LMFDB - Embedded newform 630.2.bi.b.479.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(479,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.479"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [48,48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			479.24
Character	$\chi$	$=$	630.479
Dual form			630.2.bi.b.509.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(1.70267 + 0.317671i) q^{3} +1.00000 q^{4} +(1.22943 + 1.86775i) q^{5} +(1.70267 + 0.317671i) q^{6} +(-0.691773 - 2.55371i) q^{7} +1.00000 q^{8} +(2.79817 + 1.08178i) q^{9} +(1.22943 + 1.86775i) q^{10} +(-3.10680 + 1.79371i) q^{11} +(1.70267 + 0.317671i) q^{12} +(2.03087 + 3.51756i) q^{13} +(-0.691773 - 2.55371i) q^{14} +(1.49999 + 3.57072i) q^{15} +1.00000 q^{16} +(-4.57132 - 2.63925i) q^{17} +(2.79817 + 1.08178i) q^{18} +(3.13968 - 1.81269i) q^{19} +(1.22943 + 1.86775i) q^{20} +(-0.366620 - 4.56789i) q^{21} +(-3.10680 + 1.79371i) q^{22} +(2.39862 - 4.15452i) q^{23} +(1.70267 + 0.317671i) q^{24} +(-1.97699 + 4.59255i) q^{25} +(2.03087 + 3.51756i) q^{26} +(4.42071 + 2.73081i) q^{27} +(-0.691773 - 2.55371i) q^{28} +(-6.99680 - 4.03961i) q^{29} +(1.49999 + 3.57072i) q^{30} -3.52560i q^{31} +1.00000 q^{32} +(-5.85967 + 2.06716i) q^{33} +(-4.57132 - 2.63925i) q^{34} +(3.91921 - 4.43168i) q^{35} +(2.79817 + 1.08178i) q^{36} +(-0.879847 + 0.507980i) q^{37} +(3.13968 - 1.81269i) q^{38} +(2.34047 + 6.63440i) q^{39} +(1.22943 + 1.86775i) q^{40} +(-4.80160 - 8.31661i) q^{41} +(-0.366620 - 4.56789i) q^{42} +(4.43909 + 2.56291i) q^{43} +(-3.10680 + 1.79371i) q^{44} +(1.41967 + 6.55626i) q^{45} +(2.39862 - 4.15452i) q^{46} +11.5014i q^{47} +(1.70267 + 0.317671i) q^{48} +(-6.04290 + 3.53318i) q^{49} +(-1.97699 + 4.59255i) q^{50} +(-6.94503 - 5.94595i) q^{51} +(2.03087 + 3.51756i) q^{52} +(-5.71305 + 9.89529i) q^{53} +(4.42071 + 2.73081i) q^{54} +(-7.16981 - 3.59749i) q^{55} +(-0.691773 - 2.55371i) q^{56} +(5.92168 - 2.08904i) q^{57} +(-6.99680 - 4.03961i) q^{58} +7.03823 q^{59} +(1.49999 + 3.57072i) q^{60} -11.2231i q^{61} -3.52560i q^{62} +(0.826853 - 7.89407i) q^{63} +1.00000 q^{64} +(-4.07312 + 8.11776i) q^{65} +(-5.85967 + 2.06716i) q^{66} -6.99540i q^{67} +(-4.57132 - 2.63925i) q^{68} +(5.40382 - 6.31181i) q^{69} +(3.91921 - 4.43168i) q^{70} -0.828681i q^{71} +(2.79817 + 1.08178i) q^{72} +(3.51263 - 6.08405i) q^{73} +(-0.879847 + 0.507980i) q^{74} +(-4.82509 + 7.19156i) q^{75} +(3.13968 - 1.81269i) q^{76} +(6.72983 + 6.69304i) q^{77} +(2.34047 + 6.63440i) q^{78} +0.0299868 q^{79} +(1.22943 + 1.86775i) q^{80} +(6.65951 + 6.05400i) q^{81} +(-4.80160 - 8.31661i) q^{82} +(-6.89727 - 3.98214i) q^{83} +(-0.366620 - 4.56789i) q^{84} +(-0.690658 - 11.7829i) q^{85} +(4.43909 + 2.56291i) q^{86} +(-10.6300 - 9.10080i) q^{87} +(-3.10680 + 1.79371i) q^{88} +(-0.625013 - 1.08255i) q^{89} +(1.41967 + 6.55626i) q^{90} +(7.57795 - 7.61961i) q^{91} +(2.39862 - 4.15452i) q^{92} +(1.11998 - 6.00293i) q^{93} +11.5014i q^{94} +(7.24569 + 3.63556i) q^{95} +(1.70267 + 0.317671i) q^{96} +(-4.69619 + 8.13404i) q^{97} +(-6.04290 + 3.53318i) q^{98} +(-10.6338 + 1.65824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39}+ \cdots - 26 q^{99}+O(q^{100}) $ 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 42 * q^55 + 3 * q^56 - 22 * q^57 - 3 * q^58 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * q^70 - 18 * q^73 + 18 * q^75 - 12 * q^77 - 18 * q^78 + 8 * q^81 - 3 * q^82 + 9 * q^83 + 8 * q^84 - 33 * q^85 - 15 * q^87 + 6 * q^88 - 33 * q^89 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 24 * q^97 + 3 * q^98 - 26 * q^99

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.70267	+	0.317671i	0.983037	+	0.183408i
$3$	1.70267	+	0.317671i	0.983037	+	0.183408i
$4$	1.00000			0.500000
$5$	1.22943	+	1.86775i	0.549819	+	0.835284i
$5$	1.22943	+	1.86775i	0.549819	+	0.835284i
$6$	1.70267	+	0.317671i	0.695112	+	0.129689i
$7$	−0.691773	−	2.55371i	−0.261466	−	0.965213i
$7$	−0.691773	−	2.55371i	−0.261466	−	0.965213i
$8$	1.00000			0.353553
$9$	2.79817	+	1.08178i	0.932723	+	0.360593i
$10$	1.22943	+	1.86775i	0.388781	+	0.590635i
$11$	−3.10680	+	1.79371i	−0.936736	+	0.540825i	−0.888936	−	0.458032i	$-0.848554\pi$
$11$	−3.10680	+	1.79371i	−0.936736	+	0.540825i	−0.0478002	+	0.998857i	$0.515221\pi$
$12$	1.70267	+	0.317671i	0.491518	+	0.0917038i
$13$	2.03087	+	3.51756i	0.563261	+	0.975597i	0.997209	+	0.0746590i	$0.0237868\pi$
$13$	2.03087	+	3.51756i	0.563261	+	0.975597i	−0.433948	+	0.900938i	$0.642880\pi$
$14$	−0.691773	−	2.55371i	−0.184884	−	0.682509i
$15$	1.49999	+	3.57072i	0.387295	+	0.921956i
$16$	1.00000			0.250000
$17$	−4.57132	−	2.63925i	−1.10871	−	0.640112i	−0.170213	−	0.985407i	$-0.554445\pi$
$17$	−4.57132	−	2.63925i	−1.10871	−	0.640112i	−0.938494	+	0.345295i	$0.887779\pi$
$18$	2.79817	+	1.08178i	0.659535	+	0.254978i
$19$	3.13968	−	1.81269i	0.720292	−	0.415861i	−0.0945683	−	0.995518i	$-0.530147\pi$
$19$	3.13968	−	1.81269i	0.720292	−	0.415861i	0.814860	+	0.579658i	$0.196814\pi$
$20$	1.22943	+	1.86775i	0.274909	+	0.417642i
$21$	−0.366620	−	4.56789i	−0.0800030	−	0.996795i
$22$	−3.10680	+	1.79371i	−0.662372	+	0.382421i
$23$	2.39862	−	4.15452i	0.500146	−	0.866278i	−0.499854	−	0.866110i	$-0.666613\pi$
$23$	2.39862	−	4.15452i	0.500146	−	0.866278i	1.00000		0.000168492i	$-5.36327e-5\pi$
$24$	1.70267	+	0.317671i	0.347556	+	0.0648443i
$25$	−1.97699	+	4.59255i	−0.395399	+	0.918510i
$26$	2.03087	+	3.51756i	0.398286	+	0.689851i
$27$	4.42071	+	2.73081i	0.850766	+	0.525544i
$28$	−0.691773	−	2.55371i	−0.130733	−	0.482606i
$29$	−6.99680	−	4.03961i	−1.29927	−	0.750136i	−0.318995	−	0.947756i	$-0.603345\pi$
$29$	−6.99680	−	4.03961i	−1.29927	−	0.750136i	−0.980279	+	0.197620i	$0.936679\pi$
$30$	1.49999	+	3.57072i	0.273859	+	0.651921i
$31$		−	3.52560i		−	0.633216i	−0.948556	−	0.316608i	$-0.897456\pi$
$31$		−	3.52560i		−	0.633216i	0.948556	−	0.316608i	$-0.102544\pi$
$32$	1.00000			0.176777
$33$	−5.85967	+	2.06716i	−1.02004	+	0.359846i
$34$	−4.57132	−	2.63925i	−0.783974	−	0.452628i
$35$	3.91921	−	4.43168i	0.662468	−	0.749090i
$36$	2.79817	+	1.08178i	0.466362	+	0.180296i
$37$	−0.879847	+	0.507980i	−0.144646	+	0.0835114i	−0.570576	−	0.821245i	$-0.693280\pi$
$37$	−0.879847	+	0.507980i	−0.144646	+	0.0835114i	0.425930	+	0.904756i	$0.359947\pi$
$38$	3.13968	−	1.81269i	0.509323	−	0.294058i
$39$	2.34047	+	6.63440i	0.374775	+	1.06235i
$40$	1.22943	+	1.86775i	0.194390	+	0.295317i
$41$	−4.80160	−	8.31661i	−0.749883	−	1.29884i	−0.947878	−	0.318633i	$-0.896776\pi$
$41$	−4.80160	−	8.31661i	−0.749883	−	1.29884i	0.197995	−	0.980203i	$-0.436557\pi$
$42$	−0.366620	−	4.56789i	−0.0565707	−	0.704840i
$43$	4.43909	+	2.56291i	0.676955	+	0.390840i	0.798707	−	0.601720i	$-0.205518\pi$
$43$	4.43909	+	2.56291i	0.676955	+	0.390840i	−0.121752	+	0.992561i	$0.538851\pi$
$44$	−3.10680	+	1.79371i	−0.468368	+	0.270412i
$45$	1.41967	+	6.55626i	0.211631	+	0.977350i
$46$	2.39862	−	4.15452i	0.353657	−	0.612551i
$47$			11.5014i			1.67765i	0.544403	+	0.838824i	$0.316756\pi$
$47$			11.5014i			1.67765i	−0.544403	+	0.838824i	$0.683244\pi$
$48$	1.70267	+	0.317671i	0.245759	+	0.0458519i
$49$	−6.04290	+	3.53318i	−0.863272	+	0.504740i
$50$	−1.97699	+	4.59255i	−0.279589	+	0.649484i
$51$	−6.94503	−	5.94595i	−0.972498	−	0.832599i
$52$	2.03087	+	3.51756i	0.281631	+	0.487798i
$53$	−5.71305	+	9.89529i	−0.784747	+	1.35922i	0.144403	+	0.989519i	$0.453874\pi$
$53$	−5.71305	+	9.89529i	−0.784747	+	1.35922i	−0.929150	+	0.369703i	$0.879459\pi$
$54$	4.42071	+	2.73081i	0.601583	+	0.371616i
$55$	−7.16981	−	3.59749i	−0.966777	−	0.485085i
$56$	−0.691773	−	2.55371i	−0.0924420	−	0.341254i
$57$	5.92168	−	2.08904i	0.784345	−	0.276699i
$58$	−6.99680	−	4.03961i	−0.918725	−	0.530426i
$59$	7.03823			0.916299			0.458150	−	0.888875i	$-0.348512\pi$
$59$	7.03823			0.916299			0.458150	+	0.888875i	$0.348512\pi$
$60$	1.49999	+	3.57072i	0.193647	+	0.460978i
$61$		−	11.2231i		−	1.43696i	−0.695545	−	0.718482i	$-0.744837\pi$
$61$		−	11.2231i		−	1.43696i	0.695545	−	0.718482i	$-0.255163\pi$
$62$		−	3.52560i		−	0.447751i
$63$	0.826853	−	7.89407i	0.104174	−	0.994559i
$64$	1.00000			0.125000
$65$	−4.07312	+	8.11776i	−0.505209	+	1.00688i
$66$	−5.85967	+	2.06716i	−0.721275	+	0.254450i
$67$		−	6.99540i		−	0.854624i	−0.904104	−	0.427312i	$-0.859461\pi$
$67$		−	6.99540i		−	0.854624i	0.904104	−	0.427312i	$-0.140539\pi$
$68$	−4.57132	−	2.63925i	−0.554353	−	0.320056i
$69$	5.40382	−	6.31181i	0.650544	−	0.759853i
$70$	3.91921	−	4.43168i	0.468436	−	0.529687i
$71$		−	0.828681i		−	0.0983464i	−0.998790	−	0.0491732i	$-0.984341\pi$
$71$		−	0.828681i		−	0.0983464i	0.998790	−	0.0491732i	$-0.0156586\pi$
$72$	2.79817	+	1.08178i	0.329768	+	0.127489i
$73$	3.51263	−	6.08405i	0.411122	−	0.712084i	−0.583891	−	0.811832i	$-0.698470\pi$
$73$	3.51263	−	6.08405i	0.411122	−	0.712084i	0.995013	+	0.0997484i	$0.0318038\pi$
$74$	−0.879847	+	0.507980i	−0.102280	+	0.0590515i
$75$	−4.82509	+	7.19156i	−0.557153	+	0.830410i
$76$	3.13968	−	1.81269i	0.360146	−	0.207930i
$77$	6.72983	+	6.69304i	0.766935	+	0.762742i
$78$	2.34047	+	6.63440i	0.265006	+	0.751198i
