LMFDB - Embedded newform 588.2.o.f.19.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(19,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,-4,12,4,0,-8,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	588.19
Dual form			588.2.o.f.31.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.914808 - 1.07848i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.326251 + 1.97321i) q^{4} +(-0.441565 - 0.254938i) q^{5} +(0.476589 - 1.33149i) q^{6} +(2.42653 - 1.45325i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.129001 + 0.709440i) q^{10} +(-3.57438 + 2.06367i) q^{11} +(-1.87198 + 0.704063i) q^{12} +3.97722i q^{13} -0.509876i q^{15} +(-3.78712 - 1.28752i) q^{16} +(4.27680 - 2.46921i) q^{17} +(1.39140 - 0.253006i) q^{18} +(-2.52617 + 4.37545i) q^{19} +(0.647107 - 0.788127i) q^{20} +(5.49550 + 1.96705i) q^{22} +(-2.52818 - 1.45965i) q^{23} +(2.47182 + 1.37481i) q^{24} +(-2.37001 - 4.10498i) q^{25} +(4.28936 - 3.63839i) q^{26} -1.00000 q^{27} -5.82102 q^{29} +(-0.549892 + 0.466438i) q^{30} +(2.85998 + 4.95364i) q^{31} +(2.07592 + 5.26218i) q^{32} +(-3.57438 - 2.06367i) q^{33} +(-6.57546 - 2.35360i) q^{34} +(-1.54572 - 1.26915i) q^{36} +(-5.00371 + 8.66667i) q^{37} +(7.02981 - 1.27827i) q^{38} +(-3.44437 + 1.98861i) q^{39} +(-1.44196 + 0.0230915i) q^{40} +11.7494i q^{41} +9.84649i q^{43} +(-2.90591 - 7.72628i) q^{44} +(0.441565 - 0.254938i) q^{45} +(0.738599 + 4.06190i) q^{46} +(3.93580 - 6.81701i) q^{47} +(-0.778531 - 3.92350i) q^{48} +(-2.25905 + 6.31129i) q^{50} +(4.27680 + 2.46921i) q^{51} +(-7.84789 - 1.29757i) q^{52} +(-0.619363 - 1.07277i) q^{53} +(0.914808 + 1.07848i) q^{54} +2.10443 q^{55} -5.05234 q^{57} +(5.32512 + 6.27788i) q^{58} +(-2.32689 - 4.03030i) q^{59} +(1.00609 + 0.166348i) q^{60} +(-0.470524 - 0.271657i) q^{61} +(2.72608 - 7.61607i) q^{62} +(3.77611 - 7.05273i) q^{64} +(1.01394 - 1.75620i) q^{65} +(1.04424 + 5.74277i) q^{66} +(6.08041 - 3.51053i) q^{67} +(3.47697 + 9.24462i) q^{68} -2.91930i q^{69} +1.06587i q^{71} +(0.0452885 + 2.82806i) q^{72} +(-0.724896 + 0.418519i) q^{73} +(13.9243 - 2.53193i) q^{74} +(2.37001 - 4.10498i) q^{75} +(-7.80952 - 6.41216i) q^{76} +(5.29562 + 1.89550i) q^{78} +(1.08946 + 0.629001i) q^{79} +(1.34402 + 1.53401i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(12.6715 - 10.7484i) q^{82} +13.7332 q^{83} -2.51798 q^{85} +(10.6193 - 9.00765i) q^{86} +(-2.91051 - 5.04115i) q^{87} +(-5.67431 + 10.2020i) q^{88} +(4.06085 + 2.34453i) q^{89} +(-0.678894 - 0.243001i) q^{90} +(3.70502 - 4.51243i) q^{92} +(-2.85998 + 4.95364i) q^{93} +(-10.9525 + 1.99156i) q^{94} +(2.23094 - 1.28803i) q^{95} +(-3.51923 + 4.42889i) q^{96} -1.80904i q^{97} -4.12734i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 12 q^{3} + 4 q^{4} - 8 q^{6} + 8 q^{8} - 12 q^{9} - 4 q^{12} + 4 q^{16} - 4 q^{18} + 48 q^{20} + 4 q^{24} + 12 q^{25} + 24 q^{26} - 24 q^{27} + 64 q^{29} + 16 q^{31} - 4 q^{32} - 64 q^{34}+ \cdots + 4 q^{96}+O(q^{100}) $ 24 * q - 4 * q^2 + 12 * q^3 + 4 * q^4 - 8 * q^6 + 8 * q^8 - 12 * q^9 - 4 * q^12 + 4 * q^16 - 4 * q^18 + 48 * q^20 + 4 * q^24 + 12 * q^25 + 24 * q^26 - 24 * q^27 + 64 * q^29 + 16 * q^31 - 4 * q^32 - 64 * q^34 - 8 * q^36 - 32 * q^37 - 24 * q^38 - 32 * q^40 + 24 * q^44 - 24 * q^46 + 8 * q^48 - 56 * q^50 + 32 * q^52 + 32 * q^53 + 4 * q^54 - 32 * q^55 - 16 * q^58 - 16 * q^59 + 24 * q^60 - 16 * q^62 - 8 * q^64 - 8 * q^68 - 4 * q^72 + 32 * q^74 - 12 * q^75 + 64 * q^76 + 48 * q^78 - 16 * q^80 - 12 * q^81 + 32 * q^82 + 32 * q^83 + 32 * q^85 + 24 * q^86 + 32 * q^87 - 24 * q^88 - 16 * q^93 + 4 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.914808	−	1.07848i	−0.646867	−	0.762603i
$2$	−0.914808	−	1.07848i	−0.646867	−	0.762603i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.326251	+	1.97321i	−0.163126	+	0.986605i
$5$	−0.441565	−	0.254938i	−0.197474	−	0.114012i	0.398003	−	0.917384i	$-0.369703\pi$
$5$	−0.441565	−	0.254938i	−0.197474	−	0.114012i	−0.595477	+	0.803373i	$0.703037\pi$
$6$	0.476589	−	1.33149i	0.194567	−	0.543578i
$7$		0			0
$7$		0			0
$8$	2.42653	−	1.45325i	0.857908	−	0.513803i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.129001	+	0.709440i	0.0407938	+	0.224345i
$11$	−3.57438	+	2.06367i	−1.07772	+	0.622220i	−0.930279	−	0.366852i	$-0.880436\pi$
$11$	−3.57438	+	2.06367i	−1.07772	+	0.622220i	−0.147437	+	0.989071i	$0.547102\pi$
$12$	−1.87198	+	0.704063i	−0.540393	+	0.203246i
$13$			3.97722i			1.10308i	0.834148	+	0.551541i	$0.185960\pi$
$13$			3.97722i			1.10308i	−0.834148	+	0.551541i	$0.814040\pi$
$14$		0			0
$15$		−	0.509876i		−	0.131649i
$16$	−3.78712	−	1.28752i	−0.946780	−	0.321881i
$17$	4.27680	−	2.46921i	1.03728	−	0.598872i	0.118217	−	0.992988i	$-0.462282\pi$
$17$	4.27680	−	2.46921i	1.03728	−	0.598872i	0.919061	+	0.394115i	$0.128949\pi$
$18$	1.39140	−	0.253006i	0.327956	−	0.0596340i
$19$	−2.52617	+	4.37545i	−0.579543	+	1.00380i	0.415989	+	0.909370i	$0.363436\pi$
$19$	−2.52617	+	4.37545i	−0.579543	+	1.00380i	−0.995532	+	0.0944280i	$0.969898\pi$
$20$	0.647107	−	0.788127i	0.144698	−	0.176231i
$21$		0			0
$22$	5.49550	+	1.96705i	1.17165	+	0.419376i
$23$	−2.52818	−	1.45965i	−0.527163	−	0.304358i	0.212697	−	0.977118i	$-0.431775\pi$
$23$	−2.52818	−	1.45965i	−0.527163	−	0.304358i	−0.739860	+	0.672760i	$0.765108\pi$
$24$	2.47182	+	1.37481i	0.504558	+	0.280632i
$25$	−2.37001	−	4.10498i	−0.474003	−	0.820997i
$26$	4.28936	−	3.63839i	0.841213	−	0.713547i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−5.82102			−1.08094			−0.540469	−	0.841364i	$-0.681753\pi$
$29$	−5.82102			−1.08094			−0.540469	+	0.841364i	$0.681753\pi$
$30$	−0.549892	+	0.466438i	−0.100396	+	0.0851596i
$31$	2.85998	+	4.95364i	0.513668	+	0.889700i	0.999874	+	0.0158555i	$0.00504716\pi$
$31$	2.85998	+	4.95364i	0.513668	+	0.889700i	−0.486206	+	0.873844i	$0.661620\pi$
$32$	2.07592	+	5.26218i	0.366974	+	0.930231i
$33$	−3.57438	−	2.06367i	−0.622220	−	0.359239i
$34$	−6.57546	−	2.35360i	−1.12768	−	0.403640i
$35$		0			0
$36$	−1.54572	−	1.26915i	−0.257621	−	0.211525i
$37$	−5.00371	+	8.66667i	−0.822604	+	1.42479i	0.0811323	+	0.996703i	$0.474146\pi$
$37$	−5.00371	+	8.66667i	−0.822604	+	1.42479i	−0.903737	+	0.428089i	$0.859187\pi$
$38$	7.02981	−	1.27827i	1.14039	−	0.207363i
$39$	−3.44437	+	1.98861i	−0.551541	+	0.318432i
$40$	−1.44196	+	0.0230915i	−0.227994	+	0.00365109i
$41$			11.7494i			1.83495i	0.397797	+	0.917474i	$0.369775\pi$
$41$			11.7494i			1.83495i	−0.397797	+	0.917474i	$0.630225\pi$
$42$		0			0
$43$			9.84649i			1.50158i	0.660544	+	0.750788i	$0.270326\pi$
$43$			9.84649i			1.50158i	−0.660544	+	0.750788i	$0.729674\pi$
$44$	−2.90591	−	7.72628i	−0.438082	−	1.16478i
$45$	0.441565	−	0.254938i	0.0658247	−	0.0380039i
$46$	0.738599	+	4.06190i	0.108900	+	0.598895i
$47$	3.93580	−	6.81701i	0.574096	−	0.994364i	−0.422043	−	0.906576i	$-0.638687\pi$
$47$	3.93580	−	6.81701i	0.574096	−	0.994364i	0.996139	−	0.0877879i	$-0.0279798\pi$
$48$	−0.778531	−	3.92350i	−0.112371	−	0.566309i
$49$		0			0
$50$	−2.25905	+	6.31129i	−0.319477	+	0.892552i
$51$	4.27680	+	2.46921i	0.598872	+	0.345759i
$52$	−7.84789	−	1.29757i	−1.08831	−	0.179941i
$53$	−0.619363	−	1.07277i	−0.0850761	−	0.147356i	0.820348	−	0.571865i	$-0.193780\pi$
$53$	−0.619363	−	1.07277i	−0.0850761	−	0.147356i	−0.905424	+	0.424509i	$0.860447\pi$
$54$	0.914808	+	1.07848i	0.124490	+	0.146763i
$55$	2.10443			0.283761
$56$		0			0
$57$	−5.05234			−0.669199
$58$	5.32512	+	6.27788i	0.699223	+	0.824325i
$59$	−2.32689	−	4.03030i	−0.302936	−	0.524700i	0.673864	−	0.738856i	$-0.264633\pi$
$59$	−2.32689	−	4.03030i	−0.302936	−	0.524700i	−0.976800	+	0.214155i	$0.931300\pi$
$60$	1.00609	+	0.166348i	0.129886	+	0.0214754i
$61$	−0.470524	−	0.271657i	−0.0602444	−	0.0347821i	0.469575	−	0.882892i	$-0.344407\pi$
$61$	−0.470524	−	0.271657i	−0.0602444	−	0.0347821i	−0.529820	+	0.848110i	$0.677740\pi$
$62$	2.72608	−	7.61607i	0.346212	−	0.967242i
$63$		0			0
$64$	3.77611	−	7.05273i	0.472014	−	0.881591i
$65$	1.01394	−	1.75620i	0.125764	−	0.217830i
$66$	1.04424	+	5.74277i	0.128537	+	0.706886i
$67$	6.08041	−	3.51053i	0.742841	−	0.428879i	−0.0802606	−	0.996774i	$-0.525575\pi$
$67$	6.08041	−	3.51053i	0.742841	−	0.428879i	0.823101	+	0.567895i	$0.192242\pi$
$68$	3.47697	+	9.24462i	0.421644	+	1.12107i
$69$		−	2.91930i		−	0.351442i
$70$		0			0
$71$			1.06587i			0.126496i	0.997998	+	0.0632478i	$0.0201458\pi$
$71$			1.06587i			0.126496i	−0.997998	+	0.0632478i	$0.979854\pi$
$72$	0.0452885	+	2.82806i	0.00533731	+	0.333291i
