LMFDB - Embedded newform 483.2.j.a.229.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(229,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("483.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.j (of order $6$, degree $2$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.4
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20973 + 2.09532i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.92691 - 3.33751i) q^{4} +(1.20224 - 2.08234i) q^{5} +2.41947i q^{6} +(-0.190002 + 2.63892i) q^{7} +4.48526 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.20973 + 2.09532i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.92691 - 3.33751i) q^{4} +(1.20224 - 2.08234i) q^{5} +2.41947i q^{6} +(-0.190002 + 2.63892i) q^{7} +4.48526 q^{8} +(0.500000 - 0.866025i) q^{9} +(2.90878 + 5.03816i) q^{10} +(-0.990601 + 0.571924i) q^{11} +(-3.33751 - 1.92691i) q^{12} -6.80155i q^{13} +(-5.29953 - 3.59051i) q^{14} -2.40448i q^{15} +(-1.57215 + 2.72304i) q^{16} +(2.36069 + 4.08884i) q^{17} +(1.20973 + 2.09532i) q^{18} +(2.65230 - 4.59392i) q^{19} -9.26644 q^{20} +(1.15491 + 2.38037i) q^{21} -2.76750i q^{22} +(4.71048 + 0.900791i) q^{23} +(3.88435 - 2.24263i) q^{24} +(-0.390766 - 0.676827i) q^{25} +(14.2514 + 8.22807i) q^{26} -1.00000i q^{27} +(9.17353 - 4.45083i) q^{28} +1.58171 q^{29} +(5.03816 + 2.90878i) q^{30} +(7.50051 - 4.33042i) q^{31} +(0.681496 + 1.18039i) q^{32} +(-0.571924 + 0.990601i) q^{33} -11.4232 q^{34} +(5.26671 + 3.56827i) q^{35} -3.85382 q^{36} +(-3.60593 - 2.08189i) q^{37} +(6.41716 + 11.1148i) q^{38} +(-3.40078 - 5.89032i) q^{39} +(5.39236 - 9.33985i) q^{40} -3.66283i q^{41} +(-6.38478 - 0.459704i) q^{42} +3.29523i q^{43} +(3.81760 + 2.20409i) q^{44} +(-1.20224 - 2.08234i) q^{45} +(-7.58587 + 8.78024i) q^{46} +(2.95024 + 1.70332i) q^{47} +3.14430i q^{48} +(-6.92780 - 1.00280i) q^{49} +1.89089 q^{50} +(4.08884 + 2.36069i) q^{51} +(-22.7002 + 13.1060i) q^{52} +(-6.60961 + 3.81606i) q^{53} +(2.09532 + 1.20973i) q^{54} +2.75036i q^{55} +(-0.852209 + 11.8362i) q^{56} -5.30461i q^{57} +(-1.91345 + 3.31419i) q^{58} +(-2.68538 + 1.55040i) q^{59} +(-8.02498 + 4.63322i) q^{60} +(6.23164 - 10.7935i) q^{61} +20.9546i q^{62} +(2.19037 + 1.48401i) q^{63} -9.58632 q^{64} +(-14.1632 - 8.17710i) q^{65} +(-1.38375 - 2.39673i) q^{66} +(-5.51061 + 3.18155i) q^{67} +(9.09770 - 15.7577i) q^{68} +(4.52979 - 1.57513i) q^{69} +(-13.8480 + 6.71878i) q^{70} -5.00666 q^{71} +(2.24263 - 3.88435i) q^{72} +(0.707889 - 0.408700i) q^{73} +(8.72444 - 5.03706i) q^{74} +(-0.676827 - 0.390766i) q^{75} -20.4430 q^{76} +(-1.32105 - 2.72278i) q^{77} +16.4561 q^{78} +(9.42565 + 5.44190i) q^{79} +(3.78021 + 6.54751i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.67481 + 4.43105i) q^{82} +15.4316 q^{83} +(5.71910 - 8.44130i) q^{84} +11.3525 q^{85} +(-6.90457 - 3.98635i) q^{86} +(1.36980 - 0.790854i) q^{87} +(-4.44311 + 2.56523i) q^{88} +(-8.96702 + 15.5313i) q^{89} +5.81756 q^{90} +(17.9488 + 1.29231i) q^{91} +(-6.07027 - 17.4570i) q^{92} +(4.33042 - 7.50051i) q^{93} +(-7.13801 + 4.12113i) q^{94} +(-6.37741 - 11.0460i) q^{95} +(1.18039 + 0.681496i) q^{96} -5.04561 q^{97} +(10.4820 - 13.3028i) q^{98} +1.14385i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9	$ 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50} - 108 q^{52} - 24 q^{58} + 36 q^{59} + 168 q^{64} - 40 q^{70} - 16 q^{71} - 12 q^{72} + 48 q^{73} - 48 q^{75} - 32 q^{78} - 32 q^{81} - 24 q^{82} + 88 q^{85} + 36 q^{87} + 152 q^{92} + 24 q^{93} - 108 q^{94} - 44 q^{95} + 60 q^{96} + 112 q^{98}+O(q^{100}) $ 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.20973	+	2.09532i	−0.855411	+	1.48162i	0.0208525	+	0.999783i	$0.493362\pi$
$2$	−1.20973	+	2.09532i	−0.855411	+	1.48162i	−0.876263	+	0.481833i	$0.839971\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−1.92691	−	3.33751i	−0.963455	−	1.66875i
$5$	1.20224	−	2.08234i	0.537658	−	0.931252i	−0.461371	−	0.887207i	$-0.652642\pi$
$5$	1.20224	−	2.08234i	0.537658	−	0.931252i	0.999030	−	0.0440445i	$-0.0140243\pi$
$6$			2.41947i			0.987743i
$7$	−0.190002	+	2.63892i	−0.0718140	+	0.997418i
$7$	−0.190002	+	2.63892i	−0.0718140	+	0.997418i
$8$	4.48526			1.58578
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	2.90878	+	5.03816i	0.919838	+	1.59321i
$11$	−0.990601	+	0.571924i	−0.298677	+	0.172442i	−0.641849	−	0.766831i	$-0.721832\pi$
$11$	−0.990601	+	0.571924i	−0.298677	+	0.172442i	0.343171	+	0.939273i	$0.388499\pi$
$12$	−3.33751	−	1.92691i	−0.963455	−	0.556251i
$13$		−	6.80155i		−	1.88641i	−0.332209	−	0.943206i	$-0.607794\pi$
$13$		−	6.80155i		−	1.88641i	0.332209	−	0.943206i	$-0.392206\pi$
$14$	−5.29953	−	3.59051i	−1.41636	−	0.959603i
$15$		−	2.40448i		−	0.620834i
$16$	−1.57215	+	2.72304i	−0.393037	+	0.680761i
$17$	2.36069	+	4.08884i	0.572552	+	0.991690i	0.996303	+	0.0859109i	$0.0273801\pi$
$17$	2.36069	+	4.08884i	0.572552	+	0.991690i	−0.423750	+	0.905779i	$0.639287\pi$
$18$	1.20973	+	2.09532i	0.285137	+	0.493872i
$19$	2.65230	−	4.59392i	0.608480	−	1.05392i	−0.383011	−	0.923744i	$-0.625113\pi$
$19$	2.65230	−	4.59392i	0.608480	−	1.05392i	0.991491	−	0.130174i	$-0.0415537\pi$
$20$	−9.26644			−2.07204
$21$	1.15491	+	2.38037i	0.252023	+	0.519440i
$22$		−	2.76750i		−	0.590033i
$23$	4.71048	+	0.900791i	0.982202	+	0.187828i
$23$	4.71048	+	0.900791i	0.982202	+	0.187828i
$24$	3.88435	−	2.24263i	0.792890	−	0.457775i
$25$	−0.390766	−	0.676827i	−0.0781532	−	0.135365i
$26$	14.2514	+	8.22807i	2.79494	+	1.61366i
$27$		−	1.00000i		−	0.192450i
$28$	9.17353	−	4.45083i	1.73363	−	0.841128i
$29$	1.58171			0.293716			0.146858	−	0.989158i	$-0.453084\pi$
$29$	1.58171			0.293716			0.146858	+	0.989158i	$0.453084\pi$
$30$	5.03816	+	2.90878i	0.919838	+	0.531069i
$31$	7.50051	−	4.33042i	1.34713	−	0.777766i	0.359289	−	0.933227i	$-0.383019\pi$
$31$	7.50051	−	4.33042i	1.34713	−	0.777766i	0.987842	+	0.155460i	$0.0496861\pi$
$32$	0.681496	+	1.18039i	0.120473	+	0.208665i
$33$	−0.571924	+	0.990601i	−0.0995592	+	0.172442i
$34$	−11.4232			−1.95907
$35$	5.26671	+	3.56827i	0.890236	+	0.603147i
$36$	−3.85382			−0.642304
$37$	−3.60593	−	2.08189i	−0.592812	−	0.342260i	0.173397	−	0.984852i	$-0.444526\pi$
$37$	−3.60593	−	2.08189i	−0.592812	−	0.342260i	−0.766208	+	0.642592i	$0.777859\pi$
$38$	6.41716	+	11.1148i	1.04100	+	1.80307i
$39$	−3.40078	−	5.89032i	−0.544560	−	0.943206i
$40$	5.39236	−	9.33985i	0.852608	−	1.47676i
$41$		−	3.66283i		−	0.572039i	−0.958224	−	0.286019i	$-0.907668\pi$
$41$		−	3.66283i		−	0.572039i	0.958224	−	0.286019i	$-0.0923322\pi$
$42$	−6.38478	−	0.459704i	−0.985193	−	0.0709338i
$43$			3.29523i			0.502518i	0.967920	+	0.251259i	$0.0808446\pi$
$43$			3.29523i			0.502518i	−0.967920	+	0.251259i	$0.919155\pi$
$44$	3.81760	+	2.20409i	0.575525	+	0.332279i
$45$	−1.20224	−	2.08234i	−0.179219	−	0.310417i
$46$	−7.58587	+	8.78024i	−1.11847	+	1.29458i
$47$	2.95024	+	1.70332i	0.430337	+	0.248455i	0.699490	−	0.714642i	$-0.253410\pi$
$47$	2.95024	+	1.70332i	0.430337	+	0.248455i	−0.269153	+	0.963097i	$0.586744\pi$
$48$			3.14430i			0.453841i
$49$	−6.92780	−	1.00280i	−0.989685	−	0.143257i
$50$	1.89089			0.267412
$51$	4.08884	+	2.36069i	0.572552	+	0.330563i
$52$	−22.7002	+	13.1060i	−3.14796	+	1.81747i
$53$	−6.60961	+	3.81606i	−0.907899	+	0.524176i	−0.879755	−	0.475428i	$-0.842293\pi$
$53$	−6.60961	+	3.81606i	−0.907899	+	0.524176i	−0.0281446	+	0.999604i	$0.508960\pi$
$54$	2.09532	+	1.20973i	0.285137	+	0.164624i
$55$			2.75036i			0.370859i
$56$	−0.852209	+	11.8362i	−0.113881	+	1.58169i
$57$		−	5.30461i		−	0.702612i
$58$	−1.91345	+	3.31419i	−0.251248	+	0.435174i
$59$	−2.68538	+	1.55040i	−0.349606	+	0.201845i	−0.664512	−	0.747278i	$-0.731360\pi$
$59$	−2.68538	+	1.55040i	−0.349606	+	0.201845i	0.314906	+	0.949123i	$0.398027\pi$
$60$	−8.02498	+	4.63322i	−1.03602	+	0.598146i
$61$	6.23164	−	10.7935i	0.797880	−	1.38197i	−0.123114	−	0.992392i	$-0.539288\pi$
$61$	6.23164	−	10.7935i	0.797880	−	1.38197i	0.920994	−	0.389576i	$-0.127378\pi$
$62$			20.9546i			2.66124i
$63$	2.19037	+	1.48401i	0.275961	+	0.186967i
$64$	−9.58632			−1.19829
$65$	−14.1632	−	8.17710i	−1.75672	−	1.01424i
$66$	−1.38375	−	2.39673i	−0.170328	−	0.295017i
$67$	−5.51061	+	3.18155i	−0.673228	+	0.388688i	−0.797299	−	0.603585i	$-0.793738\pi$
$67$	−5.51061	+	3.18155i	−0.673228	+	0.388688i	0.124071	+	0.992273i	$0.460405\pi$
$68$	9.09770	−	15.7577i	1.10326	−	1.91090i
$69$	4.52979	−	1.57513i	0.545322	−	0.189623i
$70$	−13.8480	+	6.71878i	−1.65515	+	0.803048i
$71$	−5.00666			−0.594181			−0.297090	−	0.954849i	$-0.596016\pi$
$71$	−5.00666			−0.594181			−0.297090	+	0.954849i	$0.596016\pi$
