LMFDB - Embedded newform 192.2.s.a.107.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(11,192)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			107.7
Character	$\chi$	$=$	192.107
Dual form			192.2.s.a.131.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04386 - 0.954131i) q^{2} +(1.68284 + 0.409950i) q^{3} +(0.179269 + 1.99195i) q^{4} +(0.0417075 + 0.0624196i) q^{5} +(-1.36549 - 2.03358i) q^{6} +(-0.100307 + 0.242162i) q^{7} +(1.71345 - 2.25035i) q^{8} +(2.66388 + 1.37976i) q^{9} +O(q^{10})$	\(q+(-1.04386 - 0.954131i) q^{2} +(1.68284 + 0.409950i) q^{3} +(0.179269 + 1.99195i) q^{4} +(0.0417075 + 0.0624196i) q^{5} +(-1.36549 - 2.03358i) q^{6} +(-0.100307 + 0.242162i) q^{7} +(1.71345 - 2.25035i) q^{8} +(2.66388 + 1.37976i) q^{9} +(0.0160199 - 0.104951i) q^{10} +(2.15600 + 0.428854i) q^{11} +(-0.514919 + 3.42562i) q^{12} +(0.751836 + 0.502361i) q^{13} +(0.335761 - 0.157077i) q^{14} +(0.0445980 + 0.122140i) q^{15} +(-3.93573 + 0.714188i) q^{16} +(1.66843 + 1.66843i) q^{17} +(-1.46424 - 3.98196i) q^{18} +(-1.06552 - 0.711956i) q^{19} +(-0.116860 + 0.0942690i) q^{20} +(-0.268075 + 0.366399i) q^{21} +(-1.84137 - 2.50477i) q^{22} +(-0.745366 - 1.79947i) q^{23} +(3.80599 - 3.08455i) q^{24} +(1.91126 - 4.61419i) q^{25} +(-0.305490 - 1.24174i) q^{26} +(3.91725 + 3.41396i) q^{27} +(-0.500357 - 0.156394i) q^{28} +(-1.26847 - 6.37705i) q^{29} +(0.0699837 - 0.170049i) 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} +(-2.27086 + 5.55367i) q^{36} +(2.54831 + 3.81381i) q^{37} +(0.432947 + 1.75982i) q^{38} +(1.05928 + 1.15361i) q^{39} +(0.211930 + 0.0130964i) q^{40} +(-4.77720 + 1.97878i) q^{41} +(0.629424 - 0.126689i) q^{42} +(-9.37912 - 1.86562i) q^{43} +(-0.467754 + 4.37152i) q^{44} +(0.0249798 + 0.223825i) q^{45} +(-0.938878 + 2.58957i) q^{46} +(-8.04483 + 8.04483i) q^{47} +(-6.91597 - 0.411587i) q^{48} +(4.90117 + 4.90117i) q^{49} +(-6.39762 + 2.99296i) q^{50} +(2.12372 + 3.49166i) q^{51} +(-0.865897 + 1.58768i) q^{52} +(1.29422 - 6.50649i) q^{53} +(-0.831673 - 7.30125i) q^{54} +(0.0631522 + 0.152463i) q^{55} +(0.373080 + 0.640659i) q^{56} +(-1.50123 - 1.63491i) q^{57} +(-4.76044 + 7.86701i) q^{58} +(-3.86117 + 2.57995i) q^{59} +(-0.235302 + 0.110733i) 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} +(-2.07189 - 4.96998i) q^{66} +(1.79590 - 0.357228i) q^{67} +(-3.02433 + 3.62252i) q^{68} +(-0.516636 - 3.33378i) q^{69} +(0.0238084 + 0.0144068i) q^{70} +(-5.21738 - 2.16111i) q^{71} +(7.66937 - 3.63053i) q^{72} +(10.0231 - 4.15171i) q^{73} +(0.978810 - 6.41248i) q^{74} +(5.10793 - 6.98141i) q^{75} +(1.22717 - 2.25009i) q^{76} +(-0.320114 + 0.479085i) q^{77} +(-0.00503859 - 2.21489i) q^{78} +(-5.93698 + 5.93698i) q^{79} +(-0.208728 - 0.215880i) q^{80} +(5.19254 + 7.35102i) q^{81} +(6.87472 + 2.49251i) q^{82} +(6.79190 - 10.1648i) q^{83} +(-0.777906 - 0.468308i) q^{84} +(-0.0345567 + 0.173728i) q^{85} +(8.01040 + 10.8963i) q^{86} +(0.479635 - 11.2516i) q^{87} +(4.65927 - 4.11693i) q^{88} +(-13.5709 - 5.62127i) q^{89} +(0.187483 - 0.257475i) q^{90} +(-0.197067 + 0.131676i) q^{91} +(3.45084 - 1.80732i) q^{92} +(-17.0311 - 4.14888i) q^{93} +(16.0735 - 0.721820i) q^{94} -0.0962031i q^{95} +(6.82656 + 7.02837i) q^{96} +13.0044i q^{97} +(-0.439755 - 9.79246i) q^{98} +(5.15161 + 4.11717i) 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}+O(q^{10}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{16}\right)$

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
$3$	1.68284	+	0.409950i	0.971587	+	0.236685i
$3$	1.68284	+	0.409950i	0.971587	+	0.236685i
$4$	0.179269	+	1.99195i	0.0896343	+	0.995975i
$5$	0.0417075	+	0.0624196i	0.0186521	+	0.0279149i	0.840679	−	0.541535i	$-0.182156\pi$
$5$	0.0417075	+	0.0624196i	0.0186521	+	0.0279149i	−0.822026	+	0.569449i	$0.807156\pi$
$6$	−1.36549	−	2.03358i	−0.557460	−	0.830204i
$7$	−0.100307	+	0.242162i	−0.0379125	+	0.0915288i	−0.941702	−	0.336449i	$-0.890774\pi$
$7$	−0.100307	+	0.242162i	−0.0379125	+	0.0915288i	0.903789	+	0.427978i	$0.140774\pi$
$8$	1.71345	−	2.25035i	0.605796	−	0.795620i
$9$	2.66388	+	1.37976i	0.887961	+	0.459919i
$10$	0.0160199	−	0.104951i	0.00506595	−	0.0331886i
$11$	2.15600	+	0.428854i	0.650058	+	0.129304i	0.509095	−	0.860710i	$-0.329980\pi$
$11$	2.15600	+	0.428854i	0.650058	+	0.129304i	0.140963	+	0.990015i	$0.454980\pi$
$12$	−0.514919	+	3.42562i	−0.148644	+	0.988891i
$13$	0.751836	+	0.502361i	0.208522	+	0.139330i	0.655446	−	0.755242i	$-0.272481\pi$
$13$	0.751836	+	0.502361i	0.208522	+	0.139330i	−0.446924	+	0.894572i	$0.647481\pi$
$14$	0.335761	−	0.157077i	0.0897358	−	0.0419805i
$15$	0.0445980	+	0.122140i	0.0115151	+	0.0315364i
$16$	−3.93573	+	0.714188i	−0.983931	+	0.178547i
$17$	1.66843	+	1.66843i	0.404653	+	0.404653i	0.879869	−	0.475216i	$-0.157630\pi$
$17$	1.66843	+	1.66843i	0.404653	+	0.404653i	−0.475216	+	0.879869i	$0.657630\pi$
$18$	−1.46424	−	3.98196i	−0.345125	−	0.938557i
$19$	−1.06552	−	0.711956i	−0.244446	−	0.163334i	0.427312	−	0.904104i	$-0.359461\pi$
$19$	−1.06552	−	0.711956i	−0.244446	−	0.163334i	−0.671758	+	0.740770i	$0.734461\pi$
$20$	−0.116860	+	0.0942690i	−0.0261307	+	0.0210792i
$21$	−0.268075	+	0.366399i	−0.0584987	+	0.0799549i
$22$	−1.84137	−	2.50477i	−0.392581	−	0.534018i
$23$	−0.745366	−	1.79947i	−0.155419	−	0.375216i	0.826921	−	0.562318i	$-0.190090\pi$
$23$	−0.745366	−	1.79947i	−0.155419	−	0.375216i	−0.982340	+	0.187102i	$0.940090\pi$
$24$	3.80599	−	3.08455i	0.776894	−	0.629631i
$25$	1.91126	−	4.61419i	0.382252	−	0.922838i
$26$	−0.305490	−	1.24174i	−0.0599116	−	0.243526i
$27$	3.91725	+	3.41396i	0.753875	+	0.657018i
$28$	−0.500357	−	0.156394i	−0.0945586	−	0.0295557i
$29$	−1.26847	−	6.37705i	−0.235550	−	1.18419i	−0.899672	−	0.436566i	$-0.856195\pi$
$29$	−1.26847	−	6.37705i	−0.235550	−	1.18419i	0.664123	−	0.747624i	$-0.268805\pi$
$30$	0.0699837	−	0.170049i	0.0127772	−	0.0310465i
$31$	−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
$36$	−2.27086	+	5.55367i	−0.378476	+	0.925611i
$37$	2.54831	+	3.81381i	0.418939	+	0.626986i	0.979576	−	0.201075i	$-0.0644436\pi$
$37$	2.54831	+	3.81381i	0.418939	+	0.626986i	−0.560637	+	0.828062i	$0.689444\pi$
$38$	0.432947	+	1.75982i	0.0702333	+	0.285481i
$39$	1.05928	+	1.15361i	0.169620	+	0.184725i
$40$	0.211930	+	0.0130964i	0.0335090	+	0.00207072i
$41$	−4.77720	+	1.97878i	−0.746073	+	0.309033i	−0.723138	−	0.690704i	$-0.757301\pi$
$41$	−4.77720	+	1.97878i	−0.746073	+	0.309033i	−0.0229347	+	0.999737i	$0.507301\pi$
$42$	0.629424	−	0.126689i	0.0971223	−	0.0195486i
$43$	−9.37912	−	1.86562i	−1.43030	−	0.284505i	−0.581643	−	0.813444i	$-0.697590\pi$
$43$	−9.37912	−	1.86562i	−1.43030	−	0.284505i	−0.848659	+	0.528940i	$0.822590\pi$
$44$	−0.467754	+	4.37152i	−0.0705165	+	0.659031i
$45$	0.0249798	+	0.223825i	0.00372377	+	0.0333658i
$46$	−0.938878	+	2.58957i	−0.138430	+	0.381811i
$47$	−8.04483	+	8.04483i	−1.17346	+	1.17346i	−0.192080	+	0.981379i	$0.561523\pi$
$47$	−8.04483	+	8.04483i	−1.17346	+	1.17346i	−0.981379	+	0.192080i	$0.938477\pi$
$48$	−6.91597	−	0.411587i	−0.998234	−	0.0594075i
$49$	4.90117	+	4.90117i	0.700167	+	0.700167i
$50$	−6.39762	+	2.99296i	−0.904760	+	0.423268i
$51$	2.12372	+	3.49166i	0.297380	+	0.488931i
$52$	−0.865897	+	1.58768i	−0.120078	+	0.220171i
$53$	1.29422	−	6.50649i	0.177775	−	0.893735i	−0.784181	−	0.620532i	$-0.786917\pi$
$53$	1.29422	−	6.50649i	0.177775	−	0.893735i	0.961956	−	0.273203i	$-0.0880831\pi$
$54$	−0.831673	−	7.30125i	−0.113176	−	0.993575i
$55$	0.0631522	+	0.152463i	0.00851544	+	0.0205581i
$56$	0.373080	+	0.640659i	0.0498549	+	0.0856117i
$57$	−1.50123	−	1.63491i	−0.198842	−	0.216550i
$58$	−4.76044	+	7.86701i	−0.625076	+	1.03299i
$59$	−3.86117	+	2.57995i	−0.502681	+	0.335881i	−0.780920	−	0.624631i	$-0.785249\pi$
$59$	−3.86117	+	2.57995i	−0.502681	+	0.335881i	0.278239	+	0.960512i	$0.410249\pi$
$60$	−0.235302	+	0.110733i	−0.0303773	+	0.0142955i
$61$	−0.853477	−	4.29072i	−0.109277	−	0.549370i	−0.996173	−	0.0874022i	$-0.972143\pi$
$61$	−0.853477	−	4.29072i	−0.109277	−	0.549370i	0.886897	−	0.461968i	$-0.152857\pi$
$62$	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
$66$	−2.07189	−	4.96998i	−0.255032	−	0.611762i
$67$	1.79590	−	0.357228i	0.219405	−	0.0436423i	−0.0841638	−	0.996452i	$-0.526822\pi$
$67$	1.79590	−	0.357228i	0.219405	−	0.0436423i	0.303568	+	0.952810i	$0.401822\pi$
$68$	−3.02433	+	3.62252i	−0.366753	+	0.439295i
$69$	−0.516636	−	3.33378i	−0.0621957	−	0.401340i
$70$	0.0238084	+	0.0144068i	0.00284565	+	0.00172194i
$71$	−5.21738	−	2.16111i	−0.619190	−	0.256477i	0.0509625	−	0.998701i	$-0.483771\pi$
$71$	−5.21738	−	2.16111i	−0.619190	−	0.256477i	−0.670152	+	0.742224i	$0.733771\pi$
$72$	7.66937	−	3.63053i	0.903844	−	0.427862i
$73$	10.0231	−	4.15171i	1.17312	−	0.485921i	0.290895	−	0.956755i	$-0.406047\pi$
$73$	10.0231	−	4.15171i	1.17312	−	0.485921i	0.882222	+	0.470834i	$0.156047\pi$
