LMFDB - Embedded newform 192.2.s.a.131.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [192,2,Mod(11,192)] 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("192.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(192, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			131.24
Character	$\chi$	$=$	192.131
Dual form			192.2.s.a.107.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.04386 - 0.954131i) q^{2} +(1.39786 + 1.02274i) q^{3} +(0.179269 - 1.99195i) q^{4} +(-0.0417075 + 0.0624196i) q^{5} +(2.43499 - 0.266149i) q^{6} +(-0.100307 - 0.242162i) q^{7} +(-1.71345 - 2.25035i) q^{8} +(0.908014 + 2.85929i) q^{9} +(0.0160199 + 0.104951i) q^{10} +(-2.15600 + 0.428854i) q^{11} +(2.28783 - 2.60112i) q^{12} +(0.751836 - 0.502361i) q^{13} +(-0.335761 - 0.157077i) q^{14} +(-0.122140 + 0.0445980i) q^{15} +(-3.93573 - 0.714188i) q^{16} +(-1.66843 + 1.66843i) q^{17} +(3.67597 + 2.11832i) q^{18} +(-1.06552 + 0.711956i) q^{19} +(0.116860 + 0.0942690i) q^{20} +(0.107454 - 0.441097i) q^{21} +(-1.84137 + 2.50477i) q^{22} +(0.745366 - 1.79947i) q^{23} +(-0.0936376 - 4.89808i) q^{24} +(1.91126 + 4.61419i) q^{25} +(0.305490 - 1.24174i) q^{26} +(-1.65503 + 4.92553i) q^{27} +(-0.500357 + 0.156394i) q^{28} +(1.26847 - 6.37705i) q^{29} +(-0.0849442 + 0.163091i) q^{30} -10.1205 q^{31} +(-4.78976 + 3.00969i) q^{32} +(-3.45238 - 1.60554i) q^{33} +(-0.149699 + 3.33350i) q^{34} +(0.0192992 + 0.00383886i) q^{35} +(5.85833 - 1.29614i) q^{36} +(2.54831 - 3.81381i) q^{37} +(-0.432947 + 1.75982i) q^{38} +(1.56474 + 0.0667024i) q^{39} +(0.211930 - 0.0130964i) q^{40} +(4.77720 + 1.97878i) q^{41} +(-0.308697 - 0.562966i) q^{42} +(-9.37912 + 1.86562i) q^{43} +(0.467754 + 4.37152i) q^{44} +(-0.216346 - 0.0625756i) q^{45} +(-0.938878 - 2.58957i) q^{46} +(8.04483 + 8.04483i) q^{47} +(-4.77116 - 5.02355i) q^{48} +(4.90117 - 4.90117i) q^{49} +(6.39762 + 2.99296i) q^{50} +(-4.03859 + 0.625860i) q^{51} +(-0.865897 - 1.58768i) q^{52} +(-1.29422 - 6.50649i) q^{53} +(2.97200 + 6.72066i) q^{54} +(0.0631522 - 0.152463i) q^{55} +(-0.373080 + 0.640659i) q^{56} +(-2.21759 - 0.0945320i) q^{57} +(-4.76044 - 7.86701i) q^{58} +(3.86117 + 2.57995i) q^{59} +(0.0669410 + 0.251292i) q^{60} +(-0.853477 + 4.29072i) q^{61} +(-10.5643 + 9.65624i) q^{62} +(0.601331 - 0.506693i) q^{63} +(-2.12818 + 7.71173i) q^{64} +0.0678815i q^{65} +(-5.13569 + 1.61807i) q^{66} +(1.79590 + 0.357228i) q^{67} +(3.02433 + 3.62252i) q^{68} +(2.88230 - 1.75309i) q^{69} +(0.0238084 - 0.0144068i) q^{70} +(5.21738 - 2.16111i) q^{71} +(4.87857 - 6.94259i) q^{72} +(10.0231 + 4.15171i) q^{73} +(-0.978810 - 6.41248i) q^{74} +(-2.04744 + 8.40470i) q^{75} +(1.22717 + 2.25009i) q^{76} +(0.320114 + 0.479085i) q^{77} +(1.69701 - 1.42334i) q^{78} +(-5.93698 - 5.93698i) q^{79} +(0.208728 - 0.215880i) q^{80} +(-7.35102 + 5.19254i) q^{81} +(6.87472 - 2.49251i) q^{82} +(-6.79190 - 10.1648i) q^{83} +(-0.859379 - 0.293117i) q^{84} +(-0.0345567 - 0.173728i) q^{85} +(-8.01040 + 10.8963i) q^{86} +(8.29520 - 7.61690i) q^{87} +(4.65927 + 4.11693i) q^{88} +(13.5709 - 5.62127i) q^{89} +(-0.285540 + 0.141103i) q^{90} +(-0.197067 - 0.131676i) q^{91} +(-3.45084 - 1.80732i) q^{92} +(-14.1470 - 10.3506i) q^{93} +(16.0735 + 0.721820i) q^{94} -0.0962031i q^{95} +(-9.77352 - 0.691552i) q^{96} -13.0044i q^{97} +(0.439755 - 9.79246i) q^{98} +(-3.18389 - 5.77520i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{16}\right)$

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 $

$2$	1.04386	−	0.954131i	0.738117	−	0.674672i
$2$	1.04386	−	0.954131i	0.738117	−	0.674672i
$3$	1.39786	+	1.02274i	0.807054	+	0.590478i
$3$	1.39786	+	1.02274i	0.807054	+	0.590478i
$4$	0.179269	−	1.99195i	0.0896343	−	0.995975i
$5$	−0.0417075	+	0.0624196i	−0.0186521	+	0.0279149i	−0.840679	−	0.541535i	$-0.817844\pi$
$5$	−0.0417075	+	0.0624196i	−0.0186521	+	0.0279149i	0.822026	+	0.569449i	$0.192844\pi$
$6$	2.43499	−	0.266149i	0.994080	−	0.108655i
$7$	−0.100307	−	0.242162i	−0.0379125	−	0.0915288i	0.903789	−	0.427978i	$-0.140774\pi$
$7$	−0.100307	−	0.242162i	−0.0379125	−	0.0915288i	−0.941702	+	0.336449i	$0.890774\pi$
$8$	−1.71345	−	2.25035i	−0.605796	−	0.795620i
$9$	0.908014	+	2.85929i	0.302671	+	0.953095i
$10$	0.0160199	+	0.104951i	0.00506595	+	0.0331886i
$11$	−2.15600	+	0.428854i	−0.650058	+	0.129304i	−0.509095	−	0.860710i	$-0.670020\pi$
$11$	−2.15600	+	0.428854i	−0.650058	+	0.129304i	−0.140963	+	0.990015i	$0.545020\pi$
$12$	2.28783	−	2.60112i	0.660441	−	0.750878i
$13$	0.751836	−	0.502361i	0.208522	−	0.139330i	−0.446924	−	0.894572i	$-0.647481\pi$
$13$	0.751836	−	0.502361i	0.208522	−	0.139330i	0.655446	+	0.755242i	$0.272481\pi$
$14$	−0.335761	−	0.157077i	−0.0897358	−	0.0419805i
$15$	−0.122140	+	0.0445980i	−0.0315364	+	0.0115151i
$16$	−3.93573	−	0.714188i	−0.983931	−	0.178547i
$17$	−1.66843	+	1.66843i	−0.404653	+	0.404653i	−0.879869	−	0.475216i	$-0.842370\pi$
$17$	−1.66843	+	1.66843i	−0.404653	+	0.404653i	0.475216	+	0.879869i	$0.342370\pi$
$18$	3.67597	+	2.11832i	0.866434	+	0.499292i
$19$	−1.06552	+	0.711956i	−0.244446	+	0.163334i	−0.671758	−	0.740770i	$-0.734461\pi$
$19$	−1.06552	+	0.711956i	−0.244446	+	0.163334i	0.427312	+	0.904104i	$0.359461\pi$
$20$	0.116860	+	0.0942690i	0.0261307	+	0.0210792i
$21$	0.107454	−	0.441097i	0.0234484	−	0.0962552i
$22$	−1.84137	+	2.50477i	−0.392581	+	0.534018i
$23$	0.745366	−	1.79947i	0.155419	−	0.375216i	−0.826921	−	0.562318i	$-0.809910\pi$
$23$	0.745366	−	1.79947i	0.155419	−	0.375216i	0.982340	+	0.187102i	$0.0599096\pi$
$24$	−0.0936376	−	4.89808i	−0.0191137	−	0.999817i
$25$	1.91126	+	4.61419i	0.382252	+	0.922838i
$26$	0.305490	−	1.24174i	0.0599116	−	0.243526i
$27$	−1.65503	+	4.92553i	−0.318510	+	0.947920i
$28$	−0.500357	+	0.156394i	−0.0945586	+	0.0295557i
$29$	1.26847	−	6.37705i	0.235550	−	1.18419i	−0.664123	−	0.747624i	$-0.731195\pi$
$29$	1.26847	−	6.37705i	0.235550	−	1.18419i	0.899672	−	0.436566i	$-0.143805\pi$
$30$	−0.0849442	+	0.163091i	−0.0155086	+	0.0297763i
$31$	−10.1205			−1.81769			−0.908844	−	0.417137i	$-0.863033\pi$
$31$	−10.1205			−1.81769			−0.908844	+	0.417137i	$0.863033\pi$
$32$	−4.78976	+	3.00969i	−0.846718	+	0.532043i
$33$	−3.45238	−	1.60554i	−0.600983	−	0.279489i
$34$	−0.149699	+	3.33350i	−0.0256732	+	0.571690i
$35$	0.0192992	+	0.00383886i	0.00326217	+	0.000648885i
$36$	5.85833	−	1.29614i	0.976388	−	0.216023i
$37$	2.54831	−	3.81381i	0.418939	−	0.626986i	−0.560637	−	0.828062i	$-0.689444\pi$
$37$	2.54831	−	3.81381i	0.418939	−	0.626986i	0.979576	+	0.201075i	$0.0644436\pi$
$38$	−0.432947	+	1.75982i	−0.0702333	+	0.285481i
$39$	1.56474	+	0.0667024i	0.250559	+	0.0106809i
$40$	0.211930	−	0.0130964i	0.0335090	−	0.00207072i
$41$	4.77720	+	1.97878i	0.746073	+	0.309033i	0.723138	−	0.690704i	$-0.242699\pi$
$41$	4.77720	+	1.97878i	0.746073	+	0.309033i	0.0229347	+	0.999737i	$0.492699\pi$
$42$	−0.308697	−	0.562966i	−0.0476331	−	0.0868676i
$43$	−9.37912	+	1.86562i	−1.43030	+	0.284505i	−0.848659	−	0.528940i	$-0.822590\pi$
$43$	−9.37912	+	1.86562i	−1.43030	+	0.284505i	−0.581643	+	0.813444i	$0.697590\pi$
$44$	0.467754	+	4.37152i	0.0705165	+	0.659031i
$45$	−0.216346	−	0.0625756i	−0.0322510	−	0.00932823i
$46$	−0.938878	−	2.58957i	−0.138430	−	0.381811i
$47$	8.04483	+	8.04483i	1.17346	+	1.17346i	0.981379	+	0.192080i	$0.0615232\pi$
$47$	8.04483	+	8.04483i	1.17346	+	1.17346i	0.192080	+	0.981379i	$0.438477\pi$
$48$	−4.77116	−	5.02355i	−0.688657	−	0.725087i
$49$	4.90117	−	4.90117i	0.700167	−	0.700167i
$50$	6.39762	+	2.99296i	0.904760	+	0.423268i
$51$	−4.03859	+	0.625860i	−0.565516	+	0.0876380i
$52$	−0.865897	−	1.58768i	−0.120078	−	0.220171i
$53$	−1.29422	−	6.50649i	−0.177775	−	0.893735i	−0.961956	−	0.273203i	$-0.911917\pi$
$53$	−1.29422	−	6.50649i	−0.177775	−	0.893735i	0.784181	−	0.620532i	$-0.213083\pi$
$54$	2.97200	+	6.72066i	0.404437	+	0.914566i
$55$	0.0631522	−	0.152463i	0.00851544	−	0.0205581i
$56$	−0.373080	+	0.640659i	−0.0498549	+	0.0856117i
$57$	−2.21759	−	0.0945320i	−0.293727	−	0.0125211i
$58$	−4.76044	−	7.86701i	−0.625076	−	1.03299i
$59$	3.86117	+	2.57995i	0.502681	+	0.335881i	0.780920	−	0.624631i	$-0.214751\pi$
$59$	3.86117	+	2.57995i	0.502681	+	0.335881i	−0.278239	+	0.960512i	$0.589751\pi$
$60$	0.0669410	+	0.251292i	0.00864205	+	0.0324416i
$61$	−0.853477	+	4.29072i	−0.109277	+	0.549370i	0.886897	+	0.461968i	$0.152857\pi$
$61$	−0.853477	+	4.29072i	−0.109277	+	0.549370i	−0.996173	+	0.0874022i	$0.972143\pi$
$62$	−10.5643	+	9.65624i	−1.34167	+	1.22634i
$63$	0.601331	−	0.506693i	0.0757606	−	0.0638373i
$64$	−2.12818	+	7.71173i	−0.266022	+	0.963967i
$65$			0.0678815i			0.00841967i
$66$	−5.13569	+	1.61807i	−0.632159	+	0.199171i
$67$	1.79590	+	0.357228i	0.219405	+	0.0436423i	0.303568	−	0.952810i	$-0.401822\pi$
$67$	1.79590	+	0.357228i	0.219405	+	0.0436423i	−0.0841638	+	0.996452i	$0.526822\pi$
$68$	3.02433	+	3.62252i	0.366753	+	0.439295i
$69$	2.88230	−	1.75309i	0.346989	−	0.211048i
$70$	0.0238084	−	0.0144068i	0.00284565	−	0.00172194i
$71$	5.21738	−	2.16111i	0.619190	−	0.256477i	−0.0509625	−	0.998701i	$-0.516229\pi$
$71$	5.21738	−	2.16111i	0.619190	−	0.256477i	0.670152	+	0.742224i	$0.266229\pi$
$72$	4.87857	−	6.94259i	0.574944	−	0.818192i
$73$	10.0231	+	4.15171i	1.17312	+	0.485921i	0.882222	−	0.470834i	$-0.156047\pi$
$73$	10.0231	+	4.15171i	1.17312	+	0.485921i	0.290895	+	0.956755i	$0.406047\pi$
$74$	−0.978810	−	6.41248i	−0.113784	−	0.745436i
$75$	−2.04744	+	8.40470i	−0.236418	+	0.970491i