$72$	2.24263	−	3.88435i	0.264297	−	0.457775i
$73$	0.707889	−	0.408700i	0.0828521	−	0.0478347i	−0.458002	−	0.888951i	$-0.651435\pi$
$73$	0.707889	−	0.408700i	0.0828521	−	0.0478347i	0.540854	+	0.841117i	$0.318101\pi$
$74$	8.72444	−	5.03706i	1.01420	−	0.585546i
$75$	−0.676827	−	0.390766i	−0.0781532	−	0.0451218i
$76$	−20.4430			−2.34497
$77$	−1.32105	−	2.72278i	−0.150547	−	0.310290i
$78$	16.4561			1.86329
$79$	9.42565	+	5.44190i	1.06047	+	0.612262i	0.925562	−	0.378596i	$-0.123593\pi$
$79$	9.42565	+	5.44190i	1.06047	+	0.612262i	0.134907	+	0.990858i	$0.456926\pi$
$80$	3.78021	+	6.54751i	0.422640	+	0.732034i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.67481	+	4.43105i	0.847541	+	0.489328i
$83$	15.4316			1.69384			0.846921	−	0.531718i	$-0.178453\pi$
$83$	15.4316			1.69384			0.846921	+	0.531718i	$0.178453\pi$
$84$	5.71910	−	8.44130i	0.624005	−	0.921021i
$85$	11.3525			1.23135
$86$	−6.90457	−	3.98635i	−0.744539	−	0.429860i
$87$	1.36980	−	0.790854i	0.146858	−	0.0847885i
$88$	−4.44311	+	2.56523i	−0.473637	+	0.273454i
$89$	−8.96702	+	15.5313i	−0.950502	+	1.64632i	−0.206161	+	0.978518i	$0.566097\pi$
$89$	−8.96702	+	15.5313i	−0.950502	+	1.64632i	−0.744341	+	0.667800i	$0.767236\pi$
$90$	5.81756			0.613225
$91$	17.9488	+	1.29231i	1.88154	+	0.135471i
$92$	−6.07027	−	17.4570i	−0.632869	−	1.82002i
$93$	4.33042	−	7.50051i	0.449044	−	0.777766i
$94$	−7.13801	+	4.12113i	−0.736230	+	0.425062i
$95$	−6.37741	−	11.0460i	−0.654309	−	1.13330i
$96$	1.18039	+	0.681496i	0.120473	+	0.0695549i
$97$	−5.04561			−0.512304			−0.256152	−	0.966636i	$-0.582455\pi$
$97$	−5.04561			−0.512304			−0.256152	+	0.966636i	$0.582455\pi$
$98$	10.4820	−	13.3028i	1.05884	−	1.34379i
$99$			1.14385i			0.114961i
$100$	−1.50594	+	2.60837i	−0.150594	+	0.260837i
$101$	−3.81852	+	2.20463i	−0.379957	+	0.219369i	−0.677800	−	0.735247i	$-0.737066\pi$
$101$	−3.81852	+	2.20463i	−0.379957	+	0.219369i	0.297842	+	0.954615i	$0.403733\pi$
$102$	−9.89282	+	5.71162i	−0.979535	+	0.565535i
$103$	−6.78507	+	11.7521i	−0.668553	+	1.15797i	0.309756	+	0.950816i	$0.399753\pi$
$103$	−6.78507	+	11.7521i	−0.668553	+	1.15797i	−0.978309	+	0.207152i	$0.933581\pi$
$104$		−	30.5067i		−	2.99143i
$105$	6.34523	+	0.456856i	0.619232	+	0.0445846i
$106$		−	18.4657i		−	1.79354i
$107$	−7.83558	−	4.52388i	−0.757494	−	0.437340i	0.0709011	−	0.997483i	$-0.477413\pi$
$107$	−7.83558	−	4.52388i	−0.757494	−	0.437340i	−0.828395	+	0.560144i	$0.810746\pi$
$108$	−3.33751	+	1.92691i	−0.321152	+	0.185417i
$109$	−0.577034	+	0.333151i	−0.0552698	+	0.0319100i	−0.527380	−	0.849629i	$-0.676826\pi$
$109$	−0.577034	+	0.333151i	−0.0552698	+	0.0319100i	0.472110	+	0.881539i	$0.343492\pi$
$110$	−5.76289	−	3.32720i	−0.549470	−	0.317236i
$111$	−4.16377			−0.395208
$112$	−6.88718	−	4.66616i	−0.650778	−	0.440911i
$113$		−	4.64196i		−	0.436679i	−0.975873	−	0.218340i	$-0.929936\pi$
$113$		−	4.64196i		−	0.436679i	0.975873	−	0.218340i	$-0.0700641\pi$
$114$	11.1148	+	6.41716i	1.04100	+	0.601022i
$115$	7.53888	−	8.72585i	0.703004	−	0.813690i
$116$	−3.04781	−	5.27897i	−0.282982	−	0.490140i
$117$	−5.89032	−	3.40078i	−0.544560	−	0.314402i
$118$		−	7.50230i		−	0.690642i
$119$	−11.2387	+	5.45280i	−1.03025	+	0.499857i
$120$		−	10.7847i		−	0.984507i
$121$	−4.84581	+	8.39318i	−0.440528	+	0.763017i
$122$	15.0773	+	26.1146i	1.36503	+	2.36430i
$123$	−1.83142	−	3.17211i	−0.165133	−	0.286019i
$124$	−28.9056	−	16.6887i	−2.59580	−	1.49869i
$125$	10.1432			0.907238
$126$	−5.75923	+	2.79428i	−0.513073	+	0.248934i
$127$	1.16424			0.103310			0.0516550	−	0.998665i	$-0.483550\pi$
$127$	1.16424			0.103310			0.0516550	+	0.998665i	$0.483550\pi$
$128$	10.2339	−	17.7256i	0.904557	−	1.56674i
$129$	1.64762	+	2.85375i	0.145065	+	0.251259i
$130$	34.2673	−	19.7842i	3.00544	−	1.73519i
$131$	−18.4674	−	10.6622i	−1.61351	−	0.931558i	−0.988549	−	0.150898i	$-0.951784\pi$
$131$	−18.4674	−	10.6622i	−1.61351	−	0.931558i	−0.624956	−	0.780660i	$-0.714883\pi$
$132$	4.40819			0.383683
$133$	11.6191	+	7.87207i	1.00750	+	0.682595i
$134$		−	15.3953i		−	1.32995i
$135$	−2.08234	−	1.20224i	−0.179219	−	0.103472i
$136$	10.5883	+	18.3395i	0.907942	+	1.57260i
$137$	5.69744	−	3.28942i	0.486765	−	0.281034i	−0.236467	−	0.971640i	$-0.575989\pi$
$137$	5.69744	−	3.28942i	0.486765	−	0.281034i	0.723231	+	0.690606i	$0.242656\pi$
$138$	−2.17943	+	11.3968i	−0.185526	+	0.970163i
$139$		−	13.4080i		−	1.13725i	−0.822597	−	0.568624i	$-0.807476\pi$
$139$		−	13.4080i		−	1.13725i	0.822597	−	0.568624i	$-0.192524\pi$
$140$	1.76064	−	24.4534i	0.148801	−	2.06669i
$141$	3.40665			0.286891
$142$	6.05672	−	10.4905i	0.508269	−	0.880347i
$143$	3.88997	+	6.73763i	0.325296	+	0.563429i
$144$	1.57215	+	2.72304i	0.131012	+	0.226920i
$145$	1.90159	−	3.29366i	0.157919	−	0.273524i
$146$			1.97767i			0.163673i
$147$	−6.50105	+	2.59545i	−0.536198	+	0.214069i
$148$			16.0464i			1.31901i
$149$	−12.4766	−	7.20340i	−1.02213	−	0.590125i	−0.107407	−	0.994215i	$-0.534255\pi$
$149$	−12.4766	−	7.20340i	−1.02213	−	0.590125i	−0.914719	+	0.404090i	$0.867588\pi$
$150$	1.63756	−	0.945446i	0.133706	−	0.0771953i
$151$	1.63256	+	2.82767i	0.132856	+	0.230113i	0.924776	−	0.380511i	$-0.124252\pi$
$151$	1.63256	+	2.82767i	0.132856	+	0.230113i	−0.791921	+	0.610624i	$0.790919\pi$
$152$	11.8963	−	20.6049i	0.964915	−	1.67128i
$153$	4.72139			0.381702
$154$	7.30322	+	0.525831i	0.588510	+	0.0423727i
$155$		−	20.8248i		−	1.67269i
$156$	−13.1060	+	22.7002i	−1.04932	+	1.81747i
$157$	0.833234	+	1.44320i	0.0664993	+	0.115180i	0.897358	−	0.441303i	$-0.145484\pi$
$157$	0.833234	+	1.44320i	0.0664993	+	0.115180i	−0.830859	+	0.556483i	$0.812150\pi$
$158$	−22.8051	+	13.1665i	−1.81427	+	1.04747i
$159$	−3.81606	+	6.60961i	−0.302633	+	0.524176i
$160$	3.27729			0.259093
$161$	−3.27211	+	12.2594i	−0.257879	+	0.966177i
$162$	2.41947			0.190091
$163$	6.14786	−	10.6484i	0.481538	−	0.834048i	−0.518238	−	0.855237i	$-0.673412\pi$
$163$	6.14786	−	10.6484i	0.481538	−	0.834048i	0.999775	+	0.0211888i	$0.00674510\pi$
$164$	−12.2247	+	7.05796i	−0.954592	+	0.551134i
$165$	1.37518	+	2.38188i	0.107058	+	0.185429i
$166$	−18.6682	+	32.3342i	−1.44893	+	2.50962i
$167$		−	0.110751i		−	0.00857015i	−0.999991	−	0.00428507i	$-0.998636\pi$
$167$		−	0.110751i		−	0.00857015i	0.999991	−	0.00428507i	$-0.00136399\pi$
$168$	5.18009	+	10.6766i	0.399653	+	0.823717i
$169$	−33.2611			−2.55855
$170$	−13.7335	+	23.7871i	−1.05331	+	1.82439i
$171$	−2.65230	−	4.59392i	−0.202827	−	0.351306i
$172$	10.9979	−	6.34962i	0.838579	−	0.484154i
$173$	11.6965	+	6.75299i	0.889270	+	0.513420i	0.873704	−	0.486459i	$-0.161712\pi$
$173$	11.6965	+	6.75299i	0.889270	+	0.513420i	0.0155661	+	0.999879i	$0.495045\pi$
$174$			3.82689i			0.290116i
$175$	1.86034	−	0.902602i	0.140628	−	0.0682303i
$176$		−	3.59660i		−	0.271104i
$177$	−1.55040	+	2.68538i	−0.116535	+	0.201845i
$178$	−21.6954	−	37.5776i	−1.62614	−	2.81656i
$179$	9.01777	+	15.6192i	0.674020	+	1.16744i	0.976754	+	0.214362i	$0.0687672\pi$
$179$	9.01777	+	15.6192i	0.674020	+	1.16744i	−0.302734	+	0.953075i	$0.597899\pi$
$180$	−4.63322	+	8.02498i	−0.345340	+	0.598146i
$181$	−25.0465			−1.86169			−0.930847	−	0.365408i	$-0.880929\pi$
$181$	−25.0465			−1.86169			−0.930847	+	0.365408i	$0.880929\pi$
$182$	−24.4210	+	36.0450i	−1.81021	+	2.67184i
$183$		−	12.4633i		−	0.921312i
$184$	21.1277	+	4.04028i	1.55756	+	0.297854i
$185$	−8.67040	+	5.00586i	−0.637460	+	0.368038i
$186$	10.4773	+	18.1472i	0.768233	+	1.33062i
$187$	−4.67701	−	2.70027i	−0.342017	−	0.197464i
$188$		−	13.1286i		−	0.957502i
$189$	2.63892	+	0.190002i	0.191953	+	0.0138206i
$190$	30.8599			2.23881
$191$	−1.72096	−	0.993597i	−0.124524	−	0.0718941i	0.436444	−	0.899731i	$-0.356238\pi$
$191$	−1.72096	−	0.993597i	−0.124524	−	0.0718941i	−0.560968	+	0.827837i	$0.689571\pi$
$192$	−8.30199	+	4.79316i	−0.599145	+	0.345916i
$193$	8.25485	+	14.2978i	0.594197	+	1.02918i	0.993660	+	0.112430i	$0.0358633\pi$
$193$	8.25485	+	14.2978i	0.594197	+	1.02918i	−0.399463	+	0.916749i	$0.630803\pi$
$194$	6.10385	−	10.5722i	0.438231	−	0.759038i
$195$	−16.3542			−1.17115
$196$	10.0024	+	25.0539i	0.714457	+	1.78956i
$197$	3.10624			0.221311			0.110655	−	0.993859i	$-0.464705\pi$
$197$	3.10624			0.221311			0.110655	+	0.993859i	$0.464705\pi$
$198$	−2.39673	−	1.38375i	−0.170328	−	0.0983389i
$199$	−1.48773	−	2.57682i	−0.105462	−	0.182666i	0.808465	−	0.588545i	$-0.200299\pi$
$199$	−1.48773	−	2.57682i	−0.105462	−	0.182666i	−0.913927	+	0.405879i	$0.866966\pi$
$200$	−1.75269	−	3.03574i	−0.123934	−	0.214660i
$201$	−3.18155	+	5.51061i	−0.224409	+	0.388688i
$202$		−	10.6680i		−	0.750601i
$203$	−0.300528	+	4.17400i	−0.0210929	+	0.292958i
$204$		−	18.1954i		−	1.27393i
