LMFDB - Embedded newform 59.2.c.a.20.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [59,2,Mod(3,59)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(59, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([50]))

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

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

chi := DirichletCharacter("59.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	59.c (of order $29$, degree $28$, 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:	$0.471117371926$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$4$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			20.3
Character	$\chi$	$=$	59.20
Dual form			59.2.c.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.554859 - 0.256705i) q^{2} +(2.89290 - 0.974731i) q^{3} +(-1.05280 - 1.23945i) q^{4} +(-2.81882 + 1.69603i) q^{5} +(-1.85537 - 0.201783i) q^{6} +(0.0467597 + 0.862432i) q^{7} +(0.593097 + 2.13614i) q^{8} +(5.03048 - 3.82407i) q^{9} +O(q^{10})$	\(q+(-0.554859 - 0.256705i) q^{2} +(2.89290 - 0.974731i) q^{3} +(-1.05280 - 1.23945i) q^{4} +(-2.81882 + 1.69603i) q^{5} +(-1.85537 - 0.201783i) q^{6} +(0.0467597 + 0.862432i) q^{7} +(0.593097 + 2.13614i) q^{8} +(5.03048 - 3.82407i) q^{9} +(1.99943 - 0.217451i) q^{10} +(0.631059 + 3.84929i) q^{11} +(-4.25378 - 2.55942i) q^{12} +(-1.31325 - 0.998305i) q^{13} +(0.195446 - 0.490531i) q^{14} +(-6.50140 + 7.65404i) q^{15} +(-0.306918 + 1.87211i) q^{16} +(0.182290 - 3.36214i) q^{17} +(-3.77286 + 0.830470i) q^{18} +(-3.16614 - 2.99913i) q^{19} +(5.06981 + 1.70822i) q^{20} +(0.975910 + 2.44935i) q^{21} +(0.637984 - 2.29781i) q^{22} +(-2.04440 - 0.450007i) q^{23} +(3.79793 + 5.60153i) q^{24} +(2.72721 - 5.14406i) q^{25} +(0.472397 + 0.891036i) q^{26} +(5.68582 - 8.38596i) q^{27} +(1.01972 - 0.965926i) q^{28} +(-3.93910 + 1.82242i) q^{29} +(5.57219 - 2.57797i) q^{30} +(5.88624 - 5.57574i) q^{31} +(3.13912 - 4.62986i) q^{32} +(5.57761 + 10.5205i) q^{33} +(-0.964222 + 1.81872i) q^{34} +(-1.59452 - 2.35174i) q^{35} +(-10.0359 - 2.20906i) q^{36} +(-0.331878 + 1.19532i) q^{37} +(0.986869 + 2.47686i) q^{38} +(-4.77217 - 1.60793i) q^{39} +(-5.29479 - 5.01550i) q^{40} +(-3.25469 + 0.716412i) q^{41} +(0.0872680 - 1.60956i) q^{42} +(-0.471222 + 2.87433i) q^{43} +(4.10664 - 4.83471i) q^{44} +(-7.69430 + 19.3112i) q^{45} +(1.01884 + 0.774499i) q^{46} +(5.86181 + 3.52693i) q^{47} +(0.936927 + 5.71500i) q^{48} +(6.21736 - 0.676179i) q^{49} +(-2.83372 + 2.15414i) q^{50} +(-2.74983 - 9.90400i) q^{51} +(0.145236 + 2.67873i) q^{52} +(2.19994 + 0.239258i) q^{53} +(-5.30754 + 3.19344i) q^{54} +(-8.30736 - 9.78018i) q^{55} +(-1.81454 + 0.611391i) q^{56} +(-12.0827 - 5.59003i) q^{57} +2.65347 q^{58} +(-3.82919 - 6.65863i) q^{59} +16.3315 q^{60} +(10.6495 + 4.92699i) q^{61} +(-4.69735 + 1.58272i) q^{62} +(3.53322 + 4.15963i) q^{63} +(0.320821 - 0.193031i) q^{64} +(5.39497 + 0.586739i) q^{65} +(-0.394124 - 7.26919i) q^{66} +(1.13948 + 4.10403i) q^{67} +(-4.35913 + 3.31372i) q^{68} +(-6.35288 + 0.690918i) q^{69} +(0.281029 + 1.71420i) q^{70} +(-9.08556 - 5.46660i) q^{71} +(11.1523 + 8.47777i) q^{72} +(-4.53863 + 11.3911i) q^{73} +(0.490989 - 0.578038i) q^{74} +(2.87546 - 17.5395i) q^{75} +(-0.383962 + 7.08177i) q^{76} +(-3.29024 + 0.724237i) q^{77} +(2.23512 + 2.11722i) q^{78} +(-9.88675 - 3.33123i) q^{79} +(-2.31002 - 5.79770i) q^{80} +(3.20295 - 11.5360i) q^{81} +(1.98980 + 0.437988i) q^{82} +(3.22744 + 4.76012i) q^{83} +(2.00842 - 3.78827i) q^{84} +(5.18844 + 9.78644i) q^{85} +(0.999317 - 1.47388i) q^{86} +(-9.61904 + 9.11164i) q^{87} +(-7.84835 + 3.63103i) q^{88} +(2.24597 - 1.03910i) q^{89} +(9.22654 - 8.73984i) q^{90} +(0.799563 - 1.17927i) q^{91} +(1.59459 + 3.00771i) q^{92} +(11.5934 - 21.8676i) q^{93} +(-2.34709 - 3.46170i) q^{94} +(14.0114 + 3.08414i) q^{95} +(4.56829 - 16.4535i) q^{96} +(3.53517 + 8.87260i) q^{97} +(-3.62334 - 1.22084i) q^{98} +(17.8945 + 16.9506i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 26 q^{2} - 23 q^{3} - 30 q^{4} - 25 q^{5} - 13 q^{6} - 23 q^{7} - 8 q^{8} - 21 q^{9}+O(q^{10}) $ 112 * q - 26 * q^2 - 23 * q^3 - 30 * q^4 - 25 * q^5 - 13 * q^6 - 23 * q^7 - 8 * q^8 - 21 * q^9	\( 112 q - 26 q^{2} - 23 q^{3} - 30 q^{4} - 25 q^{5} - 13 q^{6} - 23 q^{7} - 8 q^{8} - 21 q^{9} - 3 q^{10} - 15 q^{11} + 21 q^{12} - 23 q^{13} + 13 q^{14} + 4 q^{15} - 8 q^{16} - 10 q^{17} + 12 q^{18} - 15 q^{19} + 7 q^{20} - 12 q^{21} - q^{22} + 3 q^{23} + 25 q^{24} - 5 q^{25} + 5 q^{26} + 22 q^{27} + 29 q^{28} - 13 q^{29} + 29 q^{30} + 3 q^{31} + 36 q^{32} + 33 q^{33} + 27 q^{34} + 28 q^{35} + 20 q^{36} - 9 q^{37} + 31 q^{38} + 45 q^{39} + 79 q^{40} + 23 q^{41} + 33 q^{42} + 19 q^{43} + 43 q^{44} + 19 q^{45} - 31 q^{46} + 10 q^{47} - 25 q^{48} - 31 q^{49} - 60 q^{50} - 61 q^{51} - 75 q^{52} - 23 q^{53} - 86 q^{54} - 24 q^{55} - 103 q^{56} - 91 q^{57} + 12 q^{58} - 33 q^{59} - 210 q^{60} - 47 q^{61} - 39 q^{62} - 58 q^{63} - 152 q^{64} - 16 q^{65} - 116 q^{66} - 19 q^{67} - 5 q^{68} - 45 q^{69} + 23 q^{70} - 18 q^{71} - 36 q^{72} + 24 q^{73} + 19 q^{74} + 58 q^{75} + 97 q^{76} + 65 q^{77} + 119 q^{78} + 41 q^{79} + 107 q^{80} + 95 q^{81} + 145 q^{82} + 49 q^{83} + 167 q^{84} + 39 q^{85} + 111 q^{86} + 80 q^{87} + 175 q^{88} + 51 q^{89} + 213 q^{90} + 77 q^{91} + 135 q^{92} + 93 q^{93} + 151 q^{94} + 65 q^{95} + 181 q^{96} + 91 q^{97} + 31 q^{98} + 44 q^{99}+O(q^{100}) \) 112 * q - 26 * q^2 - 23 * q^3 - 30 * q^4 - 25 * q^5 - 13 * q^6 - 23 * q^7 - 8 * q^8 - 21 * q^9 - 3 * q^10 - 15 * q^11 + 21 * q^12 - 23 * q^13 + 13 * q^14 + 4 * q^15 - 8 * q^16 - 10 * q^17 + 12 * q^18 - 15 * q^19 + 7 * q^20 - 12 * q^21 - q^22 + 3 * q^23 + 25 * q^24 - 5 * q^25 + 5 * q^26 + 22 * q^27 + 29 * q^28 - 13 * q^29 + 29 * q^30 + 3 * q^31 + 36 * q^32 + 33 * q^33 + 27 * q^34 + 28 * q^35 + 20 * q^36 - 9 * q^37 + 31 * q^38 + 45 * q^39 + 79 * q^40 + 23 * q^41 + 33 * q^42 + 19 * q^43 + 43 * q^44 + 19 * q^45 - 31 * q^46 + 10 * q^47 - 25 * q^48 - 31 * q^49 - 60 * q^50 - 61 * q^51 - 75 * q^52 - 23 * q^53 - 86 * q^54 - 24 * q^55 - 103 * q^56 - 91 * q^57 + 12 * q^58 - 33 * q^59 - 210 * q^60 - 47 * q^61 - 39 * q^62 - 58 * q^63 - 152 * q^64 - 16 * q^65 - 116 * q^66 - 19 * q^67 - 5 * q^68 - 45 * q^69 + 23 * q^70 - 18 * q^71 - 36 * q^72 + 24 * q^73 + 19 * q^74 + 58 * q^75 + 97 * q^76 + 65 * q^77 + 119 * q^78 + 41 * q^79 + 107 * q^80 + 95 * q^81 + 145 * q^82 + 49 * q^83 + 167 * q^84 + 39 * q^85 + 111 * q^86 + 80 * q^87 + 175 * q^88 + 51 * q^89 + 213 * q^90 + 77 * q^91 + 135 * q^92 + 93 * q^93 + 151 * q^94 + 65 * q^95 + 181 * q^96 + 91 * q^97 + 31 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/59\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{29}\right)$

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 $

$2$	−0.554859	−	0.256705i	−0.392344	−	0.181518i	0.213791	−	0.976879i	$-0.431419\pi$
$2$	−0.554859	−	0.256705i	−0.392344	−	0.181518i	−0.606135	+	0.795362i	$0.707281\pi$
$3$	2.89290	−	0.974731i	1.67022	−	0.562761i	0.684182	−	0.729311i	$-0.260159\pi$
$3$	2.89290	−	0.974731i	1.67022	−	0.562761i	0.986033	+	0.166550i	$0.0532627\pi$
$4$	−1.05280	−	1.23945i	−0.526401	−	0.619727i
$5$	−2.81882	+	1.69603i	−1.26062	+	0.758488i	−0.979550	−	0.201201i	$-0.935516\pi$
$5$	−2.81882	+	1.69603i	−1.26062	+	0.758488i	−0.281066	+	0.959688i	$0.590688\pi$
$6$	−1.85537	−	0.201783i	−0.757451	−	0.0823777i
$7$	0.0467597	+	0.862432i	0.0176735	+	0.325969i	0.993979	+	0.109571i	$0.0349478\pi$
$7$	0.0467597	+	0.862432i	0.0176735	+	0.325969i	−0.976305	+	0.216397i	$0.930569\pi$
$8$	0.593097	+	2.13614i	0.209691	+	0.755240i
$9$	5.03048	−	3.82407i	1.67683	−	1.27469i
$10$	1.99943	−	0.217451i	0.632275	−	0.0687640i
$11$	0.631059	+	3.84929i	0.190272	+	1.16061i	0.893306	+	0.449449i	$0.148380\pi$
$11$	0.631059	+	3.84929i	0.190272	+	1.16061i	−0.703034	+	0.711156i	$0.748172\pi$
$12$	−4.25378	−	2.55942i	−1.22796	−	0.738840i
$13$	−1.31325	−	0.998305i	−0.364230	−	0.276880i	0.407012	−	0.913423i	$-0.366571\pi$
$13$	−1.31325	−	0.998305i	−0.364230	−	0.276880i	−0.771241	+	0.636543i	$0.780364\pi$
$14$	0.195446	−	0.490531i	0.0522350	−	0.131100i
$15$	−6.50140	+	7.65404i	−1.67865	+	1.97626i
$16$	−0.306918	+	1.87211i	−0.0767294	+	0.468029i
$17$	0.182290	−	3.36214i	0.0442117	−	0.815438i	−0.889395	−	0.457139i	$-0.848874\pi$
$17$	0.182290	−	3.36214i	0.0442117	−	0.815438i	0.933607	−	0.358299i	$-0.116643\pi$
$18$	−3.77286	+	0.830470i	−0.889272	+	0.195744i
$19$	−3.16614	−	2.99913i	−0.726362	−	0.688047i	0.232284	−	0.972648i	$-0.425380\pi$
$19$	−3.16614	−	2.99913i	−0.726362	−	0.688047i	−0.958646	+	0.284601i	$0.908139\pi$
$20$	5.06981	+	1.70822i	1.13364	+	0.381969i
$21$	0.975910	+	2.44935i	0.212961	+	0.534492i
$22$	0.637984	−	2.29781i	0.136019	−	0.489895i
$23$	−2.04440	−	0.450007i	−0.426287	−	0.0938330i	−0.00335541	−	0.999994i	$-0.501068\pi$
$23$	−2.04440	−	0.450007i	−0.426287	−	0.0938330i	−0.422932	+	0.906161i	$0.638999\pi$
$24$	3.79793	+	5.60153i	0.775249	+	1.14341i
$25$	2.72721	−	5.14406i	0.545442	−	1.02881i
$26$	0.472397	+	0.891036i	0.0926447	+	0.174747i
$27$	5.68582	−	8.38596i	1.09424	−	1.61388i
$28$	1.01972	−	0.965926i	0.192708	−	0.182543i
$29$	−3.93910	+	1.82242i	−0.731472	+	0.338415i	−0.750022	−	0.661413i	$-0.769957\pi$
$29$	−3.93910	+	1.82242i	−0.731472	+	0.338415i	0.0185498	+	0.999828i	$0.494095\pi$
$30$	5.57219	−	2.57797i	1.01734	−	0.470670i
$31$	5.88624	−	5.57574i	1.05720	−	1.00143i	0.0572045	−	0.998362i	$-0.481781\pi$
$31$	5.88624	−	5.57574i	1.05720	−	1.00143i	0.999995	−	0.00307034i	$-0.000977320\pi$
$32$	3.13912	−	4.62986i	0.554924	−	0.818451i
$33$	5.57761	+	10.5205i	0.970938	+	1.83138i
$34$	−0.964222	+	1.81872i	−0.165363	+	0.311907i
$35$	−1.59452	−	2.35174i	−0.269523	−	0.397516i
$36$	−10.0359	−	2.20906i	−1.67264	−	0.368177i
$37$	−0.331878	+	1.19532i	−0.0545604	+	0.196509i	−0.985808	−	0.167879i	$-0.946308\pi$
$37$	−0.331878	+	1.19532i	−0.0545604	+	0.196509i	0.931247	+	0.364388i	$0.118722\pi$
$38$	0.986869	+	2.47686i	0.160091	+	0.401799i
$39$	−4.77217	−	1.60793i	−0.764159	−	0.257475i
$40$	−5.29479	−	5.01550i	−0.837180	−	0.793019i
$41$	−3.25469	+	0.716412i	−0.508297	+	0.111885i	−0.461713	−	0.887030i	$-0.652765\pi$
