LMFDB - Embedded newform 65.2.o.a.32.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(2,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("65.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.o (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.2
Root			$1.58474i$ of defining polynomial
Character	$\chi$	$=$	65.32
Dual form			65.2.o.a.63.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.792369 + 1.37242i) q^{2} +(-0.0510678 - 0.190588i) q^{3} +(-0.255697 - 0.442881i) q^{4} +(0.0672627 + 2.23506i) q^{5} +(0.302032 + 0.0809291i) q^{6} +(-0.474866 + 0.274164i) q^{7} -2.35905 q^{8} +(2.56436 - 1.48053i) q^{9} +O(q^{10})$	\(q+(-0.792369 + 1.37242i) q^{2} +(-0.0510678 - 0.190588i) q^{3} +(-0.255697 - 0.442881i) q^{4} +(0.0672627 + 2.23506i) q^{5} +(0.302032 + 0.0809291i) q^{6} +(-0.474866 + 0.274164i) q^{7} -2.35905 q^{8} +(2.56436 - 1.48053i) q^{9} +(-3.12074 - 1.67868i) q^{10} +(0.147928 - 0.0396372i) q^{11} +(-0.0713497 + 0.0713497i) q^{12} +(1.63157 - 3.21528i) q^{13} -0.868956i q^{14} +(0.422539 - 0.126959i) q^{15} +(2.38063 - 4.12338i) q^{16} +(3.03602 + 0.813499i) q^{17} +4.69252i q^{18} +(1.18079 - 4.40678i) q^{19} +(0.972665 - 0.601287i) q^{20} +(0.0765027 + 0.0765027i) q^{21} +(-0.0628146 + 0.234427i) q^{22} +(-3.41860 + 0.916011i) q^{23} +(0.120472 + 0.449606i) q^{24} +(-4.99095 + 0.300672i) q^{25} +(3.11992 + 4.78688i) q^{26} +(-0.831688 - 0.831688i) q^{27} +(0.242844 + 0.140206i) q^{28} +(-2.02878 - 1.17132i) q^{29} +(-0.160566 + 0.680501i) q^{30} +(-6.61000 + 6.61000i) q^{31} +(1.41363 + 2.44848i) q^{32} +(-0.0151087 - 0.0261691i) q^{33} +(-3.52211 + 3.52211i) q^{34} +(-0.644713 - 1.04291i) q^{35} +(-1.31140 - 0.757137i) q^{36} +(5.89447 + 3.40317i) q^{37} +(5.11234 + 5.11234i) q^{38} +(-0.696113 - 0.146759i) q^{39} +(-0.158676 - 5.27261i) q^{40} +(0.926064 + 3.45612i) q^{41} +(-0.165612 + 0.0443757i) q^{42} +(1.84023 - 6.86784i) q^{43} +(-0.0553794 - 0.0553794i) q^{44} +(3.48156 + 5.63190i) q^{45} +(1.45164 - 5.41759i) q^{46} -9.13956i q^{47} +(-0.907439 - 0.243147i) q^{48} +(-3.34967 + 5.80180i) q^{49} +(3.54203 - 7.08794i) q^{50} -0.620172i q^{51} +(-1.84117 + 0.0995483i) q^{52} +(-3.70952 + 3.70952i) q^{53} +(1.80043 - 0.482424i) q^{54} +(0.0985415 + 0.327962i) q^{55} +(1.12023 - 0.646766i) q^{56} -0.900179 q^{57} +(3.21508 - 1.85623i) q^{58} +(3.67728 + 0.985325i) q^{59} +(-0.164270 - 0.154672i) q^{60} +(-3.92486 - 6.79805i) q^{61} +(-3.83416 - 14.3093i) q^{62} +(-0.811818 + 1.40611i) q^{63} +5.04207 q^{64} +(7.29606 + 3.43037i) q^{65} +0.0478868 q^{66} +(-2.44516 + 4.23514i) q^{67} +(-0.416019 - 1.55261i) q^{68} +(0.349161 + 0.604765i) q^{69} +(1.94217 - 0.0584483i) q^{70} +(-15.1045 - 4.04725i) q^{71} +(-6.04945 + 3.49265i) q^{72} +3.91807 q^{73} +(-9.34119 + 5.39314i) q^{74} +(0.312181 + 0.935860i) q^{75} +(-2.25360 + 0.603851i) q^{76} +(-0.0593789 + 0.0593789i) q^{77} +(0.752994 - 0.839074i) q^{78} +11.1394i q^{79} +(9.37611 + 5.04350i) q^{80} +(4.32557 - 7.49210i) q^{81} +(-5.47704 - 1.46757i) q^{82} -13.4251i q^{83} +(0.0143200 - 0.0534431i) q^{84} +(-1.61401 + 6.84039i) q^{85} +(7.96744 + 7.96744i) q^{86} +(-0.119633 + 0.446477i) q^{87} +(-0.348970 + 0.0935062i) q^{88} +(-2.35372 - 8.78419i) q^{89} +(-10.4880 + 0.315631i) q^{90} +(0.106738 + 1.97414i) q^{91} +(1.27981 + 1.27981i) q^{92} +(1.59734 + 0.922226i) q^{93} +(12.5433 + 7.24190i) q^{94} +(9.92882 + 2.34273i) q^{95} +(0.394459 - 0.394459i) q^{96} +(3.78550 + 6.55668i) q^{97} +(-5.30835 - 9.19433i) q^{98} +(0.320657 - 0.320657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21} + 16 q^{22} - 2 q^{23} - 32 q^{24} - 18 q^{25} - 24 q^{26} + 4 q^{27} + 6 q^{28} + 14 q^{30} - 6 q^{32} - 18 q^{33} - 2 q^{34} - 20 q^{35} + 36 q^{36} + 42 q^{37} + 8 q^{38} - 4 q^{39} - 16 q^{40} + 10 q^{41} - 56 q^{42} - 22 q^{43} + 36 q^{44} + 52 q^{45} + 4 q^{46} + 28 q^{48} - 18 q^{49} + 44 q^{50} + 46 q^{52} - 10 q^{53} + 48 q^{54} + 26 q^{55} - 12 q^{57} - 90 q^{58} + 16 q^{59} - 92 q^{60} - 16 q^{61} - 40 q^{62} - 32 q^{63} - 20 q^{64} + 8 q^{65} - 32 q^{66} - 58 q^{67} + 28 q^{68} + 16 q^{69} + 32 q^{70} - 16 q^{71} - 66 q^{72} + 72 q^{73} - 18 q^{74} - 34 q^{75} - 64 q^{76} + 28 q^{77} + 32 q^{78} - 34 q^{80} - 14 q^{81} + 22 q^{82} + 40 q^{84} - 6 q^{85} + 60 q^{86} + 62 q^{87} + 50 q^{88} + 6 q^{89} - 46 q^{90} + 8 q^{91} - 8 q^{92} + 48 q^{93} + 48 q^{94} + 14 q^{95} + 56 q^{96} - 22 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{12}\right)$

Coefficient data

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

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

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

$2$	−0.792369	+	1.37242i	−0.560290	+	0.970450i	0.437181	+	0.899373i	$0.355977\pi$
$2$	−0.792369	+	1.37242i	−0.560290	+	0.970450i	−0.997471	+	0.0710765i	$0.977357\pi$
$3$	−0.0510678	−	0.190588i	−0.0294840	−	0.110036i	0.949616	−	0.313417i	$-0.101474\pi$
$3$	−0.0510678	−	0.190588i	−0.0294840	−	0.110036i	−0.979100	+	0.203381i	$0.934807\pi$
$4$	−0.255697	−	0.442881i	−0.127849	−	0.221440i
$5$	0.0672627	+	2.23506i	0.0300808	+	0.999547i
$5$	0.0672627	+	2.23506i	0.0300808	+	0.999547i
$6$	0.302032	+	0.0809291i	0.123304	+	0.0330392i
$7$	−0.474866	+	0.274164i	−0.179482	+	0.103624i	−0.587049	−	0.809551i	$-0.699711\pi$
$7$	−0.474866	+	0.274164i	−0.179482	+	0.103624i	0.407567	+	0.913175i	$0.366377\pi$
$8$	−2.35905			−0.834050
$9$	2.56436	−	1.48053i	0.854787	−	0.493511i
$10$	−3.12074	−	1.67868i	−0.986865	−	0.530844i
$11$	0.147928	−	0.0396372i	0.0446020	−	0.0119511i	−0.236449	−	0.971644i	$-0.575984\pi$
$11$	0.147928	−	0.0396372i	0.0446020	−	0.0119511i	0.281051	+	0.959693i	$0.409317\pi$
$12$	−0.0713497	+	0.0713497i	−0.0205969	+	0.0205969i
$13$	1.63157	−	3.21528i	0.452515	−	0.891757i
$13$	1.63157	−	3.21528i	0.452515	−	0.891757i
$14$		−	0.868956i		−	0.232238i
$15$	0.422539	−	0.126959i	0.109099	−	0.0327807i
$16$	2.38063	−	4.12338i	0.595158	−	1.03084i
$17$	3.03602	+	0.813499i	0.736343	+	0.197303i	0.607452	−	0.794356i	$-0.292192\pi$
$17$	3.03602	+	0.813499i	0.736343	+	0.197303i	0.128891	+	0.991659i	$0.458858\pi$
$18$			4.69252i			1.10604i
$19$	1.18079	−	4.40678i	0.270893	−	1.01098i	−0.687652	−	0.726041i	$-0.741358\pi$
$19$	1.18079	−	4.40678i	0.270893	−	1.01098i	0.958544	−	0.284944i	$-0.0919750\pi$
$20$	0.972665	−	0.601287i	0.217494	−	0.134452i
$21$	0.0765027	+	0.0765027i	0.0166942	+	0.0166942i
$22$	−0.0628146	+	0.234427i	−0.0133921	+	0.0499801i
$23$	−3.41860	+	0.916011i	−0.712828	+	0.191002i	−0.596969	−	0.802264i	$-0.703629\pi$
$23$	−3.41860	+	0.916011i	−0.712828	+	0.191002i	−0.115858	+	0.993266i	$0.536962\pi$
$24$	0.120472	+	0.449606i	0.0245912	+	0.0917754i
$25$	−4.99095	+	0.300672i	−0.998190	+	0.0601343i
$26$	3.11992	+	4.78688i	0.611866	+	0.938785i
$27$	−0.831688	−	0.831688i	−0.160058	−	0.160058i
$28$	0.242844	+	0.140206i	0.0458932	+	0.0264964i
$29$	−2.02878	−	1.17132i	−0.376735	−	0.217508i	0.299662	−	0.954045i	$-0.403126\pi$
$29$	−2.02878	−	1.17132i	−0.376735	−	0.217508i	−0.676397	+	0.736538i	$0.736459\pi$
$30$	−0.160566	+	0.680501i	−0.0293152	+	0.124242i
$31$	−6.61000	+	6.61000i	−1.18719	+	1.18719i	−0.209350	+	0.977841i	$0.567135\pi$
$31$	−6.61000	+	6.61000i	−1.18719	+	1.18719i	−0.977841	+	0.209350i	$0.932865\pi$
$32$	1.41363	+	2.44848i	0.249897	+	0.432834i
$33$	−0.0151087	−	0.0261691i	−0.00263009	−	0.00455546i
$34$	−3.52211	+	3.52211i	−0.604038	+	0.604038i
$35$	−0.644713	−	1.04291i	−0.108976	−	0.176284i
$36$	−1.31140	−	0.757137i	−0.218567	−	0.126190i
$37$	5.89447	+	3.40317i	0.969045	+	0.559478i	0.898945	−	0.438062i	$-0.144335\pi$
$37$	5.89447	+	3.40317i	0.969045	+	0.559478i	0.0700997	+	0.997540i	$0.477668\pi$
$38$	5.11234	+	5.11234i	0.829332	+	0.829332i
$39$	−0.696113	−	0.146759i	−0.111467	−	0.0235003i
$40$	−0.158676	−	5.27261i	−0.0250889	−	0.833672i
$41$	0.926064	+	3.45612i	0.144627	+	0.539755i	0.999772	+	0.0213659i	$0.00680149\pi$
$41$	0.926064	+	3.45612i	0.144627	+	0.539755i	−0.855145	+	0.518389i	$0.826532\pi$
$42$	−0.165612	+	0.0443757i	−0.0255545	+	0.00684732i
$43$	1.84023	−	6.86784i	0.280633	−	1.04734i	−0.671339	−	0.741150i	$-0.734281\pi$
$43$	1.84023	−	6.86784i	0.280633	−	1.04734i	0.951972	−	0.306185i	$-0.0990527\pi$
$44$	−0.0553794	−	0.0553794i	−0.00834876	−	0.00834876i
$45$	3.48156	+	5.63190i	0.519001	+	0.839555i
$46$	1.45164	−	5.41759i	0.214032	−	0.798780i
$47$		−	9.13956i		−	1.33314i	−0.745442	−	0.666571i	$-0.767761\pi$
$47$		−	9.13956i		−	1.33314i	0.745442	−	0.666571i	$-0.232239\pi$
$48$	−0.907439	−	0.243147i	−0.130978	−	0.0350953i
$49$	−3.34967	+	5.80180i	−0.478524	+	0.828828i
$50$	3.54203	−	7.08794i	0.500918	−	1.00239i
$51$		−	0.620172i		−	0.0868415i
$52$	−1.84117	+	0.0995483i	−0.255324	+	0.0138049i
$53$	−3.70952	+	3.70952i	−0.509541	+	0.509541i	−0.914386	−	0.404844i	$-0.867326\pi$
$53$	−3.70952	+	3.70952i	−0.509541	+	0.509541i	0.404844	+	0.914386i	$0.367326\pi$
$54$	1.80043	−	0.482424i	0.245008	−	0.0656496i
$55$	0.0985415	+	0.327962i	0.0132873	+	0.0442223i
$56$	1.12023	−	0.646766i	0.149697	−	0.0864278i
$57$	−0.900179			−0.119232
$58$	3.21508	−	1.85623i	0.422161	−	0.243735i
$59$	3.67728	+	0.985325i	0.478742	+	0.128278i	0.490117	−	0.871657i	$-0.336954\pi$
$59$	3.67728	+	0.985325i	0.478742	+	0.128278i	−0.0113750	+	0.999935i	$0.503621\pi$
$60$	−0.164270	−	0.154672i	−0.0212071	−	0.0199680i
$61$	−3.92486	−	6.79805i	−0.502526	−	0.870401i	−0.999996	−	0.00291945i	$-0.999071\pi$
$61$	−3.92486	−	6.79805i	−0.502526	−	0.870401i	0.497470	−	0.867481i	$-0.334263\pi$
$62$	−3.83416	−	14.3093i	−0.486939	−	1.81728i
$63$	−0.811818	+	1.40611i	−0.102279	+	0.177153i
$64$	5.04207			0.630258
$65$	7.29606	+	3.43037i	0.904965	+	0.425485i