$74$	0.978810	−	6.41248i	0.113784	−	0.745436i
$75$	5.10793	−	6.98141i	0.589813	−	0.806144i
$76$	1.22717	−	2.25009i	0.140766	−	0.258103i
$77$	−0.320114	+	0.479085i	−0.0364804	+	0.0545967i
$78$	−0.00503859	−	2.21489i	−0.000570508	−	0.250786i
$79$	−5.93698	+	5.93698i	−0.667963	+	0.667963i	−0.957244	−	0.289281i	$-0.906584\pi$
$79$	−5.93698	+	5.93698i	−0.667963	+	0.667963i	0.289281	+	0.957244i	$0.406584\pi$
$80$	−0.208728	−	0.215880i	−0.0233365	−	0.0241361i
$81$	5.19254	+	7.35102i	0.576949	+	0.816780i
$82$	6.87472	+	2.49251i	0.759186	+	0.275252i
$83$	6.79190	−	10.1648i	0.745508	−	1.11573i	−0.243790	−	0.969828i	$-0.578391\pi$
$83$	6.79190	−	10.1648i	0.745508	−	1.11573i	0.989299	−	0.145904i	$-0.0466091\pi$
$84$	−0.777906	−	0.468308i	−0.0848765	−	0.0510965i
$85$	−0.0345567	+	0.173728i	−0.00374820	+	0.0188435i
$86$	8.01040	+	10.8963i	0.863783	+	1.17498i
$87$	0.479635	−	11.2516i	0.0514222	−	1.20629i
$88$	4.65927	−	4.11693i	0.496680	−	0.438867i
$89$	−13.5709	−	5.62127i	−1.43852	−	0.595853i	−0.479079	−	0.877772i	$-0.659029\pi$
$89$	−13.5709	−	5.62127i	−1.43852	−	0.595853i	−0.959438	+	0.281919i	$0.909029\pi$
$90$	0.187483	−	0.257475i	0.0197624	−	0.0271402i
$91$	−0.197067	+	0.131676i	−0.0206583	+	0.0138034i
$92$	3.45084	−	1.80732i	0.359775	−	0.188426i
$93$	−17.0311	−	4.14888i	−1.76604	−	0.430219i
$94$	16.0735	−	0.721820i	1.65785	−	0.0744500i
$95$		−	0.0962031i		−	0.00987023i
$96$	6.82656	+	7.02837i	0.696733	+	0.717331i
$97$			13.0044i			1.32039i	0.751092	+	0.660197i	$0.229527\pi$
$97$			13.0044i			1.32039i	−0.751092	+	0.660197i	$0.770473\pi$
$98$	−0.439755	−	9.79246i	−0.0444220	−	0.989188i
$99$	5.15161	+	4.11717i	0.517756	+	0.413791i
$100$	9.53386	+	2.97995i	0.953386	+	0.297995i
$101$	9.68443	−	6.47093i	0.963637	−	0.643882i	0.0290356	−	0.999578i	$-0.490756\pi$
$101$	9.68443	−	6.47093i	0.963637	−	0.643882i	0.934601	+	0.355697i	$0.115756\pi$
$102$	1.11465	−	5.67110i	0.110366	−	0.561523i
$103$	12.4024	+	5.13724i	1.22204	+	0.506187i	0.898059	−	0.439875i	$-0.144977\pi$
$103$	12.4024	+	5.13724i	1.22204	+	0.506187i	0.323985	+	0.946062i	$0.394977\pi$
$104$	2.41872	−	0.831127i	0.237175	−	0.0814987i
$105$	−0.0340512	−	0.00145155i	−0.00332306	−	0.000141656i
$106$	−7.55902	+	5.55698i	−0.734197	+	0.539741i
$107$	2.77724	−	13.9621i	0.268486	−	1.34977i	−0.577424	−	0.816445i	$-0.695942\pi$
$107$	2.77724	−	13.9621i	0.268486	−	1.34977i	0.845910	−	0.533326i	$-0.179058\pi$
$108$	−6.09821	+	8.41498i	−0.586800	+	0.809732i
$109$	5.47007	−	8.18653i	0.523937	−	0.784128i	−0.471262	−	0.881993i	$-0.656201\pi$
$109$	5.47007	−	8.18653i	0.523937	−	0.784128i	0.995200	+	0.0978654i	$0.0312015\pi$
$110$	0.0795478	−	0.219405i	0.00758459	−	0.0209194i
$111$	2.72491	+	7.46270i	0.258637	+	0.708328i
$112$	0.221831	−	1.02472i	0.0209611	−	0.0968272i
$113$	−7.56860	+	7.56860i	−0.711994	+	0.711994i	−0.966952	−	0.254958i	$-0.917938\pi$
$113$	−7.56860	+	7.56860i	−0.711994	+	0.711994i	0.254958	+	0.966952i	$0.417938\pi$
$114$	0.00714080	+	3.13898i	0.000668797	+	0.293993i
$115$	0.0812350	−	0.121577i	0.00757521	−	0.0113371i
$116$	12.4754	−	3.66994i	1.15831	−	0.340746i
$117$	1.30967	+	2.37558i	0.121079	+	0.219623i
$118$	6.49211	+	0.990964i	0.597647	+	0.0912256i
$119$	−0.571385	+	0.236676i	−0.0523788	+	0.0216960i
$120$	0.351275	+	0.108920i	0.0320668	+	0.00994296i
$121$	−5.69827	−	2.36030i	−0.518024	−	0.214573i
$122$	−3.20300	+	5.29322i	−0.289986	+	0.479226i
$123$	−8.85044	+	1.37155i	−0.798018	+	0.123669i
$124$	−1.81428	−	20.1594i	−0.162927	−	1.81037i
$125$	0.735875	−	0.146375i	0.0658186	−	0.0130921i
$126$	1.11115	+	0.0448346i	0.0989895	+	0.00399418i
$127$		−	0.413244i		−	0.0366695i	−0.999832	−	0.0183347i	$-0.994164\pi$
$127$		−	0.413244i		−	0.0366695i	0.999832	−	0.0183347i	$-0.00583646\pi$
$128$	−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	−0.999173	−	0.0406521i	$-0.987056\pi$
$131$	−1.04858	−	5.27154i	−0.0916144	−	0.460577i	0.907559	−	0.419925i	$-0.137944\pi$
$132$	−2.57926	+	7.16480i	−0.224495	+	0.623616i
$133$	0.279288	−	0.186614i	0.0242173	−	0.0161815i
$134$	−2.21551	−	1.34063i	−0.191391	−	0.115813i
$135$	−0.0497199	+	0.386901i	−0.00427921	+	0.0332991i
$136$	6.61332	−	0.895784i	0.567087	−	0.0768129i
$137$	5.79645	+	13.9939i	0.495224	+	1.19558i	0.952028	+	0.306010i	$0.0989941\pi$
$137$	5.79645	+	13.9939i	0.495224	+	1.19558i	−0.456804	+	0.889567i	$0.651006\pi$
$138$	−2.64157	+	3.97292i	−0.224865	+	0.338198i
$139$	1.71904	−	8.64218i	0.145807	−	0.733021i	−0.836827	−	0.547467i	$-0.815592\pi$
$139$	1.71904	−	8.64218i	0.145807	−	0.733021i	0.982634	−	0.185554i	$-0.0594078\pi$
$140$	−0.0111066	−	0.0377549i	−0.000938675	−	0.00319087i
$141$	−16.8361	+	10.2402i	−1.41786	+	0.862377i
$142$	3.38421	+	7.23395i	0.283997	+	0.607060i
$143$	1.40552	+	1.40552i	0.117535	+	0.117535i
$144$	−11.4697	−	3.52783i	−0.955810	−	0.293986i
$145$	0.345148	−	0.345148i	0.0286630	−	0.0286630i
$146$	−14.4240	−	5.22958i	−1.19374	−	0.432803i
$147$	6.23863	+	10.2571i	0.514554	+	0.845991i
$148$	−7.14008	+	5.75979i	−0.586911	+	0.473452i
$149$	−6.01868	−	1.19719i	−0.493069	−	0.0980776i	−0.0577083	−	0.998333i	$-0.518379\pi$
$149$	−6.01868	−	1.19719i	−0.493069	−	0.0980776i	−0.435361	+	0.900256i	$0.643379\pi$
$150$	−11.9931	+	2.41395i	−0.979234	+	0.197099i
$151$	7.84809	−	3.25079i	0.638669	−	0.264545i	−0.0397624	−	0.999209i	$-0.512660\pi$
$151$	7.84809	−	3.25079i	0.638669	−	0.264545i	0.678431	+	0.734664i	$0.262660\pi$
$152$	−3.42786	+	1.17789i	−0.278036	+	0.0955395i
$153$	2.14247	+	6.74652i	0.173208	+	0.545424i
$154$	0.791262	−	0.194664i	0.0637617	−	0.0156865i
$155$	−0.422098	−	0.631715i	−0.0339038	−	0.0507406i
$156$	−2.10803	+	2.31683i	−0.168778	+	0.185495i
$157$	−12.5487	+	2.49608i	−1.00149	+	0.199209i	−0.668493	−	0.743718i	$-0.733060\pi$
$157$	−12.5487	+	2.49608i	−1.00149	+	0.199209i	−0.332998	+	0.942927i	$0.608060\pi$
$158$	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
$162$	1.59358	−	12.6278i	0.125203	−	0.992131i
$163$	1.41044	+	7.09076i	0.110474	+	0.555391i	0.995888	+	0.0905883i	$0.0288747\pi$
$163$	1.41044	+	7.09076i	0.110474	+	0.555391i	−0.885414	+	0.464803i	$0.846125\pi$
$164$	−4.79803	−	9.16120i	−0.374663	−	0.715370i
$165$	0.0437728	+	0.282460i	0.00340770	+	0.0219894i
$166$	−16.7883	+	4.13022i	−1.30303	+	0.320567i
$167$	−5.06460	+	12.2270i	−0.391911	+	0.946156i	0.597613	+	0.801785i	$0.296116\pi$
$167$	−5.06460	+	12.2270i	−0.391911	+	0.946156i	−0.989524	+	0.144371i	$0.953884\pi$
$168$	0.365195	+	1.23107i	0.0281754	+	0.0949791i
$169$	−4.66199	−	11.2550i	−0.358615	−	0.865773i
$170$	0.201832	−	0.148376i	0.0154798	−	0.0113799i
$171$	−1.85609	−	3.36672i	−0.141939	−	0.257460i
$172$	2.03484	−	19.0172i	0.155155	−	1.45005i
$173$	20.0687	+	13.4095i	1.52580	+	1.01950i	0.983830	+	0.179104i	$0.0573200\pi$
$173$	20.0687	+	13.4095i	1.52580	+	1.01950i	0.541966	+	0.840400i	$0.317680\pi$
$174$	−11.2361	+	11.2874i	−0.851808	+	0.855693i
$175$	0.925671	+	0.925671i	0.0699742	+	0.0699742i
$176$	−8.79170	−	0.148066i	−0.662699	−	0.0111609i
$177$	−7.55536	+	2.75875i	−0.567896	+	0.207360i
$178$	8.80268	+	18.8162i	0.659789	+	1.41034i
$179$	10.2002	+	6.81555i	0.762398	+	0.509418i	0.874941	−	0.484229i	$-0.160900\pi$
$179$	10.2002	+	6.81555i	0.762398	+	0.509418i	−0.112543	+	0.993647i	$0.535900\pi$
$180$	−0.441369	+	0.0898833i	−0.0328977	+	0.00669951i
$181$	10.3436	+	2.05747i	0.768834	+	0.152931i	0.563897	−	0.825845i	$-0.309301\pi$
$181$	10.3436	+	2.05747i	0.768834	+	0.152931i	0.204936	+	0.978775i	$0.434301\pi$
$182$	0.331346	+	0.0505771i	0.0245610	+	0.00374903i
$183$	0.322716	−	7.57046i	0.0238559	−	0.559625i
$184$	−5.32659	−	1.40597i	−0.392682	−	0.103649i
$185$	−0.131773	+	0.318128i	−0.00968815	+	0.0233893i
$186$	13.8194	+	20.5807i	1.01329	+	1.50905i
$187$	2.88161	+	4.31264i	0.210724	+	0.315371i
$188$	−17.4671	−	14.5827i	−1.27392	−	1.06355i
$189$	−1.21966	+	0.606166i	−0.0887173	+	0.0440921i
$190$	−0.0917903	+	0.100422i	−0.00665917	+	0.00728539i
$191$	27.5926			1.99653			0.998265	−	0.0588807i	$-0.0187532\pi$
$191$	27.5926			1.99653			0.998265	+	0.0588807i	$0.0187532\pi$
$192$	−0.419955	−	13.8500i	−0.0303076	−	0.999541i
$193$	−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
$195$	−0.0278280	+	0.114234i	−0.00199280	+	0.00818043i
$196$	−8.88425	+	10.6415i	−0.634589	+	0.760107i
$197$	7.59394	+	11.3651i	0.541046	+	0.809732i	0.996763	−	0.0803923i	$-0.0256173\pi$
$197$	7.59394	+	11.3651i	0.541046	+	0.809732i	−0.455718	+	0.890124i	$0.650617\pi$
$198$	−1.44921	−	9.21304i	−0.102991	−	0.654742i
$199$	4.56453	−	11.0197i	0.323571	−	0.781169i	−0.675470	−	0.737387i	$-0.736059\pi$
$199$	4.56453	−	11.0197i	0.323571	−	0.781169i	0.999041	−	0.0437818i	$-0.0139407\pi$
$200$	−7.10871	−	12.2072i	−0.502662	−	0.863179i
$201$	3.16866	+	0.135075i	0.223500	+	0.00952743i
$202$	−16.2833	−	2.48550i	−1.14569	−	0.174879i
$203$	1.67152	+	0.332486i	0.117318	+	0.0233359i