$73$	−0.724896	+	0.418519i	−0.0848426	+	0.0489839i	−0.541821	−	0.840494i	$-0.682265\pi$
$73$	−0.724896	+	0.418519i	−0.0848426	+	0.0489839i	0.456978	+	0.889478i	$0.348932\pi$
$74$	13.9243	−	2.53193i	1.61867	−	0.294331i
$75$	2.37001	−	4.10498i	0.273666	−	0.474003i
$76$	−7.80952	−	6.41216i	−0.895814	−	0.735525i
$77$		0			0
$78$	5.29562	+	1.89550i	0.599611	+	0.214623i
$79$	1.08946	+	0.629001i	0.122574	+	0.0707682i	0.560033	−	0.828470i	$-0.310788\pi$
$79$	1.08946	+	0.629001i	0.122574	+	0.0707682i	−0.437459	+	0.899238i	$0.644122\pi$
$80$	1.34402	+	1.53401i	0.150266	+	0.171507i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	12.6715	−	10.7484i	1.39934	−	1.18697i
$83$	13.7332			1.50741			0.753705	−	0.657213i	$-0.228265\pi$
$83$	13.7332			1.50741			0.753705	+	0.657213i	$0.228265\pi$
$84$		0			0
$85$	−2.51798			−0.273114
$86$	10.6193	−	9.00765i	1.14511	−	0.971320i
$87$	−2.91051	−	5.04115i	−0.312040	−	0.540469i
$88$	−5.67431	+	10.2020i	−0.604884	+	1.08754i
$89$	4.06085	+	2.34453i	0.430449	+	0.248520i	0.699538	−	0.714596i	$-0.253389\pi$
$89$	4.06085	+	2.34453i	0.430449	+	0.248520i	−0.269089	+	0.963115i	$0.586723\pi$
$90$	−0.678894	−	0.243001i	−0.0715617	−	0.0256146i
$91$		0			0
$92$	3.70502	−	4.51243i	0.386275	−	0.470453i
$93$	−2.85998	+	4.95364i	−0.296567	+	0.513668i
$94$	−10.9525	+	1.99156i	−1.12967	+	0.205414i
$95$	2.23094	−	1.28803i	0.228889	−	0.132149i
$96$	−3.51923	+	4.42889i	−0.359180	+	0.452021i
$97$		−	1.80904i		−	0.183680i	−0.995774	−	0.0918402i	$-0.970725\pi$
$97$		−	1.80904i		−	0.183680i	0.995774	−	0.0918402i	$-0.0292749\pi$
$98$		0			0
$99$		−	4.12734i		−	0.414813i
$100$	8.87322	−	3.33728i	0.887322	−	0.333728i
$101$	−5.16423	+	2.98157i	−0.513860	+	0.296677i	−0.734419	−	0.678697i	$-0.762545\pi$
$101$	−5.16423	+	2.98157i	−0.513860	+	0.296677i	0.220559	+	0.975374i	$0.429212\pi$
$102$	−1.24945	−	6.87132i	−0.123714	−	0.680362i
$103$	−5.54683	+	9.60738i	−0.546545	+	0.946644i	0.451963	+	0.892037i	$0.350724\pi$
$103$	−5.54683	+	9.60738i	−0.546545	+	0.946644i	−0.998508	+	0.0546070i	$0.982609\pi$
$104$	5.77990	+	9.65084i	0.566766	+	0.946343i
$105$		0			0
$106$	−0.590364	+	1.64935i	−0.0573412	+	0.160199i
$107$	−0.544929	−	0.314615i	−0.0526802	−	0.0304150i	0.473429	−	0.880832i	$-0.343016\pi$
$107$	−0.544929	−	0.314615i	−0.0526802	−	0.0304150i	−0.526109	+	0.850417i	$0.676350\pi$
$108$	0.326251	−	1.97321i	0.0313935	−	0.189872i
$109$	−7.90877	−	13.6984i	−0.757523	−	1.31207i	−0.944110	−	0.329629i	$-0.893076\pi$
$109$	−7.90877	−	13.6984i	−0.757523	−	1.31207i	0.186588	−	0.982438i	$-0.440257\pi$
$110$	−1.92515	−	2.26959i	−0.183556	−	0.216397i
$111$	−10.0074			−0.949862
$112$		0			0
$113$	−3.72346			−0.350273			−0.175137	−	0.984544i	$-0.556037\pi$
$113$	−3.72346			−0.350273			−0.175137	+	0.984544i	$0.556037\pi$
$114$	4.62192	+	5.44886i	0.432883	+	0.510333i
$115$	0.744239	+	1.28906i	0.0694006	+	0.120205i
$116$	1.89912	−	11.4861i	0.176328	−	1.06646i
$117$	−3.44437	−	1.98861i	−0.318432	−	0.183847i
$118$	−2.21795	+	6.19647i	−0.204179	+	0.570431i
$119$		0			0
$120$	−0.740978	−	1.23723i	−0.0676418	−	0.112943i
$121$	3.01746	−	5.22640i	0.274315	−	0.475127i
$122$	0.137462	+	0.755966i	0.0124452	+	0.0684420i
$123$	−10.1753	+	5.87470i	−0.917474	+	0.529704i
$124$	−10.7076	+	4.02722i	−0.961575	+	0.361655i
$125$			4.96620i			0.444191i
$126$		0			0
$127$		−	14.0834i		−	1.24970i	−0.780746	−	0.624848i	$-0.785161\pi$
$127$		−	14.0834i		−	1.24970i	0.780746	−	0.624848i	$-0.214839\pi$
$128$	−11.0607	+	2.37943i	−0.977634	+	0.210314i
$129$	−8.52731	+	4.92324i	−0.750788	+	0.433467i
$130$	−2.82160	+	0.513067i	−0.247470	+	0.0449989i
$131$	1.68181	−	2.91299i	0.146941	−	0.254509i	−0.783155	−	0.621827i	$-0.786391\pi$
$131$	1.68181	−	2.91299i	0.146941	−	0.254509i	0.930095	+	0.367318i	$0.119724\pi$
$132$	5.23820	−	6.37973i	0.455927	−	0.555284i
$133$		0			0
$134$	−9.34846	−	3.34616i	−0.807584	−	0.289064i
$135$	0.441565	+	0.254938i	0.0380039	+	0.0219416i
$136$	6.78941	−	12.2069i	0.582187	−	1.04673i
$137$	0.243728	+	0.422150i	0.0208231	+	0.0360667i	0.876249	−	0.481858i	$-0.160038\pi$
$137$	0.243728	+	0.422150i	0.0208231	+	0.0360667i	−0.855426	+	0.517925i	$0.826705\pi$
$138$	−3.14841	+	2.67060i	−0.268011	+	0.227336i
$139$	16.2489			1.37821			0.689105	−	0.724662i	$-0.258004\pi$
$139$	16.2489			1.37821			0.689105	+	0.724662i	$0.258004\pi$
$140$		0			0
$141$	7.87161			0.662909
$142$	1.14952	−	0.975068i	0.0964659	−	0.0818259i
$143$	−8.20766	−	14.2161i	−0.686359	−	1.18881i
$144$	3.00859	−	2.63598i	0.250716	−	0.219665i
$145$	2.57036	+	1.48400i	0.213457	+	0.123239i
$146$	1.11451	+	0.398923i	0.0922372	+	0.0330151i
$147$		0			0
$148$	−15.4687	−	12.7009i	−1.27152	−	1.04401i
$149$	7.87372	−	13.6377i	0.645040	−	1.11724i	−0.339252	−	0.940696i	$-0.610174\pi$
$149$	7.87372	−	13.6377i	0.645040	−	1.11724i	0.984292	−	0.176547i	$-0.0564928\pi$
$150$	−6.59526	+	1.19925i	−0.538501	+	0.0979187i
$151$	21.0293	−	12.1413i	1.71134	−	0.988041i	0.778573	−	0.627554i	$-0.215944\pi$
$151$	21.0293	−	12.1413i	1.71134	−	0.988041i	0.932764	−	0.360487i	$-0.117389\pi$
$152$	0.228813	+	14.2883i	0.0185592	+	1.15894i
$153$			4.93843i			0.399248i
$154$		0			0
$155$		−	2.91647i		−	0.234257i
$156$	−2.80021	−	7.44525i	−0.224196	−	0.596097i
$157$	3.25493	−	1.87923i	0.259771	−	0.149979i	−0.364459	−	0.931219i	$-0.618746\pi$
$157$	3.25493	−	1.87923i	0.259771	−	0.149979i	0.624230	+	0.781240i	$0.285413\pi$
$158$	−0.318282	−	1.75038i	−0.0253211	−	0.139253i
$159$	0.619363	−	1.07277i	0.0491187	−	0.0850761i
$160$	0.424877	−	2.85283i	0.0335895	−	0.225536i
$161$		0			0
$162$	−0.476589	+	1.33149i	−0.0374444	+	0.104612i
$163$	7.00593	+	4.04488i	0.548747	+	0.316819i	0.748616	−	0.663003i	$-0.230719\pi$
$163$	7.00593	+	4.04488i	0.548747	+	0.316819i	−0.199870	+	0.979822i	$0.564052\pi$
$164$	−23.1840	−	3.83325i	−1.81037	−	0.299327i
$165$	1.05221	+	1.82249i	0.0819148	+	0.141881i
$166$	−12.5632	−	14.8110i	−0.975094	−	1.14956i
$167$	−23.7606			−1.83865			−0.919327	−	0.393495i	$-0.871266\pi$
$167$	−23.7606			−1.83865			−0.919327	+	0.393495i	$0.871266\pi$
$168$		0			0
$169$	−2.81825			−0.216789
$170$	2.30347	+	2.71560i	0.176668	+	0.208277i
$171$	−2.52617	−	4.37545i	−0.193181	−	0.334599i
$172$	−19.4292	−	3.21243i	−1.48146	−	0.244945i
$173$	−7.56294	−	4.36647i	−0.575000	−	0.331976i	0.184144	−	0.982899i	$-0.441049\pi$
$173$	−7.56294	−	4.36647i	−0.575000	−	0.331976i	−0.759144	+	0.650923i	$0.774382\pi$
$174$	−2.77424	+	7.75063i	−0.210315	+	0.587574i
$175$		0			0
$176$	16.1936	−	3.21326i	1.22064	−	0.242209i
$177$	2.32689	−	4.03030i	0.174900	−	0.302936i
$178$	−1.18636	−	6.52435i	−0.0889214	−	0.489021i
$179$	−9.34938	+	5.39787i	−0.698806	+	0.403456i	−0.806902	−	0.590685i	$-0.798858\pi$
$179$	−9.34938	+	5.39787i	−0.698806	+	0.403456i	0.108097	+	0.994140i	$0.465524\pi$
$180$	0.358985	+	0.954475i	0.0267571	+	0.0711424i
$181$		−	26.0627i		−	1.93722i	−0.248580	−	0.968611i	$-0.579964\pi$
$181$		−	26.0627i		−	1.93722i	0.248580	−	0.968611i	$-0.420036\pi$
$182$		0			0
$183$		−	0.543314i		−	0.0401629i
$184$	−8.25596	+	0.132211i	−0.608637	+	0.00974670i
$185$	4.41893	−	2.55127i	0.324886	−	0.187573i
$186$	7.95875	−	1.44719i	0.583564	−	0.106113i
$187$	−10.1913	+	17.6518i	−0.745260	+	1.29083i
$188$	12.1673	+	9.99023i	0.887395	+	0.728612i
$189$		0			0
$190$	−3.43000	−	1.22772i	−0.248838	−	0.0890685i
$191$	−1.51959	−	0.877337i	−0.109954	−	0.0634819i	0.444015	−	0.896020i	$-0.353554\pi$
$191$	−1.51959	−	0.877337i	−0.109954	−	0.0634819i	−0.553968	+	0.832538i	$0.686887\pi$
$192$	7.99590	−	0.256158i	0.577054	−	0.0184866i
$193$	7.46342	+	12.9270i	0.537229	+	0.930507i	0.999052	+	0.0435354i	$0.0138621\pi$
$193$	7.46342	+	12.9270i	0.537229	+	0.930507i	−0.461823	+	0.886972i	$0.652805\pi$
$194$	−1.95102	+	1.65493i	−0.140075	+	0.118817i
$195$	2.02789			0.145220
$196$		0			0
$197$	12.1669			0.866855			0.433428	−	0.901188i	$-0.357304\pi$
$197$	12.1669			0.866855			0.433428	+	0.901188i	$0.357304\pi$
$198$	−4.45126	+	3.77572i	−0.316338	+	0.268329i
$199$	10.7268	+	18.5793i	0.760401	+	1.31705i	0.942644	+	0.333800i	$0.108331\pi$
$199$	10.7268	+	18.5793i	0.760401	+	1.31705i	−0.182242	+	0.983254i	$0.558336\pi$
$200$	−11.7165	−	6.51664i	−0.828481	−	0.460796i
$201$	6.08041	+	3.51053i	0.428879	+	0.247614i
$202$	7.93985	+	2.84197i	0.558646	+	0.199960i
$203$		0			0
$204$	−6.26759	+	7.63345i	−0.438819	+	0.534449i
$205$	2.99536	−	5.18812i	0.209205	−	0.362354i
$206$	15.4357	−	2.80676i	1.07546	−	0.195556i
$207$	2.52818	−	1.45965i	0.175721	−	0.101453i