$41$	−3.25469	+	0.716412i	−0.508297	+	0.111885i	−0.0465849	+	0.998914i	$0.514834\pi$
$42$	0.0872680	−	1.60956i	0.0134657	−	0.248361i
$43$	−0.471222	+	2.87433i	−0.0718607	+	0.438331i	0.926251	+	0.376907i	$0.123012\pi$
$43$	−0.471222	+	2.87433i	−0.0718607	+	0.438331i	−0.998112	+	0.0614239i	$0.980436\pi$
$44$	4.10664	−	4.83471i	0.619099	−	0.728860i
$45$	−7.69430	+	19.3112i	−1.14700	+	2.87875i
$46$	1.01884	+	0.774499i	0.150219	+	0.114194i
$47$	5.86181	+	3.52693i	0.855032	+	0.514456i	0.874315	−	0.485358i	$-0.161311\pi$
$47$	5.86181	+	3.52693i	0.855032	+	0.514456i	−0.0192832	+	0.999814i	$0.506138\pi$
$48$	0.936927	+	5.71500i	0.135234	+	0.824889i
$49$	6.21736	−	0.676179i	0.888195	−	0.0965970i
$50$	−2.83372	+	2.15414i	−0.400749	+	0.304641i
$51$	−2.74983	−	9.90400i	−0.385053	−	1.38684i
$52$	0.145236	+	2.67873i	0.0201407	+	0.371473i
$53$	2.19994	+	0.239258i	0.302185	+	0.0328645i	0.257955	−	0.966157i	$-0.416951\pi$
$53$	2.19994	+	0.239258i	0.302185	+	0.0328645i	0.0442293	+	0.999021i	$0.485917\pi$
$54$	−5.30754	+	3.19344i	−0.722265	+	0.434573i
$55$	−8.30736	−	9.78018i	−1.12016	−	1.31876i
$56$	−1.81454	+	0.611391i	−0.242478	+	0.0817005i
$57$	−12.0827	−	5.59003i	−1.60039	−	0.740418i
$58$	2.65347			0.348417
$59$	−3.82919	−	6.65863i	−0.498518	−	0.866879i
$59$	−3.82919	−	6.65863i	−0.498518	−	0.866879i
$60$	16.3315			2.10839
$61$	10.6495	+	4.92699i	1.36353	+	0.630837i	0.958927	−	0.283655i	$-0.0915469\pi$
$61$	10.6495	+	4.92699i	1.36353	+	0.630837i	0.404605	+	0.914491i	$0.367409\pi$
$62$	−4.69735	+	1.58272i	−0.596564	+	0.201006i
$63$	3.53322	+	4.15963i	0.445144	+	0.524064i
$64$	0.320821	−	0.193031i	0.0401026	−	0.0241289i
$65$	5.39497	+	0.586739i	0.669164	+	0.0727760i
$66$	−0.394124	−	7.26919i	−0.0485133	−	0.894776i
$67$	1.13948	+	4.10403i	0.139209	+	0.501387i	0.999971	−	0.00762130i	$-0.00242596\pi$
$67$	1.13948	+	4.10403i	0.139209	+	0.501387i	−0.860761	+	0.509009i	$0.830012\pi$
$68$	−4.35913	+	3.31372i	−0.528622	+	0.401848i
$69$	−6.35288	+	0.690918i	−0.764797	+	0.0831767i
$70$	0.281029	+	1.71420i	0.0335894	+	0.204886i
$71$	−9.08556	−	5.46660i	−1.07826	−	0.648766i	−0.138415	−	0.990374i	$-0.544201\pi$
$71$	−9.08556	−	5.46660i	−1.07826	−	0.648766i	−0.939842	+	0.341608i	$0.889028\pi$
$72$	11.1523	+	8.47777i	1.31431	+	0.999114i
$73$	−4.53863	+	11.3911i	−0.531207	+	1.33323i	0.381408	+	0.924407i	$0.375439\pi$
$73$	−4.53863	+	11.3911i	−0.531207	+	1.33323i	−0.912614	+	0.408822i	$0.865940\pi$
$74$	0.490989	−	0.578038i	0.0570764	−	0.0671955i
$75$	2.87546	−	17.5395i	0.332030	−	2.02529i
$76$	−0.383962	+	7.08177i	−0.0440435	+	0.812335i
$77$	−3.29024	+	0.724237i	−0.374958	+	0.0825345i
$78$	2.23512	+	2.11722i	0.253077	+	0.239727i
$79$	−9.88675	−	3.33123i	−1.11235	−	0.374793i	−0.297647	−	0.954676i	$-0.596202\pi$
$79$	−9.88675	−	3.33123i	−1.11235	−	0.374793i	−0.814700	+	0.579883i	$0.803098\pi$
$80$	−2.31002	−	5.79770i	−0.258268	−	0.648203i
$81$	3.20295	−	11.5360i	0.355883	−	1.28177i
$82$	1.98980	+	0.437988i	0.219737	+	0.0483677i
$83$	3.22744	+	4.76012i	0.354258	+	0.522491i	0.962508	−	0.271254i	$-0.0874385\pi$
$83$	3.22744	+	4.76012i	0.354258	+	0.522491i	−0.608250	+	0.793746i	$0.708128\pi$
$84$	2.00842	−	3.78827i	0.219136	−	0.413335i
$85$	5.18844	+	9.78644i	0.562765	+	1.06149i
$86$	0.999317	−	1.47388i	0.107759	−	0.158933i
$87$	−9.61904	+	9.11164i	−1.03127	+	0.976870i
$88$	−7.84835	+	3.63103i	−0.836637	+	0.387069i
$89$	2.24597	−	1.03910i	0.238073	−	0.110144i	−0.297225	−	0.954807i	$-0.596061\pi$
$89$	2.24597	−	1.03910i	0.238073	−	0.110144i	0.535298	+	0.844663i	$0.320199\pi$
$90$	9.22654	−	8.73984i	0.972562	−	0.921260i
$91$	0.799563	−	1.17927i	0.0838170	−	0.123621i
$92$	1.59459	+	3.00771i	0.166247	+	0.313576i
$93$	11.5934	−	21.8676i	1.20218	−	2.26756i
$94$	−2.34709	−	3.46170i	−0.242084	−	0.357047i
$95$	14.0114	+	3.08414i	1.43754	+	0.316426i
$96$	4.56829	−	16.4535i	0.466250	−	1.67928i
$97$	3.53517	+	8.87260i	0.358942	+	0.900876i	0.991938	+	0.126721i	$0.0404454\pi$
$97$	3.53517	+	8.87260i	0.358942	+	0.900876i	−0.632997	+	0.774155i	$0.718175\pi$
$98$	−3.62334	−	1.22084i	−0.366012	−	0.123324i
$99$	17.8945	+	16.9506i	1.79846	+	1.70360i
$100$	−9.24704	+	2.03543i	−0.924704	+	0.203543i
$101$	0.496317	−	9.15403i	0.0493854	−	0.910860i	−0.863931	−	0.503610i	$-0.832005\pi$
$101$	0.496317	−	9.15403i	0.0493854	−	0.910860i	0.913317	−	0.407250i	$-0.133512\pi$
$102$	−1.01664	+	6.20122i	−0.100662	+	0.614012i
$103$	0.373198	−	0.439363i	0.0367723	−	0.0432917i	−0.743468	−	0.668771i	$-0.766821\pi$
$103$	0.373198	−	0.439363i	0.0367723	−	0.0432917i	0.780241	+	0.625479i	$0.215097\pi$
$104$	1.35364	−	3.39737i	0.132735	−	0.333140i
$105$	−6.90509	−	5.24911i	−0.673868	−	0.512261i
$106$	−1.15924	−	0.697489i	−0.112595	−	0.0677461i
$107$	0.758075	+	4.62405i	0.0732859	+	0.447024i	0.997824	+	0.0659343i	$0.0210028\pi$
$107$	0.758075	+	4.62405i	0.0732859	+	0.447024i	−0.924538	+	0.381090i	$0.875549\pi$
$108$	−16.3801	+	1.78144i	−1.57617	+	0.171419i
$109$	−3.62962	+	2.75917i	−0.347655	+	0.264280i	−0.764399	−	0.644743i	$-0.776964\pi$
$109$	−3.62962	+	2.75917i	−0.347655	+	0.264280i	0.416744	+	0.909024i	$0.363171\pi$
$110$	2.09879	+	7.55916i	0.200112	+	0.720738i
$111$	0.205023	+	3.78142i	0.0194599	+	0.358917i
$112$	−1.62892	−	0.177156i	−0.153919	−	0.0167397i
$113$	6.98819	−	4.20465i	0.657393	−	0.395540i	−0.147415	−	0.989075i	$-0.547095\pi$
$113$	6.98819	−	4.20465i	0.657393	−	0.395540i	0.804809	+	0.593534i	$0.202268\pi$
$114$	5.26918	+	6.20336i	0.493504	+	0.580998i
$115$	6.52604	−	2.19888i	0.608556	−	0.205046i
$116$	6.40590	+	2.96368i	0.594773	+	0.275171i
$117$	−10.4239			−0.963686
$118$	0.415355	+	4.67757i	0.0382366	+	0.430605i
$119$	2.90814			0.266588
$120$	−20.2061	−	9.34832i	−1.84455	−	0.853381i
$121$	−3.99463	+	1.34595i	−0.363148	+	0.122359i
$122$	−4.64420	−	5.46757i	−0.420466	−	0.495011i
$123$	−8.71718	+	5.24495i	−0.786002	+	0.472922i
$124$	−13.1079	−	1.42557i	−1.17713	−	0.128020i
$125$	0.146451	+	2.70113i	0.0130990	+	0.241597i
$126$	−0.892642	−	3.21500i	−0.0795228	−	0.286415i
$127$	−6.40397	+	4.86817i	−0.568260	+	0.431980i	−0.849448	−	0.527673i	$-0.823065\pi$
$127$	−6.40397	+	4.86817i	−0.568260	+	0.431980i	0.281188	+	0.959653i	$0.409272\pi$
$128$	−11.3494	+	1.23432i	−1.00316	+	0.109100i
$129$	1.43850	+	8.77446i	0.126653	+	0.772548i
$130$	−2.84283	−	1.71047i	−0.249333	−	0.150018i
$131$	−6.48615	−	4.93064i	−0.566697	−	0.430792i	0.282196	−	0.959357i	$-0.408937\pi$
$131$	−6.48615	−	4.93064i	−0.566697	−	0.430792i	−0.848893	+	0.528565i	$0.822730\pi$
$132$	7.16755	−	17.9892i	0.623855	−	1.56576i
$133$	2.43849	−	2.87082i	0.211444	−	0.248931i
$134$	0.421276	−	2.56967i	0.0363927	−	0.221985i
$135$	−1.80449	+	33.2819i	−0.155306	+	2.86445i
$136$	7.29011	−	1.60467i	0.625122	−	0.137600i
$137$	−5.89436	−	5.58343i	−0.503589	−	0.477025i	0.393219	−	0.919445i	$-0.371361\pi$
$137$	−5.89436	−	5.58343i	−0.503589	−	0.477025i	−0.896808	+	0.442420i	$0.854120\pi$
$138$	3.70232	+	1.24746i	0.315162	+	0.106190i
$139$	1.57818	+	3.96094i	0.133860	+	0.335963i	0.980593	−	0.196055i	$-0.0628132\pi$
$139$	1.57818	+	3.96094i	0.133860	+	0.335963i	−0.846733	+	0.532018i	$0.821434\pi$
$140$	−1.23616	+	4.45224i	−0.104475	+	0.376283i
$141$	20.3954	+	4.48937i	1.71760	+	0.378073i
$142$	3.63790	+	5.36550i	0.305286	+	0.450263i
$143$	3.01403	−	5.68507i	0.252046	−	0.475409i
$144$	5.61516	+	10.5913i	0.467930	+	0.882609i
$145$	8.01275	−	11.8179i	0.665422	−	0.981424i
$146$	5.44246	−	5.15537i	0.450421	−	0.426661i
$147$	17.3271	−	8.01637i	1.42912	−	0.661179i
$148$	1.83094	−	0.847084i	0.150503	−	0.0696299i
$149$	−6.70502	+	6.35133i	−0.549296	+	0.520321i	−0.911238	−	0.411880i	$-0.864872\pi$
$149$	−6.70502	+	6.35133i	−0.549296	+	0.520321i	0.361942	+	0.932201i	$0.382114\pi$
$150$	−6.09796	+	8.99382i	−0.497897	+	0.734342i
$151$	−10.4138	−	19.6425i	−0.847464	−	1.59849i	−0.800301	−	0.599599i	$-0.795327\pi$
$151$	−10.4138	−	19.6425i	−0.847464	−	1.59849i	−0.0471626	−	0.998887i	$-0.515018\pi$
$152$	4.52873	−	8.54209i	0.367328	−	0.692855i
$153$	−11.9400	−	17.6102i	−0.965295	−	1.42370i
$154$	2.01154	+	0.442773i	0.162094	+	0.0356796i
$155$	−7.13565	+	25.7003i	−0.573149	+	2.06430i
$156$	3.03119	+	7.60772i	0.242690	+	0.609105i
$157$	7.71264	+	2.59869i	0.615536	+	0.207398i	0.609761	−	0.792585i	$-0.291265\pi$
$157$	7.71264	+	2.59869i	0.615536	+	0.207398i	0.00577445	+	0.999983i	$0.498162\pi$
$158$	4.63061	+	4.38634i	0.368391	+	0.348959i
$159$	6.59740	−	1.45220i	0.523208	−	0.115167i
$160$	−0.996253	+	18.3748i	−0.0787607	+	1.45266i
$161$	0.292505	−	1.78420i	0.0230526	−	0.140615i
$162$	−4.73852	+	5.57862i	−0.372294	+	0.438298i
$163$	5.39519	−	13.5409i	0.422584	−	1.06061i	−0.551451	−	0.834207i	$-0.685926\pi$
$163$	5.39519	−	13.5409i	0.422584	−	1.06061i	0.974035	−	0.226398i	$-0.0726950\pi$
$164$	4.31450	+	3.27980i	0.336906	+	0.256109i
$165$	−33.5654	−	20.1956i	−2.61306	−	1.57223i
$166$	−0.568828	−	3.46970i	−0.0441496	−	0.269301i
$167$	16.8909	−	1.83700i	1.30706	−	0.142151i	0.572056	−	0.820215i	$-0.306146\pi$
$167$	16.8909	−	1.83700i	1.30706	−	0.142151i	0.735004	+	0.678063i	$0.237180\pi$
$168$	−4.65334	+	3.53738i	−0.359013	+	0.272915i
$169$	−2.74986	−	9.90410i	−0.211528	−	0.761854i
$170$	−0.366624	−	6.76199i	−0.0281188	−	0.518621i
$171$	−27.3961	−	2.97950i	−2.09503	−	0.227848i
$172$	4.05870	−	2.44204i	0.309473	−	0.186204i
$173$	12.2858	+	14.4639i	0.934071	+	1.09967i	0.994833	+	0.101521i	$0.0323709\pi$
$173$	12.2858	+	14.4639i	0.934071	+	1.09967i	−0.0607624	+	0.998152i	$0.519353\pi$
$174$	7.67621	−	2.58642i	0.581932	−	0.196076i
$175$	4.56392	+	2.11150i	0.345000	+	0.159614i
$176$	−7.40000			−0.557796
$177$	−17.5678	−	15.5303i	−1.32048	−	1.16733i
$178$	−1.51294			−0.113400
$179$	−16.2981	−	7.54030i	−1.21818	−	0.563588i	−0.297802	−	0.954628i	$-0.596254\pi$
$179$	−16.2981	−	7.54030i	−1.21818	−	0.563588i	−0.920374	+	0.391039i	$0.872116\pi$
$180$	32.0359	−	10.7942i	2.38782	−	0.804550i
$181$	15.3849	+	18.1125i	1.14355	+	1.34629i	0.929220	+	0.369526i	$0.120480\pi$
$181$	15.3849	+	18.1125i	1.14355	+	1.34629i	0.214327	+	0.976762i	$0.431244\pi$
$182$	−0.746369	+	0.449075i	−0.0553245	+	0.0332877i
$183$	35.6105	+	3.87287i	2.63240	+	0.286291i