$205$	−7.62727	−	4.40361i	−0.532712	−	0.307561i
$206$	−16.4163	−	28.4338i	−1.14377	−	1.98108i
$207$	3.13535	−	3.62900i	0.217922	−	0.252233i
$208$	18.5209	+	10.6931i	1.28420	+	0.741430i
$209$			6.06766i			0.419709i
$210$	−8.63330	+	12.7426i	−0.595755	+	0.879325i
$211$	3.77351			0.259779			0.129890	−	0.991528i	$-0.458538\pi$
$211$	3.77351			0.259779			0.129890	+	0.991528i	$0.458538\pi$
$212$	25.4722	+	14.7064i	1.74944	+	1.01004i
$213$	−4.33589	+	2.50333i	−0.297090	+	0.171525i
$214$	18.9579	−	10.9454i	1.29594	−	0.748210i
$215$	6.86180	+	3.96166i	0.467971	+	0.270183i
$216$		−	4.48526i		−	0.305183i
$217$	10.0025	+	20.6160i	0.679015	+	1.39951i
$218$		−	1.61209i		−	0.109185i
$219$	0.408700	−	0.707889i	0.0276174	−	0.0478347i
$220$	9.17935	−	5.29970i	0.618872	−	0.357306i
$221$	27.8105	−	16.0564i	1.87074	−	1.08007i
$222$	5.03706	−	8.72444i	0.338065	−	0.585546i
$223$			17.8871i			1.19781i	0.800821	+	0.598904i	$0.204397\pi$
$223$			17.8871i			1.19781i	−0.800821	+	0.598904i	$0.795603\pi$
$224$	−3.24443	+	1.57414i	−0.216778	+	0.105177i
$225$	−0.781532			−0.0521021
$226$	9.72640	+	5.61554i	0.646991	+	0.373540i
$227$	−5.56446	−	9.63794i	−0.369327	−	0.639692i	0.620134	−	0.784496i	$-0.287078\pi$
$227$	−5.56446	−	9.63794i	−0.369327	−	0.639692i	−0.989460	+	0.144804i	$0.953745\pi$
$228$	−17.7042	+	10.2215i	−1.17249	+	0.676936i
$229$	1.54019	−	2.66768i	0.101778	−	0.176285i	−0.810639	−	0.585546i	$-0.800880\pi$
$229$	1.54019	−	2.66768i	0.101778	−	0.176285i	0.912417	+	0.409261i	$0.134213\pi$
$230$	9.16342	+	26.3523i	0.604218	+	1.73762i
$231$	−2.50545	−	1.69748i	−0.164847	−	0.111686i
$232$	7.09438			0.465769
$233$	−2.44017	+	4.22649i	−0.159861	+	0.276887i	−0.934818	−	0.355126i	$-0.884438\pi$
$233$	−2.44017	+	4.22649i	−0.159861	+	0.276887i	0.774958	+	0.632013i	$0.217771\pi$
$234$	14.2514	−	8.22807i	0.931645	−	0.537886i
$235$	7.09380	−	4.09561i	0.462749	−	0.267168i
$236$	10.3490	+	5.97498i	0.673660	+	0.388938i
$237$	10.8838			0.706979
$238$	2.17044	−	30.1450i	0.140689	−	1.95401i
$239$	22.2053			1.43634			0.718170	−	0.695868i	$-0.244980\pi$
$239$	22.2053			1.43634			0.718170	+	0.695868i	$0.244980\pi$
$240$	6.54751	+	3.78021i	0.422640	+	0.244011i
$241$	8.64871	+	14.9800i	0.557112	+	0.964947i	0.997736	+	0.0672550i	$0.0214241\pi$
$241$	8.64871	+	14.9800i	0.557112	+	0.964947i	−0.440623	+	0.897692i	$0.645243\pi$
$242$	−11.7243	−	20.3070i	−0.753665	−	1.30539i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−48.0313			−3.07489
$245$	−10.4171	+	13.2204i	−0.665521	+	0.844623i
$246$	8.86211			0.565027
$247$	−31.2458	−	18.0398i	−1.98812	−	1.14784i
$248$	33.6417	−	19.4231i	2.13625	−	1.23337i
$249$	13.3642	−	7.71582i	0.846921	−	0.488970i
$250$	−12.2706	+	21.2533i	−0.776061	+	1.34418i
$251$	−5.02060			−0.316897			−0.158449	−	0.987367i	$-0.550649\pi$
$251$	−5.02060			−0.316897			−0.158449	+	0.987367i	$0.550649\pi$
$252$	0.732234	−	10.1699i	0.0461264	−	0.640645i
$253$	−5.18139	+	1.80171i	−0.325751	+	0.113272i
$254$	−1.40842	+	2.43946i	−0.0883724	+	0.153066i
$255$	9.83155	−	5.67625i	0.615675	−	0.355460i
$256$	15.1743	+	26.2826i	0.948391	+	1.64266i
$257$	−15.6089	−	9.01179i	−0.973655	−	0.562140i	−0.0733066	−	0.997309i	$-0.523355\pi$
$257$	−15.6089	−	9.01179i	−0.973655	−	0.562140i	−0.900349	+	0.435169i	$0.856689\pi$
$258$	−7.97271			−0.496359
$259$	6.17907	−	9.12021i	0.383948	−	0.566702i
$260$			63.0262i			3.90872i
$261$	0.790854	−	1.36980i	0.0489527	−	0.0847885i
$262$	44.6813	−	25.7968i	2.76042	−	1.59373i
$263$	−11.5795	+	6.68544i	−0.714024	+	0.412242i	−0.812549	−	0.582893i	$-0.801921\pi$
$263$	−11.5795	+	6.68544i	−0.714024	+	0.412242i	0.0985253	+	0.995135i	$0.468587\pi$
$264$	−2.56523	+	4.44311i	−0.157879	+	0.273454i
$265$			18.3513i			1.12731i
$266$	−30.5505	+	14.8225i	−1.87317	+	0.908828i
$267$			17.9340i			1.09755i
$268$	21.2369	+	12.2611i	1.29725	+	0.748968i
$269$	−27.3022	+	15.7630i	−1.66465	+	0.961084i	−0.694195	+	0.719787i	$0.744240\pi$
$269$	−27.3022	+	15.7630i	−1.66465	+	0.961084i	−0.970451	+	0.241297i	$0.922427\pi$
$270$	5.03816	−	2.90878i	0.306613	−	0.177023i
$271$	9.26539	+	5.34938i	0.562832	+	0.324951i	0.754282	−	0.656551i	$-0.227985\pi$
$271$	9.26539	+	5.34938i	0.562832	+	0.324951i	−0.191449	+	0.981503i	$0.561319\pi$
$272$	−14.8455			−0.900138
$273$	16.1902	−	7.85521i	0.979877	−	0.475419i
$274$			15.9173i			0.961597i
$275$	0.774186	+	0.446977i	0.0466852	+	0.0269537i
$276$	−13.9855	−	12.0831i	−0.841828	−	0.727315i
$277$	10.7307	+	18.5861i	0.644746	+	1.11673i	0.984360	+	0.176168i	$0.0563700\pi$
$277$	10.7307	+	18.5861i	0.644746	+	1.11673i	−0.339615	+	0.940565i	$0.610297\pi$
$278$	28.0940	+	16.2201i	1.68496	+	0.972814i
$279$		−	8.66084i		−	0.518511i
$280$	23.6226	+	16.0046i	1.41172	+	0.956458i
$281$		−	6.20806i		−	0.370342i	−0.982706	−	0.185171i	$-0.940716\pi$
$281$		−	6.20806i		−	0.370342i	0.982706	−	0.185171i	$-0.0592838\pi$
$282$	−4.12113	+	7.13801i	−0.245410	+	0.425062i
$283$	6.15498	+	10.6607i	0.365876	+	0.633715i	0.988916	−	0.148474i	$-0.0474363\pi$
$283$	6.15498	+	10.6607i	0.365876	+	0.633715i	−0.623041	+	0.782189i	$0.714103\pi$
$284$	9.64738	+	16.7098i	0.572467	+	0.991541i
$285$	−11.0460	−	6.37741i	−0.654309	−	0.377765i
$286$	−18.8233			−1.11305
$287$	9.66593	+	0.695946i	0.570562	+	0.0410804i
$288$	1.36299			0.0803151
$289$	−2.64576	+	4.58258i	−0.155633	+	0.269564i
$290$	4.60085	+	7.96890i	0.270171	+	0.467950i
$291$	−4.36963	+	2.52281i	−0.256152	+	0.147889i
$292$	−2.72808	−	1.57506i	−0.159649	−	0.0921732i
$293$	10.2946			0.601416			0.300708	−	0.953716i	$-0.402777\pi$
$293$	10.2946			0.601416			0.300708	+	0.953716i	$0.402777\pi$
$294$	2.42624	−	16.7616i	0.141501	−	0.977555i
$295$			7.45583i			0.434095i
$296$	−16.1736	−	9.33780i	−0.940069	−	0.542749i
$297$	0.571924	+	0.990601i	0.0331864	+	0.0574805i
$298$	30.1868	−	17.4284i	1.74868	−	1.00960i
$299$	6.12678	−	32.0385i	0.354321	−	1.85284i
$300$			3.01189i			0.173891i
$301$	−8.69585	−	0.626101i	−0.501221	−	0.0360878i
$302$	−7.89984			−0.454585
$303$	−2.20463	+	3.81852i	−0.126652	+	0.219369i
$304$	8.33964	+	14.4447i	0.478311	+	0.828459i
$305$	−14.9839	−	25.9528i	−0.857974	−	1.48605i
$306$	−5.71162	+	9.89282i	−0.326512	+	0.565535i
$307$		−	13.6086i		−	0.776682i	−0.921516	−	0.388341i	$-0.873048\pi$
$307$		−	13.6086i		−	0.776682i	0.921516	−	0.388341i	$-0.126952\pi$
$308$	−6.54178	+	9.65556i	−0.372752	+	0.550177i
$309$			13.5701i			0.771978i
$310$	43.6347	+	25.1925i	2.47828	+	1.43084i
$311$	−3.12593	+	1.80476i	−0.177255	+	0.102338i	−0.586002	−	0.810309i	$-0.699299\pi$
$311$	−3.12593	+	1.80476i	−0.177255	+	0.102338i	0.408747	+	0.912648i	$0.365966\pi$
$312$	−15.2534	−	26.4196i	−0.863552	−	1.49572i
$313$	−1.89402	+	3.28054i	−0.107056	+	0.185427i	−0.914576	−	0.404413i	$-0.867476\pi$
$313$	−1.89402	+	3.28054i	−0.107056	+	0.185427i	0.807520	+	0.589840i	$0.200809\pi$
$314$	−4.03196			−0.227537
$315$	5.72356	−	2.77697i	0.322486	−	0.156464i
$316$		−	41.9443i		−	2.35955i
$317$	0.256009	−	0.443420i	0.0143789	−	0.0249050i	−0.858746	−	0.512401i	$-0.828756\pi$
$317$	0.256009	−	0.443420i	0.0143789	−	0.0249050i	0.873125	+	0.487496i	$0.162090\pi$
$318$	−9.23283	−	15.9917i	−0.517751	−	0.896771i
$319$	−1.56684	+	0.904617i	−0.0877263	+	0.0506488i
$320$	−11.5251	+	19.9620i	−0.644270	+	1.11591i
$321$	−9.04775			−0.504996
$322$	−21.7290	−	21.6868i	−1.21091	−	1.20856i
$323$	25.0451			1.39355
$324$	−1.92691	+	3.33751i	−0.107051	+	0.185417i
$325$	−4.60347	+	2.65782i	−0.255355	+	0.147429i
$326$	14.8746	+	25.7635i	0.823825	+	1.42691i
$327$	−0.333151	+	0.577034i	−0.0184233	+	0.0319100i
$328$		−	16.4288i		−	0.907127i
$329$	−5.05548	+	7.46182i	−0.278718	+	0.411383i
$330$	−6.65441			−0.366313
$331$	−9.48984	+	16.4369i	−0.521609	+	0.903453i	0.478075	+	0.878319i	$0.341335\pi$
$331$	−9.48984	+	16.4369i	−0.521609	+	0.903453i	−0.999684	+	0.0251340i	$0.991999\pi$
$332$	−29.7354	−	51.5032i	−1.63194	−	2.82661i
$333$	−3.60593	+	2.08189i	−0.197604	+	0.114087i
$334$	0.232058	+	0.133979i	0.0126977	+	0.00733100i
$335$			15.3000i			0.835926i
$336$	−8.29756	−	0.597423i	−0.452669	−	0.0325921i
$337$		−	13.1089i		−	0.714088i	−0.934088	−	0.357044i	$-0.883785\pi$
$337$		−	13.1089i		−	0.714088i	0.934088	−	0.357044i	$-0.116215\pi$
$338$	40.2371	−	69.6927i	2.18861	−	3.79078i
$339$	−2.32098	−	4.02006i	−0.126058	−	0.218340i
$340$	−21.8752	−	37.8890i	−1.18635	−	2.05482i
$341$	−4.95334	+	8.57944i	−0.268238	+	0.464603i
$342$	12.8343			0.694000
$343$	3.96260	−	18.0914i	0.213961	−	0.976842i
$344$			14.7800i			0.796883i
$345$	2.16594	−	11.3263i	0.116610	−	0.609785i
$346$	−28.2993	+	16.3386i	−1.52138	+	0.878370i
