LMFDB - Embedded newform 756.2.cf.a.491.46

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(155,756)] 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("756.155"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 7, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			491.46
Character	$\chi$	$=$	756.491
Dual form			756.2.cf.a.659.46

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.381855 - 1.36169i) q^{2} +(1.51360 - 0.842029i) q^{3} +(-1.70837 + 1.03993i) q^{4} +(-1.15117 - 3.16281i) q^{5} +(-1.72455 - 1.73951i) q^{6} +(-0.984808 + 0.173648i) q^{7} +(2.06841 + 1.92916i) q^{8} +(1.58197 - 2.54899i) q^{9} +(-3.86718 + 2.77527i) q^{10} +(-2.52494 - 0.919002i) q^{11} +(-1.71014 + 3.01254i) q^{12} +(1.75210 + 1.47018i) q^{13} +(0.612508 + 1.27469i) q^{14} +(-4.40559 - 3.81792i) q^{15} +(1.83708 - 3.55319i) q^{16} +(-4.09050 - 2.36165i) q^{17} +(-4.07501 - 1.18081i) q^{18} +(-3.50980 + 2.02638i) q^{19} +(5.25574 + 4.20613i) q^{20} +(-1.34439 + 1.09207i) q^{21} +(-0.287232 + 3.78909i) q^{22} +(0.542808 - 3.07842i) q^{23} +(4.75516 + 1.17832i) q^{24} +(-4.84798 + 4.06793i) q^{25} +(1.33288 - 2.94720i) q^{26} +(0.248152 - 5.19022i) q^{27} +(1.50184 - 1.32079i) q^{28} +(-0.207583 - 0.247388i) q^{29} +(-3.51651 + 7.45692i) q^{30} +(2.34834 + 0.414075i) q^{31} +(-5.53982 - 1.14473i) q^{32} +(-4.59557 + 0.735068i) q^{33} +(-1.65385 + 6.47178i) q^{34} +(1.68290 + 2.91486i) q^{35} +(-0.0518239 + 5.99978i) q^{36} +(-1.29177 + 2.23741i) q^{37} +(4.09953 + 4.00546i) q^{38} +(3.88991 + 0.749955i) q^{39} +(3.72049 - 8.76280i) q^{40} +(5.06829 - 6.04015i) q^{41} +(2.00042 + 1.41362i) q^{42} +(-3.74287 + 10.2835i) q^{43} +(5.26924 - 1.05576i) q^{44} +(-9.88311 - 2.06917i) q^{45} +(-4.39911 + 0.436375i) q^{46} +(1.41707 + 8.03658i) q^{47} +(-0.211278 - 6.92498i) q^{48} +(0.939693 - 0.342020i) q^{49} +(7.39047 + 5.04806i) q^{50} +(-8.17996 - 0.130277i) q^{51} +(-4.52213 - 0.689561i) q^{52} -2.58322i q^{53} +(-7.16221 + 1.64401i) q^{54} +9.04383i q^{55} +(-2.37198 - 1.54068i) q^{56} +(-3.60616 + 6.02249i) q^{57} +(-0.257598 + 0.377129i) q^{58} +(-1.37336 + 0.499862i) q^{59} +(11.4968 + 1.94091i) q^{60} +(-2.54518 - 14.4345i) q^{61} +(-0.332884 - 3.35581i) q^{62} +(-1.11531 + 2.78497i) q^{63} +(0.556651 + 7.98061i) q^{64} +(2.63296 - 7.23399i) q^{65} +(2.75577 + 5.97703i) q^{66} +(8.59298 - 10.2407i) q^{67} +(9.44406 - 0.219260i) q^{68} +(-1.77052 - 5.11655i) q^{69} +(3.32651 - 3.40463i) q^{70} +(-1.13411 + 1.96434i) q^{71} +(8.18960 - 2.22048i) q^{72} +(-7.35814 - 12.7447i) q^{73} +(3.53992 + 0.904619i) q^{74} +(-3.91258 + 10.2394i) q^{75} +(3.88875 - 7.11178i) q^{76} +(2.64616 + 0.466589i) q^{77} +(-0.464180 - 5.58321i) q^{78} +(0.624986 + 0.744830i) q^{79} +(-13.3529 - 1.72003i) q^{80} +(-3.99472 - 8.06488i) q^{81} +(-10.1601 - 4.59495i) q^{82} +(6.80175 - 5.70735i) q^{83} +(1.16104 - 3.26374i) q^{84} +(-2.76060 + 15.6561i) q^{85} +(15.4321 + 1.16983i) q^{86} +(-0.522506 - 0.199656i) q^{87} +(-3.44970 - 6.77189i) q^{88} +(-13.1141 + 7.57142i) q^{89} +(0.956359 + 14.2478i) q^{90} +(-1.98077 - 1.14360i) q^{91} +(2.27403 + 5.82357i) q^{92} +(3.90311 - 1.35062i) q^{93} +(10.4022 - 4.99840i) q^{94} +(10.4495 + 8.76813i) q^{95} +(-9.34897 + 2.93203i) q^{96} +(-6.09370 - 2.21792i) q^{97} +(-0.824550 - 1.14896i) q^{98} +(-6.33691 + 4.98221i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$

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 $

$2$	−0.381855	−	1.36169i	−0.270012	−	0.962857i
$2$	−0.381855	−	1.36169i	−0.270012	−	0.962857i
$3$	1.51360	−	0.842029i	0.873878	−	0.486146i
$3$	1.51360	−	0.842029i	0.873878	−	0.486146i
$4$	−1.70837	+	1.03993i	−0.854187	+	0.519966i
$5$	−1.15117	−	3.16281i	−0.514819	−	1.41445i	−0.876160	−	0.482020i	$-0.839903\pi$
$5$	−1.15117	−	3.16281i	−0.514819	−	1.41445i	0.361341	−	0.932434i	$-0.382319\pi$
$6$	−1.72455	−	1.73951i	−0.704046	−	0.710154i
$7$	−0.984808	+	0.173648i	−0.372222	+	0.0656328i
$7$	−0.984808	+	0.173648i	−0.372222	+	0.0656328i
$8$	2.06841	+	1.92916i	0.731294	+	0.682063i
$9$	1.58197	−	2.54899i	0.527325	−	0.849664i
$10$	−3.86718	+	2.77527i	−1.22291	+	0.877617i
$11$	−2.52494	−	0.919002i	−0.761297	−	0.277089i	−0.0679456	−	0.997689i	$-0.521644\pi$
$11$	−2.52494	−	0.919002i	−0.761297	−	0.277089i	−0.693351	+	0.720600i	$0.743867\pi$
$12$	−1.71014	+	3.01254i	−0.493676	+	0.869646i
