LMFDB - Embedded newform 81.2.g.a.58.3

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 $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, 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:	$0.646788256372$
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			58.3
Character	$\chi$	$=$	81.58
Dual form			81.2.g.a.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.886934 + 1.19136i) q^{2} +(-0.340526 + 1.69825i) q^{3} +(-0.0590788 - 0.197337i) q^{4} +(-1.33926 - 0.880846i) q^{5} +(-1.72120 - 1.91192i) q^{6} +(1.30515 + 1.38337i) q^{7} +(-2.50387 - 0.911335i) q^{8} +(-2.76808 - 1.15659i) q^{9} +(2.23724 - 0.814290i) q^{10} +(3.62327 + 1.81967i) q^{11} +(0.355245 - 0.0331322i) q^{12} +(-0.669348 + 1.55172i) q^{13} +(-2.80567 + 0.327936i) q^{14} +(1.95195 - 1.97445i) q^{15} +(3.65071 - 2.40111i) q^{16} +(4.14727 + 3.47997i) q^{17} +(3.83303 - 2.27196i) q^{18} +(3.70167 - 3.10607i) q^{19} +(-0.0947016 + 0.316325i) q^{20} +(-2.79374 + 1.74539i) q^{21} +(-5.38148 + 2.70268i) q^{22} +(-0.459550 + 0.487095i) q^{23} +(2.40030 - 3.94186i) q^{24} +(-0.962667 - 2.23171i) q^{25} +(-1.25499 - 2.17371i) q^{26} +(2.90678 - 4.30704i) q^{27} +(0.195884 - 0.339282i) q^{28} +(4.75422 + 0.555689i) q^{29} +(0.621027 + 4.07668i) q^{30} +(-4.73543 - 1.12232i) q^{31} +(-0.0674931 + 1.15881i) q^{32} +(-4.32407 + 5.53356i) q^{33} +(-7.82425 + 1.85438i) q^{34} +(-0.529392 - 3.00233i) q^{35} +(-0.0647034 + 0.614576i) q^{36} +(-2.07926 + 11.7921i) q^{37} +(0.417308 + 7.16489i) q^{38} +(-2.40728 - 1.66512i) q^{39} +(2.55060 + 3.42604i) q^{40} +(-6.04005 - 8.11319i) q^{41} +(0.398487 - 4.87640i) q^{42} +(-0.497227 - 8.53705i) q^{43} +(0.145031 - 0.822509i) q^{44} +(2.68841 + 3.98724i) q^{45} +(-0.172714 - 0.979511i) q^{46} +(-0.196235 + 0.0465086i) q^{47} +(2.83451 + 7.01744i) q^{48} +(0.196697 - 3.37715i) q^{49} +(3.51259 + 0.832500i) q^{50} +(-7.32210 + 5.85806i) q^{51} +(0.345757 + 0.0404132i) q^{52} +(2.48138 - 4.29788i) q^{53} +(2.55311 + 7.28309i) q^{54} +(-3.24965 - 5.62856i) q^{55} +(-2.00720 - 4.65322i) q^{56} +(4.01436 + 7.34404i) q^{57} +(-4.87871 + 5.17113i) q^{58} +(-1.69552 + 0.851522i) q^{59} +(-0.504950 - 0.268544i) q^{60} +(0.0518355 - 0.173143i) q^{61} +(5.53710 - 4.64618i) q^{62} +(-2.01275 - 5.33882i) q^{63} +(5.37384 + 4.50919i) q^{64} +(2.26326 - 1.48857i) q^{65} +(-2.75729 - 10.0594i) q^{66} +(13.2368 - 1.54716i) q^{67} +(0.441711 - 1.02400i) q^{68} +(-0.670719 - 0.946298i) q^{69} +(4.04639 + 2.03218i) q^{70} +(9.41216 - 3.42575i) q^{71} +(5.87689 + 5.41861i) q^{72} +(-10.9327 - 3.97917i) q^{73} +(-12.2045 - 12.9360i) q^{74} +(4.11781 - 0.874891i) q^{75} +(-0.831632 - 0.546973i) q^{76} +(2.21160 + 7.38727i) q^{77} +(4.11886 - 1.39108i) q^{78} +(-2.19201 + 2.94438i) q^{79} -7.00426 q^{80} +(6.32459 + 6.40309i) q^{81} +15.0229 q^{82} +(-3.27719 + 4.40202i) q^{83} +(0.509481 + 0.448194i) q^{84} +(-2.48896 - 8.31370i) q^{85} +(10.6117 + 6.97943i) q^{86} +(-2.56263 + 7.88461i) q^{87} +(-7.41387 - 7.85824i) q^{88} +(-6.65218 - 2.42120i) q^{89} +(-7.13468 - 0.333556i) q^{90} +(-3.02021 + 1.09927i) q^{91} +(0.123272 + 0.0619093i) q^{92} +(3.51851 - 7.65975i) q^{93} +(0.118639 - 0.275037i) q^{94} +(-7.69347 + 0.899238i) q^{95} +(-1.94497 - 0.509225i) q^{96} +(1.11799 - 0.735313i) q^{97} +(3.84894 + 3.22965i) q^{98} +(-7.92489 - 9.22765i) 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{27}\right)$

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 $

$2$	−0.886934	+	1.19136i	−0.627157	+	0.842419i	−0.996209	−	0.0869903i	$-0.972275\pi$
$2$	−0.886934	+	1.19136i	−0.627157	+	0.842419i	0.369052	+	0.929409i	$0.379683\pi$
$3$	−0.340526	+	1.69825i	−0.196602	+	0.980483i
$3$	−0.340526	+	1.69825i	−0.196602	+	0.980483i
$4$	−0.0590788	−	0.197337i	−0.0295394	−	0.0986686i
$5$	−1.33926	−	0.880846i	−0.598936	−	0.393927i	0.213529	−	0.976937i	$-0.431504\pi$
$5$	−1.33926	−	0.880846i	−0.598936	−	0.393927i	−0.812465	+	0.583010i	$0.801875\pi$
$6$	−1.72120	−	1.91192i	−0.702677	−	0.780539i
$7$	1.30515	+	1.38337i	0.493299	+	0.522866i	0.925417	−	0.378951i	$-0.123715\pi$
$7$	1.30515	+	1.38337i	0.493299	+	0.522866i	−0.432118	+	0.901817i	$0.642234\pi$
$8$	−2.50387	−	0.911335i	−0.885253	−	0.322206i
$9$	−2.76808	−	1.15659i	−0.922695	−	0.385531i
$10$	2.23724	−	0.814290i	0.707478	−	0.257501i
$11$	3.62327	+	1.81967i	1.09246	+	0.548652i	0.901426	−	0.432932i	$-0.142521\pi$
$11$	3.62327	+	1.81967i	1.09246	+	0.548652i	0.191029	+	0.981584i	$0.438817\pi$
$12$	0.355245	−	0.0331322i	0.102550	−	0.00956443i
$13$	−0.669348	+	1.55172i	−0.185644	+	0.430371i	−0.985467	−	0.169864i	$-0.945667\pi$
$13$	−0.669348	+	1.55172i	−0.185644	+	0.430371i	0.799824	+	0.600235i	$0.204926\pi$
$14$	−2.80567	+	0.327936i	−0.749848	+	0.0876447i
$15$	1.95195	−	1.97445i	0.503991	−	0.509800i
$16$	3.65071	−	2.40111i	0.912676	−	0.600277i
$17$	4.14727	+	3.47997i	1.00586	+	0.844017i	0.987785	−	0.155820i	$-0.0498020\pi$
$17$	4.14727	+	3.47997i	1.00586	+	0.844017i	0.0180743	+	0.999837i	$0.494246\pi$
$18$	3.83303	−	2.27196i	0.903453	−	0.535507i
$19$	3.70167	−	3.10607i	0.849220	−	0.712581i	−0.110397	−	0.993888i	$-0.535212\pi$
$19$	3.70167	−	3.10607i	0.849220	−	0.712581i	0.959618	+	0.281307i	$0.0907679\pi$
$20$	−0.0947016	+	0.316325i	−0.0211759	+	0.0707325i
$21$	−2.79374	+	1.74539i	−0.609645	+	0.380874i
$22$	−5.38148	+	2.70268i	−1.14734	+	0.576214i
$23$	−0.459550	+	0.487095i	−0.0958228	+	0.101566i	−0.773510	−	0.633784i	$-0.781501\pi$
$23$	−0.459550	+	0.487095i	−0.0958228	+	0.101566i	0.677687	+	0.735350i	$0.262982\pi$
$24$	2.40030	−	3.94186i	0.489960	−	0.804629i
$25$	−0.962667	−	2.23171i	−0.192533	−	0.446342i
$26$	−1.25499	−	2.17371i	−0.246124	−	0.426300i
$27$	2.90678	−	4.30704i	0.559411	−	0.828891i
$28$	0.195884	−	0.339282i	0.0370187	−	0.0641182i
$29$	4.75422	+	0.555689i	0.882837	+	0.103189i	0.545416	−	0.838165i	$-0.316372\pi$
$29$	4.75422	+	0.555689i	0.882837	+	0.103189i	0.337420	+	0.941354i	$0.390446\pi$
$30$	0.621027	+	4.07668i	0.113383	+	0.744296i
$31$	−4.73543	−	1.12232i	−0.850508	−	0.201574i	−0.217828	−	0.975987i	$-0.569897\pi$
$31$	−4.73543	−	1.12232i	−0.850508	−	0.201574i	−0.632680	+	0.774413i	$0.718045\pi$
$32$	−0.0674931	+	1.15881i	−0.0119312	+	0.204851i
$33$	−4.32407	+	5.53356i	−0.752724	+	0.963268i
$34$	−7.82425	+	1.85438i	−1.34185	+	0.318024i
$35$	−0.529392	−	3.00233i	−0.0894836	−	0.507487i
$36$	−0.0647034	+	0.614576i	−0.0107839	+	0.102429i
$37$	−2.07926	+	11.7921i	−0.341829	+	1.93861i	0.00314382	+	0.999995i	$0.498999\pi$
$37$	−2.07926	+	11.7921i	−0.341829	+	1.93861i	−0.344973	+	0.938613i	$0.612112\pi$
$38$	0.417308	+	7.16489i	0.0676962	+	1.16230i
$39$	−2.40728	−	1.66512i	−0.385473	−	0.266633i
$40$	2.55060	+	3.42604i	0.403285	+	0.541705i
$41$	−6.04005	−	8.11319i	−0.943297	−	1.26707i	−0.963621	−	0.267274i	$-0.913877\pi$
$41$	−6.04005	−	8.11319i	−0.943297	−	1.26707i	0.0203240	−	0.999793i	$-0.493530\pi$
$42$	0.398487	−	4.87640i	0.0614879	−	0.752445i
$43$	−0.497227	−	8.53705i	−0.0758264	−	1.30189i	−0.794809	−	0.606860i	$-0.792429\pi$
$43$	−0.497227	−	8.53705i	−0.0758264	−	1.30189i	0.718982	−	0.695028i	$-0.244608\pi$
$44$	0.145031	−	0.822509i	0.0218642	−	0.123998i
$45$	2.68841	+	3.98724i	0.400765	+	0.594382i
$46$	−0.172714	−	0.979511i	−0.0254653	−	0.144421i
$47$	−0.196235	+	0.0465086i	−0.0286238	+	0.00678397i	−0.244903	−	0.969548i	$-0.578756\pi$
$47$	−0.196235	+	0.0465086i	−0.0286238	+	0.00678397i	0.216279	+	0.976332i	$0.430608\pi$
$48$	2.83451	+	7.01744i	0.409127	+	1.01288i
$49$	0.196697	−	3.37715i	0.0280995	−	0.482450i
$50$	3.51259	+	0.832500i	0.496756	+	0.117733i
$51$	−7.32210	+	5.85806i	−1.02530	+	0.820293i
$52$	0.345757	+	0.0404132i	0.0479479	+	0.00560430i
$53$	2.48138	−	4.29788i	0.340844	−	0.590359i	−0.643746	−	0.765240i	$-0.722621\pi$
$53$	2.48138	−	4.29788i	0.340844	−	0.590359i	0.984590	+	0.174880i	$0.0559538\pi$
$54$	2.55311	+	7.28309i	0.347434	+	0.991103i
$55$	−3.24965	−	5.62856i	−0.438183	−	0.758955i
$56$	−2.00720	−	4.65322i	−0.268224	−	0.621812i
$57$	4.01436	+	7.34404i	0.531715	+	0.972742i
$58$	−4.87871	+	5.17113i	−0.640606	+	0.679002i
$59$	−1.69552	+	0.851522i	−0.220738	+	0.110859i	−0.555732	−	0.831362i	$-0.687562\pi$
$59$	−1.69552	+	0.851522i	−0.220738	+	0.110859i	0.334994	+	0.942220i	$0.391266\pi$
$60$	−0.504950	−	0.268544i	−0.0651888	−	0.0346688i
$61$	0.0518355	−	0.173143i	0.00663685	−	0.0221686i	−0.954607	−	0.297868i	$-0.903724\pi$
$61$	0.0518355	−	0.173143i	0.00663685	−	0.0221686i	0.961244	+	0.275700i	$0.0889095\pi$
$62$	5.53710	−	4.64618i	0.703212	−	0.590065i
$63$	−2.01275	−	5.33882i	−0.253583	−	0.672628i
$64$	5.37384	+	4.50919i	0.671730	+	0.563648i
$65$	2.26326	−	1.48857i	0.280723	−	0.184635i
$66$	−2.75729	−	10.0594i	−0.339399	−	1.23823i
$67$	13.2368	−	1.54716i	1.61713	−	0.189015i	0.741141	−	0.671350i	$-0.234285\pi$
$67$	13.2368	−	1.54716i	1.61713	−	0.189015i	0.875987	+	0.482335i	$0.160211\pi$
$68$	0.441711	−	1.02400i	0.0535654	−	0.124178i
$69$	−0.670719	−	0.946298i	−0.0807450	−	0.113921i
$70$	4.04639	+	2.03218i	0.483637	+	0.242891i
$71$	9.41216	−	3.42575i	1.11702	−	0.406561i	0.283455	−	0.958985i	$-0.408519\pi$
$71$	9.41216	−	3.42575i	1.11702	−	0.406561i	0.833563	+	0.552424i	$0.186297\pi$
$72$	5.87689	+	5.41861i	0.692598	+	0.638590i
$73$	−10.9327	−	3.97917i	−1.27957	−	0.465726i	−0.389282	−	0.921119i	$-0.627277\pi$
$73$	−10.9327	−	3.97917i	−1.27957	−	0.465726i	−0.890291	+	0.455392i	$0.849499\pi$
$74$	−12.2045	−	12.9360i	−1.41874	−	1.50378i
$75$	4.11781	−	0.874891i	0.475484	−	0.101024i
