LMFDB - Embedded newform 630.2.bf.e.209.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(209,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.209"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-16,0,-16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.16
Character	$\chi$	$=$	630.209
Dual form			630.2.bf.e.419.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.71915 + 0.210974i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22443 + 1.87103i) q^{5} +(-1.04229 + 1.38334i) q^{6} +(2.45843 + 0.977807i) q^{7} +1.00000 q^{8} +(2.91098 + 0.725392i) q^{9} +(-2.23258 + 0.124872i) q^{10} +(-1.44107 - 0.832005i) q^{11} +(-0.676868 - 1.59432i) q^{12} +(1.04814 + 1.81544i) q^{13} +(-2.07602 + 1.64016i) q^{14} +(1.71025 + 3.47492i) q^{15} +(-0.500000 + 0.866025i) q^{16} -7.45463i q^{17} +(-2.08370 + 2.15829i) q^{18} +4.66141i q^{19} +(1.00815 - 1.99591i) q^{20} +(4.02013 + 2.19967i) q^{21} +(1.44107 - 0.832005i) q^{22} +(-2.82486 - 4.89279i) q^{23} +(1.71915 + 0.210974i) q^{24} +(-2.00154 + 4.58191i) q^{25} -2.09629 q^{26} +(4.85138 + 1.86120i) q^{27} +(-0.382411 - 2.61797i) q^{28} +(-4.10738 - 2.37140i) q^{29} +(-3.86449 - 0.256341i) q^{30} +(-1.73402 + 1.00114i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.30190 - 1.73437i) q^{33} +(6.45590 + 3.72732i) q^{34} +(1.18067 + 5.79707i) q^{35} +(-0.827282 - 2.88368i) q^{36} -4.86789i q^{37} +(-4.03690 - 2.33070i) q^{38} +(1.41891 + 3.34215i) q^{39} +(1.22443 + 1.87103i) q^{40} +(4.07169 + 7.05238i) q^{41} +(-3.91503 + 2.38170i) q^{42} +(-2.25274 - 1.30062i) q^{43} +1.66401i q^{44} +(2.20706 + 6.33474i) q^{45} +5.64971 q^{46} +(8.90154 + 5.13931i) q^{47} +(-1.04229 + 1.38334i) q^{48} +(5.08779 + 4.80775i) q^{49} +(-2.96728 - 4.02433i) q^{50} +(1.57273 - 12.8157i) q^{51} +(1.04814 - 1.81544i) q^{52} -13.8374 q^{53} +(-4.03754 + 3.27082i) q^{54} +(-0.207788 - 3.71503i) q^{55} +(2.45843 + 0.977807i) q^{56} +(-0.983434 + 8.01368i) q^{57} +(4.10738 - 2.37140i) q^{58} +(0.0862901 + 0.149459i) q^{59} +(2.15424 - 3.21858i) q^{60} +(-5.17503 - 2.98781i) q^{61} -2.00228i q^{62} +(6.44716 + 4.62971i) q^{63} +1.00000 q^{64} +(-2.11336 + 4.18399i) q^{65} +(2.65296 - 1.12632i) q^{66} +(4.70611 - 2.71707i) q^{67} +(-6.45590 + 3.72732i) q^{68} +(-3.82411 - 9.00744i) q^{69} +(-5.61075 - 1.87604i) q^{70} -12.0450i q^{71} +(2.91098 + 0.725392i) q^{72} +4.79644 q^{73} +(4.21571 + 2.43394i) q^{74} +(-4.40761 + 7.45473i) q^{75} +(4.03690 - 2.33070i) q^{76} +(-2.72924 - 3.45452i) q^{77} +(-3.60384 - 0.442261i) q^{78} +(-6.30891 + 10.9273i) q^{79} +(-2.23258 + 0.124872i) q^{80} +(7.94761 + 4.22320i) q^{81} -8.14339 q^{82} +(-2.24015 - 1.29335i) q^{83} +(-0.105101 - 4.58137i) q^{84} +(13.9479 - 9.12768i) q^{85} +(2.25274 - 1.30062i) q^{86} +(-6.56091 - 4.94334i) q^{87} +(-1.44107 - 0.832005i) q^{88} -11.2248 q^{89} +(-6.58957 - 1.25600i) q^{90} +(0.801642 + 5.48801i) q^{91} +(-2.82486 + 4.89279i) q^{92} +(-3.19227 + 1.35528i) q^{93} +(-8.90154 + 5.13931i) q^{94} +(-8.72165 + 5.70757i) q^{95} +(-0.676868 - 1.59432i) q^{96} +(4.73188 - 8.19586i) q^{97} +(-6.70752 + 2.00228i) q^{98} +(-3.59141 - 3.46729i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9} - 24 q^{11} - 16 q^{15} - 16 q^{16} + 6 q^{18} + 2 q^{21} + 24 q^{22} - 24 q^{23} - 58 q^{25} - 36 q^{29} - 10 q^{30} - 16 q^{32} - 48 q^{35} - 66 q^{39}+ \cdots + 58 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9 - 24 * q^11 - 16 * q^15 - 16 * q^16 + 6 * q^18 + 2 * q^21 + 24 * q^22 - 24 * q^23 - 58 * q^25 - 36 * q^29 - 10 * q^30 - 16 * q^32 - 48 * q^35 - 66 * q^39 + 2 * q^42 - 54 * q^43 + 48 * q^46 + 32 * q^49 + 50 * q^50 - 26 * q^51 - 24 * q^53 + 110 * q^57 + 36 * q^58 + 26 * q^60 + 20 * q^63 + 32 * q^64 - 90 * q^65 - 66 * q^67 + 36 * q^70 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 60 * q^78 + 34 * q^79 + 2 * q^81 - 4 * q^84 + 4 * q^85 + 54 * q^86 - 24 * q^88 + 16 * q^91 - 24 * q^92 + 28 * q^93 + 12 * q^95 - 64 * q^98 + 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.71915	+	0.210974i	0.992554	+	0.121806i
$3$	1.71915	+	0.210974i	0.992554	+	0.121806i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.22443	+	1.87103i	0.547582	+	0.836752i
$5$	1.22443	+	1.87103i	0.547582	+	0.836752i
$6$	−1.04229	+	1.38334i	−0.425511	+	0.564748i
$7$	2.45843	+	0.977807i	0.929200	+	0.369576i
$7$	2.45843	+	0.977807i	0.929200	+	0.369576i
$8$	1.00000			0.353553
$9$	2.91098	+	0.725392i	0.970327	+	0.241797i
$10$	−2.23258	+	0.124872i	−0.706003	+	0.0394879i
$11$	−1.44107	−	0.832005i	−0.434500	−	0.250859i	0.266762	−	0.963763i	$-0.414046\pi$
$11$	−1.44107	−	0.832005i	−0.434500	−	0.250859i	−0.701262	+	0.712904i	$0.747380\pi$
$12$	−0.676868	−	1.59432i	−0.195395	−	0.460240i
$13$	1.04814	+	1.81544i	0.290703	+	0.503512i	0.973976	−	0.226651i	$-0.0727776\pi$
$13$	1.04814	+	1.81544i	0.290703	+	0.503512i	−0.683273	+	0.730163i	$0.739444\pi$
$14$	−2.07602	+	1.64016i	−0.554840	+	0.438352i
$15$	1.71025	+	3.47492i	0.441584	+	0.897220i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	7.45463i		−	1.80801i	−0.427518	−	0.904007i	$-0.640612\pi$
$17$		−	7.45463i		−	1.80801i	0.427518	−	0.904007i	$-0.359388\pi$
$18$	−2.08370	+	2.15829i	−0.491132	+	0.508713i
$19$			4.66141i			1.06940i	0.845042	+	0.534700i	$0.179575\pi$
$19$			4.66141i			1.06940i	−0.845042	+	0.534700i	$0.820425\pi$
$20$	1.00815	−	1.99591i	0.225429	−	0.446298i
$21$	4.02013	+	2.19967i	0.877265	+	0.480006i
$22$	1.44107	−	0.832005i	0.307238	−	0.177384i
$23$	−2.82486	−	4.89279i	−0.589023	−	1.02022i	−0.994361	−	0.106051i	$-0.966179\pi$
$23$	−2.82486	−	4.89279i	−0.589023	−	1.02022i	0.405337	−	0.914167i	$-0.367154\pi$
$24$	1.71915	+	0.210974i	0.350921	+	0.0430648i
$25$	−2.00154	+	4.58191i	−0.400307	+	0.916381i
$26$	−2.09629			−0.411116
$27$	4.85138	+	1.86120i	0.933649	+	0.358188i
$28$	−0.382411	−	2.61797i	−0.0722688	−	0.494750i
$29$	−4.10738	−	2.37140i	−0.762721	−	0.440357i	0.0675508	−	0.997716i	$-0.478482\pi$
$29$	−4.10738	−	2.37140i	−0.762721	−	0.440357i	−0.830272	+	0.557359i	$0.811815\pi$
$30$	−3.86449	−	0.256341i	−0.705556	−	0.0468013i
$31$	−1.73402	+	1.00114i	−0.311440	+	0.179810i	−0.647571	−	0.762005i	$-0.724215\pi$
$31$	−1.73402	+	1.00114i	−0.311440	+	0.179810i	0.336131	+	0.941815i	$0.390882\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.30190	−	1.73437i	−0.400709	−	0.301915i
$34$	6.45590	+	3.72732i	1.10718	+	0.639229i
$35$	1.18067	+	5.79707i	0.199570	+	0.979884i
$36$	−0.827282	−	2.88368i	−0.137880	−	0.480613i
$37$		−	4.86789i		−	0.800276i	−0.916455	−	0.400138i	$-0.868962\pi$
$37$		−	4.86789i		−	0.800276i	0.916455	−	0.400138i	$-0.131038\pi$
$38$	−4.03690	−	2.33070i	−0.654871	−	0.378090i
$39$	1.41891	+	3.34215i	0.227207	+	0.535172i
$40$	1.22443	+	1.87103i	0.193600	+	0.295836i
$41$	4.07169	+	7.05238i	0.635892	+	1.10140i	0.986325	+	0.164809i	$0.0527008\pi$
$41$	4.07169	+	7.05238i	0.635892	+	1.10140i	−0.350434	+	0.936587i	$0.613966\pi$
$42$	−3.91503	+	2.38170i	−0.604103	+	0.367505i
$43$	−2.25274	−	1.30062i	−0.343540	−	0.198343i	0.318296	−	0.947991i	$-0.396889\pi$
$43$	−2.25274	−	1.30062i	−0.343540	−	0.198343i	−0.661836	+	0.749648i	$0.730223\pi$
$44$			1.66401i			0.250859i
$45$	2.20706	+	6.33474i	0.329009	+	0.944327i
$46$	5.64971			0.833005
$47$	8.90154	+	5.13931i	1.29842	+	0.749645i	0.980132	−	0.198348i	$-0.0635575\pi$
$47$	8.90154	+	5.13931i	1.29842	+	0.749645i	0.318292	+	0.947993i	$0.396891\pi$
$48$	−1.04229	+	1.38334i	−0.150441	+	0.199669i
$49$	5.08779	+	4.80775i	0.726827	+	0.686821i
$50$	−2.96728	−	4.02433i	−0.419637	−	0.569127i
$51$	1.57273	−	12.8157i	0.220226	−	1.79455i
$52$	1.04814	−	1.81544i	0.145351	−	0.251756i
$53$	−13.8374			−1.90071			−0.950354	−	0.311170i	$-0.899279\pi$
$53$	−13.8374			−1.90071			−0.950354	+	0.311170i	$0.899279\pi$
$54$	−4.03754	+	3.27082i	−0.549440	+	0.445102i
$55$	−0.207788	−	3.71503i	−0.0280181	−	0.500935i
$56$	2.45843	+	0.977807i	0.328522	+	0.130665i
$57$	−0.983434	+	8.01368i	−0.130259	+	1.06144i
$58$	4.10738	−	2.37140i	0.539325	−	0.311380i
$59$	0.0862901	+	0.149459i	0.0112340	+	0.0194579i	0.871588	−	0.490240i	$-0.163091\pi$
$59$	0.0862901	+	0.149459i	0.0112340	+	0.0194579i	−0.860354	+	0.509697i	$0.829757\pi$
$60$	2.15424	−	3.21858i	0.278112	−	0.415516i
$61$	−5.17503	−	2.98781i	−0.662595	−	0.382550i	0.130670	−	0.991426i	$-0.458287\pi$
$61$	−5.17503	−	2.98781i	−0.662595	−	0.382550i	−0.793265	+	0.608876i	$0.791621\pi$
$62$		−	2.00228i		−	0.254290i
$63$	6.44716	+	4.62971i	0.812265	+	0.583288i
$64$	1.00000			0.125000
$65$	−2.11336	+	4.18399i	−0.262131	+	0.518960i
$66$	2.65296	−	1.12632i	0.326557	−	0.138640i
$67$	4.70611	−	2.71707i	0.574943	−	0.331943i	−0.184178	−	0.982893i	$-0.558962\pi$
$67$	4.70611	−	2.71707i	0.574943	−	0.331943i	0.759121	+	0.650949i	$0.225629\pi$
$68$	−6.45590	+	3.72732i	−0.782893	+	0.452003i
$69$	−3.82411	−	9.00744i	−0.460369	−	1.08437i
$70$	−5.61075	−	1.87604i	−0.670612	−	0.224230i
$71$		−	12.0450i		−	1.42947i	−0.699393	−	0.714737i	$-0.746546\pi$
$71$		−	12.0450i		−	1.42947i	0.699393	−	0.714737i	$-0.253454\pi$
$72$	2.91098	+	0.725392i	0.343062	+	0.0854883i
$73$	4.79644			0.561381			0.280691	−	0.959798i	$-0.409437\pi$
