LMFDB - Embedded newform 192.2.s.a.131.7

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			131.7
Character	$\chi$	$=$	192.131
Dual form			192.2.s.a.107.7

$q$-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 $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

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

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
$3$	1.68284	−	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	−0.822026	−	0.569449i	$-0.807156\pi$
$5$	0.0417075	−	0.0624196i	0.0186521	−	0.0279149i	0.840679	+	0.541535i	$0.182156\pi$
$6$	−1.36549	+	2.03358i	−0.557460	+	0.830204i
$7$	−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
$9$	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	0.140963	−	0.990015i	$-0.454980\pi$
$11$	2.15600	−	0.428854i	0.650058	−	0.129304i	0.509095	+	0.860710i	$0.329980\pi$
$12$	−0.514919	−	3.42562i	−0.148644	−	0.988891i
$13$	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
$15$	0.0445980	−	0.122140i	0.0115151	−	0.0315364i
$16$	−3.93573	−	0.714188i	−0.983931	−	0.178547i
$17$	1.66843	−	1.66843i	0.404653	−	0.404653i	−0.475216	−	0.879869i	$-0.657630\pi$
$17$	1.66843	−	1.66843i	0.404653	−	0.404653i	0.879869	+	0.475216i	$0.157630\pi$
$18$	−1.46424	+	3.98196i	−0.345125	+	0.938557i
$19$	−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
$21$	−0.268075	−	0.366399i	−0.0584987	−	0.0799549i
$22$	−1.84137	+	2.50477i	−0.392581	+	0.534018i
$23$	−0.745366	+	1.79947i	−0.155419	+	0.375216i	−0.982340	−	0.187102i	$-0.940090\pi$
$23$	−0.745366	+	1.79947i	−0.155419	+	0.375216i	0.826921	+	0.562318i	$0.190090\pi$
$24$	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	0.664123	+	0.747624i	$0.268805\pi$
$29$	−1.26847	+	6.37705i	−0.235550	+	1.18419i	−0.899672	+	0.436566i	$0.856195\pi$
$30$	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	−0.560637	−	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
$39$	1.05928	−	1.15361i	0.169620	−	0.184725i
$40$	0.211930	−	0.0130964i	0.0335090	−	0.00207072i
$41$	−4.77720	−	1.97878i	−0.746073	−	0.309033i	−0.0229347	−	0.999737i	$-0.507301\pi$
$41$	−4.77720	−	1.97878i	−0.746073	−	0.309033i	−0.723138	+	0.690704i	$0.757301\pi$
$42$	0.629424	+	0.126689i	0.0971223	+	0.0195486i
$43$	−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
$45$	0.0249798	−	0.223825i	0.00372377	−	0.0333658i
$46$	−0.938878	−	2.58957i	−0.138430	−	0.381811i
$47$	−8.04483	−	8.04483i	−1.17346	−	1.17346i	−0.981379	−	0.192080i	$-0.938477\pi$
$47$	−8.04483	−	8.04483i	−1.17346	−	1.17346i	−0.192080	−	0.981379i	$-0.561523\pi$
$48$	−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	0.961956	+	0.273203i	$0.0880831\pi$
$53$	1.29422	+	6.50649i	0.177775	+	0.893735i	−0.784181	+	0.620532i	$0.786917\pi$
$54$	−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	0.278239	−	0.960512i	$-0.410249\pi$
$59$	−3.86117	−	2.57995i	−0.502681	−	0.335881i	−0.780920	+	0.624631i	$0.785249\pi$
$60$	−0.235302	−	0.110733i	−0.0303773	−	0.0142955i
$61$	−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
$66$	−2.07189	+	4.96998i	−0.255032	+	0.611762i
$67$	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
$69$	−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	−0.670152	−	0.742224i	$-0.733771\pi$
$71$	−5.21738	+	2.16111i	−0.619190	+	0.256477i	0.0509625	+	0.998701i	$0.483771\pi$
$72$	7.66937	+	3.63053i	0.903844	+	0.427862i
$73$	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
$75$	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	0.289281	−	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
$81$	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	0.989299	+	0.145904i	$0.0466091\pi$
$83$	6.79190	+	10.1648i	0.745508	+	1.11573i	−0.243790	+	0.969828i	$0.578391\pi$
$84$	−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	−0.959438	−	0.281919i	$-0.909029\pi$
$89$	−13.5709	+	5.62127i	−1.43852	+	0.595853i	−0.479079	+	0.877772i	$0.659029\pi$
$90$	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	$-0.770473\pi$
$97$		−	13.0044i		−	1.32039i	0.751092	−	0.660197i	$-0.229527\pi$
$98$	−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	0.934601	−	0.355697i	$-0.115756\pi$
$101$	9.68443	+	6.47093i	0.963637	+	0.643882i	0.0290356	+	0.999578i	$0.490756\pi$