$13$	1.75210	+	1.47018i	0.485944	+	0.407756i	0.852570	−	0.522613i	$-0.175043\pi$
$13$	1.75210	+	1.47018i	0.485944	+	0.407756i	−0.366626	+	0.930368i	$0.619487\pi$
$14$	0.612508	+	1.27469i	0.163700	+	0.340675i
$15$	−4.40559	−	3.81792i	−1.13752	−	0.985782i
$16$	1.83708	−	3.55319i	0.459270	−	0.888297i
$17$	−4.09050	−	2.36165i	−0.992092	−	0.572784i	−0.0861929	−	0.996278i	$-0.527470\pi$
$17$	−4.09050	−	2.36165i	−0.992092	−	0.572784i	−0.905899	+	0.423494i	$0.860803\pi$
$18$	−4.07501	−	1.18081i	−0.960489	−	0.278319i
$19$	−3.50980	+	2.02638i	−0.805204	+	0.464885i	−0.845287	−	0.534312i	$-0.820571\pi$
$19$	−3.50980	+	2.02638i	−0.805204	+	0.464885i	0.0400839	+	0.999196i	$0.487237\pi$
$20$	5.25574	+	4.20613i	1.17522	+	0.940519i
$21$	−1.34439	+	1.09207i	−0.293370	+	0.238309i
$22$	−0.287232	+	3.78909i	−0.0612380	+	0.807838i
$23$	0.542808	−	3.07842i	0.113183	−	0.641894i	−0.874450	−	0.485115i	$-0.838778\pi$
$23$	0.542808	−	3.07842i	0.113183	−	0.641894i	0.987634	−	0.156779i	$-0.0501111\pi$
$24$	4.75516	+	1.17832i	0.970643	+	0.240524i
$25$	−4.84798	+	4.06793i	−0.969595	+	0.813587i
$26$	1.33288	−	2.94720i	0.261399	−	0.577994i
$27$	0.248152	−	5.19022i	0.0477568	−	0.998859i
$28$	1.50184	−	1.32079i	0.283821	−	0.249606i
$29$	−0.207583	−	0.247388i	−0.0385472	−	0.0459388i	0.746426	−	0.665468i	$-0.231768\pi$
$29$	−0.207583	−	0.247388i	−0.0385472	−	0.0459388i	−0.784974	+	0.619529i	$0.787324\pi$
$30$	−3.51651	+	7.45692i	−0.642023	+	1.36144i
$31$	2.34834	+	0.414075i	0.421774	+	0.0743701i	0.380507	−	0.924778i	$-0.375749\pi$
$31$	2.34834	+	0.414075i	0.421774	+	0.0743701i	0.0412669	+	0.999148i	$0.486861\pi$
$32$	−5.53982	−	1.14473i	−0.979311	−	0.202361i
$33$	−4.59557	+	0.735068i	−0.799986	+	0.127959i
$34$	−1.65385	+	6.47178i	−0.283633	+	1.10990i
$35$	1.68290	+	2.91486i	0.284462	+	0.492702i
$36$	−0.0518239	+	5.99978i	−0.00863732	+	0.999963i
$37$	−1.29177	+	2.23741i	−0.212366	+	0.367829i	−0.952455	−	0.304681i	$-0.901450\pi$
$37$	−1.29177	+	2.23741i	−0.212366	+	0.367829i	0.740089	+	0.672509i	$0.234784\pi$
$38$	4.09953	+	4.00546i	0.665032	+	0.649771i
$39$	3.88991	+	0.749955i	0.622884	+	0.120089i
$40$	3.72049	−	8.76280i	0.588262	−	1.38552i
$41$	5.06829	−	6.04015i	0.791534	−	0.943313i	−0.207859	−	0.978159i	$-0.566649\pi$
$41$	5.06829	−	6.04015i	0.791534	−	0.943313i	0.999393	+	0.0348456i	$0.0110939\pi$
$42$	2.00042	+	1.41362i	0.308671	+	0.218127i
$43$	−3.74287	+	10.2835i	−0.570782	+	1.56821i	0.232490	+	0.972599i	$0.425313\pi$
$43$	−3.74287	+	10.2835i	−0.570782	+	1.56821i	−0.803272	+	0.595613i	$0.796909\pi$
$44$	5.26924	−	1.05576i	0.794367	−	0.159163i
$45$	−9.88311	−	2.06917i	−1.47329	−	0.308453i
$46$	−4.39911	+	0.436375i	−0.648613	+	0.0643399i
$47$	1.41707	+	8.03658i	0.206700	+	1.17226i	0.894742	+	0.446584i	$0.147360\pi$
$47$	1.41707	+	8.03658i	0.206700	+	1.17226i	−0.688041	+	0.725671i	$0.741529\pi$
$48$	−0.211278	−	6.92498i	−0.0304954	−	0.999535i
$49$	0.939693	−	0.342020i	0.134242	−	0.0488600i
$50$	7.39047	+	5.04806i	1.04517	+	0.713903i
$51$	−8.17996	−	0.130277i	−1.14542	−	0.0182424i
$52$	−4.52213	−	0.689561i	−0.627106	−	0.0956249i
$53$		−	2.58322i		−	0.354833i	−0.984136	−	0.177417i	$-0.943226\pi$
$53$		−	2.58322i		−	0.354833i	0.984136	−	0.177417i	$-0.0567740\pi$
$54$	−7.16221	+	1.64401i	−0.974653	+	0.223721i
$55$			9.04383i			1.21947i
$56$	−2.37198	−	1.54068i	−0.316970	−	0.205882i
$57$	−3.60616	+	6.02249i	−0.477648	+	0.797699i
$58$	−0.257598	+	0.377129i	−0.0338243	+	0.0495195i
$59$	−1.37336	+	0.499862i	−0.178796	+	0.0650764i	−0.429867	−	0.902892i	$-0.641440\pi$
$59$	−1.37336	+	0.499862i	−0.178796	+	0.0650764i	0.251071	+	0.967969i	$0.419217\pi$
$60$	11.4968	+	1.94091i	1.48423	+	0.250571i
$61$	−2.54518	−	14.4345i	−0.325877	−	1.84814i	−0.503437	−	0.864032i	$-0.667931\pi$
$61$	−2.54518	−	14.4345i	−0.325877	−	1.84814i	0.177559	−	0.984110i	$-0.443180\pi$
$62$	−0.332884	−	3.35581i	−0.0422763	−	0.426189i
$63$	−1.11531	+	2.78497i	−0.140516	+	0.350874i
$64$	0.556651	+	7.98061i	0.0695814	+	0.997576i
$65$	2.63296	−	7.23399i	0.326578	−	0.897266i
$66$	2.75577	+	5.97703i	0.339212	+	0.735722i
$67$	8.59298	−	10.2407i	1.04980	−	1.25110i	0.0827351	−	0.996572i	$-0.473634\pi$
$67$	8.59298	−	10.2407i	1.04980	−	1.25110i	0.967065	−	0.254531i	$-0.0819211\pi$
$68$	9.44406	−	0.219260i	1.14526	−	0.0265892i
$69$	−1.77052	−	5.11655i	−0.213146	−	0.615961i
$70$	3.32651	−	3.40463i	0.397593	−	0.406931i