$73$	4.79644			0.561381			0.280691	+	0.959798i	$0.409437\pi$
$74$	4.21571	+	2.43394i	0.490067	+	0.282940i
$75$	−4.40761	+	7.45473i	−0.508947	+	0.860798i
$76$	4.03690	−	2.33070i	0.463064	−	0.267350i
$77$	−2.72924	−	3.45452i	−0.311026	−	0.393679i
$78$	−3.60384	−	0.442261i	−0.408054	−	0.0500762i
$79$	−6.30891	+	10.9273i	−0.709807	+	1.22942i	0.255121	+	0.966909i	$0.417885\pi$
$79$	−6.30891	+	10.9273i	−0.709807	+	1.22942i	−0.964928	+	0.262513i	$0.915449\pi$
$80$	−2.23258	+	0.124872i	−0.249610	+	0.0139611i
$81$	7.94761	+	4.22320i	0.883068	+	0.469245i
$82$	−8.14339			−0.899286
$83$	−2.24015	−	1.29335i	−0.245888	−	0.141964i	0.371992	−	0.928236i	$-0.378675\pi$
$83$	−2.24015	−	1.29335i	−0.245888	−	0.141964i	−0.617880	+	0.786272i	$0.712008\pi$
$84$	−0.105101	−	4.58137i	−0.0114674	−	0.499868i
$85$	13.9479	−	9.12768i	1.51286	−	0.990036i
$86$	2.25274	−	1.30062i	0.242919	−	0.140250i
$87$	−6.56091	−	4.94334i	−0.703404	−	0.529982i
$88$	−1.44107	−	0.832005i	−0.153619	−	0.0886920i
$89$	−11.2248			−1.18982			−0.594912	−	0.803791i	$-0.702813\pi$
$89$	−11.2248			−1.18982			−0.594912	+	0.803791i	$0.702813\pi$
$90$	−6.58957	−	1.25600i	−0.694602	−	0.132394i
$91$	0.801642	+	5.48801i	0.0840350	+	0.575300i
$92$	−2.82486	+	4.89279i	−0.294512	+	0.510109i
$93$	−3.19227	+	1.35528i	−0.331023	+	0.140536i
$94$	−8.90154	+	5.13931i	−0.918124	+	0.530079i
$95$	−8.72165	+	5.70757i	−0.894823	+	0.585585i
$96$	−0.676868	−	1.59432i	−0.0690826	−	0.162719i
$97$	4.73188	−	8.19586i	0.480450	−	0.832164i	−0.519298	−	0.854593i	$-0.673807\pi$
$97$	4.73188	−	8.19586i	0.480450	−	0.832164i	0.999748	+	0.0224290i	$0.00713998\pi$
$98$	−6.70752	+	2.00228i	−0.677562	+	0.202261i
$99$	−3.59141	−	3.46729i	−0.360950	−	0.348476i
$100$	4.96881	−	0.557572i	0.496881	−	0.0557572i
$101$	5.28548	−	9.15472i	0.525925	−	0.910928i	−0.473619	−	0.880730i	$-0.657053\pi$
$101$	5.28548	−	9.15472i	0.525925	−	0.910928i	0.999544	−	0.0301987i	$-0.00961400\pi$
$102$	10.3123	+	7.76985i	1.02107	+	0.769330i
$103$	7.61856	+	13.1957i	0.750679	+	1.30021i	0.947494	+	0.319773i	$0.103607\pi$
$103$	7.61856	+	13.1957i	0.750679	+	1.30021i	−0.196816	+	0.980441i	$0.563060\pi$
$104$	1.04814	+	1.81544i	0.102779	+	0.178018i
$105$	0.806730	+	10.2151i	0.0787287	+	0.996896i
$106$	6.91868	−	11.9835i	0.672002	−	1.16394i
$107$	−11.4163			−1.10366			−0.551829	−	0.833957i	$-0.686070\pi$
$107$	−11.4163			−1.10366			−0.551829	+	0.833957i	$0.686070\pi$
$108$	−0.813845	−	5.13202i	−0.0783123	−	0.493829i
$109$	−10.6147			−1.01670			−0.508351	−	0.861150i	$-0.669745\pi$
$109$	−10.6147			−1.01670			−0.508351	+	0.861150i	$0.669745\pi$
$110$	3.32121	+	1.67757i	0.316664	+	0.159950i
$111$	1.02700	−	8.36865i	0.0974781	−	0.794317i
$112$	−2.07602	+	1.64016i	−0.196166	+	0.154981i
$113$	6.87120	+	11.9013i	0.646388	+	1.11958i	0.983979	+	0.178284i	$0.0570546\pi$
$113$	6.87120	+	11.9013i	0.646388	+	1.11958i	−0.337591	+	0.941293i	$0.609612\pi$
$114$	−6.44833	−	4.85852i	−0.603942	−	0.455042i
$115$	5.69574	−	11.2763i	0.531131	−	1.05152i
$116$			4.74279i			0.440357i
$117$	1.73422	+	6.04502i	0.160329	+	0.558862i
$118$	−0.172580			−0.0158873
$119$	7.28919	−	18.3267i	0.668199	−	1.68001i
$120$	1.71025	+	3.47492i	0.156124	+	0.317215i
$121$	−4.11554	−	7.12832i	−0.374140	−	0.648029i
$122$	5.17503	−	2.98781i	0.468526	−	0.270503i
$123$	5.51200	+	12.9831i	0.497000	+	1.17065i
$124$	1.73402	+	1.00114i	0.155720	+	0.0899050i
$125$	−11.0236	+	1.86529i	−0.985985	+	0.166837i
$126$	−7.23302	+	3.26855i	−0.644369	+	0.291185i
$127$		−	14.1949i		−	1.25960i	−0.776759	−	0.629798i	$-0.783138\pi$
$127$		−	14.1949i		−	1.25960i	0.776759	−	0.629798i	$-0.216862\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−3.59841	−	2.71124i	−0.316823	−	0.238711i
$130$	−2.56676	−	3.92222i	−0.225120	−	0.344002i
$131$	1.14681	+	1.98633i	0.100197	+	0.173547i	0.911766	−	0.410710i	$-0.134719\pi$
$131$	1.14681	+	1.98633i	0.100197	+	0.173547i	−0.811569	+	0.584257i	$0.801386\pi$
$132$	−0.351062	+	2.86069i	−0.0305560	+	0.248991i
$133$	−4.55796	+	11.4598i	−0.395225	+	0.993687i
$134$			5.43415i			0.469439i
$135$	2.45782	+	11.3560i	0.211535	+	0.977370i
$136$		−	7.45463i		−	0.639229i
$137$	5.41797	−	9.38419i	0.462888	−	0.801746i	−0.536215	−	0.844081i	$-0.680147\pi$
$137$	5.41797	−	9.38419i	0.462888	−	0.801746i	0.999103	+	0.0423355i	$0.0134798\pi$
$138$	9.71273	+	1.19194i	0.826802	+	0.101465i
$139$	7.63600	−	4.40865i	0.647677	−	0.373936i	−0.139889	−	0.990167i	$-0.544674\pi$
$139$	7.63600	−	4.40865i	0.647677	−	0.373936i	0.787566	+	0.616231i	$0.211341\pi$
$140$	4.43007	−	3.92103i	0.374409	−	0.331387i
$141$	14.2189	+	10.7133i	1.19744	+	0.902219i
$142$	10.4312	+	6.02248i	0.875371	+	0.505396i
$143$		−	3.48824i		−	0.291701i
$144$	−2.08370	+	2.15829i	−0.173642	+	0.179857i
$145$	−0.592241	−	10.5887i	−0.0491830	−	0.879340i
$146$	−2.39822	+	4.15384i	−0.198478	+	0.343774i
$147$	7.73238	+	9.33865i	0.637756	+	0.770238i
$148$	−4.21571	+	2.43394i	−0.346529	+	0.200069i
$149$	12.4184	−	7.16974i	1.01735	−	0.587368i	0.104016	−	0.994576i	$-0.466831\pi$
$149$	12.4184	−	7.16974i	1.01735	−	0.587368i	0.913336	+	0.407207i	$0.133497\pi$
$150$	−4.25218	−	7.54447i	−0.347189	−	0.616003i
$151$	3.45207	−	5.97917i	0.280926	−	0.486578i	−0.690687	−	0.723154i	$-0.742692\pi$
$151$	3.45207	−	5.97917i	0.280926	−	0.486578i	0.971613	+	0.236576i	$0.0760252\pi$
$152$			4.66141i			0.378090i
$153$	5.40753	−	21.7003i	0.437173	−	1.75436i
$154$	4.35632	−	0.636335i	0.351043	−	0.0512773i
$155$	−3.99636	−	2.01859i	−0.320995	−	0.162137i
$156$	2.18493	−	2.89989i	0.174934	−	0.232177i
$157$	−7.48808	−	12.9697i	−0.597614	−	1.03510i	−0.993172	−	0.116657i	$-0.962782\pi$
$157$	−7.48808	−	12.9697i	−0.597614	−	1.03510i	0.395559	−	0.918441i	$-0.370551\pi$
$158$	−6.30891	−	10.9273i	−0.501910	−	0.869333i
$159$	−23.7886	−	2.91932i	−1.88656	−	0.231517i
$160$	1.00815	−	1.99591i	0.0797010	−	0.157790i
$161$	−2.16051	−	14.7908i	−0.170272	−	1.16568i
$162$	−7.63121	+	4.77123i	−0.599564	+	0.374863i
$163$		−	8.03539i		−	0.629380i	−0.949194	−	0.314690i	$-0.898099\pi$
$163$		−	8.03539i		−	0.629380i	0.949194	−	0.314690i	$-0.101901\pi$
$164$	4.07169	−	7.05238i	0.317946	−	0.550698i
$165$	0.426554	−	6.43055i	0.0332072	−	0.500617i
$166$	2.24015	−	1.29335i	0.173869	−	0.100384i
$167$	4.12075	−	2.37911i	0.318873	−	0.184101i	−0.332017	−	0.943273i	$-0.607729\pi$
$167$	4.12075	−	2.37911i	0.318873	−	0.184101i	0.650890	+	0.759172i	$0.274396\pi$
$168$	4.02013	+	2.19967i	0.310160	+	0.169708i
$169$	4.30279	−	7.45265i	0.330984	−	0.573281i
$170$	0.930873	+	16.6430i	0.0713947	+	1.27646i
$171$	−3.38135	+	13.5693i	−0.258578	+	1.03767i
$172$			2.60124i			0.198343i
$173$	−14.9456	−	8.62882i	−1.13629	−	0.656037i	−0.190781	−	0.981633i	$-0.561102\pi$
$173$	−14.9456	−	8.62882i	−1.13629	−	0.656037i	−0.945509	+	0.325595i	$0.894435\pi$
$174$	7.56152	−	3.21025i	0.573237	−	0.243368i
$175$	−9.40086	+	9.30719i	−0.710638	+	0.703558i
$176$	1.44107	−	0.832005i	0.108625	−	0.0627147i
$177$	0.116814	+	0.275148i	0.00878029	+	0.0206814i
$178$	5.61239	−	9.72094i	0.420666	−	0.728616i
$179$		−	0.602635i		−	0.0450430i	−0.999746	−	0.0225215i	$-0.992831\pi$
$179$		−	0.602635i		−	0.0450430i	0.999746	−	0.0225215i	$-0.00716943\pi$
$180$	4.38251	−	5.07874i	0.326653	−	0.378547i
$181$		−	12.7778i		−	0.949769i	−0.880048	−	0.474885i	$-0.842490\pi$
$181$		−	12.7778i		−	0.949769i	0.880048	−	0.474885i	$-0.157510\pi$
$182$	−5.15358	−	2.04976i	−0.382009	−	0.151939i
$183$	−8.26633	−	6.22830i	−0.611065	−	0.460409i
$184$	−2.82486	−	4.89279i	−0.208251	−	0.360702i
$185$	9.10798	−	5.96039i	0.669632	−	0.438217i
$186$	0.422428	−	3.44223i	0.0309739	−	0.252396i
$187$	−6.20229	+	10.7427i	−0.453556	+	0.785582i
$188$		−	10.2786i		−	0.749645i
$189$	10.1069	+	9.31936i	0.735169	+	0.677883i
$190$	−0.582079	−	10.4070i	−0.0422284	−	0.755000i
$191$	16.3178	+	9.42111i	1.18072	+	0.681687i	0.956180	−	0.292778i	$-0.0945798\pi$
$191$	16.3178	+	9.42111i	1.18072	+	0.681687i	0.224537	+	0.974466i	$0.427913\pi$
$192$	1.71915	+	0.210974i	0.124069	+	0.0152257i
$193$	5.89207	−	3.40179i	0.424120	−	0.244866i	−0.272718	−	0.962094i	$-0.587923\pi$
$193$	5.89207	−	3.40179i	0.424120	−	0.244866i	0.696839	+	0.717228i	$0.254589\pi$
$194$	4.73188	+	8.19586i	0.339730	+	0.588429i
$195$	−4.51591	+	6.74706i	−0.323391	+	0.483167i
$196$	1.61974	−	6.81003i	0.115696	−	0.486430i
$197$	−8.58750			−0.611834			−0.305917	−	0.952058i	$-0.598963\pi$
$197$	−8.58750			−0.611834			−0.305917	+	0.952058i	$0.598963\pi$
$198$	4.79847	−	1.37661i	0.341012	−	0.0978311i
$199$			5.10064i			0.361575i	0.983522	+	0.180788i	$0.0578646\pi$
$199$			5.10064i			0.361575i	−0.983522	+	0.180788i	$0.942135\pi$
$200$	−2.00154	+	4.58191i	−0.141530	+	0.323990i
$201$	8.66376	−	3.67820i	0.611094	−	0.259440i
$202$	5.28548	+	9.15472i	0.371885	+	0.644124i
$203$	−7.77895	−	9.84614i	−0.545975	−	0.691064i
$204$	−11.8851	+	5.04580i	−0.832120	+	0.353277i
$205$	−8.20973	+	16.2534i	−0.573392	+	1.13519i
$206$	−15.2371			−1.06162
$207$	−4.67391	−	16.2920i	−0.324859	−	1.13237i
$208$	−2.09629			−0.145351
$209$	3.87831	−	6.71743i	0.268268	−	0.464655i
$210$	−9.24994	−	4.40892i	−0.638306	−	0.304245i