$184$	−0.251250	−	4.63403i	−0.0185224	−	0.341625i
$185$	−1.09179	−	3.93226i	−0.0802698	−	0.289106i
$186$	−12.0462	+	9.15731i	−0.883273	+	0.671446i
$187$	13.0569	−	1.42002i	0.954813	−	0.103842i
$188$	−1.79985	−	10.9786i	−0.131268	−	0.800697i
$189$	7.49818	+	4.51151i	0.545413	+	0.328164i
$190$	−6.98263	−	5.30806i	−0.506573	−	0.385087i
$191$	−1.82504	+	4.58050i	−0.132055	+	0.331433i	−0.980104	−	0.198485i	$-0.936398\pi$
$191$	−1.82504	+	4.58050i	−0.132055	+	0.331433i	0.848049	+	0.529918i	$0.177777\pi$
$192$	0.739948	−	0.871134i	0.0534011	−	0.0628687i
$193$	−3.09323	+	18.8679i	−0.222656	+	1.35814i	0.604696	+	0.796456i	$0.293294\pi$
$193$	−3.09323	+	18.8679i	−0.222656	+	1.35814i	−0.827352	+	0.561684i	$0.810154\pi$
$194$	0.316122	−	5.83053i	0.0226963	−	0.418608i
$195$	16.1790	−	3.56127i	1.15860	−	0.255028i
$196$	−7.38374	−	6.99425i	−0.527410	−	0.499590i
$197$	−8.62732	−	2.90688i	−0.614671	−	0.207107i	−0.00529224	−	0.999986i	$-0.501685\pi$
$197$	−8.62732	−	2.90688i	−0.614671	−	0.207107i	−0.609379	+	0.792879i	$0.708581\pi$
$198$	−5.57762	−	13.9988i	−0.396384	−	0.994850i
$199$	2.53614	−	9.13434i	0.179782	−	0.647517i	−0.817638	−	0.575733i	$-0.804717\pi$
$199$	2.53614	−	9.13434i	0.179782	−	0.647517i	0.997420	−	0.0717840i	$-0.0228692\pi$
$200$	12.6059	+	2.77478i	0.891374	+	0.196206i
$201$	7.29672	+	10.7619i	0.514671	+	0.759083i
$202$	−2.62527	+	4.95179i	−0.184713	+	0.348407i
$203$	−1.75590	−	3.31199i	−0.123240	−	0.232456i
$204$	−9.38052	+	13.8352i	−0.656768	+	0.968660i
$205$	7.95935	−	7.53949i	0.555905	−	0.526581i
$206$	−0.319859	+	0.147982i	−0.0222856	+	0.0103104i
$207$	−12.0052	+	5.55419i	−0.834418	+	0.386043i
$208$	2.27200	−	2.15215i	0.157535	−	0.149225i
$209$	9.54649	−	14.0800i	0.660345	−	0.973935i
$210$	2.48388	+	4.68509i	0.171404	+	0.323302i
$211$	−13.0562	+	24.6267i	−0.898828	+	1.69537i	−0.200367	+	0.979721i	$0.564213\pi$
$211$	−13.0562	+	24.6267i	−0.898828	+	1.69537i	−0.698461	+	0.715648i	$0.746132\pi$
$212$	−2.01955	−	2.97861i	−0.138703	−	0.204572i
$213$	−31.6121	−	6.95834i	−2.16602	−	0.476778i
$214$	0.766393	−	2.76030i	0.0523895	−	0.188690i
$215$	−3.54666	−	8.90144i	−0.241880	−	0.607073i
$216$	21.2858	+	7.17203i	1.44832	+	0.487995i
$217$	5.08394	+	4.81576i	0.345120	+	0.326915i
$218$	2.72222	−	0.599206i	0.184372	−	0.0405834i
$219$	−2.02654	+	37.3773i	−0.136941	+	2.52572i
$220$	−3.37608	+	20.5932i	−0.227615	+	1.38839i
$221$	−3.59583	+	4.23334i	−0.241882	+	0.284765i
$222$	0.856951	−	2.15079i	0.0575148	−	0.144351i
$223$	−2.30497	−	1.75219i	−0.154352	−	0.117336i	0.525148	−	0.851011i	$-0.324010\pi$
$223$	−2.30497	−	1.75219i	−0.154352	−	0.117336i	−0.679500	+	0.733676i	$0.737803\pi$
$224$	4.13972	+	2.49079i	0.276597	+	0.166423i
$225$	−5.95209	−	36.3061i	−0.396806	−	2.42041i
$226$	−4.95681	+	0.539086i	−0.329722	+	0.0358595i
$227$	−13.3785	+	10.1700i	−0.887960	+	0.675010i	−0.946301	−	0.323287i	$-0.895212\pi$
$227$	−13.3785	+	10.1700i	−0.887960	+	0.675010i	0.0583409	+	0.998297i	$0.481419\pi$
$228$	5.79205	+	20.8611i	0.383588	+	1.38156i
$229$	−0.880892	−	16.2471i	−0.0582110	−	1.07364i	−0.871064	−	0.491169i	$-0.836570\pi$
$229$	−0.880892	−	16.2471i	−0.0582110	−	1.07364i	0.812853	−	0.582469i	$-0.197913\pi$
$230$	−4.18549	−	0.455200i	−0.275983	−	0.0300150i
$231$	−8.81240	+	5.30225i	−0.579814	+	0.348862i
$232$	−6.22921	−	7.33360i	−0.408968	−	0.481474i
$233$	5.77225	−	1.94490i	0.378153	−	0.127414i	−0.123805	−	0.992307i	$-0.539510\pi$
$233$	5.77225	−	1.94490i	0.378153	−	0.127414i	0.501958	+	0.864892i	$0.332613\pi$
$234$	5.78377	+	2.67586i	0.378097	+	0.174926i
$235$	−22.5052			−1.46808
$236$	−4.22169	+	11.7563i	−0.274808	+	0.765271i
$237$	−31.8484			−2.06878
$238$	−1.61360	−	0.746533i	−0.104594	−	0.0483905i
$239$	4.28355	−	1.44330i	0.277080	−	0.0933592i	−0.177331	−	0.984151i	$-0.556746\pi$
$239$	4.28355	−	1.44330i	0.277080	−	0.0933592i	0.454411	+	0.890792i	$0.349850\pi$
$240$	−12.3338	−	14.5205i	−0.796146	−	0.937296i
$241$	24.1172	−	14.5108i	1.55352	−	0.934724i	0.559119	−	0.829087i	$-0.311139\pi$
$241$	24.1172	−	14.5108i	1.55352	−	0.934724i	0.994405	−	0.105637i	$-0.0336881\pi$
$242$	2.56197	+	0.278631i	0.164689	+	0.0179111i
$243$	−0.333099	−	6.14364i	−0.0213683	−	0.394115i
$244$	−5.10505	−	18.3867i	−0.326818	−	1.17709i
$245$	−16.3788	+	12.4509i	−1.04641	+	0.795457i
$246$	6.18321	−	0.672465i	0.394227	−	0.0428748i
$247$	1.16388	+	7.09937i	0.0740561	+	0.451722i
$248$	15.4017	+	9.26688i	0.978007	+	0.588448i
$249$	13.9765	+	10.6247i	0.885724	+	0.673310i
$250$	0.612134	−	1.53634i	0.0387148	−	0.0971668i
$251$	−3.53436	+	4.16097i	−0.223087	+	0.262638i	−0.862307	−	0.506385i	$-0.830981\pi$
$251$	−3.53436	+	4.16097i	−0.223087	+	0.262638i	0.639220	+	0.769024i	$0.279257\pi$
$252$	1.43589	−	8.75854i	0.0904525	−	0.551736i
$253$	0.442069	−	8.15349i	0.0277926	−	0.512605i
$254$	4.80298	−	1.05722i	0.301366	−	0.0663356i
$255$	24.5488	+	23.2538i	1.53730	+	1.45621i
$256$	5.90455	+	1.98947i	0.369034	+	0.124342i
$257$	−2.21814	−	5.56710i	−0.138364	−	0.347266i	0.843424	−	0.537249i	$-0.180536\pi$
$257$	−2.21814	−	5.56710i	−0.138364	−	0.347266i	−0.981788	+	0.189982i	$0.939157\pi$
$258$	1.45428	−	5.23785i	0.0905397	−	0.326095i
$259$	−1.04640	−	0.230330i	−0.0650200	−	0.0143120i
$260$	−4.95260	−	7.30454i	−0.307147	−	0.453008i
$261$	−12.8465	+	24.2310i	−0.795178	+	1.49986i
$262$	2.33317	+	4.40083i	0.144144	+	0.271884i
$263$	4.32309	−	6.37609i	0.266573	−	0.393166i	−0.670718	−	0.741712i	$-0.734014\pi$
$263$	4.32309	−	6.37609i	0.266573	−	0.393166i	0.937292	+	0.348546i	$0.113324\pi$
$264$	−19.1652	+	18.1542i	−1.17954	+	1.11732i
$265$	−6.60702	+	3.05673i	−0.405866	+	0.187774i
$266$	−2.08997	+	0.966924i	−0.128144	+	0.0592859i
$267$	5.48453	−	5.19522i	0.335648	−	0.317943i
$268$	3.88711	−	5.73306i	0.237443	−	0.350203i
$269$	−2.56485	−	4.83783i	−0.156382	−	0.294968i	0.792924	−	0.609320i	$-0.208557\pi$
$269$	−2.56485	−	4.83783i	−0.156382	−	0.294968i	−0.949306	+	0.314352i	$0.898213\pi$
$270$	9.54486	−	18.0035i	0.580882	−	1.09566i
$271$	−5.05394	−	7.45400i	−0.307005	−	0.452798i	0.642621	−	0.766184i	$-0.277847\pi$
$271$	−5.05394	−	7.45400i	−0.307005	−	0.452798i	−0.949626	+	0.313386i	$0.898537\pi$
$272$	6.23836	+	1.37317i	0.378256	+	0.0832604i
$273$	1.16359	−	4.19086i	0.0704235	−	0.253642i
$274$	1.83724	+	4.61113i	0.110992	+	0.278569i
$275$	21.5220	+	7.25161i	1.29783	+	0.437289i
$276$	7.54469	+	7.14671i	0.454137	+	0.430181i
$277$	9.76763	−	2.15002i	0.586880	−	0.129182i	0.0884027	−	0.996085i	$-0.471824\pi$
$277$	9.76763	−	2.15002i	0.586880	−	0.129182i	0.498477	+	0.866903i	$0.333893\pi$
$278$	0.141125	−	2.60289i	0.00846410	−	0.156111i
$279$	8.28857	−	50.5580i	0.496224	−	3.02683i
$280$	4.07794	−	4.80092i	0.243703	−	0.286910i
$281$	−4.69259	+	11.7775i	−0.279937	+	0.702588i	0.720026	+	0.693947i	$0.244130\pi$
$281$	−4.69259	+	11.7775i	−0.279937	+	0.702588i	−0.999963	+	0.00864103i	$0.997249\pi$
$282$	−10.1641	−	7.72657i	−0.605265	−	0.460111i
$283$	−26.5719	−	15.9878i	−1.57953	−	0.950374i	−0.989750	−	0.142814i	$-0.954385\pi$
$283$	−26.5719	−	15.9878i	−1.57953	−	0.950374i	−0.589785	−	0.807561i	$-0.700787\pi$
$284$	2.78969	+	17.0164i	0.165538	+	1.00974i
$285$	43.5397	−	4.73523i	2.57907	−	0.280491i
$286$	−3.13175	+	2.38069i	−0.185184	+	0.140773i
$287$	−0.770045	−	2.77345i	−0.0454543	−	0.163712i
$288$	−1.91362	−	35.2946i	−0.112761	−	2.07976i
$289$	5.62962	+	0.612258i	0.331154	+	0.0360152i
$290$	−7.47966	+	4.50036i	−0.439221	+	0.264270i
$291$	18.8753	+	22.2217i	1.10649	+	1.30266i
$292$	18.8970	−	6.36715i	1.10587	−	0.372609i
$293$	−4.59598	−	2.12633i	−0.268500	−	0.124221i	0.281020	−	0.959702i	$-0.409327\pi$
$293$	−4.59598	−	2.12633i	−0.268500	−	0.124221i	−0.549520	+	0.835481i	$0.685189\pi$
$294$	−11.6719			−0.680721
$295$	22.0870	+	12.2751i	1.28596	+	0.714683i
$296$	−2.75020			−0.159852
$297$	35.8681	+	16.5943i	2.08128	+	0.962902i
$298$	5.35075	−	1.80288i	0.309961	−	0.104438i
$299$	2.23556	+	2.63191i	0.129286	+	0.152207i
$300$	−24.7667	+	14.9017i	−1.42991	+	0.860347i
$301$	−2.50095	−	0.271994i	−0.144152	−	0.0156775i
$302$	0.735858	+	13.5721i	0.0423439	+	0.780987i
$303$	−7.48692	−	26.9655i	−0.430112	−	1.54913i
$304$	6.58645	−	5.00689i	0.377759	−	0.287165i
$305$	−38.3755	+	4.17358i	−2.19737	+	0.238979i
$306$	2.10440	+	12.8363i	0.120300	+	0.733800i
$307$	−4.14617	−	2.49467i	−0.236635	−	0.142378i	0.392298	−	0.919838i	$-0.371680\pi$
$307$	−4.14617	−	2.49467i	−0.236635	−	0.142378i	−0.628932	+	0.777460i	$0.716508\pi$
$308$	4.36163	+	3.31563i	0.248527	+	0.188925i
$309$	0.651363	−	1.63480i	0.0370548	−	0.0930005i
$310$	10.5567	−	12.4283i	0.599578	−	0.705878i
$311$	3.92141	−	23.9195i	0.222362	−	1.35635i	−0.605690	−	0.795701i	$-0.707103\pi$
$311$	3.92141	−	23.9195i	0.222362	−	1.35635i	0.828053	−	0.560650i	$-0.189449\pi$
$312$	0.604410	−	11.1477i	0.0342180	−	0.631114i
$313$	−33.1029	+	7.28650i	−1.87109	+	0.411857i	−0.997233	−	0.0743338i	$-0.976317\pi$
$313$	−33.1029	+	7.28650i	−1.87109	+	0.411857i	−0.873853	+	0.486191i	$0.838386\pi$
$314$	−3.61233	−	3.42178i	−0.203855	−	0.193102i
$315$	−17.0144	−	5.73282i	−0.958653	−	0.323008i
$316$	6.27988	+	15.7613i	0.353271	+	0.886643i
$317$	−5.88706	+	21.2033i	−0.330650	+	1.19090i	0.592217	+	0.805778i	$0.298253\pi$
$317$	−5.88706	+	21.2033i	−0.330650	+	1.19090i	−0.922868	+	0.385117i	$0.874161\pi$
$318$	−4.03341	−	0.887822i	−0.226183	−	0.0497866i
$319$	−9.50084	−	14.0127i	−0.531945	−	0.784560i
$320$	−0.576950	+	1.08824i	−0.0322525	+	0.0608346i
$321$	6.70024	+	12.6380i	0.373971	+	0.705384i
$322$	−0.620312	+	0.914892i	−0.0345686	+	0.0509849i
$323$	−10.6606	+	10.0983i	−0.593173	+	0.561883i
$324$	−17.6704	+	8.17518i	−0.981687	+	0.454177i
$325$	−8.71685	+	4.03284i	−0.483524	+	0.223702i
$326$	−6.46958	+	6.12832i	−0.358317	+	0.339416i
$327$	−7.81068	+	11.5199i	−0.431932	+	0.637052i
$328$	−3.46070	−	6.52758i	−0.191085	−	0.360425i
$329$	−2.76764	+	5.22033i	−0.152585	+	0.287806i
$330$	13.4397	+	19.8221i	0.739833	+	1.09117i
$331$	−1.85821	−	0.409024i	−0.102137	−	0.0224820i	0.163608	−	0.986525i	$-0.447687\pi$
$331$	−1.85821	−	0.409024i	−0.102137	−	0.0224820i	−0.265745	+	0.964043i	$0.585618\pi$
$332$	2.50209	−	9.01173i	0.137320	−	0.494583i