$208$	5.12076	−	15.0622i	0.355061	−	1.04438i
$209$		−	20.8527i		−	1.44241i
$210$		0			0
$211$			9.90704i			0.682029i	0.940058	+	0.341014i	$0.110770\pi$
$211$			9.90704i			0.682029i	−0.940058	+	0.341014i	$0.889230\pi$
$212$	2.31887	−	0.872142i	0.159260	−	0.0598990i
$213$	−0.923071	+	0.532935i	−0.0632478	+	0.0365161i
$214$	0.159199	+	0.875508i	0.0108826	+	0.0598485i
$215$	2.51024	−	4.34787i	0.171197	−	0.296522i
$216$	−2.42653	+	1.45325i	−0.165105	+	0.0988814i
$217$		0			0
$218$	−7.53847	+	21.0609i	−0.510570	+	1.42642i
$219$	−0.724896	−	0.418519i	−0.0489839	−	0.0282809i
$220$	−0.686572	+	4.15248i	−0.0462887	+	0.279960i
$221$	9.82060	+	17.0098i	0.660605	+	1.14420i
$222$	9.15487	+	10.7928i	0.614434	+	0.724367i
$223$	−5.67517			−0.380037			−0.190019	−	0.981780i	$-0.560855\pi$
$223$	−5.67517			−0.380037			−0.190019	+	0.981780i	$0.560855\pi$
$224$		0			0
$225$	4.74003			0.316002
$226$	3.40625	+	4.01569i	0.226580	+	0.267119i
$227$	1.02352	+	1.77280i	0.0679337	+	0.117665i	0.897992	−	0.440013i	$-0.145026\pi$
$227$	1.02352	+	1.77280i	0.0679337	+	0.117665i	−0.830058	+	0.557677i	$0.811693\pi$
$228$	1.64833	−	9.96933i	0.109163	−	0.660235i
$229$	4.02788	+	2.32550i	0.266170	+	0.153673i	0.627146	−	0.778902i	$-0.284223\pi$
$229$	4.02788	+	2.32550i	0.266170	+	0.153673i	−0.360976	+	0.932575i	$0.617556\pi$
$230$	0.709393	−	1.98189i	0.0467760	−	0.130682i
$231$		0			0
$232$	−14.1249	+	8.45942i	−0.927345	+	0.555388i
$233$	−2.12177	+	3.67501i	−0.139002	+	0.240758i	−0.927119	−	0.374767i	$-0.877723\pi$
$233$	−2.12177	+	3.67501i	−0.139002	+	0.240758i	0.788117	+	0.615525i	$0.211056\pi$
$234$	1.00626	+	5.53389i	0.0657812	+	0.361762i
$235$	−3.47583	+	2.00677i	−0.226738	+	0.130907i
$236$	8.71178	−	3.27656i	0.567089	−	0.213286i
$237$			1.25800i			0.0817160i
$238$		0			0
$239$		−	11.6610i		−	0.754289i	−0.926154	−	0.377145i	$-0.876906\pi$
$239$		−	11.6610i		−	0.754289i	0.926154	−	0.377145i	$-0.123094\pi$
$240$	−0.656477	+	1.93096i	−0.0423754	+	0.124643i
$241$	8.63879	−	4.98761i	0.556474	−	0.321280i	−0.195255	−	0.980752i	$-0.562554\pi$
$241$	8.63879	−	4.98761i	0.556474	−	0.321280i	0.751729	+	0.659472i	$0.229220\pi$
$242$	−8.39698	+	1.52687i	−0.539778	+	0.0981509i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	0.689546	−	0.839814i	0.0441436	−	0.0537636i
$245$		0			0
$246$	15.6442	+	5.59964i	0.997437	+	0.357020i
$247$	−17.4021	−	10.0471i	−1.10727	−	0.639283i
$248$	14.1387	+	7.86388i	0.897810	+	0.499357i
$249$	6.86658	+	11.8933i	0.435152	+	0.753705i
$250$	5.35596	−	4.54312i	0.338741	−	0.287332i
$251$	−11.8869			−0.750292			−0.375146	−	0.926966i	$-0.622407\pi$
$251$	−11.8869			−0.750292			−0.375146	+	0.926966i	$0.622407\pi$
$252$		0			0
$253$	12.0489			0.757509
$254$	−15.1887	+	12.8836i	−0.953021	+	0.808387i
$255$	−1.25899	−	2.18064i	−0.0788411	−	0.136557i
$256$	12.6846	+	9.75202i	0.792785	+	0.609501i
$257$	17.9758	+	10.3783i	1.12130	+	0.647381i	0.941732	−	0.336365i	$-0.109198\pi$
$257$	17.9758	+	10.3783i	1.12130	+	0.647381i	0.179565	+	0.983746i	$0.442531\pi$
$258$	13.1105	+	4.69273i	0.816223	+	0.292157i
$259$		0			0
$260$	3.13455	+	2.57368i	0.194397	+	0.159613i
$261$	2.91051	−	5.04115i	0.180156	−	0.312040i
$262$	−4.68015	+	0.851017i	−0.289140	+	0.0525760i
$263$	−1.18230	+	0.682599i	−0.0729035	+	0.0420908i	−0.536009	−	0.844212i	$-0.680069\pi$
$263$	−1.18230	+	0.682599i	−0.0729035	+	0.0420908i	0.463105	+	0.886303i	$0.346735\pi$
$264$	−11.6724	+	0.186921i	−0.718385	+	0.0115042i
$265$			0.631597i			0.0387987i
$266$		0			0
$267$			4.68906i			0.286966i
$268$	4.94327	+	13.1432i	0.301958	+	0.802852i
$269$	−20.2615	+	11.6980i	−1.23536	+	0.713238i	−0.968143	−	0.250397i	$-0.919439\pi$
$269$	−20.2615	+	11.6980i	−1.23536	+	0.713238i	−0.267222	+	0.963635i	$0.586106\pi$
$270$	−0.129001	−	0.709440i	−0.00785078	−	0.0431751i
$271$	10.4596	−	18.1165i	0.635373	−	1.10050i	−0.351063	−	0.936352i	$-0.614180\pi$
$271$	10.4596	−	18.1165i	0.635373	−	1.10050i	0.986436	−	0.164147i	$-0.0524871\pi$
$272$	−19.3759	+	3.84472i	−1.17484	+	0.233120i
$273$		0			0
$274$	0.232317	−	0.649043i	0.0140348	−	0.0392101i
$275$	16.9427	+	9.78185i	1.02168	+	0.589868i
$276$	5.76039	+	0.952424i	0.346734	+	0.0573292i
$277$	9.22359	+	15.9757i	0.554192	+	0.959888i	0.997966	+	0.0637495i	$0.0203059\pi$
$277$	9.22359	+	15.9757i	0.554192	+	0.959888i	−0.443774	+	0.896139i	$0.646361\pi$
$278$	−14.8646	−	17.5241i	−0.891519	−	1.05103i
$279$	−5.71997			−0.342446
$280$		0			0
$281$	19.9336			1.18914			0.594569	−	0.804044i	$-0.297323\pi$
$281$	19.9336			1.18914			0.594569	+	0.804044i	$0.297323\pi$
$282$	−7.20101	−	8.48940i	−0.428814	−	0.505536i
$283$	10.1479	+	17.5766i	0.603227	+	1.04482i	0.992329	+	0.123625i	$0.0394521\pi$
$283$	10.1479	+	17.5766i	0.603227	+	1.04482i	−0.389102	+	0.921195i	$0.627215\pi$
$284$	−2.10319	−	0.347742i	−0.124801	−	0.0206347i
$285$	2.23094	+	1.28803i	0.132149	+	0.0762964i
$286$	−7.82337	+	21.8568i	−0.462605	+	1.29242i
$287$		0			0
$288$	−5.59514	−	0.833296i	−0.329697	−	0.0491024i
$289$	3.69404	−	6.39827i	0.217296	−	0.376369i
$290$	−0.750921	−	4.12967i	−0.0440956	−	0.242502i
$291$	1.56668	−	0.904521i	0.0918402	−	0.0530240i
$292$	−0.589327	−	1.56691i	−0.0344878	−	0.0916967i
$293$		−	2.69416i		−	0.157394i	−0.996899	−	0.0786972i	$-0.974924\pi$
$293$		−	2.69416i		−	0.157394i	0.996899	−	0.0786972i	$-0.0250760\pi$
$294$		0			0
$295$			2.37285i			0.138153i
$296$	0.453221	+	28.3016i	0.0263429	+	1.64500i
$297$	3.57438	−	2.06367i	0.207407	−	0.119746i
$298$	−21.9110	+	3.98419i	−1.26927	+	0.230798i
$299$	5.80534	−	10.0551i	0.335731	−	0.581504i
$300$	7.32678	+	6.01579i	0.423012	+	0.347322i
$301$		0			0
$302$	−32.3319	−	11.5728i	−1.86049	−	0.665939i
$303$	−5.16423	−	2.98157i	−0.296677	−	0.171287i
$304$	15.2004	−	13.3179i	0.871803	−	0.763832i
$305$	0.138511	+	0.239909i	0.00793113	+	0.0137371i
$306$	5.32601	−	4.51772i	0.304468	−	0.258261i
$307$	6.99511			0.399232			0.199616	−	0.979874i	$-0.436031\pi$
$307$	6.99511			0.399232			0.199616	+	0.979874i	$0.436031\pi$
$308$		0			0
$309$	−11.0937			−0.631096
$310$	−3.14537	+	2.66801i	−0.178645	+	0.151533i
$311$	11.0106	+	19.0709i	0.624352	+	1.08141i	0.988666	+	0.150134i	$0.0479704\pi$
$311$	11.0106	+	19.0709i	0.624352	+	1.08141i	−0.364313	+	0.931276i	$0.618696\pi$
$312$	−5.46792	+	9.83096i	−0.309560	+	0.556569i
$313$	1.50461	+	0.868686i	0.0850455	+	0.0491010i	0.541920	−	0.840430i	$-0.317698\pi$
$313$	1.50461	+	0.868686i	0.0850455	+	0.0491010i	−0.456874	+	0.889531i	$0.651031\pi$
$314$	−5.00435	−	1.79124i	−0.282412	−	0.101086i
$315$		0			0
$316$	−1.59659	+	1.94453i	−0.0898152	+	0.109388i
$317$	−16.0648	+	27.8250i	−0.902288	+	1.56281i	−0.0777720	+	0.996971i	$0.524781\pi$
$317$	−16.0648	+	27.8250i	−0.902288	+	1.56281i	−0.824516	+	0.565838i	$0.808553\pi$
$318$	−1.72356	+	0.313405i	−0.0966526	+	0.0175749i
$319$	20.8066	−	12.0127i	1.16494	−	0.672580i
$320$	−3.46541	+	2.15157i	−0.193722	+	0.120276i
$321$		−	0.629229i		−	0.0351202i
$322$		0			0
$323$			24.9506i			1.38829i
$324$	1.87198	−	0.704063i	0.103999	−	0.0391146i
$325$	16.3264	−	9.42606i	0.905626	−	0.522864i
$326$	−2.04675	−	11.2561i	−0.113359	−	0.623416i
$327$	7.90877	−	13.6984i	0.437356	−	0.757523i
$328$	17.0748	+	28.5103i	0.942801	+	1.57422i
$329$		0			0
$330$	1.00295	−	2.80202i	0.0552105	−	0.154246i
$331$	−9.89288	−	5.71166i	−0.543762	−	0.313941i	0.202840	−	0.979212i	$-0.434983\pi$
$331$	−9.89288	−	5.71166i	−0.543762	−	0.313941i	−0.746602	+	0.665271i	$0.768316\pi$
$332$	−4.48046	+	27.0984i	−0.245897	+	1.48722i
$333$	−5.00371	−	8.66667i	−0.274201	−	0.474931i
$334$	21.7364	+	25.6254i	1.18936	+	1.40216i
$335$	−3.57986			−0.195589
$336$		0			0
$337$	7.08667			0.386036			0.193018	−	0.981195i	$-0.438172\pi$
$337$	7.08667			0.386036			0.193018	+	0.981195i	$0.438172\pi$
$338$	2.57816	+	3.03944i	0.140233	+	0.165323i
$339$	−1.86173	−	3.22461i	−0.101115	−	0.175137i
$340$	0.821495	−	4.96851i	0.0445518	−	0.269455i
$341$	−20.4453	−	11.8041i	−1.10718	−	0.639229i
$342$	−2.40789	+	6.72713i	−0.130204	+	0.363762i
$343$		0			0
$344$	14.3094	+	23.8928i	0.771513	+	1.28821i
$345$	−0.744239	+	1.28906i	−0.0400685	+	0.0694006i
$346$	2.20948	+	12.1510i	0.118783	+	0.653241i
$347$	−18.1053	+	10.4531i	−0.971942	+	0.561151i	−0.899828	−	0.436245i	$-0.856308\pi$
$347$	−18.1053	+	10.4531i	−0.971942	+	0.561151i	−0.0721145	+	0.997396i	$0.522975\pi$
$348$	10.8968	−	4.09837i	0.584131	−	0.219696i
$349$		−	1.67904i		−	0.0898768i	−0.998990	−	0.0449384i	$-0.985691\pi$