$79$	0.0299868			0.00337377			0.00168689	−	0.999999i	$-0.499463\pi$
$79$	0.0299868			0.00337377			0.00168689	+	0.999999i	$0.499463\pi$
$80$	1.22943	+	1.86775i	0.137455	+	0.208821i
$81$	6.65951	+	6.05400i	0.739946	+	0.672666i
$82$	−4.80160	−	8.31661i	−0.530248	−	0.918416i
$83$	−6.89727	−	3.98214i	−0.757074	−	0.437097i	0.0711705	−	0.997464i	$-0.477327\pi$
$83$	−6.89727	−	3.98214i	−0.757074	−	0.437097i	−0.828244	+	0.560368i	$0.810660\pi$
$84$	−0.366620	−	4.56789i	−0.0400015	−	0.498397i
$85$	−0.690658	−	11.7829i	−0.0749124	−	1.27803i
$86$	4.43909	+	2.56291i	0.478679	+	0.276366i
$87$	−10.6300	−	9.10080i	−1.13965	−	0.975708i
$88$	−3.10680	+	1.79371i	−0.331186	+	0.191210i
$89$	−0.625013	−	1.08255i	−0.0662512	−	0.114750i	0.830997	−	0.556277i	$-0.187771\pi$
$89$	−0.625013	−	1.08255i	−0.0662512	−	0.114750i	−0.897248	+	0.441526i	$0.854437\pi$
$90$	1.41967	+	6.55626i	0.149646	+	0.691090i
$91$	7.57795	−	7.61961i	0.794385	−	0.798752i
$92$	2.39862	−	4.15452i	0.250073	−	0.433139i
$93$	1.11998	−	6.00293i	0.116137	−	0.622475i
$94$			11.5014i			1.18628i
$95$	7.24569	+	3.63556i	0.743392	+	0.373000i
$96$	1.70267	+	0.317671i	0.173778	+	0.0324222i
$97$	−4.69619	+	8.13404i	−0.476826	+	0.825887i	−0.999647	−	0.0265556i	$-0.991546\pi$
$97$	−4.69619	+	8.13404i	−0.476826	+	0.825887i	0.522821	+	0.852442i	$0.324879\pi$
$98$	−6.04290	+	3.53318i	−0.610425	+	0.356905i
$99$	−10.6338	+	1.65824i	−1.06873	+	0.166660i
$100$	−1.97699	+	4.59255i	−0.197699	+	0.459255i
$101$	−5.44619	−	9.43308i	−0.541916	−	0.938626i	−0.998794	−	0.0490969i	$-0.984366\pi$
$101$	−5.44619	−	9.43308i	−0.541916	−	0.938626i	0.456878	−	0.889529i	$-0.348968\pi$
$102$	−6.94503	−	5.94595i	−0.687660	−	0.588736i
$103$	−0.292115	+	0.505958i	−0.0287830	+	0.0498536i	−0.880058	−	0.474866i	$-0.842496\pi$
$103$	−0.292115	+	0.505958i	−0.0287830	+	0.0498536i	0.851275	+	0.524720i	$0.175830\pi$
$104$	2.03087	+	3.51756i	0.199143	+	0.344926i
$105$	8.08094	−	6.30066i	0.788619	−	0.614882i
$106$	−5.71305	+	9.89529i	−0.554900	+	0.961115i
$107$	−1.34287	−	2.32592i	−0.129820	−	0.224855i	0.793787	−	0.608196i	$-0.208107\pi$
$107$	−1.34287	−	2.32592i	−0.129820	−	0.224855i	−0.923607	+	0.383341i	$0.874773\pi$
$108$	4.42071	+	2.73081i	0.425383	+	0.262772i
$109$	−0.618180	+	1.07072i	−0.0592109	+	0.102556i	−0.894111	−	0.447845i	$-0.852192\pi$
$109$	−0.618180	+	1.07072i	−0.0592109	+	0.102556i	0.834901	+	0.550401i	$0.185525\pi$
$110$	−7.16981	−	3.59749i	−0.683615	−	0.343007i
$111$	−1.65946	+	0.585420i	−0.157509	+	0.0555656i
$112$	−0.691773	−	2.55371i	−0.0653664	−	0.241303i
$113$	5.41347	+	9.37640i	0.509256	+	0.882058i	0.999943	+	0.0107214i	$0.00341278\pi$
$113$	5.41347	+	9.37640i	0.509256	+	0.882058i	−0.490686	+	0.871336i	$0.663254\pi$
$114$	5.92168	−	2.08904i	0.554616	−	0.195656i
$115$	10.7086	−	0.627687i	0.998578	−	0.0585321i
$116$	−6.99680	−	4.03961i	−0.649637	−	0.375068i
$117$	1.87749	+	12.0397i	0.173574	+	1.11307i
$118$	7.03823			0.647921
$119$	−3.57758	+	13.4996i	−0.327956	+	1.23751i
$120$	1.49999	+	3.57072i	0.136929	+	0.325961i
$121$	0.934810	−	1.61914i	0.0849827	−	0.147194i
$122$		−	11.2231i		−	1.01609i
$123$	−5.53359	−	15.6858i	−0.498947	−	1.41434i
$124$		−	3.52560i		−	0.316608i
$125$	−11.0083	+	1.95369i	−0.984614	+	0.174744i
$126$	0.826853	−	7.89407i	0.0736619	−	0.703260i
$127$			4.95940i			0.440076i	0.975491	+	0.220038i	$0.0706181\pi$
$127$			4.95940i			0.440076i	−0.975491	+	0.220038i	$0.929382\pi$
$128$	1.00000			0.0883883
$129$	6.74414	+	5.77396i	0.593789	+	0.508369i
$130$	−4.07312	+	8.11776i	−0.357237	+	0.711975i
$131$	−4.64103	+	8.03850i	−0.405489	+	0.702327i	−0.994378	−	0.105887i	$-0.966232\pi$
$131$	−4.64103	+	8.03850i	−0.405489	+	0.702327i	0.588890	+	0.808213i	$0.299565\pi$
$132$	−5.85967	+	2.06716i	−0.510019	+	0.179923i
$133$	−6.80105	−	6.76387i	−0.589725	−	0.586502i
$134$		−	6.99540i		−	0.604310i
$135$	0.334490	+	11.6141i	0.0287884	+	0.999586i
$136$	−4.57132	−	2.63925i	−0.391987	−	0.226314i
$137$	0.00306228	+	0.00530403i	0.000261628	+	0.000453154i	0.866156	−	0.499773i	$-0.166583\pi$
$137$	0.00306228	+	0.00530403i	0.000261628	+	0.000453154i	−0.865895	+	0.500227i	$0.833250\pi$
$138$	5.40382	−	6.31181i	0.460004	−	0.537297i
$139$	−7.32549	+	4.22938i	−0.621340	+	0.358731i	−0.777391	−	0.629018i	$-0.783457\pi$
$139$	−7.32549	+	4.22938i	−0.621340	+	0.358731i	0.156050	+	0.987749i	$0.450124\pi$
$140$	3.91921	−	4.43168i	0.331234	−	0.374545i
$141$	−3.65365	+	19.5830i	−0.307693	+	1.64919i
$142$		−	0.828681i		−	0.0695414i
$143$	−12.6190	−	7.28558i	−1.05525	−	0.609251i
$144$	2.79817	+	1.08178i	0.233181	+	0.0901482i
$145$	−1.05711	−	18.0347i	−0.0877885	−	1.49770i
$146$	3.51263	−	6.08405i	0.290707	−	0.503519i
$147$	−11.4115	+	4.09618i	−0.941201	+	0.337847i
$148$	−0.879847	+	0.507980i	−0.0723230	+	0.0417557i
$149$	15.0057	+	8.66353i	1.22931	+	0.709744i	0.966886	−	0.255208i	$-0.0821441\pi$
$149$	15.0057	+	8.66353i	1.22931	+	0.709744i	0.262426	+	0.964952i	$0.415477\pi$
$150$	−4.82509	+	7.19156i	−0.393967	+	0.587188i
$151$	2.82204	+	4.88791i	0.229654	+	0.397773i	0.957706	−	0.287750i	$-0.0929071\pi$
$151$	2.82204	+	4.88791i	0.229654	+	0.397773i	−0.728051	+	0.685523i	$0.759574\pi$
$152$	3.13968	−	1.81269i	0.254662	−	0.147029i
$153$	−9.93623	−	12.3302i	−0.803297	−	0.996839i
$154$	6.72983	+	6.69304i	0.542305	+	0.539340i
$155$	6.58494	−	4.33448i	0.528915	−	0.348154i
$156$	2.34047	+	6.63440i	0.187387	+	0.531177i
$157$	6.48693			0.517713			0.258857	−	0.965916i	$-0.416654\pi$
$157$	6.48693			0.517713			0.258857	+	0.965916i	$0.416654\pi$
$158$	0.0299868			0.00238562
$159$	−12.8709	+	15.0335i	−1.02073	+	1.19224i
$160$	1.22943	+	1.86775i	0.0971951	+	0.147659i
$161$	−12.2688	−	3.25139i	−0.966914	−	0.256245i
$162$	6.65951	+	6.05400i	0.523221	+	0.475647i
$163$	4.53833	−	2.62021i	0.355469	−	0.205230i	−0.311622	−	0.950206i	$-0.600872\pi$
$163$	4.53833	−	2.62021i	0.355469	−	0.205230i	0.667092	+	0.744976i	$0.267539\pi$
$164$	−4.80160	−	8.31661i	−0.374942	−	0.649418i
$165$	−11.0650	−	8.40297i	−0.861409	−	0.654171i
$166$	−6.89727	−	3.98214i	−0.535332	−	0.309074i
$167$	−18.8867	+	10.9043i	−1.46150	+	0.843797i	−0.999081	−	0.0428649i	$-0.986351\pi$
$167$	−18.8867	+	10.9043i	−1.46150	+	0.843797i	−0.462418	+	0.886662i	$0.653018\pi$
$168$	−0.366620	−	4.56789i	−0.0282853	−	0.352420i
$169$	−1.74884	+	3.02908i	−0.134526	+	0.233006i
$170$	−0.690658	−	11.7829i	−0.0529710	−	0.903704i
$171$	10.7463	−	1.67579i	0.821789	−	0.128151i
$172$	4.43909	+	2.56291i	0.338477	+	0.195420i
$173$		−	21.6843i		−	1.64863i	−0.566133	−	0.824314i	$-0.691561\pi$
$173$		−	21.6843i		−	1.64863i	0.566133	−	0.824314i	$-0.308439\pi$
$174$	−10.6300	−	9.10080i	−0.805857	−	0.689930i
$175$	13.0957	+	1.87167i	0.989940	+	0.141485i
$176$	−3.10680	+	1.79371i	−0.234184	+	0.135206i
$177$	11.9838	+	2.23584i	0.900756	+	0.168056i
$178$	−0.625013	−	1.08255i	−0.0468467	−	0.0811408i
$179$	15.1142	+	8.72620i	1.12969	+	0.652227i	0.943857	−	0.330355i	$-0.107168\pi$
$179$	15.1142	+	8.72620i	1.12969	+	0.652227i	0.185833	+	0.982581i	$0.440502\pi$
$180$	1.41967	+	6.55626i	0.105816	+	0.488675i
$181$		−	24.0491i		−	1.78755i	−0.448513	−	0.893776i	$-0.648046\pi$
$181$		−	24.0491i		−	1.78755i	0.448513	−	0.893776i	$-0.351954\pi$
$182$	7.57795	−	7.61961i	0.561715	−	0.564803i
$183$	3.56524	−	19.1092i	0.263550	−	1.41259i
$184$	2.39862	−	4.15452i	0.176828	−	0.306276i
$185$	−2.03049	−	1.01881i	−0.149285	−	0.0749044i
$186$	1.11998	−	6.00293i	0.0821209	−	0.440156i
$187$	18.9362			1.38475
$188$			11.5014i			0.838824i
$189$	3.91557	−	13.1783i	0.284816	−	0.958582i
$190$	7.24569	+	3.63556i	0.525657	+	0.263751i
$191$		−	3.22636i		−	0.233451i	−0.993164	−	0.116726i	$-0.962760\pi$
$191$		−	3.22636i		−	0.233451i	0.993164	−	0.116726i	$-0.0372398\pi$
$192$	1.70267	+	0.317671i	0.122880	+	0.0229259i
$193$			24.2271i			1.74390i	0.489593	+	0.871951i	$0.337145\pi$
$193$			24.2271i			1.74390i	−0.489593	+	0.871951i	$0.662855\pi$
$194$	−4.69619	+	8.13404i	−0.337167	+	0.583990i
$195$	−9.51397	+	12.5280i	−0.681309	+	0.897146i
$196$	−6.04290	+	3.53318i	−0.431636	+	0.252370i
$197$	−6.89656			−0.491359			−0.245680	−	0.969351i	$-0.579011\pi$
$197$	−6.89656			−0.491359			−0.245680	+	0.969351i	$0.579011\pi$
$198$	−10.6338	+	1.65824i	−0.755708	+	0.117846i
$199$	−14.5256	−	8.38638i	−1.02969	−	0.594494i	−0.112797	−	0.993618i	$-0.535981\pi$
$199$	−14.5256	−	8.38638i	−1.02969	−	0.594494i	−0.916897	+	0.399124i	$0.869314\pi$
$200$	−1.97699	+	4.59255i	−0.139795	+	0.324742i
$201$	2.22224	−	11.9109i	0.156744	−	0.840127i
$202$	−5.44619	−	9.43308i	−0.383193	−	0.663709i
$203$	−5.47580	+	20.6623i	−0.384326	+	1.45021i
$204$	−6.94503	−	5.94595i	−0.486249	−	0.416300i
$205$	9.63012	−	19.1929i	0.672597	−	1.34049i
$206$	−0.292115	+	0.505958i	−0.0203526	+	0.0352518i
$207$	11.2060	−	9.03030i	0.778871	−	0.627649i
$208$	2.03087	+	3.51756i	0.140815	+	0.243899i
$209$	−6.50291	+	11.2634i	−0.449815	+	0.779103i
$210$	8.08094	−	6.30066i	0.557638	−	0.434787i
$211$	2.37689	+	4.11690i	0.163632	+	0.283419i	0.936169	−	0.351551i	$-0.114346\pi$
$211$	2.37689	+	4.11690i	0.163632	+	0.283419i	−0.772537	+	0.634970i	$0.781012\pi$