$204$	−6.57450	+	4.85629i	−0.460307	+	0.340008i
$205$	−0.322759	−	0.215661i	−0.0225425	−	0.0150624i
$206$	−8.04471	−	17.1960i	−0.560501	−	1.19811i
$207$	0.497268	−	5.82201i	0.0345625	−	0.404657i
$208$	−3.31780	−	1.44020i	−0.230048	−	0.0998600i
$209$	−1.99193	−	1.99193i	−0.137784	−	0.137784i
$210$	0.0341596	+	0.0340045i	0.00235724	+	0.00234653i
$211$	2.76673	+	1.84867i	0.190470	+	0.127268i	0.647149	−	0.762364i	$-0.275961\pi$
$211$	2.76673	+	1.84867i	0.190470	+	0.127268i	−0.456679	+	0.889631i	$0.650961\pi$
$212$	13.1926	+	1.41161i	0.906072	+	0.0969500i
$213$	−7.89406	−	5.77566i	−0.540892	−	0.395742i
$214$	−16.2207	+	11.9246i	−1.10883	+	0.815149i
$215$	−0.274728	−	0.663251i	−0.0187363	−	0.0452334i
$216$	14.3946	−	2.96554i	0.979431	−	0.201779i
$217$	1.01515	−	2.45079i	0.0689130	−	0.166371i
$218$	−13.5210	+	3.32640i	−0.915757	+	0.225292i
$219$	18.5693	−	2.87768i	1.25479	−	0.194456i
$220$	−0.292377	+	0.153128i	−0.0197121	+	0.0103239i
$221$	0.416231	+	2.09254i	0.0279988	+	0.140759i
$222$	4.27597	−	10.3899i	0.286985	−	0.697324i
$223$	−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	$-0.714774\pi$
$227$	−13.6050	+	2.70621i	−0.902997	+	0.179617i	−0.278309	+	0.960492i	$0.589774\pi$
$228$	2.98754	−	3.28346i	0.197855	−	0.217452i
$229$	−0.0914294	−	0.136834i	−0.00604182	−	0.00904223i	0.828436	−	0.560083i	$-0.189231\pi$
$229$	−0.0914294	−	0.136834i	−0.00604182	−	0.00904223i	−0.834478	+	0.551041i	$0.814231\pi$
$230$	−0.200798	+	0.0493998i	−0.0132402	+	0.00325733i
$231$	−0.735100	+	0.674991i	−0.0483661	+	0.0444111i
$232$	−16.5241	−	8.07225i	−1.08486	−	0.529969i
$233$	15.0334	−	6.22705i	0.984873	−	0.407948i	0.168645	−	0.985677i	$-0.446061\pi$
$233$	15.0334	−	6.22705i	0.984873	−	0.407948i	0.816229	+	0.577729i	$0.196061\pi$
$234$	0.899513	−	3.72936i	0.0588030	−	0.243796i
$235$	−0.837684	−	0.166626i	−0.0546445	−	0.0108695i
$236$	−5.83131	−	7.22874i	−0.379586	−	0.470551i
$237$	−12.4248	+	7.55711i	−0.807080	+	0.490887i
$238$	0.822263	+	0.298121i	0.0532994	+	0.0193243i
$239$	−9.91200	+	9.91200i	−0.641154	+	0.641154i	−0.950839	−	0.309685i	$-0.899776\pi$
$239$	−9.91200	+	9.91200i	−0.641154	+	0.641154i	0.309685	+	0.950839i	$0.399776\pi$
$240$	−0.262756	−	0.448858i	−0.0169608	−	0.0289737i
$241$	6.54008	+	6.54008i	0.421283	+	0.421283i	0.885645	−	0.464362i	$-0.153716\pi$
$241$	6.54008	+	6.54008i	0.421283	+	0.421283i	−0.464362	+	0.885645i	$0.653716\pi$
$242$	3.69613	+	7.90070i	0.237596	+	0.507877i
$243$	5.72465	+	14.4993i	0.367236	+	0.930128i
$244$	8.39389	−	2.46927i	0.537364	−	0.158079i
$245$	−0.101514	+	0.510344i	−0.00648548	+	0.0326047i
$246$	10.5472	+	7.01278i	0.672467	+	0.447118i
$247$	−0.443436	−	1.07055i	−0.0282151	−	0.0681174i
$248$	−17.3409	+	22.7746i	−1.10115	+	1.44619i
$249$	15.5967	−	14.3214i	0.988402	−	0.907580i
$250$	−0.907807	−	0.549327i	−0.0574148	−	0.0347425i
$251$	−18.8565	+	12.5995i	−1.19021	+	0.795273i	−0.983105	−	0.183045i	$-0.941405\pi$
$251$	−18.8565	+	12.5995i	−1.19021	+	0.795273i	−0.207106	+	0.978318i	$0.566405\pi$
$252$	−1.11711	−	1.10699i	−0.0703711	−	0.0697337i
$253$	−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	$-0.00246139\pi$
$258$	9.01324	+	21.6206i	0.561140	+	1.34604i
$259$	−1.17917	+	0.234552i	−0.0732703	+	0.0145744i
$260$	−0.135217	+	0.0121690i	−0.00838577	+	0.000754691i
$261$	5.41972	−	18.7379i	0.335472	−	1.15985i
$262$	−3.93518	+	6.50321i	−0.243116	+	0.401769i
$263$	24.7866	+	10.2669i	1.52841	+	0.633087i	0.979254	−	0.202635i	$-0.0649504\pi$
$263$	24.7866	+	10.2669i	1.52841	+	0.633087i	0.549153	+	0.835722i	$0.314950\pi$
$264$	9.52852	−	5.01807i	0.586440	−	0.308841i
$265$	0.460111	−	0.190584i	0.0282644	−	0.0117075i
$266$	−0.469591	−	0.0716789i	−0.0287924	−	0.00439492i
$267$	−20.5333	−	15.0231i	−1.25661	−	0.919398i
$268$	1.03353	+	3.51331i	0.0631328	+	0.214610i
$269$	−7.89201	+	11.8112i	−0.481184	+	0.720143i	−0.990052	−	0.140701i	$-0.955064\pi$
$269$	−7.89201	+	11.8112i	−0.481184	+	0.720143i	0.508868	+	0.860845i	$0.330064\pi$
$270$	0.421055	−	0.356429i	0.0256246	−	0.0216916i
$271$	−7.91386	+	7.91386i	−0.480733	+	0.480733i	−0.905366	−	0.424633i	$-0.860403\pi$
$271$	−7.91386	+	7.91386i	−0.480733	+	0.480733i	0.424633	+	0.905366i	$0.360403\pi$
$272$	−7.75804	−	5.37490i	−0.470400	−	0.325901i
$273$	−0.385613	+	0.140802i	−0.0233384	+	0.00852172i
$274$	7.30133	−	20.1382i	0.441089	−	1.21659i
$275$	6.09949	−	9.12853i	0.367813	−	0.550471i
$276$	6.54811	−	1.62676i	0.394150	−	0.0979192i
$277$	−4.80902	+	24.1766i	−0.288946	+	1.45263i	0.514622	+	0.857417i	$0.327932\pi$
$277$	−4.80902	+	24.1766i	−0.288946	+	1.45263i	−0.803568	+	0.595213i	$0.797068\pi$
$278$	−10.0402	+	7.38101i	−0.602171	+	0.442683i
$279$	−26.9597	−	13.9638i	−1.61403	−	0.835989i
$280$	−0.0244295	+	0.0500078i	−0.00145994	+	0.00298854i
$281$	−21.3506	−	8.84369i	−1.27367	−	0.527570i	−0.359590	−	0.933110i	$-0.617084\pi$
$281$	−21.3506	−	8.84369i	−1.27367	−	0.527570i	−0.914077	+	0.405540i	$0.867084\pi$
$282$	27.3449	+	5.37461i	1.62837	+	0.320053i
$283$	−2.13260	+	1.42496i	−0.126770	+	0.0847050i	−0.617339	−	0.786698i	$-0.711789\pi$
$283$	−2.13260	+	1.42496i	−0.126770	+	0.0847050i	0.490569	+	0.871403i	$0.336789\pi$
$284$	3.36951	−	10.7802i	0.199944	−	0.639686i
$285$	0.0394384	−	0.161894i	0.00233613	−	0.00958978i
$286$	−0.126110	−	2.80820i	−0.00745701	−	0.166053i
$287$		−	1.35534i		−	0.0800034i
$288$	8.60671	+	14.6262i	0.507155	+	0.861855i
$289$		−	11.4327i		−	0.672512i
$290$	−0.689602	+	0.0309683i	−0.0404948	+	0.00181852i
$291$	−5.33114	+	21.8843i	−0.312517	+	1.28288i
$292$	10.0668	+	19.2213i	0.589116	+	1.12484i
$293$	15.6865	−	10.4814i	0.916416	−	0.612329i	−0.00538828	−	0.999985i	$-0.501715\pi$
$293$	15.6865	−	10.4814i	0.916416	−	0.612329i	0.921804	+	0.387656i	$0.126715\pi$
$294$	3.27438	−	16.6594i	0.190966	−	0.971596i
$295$	−0.322079	−	0.133409i	−0.0187522	−	0.00776740i
$296$	12.9488	+	0.800183i	0.752634	+	0.0465097i
$297$	6.98148	+	9.04043i	0.405107	+	0.524579i
$298$	5.14036	+	6.99230i	0.297773	+	0.405053i
$299$	0.343591	−	1.72735i	0.0198704	−	0.0998953i
$300$	14.8223	+	8.92318i	0.855766	+	0.515180i
$301$	1.39257	−	2.08414i	0.0802667	−	0.120128i
$302$	−11.2940	−	4.09476i	−0.649894	−	0.235627i
$303$	18.9501	−	6.91939i	1.08865	−	0.397509i
$304$	4.70206	+	2.04108i	0.269681	+	0.117064i
$305$	0.232229	−	0.232229i	0.0132974	−	0.0132974i
$306$	4.20063	−	9.08659i	0.240134	−	0.519446i
$307$	7.34995	−	11.0000i	0.419484	−	0.627802i	−0.560198	−	0.828359i	$-0.689275\pi$
$307$	7.34995	−	11.0000i	0.419484	−	0.627802i	0.979682	+	0.200556i	$0.0642750\pi$
$308$	−1.01170	−	0.551766i	−0.0576469	−	0.0314398i
$309$	18.7652	+	13.7295i	1.06751	+	0.781044i
$310$	−0.162129	+	1.06216i	−0.00920830	+	0.0603264i
$311$	−4.34991	+	1.80179i	−0.246661	+	0.102170i	−0.502589	−	0.864526i	$-0.667619\pi$
$311$	−4.34991	+	1.80179i	−0.246661	+	0.102170i	0.255928	+	0.966696i	$0.417619\pi$
$312$	4.41104	−	0.407096i	0.249726	−	0.0230473i
$313$	−8.83610	−	3.66003i	−0.499446	−	0.206877i	0.118716	−	0.992928i	$-0.462122\pi$
$313$	−8.83610	−	3.66003i	−0.499446	−	0.206877i	−0.618162	+	0.786051i	$0.712122\pi$
$314$	15.4806	+	9.36751i	0.873619	+	0.528639i
$315$	−0.0567076	−	0.0164020i	−0.00319511	−	0.000924148i
$316$	−12.8905	−	10.7619i	−0.725146	−	0.605402i
$317$	−1.84684	+	0.367359i	−0.103729	+	0.0206329i	−0.246682	−	0.969097i	$-0.579340\pi$
$317$	−1.84684	+	0.367359i	−0.103729	+	0.0206329i	0.142953	+	0.989729i	$0.454340\pi$
$318$	−14.9987	+	6.25267i	−0.841084	+	0.350632i
$319$		−	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
$324$	−13.7120	+	11.6611i	−0.761778	+	0.647838i
$325$	3.75494	−	2.50897i	0.208287	−	0.139173i
$326$	5.29321	−	8.74747i	0.293164	−	0.484477i
$327$	12.5613	−	11.5342i	0.694641	−	0.637840i
$328$	−3.73253	+	14.1409i	−0.206095	+	0.780802i
$329$	−1.14120	−	2.75511i	−0.0629166	−	0.151894i
$330$	0.223811	−	0.336612i	0.0123204	−	0.0185299i
$331$	−5.48542	+	27.5771i	−0.301506	+	1.51577i	0.471780	+	0.881716i	$0.343612\pi$
$331$	−5.48542	+	27.5771i	−0.301506	+	1.51577i	−0.773286	+	0.634057i	$0.781388\pi$
$332$	21.4653	+	11.7069i	1.17806	+	0.642500i
$333$	1.52626	+	13.6756i	0.0836383	+	0.749417i
$334$	16.9529	−	7.93096i	0.927621	−	0.433963i
$335$	0.0972006	+	0.0972006i	0.00531064	+	0.00531064i
$336$	0.793391	−	1.63350i	0.0432830	−	0.0891149i
$337$	−14.8867	+	14.8867i	−0.810928	+	0.810928i	−0.984773	−	0.173845i	$-0.944381\pi$
$337$	−14.8867	+	14.8867i	−0.810928	+	0.810928i	0.173845	+	0.984773i	$0.444381\pi$
$338$	−5.87234	+	16.1968i	−0.319413	+	0.880990i
$339$	−15.8395	+	9.63397i	−0.860281	+	0.523246i
$340$	−0.352253	−	0.0376912i	−0.0191036	−	0.00204409i
$341$	−21.8197	−	4.34020i	−1.18160	−	0.235035i
$342$	−1.27481	+	5.28532i	−0.0689337	+	0.285797i
$343$	−3.37364	+	1.39741i	−0.182159	+	0.0754528i
$344$	−20.2690	+	17.9097i	−1.09283	+	0.965625i