$66$	0.0478868			0.00589446
$67$	−2.44516	+	4.23514i	−0.298724	+	0.517405i	−0.975844	−	0.218467i	$-0.929894\pi$
$67$	−2.44516	+	4.23514i	−0.298724	+	0.517405i	0.677120	+	0.735872i	$0.263228\pi$
$68$	−0.416019	−	1.55261i	−0.0504497	−	0.188281i
$69$	0.349161	+	0.604765i	0.0420341	+	0.0728051i
$70$	1.94217	−	0.0584483i	0.232133	−	0.00698591i
$71$	−15.1045	−	4.04725i	−1.79258	−	0.480320i	−0.799799	−	0.600267i	$-0.795061\pi$
$71$	−15.1045	−	4.04725i	−1.79258	−	0.480320i	−0.992780	+	0.119947i	$0.961727\pi$
$72$	−6.04945	+	3.49265i	−0.712935	+	0.411613i
$73$	3.91807			0.458575			0.229288	−	0.973359i	$-0.426360\pi$
$73$	3.91807			0.458575			0.229288	+	0.973359i	$0.426360\pi$
$74$	−9.34119	+	5.39314i	−1.08589	+	0.626939i
$75$	0.312181	+	0.935860i	0.0360476	+	0.108064i
$76$	−2.25360	+	0.603851i	−0.258506	+	0.0692665i
$77$	−0.0593789	+	0.0593789i	−0.00676686	+	0.00676686i
$78$	0.752994	−	0.839074i	0.0852598	−	0.0950064i
$79$			11.1394i			1.25328i	0.779309	+	0.626640i	$0.215570\pi$
$79$			11.1394i			1.25328i	−0.779309	+	0.626640i	$0.784430\pi$
$80$	9.37611	+	5.04350i	1.04828	+	0.563880i
$81$	4.32557	−	7.49210i	0.480618	−	0.832455i
$82$	−5.47704	−	1.46757i	−0.604838	−	0.162066i
$83$		−	13.4251i		−	1.47360i	−0.676113	−	0.736798i	$-0.736337\pi$
$83$		−	13.4251i		−	1.47360i	0.676113	−	0.736798i	$-0.263663\pi$
$84$	0.0143200	−	0.0534431i	0.00156244	−	0.00583112i
$85$	−1.61401	+	6.84039i	−0.175063	+	0.741945i
$86$	7.96744	+	7.96744i	0.859151	+	0.859151i
$87$	−0.119633	+	0.446477i	−0.0128260	+	0.0478673i
$88$	−0.348970	+	0.0935062i	−0.0372003	+	0.00996779i
$89$	−2.35372	−	8.78419i	−0.249493	−	0.931122i	−0.971071	−	0.238789i	$-0.923250\pi$
$89$	−2.35372	−	8.78419i	−0.249493	−	0.931122i	0.721578	−	0.692333i	$-0.243417\pi$
$90$	−10.4880	+	0.315631i	−1.10554	+	0.0332705i
$91$	0.106738	+	1.97414i	0.0111891	+	0.206946i
$92$	1.27981	+	1.27981i	0.133430	+	0.133430i
$93$	1.59734	+	0.922226i	0.165637	+	0.0956304i
$94$	12.5433	+	7.24190i	1.29375	+	0.746945i
$95$	9.92882	+	2.34273i	1.01868	+	0.240359i
$96$	0.394459	−	0.394459i	0.0402593	−	0.0402593i
$97$	3.78550	+	6.55668i	0.384360	+	0.665730i	0.991680	−	0.128727i	$-0.0410890\pi$
$97$	3.78550	+	6.55668i	0.384360	+	0.665730i	−0.607321	+	0.794457i	$0.707756\pi$
$98$	−5.30835	−	9.19433i	−0.536224	−	0.928767i
$99$	0.320657	−	0.320657i	0.0322272	−	0.0322272i
$100$	1.40933	+	2.13352i	0.140933	+	0.213352i
$101$	11.7218	+	6.76758i	1.16636	+	0.673400i	0.952821	−	0.303534i	$-0.0981667\pi$
$101$	11.7218	+	6.76758i	1.16636	+	0.673400i	0.213542	+	0.976934i	$0.431500\pi$
$102$	0.851139	+	0.491405i	0.0842753	+	0.0486564i
$103$	10.3566	+	10.3566i	1.02046	+	1.02046i	0.999786	+	0.0206759i	$0.00658183\pi$
$103$	10.3566	+	10.3566i	1.02046	+	1.02046i	0.0206759	+	0.999786i	$0.493418\pi$
$104$	−3.84894	+	7.58499i	−0.377420	+	0.743770i
$105$	−0.165842	+	0.176134i	−0.0161845	+	0.0171889i
$106$	−2.15172	−	8.03034i	−0.208994	−	0.779975i
$107$	−15.5283	+	4.16078i	−1.50117	+	0.402238i	−0.913493	−	0.406855i	$-0.866625\pi$
$107$	−15.5283	+	4.16078i	−1.50117	+	0.402238i	−0.587680	+	0.809093i	$0.699959\pi$
$108$	−0.155678	+	0.580999i	−0.0149801	+	0.0559066i
$109$	−8.20821	−	8.20821i	−0.786203	−	0.786203i	0.194666	−	0.980870i	$-0.437638\pi$
$109$	−8.20821	−	8.20821i	−0.786203	−	0.786203i	−0.980870	+	0.194666i	$0.937638\pi$
$110$	−0.528183	−	0.124626i	−0.0503603	−	0.0118826i
$111$	0.347585	−	1.29721i	0.0329913	−	0.123125i
$112$			2.61073i			0.246691i
$113$	−4.40249	−	1.17964i	−0.414151	−	0.110972i	0.0457259	−	0.998954i	$-0.485440\pi$
$113$	−4.40249	−	1.17964i	−0.414151	−	0.110972i	−0.459877	+	0.887982i	$0.652107\pi$
$114$	0.713274	−	1.23543i	0.0668042	−	0.115708i
$115$	−2.27728	−	7.57915i	−0.212358	−	0.706760i
$116$			1.19801i			0.111232i
$117$	−0.576403	−	10.6607i	−0.0532884	−	0.985583i
$118$	−4.26605	+	4.26605i	−0.392722	+	0.392722i
$119$	−1.66473	+	0.446064i	−0.152606	+	0.0408907i
$120$	−0.996791	+	0.299502i	−0.0909942	+	0.0273407i
$121$	−9.50597	+	5.48827i	−0.864179	+	0.498934i
$122$	12.4397			1.12624
$123$	0.611402	−	0.352993i	0.0551283	−	0.0318283i
$124$	4.61760	+	1.23728i	0.414673	+	0.111111i
$125$	−1.00772	−	11.1348i	−0.0901335	−	0.995930i
$126$	−1.28652	−	2.22832i	−0.114612	−	0.198514i
$127$	0.629533	+	2.34945i	0.0558620	+	0.208480i	0.988216	−	0.153068i	$-0.0489152\pi$
$127$	0.629533	+	2.34945i	0.0558620	+	0.208480i	−0.932354	+	0.361547i	$0.882249\pi$
$128$	−6.82244	+	11.8168i	−0.603024	+	1.04447i
$129$	−1.40290			−0.123519
$130$	−10.4891	+	7.29517i	−0.919955	+	0.639829i
$131$	6.60705			0.577260			0.288630	−	0.957441i	$-0.406800\pi$
$131$	6.60705			0.577260			0.288630	+	0.957441i	$0.406800\pi$
$132$	−0.00772653	+	0.0133827i	−0.000672508	+	0.00116482i
$133$	0.647462	+	2.41636i	0.0561421	+	0.209525i
$134$	−3.87494	−	6.71159i	−0.334744	−	0.579793i
$135$	1.80293	−	1.91481i	0.155171	−	0.164801i
$136$	−7.16212	−	1.91909i	−0.614147	−	0.164560i
$137$	3.51216	−	2.02775i	0.300064	−	0.173242i	−0.342408	−	0.939552i	$-0.611242\pi$
$137$	3.51216	−	2.02775i	0.300064	−	0.173242i	0.642472	+	0.766309i	$0.277909\pi$
$138$	−1.10666			−0.0942050
$139$	11.1052	−	6.41160i	0.941932	−	0.543825i	0.0513668	−	0.998680i	$-0.483642\pi$
$139$	11.1052	−	6.41160i	0.941932	−	0.543825i	0.890566	+	0.454855i	$0.150309\pi$
$140$	−0.297034	+	0.552200i	−0.0251039	+	0.0466695i
$141$	−1.74189	+	0.466737i	−0.146693	+	0.0393064i
$142$	17.5229	−	17.5229i	1.47049	−	1.47049i
$143$	0.113910	−	0.540300i	0.00952562	−	0.0451822i
$144$		−	14.0984i		−	1.17487i
$145$	2.48149	−	4.61322i	0.206077	−	0.383107i
$146$	−3.10455	+	5.37725i	−0.256935	+	0.445024i
$147$	1.27681	+	0.342121i	0.105310	+	0.0282176i
$148$		−	3.48073i		−	0.286114i
$149$	1.10123	−	4.10983i	0.0902159	−	0.336690i	−0.906035	−	0.423203i	$-0.860906\pi$
$149$	1.10123	−	4.10983i	0.0902159	−	0.336690i	0.996251	+	0.0865128i	$0.0275723\pi$
$150$	−1.53176	−	0.313101i	−0.125068	−	0.0255646i
$151$	4.89430	+	4.89430i	0.398293	+	0.398293i	0.877630	−	0.479338i	$-0.159123\pi$
$151$	4.89430	+	4.89430i	0.398293	+	0.398293i	−0.479338	+	0.877630i	$0.659123\pi$
$152$	−2.78555	+	10.3958i	−0.225938	+	0.843212i
$153$	8.98987	−	2.40883i	0.726788	−	0.194742i
$154$	−0.0344430	−	0.128543i	−0.00277550	−	0.0103583i
$155$	−15.2183	−	14.3291i	−1.22236	−	1.15094i
$156$	0.112997	+	0.345821i	0.00904702	+	0.0276878i
$157$	2.29887	+	2.29887i	0.183470	+	0.183470i	0.792866	−	0.609396i	$-0.208588\pi$
$157$	2.29887	+	2.29887i	0.183470	+	0.183470i	−0.609396	+	0.792866i	$0.708588\pi$
$158$	−15.2880	−	8.82651i	−1.21625	−	0.702199i
$159$	0.896426	+	0.517552i	0.0710912	+	0.0410445i
$160$	−5.37740	+	3.32423i	−0.425121	+	0.262804i
$161$	1.37224	−	1.37224i	0.108148	−	0.108148i
$162$	6.85489	+	11.8730i	0.538571	+	0.932832i
$163$	5.43423	+	9.41236i	0.425642	+	0.737233i	0.996480	−	0.0838295i	$-0.0267151\pi$
$163$	5.43423	+	9.41236i	0.425642	+	0.737233i	−0.570839	+	0.821062i	$0.693382\pi$
$164$	1.29386	−	1.29386i	0.101033	−	0.101033i
$165$	0.0574732	−	0.0355291i	0.00447428	−	0.00276594i
$166$	18.4249	+	10.6376i	1.43005	+	0.825640i
$167$	14.1672	+	8.17941i	1.09629	+	0.632942i	0.935243	−	0.354005i	$-0.115181\pi$
$167$	14.1672	+	8.17941i	1.09629	+	0.632942i	0.161044	+	0.986947i	$0.448514\pi$
$168$	−0.180474	−	0.180474i	−0.0139238	−	0.0139238i
$169$	−7.67599	−	10.4919i	−0.590461	−	0.807066i
$170$	−8.10903	−	7.63522i	−0.621934	−	0.585594i
$171$	−3.49641	−	13.0488i	−0.267377	−	0.997865i
$172$	−3.51218	+	0.941085i	−0.267801	+	0.0717570i
$173$	−1.76871	+	6.60091i	−0.134472	+	0.501858i	0.865527	+	0.500862i	$0.166984\pi$
$173$	−1.76871	+	6.60091i	−0.134472	+	0.501858i	−1.00000		0.000995657i	$0.999683\pi$
$174$	−0.517961	−	0.517961i	−0.0392666	−	0.0392666i
$175$	2.28760	−	1.51112i	0.172926	−	0.114230i
$176$	0.188723	−	0.704325i	0.0142256	−	0.0530905i
$177$		−	0.751164i		−	0.0564609i
$178$	13.9206	+	3.73002i	1.04340	+	0.279577i
$179$	−2.83696	+	4.91376i	−0.212044	+	0.367272i	−0.952354	−	0.304994i	$-0.901345\pi$
$179$	−2.83696	+	4.91376i	−0.212044	+	0.367272i	0.740310	+	0.672266i	$0.234679\pi$
$180$	1.60404	−	2.98198i	0.119558	−	0.222264i
$181$		−	3.59115i		−	0.266928i	−0.991054	−	0.133464i	$-0.957390\pi$
$181$		−	3.59115i		−	0.266928i	0.991054	−	0.133464i	$-0.0426101\pi$
$182$	−2.79393	−	1.41776i	−0.207100	−	0.105091i
$183$	−1.09519	+	1.09519i	−0.0809588	+	0.0809588i
$184$	8.06465	−	2.16092i	0.594534	−	0.159305i
$185$	−7.20980	+	13.4034i	−0.530075	+	0.985436i
$186$	−2.53137	+	1.46149i	−0.185609	+	0.107161i
$187$	0.481358			0.0352004
$188$	−4.04773	+	2.33696i	−0.295211	+	0.170440i
$189$	0.622959	+	0.166921i	0.0453136	+	0.0121417i
$190$	−11.0825	+	11.7702i	−0.804009	+	0.853903i
$191$	11.7411	+	20.3361i	0.849553	+	1.47147i	0.881608	+	0.471982i	$0.156461\pi$
$191$	11.7411	+	20.3361i	0.849553	+	1.47147i	−0.0320553	+	0.999486i	$0.510205\pi$
$192$	−0.257487	−	0.960956i	−0.0185825	−	0.0693510i
$193$	−7.91891	+	13.7160i	−0.570016	+	0.987296i	0.426548	+	0.904465i	$0.359730\pi$
$193$	−7.91891	+	13.7160i	−0.570016	+	0.987296i	−0.996564	+	0.0828311i	$0.973604\pi$
$194$	−11.9981			−0.861411
$195$	0.281193	−	1.56572i	0.0201366	−	0.112124i
$196$	3.42601			0.244715
$197$	−2.85639	+	4.94741i	−0.203509	+	0.352488i	−0.949657	−	0.313292i	$-0.898568\pi$
$197$	−2.85639	+	4.94741i	−0.203509	+	0.352488i	0.746148	+	0.665781i	$0.231901\pi$
$198$	0.185998	+	0.694156i	0.0132183	+	0.0493315i
$199$	4.65156	+	8.05674i	0.329740	+	0.571127i	0.982460	−	0.186472i	$-0.0597055\pi$
$199$	4.65156	+	8.05674i	0.329740	+	0.571127i	−0.652720	+	0.757599i	$0.726372\pi$
$200$	11.7739	−	0.709299i	0.832541	−	0.0501550i
$201$	0.932035	+	0.249738i	0.0657407	+	0.0176152i
$202$	−18.5760	+	10.7248i	−1.30700	+	0.754597i