$211$	5.01715	+	8.68995i	0.345395	+	0.598241i	0.985425	−	0.170108i	$-0.0544118\pi$
$211$	5.01715	+	8.68995i	0.345395	+	0.598241i	−0.640031	+	0.768349i	$0.721078\pi$
$212$	6.91868	+	11.9835i	0.475177	+	0.823031i
$213$	2.54117	−	20.7072i	0.174118	−	1.41883i
$214$	5.70816	−	9.88683i	0.390202	−	0.675850i
$215$	−0.324822	−	5.80748i	−0.0221527	−	0.396067i
$216$	4.85138	+	1.86120i	0.330095	+	0.126639i
$217$	−5.24190	+	0.765693i	−0.355844	+	0.0519786i
$218$	5.30734	−	9.19258i	0.359458	−	0.622600i
$219$	8.24582	+	1.01192i	0.557201	+	0.0683794i
$220$	−3.11342	+	2.03747i	−0.209907	+	0.137366i
$221$	13.5334	−	7.81352i	0.910356	−	0.525594i
$222$	6.73396	+	5.07373i	0.451954	+	0.340526i
$223$	−8.87226	+	15.3672i	−0.594131	+	1.02906i	0.399538	+	0.916717i	$0.369171\pi$
$223$	−8.87226	+	15.3672i	−0.594131	+	1.02906i	−0.993669	+	0.112348i	$0.964163\pi$
$224$	−0.382411	−	2.61797i	−0.0255509	−	0.174920i
$225$	−9.15011	+	11.8859i	−0.610007	+	0.792396i
$226$	−13.7424			−0.914131
$227$	−0.411273	−	0.237449i	−0.0272972	−	0.0157600i	0.486289	−	0.873798i	$-0.338350\pi$
$227$	−0.411273	−	0.237449i	−0.0272972	−	0.0157600i	−0.513586	+	0.858038i	$0.671683\pi$
$228$	7.43177	−	3.15516i	0.492181	−	0.208956i
$229$	−9.51279	+	5.49221i	−0.628623	+	0.362936i	−0.780219	−	0.625507i	$-0.784892\pi$
$229$	−9.51279	+	5.49221i	−0.628623	+	0.362936i	0.151596	+	0.988443i	$0.451559\pi$
$230$	6.91769	+	10.5708i	0.456139	+	0.697018i
$231$	−3.96318	−	6.51465i	−0.260758	−	0.428633i
$232$	−4.10738	−	2.37140i	−0.269663	−	0.155690i
$233$	21.4794			1.40716			0.703582	−	0.710614i	$-0.251583\pi$
$233$	21.4794			1.40716			0.703582	+	0.710614i	$0.251583\pi$
$234$	−6.10225	−	1.52063i	−0.398916	−	0.0994067i
$235$	1.28351	+	22.9478i	0.0837269	+	1.49695i
$236$	0.0862901	−	0.149459i	0.00561701	−	0.00972894i
$237$	−13.1514	+	17.4548i	−0.854273	+	1.13381i
$238$	12.2268	+	15.4760i	0.792546	+	1.00316i
$239$	−14.6228	+	8.44250i	−0.945873	+	0.546100i	−0.891797	−	0.452437i	$-0.850555\pi$
$239$	−14.6228	+	8.44250i	−0.945873	+	0.546100i	−0.0540768	+	0.998537i	$0.517222\pi$
$240$	−3.86449	−	0.256341i	−0.249452	−	0.0165468i
$241$	8.00911	+	4.62406i	0.515912	+	0.297862i	0.735261	−	0.677784i	$-0.237060\pi$
$241$	8.00911	+	4.62406i	0.515912	+	0.297862i	−0.219348	+	0.975647i	$0.570393\pi$
$242$	8.23107			0.529113
$243$	12.7722	+	8.93707i	0.819336	+	0.573314i
$244$			5.97562i			0.382550i
$245$	−2.76581	+	15.4062i	−0.176701	+	0.984265i
$246$	−13.9997	−	1.71804i	−0.892590	−	0.109538i
$247$	−8.46249	+	4.88582i	−0.538456	+	0.310877i
$248$	−1.73402	+	1.00114i	−0.110111	+	0.0635724i
$249$	−3.57830	−	2.69608i	−0.226766	−	0.170857i
$250$	3.89643	−	10.4794i	0.246432	−	0.662775i
$251$	−9.36996			−0.591426			−0.295713	−	0.955277i	$-0.595557\pi$
$251$	−9.36996			−0.591426			−0.295713	+	0.955277i	$0.595557\pi$
$252$	0.785864	−	7.89825i	0.0495048	−	0.497543i
$253$			9.40117i			0.591047i
$254$	12.2932	+	7.09746i	0.771342	+	0.445334i
$255$	25.9042	−	12.7493i	1.62219	−	0.798390i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.62239	+	3.24609i	−0.350715	+	0.202485i	−0.665000	−	0.746843i	$-0.731569\pi$
$257$	−5.62239	+	3.24609i	−0.350715	+	0.202485i	0.314285	+	0.949329i	$0.398235\pi$
$258$	4.14721	−	1.76070i	0.258194	−	0.109616i
$259$	4.75985	−	11.9674i	0.295763	−	0.743616i
$260$	4.68012	−	0.261767i	0.290249	−	0.0162341i
$261$	−10.2363	−	9.88255i	−0.633612	−	0.611714i
$262$	−2.29362			−0.141700
$263$	−4.41420	+	7.64563i	−0.272192	+	0.471450i	−0.969423	−	0.245397i	$-0.921082\pi$
$263$	−4.41420	+	7.64563i	−0.272192	+	0.471450i	0.697231	+	0.716846i	$0.254415\pi$
$264$	−2.30190	−	1.73437i	−0.141672	−	0.106743i
$265$	−16.9429	−	25.8902i	−1.04079	−	1.59042i
$266$	−7.64546	−	9.67719i	−0.468773	−	0.593346i
$267$	−19.2971	−	2.36813i	−1.18096	−	0.144927i
$268$	−4.70611	−	2.71707i	−0.287471	−	0.165972i
$269$	11.6257			0.708833			0.354416	−	0.935088i	$-0.384680\pi$
$269$	11.6257			0.708833			0.354416	+	0.935088i	$0.384680\pi$
$270$	−11.0635	−	3.54948i	−0.673304	−	0.216014i
$271$			16.8123i			1.02128i	0.859796	+	0.510638i	$0.170591\pi$
$271$			16.8123i			1.02128i	−0.859796	+	0.510638i	$0.829409\pi$
$272$	6.45590	+	3.72732i	0.391446	+	0.226002i
$273$	0.220321	+	9.60386i	0.0133344	+	0.581252i
$274$	5.41797	+	9.38419i	0.327311	+	0.566920i
$275$	6.69653	−	4.93758i	0.403816	−	0.297747i
$276$	−5.88861	+	7.81550i	−0.354453	+	0.470438i
$277$	−1.93149	−	1.11514i	−0.116052	−	0.0670026i	0.440850	−	0.897581i	$-0.354677\pi$
$277$	−1.93149	−	1.11514i	−0.116052	−	0.0670026i	−0.556902	+	0.830578i	$0.688010\pi$
$278$			8.81729i			0.528826i
$279$	−5.77393	+	1.65645i	−0.345676	+	0.0991690i
$280$	1.18067	+	5.79707i	0.0705587	+	0.346441i
$281$	−2.79869	−	1.61582i	−0.166956	−	0.0963919i	0.414194	−	0.910189i	$-0.364064\pi$
$281$	−2.79869	−	1.61582i	−0.166956	−	0.0963919i	−0.581150	+	0.813797i	$0.697397\pi$
$282$	−16.3874	+	6.95727i	−0.975854	+	0.414299i
$283$	3.23291	+	5.59957i	0.192177	+	0.332860i	0.945971	−	0.324250i	$-0.105112\pi$
$283$	3.23291	+	5.59957i	0.192177	+	0.332860i	−0.753795	+	0.657110i	$0.771779\pi$
$284$	−10.4312	+	6.02248i	−0.618981	+	0.357369i
$285$	−16.1980	+	7.97216i	−0.959487	+	0.472230i
$286$	3.02090	+	1.74412i	0.178630	+	0.103132i
$287$	3.11412	+	21.3191i	0.183821	+	1.25843i
$288$	−0.827282	−	2.88368i	−0.0487481	−	0.169922i
$289$	−38.5715			−2.26891
$290$	9.46617	+	4.78143i	0.555872	+	0.280775i
$291$	9.86395	−	13.0917i	0.578235	−	0.767446i
$292$	−2.39822	−	4.15384i	−0.140345	−	0.243085i
$293$	−16.0415	+	9.26155i	−0.937153	+	0.541066i	−0.889067	−	0.457777i	$-0.848646\pi$
$293$	−16.0415	+	9.26155i	−0.937153	+	0.541066i	−0.0480865	+	0.998843i	$0.515312\pi$
$294$	−11.9537	+	2.02712i	−0.697154	+	0.118224i
$295$	−0.173986	+	0.344454i	−0.0101299	+	0.0200549i
$296$		−	4.86789i		−	0.282940i
$297$	−5.44268	−	6.71850i	−0.315816	−	0.389847i
$298$			14.3395i			0.830664i
$299$	5.92171	−	10.2567i	0.342461	−	0.593160i
$300$	8.65979	+	0.0897357i	0.499973	+	0.00518089i
$301$	−4.26646	−	5.40024i	−0.245915	−	0.311264i
$302$	3.45207	+	5.97917i	0.198645	+	0.344062i
$303$	11.0180	−	14.6233i	0.632965	−	0.840085i
$304$	−4.03690	−	2.33070i	−0.231532	−	0.133675i
$305$	−0.746186	−	13.3410i	−0.0427265	−	0.763905i
$306$	16.0892	+	15.5332i	0.919760	+	0.887974i
$307$	−3.44142			−0.196412			−0.0982062	−	0.995166i	$-0.531310\pi$
$307$	−3.44142			−0.196412			−0.0982062	+	0.995166i	$0.531310\pi$
$308$	−1.62708	+	4.09086i	−0.0927115	+	0.233098i
$309$	10.3135	+	24.2928i	0.586716	+	1.38197i
$310$	3.74633	−	2.45165i	0.212777	−	0.139245i
$311$	16.6186	+	28.7842i	0.942352	+	1.63220i	0.760967	+	0.648790i	$0.224725\pi$
$311$	16.6186	+	28.7842i	0.942352	+	1.63220i	0.181385	+	0.983412i	$0.441942\pi$
$312$	1.41891	+	3.34215i	0.0803300	+	0.189212i
$313$	0.967111	−	1.67509i	0.0546644	−	0.0946815i	−0.837398	−	0.546593i	$-0.815924\pi$
$313$	0.967111	−	1.67509i	0.0546644	−	0.0946815i	0.892063	+	0.451912i	$0.149258\pi$
$314$	14.9762			0.845153
$315$	−0.768233	+	17.7316i	−0.0432851	+	0.999063i
$316$	12.6178			0.709807
$317$	5.12038	−	8.86877i	0.287589	−	0.498120i	−0.685644	−	0.727937i	$-0.740479\pi$
$317$	5.12038	−	8.86877i	0.287589	−	0.498120i	0.973234	+	0.229817i	$0.0738128\pi$
$318$	14.4225	−	19.1418i	0.808773	−	1.07342i
$319$	3.94603	+	6.83472i	0.220935	+	0.382671i
$320$	1.22443	+	1.87103i	0.0684478	+	0.104594i
$321$	−19.6264	−	2.40854i	−1.09544	−	0.134432i
$322$	13.8894	+	5.52433i	0.774028	+	0.307859i
$323$	34.7491			1.93349
$324$	−0.316404	−	8.99444i	−0.0175780	−	0.499691i
$325$	−10.4161	+	1.16883i	−0.577779	+	0.0648351i
$326$	6.95885	+	4.01770i	0.385415	+	0.222520i
$327$	−18.2483	−	2.23942i	−1.00913	−	0.123840i
$328$	4.07169	+	7.05238i	0.224822	+	0.389402i
$329$	16.8586	+	21.3386i	0.929444	+	1.17644i
$330$	5.35574	+	3.58468i	0.294824	+	0.197330i
$331$	−2.81788	+	4.88070i	−0.154884	+	0.268268i	−0.933017	−	0.359832i	$-0.882834\pi$
$331$	−2.81788	+	4.88070i	−0.154884	+	0.268268i	0.778133	+	0.628100i	$0.216167\pi$
$332$			2.58670i			0.141964i
$333$	3.53113	−	14.1703i	0.193505	−	0.776529i
$334$			4.75823i			0.260359i
$335$	10.8460	+	5.47842i	0.592583	+	0.299318i
$336$	−3.91503	+	2.38170i	−0.213583	+	0.129933i
$337$	−11.8563	+	6.84524i	−0.645854	+	0.372884i	−0.786866	−	0.617124i	$-0.788298\pi$
$337$	−11.8563	+	6.84524i	−0.645854	+	0.372884i	0.141012	+	0.990008i	$0.454964\pi$
$338$	4.30279	+	7.45265i	0.234041	+	0.405371i
$339$	9.30180	+	21.9098i	0.505204	+	1.18997i
$340$	−14.8787	−	7.51536i	−0.806913	−	0.407578i
$341$	3.33181			0.180428
$342$	−10.0607	−	9.71297i	−0.544018	−	0.525217i
$343$	7.80693	+	16.7944i	0.421535	+	0.906812i
$344$	−2.25274	−	1.30062i	−0.121460	−	0.0701248i
$345$	12.1709	−	18.1840i	0.655257	−	0.978995i
$346$	14.9456	−	8.62882i	0.803478	−	0.463888i
$347$	4.89520	+	8.47874i	0.262788	+	0.455163i	0.966982	−	0.254845i	$-0.0820246\pi$
$347$	4.89520	+	8.47874i	0.262788	+	0.455163i	−0.704193	+	0.710008i	$0.748691\pi$
$348$	−1.00060	+	8.15359i	−0.0536380	+	0.437078i
$349$	14.0539	+	8.11400i	0.752286	+	0.434332i	0.826519	−	0.562909i	$-0.190318\pi$
$349$	14.0539	+	8.11400i	0.752286	+	0.434332i	−0.0742335	+	0.997241i	$0.523651\pi$