$212$	−5.71305	+	9.89529i	−0.392374	+	0.679611i
$213$	0.263248	−	1.41097i	0.0180375	−	0.0966781i
$214$	−1.34287	−	2.32592i	−0.0917967	−	0.158997i
$215$	0.670681	+	11.4420i	0.0457400	+	0.780341i
$216$	4.42071	+	2.73081i	0.300791	+	0.185808i
$217$	−9.00336	+	2.43891i	−0.611188	+	0.165564i
$218$	−0.618180	+	1.07072i	−0.0418684	+	0.0725182i
$219$	7.91357	−	9.24326i	0.534749	−	0.624602i
$220$	−7.16981	−	3.59749i	−0.483389	−	0.242542i
$221$		−	21.4399i		−	1.44220i
$222$	−1.65946	+	0.585420i	−0.111376	+	0.0392908i
$223$	8.37432	−	14.5048i	0.560786	−	0.971310i	−0.436642	−	0.899635i	$-0.643832\pi$
$223$	8.37432	−	14.5048i	0.560786	−	0.971310i	0.997428	−	0.0716748i	$-0.0228344\pi$
$224$	−0.691773	−	2.55371i	−0.0462210	−	0.170627i
$225$	−10.5001	+	10.7121i	−0.700005	+	0.714138i
$226$	5.41347	+	9.37640i	0.360099	+	0.623709i
$227$	5.49698	−	3.17368i	0.364847	−	0.210645i	−0.306358	−	0.951916i	$-0.599110\pi$
$227$	5.49698	−	3.17368i	0.364847	−	0.210645i	0.671205	+	0.741272i	$0.265777\pi$
$228$	5.92168	−	2.08904i	0.392173	−	0.138350i
$229$	3.78920	+	2.18769i	0.250397	+	0.144567i	0.619946	−	0.784644i	$-0.287154\pi$
$229$	3.78920	+	2.18769i	0.250397	+	0.144567i	−0.369549	+	0.929211i	$0.620488\pi$
$230$	10.7086	−	0.627687i	0.706101	−	0.0413884i
$231$	9.33249	+	13.5339i	0.614033	+	0.890466i
$232$	−6.99680	−	4.03961i	−0.459363	−	0.265213i
$233$	12.2423	+	21.2043i	0.802021	+	1.38914i	0.918284	+	0.395922i	$0.129575\pi$
$233$	12.2423	+	21.2043i	0.802021	+	1.38914i	−0.116263	+	0.993218i	$0.537092\pi$
$234$	1.87749	+	12.0397i	0.122735	+	0.787059i
$235$	−21.4817	+	14.1402i	−1.40131	+	0.922402i
$236$	7.03823			0.458150
$237$	0.0510576	+	0.00952593i	0.00331654	+	0.000618776i
$238$	−3.57758	+	13.4996i	−0.231900	+	0.875048i
$239$	2.10722	−	1.21660i	0.136305	−	0.0786956i	−0.430297	−	0.902687i	$-0.641591\pi$
$239$	2.10722	−	1.21660i	0.136305	−	0.0786956i	0.566602	+	0.823992i	$0.308258\pi$
$240$	1.49999	+	3.57072i	0.0968237	+	0.230489i
$241$	1.82213	−	1.05201i	0.117374	−	0.0677659i	−0.440164	−	0.897918i	$-0.645080\pi$
$241$	1.82213	−	1.05201i	0.117374	−	0.0677659i	0.557538	+	0.830152i	$0.311746\pi$
$242$	0.934810	−	1.61914i	0.0600918	−	0.104082i
$243$	9.41577	+	12.4235i	0.604022	+	0.796968i
$244$		−	11.2231i		−	0.718482i
$245$	−14.0284	−	6.94283i	−0.896244	−	0.443561i
$246$	−5.53359	−	15.6858i	−0.352809	−	1.00009i
$247$	12.7525	+	7.36268i	0.811425	+	0.468476i
$248$		−	3.52560i		−	0.223876i
$249$	−10.4788	−	8.97133i	−0.664064	−	0.568535i
$250$	−11.0083	+	1.95369i	−0.696227	+	0.123562i
$251$	19.3343			1.22037			0.610184	−	0.792260i	$-0.291096\pi$
$251$	19.3343			1.22037			0.610184	+	0.792260i	$0.291096\pi$
$252$	0.826853	−	7.89407i	0.0520868	−	0.497280i
$253$			17.2097i			1.08197i
$254$			4.95940i			0.311181i
$255$	2.56711	−	20.2817i	0.160759	−	1.27009i
$256$	1.00000			0.0625000
$257$	22.4822	+	12.9801i	1.40240	+	0.809677i	0.994639	−	0.103412i	$-0.0329759\pi$
$257$	22.4822	+	12.9801i	1.40240	+	0.809677i	0.407762	+	0.913088i	$0.366309\pi$
$258$	6.74414	+	5.77396i	0.419872	+	0.359471i
$259$	1.90589	+	1.89547i	0.118426	+	0.117779i
$260$	−4.07312	+	8.11776i	−0.252604	+	0.503442i
$261$	−15.2083	−	18.8725i	−0.941370	−	1.16818i
$262$	−4.64103	+	8.03850i	−0.286724	+	0.496620i
$263$	3.89109	+	6.73957i	0.239935	+	0.415579i	0.960695	−	0.277605i	$-0.0895406\pi$
$263$	3.89109	+	6.73957i	0.239935	+	0.415579i	−0.720760	+	0.693184i	$0.756207\pi$
$264$	−5.85967	+	2.06716i	−0.360638	+	0.127225i
$265$	−25.5057	+	1.49503i	−1.56681	+	0.0918390i
$266$	−6.80105	−	6.76387i	−0.416999	−	0.414719i
$267$	−0.720294	−	2.04178i	−0.0440813	−	0.124955i
$268$		−	6.99540i		−	0.427312i
$269$	−9.76085	+	16.9063i	−0.595129	+	1.03079i	0.398399	+	0.917212i	$0.369566\pi$
$269$	−9.76085	+	16.9063i	−0.595129	+	1.03079i	−0.993529	+	0.113582i	$0.963767\pi$
$270$	0.334490	+	11.6141i	0.0203564	+	0.706814i
$271$	−0.125260	+	0.0723187i	−0.00760898	+	0.00439305i	−0.503800	−	0.863821i	$-0.668065\pi$
$271$	−0.125260	+	0.0723187i	−0.00760898	+	0.00439305i	0.496191	+	0.868214i	$0.334732\pi$
$272$	−4.57132	−	2.63925i	−0.277177	−	0.160028i
$273$	15.3233	−	10.5664i	0.927407	−	0.639506i
$274$	0.00306228	+	0.00530403i	0.000184999	+	0.000320428i
$275$	−2.09559	−	17.8143i	−0.126369	−	1.07424i
$276$	5.40382	−	6.31181i	0.325272	−	0.379926i
$277$	−22.2251	+	12.8317i	−1.33538	+	0.770981i	−0.986118	−	0.166044i	$-0.946900\pi$
$277$	−22.2251	+	12.8317i	−1.33538	+	0.770981i	−0.349260	+	0.937026i	$0.613567\pi$
$278$	−7.32549	+	4.22938i	−0.439354	+	0.253661i
$279$	3.81391	−	9.86522i	0.228333	−	0.590615i
$280$	3.91921	−	4.43168i	0.234218	−	0.264843i
$281$	−16.2907	−	9.40542i	−0.971819	−	0.561080i	−0.0720288	−	0.997403i	$-0.522947\pi$
$281$	−16.2907	−	9.40542i	−0.971819	−	0.561080i	−0.899790	+	0.436322i	$0.856281\pi$
$282$	−3.65365	+	19.5830i	−0.217572	+	1.16615i
$283$	30.3966			1.80689			0.903444	−	0.428706i	$-0.141030\pi$
$283$	30.3966			1.80689			0.903444	+	0.428706i	$0.141030\pi$
$284$		−	0.828681i		−	0.0491732i
$285$	11.1821	+	8.49190i	0.662370	+	0.503017i
$286$	−12.6190	−	7.28558i	−0.746177	−	0.430806i
$287$	−17.9166	+	18.0151i	−1.05758	+	1.06340i
$288$	2.79817	+	1.08178i	0.164884	+	0.0637444i
$289$	5.43128	+	9.40726i	0.319487	+	0.553368i
$290$	−1.05711	−	18.0347i	−0.0620758	−	1.05903i
$291$	−10.5800	+	12.3577i	−0.620211	+	0.724424i
$292$	3.51263	−	6.08405i	0.205561	−	0.356042i
$293$	−24.1090	+	13.9193i	−1.40846	+	0.813176i	−0.995240	−	0.0974541i	$-0.968930\pi$
$293$	−24.1090	+	13.9193i	−1.40846	+	0.813176i	−0.413222	+	0.910630i	$0.635597\pi$
$294$	−11.4115	+	4.09618i	−0.665530	+	0.238894i
$295$	8.65302	+	13.1457i	0.503799	+	0.765370i
$296$	−0.879847	+	0.507980i	−0.0511401	+	0.0295257i
$297$	−18.6326	−	0.554597i	−1.08117	−	0.0321810i
$298$	15.0057	+	8.66353i	0.869255	+	0.501865i
$299$	19.4851			1.12685
$300$	−4.82509	+	7.19156i	−0.278577	+	0.415205i
$301$	3.47409	−	13.1091i	0.200243	−	0.755597i
$302$	2.82204	+	4.88791i	0.162390	+	0.281268i
$303$	−6.27645	−	17.7915i	−0.360573	−	1.02210i
$304$	3.13968	−	1.81269i	0.180073	−	0.103965i
$305$	20.9619	−	13.7980i	1.20027	−	0.790070i
$306$	−9.93623	−	12.3302i	−0.568017	−	0.704872i
$307$	29.1963			1.66632			0.833162	−	0.553030i	$-0.186528\pi$
$307$	29.1963			1.66632			0.833162	+	0.553030i	$0.186528\pi$
$308$	6.72983	+	6.69304i	0.383468	+	0.381371i
$309$	−0.658104	+	0.768683i	−0.0374382	+	0.0437289i
$310$	6.58494	−	4.33448i	0.373999	−	0.246182i
$311$	−1.53984			−0.0873161			−0.0436580	−	0.999047i	$-0.513901\pi$
$311$	−1.53984			−0.0873161			−0.0436580	+	0.999047i	$0.513901\pi$
$312$	2.34047	+	6.63440i	0.132503	+	0.375599i
$313$	9.00202			0.508824			0.254412	−	0.967096i	$-0.418118\pi$
$313$	9.00202			0.508824			0.254412	+	0.967096i	$0.418118\pi$
$314$	6.48693			0.366078
$315$	15.7607	−	8.16087i	0.888016	−	0.459813i
$316$	0.0299868			0.00168689
$317$	17.2577			0.969287			0.484644	−	0.874712i	$-0.338949\pi$
$317$	17.2577			0.969287			0.484644	+	0.874712i	$0.338949\pi$
$318$	−12.8709	+	15.0335i	−0.721763	+	0.843039i
$319$	28.9836			1.62277
$320$	1.22943	+	1.86775i	0.0687273	+	0.104410i
$321$	−1.54759	−	4.38686i	−0.0863779	−	0.244851i
$322$	−12.2688	−	3.25139i	−0.683711	−	0.181193i
$323$	−19.1366			−1.06479
$324$	6.65951	+	6.05400i	0.369973	+	0.336333i
$325$	−20.1696	+	2.37265i	−1.11881	+	0.131611i
$326$	4.53833	−	2.62021i	0.251355	−	0.145120i
$327$	−1.39269	+	1.62670i	−0.0770161	+	0.0899569i
$328$	−4.80160	−	8.31661i	−0.265124	−	0.459208i
$329$	29.3712	−	7.95634i	1.61929	−	0.438647i
$330$	−11.0650	−	8.40297i	−0.609108	−	0.462568i
$331$	29.0182			1.59498			0.797492	−	0.603329i	$-0.206159\pi$
$331$	29.0182			1.59498			0.797492	+	0.603329i	$0.206159\pi$
$332$	−6.89727	−	3.98214i	−0.378537	−	0.218548i
$333$	−3.01148	+	0.469615i	−0.165028	+	0.0257348i
$334$	−18.8867	+	10.9043i	−1.03344	+	0.596655i
$335$	13.0657	−	8.60037i	0.713854	−	0.469888i
$336$	−0.366620	−	4.56789i	−0.0200008	−	0.249199i
$337$	0.776124	−	0.448095i	0.0422782	−	0.0244093i	−0.478712	−	0.877972i	$-0.658896\pi$
$337$	0.776124	−	0.448095i	0.0422782	−	0.0244093i	0.520990	+	0.853563i	$0.325563\pi$
$338$	−1.74884	+	3.02908i	−0.0951245	+	0.164760i
$339$	6.23874	+	17.6846i	0.338842	+	0.960497i
$340$	−0.690658	−	11.7829i	−0.0374562	−	0.639015i
$341$	6.32391	+	10.9533i	0.342459	+	0.593156i
$342$	10.7463	−	1.67579i	0.581093	−	0.0906164i
$343$	13.2030	+	12.9877i	0.712897	+	0.701269i
$344$	4.43909	+	2.56291i	0.239340	+	0.138183i
$345$	18.4325	+	2.33305i	0.992374	+	0.125607i
$346$		−	21.6843i		−	1.16576i
$347$	34.3492			1.84396			0.921982	−	0.387233i	$-0.126569\pi$
$347$	34.3492			1.84396			0.921982	+	0.387233i	$0.126569\pi$
$348$	−10.6300	−	9.10080i	−0.569827	−	0.487854i
$349$	−1.95233	−	1.12718i	−0.104506	−	0.0603366i	0.446836	−	0.894616i	$-0.352551\pi$
$349$	−1.95233	−	1.12718i	−0.104506	−	0.0603366i	−0.551342	+	0.834279i	$0.685884\pi$
$350$	13.0957	+	1.87167i	0.699994	+	0.100045i
$351$	−0.627922	+	21.0960i	−0.0335160	+	1.12602i
$352$	−3.10680	+	1.79371i	−0.165593	+	0.0956052i
$353$	5.09123	−	2.93942i	0.270979	−	0.156450i	−0.358354	−	0.933586i	$-0.616662\pi$
