LMFDB - Embedded newform 81.2.g.a.7.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,2,Mod(4,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			7.6
Character	$\chi$	$=$	81.7
Dual form			81.2.g.a.58.6

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.470263 + 0.631673i) q^{2} +(-1.10956 - 1.32999i) q^{3} +(0.395743 - 1.32187i) q^{4} +(2.32750 - 1.53082i) q^{5} +(0.318331 - 1.32633i) q^{6} +(-3.41908 + 3.62402i) q^{7} +(2.50111 - 0.910331i) q^{8} +(-0.537739 + 2.95141i) q^{9} +(2.06152 + 0.750330i) q^{10} +(1.55231 - 0.779598i) q^{11} +(-2.19718 + 0.940369i) q^{12} +(0.859891 + 1.99345i) q^{13} +(-3.89706 - 0.455501i) q^{14} +(-4.61848 - 1.39701i) q^{15} +(-0.554469 - 0.364680i) q^{16} +(-3.39468 + 2.84848i) q^{17} +(-2.11721 + 1.04827i) q^{18} +(-1.63306 - 1.37030i) q^{19} +(-1.10246 - 3.68247i) q^{20} +(8.61359 + 0.526266i) q^{21} +(1.22244 + 0.613935i) q^{22} +(0.465342 + 0.493234i) q^{23} +(-3.98587 - 2.31638i) q^{24} +(1.09345 - 2.53489i) q^{25} +(-0.854835 + 1.48062i) q^{26} +(4.52200 - 2.55959i) q^{27} +(3.43741 + 5.95378i) q^{28} +(5.71522 - 0.668013i) q^{29} +(-1.28945 - 3.57433i) q^{30} +(-5.72212 + 1.35617i) q^{31} +(-0.339908 - 5.83599i) q^{32} +(-2.75924 - 1.19954i) q^{33} +(-3.39570 - 0.804795i) q^{34} +(-2.41020 + 13.6689i) q^{35} +(3.68859 + 1.87882i) q^{36} +(0.131814 + 0.747552i) q^{37} +(0.0976137 - 1.67596i) q^{38} +(1.69716 - 3.35551i) q^{39} +(4.42779 - 5.94755i) q^{40} +(0.0737288 - 0.0990350i) q^{41} +(3.71823 + 5.68845i) q^{42} +(-0.148059 + 2.54207i) q^{43} +(-0.416216 - 2.36048i) q^{44} +(3.26650 + 7.69260i) q^{45} +(-0.0927292 + 0.525894i) q^{46} +(1.65271 + 0.391699i) q^{47} +(0.130198 + 1.14207i) q^{48} +(-1.03635 - 17.7935i) q^{49} +(2.11543 - 0.501366i) q^{50} +(7.55505 + 1.35432i) q^{51} +(2.97539 - 0.347773i) q^{52} +(-5.02192 - 8.69822i) q^{53} +(3.74336 + 1.65274i) q^{54} +(2.41957 - 4.19082i) q^{55} +(-5.25246 + 12.1766i) q^{56} +(-0.0104999 + 3.69239i) q^{57} +(3.10962 + 3.29601i) q^{58} +(-10.3931 - 5.21959i) q^{59} +(-3.67440 + 5.55220i) q^{60} +(-2.27150 - 7.58734i) q^{61} +(-3.54755 - 2.97675i) q^{62} +(-8.85739 - 12.0399i) q^{63} +(2.50983 - 2.10599i) q^{64} +(5.05301 + 3.32342i) q^{65} +(-0.539853 - 2.30704i) q^{66} +(0.462282 + 0.0540330i) q^{67} +(2.42190 + 5.61460i) q^{68} +(0.139669 - 1.16617i) q^{69} +(-9.76770 + 4.90552i) q^{70} +(11.4588 + 4.17067i) q^{71} +(1.34182 + 7.87134i) q^{72} +(-2.01159 + 0.732160i) q^{73} +(-0.410222 + 0.434809i) q^{74} +(-4.58462 + 1.35835i) q^{75} +(-2.45764 + 1.61641i) q^{76} +(-2.48219 + 8.29110i) q^{77} +(2.91770 - 0.505918i) q^{78} +(4.18797 + 5.62542i) q^{79} -1.84879 q^{80} +(-8.42167 - 3.17418i) q^{81} +0.0972297 q^{82} +(-1.97654 - 2.65495i) q^{83} +(4.10442 - 11.1778i) q^{84} +(-3.54061 + 11.8265i) q^{85} +(-1.67538 + 1.10192i) q^{86} +(-7.22985 - 6.85997i) q^{87} +(3.17281 - 3.36298i) q^{88} +(-4.72182 + 1.71860i) q^{89} +(-3.32309 + 5.68090i) q^{90} +(-10.1643 - 3.69952i) q^{91} +(0.836149 - 0.419930i) q^{92} +(8.15274 + 6.10560i) q^{93} +(0.529782 + 1.22817i) q^{94} +(-5.89863 - 0.689452i) q^{95} +(-7.38465 + 6.92748i) q^{96} +(6.27220 + 4.12529i) q^{97} +(10.7523 - 9.02224i) q^{98} +(1.46618 + 5.00072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}) $ 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 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.470263	+	0.631673i	0.332526	+	0.446660i	0.936669	−	0.350216i	$-0.113892\pi$
$2$	0.470263	+	0.631673i	0.332526	+	0.446660i	−0.604143	+	0.796876i	$0.706484\pi$
$3$	−1.10956	−	1.32999i	−0.640607	−	0.767869i
$3$	−1.10956	−	1.32999i	−0.640607	−	0.767869i
$4$	0.395743	−	1.32187i	0.197872	−	0.660937i
$5$	2.32750	−	1.53082i	1.04089	−	0.684604i	0.0905734	−	0.995890i	$-0.471130\pi$
$5$	2.32750	−	1.53082i	1.04089	−	0.684604i	0.950316	+	0.311286i	$0.100760\pi$
$6$	0.318331	−	1.32633i	0.129958	−	0.541470i
$7$	−3.41908	+	3.62402i	−1.29229	+	1.36975i	−0.401158	+	0.916009i	$0.631392\pi$
$7$	−3.41908	+	3.62402i	−1.29229	+	1.36975i	−0.891134	+	0.453740i	$0.850089\pi$
$8$	2.50111	−	0.910331i	0.884277	−	0.321851i
$9$	−0.537739	+	2.95141i	−0.179246	+	0.983804i
$10$	2.06152	+	0.750330i	0.651909	+	0.237275i
$11$	1.55231	−	0.779598i	0.468038	−	0.235058i	−0.199118	−	0.979976i	$-0.563808\pi$
$11$	1.55231	−	0.779598i	0.468038	−	0.235058i	0.667156	+	0.744918i	$0.267511\pi$
$12$	−2.19718	+	0.940369i	−0.634271	+	0.271461i
$13$	0.859891	+	1.99345i	0.238491	+	0.552884i	0.994860	−	0.101261i	$-0.0322878\pi$
$13$	0.859891	+	1.99345i	0.238491	+	0.552884i	−0.756369	+	0.654145i	$0.773029\pi$
$14$	−3.89706	−	0.455501i	−1.04153	−	0.121738i
$15$	−4.61848	−	1.39701i	−1.19249	−	0.360705i
$16$	−0.554469	−	0.364680i	−0.138617	−	0.0911700i
$17$	−3.39468	+	2.84848i	−0.823331	+	0.690857i	−0.953750	−	0.300602i	$-0.902812\pi$
$17$	−3.39468	+	2.84848i	−0.823331	+	0.690857i	0.130419	+	0.991459i	$0.458368\pi$
$18$	−2.11721	+	1.04827i	−0.499030	+	0.247079i
$19$	−1.63306	−	1.37030i	−0.374650	−	0.314369i	0.435948	−	0.899972i	$-0.356413\pi$
$19$	−1.63306	−	1.37030i	−0.374650	−	0.314369i	−0.810598	+	0.585603i	$0.800858\pi$
$20$	−1.10246	−	3.68247i	−0.246518	−	0.823426i
$21$	8.61359	+	0.526266i	1.87964	+	0.114841i
$22$	1.22244	+	0.613935i	0.260626	+	0.130891i
$23$	0.465342	+	0.493234i	0.0970305	+	0.102846i	0.774069	−	0.633101i	$-0.218218\pi$
$23$	0.465342	+	0.493234i	0.0970305	+	0.102846i	−0.677038	+	0.735948i	$0.736737\pi$
$24$	−3.98587	−	2.31638i	−0.813613	−	0.472830i
$25$	1.09345	−	2.53489i	0.218689	−	0.506978i
$26$	−0.854835	+	1.48062i	−0.167647	+	0.290373i
$27$	4.52200	−	2.55959i	0.870259	−	0.492594i
$28$	3.43741	+	5.95378i	0.649610	+	1.12516i
$29$	5.71522	−	0.668013i	1.06129	−	0.124047i	0.432509	−	0.901630i	$-0.357628\pi$
$29$	5.71522	−	0.668013i	1.06129	−	0.124047i	0.628781	+	0.777583i	$0.283554\pi$
$30$	−1.28945	−	3.57433i	−0.235421	−	0.652581i
$31$	−5.72212	+	1.35617i	−1.02772	+	0.243575i	−0.709697	−	0.704507i	$-0.751168\pi$
$31$	−5.72212	+	1.35617i	−1.02772	+	0.243575i	−0.318026	+	0.948082i	$0.603020\pi$
$32$	−0.339908	−	5.83599i	−0.0600878	−	1.03167i
$33$	−2.75924	−	1.19954i	−0.480322	−	0.208813i
$34$	−3.39570	−	0.804795i	−0.582357	−	0.138021i
$35$	−2.41020	+	13.6689i	−0.407397	+	2.31047i
$36$	3.68859	+	1.87882i	0.614765	+	0.313137i
$37$	0.131814	+	0.747552i	0.0216700	+	0.122897i	0.993724	−	0.111861i	$-0.0356813\pi$
$37$	0.131814	+	0.747552i	0.0216700	+	0.122897i	−0.972054	+	0.234758i	$0.924570\pi$
$38$	0.0976137	−	1.67596i	0.0158350	−	0.271877i
$39$	1.69716	−	3.35551i	0.271764	−	0.537311i
$40$	4.42779	−	5.94755i	0.700095	−	0.940391i
$41$	0.0737288	−	0.0990350i	0.0115145	−	0.0154667i	−0.796329	−	0.604864i	$-0.793227\pi$
$41$	0.0737288	−	0.0990350i	0.0115145	−	0.0154667i	0.807843	+	0.589398i	$0.200635\pi$
$42$	3.71823	+	5.68845i	0.573735	+	0.877748i
$43$	−0.148059	+	2.54207i	−0.0225787	+	0.387662i	0.968021	+	0.250869i	$0.0807164\pi$
$43$	−0.148059	+	2.54207i	−0.0225787	+	0.387662i	−0.990600	+	0.136792i	$0.956321\pi$
$44$	−0.416216	−	2.36048i	−0.0627469	−	0.355855i
$45$	3.26650	+	7.69260i	0.486941	+	1.14674i
$46$	−0.0927292	+	0.525894i	−0.0136722	+	0.0775388i
$47$	1.65271	+	0.391699i	0.241072	+	0.0571351i	0.349376	−	0.936983i	$-0.386394\pi$
$47$	1.65271	+	0.391699i	0.241072	+	0.0571351i	−0.108304	+	0.994118i	$0.534542\pi$
$48$	0.130198	+	1.14207i	0.0187925	+	0.164844i
$49$	−1.03635	−	17.7935i	−0.148050	−	2.54192i
$50$	2.11543	−	0.501366i	0.299167	−	0.0709039i
$51$	7.55505	+	1.35432i	1.05792	+	0.189643i
$52$	2.97539	−	0.347773i	0.412612	−	0.0482274i
$53$	−5.02192	−	8.69822i	−0.689814	−	1.19479i	−0.971898	−	0.235403i	$-0.924359\pi$
$53$	−5.02192	−	8.69822i	−0.689814	−	1.19479i	0.282084	−	0.959390i	$-0.408974\pi$
$54$	3.74336	+	1.65274i	0.509406	+	0.224910i
$55$	2.41957	−	4.19082i	0.326255	−	0.565090i
$56$	−5.25246	+	12.1766i	−0.701890	+	1.62716i
$57$	−0.0104999	+	3.69239i	−0.00139074	+	0.489069i
$58$	3.10962	+	3.29601i	0.408314	+	0.432787i
$59$	−10.3931	−	5.21959i	−1.35306	−	0.679533i	−0.383309	−	0.923620i	$-0.625215\pi$
$59$	−10.3931	−	5.21959i	−1.35306	−	0.679533i	−0.969753	+	0.244087i	$0.921512\pi$
$60$	−3.67440	+	5.55220i	−0.474363	+	0.716786i
$61$	−2.27150	−	7.58734i	−0.290836	−	0.971460i	−0.971136	−	0.238526i	$-0.923336\pi$
$61$	−2.27150	−	7.58734i	−0.290836	−	0.971460i	0.680300	−	0.732934i	$-0.261849\pi$
$62$	−3.54755	−	2.97675i	−0.450540	−	0.378048i
$63$	−8.85739	−	12.0399i	−1.11593	−	1.51688i
$64$	2.50983	−	2.10599i	0.313728	−	0.263249i
$65$	5.05301	+	3.32342i	0.626749	+	0.412220i
$66$	−0.539853	−	2.30704i	−0.0664514	−	0.283977i
$67$	0.462282	+	0.0540330i	0.0564767	+	0.00660118i	0.144284	−	0.989536i	$-0.453912\pi$
$67$	0.462282	+	0.0540330i	0.0564767	+	0.00660118i	−0.0878076	+	0.996137i	$0.527986\pi$
$68$	2.42190	+	5.61460i	0.293699	+	0.680871i
$69$	0.139669	−	1.16617i	0.0168141	−	0.140391i
$70$	−9.76770	+	4.90552i	−1.16746	+	0.586322i
$71$	11.4588	+	4.17067i	1.35991	+	0.494968i	0.916027	−	0.401116i	$-0.131378\pi$
$71$	11.4588	+	4.17067i	1.35991	+	0.494968i	0.443885	+	0.896084i	$0.353600\pi$
$72$	1.34182	+	7.87134i	0.158135	+	0.927646i
$73$	−2.01159	+	0.732160i	−0.235439	+	0.0856928i	−0.457045	−	0.889443i	$-0.651092\pi$
$73$	−2.01159	+	0.732160i	−0.235439	+	0.0856928i	0.221606	+	0.975136i	$0.428870\pi$
$74$	−0.410222	+	0.434809i	−0.0476873	+	0.0505456i
$75$	−4.58462	+	1.35835i	−0.529387	+	0.156849i
$76$	−2.45764	+	1.61641i	−0.281910	+	0.185415i
$77$	−2.48219	+	8.29110i	−0.282872	+	0.944858i