$102$	1.11465	+	5.67110i	0.110366	+	0.561523i
$103$	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
$105$	−0.0340512	+	0.00145155i	−0.00332306	+	0.000141656i
$106$	−7.55902	−	5.55698i	−0.734197	−	0.539741i
$107$	2.77724	+	13.9621i	0.268486	+	1.34977i	0.845910	+	0.533326i	$0.179058\pi$
$107$	2.77724	+	13.9621i	0.268486	+	1.34977i	−0.577424	+	0.816445i	$0.695942\pi$
$108$	−6.09821	−	8.41498i	−0.586800	−	0.809732i
$109$	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
$111$	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	0.254958	−	0.966952i	$-0.417938\pi$
$113$	−7.56860	−	7.56860i	−0.711994	−	0.711994i	−0.966952	+	0.254958i	$0.917938\pi$
$114$	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	$0.00583646\pi$
$127$			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	$0.137944\pi$
$131$	−1.04858	+	5.27154i	−0.0916144	+	0.460577i	−0.999173	+	0.0406521i	$0.987056\pi$
$132$	−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	−0.456804	−	0.889567i	$-0.651006\pi$
$137$	5.79645	−	13.9939i	0.495224	−	1.19558i	0.952028	−	0.306010i	$-0.0989941\pi$
$138$	−2.64157	−	3.97292i	−0.224865	−	0.338198i
$139$	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
$141$	−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	−0.435361	−	0.900256i	$-0.643379\pi$
$149$	−6.01868	+	1.19719i	−0.493069	+	0.0980776i	−0.0577083	+	0.998333i	$0.518379\pi$
$150$	−11.9931	−	2.41395i	−0.979234	−	0.197099i
$151$	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
$153$	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	−0.332998	−	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
$162$	1.59358	+	12.6278i	0.125203	+	0.992131i
$163$	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
$165$	0.0437728	−	0.282460i	0.00340770	−	0.0219894i
$166$	−16.7883	−	4.13022i	−1.30303	−	0.320567i
$167$	−5.06460	−	12.2270i	−0.391911	−	0.946156i	−0.989524	−	0.144371i	$-0.953884\pi$
$167$	−5.06460	−	12.2270i	−0.391911	−	0.946156i	0.597613	−	0.801785i	$-0.296116\pi$
$168$	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	0.541966	−	0.840400i	$-0.317680\pi$
$173$	20.0687	−	13.4095i	1.52580	−	1.01950i	0.983830	−	0.179104i	$-0.0573200\pi$
$174$	−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	−0.112543	−	0.993647i	$-0.535900\pi$
$179$	10.2002	−	6.81555i	0.762398	−	0.509418i	0.874941	+	0.484229i	$0.160900\pi$
$180$	−0.441369	−	0.0898833i	−0.0328977	−	0.00669951i
$181$	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
$183$	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	−0.455718	−	0.890124i	$-0.650617\pi$
$197$	7.59394	−	11.3651i	0.541046	−	0.809732i	0.996763	+	0.0803923i	$0.0256173\pi$
$198$	−1.44921	+	9.21304i	−0.102991	+	0.654742i
$199$	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
$201$	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	−0.456679	−	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
$213$	−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	−0.278309	−	0.960492i	$-0.589774\pi$
$227$	−13.6050	−	2.70621i	−0.902997	−	0.179617i	−0.624688	+	0.780874i	$0.714774\pi$
$228$	2.98754	+	3.28346i	0.197855	+	0.217452i
$229$	−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
$231$	−0.735100	−	0.674991i	−0.0483661	−	0.0444111i
$232$	−16.5241	+	8.07225i	−1.08486	+	0.529969i
$233$	15.0334	+	6.22705i	0.984873	+	0.407948i	0.816229	−	0.577729i	$-0.196061\pi$
$233$	15.0334	+	6.22705i	0.984873	+	0.407948i	0.168645	+	0.985677i	$0.446061\pi$
$234$	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	0.309685	−	0.950839i	$-0.399776\pi$
$239$	−9.91200	−	9.91200i	−0.641154	−	0.641154i	−0.950839	+	0.309685i	$0.899776\pi$
$240$	−0.262756	+	0.448858i	−0.0169608	+	0.0289737i
$241$	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
$243$	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	−0.207106	−	0.978318i	$-0.566405\pi$
$251$	−18.8565	−	12.5995i	−1.19021	−	0.795273i	−0.983105	+	0.183045i	$0.941405\pi$
$252$	−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	$0.00246139\pi$
$257$			0.247927i			0.0154652i	−0.999970	+	0.00773262i	$0.997539\pi$
$258$	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	0.549153	−	0.835722i	$-0.314950\pi$
$263$	24.7866	−	10.2669i	1.52841	−	0.633087i	0.979254	+	0.202635i	$0.0649504\pi$