$76$	1.22717	+	2.25009i	0.140766	+	0.258103i
$77$	0.320114	+	0.479085i	0.0364804	+	0.0545967i
$78$	1.69701	−	1.42334i	0.192148	−	0.161162i
$79$	−5.93698	−	5.93698i	−0.667963	−	0.667963i	0.289281	−	0.957244i	$-0.406584\pi$
$79$	−5.93698	−	5.93698i	−0.667963	−	0.667963i	−0.957244	+	0.289281i	$0.906584\pi$
$80$	0.208728	−	0.215880i	0.0233365	−	0.0241361i
$81$	−7.35102	+	5.19254i	−0.816780	+	0.576949i
$82$	6.87472	−	2.49251i	0.759186	−	0.275252i
$83$	−6.79190	−	10.1648i	−0.745508	−	1.11573i	−0.989299	−	0.145904i	$-0.953391\pi$
$83$	−6.79190	−	10.1648i	−0.745508	−	1.11573i	0.243790	−	0.969828i	$-0.421609\pi$
$84$	−0.859379	−	0.293117i	−0.0937659	−	0.0319817i
$85$	−0.0345567	−	0.173728i	−0.00374820	−	0.0188435i
$86$	−8.01040	+	10.8963i	−0.863783	+	1.17498i
$87$	8.29520	−	7.61690i	0.889339	−	0.816617i
$88$	4.65927	+	4.11693i	0.496680	+	0.438867i
$89$	13.5709	−	5.62127i	1.43852	−	0.595853i	0.479079	−	0.877772i	$-0.340971\pi$
$89$	13.5709	−	5.62127i	1.43852	−	0.595853i	0.959438	+	0.281919i	$0.0909708\pi$
$90$	−0.285540	+	0.141103i	−0.0300985	+	0.0148735i
$91$	−0.197067	−	0.131676i	−0.0206583	−	0.0138034i
$92$	−3.45084	−	1.80732i	−0.359775	−	0.188426i
$93$	−14.1470	−	10.3506i	−1.46697	−	1.07330i
$94$	16.0735	+	0.721820i	1.65785	+	0.0744500i
$95$		−	0.0962031i		−	0.00987023i
$96$	−9.77352	−	0.691552i	−0.997506	−	0.0705812i
$97$		−	13.0044i		−	1.32039i	−0.751092	−	0.660197i	$-0.770473\pi$
$97$		−	13.0044i		−	1.32039i	0.751092	−	0.660197i	$-0.229527\pi$
$98$	0.439755	−	9.79246i	0.0444220	−	0.989188i
$99$	−3.18389	−	5.77520i	−0.319993	−	0.580430i
$100$	9.53386	−	2.97995i	0.953386	−	0.297995i
$101$	−9.68443	−	6.47093i	−0.963637	−	0.643882i	−0.0290356	−	0.999578i	$-0.509244\pi$
$101$	−9.68443	−	6.47093i	−0.963637	−	0.643882i	−0.934601	+	0.355697i	$0.884244\pi$
$102$	−3.61855	+	4.50665i	−0.358290	+	0.446225i
$103$	12.4024	−	5.13724i	1.22204	−	0.506187i	0.323985	−	0.946062i	$-0.394977\pi$
$103$	12.4024	−	5.13724i	1.22204	−	0.506187i	0.898059	+	0.439875i	$0.144977\pi$
$104$	−2.41872	−	0.831127i	−0.237175	−	0.0814987i
$105$	0.0230514	+	0.0251042i	0.00224959	+	0.00244992i
$106$	−7.55902	−	5.55698i	−0.734197	−	0.539741i
$107$	−2.77724	−	13.9621i	−0.268486	−	1.34977i	−0.845910	−	0.533326i	$-0.820942\pi$
$107$	−2.77724	−	13.9621i	−0.268486	−	1.34977i	0.577424	−	0.816445i	$-0.304058\pi$
$108$	9.51472	+	4.17972i	0.915555	+	0.402194i
$109$	5.47007	+	8.18653i	0.523937	+	0.784128i	0.995200	−	0.0978654i	$-0.0312015\pi$
$109$	5.47007	+	8.18653i	0.523937	+	0.784128i	−0.471262	+	0.881993i	$0.656201\pi$
$110$	−0.0795478	−	0.219405i	−0.00758459	−	0.0209194i
$111$	7.46270	−	2.72491i	0.708328	−	0.258637i
$112$	0.221831	+	1.02472i	0.0209611	+	0.0968272i
$113$	7.56860	+	7.56860i	0.711994	+	0.711994i	0.966952	−	0.254958i	$-0.0820617\pi$
$113$	7.56860	+	7.56860i	0.711994	+	0.711994i	−0.254958	+	0.966952i	$0.582062\pi$
$114$	−2.40504	+	2.01719i	−0.225252	+	0.188927i
$115$	0.0812350	+	0.121577i	0.00757521	+	0.0113371i
$116$	−12.4754	−	3.66994i	−1.15831	−	0.340746i
$117$	2.11907	+	1.69356i	0.195908	+	0.156570i
$118$	6.49211	−	0.990964i	0.597647	−	0.0912256i
$119$	0.571385	+	0.236676i	0.0523788	+	0.0216960i
$120$	0.309642	+	0.198442i	0.0282663	+	0.0181152i
$121$	−5.69827	+	2.36030i	−0.518024	+	0.214573i
$122$	3.20300	+	5.29322i	0.289986	+	0.479226i
$123$	4.65407	+	7.65187i	0.419643	+	0.689946i
$124$	−1.81428	+	20.1594i	−0.162927	+	1.81037i
$125$	−0.735875	−	0.146375i	−0.0658186	−	0.0130921i
$126$	0.144252	−	1.10266i	0.0128510	−	0.0982331i
$127$			0.413244i			0.0366695i	0.999832	+	0.0183347i	$0.00583646\pi$
$127$			0.413244i			0.0366695i	−0.999832	+	0.0183347i	$0.994164\pi$
$128$	5.13649	+	10.0805i	0.454006	+	0.890999i
$129$	−15.0187	−	6.98451i	−1.32232	−	0.614951i
$130$	0.0647678	+	0.0708585i	0.00568052	+	0.00621470i
$131$	1.04858	−	5.27154i	0.0916144	−	0.460577i	−0.907559	−	0.419925i	$-0.862056\pi$
$131$	1.04858	−	5.27154i	0.0916144	−	0.460577i	0.999173	−	0.0406521i	$-0.0129435\pi$
$132$	−3.81706	+	6.58915i	−0.332233	+	0.573512i
$133$	0.279288	+	0.186614i	0.0242173	+	0.0161815i
$134$	2.21551	−	1.34063i	0.191391	−	0.115813i
$135$	−0.238423	−	0.308738i	−0.0205202	−	0.0265719i
$136$	6.61332	+	0.895784i	0.567087	+	0.0768129i
$137$	−5.79645	+	13.9939i	−0.495224	+	1.19558i	0.456804	+	0.889567i	$0.348994\pi$
$137$	−5.79645	+	13.9939i	−0.495224	+	1.19558i	−0.952028	+	0.306010i	$0.901006\pi$
$138$	1.33603	−	4.58007i	0.113730	−	0.389881i
$139$	1.71904	+	8.64218i	0.145807	+	0.733021i	0.982634	+	0.185554i	$0.0594078\pi$
$139$	1.71904	+	8.64218i	0.145807	+	0.733021i	−0.836827	+	0.547467i	$0.815592\pi$
$140$	0.0111066	−	0.0377549i	0.000938675	−	0.00319087i
$141$	3.01777	+	19.4733i	0.254142	+	1.63995i
$142$	3.38421	−	7.23395i	0.283997	−	0.607060i
$143$	−1.40552	+	1.40552i	−0.117535	+	0.117535i
$144$	−1.53162	−	11.9019i	−0.127635	−	0.991821i
$145$	0.345148	+	0.345148i	0.0286630	+	0.0286630i
$146$	14.4240	−	5.22958i	1.19374	−	0.432803i
$147$	11.8637	−	1.83852i	0.978505	−	0.151639i
$148$	−7.14008	−	5.75979i	−0.586911	−	0.473452i
$149$	6.01868	−	1.19719i	0.493069	−	0.0980776i	0.0577083	−	0.998333i	$-0.481621\pi$
$149$	6.01868	−	1.19719i	0.493069	−	0.0980776i	0.435361	+	0.900256i	$0.356621\pi$
$150$	5.88196	+	10.7268i	0.480260	+	0.875841i
$151$	7.84809	+	3.25079i	0.638669	+	0.264545i	0.678431	−	0.734664i	$-0.262660\pi$
$151$	7.84809	+	3.25079i	0.638669	+	0.264545i	−0.0397624	+	0.999209i	$0.512660\pi$
$152$	3.42786	+	1.17789i	0.278036	+	0.0955395i
$153$	−6.28546	−	3.25556i	−0.508150	−	0.263196i
$154$	0.791262	+	0.194664i	0.0637617	+	0.0156865i
$155$	0.422098	−	0.631715i	0.0339038	−	0.0507406i
$156$	0.413377	−	3.10493i	0.0330967	−	0.248594i
$157$	−12.5487	−	2.49608i	−1.00149	−	0.199209i	−0.332998	−	0.942927i	$-0.608060\pi$
$157$	−12.5487	−	2.49608i	−1.00149	−	0.199209i	−0.668493	+	0.743718i	$0.733060\pi$
$158$	−11.8620	−	0.532694i	−0.943691	−	0.0423788i
$159$	4.84530	−	10.4188i	0.384257	−	0.826264i
$160$	0.0119050	−	0.424501i	0.000941176	−	0.0335598i
$161$	−0.510530			−0.0402354
$162$	−2.71904	+	12.4341i	−0.213628	+	0.976915i
$163$	1.41044	−	7.09076i	0.110474	−	0.555391i	−0.885414	−	0.464803i	$-0.846125\pi$
$163$	1.41044	−	7.09076i	0.110474	−	0.555391i	0.995888	−	0.0905883i	$-0.0288747\pi$
$164$	4.79803	−	9.16120i	0.374663	−	0.715370i
$165$	0.244207	−	0.148533i	0.0190115	−	0.0115633i
$166$	−16.7883	−	4.13022i	−1.30303	−	0.320567i
$167$	5.06460	+	12.2270i	0.391911	+	0.946156i	0.989524	+	0.144371i	$0.0461160\pi$
$167$	5.06460	+	12.2270i	0.391911	+	0.946156i	−0.597613	+	0.801785i	$0.703884\pi$
$168$	−1.17674	+	0.513988i	−0.0907874	+	0.0396550i
$169$	−4.66199	+	11.2550i	−0.358615	+	0.865773i
$170$	−0.201832	−	0.148376i	−0.0154798	−	0.0113799i
$171$	−3.00319	−	2.40015i	−0.229660	−	0.183544i
$172$	2.03484	+	19.0172i	0.155155	+	1.45005i
$173$	−20.0687	+	13.4095i	−1.52580	+	1.01950i	−0.541966	+	0.840400i	$0.682320\pi$
$173$	−20.0687	+	13.4095i	−1.52580	+	1.01950i	−0.983830	+	0.179104i	$0.942680\pi$
$174$	1.39148	−	15.8657i	0.105488	−	1.20277i
$175$	0.925671	−	0.925671i	0.0699742	−	0.0699742i
$176$	8.79170	−	0.148066i	0.662699	−	0.0111609i
$177$	2.75875	+	7.55536i	0.207360	+	0.567896i
$178$	8.80268	−	18.8162i	0.659789	−	1.41034i
$179$	−10.2002	+	6.81555i	−0.762398	+	0.509418i	−0.874941	−	0.484229i	$-0.839100\pi$
$179$	−10.2002	+	6.81555i	−0.762398	+	0.509418i	0.112543	+	0.993647i	$0.464100\pi$
$180$	−0.163432	+	0.419733i	−0.0121815	+	0.0312851i
$181$	10.3436	−	2.05747i	0.768834	−	0.152931i	0.204936	−	0.978775i	$-0.434301\pi$
$181$	10.3436	−	2.05747i	0.768834	−	0.152931i	0.563897	+	0.825845i	$0.309301\pi$
$182$	−0.331346	+	0.0505771i	−0.0245610	+	0.00374903i
$183$	−5.58132	+	5.12493i	−0.412583	+	0.378846i
$184$	−5.32659	+	1.40597i	−0.392682	+	0.103649i
$185$	0.131773	+	0.318128i	0.00968815	+	0.0233893i
$186$	−24.6432	+	2.69354i	−1.80693	+	0.197500i
$187$	2.88161	−	4.31264i	0.210724	−	0.315371i
$188$	17.4671	−	14.5827i	1.27392	−	1.06355i
$189$	1.35879	−	0.0932803i	0.0988374	−	0.00678514i
$190$	−0.0917903	−	0.100422i	−0.00665917	−	0.00728539i
$191$	−27.5926			−1.99653			−0.998265	−	0.0588807i	$-0.981247\pi$
$191$	−27.5926			−1.99653			−0.998265	+	0.0588807i	$0.981247\pi$
$192$	−10.8620	+	8.60334i	−0.783896	+	0.620893i
$193$	−5.03806			−0.362648			−0.181324	−	0.983423i	$-0.558038\pi$
$193$	−5.03806			−0.362648			−0.181324	+	0.983423i	$0.558038\pi$
$194$	−12.4079	−	13.5747i	−0.890834	−	0.974606i
$195$	−0.0694250	+	0.0948887i	−0.00497163	+	0.00679512i
$196$	−8.88425	−	10.6415i	−0.634589	−	0.760107i
$197$	−7.59394	+	11.3651i	−0.541046	+	0.809732i	−0.996763	−	0.0803923i	$-0.974383\pi$
$197$	−7.59394	+	11.3651i	−0.541046	+	0.809732i	0.455718	+	0.890124i	$0.349383\pi$
$198$	−8.83382	−	2.99063i	−0.627793	−	0.212535i
$199$	4.56453	+	11.0197i	0.323571	+	0.781169i	0.999041	+	0.0437818i	$0.0139407\pi$
$199$	4.56453	+	11.0197i	0.323571	+	0.781169i	−0.675470	+	0.737387i	$0.736059\pi$
$200$	7.10871	−	12.2072i	0.502662	−	0.863179i
$201$	2.14507	+	2.33609i	0.151301	+	0.164775i
$202$	−16.2833	+	2.48550i	−1.14569	+	0.174879i
$203$	−1.67152	+	0.332486i	−0.117318	+	0.0233359i
$204$	0.522690	+	8.15686i	0.0365956	+	0.571095i
$205$	−0.322759	+	0.215661i	−0.0225425	+	0.0150624i
$206$	8.04471	−	17.1960i	0.560501	−	1.19811i
$207$	5.82201	+	0.497268i	0.404657	+	0.0345625i
$208$	−3.31780	+	1.44020i	−0.230048	+	0.0998600i
$209$	1.99193	−	1.99193i	0.137784	−	0.137784i
$210$	0.0480151	+	0.00421111i	0.00331336	+	0.000290594i