$78$	2.91770	−	0.505918i	0.330364	−	0.0572839i
$79$	4.18797	+	5.62542i	0.471184	+	0.632910i	0.972652	−	0.232266i	$-0.0746141\pi$
$79$	4.18797	+	5.62542i	0.471184	+	0.632910i	−0.501469	+	0.865176i	$0.667207\pi$
$80$	−1.84879			−0.206701
$81$	−8.42167	−	3.17418i	−0.935742	−	0.352686i
$82$	0.0972297			0.0107372
$83$	−1.97654	−	2.65495i	−0.216953	−	0.291419i	0.680301	−	0.732933i	$-0.261849\pi$
$83$	−1.97654	−	2.65495i	−0.216953	−	0.291419i	−0.897254	+	0.441514i	$0.854442\pi$
$84$	4.10442	−	11.1778i	0.447829	−	1.21960i
$85$	−3.54061	+	11.8265i	−0.384034	+	1.28276i
$86$	−1.67538	+	1.10192i	−0.180661	+	0.118823i
$87$	−7.22985	−	6.85997i	−0.775121	−	0.735466i
$88$	3.17281	−	3.36298i	0.338222	−	0.358495i
$89$	−4.72182	+	1.71860i	−0.500512	+	0.182171i	−0.579924	−	0.814670i	$-0.696918\pi$
$89$	−4.72182	+	1.71860i	−0.500512	+	0.182171i	0.0794124	+	0.996842i	$0.474696\pi$
$90$	−3.32309	+	5.68090i	−0.350285	+	0.598820i
$91$	−10.1643	−	3.69952i	−1.06551	−	0.387815i
$92$	0.836149	−	0.419930i	0.0871745	−	0.0437807i
$93$	8.15274	+	6.10560i	0.845399	+	0.633121i
$94$	0.529782	+	1.22817i	0.0546428	+	0.126676i
$95$	−5.89863	−	0.689452i	−0.605187	−	0.0707362i
$96$	−7.38465	+	6.92748i	−0.753693	+	0.707033i
$97$	6.27220	+	4.12529i	0.636846	+	0.418860i	0.826457	−	0.562999i	$-0.190353\pi$
$97$	6.27220	+	4.12529i	0.636846	+	0.418860i	−0.189612	+	0.981859i	$0.560723\pi$
$98$	10.7523	−	9.02224i	1.08615	−	0.911384i
$99$	1.46618	+	5.00072i	0.147357	+	0.502591i
$100$	−2.91808	−	2.44856i	−0.291808	−	0.244856i
$101$	−0.648115	−	2.16486i	−0.0644899	−	0.215411i	0.919671	−	0.392690i	$-0.128456\pi$
$101$	−0.648115	−	2.16486i	−0.0644899	−	0.215411i	−0.984161	+	0.177279i	$0.943270\pi$
$102$	2.69737	+	5.40921i	0.267080	+	0.535592i
$103$	−0.239343	−	0.120203i	−0.0235832	−	0.0118439i	0.436969	−	0.899477i	$-0.356052\pi$
$103$	−0.239343	−	0.120203i	−0.0235832	−	0.0118439i	−0.460552	+	0.887633i	$0.652348\pi$
$104$	3.96539	+	4.20306i	0.388838	+	0.412144i
$105$	20.8537	−	11.9610i	2.03512	−	1.16727i
$106$	3.13281	−	7.26267i	0.304285	−	0.705412i
$107$	4.97987	−	8.62539i	0.481423	−	0.833848i	−0.518350	−	0.855169i	$-0.673454\pi$
$107$	4.97987	−	8.62539i	0.481423	−	0.833848i	0.999773	+	0.0213201i	$0.00678691\pi$
$108$	−1.59391	−	6.99046i	−0.153374	−	0.672657i
$109$	6.70725	+	11.6173i	0.642438	+	1.11273i	0.984887	+	0.173198i	$0.0554102\pi$
$109$	6.70725	+	11.6173i	0.642438	+	1.11273i	−0.342449	+	0.939536i	$0.611256\pi$
$110$	3.78506	−	0.442411i	0.360892	−	0.0421822i
$111$	0.847980	−	1.00477i	0.0804867	−	0.0953683i
$112$	3.21738	−	0.762533i	0.304014	−	0.0720526i
$113$	−0.0233225	−	0.400431i	−0.00219399	−	0.0376694i	0.997033	−	0.0769692i	$-0.0245243\pi$
$113$	−0.0233225	−	0.400431i	−0.00219399	−	0.0376694i	−0.999227	+	0.0392998i	$0.987487\pi$
$114$	−2.33732	+	1.72976i	−0.218910	+	0.162007i
$115$	1.83814	+	0.435646i	0.171407	+	0.0406242i
$116$	1.37873	−	7.81916i	0.128012	−	0.725991i
$117$	−6.34590	+	1.46594i	−0.586678	+	0.135526i
$118$	−1.59040	−	9.01960i	−0.146408	−	0.830322i
$119$	1.28377	−	22.0415i	0.117683	−	2.02055i
$120$	−12.8231	+	0.710278i	−1.17058	+	0.0648392i
$121$	−4.76686	+	6.40300i	−0.433351	+	0.582091i
$122$	3.72452	−	5.00289i	0.337202	−	0.452941i
$123$	−0.213522	+	0.0118271i	−0.0192527	+	0.00106641i
$124$	−0.471807	+	8.10061i	−0.0423695	+	0.727456i
$125$	1.08327	+	6.14355i	0.0968909	+	0.549495i
$126$	3.43997	−	11.2569i	0.306457	−	1.00284i
$127$	−1.81470	+	10.2917i	−0.161029	+	0.913239i	0.792037	+	0.610474i	$0.209021\pi$
$127$	−1.81470	+	10.2917i	−0.161029	+	0.913239i	−0.953065	+	0.302765i	$0.902090\pi$
$128$	−8.86603	−	2.10129i	−0.783654	−	0.185729i
$129$	3.54520	−	2.62367i	0.312137	−	0.231001i
$130$	0.276932	+	4.75474i	0.0242885	+	0.417018i
$131$	13.0882	−	3.10197i	1.14353	−	0.271021i	0.385160	−	0.922850i	$-0.374146\pi$
$131$	13.0882	−	3.10197i	1.14353	−	0.271021i	0.758366	+	0.651829i	$0.225998\pi$
$132$	−2.67759	+	3.17266i	−0.233054	+	0.276145i
$133$	10.5496	−	1.23307i	0.914763	−	0.106920i
$134$	0.183263	+	0.317421i	0.0158315	+	0.0274210i
$135$	6.60668	−	12.8798i	0.568612	−	1.10852i
$136$	−5.89743	+	10.2146i	−0.505700	+	0.875898i
$137$	−5.66340	+	13.1292i	−0.483857	+	1.12171i	0.485096	+	0.874461i	$0.338785\pi$
$137$	−5.66340	+	13.1292i	−0.483857	+	1.12171i	−0.968953	+	0.247246i	$0.920475\pi$
$138$	0.802321	−	0.460183i	0.0682981	−	0.0391734i
$139$	0.222217	+	0.235537i	0.0188482	+	0.0199780i	0.736729	−	0.676188i	$-0.236369\pi$
$139$	0.222217	+	0.235537i	0.0188482	+	0.0199780i	−0.717881	+	0.696166i	$0.754888\pi$
$140$	17.1147	+	8.59535i	1.44646	+	0.726439i
$141$	−1.31283	−	2.63270i	−0.110560	−	0.221713i
$142$	2.75416	+	9.19954i	0.231124	+	0.772009i
$143$	2.88891	+	2.42408i	0.241583	+	0.202712i
$144$	1.37448	−	1.44036i	0.114540	−	0.120030i
$145$	12.2796	−	10.3038i	1.01976	−	0.855682i
$146$	−1.40846	−	0.926361i	−0.116565	−	0.0766662i
$147$	−22.5152	+	21.1213i	−1.85702	+	1.74206i
$148$	1.04033	+	0.121598i	0.0855149	+	0.00999526i
$149$	−1.21912	−	2.82624i	−0.0998744	−	0.231535i	0.860952	−	0.508687i	$-0.169869\pi$
$149$	−1.21912	−	2.82624i	−0.0998744	−	0.231535i	−0.960826	+	0.277152i	$0.910610\pi$
$150$	−3.01401	−	2.25720i	−0.246093	−	0.184300i
$151$	11.1937	−	5.62167i	0.910928	−	0.457485i	0.0693326	−	0.997594i	$-0.477913\pi$
$151$	11.1937	−	5.62167i	0.910928	−	0.457485i	0.841596	+	0.540108i	$0.181617\pi$
$152$	−5.33190	−	1.94065i	−0.432474	−	0.157408i
$153$	−6.58157	−	11.5508i	−0.532089	−	0.933830i
$154$	−6.40455	+	2.33106i	−0.516093	+	0.187843i
$155$	−11.2422	+	11.9160i	−0.902993	+	0.957117i
$156$	−3.76392	−	3.57136i	−0.301354	−	0.285937i
$157$	−4.86355	+	3.19881i	−0.388153	+	0.255292i	−0.728554	−	0.684988i	$-0.759807\pi$
$157$	−4.86355	+	3.19881i	−0.388153	+	0.255292i	0.340401	+	0.940280i	$0.389437\pi$
$158$	−1.58398	+	5.29086i	−0.126015	+	0.420918i
$159$	−5.99640	+	16.3303i	−0.475545	+	1.29508i
$160$	−9.72499	−	13.0629i	−0.768828	−	1.03272i
$161$	−3.37853			−0.266265
$162$	−1.95536	−	6.81244i	−0.153628	−	0.535236i
$163$	−6.75084			−0.528767			−0.264383	−	0.964418i	$-0.585168\pi$
$163$	−6.75084			−0.528767			−0.264383	+	0.964418i	$0.585168\pi$
$164$	−0.101734	−	0.136653i	−0.00794410	−	0.0106708i
$165$	−8.25841	+	1.43198i	−0.642916	+	0.111479i
$166$	0.747568	−	2.49705i	0.0580226	−	0.193809i
$167$	14.5276	−	9.55498i	1.12418	−	0.739387i	0.155536	−	0.987830i	$-0.450289\pi$
$167$	14.5276	−	9.55498i	1.12418	−	0.739387i	0.968646	+	0.248444i	$0.0799191\pi$
$168$	22.0226	−	6.52497i	1.69908	−	0.503412i
$169$	5.68670	−	6.02755i	0.437439	−	0.463658i
$170$	−9.13549	+	3.32504i	−0.700660	+	0.255019i
$171$	4.92248	−	4.08297i	0.376432	−	0.312233i
$172$	3.30170	+	1.20172i	0.251752	+	0.0916303i
$173$	−12.2830	+	6.16877i	−0.933862	+	0.469003i	−0.849592	−	0.527440i	$-0.823152\pi$
$173$	−12.2830	+	6.16877i	−0.933862	+	0.469003i	−0.0842696	+	0.996443i	$0.526856\pi$
$174$	0.933329	−	7.79289i	0.0707555	−	0.590778i
$175$	5.44791	+	12.6297i	0.411823	+	0.954713i
$176$	−1.14501	−	0.133832i	−0.0863084	−	0.0100880i
$177$	4.58976	+	19.6141i	0.344988	+	1.47429i
$178$	−3.30609	−	2.17445i	−0.247802	−	0.162982i
$179$	1.66053	−	1.39335i	0.124114	−	0.104144i	−0.578618	−	0.815599i	$-0.696408\pi$
$179$	1.66053	−	1.39335i	0.124114	−	0.104144i	0.702732	+	0.711455i	$0.251963\pi$
$180$	11.4613	−	1.27361i	0.854277	−	0.0949290i
$181$	−17.7173	−	14.8665i	−1.31691	−	1.10502i	−0.986950	−	0.161028i	$-0.948519\pi$
$181$	−17.7173	−	14.8665i	−1.31691	−	1.10502i	−0.329963	−	0.943994i	$-0.607036\pi$
$182$	−2.44303	−	8.16029i	−0.181089	−	0.604881i
$183$	−7.57070	+	11.4397i	−0.559643	+	0.845647i
$184$	1.61288	+	0.810018i	0.118903	+	0.0597153i
$185$	1.45116	+	1.53814i	0.106692	+	0.113087i
$186$	−0.0228092	+	8.02110i	−0.00167245	+	0.588136i
$187$	−3.04892	+	7.06820i	−0.222959	+	0.516878i
$188$	1.17182	−	2.02966i	0.0854640	−	0.148028i
$189$	−6.18509	+	25.1393i	−0.449899	+	1.82861i
$190$	−2.33840	−	4.05023i	−0.169646	−	0.293835i
$191$	21.7391	−	2.54094i	1.57299	−	0.183856i	0.715595	−	0.698516i	$-0.246156\pi$
$191$	21.7391	−	2.54094i	1.57299	−	0.183856i	0.857395	+	0.514660i	$0.172082\pi$
$192$	−5.58576	−	1.00131i	−0.403118	−	0.0722631i
$193$	−7.02015	+	1.66381i	−0.505322	+	0.119763i	−0.475367	−	0.879788i	$-0.657685\pi$
$193$	−7.02015	+	1.66381i	−0.505322	+	0.119763i	−0.0299550	+	0.999551i	$0.509536\pi$
$194$	0.343750	+	5.90195i	0.0246798	+	0.423736i
$195$	−1.18653	−	10.4080i	−0.0849691	−	0.745332i
$196$	−23.9308	−	5.67171i	−1.70935	−	0.405122i
$197$	2.84835	−	16.1538i	0.202936	−	1.15091i	−0.697718	−	0.716373i	$-0.745801\pi$
$197$	2.84835	−	16.1538i	0.202936	−	1.15091i	0.900654	−	0.434537i	$-0.143088\pi$
$198$	−2.46933	+	3.27780i	−0.175488	+	0.232943i
$199$	−1.40107	−	7.94587i	−0.0993193	−	0.563268i	−0.993338	−	0.115238i	$-0.963237\pi$
$199$	−1.40107	−	7.94587i	−0.0993193	−	0.563268i	0.894019	−	0.448030i	$-0.147874\pi$
$200$	0.427241	−	7.33545i	0.0302105	−	0.518695i
$201$	−0.441067	−	0.674782i	−0.0311105	−	0.0475955i
$202$	1.06270	−	1.42745i	0.0747710	−	0.100435i
$203$	−17.1199	+	22.9960i	−1.20158	+	1.61401i
$204$	4.78010	−	9.45086i	0.334674	−	0.661693i
$205$	0.0199990	−	0.343370i	0.00139679	−	0.0239820i
$206$	−0.0366255	−	0.207713i	−0.00255182	−	0.0144721i
$207$	−1.70597	+	1.10819i	−0.118573	+	0.0770242i
$208$	0.250189	−	1.41889i	0.0173475	−	0.0983824i
$209$	−3.60330	−	0.853997i	−0.249245	−	0.0590722i
$210$	17.3622	+	7.54794i	1.19810	+	0.520857i
$211$	1.39097	+	23.8821i	0.0957585	+	1.64411i	0.614311	+	0.789064i	$0.289434\pi$