$76$	−0.831632	−	0.546973i	−0.0953948	−	0.0627421i
$77$	2.21160	+	7.38727i	0.252036	+	0.841857i
$78$	4.11886	−	1.39108i	0.466369	−	0.157509i
$79$	−2.19201	+	2.94438i	−0.246620	+	0.331269i	−0.908146	−	0.418654i	$-0.862502\pi$
$79$	−2.19201	+	2.94438i	−0.246620	+	0.331269i	0.661525	+	0.749923i	$0.269909\pi$
$80$	−7.00426			−0.783100
$81$	6.32459	+	6.40309i	0.702732	+	0.711455i
$82$	15.0229			1.65900
$83$	−3.27719	+	4.40202i	−0.359718	+	0.483185i	−0.944735	−	0.327836i	$-0.893681\pi$
$83$	−3.27719	+	4.40202i	−0.359718	+	0.483185i	0.585017	+	0.811021i	$0.301088\pi$
$84$	0.509481	+	0.448194i	0.0555889	+	0.0489020i
$85$	−2.48896	−	8.31370i	−0.269965	−	0.901747i
$86$	10.6117	+	6.97943i	1.14429	+	0.752611i
$87$	−2.56263	+	7.88461i	−0.274743	+	0.845319i
$88$	−7.41387	−	7.85824i	−0.790321	−	0.837691i
$89$	−6.65218	−	2.42120i	−0.705130	−	0.256646i	−0.0355305	−	0.999369i	$-0.511312\pi$
$89$	−6.65218	−	2.42120i	−0.705130	−	0.256646i	−0.669600	+	0.742722i	$0.733534\pi$
$90$	−7.13468	−	0.333556i	−0.752061	−	0.0351598i
$91$	−3.02021	+	1.09927i	−0.316604	+	0.115234i
$92$	0.123272	+	0.0619093i	0.0128519	+	0.00645449i
$93$	3.51851	−	7.65975i	0.364852	−	0.794279i
$94$	0.118639	−	0.275037i	0.0122367	−	0.0283679i
$95$	−7.69347	+	0.899238i	−0.789333	+	0.0922598i
$96$	−1.94497	−	0.509225i	−0.198507	−	0.0519725i
$97$	1.11799	−	0.735313i	0.113515	−	0.0746597i	−0.491482	−	0.870888i	$-0.663545\pi$
$97$	1.11799	−	0.735313i	0.113515	−	0.0746597i	0.604997	+	0.796228i	$0.293174\pi$
$98$	3.84894	+	3.22965i	0.388802	+	0.326244i
$99$	−7.92489	−	9.22765i	−0.796481	−	0.927414i
$100$	−0.383526	+	0.321817i	−0.0383526	+	0.0321817i
$101$	−1.42152	+	4.74821i	−0.141447	+	0.472465i	−0.999130	−	0.0417141i	$-0.986718\pi$
$101$	−1.42152	+	4.74821i	−0.141447	+	0.472465i	0.857683	+	0.514179i	$0.171903\pi$
$102$	−0.484841	−	13.9190i	−0.0480064	−	1.37818i
$103$	−2.03699	+	1.02302i	−0.200711	+	0.100801i	−0.546316	−	0.837579i	$-0.683970\pi$
$103$	−2.03699	+	1.02302i	−0.200711	+	0.100801i	0.345605	+	0.938380i	$0.387674\pi$
$104$	3.09010	−	3.27532i	0.303010	−	0.321171i
$105$	5.27897	+	0.123332i	0.515175	+	0.0120360i
$106$	2.91950	+	6.76816i	0.283567	+	0.657382i
$107$	2.21467	+	3.83593i	0.214101	+	0.370833i	0.952994	−	0.302989i	$-0.0979846\pi$
$107$	2.21467	+	3.83593i	0.214101	+	0.370833i	−0.738893	+	0.673822i	$0.764651\pi$
$108$	−1.02167	−	0.319161i	−0.0983101	−	0.0307113i
$109$	−9.21824	+	15.9665i	−0.882947	+	1.52931i	−0.0348978	+	0.999391i	$0.511111\pi$
$109$	−9.21824	+	15.9665i	−0.882947	+	1.52931i	−0.848049	+	0.529918i	$0.822223\pi$
$110$	9.58787	+	1.12066i	0.914167	+	0.106851i
$111$	−19.3178	−	7.54661i	−1.83357	−	0.716293i
$112$	8.08633	+	1.91650i	0.764086	+	0.181092i
$113$	−0.524386	+	9.00337i	−0.0493301	+	0.846965i	0.879371	+	0.476137i	$0.157963\pi$
$113$	−0.524386	+	9.00337i	−0.0493301	+	0.846965i	−0.928701	+	0.370829i	$0.879074\pi$
$114$	−12.3099	−	1.73114i	−1.15292	−	0.162136i
$115$	1.04451	−	0.247554i	0.0974014	−	0.0230846i
$116$	−0.171216	−	0.971014i	−0.0158970	−	0.0901563i
$117$	3.64753	−	3.52114i	0.337214	−	0.325530i
$118$	0.489346	−	2.77522i	0.0450479	−	0.255479i
$119$	0.598688	+	10.2791i	0.0548817	+	0.942282i
$120$	−6.68681	+	3.16489i	−0.610420	+	0.288913i
$121$	3.24810	+	4.36296i	0.295282	+	0.396633i
$122$	0.160300	+	0.215321i	0.0145129	+	0.0194942i
$123$	15.8350	−	7.49474i	1.42779	−	0.675778i
$124$	0.0582888	+	1.00078i	0.00523449	+	0.0898728i
$125$	−2.06830	+	11.7299i	−0.184994	+	1.04915i
$126$	8.14563	+	2.33727i	0.725671	+	0.208220i
$127$	−0.304561	−	1.72725i	−0.0270254	−	0.153269i	0.968309	−	0.249756i	$-0.0803504\pi$
$127$	−0.304561	−	1.72725i	−0.0270254	−	0.153269i	−0.995334	+	0.0964872i	$0.969239\pi$
$128$	−12.3973	+	2.93821i	−1.09577	+	0.259703i
$129$	14.6673	+	2.06267i	1.29139	+	0.181608i
$130$	−0.233942	+	4.01663i	−0.0205181	+	0.352281i
$131$	6.97041	+	1.65202i	0.609008	+	0.144338i	0.523537	−	0.852003i	$-0.324612\pi$
$131$	6.97041	+	1.65202i	0.609008	+	0.144338i	0.0854711	+	0.996341i	$0.472760\pi$
$132$	1.34744	+	0.526383i	0.117279	+	0.0458158i
$133$	9.12806	+	1.06692i	0.791504	+	0.0925135i
$134$	−9.89692	+	17.1420i	−0.854964	+	1.48084i
$135$	−7.68679	+	3.20783i	−0.661573	+	0.276086i
$136$	−7.21281	−	12.4930i	−0.618493	−	1.07126i
$137$	−6.92074	−	16.0441i	−0.591279	−	1.37074i	−0.906696	−	0.421785i	$-0.861404\pi$
$137$	−6.92074	−	16.0441i	−0.591279	−	1.37074i	0.315417	−	0.948953i	$-0.397856\pi$
$138$	1.72226	+	0.0402371i	0.146609	+	0.00342521i
$139$	13.0385	−	13.8200i	1.10591	−	1.17220i	0.122188	−	0.992507i	$-0.461009\pi$
$139$	13.0385	−	13.8200i	1.10591	−	1.17220i	0.983723	−	0.179691i	$-0.0575097\pi$
$140$	−0.561196	+	0.281843i	−0.0474297	+	0.0238201i
$141$	−0.0121600	−	0.349093i	−0.00102406	−	0.0293989i
$142$	−4.26668	+	14.2517i	−0.358051	+	1.19598i
$143$	−5.24886	+	4.40431i	−0.438931	+	0.368307i
$144$	−12.8826	+	2.42409i	−1.07355	+	0.202007i
$145$	−5.87767	−	4.93195i	−0.488114	−	0.409576i
$146$	14.4372	−	9.49549i	1.19483	−	0.785852i
$147$	5.66825	+	1.48404i	0.467510	+	0.122402i
$148$	2.44986	−	0.286347i	0.201377	−	0.0235376i
$149$	2.92032	−	6.77006i	0.239242	−	0.554625i	−0.755718	−	0.654897i	$-0.772712\pi$
$149$	2.92032	−	6.77006i	0.239242	−	0.554625i	0.994960	+	0.100272i	$0.0319714\pi$
$150$	−2.60992	+	5.68176i	−0.213099	+	0.463914i
$151$	−2.38668	−	1.19863i	−0.194225	−	0.0975434i	0.349029	−	0.937112i	$-0.386512\pi$
$151$	−2.38668	−	1.19863i	−0.194225	−	0.0975434i	−0.543254	+	0.839569i	$0.682808\pi$
$152$	−12.0992	+	4.40374i	−0.981372	+	0.357190i
$153$	−7.45508	−	14.4295i	−0.602707	−	1.16656i
$154$	−10.7624	−	3.91721i	−0.867262	−	0.315658i
$155$	5.35339	+	5.67426i	0.429995	+	0.455768i
$156$	−0.186371	+	0.573419i	−0.0149216	+	0.0459103i
$157$	4.77413	+	3.14000i	0.381017	+	0.250599i	0.725542	−	0.688178i	$-0.241589\pi$
$157$	4.77413	+	3.14000i	0.381017	+	0.250599i	−0.344524	+	0.938777i	$0.611960\pi$
$158$	−1.56365	−	5.22294i	−0.124397	−	0.415515i
$159$	6.45389	+	5.67754i	0.511827	+	0.450258i
$160$	1.11113	−	1.49250i	0.0878422	−	0.117993i
$161$	−1.27361			−0.100375
$162$	−13.2379	+	1.85573i	−1.04007	+	0.145800i
$163$	16.0381			1.25620			0.628100	−	0.778132i	$-0.283833\pi$
$163$	16.0381			1.25620			0.628100	+	0.778132i	$0.283833\pi$
$164$	−1.24419	+	1.67124i	−0.0971553	+	0.130502i
$165$	10.6653	−	3.60204i	0.830290	−	0.280418i
$166$	−2.33775	−	7.80862i	−0.181444	−	0.606066i
$167$	−15.9980	−	10.5220i	−1.23796	−	0.814220i	−0.249898	−	0.968272i	$-0.580397\pi$
$167$	−15.9980	−	10.5220i	−1.23796	−	0.814220i	−0.988063	+	0.154052i	$0.950768\pi$
$168$	8.58581	−	1.82419i	0.662410	−	0.140739i
$169$	6.96132	+	7.37857i	0.535486	+	0.567582i
$170$	12.1121	+	4.40846i	0.928959	+	0.338113i
$171$	−13.8390	+	4.31654i	−1.05829	+	0.330094i
$172$	−1.65530	+	0.602480i	−0.126216	+	0.0459387i
$173$	−21.1226	−	10.6082i	−1.60592	−	0.806526i	−0.999939	−	0.0110500i	$-0.996483\pi$
$173$	−21.1226	−	10.6082i	−1.60592	−	0.806526i	−0.605986	−	0.795476i	$-0.707221\pi$
$174$	−7.12053	−	10.0462i	−0.539806	−	0.761597i
$175$	1.83087	−	4.24444i	0.138401	−	0.320849i
$176$	17.5967	−	2.05676i	1.32640	−	0.155034i
$177$	−0.868726	−	3.16937i	−0.0652975	−	0.238225i
$178$	8.78457	−	5.77770i	0.658431	−	0.433057i
$179$	−3.43489	−	2.88222i	−0.256736	−	0.215427i	0.505331	−	0.862926i	$-0.331371\pi$
$179$	−3.43489	−	2.88222i	−0.256736	−	0.215427i	−0.762066	+	0.647499i	$0.775815\pi$
$180$	0.628002	−	0.766085i	0.0468085	−	0.0571006i
$181$	2.92076	−	2.45081i	0.217098	−	0.182167i	−0.527752	−	0.849398i	$-0.676965\pi$
$181$	2.92076	−	2.45081i	0.217098	−	0.182167i	0.744851	+	0.667231i	$0.232521\pi$
$182$	1.36911	−	4.57314i	0.101485	−	0.338983i
$183$	0.276388	+	0.146989i	0.0204312	+	0.0108657i
$184$	1.59456	−	0.800819i	0.117553	−	0.0590372i
$185$	13.1717	−	13.9612i	0.968403	−	1.02645i
$186$	6.00483	+	10.9855i	0.440296	+	0.805496i
$187$	8.69424	+	20.1555i	0.635786	+	1.47392i
$188$	0.0207712	+	0.0359768i	0.00151490	+	0.00262388i
$189$	9.75202	−	1.60015i	0.709355	−	0.116394i
$190$	5.75229	−	9.96325i	0.417315	−	0.722810i
$191$	18.2731	+	2.13582i	1.32220	+	0.154543i	0.747739	−	0.663993i	$-0.231139\pi$
$191$	18.2731	+	2.13582i	1.32220	+	0.154543i	0.574457	+	0.818535i	$0.305213\pi$
$192$	−9.48764	+	7.59061i	−0.684711	+	0.547805i
$193$	−15.9799	−	3.78730i	−1.15026	−	0.272616i	−0.389107	−	0.921193i	$-0.627216\pi$
$193$	−15.9799	−	3.78730i	−1.15026	−	0.272616i	−0.761149	+	0.648577i	$0.775365\pi$
$194$	−0.115561	+	1.98410i	−0.00829677	+	0.142450i
$195$	1.75726	+	4.35048i	0.125840	+	0.311544i
$196$	−0.678058	+	0.160703i	−0.0484327	+	0.0114788i
$197$	−3.25113	−	18.4381i	−0.231633	−	1.31366i	−0.849589	−	0.527445i	$-0.823150\pi$
$197$	−3.25113	−	18.4381i	−0.231633	−	1.31366i	0.617956	−	0.786213i	$-0.287961\pi$
$198$	18.0223	−	1.25707i	1.28079	−	0.0893361i
$199$	0.155470	−	0.881713i	0.0110210	−	0.0625029i	−0.978801	−	0.204812i	$-0.934342\pi$
$199$	0.155470	−	0.881713i	0.0110210	−	0.0625029i	0.989822	+	0.142309i	$0.0454527\pi$
$200$	0.376557	+	6.46524i	0.0266266	+	0.457161i
$201$	−1.88000	+	23.0061i	−0.132605	+	1.62273i
$202$	−4.39603	−	5.90490i	−0.309304	−	0.415467i
$203$	5.43622	+	7.30212i	0.381548	+	0.512508i
$204$	1.58859	+	1.09883i	0.111224	+	0.0769338i
$205$	0.942729	+	16.1860i	0.0658431	+	1.13048i
$206$	0.587899	−	3.33414i	0.0409609	−	0.232301i
$207$	1.83544	−	0.816807i	0.127572	−	0.0567720i
$208$	1.28226	+	7.27206i	0.0889088	+	0.504227i
$209$	19.0641	−	4.51829i	1.31869	−	0.312536i
$210$	−4.82904	+	6.17977i	−0.333235	+	0.426445i