$333$	2.90147	+	7.28214i	0.159000	+	0.399059i
$334$	−9.84365	−	3.31671i	−0.538620	−	0.181482i
$335$	−10.1726	−	9.63595i	−0.555786	−	0.526468i
$336$	−4.88499	+	1.07527i	−0.266498	+	0.0586606i
$337$	1.17193	−	21.6150i	0.0638392	−	1.17744i	−0.774601	−	0.632450i	$-0.782049\pi$
$337$	1.17193	−	21.6150i	0.0638392	−	1.17744i	0.838440	−	0.544994i	$-0.183468\pi$
$338$	−1.01665	+	6.20128i	−0.0552984	+	0.337305i
$339$	16.1177	−	18.9752i	0.875394	−	1.03059i
$340$	6.66744	−	16.7340i	0.361593	−	0.907529i
$341$	25.1772	+	19.1392i	1.36342	+	1.03645i
$342$	14.4361	+	8.68591i	0.780615	+	0.469680i
$343$	1.85200	+	11.2967i	0.0999984	+	0.609963i
$344$	−6.41945	+	0.698158i	−0.346114	+	0.0376421i
$345$	16.7358	−	12.7223i	0.901028	−	0.684943i
$346$	−3.10391	−	11.1793i	−0.166867	−	0.601001i
$347$	−0.0961070	−	1.77259i	−0.00515929	−	0.0951576i	0.994820	−	0.101656i	$-0.0324142\pi$
$347$	−0.0961070	−	1.77259i	−0.00515929	−	0.0951576i	−0.999979	+	0.00649863i	$0.997931\pi$
$348$	21.4204	+	2.32961i	1.14825	+	0.124880i
$349$	−0.965567	+	0.580962i	−0.0516856	+	0.0310982i	−0.541162	−	0.840918i	$-0.682015\pi$
$349$	−0.965567	+	0.580962i	−0.0516856	+	0.0310982i	0.489477	+	0.872016i	$0.337188\pi$
$350$	−1.99030	−	2.34316i	−0.106386	−	0.125247i
$351$	−15.8386	+	5.33666i	−0.845404	+	0.284850i
$352$	19.8027	+	9.16168i	1.05549	+	0.488319i
$353$	33.0859			1.76098			0.880491	−	0.474062i	$-0.157213\pi$
$353$	33.0859			1.76098			0.880491	+	0.474062i	$0.157213\pi$
$354$	5.76095	+	13.1269i	0.306191	+	0.697685i
$355$	34.8821			1.85135
$356$	−3.65248	−	1.68982i	−0.193581	−	0.0895601i
$357$	8.41294	−	2.83465i	0.445260	−	0.150026i
$358$	7.10750	+	8.36760i	0.375643	+	0.442241i
$359$	9.44626	−	5.68363i	0.498555	−	0.299970i	−0.243977	−	0.969781i	$-0.578452\pi$
$359$	9.44626	−	5.68363i	0.498555	−	0.299970i	0.742532	+	0.669811i	$0.233625\pi$
$360$	−45.8150	−	4.98268i	−2.41466	−	0.262610i
$361$	0.00103907	+	0.0191644i	5.46877e−5	+	0.00100865i
$362$	−3.88686	−	13.9992i	−0.204289	−	0.735783i
$363$	−10.2441	+	7.78738i	−0.537677	+	0.408731i
$364$	−2.30343	+	0.250513i	−0.120733	+	0.0131305i
$365$	−6.52606	−	39.8072i	−0.341589	−	2.08360i
$366$	−18.7646	−	11.2903i	−0.980841	−	0.590153i
$367$	−1.82954	−	1.39078i	−0.0955014	−	0.0725983i	0.556334	−	0.830959i	$-0.312208\pi$
$367$	−1.82954	−	1.39078i	−0.0955014	−	0.0725983i	−0.651835	+	0.758361i	$0.726001\pi$
$368$	1.46993	−	3.68924i	0.0766253	−	0.192315i
$369$	−13.6330	+	16.0501i	−0.709708	+	0.835533i
$370$	−0.403644	+	2.46212i	−0.0209844	+	0.127999i
$371$	−0.103475	+	1.90848i	−0.00537215	+	0.0990835i
$372$	−39.3094	+	8.65266i	−2.03810	+	0.448619i
$373$	0.723584	+	0.685415i	0.0374658	+	0.0354895i	0.706203	−	0.708009i	$-0.250406\pi$
$373$	0.723584	+	0.685415i	0.0374658	+	0.0354895i	−0.668738	+	0.743498i	$0.733165\pi$
$374$	−7.60925	−	2.56385i	−0.393465	−	0.132574i
$375$	3.05654	+	7.67135i	0.157839	+	0.396147i
$376$	−4.05740	+	14.6135i	−0.209245	+	0.753631i
$377$	6.99235	+	1.53913i	0.360124	+	0.0792693i
$378$	−3.00231	−	4.42807i	−0.154422	−	0.227755i
$379$	−9.54753	+	18.0086i	−0.490424	+	0.925037i	0.507563	+	0.861615i	$0.330546\pi$
$379$	−9.54753	+	18.0086i	−0.490424	+	0.925037i	−0.997987	+	0.0634226i	$0.979798\pi$
$380$	−10.9286	−	20.6135i	−0.560624	−	1.05745i
$381$	−13.7809	+	20.3253i	−0.706015	+	1.04129i
$382$	2.18847	−	2.07303i	0.111972	−	0.106066i
$383$	−23.5937	+	10.9156i	−1.20558	+	0.557760i	−0.916689	−	0.399602i	$-0.869148\pi$
$383$	−23.5937	+	10.9156i	−1.20558	+	0.557760i	−0.288890	+	0.957362i	$0.593286\pi$
$384$	−31.6296	+	14.6334i	−1.61409	+	0.746758i
$385$	8.04629	−	7.62185i	0.410077	−	0.388445i
$386$	6.55979	−	9.67496i	0.333884	−	0.492442i
$387$	8.62116	+	16.2612i	0.438238	+	0.826605i
$388$	7.27535	−	13.7228i	0.369350	−	0.696668i
$389$	13.6598	+	20.1467i	0.692580	+	1.02148i	0.997607	+	0.0691350i	$0.0220239\pi$
$389$	13.6598	+	20.1467i	0.692580	+	1.02148i	−0.305028	+	0.952343i	$0.598666\pi$
$390$	−9.89127	−	2.17723i	−0.500864	−	0.110248i
$391$	−1.88566	+	6.79153i	−0.0953618	+	0.343462i
$392$	5.13191	+	12.8801i	0.259201	+	0.650545i
$393$	−23.5698	−	7.94159i	−1.18894	−	0.400600i
$394$	4.04073	+	3.82759i	0.203569	+	0.192831i
$395$	33.5189	−	7.37806i	1.68652	−	0.371231i
$396$	2.17009	−	40.0250i	0.109051	−	2.01133i
$397$	−2.12527	+	12.9636i	−0.106664	+	0.650623i	0.878333	+	0.478050i	$0.158656\pi$
$397$	−2.12527	+	12.9636i	−0.106664	+	0.650623i	−0.984997	+	0.172573i	$0.944792\pi$
$398$	−3.75203	+	4.41723i	−0.188072	+	0.221416i
$399$	4.25604	−	10.6819i	0.213068	−	0.534762i
$400$	8.79325	+	6.68445i	0.439662	+	0.334223i
$401$	17.8154	+	10.7192i	0.889660	+	0.535291i	0.885468	−	0.464701i	$-0.153838\pi$
$401$	17.8154	+	10.7192i	0.889660	+	0.535291i	0.00419205	+	0.999991i	$0.498666\pi$
$402$	−1.28603	−	7.84442i	−0.0641412	−	0.391244i
$403$	−13.2964	+	1.44607i	−0.662340	+	0.0720338i
$404$	−11.8685	+	9.02222i	−0.590481	+	0.448872i
$405$	10.5368	+	37.9502i	0.523578	+	1.88576i
$406$	0.124075	+	2.28844i	0.00615776	+	0.113573i
$407$	−4.81056	−	0.523180i	−0.238451	−	0.0259331i
$408$	19.5254	−	11.7481i	0.966652	−	0.581615i
$409$	−23.1163	−	27.2147i	−1.14303	−	1.34568i	−0.929535	−	0.368734i	$-0.879791\pi$
$409$	−23.1163	−	27.2147i	−1.14303	−	1.34568i	−0.213495	−	0.976944i	$-0.568485\pi$
$410$	−6.35174	+	2.14015i	−0.313690	+	0.105694i
$411$	−22.4941	−	10.4069i	−1.10955	−	0.513334i
$412$	−0.937473			−0.0461860
$413$	5.56356	−	3.61377i	0.273765	−	0.177822i
$414$	8.08697			0.397453
$415$	−17.1709	−	7.94410i	−0.842886	−	0.389961i
$416$	−8.74446	+	2.94635i	−0.428733	+	0.144457i
$417$	8.42638	+	9.92030i	0.412641	+	0.485799i
$418$	−8.91137	+	5.36179i	−0.435869	+	0.262254i
$419$	27.2597	+	2.96467i	1.33172	+	0.144834i	0.746146	−	0.665782i	$-0.231902\pi$
$419$	27.2597	+	2.96467i	1.33172	+	0.144834i	0.585578	+	0.810616i	$0.300868\pi$
$420$	0.763656	+	14.0848i	0.0372626	+	0.687268i
$421$	−1.28680	−	4.63464i	−0.0627148	−	0.225878i	0.925551	−	0.378623i	$-0.123602\pi$
$421$	−1.28680	−	4.63464i	−0.0627148	−	0.225878i	−0.988266	+	0.152745i	$0.951189\pi$
$422$	13.5661	−	10.3127i	0.660390	−	0.502015i
$423$	42.9749	−	4.67380i	2.08951	−	0.227248i
$424$	0.793687	+	4.84128i	0.0385449	+	0.235113i
$425$	−16.7979	−	10.1070i	−0.814817	−	0.490259i
$426$	15.7540	+	11.9759i	0.763283	+	0.580233i
$427$	−3.75123	+	9.41487i	−0.181535	+	0.455618i
$428$	4.93320	−	5.80781i	0.238455	−	0.280731i
$429$	3.17788	−	19.3842i	0.153429	−	0.935877i
$430$	−0.317150	+	5.84948i	−0.0152943	+	0.282087i
$431$	1.70525	−	0.375355i	0.0821392	−	0.0180802i	−0.173711	−	0.984797i	$-0.555576\pi$
$431$	1.70525	−	0.375355i	0.0821392	−	0.0180802i	0.255850	+	0.966717i	$0.417645\pi$
$432$	13.9544	+	13.2183i	0.671381	+	0.635966i
$433$	21.0612	+	7.09634i	1.01214	+	0.341028i	0.776028	−	0.630699i	$-0.217232\pi$
$433$	21.0612	+	7.09634i	1.01214	+	0.341028i	0.236108	+	0.971727i	$0.424128\pi$
$434$	−1.58464	−	3.97714i	−0.0760650	−	0.190909i
$435$	11.6608	−	41.9983i	0.559091	−	2.01366i
$436$	7.24114	+	1.59389i	0.346788	+	0.0763337i
$437$	5.12324	+	7.55621i	0.245078	+	0.361462i
$438$	10.7194	−	20.2189i	0.512191	−	0.966095i
$439$	6.10646	+	11.5180i	0.291446	+	0.549725i	0.985392	−	0.170302i	$-0.0544743\pi$
$439$	6.10646	+	11.5180i	0.291446	+	0.549725i	−0.693946	+	0.720027i	$0.744130\pi$
$440$	15.9648	−	23.5463i	0.761091	−	1.12253i
$441$	28.6906	−	27.1771i	1.36622	−	1.29415i
$442$	3.08190	−	1.42584i	0.146591	−	0.0678202i
$443$	37.6159	−	17.4030i	1.78719	−	0.826840i	0.820171	−	0.572119i	$-0.193878\pi$
$443$	37.6159	−	17.4030i	1.78719	−	0.826840i	0.967015	−	0.254721i	$-0.0819836\pi$
$444$	4.47105	−	4.23521i	0.212187	−	0.200994i
$445$	−4.56866	+	6.73827i	−0.216575	+	0.319425i
$446$	0.829137	+	1.56392i	0.0392608	+	0.0740537i
$447$	−13.2061	+	24.9093i	−0.624627	+	1.17817i
$448$	0.181478	+	0.267660i	0.00857402	+	0.0126457i
$449$	6.58499	+	1.44947i	0.310765	+	0.0684046i	0.367615	−	0.929978i	$-0.380175\pi$
$449$	6.58499	+	1.44947i	0.310765	+	0.0684046i	−0.0568497	+	0.998383i	$0.518106\pi$
$450$	−6.01740	+	21.6727i	−0.283663	+	1.02166i
$451$	−4.81158	−	12.0762i	−0.226569	−	0.568644i
$452$	−12.5686	−	4.23487i	−0.591180	−	0.199192i
$453$	−49.2722	−	46.6732i	−2.31501	−	2.19290i
$454$	10.0339	−	2.20862i	0.470912	−	0.103656i
$455$	−0.253755	+	4.68023i	−0.0118962	+	0.219413i
$456$	4.77491	−	29.1257i	0.223606	−	1.36394i
$457$	−19.9001	+	23.4282i	−0.930889	+	1.09593i	0.0642983	+	0.997931i	$0.479519\pi$
$457$	−19.9001	+	23.4282i	−0.930889	+	1.09593i	−0.995187	+	0.0979960i	$0.968757\pi$
$458$	−3.68194	+	9.24097i	−0.172046	+	0.431802i
$459$	−27.1583	−	20.6452i	−1.26764	−	0.963634i
$460$	−9.59603	−	5.77374i	−0.447417	−	0.269202i
$461$	−5.30727	−	32.3729i	−0.247184	−	1.50776i	−0.760377	−	0.649482i	$-0.774986\pi$
$461$	−5.30727	−	32.3729i	−0.247184	−	1.50776i	0.513193	−	0.858273i	$-0.328463\pi$
$462$	6.25075	−	0.679810i	0.290811	−	0.0316276i
$463$	0.0515587	−	0.0391939i	0.00239614	−	0.00182150i	−0.603975	−	0.797003i	$-0.706418\pi$
$463$	0.0515587	−	0.0391939i	0.00239614	−	0.00182150i	0.606372	+	0.795181i	$0.292624\pi$
$464$	−2.20280	−	7.93378i	−0.102263	−	0.368316i
$465$	4.40815	+	81.3036i	0.204423	+	3.77036i
$466$	−3.70205	−	0.402622i	−0.171494	−	0.0186511i
$467$	−22.3545	+	13.4503i	−1.03444	+	0.622404i	−0.928256	−	0.371942i	$-0.878692\pi$
$467$	−22.3545	+	13.4503i	−1.03444	+	0.622404i	−0.106188	+	0.994346i	$0.533864\pi$
$468$	10.9743	+	12.9199i	0.507285	+	0.597222i
$469$	−3.48616	+	1.17463i	−0.160976	+	0.0542392i
$470$	12.4872	+	5.77719i	0.575991	+	0.266482i
$471$	24.8449			1.14479
$472$	11.9527	−	12.1289i	0.550167	−	0.558278i
$473$	−11.3615			−0.522403
$474$	17.6714	+	8.17565i	0.811673	+	0.375520i
$475$	−24.0624	+	8.10757i	−1.10406	+	0.372001i
$476$	−3.06169	−	3.60450i	−0.140332	−	0.165212i
$477$	11.9817	−	7.20913i	0.548603	−	0.330084i
$478$	−2.74727	−	0.298784i	−0.125657	−	0.0136660i
$479$	−0.163608	−	3.01758i	−0.00747545	−	0.137877i	−0.999889	−	0.0149285i	$-0.995248\pi$
$479$	−0.163608	−	3.01758i	−0.00747545	−	0.137877i	0.992413	−	0.122948i	$-0.0392348\pi$
$480$	15.0284	+	54.1275i	0.685951	+	2.47057i
$481$	1.62913	−	1.23843i	0.0742820	−	0.0564677i
$482$	−17.1066	+	1.86046i	−0.779186	+	0.0847415i