$211$	1.39097	+	23.8821i	0.0957585	+	1.64411i	−0.518553	+	0.855046i	$0.673529\pi$
$212$	−13.4853	+	3.19609i	−0.926177	+	0.219508i
$213$	−7.16735	−	19.8677i	−0.491098	−	1.36131i
$214$	7.79028	−	0.910553i	0.532533	−	0.0622441i
$215$	3.54684	+	6.14331i	0.241893	+	0.418970i
$216$	8.97996	−	10.5183i	0.611009	−	0.715683i
$217$	14.6496	−	25.3739i	0.994481	−	1.72249i
$218$	−4.18416	+	9.69997i	−0.283387	+	0.656965i
$219$	3.20575	+	1.86302i	0.216625	+	0.125891i
$220$	−4.58221	−	4.85686i	−0.308932	−	0.327449i
$221$	−8.59735	−	4.31775i	−0.578321	−	0.290444i
$222$	1.03346	+	0.0631413i	0.0693612	+	0.00423777i
$223$	−3.43182	−	11.4631i	−0.229812	−	0.767624i	−0.992648	−	0.121033i	$-0.961379\pi$
$223$	−3.43182	−	11.4631i	−0.229812	−	0.767624i	0.762837	−	0.646591i	$-0.223806\pi$
$224$	22.3119	+	18.7219i	1.49078	+	1.25091i
$225$	6.89352	+	4.59032i	0.459568	+	0.306021i
$226$	0.241974	−	0.203040i	0.0160959	−	0.0135060i
$227$	20.9815	+	13.7997i	1.39259	+	0.915921i	0.999993	−	0.00378925i	$-0.00120616\pi$
$227$	20.9815	+	13.7997i	1.39259	+	0.915921i	0.392598	+	0.919710i	$0.371577\pi$
$228$	4.87672	+	1.47512i	0.322968	+	0.0976920i
$229$	25.5994	+	2.99214i	1.69166	+	0.197726i	0.906686	−	0.421806i	$-0.138604\pi$
$229$	25.5994	+	2.99214i	1.69166	+	0.197726i	0.784971	+	0.619533i	$0.212678\pi$
$230$	0.589222	+	1.36597i	0.0388521	+	0.0900694i
$231$	13.7812	−	5.89821i	0.906737	−	0.388074i
$232$	13.6863	−	6.87352i	0.898550	−	0.451269i
$233$	−8.58260	−	3.12381i	−0.562265	−	0.204648i	0.0452226	−	0.998977i	$-0.485600\pi$
$233$	−8.58260	−	3.12381i	−0.562265	−	0.204648i	−0.607488	+	0.794329i	$0.707823\pi$
$234$	−3.91023	−	3.31915i	−0.255620	−	0.216980i
$235$	4.44630	−	1.61832i	0.290044	−	0.105568i
$236$	−11.0126	+	11.6727i	−0.716861	+	0.759828i
$237$	2.83493	−	11.8117i	0.184148	−	0.767254i
$238$	14.5268	−	9.55440i	0.941630	−	0.619320i
$239$	6.24071	−	20.8454i	0.403678	−	1.34838i	−0.478759	−	0.877946i	$-0.658913\pi$
$239$	6.24071	−	20.8454i	0.403678	−	1.34838i	0.882437	−	0.470431i	$-0.155902\pi$
$240$	2.05134	+	2.45886i	0.132414	+	0.158719i
$241$	8.27944	+	11.1212i	0.533326	+	0.716381i	0.984368	−	0.176122i	$-0.0563552\pi$
$241$	8.27944	+	11.1212i	0.533326	+	0.716381i	−0.451043	+	0.892502i	$0.648948\pi$
$242$	−6.28628			−0.404097
$243$	5.12276	+	14.7227i	0.328625	+	0.944460i
$244$	−10.9284			−0.699622
$245$	−29.6507	−	39.8278i	−1.89431	−	2.54451i
$246$	−0.107883	−	0.129314i	−0.00687834	−	0.00824478i
$247$	1.32737	−	4.43374i	0.0844588	−	0.282112i
$248$	−13.0771	+	8.60095i	−0.830397	+	0.546161i
$249$	−1.33796	+	5.57461i	−0.0847898	+	0.353277i
$250$	−3.37129	+	3.57336i	−0.213219	+	0.225999i
$251$	−10.0143	+	3.64492i	−0.632099	+	0.230065i	−0.638144	−	0.769917i	$-0.720298\pi$
$251$	−10.0143	+	3.64492i	−0.632099	+	0.230065i	0.00604584	+	0.999982i	$0.498076\pi$
$252$	−19.4205	+	6.94365i	−1.22338	+	0.437409i
$253$	1.10688	+	0.402871i	0.0695888	+	0.0253283i
$254$	−7.35436	+	3.69350i	−0.461454	+	0.231751i
$255$	19.6576	−	8.41325i	1.23101	−	0.526858i
$256$	−5.43743	−	12.6054i	−0.339839	−	0.787836i
$257$	1.16759	+	0.136472i	0.0728323	+	0.00851287i	0.152431	−	0.988314i	$-0.451290\pi$
$257$	1.16759	+	0.136472i	0.0728323	+	0.00851287i	−0.0795987	+	0.996827i	$0.525364\pi$
$258$	3.32448	+	1.00559i	0.206973	+	0.0626055i
$259$	−3.15982	−	2.07825i	−0.196342	−	0.129136i
$260$	6.39284	−	5.36423i	0.396467	−	0.332675i
$261$	−1.10171	+	17.2272i	−0.0681942	+	1.06634i
$262$	8.11435	+	6.80875i	0.501306	+	0.420646i
$263$	−2.67668	−	8.94073i	−0.165051	−	0.551309i	−1.00000		0.000980948i	$-0.999688\pi$
$263$	−2.67668	−	8.94073i	−0.165051	−	0.551309i	0.834948	−	0.550328i	$-0.185497\pi$
$264$	−7.99315	−	0.488359i	−0.491944	−	0.0300564i
$265$	−25.0039	−	12.5575i	−1.53598	−	0.771398i
$266$	5.73996	+	6.08401i	0.351940	+	0.373034i
$267$	7.52488	+	4.37307i	0.460515	+	0.267627i
$268$	0.254369	−	0.589695i	0.0155381	−	0.0360213i
$269$	−1.25116	+	2.16707i	−0.0762845	+	0.132129i	−0.901644	−	0.432479i	$-0.857639\pi$
$269$	−1.25116	+	2.16707i	−0.0762845	+	0.132129i	0.825360	+	0.564607i	$0.190972\pi$
$270$	11.2427	−	1.88365i	0.684210	−	0.114635i
$271$	−2.76243	−	4.78467i	−0.167806	−	0.290648i	0.769842	−	0.638234i	$-0.220335\pi$
$271$	−2.76243	−	4.78467i	−0.167806	−	0.290648i	−0.937648	+	0.347586i	$0.887002\pi$
$272$	2.92103	−	0.341419i	0.177113	−	0.0207016i
$273$	6.35766	+	17.6233i	0.384783	+	1.06661i
$274$	−10.9567	+	2.59678i	−0.661917	+	0.156877i
$275$	−0.278833	−	4.78738i	−0.0168143	−	0.288690i
$276$	−1.48626	−	0.646130i	−0.0894624	−	0.0388924i
$277$	25.9932	+	6.16051i	1.56178	+	0.370149i	0.918482	−	0.395464i	$-0.129416\pi$
$277$	25.9932	+	6.16051i	1.56178	+	0.370149i	0.643301	+	0.765613i	$0.277564\pi$
$278$	−0.0442815	+	0.251133i	−0.00265583	+	0.0150620i
$279$	−0.925604	−	17.6176i	−0.0554144	−	1.05474i
$280$	6.41505	+	36.3816i	0.383373	+	2.17421i
$281$	−1.83046	+	31.4278i	−0.109196	+	1.87482i	0.288734	+	0.957409i	$0.406766\pi$
$281$	−1.83046	+	31.4278i	−0.109196	+	1.87482i	−0.397930	+	0.917416i	$0.630271\pi$
$282$	1.04563	−	2.06734i	0.0622663	−	0.123108i
$283$	3.99576	−	5.36724i	0.237523	−	0.319049i	−0.667338	−	0.744755i	$-0.732567\pi$
$283$	3.99576	−	5.36724i	0.237523	−	0.319049i	0.904862	+	0.425705i	$0.139974\pi$
$284$	10.0479	−	13.4966i	0.596230	−	0.800876i
$285$	5.62795	+	8.61011i	0.333371	+	0.510019i
$286$	−0.172680	+	2.96480i	−0.0102108	+	0.175312i
$287$	0.106819	+	0.605803i	0.00630535	+	0.0357594i
$288$	17.4072	+	2.13503i	1.02573	+	0.125808i
$289$	0.458026	−	2.59759i	0.0269427	−	0.152800i
$290$	12.2832	+	2.91118i	0.721297	+	0.170951i
$291$	−1.47281	−	12.9192i	−0.0863379	−	0.757339i
$292$	0.171749	+	2.94882i	0.0100509	+	0.172567i
$293$	3.65264	−	0.865692i	0.213390	−	0.0505743i	−0.122530	−	0.992465i	$-0.539101\pi$
$293$	3.65264	−	0.865692i	0.213390	−	0.0505743i	0.335920	+	0.941890i	$0.390953\pi$
$294$	−23.9298	−	4.28967i	−1.39562	−	0.250179i
$295$	−32.1801	+	3.76132i	−1.87360	+	0.218992i
$296$	1.01020	+	1.74972i	0.0587167	+	0.101700i
$297$	5.02408	−	7.49862i	0.291527	−	0.435114i
$298$	1.21195	−	2.09916i	0.0702066	−	0.121601i
$299$	−0.583094	+	1.35176i	−0.0337212	+	0.0781745i
$300$	−0.0187620	+	6.59785i	−0.00108323	+	0.380927i
$301$	−8.70627	−	9.22810i	−0.501821	−	0.531899i
$302$	8.81503	+	4.42708i	0.507248	+	0.254750i
$303$	−2.16011	+	3.26403i	−0.124095	+	0.187514i
$304$	0.405760	+	1.35533i	0.0232719	+	0.0777337i
$305$	−16.9018	−	14.1823i	−0.967793	−	0.812075i
$306$	4.20128	−	9.58934i	0.240171	−	0.548186i
$307$	−22.9491	+	19.2566i	−1.30977	+	1.09903i	−0.321406	+	0.946942i	$0.604155\pi$
$307$	−22.9491	+	19.2566i	−1.30977	+	1.09903i	−0.988367	+	0.152088i	$0.951400\pi$
$308$	9.97748	+	6.56229i	0.568520	+	0.373921i
$309$	0.105698	+	0.451696i	0.00601296	+	0.0256961i
$310$	−12.8138	−	1.49772i	−0.727775	−	0.0850647i
$311$	1.76187	+	4.08446i	0.0999062	+	0.231609i	0.960837	−	0.277113i	$-0.0893776\pi$
$311$	1.76187	+	4.08446i	0.0999062	+	0.231609i	−0.860931	+	0.508721i	$0.830118\pi$
$312$	1.19018	−	9.93748i	0.0673807	−	0.562599i
$313$	−27.9019	+	14.0129i	−1.57711	+	0.792054i	−0.999702	−	0.0244032i	$-0.992231\pi$
$313$	−27.9019	+	14.0129i	−1.57711	+	0.792054i	−0.577406	+	0.816457i	$0.695935\pi$
$314$	−4.30775	−	1.56789i	−0.243100	−	0.0884812i
$315$	−39.0465	−	14.4638i	−2.20002	−	0.814942i
$316$	9.09346	−	3.30975i	0.511547	−	0.186188i
$317$	19.0975	−	20.2421i	1.07262	−	1.13691i	0.0825140	−	0.996590i	$-0.473705\pi$
$317$	19.0975	−	20.2421i	1.07262	−	1.13691i	0.990106	−	0.140321i	$-0.0448135\pi$
$318$	−13.1353	+	3.89179i	−0.736592	+	0.218241i
$319$	8.35100	−	5.49254i	0.467566	−	0.307523i
$320$	2.61772	−	8.74380i	0.146335	−	0.488793i
$321$	−16.9972	+	2.94725i	−0.948689	+	0.164499i
$322$	−1.58880	−	2.13413i	−0.0885402	−	0.118930i
$323$	9.44699			0.525644
$324$	−7.52868	+	9.87623i	−0.418260	+	0.548680i
$325$	5.99343			0.332456
$326$	−3.17467	−	4.26433i	−0.175829	−	0.236179i
$327$	8.00875	−	21.8107i	0.442885	−	1.20613i
$328$	0.0942496	−	0.314815i	0.00520406	−	0.0173828i
$329$	−7.07027	+	4.65019i	−0.389796	+	0.256373i
$330$	−4.78817	−	4.54321i	−0.263580	−	0.250095i
$331$	−0.135248	+	0.143354i	−0.00743388	+	0.00787946i	−0.731080	−	0.682292i	$-0.760983\pi$
$331$	−0.135248	+	0.143354i	−0.00743388	+	0.00787946i	0.723646	+	0.690171i	$0.242465\pi$
$332$	−4.29171	+	1.56206i	−0.235538	+	0.0857289i
$333$	−2.27722	−	0.0129513i	−0.124791	−	0.000709729i
$334$	12.8674	+	4.68336i	0.704075	+	0.256262i
$335$	1.15868	−	0.581909i	0.0633052	−	0.0317931i
$336$	−4.58405	−	3.43300i	−0.250080	−	0.187285i
$337$	−7.09164	−	16.4403i	−0.386306	−	0.895559i	−0.994786	−	0.101989i	$-0.967479\pi$
$337$	−7.09164	−	16.4403i	−0.386306	−	0.895559i	0.608479	−	0.793570i	$-0.291780\pi$
$338$	6.48169	+	0.757601i	0.352557	+	0.0412081i
$339$	−0.506691	+	0.475322i	−0.0275197	+	0.0258160i
$340$	14.2319	+	9.36049i	0.771835	+	0.507644i
$341$	−7.82522	+	6.56614i	−0.423759	+	0.355576i
$342$	4.89397	+	1.18933i	0.264635	+	0.0643115i
$343$	41.3103	+	34.6635i	2.23055	+	1.87165i
$344$	1.94381	+	6.49278i	0.104803	+	0.350067i
$345$	−1.46012	−	2.92808i	−0.0786104	−	0.157642i
$346$	−9.67291	−	4.85792i	−0.520019	−	0.261163i
$347$	−15.4622	−	16.3889i	−0.830052	−	0.879804i	0.164248	−	0.986419i	$-0.447480\pi$
$347$	−15.4622	−	16.3889i	−0.830052	−	0.879804i	−0.994300	+	0.106615i	$0.965999\pi$
$348$	−11.9292	+	6.84216i	−0.639471	+	0.366778i
$349$	−4.69595	+	10.8864i	−0.251368	+	0.582737i	−0.996445	−	0.0842411i	$-0.973153\pi$
$349$	−4.69595	+	10.8864i	−0.251368	+	0.582737i	0.745077	+	0.666978i	$0.232413\pi$