$347$	10.7753	+	18.6634i	0.578448	+	1.00190i	0.995658	+	0.0930910i	$0.0296747\pi$
$347$	10.7753	+	18.6634i	0.578448	+	1.00190i	−0.417210	+	0.908810i	$0.636992\pi$
$348$	−5.27897	−	3.04781i	−0.282982	−	0.163380i
$349$			8.34595i			0.446749i	0.974733	+	0.223374i	$0.0717072\pi$
$349$			8.34595i			0.446749i	−0.974733	+	0.223374i	$0.928293\pi$
$350$	−0.359273	+	4.98991i	−0.0192040	+	0.266722i
$351$	−6.80155			−0.363040
$352$	−1.35018	−	0.779528i	−0.0719649	−	0.0415490i
$353$	−1.33631	+	0.771520i	−0.0711247	+	0.0410639i	−0.535141	−	0.844763i	$-0.679741\pi$
$353$	−1.33631	+	0.771520i	−0.0711247	+	0.0410639i	0.464016	+	0.885827i	$0.346408\pi$
$354$	−3.75115	−	6.49718i	−0.199371	−	0.345321i
$355$	−6.01921	+	10.4256i	−0.319466	+	0.553332i
$356$	69.1146			3.66307
$357$	−7.00657	+	10.3416i	−0.370827	+	0.547335i
$358$	−43.6364			−2.30626
$359$	13.4876	+	7.78709i	0.711851	+	0.410987i	0.811746	−	0.584011i	$-0.198517\pi$
$359$	13.4876	+	7.78709i	0.711851	+	0.410987i	−0.0998953	+	0.994998i	$0.531851\pi$
$360$	−5.39236	−	9.33985i	−0.284203	−	0.492253i
$361$	−4.56942	−	7.91447i	−0.240496	−	0.416551i
$362$	30.2996	−	52.4805i	1.59251	−	2.75832i
$363$			9.69161i			0.508678i
$364$	−30.2726	−	62.3943i	−1.58671	−	3.27035i
$365$		−	1.96542i		−	0.102875i
$366$	26.1146	+	15.0773i	1.36503	+	0.788101i
$367$	−1.41466	−	2.45027i	−0.0738448	−	0.127903i	0.826739	−	0.562586i	$-0.190194\pi$
$367$	−1.41466	−	2.45027i	−0.0738448	−	0.127903i	−0.900583	+	0.434683i	$0.856860\pi$
$368$	−9.85847	+	11.4107i	−0.513908	+	0.594821i
$369$	−3.17211	−	1.83142i	−0.165133	−	0.0953398i
$370$		−	24.2230i		−	1.25929i
$371$	−8.81443	−	18.1673i	−0.457623	−	0.943198i
$372$	−33.3773			−1.73053
$373$	−25.2312	−	14.5672i	−1.30642	−	0.754263i	−0.324925	−	0.945740i	$-0.605339\pi$
$373$	−25.2312	−	14.5672i	−1.30642	−	0.754263i	−0.981497	+	0.191476i	$0.938672\pi$
$374$	11.3159	−	6.53323i	0.585130	−	0.337825i
$375$	8.78429	−	5.07161i	0.453619	−	0.261897i
$376$	13.2326	+	7.63985i	0.682419	+	0.393995i
$377$		−	10.7581i		−	0.554069i
$378$	−3.59051	+	5.29953i	−0.184676	+	0.272578i
$379$			27.0632i			1.39014i	0.718941	+	0.695071i	$0.244627\pi$
$379$			27.0632i			1.39014i	−0.718941	+	0.695071i	$0.755373\pi$
$380$	−24.5774	+	42.5693i	−1.26079	+	2.18376i
$381$	1.00826	−	0.582122i	0.0516550	−	0.0298230i
$382$	4.16381	−	2.40398i	0.213039	−	0.122998i
$383$	−14.8732	+	25.7611i	−0.759984	+	1.31633i	0.182874	+	0.983136i	$0.441460\pi$
$383$	−14.8732	+	25.7611i	−0.759984	+	1.31633i	−0.942858	+	0.333194i	$0.891873\pi$
$384$		−	20.4678i		−	1.04449i
$385$	−7.25798	−	0.522574i	−0.369901	−	0.0266328i
$386$	−39.9447			−2.03313
$387$	2.85375	+	1.64762i	0.145065	+	0.0837530i
$388$	9.72244	+	16.8398i	0.493582	+	0.854910i
$389$	−3.21012	+	1.85337i	−0.162760	+	0.0939694i	−0.579167	−	0.815209i	$-0.696622\pi$
$389$	−3.21012	+	1.85337i	−0.162760	+	0.0939694i	0.416408	+	0.909178i	$0.363289\pi$
$390$	19.7842	−	34.2673i	1.00181	−	1.73519i
$391$	7.43680	+	21.3869i	0.376095	+	1.08158i
$392$	−31.0730	−	4.49782i	−1.56942	−	0.227174i
$393$	−21.3243			−1.07567
$394$	−3.75773	+	6.50857i	−0.189312	+	0.327897i
$395$	22.6638	−	13.0850i	1.14034	−	0.658376i
$396$	3.81760	−	2.20409i	0.191842	−	0.110760i
$397$	25.1766	+	14.5357i	1.26358	+	0.729526i	0.973764	−	0.227558i	$-0.0730742\pi$
$397$	25.1766	+	14.5357i	1.26358	+	0.729526i	0.289811	+	0.957084i	$0.406408\pi$
$398$	7.19902			0.360854
$399$	13.9984	+	1.00789i	0.700798	+	0.0504574i
$400$	2.45737			0.122869
$401$	−17.6968	−	10.2173i	−0.883736	−	0.510225i	−0.0118475	−	0.999930i	$-0.503771\pi$
$401$	−17.6968	−	10.2173i	−0.883736	−	0.510225i	−0.871888	+	0.489705i	$0.837105\pi$
$402$	−7.69766	−	13.3327i	−0.383924	−	0.664976i
$403$	−29.4536	−	51.0151i	−1.46719	−	2.54124i
$404$	14.7159	+	8.49624i	0.732144	+	0.422704i
$405$	−2.40448			−0.119480
$406$	−8.38231	−	5.67913i	−0.416007	−	0.281851i
$407$	4.76272			0.236079
$408$	18.3395	+	10.5883i	0.907942	+	0.524201i
$409$	−0.302174	+	0.174460i	−0.0149415	+	0.00862650i	−0.507452	−	0.861680i	$-0.669413\pi$
$409$	−0.302174	+	0.174460i	−0.0149415	+	0.00862650i	0.492511	+	0.870306i	$0.336079\pi$
$410$	18.4539	−	10.6544i	0.911375	−	0.526183i
$411$	3.28942	−	5.69744i	0.162255	−	0.281034i
$412$	52.2969			2.57648
$413$	−3.58116	−	7.38107i	−0.176217	−	0.363199i
$414$	3.81097	+	10.9597i	0.187299	+	0.538638i
$415$	18.5525	−	32.1340i	0.910709	−	1.57739i
$416$	8.02846	−	4.63523i	0.393628	−	0.227261i
$417$	−6.70398	−	11.6116i	−0.328295	−	0.568624i
$418$	−12.7137	−	7.34025i	−0.621847	−	0.359023i
$419$	−27.9875			−1.36728			−0.683639	−	0.729821i	$-0.739604\pi$
$419$	−27.9875			−1.36728			−0.683639	+	0.729821i	$0.739604\pi$
$420$	−10.7019	−	22.0576i	−0.522201	−	1.07630i
$421$		−	24.7322i		−	1.20537i	−0.797978	−	0.602686i	$-0.794097\pi$
$421$		−	24.7322i		−	1.20537i	0.797978	−	0.602686i	$-0.205903\pi$
$422$	−4.56494	+	7.90671i	−0.222218	+	0.384893i
$423$	2.95024	−	1.70332i	0.143446	−	0.0828184i
$424$	−29.6458	+	17.1160i	−1.43973	+	0.831227i
$425$	1.84496	−	3.19556i	0.0894936	−	0.155007i
$426$		−	12.1134i		−	0.586898i
$427$	27.2992	+	18.4956i	1.32110	+	0.895065i
$428$			34.8684i			1.68543i
$429$	6.73763	+	3.88997i	0.325296	+	0.187810i
$430$	−16.6019	+	9.58511i	−0.800615	+	0.462235i
$431$	−18.7865	+	10.8464i	−0.904915	+	0.522453i	−0.878792	−	0.477206i	$-0.841650\pi$
$431$	−18.7865	+	10.8464i	−0.904915	+	0.522453i	−0.0261234	+	0.999659i	$0.508316\pi$
$432$	2.72304	+	1.57215i	0.131012	+	0.0756401i
$433$	6.09895			0.293097			0.146548	−	0.989204i	$-0.453184\pi$
$433$	6.09895			0.293097			0.146548	+	0.989204i	$0.453184\pi$
$434$	−55.2976	−	3.98142i	−2.65437	−	0.191114i
$435$		−	3.80319i		−	0.182349i
$436$	2.22379	+	1.28390i	0.106500	+	0.0614878i
$437$	16.6318	−	19.2504i	0.795605	−	0.920871i
$438$	0.988836	+	1.71271i	0.0472484	+	0.0818366i
$439$	−10.6738	−	6.16254i	−0.509435	−	0.294122i	0.223167	−	0.974780i	$-0.428361\pi$
$439$	−10.6738	−	6.16254i	−0.509435	−	0.294122i	−0.732601	+	0.680658i	$0.761694\pi$
$440$			12.3361i			0.588100i
$441$	−4.33235	+	5.49825i	−0.206302	+	0.261821i
$442$			77.6958i			3.69561i
$443$	−7.28738	+	12.6221i	−0.346234	+	0.599695i	−0.985577	−	0.169227i	$-0.945873\pi$
$443$	−7.28738	+	12.6221i	−0.346234	+	0.599695i	0.639343	+	0.768921i	$0.279206\pi$
$444$	8.02322	+	13.8966i	0.380765	+	0.659505i
$445$	21.5610	+	37.3448i	1.02209	+	1.77031i
$446$	−37.4792	−	21.6386i	−1.77469	−	1.02462i
$447$	−14.4068			−0.681418
$448$	1.82142	−	25.2975i	0.0860540	−	1.19520i
$449$	19.1465			0.903581			0.451790	−	0.892124i	$-0.350785\pi$
$449$	19.1465			0.903581			0.451790	+	0.892124i	$0.350785\pi$
$450$	0.945446	−	1.63756i	0.0445687	−	0.0771953i
$451$	2.09486	+	3.62841i	0.0986432	+	0.170855i
$452$	−15.4926	+	8.94465i	−0.728710	+	0.420721i
$453$	2.82767	+	1.63256i	0.132856	+	0.0767043i
$454$	26.9261			1.26370
$455$	24.2698	−	35.8218i	1.13778	−	1.67935i
$456$		−	23.7925i		−	1.11419i
$457$	31.4656	+	18.1667i	1.47190	+	0.849802i	0.999501	−	0.0315831i	$-0.0100549\pi$
$457$	31.4656	+	18.1667i	1.47190	+	0.849802i	0.472399	+	0.881385i	$0.343388\pi$
$458$	3.72643	+	6.45436i	0.174125	+	0.301593i
$459$	4.08884	−	2.36069i	0.190851	−	0.110188i
$460$	−43.6494	−	8.34713i	−2.03516	−	0.389187i
$461$		−	9.22969i		−	0.429870i	−0.976628	−	0.214935i	$-0.931046\pi$
$461$		−	9.22969i		−	0.429870i	0.976628	−	0.214935i	$-0.0689539\pi$
$462$	6.58769	−	3.19623i	0.306487	−	0.148702i
$463$	40.2316			1.86972			0.934861	−	0.355013i	$-0.115524\pi$
$463$	40.2316			1.86972			0.934861	+	0.355013i	$0.115524\pi$
$464$	−2.48668	+	4.30706i	−0.115441	+	0.199950i
$465$	−10.4124	−	18.0348i	−0.482864	−	0.836345i
$466$	−5.90391	−	10.2259i	−0.273493	−	0.473704i
$467$	−7.26340	+	12.5806i	−0.336110	+	0.582159i	−0.983697	−	0.179832i	$-0.942445\pi$
$467$	−7.26340	+	12.5806i	−0.336110	+	0.582159i	0.647587	+	0.761991i	$0.275778\pi$
$468$			26.2120i			1.21165i
$469$	−7.34883	−	15.1466i	−0.339338	−	0.699403i
$470$			19.8184i			0.914154i
$471$	1.44320	+	0.833234i	0.0664993	+	0.0383934i
$472$	−12.0446	+	6.95396i	−0.554398	+	0.320082i
$473$	−1.88462	−	3.26426i	−0.0866550	−	0.150091i
$474$	−13.1665	+	22.8051i	−0.604758	+	1.04747i
$475$	−4.14572			−0.190219
$476$	39.8547	+	27.0021i	1.82674	+	1.23764i
$477$			7.63212i			0.349451i
$478$	−26.8625	+	46.5272i	−1.22866	+	2.12810i
$479$	17.4574	+	30.2372i	0.797651	+	1.38157i	0.921142	+	0.389226i	$0.127257\pi$
$479$	17.4574	+	30.2372i	0.797651	+	1.38157i	−0.123492	+	0.992346i	$0.539409\pi$
$480$	2.83822	−	1.63865i	0.129546	−	0.0747936i
$481$	−14.1601	+	24.5259i	−0.645643	+	1.11829i
$482$	−41.8505			−1.90624
$483$	3.29597	+	12.2530i	0.149972	+	0.557532i
$484$	37.3497			1.69772