$353$	5.09123	−	2.93942i	0.270979	−	0.156450i	0.629332	+	0.777136i	$0.283328\pi$
$354$	11.9838	+	2.23584i	0.636931	+	0.118834i
$355$	1.54777	−	1.01881i	0.0821472	−	0.0540727i
$356$	−0.625013	−	1.08255i	−0.0331256	−	0.0573752i
$357$	−10.3799	+	21.8489i	−0.549360	+	1.15636i
$358$	15.1142	+	8.72620i	0.798811	+	0.461194i
$359$	−5.91330	+	3.41404i	−0.312092	+	0.180186i	−0.647862	−	0.761758i	$-0.724337\pi$
$359$	−5.91330	+	3.41404i	−0.312092	+	0.180186i	0.335770	+	0.941944i	$0.391003\pi$
$360$	1.41967	+	6.55626i	0.0748230	+	0.345545i
$361$	−2.92828	+	5.07193i	−0.154120	+	0.266944i
$362$		−	24.0491i		−	1.26399i
$363$	2.10603	−	2.45990i	0.110538	−	0.129111i
$364$	7.57795	−	7.61961i	0.397193	−	0.399376i
$365$	15.6820	−	0.919209i	0.820835	−	0.0481136i
$366$	3.56524	−	19.1092i	0.186358	−	0.998852i
$367$	−0.284464	−	0.492706i	−0.0148489	−	0.0257190i	0.858505	−	0.512804i	$-0.171393\pi$
$367$	−0.284464	−	0.492706i	−0.0148489	−	0.0257190i	−0.873354	+	0.487085i	$0.838060\pi$
$368$	2.39862	−	4.15452i	0.125036	−	0.216570i
$369$	−4.43896	−	28.4655i	−0.231083	−	1.48186i
$370$	−2.03049	−	1.01881i	−0.105560	−	0.0529654i
$371$	29.2219	+	7.74419i	1.51712	+	0.402058i
$372$	1.11998	−	6.00293i	0.0580683	−	0.311237i
$373$	6.58348	+	3.80098i	0.340880	+	0.196807i	0.660661	−	0.750684i	$-0.270276\pi$
$373$	6.58348	+	3.80098i	0.340880	+	0.196807i	−0.319781	+	0.947491i	$0.603609\pi$
$374$	18.9362			0.979169
$375$	−19.3642	−	0.170530i	−0.999961	−	0.00880612i
$376$			11.5014i			0.593138i
$377$		−	32.8156i		−	1.69009i
$378$	3.91557	−	13.1783i	0.201395	−	0.677820i
$379$	−37.9897			−1.95140			−0.975700	−	0.219109i	$-0.929685\pi$
$379$	−37.9897			−1.95140			−0.975700	+	0.219109i	$0.929685\pi$
$380$	7.24569	+	3.63556i	0.371696	+	0.186500i
$381$	−1.57546	+	8.44423i	−0.0807132	+	0.432611i
$382$		−	3.22636i		−	0.165075i
$383$	−10.4289	−	6.02112i	−0.532891	−	0.307665i	0.209302	−	0.977851i	$-0.432881\pi$
$383$	−10.4289	−	6.02112i	−0.532891	−	0.307665i	−0.742193	+	0.670186i	$0.766214\pi$
$384$	1.70267	+	0.317671i	0.0868890	+	0.0162111i
$385$	−4.22707	+	20.7983i	−0.215431	+	1.05998i
$386$			24.2271i			1.23312i
$387$	9.64883	+	11.9736i	0.490478	+	0.608651i
$388$	−4.69619	+	8.13404i	−0.238413	+	0.412943i
$389$	9.93198	−	5.73423i	0.503571	−	0.290737i	−0.226616	−	0.973984i	$-0.572766\pi$
$389$	9.93198	−	5.73423i	0.503571	−	0.290737i	0.730187	+	0.683247i	$0.239433\pi$
$390$	−9.51397	+	12.5280i	−0.481758	+	0.634378i
$391$	−21.9297	+	12.6611i	−1.10903	+	0.640299i
$392$	−6.04290	+	3.53318i	−0.305213	+	0.178452i
$393$	−10.4557	+	12.2126i	−0.527422	+	0.616043i
$394$	−6.89656			−0.347444
$395$	0.0368667	+	0.0560078i	0.00185496	+	0.00281806i
$396$	−10.6338	+	1.65824i	−0.534366	+	0.0833299i
$397$	−1.89421	−	3.28087i	−0.0950678	−	0.164662i	0.814569	−	0.580067i	$-0.196973\pi$
$397$	−1.89421	−	3.28087i	−0.0950678	−	0.164662i	−0.909637	+	0.415404i	$0.863640\pi$
$398$	−14.5256	−	8.38638i	−0.728104	−	0.420371i
$399$	−9.43125	−	13.6771i	−0.472153	−	0.684713i
$400$	−1.97699	+	4.59255i	−0.0988497	+	0.229627i
$401$	10.0319	+	5.79192i	0.500970	+	0.289235i	0.729114	−	0.684392i	$-0.239932\pi$
$401$	10.0319	+	5.79192i	0.500970	+	0.289235i	−0.228144	+	0.973627i	$0.573266\pi$
$402$	2.22224	−	11.9109i	0.110835	−	0.594059i
$403$	12.4015	−	7.16002i	0.617764	−	0.356666i
$404$	−5.44619	−	9.43308i	−0.270958	−	0.469313i
$405$	−3.11995	+	19.8813i	−0.155031	+	0.987910i
$406$	−5.47580	+	20.6623i	−0.271759	+	1.02545i
$407$	1.82234	−	3.15639i	0.0903301	−	0.156456i
$408$	−6.94503	−	5.94595i	−0.343830	−	0.294368i
$409$			30.2706i			1.49679i	0.663256	+	0.748393i	$0.269174\pi$
$409$			30.2706i			1.49679i	−0.663256	+	0.748393i	$0.730826\pi$
$410$	9.63012	−	19.1929i	0.475598	−	0.947869i
$411$	0.00352912	+	0.0100038i	0.000174079	+	0.000493451i
$412$	−0.292115	+	0.505958i	−0.0143915	+	0.0249268i
$413$	−4.86886	−	17.9736i	−0.239581	−	0.884424i
$414$	11.2060	−	9.03030i	0.550745	−	0.443815i
$415$	−1.04207	−	17.7782i	−0.0511534	−	0.872695i
$416$	2.03087	+	3.51756i	0.0995715	+	0.172463i
$417$	−13.8164	+	4.87413i	−0.676594	+	0.238687i
$418$	−6.50291	+	11.2634i	−0.318067	+	0.550909i
$419$	−10.7319	−	18.5882i	−0.524287	−	0.908091i	−0.999600	−	0.0282749i	$-0.990999\pi$
$419$	−10.7319	−	18.5882i	−0.524287	−	0.908091i	0.475313	−	0.879817i	$-0.342335\pi$
$420$	8.08094	−	6.30066i	0.394310	−	0.307441i
$421$	−12.8685	+	22.2889i	−0.627173	+	1.08630i	0.360943	+	0.932588i	$0.382455\pi$
$421$	−12.8685	+	22.2889i	−0.627173	+	1.08630i	−0.988116	+	0.153708i	$0.950878\pi$
$422$	2.37689	+	4.11690i	0.115705	+	0.200408i
$423$	−12.4419	+	32.1828i	−0.604948	+	1.56478i
$424$	−5.71305	+	9.89529i	−0.277450	+	0.480558i
$425$	21.1583	−	15.7762i	1.02633	−	0.765258i
$426$	0.263248	−	1.41097i	0.0127544	−	0.0683618i
$427$	−28.6605	+	7.76380i	−1.38698	+	0.375717i
$428$	−1.34287	−	2.32592i	−0.0649101	−	0.112428i
$429$	−19.1716	−	16.4136i	−0.925612	−	0.792458i
$430$	0.670681	+	11.4420i	0.0323431	+	0.551784i
$431$	−1.05463	−	0.608890i	−0.0507997	−	0.0293292i	0.474385	−	0.880317i	$-0.342670\pi$
$431$	−1.05463	−	0.608890i	−0.0507997	−	0.0293292i	−0.525185	+	0.850988i	$0.676004\pi$
$432$	4.42071	+	2.73081i	0.212692	+	0.131386i
$433$	6.29897			0.302709			0.151355	−	0.988480i	$-0.451636\pi$
$433$	6.29897			0.302709			0.151355	+	0.988480i	$0.451636\pi$
$434$	−9.00336	+	2.43891i	−0.432175	+	0.117072i
$435$	3.92919	−	31.0430i	0.188390	−	1.48840i
$436$	−0.618180	+	1.07072i	−0.0296054	+	0.0512781i
$437$		−	17.3918i		−	0.831964i
$438$	7.91357	−	9.24326i	0.378125	−	0.441660i
$439$		−	36.3857i		−	1.73659i	−0.496046	−	0.868296i	$-0.665215\pi$
$439$		−	36.3857i		−	1.73659i	0.496046	−	0.868296i	$-0.334785\pi$
$440$	−7.16981	−	3.59749i	−0.341807	−	0.171503i
$441$	−20.7312	+	3.34936i	−0.987199	+	0.159493i
$442$		−	21.4399i		−	1.01979i
$443$	−11.5534			−0.548917			−0.274459	−	0.961599i	$-0.588499\pi$
$443$	−11.5534			−0.548917			−0.274459	+	0.961599i	$0.588499\pi$
$444$	−1.65946	+	0.585420i	−0.0787545	+	0.0277828i
$445$	1.25353	−	2.49830i	0.0594231	−	0.118431i
$446$	8.37432	−	14.5048i	0.396536	−	0.686820i
$447$	22.7975	+	19.5180i	1.07829	+	0.923169i
$448$	−0.691773	−	2.55371i	−0.0326832	−	0.120652i
$449$			8.35607i			0.394347i	0.980369	+	0.197174i	$0.0631763\pi$
$449$			8.35607i			0.394347i	−0.980369	+	0.197174i	$0.936824\pi$
$450$	−10.5001	+	10.7121i	−0.494979	+	0.504971i
$451$	29.8352	+	17.2254i	1.40489	+	0.811111i
$452$	5.41347	+	9.37640i	0.254628	+	0.441029i
$453$	3.25225	+	9.21898i	0.152804	+	0.433146i
$454$	5.49698	−	3.17368i	0.257986	−	0.148948i
$455$	23.5481	+	4.78594i	1.10395	+	0.224369i
$456$	5.92168	−	2.08904i	0.277308	−	0.0978280i
$457$		−	3.77155i		−	0.176426i	−0.996102	−	0.0882129i	$-0.971884\pi$
$457$		−	3.77155i		−	0.176426i	0.996102	−	0.0882129i	$-0.0281156\pi$
$458$	3.78920	+	2.18769i	0.177058	+	0.102224i
$459$	−13.0012	−	24.1507i	−0.606843	−	1.12726i
$460$	10.7086	−	0.627687i	0.499289	−	0.0292661i
$461$	−1.39131	+	2.40982i	−0.0647998	+	0.112237i	−0.896605	−	0.442831i	$-0.853974\pi$
$461$	−1.39131	+	2.40982i	−0.0647998	+	0.112237i	0.831805	+	0.555067i	$0.187308\pi$
$462$	9.33249	+	13.5339i	0.434187	+	0.629654i
$463$	−9.52910	+	5.50163i	−0.442855	+	0.255682i	−0.704808	−	0.709398i	$-0.748967\pi$
$463$	−9.52910	+	5.50163i	−0.442855	+	0.255682i	0.261953	+	0.965081i	$0.415633\pi$
$464$	−6.99680	−	4.03961i	−0.324818	−	0.187534i
$465$	12.5889	−	5.28835i	0.583797	−	0.245241i
$466$	12.2423	+	21.2043i	0.567114	+	0.982271i
$467$	16.4814	−	9.51552i	0.762667	−	0.440326i	−0.0675856	−	0.997713i	$-0.521530\pi$
$467$	16.4814	−	9.51552i	0.762667	−	0.440326i	0.830252	+	0.557388i	$0.188196\pi$
$468$	1.87749	+	12.0397i	0.0867869	+	0.556535i
$469$	−17.8642	+	4.83923i	−0.824894	+	0.223455i
$470$	−21.4817	+	14.1402i	−0.990878	+	0.652237i
$471$	11.0451	+	2.06071i	0.508931	+	0.0949525i
$472$	7.03823			0.323961
$473$	−18.3885			−0.845504
$474$	0.0510576	+	0.00952593i	0.00234515	+	0.000437540i
$475$	2.11776	+	18.0028i	0.0971696	+	0.826026i
$476$	−3.57758	+	13.4996i	−0.163978	+	0.618753i
$477$	−26.6906	+	21.5084i	−1.22208	+	0.984804i
$478$	2.10722	−	1.21660i	0.0963820	−	0.0556462i
$479$	0.146168	+	0.253170i	0.00667858	+	0.0115676i	0.869345	−	0.494205i	$-0.164541\pi$
$479$	0.146168	+	0.253170i	0.00667858	+	0.0115676i	−0.862667	+	0.505773i	$0.831207\pi$
$480$	1.49999	+	3.57072i	0.0684647	+	0.162980i
$481$	−3.57371	−	2.06328i	−0.162947	−	0.0940775i
$482$	1.82213	−	1.05201i	0.0829960	−	0.0479177i
$483$	−19.8568	−	9.43347i	−0.903515	−	0.429238i
$484$	0.934810	−	1.61914i	0.0424913	−	0.0735972i
$485$	−20.9660	+	1.22893i	−0.952018	+	0.0558030i
$486$	9.41577	+	12.4235i	0.427108	+	0.563541i
$487$	−17.4211	−	10.0581i	−0.789425	−	0.455775i	0.0503353	−	0.998732i	$-0.483971\pi$
$487$	−17.4211	−	10.0581i	−0.789425	−	0.455775i	−0.839760	+	0.542958i	$0.817304\pi$
$488$		−	11.2231i		−	0.508044i
$489$	8.55964	−	3.01965i	0.387080	−	0.136553i
$490$	−14.0284	−	6.94283i	−0.633740	−	0.313645i
$491$	−0.00977625	+	0.00564432i	−0.000441196	+	0.000254725i	−0.500221	−	0.865898i	$-0.666748\pi$