$350$	−5.41587	+	9.38056i	−0.289490	+	0.501412i
$351$	8.99085	+	6.81342i	0.479896	+	0.363673i
$352$	−5.07737	−	8.79426i	−0.270625	−	0.468736i
$353$	18.6770	−	2.18302i	0.994074	−	0.116191i	0.396526	−	0.918024i	$-0.370216\pi$
$353$	18.6770	−	2.18302i	0.994074	−	0.116191i	0.597548	+	0.801833i	$0.296142\pi$
$354$	−10.2313	+	12.1230i	−0.543788	+	0.644332i
$355$	33.0550	−	7.83417i	1.75438	−	0.415795i
$356$	0.403147	+	6.92177i	0.0213668	+	0.366853i
$357$	−30.7394	+	22.7491i	−1.62690	+	1.20401i
$358$	1.66103	+	0.393671i	0.0877880	+	0.0208061i
$359$	−1.61227	+	9.14366i	−0.0850926	+	0.482584i	0.912244	+	0.409647i	$0.134348\pi$
$359$	−1.61227	+	9.14366i	−0.0850926	+	0.482584i	−0.997337	+	0.0729368i	$0.976763\pi$
$360$	15.1727	+	16.2665i	0.799671	+	0.857318i
$361$	−2.51015	−	14.2358i	−0.132113	−	0.749251i
$362$	1.05902	−	18.1827i	0.0556609	−	0.955661i
$363$	13.8050	−	0.764669i	0.724577	−	0.0401347i
$364$	−8.91276	+	11.9719i	−0.467156	+	0.627499i
$365$	−3.56118	+	4.78349i	−0.186401	+	0.250379i
$366$	−10.7864	+	0.597463i	−0.563813	+	0.0312299i
$367$	1.69898	−	29.1704i	0.0886861	−	1.52268i	−0.601396	−	0.798951i	$-0.705389\pi$
$367$	1.69898	−	29.1704i	0.0886861	−	1.52268i	0.690083	−	0.723731i	$-0.257574\pi$
$368$	−0.0781452	−	0.443183i	−0.00407360	−	0.0231025i
$369$	0.252646	+	0.270859i	0.0131522	+	0.0141004i
$370$	−0.289175	+	1.63999i	−0.0150335	+	0.0852593i
$371$	48.6929	+	11.5404i	2.52801	+	0.599149i
$372$	11.2972	−	8.36064i	0.585733	−	0.433479i
$373$	−0.323556	−	5.55523i	−0.0167531	−	0.287639i	−0.996271	−	0.0862813i	$-0.972502\pi$
$373$	−0.323556	−	5.55523i	−0.0167531	−	0.287639i	0.979518	−	0.201358i	$-0.0645354\pi$
$374$	−5.89859	+	1.39799i	−0.305009	+	0.0722884i
$375$	6.96889	−	8.25739i	0.359872	−	0.426410i
$376$	4.49018	−	0.524827i	0.231564	−	0.0270659i
$377$	6.24612	+	10.8186i	0.321692	+	0.557186i
$378$	−18.7884	+	7.91511i	−0.966372	+	0.407110i
$379$	−14.7919	+	25.6203i	−0.759808	+	1.31603i	0.183140	+	0.983087i	$0.441374\pi$
$379$	−14.7919	+	25.6203i	−0.759808	+	1.31603i	−0.942948	+	0.332940i	$0.891959\pi$
$380$	−3.24571	+	7.52441i	−0.166501	+	0.385994i
$381$	15.7013	−	9.00574i	0.804404	−	0.461378i
$382$	11.8282	+	12.5371i	0.605181	+	0.641455i
$383$	−11.0692	−	5.55918i	−0.565612	−	0.284061i	0.142926	−	0.989733i	$-0.454349\pi$
$383$	−11.0692	−	5.55918i	−0.565612	−	0.284061i	−0.708538	+	0.705672i	$0.750645\pi$
$384$	7.04273	+	14.1232i	0.359398	+	0.720723i
$385$	6.91489	+	23.0973i	0.352415	+	1.17715i
$386$	−4.35230	−	3.65201i	−0.221526	−	0.185883i
$387$	−7.42307	−	1.80395i	−0.377336	−	0.0916999i
$388$	7.93530	−	6.65850i	0.402854	−	0.338034i
$389$	−15.5223	−	10.2092i	−0.787012	−	0.517626i	0.0912370	−	0.995829i	$-0.470918\pi$
$389$	−15.5223	−	10.2092i	−0.787012	−	0.517626i	−0.878249	+	0.478203i	$0.841288\pi$
$390$	6.01647	−	5.64400i	0.304656	−	0.285795i
$391$	−2.98465	−	0.348856i	−0.150940	−	0.0176424i
$392$	−18.7900	−	43.5600i	−0.949037	−	2.20011i
$393$	−18.6478	−	13.9654i	−0.940658	−	0.704460i
$394$	11.5434	−	5.79730i	0.581547	−	0.292064i
$395$	18.3590	+	6.68214i	0.923743	+	0.336215i
$396$	7.19055	+	0.0408952i	0.361339	+	0.00205506i
$397$	9.59694	−	3.49300i	0.481657	−	0.175309i	−0.0897688	−	0.995963i	$-0.528613\pi$
$397$	9.59694	−	3.49300i	0.481657	−	0.175309i	0.571426	+	0.820654i	$0.306391\pi$
$398$	4.36032	−	4.62167i	0.218563	−	0.231663i
$399$	−13.3454	−	12.6626i	−0.668104	−	0.633924i
$400$	−1.53071	+	1.00676i	−0.0765353	+	0.0503380i
$401$	−0.579017	+	1.93405i	−0.0289148	+	0.0965820i	−0.971229	−	0.238148i	$-0.923460\pi$
$401$	−0.579017	+	1.93405i	−0.0289148	+	0.0965820i	0.942314	+	0.334730i	$0.108645\pi$
$402$	0.218824	−	0.595936i	0.0109139	−	0.0297226i
$403$	−7.62385	−	10.2406i	−0.379771	−	0.510121i
$404$	−3.11815			−0.155134
$405$	−24.4605	+	5.50418i	−1.21545	+	0.273505i
$406$	−22.5768			−1.12047
$407$	0.787406	+	1.05767i	0.0390303	+	0.0524267i
$408$	20.1289	−	3.49028i	0.996530	−	0.172795i
$409$	0.249431	−	0.833158i	0.0123336	−	0.0411970i	−0.951601	−	0.307335i	$-0.900563\pi$
$409$	0.249431	−	0.833158i	0.0123336	−	0.0411970i	0.963935	+	0.266138i	$0.0857478\pi$
$410$	0.226302	−	0.148841i	0.0111763	−	0.00735075i
$411$	23.7456	−	7.03546i	1.17129	−	0.347034i
$412$	−0.253611	+	0.268812i	−0.0124945	+	0.0132434i
$413$	54.4506	−	19.8184i	2.67934	−	0.975200i
$414$	−1.50226	−	0.556476i	−0.0738323	−	0.0273493i
$415$	−8.66465	−	3.15367i	−0.425331	−	0.154808i
$416$	11.3415	−	5.69591i	0.556062	−	0.279265i
$417$	0.0666968	−	0.556889i	0.00326616	−	0.0272710i
$418$	−1.15505	−	2.67771i	−0.0564954	−	0.130971i
$419$	25.0738	+	2.93070i	1.22493	+	0.143174i	0.703860	−	0.710338i	$-0.251458\pi$
$419$	25.0738	+	2.93070i	1.22493	+	0.143174i	0.521072	+	0.853512i	$0.325532\pi$
$420$	−7.55818	−	32.2995i	−0.368801	−	1.57605i
$421$	−13.9967	−	9.20577i	−0.682157	−	0.448662i	0.160554	−	0.987027i	$-0.448672\pi$
$421$	−13.9967	−	9.20577i	−0.682157	−	0.448662i	−0.842712	+	0.538365i	$0.819042\pi$
$422$	−14.4315	+	12.1095i	−0.702516	+	0.589481i
$423$	−2.04479	+	4.66719i	−0.0994211	+	0.226927i
$424$	−20.4787	−	17.1836i	−0.994532	−	0.834511i
$425$	3.50868	+	11.7198i	0.170196	+	0.568494i
$426$	9.17937	−	13.8705i	0.444742	−	0.672027i
$427$	35.2631	+	17.7098i	1.70650	+	0.857037i
$428$	−9.43093	−	9.99621i	−0.455861	−	0.483185i
$429$	0.0185744	−	6.53189i	0.000896782	−	0.315362i
$430$	−2.21262	+	5.12942i	−0.106702	+	0.247363i
$431$	−13.1811	+	22.8303i	−0.634911	+	1.09970i	0.351623	+	0.936142i	$0.385630\pi$
$431$	−13.1811	+	22.8303i	−0.634911	+	1.09970i	−0.986534	+	0.163556i	$0.947703\pi$
$432$	−3.44074	−	0.229868i	−0.165543	−	0.0110595i
$433$	6.29345	+	10.9006i	0.302444	+	0.523848i	0.976689	−	0.214660i	$-0.0688642\pi$
$433$	6.29345	+	10.9006i	0.302444	+	0.523848i	−0.674245	+	0.738508i	$0.735531\pi$
$434$	22.9172	−	2.67863i	1.10006	−	0.128579i
$435$	−27.3289	−	4.89899i	−1.31032	−	0.234888i
$436$	18.0109	−	4.26867i	0.862568	−	0.204432i
$437$	−0.0840533	−	1.44314i	−0.00402081	−	0.0690347i
$438$	0.330730	+	2.90110i	0.0158029	+	0.138620i
$439$	8.56156	+	2.02913i	0.408621	+	0.0968449i	0.429785	−	0.902931i	$-0.358589\pi$
$439$	8.56156	+	2.02913i	0.408621	+	0.0968449i	−0.0211645	+	0.999776i	$0.506737\pi$
$440$	2.23659	−	12.6843i	0.106625	−	0.604702i
$441$	53.0731	+	6.50953i	2.52729	+	0.309978i
$442$	−1.31561	−	7.46120i	−0.0625772	−	0.354893i
$443$	0.885106	−	15.1967i	0.0420527	−	0.722017i	−0.909722	−	0.415218i	$-0.863705\pi$
$443$	0.885106	−	15.1967i	0.0420527	−	0.722017i	0.951775	−	0.306798i	$-0.0992577\pi$
$444$	−0.992593	−	1.51855i	−0.0471064	−	0.0720673i
$445$	−8.35916	+	11.2283i	−0.396262	+	0.532273i
$446$	5.62705	−	7.55845i	0.266449	−	0.357903i
$447$	−2.40618	+	4.75731i	−0.113808	+	0.225013i
$448$	−0.949147	+	16.2962i	−0.0448430	+	0.769924i
$449$	−0.214786	−	1.21811i	−0.0101364	−	0.0574862i	0.979320	−	0.202317i	$-0.0648472\pi$
$449$	−0.214786	−	1.21811i	−0.0101364	−	0.0574862i	−0.989456	+	0.144831i	$0.953736\pi$
$450$	0.342190	+	6.51311i	0.0161310	+	0.307031i
$451$	0.0372423	−	0.211212i	0.00175367	−	0.00994557i
$452$	−0.538549	−	0.127639i	−0.0253312	−	0.00600361i
$453$	−19.8968	−	8.64985i	−0.934836	−	0.406406i
$454$	1.14990	+	19.7430i	0.0539673	+	0.926583i
$455$	−29.3208	+	6.94916i	−1.37458	+	0.325782i
$456$	3.33503	+	9.24464i	0.156177	+	0.432920i
$457$	−30.7759	+	3.59718i	−1.43963	+	0.168269i	−0.799810	−	0.600253i	$-0.795067\pi$
$457$	−30.7759	+	3.59718i	−1.43963	+	0.168269i	−0.639824	+	0.768522i	$0.720993\pi$
$458$	10.1484	+	17.5776i	0.474204	+	0.821345i
$459$	−8.05981	+	21.5698i	−0.376200	+	1.00679i
$460$	1.30330	−	2.25738i	0.0607666	−	0.105251i
$461$	−6.71020	+	15.5560i	−0.312525	+	0.724514i	−0.999999	−	0.00169503i	$-0.999460\pi$
$461$	−6.71020	+	15.5560i	−0.312525	+	0.724514i	0.687474	+	0.726209i	$0.258720\pi$
$462$	10.2065	+	5.93151i	0.474851	+	0.275959i
$463$	−24.4901	−	25.9580i	−1.13815	−	1.20637i	−0.975573	−	0.219674i	$-0.929501\pi$
$463$	−24.4901	−	25.9580i	−1.13815	−	1.20637i	−0.162578	−	0.986696i	$-0.551981\pi$
$464$	−3.41252	−	1.71383i	−0.158422	−	0.0795627i
$465$	28.3221	+	1.73040i	1.31340	+	0.0802453i
$466$	−2.06285	−	6.89041i	−0.0955599	−	0.319192i
$467$	−32.1894	−	27.0101i	−1.48955	−	1.24988i	−0.895195	−	0.445675i	$-0.852964\pi$
$467$	−32.1894	−	27.0101i	−1.48955	−	1.24988i	−0.594353	−	0.804204i	$-0.702592\pi$
$468$	−0.573560	+	8.96861i	−0.0265128	+	0.414574i
$469$	−1.77640	+	1.49057i	−0.0820263	+	0.0688282i
$470$	3.11318	+	2.04757i	0.143600	+	0.0944474i
$471$	9.65079	+	2.91918i	0.444685	+	0.134509i
$472$	−30.7458	−	3.59367i	−1.41519	−	0.165412i
$473$	1.75196	+	4.06150i	0.0805552	+	0.186748i
$474$	8.79431	−	3.76387i	0.403936	−	0.172880i
$475$	−5.25923	+	2.64128i	−0.241310	+	0.121190i
$476$	−28.6281	−	10.4198i	−1.31217	−	0.477590i
$477$	28.3725	−	10.1444i	1.29909	−	0.464480i
$478$	16.1023	−	5.86074i	0.736500	−	0.268064i
$479$	−24.7671	+	26.2516i	−1.13164	+	1.19947i	−0.154247	+	0.988032i	$0.549295\pi$
$479$	−24.7671	+	26.2516i	−1.13164	+	1.19947i	−0.977392	+	0.211435i	$0.932186\pi$
$480$	−6.58306	+	27.4283i	−0.300474	+	1.25192i
$481$	−1.37686	+	0.905578i	−0.0627796	+	0.0412908i
$482$	−3.13146	+	10.4598i	−0.142634	+	0.476431i
$483$	3.74869	+	4.49340i	0.170571	+	0.204457i
$484$	6.57751	+	8.83513i	0.298978	+	0.401597i
$485$	20.9136			0.949639
$486$	−6.89087	+	10.1594i	−0.312576	+	0.460842i
$487$	27.8890			1.26377			0.631885	−	0.775062i	$-0.282282\pi$
$487$	27.8890			1.26377			0.631885	+	0.775062i	$0.282282\pi$
$488$	−12.5883	−	16.9090i	−0.569844	−	0.765434i