$203$	1.28453			0.0901563
$204$	−0.274662	+	0.158576i	−0.0192302	+	0.0111026i
$205$	−7.66233	+	2.30227i	−0.535160	+	0.160798i
$206$	−22.4198	+	6.00737i	−1.56206	+	0.418553i
$207$	−7.41034	+	7.41034i	−0.515054	+	0.515054i
$208$	−9.37363	−	14.3819i	−0.649944	−	0.997209i
$209$		−	0.698690i		−	0.0483294i
$210$	−0.110322	−	0.367168i	−0.00761292	−	0.0253370i
$211$	2.73779	−	4.74199i	0.188477	−	0.326452i	−0.756265	−	0.654265i	$-0.772978\pi$
$211$	2.73779	−	4.74199i	0.188477	−	0.326452i	0.944743	+	0.327813i	$0.106311\pi$
$212$	2.59139	+	0.694360i	0.177977	+	0.0476889i
$213$			3.08543i			0.211410i
$214$	6.59375	−	24.6082i	0.450739	−	1.68218i
$215$	15.4738	+	3.65107i	1.05530	+	0.249001i
$216$	1.96199	+	1.96199i	0.133497	+	0.133497i
$217$	1.32664	−	4.95108i	0.0900581	−	0.336102i
$218$	17.7691	−	4.76121i	1.20347	−	0.322470i
$219$	−0.200087	−	0.746736i	−0.0135206	−	0.0504597i
$220$	0.120051	−	0.127501i	0.00809385	−	0.00859612i
$221$	7.56909	−	8.43436i	0.509152	−	0.567357i
$222$	1.50490	+	1.50490i	0.101002	+	0.101002i
$223$	−16.0805	−	9.28408i	−1.07683	−	0.621708i	−0.146790	−	0.989168i	$-0.546894\pi$
$223$	−16.0805	−	9.28408i	−1.07683	−	0.621708i	−0.930039	+	0.367460i	$0.880227\pi$
$224$	−1.34257	−	0.775132i	−0.0897041	−	0.0517907i
$225$	−12.3534	+	8.16030i	−0.823563	+	0.544020i
$226$	5.10737	−	5.10737i	0.339737	−	0.339737i
$227$	−3.19333	−	5.53101i	−0.211949	−	0.367106i	0.740376	−	0.672193i	$-0.234648\pi$
$227$	−3.19333	−	5.53101i	−0.211949	−	0.367106i	−0.952324	+	0.305087i	$0.901314\pi$
$228$	0.230173	+	0.398672i	0.0152436	+	0.0264027i
$229$	−11.1149	+	11.1149i	−0.734491	+	0.734491i	−0.971506	−	0.237015i	$-0.923831\pi$
$229$	−11.1149	+	11.1149i	−0.734491	+	0.734491i	0.237015	+	0.971506i	$0.423831\pi$
$230$	12.2063	+	2.88009i	0.804857	+	0.189908i
$231$	0.0143493	+	0.00828454i	0.000944111	+	0.000545083i
$232$	4.78599	+	2.76319i	0.314215	+	0.181412i
$233$	−5.85956	−	5.85956i	−0.383873	−	0.383873i	0.488623	−	0.872495i	$-0.337500\pi$
$233$	−5.85956	−	5.85956i	−0.383873	−	0.383873i	−0.872495	+	0.488623i	$0.837500\pi$
$234$	15.0877	+	7.65615i	0.986316	+	0.500498i
$235$	20.4274	−	0.614751i	1.33254	−	0.0401019i
$236$	−0.503890	−	1.88054i	−0.0328004	−	0.122413i
$237$	2.12303	−	0.568865i	0.137906	−	0.0369517i
$238$	0.706895	−	2.63817i	0.0458212	−	0.171007i
$239$	13.8081	+	13.8081i	0.893170	+	0.893170i	0.994820	−	0.101650i	$-0.0324123\pi$
$239$	13.8081	+	13.8081i	0.893170	+	0.893170i	−0.101650	+	0.994820i	$0.532412\pi$
$240$	0.482411	−	2.04453i	0.0311395	−	0.131974i
$241$	4.43437	−	16.5493i	0.285643	−	1.06603i	−0.662725	−	0.748863i	$-0.730600\pi$
$241$	4.43437	−	16.5493i	0.285643	−	1.06603i	0.948368	−	0.317172i	$-0.102733\pi$
$242$		−	17.3950i		−	1.11819i
$243$	−5.05712	−	1.35505i	−0.324414	−	0.0869266i
$244$	−2.00715	+	3.47649i	−0.128495	+	0.222559i
$245$	−13.1926	−	7.09645i	−0.842847	−	0.453376i
$246$			1.11880i			0.0713323i
$247$	−12.2425	−	10.9865i	−0.778970	−	0.699056i
$248$	15.5933	−	15.5933i	0.990176	−	0.990176i
$249$	−2.55866	+	0.685590i	−0.162148	+	0.0434475i
$250$	16.0802	+	7.43987i	1.01700	+	0.470539i
$251$	8.61959	−	4.97652i	0.544063	−	0.314115i	−0.202661	−	0.979249i	$-0.564959\pi$
$251$	8.61959	−	4.97652i	0.544063	−	0.314115i	0.746724	+	0.665134i	$0.231626\pi$
$252$	0.830319			0.0523052
$253$	−0.469399	+	0.271008i	−0.0295109	+	0.0170381i
$254$	−3.72326	−	0.997644i	−0.233618	−	0.0625978i
$255$	1.38612	−	0.0417144i	0.0868022	−	0.00261226i
$256$	−5.76971	−	9.99343i	−0.360607	−	0.624589i
$257$	−0.712105	−	2.65761i	−0.0444199	−	0.165777i	0.940153	−	0.340753i	$-0.110682\pi$
$257$	−0.712105	−	2.65761i	−0.0444199	−	0.165777i	−0.984573	+	0.174976i	$0.944015\pi$
$258$	1.11162	−	1.92538i	0.0692062	−	0.119869i
$259$	−3.73211			−0.231902
$260$	−0.346338	−	4.10842i	−0.0214790	−	0.254794i
$261$	−6.93669			−0.429370
$262$	−5.23522	+	9.06767i	−0.323433	+	0.560202i
$263$	−1.59881	−	5.96686i	−0.0985871	−	0.367932i	0.898952	−	0.438048i	$-0.144330\pi$
$263$	−1.59881	−	5.96686i	−0.0985871	−	0.367932i	−0.997539	+	0.0701155i	$0.977663\pi$
$264$	0.0356423	+	0.0617342i	0.00219363	+	0.00379948i
$265$	−8.54049	−	8.04147i	−0.524638	−	0.493983i
$266$	−3.82930	−	1.02606i	−0.234789	−	0.0629116i
$267$	−1.55396	+	0.897179i	−0.0951008	+	0.0549065i
$268$	2.50088			0.152766
$269$	18.3796	−	10.6115i	1.12063	−	0.646994i	0.179066	−	0.983837i	$-0.442692\pi$
$269$	18.3796	−	10.6115i	1.12063	−	0.646994i	0.941561	+	0.336843i	$0.109359\pi$
$270$	1.19935	+	3.99162i	0.0729899	+	0.242922i
$271$	−12.4458	+	3.33484i	−0.756027	+	0.202577i	−0.616190	−	0.787598i	$-0.711325\pi$
$271$	−12.4458	+	3.33484i	−0.756027	+	0.202577i	−0.139837	+	0.990174i	$0.544658\pi$
$272$	10.5820	−	10.5820i	0.641629	−	0.641629i
$273$	0.370796	−	0.121158i	0.0224416	−	0.00733282i
$274$			6.42690i			0.388263i
$275$	−0.726385	+	0.242305i	−0.0438026	+	0.0146116i
$276$	0.178559	−	0.309274i	0.0107480	−	0.0186161i
$277$	−20.5514	−	5.50674i	−1.23482	−	0.330868i	−0.418363	−	0.908280i	$-0.637396\pi$
$277$	−20.5514	−	5.50674i	−1.23482	−	0.330868i	−0.816453	+	0.577412i	$0.804063\pi$
$278$			20.3214i			1.21880i
$279$	−7.16409	+	26.7367i	−0.428903	+	1.60069i
$280$	1.52091	+	2.46028i	0.0908917	+	0.147030i
$281$	−4.22655	−	4.22655i	−0.252135	−	0.252135i	0.569711	−	0.821845i	$-0.307055\pi$
$281$	−4.22655	−	4.22655i	−0.252135	−	0.252135i	−0.821845	+	0.569711i	$0.807055\pi$
$282$	0.739656	−	2.76044i	0.0440459	−	0.164382i
$283$	−1.48552	+	0.398044i	−0.0883050	+	0.0236613i	−0.302701	−	0.953086i	$-0.597888\pi$
$283$	−1.48552	+	0.398044i	−0.0883050	+	0.0236613i	0.214396	+	0.976747i	$0.431222\pi$
$284$	2.06974	+	7.72438i	0.122817	+	0.458358i
$285$	−0.0605484	−	2.01195i	−0.00358658	−	0.119178i
$286$	0.651262	+	0.584450i	0.0385100	+	0.0345593i
$287$	−1.38730	−	1.38730i	−0.0818897	−	0.0818897i
$288$	7.25011	+	4.18585i	0.427217	+	0.246654i
$289$	−6.16679	−	3.56040i	−0.362752	−	0.209435i
$290$	4.36503	+	7.06103i	0.256323	+	0.414638i
$291$	1.05631	−	1.05631i	0.0619218	−	0.0619218i
$292$	−1.00184	−	1.73524i	−0.0586282	−	0.101547i
$293$	−1.39593	−	2.41782i	−0.0815512	−	0.141251i	0.822365	−	0.568960i	$-0.192654\pi$
$293$	−1.39593	−	2.41782i	−0.0815512	−	0.141251i	−0.903916	+	0.427709i	$0.859321\pi$
$294$	−1.48124	+	1.48124i	−0.0863877	+	0.0863877i
$295$	−1.95491	+	8.28521i	−0.113819	+	0.482384i
$296$	−13.9053	−	8.02825i	−0.808232	−	0.466633i
$297$	−0.155996	−	0.0900642i	−0.00905180	−	0.00522606i
$298$	4.76785	+	4.76785i	0.276194	+	0.276194i
$299$	−2.63244	+	12.4863i	−0.152238	+	0.722100i
$300$	0.334650	−	0.377556i	0.0193210	−	0.0217982i
$301$	1.00905	+	3.76583i	0.0581607	+	0.217059i
$302$	−10.5951	+	2.83896i	−0.609682	+	0.163364i
$303$	0.691212	−	2.57964i	0.0397091	−	0.148196i
$304$	−15.3598	−	15.3598i	−0.880944	−	0.880944i
$305$	14.9300	−	9.22953i	0.854891	−	0.528481i
$306$	−3.81736	+	14.2466i	−0.218224	+	0.814423i
$307$			2.12112i			0.121058i	0.998166	+	0.0605292i	$0.0192788\pi$
$307$			2.12112i			0.121058i	−0.998166	+	0.0605292i	$0.980721\pi$
$308$	0.0414808	+	0.0111148i	0.00236359	+	0.000633322i
$309$	1.44495	−	2.50272i	0.0822001	−	0.142375i
$310$	31.7241	−	9.53204i	1.80181	−	0.541383i
$311$			21.2656i			1.20586i	0.797794	+	0.602931i	$0.206000\pi$
$311$			21.2656i			1.20586i	−0.797794	+	0.602931i	$0.794000\pi$
$312$	1.64216	+	0.346212i	0.0929692	+	0.0196004i
$313$	−14.3666	+	14.3666i	−0.812050	+	0.812050i	−0.984941	−	0.172891i	$-0.944689\pi$
$313$	−14.3666	+	14.3666i	−0.812050	+	0.812050i	0.172891	+	0.984941i	$0.444689\pi$
$314$	−4.97657	+	1.33347i	−0.280844	+	0.0752519i
$315$	−3.19734	−	1.71988i	−0.180150	−	0.0969043i
$316$	4.93342	−	2.84831i	0.277527	−	0.160230i
$317$	8.78989			0.493689			0.246845	−	0.969055i	$-0.420606\pi$
$317$	8.78989			0.493689			0.246845	+	0.969055i	$0.420606\pi$
$318$	−1.42060	+	0.820184i	−0.0796633	+	0.0459936i
$319$	−0.346541	−	0.0928554i	−0.0194026	−	0.00519890i
$320$	0.339143	+	11.2693i	0.0189587	+	0.629973i
$321$	1.58599	+	2.74701i	0.0885212	+	0.153323i
$322$	0.795974	+	2.97061i	0.0443579	+	0.165546i
$323$	7.16982	−	12.4185i	0.398940	−	0.690984i
$324$	−4.42414			−0.245786
$325$	−7.17632	+	16.5378i	−0.398071	+	0.917355i
$326$	−17.2237			−0.953930
$327$	−1.14521	+	1.98356i	−0.0633302	+	0.109691i
$328$	−2.18463	−	8.15316i	−0.120626	−	0.450183i
$329$	2.50574	+	4.34006i	0.138146	+	0.239275i
$330$	0.00322099	+	0.107030i	0.000177310	+	0.00589179i
$331$	17.5522	+	4.70310i	0.964756	+	0.258506i	0.706612	−	0.707601i	$-0.250223\pi$
$331$	17.5522	+	4.70310i	0.964756	+	0.258506i	0.258144	+	0.966107i	$0.416889\pi$
$332$	−5.94572	+	3.43276i	−0.326314	+	0.188397i
$333$	20.1541			1.10444
$334$	−22.4512	+	12.9622i	−1.22848	+	0.709261i
$335$	−9.63025	−	5.18020i	−0.526157	−	0.283025i
$336$	0.497574	−	0.133325i	0.0271449	−	0.00727345i
$337$	17.2522	−	17.2522i	0.939788	−	0.939788i	−0.0584999	−	0.998287i	$-0.518632\pi$
$337$	17.2522	−	17.2522i	0.939788	−	0.939788i	0.998287	+	0.0584999i	$0.0186317\pi$
$338$	20.4815	−	2.22128i	1.11405	−	0.120822i
$339$			0.899302i			0.0488434i
$340$	3.44218	−	1.03426i	0.186678	−	0.0560906i
$341$	−0.715803	+	1.23981i	−0.0387629	+	0.0671393i
$342$	20.6789	+	5.54089i	1.11819	+	0.299617i
$343$		−	7.51173i		−	0.405595i
$344$	−4.34120	+	16.2016i	−0.234062	+	0.873530i
$345$	−1.32820	+	0.821073i	−0.0715078	+	0.0442051i
$346$	−7.65777	−	7.65777i	−0.411684	−	0.411684i
$347$	−2.01142	+	7.50674i	−0.107979	+	0.402983i	−0.998666	−	0.0516340i	$-0.983557\pi$
$347$	−2.01142	+	7.50674i	−0.107979	+	0.402983i	0.890687	+	0.454617i	$0.150224\pi$
$348$	0.228326	−	0.0611797i	0.0122395	−	0.00327958i
$349$	−1.31241	−	4.89796i	−0.0702515	−	0.262182i	0.921863	−	0.387515i	$-0.126667\pi$
$349$	−1.31241	−	4.89796i	−0.0702515	−	0.262182i	−0.992115	+	0.125333i	$0.960000\pi$