$71$	−1.13411	+	1.96434i	−0.134594	+	0.233124i	−0.925442	−	0.378888i	$-0.876306\pi$
$71$	−1.13411	+	1.96434i	−0.134594	+	0.233124i	0.790848	+	0.612013i	$0.209640\pi$
$72$	8.18960	−	2.22048i	0.965153	−	0.261686i
$73$	−7.35814	−	12.7447i	−0.861205	−	1.49165i	−0.870766	−	0.491697i	$-0.836377\pi$
$73$	−7.35814	−	12.7447i	−0.861205	−	1.49165i	0.00956070	−	0.999954i	$-0.496957\pi$
$74$	3.53992	+	0.904619i	0.411508	+	0.105160i
$75$	−3.91258	+	10.2394i	−0.451786	+	1.18234i
$76$	3.88875	−	7.11178i	0.446070	−	0.815777i
$77$	2.64616	+	0.466589i	0.301558	+	0.0531728i
$78$	−0.464180	−	5.58321i	−0.0525580	−	0.632174i
$79$	0.624986	+	0.744830i	0.0703165	+	0.0837999i	0.800056	−	0.599925i	$-0.204803\pi$
$79$	0.624986	+	0.744830i	0.0703165	+	0.0837999i	−0.729739	+	0.683725i	$0.760359\pi$
$80$	−13.3529	−	1.72003i	−1.49289	−	0.192305i
$81$	−3.99472	−	8.06488i	−0.443857	−	0.896097i
$82$	−10.1601	−	4.59495i	−1.12200	−	0.507428i
$83$	6.80175	−	5.70735i	0.746589	−	0.626463i	−0.188009	−	0.982167i	$-0.560203\pi$
$83$	6.80175	−	5.70735i	0.746589	−	0.626463i	0.934599	+	0.355704i	$0.115759\pi$
$84$	1.16104	−	3.26374i	0.126680	−	0.356103i
$85$	−2.76060	+	15.6561i	−0.299429	+	1.69815i
$86$	15.4321	+	1.16983i	1.66408	+	0.126146i
$87$	−0.522506	−	0.199656i	−0.0560185	−	0.0214053i
$88$	−3.44970	−	6.77189i	−0.367740	−	0.721886i
$89$	−13.1141	+	7.57142i	−1.39009	+	0.802569i	−0.993325	−	0.115351i	$-0.963201\pi$
$89$	−13.1141	+	7.57142i	−1.39009	+	0.802569i	−0.396765	+	0.917920i	$0.629867\pi$
$90$	0.956359	+	14.2478i	0.100809	+	1.50185i
$91$	−1.98077	−	1.14360i	−0.207641	−	0.119882i
$92$	2.27403	+	5.82357i	0.237084	+	0.607149i
$93$	3.90311	−	1.35062i	0.404734	−	0.140053i
$94$	10.4022	−	4.99840i	1.07290	−	0.515546i
$95$	10.4495	+	8.76813i	1.07209	+	0.899592i
$96$	−9.34897	+	2.93203i	−0.954175	+	0.299249i
$97$	−6.09370	−	2.21792i	−0.618721	−	0.225196i	0.0135937	−	0.999908i	$-0.495673\pi$
$97$	−6.09370	−	2.21792i	−0.618721	−	0.225196i	−0.632315	+	0.774712i	$0.717895\pi$
$98$	−0.824550	−	1.14896i	−0.0832921	−	0.116063i
$99$	−6.33691	+	4.98221i	−0.636884	+	0.500731i
$100$	4.05178	−	11.9911i	0.405178	−	1.19911i
$101$	16.4608	−	2.90248i	1.63791	−	0.288807i	0.722511	−	0.691359i	$-0.242988\pi$
$101$	16.4608	−	2.90248i	1.63791	−	0.288807i	0.915397	+	0.402552i	$0.131877\pi$
$102$	2.94616	+	11.1883i	0.291713	+	1.10780i
$103$	0.266640	+	0.732588i	0.0262728	+	0.0721840i	0.952136	−	0.305676i	$-0.0988824\pi$
$103$	0.266640	+	0.732588i	0.0262728	+	0.0721840i	−0.925863	+	0.377860i	$0.876660\pi$
$104$	0.787831	+	6.42103i	0.0772532	+	0.629634i
$105$	5.00164	+	2.99489i	0.488110	+	0.292272i
$106$	−3.51754	+	0.986417i	−0.341654	+	0.0958093i
$107$	−0.133882			−0.0129429			−0.00647145	−	0.999979i	$-0.502060\pi$
$107$	−0.133882			−0.0129429			−0.00647145	+	0.999979i	$0.502060\pi$
$108$	4.97355	+	9.12490i	0.478580	+	0.878044i
$109$	14.5904			1.39751			0.698753	−	0.715363i	$-0.253739\pi$
$109$	14.5904			1.39751			0.698753	+	0.715363i	$0.253739\pi$
$110$	12.3149	−	3.45343i	1.17418	−	0.329272i
$111$	−0.0712586	+	4.47426i	−0.00676357	+	0.424678i
$112$	−1.19217	+	3.81821i	−0.112649	+	0.360787i
$113$	1.17728	+	3.23456i	0.110750	+	0.304282i	0.982669	−	0.185367i	$-0.0593473\pi$
$113$	1.17728	+	3.23456i	0.110750	+	0.304282i	−0.871920	+	0.489649i	$0.837125\pi$
$114$	9.57777	+	2.61074i	0.897040	+	0.244518i
$115$	−10.3613	+	1.82698i	−0.966198	+	0.170367i
$116$	0.611896	+	0.206759i	0.0568131	+	0.0191971i
$117$	6.51926	−	2.14029i	0.602706	−	0.197870i
$118$	1.20508	+	1.67921i	0.110936	+	0.154584i
$119$	4.43845	+	1.61546i	0.406872	+	0.148089i
$120$	−1.74719	−	16.3961i	−0.159496	−	1.49676i
$121$	−2.89575	−	2.42982i	−0.263250	−	0.220893i
$122$	−18.6833	+	8.97760i	−1.69151	+	0.812794i
$123$	2.58538	−	13.4100i	0.233116	−	1.20914i
$124$	−4.44245	+	1.73472i	−0.398944	+	0.155782i
$125$	3.87264	+	2.23587i	0.346379	+	0.199982i
$126$	4.21815	+	0.455249i	0.375782	+	0.0405568i
$127$	−1.04534	+	0.603529i	−0.0927592	+	0.0535546i	−0.545662	−	0.838005i	$-0.683722\pi$
$127$	−1.04534	+	0.603529i	−0.0927592	+	0.0535546i	0.452903	+	0.891560i	$0.350388\pi$
$128$	10.6545	−	3.80542i	0.941735	−	0.336355i
$129$	2.99375	+	18.7166i	0.263585	+	1.64791i
$130$	−10.8558	−	0.822924i	−0.952118	−	0.0721752i
$131$	2.39897	−	13.6053i	0.209599	−	1.18870i	−0.680437	−	0.732807i	$-0.738210\pi$
$131$	2.39897	−	13.6053i	0.209599	−	1.18870i	0.890036	−	0.455890i	$-0.150679\pi$