$345$	0.186546	−	0.171292i	0.0100433	−	0.00922204i
$346$	−8.15443	−	33.1458i	−0.438385	−	1.78193i
$347$	−10.7084	−	16.0262i	−0.574855	−	0.860332i	0.424119	−	0.905606i	$-0.360584\pi$
$347$	−10.7084	−	16.0262i	−0.574855	−	0.860332i	−0.998975	+	0.0452745i	$0.985584\pi$
$348$	22.4985	−	1.06164i	1.20605	−	0.0569100i
$349$	18.0984	−	3.59999i	0.968783	−	0.192703i	0.314755	−	0.949173i	$-0.398078\pi$
$349$	18.0984	−	3.59999i	0.968783	−	0.192703i	0.654028	+	0.756470i	$0.273078\pi$
$350$	−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	$-0.412567\pi$
$353$	10.1922			0.542474			0.271237	+	0.962513i	$0.412567\pi$
$354$	10.5189	+	4.32907i	0.559074	+	0.230087i
$355$	−0.0827081	−	0.415802i	−0.00438969	−	0.0220685i
$356$	8.76444	−	28.0404i	0.464514	−	1.48614i
$357$	−1.05857	+	0.164047i	−0.0560257	+	0.00868230i
$358$	−4.14460	−	16.8468i	−0.219049	−	0.890379i
$359$	6.12003	−	14.7751i	0.323003	−	0.779798i	−0.676074	−	0.736834i	$-0.736320\pi$
$359$	6.12003	−	14.7751i	0.323003	−	0.779798i	0.999077	−	0.0429641i	$-0.0136801\pi$
$360$	0.546486	+	0.327299i	0.0288024	+	0.0172502i
$361$	−6.64254	−	16.0365i	−0.349607	−	0.844027i
$362$	−8.83413	−	12.0168i	−0.464311	−	0.631591i
$363$	−8.62165	−	6.30800i	−0.452519	−	0.331084i
$364$	−0.297620	−	0.368943i	−0.0155995	−	0.0193379i
$365$	0.677187	+	0.452482i	0.0354456	+	0.0236840i
$366$	−7.56008	+	7.59456i	−0.395172	+	0.396974i
$367$	−9.95497	−	9.95497i	−0.519645	−	0.519645i	0.397819	−	0.917464i	$-0.369767\pi$
$367$	−9.95497	−	9.95497i	−0.519645	−	0.519645i	−0.917464	+	0.397819i	$0.869767\pi$
$368$	4.21872	+	6.54990i	0.219916	+	0.341437i
$369$	−15.4561	−	1.32014i	−0.804614	−	0.0687235i
$370$	0.441088	−	0.206351i	0.0229311	−	0.0107277i
$371$	1.44581	+	0.966058i	0.0750626	+	0.0501552i
$372$	5.21122	−	34.6688i	0.270189	−	1.79749i
$373$	−19.3566	−	3.85026i	−1.00224	−	0.199359i	−0.333420	−	0.942779i	$-0.608203\pi$
$373$	−19.3566	−	3.85026i	−1.00224	−	0.199359i	−0.668825	+	0.743420i	$0.733203\pi$
$374$	1.10683	−	7.25121i	0.0572330	−	0.374951i
$375$	1.29836	+	0.0553470i	0.0670472	+	0.00285811i
$376$	4.31930	+	31.8881i	0.222751	+	1.64450i
$377$	2.24990	−	5.43173i	0.115876	−	0.279748i
$378$	1.85151	+	0.530967i	0.0952315	+	0.0273100i
$379$	0.800844	+	1.19855i	0.0411366	+	0.0615653i	0.851468	−	0.524407i	$-0.175713\pi$
$379$	0.800844	+	1.19855i	0.0411366	+	0.0615653i	−0.810331	+	0.585972i	$0.800713\pi$
$380$	0.191632	−	0.0172462i	0.00983050	−	0.000884711i
$381$	0.169409	−	0.695423i	0.00867910	−	0.0356276i
$382$	−28.8027	−	26.3269i	−1.47367	−	1.34700i
$383$	21.7067			1.10916			0.554580	−	0.832130i	$-0.312879\pi$
$383$	21.7067			1.10916			0.554580	+	0.832130i	$0.312879\pi$
$384$	−12.7764	+	14.8581i	−0.651992	+	0.758226i
$385$	−0.0432554			−0.00220450
$386$	5.25901	+	4.80697i	0.267677	+	0.244668i
$387$	−22.4108	−	17.9107i	−1.13920	−	0.910452i
$388$	−25.9041	+	2.33128i	−1.31508	+	0.118353i
$389$	17.4324	+	26.0894i	0.883858	+	1.32279i	0.945814	+	0.324708i	$0.105266\pi$
$389$	17.4324	+	26.0894i	0.883858	+	1.32279i	−0.0619565	+	0.998079i	$0.519734\pi$
$390$	0.138042	−	0.0926917i	0.00699004	−	0.00469363i
$391$	1.75870	−	4.24588i	0.0889413	−	0.214723i
$392$	19.4273	−	2.63145i	0.981225	−	0.132908i
$393$	0.396486	−	9.30101i	0.0200001	−	0.469174i
$394$	2.91685	−	19.1092i	0.146949	−	0.962706i
$395$	−0.618201	−	0.122968i	−0.0311050	−	0.00618718i
$396$	−7.27767	+	10.9998i	−0.365717	+	0.552762i
$397$	10.9547	+	7.31968i	0.549799	+	0.367364i	0.799227	−	0.601029i	$-0.205242\pi$
$397$	10.9547	+	7.31968i	0.549799	+	0.367364i	−0.249428	+	0.968393i	$0.580242\pi$
$398$	−15.2790	+	7.14786i	−0.765866	+	0.358290i
$399$	0.546499	−	0.199547i	0.0273591	−	0.00998986i
$400$	−4.22680	+	19.5252i	−0.211340	+	0.976259i
$401$	−20.2825	−	20.2825i	−1.01286	−	1.01286i	−0.999916	−	0.0129431i	$-0.995880\pi$
$401$	−20.2825	−	20.2825i	−1.01286	−	1.01286i	−0.0129431	−	0.999916i	$-0.504120\pi$
$402$	−3.17874	−	3.16431i	−0.158541	−	0.157822i
$403$	−7.60892	−	5.08412i	−0.379027	−	0.253258i
$404$	14.6259	+	18.1309i	0.727665	+	0.902044i
$405$	−0.242280	+	0.630709i	−0.0120390	+	0.0313402i
$406$	−1.42759	−	1.94192i	−0.0708501	−	0.0963757i
$407$	3.85857	+	9.31541i	0.191262	+	0.461748i
$408$	11.4964	+	1.20367i	0.569155	+	0.0595905i
$409$	−6.31288	+	15.2406i	−0.312152	+	0.753601i	0.687473	+	0.726210i	$0.258720\pi$
$409$	−6.31288	+	15.2406i	−0.312152	+	0.753601i	−0.999625	+	0.0273914i	$0.991280\pi$
$410$	0.131145	+	0.533073i	0.00647681	+	0.0263266i
$411$	4.01770	+	25.9257i	0.198179	+	1.27882i
$412$	−8.00976	+	25.6259i	−0.394613	+	1.26250i
$413$	−0.237465	−	1.19382i	−0.0116849	−	0.0587439i
$414$	−6.07403	+	5.60287i	−0.298522	+	0.275366i
$415$	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	$-0.848937\pi$
$419$	−31.4491	+	6.25562i	−1.53639	+	0.305607i	−0.646904	+	0.762571i	$0.723937\pi$
$420$	−0.00321291	−	0.0680885i	−0.000156774	−	0.00332238i
$421$	−9.69566	−	14.5106i	−0.472537	−	0.707202i	0.516266	−	0.856428i	$-0.327322\pi$
$421$	−9.69566	−	14.5106i	−0.472537	−	0.707202i	−0.988803	+	0.149226i	$0.952322\pi$
$422$	−1.12419	−	4.56957i	−0.0547249	−	0.222443i
$423$	−32.5304	+	10.3306i	−1.58168	+	0.502289i
$424$	−12.4243	−	14.0610i	−0.603378	−	0.682862i
$425$	10.8872	−	4.50964i	0.528109	−	0.218750i
$426$	2.72952	+	13.5609i	0.132246	+	0.657029i
$427$	1.12466	+	0.223709i	0.0544262	+	0.0108260i
$428$	28.3097	+	3.02915i	1.36840	+	0.146420i
$429$	1.78906	+	2.94145i	0.0863769	+	0.142014i
$430$	−0.346053	+	0.954465i	−0.0166881	+	0.0460284i
$431$	−13.1610	+	13.1610i	−0.633944	+	0.633944i	−0.949055	−	0.315111i	$-0.897958\pi$
$431$	−13.1610	+	13.1610i	−0.633944	+	0.633944i	0.315111	+	0.949055i	$0.397958\pi$
$432$	−17.8554	−	10.6388i	−0.859070	−	0.511858i
$433$	18.5364	+	18.5364i	0.890803	+	0.890803i	0.994599	−	0.103795i	$-0.0330987\pi$
$433$	18.5364	+	18.5364i	0.890803	+	0.890803i	−0.103795	+	0.994599i	$0.533099\pi$
$434$	−3.39805	+	1.58969i	−0.163112	+	0.0763074i
$435$	0.722322	−	0.439335i	0.0346327	−	0.0210645i
$436$	17.2878	+	9.42851i	0.827934	+	0.451544i
$437$	−0.486945	+	2.44804i	−0.0232937	+	0.117105i
$438$	−22.1293	−	14.7136i	−1.05738	−	0.703044i
$439$	8.76979	+	21.1722i	0.418559	+	1.01049i	0.982765	+	0.184858i	$0.0591824\pi$
$439$	8.76979	+	21.1722i	0.418559	+	1.01049i	−0.564206	+	0.825634i	$0.690818\pi$
$440$	0.451304	+	0.119123i	0.0215151	+	0.00567896i
$441$	6.29371	+	19.8186i	0.299700	+	0.943741i
$442$	1.56207	−	2.58145i	0.0743000	−	0.122787i
$443$	5.76224	−	3.85021i	0.273773	−	0.182929i	−0.411103	−	0.911589i	$-0.634856\pi$
$443$	5.76224	−	3.85021i	0.273773	−	0.182929i	0.684876	+	0.728660i	$0.259856\pi$
$444$	−14.3768	+	6.76572i	−0.682294	+	0.321087i
$445$	−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	$-0.0501659\pi$
$450$	−21.1721	−	0.854283i	−0.998061	−	0.0402713i
$451$	−11.1482	+	2.21752i	−0.524950	+	0.104419i
$452$	−16.4331	−	13.7195i	−0.772947	−	0.645309i
$453$	14.5397	−	2.25322i	0.683136	−	0.105866i
$454$	16.7838	+	10.1561i	0.787701	+	0.476649i
$455$	−0.0164384	−	0.00680899i	−0.000770642	−	0.000319210i
$456$	−6.25141	+	0.576945i	−0.292749	+	0.0270179i
$457$	−15.3039	+	6.33908i	−0.715886	+	0.296530i	−0.710738	−	0.703457i	$-0.751639\pi$
$457$	−15.3039	+	6.33908i	−0.715886	+	0.296530i	−0.00514839	+	0.999987i	$0.501639\pi$
$458$	−0.0351182	+	0.230070i	−0.00164097	+	0.0107505i
$459$	0.839694	+	12.2316i	0.0391935	+	0.570922i
$460$	0.256738	+	0.140021i	0.0119705	+	0.00652852i
$461$	14.2247	−	21.2887i	0.662509	−	0.991515i	−0.336253	−	0.941772i	$-0.609160\pi$
$461$	14.2247	−	21.2887i	0.662509	−	0.991515i	0.998762	−	0.0497436i	$-0.0158404\pi$
$462$	1.41137	−	0.00321069i	0.0656628	−	0.000149375i
$463$	9.91878	−	9.91878i	0.460965	−	0.460965i	−0.438007	−	0.898972i	$-0.644315\pi$
$463$	9.91878	−	9.91878i	0.460965	−	0.460965i	0.898972	+	0.438007i	$0.144315\pi$
$464$	9.54679	+	24.1924i	0.443198	+	1.12310i
$465$	−0.451352	−	1.23611i	−0.0209309	−	0.0573233i
$466$	−21.6342	−	7.84372i	−1.00218	−	0.363353i
$467$	2.12128	−	3.17472i	0.0981612	−	0.146909i	−0.779138	−	0.626852i	$-0.784343\pi$
$467$	2.12128	−	3.17472i	0.0981612	−	0.146909i	0.877299	+	0.479944i	$0.159343\pi$
$468$	−4.49726	+	3.03466i	−0.207886	+	0.140277i
$469$	−0.0936346	+	0.470733i	−0.00432365	+	0.0217364i
$470$	0.715439	+	0.973194i	0.0330007	+	0.0448901i
$471$	−22.1406	−	0.943817i	−1.02019	−	0.0434888i
$472$	−0.810119	+	13.1096i	−0.0372887	+	0.603418i
$473$	−19.4213	−	8.04455i	−0.892991	−	0.369889i
$474$	20.1802	+	3.96639i	0.926908	+	0.182182i
$475$	−5.32158	+	3.55577i	−0.244171	+	0.163150i
$476$	−0.573877	−	1.09574i	−0.0263036	−	0.0502233i
$477$	12.4250	−	15.5468i	0.568903	−	0.711839i
$478$	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	$0.966140\pi$
$480$	−0.153990	+	0.719247i	−0.00702865	+	0.0328290i
$481$			4.14753i			0.189111i
$482$	−0.586806	−	13.0670i	−0.0267283	−	0.595185i
$483$	0.859139	+	0.209292i	0.0390922	+	0.00952310i