$489$	7.49049	+	8.97855i	0.338732	+	0.406024i
$490$	11.2145	−	37.4591i	0.506620	−	1.69223i
$491$	−18.1734	+	11.9528i	−0.820155	+	0.539424i	−0.888842	−	0.458214i	$-0.848489\pi$
$491$	−18.1734	+	11.9528i	−0.820155	+	0.539424i	0.0686871	+	0.997638i	$0.478119\pi$
$492$	−0.0688660	+	0.286930i	−0.00310472	+	0.0129358i
$493$	−17.4985	+	18.5474i	−0.788094	+	0.835331i
$494$	3.42489	−	1.24656i	0.154093	−	0.0560853i
$495$	11.0677	+	9.39472i	0.497458	+	0.422261i
$496$	3.66730	+	1.33479i	0.164667	+	0.0599338i
$497$	−54.2932	+	27.2671i	−2.43538	+	1.22310i
$498$	−4.15052	+	1.77638i	−0.185989	+	0.0796015i
$499$	−1.18204	−	2.74029i	−0.0529156	−	0.122672i	0.889707	−	0.456531i	$-0.150908\pi$
$499$	−1.18204	−	2.74029i	−0.0529156	−	0.122672i	−0.942623	+	0.333859i	$0.891649\pi$
$500$	8.54969	+	0.999316i	0.382354	+	0.0446908i
$501$	−28.8274	−	8.71974i	−1.28791	−	0.389569i
$502$	−7.01176	−	4.61171i	−0.312950	−	0.205831i
$503$	−30.5223	+	25.6113i	−1.36092	+	1.14195i	−0.385227	+	0.922822i	$0.625877\pi$
$503$	−30.5223	+	25.6113i	−1.36092	+	1.14195i	−0.975696	+	0.219128i	$0.929679\pi$
$504$	−33.1136	−	22.0500i	−1.47500	−	0.982185i
$505$	−4.82249	−	4.04655i	−0.214598	−	0.180069i
$506$	0.266041	+	0.888640i	0.0118270	+	0.0395049i
$507$	−14.3263	−	0.875298i	−0.636255	−	0.0388734i
$508$	12.8861	+	6.47167i	0.571730	+	0.287134i
$509$	13.6753	+	14.4950i	0.606147	+	0.642479i	0.955667	−	0.294451i	$-0.0951366\pi$
$509$	13.6753	+	14.4950i	0.606147	+	0.642479i	−0.349519	+	0.936929i	$0.613655\pi$
$510$	14.5587	+	8.46074i	0.644669	+	0.374648i
$511$	4.22444	−	9.79336i	0.186878	−	0.433233i
$512$	−3.70618	+	6.41930i	−0.163792	+	0.283695i
$513$	−10.8921	−	2.01653i	−0.480899	−	0.0890319i
$514$	0.462869	+	0.801713i	0.0204163	+	0.0353620i
$515$	−0.741079	+	0.0866197i	−0.0326559	+	0.00381692i
$516$	−2.06517	−	5.72461i	−0.0909140	−	0.252012i
$517$	2.87088	−	0.680411i	0.126261	−	0.0299244i
$518$	−0.173175	−	2.97330i	−0.00760887	−	0.130639i
$519$	21.8332	+	9.49165i	0.958371	+	0.416637i
$520$	15.6636	+	3.71234i	0.686893	+	0.162797i
$521$	−6.17183	+	35.0022i	−0.270393	+	1.53347i	0.482833	+	0.875713i	$0.339608\pi$
$521$	−6.17183	+	35.0022i	−0.270393	+	1.53347i	−0.753226	+	0.657762i	$0.771503\pi$
$522$	−11.4000	+	7.40539i	−0.498966	+	0.324125i
$523$	4.17875	+	23.6989i	0.182724	+	1.03628i	0.928845	+	0.370469i	$0.120803\pi$
$523$	4.17875	+	23.6989i	0.182724	+	1.03628i	−0.746121	+	0.665810i	$0.768086\pi$
$524$	1.07917	−	18.5286i	0.0471437	−	0.809425i
$525$	10.7525	−	21.2591i	0.469278	−	0.927822i
$526$	4.38888	−	5.89528i	0.191364	−	0.257047i
$527$	15.5617	−	20.9031i	0.677880	−	0.910551i
$528$	1.09247	+	1.67135i	0.0475435	+	0.0727360i
$529$	1.31059	−	22.5020i	0.0569824	−	0.978350i
$530$	−3.82623	−	21.6996i	−0.166201	−	0.942571i
$531$	20.9939	−	27.8675i	0.911059	−	1.20934i
$532$	2.54496	−	14.4332i	0.110338	−	0.625757i
$533$	0.260820	+	0.0618155i	0.0112974	+	0.00267753i
$534$	0.776324	+	6.80975i	0.0335948	+	0.294687i
$535$	−1.61328	−	27.6989i	−0.0697481	−	1.19753i
$536$	1.20541	−	0.285687i	0.0520656	−	0.0123398i
$537$	−3.69560	−	0.662475i	−0.159477	−	0.0285879i
$538$	−1.95726	+	0.228770i	−0.0843833	+	0.00986299i
$539$	−15.4805	−	26.8130i	−0.666792	−	1.15492i
$540$	−14.4110	−	13.8303i	−0.620149	−	0.595161i
$541$	5.32644	−	9.22567i	0.229002	−	0.396642i	−0.728511	−	0.685034i	$-0.759787\pi$
$541$	5.32644	−	9.22567i	0.229002	−	0.396642i	0.957512	+	0.288392i	$0.0931206\pi$
$542$	1.72328	−	3.99501i	0.0740212	−	0.171600i
$543$	−0.113914	+	40.0591i	−0.00488853	+	1.71910i
$544$	17.7776	+	18.8431i	0.762206	+	0.807892i
$545$	33.3951	+	16.7717i	1.43049	+	0.718419i
$546$	−8.14239	+	12.3036i	−0.348462	+	0.526544i
$547$	−3.90060	−	13.0289i	−0.166777	−	0.557076i	−0.999991	−	0.00412495i	$-0.998687\pi$
$547$	−3.90060	−	13.0289i	−0.166777	−	0.557076i	0.833214	−	0.552951i	$-0.186498\pi$
$548$	15.1139	+	12.6821i	0.645636	+	0.541753i
$549$	23.6149	−	2.62413i	1.00786	−	0.111995i
$550$	2.89293	−	2.42746i	0.123355	−	0.103507i
$551$	−10.2487	−	6.74066i	−0.436609	−	0.287162i
$552$	−0.712276	−	3.04388i	−0.0303165	−	0.129556i
$553$	−34.7056	−	4.05651i	−1.47583	−	0.172500i
$554$	8.33224	+	19.3163i	0.354003	+	0.820671i
$555$	0.435556	−	3.63670i	0.0184883	−	0.154369i
$556$	0.399291	−	0.200531i	0.0169337	−	0.00850443i
$557$	4.31357	+	1.57001i	0.182772	+	0.0665235i	0.431785	−	0.901977i	$-0.357884\pi$
$557$	4.31357	+	1.57001i	0.182772	+	0.0665235i	−0.249013	+	0.968500i	$0.580106\pi$
$558$	10.6933	−	8.86958i	0.452683	−	0.375479i
$559$	−5.19480	+	1.89075i	−0.219717	+	0.0799704i
$560$	6.32115	−	6.70003i	0.267117	−	0.283128i
$561$	12.7836	−	3.78758i	0.539724	−	0.159912i
$562$	−20.7129	+	13.6231i	−0.873720	+	0.574655i
$563$	−0.284251	+	0.949463i	−0.0119797	+	0.0400151i	−0.963770	−	0.266733i	$-0.914056\pi$
$563$	−0.284251	+	0.949463i	−0.0119797	+	0.0400151i	0.951791	+	0.306748i	$0.0992410\pi$
$564$	−3.99964	+	0.693522i	−0.168415	+	0.0292026i
$565$	−0.667271	−	0.896301i	−0.0280723	−	0.0377077i
$566$	5.26940			0.221489
$567$	40.2977	−	19.6675i	1.69234	−	0.825958i
$568$	32.4565			1.36185
$569$	−4.63945	−	6.23186i	−0.194496	−	0.261253i	0.694167	−	0.719814i	$-0.255773\pi$
$569$	−4.63945	−	6.23186i	−0.194496	−	0.261253i	−0.888663	+	0.458560i	$0.848365\pi$
$570$	−2.79216	+	7.60404i	−0.116951	+	0.318498i
$571$	−6.13681	+	20.4984i	−0.256818	+	0.857830i	0.728198	+	0.685367i	$0.240358\pi$
$571$	−6.13681	+	20.4984i	−0.256818	+	0.857830i	−0.985016	+	0.172464i	$0.944827\pi$
$572$	4.34760	−	2.85946i	0.181782	−	0.119560i
$573$	−27.5004	−	26.0935i	−1.14884	−	1.09007i
$574$	−0.332436	+	0.352362i	−0.0138756	+	0.0147073i
$575$	1.75912	−	0.640267i	0.0733604	−	0.0267010i
$576$	4.86603	+	8.54001i	0.202751	+	0.355834i
$577$	−8.13925	−	2.96244i	−0.338841	−	0.123328i	0.166995	−	0.985958i	$-0.446594\pi$
$577$	−8.13925	−	2.96244i	−0.338841	−	0.123328i	−0.505836	+	0.862630i	$0.668816\pi$
$578$	1.85622	−	0.932230i	0.0772087	−	0.0387757i
$579$	10.0021	+	7.49062i	0.415675	+	0.311300i
$580$	−8.76075	−	20.3097i	−0.363770	−	0.843314i
$581$	16.3795	+	1.91449i	0.679538	+	0.0794266i
$582$	7.46812	−	7.00577i	0.309563	−	0.290399i
$583$	−14.5767	−	9.58724i	−0.603705	−	0.397063i
$584$	−4.36471	+	3.66243i	−0.180613	+	0.151552i
$585$	−12.5260	+	13.1264i	−0.517886	+	0.542710i
$586$	2.26454	+	1.90017i	0.0935472	+	0.0784954i
$587$	−3.01536	−	10.0720i	−0.124457	−	0.415716i	0.872939	−	0.487829i	$-0.162211\pi$
$587$	−3.01536	−	10.0720i	−0.124457	−	0.415716i	−0.997396	+	0.0721128i	$0.977026\pi$
$588$	19.0095	+	38.1209i	0.783937	+	1.57208i
$589$	11.2029	+	5.62632i	0.461608	+	0.231828i
$590$	−17.5091	−	18.5585i	−0.720836	−	0.764042i
$591$	−24.6448	+	14.1354i	−1.01375	+	0.581452i
$592$	0.199531	−	0.462564i	0.00820066	−	0.0190113i
$593$	14.0175	−	24.2790i	0.575630	−	0.997020i	−0.420343	−	0.907365i	$-0.638090\pi$
$593$	14.0175	−	24.2790i	0.575630	−	0.997020i	0.995973	−	0.0896551i	$-0.0285765\pi$
$594$	7.09932	−	0.352748i	0.291288	−	0.0144734i
$595$	−30.7537	−	53.2669i	−1.26078	−	2.18373i
$596$	−4.21840	+	0.493060i	−0.172792	+	0.0201965i
$597$	−9.01334	+	10.6799i	−0.368891	+	0.437097i
$598$	−1.12808	+	0.267360i	−0.0461306	+	0.0109332i
$599$	1.35310	+	23.2319i	0.0552863	+	0.949229i	0.905914	+	0.423461i	$0.139185\pi$
$599$	1.35310	+	23.2319i	0.0552863	+	0.949229i	−0.850628	+	0.525768i	$0.823778\pi$
$600$	−10.2301	+	7.57092i	−0.417643	+	0.309082i
$601$	20.9118	+	4.95618i	0.853009	+	0.202167i	0.633786	−	0.773508i	$-0.281500\pi$
$601$	20.9118	+	4.95618i	0.853009	+	0.202167i	0.219222	+	0.975675i	$0.429648\pi$
$602$	1.73491	−	9.83915i	0.0707096	−	0.401014i
$603$	−0.408060	+	1.33533i	−0.0166175	+	0.0543788i
$604$	−3.00133	−	17.0214i	−0.122122	−	0.692589i
$605$	−1.29301	+	22.2002i	−0.0525685	+	0.902566i
$606$	−3.07762	+	0.170471i	−0.125020	+	0.00692491i
$607$	2.89262	−	3.88547i	0.117408	−	0.157706i	−0.739534	−	0.673119i	$-0.764954\pi$
$607$	2.89262	−	3.88547i	0.117408	−	0.157706i	0.856942	+	0.515413i	$0.172361\pi$
$608$	−7.44197	+	9.99631i	−0.301812	+	0.405404i
$609$	49.5801	−	2.74627i	2.00909	−	0.111284i
$610$	1.01028	−	17.3458i	0.0409050	−	0.702311i
$611$	0.640316	+	3.63141i	0.0259044	+	0.146911i
$612$	−17.8734	+	4.12885i	−0.722488	+	0.166899i
$613$	2.42381	−	13.7461i	0.0978969	−	0.555201i	−0.895924	−	0.444207i	$-0.853485\pi$
$613$	2.42381	−	13.7461i	0.0978969	−	0.555201i	0.993821	−	0.110994i	$-0.0354034\pi$
$614$	−22.9559	−	5.44066i	−0.926427	−	0.219567i
$615$	−0.478868	+	0.354392i	−0.0193098	+	0.0142905i
$616$	1.33940	+	22.9966i	0.0539659	+	0.926559i
$617$	19.6655	−	4.66081i	0.791704	−	0.187637i	0.185182	−	0.982704i	$-0.440712\pi$
$617$	19.6655	−	4.66081i	0.791704	−	0.187637i	0.606522	+	0.795067i	$0.292564\pi$
$618$	−0.235618	+	0.279182i	−0.00947795	+	0.0112304i
$619$	28.6674	−	3.35073i	1.15224	−	0.134677i	0.481552	−	0.876418i	$-0.340073\pi$
$619$	28.6674	−	3.35073i	1.15224	−	0.134677i	0.670687	+	0.741740i	$0.265999\pi$
$620$	11.3025	+	19.5764i	0.453917	+	0.786208i
$621$	3.36675	+	1.03932i	0.135103	+	0.0417063i
$622$	−1.75151	+	3.03370i	−0.0702290	+	0.121640i
$623$	9.91605	−	22.9880i	0.397278	−	0.920994i
$624$	−2.16471	+	1.24160i	−0.0866578	+	0.0497038i
$625$	21.3984	+	22.6810i	0.855937	+	0.907240i
$626$	−21.9728	−	11.0351i	−0.878209	−	0.441053i
$627$	2.86228	+	5.73991i	0.114308	+	0.229230i
$628$	2.30370	+	7.69490i	0.0919277	+	0.307060i
$629$	−2.57685	−	2.16223i	−0.102746	−	0.0862139i
$630$	−9.22576	−	31.4664i	−0.367563	−	1.25365i
$631$	−35.3851	+	29.6916i	−1.40866	+	1.18200i	−0.451558	+	0.892242i	$0.649132\pi$