$132$	7.08653	−	6.03486i	0.616804	−	0.525267i
$133$	3.10460	−	2.60507i	0.269203	−	0.225888i
$134$	−17.2259	−	7.79047i	−1.48809	−	0.672994i
$135$	−16.7014	+	5.18997i	−1.43743	+	0.446682i
$136$	−3.90482	−	12.7761i	−0.334836	−	1.09554i
$137$	−12.8892	−	15.3607i	−1.10119	−	1.31235i	−0.945890	−	0.324486i	$-0.894809\pi$
$137$	−12.8892	−	15.3607i	−1.10119	−	1.31235i	−0.155304	−	0.987867i	$-0.549636\pi$
$138$	−6.29105	+	4.36467i	−0.535530	+	0.371546i
$139$	11.5414	+	2.03506i	0.978927	+	0.172611i	0.640145	−	0.768254i	$-0.278874\pi$
$139$	11.5414	+	2.03506i	0.978927	+	0.172611i	0.338781	+	0.940865i	$0.389985\pi$
$140$	−5.90628	−	3.22958i	−0.499172	−	0.272949i
$141$	8.91191	+	10.9710i	0.750518	+	0.923922i
$142$	3.10788	+	0.794211i	0.260807	+	0.0666487i
$143$	−3.07283	−	5.32230i	−0.256963	−	0.445073i
$144$	−6.15083	−	10.3038i	−0.512569	−	0.858646i
$145$	−0.543478	+	0.941332i	−0.0451334	+	0.0781734i
$146$	−14.5445	+	14.8861i	−1.20371	+	1.23198i
$147$	1.13433	−	1.30893i	0.0935578	−	0.107959i
$148$	−0.119931	−	5.16570i	−0.00985823	−	0.424618i
$149$	−5.39206	+	6.42600i	−0.441735	+	0.526439i	−0.940270	−	0.340431i	$-0.889427\pi$
$149$	−5.39206	+	6.42600i	−0.441735	+	0.526439i	0.498535	+	0.866870i	$0.333872\pi$
$150$	15.4368	+	1.41775i	1.26041	+	0.115759i
$151$	−5.18420	+	14.2435i	−0.421884	+	1.15912i	0.528743	+	0.848782i	$0.322663\pi$
$151$	−5.18420	+	14.2435i	−0.421884	+	1.15912i	−0.950627	+	0.310335i	$0.899559\pi$
$152$	−11.1689	−	2.57959i	−0.905921	−	0.209232i
$153$	−12.4909	+	6.69058i	−1.00983	+	0.540901i
$154$	−0.375101	−	3.78141i	−0.0302265	−	0.304714i
$155$	−1.39369	−	7.90403i	−0.111944	−	0.634867i
$156$	−7.42533	+	2.76404i	−0.594502	+	0.221301i
$157$	21.2677	−	7.74082i	1.69735	−	0.617785i	0.701830	−	0.712344i	$-0.252366\pi$
$157$	21.2677	−	7.74082i	1.69735	−	0.617785i	0.995519	+	0.0945593i	$0.0301442\pi$
$158$	0.775570	−	1.13545i	0.0617010	−	0.0903317i
$159$	−2.17515	−	3.90997i	−0.172501	−	0.310081i
$160$	2.75672	+	18.8392i	0.217938	+	1.48937i
$161$			3.12591i			0.246356i
$162$	−9.45642	+	8.51916i	−0.742967	+	0.669328i
$163$		−	18.2538i		−	1.42975i	−0.699254	−	0.714874i	$-0.746484\pi$
$163$		−	18.2538i		−	1.42975i	0.699254	−	0.714874i	$-0.253516\pi$
$164$	−2.37718	+	15.5895i	−0.185627	+	1.21734i
$165$	7.61517	+	13.6887i	0.592840	+	1.06567i
$166$	−10.3689	−	7.08247i	−0.804782	−	0.549706i
$167$	18.7525	−	6.82534i	1.45111	−	0.528160i	0.508208	−	0.861234i	$-0.330308\pi$
$167$	18.7525	−	6.82534i	1.45111	−	0.528160i	0.942901	+	0.333074i	$0.108086\pi$
$168$	−4.88753	−	0.334695i	−0.377081	−	0.0258223i
$169$	−1.34902	−	7.65069i	−0.103771	−	0.588515i
$170$	22.3729	−	2.21931i	1.71592	−	0.170213i
$171$	−0.387176	+	12.1521i	−0.0296081	+	0.929297i
$172$	−4.29987	−	21.4603i	−0.327862	−	1.63633i
$173$	7.49678	−	20.5972i	0.569970	−	1.56598i	−0.234582	−	0.972096i	$-0.575372\pi$
$173$	7.49678	−	20.5972i	0.569970	−	1.56598i	0.804552	−	0.593882i	$-0.202405\pi$
$174$	−0.0723466	+	0.787728i	−0.00548458	+	0.0597175i
$175$	4.06793	−	4.84798i	0.307507	−	0.366473i
$176$	−7.90390	+	7.28329i	−0.595779	+	0.548999i
$177$	−1.65782	+	1.91300i	−0.124609	+	0.143790i
$178$	15.3176	+	14.9661i	1.14810	+	1.12175i
$179$	−7.09759	+	12.2934i	−0.530499	+	0.918851i	0.468868	+	0.883268i	$0.344662\pi$
$179$	−7.09759	+	12.2934i	−0.530499	+	0.918851i	−0.999367	+	0.0355829i	$0.988671\pi$
$180$	19.0358	−	6.74285i	1.41885	−	0.502583i
$181$	2.42892	+	4.20701i	0.180540	+	0.312704i	0.942065	−	0.335432i	$-0.108882\pi$
$181$	2.42892	+	4.20701i	0.180540	+	0.312704i	−0.761525	+	0.648136i	$0.775549\pi$
$182$	−0.800855	+	3.13388i	−0.0593633	+	0.232299i
$183$	−16.0066	−	19.7049i	−1.18324	−	1.45663i
$184$	7.06152	−	5.32027i	0.520582	−	0.392215i
$185$	8.56358	+	1.50999i	0.629607	+	0.111017i
$186$	−3.32955	−	4.79906i	−0.244134	−	0.351884i
$187$	8.15789	+	9.72219i	0.596564	+	0.710957i
$188$	−10.7784	−	12.2558i	−0.786094	−	0.893848i
$189$	0.656891	+	5.15446i	0.0477818	+	0.374932i
$190$	7.94926	−	17.5770i	0.576700	−	1.27517i
$191$	3.58450	−	3.00775i	0.259365	−	0.217633i	−0.503827	−	0.863804i	$-0.668075\pi$
$191$	3.58450	−	3.00775i	0.259365	−	0.217633i	0.763193	+	0.646171i	$0.223631\pi$
$192$	7.56245	+	11.6107i	0.545773	+	0.837933i
$193$	−2.64220	+	14.9847i	−0.190190	+	1.07862i	0.728915	+	0.684605i	$0.240025\pi$
$193$	−2.64220	+	14.9847i	−0.190190	+	1.07862i	−0.919104	+	0.394014i	$0.871086\pi$
$194$	−0.693207	+	9.14462i	−0.0497694	+	0.656546i