$484$	3.68008	−	11.7738i	0.167276	−	0.535172i
$485$	−0.811728	+	0.542380i	−0.0368587	+	0.0246282i
$486$	7.85848	−	20.5972i	0.356468	−	0.934308i
$487$	18.0003	+	7.45596i	0.815670	+	0.337862i	0.751214	−	0.660059i	$-0.229469\pi$
$487$	18.0003	+	7.45596i	0.815670	+	0.337862i	0.0644565	+	0.997921i	$0.479469\pi$
$488$	−11.1180	−	5.43131i	−0.503289	−	0.245864i
$489$	−0.533314	+	12.5108i	−0.0241173	+	0.565758i
$490$	0.592901	−	0.435868i	0.0267845	−	0.0196905i
$491$	2.10722	−	10.5937i	0.0950974	−	0.478087i	−0.903660	−	0.428251i	$-0.859130\pi$
$491$	2.10722	−	10.5937i	0.0950974	−	0.478087i	0.998757	−	0.0498362i	$-0.0158699\pi$
$492$	−4.31867	−	17.3838i	−0.194701	−	0.783720i
$493$	8.52329	−	12.7560i	0.383870	−	0.574502i
$494$	−0.558561	+	1.54059i	−0.0251308	+	0.0693146i
$495$	−0.0421318	+	0.493278i	−0.00189368	+	0.0221712i
$496$	39.8313	−	7.22791i	1.78848	−	0.324543i
$497$	1.04668	−	1.04668i	0.0469500	−	0.0469500i
$498$	−29.9452	+	0.0681216i	−1.34188	+	0.00305260i
$499$	19.8260	−	29.6718i	0.887535	−	1.32829i	−0.0564854	−	0.998403i	$-0.517989\pi$
$499$	19.8260	−	29.6718i	0.887535	−	1.32829i	0.944021	−	0.329887i	$-0.107011\pi$
$500$	0.423490	+	1.43958i	0.0189390	+	0.0643802i
$501$	−13.5354	+	18.4999i	−0.604716	+	0.826513i
$502$	31.7050	+	4.83950i	1.41506	+	0.215997i
$503$	−0.0322396	+	0.0133541i	−0.00143749	+	0.000595428i	−0.383402	−	0.923582i	$-0.625248\pi$
$503$	−0.0322396	+	0.0133541i	−0.00143749	+	0.000595428i	0.381965	+	0.924177i	$0.375248\pi$
$504$	0.109887	+	2.22140i	0.00489476	+	0.0989491i
$505$	0.807826	+	0.334612i	0.0359478	+	0.0148901i
$506$	−3.13476	+	5.18045i	−0.139357	+	0.230299i
$507$	−3.23137	−	20.8516i	−0.143510	−	0.926052i
$508$	0.823162	−	0.0740817i	0.0365219	−	0.00328684i
$509$	−3.75595	+	0.747106i	−0.166480	+	0.0331149i	−0.277626	−	0.960689i	$-0.589548\pi$
$509$	−3.75595	+	0.747106i	−0.166480	+	0.0331149i	0.111147	+	0.993804i	$0.464548\pi$
$510$	0.400477	−	0.166951i	0.0177334	−	0.00739273i
$511$			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
$516$	11.2204	−	31.1686i	0.493950	−	1.37212i
$517$	−20.7947	+	13.8946i	−0.914549	+	0.611082i
$518$	1.45468	+	0.880248i	0.0639150	+	0.0386759i
$519$	28.2752	+	30.7932i	1.24114	+	1.35167i
$520$	0.152757	+	0.116312i	0.00669885	+	0.00510060i
$521$	5.37144	+	12.9678i	0.235327	+	0.568130i	0.996788	−	0.0800804i	$-0.0255177\pi$
$521$	5.37144	+	12.9678i	0.235327	+	0.568130i	−0.761461	+	0.648210i	$0.775518\pi$
$522$	−23.5358	+	14.3885i	−1.03013	+	0.629770i
$523$	−2.63083	+	13.2261i	−0.115038	+	0.578337i	0.879669	+	0.475587i	$0.157764\pi$
$523$	−2.63083	+	13.2261i	−0.115038	+	0.578337i	−0.994707	+	0.102750i	$0.967236\pi$
$524$	10.3127	−	3.03373i	0.450511	−	0.132529i
$525$	1.17828	+	1.93723i	0.0514241	+	0.0845478i
$526$	−16.0776	−	34.3669i	−0.701018	−	1.49847i
$527$	−16.8852	−	16.8852i	−0.735533	−	0.735533i
$528$	−14.7343	−	3.85332i	−0.641228	−	0.167694i
$529$	13.5809	−	13.5809i	0.590475	−	0.590475i
$530$	−0.662132	−	0.240064i	−0.0287612	−	0.0104277i
$531$	−13.8454	+	1.54521i	−0.600839	+	0.0670563i
$532$	0.421794	+	0.522873i	0.0182871	+	0.0226694i
$533$	−4.58573	−	0.912158i	−0.198630	−	0.0395100i
$534$	7.09976	+	35.2733i	0.307237	+	1.52643i
$535$	0.987343	−	0.408971i	0.0426866	−	0.0176814i
$536$	2.27330	−	4.65351i	0.0981918	−	0.201001i
$537$	14.3712	+	15.6510i	0.620164	+	0.675392i
$538$	19.5076	−	4.79920i	0.841031	−	0.206908i
$539$	8.46501	+	12.6688i	0.364614	+	0.545683i
$540$	−0.779600	−	0.0296803i	−0.0335487	−	0.00127724i
$541$	26.2221	−	5.21590i	1.12738	−	0.224249i	0.404037	−	0.914743i	$-0.367607\pi$
$541$	26.2221	−	5.21590i	1.12738	−	0.224249i	0.723339	+	0.690494i	$0.242607\pi$
$542$	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
$546$	0.536868	+	0.220948i	0.0229758	+	0.00945572i
$547$	−6.71870	−	33.7772i	−0.287271	−	1.44421i	−0.807341	−	0.590085i	$-0.799094\pi$
$547$	−6.71870	−	33.7772i	−0.287271	−	1.44421i	0.520070	−	0.854124i	$-0.325906\pi$
$548$	−26.8360	+	14.0549i	−1.14638	+	0.600396i
$549$	3.64659	−	12.6076i	0.155633	−	0.538078i
$550$	−15.0768	+	3.70916i	−0.642877	+	0.158159i
$551$	−3.18860	+	7.69796i	−0.135839	+	0.327944i
$552$	−8.38741	−	4.54965i	−0.356992	−	0.193646i
$553$	−0.842194	−	2.03324i	−0.0358137	−	0.0864620i
$554$	28.0875	−	20.6484i	1.19333	−	0.877267i
$555$	−0.352169	+	0.481338i	−0.0149488	+	0.0204317i
$556$	17.5230	+	1.87496i	0.743139	+	0.0795161i
$557$	−11.7060	−	7.82170i	−0.495999	−	0.331416i	0.282282	−	0.959331i	$-0.408908\pi$
$557$	−11.7060	−	7.82170i	−0.495999	−	0.331416i	−0.778282	+	0.627915i	$0.783908\pi$
$558$	14.8188	+	40.2992i	0.627328	+	1.70600i
$559$	−6.11434	−	6.11434i	−0.258609	−	0.258609i
$560$	0.0732148	−	0.0288920i	0.00309389	−	0.00122091i
$561$	3.08132	+	8.43878i	0.130093	+	0.356286i
$562$	13.8489	+	29.6028i	0.584179	+	1.24872i
$563$	1.45663	+	0.973290i	0.0613897	+	0.0410193i	0.585886	−	0.810393i	$-0.300746\pi$
$563$	1.45663	+	0.973290i	0.0613897	+	0.0410193i	−0.524497	+	0.851412i	$0.675746\pi$
$564$	−23.4161	−	31.7009i	−0.985995	−	1.33485i
$565$	−0.788096	−	0.156762i	−0.0331554	−	0.00659503i
$566$	3.58572	+	0.547330i	0.150719	+	0.0230060i
$567$	−2.30099	+	0.520079i	−0.0966325	+	0.0218413i
$568$	−13.8030	+	8.03800i	−0.579161	+	0.337267i
$569$	−3.39021	+	8.18469i	−0.142125	+	0.343120i	−0.978873	−	0.204468i	$-0.934454\pi$
$569$	−3.39021	+	8.18469i	−0.142125	+	0.343120i	0.836748	+	0.547588i	$0.184454\pi$
$570$	−0.195636	+	0.131365i	−0.00819430	+	0.00550226i
$571$	18.1245	+	27.1252i	0.758486	+	1.13515i	0.986859	+	0.161581i	$0.0516593\pi$
$571$	18.1245	+	27.1252i	0.758486	+	1.13515i	−0.228373	+	0.973574i	$0.573341\pi$
$572$	−2.54775	+	3.05168i	−0.106527	+	0.127597i
$573$	46.4338	+	11.3116i	1.93980	+	0.472548i
$574$	−1.29317	+	1.41478i	−0.0539761	+	0.0590519i
$575$	−9.72770			−0.405673
$576$	4.97110	−	23.4795i	0.207129	−	0.978314i
$577$	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
$579$	−8.47824	−	2.06535i	−0.352344	−	0.0858331i
$580$	0.749392	+	0.625644i	0.0311168	+	0.0259784i
$581$	1.78026	+	2.66435i	0.0738576	+	0.110536i
$582$	26.4454	−	17.7574i	1.09620	−	0.736068i
$583$	5.58067	−	13.4729i	0.231128	−	0.557992i
$584$	7.83129	−	29.6693i	0.324061	−	1.22772i
$585$	−0.0936600	+	0.180828i	−0.00387236	+	0.00747633i
$586$	−26.3751	−	4.02593i	−1.08954	−	0.166309i
$587$	34.1088	+	6.78466i	1.40782	+	0.280033i	0.839762	−	0.542955i	$-0.182694\pi$
$587$	34.1088	+	6.78466i	1.40782	+	0.280033i	0.568059	+	0.822988i	$0.307694\pi$
$588$	−19.3132	+	14.2658i	−0.796464	+	0.588312i
$589$	10.7835	+	7.20532i	0.444327	+	0.296890i
$590$	0.208914	+	0.446565i	0.00860084	+	0.0183848i
$591$	8.12023	+	22.2388i	0.334022	+	0.914782i
$592$	−12.7532	−	13.1901i	−0.524154	−	0.542111i
$593$	−1.14918	−	1.14918i	−0.0471910	−	0.0471910i	0.683118	−	0.730308i	$-0.260624\pi$
$593$	−1.14918	−	1.14918i	−0.0471910	−	0.0471910i	−0.730308	+	0.683118i	$0.760624\pi$
$594$	1.33809	−	16.0982i	0.0549025	−	0.660515i
$595$	−0.0386042	−	0.0257945i	−0.00158262	−	0.00105747i
$596$	1.30578	−	12.2035i	0.0534869	−	0.499876i
$597$	12.1989	−	16.6732i	0.499268	−	0.682389i
$598$	−2.00678	+	1.47527i	−0.0820633	+	0.0603284i
$599$	1.00985	+	2.43798i	0.0412612	+	0.0996132i	0.943167	−	0.332320i	$-0.107831\pi$
$599$	1.00985	+	2.43798i	0.0412612	+	0.0996132i	−0.901905	+	0.431934i	$0.857831\pi$
$600$	−6.95847	−	23.4569i	−0.284078	−	0.957625i
$601$	−1.00588	+	2.42841i	−0.0410307	+	0.0990568i	−0.943066	−	0.332605i	$-0.892073\pi$
$601$	−1.00588	+	2.42841i	−0.0410307	+	0.0990568i	0.902036	+	0.431662i	$0.142073\pi$
$602$	−3.44218	+	0.846838i	−0.140293	+	0.0345145i
$603$	5.27697	+	1.52630i	0.214895	+	0.0621557i
$604$	7.88232	+	15.0502i	0.320727	+	0.612386i
$605$	−0.0903312	−	0.454126i	−0.00367249	−	0.0184628i
$606$	−26.3832	−	10.8580i	−1.07174	−	0.441076i
$607$	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
$612$	−13.0546	+	5.47713i	−0.527703	+	0.221400i
$613$	−16.8711	−	25.2494i	−0.681417	−	1.01981i	−0.997471	−	0.0710711i	$-0.977358\pi$
$613$	−16.8711	−	25.2494i	−0.681417	−	1.01981i	0.316055	−	0.948741i	$-0.397642\pi$
$614$	−18.1677	+	4.46958i	−0.733189	+	0.180377i
$615$	−0.454741	−	0.495237i	−0.0183369	−	0.0199699i
$616$	0.529610	+	1.54126i	0.0213386	+	0.0620990i
$617$	15.9796	−	6.61898i	0.643316	−	0.266470i	−0.0370828	−	0.999312i	$-0.511807\pi$
$617$	15.9796	−	6.61898i	0.643316	−	0.266470i	0.680399	+	0.732842i	$0.261807\pi$
$618$	−6.48842	−	32.2361i	−0.261003	−	1.29672i
$619$	34.6693	+	6.89615i	1.39348	+	0.277180i	0.834045	−	0.551696i	$-0.186019\pi$
$619$	34.6693	+	6.89615i	1.39348	+	0.277180i	0.559432	+	0.828876i	$0.311019\pi$
$620$	1.18268	−	0.954045i	0.0474974	−	0.0383154i
$621$	3.22355	−	9.59363i	0.129357	−	0.384979i
$622$	6.25983	+	2.26958i	0.250996	+	0.0910017i
$623$	2.72252	−	2.72252i	0.109075	−	0.109075i
$624$	−4.99291	−	3.78376i	−0.199876	−	0.151471i
