LMFDB - Embedded newform 483.2.j.a.229.3

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			229.3
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-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} +(-3.13535 - 3.62900i) 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} +(11.3968 - 2.17943i) 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} - 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}+ \cdots + 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

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	$0.347358\pi$
$5$	−1.20224	+	2.08234i	−0.537658	+	0.931252i	−0.999030	+	0.0440445i	$0.985976\pi$
$6$			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	−0.343171	−	0.939273i	$-0.611501\pi$
$11$	0.990601	−	0.571924i	0.298677	−	0.172442i	0.641849	+	0.766831i	$0.278168\pi$
$12$	−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	$-0.972620\pi$
$17$	−2.36069	−	4.08884i	−0.572552	−	0.991690i	0.423750	−	0.905779i	$-0.360713\pi$
$18$	1.20973	+	2.09532i	0.285137	+	0.493872i
$19$	−2.65230	+	4.59392i	−0.608480	+	1.05392i	0.383011	+	0.923744i	$0.374887\pi$
$19$	−2.65230	+	4.59392i	−0.608480	+	1.05392i	−0.991491	+	0.130174i	$0.958446\pi$
$20$	9.26644			2.07204
$21$	−1.15491	−	2.38037i	−0.252023	−	0.519440i
$22$			2.76750i			0.590033i
$23$	−3.13535	−	3.62900i	−0.653765	−	0.756698i
$23$	−3.13535	−	3.62900i	−0.653765	−	0.756698i
$24$	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	0.766208	−	0.642592i	$-0.222141\pi$
$37$	3.60593	+	2.08189i	0.592812	+	0.342260i	−0.173397	+	0.984852i	$0.555474\pi$
$38$	−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	$-0.919155\pi$
$43$		−	3.29523i		−	0.502518i	0.967920	−	0.251259i	$-0.0808446\pi$
$44$	−3.81760	−	2.20409i	−0.575525	−	0.332279i
$45$	1.20224	+	2.08234i	0.179219	+	0.310417i
$46$	11.3968	−	2.17943i	1.68037	−	0.321340i
$47$	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	0.0281446	−	0.999604i	$-0.491040\pi$
$53$	6.60961	−	3.81606i	0.907899	−	0.524176i	0.879755	+	0.475428i	$0.157707\pi$
$54$	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	$0.460712\pi$
$61$	−6.23164	+	10.7935i	−0.797880	+	1.38197i	−0.920994	+	0.389576i	$0.872622\pi$
$62$			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	−0.124071	−	0.992273i	$-0.539595\pi$
$67$	5.51061	−	3.18155i	0.673228	−	0.388688i	0.797299	+	0.603585i	$0.206262\pi$
$68$	−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	−0.134907	−	0.990858i	$-0.543074\pi$
$79$	−9.42565	−	5.44190i	−1.06047	−	0.612262i	−0.925562	+	0.378596i	$0.876407\pi$
$80$	−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	$-0.821547\pi$
$83$	−15.4316			−1.69384			−0.846921	+	0.531718i	$0.821547\pi$
$84$	−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	$-0.433903\pi$
$89$	8.96702	−	15.5313i	0.950502	−	1.64632i	0.744341	−	0.667800i	$-0.232764\pi$
$90$	−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	$-0.417545\pi$
$97$	5.04561			0.512304			0.256152	+	0.966636i	$0.417545\pi$
$98$	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	$-0.600247\pi$
$103$	6.78507	−	11.7521i	0.668553	−	1.15797i	0.978309	−	0.207152i	$-0.0664193\pi$
$104$		−	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	0.828395	−	0.560144i	$-0.189254\pi$
$107$	7.83558	+	4.52388i	0.757494	+	0.437340i	−0.0709011	+	0.997483i	$0.522587\pi$
$108$	−3.33751	+	1.92691i	−0.321152	+	0.185417i
$109$	0.577034	−	0.333151i	0.0552698	−	0.0319100i	−0.472110	−	0.881539i	$-0.656508\pi$
$109$	0.577034	−	0.333151i	0.0552698	−	0.0319100i	0.527380	+	0.849629i	$0.323174\pi$
$110$	−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	$0.0700641\pi$
$113$			4.64196i			0.436679i	−0.975873	+	0.218340i	$0.929936\pi$
$114$	−11.1148	−	6.41716i	−1.04100	−	0.601022i
$115$	11.3263	−	2.16594i	1.05618	−	0.201975i
$116$	−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	−0.723231	−	0.690606i	$-0.757344\pi$
$137$	−5.69744	+	3.28942i	−0.486765	+	0.281034i	0.236467	+	0.971640i	$0.424011\pi$