$349$		−	1.67904i		−	0.0898768i	0.998990	−	0.0449384i	$-0.0143092\pi$
$350$		0			0
$351$		−	3.97722i		−	0.212288i
$352$	−18.2795	−	14.5250i	−0.974302	−	0.774187i
$353$	5.38099	−	3.10672i	0.286401	−	0.165354i	−0.349916	−	0.936781i	$-0.613790\pi$
$353$	5.38099	−	3.10672i	0.286401	−	0.165354i	0.636318	+	0.771427i	$0.280457\pi$
$354$	−6.47527	+	1.17744i	−0.344157	+	0.0625800i
$355$	0.271731	−	0.470651i	0.0144220	−	0.0249796i
$356$	−5.95111	+	7.24800i	−0.315408	+	0.384143i
$357$		0			0
$358$	14.3744	+	5.14513i	0.759711	+	0.271929i
$359$	−19.5276	−	11.2743i	−1.03063	−	0.595033i	−0.113463	−	0.993542i	$-0.536194\pi$
$359$	−19.5276	−	11.2743i	−1.03063	−	0.595033i	−0.917164	+	0.398510i	$0.869528\pi$
$360$	0.700983	−	1.26032i	0.0369450	−	0.0664247i
$361$	−3.26306	−	5.65178i	−0.171740	−	0.297462i
$362$	−28.1081	+	23.8423i	−1.47733	+	1.25313i
$363$	6.03492			0.316751
$364$		0			0
$365$	0.426785			0.0223389
$366$	−0.585955	+	0.497028i	−0.0306284	+	0.0259801i
$367$	−11.1449	−	19.3036i	−0.581760	−	1.00764i	−0.995271	−	0.0971382i	$-0.969031\pi$
$367$	−11.1449	−	19.3036i	−0.581760	−	1.00764i	0.413511	−	0.910499i	$-0.364302\pi$
$368$	7.69521	+	8.78296i	0.401140	+	0.457844i
$369$	−10.1753	−	5.87470i	−0.529704	−	0.305825i
$370$	−6.79397	−	2.43181i	−0.353202	−	0.126424i
$371$		0			0
$372$	−8.84150	−	7.25948i	−0.458410	−	0.376387i
$373$	1.58233	−	2.74068i	0.0819300	−	0.141907i	−0.822149	−	0.569272i	$-0.807225\pi$
$373$	1.58233	−	2.74068i	0.0819300	−	0.141907i	0.904079	+	0.427366i	$0.140558\pi$
$374$	28.3603	−	5.15691i	1.46647	−	0.266657i
$375$	−4.30086	+	2.48310i	−0.222095	+	0.128227i
$376$	−0.356494	−	22.2614i	−0.0183848	−	1.14805i
$377$		−	23.1515i		−	1.19236i
$378$		0			0
$379$			7.23505i			0.371640i	0.982584	+	0.185820i	$0.0594941\pi$
$379$			7.23505i			0.371640i	−0.982584	+	0.185820i	$0.940506\pi$
$380$	1.81371	+	4.82233i	0.0930415	+	0.247380i
$381$	12.1965	−	7.04168i	0.624848	−	0.360756i
$382$	0.443943	+	2.44145i	0.0227141	+	0.124915i
$383$	−12.5932	+	21.8121i	−0.643482	+	1.11454i	0.341167	+	0.940003i	$0.389178\pi$
$383$	−12.5932	+	21.8121i	−0.643482	+	1.11454i	−0.984650	+	0.174542i	$0.944156\pi$
$384$	−7.59098	−	8.38910i	−0.387375	−	0.428105i
$385$		0			0
$386$	7.11398	−	19.8749i	0.362092	−	1.01161i
$387$	−8.52731	−	4.92324i	−0.433467	−	0.250263i
$388$	3.56962	+	0.590202i	0.181220	+	0.0299630i
$389$	4.09251	+	7.08843i	0.207498	+	0.359398i	0.950926	−	0.309419i	$-0.100135\pi$
$389$	4.09251	+	7.08843i	0.207498	+	0.359398i	−0.743428	+	0.668817i	$0.766801\pi$
$390$	−1.85513	−	2.18704i	−0.0939380	−	0.110745i
$391$	−14.4167			−0.729086
$392$		0			0
$393$	3.36363			0.169673
$394$	−11.1304	−	13.1218i	−0.560740	−	0.661066i
$395$	−0.320712	−	0.555490i	−0.0161368	−	0.0279497i
$396$	8.14411	+	1.34655i	0.409257	+	0.0676666i
$397$	29.0305	+	16.7608i	1.45700	+	0.841200i	0.998863	−	0.0476807i	$-0.0151830\pi$
$397$	29.0305	+	16.7608i	1.45700	+	0.841200i	0.458139	+	0.888881i	$0.348516\pi$
$398$	10.2245	−	28.5652i	0.512510	−	1.43184i
$399$		0			0
$400$	3.69026	+	18.5975i	0.184513	+	0.929876i
$401$	3.52777	−	6.11027i	0.176168	−	0.305132i	−0.764397	−	0.644746i	$-0.776963\pi$
$401$	3.52777	−	6.11027i	0.176168	−	0.305132i	0.940565	+	0.339614i	$0.110296\pi$
$402$	−1.77637	−	9.76908i	−0.0885972	−	0.487238i
$403$	−19.7017	+	11.3748i	−0.981411	+	0.566618i
$404$	−4.19843	−	11.1628i	−0.208879	−	0.555372i
$405$			0.509876i			0.0253359i
$406$		0			0
$407$		−	41.3040i		−	2.04736i
$408$	13.9662	−	0.223654i	0.691430	−	0.0110725i
$409$	−22.2668	+	12.8558i	−1.10102	+	0.635677i	−0.936490	−	0.350694i	$-0.885946\pi$
$409$	−22.2668	+	12.8558i	−1.10102	+	0.635677i	−0.164535	+	0.986371i	$0.552612\pi$
$410$	−8.33549	+	1.51569i	−0.411660	+	0.0748546i
$411$	−0.243728	+	0.422150i	−0.0120222	+	0.0208231i
$412$	−17.1477	−	14.0795i	−0.844808	−	0.693646i
$413$		0			0
$414$	−3.88701	−	1.39131i	−0.191036	−	0.0683789i
$415$	−6.06409	−	3.50110i	−0.297674	−	0.171862i
$416$	−20.9288	+	8.25637i	−1.02612	+	0.404802i
$417$	8.12443	+	14.0719i	0.397855	+	0.689105i
$418$	−22.4893	+	19.0762i	−1.09999	+	0.933049i
$419$	16.0117			0.782223			0.391111	−	0.920343i	$-0.372091\pi$
$419$	16.0117			0.782223			0.391111	+	0.920343i	$0.372091\pi$
$420$		0			0
$421$	6.19958			0.302149			0.151075	−	0.988522i	$-0.451727\pi$
$421$	6.19958			0.302149			0.151075	+	0.988522i	$0.451727\pi$
$422$	10.6846	−	9.06304i	0.520117	−	0.441182i
$423$	3.93580	+	6.81701i	0.191365	+	0.331455i
$424$	−3.06191	−	1.70302i	−0.148699	−	0.0827058i
$425$	−20.2722	−	11.7041i	−0.983345	−	0.567734i
$426$	1.41920	+	0.507983i	0.0687602	+	0.0246118i
$427$		0			0
$428$	0.798585	−	0.972616i	0.0386010	−	0.0470131i
$429$	8.20766	−	14.2161i	0.396270	−	0.686359i
$430$	−6.98549	+	1.27021i	−0.336870	+	0.0612550i
$431$	26.4566	−	15.2747i	1.27437	−	0.735758i	0.298562	−	0.954390i	$-0.403493\pi$
$431$	26.4566	−	15.2747i	1.27437	−	0.735758i	0.975807	+	0.218632i	$0.0701596\pi$
$432$	3.78712	+	1.28752i	0.182208	+	0.0619461i
$433$			23.2309i			1.11641i	0.829704	+	0.558204i	$0.188509\pi$
$433$			23.2309i			1.11641i	−0.829704	+	0.558204i	$0.811491\pi$
$434$		0			0
$435$			2.96800i			0.142305i
$436$	29.6100	−	11.1365i	1.41806	−	0.533344i
$437$	12.7732	−	7.37463i	0.611027	−	0.352777i
$438$	0.211775	+	1.16465i	0.0101190	+	0.0556492i
$439$	−1.20325	+	2.08410i	−0.0574282	+	0.0994685i	−0.893310	−	0.449441i	$-0.851623\pi$
$439$	−1.20325	+	2.08410i	−0.0574282	+	0.0994685i	0.835882	+	0.548909i	$0.184957\pi$
$440$	5.10646	−	3.05827i	0.243441	−	0.145797i
$441$		0			0
$442$	9.36079	−	26.1520i	0.445247	−	1.24393i
$443$	6.59229	+	3.80606i	0.313209	+	0.180831i	0.648362	−	0.761333i	$-0.275455\pi$
$443$	6.59229	+	3.80606i	0.313209	+	0.180831i	−0.335153	+	0.942164i	$0.608788\pi$
$444$	3.26493	−	19.7467i	0.154947	−	0.937139i
$445$	−1.19542	−	2.07053i	−0.0566683	−	0.0981524i
$446$	5.19169	+	6.12057i	0.245834	+	0.289817i
$447$	15.7474			0.744828
$448$		0			0
$449$	−16.8969			−0.797414			−0.398707	−	0.917078i	$-0.630541\pi$
$449$	−16.8969			−0.797414			−0.398707	+	0.917078i	$0.630541\pi$
$450$	−4.33622	−	5.11204i	−0.204411	−	0.240984i
$451$	−24.2469	−	41.9968i	−1.14174	−	1.97755i
$452$	1.21478	−	7.34717i	0.0571386	−	0.345582i
$453$	21.0293	+	12.1413i	0.988041	+	0.570446i
$454$	0.975602	−	2.72562i	0.0457873	−	0.127920i
$455$		0			0
$456$	−12.2597	+	7.34233i	−0.574111	+	0.343836i
$457$	−3.83930	+	6.64986i	−0.179595	+	0.311067i	−0.941742	−	0.336337i	$-0.890812\pi$
$457$	−3.83930	+	6.64986i	−0.179595	+	0.311067i	0.762147	+	0.647404i	$0.224145\pi$
$458$	−1.17673	−	6.47139i	−0.0549850	−	0.302388i
$459$	−4.27680	+	2.46921i	−0.199624	+	0.115253i
$460$	−2.78639	+	1.04798i	−0.129916	+	0.0488624i
$461$		−	4.29773i		−	0.200165i	−0.994979	−	0.100083i	$-0.968089\pi$
$461$		−	4.29773i		−	0.200165i	0.994979	−	0.100083i	$-0.0319107\pi$
$462$		0			0
$463$		−	2.92047i		−	0.135726i	−0.997695	−	0.0678628i	$-0.978382\pi$
$463$		−	2.92047i		−	0.135726i	0.997695	−	0.0678628i	$-0.0216180\pi$
$464$	22.0449	+	7.49471i	1.02341	+	0.347933i
$465$	2.52574	−	1.45824i	0.117128	−	0.0676241i
$466$	5.90445	−	1.07364i	0.273518	−	0.0497354i
$467$	−20.0755	+	34.7718i	−0.928985	+	1.60905i	−0.143961	+	0.989583i	$0.545984\pi$
$467$	−20.0755	+	34.7718i	−0.928985	+	1.60905i	−0.785024	+	0.619466i	$0.787349\pi$
$468$	5.04767	−	6.14768i	0.233329	−	0.284177i
$469$		0			0
$470$	5.34399	+	1.91281i	0.246500	+	0.0882314i
$471$	3.25493	+	1.87923i	0.149979	+	0.0865905i
$472$	−11.5033	−	6.39808i	−0.529483	−	0.294495i
$473$	−20.3199	−	35.1951i	−0.934310	−	1.61827i
$474$	1.35673	−	1.15083i	0.0623169	−	0.0528594i
$475$	23.9482			1.09882
$476$		0			0
$477$	1.23873			0.0567174
$478$	−12.5762	+	10.6676i	−0.575223	+	0.487925i
$479$	11.0116	+	19.0726i	0.503132	+	0.871450i	0.999993	+	0.00361993i	$0.00115226\pi$
$479$	11.0116	+	19.0726i	0.503132	+	0.871450i	−0.496862	+	0.867830i	$0.665514\pi$
$480$	2.68306	−	1.05846i	0.122464	−	0.0483118i
$481$	−34.4692	−	19.9008i	−1.57166	−	0.907399i
$482$	−13.2819	−	4.75408i	−0.604974	−	0.216543i
$483$		0			0
$484$	9.32833	+	7.65920i	0.424015	+	0.348146i
$485$	−0.461193	+	0.798810i	−0.0209417	+	0.0362721i
$486$	−1.39140	+	0.253006i	−0.0631151	+	0.0114766i
$487$	−17.2504	+	9.95955i	−0.781692	+	0.451310i	−0.837030	−	0.547157i	$-0.815710\pi$
$487$	−17.2504	+	9.95955i	−0.781692	+	0.451310i	0.0553374	+	0.998468i	$0.482377\pi$
$488$	−1.53653	+	0.0246059i	−0.0695553	+	0.00111386i
$489$			8.08975i			0.365831i
$490$		0			0
$491$			22.4901i			1.01496i	0.861662	+	0.507482i	$0.169424\pi$