$483$	−0.892928	−	5.44662i	−0.0406296	−	0.247830i
$484$	5.87379	+	3.53414i	0.266991	+	0.160643i
$485$	−25.0132	−	19.0145i	−1.13579	−	0.863406i
$486$	−1.39228	+	3.49436i	−0.0631551	+	0.158507i
$487$	−11.2027	+	13.1889i	−0.507645	+	0.597646i	−0.954961	−	0.296730i	$-0.904104\pi$
$487$	−11.2027	+	13.1889i	−0.507645	+	0.597646i	0.447317	+	0.894376i	$0.352380\pi$
$488$	−4.20856	+	25.6711i	−0.190512	+	1.16207i
$489$	2.40900	−	44.4313i	0.108939	−	2.00925i
$490$	12.2841	−	2.70394i	0.554941	−	0.122152i
$491$	−11.7240	−	11.1056i	−0.529098	−	0.501188i	0.375867	−	0.926673i	$-0.377345\pi$
$491$	−11.7240	−	11.1056i	−0.529098	−	0.501188i	−0.904965	+	0.425485i	$0.860103\pi$
$492$	15.6783	+	5.28265i	0.706834	+	0.238160i
$493$	5.40917	+	13.5760i	0.243617	+	0.611432i
$494$	1.17665	−	4.23792i	0.0529401	−	0.190673i
$495$	−79.1901	−	17.4311i	−3.55933	−	0.783468i
$496$	8.63184	+	12.7310i	0.387581	+	0.571639i
$497$	4.28973	−	8.09129i	0.192421	−	0.362944i
$498$	−5.02758	−	9.48302i	−0.225291	−	0.424944i
$499$	2.09302	−	3.08697i	0.0936963	−	0.138192i	−0.777952	−	0.628324i	$-0.783741\pi$
$499$	2.09302	−	3.08697i	0.0936963	−	0.138192i	0.871648	+	0.490132i	$0.163052\pi$
$500$	3.19375	−	3.02528i	0.142829	−	0.135294i
$501$	47.0732	−	21.7784i	2.10307	−	0.972986i
$502$	3.02922	−	1.40146i	0.135200	−	0.0625504i
$503$	−12.9800	+	12.2953i	−0.578750	+	0.548222i	−0.920084	−	0.391721i	$-0.871880\pi$
$503$	−12.9800	+	12.2953i	−0.578750	+	0.548222i	0.341334	+	0.939942i	$0.389121\pi$
$504$	−6.79002	+	10.0145i	−0.302451	+	0.446082i
$505$	14.1265	+	26.6454i	0.628620	+	1.18570i
$506$	−2.33833	+	4.41055i	−0.103951	+	0.196073i
$507$	−17.6089	−	25.9712i	−0.782039	−	1.15342i
$508$	12.7760	+	2.81221i	0.566842	+	0.124771i
$509$	−8.85505	+	31.8930i	−0.392493	+	1.41363i	0.458612	+	0.888637i	$0.348347\pi$
$509$	−8.85505	+	31.8930i	−0.392493	+	1.41363i	−0.851105	+	0.524996i	$0.824067\pi$
$510$	−7.65173	−	19.2044i	−0.338824	−	0.850384i
$511$	−10.0363	−	3.38162i	−0.443979	−	0.149594i
$512$	13.8109	+	13.0824i	0.610363	+	0.578167i
$513$	−43.1526	+	9.49861i	−1.90524	+	0.419374i
$514$	−0.198351	+	3.65836i	−0.00874887	+	0.161363i
$515$	−0.306807	+	1.87144i	−0.0135195	+	0.0824655i
$516$	9.36108	−	11.0207i	0.412099	−	0.485160i
$517$	−9.87704	+	24.7895i	−0.434392	+	1.09024i
$518$	0.521476	+	0.396416i	0.0229124	+	0.0174175i
$519$	49.6400	+	29.8674i	2.17895	+	1.31103i
$520$	1.94638	+	11.8724i	0.0853546	+	0.520640i
$521$	−17.5054	+	1.90383i	−0.766926	+	0.0834082i	−0.483215	−	0.875502i	$-0.660531\pi$
$521$	−17.5054	+	1.90383i	−0.766926	+	0.0834082i	−0.283711	+	0.958910i	$0.591566\pi$
$522$	13.3482	−	10.1470i	0.584236	−	0.444124i
$523$	−2.68104	−	9.65623i	−0.117234	−	0.422237i	0.881520	−	0.472146i	$-0.156521\pi$
$523$	−2.68104	−	9.65623i	−0.117234	−	0.422237i	−0.998754	+	0.0499091i	$0.984107\pi$
$524$	0.717324	+	13.2303i	0.0313365	+	0.577967i
$525$	15.2611	+	1.65975i	0.666049	+	0.0724372i
$526$	−4.03548	+	2.42807i	−0.175955	+	0.105869i
$527$	−17.6734	−	20.8067i	−0.769865	−	0.906355i
$528$	−21.4074	+	7.21301i	−0.931640	+	0.313906i
$529$	−16.8972	−	7.81746i	−0.734659	−	0.339889i
$530$	4.45064			0.193324
$531$	−44.7257	−	18.8530i	−1.94093	−	0.818151i
$532$	−6.12550			−0.265574
$533$	4.98942	+	2.30835i	0.216116	+	0.0999857i
$534$	−4.37678	+	1.47471i	−0.189402	+	0.0638169i
$535$	−9.97941	−	11.7487i	−0.431448	−	0.507939i
$536$	−8.09097	+	4.86817i	−0.349477	+	0.210273i
$537$	−54.4985	−	5.92707i	−2.35178	−	0.255772i
$538$	0.181237	+	3.34272i	0.00781369	+	0.144115i
$539$	6.52634	+	23.5057i	0.281109	+	1.01246i
$540$	43.1511	−	32.8026i	1.85693	−	1.41160i
$541$	−1.04324	+	0.113459i	−0.0448523	+	0.00487799i	−0.130518	−	0.991446i	$-0.541664\pi$
$541$	−1.04324	+	0.113459i	−0.0448523	+	0.00487799i	0.0856653	+	0.996324i	$0.472698\pi$
$542$	0.890742	+	5.43329i	0.0382607	+	0.233380i
$543$	62.1616	+	37.4014i	2.66761	+	1.60505i
$544$	−14.9940	−	11.3981i	−0.642862	−	0.488691i
$545$	5.55164	−	13.9336i	0.237806	−	0.596848i
$546$	−1.72144	+	2.02664i	−0.0736709	+	0.0867320i
$547$	−5.26270	+	32.1010i	−0.225017	+	1.37254i	0.596618	+	0.802526i	$0.296511\pi$
$547$	−5.26270	+	32.1010i	−0.225017	+	1.37254i	−0.821634	+	0.570015i	$0.806937\pi$
$548$	−0.714818	+	13.1840i	−0.0305355	+	0.563194i
$549$	72.4134	−	15.9394i	3.09053	−	0.680277i
$550$	−10.0802	−	9.54843i	−0.429819	−	0.407147i
$551$	17.9374	+	6.04382i	0.764159	+	0.257475i
$552$	−5.24377	−	13.1609i	−0.223190	−	0.560164i
$553$	2.41066	−	8.68242i	0.102512	−	0.369214i
$554$	−5.97158	−	1.31444i	−0.253708	−	0.0558453i
$555$	−6.99133	−	10.3114i	−0.296765	−	0.437696i
$556$	3.24789	−	6.12617i	0.137741	−	0.259808i
$557$	−9.43266	−	17.7919i	−0.399675	−	0.753866i	0.599234	−	0.800574i	$-0.295472\pi$
$557$	−9.43266	−	17.7919i	−0.399675	−	0.753866i	−0.998909	+	0.0467076i	$0.985127\pi$
$558$	−17.5775	+	25.9249i	−0.744114	+	1.09749i
$559$	3.48829	−	3.30428i	0.147539	−	0.139756i
$560$	4.89211	−	2.26333i	0.206729	−	0.0956432i
$561$	36.3881	−	16.8349i	1.53631	−	0.710771i
$562$	5.62708	−	5.33025i	0.237364	−	0.224843i
$563$	12.6330	−	18.6324i	0.532420	−	0.785260i	−0.462426	−	0.886658i	$-0.653021\pi$
$563$	12.6330	−	18.6324i	0.532420	−	0.785260i	0.994846	+	0.101398i	$0.0323314\pi$
$564$	−15.9080	−	30.0056i	−0.669846	−	1.26346i
$565$	−12.5673	+	23.7044i	−0.528708	+	0.997250i
$566$	10.6395	+	15.6921i	0.447212	+	0.659588i
$567$	10.0988	+	2.22290i	0.424108	+	0.0933532i
$568$	6.28881	−	22.6502i	0.263873	−	0.950383i
$569$	9.68713	+	24.3129i	0.406105	+	1.01925i	0.979765	+	0.200154i	$0.0641441\pi$
$569$	9.68713	+	24.3129i	0.406105	+	1.01925i	−0.573659	+	0.819094i	$0.694477\pi$
$570$	−25.3740	−	8.54949i	−1.06280	−	0.358099i
$571$	2.96218	+	2.80592i	0.123963	+	0.117424i	0.747170	−	0.664633i	$-0.231412\pi$
$571$	2.96218	+	2.80592i	0.123963	+	0.117424i	−0.623207	+	0.782057i	$0.714171\pi$
$572$	−10.2196	+	2.24949i	−0.427301	+	0.0940561i
$573$	−0.814894	+	15.0298i	−0.0340427	+	0.627880i
$574$	−0.284693	+	1.73655i	−0.0118828	+	0.0724821i
$575$	−7.89038	+	9.28927i	−0.329051	+	0.387389i
$576$	0.875716	−	2.19788i	0.0364882	−	0.0915784i
$577$	29.8122	+	22.6627i	1.24110	+	0.943460i	0.999637	−	0.0269505i	$-0.00857965\pi$
$577$	29.8122	+	22.6627i	1.24110	+	0.943460i	0.241463	+	0.970410i	$0.422373\pi$
$578$	−2.96648	−	1.78487i	−0.123389	−	0.0742408i
$579$	9.44270	+	57.5979i	0.392425	+	2.39369i
$580$	−23.0836	+	2.51049i	−0.958494	+	0.104243i
$581$	−3.95436	+	3.00603i	−0.164055	+	0.124711i
$582$	−4.76869	−	17.1753i	−0.197669	−	0.711938i
$583$	0.467319	+	8.61919i	0.0193544	+	0.356970i
$584$	−27.0249	−	2.93913i	−1.11830	−	0.121622i
$585$	29.3830	−	17.6792i	1.21484	−	0.730944i
$586$	2.00428	+	2.35962i	0.0827962	+	0.0974752i
$587$	−0.957172	+	0.322509i	−0.0395067	+	0.0133114i	−0.338986	−	0.940792i	$-0.610084\pi$
$587$	−0.957172	+	0.322509i	−0.0395067	+	0.0133114i	0.299479	+	0.954103i	$0.403187\pi$
$588$	−28.1779	−	13.0365i	−1.16204	−	0.537616i
$589$	−35.3590			−1.45694
$590$	−9.10411	−	12.4808i	−0.374810	−	0.513826i
$591$	−27.7914			−1.14318
$592$	−2.13591	−	0.988178i	−0.0877855	−	0.0406139i
$593$	0.117791	−	0.0396884i	0.00483710	−	0.00162981i	−0.316882	−	0.948465i	$-0.602636\pi$
$593$	0.117791	−	0.0396884i	0.00483710	−	0.00162981i	0.321719	+	0.946835i	$0.395739\pi$
$594$	−15.6419	−	18.4150i	−0.641794	−	0.755578i
$595$	−8.19752	+	4.93229i	−0.336066	+	0.202204i
$596$	14.9312	+	1.62387i	0.611607	+	0.0665163i
$597$	−1.56674	−	28.8968i	−0.0641223	−	1.18267i
$598$	−0.564798	−	2.03422i	−0.0230963	−	0.0831854i
$599$	28.1892	−	21.4289i	1.15178	−	0.875561i	0.158057	−	0.987430i	$-0.449477\pi$
$599$	28.1892	−	21.4289i	1.15178	−	0.875561i	0.993723	+	0.111869i	$0.0356838\pi$
$600$	39.1723	−	4.26025i	1.59920	−	0.173924i
$601$	−1.82016	−	11.1025i	−0.0742460	−	0.452880i	−0.997618	−	0.0689749i	$-0.978027\pi$
$601$	−1.82016	−	11.1025i	−0.0742460	−	0.452880i	0.923372	−	0.383905i	$-0.125421\pi$
$602$	1.31785	+	0.792924i	0.0537116	+	0.0323172i
$603$	21.4262	+	16.2878i	0.872543	+	0.663290i
$604$	−13.3823	+	33.5871i	−0.544519	+	1.36664i
$605$	8.97739	−	10.5690i	0.364983	−	0.429691i
$606$	−2.76798	+	16.8840i	−0.112442	+	0.685864i
$607$	1.95540	−	36.0652i	0.0793672	−	1.46384i	−0.639552	−	0.768748i	$-0.720880\pi$
$607$	1.95540	−	36.0652i	0.0793672	−	1.46384i	0.718919	−	0.695094i	$-0.244637\pi$
$608$	−23.8244	+	5.24415i	−0.966208	+	0.212679i
$609$	−8.30795	−	7.86971i	−0.336655	−	0.318897i
$610$	22.3643	+	7.53542i	0.905506	+	0.305100i
$611$	−4.17705	−	10.4836i	−0.168985	−	0.424121i
$612$	−9.25659	+	33.3392i	−0.374175	+	1.34766i
$613$	20.8802	+	4.59608i	0.843343	+	0.185634i	0.615572	−	0.788081i	$-0.288925\pi$
$613$	20.8802	+	4.59608i	0.843343	+	0.185634i	0.227771	+	0.973715i	$0.426856\pi$
$614$	1.66015	+	2.44853i	0.0669980	+	0.0988147i
$615$	15.6766	−	29.5692i	0.632142	−	1.19235i
$616$	−3.49851	−	6.59888i	−0.140959	−	0.265876i
$617$	22.4267	−	33.0769i	0.902863	−	1.33162i	−0.0402627	−	0.999189i	$-0.512819\pi$
$617$	22.4267	−	33.0769i	0.902863	−	1.33162i	0.943126	−	0.332435i	$-0.107870\pi$
$618$	−0.781076	+	0.739874i	−0.0314195	+	0.0297621i
$619$	5.22870	−	2.41905i	0.210159	−	0.0972300i	−0.311986	−	0.950087i	$-0.600994\pi$
$619$	5.22870	−	2.41905i	0.210159	−	0.0972300i	0.522145	+	0.852857i	$0.325132\pi$
$620$	39.3667	−	18.2130i	1.58101	−	0.731451i
$621$	−15.3978	+	14.5856i	−0.617894	+	0.585301i
$622$	−8.31608	+	12.2653i	−0.333445	+	0.491794i
$623$	1.00117	+	1.88841i	0.0401111	+	0.0756576i
$624$	4.47490	−	8.44055i	0.179139	−	0.337893i
$625$	11.3429	+	16.7296i	0.453718	+	0.669183i
$626$	20.2379	+	4.45470i	0.808870	+	0.178046i
$627$	13.8928	−	50.0373i	0.554825	−	1.99830i
$628$	−4.89892	−	12.2954i	−0.195488	−	0.490639i
$629$	3.95832	+	1.33371i	0.157829	+	0.0531786i
$630$	7.96894	+	7.54859i	0.317490	+	0.300743i
$631$	−17.7841	+	3.91458i	−0.707975	+	0.155837i	−0.554340	−	0.832291i	$-0.687029\pi$
$631$	−17.7841	+	3.91458i	−0.707975	+	0.155837i	−0.153635	+	0.988128i	$0.549098\pi$
$632$	1.25219	−	23.0952i	0.0498093	−	0.918679i
$633$	−13.7660	+	83.9687i	−0.547148	+	3.33746i
$634$	8.70948	−	10.2536i	0.345898	−	0.407222i
$635$	9.79510	−	24.5838i	0.388707	−	0.975580i
$636$	−8.74569	−	6.64830i	−0.346789	−	0.263622i
$637$	−8.83998	−	5.31884i	−0.350253	−	0.210740i
