.07534i −0.227131 0.149387i 0.430843 0.902427i 0.358216π-0.358216\pi
−0.657974 + 0.753040i 0.728587π0.728587\pi
194194 −18.7551 25.1925i −1.34654 1.80871i
195195 −2.82722 4.36365i −0.202462 0.312487i
196196 −11.2158 + 7.37675i −0.801129 + 0.526911i
197197 −5.18414 1.88687i −0.369355 0.134434i 0.150673 0.988584i 0.451856π-0.451856\pi
−0.520027 + 0.854150i 0.674078π0.674078\pi
198198 29.3534 + 19.8897i 2.08606 + 1.41350i
199199 15.9504 5.80546i 1.13069 0.411538i 0.292148 0.956373i 0.405630π-0.405630\pi
0.838543 + 0.544835i 0.183408π0.183408\pi
200200 10.0089 13.4443i 0.707736 0.950654i
201201 5.75267 8.61687i 0.405762 0.607787i
202202 −7.71350 + 8.17583i −0.542720 + 0.575249i
203203 4.82105 5.11001i 0.338371 0.358653i
204204 −9.70538 19.6609i −0.679513 1.37654i
205205 3.55973 4.78155i 0.248622 0.333958i
206206 32.7307 11.9130i 2.28046 0.830018i
207207 −2.48216 8.72599i −0.172522 0.606499i
208208 −10.8271 3.94075i −0.750725 0.273242i
209209 28.1203 18.4950i 1.94512 1.27933i
210210 −8.82812 + 17.2809i −0.609198 + 1.19250i
211211 11.5293 + 15.4866i 0.793712 + 1.06614i 0.996221 + 0.0868601i 0.0276833π0.0276833\pi
−0.202508 + 0.979281i 0.564909π0.564909\pi
212212 34.1194 + 22.4407i 2.34333 + 1.54123i
213213 0.0427187 6.21255i 0.00292704 0.425677i
214214 3.25906 10.8860i 0.222785 0.744153i
215215 0.558746 0.967777i 0.0381062 0.0660018i
216216 −10.4244 + 26.9010i −0.709293 + 1.83038i
217217 −6.00721 10.4048i −0.407796 0.706323i
218218 −17.3286 + 4.10695i −1.17364 + 0.278158i
219219 −19.0358 3.49165i −1.28632 0.235944i
220220 25.1761 12.6439i 1.69737 0.852452i
221221 2.53079 5.86702i 0.170239 0.394659i
222222 6.50122 + 28.2965i 0.436333 + 1.89913i
223223 0.880079 + 15.1104i 0.0589345 + 1.01187i 0.890078 + 0.455808i 0.150650π0.150650\pi
−0.831144 + 0.556058i 0.812313π0.812313\pi
224224 1.31572 + 7.46180i 0.0879100 + 0.498562i
225225 −0.402198 9.04737i −0.0268132 0.603158i
226226 −3.39230 + 19.2387i −0.225653 + 1.27974i
227227 −6.25901 0.731573i −0.415425 0.0485562i −0.0941866 0.995555i 0.530025π-0.530025\pi
−0.321238 + 0.946998i 0.604099π0.604099\pi
228228 37.5762 + 35.9429i 2.48854 + 2.38038i
229229 −2.67203 8.92519i −0.176572 0.589793i −0.999758 0.0220199i 0.992990π-0.992990\pi
0.823185 0.567773i 0.192195π-0.192195\pi
230230 −10.3340 2.44921i −0.681406 0.161496i
231231 21.1021 15.4856i 1.38842 1.01888i
232232 −4.84285 11.2270i −0.317949 0.737088i
233233 −16.1221 13.5280i −1.05619 0.886251i −0.0624612 0.998047i 0.519895π-0.519895\pi
−0.993731 + 0.111797i 0.964339π0.964339\pi
234234 −15.0746 + 5.25309i −0.985458 + 0.343406i
235235 6.23822 5.23449i 0.406937 0.341460i
236236 −6.06355 3.04523i −0.394703 0.198227i
237237 −0.998152 + 8.05878i −0.0648369 + 0.523474i
238238 −23.6857 + 2.76846i −1.53532 + 0.179453i
239239 0.953580 16.3723i 0.0616819 1.05904i −0.815462 0.578811i 0.803517π-0.803517\pi
0.877144 0.480227i 0.159446π-0.159446\pi
240240 8.39666 + 10.1476i 0.542002 + 0.655027i
241241 −1.13385 1.20181i −0.0730377 0.0774155i 0.689824 0.723977i 0.257688π-0.257688\pi
−0.762862 + 0.646562i 0.776206π0.776206\pi
242242 −28.5417 −1.83473
243243 4.82490 + 14.8230i 0.309517 + 0.950894i
244244 −4.90421 −0.313960
245245 3.06887 + 3.25281i 0.196063 + 0.207814i
246246 −11.6677 14.1008i −0.743904 0.899032i
247247 −0.881085 + 15.1277i −0.0560621 + 0.962549i
248248 −20.7688 + 2.42752i −1.31882 + 0.154148i
249249 −3.18495 + 25.7143i −0.201838 + 1.62958i
250250 −25.1660 12.6388i −1.59164 0.799350i
251251 −16.6349 + 13.9583i −1.04998 + 0.881040i −0.993092 0.117340i 0.962563π-0.962563\pi
−0.0568910 + 0.998380i 0.518119π0.518119\pi
252252 30.6170 + 26.4166i 1.92869 + 1.66409i
253253 10.9736 + 9.20793i 0.689903 + 0.578898i
254254 10.1121 + 23.4424i 0.634487 + 1.47091i
255255 −5.88867 + 4.32134i −0.368763 + 0.270613i
256256 −31.5921 7.48747i −1.97451 0.467967i
257257 −1.76523 5.89628i −0.110112 0.367800i 0.885117 0.465369i 0.154078π-0.154078\pi
−0.995229 + 0.0975692i 0.968893π0.968893\pi
258258 −2.47935 2.37158i −0.154358 0.147648i
259259 21.2876 + 2.48817i 1.32275 + 0.154607i
260260 −2.20255 + 12.4913i −0.136596 + 0.774677i
261261 −5.86248 3.04591i −0.362878 0.188537i
262262 −3.72869 21.1464i −0.230359 1.30643i
263263 −1.48444 25.4869i −0.0915345 1.57159i −0.661517 0.749930i 0.730087π-0.730087\pi
0.569983 0.821657i 0.306950π-0.306950\pi
264264 −10.2006 44.3978i −0.627802 2.73250i
265265 5.38834 12.4916i 0.331003 0.767352i
266266 50.5390 25.3816i 3.09874 1.55625i
267267 −7.05983 1.29495i −0.432055 0.0792499i
268268 −24.5933 + 5.82872i −1.50228 + 0.356046i
269269 8.19176 + 14.1885i 0.499460 + 0.865091i 1.00000 0.000622889i 0.000198272π-0.000198272\pi
−0.500539 + 0.865714i 0.666865π0.666865\pi
270270 17.9022 + 3.53885i 1.08949 + 0.215368i
271271 13.6365 23.6192i 0.828361 1.43476i −0.0709627 0.997479i 0.522607π-0.522607\pi
0.899323 0.437284i 0.144060π-0.144060\pi
272272 −4.64215 + 15.5059i −0.281472 + 0.940182i
273273 −0.0810295 + 11.7841i −0.00490413 + 0.713203i
274274 2.22773 + 1.46520i 0.134582 + 0.0885160i
275275 8.53935 + 11.4703i 0.514942 + 0.691687i
276276 −10.0683 + 19.7085i −0.606038 + 1.18631i
277277 19.1354 12.5855i 1.14973 0.756192i 0.176115 0.984370i 0.443647π-0.443647\pi
0.973620 + 0.228177i 0.0732766π0.0732766\pi
278278 −17.4624 6.35580i −1.04733 0.381196i
279279 −7.86562 + 8.11066i −0.470902 + 0.485572i
280280 23.4278 8.52704i 1.40008 0.509588i
281281 17.9072 24.0535i 1.06825 1.43491i 0.175439 0.984490i 0.443866π-0.443866\pi
0.892815 0.450424i 0.148727π-0.148727\pi
282282 −11.0671 22.4195i −0.659037 1.33506i
283283 −10.6483 + 11.2865i −0.632975 + 0.670914i −0.961887 0.273446i 0.911836π-0.911836\pi
0.328912 + 0.944360i 0.393318π0.393318\pi
284284 −10.4005 + 11.0239i −0.617155 + 0.654146i
285285 9.61799 14.4067i 0.569721 0.853379i
286286 15.0524 20.2189i 0.890068 1.19557i
287287 −12.6958 + 4.62088i −0.749407 + 0.272762i
288288 6.41074 3.10995i 0.377756 0.183255i
289289 7.54012 + 2.74438i 0.443536 + 0.161434i
290290 −6.46159 + 4.24985i −0.379438 + 0.249560i
291291 11.8553 + 18.2979i 0.694967 + 1.07264i