$491$			22.4901i			1.01496i	−0.861662	+	0.507482i	$0.830576\pi$
$492$	−8.27232	−	21.9946i	−0.372945	−	0.991592i
$493$	−24.8954	+	14.3734i	−1.12123	+	0.647343i
$494$	5.08396	+	27.9591i	0.228738	+	1.25794i
$495$	−1.05221	+	1.82249i	−0.0472935	+	0.0819148i
$496$	−4.45317	−	22.4423i	−0.199953	−	1.00769i
$497$		0			0
$498$	6.54508	−	18.2856i	0.293292	−	0.819395i
$499$	22.5407	+	13.0139i	1.00906	+	0.582581i	0.910916	−	0.412591i	$-0.135376\pi$
$499$	22.5407	+	13.0139i	1.00906	+	0.582581i	0.0981437	+	0.995172i	$0.468710\pi$
$500$	−9.79936	−	1.62023i	−0.438241	−	0.0724589i
$501$	−11.8803	−	20.5773i	−0.530773	−	0.919327i
$502$	10.8742	+	12.8198i	0.485339	+	0.572175i
$503$	−21.9468			−0.978561			−0.489281	−	0.872126i	$-0.662741\pi$
$503$	−21.9468			−0.978561			−0.489281	+	0.872126i	$0.662741\pi$
$504$		0			0
$505$	3.04046			0.135299
$506$	−11.0225	−	12.9946i	−0.490008	−	0.577679i
$507$	−1.40913	−	2.44068i	−0.0625815	−	0.108394i
$508$	27.7894	+	4.59471i	1.23296	+	0.203857i
$509$	−5.34021	−	3.08317i	−0.236701	−	0.136659i	0.376959	−	0.926230i	$-0.376970\pi$
$509$	−5.34021	−	3.08317i	−0.236701	−	0.136659i	−0.613659	+	0.789571i	$0.710303\pi$
$510$	−1.20004	+	3.35267i	−0.0531389	+	0.148459i
$511$		0			0
$512$	−1.08655	−	22.6013i	−0.0480193	−	0.998846i
$513$	2.52617	−	4.37545i	0.111533	−	0.193181i
$514$	−5.25155	−	28.8807i	−0.231636	−	1.27387i
$515$	4.89857	−	2.82819i	0.215857	−	0.124625i
$516$	−6.93255	−	18.4324i	−0.305189	−	0.811441i
$517$			32.4888i			1.42886i
$518$		0			0
$519$		−	8.73293i		−	0.383333i
$520$	−0.0918400	−	5.73499i	−0.00402745	−	0.251496i
$521$	−11.2114	+	6.47291i	−0.491181	+	0.283583i	−0.725064	−	0.688681i	$-0.758190\pi$
$521$	−11.2114	+	6.47291i	−0.491181	+	0.283583i	0.233883	+	0.972265i	$0.424857\pi$
$522$	−8.09936	+	1.47275i	−0.354499	+	0.0644606i
$523$	11.6523	−	20.1824i	0.509521	−	0.882517i	−0.490418	−	0.871487i	$-0.663156\pi$
$523$	11.6523	−	20.1824i	0.509521	−	0.882517i	0.999939	−	0.0110294i	$-0.00351083\pi$
$524$	5.19924	+	4.26894i	0.227130	+	0.186489i
$525$		0			0
$526$	1.81775	+	0.650639i	0.0792575	+	0.0283692i
$527$	24.4632	+	14.1238i	1.06563	+	0.615244i
$528$	10.8796	+	12.4175i	0.473473	+	0.540401i
$529$	−7.23886	−	12.5381i	−0.314733	−	0.545133i
$530$	0.681166	−	0.577790i	0.0295880	−	0.0250976i
$531$	4.65379			0.201957
$532$		0			0
$533$	−46.7299			−2.02410
$534$	5.05707	−	4.28959i	0.218841	−	0.185629i
$535$	0.160414	+	0.277846i	0.00693532	+	0.0120123i
$536$	9.65263	−	17.3548i	0.416930	−	0.749613i
$537$	−9.34938	−	5.39787i	−0.403456	−	0.232935i
$538$	31.1515	+	11.1503i	1.34303	+	0.480722i
$539$		0			0
$540$	−0.647107	+	0.788127i	−0.0278471	+	0.0339156i
$541$	4.70699	−	8.15275i	0.202369	−	0.350514i	−0.746922	−	0.664912i	$-0.768469\pi$
$541$	4.70699	−	8.15275i	0.202369	−	0.350514i	0.949291	+	0.314398i	$0.101803\pi$
$542$	−29.1068	+	5.29266i	−1.25025	+	0.227339i
$543$	22.5709	−	13.0313i	0.968611	−	0.559228i
$544$	21.8717	+	17.3794i	0.937743	+	0.745138i
$545$			8.06497i			0.345466i
$546$		0			0
$547$		−	15.9880i		−	0.683598i	−0.939773	−	0.341799i	$-0.888964\pi$
$547$		−	15.9880i		−	0.683598i	0.939773	−	0.341799i	$-0.111036\pi$
$548$	−0.912508	+	0.343201i	−0.0389804	+	0.0146608i
$549$	0.470524	−	0.271657i	0.0200815	−	0.0115940i
$550$	−4.94973	−	27.2209i	−0.211057	−	1.16070i
$551$	14.7049	−	25.4696i	0.626449	−	1.08504i
$552$	−4.24248	−	7.08376i	−0.180572	−	0.301505i
$553$		0			0
$554$	8.79173	−	24.5622i	0.373525	−	1.04355i
$555$	4.41893	+	2.55127i	0.187573	+	0.108295i
$556$	−5.30121	+	32.0624i	−0.224821	+	1.35975i
$557$	2.53827	+	4.39642i	0.107550	+	0.186282i	0.914777	−	0.403959i	$-0.132366\pi$
$557$	2.53827	+	4.39642i	0.107550	+	0.186282i	−0.807227	+	0.590241i	$0.799033\pi$
$558$	5.23268	+	6.16889i	0.221517	+	0.261150i
$559$	−39.1616			−1.65636
$560$		0			0
$561$	−20.3826			−0.860553
$562$	−18.2354	−	21.4980i	−0.769215	−	0.906840i
$563$	−12.5196	−	21.6846i	−0.527637	−	0.913895i	−0.999481	−	0.0322126i	$-0.989745\pi$
$563$	−12.5196	−	21.6846i	−0.527637	−	0.913895i	0.471844	−	0.881682i	$-0.343589\pi$
$564$	−2.56812	+	15.5323i	−0.108137	+	0.654030i
$565$	1.64415	+	0.949250i	0.0691699	+	0.0399353i
$566$	9.67272	−	27.0235i	0.406575	−	1.13588i
$567$		0			0
$568$	1.54898	+	2.58637i	0.0649938	+	0.108522i
$569$	−6.85736	+	11.8773i	−0.287476	+	0.497922i	−0.973206	−	0.229933i	$-0.926149\pi$
$569$	−6.85736	+	11.8773i	−0.287476	+	0.497922i	0.685731	+	0.727855i	$0.259483\pi$
$570$	−0.651759	−	3.58433i	−0.0272992	−	0.150131i
$571$	−11.0415	+	6.37481i	−0.462072	+	0.266778i	−0.712915	−	0.701250i	$-0.752626\pi$
$571$	−11.0415	+	6.37481i	−0.462072	+	0.266778i	0.250843	+	0.968028i	$0.419292\pi$
$572$	30.7291	−	11.5574i	1.28485	−	0.483240i
$573$		−	1.75467i		−	0.0733026i
$574$		0			0
$575$			13.8375i			0.577065i
$576$	4.21979	+	6.79657i	0.175825	+	0.283190i
$577$	15.3862	−	8.88324i	0.640537	−	0.369814i	−0.144284	−	0.989536i	$-0.546088\pi$
$577$	15.3862	−	8.88324i	0.640537	−	0.369814i	0.784821	+	0.619722i	$0.212755\pi$
$578$	−10.2798	+	1.86923i	−0.427582	+	0.0777496i
$579$	−7.46342	+	12.9270i	−0.310169	+	0.537229i
$580$	−3.76683	+	4.58771i	−0.156409	+	0.190494i
$581$		0			0
$582$	−2.40872	−	0.862171i	−0.0998447	−	0.0357381i
$583$	4.42768	+	2.55632i	0.183376	+	0.105872i
$584$	−1.15077	+	2.06901i	−0.0476191	+	0.0856161i
$585$	1.01394	+	1.75620i	0.0419214	+	0.0726099i
$586$	−2.90561	+	2.46464i	−0.120029	+	0.101813i
$587$	43.2377			1.78461			0.892306	−	0.451431i	$-0.149086\pi$
$587$	43.2377			1.78461			0.892306	+	0.451431i	$0.149086\pi$
$588$		0			0
$589$	−28.8992			−1.19077
$590$	2.55908	−	2.17071i	0.105356	−	0.0893665i
$591$	6.08345	+	10.5368i	0.250240	+	0.433428i
$592$	30.1082	−	26.3793i	1.23744	−	1.08418i
$593$	26.7328	+	15.4342i	1.09779	+	0.633807i	0.935639	−	0.352960i	$-0.114825\pi$
$593$	26.7328	+	15.4342i	1.09779	+	0.633807i	0.162147	+	0.986767i	$0.448158\pi$
$594$	−5.49550	−	1.96705i	−0.225483	−	0.0807089i
$595$		0			0
$596$	24.3412	+	19.9858i	0.997055	+	0.818651i
$597$	−10.7268	+	18.5793i	−0.439018	+	0.760401i
$598$	−16.1551	+	2.93757i	−0.660630	+	0.120126i
$599$	−0.134668	+	0.0777506i	−0.00550238	+	0.00317680i	−0.502749	−	0.864433i	$-0.667678\pi$
$599$	−0.134668	+	0.0777506i	−0.00550238	+	0.00317680i	0.497246	+	0.867609i	$0.334345\pi$
$600$	−0.214669	−	13.4051i	−0.00876382	−	0.547261i
$601$			22.4797i			0.916967i	0.888703	+	0.458484i	$0.151607\pi$
$601$			22.4797i			0.916967i	−0.888703	+	0.458484i	$0.848393\pi$
$602$		0			0
$603$			7.02106i			0.285919i
$604$	17.0964	+	45.4563i	0.695644	+	1.84959i
$605$	−2.66481	+	1.53853i	−0.108340	+	0.0625501i
$606$	1.50871	+	8.29709i	0.0612871	+	0.337046i
$607$	−7.45143	+	12.9063i	−0.302444	+	0.523849i	−0.976689	−	0.214659i	$-0.931136\pi$
$607$	−7.45143	+	12.9063i	−0.302444	+	0.523849i	0.674245	+	0.738508i	$0.264469\pi$
$608$	−28.2686	−	4.21009i	−1.14644	−	0.170742i
$609$		0			0
$610$	0.132026	−	0.368853i	0.00534558	−	0.0149344i
$611$	27.1127	+	15.6535i	1.09686	+	0.633275i
$612$	−9.74456	−	1.61117i	−0.393901	−	0.0651276i
$613$	−18.7577	−	32.4893i	−0.757617	−	1.31223i	−0.944063	−	0.329766i	$-0.893030\pi$
$613$	−18.7577	−	32.4893i	−0.757617	−	1.31223i	0.186446	−	0.982465i	$-0.440303\pi$
$614$	−6.39918	−	7.54411i	−0.258250	−	0.304455i
$615$	5.99073			0.241570
$616$		0			0
$617$	10.8459			0.436641			0.218321	−	0.975877i	$-0.429942\pi$
$617$	10.8459			0.436641			0.218321	+	0.975877i	$0.429942\pi$
$618$	10.1486	+	11.9643i	0.408235	+	0.481275i
$619$	11.5599	+	20.0223i	0.464632	+	0.804765i	0.999185	−	0.0403694i	$-0.0128535\pi$
$619$	11.5599	+	20.0223i	0.464632	+	0.804765i	−0.534553	+	0.845135i	$0.679520\pi$
$620$	5.75481	+	0.951503i	0.231119	+	0.0382133i
$621$	2.52818	+	1.45965i	0.101453	+	0.0585737i
$622$	10.4950	−	29.3209i	0.420813	−	1.17566i
$623$		0			0
$624$	15.6046	−	3.09639i	0.624685	−	0.123955i
$625$	−10.5840	+	18.3320i	−0.423360	+	0.733281i
$626$	−0.439565	−	2.41738i	−0.0175686	−	0.0966178i
$627$	18.0590	−	10.4264i	0.721206	−	0.416388i
$628$	2.64620	+	7.03576i	0.105595	+	0.280757i
$629$			49.4209i			1.97054i
$630$		0			0
$631$			12.0123i			0.478200i	0.970995	+	0.239100i	$0.0768524\pi$
$631$			12.0123i			0.478200i	−0.970995	+	0.239100i	$0.923148\pi$
$632$	3.55771	−	0.0569731i	0.141518	−	0.00226627i
$633$	−8.57975	+	4.95352i	−0.341014	+	0.196885i
$634$	44.7050	−	8.12897i	1.77546	−	0.322843i
$635$	−3.59038	+	6.21872i	−0.142480	+	0.246782i
$636$	1.91473	+	1.57213i	0.0759240	+	0.0623389i
$637$		0			0
$638$	−31.9895	−	11.4502i	−1.26648	−	0.453319i