$638$	1.67450	+	10.2140i	0.0662939	+	0.404375i
$639$	−66.6094	+	7.24420i	−2.63503	+	0.286576i
$640$	29.8986	−	22.7283i	1.18184	−	0.898415i
$641$	−7.33079	−	26.4031i	−0.289549	−	1.04286i	−0.955045	−	0.296460i	$-0.904194\pi$
$641$	−7.33079	−	26.4031i	−0.289549	−	1.04286i	0.665496	−	0.746401i	$-0.268220\pi$
$642$	−0.473451	−	8.73228i	−0.0186856	−	0.344636i
$643$	32.4751	+	3.53188i	1.28069	+	0.139284i	0.723049	−	0.690797i	$-0.242740\pi$
$643$	32.4751	+	3.53188i	1.28069	+	0.139284i	0.557643	+	0.830081i	$0.311706\pi$
$644$	−2.51938	+	1.51586i	−0.0992776	+	0.0597334i
$645$	−18.9366	−	22.2939i	−0.745629	−	0.877822i
$646$	8.50742	−	2.86648i	0.334720	−	0.112780i
$647$	11.9292	+	5.51901i	0.468983	+	0.216975i	0.640124	−	0.768272i	$-0.278883\pi$
$647$	11.9292	+	5.51901i	0.468983	+	0.216975i	−0.171140	+	0.985247i	$0.554745\pi$
$648$	26.5421			1.04267
$649$	23.2146	−	18.9417i	0.911251	−	0.743525i
$650$	5.87187			0.230314
$651$	19.4014	+	8.97603i	0.760400	+	0.351798i
$652$	−22.4634	+	7.56880i	−0.879734	+	0.296417i
$653$	−18.4221	−	21.6882i	−0.720912	−	0.848723i	0.272638	−	0.962117i	$-0.412104\pi$
$653$	−18.4221	−	21.6882i	−0.720912	−	0.848723i	−0.993550	+	0.113394i	$0.963828\pi$
$654$	7.29104	−	4.38687i	0.285102	−	0.171540i
$655$	26.6458	+	2.89791i	1.04114	+	0.113231i
$656$	−0.342283	−	6.31304i	−0.0133639	−	0.246483i
$657$	20.7289	+	74.6588i	0.808712	+	2.91272i
$658$	2.87573	−	2.18608i	0.112108	−	0.0852221i
$659$	−2.36068	+	0.256739i	−0.0919590	+	0.0100011i	−0.153983	−	0.988074i	$-0.549210\pi$
$659$	−2.36068	+	0.256739i	−0.0919590	+	0.0100011i	0.0620238	+	0.998075i	$0.480245\pi$
$660$	10.3062	+	62.8648i	0.401166	+	2.44701i
$661$	−2.79652	−	1.68261i	−0.108772	−	0.0654461i	0.460128	−	0.887852i	$-0.347803\pi$
$661$	−2.79652	−	1.68261i	−0.108772	−	0.0654461i	−0.568900	+	0.822406i	$0.692631\pi$
$662$	0.926048	+	0.703963i	0.0359919	+	0.0273603i
$663$	−6.27600	+	15.7516i	−0.243740	+	0.611741i
$664$	−8.25410	+	9.71748i	−0.320321	+	0.377111i
$665$	−2.00469	+	12.2281i	−0.0777387	+	0.474185i
$666$	0.259456	−	4.78538i	0.0100537	−	0.185430i
$667$	8.87321	−	1.95314i	0.343572	−	0.0756259i
$668$	−20.0597	−	19.0015i	−0.776132	−	0.735192i
$669$	−8.37596	−	2.82219i	−0.323833	−	0.109112i
$670$	3.17073	+	7.95794i	0.122496	+	0.307442i
$671$	−12.2450	+	44.1024i	−0.472711	+	1.70255i
$672$	14.4036	+	3.17048i	0.555633	+	0.122304i
$673$	−1.19515	−	1.76272i	−0.0460698	−	0.0679479i	0.803957	−	0.594688i	$-0.202724\pi$
$673$	−1.19515	−	1.76272i	−0.0460698	−	0.0679479i	−0.850026	+	0.526740i	$0.823414\pi$
$674$	−6.19893	+	11.6924i	−0.238774	+	0.450376i
$675$	−27.6315	−	52.1185i	−1.06354	−	2.00604i
$676$	−9.38062	+	13.8354i	−0.360793	+	0.532130i
$677$	22.8644	−	21.6583i	0.878750	−	0.832396i	−0.108082	−	0.994142i	$-0.534471\pi$
$677$	22.8644	−	21.6583i	0.878750	−	0.832396i	0.986832	+	0.161746i	$0.0517124\pi$
$678$	−13.8141	+	6.39108i	−0.530527	+	0.245448i
$679$	−7.48671	+	3.46372i	−0.287313	+	0.132925i
$680$	−17.8280	+	16.8875i	−0.683671	+	0.647608i
$681$	−28.7895	+	42.4613i	−1.10322	+	1.62712i
$682$	−9.05667	−	17.0827i	−0.346798	−	0.654130i
$683$	−5.55731	+	10.4822i	−0.212644	+	0.401090i	−0.966773	−	0.255637i	$-0.917715\pi$
$683$	−5.55731	+	10.4822i	−0.212644	+	0.401090i	0.754128	+	0.656727i	$0.228060\pi$
$684$	25.1497	+	37.0930i	0.961622	+	1.41829i
$685$	26.0848	+	5.74171i	0.996650	+	0.219379i
$686$	1.87232	−	6.74348i	0.0714854	−	0.257467i
$687$	−18.3849	−	46.1425i	−0.701427	−	1.76045i
$688$	−5.23645	−	1.76437i	−0.199638	−	0.0672658i
$689$	−2.65021	−	2.51041i	−0.100965	−	0.0956391i
$690$	−12.5519	+	2.76288i	−0.477843	+	0.105181i
$691$	1.54514	−	28.4984i	0.0587799	−	1.08413i	−0.809200	−	0.587533i	$-0.800099\pi$
$691$	1.54514	−	28.4984i	0.0587799	−	1.08413i	0.867980	−	0.496599i	$-0.165418\pi$
$692$	4.99290	−	30.4553i	0.189802	−	1.15774i
$693$	−13.7820	+	16.2254i	−0.523534	+	0.616351i
$694$	−0.401707	+	1.00821i	−0.0152486	+	0.0382710i
$695$	−11.1665	−	8.48855i	−0.423569	−	0.321989i
$696$	−25.1688	−	15.1435i	−0.954019	−	0.574014i
$697$	1.81538	+	11.0733i	0.0687623	+	0.419431i
$698$	0.684889	−	0.0744862i	0.0259234	−	0.00281934i
$699$	14.8028	−	11.2528i	0.559892	−	0.425619i
$700$	−2.18781	−	7.87976i	−0.0826913	−	0.297827i
$701$	−0.137246	−	2.53135i	−0.00518371	−	0.0956079i	0.994797	−	0.101881i	$-0.0324860\pi$
$701$	−0.137246	−	2.53135i	−0.00518371	−	0.0956079i	−0.999980	+	0.00627291i	$0.998003\pi$
$702$	10.1582	+	1.10477i	0.383395	+	0.0416967i
$703$	4.63568	−	2.78920i	0.174838	−	0.105197i
$704$	0.945491	+	1.11312i	0.0356345	+	0.0419522i
$705$	−65.1052	+	21.9365i	−2.45200	+	0.826176i
$706$	−18.3580	−	8.49331i	−0.690912	−	0.319650i
$707$	7.91794			0.297785
$708$	−0.753666	+	38.1248i	−0.0283245	+	1.43282i
$709$	−8.23468			−0.309260			−0.154630	−	0.987972i	$-0.549419\pi$
$709$	−8.23468			−0.309260			−0.154630	+	0.987972i	$0.549419\pi$
$710$	−19.3546	−	8.95441i	−0.726367	−	0.336053i
$711$	−62.4740	+	21.0499i	−2.34296	+	0.789434i
$712$	3.55174	+	4.18143i	0.133107	+	0.156706i
$713$	−14.5430	+	8.75021i	−0.544638	+	0.327698i
$714$	−5.39566	−	0.586814i	−0.201928	−	0.0219609i
$715$	1.14602	+	21.1371i	0.0428587	+	0.790482i
$716$	7.81280	+	28.1392i	0.291978	+	1.05161i
$717$	10.9851	−	8.35063i	0.410245	−	0.311860i
$718$	−6.70036	+	0.728708i	−0.250055	+	0.0271951i
$719$	1.97588	+	12.0523i	0.0736878	+	0.449475i	0.997739	+	0.0672070i	$0.0214088\pi$
$719$	1.97588	+	12.0523i	0.0736878	+	0.449475i	−0.924051	+	0.382269i	$0.875143\pi$
$720$	−33.7913	−	20.3316i	−1.25933	−	0.757713i
$721$	0.396371	+	0.301313i	0.0147616	+	0.0112215i
$722$	0.00434307	−	0.0109003i	0.000161632	−	0.000405667i
$723$	55.6244	−	65.4861i	2.06869	−	2.43545i
$724$	6.25235	−	38.1376i	0.232367	−	1.41737i
$725$	−1.36810	+	25.2331i	−0.0508099	+	0.937133i
$726$	7.68310	−	1.69118i	0.285147	−	0.0627655i
$727$	−1.46664	−	1.38927i	−0.0543946	−	0.0515253i	0.660019	−	0.751249i	$-0.270548\pi$
$727$	−1.46664	−	1.38927i	−0.0543946	−	0.0515253i	−0.714414	+	0.699723i	$0.753307\pi$
$728$	2.99330	+	1.00856i	0.110939	+	0.0373797i
$729$	6.34227	+	15.9179i	0.234899	+	0.589551i
$730$	−6.59766	+	23.7626i	−0.244191	+	0.879495i
$731$	9.57799	+	2.10827i	0.354255	+	0.0779773i
$732$	−32.6905	−	48.2149i	−1.20828	−	1.78207i
$733$	21.4119	−	40.3871i	0.790866	−	1.49173i	−0.0781477	−	0.996942i	$-0.524901\pi$
$733$	21.4119	−	40.3871i	0.790866	−	1.49173i	0.869013	−	0.494789i	$-0.164755\pi$
$734$	0.658117	+	1.24134i	0.0242916	+	0.0458187i
$735$	−35.2461	+	51.9840i	−1.30007	+	1.91746i
$736$	−8.50110	+	8.05267i	−0.313355	+	0.296825i
$737$	−15.0785	+	6.97607i	−0.555425	+	0.256967i
$738$	11.6845	−	5.40585i	0.430114	−	0.198992i
$739$	15.8300	−	14.9950i	0.582316	−	0.551599i	−0.338814	−	0.940853i	$-0.610026\pi$
$739$	15.8300	−	14.9950i	0.582316	−	0.551599i	0.921130	+	0.389254i	$0.127267\pi$
$740$	−3.72443	+	5.49312i	−0.136913	+	0.201931i
$741$	10.2870	+	19.4033i	0.377901	+	0.712797i
$742$	0.547331	−	1.03238i	0.0200932	−	0.0378997i
$743$	−10.2596	−	15.1318i	−0.376389	−	0.555132i	0.591566	−	0.806257i	$-0.298510\pi$
$743$	−10.2596	−	15.1318i	−0.376389	−	0.555132i	−0.967955	+	0.251124i	$0.919200\pi$
$744$	53.5882	+	11.7957i	1.96464	+	0.432450i
$745$	8.12821	−	29.2752i	0.297795	−	1.07256i
$746$	−0.225537	−	0.566056i	−0.00825751	−	0.0207248i
$747$	34.4386	+	11.6037i	1.26004	+	0.424558i
$748$	−15.5064	−	14.6884i	−0.566968	−	0.537061i
$749$	−3.95248	+	0.870007i	−0.144421	+	0.0317894i
$750$	0.273323	−	5.04115i	0.00998034	−	0.184077i
$751$	−3.12564	+	19.0655i	−0.114056	+	0.695711i	0.866456	+	0.499253i	$0.166392\pi$
$751$	−3.12564	+	19.0655i	−0.114056	+	0.695711i	−0.980512	+	0.196458i	$0.937056\pi$
$752$	−8.40191	+	9.89150i	−0.306386	+	0.360706i
$753$	−6.16872	+	15.4823i	−0.224801	+	0.564207i
$754$	−3.48466	−	2.64897i	−0.126904	−	0.0964699i
$755$	62.6690	+	37.7067i	2.28076	+	1.37229i
$756$	−2.30229	−	14.0434i	−0.0837336	−	0.510753i
$757$	25.2047	−	2.74118i	0.916080	−	0.0996297i	0.362081	−	0.932147i	$-0.382066\pi$
$757$	25.2047	−	2.74118i	0.916080	−	0.0996297i	0.554000	+	0.832517i	$0.313101\pi$
$758$	9.92042	−	7.54130i	0.360326	−	0.273912i
$759$	−6.66859	−	24.0181i	−0.242055	−	0.871802i
$760$	1.72195	+	31.7595i	0.0624617	+	1.15204i
$761$	28.8725	+	3.14007i	1.04663	+	0.113827i	0.615240	−	0.788340i	$-0.289059\pi$
$761$	28.8725	+	3.14007i	1.04663	+	0.113827i	0.431386	+	0.902167i	$0.358025\pi$
$762$	12.8640	−	7.74003i	0.466015	−	0.280392i
$763$	−2.54931	−	3.00128i	−0.0922914	−	0.108654i
$764$	7.59872	−	2.56031i	0.274912	−	0.0926286i
$765$	63.5244	+	29.3895i	2.29673	+	1.06258i
$766$	15.8932			0.574246
$767$	−1.61867	+	12.5671i	−0.0584468	+	0.453773i
$768$	19.0205			0.686342
$769$	−23.7797	−	11.0016i	−0.857517	−	0.396730i	−0.0586798	−	0.998277i	$-0.518689\pi$
$769$	−23.7797	−	11.0016i	−0.857517	−	0.396730i	−0.798837	+	0.601547i	$0.794551\pi$
$770$	−6.42112	+	2.16353i	−0.231401	+	0.0779681i
$771$	−11.8433	−	13.9430i	−0.426525	−	0.502144i
$772$	26.6424	−	16.0302i	0.958882	−	0.576940i
$773$	−11.1976	−	1.21781i	−0.402748	−	0.0438015i	−0.0954964	−	0.995430i	$-0.530444\pi$
$773$	−11.1976	−	1.21781i	−0.402748	−	0.0438015i	−0.307252	+	0.951628i	$0.599409\pi$
$774$	−0.609187	−	11.2358i	−0.0218968	−	0.403862i
$775$	−12.6290	−	45.4854i	−0.453645	−	1.63388i
$776$	−16.8564	+	12.8139i	−0.605110	+	0.459993i
$777$	−3.25163	+	0.353636i	−0.116652	+	0.0126866i
$778$	−2.40750	−	14.6851i	−0.0863132	−	0.526487i
$779$	12.4534	+	7.49297i	0.446190	+	0.268464i
$780$	−21.4473	−	16.3038i	−0.767938	−	0.583771i
$781$	15.3090	−	38.4227i	0.547799	−	1.37487i
$782$	2.78969	−	3.28428i	0.0997592	−	0.117446i
$783$	−7.11426	+	43.3951i	−0.254243	+	1.55081i
$784$	−0.642334	+	11.8472i	−0.0229405	+	0.423113i
$785$	−26.1480	+	5.75562i	−0.933263	+	0.205427i
$786$	11.0393	+	10.4569i	0.393758	+	0.372987i
$787$	2.53734	+	0.854929i	0.0904463	+	0.0304749i	0.364161	−	0.931336i	$-0.381356\pi$
$787$	2.53734	+	0.854929i	0.0904463	+	0.0304749i	−0.273715	+	0.961811i	$0.588252\pi$
$788$	5.47991	+	13.7535i	0.195214	+	0.489949i
$789$	6.29130	−	22.6592i	0.223976	−	0.806690i
$790$	−20.4922	−	4.51068i	−0.729081	−	0.160483i
$791$	3.95299	+	5.83023i	0.140552	+	0.207299i