$491$	−0.00977625	+	0.00564432i	−0.000441196	+	0.000254725i	0.499779	+	0.866153i	$0.333414\pi$
$492$	−5.53359	−	15.6858i	−0.249473	−	0.707169i
$493$	21.3231	+	36.9326i	0.960343	+	1.66336i
$494$	12.7525	+	7.36268i	0.573764	+	0.331263i
$495$	−16.1707	−	17.8225i	−0.726818	−	0.801063i
$496$		−	3.52560i		−	0.158304i
$497$	−2.11621	+	0.573259i	−0.0949252	+	0.0257142i
$498$	−10.4788	−	8.97133i	−0.469565	−	0.402015i
$499$	−5.43038	+	9.40569i	−0.243097	+	0.421057i	−0.961595	−	0.274473i	$-0.911497\pi$
$499$	−5.43038	+	9.40569i	−0.243097	+	0.421057i	0.718498	+	0.695529i	$0.244830\pi$
$500$	−11.0083	+	1.95369i	−0.492307	+	0.0873718i
$501$	−35.6218	+	12.5666i	−1.59147	+	0.561434i
$502$	19.3343			0.862930
$503$			32.7910i			1.46208i	0.682335	+	0.731040i	$0.260965\pi$
$503$			32.7910i			1.46208i	−0.682335	+	0.731040i	$0.739035\pi$
$504$	0.826853	−	7.89407i	0.0368309	−	0.351630i
$505$	10.9229	−	21.7695i	0.486064	−	0.968728i
$506$			17.2097i			0.765065i
$507$	−3.93995	+	4.60197i	−0.174979	+	0.204381i
$508$			4.95940i			0.220038i
$509$	−5.90279	+	10.2239i	−0.261637	+	0.453168i	−0.966677	−	0.255999i	$-0.917596\pi$
$509$	−5.90279	+	10.2239i	−0.261637	+	0.453168i	0.705040	+	0.709167i	$0.250929\pi$
$510$	2.56711	−	20.2817i	0.113674	−	0.898090i
$511$	−17.9668	−	4.76146i	−0.794806	−	0.210635i
$512$	1.00000			0.0441942
$513$	18.8297	+	0.560466i	0.831353	+	0.0247452i
$514$	22.4822	+	12.9801i	0.991647	+	0.572528i
$515$	−1.30414	+	0.0764428i	−0.0574673	+	0.00336847i
$516$	6.74414	+	5.77396i	0.296894	+	0.254184i
$517$	−20.6302	−	35.7325i	−0.907313	−	1.57151i
$518$	1.90589	+	1.89547i	0.0837400	+	0.0832822i
$519$	6.88848	−	36.9212i	0.302371	−	1.62066i
$520$	−4.07312	+	8.11776i	−0.178618	+	0.355987i
$521$	8.58074	−	14.8623i	0.375929	−	0.651128i	−0.614537	−	0.788888i	$-0.710657\pi$
$521$	8.58074	−	14.8623i	0.375929	−	0.651128i	0.990466	+	0.137760i	$0.0439904\pi$
$522$	−15.2083	−	18.8725i	−0.665649	−	0.826027i
$523$	19.0538	+	33.0022i	0.833166	+	1.44309i	0.895515	+	0.445031i	$0.146807\pi$
$523$	19.0538	+	33.0022i	0.833166	+	1.44309i	−0.0623491	+	0.998054i	$0.519859\pi$
$524$	−4.64103	+	8.03850i	−0.202744	+	0.351163i
$525$	21.7030	+	7.34696i	0.947199	+	0.320648i
$526$	3.89109	+	6.73957i	0.169660	+	0.293859i
$527$	−9.30493	+	16.1166i	−0.405329	+	0.702051i
$528$	−5.85967	+	2.06716i	−0.255009	+	0.0899616i
$529$	−0.00671290	−	0.0116271i	−0.000291865	−	0.000505525i
$530$	−25.5057	+	1.49503i	−1.10790	+	0.0649400i
$531$	19.6942	+	7.61380i	0.854654	+	0.330411i
$532$	−6.80105	−	6.76387i	−0.294863	−	0.293251i
$533$	19.5028	−	33.7799i	0.844760	−	1.46317i
$534$	−0.720294	−	2.04178i	−0.0311702	−	0.0883565i
$535$	2.69327	−	5.36771i	0.116440	−	0.232066i
$536$		−	6.99540i		−	0.302155i
$537$	22.9625	+	19.6592i	0.990903	+	0.848356i
$538$	−9.76085	+	16.9063i	−0.420820	+	0.728882i
$539$	12.4366	−	21.8161i	0.535682	−	0.939686i
$540$	0.334490	+	11.6141i	0.0143942	+	0.499793i
$541$	11.5592	+	20.0210i	0.496967	+	0.860772i	0.999994	−	0.00349884i	$-0.00111372\pi$
$541$	11.5592	+	20.0210i	0.496967	+	0.860772i	−0.503027	+	0.864271i	$0.667780\pi$
$542$	−0.125260	+	0.0723187i	−0.00538036	+	0.00310635i
$543$	7.63969	−	40.9476i	0.327851	−	1.75723i
$544$	−4.57132	−	2.63925i	−0.195994	−	0.113157i
$545$	−2.75985	+	0.161770i	−0.118219	+	0.00692945i
$546$	15.3233	−	10.5664i	0.655776	−	0.452199i
$547$	0.301039	+	0.173805i	0.0128715	+	0.00743136i	0.506422	−	0.862286i	$-0.330968\pi$
$547$	0.301039	+	0.173805i	0.0128715	+	0.00743136i	−0.493550	+	0.869717i	$0.664301\pi$
$548$	0.00306228	+	0.00530403i	0.000130814	+	0.000226577i
$549$	12.1409	−	31.4040i	0.518159	−	1.34029i
$550$	−2.09559	−	17.8143i	−0.0893561	−	0.759604i
$551$	−29.2903			−1.24781
$552$	5.40382	−	6.31181i	0.230002	−	0.268649i
$553$	−0.0207440	−	0.0765776i	−0.000882126	−	0.00325641i
$554$	−22.2251	+	12.8317i	−0.944255	+	0.545166i
$555$	−3.13361	−	2.37973i	−0.133014	−	0.101014i
$556$	−7.32549	+	4.22938i	−0.310670	+	0.179365i
$557$	22.4182	−	38.8295i	0.949891	−	1.64526i	0.204242	−	0.978920i	$-0.434527\pi$
$557$	22.4182	−	38.8295i	0.949891	−	1.64526i	0.745649	−	0.666339i	$-0.232140\pi$
$558$	3.81391	−	9.86522i	0.161456	−	0.417628i
$559$			20.8197i			0.880580i
$560$	3.91921	−	4.43168i	0.165617	−	0.187273i
$561$	32.2421	+	6.01549i	1.36126	+	0.253974i
$562$	−16.2907	−	9.40542i	−0.687180	−	0.396744i
$563$		−	24.6532i		−	1.03901i	−0.854468	−	0.519504i	$-0.826117\pi$
$563$		−	24.6532i		−	1.03901i	0.854468	−	0.519504i	$-0.173883\pi$
$564$	−3.65365	+	19.5830i	−0.153847	+	0.824595i
$565$	−10.8573	+	21.6387i	−0.456770	+	0.910345i
$566$	30.3966			1.27766
$567$	10.8533	−	21.1945i	0.455796	−	0.890084i
$568$		−	0.828681i		−	0.0347707i
$569$		−	37.5376i		−	1.57366i	−0.617171	−	0.786829i	$-0.711721\pi$
$569$		−	37.5376i		−	1.57366i	0.617171	−	0.786829i	$-0.288279\pi$
$570$	11.1821	+	8.49190i	0.468367	+	0.355686i
$571$	−9.36824			−0.392049			−0.196024	−	0.980599i	$-0.562803\pi$
$571$	−9.36824			−0.392049			−0.196024	+	0.980599i	$0.562803\pi$
$572$	−12.6190	−	7.28558i	−0.527627	−	0.304626i
$573$	1.02492	−	5.49343i	0.0428167	−	0.229491i
$574$	−17.9166	+	18.0151i	−0.747825	+	0.751936i
$575$	14.3378	+	19.2292i	0.597928	+	0.801914i
$576$	2.79817	+	1.08178i	0.116590	+	0.0450741i
$577$	3.63671	−	6.29897i	0.151398	−	0.262230i	−0.780343	−	0.625351i	$-0.784956\pi$
$577$	3.63671	−	6.29897i	0.151398	−	0.262230i	0.931742	+	0.363122i	$0.118289\pi$
$578$	5.43128	+	9.40726i	0.225912	+	0.391290i
$579$	−7.69624	+	41.2507i	−0.319845	+	1.71432i
$580$	−1.05711	−	18.0347i	−0.0438942	−	0.748851i
$581$	−5.39790	+	20.3684i	−0.223943	+	0.845023i
$582$	−10.5800	+	12.3577i	−0.438556	+	0.512245i
$583$		−	40.9903i		−	1.69764i
$584$	3.51263	−	6.08405i	0.145353	−	0.251760i
$585$	−20.1789	+	18.3087i	−0.834295	+	0.756970i
$586$	−24.1090	+	13.9193i	−0.995933	+	0.575002i
$587$	2.08437	+	1.20341i	0.0860313	+	0.0496702i	0.542398	−	0.840121i	$-0.317516\pi$
$587$	2.08437	+	1.20341i	0.0860313	+	0.0496702i	−0.456367	+	0.889792i	$0.650850\pi$
$588$	−11.4115	+	4.09618i	−0.470600	+	0.168924i
$589$	−6.39083	−	11.0692i	−0.263330	−	0.456100i
$590$	8.65302	+	13.1457i	0.356239	+	0.541198i
$591$	−11.7426	−	2.19084i	−0.483025	−	0.0901190i
$592$	−0.879847	+	0.507980i	−0.0361615	+	0.0208779i
$593$	−33.2409	+	19.1916i	−1.36504	+	0.788106i	−0.990290	−	0.139019i	$-0.955605\pi$
$593$	−33.2409	+	19.1916i	−1.36504	+	0.788106i	−0.374751	+	0.927126i	$0.622272\pi$
$594$	−18.6326	−	0.554597i	−0.764503	−	0.0227554i
$595$	−29.6123	+	9.91481i	−1.21398	+	0.406467i
$596$	15.0057	+	8.66353i	0.614656	+	0.354872i
$597$	−22.0682	−	18.8936i	−0.903193	−	0.773264i
$598$	19.4851			0.796804
$599$		−	18.2983i		−	0.747650i	−0.927499	−	0.373825i	$-0.878046\pi$
$599$		−	18.2983i		−	0.747650i	0.927499	−	0.373825i	$-0.121954\pi$
$600$	−4.82509	+	7.19156i	−0.196983	+	0.293594i
$601$	20.5159	+	11.8449i	0.836862	+	0.483163i	0.856196	−	0.516650i	$-0.172821\pi$
$601$	20.5159	+	11.8449i	0.836862	+	0.483163i	−0.0193342	+	0.999813i	$0.506155\pi$
$602$	3.47409	−	13.1091i	0.141594	−	0.534288i
$603$	7.56747	−	19.5743i	0.308171	−	0.797128i
$604$	2.82204	+	4.88791i	0.114827	+	0.198886i
$605$	4.17343	−	0.244628i	0.169674	−	0.00994553i
$606$	−6.27645	−	17.7915i	−0.254963	−	0.722731i
$607$	1.20113	−	2.08041i	0.0487522	−	0.0844412i	−0.840620	−	0.541626i	$-0.817809\pi$
$607$	1.20113	−	2.08041i	0.0487522	−	0.0844412i	0.889372	+	0.457185i	$0.151142\pi$
$608$	3.13968	−	1.81269i	0.127331	−	0.0735145i
$609$	−15.8873	+	33.4416i	−0.643786	+	1.35512i
$610$	20.9619	−	13.7980i	0.848722	−	0.558664i
$611$	−40.4568	+	23.3578i	−1.63671	+	0.944954i
$612$	−9.93623	−	12.3302i	−0.401648	−	0.498420i
$613$	−32.4221	−	18.7189i	−1.30951	−	0.756049i	−0.327500	−	0.944851i	$-0.606206\pi$
$613$	−32.4221	−	18.7189i	−1.30951	−	0.756049i	−0.982015	+	0.188803i	$0.939539\pi$
$614$	29.1963			1.17827
$615$	22.4939	−	29.6200i	0.907044	−	1.19439i
$616$	6.72983	+	6.69304i	0.271152	+	0.269670i
$617$	−19.7702	−	34.2430i	−0.795918	−	1.37857i	−0.922255	−	0.386582i	$-0.873655\pi$
$617$	−19.7702	−	34.2430i	−0.795918	−	1.37857i	0.126337	−	0.991987i	$-0.459678\pi$
$618$	−0.658104	+	0.768683i	−0.0264728	+	0.0309210i
$619$	4.75647	−	2.74615i	0.191179	−	0.110377i	−0.401356	−	0.915922i	$-0.631461\pi$
$619$	4.75647	−	2.74615i	0.191179	−	0.110377i	0.592534	+	0.805545i	$0.298127\pi$
$620$	6.58494	−	4.33448i	0.264458	−	0.174077i
$621$	21.9488	−	11.8158i	0.880775	−	0.474151i
$622$	−1.53984			−0.0617418
$623$	−2.33216	+	2.34498i	−0.0934362	+	0.0939498i
$624$	2.34047	+	6.63440i	0.0936937	+	0.265589i
$625$	−17.1830	−	18.1589i	−0.687320	−	0.726355i
$626$	9.00202			0.359793
$627$	−14.6503	+	17.1120i	−0.585078	+	0.683388i
$628$	6.48693			0.258857
$629$	5.36275			0.213827
$630$	15.7607	−	8.16087i	0.627922	−	0.325137i
$631$	−9.72111			−0.386991			−0.193496	−	0.981101i	$-0.561983\pi$
$631$	−9.72111			−0.386991			−0.193496	+	0.981101i	$0.561983\pi$
$632$	0.0299868			0.00119281
$633$	2.73925	+	7.76480i	0.108875	+	0.308623i
$634$	17.2577			0.685390
$635$	−9.26293	+	6.09725i	−0.367588	+	0.241962i
$636$	−12.8709	+	15.0335i	−0.510364	+	0.596119i
$637$	−24.7005	−	14.0809i	−0.978670	−	0.557905i