$639$	−0.923071	−	0.532935i	−0.0365161	−	0.0210826i
$640$	5.49061	+	1.76911i	0.217035	+	0.0699302i
$641$	−24.4903	−	42.4184i	−0.967308	−	1.67543i	−0.703281	−	0.710912i	$-0.748282\pi$
$641$	−24.4903	−	42.4184i	−0.967308	−	1.67543i	−0.264028	−	0.964515i	$-0.585051\pi$
$642$	−0.678613	+	0.575624i	−0.0267827	+	0.0227181i
$643$	16.4052			0.646958			0.323479	−	0.946235i	$-0.395147\pi$
$643$	16.4052			0.646958			0.323479	+	0.946235i	$0.395147\pi$
$644$		0			0
$645$	5.02048			0.197681
$646$	26.9088	−	22.8250i	1.05871	−	0.898039i
$647$	−9.25506	−	16.0302i	−0.363854	−	0.630214i	0.624738	−	0.780835i	$-0.285206\pi$
$647$	−9.25506	−	16.0302i	−0.363854	−	0.630214i	−0.988592	+	0.150621i	$0.951873\pi$
$648$	−2.47182	−	1.37481i	−0.0971023	−	0.0540077i
$649$	16.6344	+	9.60388i	0.652958	+	0.376985i
$650$	−25.1014	−	8.98472i	−0.984557	−	0.352410i
$651$		0			0
$652$	−10.2671	+	12.5045i	−0.402090	+	0.489715i
$653$	6.23930	−	10.8068i	0.244163	−	0.422902i	−0.717733	−	0.696318i	$-0.754820\pi$
$653$	6.23930	−	10.8068i	0.244163	−	0.422902i	0.961896	+	0.273416i	$0.0881536\pi$
$654$	−22.0085	+	4.00193i	−0.860600	+	0.156488i
$655$	−1.48526	+	0.857516i	−0.0580340	+	0.0335059i
$656$	15.1276	−	44.4964i	0.590635	−	1.73729i
$657$		−	0.837037i		−	0.0326559i
$658$		0			0
$659$		−	28.5032i		−	1.11033i	−0.831741	−	0.555163i	$-0.812656\pi$
$659$		−	28.5032i		−	1.11033i	0.831741	−	0.555163i	$-0.187344\pi$
$660$	−3.93944	+	1.48165i	−0.153343	+	0.0576732i
$661$	−3.97020	+	2.29220i	−0.154423	+	0.0891561i	−0.575220	−	0.817999i	$-0.695084\pi$
$661$	−3.97020	+	2.29220i	−0.154423	+	0.0891561i	0.420797	+	0.907155i	$0.361750\pi$
$662$	2.89016	+	15.8944i	0.112329	+	0.617752i
$663$	−9.82060	+	17.0098i	−0.381401	+	0.660605i
$664$	33.3240	−	19.9578i	1.29322	−	0.774512i
$665$		0			0
$666$	−4.76943	+	13.3248i	−0.184812	+	0.516324i
$667$	14.7166	+	8.49665i	0.569830	+	0.328991i
$668$	7.75194	−	46.8847i	0.299931	−	1.81402i
$669$	−2.83758	−	4.91484i	−0.109707	−	0.190019i
$670$	3.27489	+	3.86082i	0.126520	+	0.149157i
$671$	2.24244			0.0865685
$672$		0			0
$673$	−35.9408			−1.38542			−0.692708	−	0.721219i	$-0.743582\pi$
$673$	−35.9408			−1.38542			−0.692708	+	0.721219i	$0.743582\pi$
$674$	−6.48295	−	7.64286i	−0.249714	−	0.294392i
$675$	2.37001	+	4.10498i	0.0912219	+	0.158001i
$676$	0.919458	−	5.56100i	0.0353638	−	0.213885i
$677$	−8.81217	−	5.08771i	−0.338679	−	0.195537i	0.321009	−	0.947076i	$-0.395978\pi$
$677$	−8.81217	−	5.08771i	−0.338679	−	0.195537i	−0.659688	+	0.751540i	$0.729312\pi$
$678$	−1.77456	+	4.95774i	−0.0681516	+	0.190401i
$679$		0			0
$680$	−6.10997	+	3.65927i	−0.234307	+	0.140327i
$681$	−1.02352	+	1.77280i	−0.0392215	+	0.0679337i
$682$	5.97302	+	32.8485i	0.228719	+	1.25783i
$683$	−8.41759	+	4.85990i	−0.322090	+	0.185959i	−0.652324	−	0.757940i	$-0.726206\pi$
$683$	−8.41759	+	4.85990i	−0.322090	+	0.185959i	0.330234	+	0.943899i	$0.392872\pi$
$684$	9.45786	−	3.55717i	0.361630	−	0.136012i
$685$		−	0.248542i		−	0.00949631i
$686$		0			0
$687$			4.65100i			0.177447i
$688$	12.6776	−	37.2898i	0.483329	−	1.42166i
$689$	4.26663	−	2.46334i	0.162546	−	0.0938459i
$690$	2.07106	−	0.376593i	0.0788441	−	0.0143367i
$691$	18.0956	−	31.3425i	0.688389	−	1.19233i	−0.283970	−	0.958833i	$-0.591651\pi$
$691$	18.0956	−	31.3425i	0.688389	−	1.19233i	0.972359	−	0.233492i	$-0.0750152\pi$
$692$	11.0834	−	13.4987i	0.421327	−	0.513144i
$693$		0			0
$694$	27.8363	+	9.96366i	1.05665	+	0.378216i
$695$	−7.17493	−	4.14245i	−0.272161	−	0.157132i
$696$	−14.3885	−	8.00281i	−0.545396	−	0.303346i
$697$	29.0118	+	50.2499i	1.09890	+	1.90335i
$698$	−1.81081	+	1.53600i	−0.0685403	+	0.0581384i
$699$	−4.24354			−0.160505
$700$		0			0
$701$	28.4159			1.07325			0.536626	−	0.843820i	$-0.319699\pi$
$701$	28.4159			1.07325			0.536626	+	0.843820i	$0.319699\pi$
$702$	−4.28936	+	3.63839i	−0.161891	+	0.137322i
$703$	−25.2804	−	43.7870i	−0.953469	−	1.65146i
$704$	1.05725	+	33.0018i	0.0398466	+	1.24380i
$705$	−3.47583	−	2.00677i	−0.130907	−	0.0755794i
$706$	−8.27312	−	2.96126i	−0.311363	−	0.111448i
$707$		0			0
$708$	7.19348	+	5.90634i	0.270347	+	0.221974i
$709$	0.249479	−	0.432110i	0.00936937	−	0.0162282i	−0.861303	−	0.508092i	$-0.830351\pi$
$709$	0.249479	−	0.432110i	0.00936937	−	0.0162282i	0.870672	+	0.491864i	$0.163684\pi$
$710$	−0.756171	+	0.137499i	−0.0283786	+	0.00516024i
$711$	−1.08946	+	0.629001i	−0.0408580	+	0.0235894i
$712$	13.2610	−	0.212361i	0.496976	−	0.00795856i
$713$		−	16.6983i		−	0.625356i
$714$		0			0
$715$			8.36977i			0.313012i
$716$	−7.60088	−	20.2094i	−0.284058	−	0.755259i
$717$	10.0987	−	5.83052i	0.377145	−	0.217745i
$718$	5.70491	+	31.3740i	0.212905	+	1.17087i
$719$	3.18344	−	5.51388i	0.118722	−	0.205633i	−0.800539	−	0.599280i	$-0.795454\pi$
$719$	3.18344	−	5.51388i	0.118722	−	0.205633i	0.919262	+	0.393647i	$0.128787\pi$
$720$	−2.00050	+	0.396954i	−0.0745542	+	0.0147936i
$721$		0			0
$722$	−3.11028	+	8.68945i	−0.115753	+	0.323388i
$723$	8.63879	+	4.98761i	0.321280	+	0.185491i
$724$	51.4271	+	8.50298i	1.91127	+	0.316011i
$725$	13.7959	+	23.8952i	0.512367	+	0.887446i
$726$	−5.52080	−	6.50856i	−0.204896	−	0.241555i
$727$	−18.5763			−0.688958			−0.344479	−	0.938794i	$-0.611944\pi$
$727$	−18.5763			−0.688958			−0.344479	+	0.938794i	$0.611944\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−0.390426	−	0.460280i	−0.0144503	−	0.0170357i
$731$	24.3131	+	42.1115i	0.899252	+	1.55755i
$732$	1.07207	+	0.177257i	0.0396250	+	0.00655160i
$733$	−31.3892	−	18.1226i	−1.15939	−	0.669372i	−0.208230	−	0.978080i	$-0.566770\pi$
$733$	−31.3892	−	18.1226i	−1.15939	−	0.669372i	−0.951157	+	0.308708i	$0.900103\pi$
$734$	−10.6231	+	29.6786i	−0.392106	+	1.09546i
$735$		0			0
$736$	2.43264	−	16.3339i	0.0896682	−	0.602075i
$737$	−14.4891	+	25.0959i	−0.533714	+	0.924420i
$738$	2.97266	+	16.3481i	0.109425	+	0.601781i
$739$	−40.5899	+	23.4346i	−1.49312	+	0.862056i	−0.999969	−	0.00788486i	$-0.997490\pi$
$739$	−40.5899	+	23.4346i	−1.49312	+	0.862056i	−0.493156	+	0.869941i	$0.664157\pi$
$740$	3.59251	+	9.55182i	0.132063	+	0.351132i
$741$		−	20.0942i		−	0.738180i
$742$		0			0
$743$			38.5048i			1.41260i	0.707911	+	0.706302i	$0.249638\pi$
$743$			38.5048i			1.41260i	−0.707911	+	0.706302i	$0.750362\pi$
$744$	0.259049	+	16.1764i	0.00949720	+	0.593057i
$745$	−6.95352	+	4.01462i	−0.254757	+	0.147084i
$746$	−4.40330	+	0.800678i	−0.161216	+	0.0293149i
$747$	−6.86658	+	11.8933i	−0.251235	+	0.435152i
$748$	−31.5058	−	25.8685i	−1.15197	−	0.945845i
$749$		0			0
$750$	6.61244	+	2.36684i	0.241452	+	0.0864248i
$751$	0.866354	+	0.500190i	0.0316137	+	0.0182522i	0.515724	−	0.856755i	$-0.327523\pi$
$751$	0.866354	+	0.500190i	0.0316137	+	0.0182522i	−0.484110	+	0.875007i	$0.660856\pi$
$752$	−23.6824	+	20.7494i	−0.863610	+	0.756653i
$753$	−5.94343	−	10.2943i	−0.216591	−	0.375146i
$754$	−24.9685	+	21.1792i	−0.909298	+	0.771300i
$755$	−12.3811			−0.450593
$756$		0			0
$757$	−13.8254			−0.502491			−0.251246	−	0.967923i	$-0.580840\pi$
$757$	−13.8254			−0.502491			−0.251246	+	0.967923i	$0.580840\pi$
$758$	7.80288	−	6.61869i	0.283413	−	0.240401i
$759$	6.02446	+	10.4347i	0.218674	+	0.378755i
$760$	3.54160	−	6.36757i	0.128467	−	0.230976i
$761$	25.5450	+	14.7484i	0.926005	+	0.534629i	0.885546	−	0.464552i	$-0.153785\pi$
$761$	25.5450	+	14.7484i	0.926005	+	0.534629i	0.0404588	+	0.999181i	$0.487118\pi$
$762$	−18.7518	−	6.71198i	−0.679307	−	0.243149i
$763$		0			0
$764$	2.22694	−	2.71224i	0.0805679	−	0.0981256i
$765$	1.25899	−	2.18064i	0.0455190	−	0.0788411i
$766$	35.0443	−	6.37231i	1.26620	−	0.230241i
$767$	16.0294	−	9.25456i	0.578787	−	0.334163i
$768$	−2.10322	+	15.8612i	−0.0758933	+	0.572340i
$769$		−	33.1479i		−	1.19534i	−0.801741	−	0.597672i	$-0.796093\pi$
$769$		−	33.1479i		−	1.19534i	0.801741	−	0.597672i	$-0.203907\pi$
$770$		0			0
$771$			20.7566i			0.747531i
$772$	−27.9427	+	10.5094i	−1.00568	+	0.378243i
$773$	7.16192	−	4.13494i	0.257596	−	0.148723i	−0.365641	−	0.930756i	$-0.619150\pi$
$773$	7.16192	−	4.13494i	0.257596	−	0.148723i	0.623238	+	0.782033i	$0.285817\pi$
$774$	2.49122	+	13.7004i	0.0895450	+	0.492450i
$775$	13.5564	−	23.4804i	0.486960	−	0.843440i
$776$	−2.62900	−	4.38970i	−0.0943755	−	0.157581i
$777$		0			0
$778$	3.90089	−	10.8983i	0.139854	−	0.390721i
$779$	−51.4089	−	29.6810i	−1.84192	−	1.06343i
$780$	−0.661600	+	4.00145i	−0.0236891	+	0.143275i
$781$	−2.19960	−	3.80983i	−0.0787081	−	0.136326i
$782$	13.1886	+	15.5482i	0.471622	+	0.556003i
$783$	5.82102			0.208026
$784$		0			0