$350$	0.261271	+	4.33692i	0.0139655	+	0.231818i
$351$	−4.03106	+	1.31715i	−0.215162	+	0.0703044i
$352$	0.306166	+	0.306166i	0.0163187	+	0.0163187i
$353$	22.1857	+	12.8089i	1.18082	+	0.681749i	0.956205	−	0.292698i	$-0.0945531\pi$
$353$	22.1857	+	12.8089i	1.18082	+	0.681749i	0.224618	+	0.974447i	$0.427886\pi$
$354$	1.03091	+	0.595199i	0.0547925	+	0.0316345i
$355$	8.02986	−	34.0317i	0.426181	−	1.80622i
$356$	−3.28851	+	3.28851i	−0.174291	+	0.174291i
$357$	0.170029	+	0.294499i	0.00899888	+	0.0155865i
$358$	−4.49584	−	7.78702i	−0.237613	−	0.411557i
$359$	10.0443	−	10.0443i	0.530117	−	0.530117i	−0.390490	−	0.920607i	$-0.627694\pi$
$359$	10.0443	−	10.0443i	0.530117	−	0.530117i	0.920607	+	0.390490i	$0.127694\pi$
$360$	−8.21318	−	13.2859i	−0.432873	−	0.700231i
$361$	−1.57095	−	0.906990i	−0.0826817	−	0.0477363i
$362$	4.92858	+	2.84552i	0.259040	+	0.149557i
$363$	1.53145	+	1.53145i	0.0803801	+	0.0803801i
$364$	0.847017	−	0.552055i	0.0443957	−	0.0289355i
$365$	0.263540	+	8.75710i	0.0137943	+	0.458368i
$366$	−0.635270	−	2.37086i	−0.0332061	−	0.123927i
$367$	19.4366	−	5.20802i	1.01458	−	0.271857i	0.287040	−	0.957919i	$-0.407329\pi$
$367$	19.4366	−	5.20802i	1.01458	−	0.271857i	0.727543	+	0.686062i	$0.240662\pi$
$368$	−4.36137	+	16.2769i	−0.227352	+	0.848490i
$369$	7.49167	+	7.49167i	0.390001	+	0.390001i
$370$	−12.6823	−	20.5153i	−0.659320	−	1.06654i
$371$	0.744507	−	2.77854i	0.0386529	−	0.144255i
$372$		−	0.943243i		−	0.0489049i
$373$	−25.3125	−	6.78245i	−1.31063	−	0.351182i	−0.465170	−	0.885221i	$-0.654007\pi$
$373$	−25.3125	−	6.78245i	−1.31063	−	0.351182i	−0.845460	+	0.534039i	$0.820673\pi$
$374$	−0.381413	+	0.660627i	−0.0197224	+	0.0341602i
$375$	−2.07070	+	0.760691i	−0.106931	+	0.0392819i
$376$			21.5607i			1.11191i
$377$	−7.07618	+	4.61200i	−0.364442	+	0.237530i
$378$	−0.722700	+	0.722700i	−0.0371717	+	0.0371717i
$379$	21.7627	−	5.83130i	1.11787	−	0.299534i	0.347852	−	0.937550i	$-0.386911\pi$
$379$	21.7627	−	5.83130i	1.11787	−	0.299534i	0.770023	+	0.638016i	$0.220245\pi$
$380$	−1.50123	−	4.99631i	−0.0770112	−	0.256306i
$381$	0.415627	−	0.239962i	0.0212932	−	0.0122936i
$382$	−37.2130			−1.90398
$383$	−20.8938	+	12.0630i	−1.06762	+	0.616392i	−0.927531	−	0.373747i	$-0.878073\pi$
$383$	−20.8938	+	12.0630i	−1.06762	+	0.616392i	−0.140091	+	0.990139i	$0.544740\pi$
$384$	2.60055	+	0.696814i	0.132709	+	0.0355591i
$385$	−0.136709	−	0.128721i	−0.00696735	−	0.00656024i
$386$	−12.5494	−	21.7362i	−0.638748	−	1.10634i
$387$	−5.44905	−	20.3361i	−0.276991	−	1.03374i
$388$	1.93589	−	3.35305i	0.0982797	−	0.170225i
$389$	−14.3262			−0.726365			−0.363183	−	0.931718i	$-0.618310\pi$
$389$	−14.3262			−0.726365			−0.363183	+	0.931718i	$0.618310\pi$
$390$	1.92603	+	1.62655i	0.0975281	+	0.0823633i
$391$	−11.1241			−0.562571
$392$	7.90203	−	13.6867i	0.399113	−	0.691284i
$393$	−0.337408	−	1.25922i	−0.0170200	−	0.0635194i
$394$	−4.52662	−	7.84034i	−0.228048	−	0.394991i
$395$	−24.8972	+	0.749265i	−1.25271	+	0.0376996i
$396$	−0.224004	−	0.0600217i	−0.0112566	−	0.00301620i
$397$	29.0058	−	16.7465i	1.45576	−	0.840484i	0.456963	−	0.889486i	$-0.348937\pi$
$397$	29.0058	−	16.7465i	1.45576	−	0.840484i	0.998799	+	0.0490017i	$0.0156040\pi$
$398$	−14.7430			−0.739000
$399$	0.427464	−	0.246797i	0.0214000	−	0.0123553i
$400$	−10.6418	+	21.2954i	−0.532092	+	1.06477i
$401$	17.9170	−	4.80084i	0.894731	−	0.239743i	0.217979	−	0.975953i	$-0.430054\pi$
$401$	17.9170	−	4.80084i	0.894731	−	0.239743i	0.676752	+	0.736211i	$0.263387\pi$
$402$	−1.08126	+	1.08126i	−0.0539285	+	0.0539285i
$403$	10.4683	+	32.0376i	0.521464	+	1.59591i
$404$		−	6.92181i		−	0.344373i
$405$	17.0362	+	9.16394i	0.846536	+	0.455360i
$406$	−1.01782	+	1.76292i	−0.0505136	+	0.0874922i
$407$	1.00685	+	0.269785i	0.0499077	+	0.0133727i
$408$			1.46302i			0.0724301i
$409$	1.33873	−	4.99622i	0.0661960	−	0.247047i	−0.924897	−	0.380218i	$-0.875849\pi$
$409$	1.33873	−	4.99622i	0.0661960	−	0.247047i	0.991093	+	0.133171i	$0.0425158\pi$
$410$	2.91170	−	12.3402i	0.143799	−	0.609440i
$411$	−0.565822	−	0.565822i	−0.0279099	−	0.0279099i
$412$	1.93858	−	7.23487i	0.0955068	−	0.356436i
$413$	−2.01636	+	0.540281i	−0.0992184	+	0.0265855i
$414$	−4.29840	−	16.0418i	−0.211255	−	0.788414i
$415$	30.0058	−	0.903008i	1.47293	−	0.0443269i
$416$	10.1790	−	0.550355i	0.499065	−	0.0269834i
$417$	−1.78909	−	1.78909i	−0.0876122	−	0.0876122i
$418$	0.958899	+	0.553620i	0.0469013	+	0.0270785i
$419$	0.872048	+	0.503477i	0.0426023	+	0.0245965i	0.521150	−	0.853465i	$-0.325503\pi$
$419$	0.872048	+	0.503477i	0.0426023	+	0.0245965i	−0.478548	+	0.878062i	$0.658837\pi$
$420$	0.120412	+	0.0284114i	0.00587548	+	0.00138633i
$421$	0.294746	−	0.294746i	0.0143650	−	0.0143650i	−0.699888	−	0.714253i	$-0.746767\pi$
$421$	0.294746	−	0.294746i	0.0143650	−	0.0143650i	0.714253	+	0.699888i	$0.246767\pi$
$422$	4.33868	+	7.51482i	0.211204	+	0.365816i
$423$	−13.5314	−	23.4371i	−0.657920	−	1.13955i
$424$	8.75094	−	8.75094i	0.424983	−	0.424983i
$425$	−15.3972	−	3.14729i	−0.746875	−	0.152666i
$426$	−4.23451	−	2.44480i	−0.205163	−	0.118451i
$427$	3.72756	+	2.15211i	0.180389	+	0.104148i
$428$	5.81326	+	5.81326i	0.280995	+	0.280995i
$429$	−0.108792	+	0.00588215i	−0.00525252	+	0.000283993i
$430$	−17.2718	+	18.3436i	−0.832918	+	0.884606i
$431$	−1.07449	−	4.01004i	−0.0517562	−	0.193157i	0.935207	−	0.354100i	$-0.115213\pi$
$431$	−1.07449	−	4.01004i	−0.0517562	−	0.193157i	−0.986964	+	0.160944i	$0.948546\pi$
$432$	−5.40930	+	1.44942i	−0.260255	+	0.0697352i
$433$	3.88103	−	14.4842i	0.186511	−	0.696067i	−0.807792	−	0.589468i	$-0.799337\pi$
$433$	3.88103	−	14.4842i	0.186511	−	0.696067i	0.994302	−	0.106599i	$-0.0339960\pi$
$434$	5.74380	+	5.74380i	0.275711	+	0.275711i
$435$	−1.00595	−	0.237355i	−0.0482315	−	0.0113803i
$436$	−1.53644	+	5.73407i	−0.0735821	+	0.274612i
$437$			16.1466i			0.772399i
$438$	1.18338	+	0.317086i	0.0565441	+	0.0151509i
$439$	6.94098	−	12.0221i	0.331275	−	0.573785i	−0.651487	−	0.758660i	$-0.725855\pi$
$439$	6.94098	−	12.0221i	0.331275	−	0.573785i	0.982762	+	0.184875i	$0.0591879\pi$
$440$	−0.232464	−	0.773678i	−0.0110823	−	0.0368836i
$441$			19.8372i			0.944628i
$442$	5.57801	+	17.0711i	0.265319	+	0.811991i
$443$	10.0594	−	10.0594i	0.477938	−	0.477938i	−0.426533	−	0.904472i	$-0.640265\pi$
$443$	10.0594	−	10.0594i	0.477938	−	0.477938i	0.904472	+	0.426533i	$0.140265\pi$
$444$	−0.663384	+	0.177753i	−0.0314828	+	0.00843580i
$445$	19.4748	−	5.85154i	0.923196	−	0.277389i
$446$	25.4834	−	14.7128i	1.20667	−	0.696673i
$447$	−0.839520			−0.0397079
$448$	−2.39430	+	1.38235i	−0.113120	+	0.0653100i
$449$	−6.42946	−	1.72277i	−0.303425	−	0.0813024i	0.103894	−	0.994588i	$-0.466870\pi$
$449$	−6.42946	−	1.72277i	−0.303425	−	0.0813024i	−0.407319	+	0.913286i	$0.633536\pi$
$450$	−1.41091	−	23.4201i	−0.0665108	−	1.10404i
$451$	0.273982	+	0.474551i	0.0129013	+	0.0223457i
$452$	0.603263	+	2.25141i	0.0283751	+	0.105897i
$453$	0.682853	−	1.18274i	0.0320832	−	0.0555698i
$454$	10.1212			0.475011
$455$	−4.40514	+	0.371351i	−0.206516	+	0.0174092i
$456$	2.12357			0.0994451
$457$	−18.4793	+	32.0071i	−0.864426	+	1.49723i	0.00318917	+	0.999995i	$0.498985\pi$
$457$	−18.4793	+	32.0071i	−0.864426	+	1.49723i	−0.867616	+	0.497236i	$0.834348\pi$
$458$	−6.44722	−	24.0614i	−0.301259	−	1.12431i
$459$	−1.84844	−	3.20160i	−0.0862780	−	0.149438i
$460$	−2.77437	+	2.94653i	−0.129355	+	0.137383i
$461$	24.8502	+	6.65860i	1.15739	+	0.310122i	0.785923	−	0.618324i	$-0.212188\pi$
$461$	24.8502	+	6.65860i	1.15739	+	0.310122i	0.371468	+	0.928446i	$0.378855\pi$
$462$	−0.0227398	+	0.0131288i	−0.00105795	+	0.000610809i
$463$	15.9580			0.741632			0.370816	−	0.928706i	$-0.379078\pi$
$463$	15.9580			0.741632			0.370816	+	0.928706i	$0.379078\pi$
$464$	−9.65955	+	5.57694i	−0.448433	+	0.258903i
$465$	−1.95379	+	3.63218i	−0.0906046	+	0.168438i
$466$	12.6847	−	3.39887i	0.587609	−	0.157449i
$467$	−18.6259	+	18.6259i	−0.861902	+	0.861902i	−0.991559	−	0.129657i	$-0.958612\pi$
$467$	−18.6259	+	18.6259i	−0.861902	+	0.861902i	0.129657	+	0.991559i	$0.458612\pi$
$468$	−4.57404	+	2.98119i	−0.211435	+	0.137806i
$469$		−	2.68150i		−	0.123820i
$470$	−15.3424	+	28.5222i	−0.707690	+	1.31563i
$471$	0.320738	−	0.555534i	0.0147788	−	0.0255976i
$472$	−8.67489	−	2.32443i	−0.399294	−	0.106991i
$473$		−	1.08889i		−	0.0500671i
$474$	−0.901501	+	3.36445i	−0.0414073	+	0.154534i
$475$	−4.56829	+	22.3491i	−0.209607	+	1.02544i
$476$	0.623222	+	0.623222i	0.0285653	+	0.0285653i
$477$	−4.02047	+	15.0046i	−0.184085	+	0.687014i
$478$	−29.8916	+	8.00943i	−1.36721	+	0.366343i
$479$	−4.29638	−	16.0343i	−0.196307	−	0.732627i	−0.991925	−	0.126828i	$-0.959520\pi$
$479$	−4.29638	−	16.0343i	−0.196307	−	0.732627i	0.795618	−	0.605799i	$-0.207146\pi$
$480$	0.908170	+	0.855105i	0.0414521	+	0.0390300i
$481$	20.5593	−	13.3998i	0.937426	−	0.610980i
$482$	19.1990	+	19.1990i	0.874490	+	0.874490i
$483$	−0.331609	−	0.191455i	−0.0150888	−	0.00871149i
$484$	4.86130	+	2.80667i	0.220968	+	0.127576i
$485$	−14.3999	+	8.90183i	−0.653867	+	0.404211i
$486$	5.86681	−	5.86681i	0.266124	−	0.266124i
$487$	−13.1399	−	22.7590i	−0.595425	−	1.03131i	−0.993487	−	0.113948i	$-0.963650\pi$
$487$	−13.1399	−	22.7590i	−0.595425	−	1.03131i	0.398062	−	0.917359i	$-0.369683\pi$
$488$	9.25893	+	16.0369i	0.419132	+	0.725958i
$489$	1.51637	−	1.51637i	0.0685724	−	0.0685724i
$490$	20.1928	−	12.4829i	0.912217	−	0.563919i
$491$	−36.0301	−	20.8020i	−1.62602	−	0.938781i	−0.985265	−	0.171034i	$-0.945289\pi$
$491$	−36.0301	−	20.8020i	−1.62602	−	0.938781i	−0.640752	−	0.767748i	$-0.721377\pi$
$492$	−0.312668	−	0.180519i	−0.0140961	−	0.00813842i
$493$	−5.20655	−	5.20655i	−0.234491	−	0.234491i