$195$	−2.10598	−	13.1664i	−0.150813	−	0.942865i
$196$	−1.24967	+	1.56151i	−0.0892620	+	0.111537i
$197$	10.5214	−	6.07451i	0.749616	−	0.432791i	−0.0759393	−	0.997112i	$-0.524196\pi$
$197$	10.5214	−	6.07451i	0.749616	−	0.432791i	0.825555	+	0.564322i	$0.190862\pi$
$198$	9.20398	+	6.72640i	0.654098	+	0.478024i
$199$	−10.7197	−	6.18904i	−0.759902	−	0.438730i	0.0693586	−	0.997592i	$-0.477905\pi$
$199$	−10.7197	−	6.18904i	−0.759902	−	0.438730i	−0.829261	+	0.558862i	$0.811238\pi$
$200$	−17.8753	−	0.938379i	−1.26398	−	0.0663534i
$201$	4.38336	−	22.7359i	0.309178	−	1.60367i
$202$	−10.2379	−	21.3061i	−0.720335	−	1.49909i
$203$	0.247388	+	0.207583i	0.0173632	+	0.0145695i
$204$	14.1099	−	8.28404i	0.987891	−	0.579999i
$205$	−24.9383	−	9.07681i	−1.74177	−	0.633952i
$206$	0.895736	−	0.642822i	0.0624089	−	0.0447875i
$207$	−6.98815	−	6.25359i	−0.485710	−	0.434654i
$208$	8.44258	−	3.52468i	0.585388	−	0.244392i
$209$	10.7243	−	1.89098i	0.741814	−	0.130802i
$210$	2.16820	−	7.95427i	0.149620	−	0.548897i
$211$	−5.78462	−	15.8931i	−0.398230	−	1.09413i	−0.963146	−	0.268979i	$-0.913314\pi$
$211$	−5.78462	−	15.8931i	−0.398230	−	1.09413i	0.564916	−	0.825148i	$-0.308908\pi$
$212$	2.68638	+	4.41311i	0.184501	+	0.303094i
$213$	−0.0625616	+	3.92818i	−0.00428665	+	0.269155i
$214$	0.0511236	+	0.182306i	0.00349474	+	0.0124622i
$215$	36.8333			2.51201
$216$	10.5261	−	10.2568i	0.716209	−	0.697886i
$217$	−2.38457			−0.161875
$218$	−5.57141	−	19.8675i	−0.377344	−	1.34560i
$219$	−21.8687	−	13.0946i	−1.47775	−	0.884850i
$220$	−9.40497	−	15.4502i	−0.634083	−	1.04166i
$221$	−3.69489	−	10.1516i	−0.248545	−	0.682872i
$222$	6.11975	−	1.61149i	0.410731	−	0.108156i
$223$	−8.04634	+	1.41879i	−0.538823	+	0.0950090i	−0.436435	−	0.899736i	$-0.643759\pi$
$223$	−8.04634	+	1.41879i	−0.538823	+	0.0950090i	−0.102387	+	0.994745i	$0.532648\pi$
$224$	5.65444	+	0.165355i	0.377803	+	0.0110482i
$225$	2.69976	+	18.7928i	0.179984	+	1.25285i
$226$	3.95490	−	2.83822i	0.263076	−	0.188796i
$227$	2.43696	+	0.886979i	0.161746	+	0.0588709i	0.421624	−	0.906771i	$-0.361460\pi$
$227$	2.43696	+	0.886979i	0.161746	+	0.0588709i	−0.259878	+	0.965641i	$0.583682\pi$
$228$	−0.102311	−	14.0388i	−0.00677569	−	0.929744i
$229$	12.9969	+	10.9057i	0.858858	+	0.720668i	0.961722	−	0.274028i	$-0.0883560\pi$
$229$	12.9969	+	10.9057i	0.858858	+	0.720668i	−0.102863	+	0.994695i	$0.532800\pi$
$230$	6.44429	+	13.4112i	0.424924	+	0.884309i
$231$	4.39811	−	1.52191i	0.289375	−	0.100135i
$232$	0.0478846	−	0.912162i	0.00314378	−	0.0598864i
$233$	2.36114	+	1.36320i	0.154683	+	0.0893064i	0.575344	−	0.817912i	$-0.304868\pi$
$233$	2.36114	+	1.36320i	0.154683	+	0.0893064i	−0.420660	+	0.907218i	$0.638202\pi$
$234$	−5.40381	−	8.05990i	−0.353258	−	0.526892i
$235$	23.7869	−	13.7334i	1.55169	−	0.895867i
$236$	1.82639	−	2.28215i	0.118888	−	0.148555i
$237$	1.57315	+	0.601118i	0.102187	+	0.0390468i
$238$	0.504910	−	6.66065i	0.0327284	−	0.431746i
$239$	0.736748	−	4.17831i	0.0476563	−	0.270272i	−0.951664	−	0.307142i	$-0.900627\pi$
$239$	0.736748	−	4.17831i	0.0476563	−	0.270272i	0.999320	+	0.0368695i	$0.0117386\pi$
$240$	−21.6592	+	8.64006i	−1.39810	+	0.557714i
$241$	9.96540	−	8.36197i	0.641928	−	0.538642i	−0.262682	−	0.964883i	$-0.584607\pi$
$241$	9.96540	−	8.36197i	0.641928	−	0.538642i	0.904610	+	0.426241i	$0.140162\pi$
$242$	−2.20290	+	4.87094i	−0.141608	+	0.313116i
$243$	−12.8373	−	8.84333i	−0.823511	−	0.567300i
$244$	19.3590	+	22.0126i	1.23933	+	1.40921i
$245$	−2.16349	−	2.57835i	−0.138220	−	0.164725i
$246$	−19.2475	+	1.60021i	−1.22717	+	0.102025i
$247$	−9.12867	−	1.60963i	−0.580843	−	0.102418i
$248$	4.05851	+	5.38681i	0.257716	+	0.342063i
$249$	5.48938	−	14.3659i	0.347876	−	0.910403i
$250$	1.56576	−	6.12709i	0.0990276	−	0.387511i
$251$	−10.3433	−	17.9151i	−0.652864	−	1.13079i	−0.982425	−	0.186660i	$-0.940234\pi$
$251$	−10.3433	−	17.9151i	−0.652864	−	1.13079i	0.329560	−	0.944135i	$-0.393100\pi$
$252$	−0.990814	−	5.91763i	−0.0624154	−	0.372775i
$253$	−4.19963	+	7.27397i	−0.264028	+	0.457310i
$254$	1.22099	+	1.19297i	0.0766115	+	0.0748535i
$255$	9.00448	+	26.0217i	0.563883	+	1.62954i
$256$	−9.25026	−	13.0550i	−0.578141	−	0.815937i
$257$	−7.31745	+	8.72060i	−0.456450	+	0.543976i	−0.944358	−	0.328919i	$-0.893316\pi$
$257$	−7.31745	+	8.72060i	−0.456450	+	0.543976i	0.487908	+	0.872895i	$0.337760\pi$
$258$	24.3430	−	11.2236i	1.51553	−	0.698750i