$350$	−3.35984	−	12.7950i	−0.179591	−	0.683920i
$351$	1.70605	+	10.7582i	0.0910624	+	0.574230i
$352$			1.66401i			0.0886920i
$353$	−20.9960	−	12.1220i	−1.11750	−	0.645191i	−0.176741	−	0.984257i	$-0.556556\pi$
$353$	−20.9960	−	12.1220i	−1.11750	−	0.645191i	−0.940762	+	0.339066i	$0.889889\pi$
$354$	−0.296692	−	0.0364099i	−0.0157690	−	0.00193516i
$355$	22.5365	−	14.7482i	1.19612	−	0.782755i
$356$	5.61239	+	9.72094i	0.297456	+	0.515209i
$357$	16.3977	−	29.9686i	0.867858	−	1.58611i
$358$	0.521897	+	0.301317i	0.0275831	+	0.0159251i
$359$			31.3617i			1.65521i	0.561313	+	0.827604i	$0.310296\pi$
$359$			31.3617i			1.65521i	−0.561313	+	0.827604i	$0.689704\pi$
$360$	2.20706	+	6.33474i	0.116322	+	0.333870i
$361$	−2.72872			−0.143617
$362$	11.0659	+	6.38892i	0.581612	+	0.335794i
$363$	−5.57135	−	13.1229i	−0.292420	−	0.688776i
$364$	4.35194	−	3.43825i	0.228103	−	0.180213i
$365$	5.87292	+	8.97431i	0.307402	+	0.469737i
$366$	9.52703	−	4.04471i	0.497986	−	0.211420i
$367$	0.616195	−	1.06728i	0.0321651	−	0.0557116i	−0.849495	−	0.527597i	$-0.823093\pi$
$367$	0.616195	−	1.06728i	0.0321651	−	0.0557116i	0.881660	+	0.471885i	$0.156426\pi$
$368$	5.64971			0.294512
$369$	6.73688	+	23.4829i	0.350708	+	1.22247i
$370$	0.607862	+	10.8679i	0.0316012	+	0.564997i
$371$	−34.0182	−	13.5303i	−1.76614	−	0.702457i
$372$	2.76984	+	2.08695i	0.143610	+	0.108203i
$373$	−23.9159	+	13.8079i	−1.23832	+	0.714944i	−0.968751	−	0.248037i	$-0.920214\pi$
$373$	−23.9159	+	13.8079i	−1.23832	+	0.714944i	−0.269569	+	0.962981i	$0.586881\pi$
$374$	−6.20229	−	10.7427i	−0.320713	−	0.555491i
$375$	−19.3449	+	0.881022i	−0.998965	+	0.0454958i
$376$	8.90154	+	5.13931i	0.459062	+	0.265040i
$377$		−	9.94225i		−	0.512052i
$378$	−13.1243	+	4.09316i	−0.675039	+	0.210530i
$379$	23.2265			1.19307			0.596533	−	0.802589i	$-0.296545\pi$
$379$	23.2265			1.19307			0.596533	+	0.802589i	$0.296545\pi$
$380$	9.30373	+	4.69938i	0.477271	+	0.241073i
$381$	2.99475	−	24.4033i	0.153426	−	1.25022i
$382$	−16.3178	+	9.42111i	−0.834893	+	0.482026i
$383$	−20.6052	+	11.8964i	−1.05288	+	0.607880i	−0.923454	−	0.383709i	$-0.874646\pi$
$383$	−20.6052	+	11.8964i	−1.05288	+	0.607880i	−0.129425	+	0.991589i	$0.541313\pi$
$384$	−1.04229	+	1.38334i	−0.0531889	+	0.0705935i
$385$	3.12175	−	9.33633i	0.159099	−	0.475824i
$386$			6.80357i			0.346293i
$387$	−5.61423	−	5.42020i	−0.285387	−	0.275524i
$388$	−9.46377			−0.480450
$389$	−8.18328	−	4.72462i	−0.414909	−	0.239548i	0.277988	−	0.960585i	$-0.410332\pi$
$389$	−8.18328	−	4.72462i	−0.414909	−	0.239548i	−0.692897	+	0.721037i	$0.743666\pi$
$390$	−3.58517	−	7.28442i	−0.181542	−	0.368861i
$391$	−36.4740	+	21.0583i	−1.84457	+	1.06496i
$392$	5.08779	+	4.80775i	0.256972	+	0.242828i
$393$	1.55248	+	3.65676i	0.0783122	+	0.184459i
$394$	4.29375	−	7.43699i	0.216316	−	0.374670i
$395$	−28.1703	+	1.57561i	−1.41740	+	0.0792775i
$396$	−1.20706	+	4.84390i	−0.0606570	+	0.243415i
$397$	21.7234			1.09026			0.545132	−	0.838350i	$-0.316479\pi$
$397$	21.7234			1.09026			0.545132	+	0.838350i	$0.316479\pi$
$398$	−4.41729	−	2.55032i	−0.221419	−	0.127836i
$399$	−10.2535	+	18.7395i	−0.513319	+	0.938148i
$400$	−2.96728	−	4.02433i	−0.148364	−	0.201217i
$401$	−10.6544	+	6.15134i	−0.532057	+	0.307183i	−0.741854	−	0.670562i	$-0.766053\pi$
$401$	−10.6544	+	6.15134i	−0.532057	+	0.307183i	0.209797	+	0.977745i	$0.432720\pi$
$402$	−1.14646	+	9.34214i	−0.0571803	+	0.465943i
$403$	−3.63501	−	2.09867i	−0.181073	−	0.104542i
$404$	−10.5710			−0.525925
$405$	1.82955	+	20.0413i	0.0909110	+	0.995859i
$406$	12.4165	−	1.81369i	0.616220	−	0.0900122i
$407$	−4.05010	+	7.01498i	−0.200756	+	0.347720i
$408$	1.57273	−	12.8157i	0.0778617	−	0.634470i
$409$	−2.50285	+	1.44502i	−0.123758	+	0.0714517i	−0.560601	−	0.828086i	$-0.689430\pi$
$409$	−2.50285	+	1.44502i	−0.123758	+	0.0714517i	0.436843	+	0.899538i	$0.356097\pi$
$410$	−9.97102	−	15.2365i	−0.492433	−	0.752480i
$411$	11.2941	−	14.9898i	0.557099	−	0.739393i
$412$	7.61856	−	13.1957i	0.375339	−	0.650107i
$413$	0.0659965	+	0.451810i	0.00324748	+	0.0222321i
$414$	16.4462	+	4.09826i	0.808287	+	0.201418i
$415$	−0.323006	−	5.77502i	−0.0158558	−	0.283484i
$416$	1.04814	−	1.81544i	0.0513894	−	0.0890091i
$417$	14.0576	−	5.96815i	0.688402	−	0.292261i
$418$	3.87831	+	6.71743i	0.189694	+	0.328560i
$419$	−12.7397	−	22.0658i	−0.622374	−	1.07798i	−0.989042	−	0.147632i	$-0.952835\pi$
$419$	−12.7397	−	22.0658i	−0.622374	−	1.07798i	0.366668	−	0.930352i	$-0.380499\pi$
$420$	8.44321	−	5.80622i	0.411986	−	0.283315i
$421$	−2.96965	+	5.14359i	−0.144732	+	0.250683i	−0.929273	−	0.369394i	$-0.879565\pi$
$421$	−2.96965	+	5.14359i	−0.144732	+	0.250683i	0.784541	+	0.620077i	$0.212899\pi$
$422$	−10.0343			−0.488462
$423$	22.1842	+	21.4175i	1.07863	+	1.04136i
$424$	−13.8374			−0.672002
$425$	34.1564	+	14.9207i	1.65683	+	0.723761i
$426$	16.6623	+	12.5543i	0.807293	+	0.608258i
$427$	−9.80098	−	12.4055i	−0.474303	−	0.600345i
$428$	5.70816	+	9.88683i	0.275914	+	0.477898i
$429$	0.735926	−	5.99682i	0.0355309	−	0.289529i
$430$	5.19183	+	2.62243i	0.250372	+	0.126465i
$431$			29.4344i			1.41781i	0.705306	+	0.708903i	$0.250810\pi$
$431$			29.4344i			1.41781i	−0.705306	+	0.708903i	$0.749190\pi$
$432$	−4.03754	+	3.27082i	−0.194256	+	0.157367i
$433$	14.2559			0.685093			0.342546	−	0.939501i	$-0.388711\pi$
$433$	14.2559			0.685093			0.342546	+	0.939501i	$0.388711\pi$
$434$	1.95784	−	4.92247i	0.0939795	−	0.236286i
$435$	1.21577	−	18.3285i	0.0582919	−	0.878783i
$436$	5.30734	+	9.19258i	0.254176	+	0.440245i
$437$	22.8073	−	13.1678i	1.09102	−	0.629902i
$438$	−4.99926	+	6.63513i	−0.238874	+	0.317039i
$439$	−9.41191	−	5.43397i	−0.449206	−	0.259349i	0.258289	−	0.966068i	$-0.416841\pi$
$439$	−9.41191	−	5.43397i	−0.449206	−	0.259349i	−0.707495	+	0.706719i	$0.750175\pi$
$440$	−0.207788	−	3.71503i	−0.00990590	−	0.177107i
$441$	11.3229	+	17.6859i	0.539188	+	0.842186i
$442$			15.6270i			0.743303i
$443$	5.24859	−	9.09083i	0.249368	−	0.431918i	−0.713983	−	0.700164i	$-0.753110\pi$
$443$	5.24859	−	9.09083i	0.249368	−	0.431918i	0.963351	+	0.268245i	$0.0864438\pi$
$444$	−7.76096	+	3.29492i	−0.368319	+	0.156370i
$445$	−13.7440	−	21.0019i	−0.651527	−	0.995587i
$446$	−8.87226	−	15.3672i	−0.420114	−	0.727659i
$447$	22.8617	−	9.70595i	1.08132	−	0.459076i
$448$	2.45843	+	0.977807i	0.116150	+	0.0461970i
$449$		−	37.0684i		−	1.74937i	−0.484695	−	0.874683i	$-0.661070\pi$
$449$		−	37.0684i		−	1.74937i	0.484695	−	0.874683i	$-0.338930\pi$
$450$	−5.71847	−	13.8672i	−0.269571	−	0.653706i
$451$		−	13.5507i		−	0.638076i
$452$	6.87120	−	11.9013i	0.323194	−	0.559789i
$453$	7.19609	−	9.55081i	0.338102	−	0.448736i
$454$	0.411273	−	0.237449i	0.0193020	−	0.0111440i
$455$	−9.28670	+	8.21960i	−0.435367	+	0.385341i
$456$	−0.983434	+	8.01368i	−0.0460535	+	0.375275i
$457$	−17.5211	−	10.1158i	−0.819601	−	0.473197i	0.0306780	−	0.999529i	$-0.490233\pi$
$457$	−17.5211	−	10.1158i	−0.819601	−	0.473197i	−0.850279	+	0.526333i	$0.823567\pi$
$458$		−	10.9844i		−	0.513269i
$459$	13.8746	−	36.1653i	0.647609	−	1.68805i
$460$	−12.6134	+	0.705490i	−0.588104	+	0.0328936i
$461$	6.80701	−	11.7901i	0.317034	−	0.549119i	−0.662834	−	0.748766i	$-0.730646\pi$
$461$	6.80701	−	11.7901i	0.317034	−	0.549119i	0.979868	+	0.199648i	$0.0639798\pi$
$462$	7.62344	−	0.174888i	0.354675	−	0.00813654i
$463$	19.8188	−	11.4424i	0.921057	−	0.531773i	0.0370852	−	0.999312i	$-0.488193\pi$
$463$	19.8188	−	11.4424i	0.921057	−	0.531773i	0.883972	+	0.467539i	$0.154859\pi$
$464$	4.10738	−	2.37140i	0.190680	−	0.110089i
$465$	−6.44449	−	4.31340i	−0.298856	−	0.200029i
$466$	−10.7397	+	18.6017i	−0.497507	+	0.861708i
$467$		−	3.34545i		−	0.154809i	−0.997000	−	0.0774044i	$-0.975337\pi$
$467$		−	3.34545i		−	0.154809i	0.997000	−	0.0774044i	$-0.0246633\pi$
$468$	4.36803	−	4.52439i	0.201912	−	0.209140i
$469$	14.2264	−	2.07808i	0.656916	−	0.0959567i
$470$	−20.5151	−	10.3624i	−0.946293	−	0.477980i
$471$	−10.1369	−	23.8768i	−0.467083	−	1.10018i
$472$	0.0862901	+	0.149459i	0.00397182	+	0.00687940i
$473$	2.16425	+	3.74858i	0.0995121	+	0.172360i
$474$	−8.54060	−	20.1168i	−0.392283	−	0.923995i
$475$	−21.3581	−	9.32997i	−0.979978	−	0.428088i
$476$	−19.5160	+	2.85073i	−0.894514	+	0.130663i
$477$	−40.2803	−	10.0375i	−1.84431	−	0.459586i
$478$		−	16.8850i		−	0.772302i
$479$	−8.15257	+	14.1207i	−0.372500	+	0.645189i	−0.989949	−	0.141421i	$-0.954833\pi$
$479$	−8.15257	+	14.1207i	−0.372500	+	0.645189i	0.617449	+	0.786611i	$0.288166\pi$
$480$	2.15424	−	3.21858i	0.0983273	−	0.146907i
$481$	8.83734	−	5.10224i	0.402948	−	0.232642i
$482$	−8.00911	+	4.62406i	−0.364805	+	0.210620i
$483$	−0.593788	−	25.8834i	−0.0270183	−	1.17774i
$484$	−4.11554	+	7.12832i	−0.187070	+	0.324014i
$485$	21.1286	−	1.18176i	0.959401	−	0.0536609i
$486$	−14.1258	+	6.59250i	−0.640760	+	0.299042i
$487$			5.20248i			0.235747i	0.993029	+	0.117873i	$0.0376077\pi$
$487$			5.20248i			0.235747i	−0.993029	+	0.117873i	$0.962392\pi$
$488$	−5.17503	−	2.98781i	−0.234263	−	0.135252i
$489$	1.69525	−	13.8141i	0.0766621	−	0.624694i
$490$	−11.9592	−	10.0984i	−0.540263	−	0.456197i
$491$	−20.6633	+	11.9299i	−0.932521	+	0.538391i	−0.887608	−	0.460600i	$-0.847634\pi$