$792$	−25.5956	+	48.2785i	−0.909501	+	1.71550i
$793$	−9.06682	−	17.1018i	−0.321972	−	0.607304i
$794$	4.50704	−	6.64738i	0.159949	−	0.235907i
$795$	−16.1339	+	15.2829i	−0.572212	+	0.542028i
$796$	−13.9917	+	6.47323i	−0.495921	+	0.229437i
$797$	−44.8844	+	20.7658i	−1.58989	+	0.735561i	−0.997539	−	0.0701197i	$-0.977662\pi$
$797$	−44.8844	+	20.7658i	−1.58989	+	0.735561i	−0.592350	+	0.805681i	$0.701800\pi$
$798$	−5.10359	+	4.83437i	−0.180665	+	0.171135i
$799$	12.9266	−	19.0653i	0.457309	−	0.674480i
$800$	−15.2552	−	28.7744i	−0.539354	−	1.01733i
$801$	7.32474	−	13.8159i	0.258807	−	0.488162i
$802$	−7.13338	−	10.5209i	−0.251888	−	0.371507i
$803$	−46.7119	−	10.2821i	−1.64843	−	0.362846i
$804$	5.65683	−	20.3741i	0.199501	−	0.718537i
$805$	2.20154	+	5.52544i	0.0775940	+	0.194746i
$806$	7.74883	+	2.61089i	0.272941	+	0.0919645i
$807$	−12.1354	−	11.4953i	−0.427188	−	0.404654i
$808$	19.8487	−	4.36902i	0.698274	−	0.153702i
$809$	−2.76044	+	50.9133i	−0.0970518	+	1.79001i	0.394228	+	0.919013i	$0.371012\pi$
$809$	−2.76044	+	50.9133i	−0.0970518	+	1.79001i	−0.491279	+	0.871002i	$0.663471\pi$
$810$	3.89555	−	23.7618i	0.136876	−	0.834906i
$811$	19.6189	−	23.0971i	0.688911	−	0.811049i	−0.300867	−	0.953666i	$-0.597276\pi$
$811$	19.6189	−	23.0971i	0.688911	−	0.811049i	0.989778	+	0.142617i	$0.0455517\pi$
$812$	−2.25644	+	5.66323i	−0.0791854	+	0.198740i
$813$	−21.8862	−	16.6374i	−0.767581	−	0.583500i
$814$	2.53488	+	1.52519i	0.0888475	+	0.0534577i
$815$	7.75769	+	47.3198i	0.271740	+	1.65754i
$816$	19.3854	−	2.10829i	0.678625	−	0.0738049i
$817$	10.1124	−	7.68727i	0.353789	−	0.268944i
$818$	5.84016	+	21.0344i	0.204197	+	0.735450i
$819$	−0.487416	−	8.98987i	−0.0170317	−	0.314131i
$820$	−17.7245	−	1.92765i	−0.618965	−	0.0673165i
$821$	28.1561	−	16.9410i	0.982656	−	0.591244i	0.0689495	−	0.997620i	$-0.478035\pi$
$821$	28.1561	−	16.9410i	0.982656	−	0.591244i	0.913706	+	0.406376i	$0.133208\pi$
$822$	9.80956	+	11.5487i	0.342148	+	0.402808i
$823$	−0.0856482	+	0.0288582i	−0.00298551	+	0.00100593i	−0.320794	−	0.947149i	$-0.603950\pi$
$823$	−0.0856482	+	0.0288582i	−0.00298551	+	0.00100593i	0.317808	+	0.948155i	$0.397053\pi$
$824$	1.15988	+	0.536619i	0.0404064	+	0.0186940i
$825$	69.3294			2.41374
$826$	−4.01466	+	0.576937i	−0.139688	+	0.0200742i
$827$	22.6616			0.788021			0.394011	−	0.919106i	$-0.371087\pi$
$827$	22.6616			0.788021			0.394011	+	0.919106i	$0.371087\pi$
$828$	19.5232	+	9.03241i	0.678480	+	0.313898i
$829$	2.20038	−	0.741395i	0.0764225	−	0.0257497i	−0.280831	−	0.959757i	$-0.590610\pi$
$829$	2.20038	−	0.741395i	0.0764225	−	0.0257497i	0.357253	+	0.934008i	$0.383713\pi$
$830$	7.48813	+	8.81571i	0.259917	+	0.305998i
$831$	26.1611	−	15.7406i	0.907517	−	0.546035i
$832$	−0.614021	−	0.0667788i	−0.0212874	−	0.00231514i
$833$	−1.14004	−	21.0269i	−0.0395002	−	0.728538i
$834$	−2.12886	−	7.66746i	−0.0737164	−	0.265502i
$835$	−44.4970	+	33.8257i	−1.53988	+	1.17059i
$836$	−27.5021	+	2.99103i	−0.951180	+	0.103447i
$837$	−13.2898	−	81.0644i	−0.459364	−	2.80200i
$838$	−14.3642	−	8.64268i	−0.496205	−	0.298556i
$839$	−3.25521	−	2.47454i	−0.112382	−	0.0854308i	0.547474	−	0.836823i	$-0.315590\pi$
$839$	−3.25521	−	2.47454i	−0.112382	−	0.0854308i	−0.659856	+	0.751392i	$0.729383\pi$
$840$	7.11746	−	17.8635i	0.245576	−	0.616348i
$841$	−6.57892	+	7.74531i	−0.226859	+	0.267080i
$842$	−0.475742	+	2.90190i	−0.0163951	+	0.100006i
$843$	−2.09528	+	38.6452i	−0.0721653	+	1.33101i
$844$	44.2692	−	9.74439i	1.52381	−	0.335416i
$845$	24.5490	+	23.2541i	0.844512	+	0.799965i
$846$	−25.0448	−	8.43858i	−0.861058	−	0.290124i
$847$	−1.34758	−	3.38216i	−0.0463032	−	0.116212i
$848$	−1.12312	+	4.04510i	−0.0385680	+	0.138909i
$849$	−92.4535	−	20.3506i	−3.17300	−	0.698429i
$850$	6.72595	+	9.92003i	0.230698	+	0.340254i
$851$	1.21639	−	2.29436i	0.0416974	−	0.0786497i
$852$	24.6567	+	46.5074i	0.844724	+	1.59332i
$853$	−14.4324	+	21.2861i	−0.494155	+	0.728824i	−0.990228	−	0.139457i	$-0.955464\pi$
$853$	−14.4324	+	21.2861i	−0.494155	+	0.728824i	0.496073	+	0.868281i	$0.334775\pi$
$854$	4.49825	−	4.26097i	0.153927	−	0.145807i
$855$	82.2780	−	38.0659i	2.81385	−	1.30183i
$856$	−9.42801	+	4.36186i	−0.322243	+	0.149085i
$857$	−9.45774	+	8.95885i	−0.323070	+	0.306028i	−0.831996	−	0.554782i	$-0.812802\pi$
$857$	−9.45774	+	8.95885i	−0.323070	+	0.306028i	0.508925	+	0.860811i	$0.330043\pi$
$858$	−6.73929	+	9.93971i	−0.230076	+	0.339336i
$859$	15.8610	+	29.9171i	0.541171	+	1.02076i	0.991770	+	0.128031i	$0.0408656\pi$
$859$	15.8610	+	29.9171i	0.541171	+	1.02076i	−0.450599	+	0.892726i	$0.648790\pi$
$860$	−7.29900	+	13.7674i	−0.248894	+	0.469463i
$861$	−4.93103	−	7.27272i	−0.168049	−	0.247854i
$862$	−1.04253	−	0.229478i	−0.0355087	−	0.00781606i
$863$	−9.41164	+	33.8977i	−0.320376	+	1.15389i	0.611540	+	0.791214i	$0.290551\pi$
$863$	−9.41164	+	33.8977i	−0.320376	+	1.15389i	−0.931915	+	0.362676i	$0.881863\pi$
$864$	−20.9773	−	52.6491i	−0.713663	−	1.79116i
$865$	−59.1628	−	19.9343i	−2.01159	−	0.677785i
$866$	−9.86432	−	9.34398i	−0.335203	−	0.317521i
$867$	16.8827	−	3.71616i	0.573367	−	0.126208i
$868$	0.616536	−	11.3713i	0.0209266	−	0.385969i
$869$	6.58377	−	40.1592i	0.223339	−	1.36231i
$870$	−17.2513	+	20.3097i	−0.584872	+	0.688565i
$871$	2.60066	−	6.52716i	0.0881199	−	0.221164i
$872$	−8.04669	−	6.11693i	−0.272495	−	0.207146i
$873$	51.7130	+	31.1147i	1.75022	+	1.05307i
$874$	−0.902956	−	5.50779i	−0.0305429	−	0.186304i
$875$	−2.32269	+	0.252608i	−0.0785214	+	0.00853972i
$876$	48.4609	−	36.8390i	1.63734	−	1.24468i
$877$	9.63720	+	34.7101i	0.325425	+	1.17208i	0.927558	+	0.373679i	$0.121904\pi$
$877$	9.63720	+	34.7101i	0.325425	+	1.17208i	−0.602133	+	0.798396i	$0.705682\pi$
$878$	−0.431493	−	7.95843i	−0.0145622	−	0.268584i
$879$	−15.3683	−	1.67140i	−0.518360	−	0.0563751i
$880$	20.8593	−	12.5506i	0.703167	−	0.423081i
$881$	−13.4962	−	15.8889i	−0.454698	−	0.535312i	0.486270	−	0.873809i	$-0.338357\pi$
$881$	−13.4962	−	15.8889i	−0.454698	−	0.535312i	−0.940967	+	0.338497i	$0.890081\pi$
$882$	−22.8957	+	7.71447i	−0.770939	+	0.259760i
$883$	−1.53759	−	0.711363i	−0.0517439	−	0.0239393i	0.393847	−	0.919176i	$-0.371144\pi$
$883$	−1.53759	−	0.711363i	−0.0517439	−	0.0239393i	−0.445590	+	0.895237i	$0.647006\pi$
$884$	9.03272			0.303803
$885$	75.8605	+	13.9816i	2.55002	+	0.469988i
$886$	−25.3389			−0.851278
$887$	33.4483	+	15.4748i	1.12308	+	0.519594i	0.891409	−	0.453199i	$-0.149717\pi$
$887$	33.4483	+	15.4748i	1.12308	+	0.519594i	0.231675	+	0.972793i	$0.425579\pi$
$888$	−7.95605	+	2.68071i	−0.266988	+	0.0899586i
$889$	−4.49791	−	5.29535i	−0.150855	−	0.177600i
$890$	4.26471	−	2.56599i	0.142953	−	0.0860122i
$891$	46.4266	+	5.04919i	1.55535	+	0.169154i
$892$	0.254914	+	4.70162i	0.00853516	+	0.157422i
$893$	−7.98158	−	28.7470i	−0.267093	−	0.961983i
$894$	13.7219	−	10.4311i	0.458928	−	0.348868i
$895$	58.7300	−	6.38727i	1.96313	−	0.213503i
$896$	−1.59522	−	9.73038i	−0.0532924	−	0.325069i
$897$	9.03266	+	5.43477i	0.301592	+	0.181462i
$898$	−3.28166	−	2.49465i	−0.109510	−	0.0832475i
$899$	−13.0251	+	32.6906i	−0.434412	+	1.09029i
$900$	−38.7334	+	45.6005i	−1.29111	+	1.52002i
$901$	1.20544	−	7.35287i	0.0401591	−	0.244960i
$902$	−0.430262	+	7.93572i	−0.0143262	+	0.264231i
$903$	−7.50011	+	1.65090i	−0.249588	+	0.0549385i
$904$	13.1264	+	12.4340i	0.436578	+	0.413548i
$905$	−74.0865	−	24.9626i	−2.46272	−	0.829786i
$906$	15.3579	+	38.5454i	0.510232	+	1.28059i
$907$	3.16656	−	11.4049i	0.105144	−	0.378694i	−0.892191	−	0.451659i	$-0.850832\pi$
$907$	3.16656	−	11.4049i	0.105144	−	0.378694i	0.997334	+	0.0729651i	$0.0232462\pi$
$908$	26.6902	+	5.87495i	0.885745	+	0.194967i
$909$	−32.5090	−	47.9471i	−1.07825	−	1.59031i
$910$	1.34224	−	2.53173i	0.0444947	−	0.0839259i
$911$	−21.2453	−	40.0729i	−0.703888	−	1.32767i	−0.934966	−	0.354738i	$-0.884570\pi$
$911$	−21.2453	−	40.0729i	−0.703888	−	1.32767i	0.231078	−	0.972935i	$-0.425775\pi$
$912$	14.1736	−	20.9044i	0.469334	−	0.692215i
$913$	−16.2864	+	15.4273i	−0.539001	+	0.510569i
$914$	17.0559	−	7.89090i	0.564159	−	0.261008i
$915$	−106.948	+	49.4795i	−3.53560	+	1.63574i
$916$	−19.2101	+	18.1968i	−0.634720	+	0.601239i
$917$	3.94905	−	5.82441i	0.130409	−	0.192339i
$918$	9.76928	+	18.4268i	0.322434	+	0.608176i
$919$	−27.1248	+	51.1628i	−0.894764	+	1.68770i	−0.185643	+	0.982617i	$0.559437\pi$
$919$	−27.1248	+	51.1628i	−0.894764	+	1.68770i	−0.709121	+	0.705086i	$0.750908\pi$
$920$	8.56768	+	12.6364i	0.282468	+	0.416609i
$921$	−14.4261	−	3.17542i	−0.475356	−	0.104634i
$922$	−5.36550	+	19.3248i	−0.176703	+	0.636428i
$923$	6.47426	+	16.2492i	0.213103	+	0.534848i
$924$	15.8496	+	5.34035i	0.521414	+	0.175685i
$925$	5.24368	+	4.96708i	0.172411	+	0.163317i
$926$	−0.0386691	+	0.00851171i	−0.00127075	+	0.000279712i
$927$	0.197211	−	3.63734i	0.00647725	−	0.119466i
$928$	−3.92776	+	23.9583i	−0.128935	+	0.786469i
$929$	3.14956	−	3.70795i	0.103334	−	0.121654i	−0.708064	−	0.706148i	$-0.750431\pi$
$929$	3.14956	−	3.70795i	0.103334	−	0.121654i	0.811398	+	0.584494i	$0.198707\pi$
$930$	18.4251	−	46.2436i	0.604184	−	1.51639i
$931$	−21.7130	−	16.5058i	−0.711614	−	0.540955i
$932$	−8.48764	−	5.10685i	−0.278022	−	0.167280i
$933$	−11.9709	−	73.0190i	−0.391908	−	2.39054i
$934$	15.8563	−	1.72448i	0.518836	−	0.0564268i
$935$	−34.3966	+	26.1476i	−1.12489	+	0.855119i
$936$	−6.18235	−	22.2668i	−0.202077	−	0.727814i
$937$	−1.98456	−	36.6030i	−0.0648326	−	1.19577i	−0.832169	−	0.554522i	$-0.812901\pi$
$937$	−1.98456	−	36.6030i	−0.0648326	−	1.19577i	0.767336	−	0.641245i	$-0.221582\pi$
$938$	2.23586	+	0.243165i	0.0730035	+	0.00793961i
$939$	−88.6609	+	53.3455i	−2.89334	+	1.74086i
$940$	23.6935	+	27.8941i	0.772797	+	0.909806i
$941$	35.8735	−	12.0872i	1.16944	−	0.394031i	0.333448	−	0.942769i	$-0.391788\pi$
$941$	35.8735	−	12.0872i	1.16944	−	0.394031i	0.835995	+	0.548737i	$0.184891\pi$
$942$	−13.7854	−	6.37781i	−0.449153	−	0.207800i
$943$	6.97629			0.227179
$944$	13.6410	−	5.12503i	0.443975	−	0.166805i
$945$	−28.7877			−0.936464
$946$	6.30403	+	2.91655i	0.204962	+	0.0948254i
$947$	−29.5903	+	9.97014i	−0.961556	+	0.323986i	−0.755936	−	0.654646i	$-0.772818\pi$
$947$	−29.5903	+	9.97014i	−0.961556	+	0.323986i	−0.205620	+	0.978632i	$0.565921\pi$