292292 28.1930 + 37.8698i 1.64987 + 2.21616i
293293 6.43251 + 4.23073i 0.375791 + 0.247162i 0.723328 0.690505i 0.242612π-0.242612\pi
−0.347537 + 0.937666i 0.612982π0.612982\pi
294294 11.9376 6.78313i 0.696212 0.395600i
295295 −0.648280 + 2.16541i −0.0377443 + 0.126075i
296296 18.6508 32.3042i 1.08406 1.87764i
297297 −19.4363 15.1027i −1.12781 0.876350i
298298 −3.04574 5.27538i −0.176435 0.305595i
299299 −6.27559 + 1.48734i −0.362927 + 0.0860152i
300300 −14.3169 + 16.8259i −0.826586 + 0.971443i
301301 −2.26333 + 1.13669i −0.130456 + 0.0655177i
302302 −21.1264 + 48.9765i −1.21569 + 2.81828i
303303 5.71230 5.31551i 0.328163 0.305368i
304304 −2.23193 38.3208i −0.128010 2.19785i
305305 0.283694 + 1.60891i 0.0162443 + 0.0921258i
306306 8.59827 + 20.7116i 0.491531 + 1.18401i
307307 2.28454 12.9563i 0.130386 0.739454i −0.847577 0.530673i 0.821939π-0.821939\pi
0.977962 0.208781i 0.0669496π-0.0669496\pi
308308 −63.4202 7.41276i −3.61370 0.422381i
309309 −23.2110 + 6.77537i −1.32043 + 0.385437i
310310 3.79334 + 12.6706i 0.215447 + 0.719644i
311311 −5.33273 1.26388i −0.302391 0.0716681i 0.0766191 0.997060i 0.475587π-0.475587\pi
−0.379011 + 0.925392i 0.623736π0.623736\pi
312312 18.7760 + 8.25277i 1.06298 + 0.467221i
313313 9.57732 + 22.2027i 0.541342 + 1.25497i 0.941031 + 0.338321i 0.109859π0.109859\pi
−0.399688 + 0.916651i 0.630882π0.630882\pi
314314 12.3501 + 10.3630i 0.696959 + 0.584818i
315315 6.89532 11.5725i 0.388507 0.652039i
316316 15.1749 12.7332i 0.853653 0.716300i
317317 9.24502 + 4.64302i 0.519252 + 0.260778i 0.689067 0.724698i 0.258021π-0.258021\pi
−0.169815 + 0.985476i 0.554317π0.554317\pi
318318 −33.3309 25.1720i −1.86911 1.41158i
319319 10.3612 1.21105i 0.580116 0.0678059i
320320 −0.399312 + 6.85592i −0.0223222 + 0.383258i
321321 −2.74890 + 7.39395i −0.153429 + 0.412690i
322322 16.5181 + 17.5081i 0.920515 + 0.975689i
323323 21.2871 1.18444
324324 16.0165 34.4901i 0.889808 1.91612i
325325 −6.43816 −0.357125
326326 −11.1129 11.7790i −0.615488 0.652379i
327327 12.1893 2.06298i 0.674070 0.114083i
328328 −1.36722 + 23.4742i −0.0754920 + 1.29615i
329329 −18.3318 + 2.14268i −1.01066 + 0.118130i
330330 −26.5359 + 11.2307i −1.46075 + 0.618229i
331331 −27.4917 13.8069i −1.51108 0.758894i −0.515873 0.856665i 0.672532π-0.672532\pi
−0.995209 + 0.0977711i 0.968829π0.968829\pi
332332 48.4207 40.6298i 2.65743 2.22985i
333333 −3.22659 19.8951i −0.176816 1.09024i
334334 7.46105 + 6.26056i 0.408250 + 0.342563i
335335 3.33486 + 7.73108i 0.182203 + 0.422394i
336336 −3.26161 29.6729i −0.177935 1.61879i
337337 −32.0522 7.59650i −1.74599 0.413808i −0.771141 0.636664i 0.780314π-0.780314\pi
−0.974851 + 0.222856i 0.928462π0.928462\pi
338338 −6.04784 20.2012i −0.328959 1.09880i
339339 3.21814 13.1741i 0.174785 0.715517i
340340 17.6978 + 2.06857i 0.959796 + 0.112184i
341341 3.09789 17.5690i 0.167760 0.951414i
342342 −35.9612 39.1824i −1.94456 2.11874i
343343 2.11774 + 12.0103i 0.114347 + 0.648496i
344344 0.256304 + 4.40056i 0.0138190 + 0.237263i
345345 7.04812 + 2.16298i 0.379458 + 0.116451i
346346 −16.1387 + 37.4137i −0.867621 + 2.01137i
347347 −23.1751 + 11.6390i −1.24410 + 0.624812i −0.944268 0.329178i 0.893228π-0.893228\pi
−0.299836 + 0.953991i 0.596932π0.596932\pi
348348 5.40788 + 15.1820i 0.289893 + 0.813843i
349349 14.3802 3.40817i 0.769755 0.182435i 0.173069 0.984910i 0.444632π-0.444632\pi
0.596686 + 0.802475i 0.296484π0.296484\pi
350350 12.0141 + 20.8091i 0.642182 + 1.11229i
351351 10.6796 2.95866i 0.570037 0.157922i
352352 −5.62541 + 9.74350i −0.299836 + 0.519330i
353353 −1.98881 + 6.64309i −0.105854 + 0.353576i −0.994463 0.105089i 0.966487π-0.966487\pi
0.888609 + 0.458665i 0.151672π0.151672\pi
354354 5.98611 + 3.51118i 0.318158 + 0.186617i
355355 4.21820 + 2.77435i 0.223879 + 0.147247i
356356 10.4560 + 14.0448i 0.554167 + 0.744375i
357357 16.5326 0.848895i 0.875000 0.0449283i
358358 −45.2250 + 29.7450i −2.39022 + 1.57207i
359359 28.2850 + 10.2949i 1.49283 + 0.543344i 0.954192 0.299195i 0.0967182π-0.0967182\pi
0.538634 + 0.842540i 0.318940π0.318940\pi
360360 −13.7406 18.9967i −0.724194 1.00122i
361361 −29.5849 + 10.7680i −1.55710 + 0.566738i
362362 9.46619 12.7153i 0.497532 0.668301i
363363 19.7716 + 1.28803i 1.03774 + 0.0676042i
364364 19.7278 20.9102i 1.03402 1.09599i
365365 10.7929 11.4399i 0.564929 0.598789i
366366 5.00533 + 0.326076i 0.261633 + 0.0170443i
367367 −13.7405 + 18.4567i −0.717247 + 0.963430i 0.282744 + 0.959195i 0.408755π0.408755\pi
−0.999991 + 0.00423434i 0.998652π0.998652\pi
368368 15.3522 5.58774i 0.800288 0.291281i
369369 7.44615 + 10.2945i 0.387631 + 0.535911i
370370 −22.1715 8.06976i −1.15264 0.419527i
371371 −25.7607 + 16.9431i −1.33743 + 0.879641i
372372 27.5255 1.41334i 1.42713 0.0732784i
373373 −18.8164 25.2748i −0.974276 1.30868i −0.951079 0.308949i 0.900023π-0.900023\pi
−0.0231970 0.999731i 0.507385π-0.507385\pi
374374 −29.5846 19.4581i −1.52978 1.00615i
375375 16.8628 + 9.89094i 0.870789 + 0.510766i
376376 −9.21276 + 30.7728i −0.475112 + 1.58698i
377377 −2.34830 + 4.06738i −0.120944 + 0.209481i
378378 −29.4919 28.9970i −1.51690 1.49145i
379379 9.45804 + 16.3818i 0.485827 + 0.841477i 0.999867 0.0162889i 0.00518516π-0.00518516\pi
−0.514040 + 0.857766i 0.671852π0.671852\pi
380380 −41.1180 + 9.74514i −2.10931 + 0.499915i
381381 −5.94697 16.6955i −0.304673 0.855336i
382382 −30.7713 + 15.4539i −1.57440 + 0.790692i
383383 11.8079 27.3739i 0.603358 1.39874i −0.293302 0.956020i 0.594754π-0.594754\pi
0.896659 0.442721i 0.145987π-0.145987\pi
384384 28.0227 + 8.59983i 1.43003 + 0.438858i
385385 1.23679 + 21.2349i 0.0630327 + 1.08223i
386386 −1.63631 9.27997i −0.0832859 0.472338i
387387 1.61049 + 1.75474i 0.0818656 + 0.0891987i
388388 9.23585 52.3791i 0.468879 2.65915i
389389 −5.79263 0.677061i −0.293698 0.0343283i −0.0320318 0.999487i 0.510198π-0.510198\pi
−0.261666 + 0.965159i 0.584272π0.584272\pi
390390 3.07850 12.6024i 0.155886 0.638149i
391391 2.59845 + 8.67943i 0.131409 + 0.438938i
392392 −17.1646 4.06808i −0.866942 0.205469i
393393 1.62866 + 14.8169i 0.0821549 + 0.747416i
394394 −5.45197 12.6391i −0.274666 0.636748i