$259$	0.883624	−	2.42774i	0.0549057	−	0.150852i
$260$	3.02478	+	15.0964i	0.187589	+	0.936242i
$261$	−0.958981	+	0.137766i	−0.0593594	+	0.00852753i
$262$	−19.4421	+	1.92859i	−1.20114	+	0.119148i
$263$	0.349965	+	1.98475i	0.0215797	+	0.122385i	0.993695	−	0.112120i	$-0.0357642\pi$
$263$	0.349965	+	1.98475i	0.0215797	+	0.122385i	−0.972115	+	0.234505i	$0.924653\pi$
$264$	−10.9236	−	7.34519i	−0.672301	−	0.452065i
$265$	−8.17026	+	2.97373i	−0.501895	+	0.182675i
$266$	−4.73279	−	3.23273i	−0.290186	−	0.198211i
$267$	−13.4741	+	22.5025i	−0.824603	+	1.37713i
$268$	−4.03037	+	26.4311i	−0.246194	+	1.61454i
$269$		−	8.45381i		−	0.515438i	−0.966220	−	0.257719i	$-0.917029\pi$
$269$		−	8.45381i		−	0.515438i	0.966220	−	0.257719i	$-0.0829708\pi$
$270$	13.4446	+	20.7602i	0.818213	+	1.26343i
$271$			25.5448i			1.55174i	0.630895	+	0.775868i	$0.282688\pi$
$271$			25.5448i			1.55174i	−0.630895	+	0.775868i	$0.717312\pi$
$272$	−15.9060	+	10.1958i	−0.964441	+	0.618209i
$273$	−3.96104	−	0.0630849i	−0.239733	−	0.00381807i
$274$	−15.9946	+	23.4165i	−0.966272	+	1.41464i
$275$	15.9793	−	5.81598i	0.963586	−	0.350717i
$276$	8.34558	+	6.89976i	0.502345	+	0.415317i
$277$	2.61596	+	14.8359i	0.157178	+	0.891400i	0.956768	+	0.290854i	$0.0939393\pi$
$277$	2.61596	+	14.8359i	0.157178	+	0.891400i	−0.799590	+	0.600547i	$0.794950\pi$
$278$	−1.63602	−	16.4928i	−0.0981222	−	0.989173i
$279$	4.77048	−	5.33084i	0.285601	−	0.319149i
$280$	−2.14233	+	9.27573i	−0.128029	+	0.554331i
$281$	−5.49781	+	15.1051i	−0.327972	+	0.901096i	0.660653	+	0.750692i	$0.270280\pi$
$281$	−5.49781	+	15.1051i	−0.327972	+	0.901096i	−0.988625	+	0.150404i	$0.951943\pi$
$282$	11.5359	−	16.3245i	0.686955	−	0.972111i
$283$	−2.45975	+	2.93141i	−0.146217	+	0.174254i	−0.834182	−	0.551489i	$-0.814060\pi$
$283$	−2.45975	+	2.93141i	−0.146217	+	0.174254i	0.687965	+	0.725744i	$0.258504\pi$
$284$	−0.105293	−	4.53523i	−0.00624800	−	0.269116i
$285$	23.1993	+	4.47271i	1.37421	+	0.264940i
$286$	−6.07392	+	6.21658i	−0.359159	+	0.367594i
$287$	−3.94243	+	6.82849i	−0.232714	+	0.403073i
$288$	−11.6817	+	12.3100i	−0.688354	+	0.725375i
$289$	2.65479	+	4.59823i	0.156164	+	0.270484i
$290$	1.48933	+	0.380594i	0.0874564	+	0.0223493i
$291$	−11.0910	+	1.77402i	−0.650165	+	0.103995i
$292$	25.8241	+	14.1207i	1.51124	+	0.826352i
$293$	2.66626	+	0.470134i	0.155765	+	0.0274655i	0.250987	−	0.967991i	$-0.419245\pi$
$293$	2.66626	+	0.470134i	0.155765	+	0.0274655i	−0.0952219	+	0.995456i	$0.530356\pi$
$294$	−2.21550	−	1.04478i	−0.129211	−	0.0609326i
$295$	3.16194	+	3.76825i	0.184095	+	0.219396i
$296$	−6.98826	+	2.13585i	−0.406184	+	0.124144i
$297$	−5.39639	+	12.8769i	−0.313130	+	0.747196i
$298$	10.8092	+	4.88848i	0.626159	+	0.283182i
$299$	5.47689	−	4.59566i	0.316737	−	0.265774i
$300$	−3.96410	−	21.5615i	−0.228867	−	1.24485i
$301$	1.90030	−	10.7772i	0.109532	−	0.621185i
$302$	21.3747	+	1.62031i	1.22998	+	0.0932383i
$303$	22.4711	−	18.2536i	1.29093	−	1.04864i
$304$	0.752331	+	16.1936i	0.0431491	+	0.928767i
$305$	−42.7235	+	24.6665i	−2.44634	+	1.41240i
$306$	13.8802	+	14.4538i	0.793476	+	0.826271i
$307$	28.1937	+	16.2776i	1.60910	+	0.929013i	0.989573	+	0.144035i	$0.0460079\pi$
$307$	28.1937	+	16.2776i	1.60910	+	0.929013i	0.619525	+	0.784977i	$0.287325\pi$
$308$	−5.00585	+	1.95472i	−0.285235	+	0.111380i
$309$	1.02045	+	0.884326i	0.0580512	+	0.0503076i
$310$	−10.2306	+	4.91596i	−0.581060	+	0.279208i
$311$	20.0479	+	16.8222i	1.13681	+	0.953899i	0.999330	−	0.0366057i	$-0.0116545\pi$
$311$	20.0479	+	16.8222i	1.13681	+	0.953899i	0.137482	+	0.990504i	$0.456099\pi$
$312$	6.59915	+	9.05549i	0.373603	+	0.512666i
$313$	−1.31505	−	0.478638i	−0.0743309	−	0.0270542i	0.304587	−	0.952484i	$-0.401482\pi$
$313$	−1.31505	−	0.478638i	−0.0743309	−	0.0270542i	−0.378918	+	0.925430i	$0.623704\pi$
$314$	−18.6617	−	26.0041i	−1.05314	−	1.46750i
$315$	10.0923	+	0.321547i	0.568635	+	0.0181171i
$316$	−1.84228	−	0.622504i	−0.103637	−	0.0350186i
$317$	−16.0081	+	2.82267i	−0.899106	+	0.158537i	−0.604053	−	0.796944i	$-0.706448\pi$
$317$	−16.0081	+	2.82267i	−0.899106	+	0.158537i	−0.295053	+	0.955481i	$0.595337\pi$
$318$	−4.49356	+	4.45491i	−0.251986	+	0.249819i
$319$	0.296784	+	0.815408i	0.0166167	+	0.0456541i
$320$	24.6004	−	10.9476i	1.37520	−	0.611991i
$321$	−0.202644	+	0.112733i	−0.0113105	+	0.00629213i
$322$	4.25650	−	1.19364i	0.237205	−	0.0665191i
$323$	19.1425			1.06511