$494$	24.7787	−	8.09647i	1.11485	−	0.364277i
$495$	0.738254	+	0.695118i	0.0331821	+	0.0312432i
$496$	11.5195	+	42.9915i	0.517242	+	1.93037i
$497$	8.28224	−	2.21922i	0.371509	−	0.0995456i
$498$	1.08648	−	4.05480i	0.0486864	−	0.181700i
$499$	8.31651	+	8.31651i	0.372298	+	0.372298i	0.868314	−	0.496015i	$-0.165204\pi$
$499$	8.31651	+	8.31651i	0.372298	+	0.372298i	−0.496015	+	0.868314i	$0.665204\pi$
$500$	−4.67373	+	3.29345i	−0.209016	+	0.147287i
$501$	0.835410	−	3.11779i	0.0373234	−	0.139293i
$502$			15.7730i			0.703982i
$503$	−10.3108	−	2.76277i	−0.459736	−	0.123186i	0.0215156	−	0.999769i	$-0.493151\pi$
$503$	−10.3108	−	2.76277i	−0.459736	−	0.123186i	−0.481251	+	0.876583i	$0.659818\pi$
$504$	1.91512	−	3.31708i	0.0853062	−	0.147755i
$505$	−14.3375	+	26.6541i	−0.638010	+	1.18609i
$506$		−	0.858953i		−	0.0381851i
$507$	−1.60762	+	1.99875i	−0.0713971	+	0.0887674i
$508$	0.879556	−	0.879556i	0.0390240	−	0.0390240i
$509$	−2.91197	+	0.780260i	−0.129071	+	0.0345844i	−0.322776	−	0.946475i	$-0.604616\pi$
$509$	−2.91197	+	0.780260i	−0.129071	+	0.0345844i	0.193705	+	0.981060i	$0.437949\pi$
$510$	−1.04107	+	1.93540i	−0.0460993	+	0.0857008i
$511$	−1.86056	+	1.07419i	−0.0823062	+	0.0475195i
$512$	−9.00279			−0.397871
$513$	−4.64712	+	2.68301i	−0.205175	+	0.118458i
$514$	4.21162	+	1.12850i	0.185767	+	0.0497760i
$515$	−22.4509	+	23.8441i	−0.989304	+	1.05070i
$516$	0.358718	+	0.621318i	0.0157917	+	0.0273520i
$517$	−0.362267	−	1.35200i	−0.0159325	−	0.0594608i
$518$	2.95721	−	5.12203i	0.129932	−	0.225049i
$519$	1.34838			0.0591871
$520$	−17.2118	−	8.09242i	−0.754786	−	0.354876i
$521$	−5.84796			−0.256204			−0.128102	−	0.991761i	$-0.540888\pi$
$521$	−5.84796			−0.256204			−0.128102	+	0.991761i	$0.540888\pi$
$522$	5.49642	−	9.52007i	0.240572	−	0.416682i
$523$	0.767497	+	2.86434i	0.0335603	+	0.125249i	0.980674	−	0.195650i	$-0.0626817\pi$
$523$	0.767497	+	2.86434i	0.0335603	+	0.125249i	−0.947113	+	0.320899i	$0.896015\pi$
$524$	−1.68940	−	2.92613i	−0.0738020	−	0.127829i
$525$	−0.404823	−	0.358819i	−0.0176679	−	0.0156601i
$526$	9.45590	+	2.53370i	0.412297	+	0.110475i
$527$	−25.4453	+	14.6909i	−1.10842	+	0.639944i
$528$	−0.143873			−0.00626129
$529$	−9.07083	+	5.23704i	−0.394384	+	0.227698i
$530$	17.8035	−	5.34936i	0.773336	−	0.232361i
$531$	10.8887	−	2.91762i	0.472529	−	0.126614i
$532$	0.904605	−	0.904605i	0.0392196	−	0.0392196i
$533$	12.6233	+	2.66133i	0.546776	+	0.115275i
$534$		−	2.84359i		−	0.123054i
$535$	−10.3441	−	34.4266i	−0.447212	−	1.48839i
$536$	5.76825	−	9.99091i	0.249151	−	0.431542i
$537$	1.08138	+	0.289755i	0.0466650	+	0.0125038i
$538$			33.6329i			1.45002i
$539$	−0.265543	+	0.991021i	−0.0114378	+	0.0426863i
$540$	−1.30904	−	0.308870i	−0.0563320	−	0.0132916i
$541$	−15.4678	−	15.4678i	−0.665013	−	0.665013i	0.291544	−	0.956557i	$-0.405831\pi$
$541$	−15.4678	−	15.4678i	−0.665013	−	0.665013i	−0.956557	+	0.291544i	$0.905831\pi$
$542$	5.28484	−	19.7233i	0.227003	−	0.847188i
$543$	−0.684429	+	0.183392i	−0.0293717	+	0.00787011i
$544$	2.29997	+	8.58362i	0.0986105	+	0.368020i
$545$	17.7937	−	18.8979i	0.762198	−	0.809497i
$546$	−0.127527	+	0.604891i	−0.00545767	+	0.0258870i
$547$	1.76989	+	1.76989i	0.0756751	+	0.0756751i	0.743931	−	0.668256i	$-0.232959\pi$
$547$	1.76989	+	1.76989i	0.0756751	+	0.0756751i	−0.668256	+	0.743931i	$0.732959\pi$
$548$	−1.79610	−	1.03698i	−0.0767256	−	0.0442976i
$549$	−20.1295	−	11.6218i	−0.859106	−	0.496005i
$550$	0.243019	−	1.18890i	0.0103624	−	0.0506950i
$551$	−7.55729	+	7.55729i	−0.321952	+	0.321952i
$552$	−0.823688	−	1.42667i	−0.0350585	−	0.0607231i
$553$	−3.05402	−	5.28972i	−0.129870	−	0.224942i
$554$	23.8419	−	23.8419i	1.01295	−	1.01295i
$555$	2.92271	+	0.689619i	0.124062	+	0.0292727i
$556$	−5.67915	−	3.27886i	−0.240850	−	0.139055i
$557$	8.17068	+	4.71734i	0.346203	+	0.199880i	0.663012	−	0.748609i	$-0.269278\pi$
$557$	8.17068	+	4.71734i	0.346203	+	0.199880i	−0.316809	+	0.948489i	$0.602611\pi$
$558$	−31.0175	−	31.0175i	−1.31308	−	1.31308i
$559$	−19.0795	−	17.1222i	−0.806978	−	0.724191i
$560$	−5.83514	+	0.175605i	−0.246580	+	0.00742067i
$561$	−0.0245819	−	0.0917409i	−0.00103785	−	0.00387330i
$562$	9.14960	−	2.45163i	0.385953	−	0.103416i
$563$	−2.53443	+	9.45863i	−0.106814	+	0.398634i	−0.998545	−	0.0539320i	$-0.982825\pi$
$563$	−2.53443	+	9.45863i	−0.106814	+	0.398634i	0.891731	+	0.452566i	$0.149491\pi$
$564$	0.652105	+	0.652105i	0.0274586	+	0.0274586i
$565$	2.34045	−	9.91916i	0.0984633	−	0.417302i
$566$	0.630795	−	2.35416i	0.0265143	−	0.0989527i
$567$			4.74366i			0.199215i
$568$	35.6324	+	9.54766i	1.49510	+	0.400611i
$569$	3.20931	−	5.55868i	0.134541	−	0.233032i	−0.790881	−	0.611970i	$-0.790377\pi$
$569$	3.20931	−	5.55868i	0.134541	−	0.233032i	0.925422	+	0.378938i	$0.123711\pi$
$570$	2.80922	+	1.51111i	0.117665	+	0.0632934i
$571$			1.72174i			0.0720527i	0.999351	+	0.0360264i	$0.0114700\pi$
$571$			1.72174i			0.0720527i	−0.999351	+	0.0360264i	$0.988530\pi$
$572$	−0.268415	+	0.0877049i	−0.0112230	+	0.00366713i
$573$	3.27622	−	3.27622i	0.136866	−	0.136866i
$574$	3.00322	−	0.804709i	0.125352	−	0.0335879i
$575$	16.7867	−	5.59965i	0.700052	−	0.233521i
$576$	12.9297	−	7.46495i	0.538736	−	0.311040i
$577$	24.8642			1.03511			0.517554	−	0.855650i	$-0.326843\pi$
$577$	24.8642			1.03511			0.517554	+	0.855650i	$0.326843\pi$
$578$	9.77275	−	5.64230i	0.406493	−	0.234689i
$579$	3.01849	+	0.808803i	0.125444	+	0.0336127i
$580$	−2.67762	+	0.0805813i	−0.111182	+	0.00334596i
$581$	3.68068	+	6.37512i	0.152700	+	0.264484i
$582$	0.612715	+	2.28668i	0.0253979	+	0.0947861i
$583$	−0.401707	+	0.695777i	−0.0166370	+	0.0288161i
$584$	−9.24291			−0.382474
$585$	23.7885	−	2.00536i	0.983534	−	0.0829114i
$586$	4.42437			0.182769
$587$	13.3836	−	23.1811i	0.552400	−	0.956785i	−0.445701	−	0.895182i	$-0.647045\pi$
$587$	13.3836	−	23.1811i	0.552400	−	0.956785i	0.998101	−	0.0616029i	$-0.0196212\pi$
$588$	−0.174959	−	0.652955i	−0.00721517	−	0.0269274i
$589$	21.3238	+	36.9338i	0.878630	+	1.52183i
$590$	−9.82180	−	9.24791i	−0.404357	−	0.380731i
$591$	1.08878	+	0.291739i	0.0447866	+	0.0120005i
$592$	28.0651	−	16.2034i	1.15347	−	0.665956i
$593$	−19.8452			−0.814944			−0.407472	−	0.913218i	$-0.633590\pi$
$593$	−19.8452			−0.814944			−0.407472	+	0.913218i	$0.633590\pi$
$594$	0.247213	−	0.142728i	0.0101433	−	0.00585621i
$595$	−1.10895	−	3.69077i	−0.0454627	−	0.151307i
$596$	−2.10174	+	0.563161i	−0.0860908	+	0.0230680i
$597$	1.29797	−	1.29797i	0.0531224	−	0.0531224i
$598$	−15.0506	−	13.5066i	−0.615464	−	0.552325i
$599$		−	36.5285i		−	1.49252i	−0.665657	−	0.746258i	$-0.731849\pi$
$599$		−	36.5285i		−	1.49252i	0.665657	−	0.746258i	$-0.268151\pi$
$600$	−0.736451	−	2.20774i	−0.0300655	−	0.0901306i
$601$	−14.9478	+	25.8903i	−0.609732	+	1.05609i	0.381552	+	0.924347i	$0.375390\pi$
$601$	−14.9478	+	25.8903i	−0.609732	+	1.05609i	−0.991284	+	0.131740i	$0.957944\pi$
$602$	−5.96785	−	1.59908i	−0.243231	−	0.0651736i
$603$			14.4806i			0.589695i
$604$	0.916132	−	3.41905i	0.0372769	−	0.139119i
$605$	−12.9060	−	20.8772i	−0.524703	−	0.848780i
$606$	2.99266	+	2.99266i	0.121568	+	0.121568i
$607$	4.62475	−	17.2598i	0.187713	−	0.700553i	−0.806321	−	0.591478i	$-0.798544\pi$
$607$	4.62475	−	17.2598i	0.187713	−	0.700553i	0.994034	−	0.109075i	$-0.0347888\pi$
$608$	12.4591	−	3.33841i	0.505283	−	0.135390i
$609$	−0.0655981	−	0.244816i	−0.00265817	−	0.00992043i
$610$	0.836730	+	27.8035i	0.0338782	+	1.12573i
$611$	−29.3862	−	14.9118i	−1.18884	−	0.603266i
$612$	−3.36551	−	3.36551i	−0.136043	−	0.136043i
$613$	13.3148	+	7.68729i	0.537779	+	0.310487i	0.744178	−	0.667981i	$-0.232841\pi$
$613$	13.3148	+	7.68729i	0.537779	+	0.310487i	−0.206399	+	0.978468i	$0.566175\pi$
$614$	−2.91107	−	1.68071i	−0.117481	−	0.0678278i
$615$	0.830084	+	1.34277i	0.0334722	+	0.0541459i
$616$	0.140078	−	0.140078i	0.00564390	−	0.00564390i
$617$	−0.621849	−	1.07707i	−0.0250347	−	0.0433614i	0.853237	−	0.521524i	$-0.174636\pi$
$617$	−0.621849	−	1.07707i	−0.0250347	−	0.0433614i	−0.878271	+	0.478163i	$0.841303\pi$
$618$	2.28986	+	3.96616i	0.0921117	+	0.159542i
$619$	−28.7865	+	28.7865i	−1.15703	+	1.15703i	−0.171915	+	0.985112i	$0.554995\pi$
$619$	−28.7865	+	28.7865i	−1.15703	+	1.15703i	−0.985112	+	0.171915i	$0.945005\pi$
$620$	−2.45480	+	10.4038i	−0.0985872	+	0.417827i
$621$	3.60504	+	2.08137i	0.144665	+	0.0835226i
$622$	−29.1854	−	16.8502i	−1.17023	−	0.675631i
$623$	3.52601	+	3.52601i	0.141266	+	0.141266i
$624$	−2.26233	+	2.52095i	−0.0905658	+	0.100919i
$625$	24.8192	−	3.00128i	0.992768	−	0.120051i
$626$	−8.33343	−	31.1008i	−0.333071	−	1.24304i
$627$	−0.133162	+	0.0356806i	−0.00531797	+	0.00142495i
$628$	0.430310	−	1.60594i	0.0171712	−	0.0640839i
$629$	15.1272	+	15.1272i	0.603163	+	0.603163i
$630$	4.89388	−	3.02533i	0.194977	−	0.120532i
$631$	−5.36381	+	20.0180i	−0.213530	+	0.796904i	0.773149	+	0.634224i	$0.218680\pi$
$631$	−5.36381	+	20.0180i	−0.213530	+	0.796904i	−0.986679	+	0.162680i	$0.947986\pi$
$632$		−	26.2784i		−	1.04530i
$633$	−1.04358	−	0.279626i	−0.0414785	−	0.0111141i
$634$	−6.96483	+	12.0634i	−0.276609	+	0.479101i
$635$	−5.20880	+	1.56507i	−0.206705	+	0.0621080i
$636$		−	0.529346i		−	0.0209899i
$637$	13.1892	+	20.2361i	0.522574	+	0.801784i
$638$	0.402025	−	0.402025i	0.0159163	−	0.0159163i
$639$	−44.7256	+	11.9842i	−1.76932	+	0.474087i
$640$	−26.8701	−	14.4537i	−1.06213	−	0.571332i
$641$	−15.3071	+	8.83753i	−0.604592	+	0.349061i	−0.770846	−	0.637022i	$-0.780166\pi$
$641$	−15.3071	+	8.83753i	−0.604592	+	0.349061i	0.166254	+	0.986083i	$0.446833\pi$
$642$	−5.02675			−0.198390
$643$	2.31145	−	1.33452i	0.0911547	−	0.0526282i	−0.453730	−	0.891139i	$-0.649907\pi$
$643$	2.31145	−	1.33452i	0.0911547	−	0.0526282i	0.544884	+	0.838511i	$0.316574\pi$