$211$	2.76673	−	1.84867i	0.190470	−	0.127268i	−0.456679	−	0.889631i	$-0.650961\pi$
$211$	2.76673	−	1.84867i	0.190470	−	0.127268i	0.647149	+	0.762364i	$0.275961\pi$
$212$	−13.1926	+	1.41161i	−0.906072	+	0.0969500i
$213$	9.50341	+	2.31509i	0.651163	+	0.158627i
$214$	−16.2207	−	11.9246i	−1.10883	−	0.815149i
$215$	0.274728	−	0.663251i	0.0187363	−	0.0452334i
$216$	13.9200	−	4.71526i	0.947136	−	0.320833i
$217$	1.01515	+	2.45079i	0.0689130	+	0.166371i
$218$	13.5210	+	3.32640i	0.915757	+	0.225292i
$219$	9.76478	+	16.0545i	0.659843	+	1.08486i
$220$	−0.292377	−	0.153128i	−0.0197121	−	0.0103239i
$221$	−0.416231	+	2.09254i	−0.0279988	+	0.140759i
$222$	5.19005	−	9.96480i	0.348334	−	0.668794i
$223$	−12.6115			−0.844531			−0.422265	−	0.906472i	$-0.638765\pi$
$223$	−12.6115			−0.844531			−0.422265	+	0.906472i	$0.638765\pi$
$224$	1.20928	+	0.858007i	0.0807984	+	0.0573280i
$225$	−11.4578	+	9.65459i	−0.763856	+	0.643639i
$226$	15.1220	+	0.679090i	1.00590	+	0.0451724i
$227$	13.6050	+	2.70621i	0.902997	+	0.179617i	0.624688	−	0.780874i	$-0.285226\pi$
$227$	13.6050	+	2.70621i	0.902997	+	0.179617i	0.278309	+	0.960492i	$0.410226\pi$
$228$	−0.585847	+	4.40037i	−0.0387986	+	0.291422i
$229$	−0.0914294	+	0.136834i	−0.00604182	+	0.00904223i	−0.834478	−	0.551041i	$-0.814231\pi$
$229$	−0.0914294	+	0.136834i	−0.00604182	+	0.00904223i	0.828436	+	0.560083i	$0.189231\pi$
$230$	0.200798	+	0.0493998i	0.0132402	+	0.00325733i
$231$	−0.0425040	+	0.997085i	−0.00279656	+	0.0656034i
$232$	−16.5241	+	8.07225i	−1.08486	+	0.529969i
$233$	−15.0334	−	6.22705i	−0.984873	−	0.407948i	−0.168645	−	0.985677i	$-0.553939\pi$
$233$	−15.0334	−	6.22705i	−0.984873	−	0.407948i	−0.816229	+	0.577729i	$0.803939\pi$
$234$	3.82788	−	0.254035i	0.250237	−	0.0166068i
$235$	−0.837684	+	0.166626i	−0.0546445	+	0.0108695i
$236$	5.83131	−	7.22874i	0.379586	−	0.470551i
$237$	−2.22708	−	14.3710i	−0.144664	−	0.933499i
$238$	0.822263	−	0.298121i	0.0532994	−	0.0193243i
$239$	9.91200	+	9.91200i	0.641154	+	0.641154i	0.950839	−	0.309685i	$-0.100224\pi$
$239$	9.91200	+	9.91200i	0.641154	+	0.641154i	−0.309685	+	0.950839i	$0.600224\pi$
$240$	0.512561	−	0.0882943i	0.0330857	−	0.00569938i
$241$	6.54008	−	6.54008i	0.421283	−	0.421283i	−0.464362	−	0.885645i	$-0.653716\pi$
$241$	6.54008	−	6.54008i	0.421283	−	0.421283i	0.885645	+	0.464362i	$0.153716\pi$
$242$	−3.69613	+	7.90070i	−0.237596	+	0.507877i
$243$	−15.5863	−	0.259739i	−0.999861	−	0.0166623i
$244$	8.39389	+	2.46927i	0.537364	+	0.158079i
$245$	0.101514	+	0.510344i	0.00648548	+	0.0326047i
$246$	12.1591	+	3.54686i	0.775234	+	0.226140i
$247$	−0.443436	+	1.07055i	−0.0282151	+	0.0681174i
$248$	17.3409	+	22.7746i	1.10115	+	1.44619i
$249$	0.901814	−	21.1553i	0.0571502	−	1.34066i
$250$	−0.907807	+	0.549327i	−0.0574148	+	0.0347425i
$251$	18.8565	+	12.5995i	1.19021	+	0.795273i	0.983105	−	0.183045i	$-0.0585954\pi$
$251$	18.8565	+	12.5995i	1.19021	+	0.795273i	0.207106	+	0.978318i	$0.433595\pi$
$252$	−0.901507	−	1.28866i	−0.0567896	−	0.0811777i
$253$	−0.835295	+	4.19931i	−0.0525145	+	0.264008i
$254$	0.394289	+	0.431367i	0.0247399	+	0.0270664i
$255$	0.129373	−	0.278190i	0.00810167	−	0.0174209i
$256$	14.9799	+	5.62170i	0.936242	+	0.351356i
$257$		−	0.247927i		−	0.0154652i	−0.999970	−	0.00773262i	$-0.997539\pi$
$257$		−	0.247927i		−	0.0154652i	0.999970	−	0.00773262i	$-0.00246139\pi$
$258$	−22.3415	+	7.03901i	−1.39092	+	0.438229i
$259$	−1.17917	−	0.234552i	−0.0732703	−	0.0145744i
$260$	0.135217	+	0.0121690i	0.00838577	+	0.000754691i
$261$	19.3856	−	2.16352i	1.19994	−	0.133919i
$262$	−3.93518	−	6.50321i	−0.243116	−	0.401769i
$263$	−24.7866	+	10.2669i	−1.52841	+	0.633087i	−0.979254	−	0.202635i	$-0.935050\pi$
$263$	−24.7866	+	10.2669i	−1.52841	+	0.633087i	−0.549153	+	0.835722i	$0.685050\pi$
$264$	2.30245	+	10.5201i	0.141706	+	0.647467i
$265$	0.460111	+	0.190584i	0.0282644	+	0.0117075i
$266$	0.469591	−	0.0716789i	0.0287924	−	0.00439492i
$267$	24.7193	+	6.02179i	1.51280	+	0.368527i
$268$	1.03353	−	3.51331i	0.0631328	−	0.214610i
$269$	7.89201	+	11.8112i	0.481184	+	0.720143i	0.990052	−	0.140701i	$-0.0449358\pi$
$269$	7.89201	+	11.8112i	0.481184	+	0.720143i	−0.508868	+	0.860845i	$0.669936\pi$
$270$	−0.543455	−	0.0947906i	−0.0330736	−	0.00576877i
$271$	−7.91386	−	7.91386i	−0.480733	−	0.480733i	0.424633	−	0.905366i	$-0.360403\pi$
$271$	−7.91386	−	7.91386i	−0.480733	−	0.480733i	−0.905366	+	0.424633i	$0.860403\pi$
$272$	7.75804	−	5.37490i	0.470400	−	0.325901i
$273$	−0.140802	−	0.385613i	−0.00852172	−	0.0233384i
$274$	7.30133	+	20.1382i	0.441089	+	1.21659i
$275$	−6.09949	−	9.12853i	−0.367813	−	0.550471i
$276$	−2.97536	−	6.05568i	−0.179096	−	0.364509i
$277$	−4.80902	−	24.1766i	−0.288946	−	1.45263i	−0.803568	−	0.595213i	$-0.797068\pi$
$277$	−4.80902	−	24.1766i	−0.288946	−	1.45263i	0.514622	−	0.857417i	$-0.327932\pi$
$278$	10.0402	+	7.38101i	0.602171	+	0.442683i
$279$	−9.18951	−	28.9373i	−0.550161	−	1.73243i
$280$	−0.0244295	−	0.0500078i	−0.00145994	−	0.00298854i
$281$	21.3506	−	8.84369i	1.27367	−	0.527570i	0.359590	−	0.933110i	$-0.382916\pi$
$281$	21.3506	−	8.84369i	1.27367	−	0.527570i	0.914077	+	0.405540i	$0.132916\pi$
$282$	21.7302	+	17.4479i	1.29401	+	1.03901i
$283$	−2.13260	−	1.42496i	−0.126770	−	0.0847050i	0.490569	−	0.871403i	$-0.336789\pi$
$283$	−2.13260	−	1.42496i	−0.126770	−	0.0847050i	−0.617339	+	0.786698i	$0.711789\pi$
$284$	−3.36951	−	10.7802i	−0.199944	−	0.639686i
$285$	0.0983905	−	0.134478i	0.00582815	−	0.00796580i
$286$	−0.126110	+	2.80820i	−0.00745701	+	0.166053i
$287$		−	1.35534i		−	0.0800034i
$288$	−12.9547	−	10.9624i	−0.763364	−	0.645968i
$289$			11.4327i			0.672512i
$290$	0.689602	+	0.0309683i	0.0404948	+	0.00181852i
$291$	13.3001	−	18.1783i	0.779664	−	1.06563i
$292$	10.0668	−	19.2213i	0.589116	−	1.12484i
$293$	−15.6865	−	10.4814i	−0.916416	−	0.612329i	0.00538828	−	0.999985i	$-0.498285\pi$
$293$	−15.6865	−	10.4814i	−0.916416	−	0.612329i	−0.921804	+	0.387656i	$0.873285\pi$
$294$	10.6298	−	13.2387i	0.619945	−	0.772098i
$295$	−0.322079	+	0.133409i	−0.0187522	+	0.00776740i
$296$	−12.9488	+	0.800183i	−0.752634	+	0.0465097i
$297$	1.45589	−	11.3292i	0.0844795	−	0.657387i
$298$	5.14036	−	6.99230i	0.297773	−	0.405053i
$299$	−0.343591	−	1.72735i	−0.0198704	−	0.0998953i
$300$	16.3747	+	5.58509i	0.945394	+	0.322456i
$301$	1.39257	+	2.08414i	0.0802667	+	0.120128i
$302$	11.2940	−	4.09476i	0.649894	−	0.235627i
$303$	−6.91939	−	18.9501i	−0.397509	−	1.08865i
$304$	4.70206	−	2.04108i	0.269681	−	0.117064i
$305$	−0.232229	−	0.232229i	−0.0132974	−	0.0132974i
$306$	−9.66734	+	2.59883i	−0.552645	+	0.148565i
$307$	7.34995	+	11.0000i	0.419484	+	0.627802i	0.979682	−	0.200556i	$-0.0642750\pi$
$307$	7.34995	+	11.0000i	0.419484	+	0.627802i	−0.560198	+	0.828359i	$0.689275\pi$
$308$	1.01170	−	0.551766i	0.0576469	−	0.0314398i
$309$	22.5908	+	5.50327i	1.28515	+	0.313070i
$310$	−0.162129	−	1.06216i	−0.00920830	−	0.0603264i
$311$	4.34991	+	1.80179i	0.246661	+	0.102170i	0.502589	−	0.864526i	$-0.332381\pi$
$311$	4.34991	+	1.80179i	0.246661	+	0.102170i	−0.255928	+	0.966696i	$0.582381\pi$
$312$	−2.53101	−	3.63552i	−0.143290	−	0.205821i
$313$	−8.83610	+	3.66003i	−0.499446	+	0.206877i	−0.618162	−	0.786051i	$-0.712122\pi$
$313$	−8.83610	+	3.66003i	−0.499446	+	0.206877i	0.118716	+	0.992928i	$0.462122\pi$
$314$	−15.4806	+	9.36751i	−0.873619	+	0.528639i
$315$	0.00654758	+	0.0586678i	0.000368914	+	0.00330555i
$316$	−12.8905	+	10.7619i	−0.725146	+	0.605402i
$317$	1.84684	+	0.367359i	0.103729	+	0.0206329i	0.246682	−	0.969097i	$-0.420660\pi$
$317$	1.84684	+	0.367359i	0.103729	+	0.0206329i	−0.142953	+	0.989729i	$0.545660\pi$
$318$	−4.88310	−	15.4988i	−0.273831	−	0.869127i
$319$			14.2929i			0.800249i
$320$	−0.392603	−	0.454477i	−0.0219472	−	0.0254060i
$321$	10.3974	−	22.3575i	0.580327	−	1.24787i
$322$	−0.532920	+	0.487112i	−0.0296984	+	0.0271457i
$323$	0.589892	−	2.96559i	0.0328225	−	0.165010i
$324$	9.02547	+	15.5737i	0.501415	+	0.865207i
$325$	3.75494	+	2.50897i	0.208287	+	0.139173i
$326$	−5.29321	−	8.74747i	−0.293164	−	0.484477i
$327$	−0.726304	+	17.0381i	−0.0401647	+	0.942207i
$328$	−3.73253	−	14.1409i	−0.206095	−	0.780802i
$329$	1.14120	−	2.75511i	0.0629166	−	0.151894i
$330$	0.113197	−	0.388053i	0.00623129	−	0.0213616i
$331$	−5.48542	−	27.5771i	−0.301506	−	1.51577i	−0.773286	−	0.634057i	$-0.781388\pi$
$331$	−5.48542	−	27.5771i	−0.301506	−	1.51577i	0.471780	−	0.881716i	$-0.343612\pi$
$332$	−21.4653	+	11.7069i	−1.17806	+	0.642500i
$333$	13.2187	+	3.82334i	0.724378	+	0.209518i
$334$	16.9529	+	7.93096i	0.927621	+	0.433963i
$335$	−0.0972006	+	0.0972006i	−0.00531064	+	0.00531064i
$336$	−0.737935	+	1.65929i	−0.0402576	+	0.0905218i
$337$	−14.8867	−	14.8867i	−0.810928	−	0.810928i	0.173845	−	0.984773i	$-0.444381\pi$
$337$	−14.8867	−	14.8867i	−0.810928	−	0.810928i	−0.984773	+	0.173845i	$0.944381\pi$
$338$	5.87234	+	16.1968i	0.319413	+	0.880990i
$339$	2.83913	+	18.3205i	0.154200	+	0.995034i
$340$	−0.352253	+	0.0376912i	−0.0191036	+	0.00204409i
$341$	21.8197	−	4.34020i	1.18160	−	0.235035i
$342$	−5.42496	+	0.360023i	−0.293348	+	0.0194678i
$343$	−3.37364	−	1.39741i	−0.182159	−	0.0754528i
$344$	20.2690	+	17.9097i	1.09283	+	0.965625i
$345$	−0.0107862	+	0.253029i	−0.000580710	+	0.0136226i
$346$	−8.15443	+	33.1458i	−0.438385	+	1.78193i
$347$	10.7084	−	16.0262i	0.574855	−	0.860332i	−0.424119	−	0.905606i	$-0.639416\pi$
$347$	10.7084	−	16.0262i	0.574855	−	0.860332i	0.998975	+	0.0452745i	$0.0144162\pi$