395395 −5.05517 4.24179i −0.254353 0.213428i
396396 9.61267 + 59.2714i 0.483055 + 2.97850i
397397 4.50462 3.77983i 0.226081 0.189704i −0.522710 0.852510i 0.675079π-0.675079\pi
0.748791 + 0.662806i 0.230635π0.230635\pi
398398 37.8463 + 19.0071i 1.89706 + 0.952742i
399399 −36.1551 + 15.3018i −1.81002 + 0.766047i
400400 16.1986 1.89335i 0.809931 0.0946674i
401401 −0.623901 + 10.7120i −0.0311561 + 0.534930i 0.946234 + 0.323484i 0.104854π0.104854\pi
−0.977390 + 0.211446i 0.932183π0.932183\pi
402402 25.4880 4.31373i 1.27123 0.215149i
403403 5.51187 + 5.84225i 0.274566 + 0.291023i
404404 −19.0349 −0.947023
405405 −12.2416 3.25934i −0.608289 0.161958i
406406 17.5285 0.869924
407407 21.8396 + 23.1486i 1.08255 + 1.14743i
408408 10.0401 27.0057i 0.497059 1.33698i
409409 −0.193574 + 3.32353i −0.00957161 + 0.164338i 0.990135 + 0.140117i 0.0447478π0.0447478\pi
−0.999707 + 0.0242216i 0.992289π0.992289\pi
410410 14.7727 1.72669i 0.729573 0.0852749i
411411 −1.47708 1.11552i −0.0728592 0.0550243i
412412 52.7115 + 26.4727i 2.59691 + 1.30422i
413413 3.92444 3.29300i 0.193109 0.162038i
414414 11.5863 19.4454i 0.569434 0.955692i
415415 −16.1303 13.5349i −0.791805 0.664403i
416416 −2.00629 4.65111i −0.0983665 0.228039i
417417 11.8098 + 5.19087i 0.578331 + 0.254198i
418418 81.7133 + 19.3664i 3.99673 + 0.947242i
419419 −0.820143 2.73947i −0.0400666 0.133832i 0.935616 0.353019i 0.114845π-0.114845\pi
−0.975683 + 0.219187i 0.929660π0.929660\pi
420420 −31.5457 + 9.20830i −1.53927 + 0.449319i
421421 6.24383 + 0.729799i 0.304306 + 0.0355682i 0.266875 0.963731i 0.414009π-0.414009\pi
0.0374302 + 0.999299i 0.488083π0.488083\pi
422422 −8.36498 + 47.4401i −0.407201 + 2.30935i
423423 6.65472 + 16.0300i 0.323564 + 0.779405i
424424 9.31841 + 52.8473i 0.452542 + 2.56649i
425425 0.525874 + 9.02891i 0.0255086 + 0.437967i
426426 11.3479 10.5597i 0.549808 0.511617i
427427 1.46659 3.39993i 0.0709731 0.164534i
428428 17.1967 8.63649i 0.831233 0.417461i
429429 −11.3396 + 13.3269i −0.547483 + 0.643427i
430430 2.71305 0.643004i 0.130835 0.0310084i
431431 −8.66111 15.0015i −0.417191 0.722596i 0.578465 0.815707i 0.303652π-0.303652\pi
−0.995656 + 0.0931115i 0.970319π0.970319\pi
432432 −26.0002 + 10.5848i −1.25094 + 0.509261i
433433 −6.83316 + 11.8354i −0.328381 + 0.568772i −0.982191 0.187887i 0.939836π-0.939836\pi
0.653810 + 0.756659i 0.273170π0.273170\pi
434434 8.59739 28.7173i 0.412688 1.37847i
435435 4.66790 2.65238i 0.223808 0.127172i
436436 −25.1969 16.5723i −1.20671 0.793668i
437437 −12.8308 17.2348i −0.613781 0.824451i
438438 −26.2565 40.5252i −1.25458 1.93637i
439439 31.1535 20.4900i 1.48688 0.977934i 0.492696 0.870202i 0.336012π-0.336012\pi
0.994180 0.107732i 0.0343588π-0.0343588\pi
440440 34.7876 + 12.6617i 1.65843 + 0.603621i
441441 −8.57556 + 4.16013i −0.408360 + 0.198102i
442442 14.9809 5.45261i 0.712570 0.259354i
443443 −2.66634 + 3.58151i −0.126682 + 0.170163i −0.860939 0.508708i 0.830123π-0.830123\pi
0.734257 + 0.678871i 0.237531π0.237531\pi
444444 −27.2999 + 40.8922i −1.29559 + 1.94066i
445445 4.00280 4.24272i 0.189751 0.201124i
446446 −25.9160 + 27.4693i −1.22716 + 1.30071i
447447 1.87180 + 3.79184i 0.0885330 + 0.179348i
448448 9.29471 12.4850i 0.439134 0.589859i
449449 −3.44438 + 1.25365i −0.162550 + 0.0591635i −0.422014 0.906589i 0.638677π-0.638677\pi
0.259463 + 0.965753i 0.416454π0.416454\pi
450450 15.7309 16.2209i 0.741559 0.764662i
451451 −18.8517 6.86146i −0.887693 0.323094i
452452 −27.6402 + 18.1793i −1.30009 + 0.855080i
453453 16.8450 32.9739i 0.791448 1.54925i
454454 −9.38905 12.6117i −0.440650 0.591896i
455455 −8.00114 5.26243i −0.375099 0.246707i
456456 −0.469830 + 68.3269i −0.0220018 + 3.19970i
457457 5.26887 17.5993i 0.246467 0.823259i −0.741813 0.670607i 0.766034π-0.766034\pi
0.988280 0.152651i 0.0487812π-0.0487812\pi
458458 11.6227 20.1311i 0.543092 0.940664i
459459 −5.02157 14.7355i −0.234387 0.687795i
460460 −8.99256 15.5756i −0.419280 0.726215i
461461 −11.7380 + 2.78196i −0.546694 + 0.129569i −0.494676 0.869077i 0.664713π-0.664713\pi
−0.0520176 + 0.998646i 0.516565π0.516565\pi
462462 64.2351 + 11.7824i 2.98849 + 0.548165i
463463 2.46047 1.23569i 0.114348 0.0574275i −0.390706 0.920516i 0.627769π-0.627769\pi
0.505053 + 0.863088i 0.331473π0.331473\pi
464464 4.71226 10.9242i 0.218761 0.507145i
465465 −2.05594 8.94846i −0.0953420 0.414975i
466466 −3.05322 52.4217i −0.141438 2.42839i
467467 5.46587 + 30.9985i 0.252930 + 1.43444i 0.801330 + 0.598223i 0.204126π0.204126\pi
−0.548399 + 0.836216i 0.684763π0.684763\pi
468468 −23.9893 12.4639i −1.10891 0.576144i
469469 3.31368 18.7928i 0.153011 0.867771i
470470 20.1809 + 2.35881i 0.930874 + 0.108804i
471471 −8.08760 7.73605i −0.372657 0.356459i
472472 −2.55718 8.54159i −0.117704 0.393158i
473473 −3.65944 0.867304i −0.168261 0.0398787i
474474 −16.3344 + 11.9868i −0.750264 + 0.550573i
475475 −8.49548 19.6947i −0.389799 0.903656i
476476 −30.9360 25.9584i −1.41795 1.18980i
477477 21.9532 + 18.9414i 1.00517 + 0.867269i
478478 31.3458 26.3023i 1.43372 1.20304i
479479 2.49117 + 1.25111i 0.113825 + 0.0571648i 0.504800 0.863236i 0.331566π-0.331566\pi
−0.390976 + 0.920401i 0.627862π0.627862\pi
480480 −0.711753 + 5.74648i −0.0324869 + 0.262290i
481481 −14.2314 + 1.66341i −0.648895 + 0.0758450i
482482 0.239701 4.11551i 0.0109181 0.187456i
483483 −10.6524 12.8737i −0.484700 0.585776i
484484 −33.1691 35.1572i −1.50769 1.59806i
485485 −17.7181 −0.804538
486486 −18.6400 + 34.1364i −0.845528 + 1.54846i
487487 −31.6987 −1.43640 −0.718202 0.695835i 0.755035π-0.755035\pi
−0.718202 + 0.695835i 0.755035π0.755035\pi
488488 −4.42238 4.68745i −0.200192 0.212191i
489489 7.16664 + 8.66112i 0.324087 + 0.391670i
490490 −0.648772 + 11.1390i −0.0293085 + 0.503208i
491491 34.9560 4.08577i 1.57754 0.184388i 0.718217 0.695819i 0.244959π-0.244959\pi
0.859324 + 0.511431i 0.170884π0.170884\pi
492492 3.80977 30.7589i 0.171758 1.38672i
493493 5.89592 + 2.96104i 0.265539 + 0.133359i
494494 −28.9628 + 24.3027i −1.30310 + 1.09343i
495495 18.8889 6.58227i 0.848993 0.295851i
496496 −15.5862 13.0783i −0.699839 0.587235i