$631$	−35.3851	+	29.6916i	−1.40866	+	1.18200i	−0.957099	+	0.289762i	$0.906424\pi$
$632$	15.5956	+	10.2574i	0.620359	+	0.408017i
$633$	30.2195	−	28.3486i	1.20112	−	1.12676i
$634$	21.7672	+	2.54422i	0.864487	+	0.101044i
$635$	11.5310	+	26.7319i	0.457594	+	1.06082i
$636$	19.2136	+	14.3891i	0.761869	+	0.570565i
$637$	34.5793	−	17.3664i	1.37008	−	0.688080i
$638$	7.39666	+	2.69216i	0.292836	+	0.106584i
$639$	−18.4712	+	31.5770i	−0.730710	+	1.24917i
$640$	−23.8524	+	8.68156i	−0.942848	+	0.343169i
$641$	17.0820	−	18.1058i	0.674698	−	0.715138i	−0.296068	−	0.955167i	$-0.595675\pi$
$641$	17.0820	−	18.1058i	0.674698	−	0.715138i	0.970766	+	0.240029i	$0.0771570\pi$
$642$	−9.85483	−	9.35067i	−0.388939	−	0.369041i
$643$	−1.84993	+	1.21672i	−0.0729540	+	0.0479826i	−0.585462	−	0.810700i	$-0.699087\pi$
$643$	−1.84993	+	1.21672i	−0.0729540	+	0.0479826i	0.512508	+	0.858682i	$0.328716\pi$
$644$	−1.33703	+	4.46599i	−0.0526863	+	0.175985i
$645$	4.23509	−	11.5337i	0.166756	−	0.454137i
$646$	4.44257	+	5.96741i	0.174791	+	0.234784i
$647$	26.5378			1.04331			0.521654	−	0.853157i	$-0.325315\pi$
$647$	26.5378			1.04331			0.521654	+	0.853157i	$0.325315\pi$
$648$	−23.9531	−	0.272469i	−0.940967	−	0.0107036i
$649$	−20.2024			−0.793015
$650$	2.81849	+	3.78589i	0.110550	+	0.148495i
$651$	−50.0017	+	8.67011i	−1.95972	+	0.339808i
$652$	−2.67160	+	8.92377i	−0.104628	+	0.349482i
$653$	−0.177323	+	0.116627i	−0.00693920	+	0.00456398i	−0.552974	−	0.833199i	$-0.686507\pi$
$653$	−0.177323	+	0.116627i	−0.00693920	+	0.00456398i	0.546035	+	0.837763i	$0.316137\pi$
$654$	17.5434	−	5.19785i	0.686003	−	0.203252i
$655$	25.7143	−	27.2556i	1.00474	−	1.06496i
$656$	−0.0769964	+	0.0280244i	−0.00300620	+	0.00109417i
$657$	−1.07919	−	6.33075i	−0.0421034	−	0.246986i
$658$	−6.26228	−	2.27928i	−0.244129	−	0.0888558i
$659$	−24.1950	+	12.1512i	−0.942505	+	0.473344i	−0.852575	−	0.522604i	$-0.824960\pi$
$659$	−24.1950	+	12.1512i	−0.942505	+	0.473344i	−0.0899295	+	0.995948i	$0.528664\pi$
$660$	−1.37531	+	11.4833i	−0.0535340	+	0.446986i
$661$	14.1708	+	32.8515i	0.551179	+	1.27778i	0.935091	+	0.354407i	$0.115317\pi$
$661$	14.1708	+	32.8515i	0.551179	+	1.27778i	−0.383912	+	0.923370i	$0.625423\pi$
$662$	−0.154155	−	0.0180181i	−0.00599140	−	0.000700294i
$663$	3.79675	+	16.2252i	0.147453	+	0.630135i
$664$	−7.36043	−	4.84103i	−0.285640	−	0.187868i
$665$	22.6665	−	19.0195i	0.878969	−	0.737543i
$666$	−1.06271	−	1.44455i	−0.0411792	−	0.0559751i
$667$	2.98902	+	2.50808i	0.115735	+	0.0971134i
$668$	−6.88127	−	22.9850i	−0.266244	−	0.889317i
$669$	−11.4379	+	17.2833i	−0.442216	+	0.668210i
$670$	0.912458	+	0.458254i	0.0352513	+	0.0177039i
$671$	−9.44115	−	10.0070i	−0.364471	−	0.386317i
$672$	0.143456	−	50.4477i	0.00553393	−	1.94606i
$673$	−11.3090	+	26.2172i	−0.435930	+	1.01060i	0.548711	+	0.836012i	$0.315119\pi$
$673$	−11.3090	+	26.2172i	−0.435930	+	1.01060i	−0.984642	+	0.174588i	$0.944141\pi$
$674$	7.04994	−	12.2109i	0.271554	−	0.470345i
$675$	−1.54373	−	14.2616i	−0.0594182	−	0.548928i
$676$	−5.71719	−	9.90247i	−0.219892	−	0.380864i
$677$	−14.6253	+	1.70945i	−0.562097	+	0.0656997i	−0.392397	−	0.919796i	$-0.628354\pi$
$677$	−14.6253	+	1.70945i	−0.562097	+	0.0656997i	−0.169700	+	0.985496i	$0.554280\pi$
$678$	−0.538526	−	0.0965365i	−0.0206820	−	0.00370746i
$679$	−36.3953	+	8.62584i	−1.39672	+	0.331030i
$680$	1.91053	+	32.8025i	0.0732654	+	1.25792i
$681$	−4.92679	−	43.2168i	−0.188795	−	1.65607i
$682$	−7.82757	−	1.85517i	−0.299733	−	0.0710380i
$683$	0.764140	−	4.33365i	0.0292390	−	0.165823i	−0.966692	−	0.255943i	$-0.917614\pi$
$683$	0.764140	−	4.33365i	0.0292390	−	0.165823i	0.995931	+	0.0901204i	$0.0287252\pi$
$684$	−3.44914	−	8.12271i	−0.131881	−	0.310580i
$685$	6.91695	+	39.2280i	0.264283	+	1.49882i
$686$	−2.46926	+	42.3956i	−0.0942769	+	1.61867i
$687$	−24.4247	−	37.3669i	−0.931859	−	1.42564i
$688$	1.00913	−	1.35550i	0.0384729	−	0.0516781i
$689$	13.0212	−	17.4905i	0.496068	−	0.666334i
$690$	1.16294	−	2.29929i	0.0442726	−	0.0875324i
$691$	−0.176090	+	3.02335i	−0.00669878	+	0.115014i	−1.00000		0.000541509i	$-0.999828\pi$
$691$	−0.176090	+	3.02335i	−0.00669878	+	0.115014i	0.993301	+	0.115555i	$0.0368647\pi$
$692$	3.29341	+	18.6779i	0.125197	+	0.710026i
$693$	−23.1357	−	11.7844i	−0.878852	−	0.447653i
$694$	3.08116	−	17.4741i	0.116959	−	0.663309i
$695$	0.877776	+	0.208037i	0.0332959	+	0.00789128i
$696$	−24.3275	−	10.5760i	−0.922132	−	0.400883i
$697$	0.0318129	+	0.546207i	0.00120500	+	0.0206891i
$698$	−9.08500	+	2.15318i	−0.343872	+	0.0814992i
$699$	5.36831	+	14.8808i	0.203048	+	0.562845i
$700$	18.8508	−	2.20334i	0.712493	−	0.0832785i
$701$	−21.6147	−	37.4378i	−0.816377	−	1.41401i	−0.908335	−	0.418243i	$-0.862646\pi$
$701$	−21.6147	−	37.4378i	−0.816377	−	1.41401i	0.0919585	−	0.995763i	$-0.470687\pi$
$702$	−0.0757854	+	8.88338i	−0.00286034	+	0.335282i
$703$	0.809112	−	1.40142i	0.0305162	−	0.0528557i
$704$	2.25419	−	5.22581i	0.0849581	−	0.196955i
$705$	−7.08580	−	4.11790i	−0.266867	−	0.155089i
$706$	10.1620	+	10.7711i	0.382453	+	0.405377i
$707$	10.0614	+	5.05304i	0.378399	+	0.190039i
$708$	27.7438	+	1.69507i	1.04267	+	0.0637045i
$709$	9.22829	+	30.8246i	0.346576	+	1.15764i	0.936642	+	0.350289i	$0.113917\pi$
$709$	9.22829	+	30.8246i	0.346576	+	1.15764i	−0.590066	+	0.807355i	$0.700898\pi$
$710$	20.4932	+	17.1958i	0.769095	+	0.645347i
$711$	−18.8550	+	9.33543i	−0.707117	+	0.350106i
$712$	−10.2453	+	8.59684i	−0.383959	+	0.322180i
$713$	−3.33165	−	2.19126i	−0.124771	−	0.0820633i
$714$	−28.8256	−	8.71921i	−1.07877	−	0.326308i
$715$	10.4348	+	1.21965i	0.390238	+	0.0456123i
$716$	−1.18469	−	2.74642i	−0.0442739	−	0.102638i
$717$	−34.6486	+	14.8292i	−1.29398	+	0.553808i
$718$	−6.53400	+	3.28150i	−0.243847	+	0.122464i
$719$	−9.54600	−	3.47446i	−0.356006	−	0.129576i	0.157825	−	0.987467i	$-0.449552\pi$
$719$	−9.54600	−	3.47446i	−0.356006	−	0.129576i	−0.513831	+	0.857892i	$0.671774\pi$
$720$	0.994164	−	5.45653i	0.0370503	−	0.203353i
$721$	1.25395	−	0.456400i	0.0466995	−	0.0169972i
$722$	7.81193	−	8.28016i	0.290730	−	0.308156i
$723$	5.60453	−	23.3513i	0.208435	−	0.868443i
$724$	−26.6632	+	17.5366i	−0.990929	+	0.651744i
$725$	4.55594	−	15.2179i	0.169203	−	0.565179i
$726$	6.97503	+	8.36068i	0.258868	+	0.310294i
$727$	8.41672	+	11.3056i	0.312159	+	0.419302i	0.930320	−	0.366749i	$-0.119529\pi$
$727$	8.41672	+	11.3056i	0.312159	+	0.419302i	−0.618161	+	0.786052i	$0.712122\pi$
$728$	−28.7900			−1.06703
$729$	13.8970	−	23.1490i	0.514703	−	0.857369i
$730$	−4.69629			−0.173818
$731$	−6.73840	−	9.05125i	−0.249229	−	0.334772i
$732$	12.1258	+	14.5347i	0.448182	+	0.537218i
$733$	4.50233	−	15.0388i	0.166297	−	0.555471i	−0.833698	−	0.552221i	$-0.813780\pi$
$733$	4.50233	−	15.0388i	0.166297	−	0.555471i	0.999995	−	0.00324994i	$-0.00103449\pi$
$734$	19.2251	−	12.6446i	0.709612	−	0.466719i
$735$	−20.0712	+	83.6266i	−0.740337	+	3.08461i
$736$	2.72033	−	2.88339i	0.100273	−	0.106283i
$737$	0.759727	−	0.276518i	0.0279849	−	0.0101857i
$738$	−0.0522842	+	0.286965i	−0.00192461	+	0.0105633i
$739$	−3.42025	−	1.24487i	−0.125816	−	0.0457933i	0.278345	−	0.960481i	$-0.410214\pi$
$739$	−3.42025	−	1.24487i	−0.125816	−	0.0457933i	−0.404161	+	0.914688i	$0.632436\pi$
$740$	2.60752	−	1.30955i	0.0958544	−	0.0481399i
$741$	−7.36963	+	3.15412i	−0.270730	+	0.115870i
$742$	15.6087	+	36.1850i	0.573013	+	1.32839i
$743$	−23.1239	−	2.70280i	−0.848334	−	0.0991560i	−0.319193	−	0.947690i	$-0.603412\pi$
$743$	−23.1239	−	2.70280i	−0.848334	−	0.0991560i	−0.529141	+	0.848534i	$0.677486\pi$
$744$	25.9490	+	7.84910i	0.951338	+	0.287762i
$745$	−7.16398	−	4.71182i	−0.262468	−	0.172628i
$746$	3.35694	−	2.81680i	0.122906	−	0.103130i
$747$	8.89872	−	4.40591i	0.325587	−	0.161204i
$748$	8.13668	+	6.82748i	0.297506	+	0.249637i
$749$	14.2320	+	47.5381i	0.520025	+	1.73700i
$750$	8.49318	+	0.518909i	0.310127	+	0.0189479i
$751$	7.05894	+	3.54513i	0.257584	+	0.129364i	0.572906	−	0.819621i	$-0.305816\pi$
$751$	7.05894	+	3.54513i	0.257584	+	0.129364i	−0.315322	+	0.948985i	$0.602112\pi$
$752$	−0.773530	−	0.819894i	−0.0282077	−	0.0298985i
$753$	15.9592	+	9.27467i	0.581586	+	0.337988i
$754$	−3.89650	+	9.03309i	−0.141902	+	0.328966i
$755$	17.4475	−	30.2200i	0.634980	−	1.09982i
$756$	30.7832	+	18.1246i	1.11958	+	0.659185i
$757$	−2.12074	−	3.67323i	−0.0770795	−	0.133506i	0.824909	−	0.565265i	$-0.191226\pi$
$757$	−2.12074	−	3.67323i	−0.0770795	−	0.133506i	−0.901989	+	0.431760i	$0.857893\pi$
$758$	−23.1397	+	2.70465i	−0.840473	+	0.0982372i
$759$	−0.692338	−	1.91915i	−0.0251303	−	0.0696606i
$760$	−15.3808	+	3.64531i	−0.557920	+	0.132229i
$761$	−2.37743	−	40.8189i	−0.0861818	−	1.47968i	−0.713354	−	0.700803i	$-0.752825\pi$
$761$	−2.37743	−	40.8189i	−0.0861818	−	1.47968i	0.627173	−	0.778880i	$-0.284212\pi$
$762$	13.0724	+	5.68305i	0.473565	+	0.205875i
$763$	−65.0339	−	15.4133i	−2.35438	−	0.557999i
$764$	5.24431	−	29.7420i	0.189733	−	1.07603i
$765$	−33.0009	−	16.8094i	−1.19315	−	0.607744i
$766$	−1.69387	−	9.60642i	−0.0612020	−	0.347094i
$767$	1.46810	−	25.2064i	0.0530101	−	0.910149i
$768$	−10.7318	+	21.2182i	−0.387252	+	0.765645i
$769$	19.5244	−	26.2258i	0.704066	−	0.945725i	−0.295889	−	0.955222i	$-0.595616\pi$
$769$	19.5244	−	26.2258i	0.704066	−	0.945725i	0.999955	+	0.00949722i	$0.00302310\pi$
$770$	−11.3381	+	15.2298i	−0.408598	+	0.548843i
$771$	−1.11401	−	1.70430i	−0.0401201	−	0.0613790i
$772$	−0.578834	+	9.93820i	−0.0208327	+	0.357684i
$773$	−6.74796	−	38.2696i	−0.242707	−	1.37646i	−0.825757	−	0.564025i	$-0.809252\pi$