$485$	−6.06604	+	10.5067i	−0.275445	+	0.477084i
$486$	2.09532	−	1.20973i	0.0950457	−	0.0548746i
$487$	0.0519081	+	0.0899075i	0.00235218	+	0.00407410i	0.867199	−	0.497962i	$-0.165918\pi$
$487$	0.0519081	+	0.0899075i	0.00235218	+	0.00407410i	−0.864847	+	0.502036i	$0.832585\pi$
$488$	27.9505	−	48.4118i	1.26526	−	2.19150i
$489$		−	12.2957i		−	0.556032i
$490$	−15.0992	−	37.8203i	−0.682112	−	1.70855i
$491$	−15.3488			−0.692682			−0.346341	−	0.938109i	$-0.612576\pi$
$491$	−15.3488			−0.692682			−0.346341	+	0.938109i	$0.612576\pi$
$492$	−7.05796	+	12.2247i	−0.318197	+	0.551134i
$493$	3.73393	+	6.46736i	0.168168	+	0.291275i
$494$	75.5982	−	43.6466i	3.40132	−	1.96376i
$495$	2.38188	+	1.37518i	0.107058	+	0.0618098i
$496$			27.2323i			1.22277i
$497$	0.951274	−	13.2122i	0.0426705	−	0.592646i
$498$			37.3364i			1.67308i
$499$	12.6878	−	21.9759i	0.567983	−	0.983775i	−0.428782	−	0.903408i	$-0.641057\pi$
$499$	12.6878	−	21.9759i	0.567983	−	0.983775i	0.996765	−	0.0803674i	$-0.0256093\pi$
$500$	−19.5451	−	33.8531i	−0.874083	−	1.51396i
$501$	−0.0553753	−	0.0959129i	−0.00247399	−	0.00428507i
$502$	6.07359	−	10.5198i	0.271077	−	0.469520i
$503$	26.2400			1.16999			0.584993	−	0.811039i	$-0.301097\pi$
$503$	26.2400			1.16999			0.584993	+	0.811039i	$0.301097\pi$
$504$	9.82439	+	6.65616i	0.437613	+	0.296489i
$505$			10.6020i			0.471781i
$506$	2.49294	−	13.0362i	0.110825	−	0.579532i
$507$	−28.8050	+	16.6306i	−1.27927	+	0.738589i
$508$	−2.24339	−	3.88567i	−0.0995345	−	0.172399i
$509$	34.2508	+	19.7747i	1.51814	+	0.876498i	0.999772	+	0.0213398i	$0.00679318\pi$
$509$	34.2508	+	19.7747i	1.51814	+	0.876498i	0.518367	+	0.855158i	$0.326540\pi$
$510$			27.4670i			1.21626i
$511$	0.944026	+	1.94572i	0.0417612	+	0.0860734i
$512$	−32.4917			−1.43594
$513$	−4.59392	−	2.65230i	−0.202827	−	0.117102i
$514$	37.7652	−	21.8037i	1.66575	−	0.961722i
$515$	16.3146	+	28.2577i	0.718906	+	1.24518i
$516$	6.34962	−	10.9979i	0.279526	−	0.484154i
$517$	−3.89668			−0.171376
$518$	11.6347	+	23.9801i	0.511201	+	1.05363i
$519$	13.5060			0.592846
$520$	−63.5255	−	36.6765i	−2.78578	−	1.60837i
$521$	−2.09658	−	3.63139i	−0.0918529	−	0.159094i	0.816438	−	0.577433i	$-0.195946\pi$
$521$	−2.09658	−	3.63139i	−0.0918529	−	0.159094i	−0.908291	+	0.418339i	$0.862612\pi$
$522$	1.91345	+	3.31419i	0.0837493	+	0.145058i
$523$	9.78853	−	16.9542i	0.428022	−	0.741356i	−0.568675	−	0.822562i	$-0.692544\pi$
$523$	9.78853	−	16.9542i	0.428022	−	0.741356i	0.996697	+	0.0812059i	$0.0258771\pi$
$524$			82.1802i			3.59006i
$525$	1.15980	−	1.71184i	0.0506178	−	0.0747110i
$526$		−	32.3504i		−	1.41054i
$527$	35.4128	+	20.4456i	1.54261	+	0.890624i
$528$	−1.79830	−	3.11475i	−0.0782610	−	0.135552i
$529$	21.3772	+	8.48631i	0.929441	+	0.368970i
$530$	−38.4518	−	22.2002i	−1.67024	−	0.964313i
$531$			3.10081i			0.134563i
$532$	3.88421	−	53.9475i	0.168402	−	2.33892i
$533$	−24.9130			−1.07910
$534$	−37.5776	−	21.6954i	−1.62614	−	0.938852i
$535$	−18.8405	+	10.8776i	−0.814546	+	0.470279i
$536$	−24.7165	+	14.2701i	−1.06759	+	0.616374i
$537$	15.6192	+	9.01777i	0.674020	+	0.389146i
$538$		−	76.2759i		−	3.28849i
$539$	7.43621	−	2.96880i	0.320300	−	0.127875i
$540$			9.26644i			0.398764i
$541$	−14.7359	+	25.5234i	−0.633546	+	1.09733i	0.353275	+	0.935520i	$0.385068\pi$
$541$	−14.7359	+	25.5234i	−0.633546	+	1.09733i	−0.986821	+	0.161815i	$0.948265\pi$
$542$	−22.4173	+	12.9426i	−0.962906	+	0.555934i
$543$	−21.6909	+	12.5233i	−0.930847	+	0.537425i
$544$	−3.21761	+	5.57306i	−0.137954	+	0.238943i
$545$			1.60211i			0.0686268i
$546$	−3.12670	+	43.4264i	−0.133810	+	1.85848i
$547$	17.4998			0.748236			0.374118	−	0.927381i	$-0.377945\pi$
$547$	17.4998			0.748236			0.374118	+	0.927381i	$0.377945\pi$
$548$	−21.9569	−	12.6768i	−0.937952	−	0.541527i
$549$	−6.23164	−	10.7935i	−0.265960	−	0.460656i
$550$	−1.87312	+	1.08145i	−0.0798701	+	0.0461130i
$551$	4.19517	−	7.26625i	0.178720	−	0.309553i
$552$	20.3173	−	7.06487i	0.864761	−	0.300701i
$553$	−16.1516	+	23.8396i	−0.686838	+	1.01376i
$554$	−51.9252			−2.20609
$555$	−5.00586	+	8.67040i	−0.212487	+	0.368038i
$556$	−44.7492	+	25.8359i	−1.89779	+	1.09569i
$557$	−11.7486	+	6.78304i	−0.497803	+	0.287407i	−0.727806	−	0.685783i	$-0.759460\pi$
$557$	−11.7486	+	6.78304i	−0.497803	+	0.287407i	0.230003	+	0.973190i	$0.426126\pi$
$558$	18.1472	+	10.4773i	0.768233	+	0.443540i
$559$	22.4127			0.947956
$560$	−17.9966	+	8.73162i	−0.760495	+	0.368978i
$561$	−5.40055			−0.228011
$562$	13.0079	+	7.51009i	0.548704	+	0.316794i
$563$	2.68298	+	4.64705i	0.113074	+	0.195850i	0.917008	−	0.398868i	$-0.130597\pi$
$563$	2.68298	+	4.64705i	0.113074	+	0.195850i	−0.803934	+	0.594718i	$0.797264\pi$
$564$	−6.56430	−	11.3697i	−0.276407	−	0.478751i
$565$	−9.66616	−	5.58076i	−0.406658	−	0.234784i
$566$	−29.7835			−1.25190
$567$	2.38037	−	1.15491i	0.0999663	−	0.0485018i
$568$	−22.4562			−0.942239
$569$	1.66209	+	0.959610i	0.0696786	+	0.0402289i	0.534435	−	0.845210i	$-0.320525\pi$
$569$	1.66209	+	0.959610i	0.0696786	+	0.0402289i	−0.464756	+	0.885439i	$0.653858\pi$
$570$	26.7254	−	15.4299i	1.11941	−	0.646289i
$571$	25.4494	−	14.6932i	1.06503	−	0.614893i	0.138208	−	0.990403i	$-0.455866\pi$
$571$	25.4494	−	14.6932i	1.06503	−	0.614893i	0.926818	+	0.375510i	$0.122533\pi$
$572$	14.9913	−	25.9656i	0.626816	−	1.08568i
$573$	−1.98719			−0.0830162
$574$	−13.1514	+	19.4113i	−0.548930	+	0.810212i
$575$	−1.23101	−	3.54017i	−0.0513368	−	0.147635i
$576$	−4.79316	+	8.30199i	−0.199715	+	0.345916i
$577$	8.74852	−	5.05096i	0.364206	−	0.210274i	−0.306718	−	0.951800i	$-0.599231\pi$
$577$	8.74852	−	5.05096i	0.364206	−	0.210274i	0.670924	+	0.741526i	$0.265898\pi$
$578$	−6.40132	−	11.0874i	−0.266260	−	0.461175i
$579$	14.2978	+	8.25485i	0.594197	+	0.343060i
$580$	−14.6568			−0.608591
$581$	−2.93204	+	40.7229i	−0.121642	+	1.68947i
$582$		−	12.2077i		−	0.506025i
$583$	4.36499	−	7.56038i	0.180779	−	0.313119i
$584$	3.17507	−	1.83313i	0.131385	−	0.0758553i
$585$	−14.1632	+	8.17710i	−0.585575	+	0.338082i
$586$	−12.4537	+	21.5705i	−0.514458	+	0.891067i
$587$		−	32.3785i		−	1.33640i	−0.743980	−	0.668202i	$-0.767064\pi$
$587$		−	32.3785i		−	1.33640i	0.743980	−	0.668202i	$-0.232936\pi$
$588$	21.1893	+	16.6961i	0.873831	+	0.688536i
$589$		−	45.9423i		−	1.89302i
$590$	−15.6223	−	9.01957i	−0.643162	−	0.371330i
$591$	2.69009	−	1.55312i	0.110655	−	0.0638869i
$592$	11.3381	−	6.54608i	0.465994	−	0.269042i
$593$	−31.9504	−	18.4466i	−1.31205	−	0.757510i	−0.329611	−	0.944117i	$-0.606917\pi$
$593$	−31.9504	−	18.4466i	−1.31205	−	0.757510i	−0.982435	+	0.186607i	$0.940251\pi$
$594$	−2.76750			−0.113552
$595$	−2.15700	+	29.9583i	−0.0884282	+	1.22817i
$596$			55.5212i			2.27424i
$597$	−2.57682	−	1.48773i	−0.105462	−	0.0608887i
$598$	59.7192	+	51.5957i	2.44210	+	2.10990i
$599$	5.03354	+	8.71835i	0.205665	+	0.356222i	0.950344	−	0.311200i	$-0.100731\pi$
$599$	5.03354	+	8.71835i	0.205665	+	0.356222i	−0.744679	+	0.667422i	$0.767398\pi$
$600$	−3.03574	−	1.75269i	−0.123934	−	0.0715532i
$601$			31.6780i			1.29217i	0.763264	+	0.646087i	$0.223596\pi$
$601$			31.6780i			1.29217i	−0.763264	+	0.646087i	$0.776404\pi$
$602$	11.8315	−	17.4632i	0.482218	−	0.711746i
$603$			6.36310i			0.259126i
$604$	6.29159	−	10.8974i	0.256001	−	0.443407i
$605$	11.6517	+	20.1813i	0.473707	+	0.820485i
$606$	−5.33402	−	9.23880i	−0.216680	−	0.375300i
$607$	−1.01148	−	0.583980i	−0.0410548	−	0.0237030i	0.479332	−	0.877634i	$-0.340879\pi$
$607$	−1.01148	−	0.583980i	−0.0410548	−	0.0237030i	−0.520387	+	0.853931i	$0.674212\pi$
$608$	7.23014			0.293221
$609$	1.82674	+	3.76506i	0.0740231	+	0.152568i
$610$	72.5060			2.93568
$611$	11.5852	−	20.0662i	0.468689	−	0.811792i
$612$	−9.09770	−	15.7577i	−0.367753	−	0.636966i
$613$	−12.1321	+	7.00446i	−0.490010	+	0.282908i	−0.724579	−	0.689192i	$-0.757966\pi$
$613$	−12.1321	+	7.00446i	−0.490010	+	0.282908i	0.234568	+	0.972100i	$0.424632\pi$
$614$	28.5143	+	16.4628i	1.15074	+	0.664383i
$615$	−8.80722			−0.355141
$616$	−5.92523	−	12.2124i	−0.238734	−	0.492052i
$617$		−	38.3891i		−	1.54549i	−0.634717	−	0.772744i	$-0.718883\pi$
$617$		−	38.3891i		−	1.54549i	0.634717	−	0.772744i	$-0.281117\pi$
$618$	−28.4338	−	16.4163i	−1.14377	−	0.660359i
$619$	−21.5526	−	37.3302i	−0.866271	−	1.50043i	−0.865780	−	0.500426i	$-0.833177\pi$
$619$	−21.5526	−	37.3302i	−0.866271	−	1.50043i	−0.000491575	−	1.00000i	$-0.500156\pi$
$620$	−69.5030	+	40.1276i	−2.79131	+	1.61156i
$621$	0.900791	−	4.71048i	0.0361475	−	0.189025i
$622$		−	8.73310i		−	0.350166i
$623$	−39.2822	−	26.6142i	−1.57381	−	1.06628i
$624$	21.3861			0.856130
$625$	14.1484	−	24.5058i	0.565937	−	0.980232i
$626$	−4.58252	−	7.93715i	−0.183154	−	0.317232i