$348$	−13.6854	−	17.8891i	−0.733615	−	0.958956i
$349$	18.0984	+	3.59999i	0.968783	+	0.192703i	0.654028	−	0.756470i	$-0.273078\pi$
$349$	18.0984	+	3.59999i	0.968783	+	0.192703i	0.314755	+	0.949173i	$0.398078\pi$
$350$	0.0830555	−	1.84948i	0.00443950	−	0.0988588i
$351$	1.23009	+	4.53461i	0.0656572	+	0.242040i
$352$	9.03599	−	8.54299i	0.481620	−	0.455343i
$353$	−10.1922			−0.542474			−0.271237	−	0.962513i	$-0.587433\pi$
$353$	−10.1922			−0.542474			−0.271237	+	0.962513i	$0.587433\pi$
$354$	10.0885	+	5.25450i	0.536200	+	0.279273i
$355$	−0.0827081	+	0.415802i	−0.00438969	+	0.0220685i
$356$	−8.76444	−	28.0404i	−0.464514	−	1.48614i
$357$	0.556659	+	0.915217i	0.0294615	+	0.0484384i
$358$	−4.14460	+	16.8468i	−0.219049	+	0.890379i
$359$	−6.12003	−	14.7751i	−0.323003	−	0.779798i	−0.999077	−	0.0429641i	$-0.986320\pi$
$359$	−6.12003	−	14.7751i	−0.323003	−	0.779798i	0.676074	−	0.736834i	$-0.263680\pi$
$360$	0.229881	+	0.594076i	0.0121158	+	0.0313106i
$361$	−6.64254	+	16.0365i	−0.349607	+	0.844027i
$362$	8.83413	−	12.0168i	0.464311	−	0.631591i
$363$	−10.3793	−	2.52847i	−0.544774	−	0.132710i
$364$	−0.297620	+	0.368943i	−0.0155995	+	0.0193379i
$365$	−0.677187	+	0.452482i	−0.0354456	+	0.0236840i
$366$	−0.936237	+	10.6750i	−0.0489379	+	0.557991i
$367$	−9.95497	+	9.95497i	−0.519645	+	0.519645i	−0.917464	−	0.397819i	$-0.869767\pi$
$367$	−9.95497	+	9.95497i	−0.519645	+	0.519645i	0.397819	+	0.917464i	$0.369767\pi$
$368$	−4.21872	+	6.54990i	−0.219916	+	0.341437i
$369$	−1.32014	+	15.4561i	−0.0687235	+	0.804614i
$370$	0.441088	+	0.206351i	0.0229311	+	0.0107277i
$371$	−1.44581	+	0.966058i	−0.0750626	+	0.0501552i
$372$	−23.1539	+	26.3245i	−1.20048	+	1.36486i
$373$	−19.3566	+	3.85026i	−1.00224	+	0.199359i	−0.668825	−	0.743420i	$-0.733203\pi$
$373$	−19.3566	+	3.85026i	−1.00224	+	0.199359i	−0.333420	+	0.942779i	$0.608203\pi$
$374$	−1.10683	−	7.25121i	−0.0572330	−	0.374951i
$375$	−0.878945	−	0.957218i	−0.0453885	−	0.0494305i
$376$	4.31930	−	31.8881i	0.222751	−	1.64450i
$377$	−2.24990	−	5.43173i	−0.115876	−	0.279748i
$378$	1.32938	−	1.39383i	0.0683759	−	0.0716911i
$379$	0.800844	−	1.19855i	0.0411366	−	0.0615653i	−0.810331	−	0.585972i	$-0.800713\pi$
$379$	0.800844	−	1.19855i	0.0411366	−	0.0615653i	0.851468	+	0.524407i	$0.175713\pi$
$380$	−0.191632	−	0.0172462i	−0.00983050	−	0.000884711i
$381$	−0.422641	+	0.577657i	−0.0216525	+	0.0295942i
$382$	−28.8027	+	26.3269i	−1.47367	+	1.34700i
$383$	−21.7067			−1.10916			−0.554580	−	0.832130i	$-0.687121\pi$
$383$	−21.7067			−1.10916			−0.554580	+	0.832130i	$0.687121\pi$
$384$	−3.12962	+	19.3444i	−0.159708	+	0.987164i
$385$	−0.0432554			−0.00220450
$386$	−5.25901	+	4.80697i	−0.267677	+	0.244668i
$387$	−13.8507	−	25.1236i	−0.704071	−	1.27710i
$388$	−25.9041	−	2.33128i	−1.31508	−	0.118353i
$389$	−17.4324	+	26.0894i	−0.883858	+	1.32279i	0.0619565	+	0.998079i	$0.480266\pi$
$389$	−17.4324	+	26.0894i	−0.883858	+	1.32279i	−0.945814	+	0.324708i	$0.894734\pi$
$390$	0.0180666	+	0.165291i	0.000914836	+	0.00836982i
$391$	1.75870	+	4.24588i	0.0889413	+	0.214723i
$392$	−19.4273	−	2.63145i	−0.981225	−	0.132908i
$393$	6.85717	−	6.29645i	0.345898	−	0.317614i
$394$	2.91685	+	19.1092i	0.146949	+	0.962706i
$395$	0.618201	−	0.122968i	0.0311050	−	0.00618718i
$396$	−12.0747	+	5.30684i	−0.606776	+	0.266679i
$397$	10.9547	−	7.31968i	0.549799	−	0.367364i	−0.249428	−	0.968393i	$-0.580242\pi$
$397$	10.9547	−	7.31968i	0.549799	−	0.367364i	0.799227	+	0.601029i	$0.205242\pi$
$398$	15.2790	+	7.14786i	0.765866	+	0.358290i
$399$	0.199547	+	0.546499i	0.00998986	+	0.0273591i
$400$	−4.22680	−	19.5252i	−0.211340	−	0.976259i
$401$	20.2825	−	20.2825i	1.01286	−	1.01286i	0.0129431	−	0.999916i	$-0.495880\pi$
$401$	20.2825	−	20.2825i	1.01286	−	1.01286i	0.999916	−	0.0129431i	$-0.00412004\pi$
$402$	4.46808	+	0.391867i	0.222848	+	0.0195446i
$403$	−7.60892	+	5.08412i	−0.379027	+	0.253258i
$404$	−14.6259	+	18.1309i	−0.727665	+	0.902044i
$405$	−0.0175239	−	0.675416i	−0.000870767	−	0.0335617i
$406$	−1.42759	+	1.94192i	−0.0708501	+	0.0963757i
$407$	−3.85857	+	9.31541i	−0.191262	+	0.461748i
$408$	8.32833	+	8.01587i	0.412314	+	0.396845i
$409$	−6.31288	−	15.2406i	−0.312152	−	0.753601i	−0.999625	−	0.0273914i	$-0.991280\pi$
$409$	−6.31288	−	15.2406i	−0.312152	−	0.753601i	0.687473	−	0.726210i	$-0.258720\pi$
$410$	−0.131145	+	0.533073i	−0.00647681	+	0.0263266i
$411$	−22.4147	+	13.6332i	−1.10563	+	0.672476i
$412$	−8.00976	−	25.6259i	−0.394613	−	1.26250i
$413$	0.237465	−	1.19382i	0.0116849	−	0.0587439i
$414$	6.55179	−	5.03588i	0.322003	−	0.247500i
$415$	0.917756			0.0450509
$416$	−2.08916	+	4.66898i	−0.102430	+	0.228916i
$417$	−6.43572	+	13.8387i	−0.315159	+	0.677683i
$418$	0.178725	−	3.97984i	0.00874172	−	0.194661i
$419$	31.4491	+	6.25562i	1.53639	+	0.305607i	0.889485	−	0.456964i	$-0.151063\pi$
$419$	31.4491	+	6.25562i	1.53639	+	0.305607i	0.646904	+	0.762571i	$0.276063\pi$
$420$	0.0541388	−	0.0414169i	0.00264170	−	0.00202094i
$421$	−9.69566	+	14.5106i	−0.472537	+	0.707202i	−0.988803	−	0.149226i	$-0.952322\pi$
$421$	−9.69566	+	14.5106i	−0.472537	+	0.707202i	0.516266	+	0.856428i	$0.327322\pi$
$422$	1.12419	−	4.56957i	0.0547249	−	0.222443i
$423$	−15.6976	+	30.3073i	−0.763246	+	1.47359i
$424$	−12.4243	+	14.0610i	−0.603378	+	0.682862i
$425$	−10.8872	−	4.50964i	−0.528109	−	0.218750i
$426$	12.1291	−	6.65088i	0.587656	−	0.322236i
$427$	1.12466	−	0.223709i	0.0544262	−	0.0108260i
$428$	−28.3097	+	3.02915i	−1.36840	+	0.146420i
$429$	−3.40219	+	0.527237i	−0.164259	+	0.0254553i
$430$	−0.346053	−	0.954465i	−0.0166881	−	0.0460284i
$431$	13.1610	+	13.1610i	0.633944	+	0.633944i	0.949055	−	0.315111i	$-0.102042\pi$
$431$	13.1610	+	13.1610i	0.633944	+	0.633944i	−0.315111	+	0.949055i	$0.602042\pi$
$432$	10.0315	−	18.2036i	0.482640	−	0.875819i
$433$	18.5364	−	18.5364i	0.890803	−	0.890803i	−0.103795	−	0.994599i	$-0.533099\pi$
$433$	18.5364	−	18.5364i	0.890803	−	0.890803i	0.994599	+	0.103795i	$0.0330987\pi$
$434$	3.39805	+	1.58969i	0.163112	+	0.0763074i
$435$	0.129472	+	0.835465i	0.00620771	+	0.0400575i
$436$	17.2878	−	9.42851i	0.827934	−	0.451544i
$437$	0.486945	+	2.44804i	0.0232937	+	0.117105i
$438$	25.5111	+	7.44172i	1.21897	+	0.355579i
$439$	8.76979	−	21.1722i	0.418559	−	1.01049i	−0.564206	−	0.825634i	$-0.690818\pi$
$439$	8.76979	−	21.1722i	0.418559	−	1.01049i	0.982765	−	0.184858i	$-0.0591824\pi$
$440$	−0.451304	+	0.119123i	−0.0215151	+	0.00567896i
$441$	18.4642	+	9.56351i	0.879246	+	0.455405i
$442$	1.56207	+	2.58145i	0.0743000	+	0.122787i
$443$	−5.76224	−	3.85021i	−0.273773	−	0.182929i	0.411103	−	0.911589i	$-0.365144\pi$
$443$	−5.76224	−	3.85021i	−0.273773	−	0.182929i	−0.684876	+	0.728660i	$0.740144\pi$
$444$	−4.09006	−	15.3538i	−0.194106	−	0.728659i
$445$	−0.215132	+	1.08154i	−0.0101982	+	0.0512700i
$446$	−13.1646	+	12.0331i	−0.623363	+	0.569781i
$447$	9.63767	+	4.48203i	0.455846	+	0.211993i
$448$	2.08096	−	0.258176i	0.0983163	−	0.0121977i
$449$		−	6.65138i		−	0.313898i	−0.987607	−	0.156949i	$-0.949834\pi$
$449$		−	6.65138i		−	0.313898i	0.987607	−	0.156949i	$-0.0501659\pi$
$450$	−2.74859	+	21.0103i	−0.129570	+	0.990434i
$451$	−11.1482	−	2.21752i	−0.524950	−	0.104419i
$452$	16.4331	−	13.7195i	0.772947	−	0.645309i
$453$	7.64582	+	12.5707i	0.359232	+	0.590622i
$454$	16.7838	−	10.1561i	0.787701	−	0.476649i
$455$	0.0164384	−	0.00680899i	0.000770642	−	0.000319210i
$456$	3.58699	+	5.15233i	0.167976	+	0.241280i
$457$	−15.3039	−	6.33908i	−0.715886	−	0.296530i	−0.00514839	−	0.999987i	$-0.501639\pi$
$457$	−15.3039	−	6.33908i	−0.715886	−	0.296530i	−0.710738	+	0.703457i	$0.751639\pi$
$458$	0.0351182	+	0.230070i	0.00164097	+	0.0107505i
$459$	−5.45661	−	10.9792i	−0.254693	−	0.512465i
$460$	0.256738	−	0.140021i	0.0119705	−	0.00652852i
$461$	−14.2247	−	21.2887i	−0.662509	−	0.991515i	−0.998762	−	0.0497436i	$-0.984160\pi$
$461$	−14.2247	−	21.2887i	−0.662509	−	0.991515i	0.336253	−	0.941772i	$-0.390840\pi$
$462$	0.906981	+	1.08137i	0.0421966	+	0.0503097i
$463$	9.91878	+	9.91878i	0.460965	+	0.460965i	0.898972	−	0.438007i	$-0.144315\pi$
$463$	9.91878	+	9.91878i	0.460965	+	0.460965i	−0.438007	+	0.898972i	$0.644315\pi$
$464$	−9.54679	+	24.1924i	−0.443198	+	1.12310i
$465$	1.23611	−	0.451352i	0.0573233	−	0.0209309i
$466$	−21.6342	+	7.84372i	−1.00218	+	0.363353i
$467$	−2.12128	−	3.17472i	−0.0981612	−	0.146909i	0.779138	−	0.626852i	$-0.215657\pi$
$467$	−2.12128	−	3.17472i	−0.0981612	−	0.146909i	−0.877299	+	0.479944i	$0.840657\pi$
$468$	3.75338	−	3.91748i	0.173500	−	0.181085i
$469$	−0.0936346	−	0.470733i	−0.00432365	−	0.0217364i
$470$	−0.715439	+	0.973194i	−0.0330007	+	0.0448901i
$471$	−14.9884	−	16.3232i	−0.690629	−	0.752131i
$472$	−0.810119	−	13.1096i	−0.0372887	−	0.603418i
$473$	19.4213	−	8.04455i	0.892991	−	0.369889i
$474$	−16.0366	−	12.8764i	−0.736585	−	0.591431i
$475$	−5.32158	−	3.55577i	−0.244171	−	0.163150i
$476$	0.573877	−	1.09574i	0.0263036	−	0.0502233i
$477$	17.4287	−	9.60853i	0.798007	−	0.439944i
$478$	19.8040	+	0.889350i	0.905815	+	0.0406779i
$479$			4.64745i			0.212347i	0.994348	+	0.106174i	$0.0338599\pi$
$479$			4.64745i			0.212347i	−0.994348	+	0.106174i	$0.966140\pi$
$480$	0.450795	−	0.581217i	0.0205759	−	0.0265288i
$481$		−	4.14753i		−	0.189111i
$482$	0.586806	−	13.0670i	0.0267283	−	0.595185i
$483$	−0.713648	−	0.522138i	−0.0324721	−	0.0237581i
$484$	3.68008	+	11.7738i	0.167276	+	0.535172i
$485$	0.811728	+	0.542380i	0.0368587	+	0.0246282i