$638$	28.9836			1.14747
$639$	0.896449	−	2.31879i	0.0354630	−	0.0917300i
$640$	1.22943	+	1.86775i	0.0485976	+	0.0738294i
$641$	−27.9609	+	16.1432i	−1.10439	+	0.637619i	−0.937370	−	0.348335i	$-0.886747\pi$
$641$	−27.9609	+	16.1432i	−1.10439	+	0.637619i	−0.167018	+	0.985954i	$0.553414\pi$
$642$	−1.54759	−	4.38686i	−0.0610784	−	0.173136i
$643$	−14.1941	−	24.5848i	−0.559759	−	0.969532i	−0.997516	−	0.0704382i	$-0.977560\pi$
$643$	−14.1941	−	24.5848i	−0.559759	−	0.969532i	0.437757	−	0.899093i	$-0.355773\pi$
$644$	−12.2688	−	3.25139i	−0.483457	−	0.128123i
$645$	−2.49286	+	19.6951i	−0.0981562	+	0.775493i
$646$	−19.1366			−0.752920
$647$	−3.35941	−	1.93956i	−0.132072	−	0.0762519i	0.432508	−	0.901630i	$-0.357629\pi$
$647$	−3.35941	−	1.93956i	−0.132072	−	0.0762519i	−0.564580	+	0.825378i	$0.690962\pi$
$648$	6.65951	+	6.05400i	0.261610	+	0.237824i
$649$	−21.8664	+	12.6246i	−0.858330	+	0.495557i
$650$	−20.1696	+	2.37265i	−0.791117	+	0.0930631i
$651$	−16.1045	+	1.29255i	−0.631186	+	0.0506592i
$652$	4.53833	−	2.62021i	0.177735	−	0.102615i
$653$	−10.5947	+	18.3505i	−0.414602	+	0.718111i	−0.995387	−	0.0959461i	$-0.969412\pi$
$653$	−10.5947	+	18.3505i	−0.414602	+	0.718111i	0.580785	+	0.814057i	$0.302746\pi$
$654$	−1.39269	+	1.62670i	−0.0544586	+	0.0636091i
$655$	−20.7197	+	1.21450i	−0.809587	+	0.0474543i
$656$	−4.80160	−	8.31661i	−0.187471	−	0.324709i
$657$	16.4105	−	13.2243i	0.640235	−	0.515930i
$658$	29.3712	−	7.95634i	1.14501	−	0.310170i
$659$	3.78622	+	2.18598i	0.147490	+	0.0851535i	0.571929	−	0.820303i	$-0.306195\pi$
$659$	3.78622	+	2.18598i	0.147490	+	0.0851535i	−0.424439	+	0.905457i	$0.639529\pi$
$660$	−11.0650	−	8.40297i	−0.430705	−	0.327085i
$661$		−	21.7460i		−	0.845820i	−0.906172	−	0.422910i	$-0.861009\pi$
$661$		−	21.7460i		−	0.845820i	0.906172	−	0.422910i	$-0.138991\pi$
$662$	29.0182			1.12782
$663$	6.81083	−	36.5050i	0.264511	−	1.41774i
$664$	−6.89727	−	3.98214i	−0.267666	−	0.154537i
$665$	4.27180	−	21.0184i	0.165653	−	0.815058i
$666$	−3.01148	+	0.469615i	−0.116693	+	0.0181972i
$667$	−33.5653	+	19.3789i	−1.29965	+	0.750355i
$668$	−18.8867	+	10.9043i	−0.730750	+	0.421898i
$669$	18.8665	−	22.0365i	0.729419	−	0.851982i
$670$	13.0657	−	8.60037i	0.504771	−	0.332261i
$671$	20.1309	+	34.8678i	0.777146	+	1.34606i
$672$	−0.366620	−	4.56789i	−0.0141427	−	0.176210i
$673$	−33.8278	−	19.5305i	−1.30397	−	0.752845i	−0.322884	−	0.946439i	$-0.604652\pi$
$673$	−33.8278	−	19.5305i	−1.30397	−	0.752845i	−0.981082	+	0.193594i	$0.937986\pi$
$674$	0.776124	−	0.448095i	0.0298952	−	0.0172600i
$675$	−21.2811	+	14.9035i	−0.819109	+	0.573637i
$676$	−1.74884	+	3.02908i	−0.0672632	+	0.116503i
$677$		−	10.7467i		−	0.413027i	−0.978444	−	0.206514i	$-0.933788\pi$
$677$		−	10.7467i		−	0.413027i	0.978444	−	0.206514i	$-0.0662118\pi$
$678$	6.23874	+	17.6846i	0.239597	+	0.679174i
$679$	24.0207	+	6.36581i	0.921830	+	0.244298i
$680$	−0.690658	−	11.7829i	−0.0264855	−	0.451852i
$681$	10.3677	−	3.65750i	0.397292	−	0.140156i
$682$	6.32391	+	10.9533i	0.242155	+	0.419425i
$683$	−6.84384	+	11.8539i	−0.261872	+	0.453576i	−0.966739	−	0.255763i	$-0.917673\pi$
$683$	−6.84384	+	11.8539i	−0.261872	+	0.453576i	0.704867	+	0.709339i	$0.251007\pi$
$684$	10.7463	−	1.67579i	0.410895	−	0.0640755i
$685$	−0.00614174	+	0.0122405i	−0.000234664	+	0.000467686i
$686$	13.2030	+	12.9877i	0.504094	+	0.495872i
$687$	5.75678	+	4.92864i	0.219635	+	0.188039i
$688$	4.43909	+	2.56291i	0.169239	+	0.0977100i
$689$	−46.4098			−1.76807
$690$	18.4325	+	2.33305i	0.701715	+	0.0888179i
$691$		−	28.1003i		−	1.06899i	−0.845173	−	0.534493i	$-0.820503\pi$
$691$		−	28.1003i		−	1.06899i	0.845173	−	0.534493i	$-0.179497\pi$
$692$		−	21.6843i		−	0.824314i
$693$	11.5908	+	26.0084i	0.440299	+	0.987979i
$694$	34.3492			1.30388
$695$	−16.9056	−	8.48247i	−0.641267	−	0.321759i
$696$	−10.6300	−	9.10080i	−0.402928	−	0.344965i
$697$			50.6904i			1.92004i
$698$	−1.95233	−	1.12718i	−0.0738969	−	0.0426644i
$699$	14.1086	+	39.9930i	0.533637	+	1.51267i
$700$	13.0957	+	1.87167i	0.494970	+	0.0707426i
$701$		−	47.4955i		−	1.79388i	−0.442151	−	0.896941i	$-0.645784\pi$
$701$		−	47.4955i		−	1.79388i	0.442151	−	0.896941i	$-0.354216\pi$
$702$	−0.627922	+	21.0960i	−0.0236994	+	0.796219i
$703$	−1.84163	+	3.18979i	−0.0694582	+	0.120305i
$704$	−3.10680	+	1.79371i	−0.117092	+	0.0676031i
$705$	−41.0682	+	17.2519i	−1.54672	+	0.649744i
$706$	5.09123	−	2.93942i	0.191611	−	0.110627i
$707$	−20.3218	+	20.4336i	−0.764282	+	0.768483i
$708$	11.9838	+	2.23584i	0.450378	+	0.0840281i
$709$	−32.5456			−1.22227			−0.611137	−	0.791525i	$-0.709288\pi$
$709$	−32.5456			−1.22227			−0.611137	+	0.791525i	$0.709288\pi$
$710$	1.54777	−	1.01881i	0.0580868	−	0.0382352i
$711$	0.0839081	+	0.0324390i	0.00314680	+	0.00121656i
$712$	−0.625013	−	1.08255i	−0.0234233	−	0.0405704i
$713$	−14.6472	−	8.45655i	−0.548541	−	0.316700i
$714$	−10.3799	+	21.8489i	−0.388456	+	0.817673i
$715$	−1.90654	−	32.5263i	−0.0713007	−	1.21641i
$716$	15.1142	+	8.72620i	0.564845	+	0.326113i
$717$	3.97438	−	1.40207i	0.148426	−	0.0523614i
$718$	−5.91330	+	3.41404i	−0.220682	+	0.127411i
$719$	1.35013	+	2.33850i	0.0503515	+	0.0872114i	0.890103	−	0.455760i	$-0.150633\pi$
$719$	1.35013	+	2.33850i	0.0503515	+	0.0872114i	−0.839751	+	0.542971i	$0.817299\pi$
$720$	1.41967	+	6.55626i	0.0529079	+	0.244337i
$721$	1.49415	+	0.395970i	0.0556450	+	0.0147467i
$722$	−2.92828	+	5.07193i	−0.108979	+	0.188758i
$723$	3.43669	−	1.21239i	0.127812	−	0.0450891i
$724$		−	24.0491i		−	0.893776i
$725$	32.3847	−	24.1469i	1.20274	−	0.896793i
$726$	2.10603	−	2.45990i	0.0781619	−	0.0912953i
$727$	13.0226	−	22.5558i	0.482982	−	0.836549i	−0.516827	−	0.856090i	$-0.672887\pi$
$727$	13.0226	−	22.5558i	0.482982	−	0.836549i	0.999809	+	0.0195409i	$0.00622045\pi$
$728$	7.57795	−	7.61961i	0.280858	−	0.282401i
$729$	12.0854	+	24.1442i	0.447606	+	0.894231i
$730$	15.6820	−	0.919209i	0.580418	−	0.0340214i
$731$	−13.5283	−	23.4317i	−0.500363	−	0.866654i
$732$	3.56524	−	19.1092i	0.131775	−	0.706295i
$733$	−9.72720	+	16.8480i	−0.359282	+	0.622295i	−0.987841	−	0.155467i	$-0.950312\pi$
$733$	−9.72720	+	16.8480i	−0.359282	+	0.622295i	0.628559	+	0.777762i	$0.283645\pi$
$734$	−0.284464	−	0.492706i	−0.0104998	−	0.0181861i
$735$	−21.6803	−	16.2778i	−0.799688	−	0.600415i
$736$	2.39862	−	4.15452i	0.0884141	−	0.153138i
$737$	12.5477	+	21.7333i	0.462202	+	0.800557i
$738$	−4.43896	−	28.4655i	−0.163400	−	1.04783i
$739$	5.50909	−	9.54203i	0.202655	−	0.351009i	−0.746728	−	0.665130i	$-0.768376\pi$
$739$	5.50909	−	9.54203i	0.202655	−	0.351009i	0.949383	+	0.314120i	$0.101710\pi$
$740$	−2.03049	−	1.01881i	−0.0746424	−	0.0374522i
$741$	19.3745	+	16.5873i	0.711738	+	0.609351i
$742$	29.2219	+	7.74419i	1.07277	+	0.284298i
$743$	−7.57857	−	13.1265i	−0.278031	−	0.481563i	0.692865	−	0.721068i	$-0.256348\pi$
$743$	−7.57857	−	13.1265i	−0.278031	−	0.481563i	−0.970895	+	0.239504i	$0.923015\pi$
$744$	1.11998	−	6.00293i	0.0410605	−	0.220078i
$745$	2.26713	+	38.6781i	0.0830613	+	1.41706i
$746$	6.58348	+	3.80098i	0.241039	+	0.139164i
$747$	−14.9919	−	18.6040i	−0.548526	−	0.680685i
$748$	18.9362			0.692377
$749$	−5.01077	+	5.03831i	−0.183090	+	0.184096i
$750$	−19.3642	−	0.170530i	−0.707079	−	0.00622687i
$751$	−7.79754	+	13.5057i	−0.284536	+	0.492831i	−0.972497	−	0.232917i	$-0.925173\pi$
$751$	−7.79754	+	13.5057i	−0.284536	+	0.492831i	0.687960	+	0.725748i	$0.258506\pi$
$752$			11.5014i			0.419412i
$753$	32.9199	+	6.14194i	1.19967	+	0.223825i
$754$		−	32.8156i		−	1.19507i
$755$	−5.65990	+	11.2802i	−0.205985	+	0.410529i
$756$	3.91557	−	13.1783i	0.142408	−	0.479291i
$757$			2.00202i			0.0727648i	0.999338	+	0.0363824i	$0.0115834\pi$
$757$			2.00202i			0.0727648i	−0.999338	+	0.0363824i	$0.988417\pi$
$758$	−37.9897			−1.37985
$759$	−5.46703	+	29.3025i	−0.198441	+	1.06361i
$760$	7.24569	+	3.63556i	0.262829	+	0.131875i
$761$	−8.46103	+	14.6549i	−0.306712	+	0.531241i	−0.977641	−	0.210281i	$-0.932562\pi$
$761$	−8.46103	+	14.6549i	−0.306712	+	0.531241i	0.670929	+	0.741522i	$0.265896\pi$
$762$	−1.57546	+	8.44423i	−0.0570729	+	0.305902i
$763$	3.16195	+	0.837960i	0.114470	+	0.0303362i
$764$		−	3.22636i		−	0.116726i
$765$	10.8139	−	33.7176i	0.390976	−	1.21906i
$766$	−10.4289	−	6.02112i	−0.376811	−	0.217552i
$767$	14.2937	+	24.7574i	0.516116	+	0.893939i
$768$	1.70267	+	0.317671i	0.0614398	+	0.0114630i
$769$	10.5316	−	6.08042i	0.379779	−	0.219265i	−0.297943	−	0.954584i	$-0.596301\pi$
$769$	10.5316	−	6.08042i	0.379779	−	0.219265i	0.677722	+	0.735318i	$0.262967\pi$
$770$	−4.22707	+	20.7983i	−0.152333	+	0.749518i
$771$	34.1564	+	29.2428i	1.23011	+	1.05315i
$772$			24.2271i			0.871951i
$773$	19.6768	+	11.3604i	0.707726	+	0.408606i	0.810219	−	0.586128i	$-0.199348\pi$
$773$	19.6768	+	11.3604i	0.707726	+	0.408606i	−0.102492	+	0.994734i	$0.532682\pi$
$774$	9.64883	+	11.9736i	0.346820	+	0.430381i
$775$	16.1915	+	6.97008i	0.581615	+	0.250373i
$776$	−4.69619	+	8.13404i	−0.168583	+	0.291995i
$777$	2.64297	+	3.83281i	0.0948159	+	0.137501i
$778$	9.93198	−	5.73423i	0.356079	−	0.205582i
$779$	−30.1509	−	17.4077i	−1.08027	−	0.623694i