$264$	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	0.508868	−	0.860845i	$-0.330064\pi$
$269$	−7.89201	−	11.8112i	−0.481184	−	0.720143i	−0.990052	+	0.140701i	$0.955064\pi$
$270$	0.421055	+	0.356429i	0.0256246	+	0.0216916i
$271$	−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
$273$	−0.385613	−	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	−0.803568	−	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
$279$	−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	−0.914077	−	0.405540i	$-0.867084\pi$
$281$	−21.3506	+	8.84369i	−1.27367	+	0.527570i	−0.359590	+	0.933110i	$0.617084\pi$
$282$	27.3449	−	5.37461i	1.62837	−	0.320053i
$283$	−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
$285$	0.0394384	+	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	0.921804	−	0.387656i	$-0.126715\pi$
$293$	15.6865	+	10.4814i	0.916416	+	0.612329i	−0.00538828	+	0.999985i	$0.501715\pi$
$294$	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	0.979682	−	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
$309$	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	0.255928	−	0.966696i	$-0.417619\pi$
$311$	−4.34991	−	1.80179i	−0.246661	−	0.102170i	−0.502589	+	0.864526i	$0.667619\pi$
$312$	4.41104	+	0.407096i	0.249726	+	0.0230473i
$313$	−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
$315$	−0.0567076	+	0.0164020i	−0.00319511	+	0.000924148i
$316$	−12.8905	+	10.7619i	−0.725146	+	0.605402i
$317$	−1.84684	−	0.367359i	−0.103729	−	0.0206329i	0.142953	−	0.989729i	$-0.454340\pi$
$317$	−1.84684	−	0.367359i	−0.103729	−	0.0206329i	−0.246682	+	0.969097i	$0.579340\pi$
$318$	−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	−0.773286	−	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
$333$	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	0.173845	−	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
$339$	−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	−0.998975	−	0.0452745i	$-0.985584\pi$
$347$	−10.7084	+	16.0262i	−0.574855	+	0.860332i	0.424119	+	0.905606i	$0.360584\pi$
$348$	22.4985	+	1.06164i	1.20605	+	0.0569100i
$349$	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	$-0.412567\pi$
$353$	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	0.999077	+	0.0429641i	$0.0136801\pi$
$359$	6.12003	+	14.7751i	0.323003	+	0.779798i	−0.676074	+	0.736834i	$0.736320\pi$
$360$	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	−0.917464	−	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
$369$	−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	−0.668825	−	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
$375$	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	−0.810331	−	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
$381$	0.169409	+	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	−0.0619565	−	0.998079i	$-0.519734\pi$
$389$	17.4324	−	26.0894i	0.883858	−	1.32279i	0.945814	−	0.324708i	$-0.105266\pi$
$390$	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	−0.249428	−	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
$399$	0.546499	+	0.199547i	0.0273591	+	0.00998986i
$400$	−4.22680	−	19.5252i	−0.211340	−	0.976259i
$401$	−20.2825	+	20.2825i	−1.01286	+	1.01286i	−0.0129431	+	0.999916i	$0.504120\pi$
$401$	−20.2825	+	20.2825i	−1.01286	+	1.01286i	−0.999916	+	0.0129431i	$0.995880\pi$
$402$	−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	−0.999625	−	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
$411$	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	−0.646904	−	0.762571i	$-0.723937\pi$
$419$	−31.4491	−	6.25562i	−1.53639	−	0.305607i	−0.889485	+	0.456964i	$0.848937\pi$
$420$	−0.00321291	+	0.0680885i	−0.000156774	+	0.00332238i
$421$	−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
$423$	−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	0.315111	−	0.949055i	$-0.397958\pi$
$431$	−13.1610	−	13.1610i	−0.633944	−	0.633944i	−0.949055	+	0.315111i	$0.897958\pi$
$432$	−17.8554	+	10.6388i	−0.859070	+	0.511858i
$433$	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
$435$	0.722322	+	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	−0.564206	−	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