$486$	−16.5177	+	14.6002i	−0.749256	+	0.662280i
$487$	18.0003	−	7.45596i	0.815670	−	0.337862i	0.0644565	−	0.997921i	$-0.479469\pi$
$487$	18.0003	−	7.45596i	0.815670	−	0.337862i	0.751214	+	0.660059i	$0.229469\pi$
$488$	11.1180	−	5.43131i	0.503289	−	0.245864i
$489$	9.22358	−	8.46936i	0.417105	−	0.382998i
$490$	0.592901	+	0.435868i	0.0267845	+	0.0196905i
$491$	−2.10722	−	10.5937i	−0.0950974	−	0.478087i	−0.998757	−	0.0498362i	$-0.984130\pi$
$491$	−2.10722	−	10.5937i	−0.0950974	−	0.478087i	0.903660	−	0.428251i	$-0.140870\pi$
$492$	16.0765	−	7.89893i	0.724783	−	0.356111i
$493$	8.52329	+	12.7560i	0.383870	+	0.574502i
$494$	0.558561	+	1.54059i	0.0251308	+	0.0693146i
$495$	0.493278	+	0.0421318i	0.0221712	+	0.00189368i
$496$	39.8313	+	7.22791i	1.78848	+	0.324543i
$497$	−1.04668	−	1.04668i	−0.0469500	−	0.0469500i
$498$	−19.2436	−	22.9435i	−0.862324	−	1.02812i
$499$	19.8260	+	29.6718i	0.887535	+	1.32829i	0.944021	+	0.329887i	$0.107011\pi$
$499$	19.8260	+	29.6718i	0.887535	+	1.32829i	−0.0564854	+	0.998403i	$0.517989\pi$
$500$	−0.423490	+	1.43958i	−0.0189390	+	0.0643802i
$501$	−5.42546	+	22.2714i	−0.242391	+	0.995013i
$502$	31.7050	−	4.83950i	1.41506	−	0.215997i
$503$	0.0322396	+	0.0133541i	0.00143749	+	0.000595428i	0.383402	−	0.923582i	$-0.374752\pi$
$503$	0.0322396	+	0.0133541i	0.00143749	+	0.000595428i	−0.381965	+	0.924177i	$0.624752\pi$
$504$	−2.17059	−	0.485015i	−0.0966858	−	0.0216043i
$505$	0.807826	−	0.334612i	0.0359478	−	0.0148901i
$506$	3.13476	+	5.18045i	0.139357	+	0.230299i
$507$	−18.0278	+	10.9650i	−0.800641	+	0.486971i
$508$	0.823162	+	0.0740817i	0.0365219	+	0.00328684i
$509$	3.75595	+	0.747106i	0.166480	+	0.0331149i	0.277626	−	0.960689i	$-0.410452\pi$
$509$	3.75595	+	0.747106i	0.166480	+	0.0331149i	−0.111147	+	0.993804i	$0.535452\pi$
$510$	−0.130383	−	0.413829i	−0.00577345	−	0.0183247i
$511$		−	2.84367i		−	0.125796i
$512$	21.0007	−	8.42452i	0.928107	−	0.372315i
$513$	−1.74330	−	6.42655i	−0.0769688	−	0.283739i
$514$	−0.236555	−	0.258800i	−0.0104340	−	0.0114152i
$515$	−0.196608	+	0.988414i	−0.00866357	+	0.0435547i
$516$	−16.6052	+	28.6644i	−0.731002	+	1.26188i
$517$	−20.7947	−	13.8946i	−0.914549	−	0.611082i
$518$	−1.45468	+	0.880248i	−0.0639150	+	0.0386759i
$519$	−41.7676	−	1.78048i	−1.83339	−	0.0781545i
$520$	0.152757	−	0.116312i	0.00669885	−	0.00510060i
$521$	−5.37144	+	12.9678i	−0.235327	+	0.568130i	−0.996788	−	0.0800804i	$-0.974482\pi$
$521$	−5.37144	+	12.9678i	−0.235327	+	0.568130i	0.761461	+	0.648210i	$0.224482\pi$
$522$	18.1715	−	20.7548i	0.795345	−	0.908413i
$523$	−2.63083	−	13.2261i	−0.115038	−	0.578337i	−0.994707	−	0.102750i	$-0.967236\pi$
$523$	−2.63083	−	13.2261i	−0.115038	−	0.578337i	0.879669	−	0.475587i	$-0.157764\pi$
$524$	−10.3127	−	3.03373i	−0.450511	−	0.132529i
$525$	2.24068	−	0.347238i	0.0977911	−	0.0151547i
$526$	−16.0776	+	34.3669i	−0.701018	+	1.49847i
$527$	16.8852	−	16.8852i	0.735533	−	0.735533i
$528$	12.4410	+	8.78463i	0.541424	+	0.382302i
$529$	13.5809	+	13.5809i	0.590475	+	0.590475i
$530$	0.662132	−	0.240064i	0.0287612	−	0.0104277i
$531$	−3.87082	+	13.3828i	−0.167979	+	0.580764i
$532$	0.421794	−	0.522873i	0.0182871	−	0.0226694i
$533$	4.58573	−	0.912158i	0.198630	−	0.0395100i
$534$	31.5490	−	17.2996i	1.36526	−	0.748627i
$535$	0.987343	+	0.408971i	0.0426866	+	0.0176814i
$536$	−2.27330	−	4.65351i	−0.0981918	−	0.201001i
$537$	−21.2289	−	0.904954i	−0.916096	−	0.0390516i
$538$	19.5076	+	4.79920i	0.841031	+	0.206908i
$539$	−8.46501	+	12.6688i	−0.364614	+	0.545683i
$540$	−0.657731	+	0.419580i	−0.0283043	+	0.0180558i
$541$	26.2221	+	5.21590i	1.12738	+	0.224249i	0.723339	−	0.690494i	$-0.242607\pi$
$541$	26.2221	+	5.21590i	1.12738	+	0.224249i	0.404037	+	0.914743i	$0.367607\pi$
$542$	−15.8118	−	0.710069i	−0.679175	−	0.0305001i
$543$	16.5631	+	7.70274i	0.710792	+	0.330556i
$544$	2.96992	−	13.0128i	0.127334	−	0.557920i
$545$	−0.739143			−0.0316614
$546$	−0.514902	−	0.268181i	−0.0220358	−	0.0114771i
$547$	−6.71870	+	33.7772i	−0.287271	+	1.44421i	0.520070	+	0.854124i	$0.325906\pi$
$547$	−6.71870	+	33.7772i	−0.287271	+	1.44421i	−0.807341	+	0.590085i	$0.799094\pi$
$548$	26.8360	+	14.0549i	1.14638	+	0.600396i
$549$	−13.0434	+	1.45570i	−0.556677	+	0.0621276i
$550$	−15.0768	−	3.70916i	−0.642877	−	0.158159i
$551$	3.18860	+	7.69796i	0.135839	+	0.327944i
$552$	−8.88376	−	3.48237i	−0.378118	−	0.148219i
$553$	−0.842194	+	2.03324i	−0.0358137	+	0.0864620i
$554$	−28.0875	−	20.6484i	−1.19333	−	0.877267i
$555$	−0.141162	+	0.579468i	−0.00599199	+	0.0245970i
$556$	17.5230	−	1.87496i	0.743139	−	0.0795161i
$557$	11.7060	−	7.82170i	0.495999	−	0.331416i	−0.282282	−	0.959331i	$-0.591092\pi$
$557$	11.7060	−	7.82170i	0.495999	−	0.331416i	0.778282	+	0.627915i	$0.216092\pi$
$558$	−37.2025	−	21.4383i	−1.57491	−	0.907557i
$559$	−6.11434	+	6.11434i	−0.258609	+	0.258609i
$560$	−0.0732148	−	0.0288920i	−0.00309389	−	0.00122091i
$561$	8.43878	−	3.08132i	0.356286	−	0.130093i
$562$	13.8489	−	29.6028i	0.584179	−	1.24872i
$563$	−1.45663	+	0.973290i	−0.0613897	+	0.0410193i	−0.585886	−	0.810393i	$-0.699254\pi$
$563$	−1.45663	+	0.973290i	−0.0613897	+	0.0410193i	0.524497	+	0.851412i	$0.324254\pi$
$564$	39.3308	−	2.52031i	1.65612	−	0.106124i
$565$	−0.788096	+	0.156762i	−0.0331554	+	0.00659503i
$566$	−3.58572	+	0.547330i	−0.150719	+	0.0230060i
$567$	1.99480	+	1.25929i	0.0837736	+	0.0528854i
$568$	−13.8030	−	8.03800i	−0.579161	−	0.337267i
$569$	3.39021	+	8.18469i	0.142125	+	0.343120i	0.978873	−	0.204468i	$-0.0655463\pi$
$569$	3.39021	+	8.18469i	0.142125	+	0.343120i	−0.836748	+	0.547588i	$0.815546\pi$
$570$	−0.0256043	−	0.234253i	−0.00107245	−	0.00981179i
$571$	18.1245	−	27.1252i	0.758486	−	1.13515i	−0.228373	−	0.973574i	$-0.573341\pi$
$571$	18.1245	−	27.1252i	0.758486	−	1.13515i	0.986859	−	0.161581i	$-0.0516593\pi$
$572$	2.54775	+	3.05168i	0.106527	+	0.127597i
$573$	−38.5705	−	28.2200i	−1.61131	−	1.17891i
$574$	−1.29317	−	1.41478i	−0.0539761	−	0.0590519i
$575$	9.72770			0.405673
$576$	−23.9825	+	0.917290i	−0.999269	+	0.0382204i
$577$	18.8087			0.783017			0.391509	−	0.920174i	$-0.371953\pi$
$577$	18.8087			0.783017			0.391509	+	0.920174i	$0.371953\pi$
$578$	10.9083	+	11.9341i	0.453725	+	0.496393i
$579$	−7.04250	−	5.15262i	−0.292676	−	0.214136i
$580$	0.749392	−	0.625644i	0.0311168	−	0.0259784i
$581$	−1.78026	+	2.66435i	−0.0738576	+	0.110536i
$582$	−3.46110	−	31.6655i	−0.143467	−	1.31258i
$583$	5.58067	+	13.4729i	0.231128	+	0.557992i
$584$	−7.83129	−	29.6693i	−0.324061	−	1.22772i
$585$	−0.194093	+	0.0616373i	−0.00802474	+	0.00254839i
$586$	−26.3751	+	4.02593i	−1.08954	+	0.166309i
$587$	−34.1088	+	6.78466i	−1.40782	+	0.280033i	−0.839762	−	0.542955i	$-0.817306\pi$
$587$	−34.1088	+	6.78466i	−1.40782	+	0.280033i	−0.568059	+	0.822988i	$0.692306\pi$
$588$	−1.53545	−	23.9616i	−0.0633209	−	0.988158i
$589$	10.7835	−	7.20532i	0.444327	−	0.296890i
$590$	−0.208914	+	0.446565i	−0.00860084	+	0.0183848i
$591$	−22.2388	+	8.12023i	−0.914782	+	0.334022i
$592$	−12.7532	+	13.1901i	−0.524154	+	0.542111i
$593$	1.14918	−	1.14918i	0.0471910	−	0.0471910i	−0.683118	−	0.730308i	$-0.739376\pi$
$593$	1.14918	−	1.14918i	0.0471910	−	0.0471910i	0.730308	+	0.683118i	$0.239376\pi$
$594$	−9.28980	−	13.2152i	−0.381165	−	0.542225i
$595$	−0.0386042	+	0.0257945i	−0.00158262	+	0.00105747i
$596$	−1.30578	−	12.2035i	−0.0534869	−	0.499876i
$597$	−4.88975	+	20.0724i	−0.200124	+	0.821507i
$598$	−2.00678	−	1.47527i	−0.0820633	−	0.0603284i
$599$	−1.00985	+	2.43798i	−0.0412612	+	0.0996132i	−0.943167	−	0.332320i	$-0.892169\pi$
$599$	−1.00985	+	2.43798i	−0.0412612	+	0.0996132i	0.901905	+	0.431934i	$0.142169\pi$
$600$	22.4217	−	9.79358i	0.915363	−	0.399821i
$601$	−1.00588	−	2.42841i	−0.0410307	−	0.0990568i	0.902036	−	0.431662i	$-0.142073\pi$
$601$	−1.00588	−	2.42841i	−0.0410307	−	0.0990568i	−0.943066	+	0.332605i	$0.892073\pi$
$602$	3.44218	+	0.846838i	0.140293	+	0.0345145i
$603$	0.609290	+	5.45937i	0.0248122	+	0.222323i
$604$	7.88232	−	15.0502i	0.320727	−	0.612386i
$605$	0.0903312	−	0.454126i	0.00367249	−	0.0184628i
$606$	−25.3037	−	13.1791i	−1.02789	−	0.535366i
$607$	42.0620			1.70725			0.853623	−	0.520892i	$-0.174400\pi$
$607$	42.0620			1.70725			0.853623	+	0.520892i	$0.174400\pi$
$608$	2.96081	−	6.61697i	0.120077	−	0.268354i
$609$	−2.67659	−	1.24476i	−0.108461	−	0.0504402i
$610$	−0.463990	−	0.0208366i	−0.0187864	−	0.000843651i
$611$	10.0898	+	2.00699i	0.408190	+	0.0811940i
$612$	−7.61169	+	11.9367i	−0.307684	+	0.482513i
$613$	−16.8711	+	25.2494i	−0.681417	+	1.01981i	0.316055	+	0.948741i	$0.397642\pi$
$613$	−16.8711	+	25.2494i	−0.681417	+	1.01981i	−0.997471	+	0.0710711i	$0.977358\pi$
$614$	18.1677	+	4.46958i	0.733189	+	0.180377i
$615$	−0.671736	−	0.0286350i	−0.0270870	−	0.00115467i
$616$	0.529610	−	1.54126i	0.0213386	−	0.0620990i
$617$	−15.9796	−	6.61898i	−0.643316	−	0.266470i	0.0370828	−	0.999312i	$-0.488193\pi$
$617$	−15.9796	−	6.61898i	−0.643316	−	0.266470i	−0.680399	+	0.732842i	$0.738193\pi$
$618$	28.8324	−	15.8100i	1.15981	−	0.635971i
$619$	34.6693	−	6.89615i	1.39348	−	0.277180i	0.559432	−	0.828876i	$-0.311019\pi$
$619$	34.6693	−	6.89615i	1.39348	−	0.277180i	0.834045	+	0.551696i	$0.186019\pi$
$620$	−1.18268	−	0.954045i	−0.0474974	−	0.0383154i
$621$	7.62976	+	6.64950i	0.306172	+	0.266835i
$622$	6.25983	−	2.26958i	0.250996	−	0.0910017i
$623$	−2.72252	−	2.72252i	−0.109075	−	0.109075i
$624$	−6.11076	−	1.38004i	−0.244626	−	0.0552460i
$625$	−17.6179	+	17.6179i	−0.704717	+	0.704717i