$491$	−20.6633	+	11.9299i	−0.932521	+	0.538391i	−0.0449127	+	0.998991i	$0.514301\pi$
$492$	8.48773	−	11.2651i	0.382656	−	0.507870i
$493$	−17.6779	+	30.6190i	−0.796172	+	1.37901i
$494$		−	9.77165i		−	0.439647i
$495$	2.08999	−	10.9651i	0.0939380	−	0.492845i
$496$		−	2.00228i		−	0.0899050i
$497$	11.7777	−	29.6117i	0.528300	−	1.32827i
$498$	4.12403	−	1.75086i	0.184802	−	0.0784578i
$499$	16.1660	+	28.0003i	0.723688	+	1.25346i	0.959512	+	0.281668i	$0.0908877\pi$
$499$	16.1660	+	28.0003i	0.723688	+	1.25346i	−0.235824	+	0.971796i	$0.575779\pi$
$500$	7.12721	+	8.61411i	0.318738	+	0.385235i
$501$	7.58613	−	3.22069i	0.338923	−	0.143890i
$502$	4.68498	−	8.11462i	0.209101	−	0.362173i
$503$		−	10.0768i		−	0.449301i	−0.974439	−	0.224651i	$-0.927876\pi$
$503$		−	10.0768i		−	0.449301i	0.974439	−	0.224651i	$-0.0721241\pi$
$504$	6.44716	+	4.62971i	0.287179	+	0.206223i
$505$	23.6005	−	1.32001i	1.05021	−	0.0587399i
$506$	−8.14166	−	4.70059i	−0.361941	−	0.208967i
$507$	8.96947	−	11.9045i	0.398348	−	0.528697i
$508$	−12.2932	+	7.09746i	−0.545421	+	0.314899i
$509$	10.5573	+	18.2858i	0.467944	+	0.810503i	0.999329	−	0.0366275i	$-0.0116615\pi$
$509$	10.5573	+	18.2858i	0.467944	+	0.810503i	−0.531385	+	0.847131i	$0.678328\pi$
$510$	−1.91093	+	28.8084i	−0.0846174	+	1.27566i
$511$	11.7917	+	4.69000i	0.521636	+	0.207473i
$512$	1.00000			0.0441942
$513$	−8.67582	+	22.6143i	−0.383047	+	0.998445i
$514$		−	6.49218i		−	0.286358i
$515$	−15.3612	+	30.4118i	−0.676898	+	1.34011i
$516$	−0.548793	+	4.47194i	−0.0241593	+	0.196866i
$517$	−8.55186	−	14.8122i	−0.376110	−	0.651442i
$518$	7.98412	+	10.1058i	0.350802	+	0.444025i
$519$	−23.8733	−	17.9874i	−1.04792	−	0.789559i
$520$	−2.11336	+	4.18399i	−0.0926772	+	0.183480i
$521$	21.9402			0.961216			0.480608	−	0.876936i	$-0.340416\pi$
$521$	21.9402			0.961216			0.480608	+	0.876936i	$0.340416\pi$
$522$	13.6767	−	3.92363i	0.598613	−	0.171733i
$523$	7.10550			0.310702			0.155351	−	0.987859i	$-0.450349\pi$
$523$	7.10550			0.310702			0.155351	+	0.987859i	$0.450349\pi$
$524$	1.14681	−	1.98633i	0.0500986	−	0.0867733i
$525$	−18.1251	+	14.0172i	−0.791044	+	0.611759i
$526$	−4.41420	−	7.64563i	−0.192468	−	0.333365i
$527$	7.46313	+	12.9265i	0.325099	+	0.563088i
$528$	2.65296	−	1.12632i	0.115455	−	0.0490166i
$529$	−4.45963	+	7.72430i	−0.193897	+	0.335839i
$530$	30.8930	−	1.72790i	1.34191	−	0.0750551i
$531$	0.142773	+	0.497666i	0.00619580	+	0.0215969i
$532$	12.2034	−	1.78257i	0.529085	−	0.0772843i
$533$	−8.53543	+	14.7838i	−0.369711	+	0.640358i
$534$	11.6994	−	15.5277i	0.506284	−	0.671951i
$535$	−13.9785	−	21.3603i	−0.604344	−	0.923488i
$536$	4.70611	−	2.71707i	0.203273	−	0.117360i
$537$	0.127140	−	1.03602i	0.00548650	−	0.0447076i
$538$	−5.81286	+	10.0682i	−0.250610	+	0.434070i
$539$	−3.33181	−	11.1614i	−0.143511	−	0.480755i
$540$	8.60569	−	7.80654i	0.370330	−	0.335940i
$541$	−36.7965			−1.58200			−0.791002	−	0.611813i	$-0.790441\pi$
$541$	−36.7965			−1.58200			−0.791002	+	0.611813i	$0.790441\pi$
$542$	−14.5599	−	8.40617i	−0.625402	−	0.361076i
$543$	2.69579	−	21.9671i	0.115687	−	0.942697i
$544$	−6.45590	+	3.72732i	−0.276794	+	0.159807i
$545$	−12.9970	−	19.8604i	−0.556728	−	0.850727i
$546$	−8.42735	−	4.61113i	−0.360657	−	0.197338i
$547$	−14.6902	−	8.48140i	−0.628108	−	0.362638i	0.151911	−	0.988394i	$-0.451457\pi$
$547$	−14.6902	−	8.48140i	−0.628108	−	0.362638i	−0.780019	+	0.625756i	$0.784791\pi$
$548$	−10.8359			−0.462888
$549$	−12.8971	−	12.4514i	−0.550434	−	0.531412i
$550$	0.927806	+	8.26815i	0.0395618	+	0.352555i
$551$	11.0540	−	19.1462i	0.470918	−	0.815654i
$552$	−3.82411	−	9.00744i	−0.162765	−	0.383382i
$553$	−26.1949	+	20.6953i	−1.11392	+	0.880052i
$554$	1.93149	−	1.11514i	0.0820610	−	0.0473780i
$555$	16.9155	−	8.32529i	0.718023	−	0.353389i
$556$	−7.63600	−	4.40865i	−0.323839	−	0.186968i
$557$	2.63451			0.111628			0.0558139	−	0.998441i	$-0.482225\pi$
$557$	2.63451			0.111628			0.0558139	+	0.998441i	$0.482225\pi$
$558$	1.45244	−	5.82859i	0.0614866	−	0.246744i
$559$		−	5.45295i		−	0.230635i
$560$	−5.61075	−	1.87604i	−0.237097	−	0.0792772i
$561$	−12.9291	+	17.1598i	−0.545867	+	0.724487i
$562$	2.79869	−	1.61582i	0.118055	−	0.0681594i
$563$	−20.7641	+	11.9882i	−0.875104	+	0.505242i	−0.869041	−	0.494740i	$-0.835263\pi$
$563$	−20.7641	+	11.9882i	−0.875104	+	0.505242i	−0.00606320	+	0.999982i	$0.501930\pi$
$564$	2.16852	−	17.6705i	0.0913110	−	0.744063i
$565$	−13.8544	+	27.4285i	−0.582857	+	1.15393i
$566$	−6.46583			−0.271779
$567$	15.4092	+	18.1537i	0.647125	+	0.762384i
$568$		−	12.0450i		−	0.505396i
$569$	36.5400	+	21.0964i	1.53184	+	0.884407i	0.999277	+	0.0380144i	$0.0121033\pi$
$569$	36.5400	+	21.0964i	1.53184	+	0.884407i	0.532560	+	0.846392i	$0.321230\pi$
$570$	1.19491	−	18.0140i	0.0500493	−	0.754522i
$571$	12.7469	+	22.0783i	0.533441	+	0.923947i	0.999237	+	0.0390547i	$0.0124347\pi$
$571$	12.7469	+	22.0783i	0.533441	+	0.923947i	−0.465796	+	0.884892i	$0.654232\pi$
$572$	−3.02090	+	1.74412i	−0.126310	+	0.0729253i
$573$	26.0653	+	19.6390i	1.08889	+	0.820429i
$574$	−20.0200	−	7.96266i	−0.835617	−	0.332355i
$575$	28.0724	−	3.15012i	1.17070	−	0.131369i
$576$	2.91098	+	0.725392i	0.121291	+	0.0302247i
$577$	32.7696			1.36422			0.682108	−	0.731251i	$-0.261063\pi$
$577$	32.7696			1.36422			0.682108	+	0.731251i	$0.261063\pi$
$578$	19.2858	−	33.4039i	0.802182	−	1.38942i
$579$	10.8471	−	4.60512i	0.450788	−	0.191382i
$580$	−8.87393	+	5.80722i	−0.368470	+	0.241132i
$581$	−4.24261	−	5.37005i	−0.176013	−	0.222787i
$582$	6.40573	+	15.0883i	0.265526	+	0.625428i
$583$	19.9407	+	11.5128i	0.825858	+	0.476810i
$584$	4.79644			0.198478
$585$	−9.18700	+	10.6465i	−0.379836	+	0.440178i
$586$		−	18.5231i		−	0.765182i
$587$	19.1726	+	11.0693i	0.791337	+	0.456879i	0.840433	−	0.541915i	$-0.182301\pi$
$587$	19.1726	+	11.0693i	0.791337	+	0.456879i	−0.0490959	+	0.998794i	$0.515634\pi$
$588$	4.22131	−	11.3658i	0.174084	−	0.468716i
$589$	−4.66672	−	8.08300i	−0.192289	−	0.333054i
$590$	−0.211313	−	0.322903i	−0.00869960	−	0.0132937i
$591$	−14.7632	−	1.81174i	−0.607278	−	0.0745249i
$592$	4.21571	+	2.43394i	0.173265	+	0.100034i
$593$		−	26.0392i		−	1.06930i	−0.845073	−	0.534650i	$-0.820443\pi$
$593$		−	26.0392i		−	1.06930i	0.845073	−	0.534650i	$-0.179557\pi$
$594$	8.53973	−	1.35425i	0.350389	−	0.0555654i
$595$	43.2150	−	8.80148i	1.77164	−	0.360825i
$596$	−12.4184	−	7.16974i	−0.508676	−	0.293684i
$597$	−1.07610	+	8.76879i	−0.0440419	+	0.358883i
$598$	5.92171	+	10.2567i	0.242157	+	0.419428i
$599$	18.1227	−	10.4631i	0.740472	−	0.427512i	−0.0817689	−	0.996651i	$-0.526057\pi$
$599$	18.1227	−	10.4631i	0.740472	−	0.427512i	0.822241	+	0.569140i	$0.192724\pi$
$600$	−4.40761	+	7.45473i	−0.179940	+	0.304338i
$601$	−25.4768	−	14.7091i	−1.03922	−	0.599995i	−0.119609	−	0.992821i	$-0.538164\pi$
$601$	−25.4768	−	14.7091i	−1.03922	−	0.599995i	−0.919613	+	0.392826i	$0.871497\pi$
$602$	6.80997	−	0.994743i	0.277554	−	0.0405427i
$603$	15.6703	−	4.49557i	0.638146	−	0.183074i
$604$	−6.90415			−0.280926
$605$	8.29813	−	16.4284i	0.337367	−	0.667911i
$606$	7.15515	+	16.8535i	0.290658	+	0.684625i
$607$	−6.62507	−	11.4750i	−0.268903	−	0.465754i	0.699676	−	0.714461i	$-0.253328\pi$
$607$	−6.62507	−	11.4750i	−0.268903	−	0.465754i	−0.968579	+	0.248707i	$0.919994\pi$
$608$	4.03690	−	2.33070i	0.163718	−	0.0945225i
$609$	−11.2959	−	18.5682i	−0.457734	−	0.752421i
$610$	11.9268	+	6.02430i	0.482901	+	0.243917i
$611$			21.5469i			0.871695i
$612$	−21.4968	+	6.16708i	−0.868955	+	0.249290i
$613$			17.3252i			0.699759i	0.936795	+	0.349880i	$0.113778\pi$
$613$			17.3252i			0.699759i	−0.936795	+	0.349880i	$0.886222\pi$
$614$	1.72071	−	2.98036i	0.0694423	−	0.120278i
$615$	−17.5428	+	26.2101i	−0.707395	+	1.05689i
$616$	−2.72924	−	3.45452i	−0.109964	−	0.139187i
$617$	9.93911	+	17.2150i	0.400133	+	0.693052i	0.993742	−	0.111703i	$-0.0356304\pi$
$617$	9.93911	+	17.2150i	0.400133	+	0.693052i	−0.593608	+	0.804754i	$0.702297\pi$
$618$	−26.1949	−	3.21463i	−1.05371	−	0.129311i
$619$	30.8618	+	17.8181i	1.24044	+	0.716168i	0.969184	−	0.246339i	$-0.0792276\pi$
$619$	30.8618	+	17.8181i	1.24044	+	0.716168i	0.271256	+	0.962507i	$0.412561\pi$
$620$	0.250028	+	4.47025i	0.0100414	+	0.179529i
$621$	−4.59799	−	28.9945i	−0.184511	−	1.16351i
$622$	−33.2371			−1.33269
$623$	−27.5954	−	10.9757i	−1.10559	−	0.439731i
$624$	−3.60384	−	0.442261i	−0.144269	−	0.0177046i
$625$	−16.9877	−	18.3417i	−0.679509	−	0.733668i
$626$	0.967111	+	1.67509i	0.0386535	+	0.0669499i
$627$	8.08462	−	10.7301i	0.322869	−	0.428518i
$628$	−7.48808	+	12.9697i	−0.298807	+	0.517549i
$629$	−36.2883			−1.44691
$630$	−14.9719	−	9.53111i	−0.596495	−	0.379729i
$631$	28.1609			1.12107			0.560533	−	0.828132i	$-0.310596\pi$
$631$	28.1609			1.12107			0.560533	+	0.828132i	$0.310596\pi$
$632$	−6.30891	+	10.9273i	−0.250955	+	0.434666i
$633$	6.79189	+	15.9978i	0.269954	+	0.635857i
$634$	5.12038	+	8.86877i	0.203356	+	0.352224i
$635$	26.5592	−	17.3807i	1.05397	−	0.689732i
$636$	9.36608	+	22.0612i	0.371389	+	0.874782i
$637$	−3.39543	+	14.2758i	−0.134532	+	0.565626i
$638$	−7.89205			−0.312449
$639$	8.73732	−	35.0627i	0.345643	−	1.38706i