$441$	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	0.684876	−	0.728660i	$-0.259856\pi$
$443$	5.76224	+	3.85021i	0.273773	+	0.182929i	−0.411103	+	0.911589i	$0.634856\pi$
$444$	−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	$0.0501659\pi$
$449$			6.65138i			0.313898i	−0.987607	+	0.156949i	$0.949834\pi$
$450$	−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	−0.00514839	−	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
$459$	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	0.998762	+	0.0497436i	$0.0158404\pi$
$461$	14.2247	+	21.2887i	0.662509	+	0.991515i	−0.336253	+	0.941772i	$0.609160\pi$
$462$	1.41137	+	0.00321069i	0.0656628	+	0.000149375i
$463$	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
$465$	−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	0.877299	−	0.479944i	$-0.159343\pi$
$467$	2.12128	+	3.17472i	0.0981612	+	0.146909i	−0.779138	+	0.626852i	$0.784343\pi$
$468$	−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	$-0.966140\pi$
$479$		−	4.64745i		−	0.212347i	0.994348	−	0.106174i	$-0.0338599\pi$
$480$	−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	0.0644565	−	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
$489$	−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	0.998757	+	0.0498362i	$0.0158699\pi$
$491$	2.10722	+	10.5937i	0.0950974	+	0.478087i	−0.903660	+	0.428251i	$0.859130\pi$
$492$	−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	0.944021	+	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
$501$	−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	0.381965	−	0.924177i	$-0.375248\pi$
$503$	−0.0322396	−	0.0133541i	−0.00143749	−	0.000595428i	−0.383402	+	0.923582i	$0.625248\pi$
$504$	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	0.111147	−	0.993804i	$-0.464548\pi$
$509$	−3.75595	−	0.747106i	−0.166480	−	0.0331149i	−0.277626	+	0.960689i	$0.589548\pi$
$510$	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	−0.761461	−	0.648210i	$-0.775518\pi$
$521$	5.37144	−	12.9678i	0.235327	−	0.568130i	0.996788	+	0.0800804i	$0.0255177\pi$
$522$	−23.5358	−	14.3885i	−1.03013	−	0.629770i
$523$	−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
$525$	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	0.723339	−	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
$546$	0.536868	−	0.220948i	0.0229758	−	0.00945572i
$547$	−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
$549$	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	−0.778282	−	0.627915i	$-0.783908\pi$
$557$	−11.7060	+	7.82170i	−0.495999	+	0.331416i	0.282282	+	0.959331i	$0.408908\pi$
$558$	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	−0.524497	−	0.851412i	$-0.675746\pi$
$563$	1.45663	−	0.973290i	0.0613897	−	0.0410193i	0.585886	+	0.810393i	$0.300746\pi$
$564$	−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	0.836748	−	0.547588i	$-0.184454\pi$
$569$	−3.39021	−	8.18469i	−0.142125	−	0.343120i	−0.978873	+	0.204468i	$0.934454\pi$
$570$	−0.195636	−	0.131365i	−0.00819430	−	0.00550226i
$571$	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
$573$	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	0.568059	−	0.822988i	$-0.307694\pi$
$587$	34.1088	−	6.78466i	1.40782	−	0.280033i	0.839762	+	0.542955i	$0.182694\pi$
$588$	−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	−0.730308	−	0.683118i	$-0.760624\pi$
$593$	−1.14918	+	1.14918i	−0.0471910	+	0.0471910i	0.683118	+	0.730308i	$0.260624\pi$
$594$	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	−0.901905	−	0.431934i	$-0.857831\pi$
$599$	1.00985	−	2.43798i	0.0412612	−	0.0996132i	0.943167	+	0.332320i	$0.107831\pi$
$600$	−6.95847	+	23.4569i	−0.284078	+	0.957625i
$601$	−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
$603$	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	0.316055	+	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
$615$	−0.454741	+	0.495237i	−0.0183369	+	0.0199699i
$616$	0.529610	−	1.54126i	0.0213386	−	0.0620990i
$617$	15.9796	+	6.61898i	0.643316	+	0.266470i	0.680399	−	0.732842i	$-0.261807\pi$
$617$	15.9796	+	6.61898i	0.643316	+	0.266470i	−0.0370828	+	0.999312i	$0.511807\pi$
$618$	−6.48842	+	32.2361i	−0.261003	+	1.29672i
$619$	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