$625$	−17.6179	−	17.6179i	−0.704717	−	0.704717i
$626$	5.73146	+	12.2513i	0.229075	+	0.489662i
$627$	−2.53550	−	4.16868i	−0.101258	−	0.166481i
$628$	−7.22165	−	24.5488i	−0.288175	−	0.979604i
$629$	−2.11140	+	10.6147i	−0.0841870	+	0.423237i
$630$	0.0435449	+	0.0712278i	0.00173487	+	0.00283778i
$631$	1.74700	+	4.21763i	0.0695470	+	0.167901i	0.954831	−	0.297150i	$-0.0960360\pi$
$631$	1.74700	+	4.21763i	0.0695470	+	0.167901i	−0.885284	+	0.465051i	$0.846036\pi$
$632$	3.18759	+	23.5330i	0.126795	+	0.936094i
$633$	3.89810	+	4.24523i	0.154935	+	0.168733i
$634$	2.27834	+	1.37866i	0.0904845	+	0.0547534i
$635$	0.0257945	−	0.0172354i	0.00102363	−	0.000683964i
$636$	21.6223	+	7.78382i	0.857381	+	0.308649i
$637$	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	$0.785695\pi$
$642$	−32.1854	+	13.4175i	−1.27025	+	0.529545i
$643$	24.3933	−	4.85212i	0.961976	−	0.191349i	0.310969	−	0.950420i	$-0.399347\pi$
$643$	24.3933	−	4.85212i	0.961976	−	0.191349i	0.651008	+	0.759071i	$0.274347\pi$
$644$	0.0915220	+	1.01695i	0.00360647	+	0.0400734i
$645$	−0.190422	−	1.22877i	−0.00749787	−	0.0483827i
$646$	−2.21380	+	3.65848i	−0.0871006	+	0.143941i
$647$	−17.3176	−	7.17319i	−0.680826	−	0.282007i	0.0153463	−	0.999882i	$-0.495115\pi$
$647$	−17.3176	−	7.17319i	−0.680826	−	0.282007i	−0.696172	+	0.717875i	$0.745115\pi$
$648$	25.4396	+	0.910562i	0.999360	+	0.0357703i
$649$	−9.43108	+	3.90648i	−0.370202	+	0.153343i
$650$	−6.31351	−	0.963702i	−0.247636	−	0.0377995i
$651$	2.71304	−	3.70813i	0.106332	−	0.145333i
$652$	−13.8716	+	4.08067i	−0.543253	+	0.159812i
$653$	18.8122	−	28.1544i	0.736178	−	1.10177i	−0.254702	−	0.967020i	$-0.581977\pi$
$653$	18.8122	−	28.1544i	0.736178	−	1.10177i	0.990880	−	0.134748i	$-0.0430225\pi$
$654$	−24.1173	+	0.0548638i	−0.943060	+	0.00214535i
$655$	0.285314	−	0.285314i	0.0111482	−	0.0111482i
$656$	17.3885	−	11.1998i	0.678907	−	0.437277i
$657$	32.4288	+	2.76980i	1.26517	+	0.108060i
$658$	−1.43748	+	3.96479i	−0.0560389	+	0.154564i
$659$	2.59960	−	3.89057i	0.101266	−	0.151555i	−0.777376	−	0.629036i	$-0.783450\pi$
$659$	2.59960	−	3.89057i	0.101266	−	0.151555i	0.878642	+	0.477481i	$0.158450\pi$
$660$	−0.554798	+	0.137829i	−0.0215955	+	0.00536500i
$661$	−5.49642	+	27.6324i	−0.213786	+	1.07477i	0.713567	+	0.700587i	$0.247078\pi$
$661$	−5.49642	+	27.6324i	−0.213786	+	1.07477i	−0.927353	+	0.374187i	$0.877922\pi$
$662$	32.0381	−	23.5527i	1.24520	−	0.915401i
$663$	−0.157385	+	3.69203i	−0.00611233	+	0.143387i
$664$	−11.2368	−	32.7011i	−0.436073	−	1.26905i
$665$	0.0232968	+	0.00964984i	0.000903410	+	0.000374205i
$666$	11.4551	−	15.7316i	0.443876	−	0.609586i
$667$	−10.5299	+	7.03582i	−0.407718	+	0.272428i
$668$	−25.2636	−	7.89651i	−0.977476	−	0.305525i
$669$	−21.2232	−	5.17009i	−0.820535	−	0.199887i
$670$	−0.00872129	−	0.194205i	−0.000336933	−	0.00750281i
$671$		−	9.61679i		−	0.371252i
$672$	−2.38676	+	0.948142i	−0.0920713	+	0.0365754i
$673$		−	11.0254i		−	0.424996i	−0.977161	−	0.212498i	$-0.931840\pi$
$673$		−	11.0254i		−	0.424996i	0.977161	−	0.212498i	$-0.0681599\pi$
$674$	29.7433	−	1.33570i	1.14567	−	0.0514492i
$675$	23.2396	−	11.5500i	0.894491	−	0.444558i
$676$	21.5837	−	11.3041i	0.830144	−	0.434774i
$677$	−10.9422	+	7.31133i	−0.420542	+	0.280997i	−0.747782	−	0.663944i	$-0.768881\pi$
$677$	−10.9422	+	7.31133i	−0.420542	+	0.280997i	0.327240	+	0.944941i	$0.393881\pi$
$678$	25.7262	+	5.05644i	0.988008	+	0.194192i
$679$	−3.14917	−	1.30443i	−0.120854	−	0.0500594i
$680$	0.331739	+	0.375440i	0.0127216	+	0.0143975i
$681$	−24.0045	−	1.02327i	−0.919853	−	0.0392118i
$682$	18.6355	+	25.3494i	0.713589	+	0.970677i
$683$	−6.11205	+	30.7273i	−0.233871	+	1.17575i	0.668140	+	0.744036i	$0.267091\pi$
$683$	−6.11205	+	30.7273i	−0.233871	+	1.17575i	−0.902011	+	0.431713i	$0.857909\pi$
$684$	6.37360	−	4.30078i	0.243701	−	0.164444i
$685$	−0.631737	+	0.945461i	−0.0241374	+	0.0361242i
$686$	4.85490	+	1.76020i	0.185361	+	0.0672048i
$687$	−0.0977658	−	0.267750i	−0.00373000	−	0.0102153i
$688$	38.2460	+	0.644123i	1.45812	+	0.0245570i
$689$	4.24165	−	4.24165i	0.161594	−	0.161594i
$690$	−0.358162		0.000814773i	−0.0136350		3.10179e-5i
$691$	3.78957	−	5.67149i	0.144162	−	0.215754i	−0.752361	−	0.658751i	$-0.771085\pi$
$691$	3.78957	−	5.67149i	0.144162	−	0.215754i	0.896523	+	0.442998i	$0.146085\pi$
$692$	−23.1133	+	42.3798i	−0.878637	+	1.61104i
$693$	−1.51377	+	0.834545i	−0.0575032	+	0.0317017i
$694$	−4.11311	+	26.9462i	−0.156131	+	1.02286i
$695$	0.611138	−	0.253142i	0.0231818	−	0.00960222i
$696$	−24.4981	−	20.3583i	−0.928600	−	0.771680i
$697$	−11.2719	−	4.66896i	−0.426952	−	0.176849i
$698$	−22.3269	−	13.5103i	−0.845087	−	0.511374i
$699$	27.8516	−	4.31616i	1.05344	−	0.163252i
$700$	−1.67795	+	2.00983i	−0.0634204	+	0.0759646i
$701$	−45.6378	+	9.07793i	−1.72372	+	0.342869i	−0.954974	−	0.296689i	$-0.904118\pi$
$701$	−45.6378	+	9.07793i	−1.72372	+	0.342869i	−0.768743	+	0.639558i	$0.779118\pi$
$702$	3.04258	−	5.90715i	0.114835	−	0.222951i
$703$		−	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
$708$	−6.84973	−	14.5553i	−0.257429	−	0.547023i
$709$	−32.9914	+	22.0441i	−1.23902	+	0.827885i	−0.990062	−	0.140630i	$-0.955087\pi$
$709$	−32.9914	+	22.0441i	−1.23902	+	0.827885i	−0.248955	+	0.968515i	$0.580087\pi$
$710$	−0.310394	+	0.512951i	−0.0116489	+	0.0192507i
$711$	−24.0070	+	7.62383i	−0.900334	+	0.285916i
$712$	−35.9030	+	20.9077i	−1.34552	+	0.783547i
$713$	7.54344	+	18.2115i	0.282504	+	0.682025i
$714$	1.26152	+	0.838776i	0.0472112	+	0.0313904i
$715$	−0.0291113	+	0.146352i	−0.00108870	+	0.00547327i
$716$	−11.7477	+	21.5401i	−0.439030	+	0.804990i
$717$	−20.7437	+	12.6169i	−0.774687	+	0.471185i
$718$	−20.4858	+	9.58372i	−0.764522	+	0.357661i
$719$	−27.3837	−	27.3837i	−1.02124	−	1.02124i	−0.999770	−	0.0214686i	$-0.993166\pi$
$719$	−27.3837	−	27.3837i	−1.02124	−	1.02124i	−0.0214686	−	0.999770i	$-0.506834\pi$
$720$	−0.258167	−	0.863072i	−0.00962130	−	0.0321648i
$721$	−2.48809	+	2.48809i	−0.0926614	+	0.0926614i
$722$	−8.36708	+	23.0776i	−0.311390	+	0.858861i
$723$	8.32478	+	13.6870i	0.309602	+	0.509025i
$724$	−2.24409	+	20.9728i	−0.0834011	+	0.779447i
$725$	−31.8493	−	6.33523i	−1.18285	−	0.235284i
$726$	2.98110	+	14.8108i	0.110639	+	0.549681i
$727$	0.372141	−	0.154146i	0.0138019	−	0.00571695i	−0.375772	−	0.926712i	$-0.622622\pi$
$727$	0.372141	−	0.154146i	0.0138019	−	0.00571695i	0.389574	+	0.920995i	$0.372622\pi$
$728$	−0.0413471	+	0.669092i	−0.00153243	+	0.0247982i
$729$	3.68969	+	26.7467i	0.136655	+	0.990619i
$730$	−0.275158	−	1.11845i	−0.0101841	−	0.0413957i
$731$	−12.5357	−	18.7610i	−0.463650	−	0.693902i
$732$	15.1378	−	0.714313i	0.559510	−	0.0264018i
$733$	−20.6905	+	4.11560i	−0.764223	+	0.152013i	−0.561787	−	0.827282i	$-0.689886\pi$
$733$	−20.6905	+	4.11560i	−0.764223	+	0.152013i	−0.202436	+	0.979295i	$0.564886\pi$
$734$	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
$738$	14.8744	+	16.1252i	0.547533	+	0.593577i
$739$	−1.24476	−	6.25783i	−0.0457892	−	0.230198i	0.951114	−	0.308841i	$-0.0999412\pi$
$739$	−1.24476	−	6.25783i	−0.0457892	−	0.230198i	−0.996903	+	0.0786433i	$0.974941\pi$
$740$	−0.657319	−	0.205455i	−0.0241635	−	0.00755268i
$741$	−0.307359	−	1.98335i	−0.0112911	−	0.0728600i
$742$	−0.587469	−	2.38791i	−0.0215667	−	0.0876631i
$743$	14.4970	−	34.9988i	0.531843	−	1.28398i	−0.398459	−	0.917186i	$-0.630455\pi$
$743$	14.4970	−	34.9988i	0.531843	−	1.28398i	0.930302	−	0.366795i	$-0.119545\pi$
$744$	−38.5183	+	31.2170i	−1.41215	+	1.14447i
$745$	−0.176296	−	0.425615i	−0.00645897	−	0.0155933i
$746$	16.5318	+	22.4878i	0.605272	+	0.823337i
$747$	32.1178	−	17.7067i	1.17513	−	0.647853i
$748$	−8.07397	+	6.51315i	−0.295214	+	0.238144i
$749$	3.10253	+	2.07304i	0.113364	+	0.0757474i
$750$	−1.30250	−	1.29658i	−0.0475604	−	0.0473445i
$751$	16.0660	+	16.0660i	0.586258	+	0.586258i	0.936616	−	0.350358i	$-0.113940\pi$
$751$	16.0660	+	16.0660i	0.586258	+	0.586258i	−0.350358	+	0.936616i	$0.613940\pi$
$752$	25.9167	−	37.4078i	0.945085	−	1.36412i
$753$	−36.8976	+	13.4727i	−1.34462	+	0.490972i
$754$	−7.53115	+	3.52325i	−0.274268	+	0.128309i
$755$	0.530237	+	0.354293i	0.0192973	+	0.0128940i
$756$	−1.42610	−	2.32084i	−0.0518667	−	0.0844081i
$757$	−46.1515	−	9.18010i	−1.67740	−	0.333656i	−0.737566	−	0.675276i	$-0.764025\pi$
$757$	−46.1515	−	9.18010i	−1.67740	−	0.333656i	−0.939838	+	0.341619i	$0.889025\pi$
$758$	0.307606	−	2.01522i	0.0111728	−	0.0731961i
$759$	0.315841	−	7.40918i	0.0114643	−	0.268936i
$760$	−0.216491	−	0.164839i	−0.00785295	−	0.00597934i
$761$	−13.3019	+	32.1135i	−0.482192	+	1.16412i	0.476373	+	0.879243i	$0.341951\pi$
$761$	−13.3019	+	32.1135i	−0.482192	+	1.16412i	−0.958566	+	0.284872i	$0.908049\pi$
$762$	−0.840363	+	0.564282i	−0.0304431	+	0.0204418i
$763$	1.43379	+	2.14581i	0.0519065	+	0.0776836i
$764$	4.94649	+	54.9631i	0.178958	+	1.98849i
$765$	−0.331758	+	0.415112i	−0.0119947	+	0.0150084i