$644$	−0.958617	−	0.256861i	−0.0377748	−	0.0101217i
$645$	−0.0943630	−	3.13556i	−0.00371554	−	0.123463i
$646$	11.3623	+	19.6801i	0.447043	+	0.774302i
$647$	10.9143	+	40.7326i	0.429084	+	1.60136i	0.754839	+	0.655910i	$0.227715\pi$
$647$	10.9143	+	40.7326i	0.429084	+	1.60136i	−0.325755	+	0.945454i	$0.605619\pi$
$648$	−10.2042	+	17.6742i	−0.400860	+	0.694309i
$649$	0.583029			0.0228859
$650$	−17.0106	−	22.9530i	−0.667212	−	0.900292i
$651$	−1.01136			−0.0396385
$652$	2.77904	−	4.81343i	0.108835	−	0.188508i
$653$	6.53917	+	24.4045i	0.255898	+	0.955023i	0.967589	+	0.252531i	$0.0812629\pi$
$653$	6.53917	+	24.4045i	0.255898	+	0.955023i	−0.711691	+	0.702492i	$0.752070\pi$
$654$	−1.81485	−	3.14342i	−0.0709664	−	0.122917i
$655$	0.444408	+	14.7671i	0.0173644	+	0.576999i
$656$	16.4555	+	4.40924i	0.642479	+	0.172152i
$657$	10.0473	−	5.80083i	0.391984	−	0.226312i
$658$	−7.94187			−0.309606
$659$	32.7551	−	18.9112i	1.27596	−	0.736675i	0.299856	−	0.953985i	$-0.403061\pi$
$659$	32.7551	−	18.9112i	1.27596	−	0.736675i	0.976103	+	0.217310i	$0.0697281\pi$
$660$	−0.0304309	−	0.0163691i	−0.00118452	−	0.000637165i
$661$	−16.6205	+	4.45346i	−0.646463	+	0.173219i	−0.567129	−	0.823629i	$-0.691946\pi$
$661$	−16.6205	+	4.45346i	−0.646463	+	0.173219i	−0.0793341	+	0.996848i	$0.525279\pi$
$662$	−20.3625	+	20.3625i	−0.791409	+	0.791409i
$663$	−1.99402	−	1.01185i	−0.0774415	−	0.0392970i
$664$			31.6705i			1.22905i
$665$	−5.35715	+	1.60964i	−0.207741	+	0.0624193i
$666$	−15.9694	+	27.6599i	−0.618804	+	1.07180i
$667$	8.00852	+	2.14588i	0.310091	+	0.0830887i
$668$		−	8.36582i		−	0.323683i
$669$	−0.948235	+	3.53886i	−0.0366609	+	0.136820i
$670$	14.7401	−	9.11214i	0.569461	−	0.352033i
$671$	−0.850052	−	0.850052i	−0.0328159	−	0.0328159i
$672$	−0.0791687	+	0.295461i	−0.00305400	+	0.0113977i
$673$	30.3909	−	8.14322i	1.17148	−	0.313898i	0.379940	−	0.925011i	$-0.375945\pi$
$673$	30.3909	−	8.14322i	1.17148	−	0.313898i	0.791543	+	0.611113i	$0.209278\pi$
$674$	10.0072	+	37.3474i	0.385464	+	1.43857i
$675$	4.40098	+	3.90085i	0.169394	+	0.150144i
$676$	−2.68392	+	6.08229i	−0.103228	+	0.233934i
$677$	−28.8731	−	28.8731i	−1.10968	−	1.10968i	−0.993191	−	0.116494i	$-0.962835\pi$
$677$	−28.8731	−	28.8731i	−1.10968	−	1.10968i	−0.116494	−	0.993191i	$-0.537165\pi$
$678$	−1.23422	−	0.712579i	−0.0474001	−	0.0273664i
$679$	−3.59521	−	2.07570i	−0.137972	−	0.0796579i
$680$	3.80752	−	16.1368i	0.146012	−	0.618819i
$681$	−0.891066	+	0.891066i	−0.0341457	+	0.0341457i
$682$	−1.13436	−	1.96477i	−0.0434369	−	0.0752349i
$683$	15.8896	+	27.5215i	0.607998	+	1.05308i	0.991570	+	0.129572i	$0.0413603\pi$
$683$	15.8896	+	27.5215i	0.607998	+	1.05308i	−0.383572	+	0.923511i	$0.625306\pi$
$684$	−4.88503	+	4.88503i	−0.186784	+	0.186784i
$685$	4.76837	+	7.71348i	0.182190	+	0.294717i
$686$	10.3093	+	5.95206i	0.393610	+	0.227251i
$687$	2.68597	+	1.55074i	0.102476	+	0.0591646i
$688$	−23.9378	−	23.9378i	−0.912619	−	0.912619i
$689$	5.87480	+	17.9794i	0.223812	+	0.684962i
$690$	−0.0744368	−	2.47344i	−0.00283376	−	0.0941623i
$691$	−6.94735	−	25.9278i	−0.264289	−	0.986342i	−0.962684	−	0.270629i	$-0.912768\pi$
$691$	−6.94735	−	25.9278i	−0.264289	−	0.986342i	0.698394	−	0.715713i	$-0.253898\pi$
$692$	3.37567	−	0.904508i	0.128324	−	0.0343842i
$693$	−0.0643565	+	0.240182i	−0.00244470	+	0.00912374i
$694$	−8.70863	−	8.70863i	−0.330575	−	0.330575i
$695$	15.0773	+	24.3895i	0.571913	+	0.925147i
$696$	0.282220	−	1.05326i	0.0106975	−	0.0399237i
$697$			11.2462i			0.425980i
$698$	7.76199	+	2.07982i	0.293796	+	0.0787223i
$699$	−0.817526	+	1.41600i	−0.0309217	+	0.0535579i
$700$	−1.25418	−	0.626745i	−0.0474035	−	0.0236887i
$701$		−	39.3253i		−	1.48530i	−0.669681	−	0.742649i	$-0.733569\pi$
$701$		−	39.3253i		−	1.48530i	0.669681	−	0.742649i	$-0.266431\pi$
$702$	1.38640	−	6.57599i	0.0523261	−	0.248195i
$703$	21.9572	−	21.9572i	0.828131	−	0.828131i
$704$	0.745863	−	0.199854i	0.0281108	−	0.00753226i
$705$	−1.16035	−	3.86182i	−0.0437012	−	0.145445i
$706$	−35.1585	+	20.2987i	−1.32321	+	0.763953i
$707$	−7.42171			−0.279122
$708$	−0.332676	+	0.192071i	−0.0125027	+	0.00721845i
$709$	−36.2309	−	9.70804i	−1.36068	−	0.364593i	−0.496614	−	0.867972i	$-0.665424\pi$
$709$	−36.2309	−	9.70804i	−1.36068	−	0.364593i	−0.864066	+	0.503378i	$0.832090\pi$
$710$	40.3433	+	37.9861i	1.51406	+	1.42559i
$711$	16.4923	+	28.5654i	0.618508	+	1.07129i
$712$	5.55253	+	20.7223i	0.208090	+	0.776602i
$713$	16.5421	−	28.6518i	0.619507	−	1.07302i
$714$	−0.538902			−0.0201679
$715$	1.21526	+	0.218253i	0.0454483	+	0.00816220i
$716$	2.90161			0.108438
$717$	1.92650	−	3.33680i	0.0719465	−	0.124615i
$718$	5.82623	+	21.7438i	0.217433	+	0.811471i
$719$	−14.5578	−	25.2148i	−0.542913	−	0.940353i	−0.998735	−	0.0502820i	$-0.983988\pi$
$719$	−14.5578	−	25.2148i	−0.542913	−	0.940353i	0.455822	−	0.890071i	$-0.349345\pi$
$720$	31.5108	−	0.948298i	1.17434	−	0.0353410i
$721$	−7.75737	−	2.07858i	−0.288900	−	0.0774104i
$722$	2.48955	−	1.43734i	0.0926514	−	0.0534923i
$723$	−3.38055			−0.125724
$724$	−1.59045	+	0.918247i	−0.0591086	+	0.0341264i
$725$	10.4777	+	5.23598i	0.389132	+	0.194459i
$726$	−3.31526	+	0.888322i	−0.123041	+	0.0329687i
$727$	15.6053	−	15.6053i	0.578768	−	0.578768i	−0.355796	−	0.934564i	$-0.615790\pi$
$727$	15.6053	−	15.6053i	0.578768	−	0.578768i	0.934564	+	0.355796i	$0.115790\pi$
$728$	−0.251799	−	4.65710i	−0.00933231	−	0.172603i
$729$		−	24.9204i		−	0.922977i
$730$	−12.2273	−	6.57717i	−0.452552	−	0.243432i
$731$	11.1740	−	19.3539i	0.413284	−	0.715829i
$732$	0.765076	+	0.205002i	0.0282780	+	0.00757708i
$733$		−	34.8651i		−	1.28777i	−0.765121	−	0.643886i	$-0.777321\pi$
$733$		−	34.8651i		−	1.28777i	0.765121	−	0.643886i	$-0.222679\pi$
$734$	−8.25335	+	30.8019i	−0.304637	+	1.13692i
$735$	−0.678777	+	2.87676i	−0.0250371	+	0.106111i
$736$	−7.07547	−	7.07547i	−0.260805	−	0.260805i
$737$	−0.193839	+	0.723416i	−0.00714014	+	0.0266474i
$738$	−16.2179	+	4.34557i	−0.596989	+	0.159963i
$739$	8.85631	+	33.0522i	0.325785	+	1.21584i	0.913521	+	0.406792i	$0.133353\pi$
$739$	8.85631	+	33.0522i	0.325785	+	1.21584i	−0.587736	+	0.809053i	$0.699981\pi$
$740$	7.77962	−	0.234123i	0.285985	−	0.00860654i
$741$	−1.46870	+	2.89432i	−0.0539541	+	0.106326i
$742$	3.22341	+	3.22341i	0.118335	+	0.118335i
$743$	−2.70989	−	1.56456i	−0.0994162	−	0.0573980i	0.449468	−	0.893297i	$-0.351614\pi$
$743$	−2.70989	−	1.56456i	−0.0994162	−	0.0573980i	−0.548884	+	0.835899i	$0.684947\pi$
$744$	−3.76821	−	2.17558i	−0.138149	−	0.0797605i
$745$	9.25977	+	2.18486i	0.339252	+	0.0800472i
$746$	29.3652	−	29.3652i	1.07514	−	1.07514i
$747$	−19.8763	−	34.4268i	−0.727236	−	1.25961i
$748$	−0.123082	−	0.213184i	−0.00450032	−	0.00779478i
$749$	6.23310	−	6.23310i	0.227753	−	0.227753i
$750$	0.596768	−	3.44463i	0.0217909	−	0.125780i
$751$	6.28199	+	3.62691i	0.229233	+	0.132348i	0.610218	−	0.792233i	$-0.291082\pi$
$751$	6.28199	+	3.62691i	0.229233	+	0.132348i	−0.380985	+	0.924581i	$0.624415\pi$
$752$	−37.6858	−	21.7579i	−1.37426	−	0.793430i
$753$	−1.38865	−	1.38865i	−0.0506051	−	0.0506051i
$754$	−0.722668	−	13.3659i	−0.0263180	−	0.486758i
$755$	−10.6098	+	11.2682i	−0.386131	+	0.410093i
$756$	−0.0853627	−	0.318578i	−0.00310461	−	0.0115866i
$757$	−15.9782	+	4.28134i	−0.580737	+	0.155608i	−0.537216	−	0.843445i	$-0.680524\pi$
$757$	−15.9782	+	4.28134i	−0.580737	+	0.155608i	−0.0435205	+	0.999053i	$0.513857\pi$
$758$	−9.24108	+	34.4882i	−0.335651	+	1.25267i
$759$	0.0756220	+	0.0756220i	0.00274490	+	0.00274490i
$760$	−23.4226	−	5.52661i	−0.849626	−	0.200471i
$761$	−5.99332	+	22.3674i	−0.217258	+	0.810817i	0.768102	+	0.640328i	$0.221201\pi$
$761$	−5.99332	+	22.3674i	−0.217258	+	0.810817i	−0.985360	+	0.170489i	$0.945465\pi$
$762$			0.760555i			0.0275520i
$763$	6.14819	+	1.64740i	0.222579	+	0.0596400i
$764$	6.00431	−	10.3998i	0.217228	−	0.376251i
$765$	5.98855	+	19.9308i	0.216516	+	0.720601i
$766$		−	38.2335i		−	1.38143i
$767$	9.16782	−	10.2159i	0.331031	−	0.368873i
$768$	−1.60998	+	1.60998i	−0.0580951	+	0.0580951i
$769$	5.69177	−	1.52511i	0.205251	−	0.0549967i	−0.154729	−	0.987957i	$-0.549450\pi$
$769$	5.69177	−	1.52511i	0.205251	−	0.0549967i	0.359979	+	0.932960i	$0.382784\pi$
$770$	0.284984	−	0.0856282i	0.0102701	−	0.00308583i
$771$	−0.470143	+	0.271437i	−0.0169318	+	0.00977557i
$772$	8.09938			0.291503
$773$	7.00612	−	4.04499i	0.251993	−	0.145488i	−0.368684	−	0.929555i	$-0.620191\pi$
$773$	7.00612	−	4.04499i	0.251993	−	0.145488i	0.620676	+	0.784067i	$0.286858\pi$
$774$	32.2274	+	8.63532i	1.15839	+	0.310390i
$775$	31.0027	−	34.9776i	1.11365	−	1.25643i
$776$	−8.93019	−	15.4675i	−0.320575	−	0.555252i
$777$	0.190591	+	0.711294i	0.00683740	+	0.0255175i
$778$	11.3516	−	19.6616i	0.406975	−	0.704901i
$779$	16.3238			0.584863
$780$	−0.765329	+	0.275816i	−0.0274032	+	0.00987580i
$781$	−2.39481			−0.0856930
$782$	8.81441	−	15.2670i	0.315203	−	0.545947i
$783$	0.713141	+	2.66148i	0.0254856	+	0.0951135i
$784$	15.9487	+	27.6239i	0.569595	+	0.986567i
$785$	−4.98347	+	5.29272i	−0.177868	+	0.188905i
$786$	1.99554	+	0.534703i	0.0711785	+	0.0190722i
$787$	−14.0397	+	8.10582i	−0.500461	+	0.288941i	−0.728904	−	0.684616i	$-0.759970\pi$
$787$	−14.0397	+	8.10582i	−0.500461	+	0.288941i	0.228443	+	0.973557i	$0.426637\pi$
$788$	2.92148			0.104073
$789$	−1.05556	+	0.609429i	−0.0375790	+	0.0216962i
$790$	18.6994	−	34.7632i	0.665296	−	1.23682i
$791$	2.41401	−	0.646831i	0.0858322	−	0.0229987i
$792$	−0.756445	+	0.756445i	−0.0268791	+	0.0268791i
$793$	−28.2613	+	1.52803i	−1.00359	+	0.0542618i
$794$			53.0777i			1.88366i
$795$	−1.09646	+	2.03837i	−0.0388875	+	0.0722937i
$796$	2.37878	−	4.12017i	0.0843137	−	0.146036i