$640$	−2.23258	+	0.124872i	−0.0882504	+	0.00493599i
$641$	25.4170	+	14.6745i	1.00391	+	0.579608i	0.909403	−	0.415916i	$-0.136539\pi$
$641$	25.4170	+	14.6745i	1.00391	+	0.579608i	0.0945076	+	0.995524i	$0.469872\pi$
$642$	11.8991	−	15.7927i	0.469619	−	0.623288i
$643$	16.7337	+	28.9836i	0.659912	+	1.14300i	0.980638	+	0.195830i	$0.0627400\pi$
$643$	16.7337	+	28.9836i	0.659912	+	1.14300i	−0.320726	+	0.947172i	$0.603927\pi$
$644$	−11.7289	+	9.26644i	−0.462185	+	0.365149i
$645$	0.666805	−	10.0525i	0.0262554	−	0.395816i
$646$	−17.3745	+	30.0936i	−0.683592	+	1.18402i
$647$			19.6226i			0.771445i	0.922615	+	0.385723i	$0.126048\pi$
$647$			19.6226i			0.771445i	−0.922615	+	0.385723i	$0.873952\pi$
$648$	7.94761	+	4.22320i	0.312212	+	0.165903i
$649$		−	0.287175i		−	0.0112726i
$650$	4.19579	−	9.60499i	0.164572	−	0.376739i
$651$	−9.17318	+	0.210441i	−0.359525	+	0.00824782i
$652$	−6.95885	+	4.01770i	−0.272530	+	0.157345i
$653$	−9.70880	−	16.8161i	−0.379935	−	0.658066i	0.611118	−	0.791540i	$-0.290720\pi$
$653$	−9.70880	−	16.8161i	−0.379935	−	0.658066i	−0.991052	+	0.133474i	$0.957387\pi$
$654$	11.0635	−	14.6838i	0.432618	−	0.574180i
$655$	−2.31231	+	4.57785i	−0.0903492	+	0.178871i
$656$	−8.14339			−0.317946
$657$	13.9624	+	3.47930i	0.544723	+	0.135741i
$658$	−26.9091	+	3.93065i	−1.04903	+	0.153233i
$659$	−10.8291	−	6.25219i	−0.421842	−	0.243551i	0.274023	−	0.961723i	$-0.411646\pi$
$659$	−10.8291	−	6.25219i	−0.421842	−	0.243551i	−0.695865	+	0.718172i	$0.744979\pi$
$660$	−5.78229	+	2.84587i	−0.225076	+	0.110775i
$661$	3.75358	−	2.16713i	0.145997	−	0.0842916i	−0.425222	−	0.905089i	$-0.639804\pi$
$661$	3.75358	−	2.16713i	0.145997	−	0.0842916i	0.571219	+	0.820798i	$0.306471\pi$
$662$	−2.81788	−	4.88070i	−0.109520	−	0.189694i
$663$	24.9145	−	10.5775i	0.967598	−	0.410794i
$664$	−2.24015	−	1.29335i	−0.0869347	−	0.0501918i
$665$	−27.0225	+	5.50360i	−1.04789	+	0.213420i
$666$	10.5063	+	10.1432i	0.407111	+	0.393041i
$667$			26.7954i			1.03752i
$668$	−4.12075	−	2.37911i	−0.159436	−	0.0920507i
$669$	−18.4949	+	24.5468i	−0.715053	+	0.949034i
$670$	−10.1675	+	6.65374i	−0.392804	+	0.257056i
$671$	4.97174	+	8.61131i	0.191932	+	0.332436i
$672$	−0.105101	−	4.58137i	−0.00405434	−	0.176730i
$673$	−1.47592	−	0.852124i	−0.0568926	−	0.0328470i	0.471284	−	0.881982i	$-0.343791\pi$
$673$	−1.47592	−	0.852124i	−0.0568926	−	0.0328470i	−0.528177	+	0.849135i	$0.677124\pi$
$674$		−	13.6905i		−	0.527338i
$675$	−18.2381	+	18.5033i	−0.701983	+	0.712193i
$676$	−8.60558			−0.330984
$677$	5.08519	+	2.93594i	0.195440	+	0.112837i	0.594527	−	0.804076i	$-0.297339\pi$
$677$	5.08519	+	2.93594i	0.195440	+	0.112837i	−0.399087	+	0.916913i	$0.630673\pi$
$678$	−23.6253	−	2.89928i	−0.907324	−	0.111346i
$679$	19.6470	−	15.5221i	0.753983	−	0.595684i
$680$	13.9479	−	9.12768i	0.534876	−	0.350031i
$681$	−0.656947	−	0.494979i	−0.0251742	−	0.0189676i
$682$	−1.66591	+	2.88543i	−0.0637908	+	0.110489i
$683$	10.9483			0.418926			0.209463	−	0.977817i	$-0.432828\pi$
$683$	10.9483			0.418926			0.209463	+	0.977817i	$0.432828\pi$
$684$	13.4420	−	3.85630i	0.513968	−	0.147449i
$685$	24.1921	−	1.35310i	0.924332	−	0.0516994i
$686$	−18.4478	−	1.63620i	−0.704342	−	0.0624702i
$687$	−17.5127	+	7.43501i	−0.668150	+	0.283663i
$688$	2.25274	−	1.30062i	0.0858850	−	0.0495857i
$689$	−14.5035	−	25.1209i	−0.552541	−	0.957029i
$690$	9.66241	+	19.6323i	0.367842	+	0.747388i
$691$	−34.4759	−	19.9047i	−1.31153	−	0.757210i	−0.329177	−	0.944268i	$-0.606771\pi$
$691$	−34.4759	−	19.9047i	−1.31153	−	0.757210i	−0.982349	+	0.187058i	$0.940105\pi$
$692$			17.2576i			0.656037i
$693$	−5.43890	−	12.0358i	−0.206607	−	0.457203i
$694$	−9.79041			−0.371639
$695$	17.5985	+	8.88913i	0.667549	+	0.337184i
$696$	−6.56091	−	4.94334i	−0.248691	−	0.187377i
$697$	52.5729	−	30.3530i	1.99134	−	1.14970i
$698$	−14.0539	+	8.11400i	−0.531946	+	0.307119i
$699$	36.9264	+	4.53159i	1.39669	+	0.171400i
$700$	12.7607	+	3.48779i	0.482309	+	0.131826i
$701$		−	7.84396i		−	0.296262i	−0.988968	−	0.148131i	$-0.952674\pi$
$701$		−	7.84396i		−	0.296262i	0.988968	−	0.148131i	$-0.0473258\pi$
$702$	−10.1699	−	3.90161i	−0.383838	−	0.147257i
$703$	22.6912			0.855815
$704$	−1.44107	−	0.832005i	−0.0543125	−	0.0313574i
$705$	−2.63483	+	39.7216i	−0.0992335	+	1.49600i
$706$	20.9960	−	12.1220i	0.790194	−	0.456219i
$707$	21.9455	−	17.3381i	0.825347	−	0.652066i
$708$	0.179878	−	0.238738i	0.00676022	−	0.00897232i
$709$	10.3461	−	17.9200i	0.388557	−	0.673001i	−0.603698	−	0.797213i	$-0.706307\pi$
$709$	10.3461	−	17.9200i	0.388557	−	0.673001i	0.992256	+	0.124212i	$0.0396402\pi$
$710$	1.50408	+	26.8913i	0.0564470	+	1.00921i
$711$	−26.2917	+	27.2329i	−0.986016	+	1.02131i
$712$	−11.2248			−0.420666
$713$	9.79674	+	5.65615i	0.366891	+	0.211825i
$714$	17.7547	+	29.1851i	0.664454	+	1.09223i
$715$	6.52661	−	4.27111i	0.244082	−	0.159730i
$716$	−0.521897	+	0.301317i	−0.0195042	+	0.0112608i
$717$	−26.9201	+	11.4289i	−1.00535	+	0.426821i
$718$	−27.1600	−	15.6809i	−1.01360	−	0.585204i
$719$	−21.2881			−0.793910			−0.396955	−	0.917838i	$-0.629933\pi$
$719$	−21.2881			−0.793910			−0.396955	+	0.917838i	$0.629933\pi$
$720$	−6.58957	−	1.25600i	−0.245579	−	0.0468082i
$721$	5.82684	+	39.8903i	0.217003	+	1.48559i
$722$	1.36436	−	2.36314i	0.0507763	−	0.0879471i
$723$	12.7933	+	9.63919i	0.475790	+	0.358485i
$724$	−11.0659	+	6.38892i	−0.411262	+	0.237442i
$725$	19.0866	−	14.0732i	0.708858	−	0.522665i
$726$	14.1505	+	1.73654i	0.525174	+	0.0644490i
$727$	4.79802	−	8.31041i	0.177949	−	0.308216i	−0.763229	−	0.646128i	$-0.776387\pi$
$727$	4.79802	−	8.31041i	0.177949	−	0.308216i	0.941178	+	0.337912i	$0.109721\pi$
$728$	0.801642	+	5.48801i	0.0297108	+	0.203399i
$729$	20.0719	+	18.0588i	0.743402	+	0.668844i
$730$	−10.7084	+	0.598941i	−0.396337	+	0.0221678i
$731$	−9.69565	+	16.7934i	−0.358607	+	0.621125i
$732$	−1.26070	+	10.2730i	−0.0465967	+	0.379701i
$733$	−22.1972	−	38.4466i	−0.819871	−	1.42006i	−0.905777	−	0.423754i	$-0.860712\pi$
$733$	−22.1972	−	38.4466i	−0.819871	−	1.42006i	0.0859066	−	0.996303i	$-0.472621\pi$
$734$	0.616195	+	1.06728i	0.0227442	+	0.0393941i
$735$	−8.00515	+	25.9021i	−0.295274	+	0.955412i
$736$	−2.82486	+	4.89279i	−0.104126	+	0.180351i
$737$	−9.04247			−0.333084
$738$	−23.7052	−	5.90715i	−0.872602	−	0.217445i
$739$	−17.8223			−0.655603			−0.327801	−	0.944747i	$-0.606308\pi$
$739$	−17.8223			−0.655603			−0.327801	+	0.944747i	$0.606308\pi$
$740$	−9.71584	−	4.90754i	−0.357161	−	0.180405i
$741$	−15.5791	+	6.61412i	−0.572313	+	0.242976i
$742$	28.7267	−	22.6955i	1.05459	−	0.833179i
$743$	−25.2903	−	43.8041i	−0.927811	−	1.60702i	−0.786976	−	0.616983i	$-0.788355\pi$
$743$	−25.2903	−	43.8041i	−0.927811	−	1.60702i	−0.140835	−	0.990033i	$-0.544979\pi$
$744$	−3.19227	+	1.35528i	−0.117034	+	0.0496870i
$745$	28.6203	+	14.4563i	1.04857	+	0.529638i
$746$		−	27.6157i		−	1.01108i
$747$	−5.58285	−	5.38991i	−0.204266	−	0.197206i
$748$	12.4046			0.453556
$749$	−28.0663	−	11.1630i	−1.02552	−	0.407886i
$750$	8.90945	−	17.1937i	0.325327	−	0.627824i
$751$	−22.2173	−	38.4816i	−0.810722	−	1.40421i	−0.912359	−	0.409390i	$-0.865741\pi$
$751$	−22.2173	−	38.4816i	−0.810722	−	1.40421i	0.101637	−	0.994822i	$-0.467592\pi$
$752$	−8.90154	+	5.13931i	−0.324606	+	0.187411i
$753$	−16.1084	−	1.97681i	−0.587023	−	0.0720391i
$754$	8.61024	+	4.97113i	0.313567	+	0.181038i
$755$	15.4140	−	0.862134i	0.560975	−	0.0313763i
$756$	3.01734	−	13.4125i	0.109740	−	0.487809i
$757$			26.2968i			0.955774i	0.878421	+	0.477887i	$0.158597\pi$
$757$			26.2968i			0.955774i	−0.878421	+	0.477887i	$0.841403\pi$
$758$	−11.6133	+	20.1148i	−0.421812	+	0.730601i
$759$	−1.98340	+	16.1621i	−0.0719928	+	0.586646i
$760$	−8.72165	+	5.70757i	−0.316368	+	0.207035i
$761$	−11.6947	−	20.2558i	−0.423932	−	0.734272i	0.572388	−	0.819983i	$-0.306017\pi$
$761$	−11.6947	−	20.2558i	−0.423932	−	0.734272i	−0.996320	+	0.0857107i	$0.972684\pi$
$762$	19.6365	+	14.7952i	0.711354	+	0.535972i
$763$	−26.0955	−	10.3791i	−0.944720	−	0.375749i
$764$		−	18.8422i		−	0.681687i
$765$	47.2231	−	16.4528i	1.70736	−	0.594854i
$766$		−	23.7929i		−	0.859672i
$767$	−0.180889	+	0.313309i	−0.00653152	+	0.0113129i
$768$	−0.676868	−	1.59432i	−0.0244244	−	0.0575300i
$769$	−21.6845	+	12.5196i	−0.781963	+	0.451467i	−0.837126	−	0.547011i	$-0.815766\pi$
$769$	−21.6845	+	12.5196i	−0.781963	+	0.451467i	0.0551625	+	0.998477i	$0.482432\pi$
$770$	6.52462	+	7.37168i	0.235131	+	0.265657i
$771$	−10.3506	+	4.39435i	−0.372768	+	0.158259i
$772$	−5.89207	−	3.40179i	−0.212060	−	0.122433i
$773$			55.5416i			1.99769i	0.0480317	+	0.998846i	$0.484705\pi$
$773$			55.5416i			1.99769i	−0.0480317	+	0.998846i	$0.515295\pi$
$774$	7.50115	−	2.15196i	0.269623	−	0.0773506i
$775$	−1.11642	−	9.94895i	−0.0401028	−	0.357377i
$776$	4.73188	−	8.19586i	0.169865	−	0.294214i
$777$	10.7077	−	19.5696i	0.384137	−	0.702054i
$778$	8.18328	−	4.72462i	0.293385	−	0.169386i
$779$	−32.8740	+	18.9798i	−1.17783	+	0.680023i
$780$	8.10108	+	0.537364i	0.290065	+	0.0192407i
$781$	−10.0215	+	17.3577i	−0.358596	+	0.621107i
$782$		−	42.1165i		−	1.50608i
$783$	−15.5128	−	19.1492i	−0.554383	−	0.684337i
$784$	−6.70752	+	2.00228i	−0.239554	+	0.0715100i