$766$	−22.6587	−	20.7110i	−0.818691	−	0.748320i
$767$	−4.19903			−0.151618
$768$	27.5133	−	3.31941i	0.992801	−	0.119779i
$769$	−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
$771$	0.101638	−	0.417220i	0.00366039	−	0.0150258i
$772$	−0.903167	−	10.0356i	−0.0325057	−	0.361188i
$773$	−3.03986	−	4.54947i	−0.109336	−	0.163633i	0.772766	−	0.634691i	$-0.218872\pi$
$773$	−3.03986	−	4.54947i	−0.109336	−	0.163633i	−0.882103	+	0.471057i	$0.843872\pi$
$774$	6.30444	+	40.0790i	0.226608	+	1.44061i
$775$	−19.3428	+	46.6977i	−0.694815	+	1.67743i
$776$	29.2644	+	22.2824i	1.05053	+	0.799890i
$777$	−2.08051	−	0.0886888i	−0.0746380	−	0.00318169i
$778$	6.69582	−	43.8664i	0.240057	−	1.57269i
$779$	6.49899	+	1.29273i	0.232851	+	0.0463168i
$780$	−0.232536	−	0.0349535i	−0.00832613	−	0.00125154i
$781$	−10.3219	−	6.89685i	−0.369345	−	0.246789i
$782$	−5.88695	+	2.75405i	−0.210517	+	0.0984847i
$783$	16.8021	−	29.3110i	0.600458	−	1.04749i
$784$	−22.7900	−	15.7893i	−0.813929	−	0.563903i
$785$	−0.679177	−	0.679177i	−0.0242409	−	0.0242409i
$786$	−9.28826	+	9.33061i	−0.331301	+	0.332812i
$787$	−4.45487	−	2.97665i	−0.158799	−	0.106106i	0.473632	−	0.880723i	$-0.342943\pi$
$787$	−4.45487	−	2.97665i	−0.158799	−	0.106106i	−0.632431	+	0.774617i	$0.717943\pi$
$788$	−21.2774	+	17.1642i	−0.757976	+	0.611448i
$789$	37.5029	+	27.4389i	1.33514	+	0.976849i
$790$	0.527985	+	0.718205i	0.0187849	+	0.0255526i
$791$	−1.07365	−	2.59201i	−0.0381745	−	0.0921614i
$792$	18.0921	−	4.53837i	0.642875	−	0.161264i
$793$	1.51381	−	3.65467i	0.0537571	−	0.129781i
$794$	−4.45117	−	18.0929i	−0.157966	−	0.642092i
$795$	0.852422	−	0.132100i	0.0302323	−	0.00468510i
$796$	22.7691	+	7.11681i	0.807028	+	0.252249i
$797$	−1.68618	−	8.47701i	−0.0597276	−	0.300271i	0.939362	−	0.342927i	$-0.111418\pi$
$797$	−1.68618	−	8.47701i	−0.0597276	−	0.300271i	−0.999090	+	0.0426555i	$0.986418\pi$
$798$	−0.760860	−	0.313133i	−0.0269341	−	0.0110848i
$799$	−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
$804$	0.298980	+	6.33603i	0.0105442	+	0.223454i
$805$	0.0212929	+	0.0318671i	0.000750476	+	0.00112317i
$806$	3.09170	+	12.5670i	0.108900	+	0.442653i
$807$	−18.1230	+	16.6410i	−0.637959	+	0.585793i
$808$	2.03191	−	32.8810i	0.0714823	−	1.15675i
$809$	13.8531	−	5.73816i	0.487050	−	0.201743i	−0.125625	−	0.992078i	$-0.540094\pi$
$809$	13.8531	−	5.73816i	0.487050	−	0.201743i	0.612675	+	0.790335i	$0.290094\pi$
$810$	0.854684	−	0.427202i	0.0300306	−	0.0150103i
$811$	−20.2295	−	4.02389i	−0.710352	−	0.141298i	−0.173327	−	0.984864i	$-0.555452\pi$
$811$	−20.2295	−	4.02389i	−0.710352	−	0.141298i	−0.537025	+	0.843566i	$0.680452\pi$
$812$	−0.362644	+	3.38919i	−0.0127263	+	0.118937i
$813$	−16.5620	+	10.0735i	−0.580856	+	0.353292i
$814$	4.86033	−	13.4055i	0.170355	−	0.469863i
$815$	−0.383776	+	0.383776i	−0.0134431	+	0.0134431i
$816$	−10.8521	−	12.2255i	−0.379899	−	0.427978i
$817$	8.66537	+	8.66537i	0.303163	+	0.303163i
$818$	21.1313	−	9.88572i	0.738839	−	0.345646i
$819$	−0.706645	+	0.0788648i	−0.0246922	+	0.00275576i
$820$	0.371725	−	0.681582i	0.0129812	−	0.0238019i
$821$	9.97627	−	50.1541i	0.348174	−	1.75039i	−0.268602	−	0.963251i	$-0.586562\pi$
$821$	9.97627	−	50.1541i	0.348174	−	1.75039i	0.616776	−	0.787138i	$-0.288438\pi$
$822$	20.5426	−	30.8961i	0.716505	−	1.07762i
$823$	−6.20664	−	14.9842i	−0.216350	−	0.522315i	0.778025	−	0.628233i	$-0.216222\pi$
$823$	−6.20664	−	14.9842i	−0.216350	−	0.522315i	−0.994375	+	0.105919i	$0.966222\pi$
$824$	32.8115	−	19.1074i	1.14304	−	0.665637i
$825$	14.0067	−	12.8613i	0.487650	−	0.447775i
$826$	−0.891178	+	1.47274i	−0.0310080	+	0.0512433i
$827$	20.0660	−	13.4077i	0.697763	−	0.466230i	−0.155416	−	0.987849i	$-0.549672\pi$
$827$	20.0660	−	13.4077i	0.697763	−	0.466230i	0.853178	+	0.521619i	$0.174672\pi$
$828$	11.6863	−	0.0531700i	0.406127	−	0.00184779i
$829$	0.773289	+	3.88759i	0.0268575	+	0.135022i	0.991888	−	0.127117i	$-0.0405723\pi$
$829$	0.773289	+	3.88759i	0.0268575	+	0.135022i	−0.965030	+	0.262138i	$0.915572\pi$
$830$	−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
$834$	−19.9219	+	8.30505i	−0.689838	+	0.287580i
$835$	−0.974438	+	0.193828i	−0.0337218	+	0.00670769i
$836$	3.61073	−	4.32491i	0.124880	−	0.149580i
$837$	−39.6443	−	34.5509i	−1.37031	−	1.19425i
$838$	38.7970	+	23.4766i	1.34022	+	0.810986i
$839$	−38.8599	−	16.0963i	−1.34159	−	0.555705i	−0.407652	−	0.913137i	$-0.633652\pi$
$839$	−38.8599	−	16.0963i	−1.34159	−	0.555705i	−0.933939	+	0.357432i	$0.883652\pi$
$840$	−0.0616115	+	0.0741401i	−0.00212580	+	0.00255808i
$841$	−12.2653	+	5.08045i	−0.422941	+	0.175188i
$842$	−3.72412	+	24.3979i	−0.128342	+	0.840806i
$843$	−32.3041	−	23.6352i	−1.11261	−	0.814038i
$844$	−3.18647	+	5.84260i	−0.109683	+	0.201110i
$845$	0.508096	−	0.760419i	0.0174790	−	0.0261592i
$846$	43.8137	+	20.2546i	1.50635	+	0.696369i
$847$	1.14315	−	1.14315i	0.0392792	−	0.0392792i
$848$	−0.446842	+	26.5321i	−0.0153446	+	0.911115i
$849$	−4.17298	+	1.52371i	−0.143216	+	0.0522937i
$850$	−15.6675	−	5.68044i	−0.537391	−	0.194837i
$851$	4.96342	−	7.42829i	0.170144	−	0.254638i
$852$	10.0897	−	16.7600i	0.345666	−	0.574187i
$853$	10.2912	−	51.7372i	0.352363	−	1.77145i	−0.245046	−	0.969511i	$-0.578803\pi$
$853$	10.2912	−	51.7372i	0.352363	−	1.77145i	0.597409	−	0.801937i	$-0.296197\pi$
$854$	−0.960536	−	1.30659i	−0.0328689	−	0.0447107i
$855$	0.132737	−	0.256274i	0.00453951	−	0.00876437i
$856$	−26.6611	−	30.1732i	−0.911257	−	1.03130i
$857$	35.5270	+	14.7158i	1.21358	+	0.502681i	0.895363	−	0.445338i	$-0.146916\pi$
$857$	35.5270	+	14.7158i	1.21358	+	0.502681i	0.318216	+	0.948018i	$0.396916\pi$
$858$	0.939000	−	4.77745i	0.0320569	−	0.163099i
$859$	31.9131	−	21.3237i	1.08886	−	0.727554i	0.124520	−	0.992217i	$-0.460261\pi$
$859$	31.9131	−	21.3237i	1.08886	−	0.727554i	0.964341	+	0.264663i	$0.0852608\pi$
$860$	1.27191	−	0.666144i	0.0433719	−	0.0227153i
$861$	0.555623	−	2.28082i	0.0189356	−	0.0777302i
$862$	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	$-0.413389\pi$
$864$	8.48771	+	28.1418i	0.288758	+	0.957402i
$865$			1.81196i			0.0616084i
$866$	−1.66317	−	37.0355i	−0.0565169	−	1.25852i
$867$	4.68683	−	19.2394i	0.159173	−	0.653403i
$868$	5.06384	+	1.58278i	0.171878	+	0.0537231i
$869$	−15.3462	+	10.2540i	−0.520585	+	0.347844i
$870$	−1.17318	−	0.230587i	−0.0397746	−	0.00781765i
$871$	1.52968	+	0.633615i	0.0518313	+	0.0214692i
$872$	−9.04991	−	26.3368i	−0.306469	−	0.891877i
$873$	−17.9429	+	34.6421i	−0.607275	+	1.17246i
$874$	2.84405	−	2.09079i	0.0962013	−	0.0707219i
$875$	−0.0383669	+	0.192884i	−0.00129704	+	0.00652066i
$876$	9.06108	+	36.4732i	0.306145	+	1.23231i
$877$	−18.4579	+	27.6242i	−0.623279	+	0.932802i	0.376700	+	0.926335i	$0.377059\pi$
$877$	−18.4579	+	27.6242i	−0.623279	+	0.932802i	−0.999979	+	0.00646722i	$0.997941\pi$
$878$	11.0466	−	30.4682i	0.372805	−	1.02825i
$879$	30.6947	−	11.2078i	1.03531	−	0.378030i
$880$	−0.357437	−	0.554950i	−0.0120492	−	0.0187074i
$881$	28.1610	−	28.1610i	0.948767	−	0.948767i	−0.0499827	−	0.998750i	$-0.515917\pi$
$881$	28.1610	−	28.1610i	0.948767	−	0.948767i	0.998750	+	0.0499827i	$0.0159166\pi$
$882$	12.3398	−	26.6927i	0.415502	−	0.898791i
$883$	−7.45192	+	11.1526i	−0.250777	+	0.375314i	−0.935405	−	0.353578i	$-0.884965\pi$
$883$	−7.45192	+	11.1526i	−0.250777	+	0.375314i	0.684628	+	0.728893i	$0.259965\pi$
$884$	−4.09361	+	1.20424i	−0.137683	+	0.0405029i
$885$	−0.487315	−	0.356542i	−0.0163809	−	0.0119850i
$886$	−9.68855	−	1.47887i	−0.325493	−	0.0496837i
$887$	−23.8945	+	9.89741i	−0.802298	+	0.332323i	−0.745876	−	0.666085i	$-0.767969\pi$
$887$	−23.8945	+	9.89741i	−0.802298	+	0.332323i	−0.0564213	+	0.998407i	$0.517969\pi$
$888$	21.4627	+	6.65494i	0.720241	+	0.223325i
$889$	0.100072	+	0.0414513i	0.00335631	+	0.00139023i
$890$	−0.807366	+	1.33424i	−0.0270630	+	0.0447237i
$891$	8.04258	+	18.0756i	0.269437	+	0.605556i
$892$	−2.26085	−	25.1215i	−0.0756989	−	0.841131i
$893$	14.2995	−	2.84434i	0.478514	−	0.0951823i
$894$	5.78389	+	13.8742i	0.193442	+	0.464022i
$895$			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
$900$	21.2855	+	21.0927i	0.709516	+	0.703089i
$901$	13.0149	−	8.69629i	0.433590	−	0.289715i
$902$	13.7529	+	8.32210i	0.457923	+	0.277096i
$903$	3.19787	−	2.93638i	0.106418	−	0.0977164i
$904$	4.06360	+	30.0004i	0.135153	+	0.997799i
$905$	0.302979	+	0.731455i	0.0100714	+	0.0243144i
$906$	−17.3272	−	11.5208i	−0.575659	−	0.382752i
$907$	−0.344578	+	1.73231i	−0.0114415	+	0.0575205i	−0.986084	−	0.166246i	$-0.946835\pi$
$907$	−0.344578	+	1.73231i	−0.0114415	+	0.0575205i	0.974643	+	0.223767i	$0.0718354\pi$
$908$	−7.82958	−	26.6154i	−0.259834	−	0.883262i
$909$	34.7265	−	3.87563i	1.15181	−	0.128547i
$910$	0.0106626	+	0.0227919i	0.000353462	+	0.000755546i
$911$	16.1986	+	16.1986i	0.536684	+	0.536684i	0.922554	−	0.385869i	$-0.126098\pi$
$911$	16.1986	+	16.1986i	0.536684	+	0.536684i	−0.385869	+	0.922554i	$0.626098\pi$