$211$	−0.869893	+	14.9355i	−0.0598859	+	1.02820i	0.825814	+	0.563943i	$0.190716\pi$
$211$	−0.869893	+	14.9355i	−0.0598859	+	1.02820i	−0.885700	+	0.464258i	$0.846321\pi$
$212$	−0.994728	−	0.235755i	−0.0683182	−	0.0161917i
$213$	2.61268	+	17.1507i	0.179018	+	1.17515i
$214$	−6.53424	−	0.763743i	−0.446672	−	0.0522084i
$215$	−6.85392	+	11.8713i	−0.467433	+	0.809618i
$216$	−11.2034	+	8.13523i	−0.762293	+	0.553532i
$217$	−4.62784	−	8.01565i	−0.314158	−	0.544138i
$218$	−10.8458	−	25.1434i	−0.734571	−	1.70293i
$219$	10.4805	−	17.2114i	0.708204	−	1.16304i
$220$	−0.918738	+	0.973805i	−0.0619413	+	0.0656539i
$221$	−8.17592	+	4.10610i	−0.549972	+	0.276206i
$222$	26.1244	−	16.3211i	1.75335	−	1.09540i
$223$	1.77843	−	5.94037i	0.119093	−	0.397797i	−0.877568	−	0.479452i	$-0.840835\pi$
$223$	1.77843	−	5.94037i	0.119093	−	0.397797i	0.996661	+	0.0816552i	$0.0260206\pi$
$224$	−1.69116	+	1.41905i	−0.112995	+	0.0948142i
$225$	0.0835609	+	7.29098i	0.00557072	+	0.486065i
$226$	−10.2612	−	8.61013i	−0.682562	−	0.572737i
$227$	−11.9336	+	7.84886i	−0.792061	+	0.520947i	−0.879884	−	0.475189i	$-0.842380\pi$
$227$	−11.9336	+	7.84886i	−0.792061	+	0.520947i	0.0878224	+	0.996136i	$0.472009\pi$
$228$	1.21209	−	1.22606i	0.0802725	−	0.0811977i
$229$	−19.4011	+	2.26766i	−1.28206	+	0.149851i	−0.729707	−	0.683760i	$-0.760343\pi$
$229$	−19.4011	+	2.26766i	−1.28206	+	0.149851i	−0.552351	+	0.833611i	$0.686269\pi$
$230$	−0.631489	+	1.46396i	−0.0416392	+	0.0965304i
$231$	−13.2985	+	1.24029i	−0.874978	+	0.0816054i
$232$	−11.3975	−	5.72406i	−0.748286	−	0.375803i
$233$	8.91628	−	3.24526i	0.584125	−	0.212604i	−0.0330187	−	0.999455i	$-0.510512\pi$
$233$	8.91628	−	3.24526i	0.584125	−	0.212604i	0.617143	+	0.786851i	$0.288290\pi$
$234$	0.959828	+	7.46854i	0.0627459	+	0.488234i
$235$	0.303777	+	0.110566i	0.0198162	+	0.00721252i
$236$	0.268206	+	0.284282i	0.0174587	+	0.0185052i
$237$	−4.25385	−	4.72521i	−0.276317	−	0.306935i
$238$	−12.7771	−	8.40362i	−0.828215	−	0.544726i
$239$	−3.15591	−	10.5415i	−0.204139	−	0.681871i	−0.997339	−	0.0729094i	$-0.976772\pi$
$239$	−3.15591	−	10.5415i	−0.204139	−	0.681871i	0.793200	−	0.608961i	$-0.208414\pi$
$240$	2.38513	−	11.8950i	0.153959	−	0.767816i
$241$	−1.30807	+	1.75705i	−0.0842605	+	0.113181i	−0.842255	−	0.539080i	$-0.818772\pi$
$241$	−1.30807	+	1.75705i	−0.0842605	+	0.113181i	0.757994	+	0.652261i	$0.226180\pi$
$242$	−8.07871			−0.519319
$243$	−13.0277	+	8.56029i	−0.835728	+	0.549143i
$244$	−0.0372298			−0.00238340
$245$	−3.23818	+	4.34963i	−0.206880	+	0.277888i
$246$	−5.11566	+	25.5125i	−0.326163	+	1.62662i
$247$	2.34205	+	7.82301i	0.149021	+	0.497766i
$248$	10.8341	+	7.12570i	0.687966	+	0.452483i
$249$	−6.35976	−	7.06447i	−0.403033	−	0.447693i
$250$	−12.1401	−	12.8677i	−0.767806	−	0.813827i
$251$	6.59388	+	2.39998i	0.416202	+	0.151485i	0.541629	−	0.840618i	$-0.317808\pi$
$251$	6.59388	+	2.39998i	0.416202	+	0.151485i	−0.125427	+	0.992103i	$0.540030\pi$
$252$	−0.934635	+	0.712602i	−0.0588765	+	0.0448897i
$253$	−2.55143	+	0.928643i	−0.160407	+	0.0583833i
$254$	2.32790	+	1.16912i	0.146066	+	0.0733570i
$255$	14.9663	−	1.39584i	0.937224	−	0.0874108i
$256$	1.93807	−	4.49296i	0.121130	−	0.280810i
$257$	0.464504	−	0.0542928i	0.0289750	−	0.00338669i	−0.101593	−	0.994826i	$-0.532394\pi$
$257$	0.464504	−	0.0542928i	0.0289750	−	0.00338669i	0.130568	+	0.991439i	$0.458320\pi$
$258$	−15.4664	+	15.6446i	−0.962893	+	0.973992i
$259$	−19.0266	+	12.5140i	−1.18226	+	0.777582i
$260$	−0.427461	−	0.358683i	−0.0265100	−	0.0222446i
$261$	−12.5174	−	7.03689i	−0.774806	−	0.435573i
$262$	−8.15045	+	6.83904i	−0.503536	+	0.422517i
$263$	−5.47384	+	18.2839i	−0.337532	+	1.12743i	0.605810	+	0.795610i	$0.292849\pi$
$263$	−5.47384	+	18.2839i	−0.337532	+	1.12743i	−0.943341	+	0.331824i	$0.892336\pi$
$264$	15.8698	−	9.91464i	0.976721	−	0.610204i
$265$	−7.10899	+	3.57027i	−0.436702	+	0.219320i
$266$	−9.36708	+	9.92852i	−0.574332	+	0.608757i
$267$	6.37703	−	10.4726i	0.390268	−	0.640911i
$268$	−1.08732	−	2.52070i	−0.0664189	−	0.153976i
$269$	−2.12061	−	3.67300i	−0.129296	−	0.223947i	0.794108	−	0.607776i	$-0.207938\pi$
$269$	−2.12061	−	3.67300i	−0.129296	−	0.223947i	−0.923404	+	0.383830i	$0.874605\pi$
$270$	2.99600	−	12.0029i	0.182331	−	0.730471i
$271$	−3.83162	+	6.63656i	−0.232754	+	0.403142i	−0.958618	−	0.284697i	$-0.908107\pi$
$271$	−3.83162	+	6.63656i	−0.232754	+	0.403142i	0.725863	+	0.687839i	$0.241440\pi$
$272$	23.4962	+	2.74631i	1.42467	+	0.166520i
$273$	−0.838368	−	5.50339i	−0.0507403	−	0.333080i
$274$	25.2525	+	5.98496i	1.52556	+	0.361564i
$275$	0.572988	−	9.83782i	0.0345525	−	0.593243i
$276$	−0.147114	+	0.188264i	−0.00885525	+	0.0113322i
$277$	14.4352	−	3.42121i	0.867329	−	0.205561i	0.227219	−	0.973844i	$-0.427037\pi$
$277$	14.4352	−	3.42121i	0.867329	−	0.205561i	0.640110	+	0.768283i	$0.278889\pi$
$278$	4.90030	+	27.7910i	0.293901	+	1.66679i
$279$	11.8100	+	8.58363i	0.707046	+	0.513888i
$280$	−1.41060	+	7.99991i	−0.0842995	+	0.478086i
$281$	−0.0647163	−	1.11114i	−0.00386065	−	0.0662848i	0.995828	−	0.0912552i	$-0.0290879\pi$
$281$	−0.0647163	−	1.11114i	−0.00386065	−	0.0662848i	−0.999688	+	0.0249704i	$0.992051\pi$
$282$	0.426681	+	0.295136i	0.0254085	+	0.0175751i
$283$	−3.94683	−	5.30152i	−0.234615	−	0.315142i	0.669187	−	0.743094i	$-0.266643\pi$
$283$	−3.94683	−	5.30152i	−0.234615	−	0.315142i	−0.903802	+	0.427952i	$0.859235\pi$
$284$	−1.23209	−	1.65498i	−0.0731109	−	0.0982050i
$285$	1.09270	−	13.3716i	0.0647257	−	0.792067i
$286$	−0.591730	−	10.1596i	−0.0349897	−	0.600751i
$287$	3.34043	−	18.9445i	0.197179	−	1.11826i
$288$	1.52710	−	3.12963i	0.0899852	−	0.184415i
$289$	2.13761	+	12.1230i	0.125742	+	0.713117i
$290$	11.0888	−	2.62810i	0.651159	−	0.154328i
$291$	0.868039	+	2.14901i	0.0508853	+	0.125977i
$292$	−0.139348	+	2.39251i	−0.00815470	+	0.140011i
$293$	3.02889	+	0.717859i	0.176949	+	0.0419378i	0.318135	−	0.948045i	$-0.396943\pi$
$293$	3.02889	+	0.717859i	0.176949	+	0.0419378i	−0.141186	+	0.989983i	$0.545092\pi$
$294$	−6.79540	+	5.43668i	−0.396316	+	0.317074i
$295$	3.02080	+	0.353081i	0.175878	+	0.0205572i
$296$	15.9528	−	27.6310i	0.927235	−	1.60602i
$297$	18.3695	−	10.3162i	1.06590	−	0.598605i
$298$	5.47544	+	9.48374i	0.317184	+	0.549379i
$299$	−0.448237	−	1.03913i	−0.0259222	−	0.0600945i
$300$	−0.415924	−	0.760909i	−0.0240134	−	0.0439311i
$301$	11.1610	−	11.8299i	0.643308	−	0.681867i
$302$	3.54483	−	1.78028i	0.203982	−	0.102444i
$303$	−7.57957	−	4.03098i	−0.435435	−	0.231574i
$304$	6.05570	−	20.2274i	0.347318	−	1.16012i
$305$	−0.221933	+	0.186224i	−0.0127079	+	0.0106632i
$306$	23.8029	+	3.91639i	1.36072	+	0.223885i
$307$	−5.76257	−	4.83537i	−0.328887	−	0.275969i	0.463359	−	0.886171i	$-0.346644\pi$
$307$	−5.76257	−	4.83537i	−0.328887	−	0.275969i	−0.792246	+	0.610202i	$0.791088\pi$
$308$	1.32712	−	0.872863i	0.0756199	−	0.0497360i
$309$	−1.04369	−	3.80768i	−0.0593732	−	0.216611i
$310$	−11.5082	+	1.34511i	−0.653621	+	0.0763974i
$311$	−6.09456	+	14.1288i	−0.345591	+	0.801169i	0.653433	+	0.756984i	$0.273328\pi$
$311$	−6.09456	+	14.1288i	−0.345591	+	0.801169i	−0.999023	+	0.0441844i	$0.985931\pi$
$312$	4.51004	+	6.36309i	0.255331	+	0.360239i
$313$	−3.54777	−	1.78176i	−0.200532	−	0.100711i	0.345699	−	0.938345i	$-0.387642\pi$
$313$	−3.54777	−	1.78176i	−0.200532	−	0.100711i	−0.546231	+	0.837635i	$0.683938\pi$
$314$	−7.97521	+	2.90274i	−0.450067	+	0.163811i
$315$	−2.00707	+	8.92300i	−0.113086	+	0.502754i
$316$	0.710537	+	0.258614i	0.0399708	+	0.0145482i
$317$	−5.88460	−	6.23731i	−0.330512	−	0.350323i	0.540712	−	0.841208i	$-0.318155\pi$
$317$	−5.88460	−	6.23731i	−0.330512	−	0.350323i	−0.871224	+	0.490885i	$0.836673\pi$
$318$	−12.4882	+	2.65330i	−0.700302	+	0.148790i
$319$	16.2146	+	10.6645i	0.907845	+	0.597099i
$320$	−3.22508	−	10.7725i	−0.180287	−	0.602202i
$321$	−7.26851	+	2.45483i	−0.405689	+	0.137015i
$322$	1.12961	−	1.51733i	0.0629508	−	0.0845576i
$323$	26.1608			1.45563
$324$	0.889919	−	1.62636i	0.0494399	−	0.0903535i
$325$	4.10736			0.227835
$326$	−14.2247	+	19.1071i	−0.787836	+	1.05825i
$327$	−23.9759	−	21.0918i	−1.32587	−	1.16638i
$328$	7.72967	+	25.8189i	0.426800	+	1.42561i
$329$	−0.320454	−	0.210766i	−0.0176672	−	0.0116199i
$330$	−5.16807	+	15.9010i	−0.284493	+	0.875318i
$331$	6.40317	+	6.78697i	0.351950	+	0.373045i	0.879027	−	0.476772i	$-0.158193\pi$
$331$	6.40317	+	6.78697i	0.351950	+	0.373045i	−0.527077	+	0.849818i	$0.676712\pi$
$332$	1.06230	+	0.386644i	0.0583010	+	0.0212198i
$333$	19.3942	−	30.2366i	1.06280	−	1.65696i
$334$	26.7247	−	9.72699i	1.46231	−	0.532237i
$335$	−19.0903	−	9.58751i	−1.04301	−	0.523822i
$336$	−6.00828	+	13.0800i	−0.327779	+	0.713571i
$337$	1.74575	−	4.04710i	0.0950970	−	0.220460i	−0.864027	−	0.503445i	$-0.832066\pi$
$337$	1.74575	−	4.04710i	0.0950970	−	0.220460i	0.959124	+	0.282986i	$0.0913249\pi$
$338$	−14.9648	+	1.74913i	−0.813976	+	0.0951401i
$339$	−15.1114	−	3.95641i	−0.820737	−	0.214883i
$340$	−1.49356	+	0.982327i	−0.0809994	+	0.0532742i
$341$	−15.1155	−	12.6834i	−0.818548	−	0.686844i
$342$	7.13172	−	20.3157i	0.385639	−	1.09855i
$343$	15.1270	−	12.6931i	0.816782	−	0.685362i
$344$	−6.53512	+	21.8288i	−0.352350	+	1.17693i
$345$	0.0647248	+	1.85814i	0.00348466	+	0.100039i
$346$	31.3726	−	15.7559i	1.68660	−	0.847042i
$347$	−13.7512	+	14.5754i	−0.738201	+	0.782448i	−0.982302	−	0.187302i	$-0.940026\pi$
$347$	−13.7512	+	14.5754i	−0.738201	+	0.782448i	0.244101	+	0.969750i	$0.421507\pi$
$348$	1.70732	+	0.0398880i	0.0915222	+	0.00213822i