$324$	15.2114	+	9.62359i	0.845078	+	0.534644i
$325$	−14.4747			−0.802914
$326$	−24.8559	+	6.97030i	−1.37664	+	0.386049i
$327$	22.0840	−	12.2855i	1.22125	−	0.679391i
$328$	22.1358	−	2.71596i	1.22224	−	0.149964i
$329$	−2.79107	−	7.66841i	−0.153877	−	0.422773i
$330$	15.7319	−	15.5966i	0.866011	−	0.858563i
$331$	−12.7600	+	2.24994i	−0.701355	+	0.123668i	−0.512944	−	0.858422i	$-0.671445\pi$
$331$	−12.7600	+	2.24994i	−0.701355	+	0.123668i	−0.188412	+	0.982090i	$0.560334\pi$
$332$	−5.68468	+	16.8236i	−0.311987	+	0.923318i
$333$	3.65960	+	6.83225i	0.200545	+	0.374405i
$334$	−16.4547	−	22.9287i	−0.900360	−	1.25460i
$335$	−42.2815	−	15.3892i	−2.31008	−	0.840801i
$336$	1.41058	+	6.78309i	0.0769534	+	0.370048i
$337$	14.7482	+	12.3752i	0.803384	+	0.674119i	0.949019	−	0.315219i	$-0.102078\pi$
$337$	14.7482	+	12.3752i	0.803384	+	0.674119i	−0.145635	+	0.989338i	$0.546523\pi$
$338$	−9.90270	+	4.75840i	−0.538636	+	0.258823i
$339$	4.50553	+	3.90452i	0.244707	+	0.212065i
$340$	−11.5652	−	29.6174i	−0.627211	−	1.60623i
$341$	−5.54887	−	3.20364i	−0.300488	−	0.173487i
$342$	16.6952	−	4.11314i	0.902775	−	0.222413i
$343$	−0.866025	+	0.500000i	−0.0467610	+	0.0269975i
$344$	−27.5803	+	14.0498i	−1.48703	+	0.757514i
$345$	−14.1445	+	11.4899i	−0.761516	+	0.618593i
$346$	−30.9096	−	2.34310i	−1.66171	−	0.125966i
$347$	−3.30321	+	18.7334i	−0.177325	+	1.00566i	0.758100	+	0.652138i	$0.226128\pi$
$347$	−3.30321	+	18.7334i	−0.177325	+	1.00566i	−0.935425	+	0.353524i	$0.884983\pi$
$348$	1.10026	−	0.202284i	0.0589803	−	0.0108436i
$349$	−10.9659	+	9.20149i	−0.586992	+	0.492544i	−0.887235	−	0.461318i	$-0.847377\pi$
$349$	−10.9659	+	9.20149i	−0.586992	+	0.492544i	0.300243	+	0.953863i	$0.402932\pi$
$350$	−8.15478	−	3.68802i	−0.435891	−	0.197133i
$351$	8.06537	−	8.72895i	0.430498	−	0.465917i
$352$	12.9357	+	7.98146i	0.689475	+	0.425413i
$353$	8.84279	+	10.5384i	0.470654	+	0.560904i	0.948188	−	0.317709i	$-0.102914\pi$
$353$	8.84279	+	10.5384i	0.470654	+	0.560904i	−0.477534	+	0.878613i	$0.658469\pi$
$354$	3.23795	+	1.52694i	0.172095	+	0.0811559i
$355$	7.51840	+	1.32570i	0.399035	+	0.0703607i
$356$	14.5300	−	26.5726i	0.770088	−	1.40834i
$357$	8.07831	−	1.29214i	0.427550	−	0.0683872i
$358$	19.4500	+	4.97040i	1.02796	+	0.262694i
$359$	−1.26798	−	2.19621i	−0.0669216	−	0.115912i	0.830623	−	0.556835i	$-0.187984\pi$
$359$	−1.26798	−	2.19621i	−0.0669216	−	0.115912i	−0.897545	+	0.440923i	$0.854651\pi$
$360$	−16.4506	−	23.3460i	−0.867021	−	1.23044i
$361$	−1.28753	+	2.23007i	−0.0677648	+	0.117372i
$362$	4.80113	−	4.91389i	0.252342	−	0.258268i
$363$	−6.42899	−	1.23947i	−0.337434	−	0.0650555i
$364$	4.57317	−	0.106174i	0.239699	−	0.00556503i
$365$	−31.8386	+	37.9437i	−1.66651	+	1.98607i
$366$	−20.7196	+	29.3204i	−1.08303	+	1.53260i
$367$	−8.56463	+	23.5311i	−0.447070	+	1.22832i	0.487684	+	0.873020i	$0.337842\pi$
$367$	−8.56463	+	23.5311i	−0.447070	+	1.22832i	−0.934754	+	0.355295i	$0.884380\pi$
$368$	−9.94100	−	7.58400i	−0.518211	−	0.395343i
$369$	−7.37840	−	22.4744i	−0.384104	−	1.16997i
$370$	−1.21391	−	12.2375i	−0.0631083	−	0.636197i
$371$	0.448572	+	2.54398i	0.0232887	+	0.132077i
$372$	−5.26341	+	6.36634i	−0.272895	+	0.330079i
$373$	33.1271	−	12.0573i	1.71526	−	0.624302i	0.717843	−	0.696205i	$-0.245129\pi$
$373$	33.1271	−	12.0573i	1.71526	−	0.624302i	0.997412	+	0.0719028i	$0.0229072\pi$
$374$	10.1234	−	14.8209i	0.523471	−	0.766373i
$375$	7.74430	+	0.123338i	0.399914	+	0.00636916i
$376$	−12.5728	+	19.3567i	−0.648393	+	0.998246i
$377$		−	0.738633i		−	0.0380415i
$378$	6.76792	−	2.86274i	0.348104	−	0.147243i
$379$			20.0699i			1.03092i	0.856913	+	0.515461i	$0.172379\pi$
$379$			20.0699i			1.03092i	−0.856913	+	0.515461i	$0.827621\pi$
$380$	−26.9698	−	4.11252i	−1.38352	−	0.210968i
$381$	−1.07404	+	1.79371i	−0.0550249	+	0.0918946i
$382$	−5.46437	−	3.73243i	−0.279581	−	0.190968i
$383$	2.61524	−	0.951871i	0.133633	−	0.0486383i	−0.274338	−	0.961633i	$-0.588459\pi$
$383$	2.61524	−	0.951871i	0.133633	−	0.0486383i	0.407971	+	0.912995i	$0.366237\pi$
$384$	12.9224	−	14.7313i	0.659444	−	0.751753i
$385$	−1.57044	−	8.90644i	−0.0800373	−	0.453914i
$386$	21.4133	−	2.12412i	1.08991	−	0.108115i
$387$	20.2913	+	25.8087i	1.03147	+	1.31193i
$388$	12.7168	−	2.54799i	0.645598	−	0.129355i
$389$	−0.590528	+	1.62246i	−0.0299409	+	0.0822621i	−0.953762	−	0.300561i	$-0.902826\pi$