$797$	−16.1019	−	4.31449i	−0.570358	−	0.152827i	−0.0378972	−	0.999282i	$-0.512066\pi$
$797$	−16.1019	−	4.31449i	−0.570358	−	0.152827i	−0.532461	+	0.846455i	$0.678733\pi$
$798$			0.782216i			0.0276901i
$799$	7.43502	−	27.7479i	0.263032	−	0.981649i
$800$	−7.79154	−	11.7952i	−0.275473	−	0.417023i
$801$	−19.0411	−	19.0411i	−0.672783	−	0.672783i
$802$	−7.60807	+	28.3937i	−0.268650	+	1.00262i
$803$	0.579592	−	0.155301i	0.0204534	−	0.00548047i
$804$	−0.127715	−	0.476638i	−0.00450415	−	0.0168097i
$805$	3.15933	+	2.97473i	0.111352	+	0.104846i
$806$	−52.2639	−	11.0186i	−1.84092	−	0.388115i
$807$	−2.96103	−	2.96103i	−0.104233	−	0.104233i
$808$	−27.6523	−	15.9651i	−0.972804	−	0.561649i
$809$	20.8943	+	12.0633i	0.734603	+	0.424123i	0.820104	−	0.572215i	$-0.193916\pi$
$809$	20.8943	+	12.0633i	0.734603	+	0.424123i	−0.0855005	+	0.996338i	$0.527249\pi$
$810$	−26.0758	+	16.1197i	−0.916209	+	0.566388i
$811$	17.7808	−	17.7808i	0.624369	−	0.624369i	−0.322276	−	0.946646i	$-0.604448\pi$
$811$	17.7808	−	17.7808i	0.624369	−	0.624369i	0.946646	+	0.322276i	$0.104448\pi$
$812$	−0.328451	−	0.568894i	−0.0115264	−	0.0199642i
$813$	1.27116	+	2.20171i	0.0445815	+	0.0772173i
$814$	−1.16806	+	1.16806i	−0.0409403	+	0.0409403i
$815$	−20.6716	+	12.7789i	−0.724096	+	0.447625i
$816$	−2.55720	−	1.47640i	−0.0895200	−	0.0516844i
$817$	−28.0921	−	16.2190i	−0.982819	−	0.567431i
$818$	5.79615	+	5.79615i	0.202658	+	0.202658i
$819$	3.19650	+	4.90438i	0.111695	+	0.171373i
$820$	2.97887	+	2.80481i	0.104027	+	0.0979484i
$821$	10.2562	+	38.2768i	0.357945	+	1.33587i	0.876737	+	0.480970i	$0.159715\pi$
$821$	10.2562	+	38.2768i	0.357945	+	1.33587i	−0.518792	+	0.854901i	$0.673618\pi$
$822$	1.22489	−	0.328208i	0.0427229	−	0.0114476i
$823$	10.3383	−	38.5831i	0.360371	−	1.34492i	−0.513219	−	0.858258i	$-0.671547\pi$
$823$	10.3383	−	38.5831i	0.360371	−	1.34492i	0.873589	−	0.486664i	$-0.161786\pi$
$824$	−24.4316	−	24.4316i	−0.851116	−	0.851116i
$825$	0.0832753	+	0.126066i	0.00289927	+	0.00438905i
$826$	0.856204	−	3.19540i	0.0297912	−	0.111182i
$827$			25.6019i			0.890264i	0.895465	+	0.445132i	$0.146843\pi$
$827$			25.6019i			0.890264i	−0.895465	+	0.445132i	$0.853157\pi$
$828$	5.17670	+	1.38709i	0.179903	+	0.0482048i
$829$	9.41684	−	16.3104i	0.327060	−	0.566485i	−0.654867	−	0.755744i	$-0.727275\pi$
$829$	9.41684	−	16.3104i	0.327060	−	0.566485i	0.981927	+	0.189259i	$0.0606086\pi$
$830$	−22.5364	+	41.8962i	−0.782249	+	1.45424i
$831$			4.19807i			0.145629i
$832$	8.22646	−	16.2116i	0.285201	−	0.562037i
$833$	−14.8894	+	14.8894i	−0.515888	+	0.515888i
$834$	3.87301	−	1.03777i	0.134111	−	0.0359351i
$835$	−17.3285	+	32.2146i	−0.599678	+	1.11483i
$836$	−0.309436	+	0.178653i	−0.0107021	+	0.00617885i
$837$	10.9949			0.380040
$838$	−1.38197	+	0.797879i	−0.0477393	+	0.0275623i
$839$	−24.0857	−	6.45374i	−0.831530	−	0.222808i	−0.182149	−	0.983271i	$-0.558305\pi$
$839$	−24.0857	−	6.45374i	−0.831530	−	0.222808i	−0.649381	+	0.760463i	$0.724972\pi$
$840$	0.391229	−	0.415508i	0.0134987	−	0.0143364i
$841$	−11.7560	−	20.3621i	−0.405381	−	0.702140i
$842$	0.170969	+	0.638063i	0.00589196	+	0.0219891i
$843$	−0.589688	+	1.02137i	−0.0203099	+	0.0351778i
$844$	−2.80018			−0.0963863
$845$	22.9336	−	17.8620i	0.788940	−	0.614471i
$846$	42.8875			1.47450
$847$	3.00937	−	5.21239i	0.103403	−	0.179100i
$848$	6.46474	+	24.1267i	0.222000	+	0.828516i
$849$	0.151725	+	0.262795i	0.00520717	+	0.00901909i
$850$	16.5197	−	18.6377i	0.566621	−	0.639268i
$851$	−23.2682	−	6.23469i	−0.797623	−	0.213722i
$852$	1.36648	−	0.788935i	0.0468147	−	0.0270285i
$853$	2.14143			0.0733210			0.0366605	−	0.999328i	$-0.488328\pi$
$853$	2.14143			0.0733210			0.0366605	+	0.999328i	$0.488328\pi$
$854$	−5.90721	+	3.41053i	−0.202140	+	0.116706i
$855$	28.9296	−	8.69237i	0.989370	−	0.297273i
$856$	36.6319	−	9.81549i	1.25205	−	0.335487i
$857$	−36.4384	+	36.4384i	−1.24471	+	1.24471i	−0.286686	+	0.958025i	$0.592554\pi$
$857$	−36.4384	+	36.4384i	−1.24471	+	1.24471i	−0.958025	+	0.286686i	$0.907446\pi$
$858$	0.0781304	−	0.153969i	0.00266733	−	0.00525642i
$859$			4.40721i			0.150372i	0.997170	+	0.0751861i	$0.0239551\pi$
$859$			4.40721i			0.150372i	−0.997170	+	0.0751861i	$0.976045\pi$
$860$	−2.33962	−	7.78661i	−0.0797802	−	0.265521i
$861$	−0.193556	+	0.335249i	−0.00659637	+	0.0114252i
$862$	6.35486	+	1.70278i	0.216447	+	0.0579969i
$863$		−	53.8912i		−	1.83448i	−0.398338	−	0.917239i	$-0.630413\pi$
$863$		−	53.8912i		−	1.83448i	0.398338	−	0.917239i	$-0.369587\pi$
$864$	0.860671	−	3.21207i	0.0292806	−	0.109277i
$865$	−14.8724	−	3.50917i	−0.505676	−	0.119315i
$866$	16.8033	+	16.8033i	0.570998	+	0.570998i
$867$	−0.363644	+	1.35714i	−0.0123500	+	0.0460908i
$868$	−2.53196	+	0.678436i	−0.0859403	+	0.0230276i
$869$	0.441535	+	1.64783i	0.0149780	+	0.0558988i
$870$	1.12283	−	1.19251i	0.0380676	−	0.0404300i
$871$	9.62771	+	14.7718i	0.326222	+	0.500522i
$872$	19.3636	+	19.3636i	0.655733	+	0.655733i
$873$	19.4148	+	11.2091i	0.657091	+	0.379372i
$874$	−22.1600	−	12.7941i	−0.749574	−	0.432767i
$875$	3.53130	+	5.01127i	0.119380	+	0.169412i
$876$	−0.279553	+	0.279553i	−0.00944522	+	0.00944522i
$877$	6.56696	+	11.3743i	0.221750	+	0.384083i	0.955340	−	0.295510i	$-0.0954896\pi$
$877$	6.56696	+	11.3743i	0.221750	+	0.384083i	−0.733589	+	0.679593i	$0.762156\pi$
$878$	10.9996	+	19.0519i	0.371220	+	0.642971i
$879$	−0.389521	+	0.389521i	−0.0131382	+	0.0131382i
$880$	1.58690	+	0.374433i	0.0534944	+	0.0126221i
$881$	31.7049	+	18.3049i	1.06817	+	0.616706i	0.927680	−	0.373376i	$-0.121800\pi$
$881$	31.7049	+	18.3049i	1.06817	+	0.616706i	0.140486	+	0.990083i	$0.455133\pi$
$882$	−27.2250	−	15.7184i	−0.916714	−	0.529265i
$883$	7.40474	+	7.40474i	0.249189	+	0.249189i	0.820638	−	0.571449i	$-0.193618\pi$
$883$	7.40474	+	7.40474i	0.249189	+	0.249189i	−0.571449	+	0.820638i	$0.693618\pi$
$884$	−5.67081	−	1.19556i	−0.190730	−	0.0402111i
$885$	1.67889	−	0.0505253i	0.0564354	−	0.00169839i
$886$	5.83502	+	21.7766i	0.196031	+	0.731599i
$887$	52.7370	−	14.1308i	1.77074	−	0.474467i	0.781891	−	0.623416i	$-0.214255\pi$
$887$	52.7370	−	14.1308i	1.77074	−	0.474467i	0.988845	+	0.148948i	$0.0475888\pi$
$888$	−0.819971	+	3.06017i	−0.0275164	+	0.102693i
$889$	−0.943078	−	0.943078i	−0.0316298	−	0.0316298i
$890$	−7.40047	+	31.3643i	−0.248064	+	1.05133i
$891$	0.342907	−	1.27975i	0.0114878	−	0.0428731i
$892$			9.49566i			0.317938i
$893$	−40.2760	−	10.7919i	−1.34779	−	0.361138i
$894$	0.665210	−	1.15218i	0.0222479	−	0.0385346i
$895$	−11.1734	−	6.01025i	−0.373484	−	0.200901i
$896$		−	7.48186i		−	0.249951i
$897$	2.51416	−	0.135936i	0.0839455	−	0.00453876i
$898$	7.45887	−	7.45887i	0.248906	−	0.248906i
$899$	21.1526	−	5.66782i	0.705479	−	0.189032i
$900$	6.77279	+	3.38453i	0.225760	+	0.112818i
$901$	−14.2799	+	8.24448i	−0.475731	+	0.274664i
$902$	−0.868379			−0.0289139
$903$	0.666190	−	0.384625i	0.0221694	−	0.0127995i
$904$	10.3857	+	2.78284i	0.345423	+	0.0925558i
$905$	8.02642	−	0.241550i	0.266807	−	0.00802940i
$906$	1.08214	+	1.87433i	0.0359518	+	0.0622703i
$907$	10.6057	+	39.5809i	0.352155	+	1.31426i	0.884027	+	0.467437i	$0.154822\pi$
$907$	10.6057	+	39.5809i	0.352155	+	1.31426i	−0.531871	+	0.846825i	$0.678511\pi$
$908$	−1.63305	+	2.82853i	−0.0541947	+	0.0938680i
$909$	40.0785			1.32932
$910$	2.98084	−	6.33996i	0.0988140	−	0.210168i
$911$	24.2232			0.802551			0.401276	−	0.915957i	$-0.368567\pi$
$911$	24.2232			0.802551			0.401276	+	0.915957i	$0.368567\pi$
$912$	−2.14299	+	3.71178i	−0.0709616	+	0.122909i
$913$	−0.532133	−	1.98595i	−0.0176110	−	0.0657253i
$914$	−29.2849	−	50.7229i	−0.968658	−	1.67777i
$915$	−2.52148	−	2.37415i	−0.0833575	−	0.0784869i
$916$	7.76460	+	2.08052i	0.256550	+	0.0687423i
$917$	−3.13746	+	1.81141i	−0.103608	+	0.0598182i
$918$	5.85860			0.193363
$919$	−30.2077	+	17.4404i	−0.996460	+	0.575307i	−0.907199	−	0.420702i	$-0.861784\pi$
$919$	−30.2077	+	17.4404i	−0.996460	+	0.575307i	−0.0892612	+	0.996008i	$0.528451\pi$
$920$	5.37222	+	17.8796i	0.177117	+	0.589473i
$921$	0.404259	−	0.108321i	0.0133208	−	0.00356929i
$922$	−28.8290	+	28.8290i	−0.949432	+	0.949432i
$923$	−37.6571	+	41.9619i	−1.23950	+	1.38119i
$924$		−	0.00847334i		−	0.000278753i
$925$	−30.4422	−	15.2128i	−1.00093	−	0.500193i
$926$	−12.6446	+	21.9012i	−0.415529	+	0.719717i
$927$	41.8912	+	11.2247i	1.37589	+	0.368668i
$928$		−	6.62322i		−	0.217418i
$929$	2.24604	−	8.38235i	0.0736903	−	0.275016i	−0.919243	−	0.393691i	$-0.871198\pi$
$929$	2.24604	−	8.38235i	0.0736903	−	0.275016i	0.992933	+	0.118675i	$0.0378647\pi$
$930$	−3.43677	−	5.55945i	−0.112696	−	0.182302i
$931$	21.6120	+	21.6120i	0.708304	+	0.708304i
$932$	−1.09681	+	4.09336i	−0.0359273	+	0.134083i
$933$	4.05296	−	1.08599i	0.132688	−	0.0355536i
$934$	−10.8040	−	40.3211i	−0.353518	−	1.31935i
$935$	0.0323774	+	1.07586i	0.00105885	+	0.0351844i
$936$	1.35976	+	25.1491i	0.0444452	+	0.822026i
$937$	−25.8920	−	25.8920i	−0.845856	−	0.845856i	0.143757	−	0.989613i	$-0.454082\pi$
$937$	−25.8920	−	25.8920i	−0.845856	−	0.845856i	−0.989613	+	0.143757i	$0.954082\pi$
$938$	3.68015	+	2.12474i	0.120161	+	0.0693751i
$939$	3.47178	+	2.00443i	0.113297	+	0.0654122i
$940$	−5.49550	−	8.88972i	−0.179243	−	0.289951i
$941$	−20.9205	+	20.9205i	−0.681989	+	0.681989i	−0.960448	−	0.278459i	$-0.910176\pi$
$941$	−20.9205	+	20.9205i	−0.681989	+	0.681989i	0.278459	+	0.960448i	$0.410176\pi$
$942$	0.508285	+	0.880376i	0.0165608	+	0.0286842i
$943$	−6.33169	−	10.9668i	−0.206188	−	0.357128i
$944$	12.8171	−	12.8171i	0.417162	−	0.417162i
$945$	−0.331177	+	1.40358i	−0.0107732	+	0.0456583i
$946$	1.49442	+	0.862801i	0.0485876	+	0.0280521i
$947$	23.9064	+	13.8023i	0.776852	+	0.448516i	0.835314	−	0.549774i	$-0.185286\pi$