$626$	−5.73146	+	12.2513i	−0.229075	+	0.489662i
$627$	4.82165	−	0.747211i	0.192558	−	0.0298407i
$628$	−7.22165	+	24.5488i	−0.288175	+	0.979604i
$629$	2.11140	+	10.6147i	0.0841870	+	0.423237i
$630$	0.0628114	+	0.0549934i	0.00250247	+	0.00219099i
$631$	1.74700	−	4.21763i	0.0695470	−	0.167901i	−0.885284	−	0.465051i	$-0.846036\pi$
$631$	1.74700	−	4.21763i	0.0695470	−	0.167901i	0.954831	+	0.297150i	$0.0960360\pi$
$632$	−3.18759	+	23.5330i	−0.126795	+	0.936094i
$633$	5.75820	+	0.245462i	0.228868	+	0.00975626i
$634$	2.27834	−	1.37866i	0.0904845	−	0.0547534i
$635$	−0.0257945	−	0.0172354i	−0.00102363	−	0.000683964i
$636$	−19.8851	−	11.5193i	−0.788496	−	0.456772i
$637$	1.22272	−	6.14703i	0.0484459	−	0.243554i
$638$	13.6373	+	14.9197i	0.539906	+	0.590678i
$639$	10.9167	+	12.9557i	0.431858	+	0.512518i
$640$	−0.843451	−	0.0998140i	−0.0333403	−	0.00394549i
$641$			31.5734i			1.24708i	0.781793	+	0.623538i	$0.214305\pi$
$641$			31.5734i			1.24708i	−0.781793	+	0.623538i	$0.785695\pi$
$642$	−10.4786	−	33.2585i	−0.413555	−	1.31261i
$643$	24.3933	+	4.85212i	0.961976	+	0.191349i	0.651008	−	0.759071i	$-0.274347\pi$
$643$	24.3933	+	4.85212i	0.961976	+	0.191349i	0.310969	+	0.950420i	$0.399347\pi$
$644$	−0.0915220	+	1.01695i	−0.00360647	+	0.0400734i
$645$	1.06236	−	0.646157i	0.0418305	−	0.0254424i
$646$	−2.21380	−	3.65848i	−0.0871006	−	0.143941i
$647$	17.3176	−	7.17319i	0.680826	−	0.282007i	−0.0153463	−	0.999882i	$-0.504885\pi$
$647$	17.3176	−	7.17319i	0.680826	−	0.282007i	0.696172	+	0.717875i	$0.254885\pi$
$648$	24.2807	+	7.64524i	0.953834	+	0.300333i
$649$	−9.43108	−	3.90648i	−0.370202	−	0.153343i
$650$	6.31351	−	0.963702i	0.247636	−	0.0377995i
$651$	−1.08748	+	4.46410i	−0.0426218	+	0.174962i
$652$	−13.8716	−	4.08067i	−0.543253	−	0.159812i
$653$	−18.8122	−	28.1544i	−0.736178	−	1.10177i	−0.990880	−	0.134748i	$-0.956977\pi$
$653$	−18.8122	−	28.1544i	−0.736178	−	1.10177i	0.254702	−	0.967020i	$-0.418023\pi$
$654$	15.4984	+	18.4783i	0.606035	+	0.722557i
$655$	0.285314	+	0.285314i	0.0111482	+	0.0111482i
$656$	−17.3885	−	11.1998i	−0.678907	−	0.437277i
$657$	−2.76980	+	32.4288i	−0.108060	+	1.26517i
$658$	−1.43748	−	3.96479i	−0.0560389	−	0.154564i
$659$	−2.59960	−	3.89057i	−0.101266	−	0.151555i	0.777376	−	0.629036i	$-0.216550\pi$
$659$	−2.59960	−	3.89057i	−0.101266	−	0.151555i	−0.878642	+	0.477481i	$0.841550\pi$
$660$	−0.252092	−	0.513076i	−0.00981268	−	0.0199715i
$661$	−5.49642	−	27.6324i	−0.213786	−	1.07477i	−0.927353	−	0.374187i	$-0.877922\pi$
$661$	−5.49642	−	27.6324i	−0.213786	−	1.07477i	0.713567	−	0.700587i	$-0.247078\pi$
$662$	−32.0381	−	23.5527i	−1.24520	−	0.915401i
$663$	−2.72195	+	2.49937i	−0.105712	+	0.0970676i
$664$	−11.2368	+	32.7011i	−0.436073	+	1.26905i
$665$	−0.0232968	+	0.00964984i	−0.000903410	+	0.000374205i
$666$	17.4463	−	8.62132i	0.676032	−	0.334069i
$667$	−10.5299	−	7.03582i	−0.407718	−	0.272428i
$668$	25.2636	−	7.89651i	0.977476	−	0.305525i
$669$	−17.6291	−	12.8983i	−0.681581	−	0.498677i
$670$	−0.00872129	+	0.194205i	−0.000336933	+	0.00750281i
$671$		−	9.61679i		−	0.371252i
$672$	0.812885	+	2.43615i	0.0313577	+	0.0939765i
$673$			11.0254i			0.424996i	0.977161	+	0.212498i	$0.0681599\pi$
$673$			11.0254i			0.424996i	−0.977161	+	0.212498i	$0.931840\pi$
$674$	−29.7433	−	1.33570i	−1.14567	−	0.0514492i
$675$	−25.8905	+	1.77737i	−0.996527	+	0.0684111i
$676$	21.5837	+	11.3041i	0.830144	+	0.434774i
$677$	10.9422	+	7.31133i	0.420542	+	0.280997i	0.747782	−	0.663944i	$-0.231119\pi$
$677$	10.9422	+	7.31133i	0.420542	+	0.280997i	−0.327240	+	0.944941i	$0.606119\pi$
$678$	20.4438	+	16.4151i	0.785140	+	0.630417i
$679$	−3.14917	+	1.30443i	−0.120854	+	0.0500594i
$680$	−0.331739	+	0.375440i	−0.0127216	+	0.0143975i
$681$	16.2501	+	17.6973i	0.622707	+	0.678161i
$682$	18.6355	−	25.3494i	0.713589	−	0.970677i
$683$	6.11205	+	30.7273i	0.233871	+	1.17575i	0.902011	+	0.431713i	$0.142091\pi$
$683$	6.11205	+	30.7273i	0.233871	+	1.17575i	−0.668140	+	0.744036i	$0.732909\pi$
$684$	−5.31936	+	5.55193i	−0.203391	+	0.212283i
$685$	−0.631737	−	0.945461i	−0.0241374	−	0.0361242i
$686$	−4.85490	+	1.76020i	−0.185361	+	0.0672048i
$687$	−0.267750	+	0.0977658i	−0.0102153	+	0.00373000i
$688$	38.2460	−	0.644123i	1.45812	−	0.0245570i
$689$	−4.24165	−	4.24165i	−0.161594	−	0.161594i
$690$	0.230164	+	0.274418i	0.00876219	+	0.0104469i
$691$	3.78957	+	5.67149i	0.144162	+	0.215754i	0.896523	−	0.442998i	$-0.146085\pi$
$691$	3.78957	+	5.67149i	0.144162	+	0.215754i	−0.752361	+	0.658751i	$0.771085\pi$
$692$	23.1133	+	42.3798i	0.878637	+	1.61104i
$693$	−1.07917	+	1.35031i	−0.0409943	+	0.0512941i
$694$	−4.11311	−	26.9462i	−0.156131	−	1.02286i
$695$	−0.611138	−	0.253142i	−0.0231818	−	0.00960222i
$696$	−31.3541	−	5.61597i	−1.18848	−	0.212873i
$697$	−11.2719	+	4.66896i	−0.426952	+	0.176849i
$698$	22.3269	−	13.5103i	0.845087	−	0.511374i
$699$	−14.6460	−	24.0798i	−0.553961	−	0.910782i
$700$	−1.67795	−	2.00983i	−0.0634204	−	0.0759646i
$701$	45.6378	+	9.07793i	1.72372	+	0.342869i	0.954974	−	0.296689i	$-0.0958824\pi$
$701$	45.6378	+	9.07793i	1.72372	+	0.342869i	0.768743	+	0.639558i	$0.220882\pi$
$702$	5.61065	+	3.55982i	0.211760	+	0.134357i
$703$			5.87796i			0.221692i
$704$	1.28114	−	17.5392i	0.0482846	−	0.661032i
$705$	−1.34138	−	0.623813i	−0.0505192	−	0.0234941i
$706$	−10.6392	+	9.72466i	−0.400410	+	0.365992i
$707$	−0.595600	+	2.99429i	−0.0223999	+	0.112612i
$708$	15.5445	−	4.14085i	0.584196	−	0.155623i
$709$	−32.9914	−	22.0441i	−1.23902	−	0.827885i	−0.248955	−	0.968515i	$-0.580087\pi$
$709$	−32.9914	−	22.0441i	−1.23902	−	0.827885i	−0.990062	+	0.140630i	$0.955087\pi$
$710$	0.310394	+	0.512951i	0.0116489	+	0.0192507i
$711$	11.5847	−	22.3664i	0.434459	−	0.838805i
$712$	−35.9030	−	20.9077i	−1.34552	−	0.783547i
$713$	−7.54344	+	18.2115i	−0.282504	+	0.682025i
$714$	1.45431	+	0.424229i	0.0544261	+	0.0158764i
$715$	−0.0291113	−	0.146352i	−0.00108870	−	0.00547327i
$716$	11.7477	+	21.5401i	0.439030	+	0.804990i
$717$	3.71819	+	23.9929i	0.138858	+	0.896033i
$718$	−20.4858	−	9.58372i	−0.764522	−	0.357661i
$719$	27.3837	−	27.3837i	1.02124	−	1.02124i	0.0214686	−	0.999770i	$-0.493166\pi$
$719$	27.3837	−	27.3837i	1.02124	−	1.02124i	0.999770	−	0.0214686i	$-0.00683420\pi$
$720$	0.806789	+	0.400793i	0.0300673	+	0.0149367i
$721$	−2.48809	−	2.48809i	−0.0926614	−	0.0926614i
$722$	8.36708	+	23.0776i	0.311390	+	0.858861i
$723$	15.8309	−	2.45331i	0.588757	−	0.0912397i
$724$	−2.24409	−	20.9728i	−0.0834011	−	0.779447i
$725$	31.8493	−	6.33523i	1.18285	−	0.235284i
$726$	−13.2470	+	7.26389i	−0.491643	+	0.269588i
$727$	0.372141	+	0.154146i	0.0138019	+	0.00571695i	0.389574	−	0.920995i	$-0.372622\pi$
$727$	0.372141	+	0.154146i	0.0138019	+	0.00571695i	−0.375772	+	0.926712i	$0.622622\pi$
$728$	0.0413471	+	0.669092i	0.00153243	+	0.0247982i
$729$	−21.5218	−	16.3038i	−0.797103	−	0.603843i
$730$	−0.275158	+	1.11845i	−0.0101841	+	0.0413957i
$731$	12.5357	−	18.7610i	0.463650	−	0.693902i
$732$	9.20805	+	12.0364i	0.340339	+	0.444880i
$733$	−20.6905	−	4.11560i	−0.764223	−	0.152013i	−0.202436	−	0.979295i	$-0.564886\pi$
$733$	−20.6905	−	4.11560i	−0.764223	−	0.152013i	−0.561787	+	0.827282i	$0.689886\pi$
$734$	−0.893206	+	19.8899i	−0.0329688	+	0.734149i
$735$	−0.380047	+	0.817211i	−0.0140182	+	0.0301433i
$736$	1.84573	+	10.8624i	0.0680344	+	0.400392i
$737$	−4.02516			−0.148269
$738$	13.3691	+	17.3935i	0.492125	+	0.640265i
$739$	−1.24476	+	6.25783i	−0.0457892	+	0.230198i	−0.996903	−	0.0786433i	$-0.974941\pi$
$739$	−1.24476	+	6.25783i	−0.0457892	+	0.230198i	0.951114	+	0.308841i	$0.0999412\pi$
$740$	0.657319	−	0.205455i	0.0241635	−	0.00755268i
$741$	−1.71475	+	1.04296i	−0.0629929	+	0.0383139i
$742$	−0.587469	+	2.38791i	−0.0215667	+	0.0876631i
$743$	−14.4970	−	34.9988i	−0.531843	−	1.28398i	−0.930302	−	0.366795i	$-0.880455\pi$
$743$	−14.4970	−	34.9988i	−0.531843	−	1.28398i	0.398459	−	0.917186i	$-0.369545\pi$
$744$	0.947655	+	49.5708i	0.0347427	+	1.81736i
$745$	−0.176296	+	0.425615i	−0.00645897	+	0.0155933i
$746$	−16.5318	+	22.4878i	−0.605272	+	0.823337i
$747$	22.8969	−	28.6498i	0.837755	−	1.04824i
$748$	−8.07397	−	6.51315i	−0.295214	−	0.238144i
$749$	−3.10253	+	2.07304i	−0.113364	+	0.0757474i
$750$	−1.83080	−	0.160568i	−0.0668515	−	0.00586312i
$751$	16.0660	−	16.0660i	0.586258	−	0.586258i	−0.350358	−	0.936616i	$-0.613940\pi$
$751$	16.0660	−	16.0660i	0.586258	−	0.586258i	0.936616	+	0.350358i	$0.113940\pi$
$752$	−25.9167	−	37.4078i	−0.945085	−	1.36412i
$753$	13.4727	+	36.8976i	0.490972	+	1.34462i
$754$	−7.53115	−	3.52325i	−0.274268	−	0.128309i
$755$	−0.530237	+	0.354293i	−0.0192973	+	0.0128940i
$756$	0.0577788	−	2.72336i	0.00210140	−	0.0990478i
$757$	−46.1515	+	9.18010i	−1.67740	+	0.333656i	−0.939838	−	0.341619i	$-0.889025\pi$
$757$	−46.1515	+	9.18010i	−1.67740	+	0.333656i	−0.737566	+	0.675276i	$0.764025\pi$
$758$	−0.307606	−	2.01522i	−0.0111728	−	0.0731961i
$759$	−5.46242	+	5.01575i	−0.198273	+	0.182060i
$760$	−0.216491	+	0.164839i	−0.00785295	+	0.00597934i
$761$	13.3019	+	32.1135i	0.482192	+	1.16412i	0.958566	+	0.284872i	$0.0919511\pi$
$761$	13.3019	+	32.1135i	0.482192	+	1.16412i	−0.476373	+	0.879243i	$0.658049\pi$
$762$	0.109984	+	1.00624i	0.00398431	+	0.0364524i
$763$	1.43379	−	2.14581i	0.0519065	−	0.0776836i
$764$	−4.94649	+	54.9631i	−0.178958	+	1.98849i
$765$	0.465361	−	0.256555i	0.0168252	−	0.00927578i
$766$	−22.6587	+	20.7110i	−0.818691	+	0.748320i
$767$	4.19903			0.151618
$768$	15.1902	+	23.1788i	0.548129	+	0.836394i