$627$	3.03383	+	5.25475i	0.121160	+	0.209854i
$628$	3.21113	−	5.56185i	0.128138	−	0.221942i
$629$		−	19.6588i		−	0.783847i
$630$	−1.10535	+	15.3521i	−0.0440382	+	0.611642i
$631$		−	15.9937i		−	0.636701i	−0.947973	−	0.318350i	$-0.896871\pi$
$631$		−	15.9937i		−	0.636701i	0.947973	−	0.318350i	$-0.103129\pi$
$632$	42.2765	+	24.4084i	1.68167	+	0.970913i
$633$	3.26796	−	1.88676i	0.129890	−	0.0749918i
$634$	0.619405	+	1.07284i	0.0245997	+	0.0426080i
$635$	1.39970	−	2.42435i	0.0555454	−	0.0962075i
$636$	29.4128			1.16629
$637$	−6.82060	+	47.1198i	−0.270242	+	1.86695i
$638$		−	4.37738i		−	0.173302i
$639$	−2.50333	+	4.33589i	−0.0990301	+	0.171525i
$640$	−24.6072	−	42.6209i	−0.972686	−	1.68474i
$641$	−4.02600	+	2.32441i	−0.159017	+	0.0918087i	−0.577397	−	0.816464i	$-0.695932\pi$
$641$	−4.02600	+	2.32441i	−0.159017	+	0.0918087i	0.418380	+	0.908272i	$0.362598\pi$
$642$	10.9454	−	18.9579i	0.431979	−	0.748210i
$643$	15.8839			0.626402			0.313201	−	0.949687i	$-0.398599\pi$
$643$	15.8839			0.626402			0.313201	+	0.949687i	$0.398599\pi$
$644$	47.2210	−	12.7021i	1.86077	−	0.500533i
$645$	7.92333			0.311981
$646$	−30.2979	+	52.4775i	−1.19206	+	2.06470i
$647$	−2.91855	+	1.68502i	−0.114740	+	0.0662451i	−0.556272	−	0.831001i	$-0.687769\pi$
$647$	−2.91855	+	1.68502i	−0.114740	+	0.0662451i	0.441532	+	0.897246i	$0.354435\pi$
$648$	−2.24263	−	3.88435i	−0.0880989	−	0.152592i
$649$	1.77342	−	3.07166i	0.0696130	−	0.120573i
$650$		−	12.8610i		−	0.504450i
$651$	18.9704	+	12.8527i	0.743510	+	0.503739i
$652$	−47.3855			−1.85576
$653$	23.1295	−	40.0615i	0.905128	−	1.56773i	0.0843827	−	0.996433i	$-0.473108\pi$
$653$	23.1295	−	40.0615i	0.905128	−	1.56773i	0.820745	−	0.571294i	$-0.193558\pi$
$654$	−0.806047	−	1.39611i	−0.0315189	−	0.0545924i
$655$	−44.4046	+	25.6370i	−1.73503	+	1.00172i
$656$	9.97406	+	5.75853i	0.389422	+	0.224833i
$657$		−	0.817399i		−	0.0318898i
$658$	−9.51910	−	19.6197i	−0.371093	−	0.764854i
$659$			1.39884i			0.0544910i	0.999629	+	0.0272455i	$0.00867358\pi$
$659$			1.39884i			0.0544910i	−0.999629	+	0.0272455i	$0.991326\pi$
$660$	5.29970	−	9.17935i	0.206291	−	0.357306i
$661$	5.30263	+	9.18443i	0.206248	+	0.357233i	0.950530	−	0.310633i	$-0.100541\pi$
$661$	5.30263	+	9.18443i	0.206248	+	0.357233i	−0.744281	+	0.667866i	$0.767208\pi$
$662$	−22.9604	−	39.7685i	−0.892380	−	1.54565i
$663$	16.0564	−	27.8105i	0.623578	−	1.08007i
$664$	69.2149			2.68606
$665$	30.3612	−	14.7307i	1.17736	−	0.571233i
$666$		−	10.0741i		−	0.390364i
$667$	7.45060	+	1.42479i	0.288488	+	0.0551681i
$668$	−0.369631	+	0.213407i	−0.0143015	+	0.00825695i
$669$	8.94355	+	15.4907i	0.345777	+	0.598904i
$670$	−32.0583	−	18.5089i	−1.23852	−	0.715060i
$671$			14.2561i			0.550351i
$672$	−2.02269	+	2.98546i	−0.0780269	+	0.115167i
$673$	−36.9524			−1.42441			−0.712204	−	0.701972i	$-0.752303\pi$
$673$	−36.9524			−1.42441			−0.712204	+	0.701972i	$0.752303\pi$
$674$	27.4674	+	15.8583i	1.05800	+	0.610838i
$675$	−0.676827	+	0.390766i	−0.0260511	+	0.0150406i
$676$	64.0912	+	111.009i	2.46505	+	4.26959i
$677$	−22.9098	+	39.6810i	−0.880497	+	1.52507i	−0.0297074	+	0.999559i	$0.509458\pi$
$677$	−22.9098	+	39.6810i	−0.880497	+	1.52507i	−0.850789	+	0.525507i	$0.823876\pi$
$678$	11.2311			0.431327
$679$	0.958676	−	13.3150i	0.0367906	−	0.510981i
$680$	50.9189			1.95265
$681$	−9.63794	−	5.56446i	−0.369327	−	0.213231i
$682$	−11.9844	−	20.7577i	−0.458908	−	0.794852i
$683$	−23.9748	−	41.5255i	−0.917369	−	1.58893i	−0.803396	−	0.595445i	$-0.796976\pi$
$683$	−23.9748	−	41.5255i	−0.917369	−	1.58893i	−0.113973	−	0.993484i	$-0.536358\pi$
$684$	−10.2215	+	17.7042i	−0.390829	+	0.676936i
$685$		−	15.8187i		−	0.604401i
$686$	33.1135	+	30.1887i	1.26428	+	1.15261i
$687$		−	3.08037i		−	0.117523i
$688$	−8.97306	−	5.18060i	−0.342095	−	0.197509i
$689$	25.9551	+	44.9556i	0.988811	+	1.71267i
$690$	21.1119	+	18.2401i	0.803717	+	0.694388i
$691$	32.4085	+	18.7110i	1.23288	+	0.711802i	0.967629	−	0.252378i	$-0.0812127\pi$
$691$	32.4085	+	18.7110i	1.23288	+	0.711802i	0.265248	+	0.964180i	$0.414546\pi$
$692$		−	52.0496i		−	1.97863i
$693$	−3.01852	−	0.217333i	−0.114664	−	0.00825581i
$694$	−52.1409			−1.97924
$695$	−27.9200	−	16.1196i	−1.05906	−	0.611451i
$696$	6.14391	−	3.54719i	0.232884	−	0.134456i
$697$	14.9768	−	8.64683i	0.567285	−	0.327522i
$698$	−17.4874	−	10.0964i	−0.661909	−	0.382154i
$699$			4.88034i			0.184591i
$700$	−6.59715	−	4.46966i	−0.249349	−	0.168937i
$701$		−	15.5586i		−	0.587639i	−0.955861	−	0.293819i	$-0.905074\pi$
$701$		−	15.5586i		−	0.587639i	0.955861	−	0.293819i	$-0.0949265\pi$
$702$	8.22807	−	14.2514i	0.310548	−	0.537886i
$703$	−19.1281	+	11.0436i	−0.721428	+	0.416517i
$704$	9.49621	−	5.48264i	0.357902	−	0.206635i
$705$	4.09561	−	7.09380i	0.154250	−	0.267168i
$706$		−	3.73334i		−	0.140506i
$707$	−5.09231	−	10.4957i	−0.191516	−	0.394730i
$708$	11.9500			0.449107
$709$	−10.1843	−	5.87992i	−0.382480	−	0.220825i	0.296417	−	0.955059i	$-0.404208\pi$
$709$	−10.1843	−	5.87992i	−0.382480	−	0.220825i	−0.678897	+	0.734234i	$0.737542\pi$
$710$	−14.5633	−	25.2243i	−0.546550	−	0.946652i
$711$	9.42565	−	5.44190i	0.353490	−	0.204087i
$712$	−40.2194	+	69.6621i	−1.50729	+	2.61070i
$713$	39.2317	−	13.6419i	1.46924	−	0.510895i
$714$	−13.1929	−	27.1916i	−0.493730	−	1.01762i
$715$	18.7067			0.699592
$716$	34.7529	−	60.1938i	1.29878	−	2.24955i
$717$	19.2303	−	11.1026i	0.718170	−	0.414636i
$718$	−32.6329	+	18.8406i	−1.21785	+	0.703126i
$719$	12.8005	+	7.39039i	0.477379	+	0.275615i	0.719324	−	0.694675i	$-0.244452\pi$
$719$	12.8005	+	7.39039i	0.477379	+	0.275615i	−0.241944	+	0.970290i	$0.577785\pi$
$720$	7.56041			0.281760
$721$	−29.7236	−	20.1382i	−1.10697	−	0.749985i
$722$	22.1111			0.822891
$723$	14.9800	+	8.64871i	0.557112	+	0.321649i
$724$	48.2625	+	83.5930i	1.79366	+	3.10671i
$725$	−0.618078	−	1.07054i	−0.0229548	−	0.0397590i
$726$	−20.3070	−	11.7243i	−0.753665	−	0.435128i
$727$	5.54422			0.205624			0.102812	−	0.994701i	$-0.467216\pi$
$727$	5.54422			0.205624			0.102812	+	0.994701i	$0.467216\pi$
$728$	80.5049	+	5.79634i	2.98371	+	0.214827i
$729$	−1.00000			−0.0370370
$730$	4.11819	+	2.37764i	0.152421	+	0.0880003i
$731$	−13.4737	+	7.77904i	−0.498342	+	0.287718i
$732$	−41.5963	+	24.0156i	−1.53744	+	0.887643i
$733$	1.94680	−	3.37195i	0.0719066	−	0.124546i	−0.827830	−	0.560979i	$-0.810425\pi$
$733$	1.94680	−	3.37195i	0.0719066	−	0.124546i	0.899737	+	0.436433i	$0.143758\pi$
$734$	6.84546			0.252671
$735$	−2.41121	+	16.6578i	−0.0889390	+	0.614431i
$736$	2.14689	+	6.17406i	0.0791354	+	0.227579i
$737$	3.63921	−	6.30330i	0.134052	−	0.232185i
$738$	7.67481	−	4.43105i	0.282514	−	0.163109i
$739$	−6.44990	−	11.1716i	−0.237263	−	0.410952i	0.722665	−	0.691199i	$-0.242917\pi$
$739$	−6.44990	−	11.1716i	−0.237263	−	0.410952i	−0.959928	+	0.280247i	$0.909584\pi$
$740$	33.4142	+	19.2917i	1.22833	+	0.709176i
$741$	−36.0796			−1.32542
$742$	48.7294	+	3.50851i	1.78891	+	0.128801i
$743$		−	11.4769i		−	0.421048i	−0.977589	−	0.210524i	$-0.932483\pi$
$743$		−	11.4769i		−	0.421048i	0.977589	−	0.210524i	$-0.0675170\pi$
$744$	19.4231	−	33.6417i	0.712084	−	1.23337i
$745$	−29.9999	+	17.3204i	−1.09911	+	0.634572i
$746$	61.0461	−	35.2450i	2.23506	−	1.29041i
$747$	7.71582	−	13.3642i	0.282307	−	0.488970i
$748$			20.8128i			0.760990i
$749$	13.4269	−	19.8179i	0.490609	−	0.724131i
$750$			24.5412i			0.896118i
$751$	−32.4210	−	18.7183i	−1.18306	−	0.683040i	−0.226340	−	0.974048i	$-0.572676\pi$
$751$	−32.4210	−	18.7183i	−1.18306	−	0.683040i	−0.956721	+	0.291008i	$0.906009\pi$
$752$	−9.27644	+	5.35576i	−0.338277	+	0.195304i
$753$	−4.34797	+	2.51030i	−0.158449	+	0.0914804i
$754$	22.5416	+	13.0144i	0.820917	+	0.473957i
$755$	7.85091			0.285724
$756$	−4.45083	−	9.17353i	−0.161875	−	0.333638i
$757$			5.60256i			0.203628i	0.994803	+	0.101814i	$0.0324647\pi$
$757$			5.60256i			0.203628i	−0.994803	+	0.101814i	$0.967535\pi$
$758$	−56.7060	−	32.7392i	−2.05965	−	1.18914i
$759$	−3.58636	+	4.15102i	−0.130177	+	0.150672i
$760$	−28.6044	−	49.5442i	−1.03759	−	1.79716i
$761$	8.44160	+	4.87376i	0.306008	+	0.176674i	0.645139	−	0.764065i	$-0.276800\pi$
$761$	8.44160	+	4.87376i	0.306008	+	0.176674i	−0.339131	+	0.940739i	$0.610133\pi$
$762$			2.81685i			0.102044i
$763$	−0.769520	−	1.58605i	−0.0278585	−	0.0574187i
$764$			7.65829i			0.277067i
$765$	5.67625	−	9.83155i	0.205225	−	0.355460i
$766$	−35.9852	−	62.3281i	−1.30020	−	2.25201i
$767$	10.5451	+	18.2647i	0.380763	+	0.659501i
$768$	26.2826	+	15.1743i	0.948391	+	0.547554i
$769$	−33.3000			−1.20083			−0.600415	−	0.799689i	$-0.704998\pi$
$769$	−33.3000			−1.20083			−0.600415	+	0.799689i	$0.704998\pi$