$947$	23.9064	+	13.8023i	0.776852	+	0.448516i	−0.0584612	+	0.998290i	$0.518619\pi$
$948$	−0.794793	−	0.794793i	−0.0258137	−	0.0258137i
$949$	6.39258	−	12.5977i	0.207512	−	0.408937i
$950$	−27.0526	−	23.9783i	−0.877702	−	0.777960i
$951$	−0.448880	−	1.67524i	−0.0145559	−	0.0543235i
$952$	3.92719	−	1.05229i	0.127281	−	0.0341048i
$953$	−7.47941	+	27.9135i	−0.242282	+	0.904208i	0.732448	+	0.680822i	$0.238377\pi$
$953$	−7.47941	+	27.9135i	−0.242282	+	0.904208i	−0.974730	+	0.223385i	$0.928289\pi$
$954$	−17.4070	−	17.4070i	−0.563572	−	0.563572i
$955$	−44.6626	+	27.6098i	−1.44525	+	0.893431i
$956$	2.58464	−	9.64602i	0.0835933	−	0.311974i
$957$			0.0707884i			0.00228826i
$958$	25.4102	+	6.80864i	0.820966	+	0.219977i
$959$	−1.11187	+	1.92582i	−0.0359042	+	0.0621878i
$960$	2.13047	−	0.640135i	0.0687607	−	0.0206603i
$961$		−	56.3841i		−	1.81884i
$962$	2.09966	+	38.8337i	0.0676957	+	1.25205i
$963$	−33.6599	+	33.6599i	−1.08467	+	1.08467i
$964$	−8.46323	+	2.26771i	−0.272582	+	0.0730382i
$965$	−31.1886	−	16.7766i	−1.00400	−	0.540059i
$966$	0.525514	−	0.303406i	0.0169081	−	0.00976192i
$967$	4.31688			0.138822			0.0694108	−	0.997588i	$-0.477888\pi$
$967$	4.31688			0.138822			0.0694108	+	0.997588i	$0.477888\pi$
$968$	22.4250	−	12.9471i	0.720768	−	0.416136i
$969$	−2.73296	−	0.732295i	−0.0877954	−	0.0235247i
$970$	−0.807022	−	26.8163i	−0.0259119	−	0.861021i
$971$	6.77930	+	11.7421i	0.217558	+	0.376822i	0.954061	−	0.299613i	$-0.0968575\pi$
$971$	6.77930	+	11.7421i	0.217558	+	0.376822i	−0.736503	+	0.676435i	$0.763524\pi$
$972$	0.692966	+	2.58618i	0.0222269	+	0.0829519i
$973$	−3.51566	+	6.08930i	−0.112707	+	0.195214i
$974$	41.6466			1.33444
$975$	3.51839	+	0.523167i	0.112679	+	0.0167548i
$976$	−37.3745			−1.19633
$977$	23.8254	−	41.2668i	0.762242	−	1.32024i	−0.179450	−	0.983767i	$-0.557432\pi$
$977$	23.8254	−	41.2668i	0.762242	−	1.32024i	0.941692	−	0.336475i	$-0.109235\pi$
$978$	0.879575	+	3.28262i	0.0281257	+	0.104967i
$979$	−0.696362	−	1.20613i	−0.0222558	−	0.0385482i
$980$	0.230442	+	7.65731i	0.00736121	+	0.244604i
$981$	−33.2013	−	8.89627i	−1.06004	−	0.284036i
$982$	57.0983	−	32.9657i	1.82208	−	1.05198i
$983$	7.39039			0.235717			0.117858	−	0.993030i	$-0.462397\pi$
$983$	7.39039			0.235717			0.117858	+	0.993030i	$0.462397\pi$
$984$	−1.44233	+	0.832728i	−0.0459797	+	0.0265464i
$985$	−11.2499	−	6.05141i	−0.358450	−	0.192814i
$986$	11.2711	−	3.02008i	0.358945	−	0.0961789i
$987$	0.699200	−	0.699200i	0.0222558	−	0.0222558i
$988$	−1.73535	+	8.23118i	−0.0552090	+	0.261869i
$989$			25.1641i			0.800171i
$990$	−1.53897	+	0.462408i	−0.0489115	+	0.0146963i
$991$	−10.0052	+	17.3296i	−0.317827	+	0.550493i	−0.980034	−	0.198828i	$-0.936287\pi$
$991$	−10.0052	+	17.3296i	−0.317827	+	0.550493i	0.662207	+	0.749321i	$0.269620\pi$
$992$	−25.5285	−	6.84035i	−0.810531	−	0.217181i
$993$		−	3.58541i		−	0.113780i
$994$	−3.51688	+	13.1252i	−0.111549	+	0.416306i
$995$	−17.6944	+	10.9384i	−0.560950	+	0.346771i
$996$	0.957877	+	0.957877i	0.0303515	+	0.0303515i
$997$	8.75402	−	32.6705i	0.277243	−	1.03468i	−0.677081	−	0.735909i	$-0.736755\pi$
$997$	8.75402	−	32.6705i	0.277243	−	1.03468i	0.954324	−	0.298775i	$-0.0965781\pi$
$998$	−18.0035	+	4.82403i	−0.569892	+	0.152702i
$999$	−2.07198	−	7.73273i	−0.0655545	−	0.244653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.o.a.32.2	✓	20
3.2	odd	2		585.2.cf.a.487.4		20
5.2	odd	4		325.2.x.b.318.2		20
5.3	odd	4		65.2.t.a.58.4	yes	20
5.4	even	2		325.2.s.b.32.4		20
13.2	odd	12		845.2.t.g.427.2		20
13.3	even	3		845.2.o.e.587.2		20
13.4	even	6		845.2.k.d.577.4		20
13.5	odd	4		845.2.t.e.657.4		20
13.6	odd	12		845.2.f.d.437.4		20
13.7	odd	12		845.2.f.e.437.7		20
13.8	odd	4		845.2.t.f.657.2		20
13.9	even	3		845.2.k.e.577.7		20
13.10	even	6		845.2.o.f.587.4		20
13.11	odd	12		65.2.t.a.37.4	yes	20
13.12	even	2		845.2.o.g.357.4		20
15.8	even	4		585.2.dp.a.253.2		20
39.11	even	12		585.2.dp.a.37.2		20
65.3	odd	12		845.2.t.f.418.2		20
65.8	even	4		845.2.o.e.488.2		20
65.18	even	4		845.2.o.f.488.4		20
65.23	odd	12		845.2.t.e.418.4		20
65.24	odd	12		325.2.x.b.232.2		20
65.28	even	12		845.2.o.g.258.4		20
65.33	even	12		845.2.k.e.268.7		20
65.37	even	12		325.2.s.b.193.4		20
65.38	odd	4		845.2.t.g.188.2		20
65.43	odd	12		845.2.f.d.408.7		20
65.48	odd	12		845.2.f.e.408.4		20
65.58	even	12		845.2.k.d.268.4		20
65.63	even	12	inner	65.2.o.a.63.2	yes	20
195.128	odd	12		585.2.cf.a.388.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.2	✓	20	1.1	even	1	trivial
65.2.o.a.63.2	yes	20	65.63	even	12	inner
65.2.t.a.37.4	yes	20	13.11	odd	12
65.2.t.a.58.4	yes	20	5.3	odd	4
325.2.s.b.32.4		20	5.4	even	2
325.2.s.b.193.4		20	65.37	even	12
325.2.x.b.232.2		20	65.24	odd	12
325.2.x.b.318.2		20	5.2	odd	4
585.2.cf.a.388.4		20	195.128	odd	12
585.2.cf.a.487.4		20	3.2	odd	2
585.2.dp.a.37.2		20	39.11	even	12
585.2.dp.a.253.2		20	15.8	even	4
845.2.f.d.408.7		20	65.43	odd	12
845.2.f.d.437.4		20	13.6	odd	12
845.2.f.e.408.4		20	65.48	odd	12
845.2.f.e.437.7		20	13.7	odd	12
845.2.k.d.268.4		20	65.58	even	12
845.2.k.d.577.4		20	13.4	even	6
845.2.k.e.268.7		20	65.33	even	12
845.2.k.e.577.7		20	13.9	even	3
845.2.o.e.488.2		20	65.8	even	4
845.2.o.e.587.2		20	13.3	even	3
845.2.o.f.488.4		20	65.18	even	4
845.2.o.f.587.4		20	13.10	even	6
845.2.o.g.258.4		20	65.28	even	12
845.2.o.g.357.4		20	13.12	even	2
845.2.t.e.418.4		20	65.23	odd	12
845.2.t.e.657.4		20	13.5	odd	4
845.2.t.f.418.2		20	65.3	odd	12
845.2.t.f.657.2		20	13.8	odd	4
845.2.t.g.188.2		20	65.38	odd	4
845.2.t.g.427.2		20	13.2	odd	12

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.792369 + 1.37242i) q^{2} +(-0.0510678 - 0.190588i) q^{3} +(-0.255697 - 0.442881i) q^{4} +(0.0672627 + 2.23506i) q^{5} +(0.302032 + 0.0809291i) q^{6} +(-0.474866 + 0.274164i) q^{7} -2.35905 q^{8} +(2.56436 - 1.48053i) q^{9} +O(q^{10})\)	\(q+(-0.792369 + 1.37242i) q^{2} +(-0.0510678 - 0.190588i) q^{3} +(-0.255697 - 0.442881i) q^{4} +(0.0672627 + 2.23506i) q^{5} +(0.302032 + 0.0809291i) q^{6} +(-0.474866 + 0.274164i) q^{7} -2.35905 q^{8} +(2.56436 - 1.48053i) q^{9} +(-3.12074 - 1.67868i) q^{10} +(0.147928 - 0.0396372i) q^{11} +(-0.0713497 + 0.0713497i) q^{12} +(1.63157 - 3.21528i) q^{13} -0.868956i q^{14} +(0.422539 - 0.126959i) q^{15} +(2.38063 - 4.12338i) q^{16} +(3.03602 + 0.813499i) q^{17} +4.69252i q^{18} +(1.18079 - 4.40678i) q^{19} +(0.972665 - 0.601287i) q^{20} +(0.0765027 + 0.0765027i) q^{21} +(-0.0628146 + 0.234427i) q^{22} +(-3.41860 + 0.916011i) q^{23} +(0.120472 + 0.449606i) q^{24} +(-4.99095 + 0.300672i) q^{25} +(3.11992 + 4.78688i) q^{26} +(-0.831688 - 0.831688i) q^{27} +(0.242844 + 0.140206i) q^{28} +(-2.02878 - 1.17132i) q^{29} +(-0.160566 + 0.680501i) q^{30} +(-6.61000 + 6.61000i) q^{31} +(1.41363 + 2.44848i) q^{32} +(-0.0151087 - 0.0261691i) q^{33} +(-3.52211 + 3.52211i) q^{34} +(-0.644713 - 1.04291i) q^{35} +(-1.31140 - 0.757137i) q^{36} +(5.89447 + 3.40317i) q^{37} +(5.11234 + 5.11234i) q^{38} +(-0.696113 - 0.146759i) q^{39} +(-0.158676 - 5.27261i) q^{40} +(0.926064 + 3.45612i) q^{41} +(-0.165612 + 0.0443757i) q^{42} +(1.84023 - 6.86784i) q^{43} +(-0.0553794 - 0.0553794i) q^{44} +(3.48156 + 5.63190i) q^{45} +(1.45164 - 5.41759i) q^{46} -9.13956i q^{47} +(-0.907439 - 0.243147i) q^{48} +(-3.34967 + 5.80180i) q^{49} +(3.54203 - 7.08794i) q^{50} -0.620172i q^{51} +(-1.84117 + 0.0995483i) q^{52} +(-3.70952 + 3.70952i) q^{53} +(1.80043 - 0.482424i) q^{54} +(0.0985415 + 0.327962i) q^{55} +(1.12023 - 0.646766i) q^{56} -0.900179 q^{57} +(3.21508 - 1.85623i) q^{58} +(3.67728 + 0.985325i) q^{59} +(-0.164270 - 0.154672i) q^{60} +(-3.92486 - 6.79805i) q^{61} +(-3.83416 - 14.3093i) q^{62} +(-0.811818 + 1.40611i) q^{63} +5.04207 q^{64} +(7.29606 + 3.43037i) q^{65} +0.0478868 q^{66} +(-2.44516 + 4.23514i) q^{67} +(-0.416019 - 1.55261i) q^{68} +(0.349161 + 0.604765i) q^{69} +(1.94217 - 0.0584483i) q^{70} +(-15.1045 - 4.04725i) q^{71} +(-6.04945 + 3.49265i) q^{72} +3.91807 q^{73} +(-9.34119 + 5.39314i) q^{74} +(0.312181 + 0.935860i) q^{75} +(-2.25360 + 0.603851i) q^{76} +(-0.0593789 + 0.0593789i) q^{77} +(0.752994 - 0.839074i) q^{78} +11.1394i q^{79} +(9.37611 + 5.04350i) q^{80} +(4.32557 - 7.49210i) q^{81} +(-5.47704 - 1.46757i) q^{82} -13.4251i q^{83} +(0.0143200 - 0.0534431i) q^{84} +(-1.61401 + 6.84039i) q^{85} +(7.96744 + 7.96744i) q^{86} +(-0.119633 + 0.446477i) q^{87} +(-0.348970 + 0.0935062i) q^{88} +(-2.35372 - 8.78419i) q^{89} +(-10.4880 + 0.315631i) q^{90} +(0.106738 + 1.97414i) q^{91} +(1.27981 + 1.27981i) q^{92} +(1.59734 + 0.922226i) q^{93} +(12.5433 + 7.24190i) q^{94} +(9.92882 + 2.34273i) q^{95} +(0.394459 - 0.394459i) q^{96} +(3.78550 + 6.55668i) q^{97} +(-5.30835 - 9.19433i) q^{98} +(0.320657 - 0.320657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21} + 16 q^{22} - 2 q^{23} - 32 q^{24} - 18 q^{25} - 24 q^{26} + 4 q^{27} + 6 q^{28} + 14 q^{30} - 6 q^{32} - 18 q^{33} - 2 q^{34} - 20 q^{35} + 36 q^{36} + 42 q^{37} + 8 q^{38} - 4 q^{39} - 16 q^{40} + 10 q^{41} - 56 q^{42} - 22 q^{43} + 36 q^{44} + 52 q^{45} + 4 q^{46} + 28 q^{48} - 18 q^{49} + 44 q^{50} + 46 q^{52} - 10 q^{53} + 48 q^{54} + 26 q^{55} - 12 q^{57} - 90 q^{58} + 16 q^{59} - 92 q^{60} - 16 q^{61} - 40 q^{62} - 32 q^{63} - 20 q^{64} + 8 q^{65} - 32 q^{66} - 58 q^{67} + 28 q^{68} + 16 q^{69} + 32 q^{70} - 16 q^{71} - 66 q^{72} + 72 q^{73} - 18 q^{74} - 34 q^{75} - 64 q^{76} + 28 q^{77} + 32 q^{78} - 34 q^{80} - 14 q^{81} + 22 q^{82} + 40 q^{84} - 6 q^{85} + 60 q^{86} + 62 q^{87} + 50 q^{88} + 6 q^{89} - 46 q^{90} + 8 q^{91} - 8 q^{92} + 48 q^{93} + 48 q^{94} + 14 q^{95} + 56 q^{96} - 22 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

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