497497 −4.53226 10.5070i −0.203300 0.471302i
498498 −52.1206 + 38.2482i −2.33558 + 1.71394i
499499 −7.77433 1.84255i −0.348027 0.0824838i 0.0528848 0.998601i 0.483158π-0.483158\pi
−0.400912 + 0.916117i 0.631307π0.631307\pi
500500 −13.6778 45.6870i −0.611689 2.04318i
501501 −4.88593 4.67355i −0.218287 0.208799i
502502 −53.8144 6.29000i −2.40185 0.280736i
503503 −2.70376 + 15.3338i −0.120555 + 0.683700i 0.863294 + 0.504701i 0.168397π0.168397\pi
−0.983849 + 0.178999i 0.942714π0.942714\pi
504504 2.35988 + 53.0850i 0.105117 + 2.36459i
505505 1.10111 + 6.24473i 0.0489989 + 0.277887i
506506 2.07819 + 35.6812i 0.0923868 + 1.58622i
507507 3.27785 + 14.2668i 0.145574 + 0.633611i
508508 −17.1244 + 39.6989i −0.759774 + 1.76136i
509509 −15.4415 + 7.75504i −0.684435 + 0.343736i −0.756804 0.653642i 0.773240π-0.773240\pi
0.0723693 + 0.997378i 0.476944π0.476944\pi
510510 −17.9252 3.28793i −0.793739 0.145592i
511511 −34.6849 + 8.22048i −1.53437 + 0.363653i
512512 −23.5802 40.8420i −1.04211 1.80498i
513513 23.1430 + 28.7655i 1.02179 + 1.27003i
514514 7.67834 13.2993i 0.338677 0.586606i
515515 5.63561 18.8243i 0.248335 0.829496i
516516 0.0399515 5.81011i 0.00175877 0.255776i
517517 −22.8973 15.0598i −1.00702 0.662329i
518518 31.9333 + 42.8939i 1.40307 + 1.88465i
519519 12.8681 25.1891i 0.564846 1.10568i
520520 −13.9253 + 9.15885i −0.610667 + 0.401642i
521521 −33.0219 12.0190i −1.44672 0.526562i −0.505045 0.863093i 0.668524π-0.668524\pi
−0.941672 + 0.336531i 0.890746π0.890746\pi
522522 −4.50996 15.8547i −0.197395 0.693940i
523523 2.55225 0.928943i 0.111602 0.0406198i −0.285616 0.958344i 0.592198π-0.592198\pi
0.397218 + 0.917724i 0.369976π0.369976\pi
524524 21.7146 29.1678i 0.948607 1.27420i
525525 −7.38342 14.9572i −0.322239 0.652784i
526526 43.7128 46.3328i 1.90597 2.02021i
527527 7.74298 8.20708i 0.337290 0.357506i
528528 24.6117 36.8656i 1.07109 1.60437i
529529 −8.27369 + 11.1135i −0.359726 + 0.483195i
530530 31.8961 11.6092i 1.38548 0.504273i
531531 −3.98828 2.70243i −0.173076 0.117275i
532532 89.9974 + 32.7564i 3.90188 + 1.42017i
533533 7.54627 4.96326i 0.326865 0.214983i
534534 −9.73778 15.0297i −0.421395 0.650397i
535535 −3.82812 5.14206i −0.165504 0.222311i
536536 −27.7482 18.2503i −1.19854 0.788291i
537537 32.6709 18.5642i 1.40985 0.801104i
538538 −11.7239 + 39.1605i −0.505452 + 1.68833i
539539 7.52504 13.0337i 0.324126 0.561403i
540540 16.4455 + 26.1642i 0.707702 + 1.12593i
541541 19.9581 + 34.5684i 0.858065 + 1.48621i 0.873772 + 0.486336i 0.161667π0.161667\pi
−0.0157071 + 0.999877i 0.505000π0.505000\pi
542542 66.2135 15.6929i 2.84412 0.674068i
543543 −7.13129 + 8.38102i −0.306033 + 0.359664i
544544 −6.35886 + 3.19354i −0.272634 + 0.136922i
545545 −3.97924 + 9.22493i −0.170452 + 0.395152i
546546 −21.5249 + 20.0297i −0.921179 + 0.857193i
547547 0.540346 + 9.27738i 0.0231035 + 0.396672i 0.989960 + 0.141350i 0.0451444π0.0451444\pi
−0.966856 + 0.255322i 0.917819π0.917819\pi
548548 0.784096 + 4.44683i 0.0334949 + 0.189959i
549549 −3.45261 0.451762i −0.147354 0.0192807i
550550 −6.19562 + 35.1371i −0.264182 + 1.49825i
551551 −15.5411 1.81649i −0.662071 0.0773850i
552552 −27.9165 + 8.14890i −1.18820 + 0.346840i
553553 4.28954 + 14.3281i 0.182410 + 0.609292i
554554 55.6045 + 13.1785i 2.36241 + 0.559901i
555555 14.9946 + 6.59069i 0.636485 + 0.279759i
556556 −12.4646 28.8962i −0.528617 1.22547i
557557 28.8895 + 24.2411i 1.22409 + 1.02713i 0.998601 + 0.0528835i 0.0168412π0.0168412\pi
0.225485 + 0.974247i 0.427603π0.427603\pi
558558 −28.1871 0.387659i −1.19326 0.0164109i
559559 1.29707 1.08837i 0.0548602 0.0460332i
560560 21.6787 + 10.8875i 0.916093 + 0.460079i
561561 19.6159 + 14.8142i 0.828184 + 0.625457i
562562 74.3141 8.68607i 3.13475 0.366400i
563563 2.31955 39.8251i 0.0977572 1.67843i −0.491806 0.870705i 0.663663π-0.663663\pi
0.589564 0.807722i 0.299300π-0.299300\pi
564564 14.7546 39.6866i 0.621279 1.67111i
565565 7.56291 + 8.01622i 0.318174 + 0.337245i
566566 −38.7153 −1.62732
567567 19.1212 + 21.4179i 0.803015 + 0.899467i
568568 −19.9153 −0.835626
569569 −21.4166 22.7003i −0.897831 0.951646i 0.101234 0.994863i 0.467721π-0.467721\pi
−0.999066 + 0.0432171i 0.986239π0.986239\pi
570570 42.6138 7.21220i 1.78490 0.302086i
571571 1.25067 21.4732i 0.0523390 0.898627i −0.865311 0.501236i 0.832879π-0.832879\pi
0.917650 0.397390i 0.130084π-0.130084\pi
572572 42.3982 4.95563i 1.77276 0.207205i
573573 22.0135 9.31669i 0.919626 0.389210i
574574 −30.1239 15.1288i −1.25735 0.631464i
575575 6.99316 5.86796i 0.291635 0.244711i
576576 −13.6842 5.19485i −0.570176 0.216452i
577577 1.05985 + 0.889324i 0.0441223 + 0.0370230i 0.664582 0.747215i 0.268610π-0.268610\pi
−0.620460 + 0.784238i 0.713054π0.713054\pi
578578 7.92966 + 18.3830i 0.329831 + 0.764633i
579579 0.714726 + 6.50232i 0.0297030 + 0.270227i
580580 −12.7441 3.02040i −0.529170 0.125415i
581581 13.6873 + 45.7187i 0.567844 + 1.89673i
582582 −12.9089 + 52.8451i −0.535092 + 2.19050i
583583 −45.4740 5.31515i −1.88334 0.220131i
584584 −10.7729 + 61.0961i −0.445785 + 2.52817i
585585 −2.70128 + 8.59109i −0.111684 + 0.355198i
586586 3.33572 + 18.9178i 0.137797 + 0.781488i
587587 0.466073 + 8.00217i 0.0192369 + 0.330285i 0.994173 + 0.107799i 0.0343802π0.0343802\pi
−0.974936 + 0.222486i 0.928583π0.928583\pi
588588 22.2283 + 6.82161i 0.916680 + 0.281318i
589589 −10.5986 + 24.5703i −0.436707 + 1.01240i
590590 −5.03985 + 2.53111i −0.207487 + 0.104204i
591591 3.20634 + 9.00145i 0.131891 + 0.370270i
592592 35.3175 8.37039i 1.45154 0.344021i
593593 −10.7066 18.5444i −0.439668 0.761527i 0.557996 0.829844i 0.311571π-0.311571\pi
−0.997664 + 0.0683166i 0.978237π0.978237\pi
594594 −5.86999 61.1327i −0.240849 2.50831i
595595 −6.72652 + 11.6507i −0.275761 + 0.477631i
596596 2.95859 9.88237i 0.121188 0.404798i
597597 −25.3594 14.8747i −1.03789 0.608779i
598598 −13.4444 8.84252i −0.549782 0.361598i
599599 −13.8938 18.6626i −0.567684 0.762531i 0.421876 0.906653i 0.361372π-0.361372\pi
−0.989560 + 0.144122i 0.953964π0.953964\pi
600600 −28.9925 + 1.48867i −1.18361 + 0.0607745i