$621$	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	−0.885284	−	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
$633$	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	$-0.785695\pi$
$641$		−	31.5734i		−	1.24708i	0.781793	−	0.623538i	$-0.214305\pi$
$642$	−32.1854	−	13.4175i	−1.27025	−	0.529545i
$643$	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
$645$	−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	−0.696172	−	0.717875i	$-0.745115\pi$
$647$	−17.3176	+	7.17319i	−0.680826	+	0.282007i	0.0153463	+	0.999882i	$0.495115\pi$
$648$	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	0.990880	+	0.134748i	$0.0430225\pi$
$653$	18.8122	+	28.1544i	0.736178	+	1.10177i	−0.254702	+	0.967020i	$0.581977\pi$
$654$	−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	0.878642	−	0.477481i	$-0.158450\pi$
$659$	2.59960	+	3.89057i	0.101266	+	0.151555i	−0.777376	+	0.629036i	$0.783450\pi$
$660$	−0.554798	−	0.137829i	−0.0215955	−	0.00536500i
$661$	−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
$663$	−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	$0.0681599\pi$
$673$			11.0254i			0.424996i	−0.977161	+	0.212498i	$0.931840\pi$
$674$	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	0.327240	−	0.944941i	$-0.393881\pi$
$677$	−10.9422	−	7.31133i	−0.420542	−	0.280997i	−0.747782	+	0.663944i	$0.768881\pi$
$678$	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	−0.902011	−	0.431713i	$-0.857909\pi$
$683$	−6.11205	−	30.7273i	−0.233871	−	1.17575i	0.668140	−	0.744036i	$-0.267091\pi$
$684$	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	0.896523	−	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
$693$	−1.51377	−	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	−0.768743	−	0.639558i	$-0.779118\pi$
$701$	−45.6378	−	9.07793i	−1.72372	−	0.342869i	−0.954974	+	0.296689i	$0.904118\pi$
$702$	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	−0.248955	−	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
$711$	−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	−0.0214686	+	0.999770i	$0.506834\pi$
$719$	−27.3837	+	27.3837i	−1.02124	+	1.02124i	−0.999770	+	0.0214686i	$0.993166\pi$
$720$	−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	0.389574	−	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
$729$	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	−0.202436	−	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
$738$	14.8744	−	16.1252i	0.547533	−	0.593577i
$739$	−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
$741$	−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	0.930302	+	0.366795i	$0.119545\pi$
$743$	14.4970	+	34.9988i	0.531843	+	1.28398i	−0.398459	+	0.917186i	$0.630455\pi$
$744$	−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	−0.350358	−	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
$753$	−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	−0.939838	−	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
$759$	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	−0.958566	−	0.284872i	$-0.908049\pi$
$761$	−13.3019	−	32.1135i	−0.482192	−	1.16412i	0.476373	−	0.879243i	$-0.341951\pi$
$762$	−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	−0.882103	−	0.471057i	$-0.843872\pi$
$773$	−3.03986	+	4.54947i	−0.109336	+	0.163633i	0.772766	+	0.634691i	$0.218872\pi$
$774$	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	−0.632431	−	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
$789$	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	−0.999090	−	0.0426555i	$-0.986418\pi$
$797$	−1.68618	+	8.47701i	−0.0597276	+	0.300271i	0.939362	+	0.342927i	$0.111418\pi$
$798$	−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	0.612675	−	0.790335i	$-0.290094\pi$
$809$	13.8531	+	5.73816i	0.487050	+	0.201743i	−0.125625	+	0.992078i	$0.540094\pi$
$810$	0.854684	+	0.427202i	0.0300306	+	0.0150103i
$811$	−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
$813$	−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	0.616776	+	0.787138i	$0.288438\pi$
$821$	9.97627	+	50.1541i	0.348174	+	1.75039i	−0.268602	+	0.963251i	$0.586562\pi$
$822$	20.5426	+	30.8961i	0.716505	+	1.07762i
$823$	−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