$138$	8.78024	−	7.58587i	0.747423	−	0.645752i
$139$		−	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	0.914719	−	0.404090i	$-0.132412\pi$
$149$	12.4766	+	7.20340i	1.02213	+	0.590125i	0.107407	+	0.994215i	$0.465745\pi$
$150$	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	0.830859	−	0.556483i	$-0.187850\pi$
$157$	−0.833234	−	1.44320i	−0.0664993	−	0.115180i	−0.897358	+	0.441303i	$0.854516\pi$
$158$	22.8051	−	13.1665i	1.81427	−	1.04747i
$159$	3.81606	−	6.60961i	0.302633	−	0.524176i
$160$	−3.27729			−0.259093
$161$	−10.1724	+	7.58441i	−0.801694	+	0.597735i
$162$	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	$-0.119071\pi$
$181$	25.0465			1.86169			0.930847	+	0.365408i	$0.119071\pi$
$182$	24.4210	−	36.0450i	1.81021	−	2.67184i
$183$			12.4633i			0.921312i
$184$	−14.0628	−	16.2770i	−1.03673	−	1.19996i
$185$	−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	0.560968	−	0.827837i	$-0.310429\pi$
$191$	1.72096	+	0.993597i	0.124524	+	0.0718941i	−0.436444	+	0.899731i	$0.643762\pi$
$192$	−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	0.913927	−	0.405879i	$-0.133034\pi$
$199$	1.48773	+	2.57682i	0.105462	+	0.182666i	−0.808465	+	0.588545i	$0.799701\pi$
$200$	−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
$207$	−4.71048	+	0.900791i	−0.327401	+	0.0626093i
$208$	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	0.989460	−	0.144804i	$-0.0462551\pi$
$227$	5.56446	+	9.63794i	0.369327	+	0.639692i	−0.620134	+	0.784496i	$0.712922\pi$
$228$	17.7042	−	10.2215i	1.17249	−	0.676936i
$229$	−1.54019	+	2.66768i	−0.101778	+	0.176285i	−0.912417	−	0.409261i	$-0.865787\pi$
$229$	−1.54019	+	2.66768i	−0.101778	+	0.176285i	0.810639	+	0.585546i	$0.199120\pi$
$230$	−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	$-0.978576\pi$
$241$	−8.64871	−	14.9800i	−0.557112	−	0.964947i	0.440623	−	0.897692i	$-0.354757\pi$
$242$	−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	$-0.449351\pi$
$251$	5.02060			0.316897			0.158449	+	0.987367i	$0.449351\pi$
$252$	−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	−0.0985253	−	0.995135i	$-0.531413\pi$
$263$	11.5795	−	6.68544i	0.714024	−	0.412242i	0.812549	+	0.582893i	$0.198079\pi$
$264$	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
$276$	3.47149	+	18.1533i	0.208959	+	1.09270i
$277$	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	$0.0592838\pi$
$281$			6.20806i			0.370342i	−0.982706	+	0.185171i	$0.940716\pi$
$282$	−4.12113	+	7.13801i	−0.245410	+	0.425062i
$283$	−6.15498	−	10.6607i	−0.365876	−	0.633715i	0.623041	−	0.782189i	$-0.285897\pi$
$283$	−6.15498	−	10.6607i	−0.365876	−	0.633715i	−0.988916	+	0.148474i	$0.952564\pi$
$284$	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	$-0.597223\pi$
$293$	−10.2946			−0.601416			−0.300708	+	0.953716i	$0.597223\pi$
$294$	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
$299$	−24.6828	+	21.3252i	−1.42744	+	1.23327i
$300$			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	−0.807520	−	0.589840i	$-0.799191\pi$
$313$	1.89402	−	3.28054i	0.107056	−	0.185427i	0.914576	+	0.404413i	$0.132524\pi$
$314$	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
$322$	−3.58593	−	30.4894i	−0.199836	−	1.69911i
$323$	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	$0.116215\pi$
$337$			13.1089i			0.714088i	−0.934088	+	0.357044i	$0.883785\pi$
$338$	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
$345$	8.72585	−	7.53888i	0.469784	−	0.405880i
$346$	−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	0.0998953	−	0.994998i	$-0.468149\pi$
$359$	−13.4876	−	7.78709i	−0.711851	−	0.410987i	−0.811746	+	0.584011i	$0.801483\pi$
$360$	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	0.900583	−	0.434683i	$-0.143140\pi$
$367$	1.41466	+	2.45027i	0.0738448	+	0.127903i	−0.826739	+	0.562586i	$0.809806\pi$
$368$	14.8111	−	2.83236i	0.772084	−	0.147647i
$369$	−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	0.981497	−	0.191476i	$-0.0613276\pi$