$785$	15.0982	−	29.8910i	0.538877	−	1.06686i
$786$	−3.94308	−	0.483893i	−0.140645	−	0.0172599i
$787$	7.49527	+	12.9822i	0.267177	+	0.462765i	0.968132	−	0.250441i	$-0.0805757\pi$
$787$	7.49527	+	12.9822i	0.267177	+	0.462765i	−0.700954	+	0.713206i	$0.747242\pi$
$788$	4.29375	+	7.43699i	0.152959	+	0.264932i
$789$	−9.20172	+	12.2127i	−0.327590	+	0.434785i
$790$	12.7206	−	25.1840i	0.452579	−	0.896005i
$791$	5.25524	+	35.9772i	0.186855	+	1.27920i
$792$	−3.59141	−	3.46729i	−0.127615	−	0.123205i
$793$		−	12.5266i		−	0.444833i
$794$	−10.8617	+	18.8130i	−0.385467	+	0.667648i
$795$	−23.6653	−	48.0837i	−0.839323	−	1.70535i
$796$	4.41729	−	2.55032i	0.156567	−	0.0903938i
$797$	−43.9990	+	25.4028i	−1.55852	+	0.899814i	−0.561124	+	0.827732i	$0.689631\pi$
$797$	−43.9990	+	25.4028i	−1.55852	+	0.899814i	−0.997399	+	0.0720822i	$0.977036\pi$
$798$	−11.1021	−	18.2496i	−0.393010	−	0.646028i
$799$	38.3116	−	66.3577i	1.35537	−	2.34757i
$800$	4.96881	−	0.557572i	0.175674	−	0.0197132i
$801$	−32.6751	−	8.14237i	−1.15452	−	0.287696i
$802$		−	12.3027i		−	0.434423i
$803$	−6.91203	−	3.99066i	−0.243920	−	0.140827i
$804$	−7.51730	−	5.66393i	−0.265115	−	0.199752i
$805$	25.0286	−	22.1527i	0.882144	−	0.780779i
$806$	3.63501	−	2.09867i	0.128038	−	0.0739227i
$807$	19.9864	+	2.45272i	0.703555	+	0.0863398i
$808$	5.28548	−	9.15472i	0.185942	−	0.322062i
$809$			38.3573i			1.34857i	0.738471	+	0.674285i	$0.235548\pi$
$809$			38.3573i			1.34857i	−0.738471	+	0.674285i	$0.764452\pi$
$810$	−18.2710	−	8.43620i	−0.641979	−	0.296418i
$811$		−	0.237330i		−	0.00833379i	−0.999991	−	0.00416689i	$-0.998674\pi$
$811$		−	0.237330i		−	0.00833379i	0.999991	−	0.00416689i	$-0.00132637\pi$
$812$	−4.63754	+	11.6598i	−0.162746	+	0.409180i
$813$	−3.54696	+	28.9030i	−0.124397	+	1.01367i
$814$	−4.05010	−	7.01498i	−0.141956	−	0.245875i
$815$	15.0345	−	9.83878i	0.526635	−	0.344638i
$816$	10.3123	+	7.76985i	0.361003	+	0.271999i
$817$	6.06273	−	10.5009i	0.212108	−	0.367382i
$818$		−	2.89004i		−	0.101048i
$819$	−1.64740	+	16.5570i	−0.0575647	+	0.578548i
$820$	18.1807	−	1.01688i	0.634899	−	0.0355110i
$821$	34.0959	+	19.6853i	1.18995	+	0.687020i	0.958296	−	0.285777i	$-0.0922516\pi$
$821$	34.0959	+	19.6853i	1.18995	+	0.687020i	0.231658	+	0.972797i	$0.425585\pi$
$822$	7.33450	+	17.2759i	0.255820	+	0.602567i
$823$	12.0228	−	6.94134i	0.419087	−	0.241960i	−0.275600	−	0.961273i	$-0.588876\pi$
$823$	12.0228	−	6.94134i	0.419087	−	0.241960i	0.694687	+	0.719312i	$0.255543\pi$
$824$	7.61856	+	13.1957i	0.265405	+	0.459695i
$825$	12.5541	−	7.07567i	0.437076	−	0.246343i
$826$	−0.424277	−	0.168750i	−0.0147625	−	0.00587157i
$827$	−53.7207			−1.86805			−0.934027	−	0.357204i	$-0.883730\pi$
$827$	−53.7207			−1.86805			−0.934027	+	0.357204i	$0.883730\pi$
$828$	−11.7723	+	12.1937i	−0.409116	+	0.423760i
$829$		−	40.2685i		−	1.39858i	−0.714836	−	0.699292i	$-0.753499\pi$
$829$		−	40.2685i		−	1.39858i	0.714836	−	0.699292i	$-0.246501\pi$
$830$	5.16281	+	2.60778i	0.179204	+	0.0905172i
$831$	−3.08526	−	2.32460i	−0.107026	−	0.0806394i
$832$	1.04814	+	1.81544i	0.0363378	+	0.0629390i
$833$	35.8400	−	37.9276i	1.24178	−	1.31411i
$834$	−1.86022	+	15.1583i	−0.0644140	+	0.524888i
$835$	9.49697	+	4.79699i	0.328656	+	0.166007i
$836$	−7.75663			−0.268268
$837$	−10.2757	+	1.62955i	−0.355182	+	0.0563253i
$838$	25.4794			0.880170
$839$	−12.6898	+	21.9794i	−0.438100	+	0.758812i	−0.997543	−	0.0700572i	$-0.977682\pi$
$839$	−12.6898	+	21.9794i	−0.438100	+	0.758812i	0.559443	+	0.828869i	$0.311015\pi$
$840$	0.806730	+	10.2151i	0.0278348	+	0.352456i
$841$	−3.25296	−	5.63429i	−0.112171	−	0.194286i
$842$	−2.96965	−	5.14359i	−0.102341	−	0.177260i
$843$	−4.47048	−	3.36830i	−0.153971	−	0.116010i
$844$	5.01715	−	8.68995i	0.172697	−	0.299120i
$845$	19.2126	−	1.07460i	0.660935	−	0.0369672i
$846$	−29.6402	+	8.50332i	−1.01905	+	0.292350i
$847$	−3.14765	−	21.5487i	−0.108155	−	0.740422i
$848$	6.91868	−	11.9835i	0.237589	−	0.411516i
$849$	4.37652	+	10.3086i	0.150202	+	0.353790i
$850$	−29.9999	+	22.1200i	−1.02899	+	0.758709i
$851$	−23.8176	+	13.7511i	−0.816456	+	0.471381i
$852$	−19.2035	+	8.15286i	−0.657901	+	0.279312i
$853$	−17.2962	+	29.9580i	−0.592212	+	1.02574i	0.401722	+	0.915762i	$0.368412\pi$
$853$	−17.2962	+	29.9580i	−0.592212	+	1.02574i	−0.993934	+	0.109979i	$0.964921\pi$
$854$	15.6440	−	2.28514i	0.535326	−	0.0781959i
$855$	−29.5288	+	10.2880i	−1.00986	+	0.351843i
$856$	−11.4163			−0.390202
$857$	16.9137	+	9.76512i	0.577761	+	0.333570i	0.760243	−	0.649639i	$-0.225080\pi$
$857$	16.9137	+	9.76512i	0.577761	+	0.333570i	−0.182482	+	0.983209i	$0.558413\pi$
$858$	4.82544	+	3.63574i	0.164738	+	0.124122i
$859$	43.4126	−	25.0643i	1.48122	−	0.855182i	0.481446	−	0.876476i	$-0.340112\pi$
$859$	43.4126	−	25.0643i	1.48122	−	0.855182i	0.999773	+	0.0212940i	$0.00677859\pi$
$860$	−4.86701	+	3.18504i	−0.165964	+	0.108609i
$861$	0.855875	+	37.3079i	0.0291681	+	1.27145i
$862$	−25.4910	−	14.7172i	−0.868225	−	0.501270i
$863$	−17.7867			−0.605465			−0.302733	−	0.953076i	$-0.597899\pi$
$863$	−17.7867			−0.605465			−0.302733	+	0.953076i	$0.597899\pi$
$864$	−0.813845	−	5.13202i	−0.0276876	−	0.174595i
$865$	−2.15499	−	38.5290i	−0.0732720	−	1.31003i
$866$	−7.12793	+	12.3459i	−0.242217	+	0.419532i
$867$	−66.3104	−	8.13757i	−2.25202	−	0.276366i
$868$	3.28406	+	4.15678i	0.111468	+	0.141090i
$869$	18.1832	−	10.4981i	0.616823	−	0.356123i
$870$	15.2650	+	10.2171i	0.517533	+	0.346393i
$871$	9.86535	+	5.69576i	0.334275	+	0.192994i
$872$	−10.6147			−0.359458
$873$	19.7196	−	20.4255i	0.667409	−	0.691299i
$874$			26.3356i			0.890815i
$875$	−28.9248	−	6.19331i	−0.977836	−	0.209372i
$876$	−3.24656	−	7.64705i	−0.109691	−	0.258370i
$877$	18.1879	−	10.5008i	0.614163	−	0.354587i	−0.160430	−	0.987047i	$-0.551288\pi$
$877$	18.1879	−	10.5008i	0.614163	−	0.354587i	0.774593	+	0.632460i	$0.217955\pi$
$878$	9.41191	−	5.43397i	0.317637	−	0.183388i
$879$	−29.5317	+	12.5377i	−0.996080	+	0.422886i
$880$	3.32121	+	1.67757i	0.111958	+	0.0565507i
$881$	57.9674			1.95297			0.976486	−	0.215580i	$-0.0691642\pi$
$881$	57.9674			1.95297			0.976486	+	0.215580i	$0.0691642\pi$
$882$	−20.9779	+	0.963010i	−0.706363	+	0.0324262i
$883$		−	42.6213i		−	1.43432i	−0.696908	−	0.717161i	$-0.745441\pi$
$883$		−	42.6213i		−	1.43432i	0.696908	−	0.717161i	$-0.254559\pi$
$884$	−13.5334	−	7.81352i	−0.455178	−	0.262797i
$885$	−0.371780	+	0.555463i	−0.0124972	+	0.0186717i
$886$	5.24859	+	9.09083i	0.176330	+	0.305412i
$887$	3.27263	−	1.88945i	0.109884	−	0.0634416i	−0.444051	−	0.896002i	$-0.646459\pi$
$887$	3.27263	−	1.88945i	0.109884	−	0.0634416i	0.553935	+	0.832560i	$0.313126\pi$
$888$	1.02700	−	8.36865i	0.0344637	−	0.280833i
$889$	13.8799	−	34.8973i	0.465517	−	1.17042i
$890$	25.0602	−	1.40166i	0.840020	−	0.0469837i
$891$	−7.93937	−	12.6984i	−0.265979	−	0.425412i
$892$	17.7445			0.594131
$893$	−23.9564	+	41.4937i	−0.801671	+	1.38853i
$894$	−3.02525	+	24.6518i	−0.101180	+	0.824479i
$895$	1.12755	−	0.737885i	0.0376898	−	0.0246648i
$896$	−2.07602	+	1.64016i	−0.0693550	+	0.0547940i
$897$	12.3442	−	16.3835i	0.412161	−	0.547030i
$898$	32.1022	+	18.5342i	1.07126	+	0.618494i
$899$	9.49639			0.316722
$900$	14.8686	+	1.98126i	0.495619	+	0.0660419i
$901$			103.152i			3.43651i
$902$	11.7352	+	6.77533i	0.390740	+	0.225594i
$903$	−6.19539	−	10.1839i	−0.206170	−	0.338901i
$904$	6.87120	+	11.9013i	0.228533	+	0.395830i
$905$	23.9078	−	15.6456i	0.794721	−	0.520077i
$906$	4.67320	+	11.0074i	0.155257	+	0.365696i
$907$	43.9682	+	25.3850i	1.45994	+	0.842896i	0.999008	−	0.0445394i	$-0.0141820\pi$
$907$	43.9682	+	25.3850i	1.45994	+	0.842896i	0.460932	+	0.887436i	$0.347515\pi$
$908$			0.474897i			0.0157600i
$909$	22.0267	−	22.8152i	0.730579	−	0.756731i
$910$	−2.47503	−	12.1523i	−0.0820464	−	0.402845i
$911$	−6.59422	−	3.80717i	−0.218476	−	0.126137i	0.386768	−	0.922177i	$-0.373591\pi$
$911$	−6.59422	−	3.80717i	−0.218476	−	0.126137i	−0.605244	+	0.796040i	$0.706925\pi$
$912$	−6.44833	−	4.85852i	−0.213526	−	0.160882i
$913$	2.15215	+	3.72763i	0.0712257	+	0.123367i
$914$	17.5211	−	10.1158i	0.579545	−	0.334601i
$915$	1.53180	−	23.0927i	0.0506396	−	0.763421i
$916$	9.51279	+	5.49221i	0.314312	+	0.181468i
$917$	0.877104	+	6.00462i	0.0289645	+	0.198290i
$918$	24.3828	+	30.0984i	0.804751	+	0.993394i
$919$	−10.4157			−0.343581			−0.171791	−	0.985133i	$-0.554955\pi$
$919$	−10.4157			−0.343581			−0.171791	+	0.985133i	$0.554955\pi$
$920$	5.69574	−	11.2763i	0.187783	−	0.371768i
$921$	−5.91634	−	0.726049i	−0.194950	−	0.0239241i
$922$	6.80701	+	11.7901i	0.224177	+	0.388286i
$923$	21.8669	−	12.6249i	0.719757	−	0.415552i
$924$	−3.66026	+	6.68954i	−0.120414	+	0.220070i
$925$	22.3042	+	9.74324i	0.733357	+	0.320356i
$926$			22.8848i			0.752040i
$927$	12.6054	+	43.9389i	0.414015	+	1.44314i
$928$			4.74279i			0.155690i
$929$	−21.5567	+	37.3374i	−0.707253	+	1.22500i	0.258619	+	0.965980i	$0.416733\pi$
$929$	−21.5567	+	37.3374i	−0.707253	+	1.22500i	−0.965872	+	0.259019i	$0.916601\pi$
$930$	6.95775	−	3.42439i	0.228154	−	0.112290i
$931$	−22.4109	+	23.7162i	−0.734487	+	0.777269i
$932$	−10.7397	−	18.6017i	−0.351791	−	0.609320i