$770$	9.87518	−	14.5756i	0.355877	−	0.525269i
$771$	−18.0236			−0.649104
$772$	31.8127	−	55.1012i	1.14496	−	1.98314i
$773$	2.26626	+	3.92528i	0.0815118	+	0.141183i	0.903900	−	0.427745i	$-0.140692\pi$
$773$	2.26626	+	3.92528i	0.0815118	+	0.141183i	−0.822388	+	0.568927i	$0.807358\pi$
$774$	−6.90457	+	3.98635i	−0.248180	+	0.143287i
$775$	−5.86189	−	3.38436i	−0.210565	−	0.121570i
$776$	−22.6309			−0.812401
$777$	0.791125	−	10.9879i	0.0283815	−	0.394187i
$778$		−	8.96832i		−	0.321530i
$779$	−16.8268	−	9.71495i	−0.602882	−	0.348074i
$780$	31.5131	+	54.5823i	1.12835	+	1.95436i
$781$	4.95960	−	2.86343i	0.177468	−	0.102461i
$782$	−53.8089	−	10.2900i	−1.92420	−	0.367968i
$783$		−	1.58171i		−	0.0565257i
$784$	13.6222	−	17.2881i	0.486507	−	0.617434i
$785$	4.00699			0.143016
$786$	25.7968	−	44.6813i	0.920140	−	1.59373i
$787$	21.5140	+	37.2634i	0.766893	+	1.32830i	0.939240	+	0.343261i	$0.111532\pi$
$787$	21.5140	+	37.2634i	0.766893	+	1.32830i	−0.172347	+	0.985036i	$0.555135\pi$
$788$	−5.98545	−	10.3671i	−0.213223	−	0.369313i
$789$	−6.68544	+	11.5795i	−0.238008	+	0.412242i
$790$			63.3173i			2.25273i
$791$	12.2498	+	0.881982i	0.435552	+	0.0313597i
$792$			5.13046i			0.182303i
$793$	−73.4127	−	42.3848i	−2.60696	−	1.50513i
$794$	−60.9139	+	35.1686i	−2.16175	+	1.24809i
$795$	9.17564	+	15.8927i	0.325426	+	0.563655i
$796$	−5.73344	+	9.93061i	−0.203216	+	0.351981i
$797$	−10.4818			−0.371284			−0.185642	−	0.982617i	$-0.559436\pi$
$797$	−10.4818			−0.371284			−0.185642	+	0.982617i	$0.559436\pi$
$798$	−19.0462	+	28.1119i	−0.674229	+	0.995151i
$799$			16.0841i			0.569014i
$800$	0.532611	−	0.922509i	0.0188306	−	0.0326156i
$801$	8.96702	+	15.5313i	0.316834	+	0.548773i
$802$	42.8168	−	24.7203i	1.51191	−	0.872904i
$803$	−0.467490	+	0.809717i	−0.0164974	+	0.0285743i
$804$	24.5223			0.864834
$805$	21.5944	+	21.5524i	0.761104	+	0.759623i
$806$	142.524			5.02019
$807$	−15.7630	+	27.3022i	−0.554882	+	0.961084i
$808$	−17.1271	+	9.88833i	−0.602529	+	0.347870i
$809$	−15.1799	−	26.2924i	−0.533697	−	0.924391i	−0.999225	−	0.0393575i	$-0.987469\pi$
$809$	−15.1799	−	26.2924i	−0.533697	−	0.924391i	0.465528	−	0.885033i	$-0.345864\pi$
$810$	2.90878	−	5.03816i	0.102204	−	0.177023i
$811$		−	37.2155i		−	1.30681i	−0.757006	−	0.653407i	$-0.773339\pi$
$811$		−	37.2155i		−	1.30681i	0.757006	−	0.653407i	$-0.226661\pi$
$812$	14.5099	−	7.03992i	0.509196	−	0.247053i
$813$	10.6988			0.375222
$814$	−5.76162	+	9.97943i	−0.201945	+	0.349779i
$815$	−14.7824	−	25.6039i	−0.517806	−	0.896866i
$816$	−12.8565	+	7.42273i	−0.450069	+	0.259848i
$817$	15.1380	+	8.73995i	0.529613	+	0.305772i
$818$		−	0.844202i		−	0.0295168i
$819$	10.0935	−	14.8979i	0.352697	−	0.520576i
$820$			33.9415i			1.18529i
$821$	15.6073	−	27.0327i	0.544700	−	0.943448i	−0.453926	−	0.891039i	$-0.649977\pi$
$821$	15.6073	−	27.0327i	0.544700	−	0.943448i	0.998626	−	0.0524082i	$-0.0166897\pi$
$822$	7.95863	+	13.7848i	0.277589	+	0.480799i
$823$	−0.357986	−	0.620051i	−0.0124786	−	0.0216136i	0.859719	−	0.510768i	$-0.170639\pi$
$823$	−0.357986	−	0.620051i	−0.0124786	−	0.0216136i	−0.872197	+	0.489154i	$0.837306\pi$
$824$	−30.4328	+	52.7112i	−1.06018	+	1.83628i
$825$	0.893954			0.0311235
$826$	19.7980	+	1.42545i	0.688859	+	0.0495978i
$827$			16.7957i			0.584044i	0.956412	+	0.292022i	$0.0943280\pi$
$827$			16.7957i			0.584044i	−0.956412	+	0.292022i	$0.905672\pi$
$828$	−18.1533	−	3.47149i	−0.630872	−	0.120643i
$829$	−26.8983	+	15.5298i	−0.934217	+	0.539371i	−0.888143	−	0.459567i	$-0.848004\pi$
$829$	−26.8983	+	15.5298i	−0.934217	+	0.539371i	−0.0460744	+	0.998938i	$0.514671\pi$
$830$	44.8873	+	77.7471i	1.55806	+	2.69864i
$831$	18.5861	+	10.7307i	0.644746	+	0.372244i
$832$			65.2018i			2.26047i
$833$	−12.2541	−	30.6940i	−0.424580	−	1.06348i
$834$	32.4401			1.12331
$835$	−0.230621	−	0.133149i	−0.00798096	−	0.00460781i
$836$	20.2509	−	11.6918i	0.700391	−	0.404371i
$837$	−4.33042	−	7.50051i	−0.149681	−	0.259255i
$838$	33.8574	−	58.6427i	1.16958	−	2.02578i
$839$	14.7416			0.508936			0.254468	−	0.967081i	$-0.418100\pi$
$839$	14.7416			0.508936			0.254468	+	0.967081i	$0.418100\pi$
$840$	28.4600	+	2.04912i	0.981965	+	0.0707014i
$841$	−26.4982			−0.913731
$842$	51.8218	+	29.9193i	1.78590	+	1.03109i
$843$	−3.10403	−	5.37633i	−0.106908	−	0.185171i
$844$	−7.27122	−	12.5941i	−0.250286	−	0.433508i
$845$	−39.9879	+	69.2610i	−1.37562	+	2.38265i
$846$			8.24227i			0.283375i
$847$	−21.2282	−	14.3824i	−0.729410	−	0.494186i
$848$		−	23.9977i		−	0.824083i
$849$	10.6607	+	6.15498i	0.365876	+	0.211238i
$850$	4.46382	+	7.73156i	0.153108	+	0.265190i
$851$	−15.1103	−	13.0549i	−0.517975	−	0.447515i
$852$	16.7098	+	9.64738i	0.572467	+	0.330514i
$853$			23.7091i			0.811783i	0.913921	+	0.405891i	$0.133039\pi$
$853$			23.7091i			0.811783i	−0.913921	+	0.405891i	$0.866961\pi$
$854$	−71.7790	+	34.8258i	−2.45623	+	1.19172i
$855$	−12.7548			−0.436206
$856$	−35.1446	−	20.2908i	−1.20122	−	0.693524i
$857$	22.6558	−	13.0803i	0.773906	−	0.446815i	−0.0603600	−	0.998177i	$-0.519225\pi$
$857$	22.6558	−	13.0803i	0.773906	−	0.446815i	0.834266	+	0.551362i	$0.185892\pi$
$858$	−16.3015	+	9.41166i	−0.556523	+	0.321309i
$859$	3.87240	+	2.23573i	0.132125	+	0.0762821i	0.564605	−	0.825361i	$-0.309028\pi$
$859$	3.87240	+	2.23573i	0.132125	+	0.0762821i	−0.432481	+	0.901643i	$0.642362\pi$
$860$		−	30.5351i		−	1.04124i
$861$	8.71891	−	4.23026i	0.297140	−	0.144167i
$862$		−	52.4850i		−	1.78765i
$863$	0.281597	−	0.487740i	0.00958567	−	0.0166029i	−0.861193	−	0.508278i	$-0.830282\pi$
$863$	0.281597	−	0.487740i	0.00958567	−	0.0166029i	0.870778	+	0.491676i	$0.163615\pi$
$864$	1.18039	−	0.681496i	0.0401575	−	0.0231850i
$865$	28.1241	−	16.2374i	0.956247	−	0.552089i
$866$	−7.37810	+	12.7792i	−0.250718	+	0.434256i
$867$			5.29151i			0.179709i
$868$	49.5322	−	73.1087i	1.68123	−	2.48147i
$869$	−12.4494			−0.422318
$870$	7.96890	+	4.60085i	0.270171	+	0.155983i
$871$	21.6395	+	37.4807i	0.733226	+	1.26998i
$872$	−2.58815	+	1.49427i	−0.0876457	+	0.0506023i
$873$	−2.52281	+	4.36963i	−0.0853840	+	0.147889i
$874$	20.2157	+	58.1367i	0.683807	+	1.96650i
$875$	−1.92723	+	26.7672i	−0.0651524	+	0.904896i
$876$	−3.15011			−0.106432
$877$	−2.65923	+	4.60592i	−0.0897958	+	0.155531i	−0.907425	−	0.420215i	$-0.861955\pi$
$877$	−2.65923	+	4.60592i	−0.0897958	+	0.155531i	0.817629	+	0.575746i	$0.195288\pi$
$878$	25.8250	−	14.9101i	0.871552	−	0.503191i
$879$	8.91537	−	5.14729i	0.300708	−	0.173614i
$880$	−7.48935	−	4.32398i	−0.252466	−	0.145761i
$881$	−13.4765			−0.454036			−0.227018	−	0.973891i	$-0.572898\pi$
$881$	−13.4765			−0.454036			−0.227018	+	0.973891i	$0.572898\pi$
$882$	−6.27960	−	15.7291i	−0.211445	−	0.529626i
$883$	−38.2581			−1.28749			−0.643744	−	0.765241i	$-0.722620\pi$
$883$	−38.2581			−1.28749			−0.643744	+	0.765241i	$0.722620\pi$
$884$	−107.177	−	61.8785i	−3.60474	−	2.08120i
$885$	3.72791	+	6.45694i	0.125312	+	0.217048i
$886$	−17.6316	−	30.5388i	−0.592345	−	1.02597i
$887$	0.549748	+	0.317397i	0.0184587	+	0.0106572i	0.509201	−	0.860648i	$-0.329941\pi$
$887$	0.549748	+	0.317397i	0.0184587	+	0.0106572i	−0.490742	+	0.871305i	$0.663274\pi$
$888$	−18.6756			−0.626712
$889$	−0.221209	+	3.07235i	−0.00741910	+	0.103043i
$890$	−104.332			−3.49723
$891$	0.990601	+	0.571924i	0.0331864	+	0.0191602i
$892$	59.6983	−	34.4668i	1.99885	−	1.15403i
$893$	15.6499	−	9.03545i	0.523703	−	0.302360i
$894$	17.4284	−	30.1868i	0.582892	−	1.00960i
$895$	43.3661			1.44957
$896$	44.8321	+	30.3743i	1.49773	+	1.01474i
$897$	−10.7133	−	30.8096i	−0.357708	−	1.02870i
$898$	−23.1622	+	40.1181i	−0.772933	+	1.33876i
$899$	11.8636	−	6.84946i	0.395674	−	0.228442i
$900$	1.50594	+	2.60837i	0.0501981	+	0.0869456i
$901$	−31.2065	−	18.0171i	−1.03964	−	0.600236i
$902$	−10.1369			−0.337522
$903$	−7.84388	+	3.80571i	−0.261028	+	0.126646i
$904$		−	20.8204i		−	0.692477i
$905$	−30.1120	+	52.1555i	−1.00096	+	1.73371i
$906$	−6.84146	+	3.94992i	−0.227292	+	0.131227i
$907$	−36.5902	+	21.1253i	−1.21496	+	0.701456i	−0.963835	−	0.266500i	$-0.914133\pi$
$907$	−36.5902	+	21.1253i	−1.21496	+	0.701456i	−0.251122	+	0.967955i	$0.580800\pi$
$908$	−21.4445	+	37.1429i	−0.711659	+	1.23263i
$909$			4.40925i			0.146246i
$910$	45.6982	+	94.1877i	1.51488	+	3.12229i
$911$		−	3.22479i		−	0.106842i	−0.998572	−	0.0534211i	$-0.982987\pi$
$911$		−	3.22479i		−	0.106842i	0.998572	−	0.0534211i	$-0.0170126\pi$
$912$	14.4447	+	8.33964i	0.478311	+	0.276153i
$913$	−15.2866	+	8.82572i	−0.505913	+	0.292089i
$914$	−76.1301	+	43.9537i	−2.51816	+	1.45386i
$915$	−25.9528	−	14.9839i	−0.857974	−	0.495351i
$916$	−11.8712			−0.392235
$917$	31.6455	−	46.7082i	1.04502	−	1.54244i