$373$	25.2312	+	14.5672i	1.30642	+	0.754263i	0.324925	+	0.945740i	$0.394661\pi$
$374$	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	$-0.755373\pi$
$379$		−	27.0632i		−	1.39014i	0.718941	−	0.695071i	$-0.244627\pi$
$380$	−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	$-0.558540\pi$
$383$	14.8732	−	25.7611i	0.759984	−	1.31633i	0.942858	−	0.333194i	$-0.108127\pi$
$384$		−	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	−0.416408	−	0.909178i	$-0.636711\pi$
$389$	3.21012	−	1.85337i	0.162760	−	0.0939694i	0.579167	+	0.815209i	$0.303378\pi$
$390$	−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	0.871888	−	0.489705i	$-0.162895\pi$
$401$	17.6968	+	10.2173i	0.883736	+	0.510225i	0.0118475	+	0.999930i	$0.496229\pi$
$402$	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	$-0.260396\pi$
$419$	27.9875			1.36728			0.683639	+	0.729821i	$0.260396\pi$
$420$	−10.7019	−	22.0576i	−0.522201	−	1.07630i
$421$			24.7322i			1.20537i	0.797978	+	0.602686i	$0.205903\pi$
$421$			24.7322i			1.20537i	−0.797978	+	0.602686i	$0.794097\pi$
$422$	−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	0.0261234	−	0.999659i	$-0.491684\pi$
$431$	18.7865	−	10.8464i	0.904915	−	0.522453i	0.878792	+	0.477206i	$0.158350\pi$
$432$	2.72304	+	1.57215i	0.131012	+	0.0756401i
$433$	−6.09895			−0.293097			−0.146548	−	0.989204i	$-0.546816\pi$
$433$	−6.09895			−0.293097			−0.146548	+	0.989204i	$0.546816\pi$
$434$	55.2976	+	3.98142i	2.65437	+	0.191114i
$435$			3.80319i			0.182349i
$436$	−2.22379	−	1.28390i	−0.106500	−	0.0614878i
$437$	24.9872	−	4.77834i	1.19530	−	0.228579i
$438$	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	−0.472399	−	0.881385i	$-0.656612\pi$
$457$	−31.4656	−	18.1667i	−1.47190	−	0.849802i	−0.999501	+	0.0315831i	$0.989945\pi$
$458$	−3.72643	−	6.45436i	−0.174125	−	0.301593i
$459$	−4.08884	+	2.36069i	−0.190851	+	0.110188i
$460$	−29.0535	−	33.6279i	−1.35463	−	1.56791i
$461$		−	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	−0.647587	−	0.761991i	$-0.724222\pi$
$467$	7.26340	−	12.5806i	0.336110	−	0.582159i	0.983697	+	0.179832i	$0.0575553\pi$
$468$			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	$-0.872743\pi$
$479$	−17.4574	−	30.2372i	−0.797651	−	1.38157i	0.123492	−	0.992346i	$-0.460591\pi$
$480$	−2.83822	+	1.63865i	−0.129546	+	0.0747936i
$481$	14.1601	−	24.5259i	0.645643	−	1.11829i
$482$	41.8505			1.90624
$483$	−5.01731	+	11.6545i	−0.228296	+	0.530297i
$484$	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	$-0.698903\pi$
$503$	−26.2400			−1.16999			−0.584993	+	0.811039i	$0.698903\pi$
$504$	−9.82439	−	6.65616i	−0.437613	−	0.296489i
$505$		−	10.6020i		−	0.471781i
$506$	10.0433	−	8.67707i	0.446477	−	0.385743i
$507$	−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	0.908291	−	0.418339i	$-0.137388\pi$
$521$	2.09658	+	3.63139i	0.0918529	+	0.159094i	−0.816438	+	0.577433i	$0.804054\pi$
$522$	1.91345	+	3.31419i	0.0837493	+	0.145058i
$523$	−9.78853	+	16.9542i	−0.428022	+	0.741356i	−0.996697	−	0.0812059i	$-0.974123\pi$
$523$	−9.78853	+	16.9542i	−0.428022	+	0.741356i	0.568675	+	0.822562i	$0.307456\pi$
$524$			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
$529$	−3.33922	+	22.7563i	−0.145183	+	0.989405i
$530$	−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	−0.230003	−	0.973190i	$-0.573874\pi$
$557$	11.7486	−	6.78304i	0.497803	−	0.287407i	0.727806	+	0.685783i	$0.240540\pi$
$558$	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	0.803934	−	0.594718i	$-0.202736\pi$
$563$	−2.68298	−	4.64705i	−0.113074	−	0.195850i	−0.917008	+	0.398868i	$0.869403\pi$
$564$	−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	0.464756	−	0.885439i	$-0.346142\pi$
$569$	−1.66209	−	0.959610i	−0.0696786	−	0.0402289i	−0.534435	+	0.845210i	$0.679475\pi$
$570$	26.7254	−	15.4299i	1.11941	−	0.646289i
$571$	−25.4494	+	14.6932i	−1.06503	+	0.614893i	−0.926818	−	0.375510i	$-0.877467\pi$
$571$	−25.4494	+	14.6932i	−1.06503	+	0.614893i	−0.138208	+	0.990403i	$0.544134\pi$