$349$	−13.3272	−	30.8958i	−0.713387	−	1.65382i	−0.755872	−	0.654719i	$-0.772787\pi$
$349$	−13.3272	−	30.8958i	−0.713387	−	1.65382i	0.0424857	−	0.999097i	$-0.486472\pi$
$350$	3.43279	+	5.94576i	0.183490	+	0.317814i
$351$	4.73769	+	7.39344i	0.252879	+	0.394633i
$352$	−2.35320	+	4.07587i	−0.125426	+	0.217244i
$353$	−8.01065	−	0.936311i	−0.426364	−	0.0498348i	−0.0997947	−	0.995008i	$-0.531819\pi$
$353$	−8.01065	−	0.936311i	−0.426364	−	0.0498348i	−0.326569	+	0.945173i	$0.605893\pi$
$354$	4.54637	+	1.77606i	0.241637	+	0.0943966i
$355$	−15.6229	−	3.70270i	−0.829178	−	0.196519i
$356$	−0.0847886	+	1.45576i	−0.00449379	+	0.0771554i
$357$	−17.6603	−	2.48357i	−0.934682	−	0.131444i
$358$	6.48028	−	1.53585i	0.342493	−	0.0811724i
$359$	−2.83469	−	16.0764i	−0.149609	−	0.848477i	−0.963550	−	0.267529i	$-0.913793\pi$
$359$	−2.83469	−	16.0764i	−0.149609	−	0.848477i	0.813940	−	0.580948i	$-0.197318\pi$
$360$	−3.09773	−	12.4336i	−0.163265	−	0.655307i
$361$	0.755367	−	4.28390i	0.0397562	−	0.225468i
$362$	0.329272	+	5.65339i	0.0173062	+	0.297135i
$363$	−8.51545	+	4.03038i	−0.446945	+	0.211540i
$364$	0.395357	+	0.531056i	0.0207223	+	0.0278349i
$365$	11.1367	+	14.9592i	0.582920	+	0.782998i
$366$	−0.420254	+	0.198907i	−0.0219670	+	0.0103971i
$367$	−0.765272	−	13.1392i	−0.0399469	−	0.685861i	−0.957533	−	0.288324i	$-0.906902\pi$
$367$	−0.765272	−	13.1392i	−0.0399469	−	0.685861i	0.917586	−	0.397537i	$-0.130135\pi$
$368$	−0.508116	+	2.88167i	−0.0264874	+	0.150217i
$369$	7.33570	+	29.4439i	0.381881	+	1.53279i
$370$	4.95036	+	28.0749i	0.257357	+	1.45954i
$371$	9.18414	−	2.17668i	0.476817	−	0.113008i
$372$	−1.71942	−	0.241803i	−0.0891479	−	0.0125369i
$373$	−0.0126555	+	0.217287i	−0.000655279	+	0.0112507i	−0.998620	−	0.0525186i	$-0.983275\pi$
$373$	−0.0126555	+	0.217287i	−0.000655279	+	0.0112507i	0.997965	+	0.0637693i	$0.0203122\pi$
$374$	−31.7237	−	7.51866i	−1.64039	−	0.388780i
$375$	−19.2160	−	7.50681i	−0.992307	−	0.387650i
$376$	0.533733	+	0.0623844i	0.0275252	+	0.00321723i
$377$	−4.04451	+	7.00529i	−0.208303	+	0.360791i
$378$	−6.74305	+	13.0374i	−0.346825	+	0.670571i
$379$	12.0931	+	20.9458i	0.621180	+	1.07592i	0.989266	+	0.146124i	$0.0466797\pi$
$379$	12.0931	+	20.9458i	0.621180	+	1.07592i	−0.368086	+	0.929792i	$0.619987\pi$
$380$	0.631974	+	1.46508i	0.0324196	+	0.0751571i
$381$	3.03701	+	0.0709534i	0.155591	+	0.00363505i
$382$	−18.7516	+	19.8755i	−0.959414	+	1.01692i
$383$	−7.55923	+	3.79639i	−0.386258	+	0.193986i	−0.631322	−	0.775521i	$-0.717487\pi$
$383$	−7.55923	+	3.79639i	−0.386258	+	0.193986i	0.245064	+	0.969507i	$0.421191\pi$
$384$	−0.768215	−	22.0542i	−0.0392028	−	1.12545i
$385$	3.54513	−	11.8416i	0.180677	−	0.603502i
$386$	18.6851	−	15.6787i	0.951048	−	0.798024i
$387$	−8.49753	+	24.2064i	−0.431954	+	1.23048i
$388$	−0.211154	−	0.177179i	−0.0107197	−	0.00899491i
$389$	20.9831	−	13.8008i	1.06389	−	0.699729i	0.108204	−	0.994129i	$-0.465490\pi$
$389$	20.9831	−	13.8008i	1.06389	−	0.699729i	0.955682	+	0.294399i	$0.0951196\pi$
$390$	−6.74156	−	1.76506i	−0.341372	−	0.0893770i
$391$	−3.60095	+	0.420891i	−0.182108	+	0.0212854i
$392$	−3.57022	+	8.27670i	−0.180323	+	0.418036i
$393$	−5.17914	+	11.2749i	−0.261253	+	0.568745i
$394$	24.8499	+	12.4801i	1.25192	+	0.628738i
$395$	5.52922	−	2.01247i	0.278205	−	0.101258i
$396$	−1.35276	+	2.10903i	−0.0679790	+	0.105983i
$397$	23.8173	+	8.66880i	1.19536	+	0.435074i	0.861602	−	0.507585i	$-0.169462\pi$
$397$	23.8173	+	8.66880i	1.19536	+	0.435074i	0.333756	+	0.942660i	$0.391684\pi$
$398$	0.912545	+	0.967242i	0.0457418	+	0.0484834i
$399$	−4.92023	+	15.1384i	−0.246319	+	0.757868i
$400$	−8.87299	−	5.83586i	−0.443650	−	0.291793i
$401$	6.80813	+	22.7407i	0.339982	+	1.13562i	0.941572	+	0.336813i	$0.109349\pi$
$401$	6.80813	+	22.7407i	0.339982	+	1.13562i	−0.601590	+	0.798805i	$0.705466\pi$
$402$	−25.7411	−	22.6447i	−1.28385	−	1.12941i
$403$	4.91118	−	6.59686i	0.244643	−	0.328613i
$404$	1.02098			0.0507957
$405$	−2.83014	−	14.1464i	−0.140631	−	0.702941i
$406$	−13.5210			−0.671037
$407$	−28.9915	+	38.9423i	−1.43705	+	1.93030i
$408$	23.6723	−	7.99496i	1.17195	−	0.395810i
$409$	−2.69238	−	8.99318i	−0.133130	−	0.444684i	0.865266	−	0.501314i	$-0.167150\pi$
$409$	−2.69238	−	8.99318i	−0.133130	−	0.444684i	−0.998395	+	0.0566295i	$0.981965\pi$
$410$	−20.1195	−	13.2328i	−0.993633	−	0.653523i
$411$	29.6035	−	6.28971i	1.46023	−	0.310248i
$412$	0.322222	+	0.341536i	0.0158748	+	0.0168263i
$413$	−3.39087	−	1.23418i	−0.166854	−	0.0607298i
$414$	−0.654808	+	2.91113i	−0.0321820	+	0.143074i
$415$	8.26652	−	3.00877i	0.405787	−	0.147695i
$416$	−1.75298	−	0.880379i	−0.0859469	−	0.0431642i
$417$	19.0298	+	26.8487i	0.931895	+	1.31478i
$418$	−11.5257	+	26.7197i	−0.563743	+	1.30690i
$419$	11.6606	−	1.36293i	0.569659	−	0.0665836i	0.173613	−	0.984814i	$-0.444456\pi$
$419$	11.6606	−	1.36293i	0.569659	−	0.0665836i	0.396047	+	0.918230i	$0.370382\pi$
$420$	−0.287538	−	1.04902i	−0.0140304	−	0.0511871i
$421$	−5.65294	+	3.71800i	−0.275507	+	0.181204i	−0.679742	−	0.733451i	$-0.737908\pi$
$421$	−5.65294	+	3.71800i	−0.275507	+	0.181204i	0.404235	+	0.914655i	$0.367538\pi$
$422$	−17.0220	−	14.2831i	−0.828618	−	0.695293i
$423$	0.596987	+	0.0982244i	0.0290265	+	0.00477584i
$424$	−10.1299	+	8.49998i	−0.491950	+	0.412795i
$425$	3.77386	−	12.6056i	0.183059	−	0.611459i
$426$	−22.7500	−	12.0989i	−1.10224	−	0.586195i
$427$	0.307174	−	0.154268i	0.0148652	−	0.00746557i
$428$	0.626131	−	0.663660i	0.0302652	−	0.0320792i
$429$	−5.69224	−	10.4136i	−0.274824	−	0.502775i
$430$	−8.06405	−	18.6946i	−0.388883	−	0.901532i
$431$	3.90563	+	6.76475i	0.188128	+	0.325846i	0.944626	−	0.328149i	$-0.106425\pi$
$431$	3.90563	+	6.76475i	0.188128	+	0.325846i	−0.756498	+	0.653996i	$0.773092\pi$
$432$	0.270143	−	22.7032i	0.0129972	−	1.09231i
$433$	−2.20878	+	3.82573i	−0.106147	+	0.183853i	−0.914206	−	0.405249i	$-0.867185\pi$
$433$	−2.20878	+	3.82573i	−0.106147	+	0.183853i	0.808059	+	0.589102i	$0.200518\pi$
$434$	13.6541	+	1.59594i	0.655419	+	0.0766074i
$435$	10.3772	−	8.30228i	0.497547	−	0.398064i
$436$	3.69538	+	0.875820i	0.176976	+	0.0419442i
$437$	−0.188153	+	3.23046i	−0.00900056	+	0.154534i
$438$	11.2094	+	27.7514i	0.535608	+	1.32601i
$439$	−14.6281	+	3.46693i	−0.698162	+	0.165468i	−0.564346	−	0.825539i	$-0.690871\pi$
$439$	−14.6281	+	3.46693i	−0.698162	+	0.165468i	−0.133817	+	0.991006i	$0.542723\pi$
$440$	3.00721	+	17.0547i	0.143363	+	0.813052i
$441$	−4.45046	+	9.12074i	−0.211927	+	0.434321i
$442$	2.35966	−	13.3823i	0.112238	−	0.636531i
$443$	−0.660317	−	11.3372i	−0.0313726	−	0.538647i	−0.976979	−	0.213334i	$-0.931568\pi$
$443$	−0.660317	−	11.3372i	−0.0313726	−	0.538647i	0.945607	−	0.325312i	$-0.105469\pi$
$444$	−0.347951	+	4.25797i	−0.0165130	+	0.202074i
$445$	6.77632	+	9.10217i	0.321228	+	0.431484i
$446$	5.49977	+	7.38748i	0.260422	+	0.349807i
$447$	10.5028	+	7.26480i	0.496765	+	0.343613i
$448$	0.775753	+	13.3192i	0.0366509	+	0.629272i
$449$	−1.16004	+	6.57891i	−0.0547457	+	0.310478i	−0.999868	−	0.0162381i	$-0.994831\pi$
$449$	−1.16004	+	6.57891i	−0.0547457	+	0.310478i	0.945122	+	0.326716i	$0.105942\pi$
$450$	−8.76029	−	6.36707i	−0.412964	−	0.300147i
$451$	−7.12134	−	40.3871i	−0.335331	−	1.90176i
$452$	1.80768	−	0.428428i	0.0850260	−	0.0201515i
$453$	2.84830	−	3.64500i	0.133825	−	0.171257i
$454$	1.23352	−	21.1786i	0.0578917	−	0.993963i
$455$	5.01314	+	1.18814i	0.235020	+	0.0557007i
$456$	−3.35856	−	22.0470i	−0.157279	−	1.03244i
$457$	−11.9315	−	1.39459i	−0.558133	−	0.0652364i	−0.167650	−	0.985847i	$-0.553618\pi$
$457$	−11.9315	−	1.39459i	−0.558133	−	0.0652364i	−0.390483	+	0.920610i	$0.627692\pi$
$458$	14.5059	−	25.1249i	0.677815	−	1.17401i
$459$	27.0436	−	7.74693i	1.26229	−	0.361596i
$460$	−0.110560	−	0.191496i	−0.00515490	−	0.00892855i
$461$	2.77206	+	6.42636i	0.129108	+	0.299305i	0.970493	−	0.241131i	$-0.0775184\pi$
$461$	2.77206	+	6.42636i	0.129108	+	0.299305i	−0.841385	+	0.540436i	$0.818259\pi$
$462$	10.3173	−	16.9434i	0.480003	−	0.788277i
$463$	−19.2377	+	20.3908i	−0.894052	+	0.947639i	−0.998902	−	0.0468486i	$-0.985082\pi$
$463$	−19.2377	+	20.3908i	−0.894052	+	0.947639i	0.104850	+	0.994488i	$0.466564\pi$
$464$	18.6905	−	9.38674i	0.867686	−	0.435768i
$465$	−11.4593	+	7.15915i	−0.531411	+	0.331997i
$466$	−4.04188	+	13.5008i	−0.187237	+	0.625414i
$467$	−10.9662	+	9.20178i	−0.507458	+	0.425807i	−0.860233	−	0.509900i	$-0.829682\pi$
$467$	−10.9662	+	9.20178i	−0.507458	+	0.425807i	0.352776	+	0.935708i	$0.385238\pi$
$468$	−0.910343	−	0.511767i	−0.0420806	−	0.0236565i
$469$	19.4162	+	16.2921i	0.896557	+	0.752300i
$470$	−0.401154	+	0.263843i	−0.0185039	+	0.0121702i
$471$	−6.95820	+	7.03841i	−0.320617	+	0.324313i
$472$	5.02139	−	0.586916i	0.231128	−	0.0270150i
$473$	13.7331	−	31.8368i	0.631447	−	1.46386i
$474$	9.40231	−	0.876913i	0.431862	−	0.0402779i
$475$	−10.4953	−	5.27095i	−0.481558	−	0.241848i
$476$	1.99307	−	0.725420i	0.0913524	−	0.0332496i
$477$	−11.8396	+	9.02695i	−0.542097	+	0.413316i
$478$	15.3578	+	5.58977i	0.702448	+	0.255670i
$479$	15.4383	+	16.3636i	0.705392	+	0.747672i	0.976650	−	0.214835i	$-0.0689212\pi$
$479$	15.4383	+	16.3636i	0.705392	+	0.747672i	−0.271258	+	0.962507i	$0.587440\pi$
$480$	2.15627	+	2.39520i	0.0984198	+	0.109325i
$481$	−16.9063	−	11.1195i	−0.770862	−	0.507004i
$482$	−0.933101	−	3.11677i	−0.0425016	−	0.141965i
$483$	0.433698	−	2.16291i	0.0197339	−	0.0984158i
$484$	0.669080	−	0.898730i	0.0304127	−	0.0408514i
$485$	−2.14498			−0.0973984
$486$	1.35634	−	23.1131i	0.0615249	−	1.04843i