$769$	−29.4345			−1.06144			−0.530718	−	0.847549i	$-0.678078\pi$
$769$	−29.4345			−1.06144			−0.530718	+	0.847549i	$0.678078\pi$
$770$	−0.0451524	+	0.0412713i	−0.00162718	+	0.00148732i
$771$	0.253564	−	0.346566i	0.00913189	−	0.0124813i
$772$	−0.903167	+	10.0356i	−0.0325057	+	0.361188i
$773$	3.03986	−	4.54947i	0.109336	−	0.163633i	−0.772766	−	0.634691i	$-0.781128\pi$
$773$	3.03986	−	4.54947i	0.109336	−	0.163633i	0.882103	+	0.471057i	$0.156128\pi$
$774$	−38.4293	−	13.0100i	−1.38131	−	0.467634i
$775$	−19.3428	−	46.6977i	−0.694815	−	1.67743i
$776$	−29.2644	+	22.2824i	−1.05053	+	0.799890i
$777$	−1.40843	−	1.53386i	−0.0505272	−	0.0550268i
$778$	6.69582	+	43.8664i	0.240057	+	1.57269i
$779$	−6.49899	+	1.29273i	−0.232851	+	0.0463168i
$780$	0.176568	+	0.155302i	0.00632214	+	0.00556069i
$781$	−10.3219	+	6.89685i	−0.369345	+	0.246789i
$782$	5.88695	+	2.75405i	0.210517	+	0.0984847i
$783$	29.3110	+	16.8021i	1.04749	+	0.600458i
$784$	−22.7900	+	15.7893i	−0.813929	+	0.563903i
$785$	0.679177	−	0.679177i	0.0242409	−	0.0242409i
$786$	1.15025	−	13.1152i	0.0410282	−	0.467804i
$787$	−4.45487	+	2.97665i	−0.158799	+	0.106106i	−0.632431	−	0.774617i	$-0.717943\pi$
$787$	−4.45487	+	2.97665i	−0.158799	+	0.106106i	0.473632	+	0.880723i	$0.342943\pi$
$788$	21.2774	+	17.1642i	0.757976	+	0.611448i
$789$	−45.1485	−	10.9985i	−1.60733	−	0.391556i
$790$	0.527985	−	0.718205i	0.0187849	−	0.0255526i
$791$	1.07365	−	2.59201i	0.0381745	−	0.0921614i
$792$	−7.54081	+	17.0604i	−0.267951	+	0.606215i
$793$	1.51381	+	3.65467i	0.0537571	+	0.129781i
$794$	4.45117	−	18.0929i	0.157966	−	0.642092i
$795$	0.448252	+	0.736983i	0.0158979	+	0.0261381i
$796$	22.7691	−	7.11681i	0.807028	−	0.252249i
$797$	1.68618	−	8.47701i	0.0597276	−	0.300271i	−0.939362	−	0.342927i	$-0.888582\pi$
$797$	1.68618	−	8.47701i	0.0597276	−	0.300271i	0.999090	+	0.0426555i	$0.0135818\pi$
$798$	0.729730	+	0.380071i	0.0258322	+	0.0134544i
$799$	−26.8444			−0.949688
$800$	−23.0417	−	16.3486i	−0.814649	−	0.578009i
$801$	28.3954	+	33.6990i	1.00330	+	1.19070i
$802$	1.81984	−	40.5241i	0.0642608	−	1.43096i
$803$	−23.3903	−	4.65262i	−0.825425	−	0.164187i
$804$	5.03792	−	3.85408i	0.177674	−	0.135923i
$805$	0.0212929	−	0.0318671i	0.000750476	−	0.00112317i
$806$	−3.09170	+	12.5670i	−0.108900	+	0.442653i
$807$	−1.04788	+	24.5819i	−0.0368873	+	0.865323i
$808$	2.03191	+	32.8810i	0.0714823	+	1.15675i
$809$	−13.8531	−	5.73816i	−0.487050	−	0.201743i	0.125625	−	0.992078i	$-0.459906\pi$
$809$	−13.8531	−	5.73816i	−0.487050	−	0.201743i	−0.612675	+	0.790335i	$0.709906\pi$
$810$	−0.662727	−	0.688316i	−0.0232859	−	0.0241850i
$811$	−20.2295	+	4.02389i	−0.710352	+	0.141298i	−0.537025	−	0.843566i	$-0.680452\pi$
$811$	−20.2295	+	4.02389i	−0.710352	+	0.141298i	−0.173327	+	0.984864i	$0.555452\pi$
$812$	0.362644	+	3.38919i	0.0127263	+	0.118937i
$813$	−2.96865	−	19.1563i	−0.104115	−	0.671840i
$814$	4.86033	+	13.4055i	0.170355	+	0.469863i
$815$	0.383776	+	0.383776i	0.0134431	+	0.0134431i
$816$	16.3418	+	0.421098i	0.572076	+	0.0147414i
$817$	8.66537	−	8.66537i	0.303163	−	0.303163i
$818$	−21.1313	−	9.88572i	−0.738839	−	0.345646i
$819$	0.197560	−	0.683036i	0.00690330	−	0.0238672i
$820$	0.371725	+	0.681582i	0.0129812	+	0.0238019i
$821$	−9.97627	−	50.1541i	−0.348174	−	1.75039i	−0.616776	−	0.787138i	$-0.711562\pi$
$821$	−9.97627	−	50.1541i	−0.348174	−	1.75039i	0.268602	−	0.963251i	$-0.413438\pi$
$822$	−10.3898	+	35.6176i	−0.362387	+	1.24231i
$823$	−6.20664	+	14.9842i	−0.216350	+	0.522315i	−0.994375	−	0.105919i	$-0.966222\pi$
$823$	−6.20664	+	14.9842i	−0.216350	+	0.522315i	0.778025	+	0.628233i	$0.216222\pi$
$824$	−32.8115	−	19.1074i	−1.14304	−	0.665637i
$825$	0.809877	−	18.9986i	0.0281963	−	0.661445i
$826$	−0.891178	−	1.47274i	−0.0310080	−	0.0512433i
$827$	−20.0660	−	13.4077i	−0.697763	−	0.466230i	0.155416	−	0.987849i	$-0.450328\pi$
$827$	−20.0660	−	13.4077i	−0.697763	−	0.466230i	−0.853178	+	0.521619i	$0.825328\pi$
$828$	2.03424	−	11.5080i	0.0706946	−	0.399931i
$829$	0.773289	−	3.88759i	0.0268575	−	0.135022i	−0.965030	−	0.262138i	$-0.915572\pi$
$829$	0.773289	−	3.88759i	0.0268575	−	0.135022i	0.991888	+	0.127117i	$0.0405723\pi$
$830$	0.958005	−	0.875659i	0.0332528	−	0.0303946i
$831$	18.0040	−	38.7138i	0.624551	−	1.34297i
$832$	2.27403	+	6.86707i	0.0788379	+	0.238073i
$833$			16.3545i			0.566649i
$834$	6.48594	+	20.5861i	0.224590	+	0.712838i
$835$	−0.974438	−	0.193828i	−0.0337218	−	0.00670769i
$836$	−3.61073	−	4.32491i	−0.124880	−	0.149580i
$837$	16.7496	−	49.8486i	0.578951	−	1.72302i
$838$	38.7970	−	23.4766i	1.34022	−	0.810986i
$839$	38.8599	−	16.0963i	1.34159	−	0.555705i	0.407652	−	0.913137i	$-0.366348\pi$
$839$	38.8599	−	16.0963i	1.34159	−	0.555705i	0.933939	+	0.357432i	$0.116348\pi$
$840$	0.0169959	−	0.0948888i	0.000586415	−	0.00327397i
$841$	−12.2653	−	5.08045i	−0.422941	−	0.175188i
$842$	3.72412	+	24.3979i	0.128342	+	0.840806i
$843$	38.8898	+	9.47381i	1.33944	+	0.326295i
$844$	−3.18647	−	5.84260i	−0.109683	−	0.201110i
$845$	−0.508096	−	0.760419i	−0.0174790	−	0.0261592i
$846$	12.5310	+	46.6140i	0.430826	+	1.60262i
$847$	1.14315	+	1.14315i	0.0392792	+	0.0392792i
$848$	0.446842	+	26.5321i	0.0153446	+	0.911115i
$849$	−1.52371	−	4.17298i	−0.0522937	−	0.143216i
$850$	−15.6675	+	5.68044i	−0.537391	+	0.194837i
$851$	−4.96342	−	7.42829i	−0.170144	−	0.254638i
$852$	6.31521	−	18.5153i	0.216355	−	0.634324i
$853$	10.2912	+	51.7372i	0.352363	+	1.77145i	0.597409	+	0.801937i	$0.296197\pi$
$853$	10.2912	+	51.7372i	0.352363	+	1.77145i	−0.245046	+	0.969511i	$0.578803\pi$
$854$	0.960536	−	1.30659i	0.0328689	−	0.0447107i
$855$	0.275072	−	0.0873537i	0.00940726	−	0.00298743i
$856$	−26.6611	+	30.1732i	−0.911257	+	1.03130i
$857$	−35.5270	+	14.7158i	−1.21358	+	0.502681i	−0.895363	−	0.445338i	$-0.853084\pi$
$857$	−35.5270	+	14.7158i	−1.21358	+	0.502681i	−0.318216	+	0.948018i	$0.603084\pi$
$858$	−3.04834	+	3.79649i	−0.104069	+	0.129610i
$859$	31.9131	+	21.3237i	1.08886	+	0.727554i	0.964341	−	0.264663i	$-0.0852608\pi$
$859$	31.9131	+	21.3237i	1.08886	+	0.727554i	0.124520	+	0.992217i	$0.460261\pi$
$860$	−1.27191	−	0.666144i	−0.0433719	−	0.0227153i
$861$	1.38616	−	1.89458i	0.0472402	−	0.0645670i
$862$	26.2955	+	1.18087i	0.895630	+	0.0402205i
$863$		−	56.5922i		−	1.92642i	−0.268751	−	0.963210i	$-0.586611\pi$
$863$		−	56.5922i		−	1.92642i	0.268751	−	0.963210i	$-0.413389\pi$
$864$	−6.89715	−	28.5732i	−0.234646	−	0.972081i
$865$		−	1.81196i		−	0.0616084i
$866$	1.66317	−	37.0355i	0.0565169	−	1.25852i
$867$	−11.6927	+	15.9813i	−0.397103	+	0.542753i
$868$	5.06384	−	1.58278i	0.171878	−	0.0537231i
$869$	15.3462	+	10.2540i	0.520585	+	0.347844i
$870$	0.932293	+	0.748571i	0.0316077	+	0.0253789i
$871$	1.52968	−	0.633615i	0.0518313	−	0.0214692i
$872$	9.04991	−	26.3368i	0.306469	−	0.891877i
$873$	37.1832	−	11.8082i	1.25846	−	0.399645i
$874$	2.84405	+	2.09079i	0.0962013	+	0.0707219i
$875$	0.0383669	+	0.192884i	0.00129704	+	0.00652066i
$876$	33.7303	−	16.5729i	1.13964	−	0.559945i
$877$	−18.4579	−	27.6242i	−0.623279	−	0.932802i	−0.999979	−	0.00646722i	$-0.997941\pi$
$877$	−18.4579	−	27.6242i	−0.623279	−	0.932802i	0.376700	−	0.926335i	$-0.377059\pi$
$878$	−11.0466	−	30.4682i	−0.372805	−	1.02825i
$879$	−11.2078	−	30.6947i	−0.378030	−	1.03531i
$880$	−0.357437	+	0.554950i	−0.0120492	+	0.0187074i
$881$	−28.1610	−	28.1610i	−0.948767	−	0.948767i	0.0499827	−	0.998750i	$-0.484083\pi$
$881$	−28.1610	−	28.1610i	−0.948767	−	0.948767i	−0.998750	+	0.0499827i	$0.984083\pi$
$882$	28.3987	−	7.63430i	0.956236	−	0.257060i
$883$	−7.45192	−	11.1526i	−0.250777	−	0.375314i	0.684628	−	0.728893i	$-0.259965\pi$
$883$	−7.45192	−	11.1526i	−0.250777	−	0.375314i	−0.935405	+	0.353578i	$0.884965\pi$
$884$	4.09361	+	1.20424i	0.137683	+	0.0405029i
$885$	−0.586663	−	0.142915i	−0.0197205	−	0.00480403i
$886$	−9.68855	+	1.47887i	−0.325493	+	0.0496837i
$887$	23.8945	+	9.89741i	0.802298	+	0.332323i	0.745876	−	0.666085i	$-0.232031\pi$
$887$	23.8945	+	9.89741i	0.802298	+	0.332323i	0.0564213	+	0.998407i	$0.482031\pi$
$888$	−18.9190	−	12.1247i	−0.634879	−	0.406878i
$889$	0.100072	−	0.0414513i	0.00335631	−	0.00139023i
$890$	0.807366	+	1.33424i	0.0270630	+	0.0447237i
$891$	13.6219	−	14.3476i	0.456352	−	0.480663i
$892$	−2.26085	+	25.1215i	−0.0756989	+	0.841131i
$893$	−14.2995	−	2.84434i	−0.478514	−	0.0951823i
$894$	14.3368	−	4.51701i	0.479494	−	0.151071i
$895$		−	0.920951i		−	0.0307840i
$896$	1.92589	−	2.25501i	0.0643395	−	0.0753346i
$897$	1.28634	−	2.76599i	0.0429495	−	0.0923539i
$898$	−6.34629	−	6.94308i	−0.211778	−	0.231694i
$899$	−12.8375	+	64.5387i	−0.428156	+	2.15249i
$900$	17.1774	+	24.5542i	0.572581	+	0.818473i
$901$	13.0149	+	8.69629i	0.433590	+	0.289715i
$902$	−13.7529	+	8.32210i	−0.457923	+	0.277096i
$903$	−0.184903	+	4.33756i	−0.00615319	+	0.144345i
$904$	4.06360	−	30.0004i	0.135153	−	0.997799i
$905$	−0.302979	+	0.731455i	−0.0100714	+	0.0243144i
$906$	19.9752	+	5.82687i	0.663632	+	0.193585i
$907$	−0.344578	−	1.73231i	−0.0114415	−	0.0575205i	0.974643	−	0.223767i	$-0.0718354\pi$
$907$	−0.344578	−	1.73231i	−0.0114415	−	0.0575205i	−0.986084	+	0.166246i	$0.946835\pi$
$908$	7.82958	−	26.6154i	0.259834	−	0.883262i
$909$	9.70864	−	33.5662i	0.322015	−	1.11332i
$910$	0.0106626	−	0.0227919i	0.000353462	−	0.000755546i
$911$	−16.1986	+	16.1986i	−0.536684	+	0.536684i	−0.922554	−	0.385869i	$-0.873902\pi$
$911$	−16.1986	+	16.1986i	−0.536684	+	0.536684i	0.385869	+	0.922554i	$0.373902\pi$