$572$	−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
$598$	−14.8235	−	77.5162i	−0.606180	−	3.16987i
$599$	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	−0.234568	−	0.972100i	$-0.575368\pi$
$613$	12.1321	−	7.00446i	0.490010	−	0.282908i	0.724579	+	0.689192i	$0.242034\pi$
$614$	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	$0.281117\pi$
$617$			38.3891i			1.54549i	−0.634717	+	0.772744i	$0.718883\pi$
$618$	28.4338	+	16.4163i	1.14377	+	0.660359i
$619$	21.5526	+	37.3302i	0.866271	+	1.50043i	0.865780	+	0.500426i	$0.166823\pi$
$619$	21.5526	+	37.3302i	0.866271	+	1.50043i	0.000491575		1.00000i	$0.499844\pi$
$620$	69.5030	−	40.1276i	2.79131	−	1.61156i
$621$	−3.62900	+	3.13535i	−0.145627	+	0.125817i
$622$		−	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	$0.103129\pi$
$631$			15.9937i			0.636701i	−0.947973	+	0.318350i	$0.896871\pi$
$632$	−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	−0.418380	−	0.908272i	$-0.637402\pi$
$641$	4.02600	−	2.32441i	0.159017	−	0.0918087i	0.577397	+	0.816464i	$0.304068\pi$
$642$	−10.9454	+	18.9579i	−0.431979	+	0.748210i
$643$	−15.8839			−0.626402			−0.313201	−	0.949687i	$-0.601401\pi$
$643$	−15.8839			−0.626402			−0.313201	+	0.949687i	$0.601401\pi$
$644$	44.9142	+	19.3358i	1.76987	+	0.761938i
$645$	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	$-0.991326\pi$
$659$		−	1.39884i		−	0.0544910i	0.999629	−	0.0272455i	$-0.00867358\pi$
$660$	5.29970	−	9.17935i	0.206291	−	0.357306i
$661$	−5.30263	−	9.18443i	−0.206248	−	0.357233i	0.744281	−	0.667866i	$-0.232792\pi$
$661$	−5.30263	−	9.18443i	−0.206248	−	0.357233i	−0.950530	+	0.310633i	$0.899459\pi$
$662$	−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
$667$	−4.95920	−	5.74001i	−0.192021	−	0.222254i
$668$	−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	$-0.490542\pi$
$677$	22.9098	−	39.6810i	0.880497	−	1.52507i	0.850789	−	0.525507i	$-0.176124\pi$
$678$	−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
$690$	5.24041	+	27.4035i	0.199499	+	1.04323i
$691$	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	$0.0949265\pi$
$701$			15.5586i			0.587639i	−0.955861	+	0.293819i	$0.905074\pi$
$702$	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	0.678897	−	0.734234i	$-0.262458\pi$
$709$	10.1843	+	5.87992i	0.382480	+	0.220825i	−0.296417	+	0.955059i	$0.595792\pi$
$710$	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	$-0.532784\pi$
$727$	−5.54422			−0.205624			−0.102812	+	0.994701i	$0.532784\pi$
$728$	−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	−0.899737	−	0.436433i	$-0.856242\pi$
$733$	−1.94680	+	3.37195i	−0.0719066	+	0.124546i	0.827830	+	0.560979i	$0.189575\pi$
$734$	−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	$0.0675170\pi$
$743$			11.4769i			0.421048i	−0.977589	+	0.210524i	$0.932483\pi$
$744$	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	0.956721	−	0.291008i	$-0.0939907\pi$
$751$	32.4210	+	18.7183i	1.18306	+	0.683040i	0.226340	+	0.974048i	$0.427324\pi$
$752$	−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	$-0.967535\pi$
$757$		−	5.60256i		−	0.203628i	0.994803	−	0.101814i	$-0.0324647\pi$
$758$	56.7060	+	32.7392i	2.05965	+	1.18914i
$759$	−5.38807	+	1.03037i	−0.195574	+	0.0374000i
$760$	−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	$-0.295002\pi$
$769$	33.3000			1.20083			0.600415	+	0.799689i	$0.295002\pi$
$770$	−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	0.822388	−	0.568927i	$-0.192642\pi$
$773$	−2.26626	−	3.92528i	−0.0815118	−	0.141183i	−0.903900	+	0.427745i	$0.859308\pi$

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} +(-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} +(-3.13535 - 3.62900i) 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} +(11.3968 - 2.17943i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) \) 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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