601601 26.3770 17.3485i 1.07594 0.707658i 0.117537 0.993069i 0.462500π-0.462500\pi
0.958405 + 0.285410i 0.0921298π0.0921298\pi
602602 −5.93821 2.16133i −0.242023 0.0880893i
603603 −17.8509 + 1.83801i −0.726943 + 0.0748494i
604604 −84.8800 + 30.8938i −3.45372 + 1.25705i
605605 −9.61519 + 12.9154i −0.390913 + 0.525087i
606606 19.4274 + 1.26561i 0.789185 + 0.0514120i
607607 3.23033 3.42395i 0.131115 0.138974i −0.658489 0.752590i 0.728804π-0.728804\pi
0.789605 + 0.613616i 0.210286π0.210286\pi
608608 11.5806 12.2747i 0.469656 0.497806i
609609 −12.1424 0.791026i −0.492036 0.0320540i
610610 −2.43416 + 3.26965i −0.0985563 + 0.132384i
611611 11.5946 4.22010i 0.469069 0.170727i
612612 −15.5200 + 34.6608i −0.627357 + 1.40108i
613613 41.2145 + 15.0009i 1.66464 + 0.605879i 0.991082 0.133255i 0.0425429π-0.0425429\pi
0.673558 + 0.739134i 0.264765π0.264765\pi
614614 27.4251 18.0378i 1.10679 0.727946i
615615 −10.3114 + 0.529454i −0.415795 + 0.0213496i
616616 −50.1041 67.3015i −2.01875 2.71166i
617617 14.8817 + 9.78784i 0.599114 + 0.394044i 0.812531 0.582918i 0.198089π-0.198089\pi
−0.213417 + 0.976961i 0.568459π0.568459\pi
618618 −52.0383 30.5233i −2.09329 1.22783i
619619 −1.60750 + 5.36943i −0.0646109 + 0.215816i −0.984198 0.177070i 0.943338π-0.943338\pi
0.919587 + 0.392886i 0.128523π0.128523\pi
620620 −11.1991 + 19.3975i −0.449768 + 0.779021i
621621 −8.90364 + 12.9475i −0.357291 + 0.519565i
622622 −6.83702 11.8421i −0.274139 0.474823i
623623 −12.8637 + 3.04874i −0.515372 + 0.122145i
624624 6.69646 + 18.7996i 0.268073 + 0.752586i
625625 −0.708810 + 0.355978i −0.0283524 + 0.0142391i
626626 −23.8959 + 55.3970i −0.955074 + 2.21411i
627627 −55.7309 17.1032i −2.22568 0.683035i
628628 1.58747 + 27.2558i 0.0633470 + 1.08763i
629629 3.49521 + 19.8223i 0.139363 + 0.790367i
630630 32.8085 7.30074i 1.30712 0.290868i
631631 −2.84022 + 16.1077i −0.113067 + 0.641237i 0.874622 + 0.484806i 0.161110π0.161110\pi
−0.987689 + 0.156431i 0.950001π0.950001\pi
632632 25.8544 + 3.02195i 1.02843 + 0.120207i
633633 7.93551 32.4855i 0.315408 1.29118i
634634 7.40308 + 24.7280i 0.294014 + 0.982075i
635635 14.0145 + 3.32150i 0.556149 + 0.131810i
636636 −7.72833 70.3096i −0.306448 2.78796i
637637 2.68379 + 6.22172i 0.106336 + 0.246514i
638638 19.9384 + 16.7303i 0.789369 + 0.662360i
639639 −8.33752 + 6.80284i −0.329827 + 0.269116i
640640 −18.2480 + 15.3119i −0.721314 + 0.605255i
641641 20.8476 + 10.4700i 0.823429 + 0.413541i 0.810044 0.586369i 0.199443π-0.199443\pi
0.0133847 + 0.999910i 0.495739π0.495739\pi
642642 −18.1255 + 7.67119i −0.715357 + 0.302758i
643643 14.4953 1.69426i 0.571638 0.0668149i 0.174637 0.984633i 0.444125π-0.444125\pi
0.397002 + 0.917818i 0.370051π0.370051\pi
644644 −2.37012 + 40.6933i −0.0933957 + 1.60354i
645645 −1.90841 + 0.322991i −0.0751438 + 0.0127177i
646646 36.4479 + 38.6325i 1.43402 + 1.51998i
647647 1.33592 0.0525205 0.0262602 0.999655i 0.491640π-0.491640\pi
0.0262602 + 0.999655i 0.491640π0.491640\pi
648648 47.4087 15.7929i 1.86239 0.620405i
649649 7.60705 0.298603
650650 −11.0235 11.6842i −0.432377 0.458292i
651651 −7.25159 + 19.5052i −0.284212 + 0.764470i
652652 1.59455 27.3774i 0.0624475 1.07218i
653653 −16.3676 + 1.91310i −0.640514 + 0.0748654i −0.430150 0.902758i 0.641539π-0.641539\pi
−0.210365 + 0.977623i 0.567465π0.567465\pi
654654 24.6146 + 18.5893i 0.962507 + 0.726900i
655655 −10.8251 5.43657i −0.422972 0.212424i
656656 −17.5271 + 14.7069i −0.684316 + 0.574210i
657657 16.3597 + 29.2578i 0.638252 + 1.14145i
658658 −35.2765 29.6005i −1.37522 1.15395i
659659 −17.8283 41.3307i −0.694493 1.61002i −0.788929 0.614484i 0.789364π-0.789364\pi
0.0944361 0.995531i 0.469895π-0.469895\pi
660660 −44.6719 19.6350i −1.73885 0.764290i
661661 24.2010 + 5.73574i 0.941310 + 0.223094i 0.672499 0.740098i 0.265221π-0.265221\pi
0.268811 + 0.963193i 0.413369π0.413369\pi
662662 −22.0144 73.5332i −0.855614 2.85795i
663663 −10.6237 + 3.10110i −0.412591 + 0.120437i
664664 82.4975 + 9.64257i 3.20152 + 0.374204i
665665 5.54020 31.4200i 0.214840 1.21842i
666666 30.5817 39.9203i 1.18502 1.54688i
667667 −1.15641 6.55832i −0.0447764 0.253939i
668668 0.959034 + 16.4660i 0.0371061 + 0.637087i
669669 19.1923 17.8592i 0.742017 0.690475i
670670 −8.32066 + 19.2895i −0.321455 + 0.745217i
671671 4.91333 2.46757i 0.189677 0.0952594i
672672 8.50461 9.99501i 0.328072 0.385566i
673673 1.92706 0.456722i 0.0742827 0.0176053i −0.193306 0.981138i 0.561921π-0.561921\pi
0.267589 + 0.963533i 0.413773π0.413773\pi
674674 −41.0936 71.1762i −1.58287 2.74161i
675675 −11.6292 + 10.5267i −0.447607 + 0.405175i
676676 17.8551 30.9260i 0.686735 1.18946i
677677 −8.17155 + 27.2949i −0.314058 + 1.04903i 0.644613 + 0.764509i 0.277019π0.277019\pi
−0.958671 + 0.284518i 0.908167π0.908167\pi
678678 29.4189 16.7163i 1.12983 0.641987i
679679 33.5508 + 22.0667i 1.28756 + 0.846842i
680680 13.9818 + 18.7809i 0.536179 + 0.720214i
681681 5.93489 + 9.16014i 0.227426 + 0.351017i
682682 37.1891 24.4596i 1.42404 0.936608i
683683 27.6811 + 10.0751i 1.05919 + 0.385512i 0.812123 0.583487i 0.198312π-0.198312\pi
0.247064 + 0.968999i 0.420534π0.420534\pi
684684 6.47273 89.8314i 0.247491 3.43479i
685685 1.41350 0.514472i 0.0540071 0.0196570i
686686 −18.1707 + 24.4075i −0.693762 + 0.931884i
687687 −8.95981 + 13.4208i −0.341838 + 0.512036i
688688 −2.94340 + 3.11982i −0.112216 + 0.118942i
689689 14.1454 14.9932i 0.538895 0.571196i
690690 8.14239 + 16.4947i 0.309976 + 0.627941i
691691 29.0246 38.9868i 1.10415 1.48313i 0.246320 0.969189i 0.420779π-0.420779\pi
0.857827 0.513938i 0.171814π-0.171814\pi
692692 −64.8408 + 23.6001i −2.46488 + 0.897141i
693693 −43.9656 11.0607i −1.67011 0.420163i
694694 −60.8034 22.1306i −2.30807 0.840067i
695695 −8.75884 + 5.76078i −0.332242 + 0.218519i
696696 −9.63445 + 18.8593i −0.365193 + 0.714860i
697697 −7.57688 10.1775i −0.286995 0.385501i
698698 30.8072 + 20.2622i 1.16607 + 0.766936i
699699 −0.250649 + 36.4517i −0.00948041 + 1.37873i
700700 −11.6703 + 38.9816i −0.441097 + 1.47337i
701701 3.03784 5.26170i 0.114738 0.198732i −0.802937 0.596064i 0.796731π-0.796731\pi
0.917675 + 0.397332i 0.130064π0.130064\pi