$487$	−41.7203			−1.89053			−0.945264	−	0.326307i	$-0.894196\pi$
$487$	−41.7203			−1.89053			−0.945264	+	0.326307i	$0.894196\pi$
$488$	−0.287580	+	0.386288i	−0.0130182	+	0.0174864i
$489$	−5.46138	+	27.2367i	−0.246972	+	1.23168i
$490$	−2.30992	−	7.71567i	−0.104352	−	0.348559i
$491$	9.24805	+	6.08254i	0.417359	+	0.274501i	0.740772	−	0.671757i	$-0.234460\pi$
$491$	9.24805	+	6.08254i	0.417359	+	0.274501i	−0.323413	+	0.946258i	$0.604830\pi$
$492$	−2.41450	−	2.68205i	−0.108854	−	0.120916i
$493$	17.7832	+	18.8491i	0.800917	+	0.848922i
$494$	−11.3973	−	4.14826i	−0.512787	−	0.186639i
$495$	2.48536	+	19.3389i	0.111708	+	0.869217i
$496$	−19.9825	+	7.27302i	−0.897239	+	0.326568i
$497$	17.0233	+	8.54944i	0.763601	+	0.383495i
$498$	14.0570	−	1.31104i	0.629910	−	0.0587490i
$499$	3.09519	−	7.17545i	0.138560	−	0.321217i	−0.834781	−	0.550582i	$-0.814406\pi$
$499$	3.09519	−	7.17545i	0.138560	−	0.321217i	0.973340	+	0.229365i	$0.0736650\pi$
$500$	2.43694	−	0.284837i	0.108983	−	0.0127383i
$501$	23.3167	−	23.5855i	1.04171	−	1.05372i
$502$	−8.70757	+	5.72706i	−0.388638	+	0.255611i
$503$	18.1547	+	15.2336i	0.809478	+	0.679233i	0.950483	−	0.310776i	$-0.100589\pi$
$503$	18.1547	+	15.2336i	0.809478	+	0.679233i	−0.141005	+	0.990009i	$0.545033\pi$
$504$	0.174228	+	15.2020i	0.00776073	+	0.677152i
$505$	6.08624	−	5.10696i	0.270834	−	0.227257i
$506$	1.15660	−	3.86331i	0.0514171	−	0.171745i
$507$	−14.9011	+	9.30945i	−0.661783	+	0.413447i
$508$	−0.322858	+	0.162145i	−0.0143245	+	0.00719403i
$509$	−8.55338	+	9.06605i	−0.379122	+	0.401846i	−0.888634	−	0.458618i	$-0.848345\pi$
$509$	−8.55338	+	9.06605i	−0.379122	+	0.401846i	0.509512	+	0.860464i	$0.329826\pi$
$510$	−11.6111	+	19.0682i	−0.514150	+	0.844355i
$511$	−8.76405	−	20.3174i	−0.387699	−	0.898787i
$512$	−9.10692	−	15.7736i	−0.402473	−	0.697103i
$513$	−2.61802	−	24.9719i	−0.115588	−	1.10254i
$514$	−0.347303	+	0.601546i	−0.0153189	+	0.0265331i
$515$	3.62919	+	0.424191i	0.159921	+	0.0186921i
$516$	−0.459488	−	3.01627i	−0.0202278	−	0.132784i
$517$	−0.795643	−	0.188571i	−0.0349923	−	0.00829333i
$518$	1.96668	−	33.7666i	0.0864111	−	1.48362i
$519$	25.2081	−	32.2591i	1.10651	−	1.41602i
$520$	−7.02351	+	1.66460i	−0.308001	+	0.0729977i
$521$	3.66734	+	20.7985i	0.160669	+	0.911200i	0.953418	+	0.301652i	$0.0975380\pi$
$521$	3.66734	+	20.7985i	0.160669	+	0.911200i	−0.792749	+	0.609548i	$0.791351\pi$
$522$	19.4856	−	8.67144i	0.852860	−	0.379539i
$523$	7.23247	−	41.0174i	0.316254	−	1.79356i	−0.248848	−	0.968543i	$-0.580052\pi$
$523$	7.23247	−	41.0174i	0.316254	−	1.79356i	0.565102	−	0.825021i	$-0.308837\pi$
$524$	−0.0857995	−	1.47312i	−0.00374817	−	0.0643536i
$525$	6.58464	+	4.55461i	0.287377	+	0.198779i
$526$	−16.9278	−	22.7379i	−0.738086	−	0.991421i
$527$	−15.7335	−	21.1337i	−0.685360	−	0.920598i
$528$	−2.49924	+	30.5839i	−0.108765	+	1.33099i
$529$	1.31126	+	22.5134i	0.0570111	+	0.978843i
$530$	2.05173	−	11.6360i	0.0891217	−	0.505434i
$531$	5.67820	−	0.396059i	0.246413	−	0.0171875i
$532$	−0.328733	−	1.86434i	−0.0142524	−	0.0808293i
$533$	16.6323	−	3.94193i	0.720426	−	0.170744i
$534$	6.82059	+	16.8858i	0.295156	+	0.730721i
$535$	0.412835	−	7.08810i	0.0178484	−	0.306445i
$536$	−34.5531	−	8.18925i	−1.49247	−	0.353722i
$537$	6.06438	−	4.85183i	0.261697	−	0.209372i
$538$	6.25670	+	0.731303i	0.269746	+	0.0315287i
$539$	6.85799	−	11.8784i	0.295395	−	0.511638i
$540$	1.08715	+	1.32737i	0.0467835	+	0.0571211i
$541$	−4.87647	−	8.44629i	−0.209656	−	0.363134i	0.741950	−	0.670455i	$-0.233901\pi$
$541$	−4.87647	−	8.44629i	−0.209656	−	0.363134i	−0.951606	+	0.307320i	$0.900568\pi$
$542$	−4.50813	−	10.4510i	−0.193641	−	0.448910i
$543$	3.16749	+	5.79474i	0.135930	+	0.248676i
$544$	−4.31254	+	4.57103i	−0.184899	+	0.195981i
$545$	26.4096	−	13.2634i	1.13126	−	0.568142i
$546$	7.30010	+	3.88235i	0.312415	+	0.166149i
$547$	−0.198805	+	0.664056i	−0.00850030	+	0.0283930i	−0.962134	−	0.272575i	$-0.912125\pi$
$547$	−0.198805	+	0.664056i	−0.00850030	+	0.0283930i	0.953634	+	0.300968i	$0.0973098\pi$
$548$	−2.75722	+	2.31358i	−0.117783	+	0.0988314i
$549$	−0.343740	+	0.419321i	−0.0146705	+	0.0178962i
$550$	11.2122	+	9.40814i	0.478089	+	0.401164i
$551$	19.3245	−	12.7100i	0.823253	−	0.541462i
$552$	0.817000	+	2.98066i	0.0347738	+	0.126865i
$553$	−6.93407	+	0.810476i	−0.294867	+	0.0344650i
$554$	−8.72721	+	20.2319i	−0.370783	+	0.859573i
$555$	19.2242	+	27.1229i	0.816024	+	1.15130i
$556$	−3.49750	−	1.75651i	−0.148327	−	0.0744926i
$557$	−28.7125	+	10.4505i	−1.21659	+	0.442801i	−0.868984	−	0.494841i	$-0.835226\pi$
$557$	−28.7125	+	10.4505i	−1.21659	+	0.442801i	−0.347602	+	0.937642i	$0.613004\pi$
$558$	−20.7009	+	6.45684i	−0.876339	+	0.273340i
$559$	13.5800	+	4.94270i	0.574371	+	0.209054i
$560$	−9.14158	−	9.68950i	−0.386302	−	0.409456i
$561$	−37.1897	+	7.90150i	−1.57015	+	0.333602i
$562$	1.38116	+	0.908405i	0.0582608	+	0.0383187i
$563$	2.79565	+	9.33813i	0.117823	+	0.393555i	0.996473	−	0.0839099i	$-0.0267408\pi$
$563$	2.79565	+	9.33813i	0.117823	+	0.393555i	−0.878651	+	0.477465i	$0.841556\pi$
$564$	−0.0681706	+	0.0230236i	−0.00287050	+	0.000969470i
$565$	8.63287	−	11.5960i	0.363188	−	0.487846i
$566$	9.81660			0.412622
$567$	−0.603363	+	17.1062i	−0.0253389	+	0.718394i
$568$	−26.6889			−1.11984
$569$	−11.7532	+	15.7873i	−0.492720	+	0.661838i	−0.977041	−	0.213053i	$-0.931659\pi$
$569$	−11.7532	+	15.7873i	−0.492720	+	0.661838i	0.484321	+	0.874891i	$0.339067\pi$
$570$	14.9613	+	13.1615i	0.626658	+	0.551277i
$571$	9.46443	+	31.6134i	0.396074	+	1.32298i	0.890984	+	0.454035i	$0.150016\pi$
$571$	9.46443	+	31.6134i	0.396074	+	1.32298i	−0.494910	+	0.868944i	$0.664799\pi$
$572$	1.17923	+	0.775592i	0.0493061	+	0.0324292i
$573$	−9.84961	+	30.3049i	−0.411473	+	1.26601i
$574$	19.6070	+	20.7822i	0.818381	+	0.867433i
$575$	1.52945	+	0.556674i	0.0637824	+	0.0232149i
$576$	−9.65995	−	18.6972i	−0.402498	−	0.779048i
$577$	−19.1279	+	6.96197i	−0.796303	+	0.289831i	−0.707954	−	0.706259i	$-0.750381\pi$
$577$	−19.1279	+	6.96197i	−0.796303	+	0.289831i	−0.0883494	+	0.996090i	$0.528159\pi$
$578$	−16.3388	−	8.20563i	−0.679603	−	0.341309i
$579$	11.8733	−	25.8481i	0.493438	−	1.07421i
$580$	−0.626011	+	1.45126i	−0.0259937	+	0.0602601i
$581$	−10.3668	+	1.21171i	−0.430089	+	0.0502702i
$582$	−3.33014	−	0.871887i	−0.138039	−	0.0361409i
$583$	16.8114	−	11.0571i	0.696259	−	0.457937i
$584$	23.7477	+	19.9267i	0.982686	+	0.824571i
$585$	−7.98658	+	1.50282i	−0.330204	+	0.0621339i
$586$	−3.54165	+	2.97180i	−0.146304	+	0.122764i
$587$	10.0799	−	33.6693i	0.416043	−	1.38968i	−0.451479	−	0.892281i	$-0.649104\pi$
$587$	10.0799	−	33.6693i	0.416043	−	1.38968i	0.867522	−	0.497398i	$-0.165711\pi$
$588$	−0.0420168	−	1.20623i	−0.00173274	−	0.0497442i
$589$	−21.0150	+	10.5541i	−0.865907	+	0.434875i
$590$	−3.09990	+	3.28570i	−0.127621	+	0.135270i
$591$	32.4195	+	0.757413i	1.33356	+	0.0311558i
$592$	20.7233	+	48.0420i	0.851722	+	1.97451i
$593$	−4.46816	−	7.73909i	−0.183485	−	0.317806i	0.759580	−	0.650414i	$-0.225405\pi$
$593$	−4.46816	−	7.73909i	−0.183485	−	0.317806i	−0.943065	+	0.332608i	$0.892071\pi$
$594$	−4.00224	+	31.0344i	−0.164214	+	1.27336i
$595$	8.25249	−	14.2937i	0.338319	−	0.585986i
$596$	−1.50851	−	0.176320i	−0.0617911	−	0.00722234i
$597$	1.44442	+	0.564272i	0.0591163	+	0.0230941i
$598$	1.63554	+	0.387629i	0.0668821	+	0.0158513i
$599$	2.30662	−	39.6032i	0.0942460	−	1.61814i	−0.537705	−	0.843133i	$-0.680709\pi$
$599$	2.30662	−	39.6032i	0.0942460	−	1.61814i	0.631951	−	0.775008i	$-0.282254\pi$
$600$	−11.1078	−	1.56209i	−0.453474	−	0.0637721i
$601$	23.0255	−	5.45715i	0.939231	−	0.222602i	0.267636	−	0.963520i	$-0.413758\pi$
$601$	23.0255	−	5.45715i	0.939231	−	0.222602i	0.671595	+	0.740918i	$0.265609\pi$
$602$	4.19466	+	23.7891i	0.170962	+	0.969572i
$603$	−38.4299	−	11.0269i	−1.56499	−	0.449049i
$604$	−0.0955328	+	0.541794i	−0.00388718	+	0.0220453i
$605$	−0.506964	−	8.70423i	−0.0206110	−	0.353877i
$606$	11.5249	−	5.45478i	0.468169	−	0.221585i
$607$	10.6054	+	14.2455i	0.430460	+	0.578208i	0.963441	−	0.267919i	$-0.0863359\pi$
$607$	10.6054	+	14.2455i	0.430460	+	0.578208i	−0.532982	+	0.846127i	$0.678928\pi$
$608$	3.34951	+	4.49917i	0.135841	+	0.182466i
$609$	−14.2520	+	6.74549i	−0.577519	+	0.273341i
$610$	−0.0250197	−	0.429571i	−0.00101302	−	0.0173928i
$611$	0.0591812	−	0.335633i	0.00239422	−	0.0135783i
$612$	−2.40705	+	2.32364i	−0.0972991	+	0.0939278i
$613$	−0.410662	−	2.32898i	−0.0165865	−	0.0940666i	0.975391	−	0.220483i	$-0.0707635\pi$
$613$	−0.410662	−	2.32898i	−0.0165865	−	0.0940666i	−0.991977	+	0.126417i	$0.959652\pi$
$614$	10.8717	−	2.57664i	0.438745	−	0.103985i
$615$	−27.8089	−	3.91077i	−1.12136	−	0.157698i
$616$	1.19470	−	20.5123i	0.0481360	−	0.826464i
$617$	32.8897	+	7.79500i	1.32409	+	0.313815i	0.831053	−	0.556194i	$-0.187739\pi$
$617$	32.8897	+	7.79500i	1.32409	+	0.313815i	0.493036	+	0.870009i	$0.335887\pi$
$618$	5.46200	+	2.13376i	0.219714	+	0.0858323i
$619$	−47.1703	−	5.51342i	−1.89594	−	0.221603i	−0.913319	−	0.407246i	$-0.866489\pi$
$619$	−47.1703	−	5.51342i	−1.89594	−	0.221603i	−0.982617	+	0.185643i	$0.940563\pi$
$620$	0.803470	−	1.39165i	0.0322681	−	0.0558901i
$621$	0.762125	+	3.39518i	0.0305830	+	0.136244i
$622$	−11.4270	−	19.7921i	−0.458180	−	0.793591i
$623$	−5.33265	−	12.3625i	−0.213648	−	0.495292i
$624$	−12.7864	−	0.298727i	−0.511866	−	0.0119587i
$625$	4.76272	−	5.04819i	0.190509	−	0.201928i
$626$	5.26935	−	2.64637i	0.210606	−	0.105770i
$627$	1.18134	+	33.9142i	0.0471780	+	1.35440i
$628$	0.337588	−	1.12762i	0.0134712	−	0.0449970i