$912$	7.07605	+	5.36242i	0.234311	+	0.177567i
$913$	19.0025	−	19.0025i	0.628893	−	0.628893i
$914$	22.0234	+	7.98484i	0.728469	+	0.264115i
$915$	0.486005	−	0.295601i	0.0160668	−	0.00977227i
$916$	0.256176	−	0.206653i	0.00846428	−	0.00682800i
$917$	1.38175	+	0.274847i	0.0456294	+	0.00907625i
$918$	10.7940	−	13.5692i	0.356256	−	0.447850i
$919$	−25.4121	+	10.5260i	−0.838266	+	0.347221i	−0.760170	−	0.649725i	$-0.774884\pi$
$919$	−25.4121	+	10.5260i	−0.838266	+	0.347221i	−0.0780965	+	0.996946i	$0.524884\pi$
$920$	−0.134399	−	0.391123i	−0.00443099	−	0.0128950i
$921$	16.8782	−	15.4981i	0.556156	−	0.510679i
$922$	−35.1608	+	8.65016i	−1.15796	+	0.284878i
$923$	−2.83696	−	4.24581i	−0.0933797	−	0.139753i
$924$	−1.47633	−	1.34328i	−0.0485676	−	0.0441906i
$925$	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	$-0.766396\pi$
$929$	−45.2667			−1.48515			−0.742576	+	0.669762i	$0.766396\pi$
$930$	−0.708267	+	1.72097i	−0.0232250	+	0.0564329i
$931$	−1.73286	−	8.71169i	−0.0567923	−	0.285514i
$932$	15.0990	+	28.8295i	0.494584	+	0.944343i
$933$	−8.05884	+	1.24888i	−0.263835	+	0.0408865i
$934$	−5.24341	+	1.28997i	−0.171570	+	0.0422091i
$935$	−0.149008	+	0.359738i	−0.00487310	+	0.0117647i
$936$	7.58995	+	1.12323i	0.248085	+	0.0367138i
$937$	16.4387	+	39.6866i	0.537030	+	1.29650i	0.926787	+	0.375587i	$0.122559\pi$
$937$	16.4387	+	39.6866i	0.537030	+	1.29650i	−0.389758	+	0.920917i	$0.627441\pi$
$938$	0.546882	−	0.402038i	0.0178563	−	0.0131270i
$939$	−13.3693	−	9.78160i	−0.436290	−	0.319210i
$940$	0.181740	−	1.69850i	0.00592769	−	0.0553988i
$941$	−13.4371	−	8.97839i	−0.438037	−	0.292687i	0.316931	−	0.948449i	$-0.397348\pi$
$941$	−13.4371	−	8.97839i	−0.438037	−	0.292687i	−0.754968	+	0.655762i	$0.772348\pi$
$942$	22.2111	+	22.1102i	0.723676	+	0.720391i
$943$	7.12152	+	7.12152i	0.231908	+	0.231908i
$944$	13.3539	−	12.9116i	0.434633	−	0.420236i
$945$	−0.0887057	−	0.0508492i	−0.00288560	−	0.00165412i
$946$	12.5974	+	26.9278i	0.409578	+	0.875498i
$947$	−11.2306	−	7.50405i	−0.364946	−	0.243849i	0.359554	−	0.933124i	$-0.382929\pi$
$947$	−11.2306	−	7.50405i	−0.364946	−	0.243849i	−0.724499	+	0.689276i	$0.757929\pi$
$948$	−17.2808	−	23.3949i	−0.561253	−	0.759831i
$949$	9.62140	+	1.91381i	0.312324	+	0.0621250i
$950$	8.94763	+	1.36578i	0.290299	+	0.0443117i
$951$	−3.25853	−	0.138906i	−0.105665	−	0.00450432i
$952$	−0.446437	+	1.69135i	−0.0144691	+	0.0548170i
$953$	16.3000	−	39.3517i	0.528009	−	1.27473i	−0.404817	−	0.914398i	$-0.632665\pi$
$953$	16.3000	−	39.3517i	0.528009	−	1.27473i	0.932826	−	0.360328i	$-0.117335\pi$
$954$	−27.8036	+	4.37352i	−0.900175	+	0.141598i
$955$	1.15082	+	1.72232i	0.0372396	+	0.0557329i
$956$	−21.5211	−	17.9673i	−0.696042	−	0.581103i
$957$	5.85937	−	24.0526i	0.189407	−	0.777511i
$958$	4.43427	−	4.85126i	0.143265	−	0.156737i
$959$	−3.97022			−0.128205
$960$	0.846999	−	0.603863i	0.0273368	−	0.0194896i
$961$	71.4236			2.30399
$962$	3.95728	−	4.32942i	0.127588	−	0.139586i
$963$	26.6626	−	33.3616i	0.859191	−	1.07506i
$964$	−11.8551	+	14.1999i	−0.381826	+	0.457349i
$965$	−0.210125	−	0.314474i	−0.00676416	−	0.0101233i
$966$	−0.697125	−	1.03820i	−0.0224296	−	0.0334036i
$967$	1.80085	−	4.34765i	0.0579116	−	0.139811i	−0.892275	−	0.451492i	$-0.850892\pi$
$967$	1.80085	−	4.34765i	0.0579116	−	0.139811i	0.950187	+	0.311681i	$0.100892\pi$
$968$	−15.0752	+	8.77886i	−0.484535	+	0.282163i
$969$	0.223049	−	5.23242i	0.00716538	−	0.168090i
$970$	1.36483	+	0.208329i	0.0438220	+	0.00668905i
$971$	49.1172	+	9.77002i	1.57625	+	0.313535i	0.904245	−	0.427015i	$-0.140435\pi$
$971$	49.1172	+	9.77002i	1.57625	+	0.313535i	0.672002	+	0.740550i	$0.265435\pi$
$972$	−27.8555	+	14.0025i	−0.893467	+	0.449130i
$973$	1.92038	+	1.28316i	0.0615646	+	0.0411361i
$974$	−11.6757	−	24.9576i	−0.374114	−	0.799692i
$975$	7.34751	−	2.68286i	0.235309	−	0.0859201i
$976$	6.42343	+	16.2775i	0.205609	+	0.521032i
$977$	14.3409	+	14.3409i	0.458806	+	0.458806i	0.898263	−	0.439457i	$-0.144829\pi$
$977$	14.3409	+	14.3409i	0.458806	+	0.458806i	−0.439457	+	0.898263i	$0.644829\pi$
$978$	12.4936	−	12.5506i	0.399503	−	0.401324i
$979$	−26.8482	−	17.9394i	−0.858073	−	0.573346i
$980$	−1.03478	−	0.110722i	−0.0330548	−	0.00353687i
$981$	25.8670	−	14.2606i	0.825871	−	0.455306i
$982$	−12.3074	+	9.04773i	−0.392745	+	0.288725i
$983$	20.8007	+	50.2173i	0.663439	+	1.60168i	0.792378	+	0.610030i	$0.208843\pi$
$983$	20.8007	+	50.2173i	0.663439	+	1.60168i	−0.128939	+	0.991652i	$0.541157\pi$
$984$	−12.0783	+	22.2667i	−0.385043	+	0.709837i
$985$	−0.392683	+	0.948021i	−0.0125119	+	0.0302065i
$986$	−21.0680	+	5.18309i	−0.670942	+	0.165063i
$987$	−0.791003	−	5.10423i	−0.0251779	−	0.162470i
$988$	2.05298	−	1.07522i	0.0653141	−	0.0342072i
$989$	3.63374	+	18.2680i	0.115546	+	0.580890i
$990$	0.514631	−	0.474712i	0.0163561	−	0.0150873i
$991$	−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
$996$	31.3234	+	28.5005i	0.992521	+	0.903074i
$997$	34.7772	+	52.0478i	1.10141	+	1.64837i	0.660525	+	0.750804i	$0.270334\pi$
$997$	34.7772	+	52.0478i	1.10141	+	1.64837i	0.440881	+	0.897566i	$0.354666\pi$
$998$	−49.0063	+	12.0564i	−1.55127	+	0.381639i
$999$	−3.03786	+	23.6395i	−0.0961137	+	0.747920i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.7	✓	240	1.1	even	1	trivial
192.2.s.a.107.24	yes	240	3.2	odd	2	inner
192.2.s.a.131.7	yes	240	192.131	even	16	inner
192.2.s.a.131.24	yes	240	64.3	odd	16	inner
768.2.s.a.335.2		240	4.3	odd	2
768.2.s.a.335.5		240	12.11	even	2
768.2.s.a.431.2		240	192.125	odd	16
768.2.s.a.431.5		240	64.61	even	16

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

\(f(q)\)	\(=\)	\(q+(-1.04386 - 0.954131i) q^{2} +(1.68284 + 0.409950i) q^{3} +(0.179269 + 1.99195i) q^{4} +(0.0417075 + 0.0624196i) q^{5} +(-1.36549 - 2.03358i) q^{6} +(-0.100307 + 0.242162i) q^{7} +(1.71345 - 2.25035i) q^{8} +(2.66388 + 1.37976i) q^{9} +O(q^{10})\)	\(q+(-1.04386 - 0.954131i) q^{2} +(1.68284 + 0.409950i) q^{3} +(0.179269 + 1.99195i) q^{4} +(0.0417075 + 0.0624196i) q^{5} +(-1.36549 - 2.03358i) q^{6} +(-0.100307 + 0.242162i) q^{7} +(1.71345 - 2.25035i) q^{8} +(2.66388 + 1.37976i) q^{9} +(0.0160199 - 0.104951i) q^{10} +(2.15600 + 0.428854i) q^{11} +(-0.514919 + 3.42562i) q^{12} +(0.751836 + 0.502361i) q^{13} +(0.335761 - 0.157077i) q^{14} +(0.0445980 + 0.122140i) q^{15} +(-3.93573 + 0.714188i) q^{16} +(1.66843 + 1.66843i) q^{17} +(-1.46424 - 3.98196i) q^{18} +(-1.06552 - 0.711956i) q^{19} +(-0.116860 + 0.0942690i) q^{20} +(-0.268075 + 0.366399i) q^{21} +(-1.84137 - 2.50477i) q^{22} +(-0.745366 - 1.79947i) q^{23} +(3.80599 - 3.08455i) q^{24} +(1.91126 - 4.61419i) q^{25} +(-0.305490 - 1.24174i) q^{26} +(3.91725 + 3.41396i) q^{27} +(-0.500357 - 0.156394i) q^{28} +(-1.26847 - 6.37705i) q^{29} +(0.0699837 - 0.170049i) 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} +(-2.27086 + 5.55367i) q^{36} +(2.54831 + 3.81381i) q^{37} +(0.432947 + 1.75982i) q^{38} +(1.05928 + 1.15361i) q^{39} +(0.211930 + 0.0130964i) q^{40} +(-4.77720 + 1.97878i) q^{41} +(0.629424 - 0.126689i) q^{42} +(-9.37912 - 1.86562i) q^{43} +(-0.467754 + 4.37152i) q^{44} +(0.0249798 + 0.223825i) q^{45} +(-0.938878 + 2.58957i) q^{46} +(-8.04483 + 8.04483i) q^{47} +(-6.91597 - 0.411587i) q^{48} +(4.90117 + 4.90117i) q^{49} +(-6.39762 + 2.99296i) q^{50} +(2.12372 + 3.49166i) q^{51} +(-0.865897 + 1.58768i) q^{52} +(1.29422 - 6.50649i) q^{53} +(-0.831673 - 7.30125i) q^{54} +(0.0631522 + 0.152463i) q^{55} +(0.373080 + 0.640659i) q^{56} +(-1.50123 - 1.63491i) q^{57} +(-4.76044 + 7.86701i) q^{58} +(-3.86117 + 2.57995i) q^{59} +(-0.235302 + 0.110733i) 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} +(-2.07189 - 4.96998i) q^{66} +(1.79590 - 0.357228i) q^{67} +(-3.02433 + 3.62252i) q^{68} +(-0.516636 - 3.33378i) q^{69} +(0.0238084 + 0.0144068i) q^{70} +(-5.21738 - 2.16111i) q^{71} +(7.66937 - 3.63053i) q^{72} +(10.0231 - 4.15171i) q^{73} +(0.978810 - 6.41248i) q^{74} +(5.10793 - 6.98141i) q^{75} +(1.22717 - 2.25009i) q^{76} +(-0.320114 + 0.479085i) q^{77} +(-0.00503859 - 2.21489i) q^{78} +(-5.93698 + 5.93698i) q^{79} +(-0.208728 - 0.215880i) q^{80} +(5.19254 + 7.35102i) q^{81} +(6.87472 + 2.49251i) q^{82} +(6.79190 - 10.1648i) q^{83} +(-0.777906 - 0.468308i) q^{84} +(-0.0345567 + 0.173728i) q^{85} +(8.01040 + 10.8963i) q^{86} +(0.479635 - 11.2516i) q^{87} +(4.65927 - 4.11693i) q^{88} +(-13.5709 - 5.62127i) q^{89} +(0.187483 - 0.257475i) q^{90} +(-0.197067 + 0.131676i) q^{91} +(3.45084 - 1.80732i) q^{92} +(-17.0311 - 4.14888i) q^{93} +(16.0735 - 0.721820i) q^{94} -0.0962031i q^{95} +(6.82656 + 7.02837i) q^{96} +13.0044i q^{97} +(-0.439755 - 9.79246i) q^{98} +(5.15161 + 4.11717i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) \) 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

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