$825$	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	0.853178	−	0.521619i	$-0.174672\pi$
$827$	20.0660	+	13.4077i	0.697763	+	0.466230i	−0.155416	+	0.987849i	$0.549672\pi$
$828$	11.6863	+	0.0531700i	0.406127	+	0.00184779i
$829$	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
$834$	−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	−0.933939	−	0.357432i	$-0.883652\pi$
$839$	−38.8599	+	16.0963i	−1.34159	+	0.555705i	−0.407652	+	0.913137i	$0.633652\pi$
$840$	−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	0.597409	+	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
$855$	0.132737	+	0.256274i	0.00453951	+	0.00876437i
$856$	−26.6611	+	30.1732i	−0.911257	+	1.03130i
$857$	35.5270	−	14.7158i	1.21358	−	0.502681i	0.318216	−	0.948018i	$-0.396916\pi$
$857$	35.5270	−	14.7158i	1.21358	−	0.502681i	0.895363	+	0.445338i	$0.146916\pi$
$858$	0.939000	+	4.77745i	0.0320569	+	0.163099i
$859$	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
$861$	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	$0.413389\pi$
$863$			56.5922i			1.92642i	−0.268751	+	0.963210i	$0.586611\pi$
$864$	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	−0.999979	−	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
$879$	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	0.998750	−	0.0499827i	$-0.0159166\pi$
$881$	28.1610	+	28.1610i	0.948767	+	0.948767i	−0.0499827	+	0.998750i	$0.515917\pi$
$882$	12.3398	+	26.6927i	0.415502	+	0.898791i
$883$	−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
$885$	−0.487315	+	0.356542i	−0.0163809	+	0.0119850i
$886$	−9.68855	+	1.47887i	−0.325493	+	0.0496837i
$887$	−23.8945	−	9.89741i	−0.802298	−	0.332323i	−0.0564213	−	0.998407i	$-0.517969\pi$
$887$	−23.8945	−	9.89741i	−0.802298	−	0.332323i	−0.745876	+	0.666085i	$0.767969\pi$
$888$	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	0.974643	−	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
$909$	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	−0.385869	−	0.922554i	$-0.626098\pi$
$911$	16.1986	−	16.1986i	0.536684	−	0.536684i	0.922554	+	0.385869i	$0.126098\pi$
$912$	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	−0.0780965	−	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
$921$	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	−0.389758	−	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
$939$	−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	−0.754968	−	0.655762i	$-0.772348\pi$
$941$	−13.4371	+	8.97839i	−0.438037	+	0.292687i	0.316931	+	0.948449i	$0.397348\pi$
$942$	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	−0.724499	−	0.689276i	$-0.757929\pi$
$947$	−11.2306	+	7.50405i	−0.364946	+	0.243849i	0.359554	+	0.933124i	$0.382929\pi$
$948$	−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	0.932826	+	0.360328i	$0.117335\pi$
$953$	16.3000	+	39.3517i	0.528009	+	1.27473i	−0.404817	+	0.914398i	$0.632665\pi$
$954$	−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	0.950187	−	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
$969$	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	0.672002	−	0.740550i	$-0.265435\pi$
$971$	49.1172	−	9.77002i	1.57625	−	0.313535i	0.904245	+	0.427015i	$0.140435\pi$
$972$	−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	−0.439457	−	0.898263i	$-0.644829\pi$
$977$	14.3409	−	14.3409i	0.458806	−	0.458806i	0.898263	+	0.439457i	$0.144829\pi$
$978$	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	−0.128939	−	0.991652i	$-0.541157\pi$
$983$	20.8007	−	50.2173i	0.663439	−	1.60168i	0.792378	−	0.610030i	$-0.208843\pi$
$984$	−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	0.440881	−	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
$999$	−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.131.7	yes	240
3.2	odd	2	inner	192.2.s.a.131.24	yes	240
4.3	odd	2		768.2.s.a.431.2		240
12.11	even	2		768.2.s.a.431.5		240
64.21	even	16		768.2.s.a.335.5		240
64.43	odd	16	inner	192.2.s.a.107.24	yes	240
192.107	even	16	inner	192.2.s.a.107.7	✓	240
192.149	odd	16		768.2.s.a.335.2		240

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

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

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