$785$	−1.91635			−0.0683974
$786$	−3.07708	−	3.62762i	−0.109756	−	0.129393i
$787$	−3.77375	−	6.53633i	−0.134520	−	0.232995i	0.790894	−	0.611953i	$-0.209616\pi$
$787$	−3.77375	−	6.53633i	−0.134520	−	0.232995i	−0.925414	+	0.378958i	$0.876283\pi$
$788$	−3.96946	+	24.0078i	−0.141406	+	0.855244i
$789$	−1.18230	−	0.682599i	−0.0420908	−	0.0243012i
$790$	−0.305696	+	0.854050i	−0.0108762	+	0.0303857i
$791$		0			0
$792$	−5.99807	−	10.0151i	−0.213132	−	0.355872i
$793$	1.08044	−	1.87138i	0.0383675	−	0.0664545i
$794$	−8.48116	−	46.6419i	−0.300985	−	1.65526i
$795$	−0.546979	+	0.315798i	−0.0193993	+	0.0112002i
$796$	−40.1606	+	15.1047i	−1.42345	+	0.535371i
$797$			36.4436i			1.29090i	0.763803	+	0.645450i	$0.223330\pi$
$797$			36.4436i			1.29090i	−0.763803	+	0.645450i	$0.776670\pi$
$798$		0			0
$799$		−	38.8734i		−	1.37524i
$800$	16.6812	−	20.9930i	0.589770	−	0.742216i
$801$	−4.06085	+	2.34453i	−0.143483	+	0.0828399i
$802$	−9.81705	+	1.78509i	−0.346652	+	0.0630337i
$803$	1.72737	−	2.99189i	0.0609575	−	0.105581i
$804$	−8.91075	+	10.8526i	−0.314258	+	0.382742i
$805$		0			0
$806$	30.2908	+	10.8422i	1.06695	+	0.381900i
$807$	−20.2615	−	11.6980i	−0.713238	−	0.411788i
$808$	−8.19819	+	14.7398i	−0.288411	+	0.518544i
$809$	−12.6239	−	21.8652i	−0.443832	−	0.768740i	0.554138	−	0.832425i	$-0.313048\pi$
$809$	−12.6239	−	21.8652i	−0.443832	−	0.768740i	−0.997970	+	0.0636848i	$0.979715\pi$
$810$	0.549892	−	0.466438i	0.0193212	−	0.0163890i
$811$	−15.1794			−0.533021			−0.266510	−	0.963832i	$-0.585871\pi$
$811$	−15.1794			−0.533021			−0.266510	+	0.963832i	$0.585871\pi$
$812$		0			0
$813$	20.9191			0.733666
$814$	−44.5456	+	37.7852i	−1.56132	+	1.32437i
$815$	−2.06238	−	3.57215i	−0.0722421	−	0.125127i
$816$	−13.0176	−	14.8577i	−0.455707	−	0.520124i
$817$	−43.0828	−	24.8739i	−1.50728	−	0.870227i
$818$	34.2346	+	12.2539i	1.19699	+	0.428446i
$819$		0			0
$820$	9.26002	+	7.60312i	0.323374	+	0.265512i
$821$	23.3325	−	40.4131i	0.814311	−	1.41043i	−0.0955108	−	0.995428i	$-0.530448\pi$
$821$	23.3325	−	40.4131i	0.814311	−	1.41043i	0.909822	−	0.414999i	$-0.136218\pi$
$822$	0.678246	−	0.123329i	0.0236566	−	0.00430161i
$823$	−21.1099	+	12.1878i	−0.735846	+	0.424841i	−0.820557	−	0.571565i	$-0.806337\pi$
$823$	−21.1099	+	12.1878i	−0.735846	+	0.424841i	0.0847109	+	0.996406i	$0.473003\pi$
$824$	0.502415	+	31.3736i	0.0175025	+	1.09295i
$825$			19.5637i			0.681120i
$826$		0			0
$827$			42.9409i			1.49320i	0.665273	+	0.746600i	$0.268315\pi$
$827$			42.9409i			1.49320i	−0.665273	+	0.746600i	$0.731685\pi$
$828$	2.05537	+	5.46485i	0.0714290	+	0.189917i
$829$	42.2789	−	24.4097i	1.46841	−	0.847784i	0.469032	−	0.883181i	$-0.344603\pi$
$829$	42.2789	−	24.4097i	1.46841	−	0.847784i	0.999373	+	0.0353964i	$0.0112694\pi$
$830$	1.77160	+	9.74285i	0.0614931	+	0.338179i
$831$	−9.22359	+	15.9757i	−0.319963	+	0.554192i
$832$	28.0502	+	15.0184i	0.972467	+	0.520670i
$833$		0			0
$834$	7.74403	−	21.6352i	0.268154	−	0.749165i
$835$	10.4919	+	6.05748i	0.363086	+	0.209628i
$836$	41.1468	+	6.80322i	1.42309	+	0.235294i
$837$	−2.85998	−	4.95364i	−0.0988555	−	0.171223i
$838$	−14.6476	−	17.2684i	−0.505994	−	0.596525i
$839$	42.1517			1.45524			0.727620	−	0.685981i	$-0.240626\pi$
$839$	42.1517			1.45524			0.727620	+	0.685981i	$0.240626\pi$
$840$		0			0
$841$	4.88432			0.168425
$842$	−5.67143	−	6.68615i	−0.195450	−	0.230420i
$843$	9.96680	+	17.2630i	0.343275	+	0.594569i
$844$	−19.5487	−	3.23218i	−0.672893	−	0.111256i
$845$	1.24444	+	0.718479i	0.0428101	+	0.0247164i
$846$	3.75153	−	10.4810i	0.128980	−	0.360343i
$847$		0			0
$848$	0.964387	+	4.86015i	0.0331172	+	0.166898i
$849$	−10.1479	+	17.5766i	−0.348273	+	0.603227i
$850$	5.92243	+	32.5702i	0.203138	+	1.11715i
$851$	25.3006	−	14.6073i	0.867293	−	0.500732i
$852$	−0.750441	−	1.99528i	−0.0257097	−	0.0683573i
$853$		−	13.5733i		−	0.464741i	−0.972627	−	0.232370i	$-0.925352\pi$
$853$		−	13.5733i		−	0.464741i	0.972627	−	0.232370i	$-0.0746481\pi$
$854$		0			0
$855$			2.57606i			0.0880995i
$856$	−1.77950	+	0.0284969i	−0.0608221	+	0.000974003i
$857$	44.0869	−	25.4536i	1.50598	−	0.869477i	0.506003	−	0.862532i	$-0.331122\pi$
$857$	44.0869	−	25.4536i	1.50598	−	0.869477i	0.999976	−	0.00694549i	$-0.00221084\pi$
$858$	−22.8402	+	4.15317i	−0.779753	+	0.141787i
$859$	−6.40910	+	11.1009i	−0.218676	+	0.378757i	−0.954403	−	0.298520i	$-0.903507\pi$
$859$	−6.40910	+	11.1009i	−0.218676	+	0.378757i	0.735728	+	0.677277i	$0.236840\pi$
$860$	7.76028	+	6.37173i	0.264624	+	0.217274i
$861$		0			0
$862$	−40.6763	−	14.5595i	−1.38544	−	0.495900i
$863$	−44.9680	−	25.9623i	−1.53073	−	0.883767i	−0.999328	−	0.0366476i	$-0.988332\pi$
$863$	−44.9680	−	25.9623i	−1.53073	−	0.883767i	−0.531402	−	0.847120i	$-0.678335\pi$
$864$	−2.07592	−	5.26218i	−0.0706241	−	0.179023i
$865$	2.22635	+	3.85616i	0.0756983	+	0.131113i
$866$	25.0542	−	21.2519i	0.851376	−	0.722168i
$867$	7.38808			0.250912
$868$		0			0
$869$	−5.19220			−0.176133
$870$	3.20094	−	2.71515i	0.108522	−	0.0920522i
$871$	13.9621	+	24.1831i	0.473089	+	0.819414i
$872$	−39.0981	−	21.7461i	−1.32403	−	0.736417i
$873$	1.56668	+	0.904521i	0.0530240	+	0.0306134i
$874$	−19.6385	−	7.02935i	−0.664282	−	0.237771i
$875$		0			0
$876$	1.06232	−	1.29383i	0.0358926	−	0.0437145i
$877$	−9.09971	+	15.7612i	−0.307275	+	0.532216i	−0.977765	−	0.209702i	$-0.932751\pi$
$877$	−9.09971	+	15.7612i	−0.307275	+	0.532216i	0.670490	+	0.741919i	$0.266084\pi$
$878$	3.34841	−	0.608860i	0.113003	−	0.0205480i
$879$	2.33321	−	1.34708i	0.0786972	−	0.0454359i
$880$	−7.96973	−	2.70950i	−0.268659	−	0.0913374i
$881$			12.1271i			0.408571i	0.978911	+	0.204286i	$0.0654872\pi$
$881$			12.1271i			0.408571i	−0.978911	+	0.204286i	$0.934513\pi$
$882$		0			0
$883$		−	28.6986i		−	0.965786i	−0.875679	−	0.482893i	$-0.839586\pi$
$883$		−	28.6986i		−	0.965786i	0.875679	−	0.482893i	$-0.160414\pi$
$884$	−36.7679	+	13.8287i	−1.23664	+	0.465108i
$885$	−2.05495	+	1.18643i	−0.0690764	+	0.0398813i
$886$	−1.92591	−	10.5915i	−0.0647022	−	0.355828i
$887$	−6.53190	+	11.3136i	−0.219320	+	0.379873i	−0.954600	−	0.297890i	$-0.903717\pi$
$887$	−6.53190	+	11.3136i	−0.219320	+	0.379873i	0.735281	+	0.677763i	$0.237050\pi$
$888$	−24.2833	+	14.5433i	−0.814894	+	0.488041i
$889$		0			0
$890$	−1.13945	+	3.18337i	−0.0381944	+	0.106707i
$891$	3.57438	+	2.06367i	0.119746	+	0.0691355i
$892$	1.85153	−	11.1983i	0.0619938	−	0.374947i
$893$	19.8850	+	34.4419i	0.665427	+	1.15255i
$894$	−14.4059	−	16.9833i	−0.481805	−	0.568008i
$895$	5.50448			0.183995
$896$		0			0
$897$	11.6107			0.387669
$898$	15.4574	+	18.2230i	0.515821	+	0.608110i
$899$	−16.6480	−	28.8352i	−0.555243	−	0.961709i
$900$	−1.54644	+	9.35307i	−0.0515480	+	0.311769i
$901$	−5.29779	−	3.05868i	−0.176495	−	0.101899i
$902$	−23.1116	+	64.5689i	−0.769532	+	2.14991i
$903$		0			0
$904$	−9.03509	+	5.41113i	−0.300503	+	0.179971i
$905$	−6.64436	+	11.5084i	−0.220866	+	0.382551i
$906$	−6.14361	−	33.7866i	−0.204108	−	1.12249i
$907$	−23.6320	+	13.6440i	−0.784688	+	0.453040i	−0.838089	−	0.545533i	$-0.816327\pi$
$907$	−23.6320	+	13.6440i	−0.784688	+	0.453040i	0.0534010	+	0.998573i	$0.482994\pi$
$908$	−3.83203	+	1.44125i	−0.127170	+	0.0478296i
$909$		−	5.96314i		−	0.197785i
$910$		0			0
$911$		−	39.9753i		−	1.32444i	−0.749309	−	0.662221i	$-0.769614\pi$
$911$		−	39.9753i		−	1.32444i	0.749309	−	0.662221i	$-0.230386\pi$
$912$	19.1338	+	6.50501i	0.633584	+	0.215402i
$913$	−49.0875	+	28.3407i	−1.62456	+	0.937941i
$914$	10.6840	−	1.94273i	0.353395	−	0.0642597i
$915$	−0.138511	+	0.239909i	−0.00457904	+	0.00793113i
$916$	−5.90280	+	7.18917i	−0.195034	+	0.237537i
$917$		0			0
$918$	6.57546	+	2.35360i	0.217023	+	0.0776805i
$919$	−27.0928	−	15.6420i	−0.893709	−	0.515983i	−0.0185550	−	0.999828i	$-0.505907\pi$
$919$	−27.0928	−	15.6420i	−0.893709	−	0.515983i	−0.875154	+	0.483845i	$0.839240\pi$
$920$	3.67925	+	2.04638i	0.121301	+	0.0674670i
$921$	3.49755	+	6.05794i	0.115248	+	0.199616i
$922$	−4.63503	+	3.93160i	−0.152647	+	0.129480i
$923$	−4.23920			−0.139535
$924$		0			0
$925$	47.4354			1.55967
$926$	−3.14967	+	2.67167i	−0.103505	+	0.0877964i
$927$	−5.54683	−	9.60738i	−0.182182	−	0.315548i
$928$	−12.0840	−	30.6313i	−0.396675	−	1.00552i
$929$	13.8363	+	7.98838i	0.453954	+	0.262090i	0.709499	−	0.704707i	$-0.248921\pi$
$929$	13.8363	+	7.98838i	0.453954	+	0.262090i	−0.255545	+	0.966797i	$0.582255\pi$
$930$	−3.88325	−	1.38996i	−0.127337	−	0.0455786i
$931$		0			0
$932$	−6.55934	−	5.38567i	−0.214858	−	0.176414i
$933$	−11.0106	+	19.0709i	−0.360470	+	0.624352i