702702 23.6553 + 14.3159i 0.892810 + 0.540320i
703703 −23.8675 41.3397i −0.900179 1.55916i
704704 22.4891 5.33001i 0.847589 0.200882i
705705 −13.8734 2.54473i −0.522501 0.0958400i
706706 −15.4614 + 7.76500i −0.581897 + 0.292240i
707707 5.69232 13.1963i 0.214082 0.496297i
708708 2.63161 + 11.4540i 0.0989018 + 0.430469i
709709 1.26191 + 21.6661i 0.0473919 + 0.813688i 0.935341 + 0.353747i 0.115092π0.115092\pi
−0.887949 + 0.459941i 0.847871π0.847871\pi
710710 2.18745 + 12.4056i 0.0820934 + 0.465575i
711711 11.8562 7.56644i 0.444642 0.283764i
712712 −3.99536 + 22.6588i −0.149733 + 0.849175i
713713 −11.3118 1.32216i −0.423632 0.0495155i
714714 29.8479 + 28.5505i 1.11703 + 1.06848i
715715 −4.07839 13.6228i −0.152523 0.509462i
716716 −89.1966 21.1400i −3.33343 0.790038i
717717 −22.9010 + 16.8057i −0.855254 + 0.627619i
718718 29.7463 + 68.9597i 1.11012 + 2.57355i
719719 −11.8323 9.92847i −0.441270 0.370269i 0.394915 0.918718i 0.370774π-0.370774\pi
−0.836184 + 0.548449i 0.815219π0.815219\pi
720720 4.27002 22.4099i 0.159134 0.835167i
721721 −34.1158 + 28.6266i −1.27054 + 1.06611i
722722 −70.1977 35.2546i −2.61249 1.31204i
723723 −0.351772 + 2.84010i −0.0130825 + 0.105624i
724724 26.6634 3.11651i 0.990938 0.115824i
725725 0.386539 6.63661i 0.0143557 0.246478i
726726 31.5155 + 38.0876i 1.16965 + 1.41356i
727727 17.6753 + 18.7348i 0.655542 + 0.694833i 0.966812 0.255488i 0.0822361π-0.0822361\pi
−0.311271 + 0.950321i 0.600755π0.600755\pi
728728 37.7756 1.40006
729729 14.4529 22.8060i 0.535294 0.844666i
730730 39.2412 1.45238
731731 −1.63228 1.73012i −0.0603721 0.0639907i
732732 5.41518 + 6.54443i 0.200151 + 0.241889i
733733 −1.69715 + 29.1389i −0.0626857 + 1.07627i 0.809507 + 0.587110i 0.199734π0.199734\pi
−0.872193 + 0.489162i 0.837303π0.837303\pi
734734 −57.0224 + 6.66496i −2.10473 + 0.246008i
735735 0.952102 7.68698i 0.0351188 0.283539i
736736 6.41842 + 3.22345i 0.236586 + 0.118818i
737737 21.7063 18.2138i 0.799563 0.670913i
738738 −5.93346 + 31.1399i −0.218414 + 1.14628i
739739 15.6599 + 13.1402i 0.576058 + 0.483370i 0.883650 0.468148i 0.155079π-0.155079\pi
−0.307592 + 0.951518i 0.599523π0.599523\pi
740740 −15.8259 36.6886i −0.581772 1.34870i
741741 21.1600 15.5281i 0.777332 0.570437i
742742 −74.8566 17.7413i −2.74807 0.651305i
743743 6.73922 + 22.5106i 0.247238 + 0.825832i 0.988052 + 0.154122i 0.0492549π0.0492549\pi
−0.740814 + 0.671710i 0.765560π0.765560\pi
744744 26.1721 + 25.0345i 0.959515 + 0.917808i
745745 −3.41322 0.398948i −0.125051 0.0146163i
746746 13.6520 77.4244i 0.499836 2.83471i
747747 37.8313 24.1434i 1.38418 0.883360i
748748 −10.4129 59.0546i −0.380734 2.15925i
749749 0.844797 + 14.5046i 0.0308682 + 0.529987i
750750 10.9221 + 47.5385i 0.398820 + 1.73586i
751751 13.9011 32.2264i 0.507259 1.17596i −0.451637 0.892202i 0.649160π-0.649160\pi
0.958896 0.283757i 0.0915810π-0.0915810\pi
752752 −27.9314 + 14.0277i −1.01855 + 0.511537i
753753 36.9947 + 6.78578i 1.34816 + 0.247288i
754754 −11.4024 + 2.70242i −0.415251 + 0.0984163i
755755 15.0453 + 26.0592i 0.547554 + 0.948391i
756756 1.44472 70.0259i 0.0525439 2.54682i
757757 −23.1445 + 40.0875i −0.841202 + 1.45701i 0.0476764 + 0.998863i 0.484818π0.484818\pi
−0.888879 + 0.458142i 0.848515π0.848515\pi
758758 −13.5361 + 45.2139i −0.491655 + 1.64224i
759759 0.170606 24.8110i 0.00619259 0.900583i
760760 −46.3926 30.5129i −1.68284 1.10682i
761761 4.23035 + 5.68235i 0.153350 + 0.205985i 0.872159 0.489223i 0.162720π-0.162720\pi
−0.718809 + 0.695208i 0.755312π0.755312\pi
762762 20.1171 39.3790i 0.728766 1.42655i
763763 19.0241 12.5123i 0.688717 0.452976i
764764 −54.7961 19.9441i −1.98245 0.721554i
765765 12.2688 + 3.08656i 0.443581 + 0.111595i
766766 69.8968 25.4404i 2.52547 0.919198i
767767 −2.04519 + 2.74716i −0.0738474 + 0.0991943i
768768 24.8921 + 50.4257i 0.898215 + 1.81958i
769769 29.7305 31.5125i 1.07211 1.13637i 0.0819197 0.996639i 0.473895π-0.473895\pi
0.990190 0.139731i 0.0446236π-0.0446236\pi
770770 −36.4202 + 38.6031i −1.31249 + 1.39116i
771771 −5.91915 + 8.86624i −0.213173 + 0.319310i
772772 9.52931 12.8001i 0.342967 0.460685i
773773 33.8164 12.3082i 1.21629 0.442694i 0.347409 0.937714i 0.387062π-0.387062\pi
0.868881 + 0.495020i 0.164839π0.164839\pi
774774 −0.427083 + 5.92726i −0.0153512 + 0.213051i
775775 −10.6833 3.88841i −0.383756 0.139676i
776776 58.3924 38.4053i 2.09617 1.37867i
777777 −20.1853 31.1548i −0.724143 1.11767i
778778 −8.68943 11.6719i −0.311531 0.418459i
779779 25.1406 + 16.5352i 0.900755 + 0.592436i
780780 19.1011 10.8536i 0.683928 0.388620i
781781 4.87314 16.2774i 0.174375 0.582452i
782782 −11.3026 + 19.5768i −0.404182 + 0.700063i
783783 2.40867 + 11.1865i 0.0860789 + 0.399771i
784784 −8.58220 14.8648i −0.306507 0.530886i
785785 8.84990 2.09747i 0.315867 0.0748618i
786786 −24.1017 + 28.3254i −0.859679 + 1.01034i
787787 18.7666 9.42494i 0.668957 0.335963i −0.0816980 0.996657i 0.526034π-0.526034\pi
0.750655 + 0.660694i 0.229738π0.229738\pi
788788 9.23273 21.4039i 0.328902 0.762481i
789789 −32.3719 + 30.1233i −1.15247 + 1.07242i
790790 −0.957355 16.4371i −0.0340611 0.584807i
791791 −4.33738 24.5985i −0.154219 0.874622i
792792 −47.9834 + 62.6359i −1.70502 + 2.22567i
793793 −0.429848 + 2.43779i −0.0152643 + 0.0865683i
794794 14.5726 + 1.70330i 0.517163 + 0.0604477i
795795 −22.6192 + 6.60261i −0.802219 + 0.234170i
796796 20.5696 + 68.7072i 0.729070 + 2.43526i
797797 −41.0669 9.73304i −1.45467 0.344762i −0.574139 0.818758i 0.694663π-0.694663\pi
−0.880527 + 0.473996i 0.842811π0.842811\pi
798798 −89.6752 39.4157i −3.17447 1.39530i
799799 −6.86535 15.9157i −0.242879 0.563056i
800800 5.49242 + 4.60868i 0.194186 + 0.162942i
801801 6.06735 + 10.8509i 0.214379 + 0.383397i
802802 −20.5087 + 17.2089i −0.724188 + 0.607666i
803803 −47.2998 23.7549i −1.66917 0.838291i
804804 34.9339 + 26.3826i 1.23202 + 0.930442i
805805 13.4872 1.57643i 0.475363 0.0555619i
806806 −1.16523 + 20.0063i −0.0410436 + 0.704692i
807807 9.88866 26.5984i 0.348097 0.936307i
808808 −17.1648 18.1936i −0.603855 0.640048i
809809 15.1427 0.532390 0.266195 0.963919i 0.414233π-0.414233\pi