$912$	8.66030	+	1.95583i	0.286771	+	0.0647639i
$913$	19.0025	+	19.0025i	0.628893	+	0.628893i
$914$	−22.0234	+	7.98484i	−0.728469	+	0.264115i
$915$	−0.0871136	−	0.562132i	−0.00287989	−	0.0185835i
$916$	0.256176	+	0.206653i	0.00846428	+	0.00682800i
$917$	−1.38175	+	0.274847i	−0.0456294	+	0.00907625i
$918$	−16.1715	−	6.25437i	−0.533739	−	0.206425i
$919$	−25.4121	−	10.5260i	−0.838266	−	0.347221i	−0.0780965	−	0.996946i	$-0.524884\pi$
$919$	−25.4121	−	10.5260i	−0.838266	−	0.347221i	−0.760170	+	0.649725i	$0.774884\pi$
$920$	0.134399	−	0.391123i	0.00443099	−	0.0128950i
$921$	−0.975911	+	22.8935i	−0.0321574	+	0.754366i
$922$	−35.1608	−	8.65016i	−1.15796	−	0.284878i
$923$	2.83696	−	4.24581i	0.0933797	−	0.139753i
$924$	1.97852	+	0.263412i	0.0650886	+	0.00866562i
$925$	22.4681	+	4.46919i	0.738747	+	0.146946i
$926$	19.8176	+	0.889959i	0.651246	+	0.0292459i
$927$	25.9504	+	30.7973i	0.852322	+	1.01152i
$928$	13.1173	+	34.3623i	0.430595	+	1.12800i
$929$	45.2667			1.48515			0.742576	−	0.669762i	$-0.233604\pi$
$929$	45.2667			1.48515			0.742576	+	0.669762i	$0.233604\pi$
$930$	0.859674	−	1.65056i	0.0281898	−	0.0541240i
$931$	−1.73286	+	8.71169i	−0.0567923	+	0.285514i
$932$	−15.0990	+	28.8295i	−0.494584	+	0.944343i
$933$	4.23780	+	6.96747i	0.138739	+	0.228105i
$934$	−5.24341	−	1.28997i	−0.171570	−	0.0422091i
$935$	0.149008	+	0.359738i	0.00487310	+	0.0117647i
$936$	0.180195	−	7.67049i	0.00588986	−	0.250718i
$937$	16.4387	−	39.6866i	0.537030	−	1.29650i	−0.389758	−	0.920917i	$-0.627441\pi$
$937$	16.4387	−	39.6866i	0.537030	−	1.29650i	0.926787	−	0.375587i	$-0.122559\pi$
$938$	−0.546882	−	0.402038i	−0.0178563	−	0.0131270i
$939$	−16.0949	−	3.92081i	−0.525236	−	0.127951i
$940$	0.181740	+	1.69850i	0.00592769	+	0.0553988i
$941$	13.4371	−	8.97839i	0.438037	−	0.292687i	−0.316931	−	0.948449i	$-0.602652\pi$
$941$	13.4371	−	8.97839i	0.438037	−	0.292687i	0.754968	+	0.655762i	$0.227652\pi$
$942$	−31.2201	−	2.73812i	−1.01721	−	0.0892129i
$943$	7.12152	−	7.12152i	0.231908	−	0.231908i
$944$	−13.3539	−	12.9116i	−0.434633	−	0.420236i
$945$	−0.0508492	+	0.0887057i	−0.00165412	+	0.00288560i
$946$	12.5974	−	26.9278i	0.409578	−	0.875498i
$947$	11.2306	−	7.50405i	0.364946	−	0.243849i	−0.359554	−	0.933124i	$-0.617071\pi$
$947$	11.2306	−	7.50405i	0.364946	−	0.243849i	0.724499	+	0.689276i	$0.242071\pi$
$948$	−29.0256	+	1.85995i	−0.942708	+	0.0604085i
$949$	9.62140	−	1.91381i	0.312324	−	0.0621250i
$950$	−8.94763	+	1.36578i	−0.290299	+	0.0443117i
$951$	2.20591	+	2.40235i	0.0715314	+	0.0779015i
$952$	−0.446437	−	1.69135i	−0.0144691	−	0.0548170i
$953$	−16.3000	−	39.3517i	−0.528009	−	1.27473i	−0.932826	−	0.360328i	$-0.882665\pi$
$953$	−16.3000	−	39.3517i	−0.528009	−	1.27473i	0.404817	−	0.914398i	$-0.367335\pi$
$954$	9.02529	−	26.6592i	0.292205	−	0.863124i
$955$	1.15082	−	1.72232i	0.0372396	−	0.0557329i
$956$	21.5211	−	17.9673i	0.696042	−	0.581103i
$957$	−14.6179	+	19.9794i	−0.472529	+	0.645844i
$958$	4.43427	+	4.85126i	0.143265	+	0.156737i
$959$	3.97022			0.128205
$960$	−0.0839918	−	1.03682i	−0.00271082	−	0.0334633i
$961$	71.4236			2.30399
$962$	−3.95728	−	4.32942i	−0.127588	−	0.139586i
$963$	37.4000	−	20.6187i	1.20520	−	0.664429i
$964$	−11.8551	−	14.1999i	−0.381826	−	0.457349i
$965$	0.210125	−	0.314474i	0.00676416	−	0.0101233i
$966$	−1.24313	+	0.135877i	−0.0399972	+	0.00437177i
$967$	1.80085	+	4.34765i	0.0579116	+	0.139811i	0.950187	−	0.311681i	$-0.100892\pi$
$967$	1.80085	+	4.34765i	0.0579116	+	0.139811i	−0.892275	+	0.451492i	$0.850892\pi$
$968$	15.0752	+	8.77886i	0.484535	+	0.282163i
$969$	3.85760	−	3.54216i	0.123924	−	0.113791i
$970$	1.36483	−	0.208329i	0.0438220	−	0.00668905i
$971$	−49.1172	+	9.77002i	−1.57625	+	0.313535i	−0.904245	−	0.427015i	$-0.859565\pi$
$971$	−49.1172	+	9.77002i	−1.57625	+	0.313535i	−0.672002	+	0.740550i	$0.734565\pi$
$972$	−3.31152	+	31.0005i	−0.106217	+	0.994343i
$973$	1.92038	−	1.28316i	0.0615646	−	0.0411361i
$974$	11.6757	−	24.9576i	0.374114	−	0.799692i
$975$	2.68286	+	7.34751i	0.0859201	+	0.235309i
$976$	6.42343	−	16.2775i	0.205609	−	0.521032i
$977$	−14.3409	+	14.3409i	−0.458806	+	0.458806i	−0.898263	−	0.439457i	$-0.855171\pi$
$977$	−14.3409	+	14.3409i	−0.458806	+	0.458806i	0.439457	+	0.898263i	$0.355171\pi$
$978$	1.54721	−	17.6413i	0.0494742	−	0.564106i
$979$	−26.8482	+	17.9394i	−0.858073	+	0.573346i
$980$	1.03478	−	0.110722i	0.0330548	−	0.00353687i
$981$	−18.4407	+	23.0740i	−0.588768	+	0.736695i
$982$	−12.3074	−	9.04773i	−0.392745	−	0.288725i
$983$	−20.8007	+	50.2173i	−0.663439	+	1.60168i	0.128939	+	0.991652i	$0.458843\pi$
$983$	−20.8007	+	50.2173i	−0.663439	+	1.60168i	−0.792378	+	0.610030i	$0.791157\pi$
$984$	9.24490	−	23.5844i	0.294717	−	0.751843i
$985$	−0.392683	−	0.948021i	−0.0125119	−	0.0302065i
$986$	21.0680	+	5.18309i	0.670942	+	0.165063i
$987$	4.41299	−	2.68410i	0.140467	−	0.0854358i
$988$	2.05298	+	1.07522i	0.0653141	+	0.0342072i
$989$	−3.63374	+	18.2680i	−0.115546	+	0.580890i
$990$	0.555110	−	0.426672i	0.0176426	−	0.0135605i
$991$	−21.0842			−0.669761			−0.334880	−	0.942261i	$-0.608696\pi$
$991$	−21.0842			−0.669761			−0.334880	+	0.942261i	$0.608696\pi$
$992$	48.4745	−	30.4594i	1.53907	−	0.967087i
$993$	20.5363	−	44.1590i	0.651700	−	1.40134i
$994$	−2.09125	−	0.0939130i	−0.0663305	−	0.00297874i
$995$	−0.878223	−	0.174689i	−0.0278415	−	0.00553803i
$996$	−41.9786	−	5.58885i	−1.33014	−	0.177089i
$997$	34.7772	−	52.0478i	1.10141	−	1.64837i	0.440881	−	0.897566i	$-0.354666\pi$
$997$	34.7772	−	52.0478i	1.10141	−	1.64837i	0.660525	−	0.750804i	$-0.270334\pi$
$998$	49.0063	+	12.0564i	1.55127	+	0.381639i
$999$	14.5675	+	18.8637i	0.460896	+	0.596822i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.131.24	yes	240
3.2	odd	2	inner	192.2.s.a.131.7	yes	240
4.3	odd	2		768.2.s.a.431.5		240
12.11	even	2		768.2.s.a.431.2		240
64.21	even	16		768.2.s.a.335.2		240
64.43	odd	16	inner	192.2.s.a.107.7	✓	240
192.107	even	16	inner	192.2.s.a.107.24	yes	240
192.149	odd	16		768.2.s.a.335.5		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.7	✓	240	64.43	odd	16	inner
192.2.s.a.107.24	yes	240	192.107	even	16	inner
192.2.s.a.131.7	yes	240	3.2	odd	2	inner
192.2.s.a.131.24	yes	240	1.1	even	1	trivial
768.2.s.a.335.2		240	64.21	even	16
768.2.s.a.335.5		240	192.149	odd	16
768.2.s.a.431.2		240	12.11	even	2
768.2.s.a.431.5		240	4.3	odd	2

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.04386 - 0.954131i) q^{2} +(1.39786 + 1.02274i) q^{3} +(0.179269 - 1.99195i) q^{4} +(-0.0417075 + 0.0624196i) q^{5} +(2.43499 - 0.266149i) q^{6} +(-0.100307 - 0.242162i) q^{7} +(-1.71345 - 2.25035i) q^{8} +(0.908014 + 2.85929i) q^{9} +(0.0160199 + 0.104951i) q^{10} +(-2.15600 + 0.428854i) q^{11} +(2.28783 - 2.60112i) q^{12} +(0.751836 - 0.502361i) q^{13} +(-0.335761 - 0.157077i) q^{14} +(-0.122140 + 0.0445980i) q^{15} +(-3.93573 - 0.714188i) q^{16} +(-1.66843 + 1.66843i) q^{17} +(3.67597 + 2.11832i) q^{18} +(-1.06552 + 0.711956i) q^{19} +(0.116860 + 0.0942690i) q^{20} +(0.107454 - 0.441097i) q^{21} +(-1.84137 + 2.50477i) q^{22} +(0.745366 - 1.79947i) q^{23} +(-0.0936376 - 4.89808i) q^{24} +(1.91126 + 4.61419i) q^{25} +(0.305490 - 1.24174i) q^{26} +(-1.65503 + 4.92553i) q^{27} +(-0.500357 + 0.156394i) q^{28} +(1.26847 - 6.37705i) q^{29} +(-0.0849442 + 0.163091i) q^{30} -10.1205 q^{31} +(-4.78976 + 3.00969i) q^{32} +(-3.45238 - 1.60554i) q^{33} +(-0.149699 + 3.33350i) q^{34} +(0.0192992 + 0.00383886i) q^{35} +(5.85833 - 1.29614i) q^{36} +(2.54831 - 3.81381i) q^{37} +(-0.432947 + 1.75982i) q^{38} +(1.56474 + 0.0667024i) q^{39} +(0.211930 - 0.0130964i) q^{40} +(4.77720 + 1.97878i) q^{41} +(-0.308697 - 0.562966i) q^{42} +(-9.37912 + 1.86562i) q^{43} +(0.467754 + 4.37152i) q^{44} +(-0.216346 - 0.0625756i) q^{45} +(-0.938878 - 2.58957i) q^{46} +(8.04483 + 8.04483i) q^{47} +(-4.77116 - 5.02355i) q^{48} +(4.90117 - 4.90117i) q^{49} +(6.39762 + 2.99296i) q^{50} +(-4.03859 + 0.625860i) q^{51} +(-0.865897 - 1.58768i) q^{52} +(-1.29422 - 6.50649i) q^{53} +(2.97200 + 6.72066i) q^{54} +(0.0631522 - 0.152463i) q^{55} +(-0.373080 + 0.640659i) q^{56} +(-2.21759 - 0.0945320i) q^{57} +(-4.76044 - 7.86701i) q^{58} +(3.86117 + 2.57995i) q^{59} +(0.0669410 + 0.251292i) q^{60} +(-0.853477 + 4.29072i) q^{61} +(-10.5643 + 9.65624i) q^{62} +(0.601331 - 0.506693i) q^{63} +(-2.12818 + 7.71173i) q^{64} +0.0678815i q^{65} +(-5.13569 + 1.61807i) q^{66} +(1.79590 + 0.357228i) q^{67} +(3.02433 + 3.62252i) q^{68} +(2.88230 - 1.75309i) q^{69} +(0.0238084 - 0.0144068i) q^{70} +(5.21738 - 2.16111i) q^{71} +(4.87857 - 6.94259i) q^{72} +(10.0231 + 4.15171i) q^{73} +(-0.978810 - 6.41248i) q^{74} +(-2.04744 + 8.40470i) q^{75} +(1.22717 + 2.25009i) q^{76} +(0.320114 + 0.479085i) q^{77} +(1.69701 - 1.42334i) q^{78} +(-5.93698 - 5.93698i) q^{79} +(0.208728 - 0.215880i) q^{80} +(-7.35102 + 5.19254i) q^{81} +(6.87472 - 2.49251i) q^{82} +(-6.79190 - 10.1648i) q^{83} +(-0.859379 - 0.293117i) q^{84} +(-0.0345567 - 0.173728i) q^{85} +(-8.01040 + 10.8963i) q^{86} +(8.29520 - 7.61690i) q^{87} +(4.65927 + 4.11693i) q^{88} +(13.5709 - 5.62127i) q^{89} +(-0.285540 + 0.141103i) q^{90} +(-0.197067 - 0.131676i) q^{91} +(-3.45084 - 1.80732i) q^{92} +(-14.1470 - 10.3506i) q^{93} +(16.0735 + 0.721820i) q^{94} -0.0962031i q^{95} +(-9.77352 - 0.691552i) q^{96} -13.0044i q^{97} +(0.439755 - 9.79246i) q^{98} +(-3.18389 - 5.77520i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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