$629$	−49.6594	+	41.6692i	−1.98005	+	1.66146i
$630$	−8.85036	−	10.3053i	−0.352607	−	0.410572i
$631$	−14.6874	−	12.3242i	−0.584695	−	0.490617i	0.301790	−	0.953374i	$-0.402416\pi$
$631$	−14.6874	−	12.3242i	−0.584695	−	0.490617i	−0.886485	+	0.462757i	$0.846860\pi$
$632$	8.17183	−	5.37470i	0.325058	−	0.213794i
$633$	−25.0679	−	6.56320i	−0.996360	−	0.260864i
$634$	12.6501	−	1.47859i	0.502401	−	0.0587223i
$635$	−1.11356	+	2.58151i	−0.0441901	+	0.102444i
$636$	0.739101	−	1.60901i	0.0293072	−	0.0638016i
$637$	5.10875	+	2.56571i	0.202416	+	0.101657i
$638$	−27.0866	+	9.85872i	−1.07237	+	0.390311i
$639$	−30.0159	−	1.40328i	−1.18741	−	0.0555129i
$640$	19.1913	+	6.98507i	0.758603	+	0.276109i
$641$	−1.44451	−	1.53109i	−0.0570547	−	0.0604744i	0.698218	−	0.715886i	$-0.253977\pi$
$641$	−1.44451	−	1.53109i	−0.0570547	−	0.0604744i	−0.755272	+	0.655411i	$0.772495\pi$
$642$	3.52210	−	10.8367i	0.139006	−	0.427690i
$643$	36.6084	+	24.0777i	1.44369	+	0.949533i	0.998537	+	0.0540808i	$0.0172228\pi$
$643$	36.6084	+	24.0777i	1.44369	+	0.949533i	0.445158	+	0.895452i	$0.353148\pi$
$644$	0.0752436	+	0.251331i	0.00296501	+	0.00990384i
$645$	−17.8265	−	15.6821i	−0.701918	−	0.617483i
$646$	−23.2029	+	31.1669i	−0.912907	+	1.22625i
$647$	2.17952			0.0856859			0.0428430	−	0.999082i	$-0.486358\pi$
$647$	2.17952			0.0856859			0.0428430	+	0.999082i	$0.486358\pi$
$648$	−10.0006	−	21.7964i	−0.392861	−	0.856242i
$649$	−7.69281			−0.301969
$650$	−3.64296	+	4.89334i	−0.142889	+	0.191933i
$651$	15.1885	−	5.12968i	0.595282	−	0.201048i
$652$	−0.947512	−	3.16491i	−0.0371075	−	0.123948i
$653$	15.6357	+	10.2838i	0.611873	+	0.402435i	0.817279	−	0.576242i	$-0.195481\pi$
$653$	15.6357	+	10.2838i	0.611873	+	0.402435i	−0.205407	+	0.978677i	$0.565852\pi$
$654$	46.3930	−	9.85690i	1.81411	−	0.385435i
$655$	−7.88003	−	8.35235i	−0.307898	−	0.326353i
$656$	−41.5311	−	15.1161i	−1.62152	−	0.590183i
$657$	25.6603	+	23.6593i	1.00110	+	0.923038i
$658$	0.535320	−	0.194841i	0.0208689	−	0.00759568i
$659$	−12.7829	−	6.41983i	−0.497953	−	0.250081i	0.182052	−	0.983289i	$-0.441726\pi$
$659$	−12.7829	−	6.41983i	−0.497953	−	0.250081i	−0.680005	+	0.733208i	$0.738022\pi$
$660$	−1.34091	−	1.89185i	−0.0521948	−	0.0736401i
$661$	9.89935	−	22.9493i	0.385040	−	0.892623i	−0.609930	−	0.792455i	$-0.708803\pi$
$661$	9.89935	−	22.9493i	0.385040	−	0.892623i	0.994971	−	0.100168i	$-0.0319381\pi$
$662$	−13.7649	+	1.60889i	−0.534989	+	0.0625312i
$663$	−4.18906	−	15.2830i	−0.162690	−	0.593541i
$664$	12.2174	−	8.03550i	0.474126	−	0.311838i
$665$	−11.2851	−	9.46931i	−0.437617	−	0.367204i
$666$	18.8213	+	49.9234i	0.729311	+	1.93449i
$667$	−2.45548	+	2.06039i	−0.0950764	+	0.0797786i
$668$	−1.13125	+	3.77862i	−0.0437692	+	0.146199i
$669$	9.48262	+	5.04306i	0.366619	+	0.194976i
$670$	28.3540	−	14.2399i	1.09541	−	0.550136i
$671$	0.502877	−	0.533018i	0.0194133	−	0.0205769i
$672$	−1.83401	−	3.35523i	−0.0707486	−	0.129431i
$673$	−11.7597	−	27.2621i	−0.453304	−	1.05088i	−0.979669	−	0.200619i	$-0.935705\pi$
$673$	−11.7597	−	27.2621i	−0.453304	−	1.05088i	0.526365	−	0.850259i	$-0.323554\pi$
$674$	3.27319	+	5.66933i	0.126078	+	0.218374i
$675$	−12.4103	−	2.34086i	−0.477674	−	0.0900997i
$676$	1.04480	−	1.80964i	0.0401846	−	0.0696017i
$677$	−38.5222	−	4.50260i	−1.48053	−	0.173049i	−0.662862	−	0.748741i	$-0.730659\pi$
$677$	−38.5222	−	4.50260i	−1.48053	−	0.173049i	−0.817666	+	0.575692i	$0.804733\pi$
$678$	18.1163	−	14.4940i	0.695753	−	0.556639i
$679$	2.47635	+	0.586906i	0.0950336	+	0.0225234i
$680$	−1.34453	+	23.0847i	−0.0515604	+	0.885258i
$681$	−9.26560	−	22.9389i	−0.355058	−	0.879022i
$682$	28.5169	−	6.75863i	1.09197	−	0.258801i
$683$	−2.81006	−	15.9367i	−0.107524	−	0.609799i	−0.990182	−	0.139784i	$-0.955359\pi$
$683$	−2.81006	−	15.9367i	−0.107524	−	0.609799i	0.882658	−	0.470016i	$-0.155752\pi$
$684$	1.66940	+	2.47593i	0.0638312	+	0.0946695i
$685$	−4.86369	+	27.5833i	−0.185832	+	1.05391i
$686$	1.70535	+	29.2797i	0.0651104	+	1.11790i
$687$	2.75551	−	33.7200i	0.105129	−	1.28650i
$688$	−22.3136	−	29.9724i	−0.850698	−	1.14269i
$689$	5.00822	+	6.72720i	0.190798	+	0.256286i
$690$	−2.27112	−	1.57094i	−0.0864601	−	0.0598046i
$691$	1.02377	+	17.5774i	0.0389460	+	0.668677i	0.960131	+	0.279551i	$0.0901857\pi$
$691$	1.02377	+	17.5774i	0.0389460	+	0.668677i	−0.921185	+	0.389125i	$0.872777\pi$
$692$	−0.845488	+	4.79500i	−0.0321406	+	0.182279i
$693$	2.42216	−	23.0065i	0.0920101	−	0.873945i
$694$	−5.16814	−	29.3100i	−0.196180	−	1.11259i
$695$	−29.6353	+	7.02369i	−1.12413	+	0.266424i
$696$	13.6020	−	17.4067i	0.515584	−	0.659798i
$697$	3.18397	−	54.6667i	0.120602	−	2.07065i
$698$	48.6284	+	11.5251i	1.84061	+	0.436233i
$699$	2.47503	+	16.2471i	0.0936143	+	0.614523i
$700$	−0.945751	−	0.110542i	−0.0357460	−	0.00417811i
$701$	−9.33660	+	16.1715i	−0.352639	+	0.610788i	−0.986711	−	0.162486i	$-0.948049\pi$
$701$	−9.33660	+	16.1715i	−0.352639	+	0.610788i	0.634072	+	0.773274i	$0.281382\pi$
$702$	−13.0103	−	0.913202i	−0.491041	−	0.0344666i
$703$	28.9303	+	50.1087i	1.09113	+	1.88989i
$704$	11.2656	+	26.1166i	0.424588	+	0.984307i
$705$	−0.291212	+	0.478238i	−0.0109677	+	0.0180115i
$706$	8.22041	−	8.71312i	0.309379	−	0.327923i
$707$	−8.42384	+	4.23061i	−0.316811	+	0.159109i
$708$	−0.574112	+	0.358675i	−0.0215764	+	0.0134798i
$709$	−9.44848	+	31.5601i	−0.354845	+	1.18527i	0.575260	+	0.817971i	$0.304901\pi$
$709$	−9.44848	+	31.5601i	−0.354845	+	1.18527i	−0.930105	+	0.367294i	$0.880284\pi$
$710$	18.2677	−	15.3285i	0.685576	−	0.575267i
$711$	9.47312	−	5.61503i	0.355270	−	0.210580i
$712$	14.4497	+	12.1247i	0.541526	+	0.454394i
$713$	2.72284	−	1.79084i	0.101971	−	0.0670675i
$714$	18.6223	−	18.8370i	0.696924	−	0.704957i
$715$	10.9091	−	1.27509i	0.407978	−	0.0476858i
$716$	−0.365839	+	0.848110i	−0.0136720	+	0.0316953i
$717$	18.9767	−	1.76987i	0.708697	−	0.0660971i
$718$	21.6669	+	10.8815i	0.808602	+	0.406095i
$719$	43.1137	−	15.6921i	1.60787	−	0.585216i	0.626852	−	0.779139i	$-0.284343\pi$
$719$	43.1137	−	15.6921i	1.60787	−	0.585216i	0.981017	+	0.193922i	$0.0621209\pi$
$720$	19.3884	+	8.10107i	0.722562	+	0.301909i
$721$	−4.07379	−	1.48274i	−0.151716	−	0.0552200i
$722$	4.43370	+	4.69945i	0.165005	+	0.174895i
$723$	−2.53847	−	2.81975i	−0.0944067	−	0.104868i
$724$	−0.656191	−	0.431584i	−0.0243871	−	0.0160397i
$725$	−3.33659	−	11.1450i	−0.123918	−	0.413915i
$726$	2.75101	−	13.7196i	0.102099	−	0.509184i
$727$	9.64105	−	12.9502i	0.357567	−	0.480295i	−0.586547	−	0.809915i	$-0.699513\pi$
$727$	9.64105	−	12.9502i	0.357567	−	0.480295i	0.944114	+	0.329620i	$0.106921\pi$
$728$	8.56403			0.317404
$729$	−10.1012	−	25.0393i	−0.374119	−	0.927381i
$730$	−27.6992			−1.02519
$731$	27.6465	−	37.1358i	1.02254	−	1.37352i
$732$	0.0126777	−	0.0632254i	0.000468582	−	0.00233688i
$733$	7.38479	+	24.6669i	0.272763	+	0.911093i	0.979128	+	0.203245i	$0.0651488\pi$
$733$	7.38479	+	24.6669i	0.272763	+	0.911093i	−0.706364	+	0.707848i	$0.749666\pi$
$734$	16.3323	+	10.7419i	0.602835	+	0.396491i
$735$	−6.28406	−	6.98039i	−0.231791	−	0.257475i
$736$	−0.533435	−	0.565408i	−0.0196627	−	0.0208412i
$737$	50.7756	+	18.4808i	1.87034	+	0.680750i
$738$	−41.5845	−	17.3753i	−1.53075	−	0.639594i
$739$	−16.9934	+	6.18508i	−0.625111	+	0.227522i	−0.635102	−	0.772428i	$-0.719042\pi$
$739$	−16.9934	+	6.18508i	−0.625111	+	0.227522i	0.00999089	+	0.999950i	$0.496820\pi$
$740$	−3.53323	−	1.77445i	−0.129884	−	0.0652302i
$741$	−14.0829	+	1.31345i	−0.517349	+	0.0482509i
$742$	−5.55252	+	12.8722i	−0.203839	+	0.472553i
$743$	44.0370	−	5.14719i	1.61556	−	0.188832i	0.740229	−	0.672355i	$-0.234717\pi$
$743$	44.0370	−	5.14719i	1.61556	−	0.188832i	0.875332	+	0.483523i	$0.160643\pi$
$744$	−15.7905	+	15.9725i	−0.578907	+	0.585580i
$745$	−9.87445	+	6.49453i	−0.361772	+	0.237941i
$746$	−0.247642	−	0.207797i	−0.00906683	−	0.00760798i
$747$	14.1629	−	8.39481i	0.518193	−	0.307150i
$748$	3.46379	−	2.90646i	0.126649	−	0.106271i
$749$	−2.41605	+	8.07017i	−0.0882805	+	0.294878i
$750$	25.9866	−	16.2351i	0.948896	−	0.592821i
$751$	2.23887	−	1.12440i	0.0816977	−	0.0410301i	−0.407481	−	0.913214i	$-0.633593\pi$
$751$	2.23887	−	1.12440i	0.0816977	−	0.0410301i	0.489179	+	0.872183i	$0.337297\pi$
$752$	−0.604725	+	0.640971i	−0.0220520	+	0.0233738i
$753$	−6.32113	+	10.3808i	−0.230355	+	0.378297i
$754$	−4.75861	−	11.0317i	−0.173298	−	0.401751i
$755$	2.14057	+	3.70758i	0.0779034	+	0.134933i
$756$	−0.891907	−	1.82990i	−0.0324384	−	0.0665529i
$757$	21.8769	−	37.8919i	0.795129	−	1.37720i	−0.127629	−	0.991822i	$-0.540737\pi$
$757$	21.8769	−	37.8919i	0.795129	−	1.37720i	0.922757	−	0.385381i	$-0.125930\pi$
$758$	−35.6798	−	4.17037i	−1.29595	−	0.151475i
$759$	−0.708240	−	4.64918i	−0.0257075	−	0.168754i
$760$	20.0830	+	4.75975i	0.728486	+	0.172654i
$761$	−2.68708	+	46.1354i	−0.0974065	+	1.67241i	0.496626	+	0.867964i	$0.334572\pi$
$761$	−2.68708	+	46.1354i	−0.0974065	+	1.67241i	−0.594033	+	0.804441i	$0.702465\pi$
$762$	−2.77816	+	3.55524i	−0.100642	+	0.128793i
$763$	−34.1187	+	8.08628i	−1.23518	+	0.292743i
$764$	−0.658078	−	3.73214i	−0.0238084	−	0.135024i
$765$	−2.72592	+	25.8917i	−0.0985557	+	0.936117i
$766$	2.18168	−	12.3729i	0.0788272	−	0.447051i
$767$	−0.186434	−	3.20094i	−0.00673173	−	0.115579i
$768$	6.97019	+	4.82129i	0.251515	+	0.173973i
$769$	17.4122	+	23.3886i	0.627899	+	0.843414i	0.996272	−	0.0862635i	$-0.0274927\pi$
$769$	17.4122	+	23.3886i	0.627899	+	0.843414i	−0.368374	+	0.929678i	$0.620085\pi$
$770$	10.9633	+	14.7262i	0.395089	+	0.530696i
$771$	−0.0659731	+	0.807331i	−0.00237596	+	0.0290753i