0.266195 + 0.963919i 0.414233π0.414233\pi
810810 −15.0450 27.7971i −0.528627 0.976692i
811811 30.4862 1.07051 0.535257 0.844689i 0.320215π-0.320215\pi
0.535257 + 0.844689i 0.320215π0.320215\pi
812812 20.3703 + 21.5913i 0.714858 + 0.757706i
813813 −46.5760 + 7.88278i −1.63349 + 0.276461i
814814 −4.61698 + 79.2704i −0.161825 + 2.77843i
815815 −9.07386 + 1.06058i −0.317844 + 0.0371506i
816816 25.8177 10.9267i 0.903799 0.382512i
817817 5.04094 + 2.53165i 0.176360 + 0.0885714i
818818 −6.36311 + 5.33928i −0.222481 + 0.186684i
819819 15.8147 12.9037i 0.552611 0.450892i
820820 19.2947 + 16.1902i 0.673800 + 0.565386i
821821 −17.6031 40.8085i −0.614352 1.42423i −0.886844 0.462070i 0.847107π-0.847107\pi
0.272492 0.962158i 0.412152π-0.412152\pi
822822 −0.504599 4.59066i −0.0175999 0.160118i
823823 −23.0619 5.46577i −0.803888 0.190525i −0.191923 0.981410i 0.561472π-0.561472\pi
−0.611965 + 0.790885i 0.709621π0.709621\pi
824824 22.2300 + 74.2535i 0.774420 + 2.58674i
825825 5.87754 24.0608i 0.204630 0.837689i
826826 12.6957 + 1.48392i 0.441740 + 0.0516320i
827827 0.904516 5.12977i 0.0314531 0.178379i −0.965034 0.262124i 0.915577π-0.915577\pi
0.996487 + 0.0837448i 0.0266881π0.0266881\pi
828828 37.4173 8.32632i 1.30034 0.289360i
829829 1.35636 + 7.69231i 0.0471084 + 0.267165i 0.999260 0.0384608i 0.0122455π-0.0122455\pi
−0.952152 + 0.305626i 0.901134π0.901134\pi
830830 −3.05477 52.4484i −0.106033 1.82051i
831831 −37.9239 11.6384i −1.31557 0.403732i
832832 −4.12143 + 9.55455i −0.142885 + 0.331245i
833833 8.50616 4.27195i 0.294721 0.148014i
834834 10.8003 + 30.3208i 0.373985 + 1.04992i
835835 5.34646 1.26713i 0.185022 0.0438510i
836836 71.1060 + 123.159i 2.45925 + 4.25955i
837837 19.5084 + 1.54057i 0.674310 + 0.0532499i
838838 3.56743 6.17897i 0.123235 0.213449i
839839 8.63105 28.8297i 0.297977 0.995312i −0.669597 0.742725i 0.733533π-0.733533\pi
0.967574 0.252588i 0.0812816π-0.0812816\pi
840840 −37.2477 21.8478i −1.28517 0.753822i
841841 20.1774 + 13.2709i 0.695772 + 0.457616i
842842 9.36628 + 12.5811i 0.322783 + 0.433573i
843843 −51.8713 + 2.66341i −1.78654 + 0.0917328i
844844 −68.1571 + 44.8277i −2.34607 + 1.54303i
845845 −11.1787 4.06870i −0.384557 0.139967i
846846 −17.6975 + 39.5239i −0.608453 + 1.35886i
847847 34.2925 12.4814i 1.17830 0.428867i
848848 −31.1810 + 41.8833i −1.07076 + 1.43828i
849849 26.8191 + 1.74715i 0.920428 + 0.0599619i
850850 −15.4856 + 16.4138i −0.531151 + 0.562987i
851851 13.9421 14.7778i 0.477929 0.506575i
852852 26.1949 + 1.70649i 0.897424 + 0.0584632i
853853 3.32810 4.47042i 0.113952 0.153064i −0.741488 0.670966i 0.765879π-0.765879\pi
0.855440 + 0.517902i 0.173287π0.173287\pi
854854 8.68141 3.15978i 0.297072 0.108125i
855855 −29.8451 + 3.07300i −1.02068 + 0.105094i
856856 23.7619 + 8.64862i 0.812165 + 0.295604i
857857 −14.6309 + 9.62290i −0.499782 + 0.328712i −0.774245 0.632886i 0.781870π-0.781870\pi
0.274463 + 0.961598i 0.411500π0.411500\pi
858858 −43.6019 + 2.23881i −1.48854 + 0.0764317i
859859 −20.0517 26.9341i −0.684154 0.918978i 0.315396 0.948960i 0.397863π-0.397863\pi
−0.999550 + 0.0299816i 0.990455π0.990455\pi
860860 3.94495 + 2.59463i 0.134522 + 0.0884763i
861861 20.1849 + 11.8395i 0.687899 + 0.403490i
862862 12.3956 41.4042i 0.422196 1.41023i
863863 −5.63576 + 9.76143i −0.191844 + 0.332283i −0.945861 0.324571i 0.894780π-0.894780\pi
0.754018 + 0.656854i 0.228113π0.228113\pi
864864 −11.2288 5.12085i −0.382010 0.174215i
865865 11.4933 + 19.9069i 0.390782 + 0.676855i
866866 −33.1791 + 7.86359i −1.12747 + 0.267216i
867867 −4.66349 13.0922i −0.158380 0.444636i
868868 45.3647 22.7830i 1.53978 0.773306i
869869 −8.79634 + 20.3922i −0.298395 + 0.691758i
870870 12.8061 + 3.93003i 0.434166 + 0.133240i
871871 0.741772 + 12.7357i 0.0251340 + 0.431534i
872872 −6.88157 39.0273i −0.233039 1.32163i
873873 11.3271 36.0246i 0.383366 1.21925i
874874 9.30925 52.7954i 0.314890 1.78583i
875875 35.7636 + 4.18016i 1.20903 + 0.141315i
876876 19.4049 79.4377i 0.655632 2.68395i
877877 −10.5547 35.2552i −0.356408 1.19049i −0.928824 0.370522i 0.879179π-0.879179\pi
0.572416 0.819963i 0.306006π-0.306006\pi
878878 90.5273 + 21.4554i 3.05515 + 0.724083i
879879 −1.45702 13.2554i −0.0491439 0.447093i
880880 14.2676 + 33.0759i 0.480959 + 1.11499i
881881 −10.8033 9.06508i −0.363974 0.305410i 0.442398 0.896819i 0.354128π-0.354128\pi
−0.806372 + 0.591408i 0.798572π0.798572\pi
882882 −22.2331 8.44021i −0.748628 0.284197i
883883 −26.7963 + 22.4847i −0.901767 + 0.756672i −0.970535 0.240961i 0.922538π-0.922538\pi
0.0687683 + 0.997633i 0.478093π0.478093\pi
884884 24.1262 + 12.1166i 0.811451 + 0.407526i
885885 3.60546 1.52592i 0.121196 0.0512934i
886886 −11.0652 + 1.29334i −0.371742 + 0.0434504i
887887 −2.54514 + 43.6983i −0.0854573 + 1.46725i 0.634336 + 0.773057i 0.281273π0.281273\pi
−0.719794 + 0.694188i 0.755764π0.755764\pi
888888 −63.7025 + 10.7814i −2.13772 + 0.361799i
889889 −22.4010 23.7436i −0.751304 0.796336i
890890 14.5535 0.487833
891891 1.30749 + 42.6131i 0.0438027 + 1.42759i
892892 −63.9539 −2.14134
893893 28.2092 + 29.9000i 0.943986 + 1.00057i
894894 −3.67666 + 9.88943i −0.122966 + 0.330752i
895895 −1.77557 + 30.4853i −0.0593507 + 1.01901i
896896 53.6240 6.26775i 1.79145 0.209391i
897897 8.91423 + 6.73216i 0.297638 + 0.224780i
898898 −8.17267 4.10447i −0.272726 0.136968i
899899 −6.35325 + 5.33101i −0.211893 + 0.177799i
900900 38.2619 + 0.526218i 1.27540 + 0.0175406i
901901 −22.1820 18.6129i −0.738988 0.620085i
902902 −19.8257 45.9610i −0.660122 1.53034i
903903 4.01601 + 1.76519i 0.133644 + 0.0587418i
904904 −42.3004 10.0254i −1.40689 0.333439i
905905 −2.56482 8.56710i −0.0852576 0.284780i
906906 88.6844 25.8873i 2.94634 0.860046i
907907 16.6087 + 1.94128i 0.551482 + 0.0644590i 0.387270 0.921966i 0.373418π-0.373418\pi
0.164212 + 0.986425i 0.447492π0.447492\pi
908908 4.62359 26.2217i 0.153439 0.870196i
909909 −13.4008 1.75344i −0.444475 0.0581581i
910910 −4.14918 23.5311i −0.137544 0.780050i
911911 1.11002 + 19.0583i 0.0367765 + 0.631429i 0.965459 + 0.260554i 0.0839052π0.0839052\pi
−0.928683 + 0.370875i 0.879058π0.879058\pi