$948$	33.5301	+	39.4747i	1.08901	+	1.28208i
$949$	17.3322	−	10.4284i	0.562626	−	0.338521i
$950$	15.4325	+	1.67838i	0.500696	+	0.0544540i
$951$	3.63682	+	67.0773i	0.117932	+	2.17513i
$952$	1.72481	+	6.21219i	0.0559013	+	0.201338i
$953$	15.7000	−	11.9349i	0.508574	−	0.386608i	−0.319184	−	0.947693i	$-0.603409\pi$
$953$	15.7000	−	11.9349i	0.508574	−	0.386608i	0.827758	+	0.561085i	$0.189616\pi$
$954$	−8.49876	+	0.924296i	−0.275157	+	0.0299252i
$955$	−2.62420	−	16.0069i	−0.0849172	−	0.517972i
$956$	−6.29864	−	3.78976i	−0.203712	−	0.122570i
$957$	−41.1435	−	31.2765i	−1.32998	−	1.01103i
$958$	−0.683847	+	1.71633i	−0.0220941	+	0.0554520i
$959$	4.53971	−	5.34456i	0.146595	−	0.172585i
$960$	−0.608313	+	3.71055i	−0.0196332	+	0.119757i
$961$	1.88061	−	34.6858i	0.0606648	−	1.11890i
$962$	−1.22185	+	0.268949i	−0.0393940	+	0.00867127i
$963$	21.4962	+	20.3623i	0.692705	+	0.656165i
$964$	−43.3761	−	14.6151i	−1.39705	−	0.470721i
$965$	−23.2812	−	58.4314i	−0.749449	−	1.88097i
$966$	−0.902726	+	3.25133i	−0.0290447	+	0.104610i
$967$	21.6134	+	4.75746i	0.695039	+	0.152990i	0.548420	−	0.836203i	$-0.315230\pi$
$967$	21.6134	+	4.75746i	0.695039	+	0.152990i	0.146620	+	0.989193i	$0.453161\pi$
$968$	−5.24434	−	7.73482i	−0.168559	−	0.248606i
$969$	−20.9970	+	39.6045i	−0.674520	+	1.27228i
$970$	8.99767	+	16.9714i	0.288898	+	0.544919i
$971$	−2.95958	+	4.36506i	−0.0949775	+	0.140081i	−0.872209	−	0.489133i	$-0.837313\pi$
$971$	−2.95958	+	4.36506i	−0.0949775	+	0.140081i	0.777231	+	0.629215i	$0.216623\pi$
$972$	−7.26407	+	6.88090i	−0.232995	+	0.220705i
$973$	−3.34225	+	1.54629i	−0.107148	+	0.0495717i
$974$	9.60159	−	4.44217i	0.307655	−	0.142336i
$975$	−21.2860	+	20.1632i	−0.681698	+	0.645739i
$976$	−12.4924	+	18.4250i	−0.399873	+	0.589768i
$977$	2.72270	+	5.13555i	0.0871068	+	0.164301i	0.923238	−	0.384229i	$-0.125533\pi$
$977$	2.72270	+	5.13555i	0.0871068	+	0.164301i	−0.836131	+	0.548530i	$0.815188\pi$
$978$	−12.7424	+	24.0347i	−0.407457	+	0.768545i
$979$	5.41714	+	7.98968i	0.173132	+	0.255351i
$980$	32.6759	+	7.19252i	1.04379	+	0.229757i
$981$	−7.70749	+	27.7599i	−0.246081	+	0.886305i
$982$	3.65432	+	9.17165i	0.116614	+	0.292679i
$983$	46.3529	+	15.6181i	1.47843	+	0.498140i	0.939007	−	0.343898i	$-0.111747\pi$
$983$	46.3529	+	15.6181i	1.47843	+	0.498140i	0.539419	+	0.842037i	$0.318644\pi$
$984$	−16.3741	−	15.5104i	−0.521987	−	0.494452i
$985$	29.2491	−	6.43820i	0.931952	−	0.205138i
$986$	0.483700	−	8.92132i	0.0154041	−	0.284113i
$987$	−2.91809	+	17.7996i	−0.0928839	+	0.566567i
$988$	7.57401	−	8.91681i	0.240961	−	0.283682i
$989$	2.25684	−	5.66423i	0.0717632	−	0.180112i
$990$	39.4647	+	30.0003i	1.25427	+	0.953471i
$991$	8.32741	+	5.01044i	0.264529	+	0.159162i	0.641639	−	0.767007i	$-0.278255\pi$
$991$	8.32741	+	5.01044i	0.264529	+	0.159162i	−0.377110	+	0.926168i	$0.623082\pi$
$992$	−7.33728	−	44.7554i	−0.232959	−	1.42099i
$993$	−5.77431	+	0.627994i	−0.183242	+	0.0199288i
$994$	−4.45727	+	3.38833i	−0.141376	+	0.107471i
$995$	8.34320	+	30.0495i	0.264497	+	0.952633i
$996$	−1.54571	−	28.5089i	−0.0489776	−	0.903338i
$997$	−2.19246	−	0.238444i	−0.0694359	−	0.00755161i	0.0733351	−	0.997307i	$-0.476636\pi$
$997$	−2.19246	−	0.238444i	−0.0694359	−	0.00755161i	−0.142771	+	0.989756i	$0.545601\pi$
$998$	−1.95377	+	1.17554i	−0.0618455	+	0.0372112i
$999$	8.13688	+	9.57948i	0.257440	+	0.303081i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	59.2.c.a.20.3	yes	112
3.2	odd	2		531.2.i.a.433.2		112
4.3	odd	2		944.2.m.c.433.1		112
59.3	even	29	inner	59.2.c.a.3.3	✓	112
59.11	odd	58		3481.2.a.q.1.30		56
59.48	even	29		3481.2.a.p.1.27		56
177.62	odd	58		531.2.i.a.298.2		112
236.3	odd	58		944.2.m.c.593.1		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
59.2.c.a.3.3	✓	112	59.3	even	29	inner
59.2.c.a.20.3	yes	112	1.1	even	1	trivial
531.2.i.a.298.2		112	177.62	odd	58
531.2.i.a.433.2		112	3.2	odd	2
944.2.m.c.433.1		112	4.3	odd	2
944.2.m.c.593.1		112	236.3	odd	58
3481.2.a.p.1.27		56	59.48	even	29
3481.2.a.q.1.30		56	59.11	odd	58

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:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	59.c (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.554859 - 0.256705i) q^{2} +(2.89290 - 0.974731i) q^{3} +(-1.05280 - 1.23945i) q^{4} +(-2.81882 + 1.69603i) q^{5} +(-1.85537 - 0.201783i) q^{6} +(0.0467597 + 0.862432i) q^{7} +(0.593097 + 2.13614i) q^{8} +(5.03048 - 3.82407i) q^{9} +O(q^{10})\)	\(q+(-0.554859 - 0.256705i) q^{2} +(2.89290 - 0.974731i) q^{3} +(-1.05280 - 1.23945i) q^{4} +(-2.81882 + 1.69603i) q^{5} +(-1.85537 - 0.201783i) q^{6} +(0.0467597 + 0.862432i) q^{7} +(0.593097 + 2.13614i) q^{8} +(5.03048 - 3.82407i) q^{9} +(1.99943 - 0.217451i) q^{10} +(0.631059 + 3.84929i) q^{11} +(-4.25378 - 2.55942i) q^{12} +(-1.31325 - 0.998305i) q^{13} +(0.195446 - 0.490531i) q^{14} +(-6.50140 + 7.65404i) q^{15} +(-0.306918 + 1.87211i) q^{16} +(0.182290 - 3.36214i) q^{17} +(-3.77286 + 0.830470i) q^{18} +(-3.16614 - 2.99913i) q^{19} +(5.06981 + 1.70822i) q^{20} +(0.975910 + 2.44935i) q^{21} +(0.637984 - 2.29781i) q^{22} +(-2.04440 - 0.450007i) q^{23} +(3.79793 + 5.60153i) q^{24} +(2.72721 - 5.14406i) q^{25} +(0.472397 + 0.891036i) q^{26} +(5.68582 - 8.38596i) q^{27} +(1.01972 - 0.965926i) q^{28} +(-3.93910 + 1.82242i) q^{29} +(5.57219 - 2.57797i) q^{30} +(5.88624 - 5.57574i) q^{31} +(3.13912 - 4.62986i) q^{32} +(5.57761 + 10.5205i) q^{33} +(-0.964222 + 1.81872i) q^{34} +(-1.59452 - 2.35174i) q^{35} +(-10.0359 - 2.20906i) q^{36} +(-0.331878 + 1.19532i) q^{37} +(0.986869 + 2.47686i) q^{38} +(-4.77217 - 1.60793i) q^{39} +(-5.29479 - 5.01550i) q^{40} +(-3.25469 + 0.716412i) q^{41} +(0.0872680 - 1.60956i) q^{42} +(-0.471222 + 2.87433i) q^{43} +(4.10664 - 4.83471i) q^{44} +(-7.69430 + 19.3112i) q^{45} +(1.01884 + 0.774499i) q^{46} +(5.86181 + 3.52693i) q^{47} +(0.936927 + 5.71500i) q^{48} +(6.21736 - 0.676179i) q^{49} +(-2.83372 + 2.15414i) q^{50} +(-2.74983 - 9.90400i) q^{51} +(0.145236 + 2.67873i) q^{52} +(2.19994 + 0.239258i) q^{53} +(-5.30754 + 3.19344i) q^{54} +(-8.30736 - 9.78018i) q^{55} +(-1.81454 + 0.611391i) q^{56} +(-12.0827 - 5.59003i) q^{57} +2.65347 q^{58} +(-3.82919 - 6.65863i) q^{59} +16.3315 q^{60} +(10.6495 + 4.92699i) q^{61} +(-4.69735 + 1.58272i) q^{62} +(3.53322 + 4.15963i) q^{63} +(0.320821 - 0.193031i) q^{64} +(5.39497 + 0.586739i) q^{65} +(-0.394124 - 7.26919i) q^{66} +(1.13948 + 4.10403i) q^{67} +(-4.35913 + 3.31372i) q^{68} +(-6.35288 + 0.690918i) q^{69} +(0.281029 + 1.71420i) q^{70} +(-9.08556 - 5.46660i) q^{71} +(11.1523 + 8.47777i) q^{72} +(-4.53863 + 11.3911i) q^{73} +(0.490989 - 0.578038i) q^{74} +(2.87546 - 17.5395i) q^{75} +(-0.383962 + 7.08177i) q^{76} +(-3.29024 + 0.724237i) q^{77} +(2.23512 + 2.11722i) q^{78} +(-9.88675 - 3.33123i) q^{79} +(-2.31002 - 5.79770i) q^{80} +(3.20295 - 11.5360i) q^{81} +(1.98980 + 0.437988i) q^{82} +(3.22744 + 4.76012i) q^{83} +(2.00842 - 3.78827i) q^{84} +(5.18844 + 9.78644i) q^{85} +(0.999317 - 1.47388i) q^{86} +(-9.61904 + 9.11164i) q^{87} +(-7.84835 + 3.63103i) q^{88} +(2.24597 - 1.03910i) q^{89} +(9.22654 - 8.73984i) q^{90} +(0.799563 - 1.17927i) q^{91} +(1.59459 + 3.00771i) q^{92} +(11.5934 - 21.8676i) q^{93} +(-2.34709 - 3.46170i) q^{94} +(14.0114 + 3.08414i) q^{95} +(4.56829 - 16.4535i) q^{96} +(3.53517 + 8.87260i) q^{97} +(-3.62334 - 1.22084i) q^{98} +(17.8945 + 16.9506i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 26 q^{2} - 23 q^{3} - 30 q^{4} - 25 q^{5} - 13 q^{6} - 23 q^{7} - 8 q^{8} - 21 q^{9}+O(q^{10}) \) 112 * q - 26 * q^2 - 23 * q^3 - 30 * q^4 - 25 * q^5 - 13 * q^6 - 23 * q^7 - 8 * q^8 - 21 * q^9	\( 112 q - 26 q^{2} - 23 q^{3} - 30 q^{4} - 25 q^{5} - 13 q^{6} - 23 q^{7} - 8 q^{8} - 21 q^{9} - 3 q^{10} - 15 q^{11} + 21 q^{12} - 23 q^{13} + 13 q^{14} + 4 q^{15} - 8 q^{16} - 10 q^{17} + 12 q^{18} - 15 q^{19} + 7 q^{20} - 12 q^{21} - q^{22} + 3 q^{23} + 25 q^{24} - 5 q^{25} + 5 q^{26} + 22 q^{27} + 29 q^{28} - 13 q^{29} + 29 q^{30} + 3 q^{31} + 36 q^{32} + 33 q^{33} + 27 q^{34} + 28 q^{35} + 20 q^{36} - 9 q^{37} + 31 q^{38} + 45 q^{39} + 79 q^{40} + 23 q^{41} + 33 q^{42} + 19 q^{43} + 43 q^{44} + 19 q^{45} - 31 q^{46} + 10 q^{47} - 25 q^{48} - 31 q^{49} - 60 q^{50} - 61 q^{51} - 75 q^{52} - 23 q^{53} - 86 q^{54} - 24 q^{55} - 103 q^{56} - 91 q^{57} + 12 q^{58} - 33 q^{59} - 210 q^{60} - 47 q^{61} - 39 q^{62} - 58 q^{63} - 152 q^{64} - 16 q^{65} - 116 q^{66} - 19 q^{67} - 5 q^{68} - 45 q^{69} + 23 q^{70} - 18 q^{71} - 36 q^{72} + 24 q^{73} + 19 q^{74} + 58 q^{75} + 97 q^{76} + 65 q^{77} + 119 q^{78} + 41 q^{79} + 107 q^{80} + 95 q^{81} + 145 q^{82} + 49 q^{83} + 167 q^{84} + 39 q^{85} + 111 q^{86} + 80 q^{87} + 175 q^{88} + 51 q^{89} + 213 q^{90} + 77 q^{91} + 135 q^{92} + 93 q^{93} + 151 q^{94} + 65 q^{95} + 181 q^{96} + 91 q^{97} + 31 q^{98} + 44 q^{99}+O(q^{100}) \) 112 * q - 26 * q^2 - 23 * q^3 - 30 * q^4 - 25 * q^5 - 13 * q^6 - 23 * q^7 - 8 * q^8 - 21 * q^9 - 3 * q^10 - 15 * q^11 + 21 * q^12 - 23 * q^13 + 13 * q^14 + 4 * q^15 - 8 * q^16 - 10 * q^17 + 12 * q^18 - 15 * q^19 + 7 * q^20 - 12 * q^21 - q^22 + 3 * q^23 + 25 * q^24 - 5 * q^25 + 5 * q^26 + 22 * q^27 + 29 * q^28 - 13 * q^29 + 29 * q^30 + 3 * q^31 + 36 * q^32 + 33 * q^33 + 27 * q^34 + 28 * q^35 + 20 * q^36 - 9 * q^37 + 31 * q^38 + 45 * q^39 + 79 * q^40 + 23 * q^41 + 33 * q^42 + 19 * q^43 + 43 * q^44 + 19 * q^45 - 31 * q^46 + 10 * q^47 - 25 * q^48 - 31 * q^49 - 60 * q^50 - 61 * q^51 - 75 * q^52 - 23 * q^53 - 86 * q^54 - 24 * q^55 - 103 * q^56 - 91 * q^57 + 12 * q^58 - 33 * q^59 - 210 * q^60 - 47 * q^61 - 39 * q^62 - 58 * q^63 - 152 * q^64 - 16 * q^65 - 116 * q^66 - 19 * q^67 - 5 * q^68 - 45 * q^69 + 23 * q^70 - 18 * q^71 - 36 * q^72 + 24 * q^73 + 19 * q^74 + 58 * q^75 + 97 * q^76 + 65 * q^77 + 119 * q^78 + 41 * q^79 + 107 * q^80 + 95 * q^81 + 145 * q^82 + 49 * q^83 + 167 * q^84 + 39 * q^85 + 111 * q^86 + 80 * q^87 + 175 * q^88 + 51 * q^89 + 213 * q^90 + 77 * q^91 + 135 * q^92 + 93 * q^93 + 151 * q^94 + 65 * q^95 + 181 * q^96 + 91 * q^97 + 31 * q^98 + 44 * q^99

Introduction

L-functions

Modular forms

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