$772$	0.196698	+	3.37717i	0.00707931	+	0.121547i
$773$	−6.90323	+	39.1502i	−0.248292	+	1.40813i	0.564429	+	0.825481i	$0.309096\pi$
$773$	−6.90323	+	39.1502i	−0.248292	+	1.40813i	−0.812721	+	0.582653i	$0.802015\pi$
$774$	−21.3017	−	31.5931i	−0.765676	−	1.13559i
$775$	2.05395	+	11.6485i	0.0737801	+	0.418427i
$776$	−3.46942	+	0.822267i	−0.124545	+	0.0295177i
$777$	−14.7728	−	36.5732i	−0.529972	−	1.31206i
$778$	−2.16892	+	37.2389i	−0.0777595	+	1.33508i
$779$	−47.5583	−	11.2715i	−1.70395	−	0.403845i
$780$	0.754693	−	0.603794i	0.0270224	−	0.0216193i
$781$	40.3365	+	4.71466i	1.44335	+	0.168704i
$782$	2.69238	−	4.66333i	0.0962792	−	0.166760i
$783$	16.2129	−	18.8614i	0.579400	−	0.674050i
$784$	−7.39082	−	12.8013i	−0.263958	−	0.457188i
$785$	−3.62796	−	8.41056i	−0.129487	−	0.300186i
$786$	−8.83894	−	16.1703i	−0.315275	−	0.576777i
$787$	10.5965	−	11.2316i	0.377725	−	0.400365i	−0.510423	−	0.859924i	$-0.670511\pi$
$787$	10.5965	−	11.2316i	0.377725	−	0.400365i	0.888147	+	0.459559i	$0.151993\pi$
$788$	−3.44644	+	1.73087i	−0.122774	+	0.0616596i
$789$	−29.1866	−	15.5221i	−1.03907	−	0.552600i
$790$	−2.50648	+	8.37222i	−0.0891765	+	0.297870i
$791$	−13.1394	+	11.0253i	−0.467184	+	0.392014i
$792$	11.4334	+	30.3271i	0.406269	+	1.07763i
$793$	0.233973	+	0.196327i	0.00830864	+	0.00697178i
$794$	−31.4521	+	20.6863i	−1.11619	+	0.734131i
$795$	−3.64241	−	13.2886i	−0.129183	−	0.471298i
$796$	−0.183180	+	0.0214106i	−0.00649263	+	0.000758879i
$797$	−10.9980	+	25.4961i	−0.389568	+	0.903120i	0.604725	+	0.796434i	$0.293283\pi$
$797$	−10.9980	+	25.4961i	−0.389568	+	0.903120i	−0.994293	+	0.106685i	$0.965976\pi$
$798$	−13.6714	−	19.2885i	−0.483961	−	0.682806i
$799$	−0.975688	−	0.490009i	−0.0345174	−	0.0173353i
$800$	2.65111	−	0.964924i	0.0937308	−	0.0341152i
$801$	15.6135	+	14.3959i	0.551675	+	0.508656i
$802$	−33.1308	−	12.0586i	−1.16989	−	0.425804i
$803$	−32.3712	−	34.3115i	−1.14235	−	1.21083i
$804$	4.65103	−	0.988182i	0.164029	−	0.0348505i
$805$	1.70570	+	1.12186i	0.0601181	+	0.0395403i
$806$	3.50334	+	11.7020i	0.123400	+	0.412184i
$807$	6.95978	−	2.35056i	0.244996	−	0.0827438i
$808$	7.88652	−	10.5934i	0.277447	−	0.372676i
$809$	−1.83050			−0.0643571			−0.0321785	−	0.999482i	$-0.510245\pi$
$809$	−1.83050			−0.0643571			−0.0321785	+	0.999482i	$0.510245\pi$
$810$	19.3636	+	9.17523i	0.680368	+	0.322385i
$811$	−14.4506			−0.507429			−0.253715	−	0.967279i	$-0.581652\pi$
$811$	−14.4506			−0.507429			−0.253715	+	0.967279i	$0.581652\pi$
$812$	1.11981	−	1.50417i	0.0392977	−	0.0527860i
$813$	−9.96575	−	8.76695i	−0.349514	−	0.307470i
$814$	−20.6808	−	69.0785i	−0.724860	−	2.42120i
$815$	−21.4792	−	14.1271i	−0.752384	−	0.494851i
$816$	−12.6650	+	38.9672i	−0.443363	+	1.36412i
$817$	−28.3572	−	30.0569i	−0.992094	−	1.05156i
$818$	13.1021	+	4.76877i	0.458104	+	0.166736i
$819$	9.63160	+	0.450290i	0.336556	+	0.0157344i
$820$	3.13841	−	1.14229i	0.109598	−	0.0398904i
$821$	−19.2932	−	9.68942i	−0.673338	−	0.338163i	0.0790618	−	0.996870i	$-0.474808\pi$
$821$	−19.2932	−	9.68942i	−0.673338	−	0.338163i	−0.752400	+	0.658707i	$0.771104\pi$
$822$	−18.7631	+	40.8470i	−0.654437	+	1.42470i
$823$	−4.35435	+	10.0945i	−0.151783	+	0.351873i	−0.977095	−	0.212805i	$-0.931740\pi$
$823$	−4.35435	+	10.0945i	−0.151783	+	0.351873i	0.825312	+	0.564678i	$0.190999\pi$
$824$	6.03268	−	0.705120i	0.210158	−	0.0245640i
$825$	16.5119	+	4.32311i	0.574872	+	0.150511i
$826$	4.47783	−	2.94511i	0.155804	−	0.102474i
$827$	−21.6075	−	18.1309i	−0.751367	−	0.630472i	0.184497	−	0.982833i	$-0.440934\pi$
$827$	−21.6075	−	18.1309i	−0.751367	−	0.630472i	−0.935864	+	0.352361i	$0.885379\pi$
$828$	−0.269622	−	0.313945i	−0.00937002	−	0.0109104i
$829$	−36.5129	+	30.6380i	−1.26815	+	1.06410i	−0.273382	+	0.961906i	$0.588142\pi$
$829$	−36.5129	+	30.6380i	−1.26815	+	1.06410i	−0.994764	+	0.102196i	$0.967413\pi$
$830$	−3.74734	+	12.5170i	−0.130072	+	0.434471i
$831$	0.894499	+	25.6796i	0.0310298	+	0.890815i
$832$	−10.5940	+	5.32050i	−0.367280	+	0.184455i
$833$	12.5681	−	13.3214i	0.435460	−	0.461561i
$834$	−48.8646	−	1.14162i	−1.69204	−	0.0395310i
$835$	12.1572	+	28.1835i	0.420717	+	0.975331i
$836$	−2.01791	−	3.49513i	−0.0697910	−	0.120882i
$837$	−18.5987	+	17.1334i	−0.642866	+	0.592215i
$838$	−8.71848	+	15.1008i	−0.301175	+	0.521650i
$839$	51.2931	+	5.99530i	1.77083	+	0.206981i	0.938022	−	0.346575i	$-0.112655\pi$
$839$	51.2931	+	5.99530i	1.77083	+	0.206981i	0.832812	+	0.553555i	$0.186729\pi$
$840$	−13.1055	−	5.11972i	−0.452182	−	0.176647i
$841$	−5.92448	−	1.40413i	−0.204292	−	0.0484182i
$842$	0.584315	−	10.0323i	0.0201368	−	0.345736i
$843$	1.90902	+	0.268466i	0.0657502	+	0.00924646i
$844$	2.99872	−	0.710709i	0.103220	−	0.0244636i
$845$	−2.82365	−	16.0137i	−0.0971364	−	0.550888i
$846$	−0.646509	+	0.624108i	−0.0222274	+	0.0214573i
$847$	−1.79636	+	10.1876i	−0.0617235	+	0.350051i
$848$	−1.26087	−	21.6484i	−0.0432986	−	0.743408i
$849$	10.3473	−	4.89739i	0.355118	−	0.168078i
$850$	11.6706	+	15.6763i	0.400298	+	0.537693i
$851$	−4.78834	−	6.43186i	−0.164142	−	0.220481i
$852$	3.23012	−	1.52882i	0.110662	−	0.0523767i
$853$	−2.28555	−	39.2414i	−0.0782558	−	1.34360i	−0.777575	−	0.628791i	$-0.783550\pi$
$853$	−2.28555	−	39.2414i	−0.0782558	−	1.34360i	0.699319	−	0.714810i	$-0.253487\pi$
$854$	−0.0886537	+	0.502780i	−0.00303367	+	0.0172048i
$855$	22.3362	+	6.40904i	0.763883	+	0.219185i
$856$	−2.04945	−	11.6230i	−0.0700487	−	0.397266i
$857$	19.0168	−	4.50706i	0.649601	−	0.153958i	0.107412	−	0.994215i	$-0.465744\pi$
$857$	19.0168	−	4.50706i	0.649601	−	0.153958i	0.542189	+	0.840256i	$0.317595\pi$
$858$	17.4550	+	2.45470i	0.595905	+	0.0838022i
$859$	−1.38709	+	23.8154i	−0.0473270	+	0.812572i	0.888231	+	0.459398i	$0.151935\pi$
$859$	−1.38709	+	23.8154i	−0.0473270	+	0.812572i	−0.935557	+	0.353174i	$0.885102\pi$
$860$	2.74758	+	0.651187i	0.0936915	+	0.0222053i
$861$	31.0350	+	12.1240i	1.05767	+	0.413184i
$862$	−11.5233	−	1.34688i	−0.392485	−	0.0458749i
$863$	−12.6584	+	21.9249i	−0.430896	+	0.746334i	−0.996951	−	0.0780339i	$-0.975136\pi$
$863$	−12.6584	+	21.9249i	−0.430896	+	0.746334i	0.566055	+	0.824368i	$0.308469\pi$
$864$	4.79486	+	3.65911i	0.163125	+	0.124485i
$865$	18.9446	+	32.8129i	0.644134	+	1.11567i
$866$	−2.59877	−	6.02462i	−0.0883098	−	0.204725i
$867$	−21.3157	−	0.497997i	−0.723920	−	0.0169129i
$868$	−1.30838	+	1.38680i	−0.0444092	+	0.0470711i
$869$	−13.3000	+	6.67953i	−0.451173	+	0.226588i
$870$	0.687135	+	19.7265i	0.0232961	+	0.668792i
$871$	−6.45925	+	21.5754i	−0.218863	+	0.731054i
$872$	37.6321	−	31.5771i	1.27438	−	1.06933i
$873$	−3.94514	+	0.742350i	−0.133523	+	0.0251247i
$874$	−3.68176	−	3.08936i	−0.124537	−	0.104499i
$875$	−18.9263	+	12.4480i	−0.639824	+	0.420819i
$876$	−4.01562	−	1.05136i	−0.135675	−	0.0355220i
$877$	41.0895	−	4.80267i	1.38749	−	0.162175i	0.610666	−	0.791888i	$-0.290902\pi$
$877$	41.0895	−	4.80267i	1.38749	−	0.162175i	0.776827	+	0.629714i	$0.216828\pi$
$878$	8.84383	−	20.5023i	0.298465	−	0.691919i
$879$	−2.25051	+	4.89935i	−0.0759080	+	0.165251i
$880$	−25.3783	−	12.7455i	−0.855502	−	0.429649i
$881$	−5.70063	+	2.07486i	−0.192059	+	0.0699038i	−0.436259	−	0.899821i	$-0.643697\pi$
$881$	−5.70063	+	2.07486i	−0.192059	+	0.0699038i	0.244200	+	0.969725i	$0.421475\pi$
$882$	−6.91882	−	13.3916i	−0.232969	−	0.450918i
$883$	13.5249	+	4.92265i	0.455148	+	0.165660i	0.559413	−	0.828889i	$-0.311027\pi$
$883$	13.5249	+	4.92265i	0.455148	+	0.165660i	−0.104265	+	0.994550i	$0.533249\pi$
$884$	1.29331	+	1.37083i	0.0434987	+	0.0461059i
$885$	−1.62828	+	5.00984i	−0.0547340	+	0.168404i
$886$	14.0923	+	9.26868i	0.473442	+	0.311387i
$887$	1.86023	+	6.21360i	0.0624604	+	0.208632i	0.983523	−	0.180782i	$-0.0578628\pi$
$887$	1.86023	+	6.21360i	0.0624604	+	0.208632i	−0.921063	+	0.389414i	$0.872678\pi$
$888$	41.4919	+	36.5008i	1.39238	+	1.22489i
$889$	1.99194	−	2.67564i	0.0668075	−	0.0897380i
$890$	−16.8541			−0.564951
$891$	11.2641	+	34.7088i	0.377362	+	1.16279i
$892$	−1.27732			−0.0427680
$893$	−0.581938	+	0.781679i	−0.0194738	+	0.0261579i
$894$	−17.9703	+	6.06920i	−0.601016	+	0.202984i
$895$	2.06143	+	6.88566i	0.0689060	+	0.230162i
$896$	−20.2449	−	13.3153i	−0.676334	−	0.444832i
$897$	1.91734	−	0.407367i	0.0640180	−	0.0136016i
$898$	−6.80897	−	7.21709i	−0.227218	−	0.240837i
$899$	−21.8896	−	7.96717i	−0.730059	−	0.265720i
$900$	1.43384	−	0.447232i	0.0477948	−	0.0149077i
$901$	25.2474	−	9.18932i	0.841114	−	0.306141i
$902$	54.4318	+	27.3367i	1.81238	+	0.910212i
$903$	16.2896	+	22.9825i	0.542083	+	0.764810i
$904$	9.51808	−	22.0654i	0.316567	−	0.733884i
$905$	−6.07045	+	0.709534i	−0.201789	+	0.0235857i
$906$	1.81625	+	6.62623i	0.0603409	+	0.220142i
$907$	−21.7933	+	14.3337i	−0.723635	+	0.475942i	−0.857125	−	0.515108i	$-0.827752\pi$
$907$	−21.7933	+	14.3337i	−0.723635	+	0.475942i	0.133491	+	0.991050i	$0.457381\pi$
$908$	2.25389	+	1.89124i	0.0747981	+	0.0627631i
$909$	9.42664	−	11.4993i	0.312662	−	0.381409i
$910$	−5.86182	+	4.91865i	−0.194318	+	0.163052i
$911$	3.60153	−	12.0299i	0.119324	−	0.398570i	−0.877370	−	0.479814i	$-0.840704\pi$
$911$	3.60153	−	12.0299i	0.119324	−	0.398570i	0.996694	+	0.0812442i	$0.0258894\pi$
$912$	32.2891	+	17.1720i	1.06920	+	0.568622i
$913$	−19.8844	+	9.98630i	−0.658076	+	0.330498i
$914$	12.2439	−	12.9778i	0.404993	−	0.429268i
$915$	−0.240681	−	0.440312i	−0.00795666	−	0.0145563i
$916$	1.59369	+	3.69458i	0.0526569	+	0.122072i
$917$	6.81205	+	11.7988i	0.224954	+	0.389631i
$918$	−14.7565	+	39.0897i	−0.487037	+	1.29015i