912912 −48.6728 + 45.2919i −1.61172 + 1.49976i
913913 −28.0678 + 65.0685i −0.928908 + 2.15345i
914914 40.9612 20.5715i 1.35488 0.680444i
915915 1.83376 2.15512i 0.0606222 0.0712460i
916916 38.3042 9.07825i 1.26561 0.299954i
917917 13.7274 + 23.7765i 0.453319 + 0.785171i
918918 18.1446 34.3436i 0.598860 1.13351i
919919 −2.23912 + 3.87828i −0.0738619 + 0.127933i −0.900591 0.434668i 0.856866π-0.856866\pi
0.826729 + 0.562600i 0.190199π0.190199\pi
920920 6.77809 22.6404i 0.223467 0.746432i
921921 −19.8121 + 11.2576i −0.652831 + 0.370951i
922922 −25.1467 16.5393i −0.828164 0.544692i
923923 4.56816 + 6.13610i 0.150363 + 0.201972i
924924 60.1360 + 92.8163i 1.97833 + 3.05343i
925925 16.9446 11.1447i 0.557136 0.366434i
926926 6.45541 + 2.34958i 0.212138 + 0.0772119i
927927 34.6708 + 23.4927i 1.13874 + 0.771601i
928928 4.91493 1.78889i 0.161340 0.0587231i
929929 −24.3387 + 32.6925i −0.798526 + 1.07261i 0.197210 + 0.980361i 0.436812π0.436812\pi
−0.995736 + 0.0922458i 0.970595π0.970595\pi
930930 12.7198 19.0528i 0.417098 0.624767i
931931 −15.4912 + 16.4197i −0.507704 + 0.538135i
932932 61.0240 64.6817i 1.99891 2.11872i
933933 4.20177 + 8.51184i 0.137560 + 0.278665i
934934 −46.8985 + 62.9956i −1.53456 + 2.06128i
935935 −18.7715 + 6.83227i −0.613894 + 0.223439i
936936 −9.71939 34.1683i −0.317688 1.11683i
937937 −25.7954 9.38877i −0.842700 0.306718i −0.115640 0.993291i 0.536892π-0.536892\pi
−0.727060 + 0.686574i 0.759114π0.759114\pi
938938 39.7796 26.1634i 1.29885 0.854266i
939939 19.0533 37.2965i 0.621780 1.21713i
940940 20.5472 + 27.5997i 0.670176 + 0.900203i
941941 2.11164 + 1.38885i 0.0688375 + 0.0452751i 0.583461 0.812141i 0.301698π-0.301698\pi
−0.514624 + 0.857416i 0.672068π0.672068\pi
942942 0.192007 27.9234i 0.00625592 0.909794i
943943 −3.67311 + 12.2690i −0.119613 + 0.399535i
944944 4.33786 7.51340i 0.141185 0.244540i
945945 −23.0567 + 3.57683i −0.750036 + 0.116354i
946946 −4.69172 8.12630i −0.152541 0.264209i
947947 −12.4238 + 2.94449i −0.403718 + 0.0956829i −0.427458 0.904035i 0.640591π-0.640591\pi
0.0237399 + 0.999718i 0.492443π0.492443\pi
948948 −33.7478 6.19022i −1.09608 0.201049i
949949 21.2954 10.6950i 0.691279 0.347173i
950950 21.1967 49.1394i 0.687711 1.59429i
951951 −4.01238 17.4638i −0.130110 0.566303i
952952 −3.08554 52.9766i −0.100003 1.71698i
953953 1.62376 + 9.20879i 0.0525987 + 0.298302i 0.999747 0.0224940i 0.00716067π-0.00716067\pi
−0.947148 + 0.320796i 0.896050π0.896050\pi
954954 3.21288 + 72.2732i 0.104021 + 2.33993i
955955 −3.37322 + 19.1305i −0.109155 + 0.619048i
956956 68.8265 + 8.04467i 2.22601 + 0.260183i
957957 −13.0568 12.4893i −0.422068 0.403722i
958958 1.99484 + 6.66324i 0.0644504 + 0.215279i
959959 −3.31732 0.786220i −0.107122 0.0253884i
960960 9.58981 7.03738i 0.309510 0.227131i
961961 −6.66071 15.4413i −0.214862 0.498105i
962962 −27.3859 22.9795i −0.882958 0.740890i
963963 12.9022 4.49606i 0.415767 0.144884i
964964 5.34797 4.48748i 0.172247 0.144532i
965965 −4.75053 2.38580i −0.152925 0.0768018i
966966 5.12465 41.3749i 0.164883 1.33121i
967967 2.13167 0.249157i 0.0685500 0.00801235i −0.0817488 0.996653i 0.526051π-0.526051\pi
0.150299 + 0.988641i 0.451976π0.451976\pi
968968 3.69299 63.4062i 0.118697 2.03795i
969969 −23.5050 28.4066i −0.755089 0.912550i
970970 −30.3371 32.1555i −0.974066 1.03245i
971971 −18.8603 −0.605255 −0.302627 0.953109i 0.597864π-0.597864\pi
−0.302627 + 0.953109i 0.597864π0.597864\pi
972972 −63.7108 + 16.7104i −2.04352 + 0.535987i
973973 23.7603 0.761719
974974 −54.2748 57.5279i −1.73908 1.84331i
975975 7.10896 + 8.59142i 0.227669 + 0.275146i
976976 0.364601 6.25996i 0.0116706 0.200376i
977977 −59.7085 + 6.97892i −1.91024 + 0.223276i −0.986975 0.160876i 0.948568π-0.948568\pi
−0.923270 + 0.384151i 0.874494π0.874494\pi
978978 −3.44773 + 27.8359i −0.110246 + 0.890095i
979979 −17.5422 8.81001i −0.560650 0.281569i
980980 −14.4748 + 12.1458i −0.462380 + 0.387983i
981981 −16.2123 13.9881i −0.517618 0.446606i
982982 67.2670 + 56.4437i 2.14657 + 1.80119i
983983 12.7239 + 29.4973i 0.405829 + 0.940817i 0.991481 + 0.130254i 0.0415793π0.0415793\pi
−0.585652 + 0.810563i 0.699161π0.699161\pi
984984 32.8349 24.0955i 1.04674 0.768138i
985985 −7.55598 1.79080i −0.240754 0.0570597i
986986 4.72125 + 15.7701i 0.150355 + 0.502221i
987987 23.1011 + 22.0970i 0.735317 + 0.703355i
988988 −63.5941 7.43309i −2.02320 0.236478i
989989 −0.416905 + 2.36439i −0.0132568 + 0.0751831i
990990 44.2875 + 23.0100i 1.40755 + 0.731307i
991991 −2.05455 11.6519i −0.0652648 0.370135i −0.999895 0.0145131i 0.995380π-0.995380\pi
0.934630 0.355622i 0.115731π-0.115731\pi
992992 −0.520093 8.92965i −0.0165130 0.283517i
993993 11.9315 + 51.9318i 0.378636 + 1.64801i
994994 11.3082 26.2154i 0.358675 0.831503i
995995 21.3507 10.7227i 0.676861 0.339933i
996996 −107.684 19.7520i −3.41211 0.625867i
997997 −41.3358 + 9.79677i −1.30912 + 0.310267i −0.825198 0.564844i 0.808936π-0.808936\pi
−0.483922 + 0.875111i 0.660788π0.660788\pi
998998 −9.96735 17.2640i −0.315511 0.546481i
999999 −22.9862 + 26.2737i −0.727252 + 0.831263i
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 81.2.g.a.22.8 144
3.2 odd 2 243.2.g.a.199.1 144
9.2 odd 6 729.2.g.a.352.1 144
9.4 even 3 729.2.g.c.595.1 144
9.5 odd 6 729.2.g.b.595.8 144
9.7 even 3 729.2.g.d.352.8 144
81.11 odd 54 243.2.g.a.127.1 144
81.16 even 27 729.2.g.d.379.8 144
81.31 even 27 6561.2.a.c.1.6 72
81.38 odd 54 729.2.g.b.136.8 144
81.43 even 27 729.2.g.c.136.1 144
81.50 odd 54 6561.2.a.d.1.67 72
81.65 odd 54 729.2.g.a.379.1 144
81.70 even 27 inner 81.2.g.a.70.8 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
81.2.g.a.22.8 144 1.1 even 1 trivial
81.2.g.a.70.8 yes 144 81.70 even 27 inner
243.2.g.a.127.1 144 81.11 odd 54
243.2.g.a.199.1 144 3.2 odd 2
729.2.g.a.352.1 144 9.2 odd 6
729.2.g.a.379.1 144 81.65 odd 54
729.2.g.b.136.8 144 81.38 odd 54
729.2.g.b.595.8 144 9.5 odd 6
729.2.g.c.136.1 144 81.43 even 27
729.2.g.c.595.1 144 9.4 even 3
729.2.g.d.352.8 144 9.7 even 3
729.2.g.d.379.8 144 81.16 even 27
6561.2.a.c.1.6 72 81.31 even 27
6561.2.a.d.1.67 72 81.50 odd 54