$773$	−6.74796	−	38.2696i	−0.242707	−	1.37646i	0.583050	−	0.812436i	$-0.301859\pi$
$774$	−2.35129	−	5.53729i	−0.0845154	−	0.199034i
$775$	−2.81909	+	15.9878i	−0.101265	+	0.574300i
$776$	19.4429	+	4.60805i	0.697958	+	0.165419i
$777$	0.741977	+	6.50848i	0.0266183	+	0.233490i
$778$	−0.850704	−	14.6060i	−0.0304992	−	0.523651i
$779$	−0.256111	+	0.0606995i	−0.00917614	+	0.00217479i
$780$	−14.2276	−	2.55045i	−0.509431	−	0.0913208i
$781$	21.0391	−	2.45911i	0.752837	−	0.0879940i
$782$	−1.18321	−	2.04938i	−0.0423115	−	0.0732856i
$783$	24.1344	−	17.6494i	0.862493	−	0.630738i
$784$	−5.91429	+	10.2439i	−0.211225	+	0.365852i
$785$	−6.42311	+	14.8904i	−0.229251	+	0.531463i
$786$	0.0521718	−	18.3467i	0.00186091	−	0.654406i
$787$	−1.56542	−	1.65925i	−0.0558011	−	0.0591457i	0.698872	−	0.715247i	$-0.253686\pi$
$787$	−1.56542	−	1.65925i	−0.0558011	−	0.0591457i	−0.754673	+	0.656101i	$0.772204\pi$
$788$	−20.2260	−	10.1579i	−0.720523	−	0.361860i
$789$	−8.92113	+	13.4803i	−0.317601	+	0.479910i
$790$	4.41265	+	14.7393i	0.156995	+	0.524399i
$791$	1.53091	+	1.28459i	0.0544329	+	0.0456746i
$792$	8.21940	+	11.1727i	0.292064	+	0.397003i
$793$	13.1718	−	11.0524i	0.467743	−	0.392483i
$794$	6.71952	+	4.41950i	0.238467	+	0.156842i
$795$	11.0422	+	47.1882i	0.391626	+	1.67359i
$796$	−11.0579	−	1.29248i	−0.391937	−	0.0458109i
$797$	13.5480	+	31.4079i	0.479896	+	1.11252i	0.970491	+	0.241136i	$0.0775200\pi$
$797$	13.5480	+	31.4079i	0.479896	+	1.11252i	−0.490596	+	0.871387i	$0.663221\pi$
$798$	1.72281	−	14.3847i	0.0609867	−	0.509212i
$799$	−6.72616	+	3.37800i	−0.237954	+	0.119505i
$800$	−15.1653	−	5.51971i	−0.536174	−	0.195151i
$801$	−2.53320	−	14.8602i	−0.0895061	−	0.525059i
$802$	−1.49398	+	0.543764i	−0.0527543	+	0.0192010i
$803$	−2.55182	+	2.70477i	−0.0900518	+	0.0954493i
$804$	−1.06653	+	0.315995i	−0.0376135	+	0.0111443i
$805$	−7.86353	+	5.17192i	−0.277153	+	0.182286i
$806$	2.88350	−	9.63156i	0.101567	−	0.339257i
$807$	4.27042	−	0.740476i	0.150326	−	0.0260660i
$808$	−3.59174	−	4.82455i	−0.126357	−	0.169727i
$809$	−22.5844			−0.794027			−0.397013	−	0.917813i	$-0.629953\pi$
$809$	−22.5844			−0.794027			−0.397013	+	0.917813i	$0.629953\pi$
$810$	−14.9797	−	12.8627i	−0.526334	−	0.451948i
$811$	15.6809			0.550631			0.275315	−	0.961354i	$-0.411218\pi$
$811$	15.6809			0.550631			0.275315	+	0.961354i	$0.411218\pi$
$812$	23.6228	+	31.7309i	0.828997	+	1.11354i
$813$	−3.29847	+	8.98290i	−0.115682	+	0.315044i
$814$	−0.297813	+	0.994766i	−0.0104384	+	0.0348665i
$815$	−15.7126	+	10.3343i	−0.550388	+	0.361996i
$816$	−3.69515	−	3.50610i	−0.129356	−	0.122738i
$817$	3.72519	−	3.94847i	0.130328	−	0.138139i
$818$	0.643582	−	0.234245i	0.0225023	−	0.00819017i
$819$	16.3846	−	28.0098i	0.572523	−	0.978741i
$820$	−0.445977	−	0.162322i	−0.0155742	−	0.00566854i
$821$	45.6834	−	22.9431i	1.59436	−	0.800718i	0.594367	−	0.804194i	$-0.297403\pi$
$821$	45.6834	−	22.9431i	1.59436	−	0.800718i	0.999994	+	0.00347568i	$0.00110635\pi$
$822$	15.6108	+	11.6910i	0.544490	+	0.407769i
$823$	1.30609	+	3.02787i	0.0455276	+	0.105545i	0.939462	−	0.342653i	$-0.111325\pi$
$823$	1.30609	+	3.02787i	0.0455276	+	0.105545i	−0.893935	+	0.448197i	$0.852066\pi$
$824$	−0.708048	−	0.0827589i	−0.0246660	−	0.00288304i
$825$	−6.05778	+	5.68275i	−0.210905	+	0.197848i
$826$	38.1249	+	25.0751i	1.32653	+	0.872475i
$827$	15.7734	−	13.2354i	0.548494	−	0.460241i	−0.325937	−	0.945392i	$-0.605680\pi$
$827$	15.7734	−	13.2354i	0.548494	−	0.460241i	0.874431	+	0.485151i	$0.161235\pi$
$828$	0.789756	+	2.69363i	0.0274459	+	0.0936102i
$829$	10.1320	+	8.50174i	0.351898	+	0.295278i	0.801552	−	0.597925i	$-0.204008\pi$
$829$	10.1320	+	8.50174i	0.351898	+	0.295278i	−0.449654	+	0.893203i	$0.648453\pi$
$830$	−2.08257	−	6.95628i	−0.0722872	−	0.241456i
$831$	−20.6477	−	41.4062i	−0.716262	−	1.43637i
$832$	6.35638	+	3.19229i	0.220368	+	0.110673i
$833$	54.2023	+	57.4511i	1.87800	+	1.99056i
$834$	0.383137	−	0.219754i	0.0132670	−	0.00760946i
$835$	19.1861	−	44.4784i	0.663963	−	1.53924i
$836$	−2.55486	+	4.42514i	−0.0883616	+	0.153047i
$837$	−22.4042	+	20.7789i	−0.774402	+	0.718223i
$838$	9.94002	+	17.2166i	0.343372	+	0.594738i
$839$	−6.26646	+	0.732444i	−0.216342	+	0.0252868i	−0.223574	−	0.974687i	$-0.571772\pi$
$839$	−6.26646	+	0.732444i	−0.216342	+	0.0252868i	0.00723124	+	0.999974i	$0.497698\pi$
$840$	41.2691	−	48.8996i	1.42392	−	1.68720i
$841$	3.99920	−	0.947828i	0.137904	−	0.0326837i
$842$	−0.767093	−	13.1705i	−0.0264358	−	0.453884i
$843$	43.8296	−	32.4366i	1.50957	−	1.11718i
$844$	32.1196	+	7.61247i	1.10560	+	0.262032i
$845$	4.00870	−	22.7345i	0.137903	−	0.782089i
$846$	−3.90973	+	0.903169i	−0.134419	+	0.0310516i
$847$	−6.90630	−	39.1676i	−0.237303	−	1.34581i
$848$	−0.387568	+	6.65429i	−0.0133091	+	0.228509i
$849$	−11.5719	+	0.640975i	−0.397147	+	0.0219982i
$850$	−5.75308	+	7.72773i	−0.197329	+	0.265059i
$851$	−0.307380	+	0.412882i	−0.0105368	+	0.0141534i
$852$	−29.0991	+	1.61181i	−0.996917	+	0.0552198i
$853$	−1.05380	+	18.0931i	−0.0360816	+	0.619496i	0.930998	+	0.365023i	$0.118939\pi$
$853$	−1.05380	+	18.0931i	−0.0360816	+	0.619496i	−0.967080	+	0.254473i	$0.918098\pi$
$854$	5.39614	+	30.6030i	0.184652	+	1.04721i
$855$	5.20678	−	17.0386i	0.178068	−	0.582706i
$856$	4.60327	−	26.1064i	0.157336	−	0.892299i
$857$	−33.0907	−	7.84263i	−1.13036	−	0.267899i	−0.377452	−	0.926029i	$-0.623200\pi$
$857$	−33.0907	−	7.84263i	−1.13036	−	0.267899i	−0.752904	+	0.658130i	$0.771348\pi$
$858$	4.13475	−	3.05997i	0.141158	−	0.104466i
$859$	−2.76746	−	47.5154i	−0.0944244	−	1.62120i	−0.629915	−	0.776664i	$-0.716910\pi$
$859$	−2.76746	−	47.5154i	−0.0944244	−	1.62120i	0.535491	−	0.844541i	$-0.320127\pi$
$860$	9.52432	−	2.25731i	0.324777	−	0.0769735i
$861$	0.687188	−	0.814246i	0.0234193	−	0.0277494i
$862$	−20.6199	+	2.41012i	−0.702316	+	0.0820890i
$863$	26.7851	+	46.3932i	0.911777	+	1.57924i	0.811553	+	0.584279i	$0.198623\pi$
$863$	26.7851	+	46.3932i	0.911777	+	1.57924i	0.100224	+	0.994965i	$0.468044\pi$
$864$	−16.4748	−	25.5203i	−0.560485	−	0.868219i
$865$	−19.1455	+	33.1610i	−0.650966	+	1.12751i
$866$	−3.92602	+	9.10154i	−0.133412	+	0.309283i
$867$	−3.96298	+	2.27303i	−0.134590	+	0.0771960i
$868$	−27.7436	−	29.4065i	−0.941679	−	0.998121i
$869$	10.8866	+	5.46745i	0.369302	+	0.185471i
$870$	−9.75720	−	19.5667i	−0.330800	−	0.663374i
$871$	0.289800	+	0.967998i	0.00981949	+	0.0327994i
$872$	27.3512	+	22.9504i	0.926227	+	0.777197i
$873$	−15.5482	+	16.2935i	−0.526228	+	0.551452i
$874$	0.872065	−	0.731749i	0.0294980	−	0.0247518i
$875$	−25.9681	−	17.0795i	−0.877882	−	0.577392i
$876$	3.73133	−	3.50033i	0.126070	−	0.118265i
$877$	14.2696	+	1.66787i	0.481848	+	0.0563200i	0.353550	−	0.935416i	$-0.384974\pi$
$877$	14.2696	+	1.66787i	0.481848	+	0.0563200i	0.128298	+	0.991736i	$0.459048\pi$
$878$	2.74444	+	6.36233i	0.0926204	+	0.214718i
$879$	−5.20420	−	3.89743i	−0.175533	−	0.131457i
$880$	−2.86988	+	1.44131i	−0.0967438	+	0.0485866i
$881$	0.647962	+	0.235839i	0.0218304	+	0.00794561i	0.352912	−	0.935656i	$-0.385191\pi$
$881$	0.647962	+	0.235839i	0.0218304	+	0.00794561i	−0.331082	+	0.943602i	$0.607414\pi$
$882$	20.8464	+	36.5861i	0.701936	+	1.23192i
$883$	−23.8383	+	8.67642i	−0.802222	+	0.291985i	−0.710407	−	0.703791i	$-0.751489\pi$
$883$	−23.8383	+	8.67642i	−0.802222	+	0.291985i	−0.0918148	+	0.995776i	$0.529267\pi$
$884$	−9.10987	+	9.65590i	−0.306398	+	0.324763i
$885$	40.7084	+	38.6258i	1.36840	+	1.29839i
$886$	10.0156	−	6.58735i	0.336480	−	0.221306i
$887$	−11.9637	+	39.9614i	−0.401700	+	1.34177i	0.483003	+	0.875619i	$0.339546\pi$
$887$	−11.9637	+	39.9614i	−0.401700	+	1.34177i	−0.884704	+	0.466154i	$0.845639\pi$
$888$	1.20622	−	3.28498i	0.0404782	−	0.110237i
$889$	−31.0926	−	41.7646i	−1.04281	−	1.40074i
$890$	−11.0236			−0.369513
$891$	−15.5476	+	1.63822i	−0.520865	+	0.0548825i
$892$	−16.5109			−0.552824
$893$	−2.16223	−	2.90437i	−0.0723562	−	0.0971912i
$894$	−4.13660	+	0.717272i	−0.138349	+	0.0239892i
$895$	1.73191	−	5.78499i	0.0578915	−	0.193371i
$896$	37.9288	−	24.9462i	1.26711	−	0.833393i
$897$	2.44481	−	0.724359i	0.0816298	−	0.0241857i
$898$	0.668442	−	0.708507i	0.0223062	−	0.0236432i
$899$	−31.7972	+	11.5732i	−1.06050	+	0.385989i
$900$	8.79589	−	7.29578i	0.293196	−	0.243193i
$901$	41.8245	+	15.2229i	1.39338	+	0.507147i
$902$	0.150930	−	0.0758001i	0.00502543	−	0.00252387i
$903$	−2.61312	+	21.8184i	−0.0869591	+	0.726071i
$904$	−0.422857	−	0.980293i	−0.0140640	−	0.0326041i
$905$	−63.9949	−	7.47993i	−2.12726	−	0.248641i
$906$	−3.89288	−	16.6360i	−0.129332	−	0.552694i
$907$	33.1694	+	21.8159i	1.10137	+	0.724384i	0.963938	−	0.266127i	$-0.0857442\pi$
$907$	33.1694	+	21.8159i	1.10137	+	0.724384i	0.137434	+	0.990511i	$0.456115\pi$
$908$	26.5448	−	22.2737i	0.880920	−	0.739180i
$909$	6.73790	−	0.748729i	0.223482	−	0.0248338i
$910$	−18.1781	−	15.2532i	−0.602598	−	0.505640i
$911$	−11.2981	−	37.7383i	−0.374323	−	1.25033i	−0.913051	−	0.407846i	$-0.866280\pi$
$911$	−11.2981	−	37.7383i	−0.374323	−	1.25033i	0.538727	−	0.842480i	$-0.318905\pi$
$912$	1.35236	−	2.04348i	0.0447811	−	0.0676665i
$913$	−5.13799	−	2.58040i	−0.170043	−	0.0853987i
$914$	−16.7450	−	17.7487i	−0.553875	−	0.587073i
$915$	−0.108671	+	38.2153i	−0.00359256	+	1.26336i
$916$	14.0860	−	32.6551i	0.465415	−	1.07895i
$917$	−33.5082	+	58.0379i	−1.10654	+	1.91658i
$918$	−17.4153	+	5.05232i	−0.574790	+	0.166751i
$919$	7.97650	+	13.8157i	0.263120	+	0.455738i	0.967069	−	0.254513i	$-0.0819150\pi$