$919$	19.5883	−	33.9279i	0.646158	−	1.11918i	−0.337875	−	0.941191i	$-0.609708\pi$
$919$	19.5883	−	33.9279i	0.646158	−	1.11918i	0.984033	−	0.177987i	$-0.0569586\pi$
$920$	−2.84094	−	0.332058i	−0.0936629	−	0.0109476i
$921$	10.1740	−	8.13970i	0.335243	−	0.268212i
$922$	−10.1147	−	2.39724i	−0.333111	−	0.0789488i
$923$	−0.984202	+	16.8981i	−0.0323954	+	0.556208i
$924$	1.03042	+	2.55101i	0.0338982	+	0.0839222i
$925$	28.3182	−	6.71153i	0.931096	−	0.220674i
$926$	−7.23016	−	41.0043i	−0.237598	−	1.34748i
$927$	6.82178	−	0.475825i	0.224057	−	0.0156281i
$928$	−0.964816	+	5.47174i	−0.0316716	+	0.179619i
$929$	−2.80667	−	48.1887i	−0.0920839	−	1.58102i	−0.655725	−	0.755000i	$-0.727637\pi$
$929$	−2.80667	−	48.1887i	−0.0920839	−	1.58102i	0.563641	−	0.826020i	$-0.309400\pi$
$930$	1.63450	−	20.0018i	0.0535972	−	0.655885i
$931$	−9.76155	−	13.1120i	−0.319922	−	0.429730i
$932$	−1.16717	−	1.56779i	−0.0382320	−	0.0513545i
$933$	−21.9188	−	15.1613i	−0.717589	−	0.496358i
$934$	−1.23628	−	21.2261i	−0.0404523	−	0.694540i
$935$	6.11005	−	34.6518i	0.199820	−	1.13324i
$936$	−12.3419	+	5.49237i	−0.403407	+	0.179524i
$937$	2.06159	+	11.6919i	0.0673494	+	0.381957i	0.999787	+	0.0206269i	$0.00656621\pi$
$937$	2.06159	+	11.6919i	0.0673494	+	0.381957i	−0.932438	+	0.361330i	$0.882323\pi$
$938$	−36.6307	+	8.68163i	−1.19603	+	0.283465i
$939$	4.23397	−	5.41825i	0.138170	−	0.176818i
$940$	0.00387194	−	0.0664786i	0.000126289	−	0.00216829i
$941$	8.47250	+	2.00802i	0.276196	+	0.0654596i	0.366379	−	0.930466i	$-0.380597\pi$
$941$	8.47250	+	2.00802i	0.276196	+	0.0654596i	−0.0901836	+	0.995925i	$0.528745\pi$
$942$	−2.21381	−	14.5323i	−0.0721297	−	0.473489i
$943$	6.72760	+	0.786343i	0.219081	+	0.0256069i
$944$	−4.14525	+	7.17978i	−0.134916	+	0.233682i
$945$	−14.4700	−	6.44702i	−0.470709	−	0.209721i
$946$	25.7488	+	44.5982i	0.837164	+	1.45001i
$947$	13.9682	+	32.3820i	0.453907	+	1.05227i	0.979483	+	0.201527i	$0.0645905\pi$
$947$	13.9682	+	32.3820i	0.453907	+	1.05227i	−0.525576	+	0.850746i	$0.676150\pi$
$948$	−0.681147	+	1.11860i	−0.0221226	+	0.0363305i
$949$	13.4923	−	14.3010i	0.437980	−	0.464231i
$950$	15.5883	−	7.82871i	0.505750	−	0.253997i
$951$	12.5964	−	7.86954i	0.408465	−	0.255187i
$952$	7.86865	−	26.2831i	0.255024	−	0.851841i
$953$	22.5161	−	18.8933i	0.729369	−	0.612013i	−0.200591	−	0.979675i	$-0.564286\pi$
$953$	22.5161	−	18.8933i	0.729369	−	0.612013i	0.929959	+	0.367662i	$0.119842\pi$
$954$	−0.253417	−	22.1115i	−0.00820467	−	0.715886i
$955$	−22.5912	−	18.9562i	−0.731032	−	0.613409i
$956$	−1.89378	+	1.24556i	−0.0612491	+	0.0402841i
$957$	−23.6325	+	23.9049i	−0.763930	+	0.772736i
$958$	−33.1877	+	3.87908i	−1.07224	+	0.125327i
$959$	13.1624	−	30.5138i	0.425035	−	0.985343i
$960$	19.3926	−	1.80866i	0.625893	−	0.0583744i
$961$	−6.53793	−	3.28347i	−0.210901	−	0.105918i
$962$	28.2421	−	10.2793i	0.910561	−	0.331417i
$963$	−1.69380	−	13.1797i	−0.0545819	−	0.424708i
$964$	0.424010	+	0.154327i	0.0136565	+	0.00497054i
$965$	18.0652	+	19.1480i	0.581540	+	0.616396i
$966$	2.19214	+	2.43505i	0.0705311	+	0.0783465i
$967$	−23.3194	−	15.3374i	−0.749901	−	0.493218i	0.116114	−	0.993236i	$-0.462956\pi$
$967$	−23.3194	−	15.3374i	−0.749901	−	0.493218i	−0.866015	+	0.500018i	$0.833327\pi$
$968$	−4.15672	−	13.8844i	−0.133602	−	0.446262i
$969$	−8.90842	+	44.4275i	−0.286180	+	1.42722i
$970$	1.90245	−	2.55544i	0.0610841	−	0.0820502i
$971$	−32.8139			−1.05305			−0.526524	−	0.850160i	$-0.676505\pi$
$971$	−32.8139			−1.05305			−0.526524	+	0.850160i	$0.676505\pi$
$972$	2.45893	+	2.06512i	0.0788701	+	0.0662387i
$973$	36.1354			1.15845
$974$	37.0032	−	49.7039i	1.18566	−	1.59262i
$975$	−1.39866	+	6.97531i	−0.0447930	+	0.223389i
$976$	−0.226498	−	0.756555i	−0.00725001	−	0.0242167i
$977$	8.44583	+	5.55491i	0.270206	+	0.177717i	0.677380	−	0.735633i	$-0.263115\pi$
$977$	8.44583	+	5.55491i	0.270206	+	0.177717i	−0.407174	+	0.913351i	$0.633486\pi$
$978$	−27.6048	−	30.6636i	−0.882703	−	0.980514i
$979$	−19.6968	−	20.8774i	−0.629514	−	0.667246i
$980$	1.04965	+	0.382042i	0.0335299	+	0.0122039i
$981$	43.9835	−	33.5347i	1.40429	−	1.07068i
$982$	−15.4489	+	5.62294i	−0.492994	+	0.179435i
$983$	44.4143	+	22.3057i	1.41660	+	0.711441i	0.981947	−	0.189159i	$-0.0605760\pi$
$983$	44.4143	+	22.3057i	1.41660	+	0.711441i	0.434649	+	0.900600i	$0.356872\pi$
$984$	−46.4790	+	4.33490i	−1.48170	+	0.138191i
$985$	−11.8870	+	27.5571i	−0.378751	+	0.878044i
$986$	−38.2287	+	4.46829i	−1.21745	+	0.142299i
$987$	0.467056	−	0.472439i	0.0148665	−	0.0150379i
$988$	1.40540	−	0.924348i	0.0447118	−	0.0294074i
$989$	4.38685	+	3.68101i	0.139494	+	0.117049i
$990$	−25.2439	−	14.1913i	−0.802303	−	0.451030i
$991$	−20.4874	+	17.1909i	−0.650802	+	0.546088i	−0.907314	−	0.420453i	$-0.861871\pi$
$991$	−20.4874	+	17.1909i	−0.650802	+	0.546088i	0.256512	+	0.966541i	$0.417427\pi$
$992$	1.62016	−	5.41172i	0.0514402	−	0.171822i
$993$	−13.7064	+	8.56303i	−0.434959	+	0.271740i
$994$	−25.2840	+	12.6981i	−0.801961	+	0.402760i
$995$	−0.984868	+	1.04390i	−0.0312224	+	0.0330938i
$996$	−1.01836	+	1.67238i	−0.0322678	+	0.0529913i
$997$	16.7707	+	38.8789i	0.531134	+	1.23131i	0.946810	+	0.321794i	$0.104286\pi$
$997$	16.7707	+	38.8789i	0.531134	+	1.23131i	−0.415675	+	0.909513i	$0.636455\pi$
$998$	5.80331	+	10.0516i	0.183701	+	0.318179i
$999$	44.7451	+	43.2325i	1.41567	+	1.36782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.58.3	yes	144
3.2	odd	2		243.2.g.a.226.6		144
9.2	odd	6		729.2.g.a.433.3		144
9.4	even	3		729.2.g.c.676.3		144
9.5	odd	6		729.2.g.b.676.6		144
9.7	even	3		729.2.g.d.433.6		144
81.7	even	27	inner	81.2.g.a.7.3	✓	144
81.13	even	27		6561.2.a.c.1.21		72
81.20	odd	54		729.2.g.b.55.6		144
81.34	even	27		729.2.g.d.298.6		144
81.47	odd	54		729.2.g.a.298.3		144
81.61	even	27		729.2.g.c.55.3		144
81.68	odd	54		6561.2.a.d.1.52		72
81.74	odd	54		243.2.g.a.100.6		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.3	✓	144	81.7	even	27	inner
81.2.g.a.58.3	yes	144	1.1	even	1	trivial
243.2.g.a.100.6		144	81.74	odd	54
243.2.g.a.226.6		144	3.2	odd	2
729.2.g.a.298.3		144	81.47	odd	54
729.2.g.a.433.3		144	9.2	odd	6
729.2.g.b.55.6		144	81.20	odd	54
729.2.g.b.676.6		144	9.5	odd	6
729.2.g.c.55.3		144	81.61	even	27
729.2.g.c.676.3		144	9.4	even	3
729.2.g.d.298.6		144	81.34	even	27
729.2.g.d.433.6		144	9.7	even	3
6561.2.a.c.1.21		72	81.13	even	27
6561.2.a.d.1.52		72	81.68	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.886934 + 1.19136i) q^{2} +(-0.340526 + 1.69825i) q^{3} +(-0.0590788 - 0.197337i) q^{4} +(-1.33926 - 0.880846i) q^{5} +(-1.72120 - 1.91192i) q^{6} +(1.30515 + 1.38337i) q^{7} +(-2.50387 - 0.911335i) q^{8} +(-2.76808 - 1.15659i) q^{9} +(2.23724 - 0.814290i) q^{10} +(3.62327 + 1.81967i) q^{11} +(0.355245 - 0.0331322i) q^{12} +(-0.669348 + 1.55172i) q^{13} +(-2.80567 + 0.327936i) q^{14} +(1.95195 - 1.97445i) q^{15} +(3.65071 - 2.40111i) q^{16} +(4.14727 + 3.47997i) q^{17} +(3.83303 - 2.27196i) q^{18} +(3.70167 - 3.10607i) q^{19} +(-0.0947016 + 0.316325i) q^{20} +(-2.79374 + 1.74539i) q^{21} +(-5.38148 + 2.70268i) q^{22} +(-0.459550 + 0.487095i) q^{23} +(2.40030 - 3.94186i) q^{24} +(-0.962667 - 2.23171i) q^{25} +(-1.25499 - 2.17371i) q^{26} +(2.90678 - 4.30704i) q^{27} +(0.195884 - 0.339282i) q^{28} +(4.75422 + 0.555689i) q^{29} +(0.621027 + 4.07668i) q^{30} +(-4.73543 - 1.12232i) q^{31} +(-0.0674931 + 1.15881i) q^{32} +(-4.32407 + 5.53356i) q^{33} +(-7.82425 + 1.85438i) q^{34} +(-0.529392 - 3.00233i) q^{35} +(-0.0647034 + 0.614576i) q^{36} +(-2.07926 + 11.7921i) q^{37} +(0.417308 + 7.16489i) q^{38} +(-2.40728 - 1.66512i) q^{39} +(2.55060 + 3.42604i) q^{40} +(-6.04005 - 8.11319i) q^{41} +(0.398487 - 4.87640i) q^{42} +(-0.497227 - 8.53705i) q^{43} +(0.145031 - 0.822509i) q^{44} +(2.68841 + 3.98724i) q^{45} +(-0.172714 - 0.979511i) q^{46} +(-0.196235 + 0.0465086i) q^{47} +(2.83451 + 7.01744i) q^{48} +(0.196697 - 3.37715i) q^{49} +(3.51259 + 0.832500i) q^{50} +(-7.32210 + 5.85806i) q^{51} +(0.345757 + 0.0404132i) q^{52} +(2.48138 - 4.29788i) q^{53} +(2.55311 + 7.28309i) q^{54} +(-3.24965 - 5.62856i) q^{55} +(-2.00720 - 4.65322i) q^{56} +(4.01436 + 7.34404i) q^{57} +(-4.87871 + 5.17113i) q^{58} +(-1.69552 + 0.851522i) q^{59} +(-0.504950 - 0.268544i) q^{60} +(0.0518355 - 0.173143i) q^{61} +(5.53710 - 4.64618i) q^{62} +(-2.01275 - 5.33882i) q^{63} +(5.37384 + 4.50919i) q^{64} +(2.26326 - 1.48857i) q^{65} +(-2.75729 - 10.0594i) q^{66} +(13.2368 - 1.54716i) q^{67} +(0.441711 - 1.02400i) q^{68} +(-0.670719 - 0.946298i) q^{69} +(4.04639 + 2.03218i) q^{70} +(9.41216 - 3.42575i) q^{71} +(5.87689 + 5.41861i) q^{72} +(-10.9327 - 3.97917i) q^{73} +(-12.2045 - 12.9360i) q^{74} +(4.11781 - 0.874891i) q^{75} +(-0.831632 - 0.546973i) q^{76} +(2.21160 + 7.38727i) q^{77} +(4.11886 - 1.39108i) q^{78} +(-2.19201 + 2.94438i) q^{79} -7.00426 q^{80} +(6.32459 + 6.40309i) q^{81} +15.0229 q^{82} +(-3.27719 + 4.40202i) q^{83} +(0.509481 + 0.448194i) q^{84} +(-2.48896 - 8.31370i) q^{85} +(10.6117 + 6.97943i) q^{86} +(-2.56263 + 7.88461i) q^{87} +(-7.41387 - 7.85824i) q^{88} +(-6.65218 - 2.42120i) q^{89} +(-7.13468 - 0.333556i) q^{90} +(-3.02021 + 1.09927i) q^{91} +(0.123272 + 0.0619093i) q^{92} +(3.51851 - 7.65975i) q^{93} +(0.118639 - 0.275037i) q^{94} +(-7.69347 + 0.899238i) q^{95} +(-1.94497 - 0.509225i) q^{96} +(1.11799 - 0.735313i) q^{97} +(3.84894 + 3.22965i) q^{98} +(-7.92489 - 9.22765i) 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

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