$933$	22.4972	+	52.9905i	0.736524	+	1.73483i
$934$	2.89724	+	1.67272i	0.0948006	+	0.0547332i
$935$	−27.6942	+	1.54898i	−0.905697	+	0.0506571i
$936$	1.73422	+	6.04502i	0.0566848	+	0.197588i
$937$	16.2891			0.532140			0.266070	−	0.963954i	$-0.414275\pi$
$937$	16.2891			0.532140			0.266070	+	0.963954i	$0.414275\pi$
$938$	−5.31355	+	13.3595i	−0.173494	+	0.436203i
$939$	2.01601	−	2.67570i	0.0657901	−	0.0873180i
$940$	19.2316	−	12.5855i	0.627267	−	0.410492i
$941$	14.8611	+	25.7402i	0.484458	+	0.839106i	0.999841	−	0.0178543i	$-0.00568350\pi$
$941$	14.8611	+	25.7402i	0.484458	+	0.839106i	−0.515383	+	0.856960i	$0.672350\pi$
$942$	25.7463	+	3.15957i	0.838860	+	0.102944i
$943$	23.0039	−	39.8439i	0.749110	−	1.29750i
$944$	−0.172580			−0.00561701
$945$	−5.06161	+	30.3213i	−0.164654	+	0.986351i
$946$	−4.32849			−0.140731
$947$	12.6233	−	21.8642i	0.410202	−	0.710490i	−0.584710	−	0.811243i	$-0.698792\pi$
$947$	12.6233	−	21.8642i	0.410202	−	0.710490i	0.994912	+	0.100752i	$0.0321249\pi$
$948$	21.6920	+	2.66202i	0.704522	+	0.0864585i
$949$	5.02736	+	8.70764i	0.163195	+	0.282662i
$950$	18.7591	−	13.8317i	0.608624	−	0.448760i
$951$	10.6738	−	14.1665i	0.346122	−	0.459381i
$952$	7.28919	−	18.3267i	0.236244	−	0.593972i
$953$	−46.4580			−1.50492			−0.752461	−	0.658636i	$-0.771134\pi$
$953$	−46.4580			−1.50492			−0.752461	+	0.658636i	$0.771134\pi$
$954$	28.8329	−	29.8650i	0.933500	−	0.966915i
$955$	2.35286	+	42.0667i	0.0761368	+	1.36125i
$956$	14.6228	+	8.44250i	0.472937	+	0.273050i
$957$	5.34188	+	12.5824i	0.172678	+	0.406732i
$958$	−8.15257	−	14.1207i	−0.263397	−	0.456218i
$959$	22.4956	−	17.7727i	0.726422	−	0.573910i
$960$	1.71025	+	3.47492i	0.0551980	+	0.112152i
$961$	−13.4954	+	23.3748i	−0.435337	+	0.754025i
$962$			10.2045i			0.329006i
$963$	−33.2327	−	8.28131i	−1.07091	−	0.266862i
$964$		−	9.24813i		−	0.297862i
$965$	13.5793	+	6.85900i	0.437133	+	0.220799i
$966$	22.7126	+	12.4275i	0.730766	+	0.399848i
$967$	−38.7680	+	22.3827i	−1.24670	+	0.719780i	−0.970449	−	0.241307i	$-0.922424\pi$
$967$	−38.7680	+	22.3827i	−1.24670	+	0.719780i	−0.276246	+	0.961087i	$0.589091\pi$
$968$	−4.11554	−	7.12832i	−0.132278	−	0.229113i
$969$	59.7390	+	7.33114i	1.91909	+	0.235510i
$970$	−9.54087	+	18.8888i	−0.306339	+	0.606483i
$971$	5.45198			0.174962			0.0874812	−	0.996166i	$-0.472118\pi$
$971$	5.45198			0.174962			0.0874812	+	0.996166i	$0.472118\pi$
$972$	1.35364	−	15.5296i	0.0434181	−	0.498111i
$973$	23.0834	−	3.37183i	0.740020	−	0.108096i
$974$	−4.50548	−	2.60124i	−0.144365	−	0.0833491i
$975$	−18.1534	−	0.188112i	−0.581374	−	0.00602440i
$976$	5.17503	−	2.98781i	0.165649	−	0.0956374i
$977$	9.53359	+	16.5127i	0.305007	+	0.528287i	0.977263	−	0.212032i	$-0.0680080\pi$
$977$	9.53359	+	16.5127i	0.305007	+	0.528287i	−0.672256	+	0.740319i	$0.734675\pi$
$978$	11.1157	+	8.37517i	0.355441	+	0.267808i
$979$	16.1757	+	9.33907i	0.516979	+	0.298478i
$980$	14.7250	−	5.30783i	0.470374	−	0.169552i
$981$	−30.8991	−	7.69981i	−0.986533	−	0.245836i
$982$		−	23.8599i		−	0.761400i
$983$	−26.7964	−	15.4709i	−0.854674	−	0.493446i	0.00755133	−	0.999971i	$-0.497596\pi$
$983$	−26.7964	−	15.4709i	−0.854674	−	0.493446i	−0.862225	+	0.506525i	$0.830930\pi$
$984$	5.51200	+	12.9831i	0.175716	+	0.413887i
$985$	−10.5148	−	16.0675i	−0.335030	−	0.511953i
$986$	−17.6779	−	30.6190i	−0.562979	−	0.975107i
$987$	24.4806	+	40.2411i	0.779227	+	1.28089i
$988$	8.46249	+	4.88582i	0.269228	+	0.155439i
$989$			14.6963i			0.467314i
$990$	8.45107	+	7.29254i	0.268593	+	0.231772i
$991$	21.5926			0.685912			0.342956	−	0.939351i	$-0.388572\pi$
$991$	21.5926			0.685912			0.342956	+	0.939351i	$0.388572\pi$
$992$	1.73402	+	1.00114i	0.0550553	+	0.0317862i
$993$	−5.87406	+	7.79618i	−0.186408	+	0.247404i
$994$	19.7557	+	25.0056i	0.626613	+	0.793130i
$995$	−9.54348	+	6.24539i	−0.302549	+	0.197992i
$996$	−0.545726	+	4.44694i	−0.0172920	+	0.140907i
$997$	−26.8955	+	46.5843i	−0.851788	+	1.47534i	0.0278059	+	0.999613i	$0.491148\pi$
$997$	−26.8955	+	46.5843i	−0.851788	+	1.47534i	−0.879593	+	0.475726i	$0.842185\pi$
$998$	−32.3319			−1.02345
$999$	9.06011	−	23.6160i	0.286649	−	0.747177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bf.e.209.16	yes	32
3.2	odd	2		1890.2.bf.f.629.4		32
5.4	even	2		630.2.bf.f.209.1	yes	32
7.6	odd	2	inner	630.2.bf.e.209.1	✓	32
9.4	even	3		1890.2.bf.e.1259.10		32
9.5	odd	6		630.2.bf.f.419.16	yes	32
15.14	odd	2		1890.2.bf.e.629.7		32
21.20	even	2		1890.2.bf.f.629.13		32
35.34	odd	2		630.2.bf.f.209.16	yes	32
45.4	even	6		1890.2.bf.f.1259.13		32
45.14	odd	6	inner	630.2.bf.e.419.1	yes	32
63.13	odd	6		1890.2.bf.e.1259.7		32
63.41	even	6		630.2.bf.f.419.1	yes	32
105.104	even	2		1890.2.bf.e.629.10		32
315.104	even	6	inner	630.2.bf.e.419.16	yes	32
315.139	odd	6		1890.2.bf.f.1259.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bf.e.209.1	✓	32	7.6	odd	2	inner
630.2.bf.e.209.16	yes	32	1.1	even	1	trivial
630.2.bf.e.419.1	yes	32	45.14	odd	6	inner
630.2.bf.e.419.16	yes	32	315.104	even	6	inner
630.2.bf.f.209.1	yes	32	5.4	even	2
630.2.bf.f.209.16	yes	32	35.34	odd	2
630.2.bf.f.419.1	yes	32	63.41	even	6
630.2.bf.f.419.16	yes	32	9.5	odd	6
1890.2.bf.e.629.7		32	15.14	odd	2
1890.2.bf.e.629.10		32	105.104	even	2
1890.2.bf.e.1259.7		32	63.13	odd	6
1890.2.bf.e.1259.10		32	9.4	even	3
1890.2.bf.f.629.4		32	3.2	odd	2
1890.2.bf.f.629.13		32	21.20	even	2
1890.2.bf.f.1259.4		32	315.139	odd	6
1890.2.bf.f.1259.13		32	45.4	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.71915 + 0.210974i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.22443 + 1.87103i) q^{5} +(-1.04229 + 1.38334i) q^{6} +(2.45843 + 0.977807i) q^{7} +1.00000 q^{8} +(2.91098 + 0.725392i) q^{9} +(-2.23258 + 0.124872i) q^{10} +(-1.44107 - 0.832005i) q^{11} +(-0.676868 - 1.59432i) q^{12} +(1.04814 + 1.81544i) q^{13} +(-2.07602 + 1.64016i) q^{14} +(1.71025 + 3.47492i) q^{15} +(-0.500000 + 0.866025i) q^{16} -7.45463i q^{17} +(-2.08370 + 2.15829i) q^{18} +4.66141i q^{19} +(1.00815 - 1.99591i) q^{20} +(4.02013 + 2.19967i) q^{21} +(1.44107 - 0.832005i) q^{22} +(-2.82486 - 4.89279i) q^{23} +(1.71915 + 0.210974i) q^{24} +(-2.00154 + 4.58191i) q^{25} -2.09629 q^{26} +(4.85138 + 1.86120i) q^{27} +(-0.382411 - 2.61797i) q^{28} +(-4.10738 - 2.37140i) q^{29} +(-3.86449 - 0.256341i) q^{30} +(-1.73402 + 1.00114i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.30190 - 1.73437i) q^{33} +(6.45590 + 3.72732i) q^{34} +(1.18067 + 5.79707i) q^{35} +(-0.827282 - 2.88368i) q^{36} -4.86789i q^{37} +(-4.03690 - 2.33070i) q^{38} +(1.41891 + 3.34215i) q^{39} +(1.22443 + 1.87103i) q^{40} +(4.07169 + 7.05238i) q^{41} +(-3.91503 + 2.38170i) q^{42} +(-2.25274 - 1.30062i) q^{43} +1.66401i q^{44} +(2.20706 + 6.33474i) q^{45} +5.64971 q^{46} +(8.90154 + 5.13931i) q^{47} +(-1.04229 + 1.38334i) q^{48} +(5.08779 + 4.80775i) q^{49} +(-2.96728 - 4.02433i) q^{50} +(1.57273 - 12.8157i) q^{51} +(1.04814 - 1.81544i) q^{52} -13.8374 q^{53} +(-4.03754 + 3.27082i) q^{54} +(-0.207788 - 3.71503i) q^{55} +(2.45843 + 0.977807i) q^{56} +(-0.983434 + 8.01368i) q^{57} +(4.10738 - 2.37140i) q^{58} +(0.0862901 + 0.149459i) q^{59} +(2.15424 - 3.21858i) q^{60} +(-5.17503 - 2.98781i) q^{61} -2.00228i q^{62} +(6.44716 + 4.62971i) q^{63} +1.00000 q^{64} +(-2.11336 + 4.18399i) q^{65} +(2.65296 - 1.12632i) q^{66} +(4.70611 - 2.71707i) q^{67} +(-6.45590 + 3.72732i) q^{68} +(-3.82411 - 9.00744i) q^{69} +(-5.61075 - 1.87604i) q^{70} -12.0450i q^{71} +(2.91098 + 0.725392i) q^{72} +4.79644 q^{73} +(4.21571 + 2.43394i) q^{74} +(-4.40761 + 7.45473i) q^{75} +(4.03690 - 2.33070i) q^{76} +(-2.72924 - 3.45452i) q^{77} +(-3.60384 - 0.442261i) q^{78} +(-6.30891 + 10.9273i) q^{79} +(-2.23258 + 0.124872i) q^{80} +(7.94761 + 4.22320i) q^{81} -8.14339 q^{82} +(-2.24015 - 1.29335i) q^{83} +(-0.105101 - 4.58137i) q^{84} +(13.9479 - 9.12768i) q^{85} +(2.25274 - 1.30062i) q^{86} +(-6.56091 - 4.94334i) q^{87} +(-1.44107 - 0.832005i) q^{88} -11.2248 q^{89} +(-6.58957 - 1.25600i) q^{90} +(0.801642 + 5.48801i) q^{91} +(-2.82486 + 4.89279i) q^{92} +(-3.19227 + 1.35528i) q^{93} +(-8.90154 + 5.13931i) q^{94} +(-8.72165 + 5.70757i) q^{95} +(-0.676868 - 1.59432i) q^{96} +(4.73188 - 8.19586i) q^{97} +(-6.70752 + 2.00228i) q^{98} +(-3.59141 - 3.46729i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9} - 24 q^{11} - 16 q^{15} - 16 q^{16} + 6 q^{18} + 2 q^{21} + 24 q^{22} - 24 q^{23} - 58 q^{25} - 36 q^{29} - 10 q^{30} - 16 q^{32} - 48 q^{35} - 66 q^{39}+ \cdots + 58 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9 - 24 * q^11 - 16 * q^15 - 16 * q^16 + 6 * q^18 + 2 * q^21 + 24 * q^22 - 24 * q^23 - 58 * q^25 - 36 * q^29 - 10 * q^30 - 16 * q^32 - 48 * q^35 - 66 * q^39 + 2 * q^42 - 54 * q^43 + 48 * q^46 + 32 * q^49 + 50 * q^50 - 26 * q^51 - 24 * q^53 + 110 * q^57 + 36 * q^58 + 26 * q^60 + 20 * q^63 + 32 * q^64 - 90 * q^65 - 66 * q^67 + 36 * q^70 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 60 * q^78 + 34 * q^79 + 2 * q^81 - 4 * q^84 + 4 * q^85 + 54 * q^86 - 24 * q^88 + 16 * q^91 - 24 * q^92 + 28 * q^93 + 12 * q^95 - 64 * q^98 + 58 * q^99

Introduction

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