$919$	7.97650	+	13.8157i	0.263120	+	0.455738i	−0.703949	+	0.710250i	$0.748582\pi$
$920$	4.99397	−	0.583711i	0.164646	−	0.0192444i
$921$	51.0744	+	9.15563i	1.68296	+	0.301688i
$922$	−12.9819	+	3.07676i	−0.427535	+	0.101328i
$923$	1.53931	+	26.4289i	0.0506670	+	0.869919i
$924$	−2.34287	−	20.5512i	−0.0770748	−	0.676085i
$925$	2.03910	+	0.483274i	0.0670450	+	0.0158900i
$926$	4.88017	−	27.6768i	0.160372	−	0.909516i
$927$	0.483471	−	0.641762i	0.0158793	−	0.0210782i
$928$	−5.84117	−	33.1269i	−0.191746	−	1.08744i
$929$	1.45951	−	25.0588i	0.0478850	−	0.822154i	−0.885802	−	0.464064i	$-0.846391\pi$
$929$	1.45951	−	25.0588i	0.0478850	−	0.822154i	0.933687	−	0.358090i	$-0.116572\pi$
$930$	12.2258	+	18.7040i	0.400899	+	0.613329i
$931$	−22.6900	+	30.4779i	−0.743634	+	0.998873i
$932$	−7.52579	+	10.1089i	−0.246515	+	0.331128i
$933$	3.47739	−	6.87523i	0.113845	−	0.225085i
$934$	1.92407	−	33.0350i	0.0629576	−	1.08094i
$935$	3.72378	+	21.1186i	0.121781	+	0.690652i
$936$	−14.5373	+	9.44334i	−0.475167	+	0.308665i
$937$	−6.76540	+	38.3685i	−0.221016	+	1.25344i	0.649140	+	0.760669i	$0.275129\pi$
$937$	−6.76540	+	38.3685i	−0.221016	+	1.25344i	−0.870156	+	0.492776i	$0.835982\pi$
$938$	−1.77693	−	0.421140i	−0.0580187	−	0.0137507i
$939$	49.5959	+	21.5610i	1.61850	+	0.703618i
$940$	−0.379624	−	6.51788i	−0.0123820	−	0.212590i
$941$	32.1821	−	7.62730i	1.04911	−	0.248643i	0.330317	−	0.943870i	$-0.392844\pi$
$941$	32.1821	−	7.62730i	1.04911	−	0.248643i	0.718790	+	0.695227i	$0.244696\pi$
$942$	2.69444	+	7.46893i	0.0877896	+	0.243351i
$943$	0.0831565	−	0.00971960i	0.00270795	−	0.000316514i
$944$	3.85915	+	6.68424i	0.125605	+	0.217554i
$945$	24.0879	+	67.9799i	0.783580	+	2.21139i
$946$	−1.74166	+	3.01664i	−0.0566261	+	0.0980793i
$947$	5.74484	−	13.3180i	0.186682	−	0.432778i	−0.799013	−	0.601313i	$-0.794644\pi$
$947$	5.74484	−	13.3180i	0.186682	−	0.432778i	0.985696	+	0.168535i	$0.0539037\pi$
$948$	−14.4917	−	8.42182i	−0.470668	−	0.273528i
$949$	−3.18928	−	3.38044i	−0.103528	−	0.109734i
$950$	−4.14165	−	2.08001i	−0.134373	−	0.0674846i
$951$	−48.1116	−	2.93948i	−1.56013	−	0.0953193i
$952$	−16.8542	−	56.2971i	−0.546249	−	1.82460i
$953$	−4.46031	−	3.74265i	−0.144484	−	0.121236i	0.567681	−	0.823249i	$-0.307841\pi$
$953$	−4.46031	−	3.74265i	−0.144484	−	0.121236i	−0.712165	+	0.702012i	$0.752285\pi$
$954$	19.7505	+	13.1516i	0.639446	+	0.425800i
$955$	46.7081	−	39.1928i	1.51144	−	1.26825i
$956$	−25.0853	−	16.4989i	−0.811316	−	0.533611i
$957$	−16.5710	−	5.01241i	−0.535664	−	0.162028i
$958$	−28.2295	−	3.29956i	−0.912054	−	0.106604i
$959$	−28.2169	−	65.4142i	−0.911172	−	2.11233i
$960$	−14.5337	+	6.22026i	−0.469072	+	0.200758i
$961$	3.20081	−	1.60751i	0.103252	−	0.0518551i
$962$	−1.21952	−	0.443868i	−0.0393188	−	0.0143109i
$963$	22.7792	+	19.3359i	0.734050	+	0.623090i
$964$	17.9774	−	6.54323i	0.579013	−	0.210743i
$965$	−13.7924	+	14.6191i	−0.443994	+	0.470606i
$966$	−1.07549	+	4.48103i	−0.0346034	+	0.144175i
$967$	38.1735	−	25.1071i	1.22758	−	0.807391i	0.240975	−	0.970531i	$-0.422533\pi$
$967$	38.1735	−	25.1071i	1.22758	−	0.807391i	0.986603	+	0.163140i	$0.0521623\pi$
$968$	−6.09360	+	20.3541i	−0.195856	+	0.654204i
$969$	−10.4820	−	12.5644i	−0.336731	−	0.403626i
$970$	9.83491	+	13.2106i	0.315780	+	0.424166i
$971$	1.52462			0.0489275			0.0244638	−	0.999701i	$-0.492212\pi$
$971$	1.52462			0.0489275			0.0244638	+	0.999701i	$0.492212\pi$
$972$	21.4888	−	0.945245i	0.689254	−	0.0303187i
$973$	−1.61337			−0.0517222
$974$	13.1152	+	17.6167i	0.420237	+	0.564476i
$975$	−6.65009	−	7.97119i	−0.212973	−	0.255282i
$976$	−1.50747	+	5.03531i	−0.0482531	+	0.161176i
$977$	−17.0393	+	11.2069i	−0.545137	+	0.358542i	−0.792012	−	0.610505i	$-0.790966\pi$
$977$	−17.0393	+	11.2069i	−0.545137	+	0.358542i	0.246876	+	0.969047i	$0.420596\pi$
$978$	−2.14900	+	8.95382i	−0.0687176	+	0.286312i
$979$	−5.98990	+	6.34892i	−0.191438	+	0.202912i
$980$	−64.3814	+	23.4329i	−2.05659	+	0.748537i
$981$	−37.8942	+	13.5488i	−1.20987	+	0.432579i
$982$	−16.0966	−	5.85868i	−0.513662	−	0.186958i
$983$	37.6795	−	18.9233i	1.20179	−	0.603561i	0.268705	−	0.963222i	$-0.413404\pi$
$983$	37.6795	−	18.9233i	1.20179	−	0.603561i	0.933083	+	0.359662i	$0.117108\pi$
$984$	−0.523277	+	0.223957i	−0.0166815	+	0.00713948i
$985$	−18.0990	−	41.9582i	−0.576683	−	1.33690i
$986$	−19.9448	−	2.33121i	−0.635171	−	0.0742409i
$987$	14.0296	+	4.24370i	0.446567	+	0.135078i
$988$	−5.33554	−	3.50924i	−0.169746	−	0.111644i
$989$	−1.32273	+	1.10990i	−0.0420604	+	0.0352929i
$990$	−0.729639	+	11.4092i	−0.0231895	+	0.362608i
$991$	−1.19365	−	1.00159i	−0.0379176	−	0.0318167i	0.623632	−	0.781718i	$-0.285656\pi$
$991$	−1.19365	−	1.00159i	−0.0379176	−	0.0318167i	−0.661550	+	0.749901i	$0.730101\pi$
$992$	9.85957	+	32.9332i	0.313042	+	1.04563i
$993$	0.340725	+	0.0208173i	0.0108126	+	0.000660618i
$994$	−42.7560	−	21.4729i	−1.35614	−	0.681078i
$995$	−15.4247	−	16.3492i	−0.488996	−	0.518305i
$996$	6.83944	+	3.97473i	0.216716	+	0.125944i
$997$	−20.7294	+	48.0562i	−0.656508	+	1.52196i	0.185587	+	0.982628i	$0.440581\pi$
$997$	−20.7294	+	48.0562i	−0.656508	+	1.52196i	−0.842095	+	0.539329i	$0.818678\pi$
$998$	1.17509	−	2.03532i	0.0371970	−	0.0644270i
$999$	2.50949	+	3.04304i	0.0793968	+	0.0962776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.7.6	✓	144
3.2	odd	2		243.2.g.a.100.3		144
9.2	odd	6		729.2.g.b.55.3		144
9.4	even	3		729.2.g.d.298.3		144
9.5	odd	6		729.2.g.a.298.6		144
9.7	even	3		729.2.g.c.55.6		144
81.4	even	27		729.2.g.c.676.6		144
81.23	odd	54		243.2.g.a.226.3		144
81.25	even	27		6561.2.a.c.1.48		72
81.31	even	27		729.2.g.d.433.3		144
81.50	odd	54		729.2.g.a.433.6		144
81.56	odd	54		6561.2.a.d.1.25		72
81.58	even	27	inner	81.2.g.a.58.6	yes	144
81.77	odd	54		729.2.g.b.676.3		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.6	✓	144	1.1	even	1	trivial
81.2.g.a.58.6	yes	144	81.58	even	27	inner
243.2.g.a.100.3		144	3.2	odd	2
243.2.g.a.226.3		144	81.23	odd	54
729.2.g.a.298.6		144	9.5	odd	6
729.2.g.a.433.6		144	81.50	odd	54
729.2.g.b.55.3		144	9.2	odd	6
729.2.g.b.676.3		144	81.77	odd	54
729.2.g.c.55.6		144	9.7	even	3
729.2.g.c.676.6		144	81.4	even	27
729.2.g.d.298.3		144	9.4	even	3
729.2.g.d.433.3		144	81.31	even	27
6561.2.a.c.1.48		72	81.25	even	27
6561.2.a.d.1.25		72	81.56	odd	54

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.470263 + 0.631673i) q^{2} +(-1.10956 - 1.32999i) q^{3} +(0.395743 - 1.32187i) q^{4} +(2.32750 - 1.53082i) q^{5} +(0.318331 - 1.32633i) q^{6} +(-3.41908 + 3.62402i) q^{7} +(2.50111 - 0.910331i) q^{8} +(-0.537739 + 2.95141i) q^{9} +(2.06152 + 0.750330i) q^{10} +(1.55231 - 0.779598i) q^{11} +(-2.19718 + 0.940369i) q^{12} +(0.859891 + 1.99345i) q^{13} +(-3.89706 - 0.455501i) q^{14} +(-4.61848 - 1.39701i) q^{15} +(-0.554469 - 0.364680i) q^{16} +(-3.39468 + 2.84848i) q^{17} +(-2.11721 + 1.04827i) q^{18} +(-1.63306 - 1.37030i) q^{19} +(-1.10246 - 3.68247i) q^{20} +(8.61359 + 0.526266i) q^{21} +(1.22244 + 0.613935i) q^{22} +(0.465342 + 0.493234i) q^{23} +(-3.98587 - 2.31638i) q^{24} +(1.09345 - 2.53489i) q^{25} +(-0.854835 + 1.48062i) q^{26} +(4.52200 - 2.55959i) q^{27} +(3.43741 + 5.95378i) q^{28} +(5.71522 - 0.668013i) q^{29} +(-1.28945 - 3.57433i) q^{30} +(-5.72212 + 1.35617i) q^{31} +(-0.339908 - 5.83599i) q^{32} +(-2.75924 - 1.19954i) q^{33} +(-3.39570 - 0.804795i) q^{34} +(-2.41020 + 13.6689i) q^{35} +(3.68859 + 1.87882i) q^{36} +(0.131814 + 0.747552i) q^{37} +(0.0976137 - 1.67596i) q^{38} +(1.69716 - 3.35551i) q^{39} +(4.42779 - 5.94755i) q^{40} +(0.0737288 - 0.0990350i) q^{41} +(3.71823 + 5.68845i) q^{42} +(-0.148059 + 2.54207i) q^{43} +(-0.416216 - 2.36048i) q^{44} +(3.26650 + 7.69260i) q^{45} +(-0.0927292 + 0.525894i) q^{46} +(1.65271 + 0.391699i) q^{47} +(0.130198 + 1.14207i) q^{48} +(-1.03635 - 17.7935i) q^{49} +(2.11543 - 0.501366i) q^{50} +(7.55505 + 1.35432i) q^{51} +(2.97539 - 0.347773i) q^{52} +(-5.02192 - 8.69822i) q^{53} +(3.74336 + 1.65274i) q^{54} +(2.41957 - 4.19082i) q^{55} +(-5.25246 + 12.1766i) q^{56} +(-0.0104999 + 3.69239i) q^{57} +(3.10962 + 3.29601i) q^{58} +(-10.3931 - 5.21959i) q^{59} +(-3.67440 + 5.55220i) q^{60} +(-2.27150 - 7.58734i) q^{61} +(-3.54755 - 2.97675i) q^{62} +(-8.85739 - 12.0399i) q^{63} +(2.50983 - 2.10599i) q^{64} +(5.05301 + 3.32342i) q^{65} +(-0.539853 - 2.30704i) q^{66} +(0.462282 + 0.0540330i) q^{67} +(2.42190 + 5.61460i) q^{68} +(0.139669 - 1.16617i) q^{69} +(-9.76770 + 4.90552i) q^{70} +(11.4588 + 4.17067i) q^{71} +(1.34182 + 7.87134i) q^{72} +(-2.01159 + 0.732160i) q^{73} +(-0.410222 + 0.434809i) q^{74} +(-4.58462 + 1.35835i) q^{75} +(-2.45764 + 1.61641i) q^{76} +(-2.48219 + 8.29110i) q^{77} +(2.91770 - 0.505918i) q^{78} +(4.18797 + 5.62542i) q^{79} -1.84879 q^{80} +(-8.42167 - 3.17418i) q^{81} +0.0972297 q^{82} +(-1.97654 - 2.65495i) q^{83} +(4.10442 - 11.1778i) q^{84} +(-3.54061 + 11.8265i) q^{85} +(-1.67538 + 1.10192i) q^{86} +(-7.22985 - 6.85997i) q^{87} +(3.17281 - 3.36298i) q^{88} +(-4.72182 + 1.71860i) q^{89} +(-3.32309 + 5.68090i) q^{90} +(-10.1643 - 3.69952i) q^{91} +(0.836149 - 0.419930i) q^{92} +(8.15274 + 6.10560i) q^{93} +(0.529782 + 1.22817i) q^{94} +(-5.89863 - 0.689452i) q^{95} +(-7.38465 + 6.92748i) q^{96} +(6.27220 + 4.12529i) q^{97} +(10.7523 - 9.02224i) q^{98} +(1.46618 + 5.00072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) \) 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 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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