$918$			11.4232i			0.377023i
$919$	21.4672	+	12.3941i	0.708139	+	0.408844i	0.810372	−	0.585916i	$-0.199265\pi$
$919$	21.4672	+	12.3941i	0.708139	+	0.408844i	−0.102232	+	0.994761i	$0.532599\pi$
$920$	33.8139	−	39.1377i	1.11481	−	1.29033i
$921$	−6.80429	−	11.7854i	−0.224209	−	0.388341i
$922$	19.3392	+	11.1655i	0.636901	+	0.367715i
$923$			34.0530i			1.12087i
$924$	−0.837564	+	11.6328i	−0.0275538	+	0.382693i
$925$			3.25412i			0.106995i
$926$	−48.6696	+	84.2981i	−1.59938	+	2.77021i
$927$	6.78507	+	11.7521i	0.222851	+	0.385989i
$928$	1.07793	+	1.86703i	0.0353847	+	0.0612882i
$929$	−40.7393	−	23.5209i	−1.33661	−	0.771695i	−0.350310	−	0.936634i	$-0.613924\pi$
$929$	−40.7393	−	23.5209i	−1.33661	−	0.771695i	−0.986304	+	0.164939i	$0.947257\pi$
$930$	50.3850			1.65219
$931$	−22.9814	+	29.1660i	−0.753185	+	0.955878i
$932$	18.8079			0.616075
$933$	−1.80476	+	3.12593i	−0.0590851	+	0.102338i
$934$	−17.5736	−	30.4383i	−0.575024	−	0.995971i
$935$	−11.2458	+	6.49276i	−0.367777	+	0.212336i
$936$	−26.4196	−	15.2534i	−0.863552	−	0.498572i
$937$	−55.0744			−1.79920			−0.899602	−	0.436712i	$-0.856143\pi$
$937$	−55.0744			−1.79920			−0.899602	+	0.436712i	$0.856143\pi$
$938$	40.6270	+	2.92514i	1.32652	+	0.0955092i
$939$			3.78804i			0.123618i
$940$	−27.3382	−	15.7837i	−0.891675	−	0.514809i
$941$	−10.4642	−	18.1245i	−0.341122	−	0.590841i	0.643519	−	0.765430i	$-0.277474\pi$
$941$	−10.4642	−	18.1245i	−0.341122	−	0.590841i	−0.984641	+	0.174589i	$0.944140\pi$
$942$	−3.49178	+	2.01598i	−0.113768	+	0.0656842i
$943$	3.29945	−	17.2537i	0.107445	−	0.561857i
$944$		−	9.74986i		−	0.317331i
$945$	3.56827	−	5.26671i	0.116076	−	0.171326i
$946$	9.11956			0.296503
$947$	−16.8910	+	29.2561i	−0.548884	+	0.950696i	0.449467	+	0.893297i	$0.351614\pi$
$947$	−16.8910	+	29.2561i	−0.548884	+	0.950696i	−0.998351	+	0.0573986i	$0.981719\pi$
$948$	−20.9721	−	36.3248i	−0.681143	−	1.17977i
$949$	−2.77979	−	4.81474i	−0.0902359	−	0.156293i
$950$	5.01522	−	8.68661i	0.162715	−	0.281831i
$951$		−	0.512018i		−	0.0166033i
$952$	−50.4084	+	24.4572i	−1.63374	+	0.792663i
$953$		−	33.0167i		−	1.06952i	−0.845005	−	0.534758i	$-0.820403\pi$
$953$		−	33.0167i		−	1.06952i	0.845005	−	0.534758i	$-0.179597\pi$
$954$	−15.9917	−	9.23283i	−0.517751	−	0.298924i
$955$	−4.13802	+	2.38909i	−0.133903	+	0.0773090i
$956$	−42.7876	−	74.1103i	−1.38385	−	2.39690i
$957$	−0.904617	+	1.56684i	−0.0292421	+	0.0506488i
$958$	−84.4754			−2.72928
$959$	7.59798	+	15.6601i	0.245352	+	0.505690i
$960$			23.0501i			0.743939i
$961$	22.0051	−	38.1139i	0.709841	−	1.22948i
$962$	−34.2598	−	59.3397i	−1.10458	−	1.91319i
$963$	−7.83558	+	4.52388i	−0.252498	+	0.145780i
$964$	33.3306	−	57.7303i	1.07351	−	1.85937i
$965$	39.6972			1.27790
$966$	−29.6613	−	7.91677i	−0.954335	−	0.254718i
$967$	−17.5469			−0.564269			−0.282135	−	0.959375i	$-0.591042\pi$
$967$	−17.5469			−0.564269			−0.282135	+	0.959375i	$0.591042\pi$
$968$	−21.7347	+	37.6456i	−0.698580	+	1.20998i
$969$	21.6897	−	12.5226i	0.696773	−	0.402282i
$970$	−14.6766	−	25.4206i	−0.471237	−	0.816206i
$971$	18.1418	−	31.4225i	0.582197	−	1.00839i	−0.413022	−	0.910721i	$-0.635527\pi$
$971$	18.1418	−	31.4225i	0.582197	−	1.00839i	0.995219	−	0.0976733i	$-0.0311400\pi$
$972$			3.85382i			0.123611i
$973$	35.3825	+	2.54754i	1.13431	+	0.0816703i
$974$	−0.251180			−0.00804833
$975$	−2.65782	+	4.60347i	−0.0851182	+	0.147429i
$976$	19.5942	+	33.9381i	0.627193	+	1.08633i
$977$	−42.0927	+	24.3022i	−1.34666	+	0.777497i	−0.987776	−	0.155883i	$-0.950178\pi$
$977$	−42.0927	+	24.3022i	−1.34666	+	0.777497i	−0.358889	+	0.933380i	$0.616844\pi$
$978$	25.7635	+	14.8746i	0.823825	+	0.475636i
$979$		−	20.5138i		−	0.655624i
$980$	64.1961	+	9.29239i	2.05067	+	0.296835i
$981$			0.666301i			0.0212734i
$982$	18.5680	−	32.1607i	0.592528	−	1.02629i
$983$	16.5900	+	28.7347i	0.529139	+	0.916496i	0.999422	+	0.0339805i	$0.0108184\pi$
$983$	16.5900	+	28.7347i	0.529139	+	0.916496i	−0.470283	+	0.882516i	$0.655848\pi$
$984$	−8.21439	−	14.2277i	−0.261865	−	0.453564i
$985$	3.73445	−	6.46826i	0.118990	−	0.206096i
$986$	−18.0682			−0.575410
$987$	−0.647269	+	8.98986i	−0.0206028	+	0.286151i
$988$			139.044i			4.42358i
$989$	−2.96832	+	15.5221i	−0.0943869	+	0.493574i
$990$	−5.76289	+	3.32720i	−0.183157	+	0.105745i
$991$	−9.20471	−	15.9430i	−0.292397	−	0.506447i	0.681979	−	0.731372i	$-0.261120\pi$
$991$	−9.20471	−	15.9430i	−0.292397	−	0.506447i	−0.974376	+	0.224925i	$0.927786\pi$
$992$	10.2231	+	5.90233i	0.324585	+	0.187399i
$993$			18.9797i			0.602302i
$994$	26.5329	+	17.9764i	0.841573	+	0.570177i
$995$	−7.15443			−0.226811
$996$	−51.5032	−	29.7354i	−1.63194	−	0.942202i
$997$	16.8062	−	9.70305i	0.532257	−	0.307299i	−0.209678	−	0.977770i	$-0.567242\pi$
$997$	16.8062	−	9.70305i	0.532257	−	0.307299i	0.741935	+	0.670472i	$0.233908\pi$
$998$	30.6977	+	53.1699i	0.971717	+	1.68306i
$999$	−2.08189	+	3.60593i	−0.0658680	+	0.114087i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.j.a.229.4	yes	64
7.3	odd	6	inner	483.2.j.a.367.3	yes	64
23.22	odd	2	inner	483.2.j.a.229.3	✓	64
161.45	even	6	inner	483.2.j.a.367.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.j.a.229.3	✓	64	23.22	odd	2	inner
483.2.j.a.229.4	yes	64	1.1	even	1	trivial
483.2.j.a.367.3	yes	64	7.3	odd	6	inner
483.2.j.a.367.4	yes	64	161.45	even	6	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20973 + 2.09532i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.92691 - 3.33751i) q^{4} +(1.20224 - 2.08234i) q^{5} +2.41947i q^{6} +(-0.190002 + 2.63892i) q^{7} +4.48526 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.20973 + 2.09532i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.92691 - 3.33751i) q^{4} +(1.20224 - 2.08234i) q^{5} +2.41947i q^{6} +(-0.190002 + 2.63892i) q^{7} +4.48526 q^{8} +(0.500000 - 0.866025i) q^{9} +(2.90878 + 5.03816i) q^{10} +(-0.990601 + 0.571924i) q^{11} +(-3.33751 - 1.92691i) q^{12} -6.80155i q^{13} +(-5.29953 - 3.59051i) q^{14} -2.40448i q^{15} +(-1.57215 + 2.72304i) q^{16} +(2.36069 + 4.08884i) q^{17} +(1.20973 + 2.09532i) q^{18} +(2.65230 - 4.59392i) q^{19} -9.26644 q^{20} +(1.15491 + 2.38037i) q^{21} -2.76750i q^{22} +(4.71048 + 0.900791i) q^{23} +(3.88435 - 2.24263i) q^{24} +(-0.390766 - 0.676827i) q^{25} +(14.2514 + 8.22807i) q^{26} -1.00000i q^{27} +(9.17353 - 4.45083i) q^{28} +1.58171 q^{29} +(5.03816 + 2.90878i) q^{30} +(7.50051 - 4.33042i) q^{31} +(0.681496 + 1.18039i) q^{32} +(-0.571924 + 0.990601i) q^{33} -11.4232 q^{34} +(5.26671 + 3.56827i) q^{35} -3.85382 q^{36} +(-3.60593 - 2.08189i) q^{37} +(6.41716 + 11.1148i) q^{38} +(-3.40078 - 5.89032i) q^{39} +(5.39236 - 9.33985i) q^{40} -3.66283i q^{41} +(-6.38478 - 0.459704i) q^{42} +3.29523i q^{43} +(3.81760 + 2.20409i) q^{44} +(-1.20224 - 2.08234i) q^{45} +(-7.58587 + 8.78024i) q^{46} +(2.95024 + 1.70332i) q^{47} +3.14430i q^{48} +(-6.92780 - 1.00280i) q^{49} +1.89089 q^{50} +(4.08884 + 2.36069i) q^{51} +(-22.7002 + 13.1060i) q^{52} +(-6.60961 + 3.81606i) q^{53} +(2.09532 + 1.20973i) q^{54} +2.75036i q^{55} +(-0.852209 + 11.8362i) q^{56} -5.30461i q^{57} +(-1.91345 + 3.31419i) q^{58} +(-2.68538 + 1.55040i) q^{59} +(-8.02498 + 4.63322i) q^{60} +(6.23164 - 10.7935i) q^{61} +20.9546i q^{62} +(2.19037 + 1.48401i) q^{63} -9.58632 q^{64} +(-14.1632 - 8.17710i) q^{65} +(-1.38375 - 2.39673i) q^{66} +(-5.51061 + 3.18155i) q^{67} +(9.09770 - 15.7577i) q^{68} +(4.52979 - 1.57513i) q^{69} +(-13.8480 + 6.71878i) q^{70} -5.00666 q^{71} +(2.24263 - 3.88435i) q^{72} +(0.707889 - 0.408700i) q^{73} +(8.72444 - 5.03706i) q^{74} +(-0.676827 - 0.390766i) q^{75} -20.4430 q^{76} +(-1.32105 - 2.72278i) q^{77} +16.4561 q^{78} +(9.42565 + 5.44190i) q^{79} +(3.78021 + 6.54751i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.67481 + 4.43105i) q^{82} +15.4316 q^{83} +(5.71910 - 8.44130i) q^{84} +11.3525 q^{85} +(-6.90457 - 3.98635i) q^{86} +(1.36980 - 0.790854i) q^{87} +(-4.44311 + 2.56523i) q^{88} +(-8.96702 + 15.5313i) q^{89} +5.81756 q^{90} +(17.9488 + 1.29231i) q^{91} +(-6.07027 - 17.4570i) q^{92} +(4.33042 - 7.50051i) q^{93} +(-7.13801 + 4.12113i) q^{94} +(-6.37741 - 11.0460i) q^{95} +(1.18039 + 0.681496i) q^{96} -5.04561 q^{97} +(10.4820 - 13.3028i) q^{98} +1.14385i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50} - 108 q^{52} - 24 q^{58} + 36 q^{59} + 168 q^{64} - 40 q^{70} - 16 q^{71} - 12 q^{72} + 48 q^{73} - 48 q^{75} - 32 q^{78} - 32 q^{81} - 24 q^{82} + 88 q^{85} + 36 q^{87} + 152 q^{92} + 24 q^{93} - 108 q^{94} - 44 q^{95} + 60 q^{96} + 112 q^{98}+O(q^{100}) \) 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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