$934$	55.8661	−	10.1585i	1.82799	−	0.332395i
$935$	9.00023	−	5.19629i	0.294339	−	0.169937i
$936$	−11.2478	+	0.180122i	−0.367647	+	0.00588748i
$937$		−	18.3690i		−	0.600089i	−0.953925	−	0.300045i	$-0.902998\pi$
$937$		−	18.3690i		−	0.600089i	0.953925	−	0.300045i	$-0.0970016\pi$
$938$		0			0
$939$			1.73737i			0.0566970i
$940$	−2.82579	−	7.51325i	−0.0921670	−	0.245055i
$941$	−30.9773	+	17.8847i	−1.00983	+	0.583026i	−0.911142	−	0.412093i	$-0.864798\pi$
$941$	−30.9773	+	17.8847i	−1.00983	+	0.583026i	−0.0986881	+	0.995118i	$0.531465\pi$
$942$	−0.950913	−	5.22952i	−0.0309824	−	0.170387i
$943$	17.1500	−	29.7046i	0.558480	−	0.967316i
$944$	3.62312	+	18.2592i	0.117922	+	0.594285i
$945$		0			0
$946$	−19.3685	+	54.1114i	−0.629724	+	1.75931i
$947$	−11.0740	−	6.39358i	−0.359857	−	0.207763i	0.309161	−	0.951010i	$-0.399952\pi$
$947$	−11.0740	−	6.39358i	−0.359857	−	0.207763i	−0.669018	+	0.743246i	$0.733285\pi$
$948$	−2.48230	−	0.410425i	−0.0806215	−	0.0133300i
$949$	−1.66454	−	2.88307i	−0.0540332	−	0.0935883i
$950$	−21.9080	−	25.8277i	−0.710790	−	0.837963i
$951$	−32.1296			−1.04187
$952$		0			0
$953$	23.6660			0.766616			0.383308	−	0.923621i	$-0.374785\pi$
$953$	23.6660			0.766616			0.383308	+	0.923621i	$0.374785\pi$
$954$	−1.13320	−	1.33595i	−0.0366886	−	0.0432528i
$955$	0.447333	+	0.774803i	0.0144754	+	0.0250720i
$956$	23.0097	+	3.80443i	0.744186	+	0.123044i
$957$	20.8066	+	12.0127i	0.672580	+	0.388314i
$958$	10.4960	−	29.3236i	0.339110	−	0.947402i
$959$		0			0
$960$	−3.59601	−	1.92535i	−0.116061	−	0.0621403i
$961$	−0.859022	+	1.48787i	−0.0277104	+	0.0479958i
$962$	10.0700	+	55.3799i	0.324671	+	1.78552i
$963$	0.544929	−	0.314615i	0.0175601	−	0.0101383i
$964$	7.02319	+	18.6734i	0.226202	+	0.601429i
$965$		−	7.61083i		−	0.245001i
$966$		0			0
$967$		−	9.30274i		−	0.299156i	−0.988750	−	0.149578i	$-0.952208\pi$
$967$		−	9.30274i		−	0.299156i	0.988750	−	0.149578i	$-0.0477915\pi$
$968$	−0.273313	−	17.0671i	−0.00878461	−	0.548559i
$969$	−21.6079	+	12.4753i	−0.694145	+	0.400765i
$970$	1.28341	−	0.233369i	0.0412077	−	0.00749303i
$971$	−12.4374	+	21.5423i	−0.399136	+	0.691325i	−0.993620	−	0.112783i	$-0.964023\pi$
$971$	−12.4374	+	21.5423i	−0.399136	+	0.691325i	0.594483	+	0.804108i	$0.297357\pi$
$972$	1.54572	+	1.26915i	0.0495792	+	0.0407079i
$973$		0			0
$974$	26.5221	+	9.49323i	0.849822	+	0.304183i
$975$	16.3264	+	9.42606i	0.522864	+	0.301875i
$976$	1.43217	+	1.63461i	0.0458425	+	0.0523226i
$977$	17.5448	+	30.3885i	0.561308	+	0.972214i	0.997383	+	0.0723036i	$0.0230350\pi$
$977$	17.5448	+	30.3885i	0.561308	+	0.972214i	−0.436075	+	0.899911i	$0.643632\pi$
$978$	8.72466	−	7.40057i	0.278984	−	0.236644i
$979$	−19.3533			−0.618536
$980$		0			0
$981$	15.8175			0.505015
$982$	24.2552	−	20.5741i	0.774015	−	0.656547i
$983$	25.1609	+	43.5799i	0.802508	+	1.38998i	0.917961	+	0.396671i	$0.129835\pi$
$983$	25.1609	+	43.5799i	0.802508	+	1.38998i	−0.115453	+	0.993313i	$0.536832\pi$
$984$	−16.1532	+	29.0424i	−0.514945	+	0.925837i
$985$	−5.37248	−	3.10180i	−0.171181	−	0.0988316i
$986$	38.2759	+	13.7004i	1.21895	+	0.436309i
$987$		0			0
$988$	25.5025	−	31.0602i	0.811344	−	0.988156i
$989$	14.3724	−	24.8937i	0.457016	−	0.791575i
$990$	2.92810	−	0.532433i	0.0930611	−	0.0169218i
$991$	−26.9804	+	15.5771i	−0.857060	+	0.494824i	−0.863027	−	0.505158i	$-0.831434\pi$
$991$	−26.9804	+	15.5771i	−0.857060	+	0.494824i	0.00596663	+	0.999982i	$0.498101\pi$
$992$	−20.1299	+	25.3331i	−0.639124	+	0.804327i
$993$		−	11.4233i		−	0.362508i
$994$		0			0
$995$		−	10.9386i		−	0.346778i
$996$	−25.7082	+	9.66902i	−0.814594	+	0.306375i
$997$	27.1914	−	15.6989i	0.861159	−	0.497191i	−0.00324095	−	0.999995i	$-0.501032\pi$
$997$	27.1914	−	15.6989i	0.861159	−	0.497191i	0.864400	+	0.502804i	$0.167698\pi$
$998$	−6.58517	−	36.2150i	−0.208450	−	1.14636i
$999$	5.00371	−	8.66667i	0.158310	−	0.274201i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.o.f.19.5		24
4.3	odd	2		588.2.o.e.19.12		24
7.2	even	3		588.2.b.c.391.4	yes	12
7.3	odd	6		588.2.o.e.31.12		24
7.4	even	3	inner	588.2.o.f.31.12		24
7.5	odd	6		588.2.b.d.391.4	yes	12
7.6	odd	2		588.2.o.e.19.5		24
21.2	odd	6		1764.2.b.l.1567.9		12
21.5	even	6		1764.2.b.m.1567.9		12
28.3	even	6	inner	588.2.o.f.31.5		24
28.11	odd	6		588.2.o.e.31.5		24
28.19	even	6		588.2.b.c.391.3	✓	12
28.23	odd	6		588.2.b.d.391.3	yes	12
28.27	even	2	inner	588.2.o.f.19.12		24
84.23	even	6		1764.2.b.m.1567.10		12
84.47	odd	6		1764.2.b.l.1567.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.3	✓	12	28.19	even	6
588.2.b.c.391.4	yes	12	7.2	even	3
588.2.b.d.391.3	yes	12	28.23	odd	6
588.2.b.d.391.4	yes	12	7.5	odd	6
588.2.o.e.19.5		24	7.6	odd	2
588.2.o.e.19.12		24	4.3	odd	2
588.2.o.e.31.5		24	28.11	odd	6
588.2.o.e.31.12		24	7.3	odd	6
588.2.o.f.19.5		24	1.1	even	1	trivial
588.2.o.f.19.12		24	28.27	even	2	inner
588.2.o.f.31.5		24	28.3	even	6	inner
588.2.o.f.31.12		24	7.4	even	3	inner
1764.2.b.l.1567.9		12	21.2	odd	6
1764.2.b.l.1567.10		12	84.47	odd	6
1764.2.b.m.1567.9		12	21.5	even	6
1764.2.b.m.1567.10		12	84.23	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.914808 - 1.07848i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.326251 + 1.97321i) q^{4} +(-0.441565 - 0.254938i) q^{5} +(0.476589 - 1.33149i) q^{6} +(2.42653 - 1.45325i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.129001 + 0.709440i) q^{10} +(-3.57438 + 2.06367i) q^{11} +(-1.87198 + 0.704063i) q^{12} +3.97722i q^{13} -0.509876i q^{15} +(-3.78712 - 1.28752i) q^{16} +(4.27680 - 2.46921i) q^{17} +(1.39140 - 0.253006i) q^{18} +(-2.52617 + 4.37545i) q^{19} +(0.647107 - 0.788127i) q^{20} +(5.49550 + 1.96705i) q^{22} +(-2.52818 - 1.45965i) q^{23} +(2.47182 + 1.37481i) q^{24} +(-2.37001 - 4.10498i) q^{25} +(4.28936 - 3.63839i) q^{26} -1.00000 q^{27} -5.82102 q^{29} +(-0.549892 + 0.466438i) q^{30} +(2.85998 + 4.95364i) q^{31} +(2.07592 + 5.26218i) q^{32} +(-3.57438 - 2.06367i) q^{33} +(-6.57546 - 2.35360i) q^{34} +(-1.54572 - 1.26915i) q^{36} +(-5.00371 + 8.66667i) q^{37} +(7.02981 - 1.27827i) q^{38} +(-3.44437 + 1.98861i) q^{39} +(-1.44196 + 0.0230915i) q^{40} +11.7494i q^{41} +9.84649i q^{43} +(-2.90591 - 7.72628i) q^{44} +(0.441565 - 0.254938i) q^{45} +(0.738599 + 4.06190i) q^{46} +(3.93580 - 6.81701i) q^{47} +(-0.778531 - 3.92350i) q^{48} +(-2.25905 + 6.31129i) q^{50} +(4.27680 + 2.46921i) q^{51} +(-7.84789 - 1.29757i) q^{52} +(-0.619363 - 1.07277i) q^{53} +(0.914808 + 1.07848i) q^{54} +2.10443 q^{55} -5.05234 q^{57} +(5.32512 + 6.27788i) q^{58} +(-2.32689 - 4.03030i) q^{59} +(1.00609 + 0.166348i) q^{60} +(-0.470524 - 0.271657i) q^{61} +(2.72608 - 7.61607i) q^{62} +(3.77611 - 7.05273i) q^{64} +(1.01394 - 1.75620i) q^{65} +(1.04424 + 5.74277i) q^{66} +(6.08041 - 3.51053i) q^{67} +(3.47697 + 9.24462i) q^{68} -2.91930i q^{69} +1.06587i q^{71} +(0.0452885 + 2.82806i) q^{72} +(-0.724896 + 0.418519i) q^{73} +(13.9243 - 2.53193i) q^{74} +(2.37001 - 4.10498i) q^{75} +(-7.80952 - 6.41216i) q^{76} +(5.29562 + 1.89550i) q^{78} +(1.08946 + 0.629001i) q^{79} +(1.34402 + 1.53401i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(12.6715 - 10.7484i) q^{82} +13.7332 q^{83} -2.51798 q^{85} +(10.6193 - 9.00765i) q^{86} +(-2.91051 - 5.04115i) q^{87} +(-5.67431 + 10.2020i) q^{88} +(4.06085 + 2.34453i) q^{89} +(-0.678894 - 0.243001i) q^{90} +(3.70502 - 4.51243i) q^{92} +(-2.85998 + 4.95364i) q^{93} +(-10.9525 + 1.99156i) q^{94} +(2.23094 - 1.28803i) q^{95} +(-3.51923 + 4.42889i) q^{96} -1.80904i q^{97} -4.12734i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 12 q^{3} + 4 q^{4} - 8 q^{6} + 8 q^{8} - 12 q^{9} - 4 q^{12} + 4 q^{16} - 4 q^{18} + 48 q^{20} + 4 q^{24} + 12 q^{25} + 24 q^{26} - 24 q^{27} + 64 q^{29} + 16 q^{31} - 4 q^{32} - 64 q^{34}+ \cdots + 4 q^{96}+O(q^{100}) \) 24 * q - 4 * q^2 + 12 * q^3 + 4 * q^4 - 8 * q^6 + 8 * q^8 - 12 * q^9 - 4 * q^12 + 4 * q^16 - 4 * q^18 + 48 * q^20 + 4 * q^24 + 12 * q^25 + 24 * q^26 - 24 * q^27 + 64 * q^29 + 16 * q^31 - 4 * q^32 - 64 * q^34 - 8 * q^36 - 32 * q^37 - 24 * q^38 - 32 * q^40 + 24 * q^44 - 24 * q^46 + 8 * q^48 - 56 * q^50 + 32 * q^52 + 32 * q^53 + 4 * q^54 - 32 * q^55 - 16 * q^58 - 16 * q^59 + 24 * q^60 - 16 * q^62 - 8 * q^64 - 8 * q^68 - 4 * q^72 + 32 * q^74 - 12 * q^75 + 64 * q^76 + 48 * q^78 - 16 * q^80 - 12 * q^81 + 32 * q^82 + 32 * q^83 + 32 * q^85 + 24 * q^86 + 32 * q^87 - 24 * q^88 - 16 * q^93 + 4 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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