$780$	−9.51397	+	12.5280i	−0.340655	+	0.448573i
$781$	1.48642	+	2.57455i	0.0531882	+	0.0921246i
$782$	−21.9297	+	12.6611i	−0.784203	+	0.452760i
$783$	−19.8995	−	36.9649i	−0.711148	−	1.32102i
$784$	−6.04290	+	3.53318i	−0.215818	+	0.126185i
$785$	7.97524	+	12.1160i	0.284648	+	0.432437i
$786$	−10.4557	+	12.2126i	−0.372944	+	0.435609i
$787$	−28.3169			−1.00939			−0.504695	−	0.863298i	$-0.668395\pi$
$787$	−28.3169			−1.00939			−0.504695	+	0.863298i	$0.668395\pi$
$788$	−6.89656			−0.245680
$789$	4.48428	+	12.7113i	0.159644	+	0.452536i
$790$	0.0368667	+	0.0560078i	0.00131166	+	0.00199267i
$791$	20.1997	−	20.3108i	0.718220	−	0.722168i
$792$	−10.6338	+	1.65824i	−0.377854	+	0.0589231i
$793$	39.4778	−	22.7925i	1.40190	−	0.809387i
$794$	−1.89421	−	3.28087i	−0.0672231	−	0.116434i
$795$	−43.9028	−	5.55689i	−1.55707	−	0.197083i
$796$	−14.5256	−	8.38638i	−0.514847	−	0.297247i
$797$	−2.25578	+	1.30238i	−0.0799040	+	0.0461326i	−0.539420	−	0.842037i	$-0.681356\pi$
$797$	−2.25578	+	1.30238i	−0.0799040	+	0.0461326i	0.459516	+	0.888170i	$0.348023\pi$
$798$	−9.43125	−	13.6771i	−0.333863	−	0.484165i
$799$	30.3550	−	52.5764i	1.07388	−	1.86002i
$800$	−1.97699	+	4.59255i	−0.0698973	+	0.162371i
$801$	−0.577809	−	3.70529i	−0.0204159	−	0.130920i
$802$	10.0319	+	5.79192i	0.354239	+	0.204520i
$803$			25.2026i			0.889379i
$804$	2.22224	−	11.9109i	0.0783722	−	0.420063i
$805$	−9.01082	−	26.9124i	−0.317590	−	0.948536i
$806$	12.4015	−	7.16002i	0.436825	−	0.252201i
$807$	−21.9901	+	25.6851i	−0.774090	+	0.904158i
$808$	−5.44619	−	9.43308i	−0.191596	−	0.331855i
$809$	−21.2398	−	12.2628i	−0.746751	−	0.431137i	0.0777677	−	0.996972i	$-0.475221\pi$
$809$	−21.2398	−	12.2628i	−0.746751	−	0.431137i	−0.824519	+	0.565835i	$0.808554\pi$
$810$	−3.11995	+	19.8813i	−0.109624	+	0.698558i
$811$			9.73361i			0.341793i	0.985289	+	0.170897i	$0.0546664\pi$
$811$			9.73361i			0.341793i	−0.985289	+	0.170897i	$0.945334\pi$
$812$	−5.47580	+	20.6623i	−0.192163	+	0.725105i
$813$	−0.236249	+	0.0833435i	−0.00828563	+	0.00292298i
$814$	1.82234	−	3.15639i	0.0638730	−	0.110631i
$815$	10.4735	+	5.25511i	0.366869	+	0.184078i
$816$	−6.94503	−	5.94595i	−0.243125	−	0.208150i
$817$	18.5831			0.650140
$818$			30.2706i			1.05839i
$819$	29.4471	−	13.1233i	1.02897	−	0.458565i
$820$	9.63012	−	19.1929i	0.336298	−	0.670245i
$821$		−	2.04290i		−	0.0712977i	−0.999364	−	0.0356488i	$-0.988650\pi$
$821$		−	2.04290i		−	0.0712977i	0.999364	−	0.0356488i	$-0.0113498\pi$
$822$	0.00352912	+	0.0100038i	0.000123092	+	0.000348923i
$823$			13.0612i			0.455284i	0.973745	+	0.227642i	$0.0731016\pi$
$823$			13.0612i			0.455284i	−0.973745	+	0.227642i	$0.926898\pi$
$824$	−0.292115	+	0.505958i	−0.0101763	+	0.0176259i
$825$	2.09099	−	30.9976i	0.0727991	−	1.07920i
$826$	−4.86886	−	17.9736i	−0.169409	−	0.625382i
$827$	−18.5995			−0.646767			−0.323384	−	0.946268i	$-0.604820\pi$
$827$	−18.5995			−0.646767			−0.323384	+	0.946268i	$0.604820\pi$
$828$	11.2060	−	9.03030i	0.389436	−	0.313824i
$829$	−26.4337	−	15.2615i	−0.918080	−	0.530053i	−0.0350576	−	0.999385i	$-0.511161\pi$
$829$	−26.4337	−	15.2615i	−0.918080	−	0.530053i	−0.883022	+	0.469332i	$0.844495\pi$
$830$	−1.04207	−	17.7782i	−0.0361709	−	0.617089i
$831$	−41.9183	+	14.7878i	−1.45413	+	0.512985i
$832$	2.03087	+	3.51756i	0.0704076	+	0.121950i
$833$	36.9489	−	0.202548i	1.28021	−	0.00701787i
$834$	−13.8164	+	4.87413i	−0.478424	+	0.168777i
$835$	−43.5864	−	21.8697i	−1.50837	−	0.756831i
$836$	−6.50291	+	11.2634i	−0.224908	+	0.389552i
$837$	9.62773	−	15.5856i	0.332783	−	0.538719i
$838$	−10.7319	−	18.5882i	−0.370727	−	0.642118i
$839$	−6.88932	+	11.9327i	−0.237846	+	0.411961i	−0.960096	−	0.279671i	$-0.909775\pi$
$839$	−6.88932	+	11.9327i	−0.237846	+	0.411961i	0.722250	+	0.691632i	$0.243108\pi$
$840$	8.08094	−	6.30066i	0.278819	−	0.217393i
$841$	18.1368	+	31.4139i	0.625408	+	1.08324i
$842$	−12.8685	+	22.2889i	−0.443478	+	0.768127i
$843$	−24.7498	−	21.1894i	−0.852428	−	0.729801i
$844$	2.37689	+	4.11690i	0.0818161	+	0.141710i
$845$	−7.80766	+	0.457650i	−0.268592	+	0.0157436i
$846$	−12.4419	+	32.1828i	−0.427763	+	1.10647i
$847$	−4.78149	−	1.26716i	−0.164294	−	0.0435401i
$848$	−5.71305	+	9.89529i	−0.196187	+	0.339806i
$849$	51.7553	+	9.65611i	1.77624	+	0.331397i
$850$	21.1583	−	15.7762i	0.725725	−	0.541119i
$851$			4.87380i			0.167072i
$852$	0.263248	−	1.41097i	0.00901873	−	0.0483391i
$853$	−2.66904	+	4.62291i	−0.0913862	+	0.158286i	−0.908095	−	0.418765i	$-0.862463\pi$
$853$	−2.66904	+	4.62291i	−0.0913862	+	0.158286i	0.816708	+	0.577051i	$0.195796\pi$
$854$	−28.6605	+	7.76380i	−0.980741	+	0.265672i
$855$	16.3418	+	18.0111i	0.558878	+	0.615968i
$856$	−1.34287	−	2.32592i	−0.0458984	−	0.0794983i
$857$	32.1904	−	18.5851i	1.09960	−	0.634856i	0.163486	−	0.986546i	$-0.447726\pi$
$857$	32.1904	−	18.5851i	1.09960	−	0.634856i	0.936117	+	0.351690i	$0.114393\pi$
$858$	−19.1716	−	16.4136i	−0.654507	−	0.560352i
$859$	33.7048	+	19.4595i	1.14999	+	0.663949i	0.948885	−	0.315621i	$-0.102213\pi$
$859$	33.7048	+	19.4595i	1.14999	+	0.663949i	0.201107	+	0.979569i	$0.435546\pi$
$860$	0.670681	+	11.4420i	0.0228700	+	0.390170i
$861$	−36.2290	+	24.9822i	−1.23468	+	0.851390i
$862$	−1.05463	−	0.608890i	−0.0359208	−	0.0207389i
$863$	2.48936	+	4.31171i	0.0847390	+	0.146772i	0.905280	−	0.424816i	$-0.139661\pi$
$863$	2.48936	+	4.31171i	0.0847390	+	0.146772i	−0.820541	+	0.571588i	$0.806328\pi$
$864$	4.42071	+	2.73081i	0.150396	+	0.0929040i
$865$	40.5009	−	26.6594i	1.37707	−	0.906446i
$866$	6.29897			0.214048
$867$	6.25927	+	17.7428i	0.212576	+	0.602578i
$868$	−9.00336	+	2.43891i	−0.305594	+	0.0827821i
$869$	−0.0931629	+	0.0537876i	−0.00316034	+	0.00182462i
$870$	3.92919	−	31.0430i	0.133212	−	1.05246i
$871$	24.6068	−	14.2067i	0.833768	−	0.481376i
$872$	−0.618180	+	1.07072i	−0.0209342	+	0.0362591i
$873$	−21.9400	+	17.6802i	−0.742555	+	0.598384i
$874$		−	17.3918i		−	0.588287i
$875$	12.6044	+	26.7606i	0.426107	+	0.904673i
$876$	7.91357	−	9.24326i	0.267375	−	0.312301i
$877$	39.7198	+	22.9323i	1.34124	+	0.774367i	0.986990	−	0.160782i	$-0.0514017\pi$
$877$	39.7198	+	22.9323i	1.34124	+	0.774367i	0.354253	+	0.935149i	$0.384735\pi$
$878$		−	36.3857i		−	1.22796i
$879$	−45.4714	+	16.0413i	−1.53371	+	0.541060i
$880$	−7.16981	−	3.59749i	−0.241694	−	0.121271i
$881$	4.17555			0.140678			0.0703390	−	0.997523i	$-0.477592\pi$
$881$	4.17555			0.140678			0.0703390	+	0.997523i	$0.477592\pi$
$882$	−20.7312	+	3.34936i	−0.698055	+	0.112779i
$883$			9.11973i			0.306903i	0.988156	+	0.153452i	$0.0490390\pi$
$883$			9.11973i			0.306903i	−0.988156	+	0.153452i	$0.950961\pi$
$884$		−	21.4399i		−	0.721101i
$885$	10.5572	+	25.1315i	0.354878	+	0.844788i
$886$	−11.5534			−0.388143
$887$	6.54685	+	3.77983i	0.219822	+	0.126914i	0.605868	−	0.795565i	$-0.292826\pi$
$887$	6.54685	+	3.77983i	0.219822	+	0.126914i	−0.386046	+	0.922480i	$0.626159\pi$
$888$	−1.65946	+	0.585420i	−0.0556878	+	0.0196454i
$889$	12.6649	−	3.43078i	0.424767	−	0.115065i
$890$	1.25353	−	2.49830i	0.0420185	−	0.0837430i
$891$	−31.5489	−	6.86332i	−1.05693	−	0.229930i
$892$	8.37432	−	14.5048i	0.280393	−	0.485655i
$893$	20.8485	+	36.1106i	0.697668	+	1.20840i
$894$	22.7975	+	19.5180i	0.762464	+	0.652779i
$895$	2.28353	+	38.9579i	0.0763301	+	1.30222i
$896$	−0.691773	−	2.55371i	−0.0231105	−	0.0853136i
$897$	33.1767	+	6.18985i	1.10774	+	0.206673i
$898$			8.35607i			0.278846i
$899$	−14.2420	+	24.6679i	−0.474998	+	0.822721i
$900$	−10.5001	+	10.7121i	−0.350003	+	0.357069i
$901$	52.2323	−	30.1563i	1.74011	−	1.00465i
$902$	29.8352	+	17.2254i	0.993404	+	0.573542i
$903$	10.0796	−	21.2169i	0.335429	−	0.706053i
$904$	5.41347	+	9.37640i	0.180049	+	0.311854i
$905$	44.9177	−	29.5667i	1.49311	−	0.982830i
$906$	3.25225	+	9.21898i	0.108049	+	0.306280i
$907$	14.6018	−	8.43037i	0.484846	−	0.279926i	−0.237588	−	0.971366i	$-0.576357\pi$
$907$	14.6018	−	8.43037i	0.484846	−	0.279926i	0.722434	+	0.691440i	$0.243023\pi$
$908$	5.49698	−	3.17368i	0.182424	−	0.105322i
$909$	−5.03487	−	32.2869i	−0.166996	−	1.07089i
$910$	23.5481	+	4.78594i	0.780612	+	0.158653i
$911$	−4.64902	−	2.68411i	−0.154029	−	0.0889286i	0.421005	−	0.907059i	$-0.361678\pi$
$911$	−4.64902	−	2.68411i	−0.154029	−	0.0889286i	−0.575033	+	0.818130i	$0.695011\pi$
$912$	5.92168	−	2.08904i	0.196086	−	0.0691749i
$913$	28.5713			0.945571
$914$		−	3.77155i		−	0.124752i
$915$	40.0744	−	16.8344i	1.32482	−	0.556529i
$916$	3.78920	+	2.18769i	0.125199	+	0.0722834i
$917$	23.7386	+	6.29104i	0.783916	+	0.207748i
$918$	−13.0012	−	24.1507i	−0.429103	−	0.797094i
$919$	−8.65286	−	14.9872i	−0.285432	−	0.494382i	0.687282	−	0.726390i	$-0.258804\pi$
$919$	−8.65286	−	14.9872i	−0.285432	−	0.494382i	−0.972714	+	0.232009i	$0.925470\pi$
$920$	10.7086	−	0.627687i	0.353051	−	0.0206942i
$921$	49.7117	+	9.27483i	1.63806	+	0.305616i
$922$	−1.39131	+	2.40982i	−0.0458204	+	0.0793632i
$923$	2.91494	−	1.68294i	0.0959464	−	0.0553947i
$924$	9.33249	+	13.5339i	0.307016	+	0.445233i
$925$	−0.593471	−	5.04501i	−0.0195132	−	0.165879i
$926$	−9.52910	+	5.50163i	−0.313146	+	0.180795i
$927$	−1.36472	+	1.09975i	−0.0448234	+	0.0361206i
$928$	−6.99680	−	4.03961i	−0.229681	−	0.132607i
$929$	10.7008			0.351083			0.175542	−	0.984472i	$-0.443832\pi$
$929$	10.7008			0.351083			0.175542	+	0.984472i	$0.443832\pi$
$930$	12.5889	−	5.28835i	0.412807	−	0.173412i
$931$	−12.5682	+	22.0470i	−0.411906	+	0.722561i
$932$	12.2423	+	21.2043i	0.401010	+	0.694570i
$933$	−2.62183	−	0.489161i	−0.0858349	−	0.0160144i
$934$	16.4814	−	9.51552i	0.539287	−	0.311357i
$935$	23.2808	+	35.3682i	0.761364	+	1.15666i
$936$	1.87749	+	12.0397i	0.0613676	+	0.393530i
$937$	−12.8760			−0.420639			−0.210320	−	0.977633i	$-0.567450\pi$
$937$	−12.8760			−0.420639			−0.210320	+	0.977633i	$0.567450\pi$
$938$	−17.8642	+	4.83923i	−0.583288	+	0.158006i
$939$	15.3275	+	2.85968i	0.500193	+	0.0933222i
$940$	−21.4817	+	14.1402i	−0.700656	+	0.461201i
$941$	−33.7847			−1.10135			−0.550675	−	0.834720i	$-0.685630\pi$
$941$	−33.7847			−1.10135			−0.550675	+	0.834720i	$0.685630\pi$
$942$	11.0451	+	2.06071i	0.359869	+	0.0671415i
$943$	−46.0687			−1.50020
$944$	7.03823			0.229075
$945$	29.4278	−	8.88854i	0.957286	−	0.289144i
$946$	−18.3885			−0.597862
$947$	−21.1866			−0.688472			−0.344236	−	0.938883i	$-0.611862\pi$
$947$	−21.1866			−0.688472			−0.344236	+	0.938883i	$0.611862\pi$
$948$	0.0510576	+	0.00952593i	0.00165827	+	0.000309388i
$949$	28.5347			0.926276
$950$	2.11776	+	18.0028i	0.0687093	+	0.584088i
$951$	29.3841	+	5.48226i	0.952845	+	0.177775i
$952$	−3.57758	+	13.4996i	−0.115950	+	0.437524i
$953$	−15.9394			−0.516328			−0.258164	−	0.966101i	$-0.583117\pi$
$953$	−15.9394			−0.516328			−0.258164	+	0.966101i	$0.583117\pi$
$954$	−26.6906	+	21.5084i	−0.864140	+	0.696362i
$955$	6.02604	−	3.96659i	0.194998	−	0.128356i
$956$	2.10722	−	1.21660i	0.0681524	−	0.0393478i
$957$	49.3495	+	9.20724i	1.59524	+	0.297628i
$958$	0.146168	+	0.253170i	0.00472247	+	0.00817956i
$959$	0.0114266	−	0.0114894i	0.000368983	−	0.000371011i
$960$	1.49999	+	3.57072i	0.0484119	+	0.115244i
$961$	18.5702			0.599038
$962$	−3.57371	−	2.06328i	−0.115221	−	0.0665228i
$963$	−1.24145	−	7.96101i	−0.0400052	−	0.256540i
$964$	1.82213	−	1.05201i	0.0586870	−	0.0338830i
$965$	−45.2501	+	29.7855i	−1.45665	+	0.958830i
$966$	−19.8568	−	9.43347i	−0.638881	−	0.303517i
$967$	48.1802	−	27.8169i	1.54937	−	0.894530i	0.551182	−	0.834385i	$-0.314177\pi$
$967$	48.1802	−	27.8169i	1.54937	−	0.894530i	0.998190	−	0.0601450i	$-0.0191563\pi$
$968$	0.934810	−	1.61914i	0.0300459	−	0.0520411i
$969$	−32.5833	−	6.07915i	−1.04673	−	0.195290i
$970$	−20.9660	+	1.22893i	−0.673178	+	0.0394586i
$971$	−28.9188	−	50.0888i	−0.928047	−	1.60743i	−0.786586	−	0.617481i	$-0.788153\pi$
$971$	−28.9188	−	50.0888i	−0.928047	−	1.60743i	−0.141462	−	0.989944i	$-0.545180\pi$
$972$	9.41577	+	12.4235i	0.302011	+	0.398484i
$973$	15.8682	+	15.7814i	0.508711	+	0.505930i
$974$	−17.4211	−	10.0581i	−0.558208	−	0.322281i
$975$	−35.0959	−	2.36745i	−1.12397	−	0.0758192i
$976$		−	11.2231i		−	0.359241i
$977$	−39.0804			−1.25029			−0.625146	−	0.780508i	$-0.714961\pi$
$977$	−39.0804			−1.25029			−0.625146	+	0.780508i	$0.714961\pi$
$978$	8.55964	−	3.01965i	0.273707	−	0.0965577i
$979$	3.88358	+	2.24219i	0.124120	+	0.0716606i
$980$	−14.0284	−	6.94283i	−0.448122	−	0.221781i
$981$	−2.88805	+	2.32732i	−0.0922084	+	0.0743056i
$982$	−0.00977625	+	0.00564432i	−0.000311973	+	0.000180118i
$983$	13.8267	−	7.98287i	0.441005	−	0.254614i	−0.263019	−	0.964791i	$-0.584718\pi$
$983$	13.8267	−	7.98287i	0.441005	−	0.254614i	0.704024	+	0.710177i	$0.251385\pi$
$984$	−5.53359	−	15.6858i	−0.176404	−	0.500044i
$985$	−8.47885	−	12.8811i	−0.270159	−	0.410425i
$986$	21.3231	+	36.9326i	0.679065	+	1.17617i
$987$	52.5370	−	4.21663i	1.67227	−	0.134217i
$988$	12.7525	+	7.36268i	0.405712	+	0.234238i
$989$	21.2953	−	12.2949i	0.677153	−	0.390954i
$990$	−16.1707	−	17.8225i	−0.513938	−	0.566437i
$991$	16.1342	−	27.9452i	0.512519	−	0.887709i	−0.487376	−	0.873192i	$-0.662046\pi$
$991$	16.1342	−	27.9452i	0.512519	−	0.887709i	0.999895	−	0.0145163i	$-0.00462085\pi$
$992$		−	3.52560i		−	0.111938i
$993$	49.4084	+	9.21824i	1.56793	+	0.292532i
$994$	−2.11621	+	0.573259i	−0.0671223	+	0.0181827i
$995$	−2.19461	−	37.4407i	−0.0695737	−	1.18695i
$996$	−10.4788	−	8.97133i	−0.332032	−	0.284268i
$997$	−19.8570	−	34.3933i	−0.628877	−	1.08925i	−0.987777	−	0.155871i	$-0.950182\pi$
$997$	−19.8570	−	34.3933i	−0.628877	−	1.08925i	0.358901	−	0.933376i	$-0.383152\pi$
$998$	−5.43038	+	9.40569i	−0.171896	+	0.297732i
$999$	−5.27675	−	0.157062i	−0.166949	−	0.00496922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bi.b.479.24	yes	48
3.2	odd	2		1890.2.bi.a.899.8		48
5.4	even	2		630.2.bi.a.479.1	yes	48
7.5	odd	6		630.2.r.a.299.17	yes	48
9.4	even	3		1890.2.r.a.1529.16		48
9.5	odd	6		630.2.r.b.59.8	yes	48
15.14	odd	2		1890.2.bi.b.899.24		48
21.5	even	6		1890.2.r.b.89.16		48
35.19	odd	6		630.2.r.b.299.8	yes	48
45.4	even	6		1890.2.r.b.1529.16		48
45.14	odd	6		630.2.r.a.59.17	✓	48
63.5	even	6		630.2.bi.a.509.1	yes	48
63.40	odd	6		1890.2.bi.b.719.24		48
105.89	even	6		1890.2.r.a.89.16		48
315.194	even	6	inner	630.2.bi.b.509.24	yes	48
315.229	odd	6		1890.2.bi.a.719.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.17	✓	48	45.14	odd	6
630.2.r.a.299.17	yes	48	7.5	odd	6
630.2.r.b.59.8	yes	48	9.5	odd	6
630.2.r.b.299.8	yes	48	35.19	odd	6
630.2.bi.a.479.1	yes	48	5.4	even	2
630.2.bi.a.509.1	yes	48	63.5	even	6
630.2.bi.b.479.24	yes	48	1.1	even	1	trivial
630.2.bi.b.509.24	yes	48	315.194	even	6	inner
1890.2.r.a.89.16		48	105.89	even	6
1890.2.r.a.1529.16		48	9.4	even	3
1890.2.r.b.89.16		48	21.5	even	6
1890.2.r.b.1529.16		48	45.4	even	6
1890.2.bi.a.719.8		48	315.229	odd	6
1890.2.bi.a.899.8		48	3.2	odd	2
1890.2.bi.b.719.24		48	63.40	odd	6
1890.2.bi.b.899.24		48	15.14	odd	2

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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.70267 + 0.317671i) q^{3} +1.00000 q^{4} +(1.22943 + 1.86775i) q^{5} +(1.70267 + 0.317671i) q^{6} +(-0.691773 - 2.55371i) q^{7} +1.00000 q^{8} +(2.79817 + 1.08178i) q^{9} +(1.22943 + 1.86775i) q^{10} +(-3.10680 + 1.79371i) q^{11} +(1.70267 + 0.317671i) q^{12} +(2.03087 + 3.51756i) q^{13} +(-0.691773 - 2.55371i) q^{14} +(1.49999 + 3.57072i) q^{15} +1.00000 q^{16} +(-4.57132 - 2.63925i) q^{17} +(2.79817 + 1.08178i) q^{18} +(3.13968 - 1.81269i) q^{19} +(1.22943 + 1.86775i) q^{20} +(-0.366620 - 4.56789i) q^{21} +(-3.10680 + 1.79371i) q^{22} +(2.39862 - 4.15452i) q^{23} +(1.70267 + 0.317671i) q^{24} +(-1.97699 + 4.59255i) q^{25} +(2.03087 + 3.51756i) q^{26} +(4.42071 + 2.73081i) q^{27} +(-0.691773 - 2.55371i) q^{28} +(-6.99680 - 4.03961i) q^{29} +(1.49999 + 3.57072i) q^{30} -3.52560i q^{31} +1.00000 q^{32} +(-5.85967 + 2.06716i) q^{33} +(-4.57132 - 2.63925i) q^{34} +(3.91921 - 4.43168i) q^{35} +(2.79817 + 1.08178i) q^{36} +(-0.879847 + 0.507980i) q^{37} +(3.13968 - 1.81269i) q^{38} +(2.34047 + 6.63440i) q^{39} +(1.22943 + 1.86775i) q^{40} +(-4.80160 - 8.31661i) q^{41} +(-0.366620 - 4.56789i) q^{42} +(4.43909 + 2.56291i) q^{43} +(-3.10680 + 1.79371i) q^{44} +(1.41967 + 6.55626i) q^{45} +(2.39862 - 4.15452i) q^{46} +11.5014i q^{47} +(1.70267 + 0.317671i) q^{48} +(-6.04290 + 3.53318i) q^{49} +(-1.97699 + 4.59255i) q^{50} +(-6.94503 - 5.94595i) q^{51} +(2.03087 + 3.51756i) q^{52} +(-5.71305 + 9.89529i) q^{53} +(4.42071 + 2.73081i) q^{54} +(-7.16981 - 3.59749i) q^{55} +(-0.691773 - 2.55371i) q^{56} +(5.92168 - 2.08904i) q^{57} +(-6.99680 - 4.03961i) q^{58} +7.03823 q^{59} +(1.49999 + 3.57072i) q^{60} -11.2231i q^{61} -3.52560i q^{62} +(0.826853 - 7.89407i) q^{63} +1.00000 q^{64} +(-4.07312 + 8.11776i) q^{65} +(-5.85967 + 2.06716i) q^{66} -6.99540i q^{67} +(-4.57132 - 2.63925i) q^{68} +(5.40382 - 6.31181i) q^{69} +(3.91921 - 4.43168i) q^{70} -0.828681i q^{71} +(2.79817 + 1.08178i) q^{72} +(3.51263 - 6.08405i) q^{73} +(-0.879847 + 0.507980i) q^{74} +(-4.82509 + 7.19156i) q^{75} +(3.13968 - 1.81269i) q^{76} +(6.72983 + 6.69304i) q^{77} +(2.34047 + 6.63440i) q^{78} +0.0299868 q^{79} +(1.22943 + 1.86775i) q^{80} +(6.65951 + 6.05400i) q^{81} +(-4.80160 - 8.31661i) q^{82} +(-6.89727 - 3.98214i) q^{83} +(-0.366620 - 4.56789i) q^{84} +(-0.690658 - 11.7829i) q^{85} +(4.43909 + 2.56291i) q^{86} +(-10.6300 - 9.10080i) q^{87} +(-3.10680 + 1.79371i) q^{88} +(-0.625013 - 1.08255i) q^{89} +(1.41967 + 6.55626i) q^{90} +(7.57795 - 7.61961i) q^{91} +(2.39862 - 4.15452i) q^{92} +(1.11998 - 6.00293i) q^{93} +11.5014i q^{94} +(7.24569 + 3.63556i) q^{95} +(1.70267 + 0.317671i) q^{96} +(-4.69619 + 8.13404i) q^{97} +(-6.04290 + 3.53318i) q^{98} +(-10.6338 + 1.65824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39}+ \cdots - 26 q^{99}+O(q^{100}) \) 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 42 * q^55 + 3 * q^56 - 22 * q^57 - 3 * q^58 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * q^70 - 18 * q^73 + 18 * q^75 - 12 * q^77 - 18 * q^78 + 8 * q^81 - 3 * q^82 + 9 * q^83 + 8 * q^84 - 33 * q^85 - 15 * q^87 + 6 * q^88 - 33 * q^89 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 24 * q^97 + 3 * q^98 - 26 * q^99

Introduction

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