$389$	−0.590528	+	1.62246i	−0.0299409	+	0.0822621i	0.923822	+	0.382823i	$0.125048\pi$
$390$	−17.1243	+	7.89534i	−0.867123	+	0.399796i
$391$	−9.49050	+	11.3103i	−0.479955	+	0.571988i
$392$	2.60348	+	1.10538i	0.131496	+	0.0558303i
$393$	−7.82493	−	22.6129i	−0.394716	−	1.14067i
$394$	−12.2892	−	12.0072i	−0.619121	−	0.604914i
$395$	1.63629	−	2.83414i	0.0823308	−	0.142601i
$396$	5.64466	−	15.1014i	0.283655	−	0.758875i
$397$	2.03793	+	3.52980i	0.102281	+	0.177155i	0.912624	−	0.408800i	$-0.134053\pi$
$397$	2.03793	+	3.52980i	0.102281	+	0.177155i	−0.810343	+	0.585956i	$0.800719\pi$
$398$	−4.33414	+	16.9602i	−0.217251	+	0.850139i
$399$	2.50558	−	6.55720i	0.125436	−	0.328271i
$400$	5.54800	+	24.6989i	0.277400	+	1.23494i
$401$	−19.5597	−	3.44890i	−0.976765	−	0.172230i	−0.337592	−	0.941293i	$-0.609612\pi$
$401$	−19.5597	−	3.44890i	−0.976765	−	0.172230i	−0.639173	+	0.769063i	$0.720723\pi$
$402$	−32.6329	+	2.71305i	−1.62758	+	0.135315i
$403$	3.50575	+	4.17799i	0.174634	+	0.208120i
$404$	−25.1028	+	22.0766i	−1.24891	+	1.09835i
$405$	−20.9091	+	21.9186i	−1.03898	+	1.08914i
$406$	0.188197	−	0.416131i	0.00934004	−	0.0206522i
$407$	5.31783	−	4.46219i	0.263595	−	0.221183i
$408$	−16.6682	−	16.0500i	−0.825199	−	0.794591i
$409$	2.61457	−	14.8280i	0.129282	−	0.733196i	−0.849390	−	0.527766i	$-0.823030\pi$
$409$	2.61457	−	14.8280i	0.129282	−	0.733196i	0.978672	−	0.205430i	$-0.0658592\pi$
$410$	−2.83694	+	37.4242i	−0.140106	+	1.84825i
$411$	−32.4432	−	12.3969i	−1.60030	−	0.611495i
$412$	−1.21736	−	0.974246i	−0.0599751	−	0.0479976i
$413$	1.26569	−	0.730749i	0.0622807	−	0.0359578i
$414$	−5.84696	+	11.9036i	−0.287362	+	0.585031i
$415$	−25.8813	−	14.9425i	−1.27046	−	0.733501i
$416$	−8.02334	−	10.1502i	−0.393377	−	0.497656i
$417$	19.1826	−	6.63791i	0.939376	−	0.325060i
$418$	−6.67004	−	13.8810i	−0.326242	−	0.678942i
$419$	−16.3487	−	13.7182i	−0.798688	−	0.670179i	0.149191	−	0.988808i	$-0.452333\pi$
$419$	−16.3487	−	13.7182i	−0.798688	−	0.670179i	−0.947879	+	0.318629i	$0.896777\pi$
$420$	−11.6591	+	0.0849683i	−0.568908	+	0.00414603i
$421$	2.17345	+	0.791071i	0.105927	+	0.0385545i	0.394440	−	0.918922i	$-0.370939\pi$
$421$	2.17345	+	0.791071i	0.105927	+	0.0385545i	−0.288513	+	0.957476i	$0.593161\pi$
$422$	−19.4325	+	13.9457i	−0.945961	+	0.678866i
$423$	22.7269	+	9.10157i	1.10502	+	0.442534i
$424$	4.98346	−	5.34317i	0.242018	−	0.259487i
$425$	29.4377	−	5.19066i	1.42794	−	0.251784i
$426$	5.37284	−	1.41481i	0.260315	−	0.0685476i
$427$	5.01303	+	13.7732i	0.242598	+	0.666532i
$428$	0.228721	−	0.139229i	0.0110556	−	0.00672987i
$429$	−9.13257	−	5.46842i	−0.440925	−	0.264018i
$430$	−14.0650	−	50.1554i	−0.678274	−	2.41871i
$431$	−34.8902			−1.68060			−0.840300	−	0.542121i	$-0.817621\pi$
$431$	−34.8902			−1.68060			−0.840300	+	0.542121i	$0.817621\pi$
$432$	−17.9860	−	10.4166i	−0.865350	−	0.501169i
$433$	31.0582			1.49256			0.746281	−	0.665631i	$-0.231838\pi$
$433$	31.0582			1.49256			0.746281	+	0.665631i	$0.231838\pi$
$434$	0.910558	+	3.24703i	0.0437082	+	0.155862i
$435$	−0.0299802	+	1.88243i	−0.00143744	+	0.0902554i
$436$	−24.9258	+	15.1730i	−1.19373	+	0.726656i
$437$	4.33291	+	11.9046i	0.207271	+	0.569473i
$438$	−9.48004	+	34.7785i	−0.452974	+	1.66178i
$439$	22.2770	−	3.92804i	1.06322	−	0.187475i	0.385438	−	0.922734i	$-0.374051\pi$
$439$	22.2770	−	3.92804i	1.06322	−	0.187475i	0.677786	+	0.735259i	$0.262939\pi$
$440$	−17.4470	+	18.7064i	−0.831755	+	0.891791i
$441$	0.614763	−	2.93634i	0.0292744	−	0.139826i
$442$	−12.4124	+	8.90772i	−0.590398	+	0.423697i
$443$	−16.0375	−	5.83717i	−0.761964	−	0.277332i	−0.0683331	−	0.997663i	$-0.521768\pi$
$443$	−16.0375	−	5.83717i	−0.761964	−	0.277332i	−0.693631	+	0.720330i	$0.743990\pi$
$444$	−4.53119	−	7.71782i	−0.215041	−	0.366271i
$445$	39.0435	+	32.7614i	1.85084	+	1.55304i
$446$	5.00448	+	10.4148i	0.236969	+	0.493156i
$447$	−2.75054	+	14.2667i	−0.130096	+	0.674790i
$448$	−1.93401	−	7.76271i	−0.0913735	−	0.366753i
$449$	16.9257	+	9.77205i	0.798773	+	0.461172i	0.843042	−	0.537848i	$-0.180763\pi$
$449$	16.9257	+	9.77205i	0.798773	+	0.461172i	−0.0442693	+	0.999020i	$0.514096\pi$
$450$	24.5590	−	10.8524i	1.15772	−	0.511585i
$451$	−18.3480	+	10.5932i	−0.863975	+	0.498816i
$452$	−5.37496	−	4.30154i	−0.252817	−	0.202327i
$453$	4.14661	+	25.9242i	0.194825	+	1.21802i
$454$	0.277223	−	3.65706i	0.0130107	−	0.171635i
$455$	−1.33679	+	7.58129i	−0.0626695	+	0.355417i
$456$	−19.0774	+	5.50011i	−0.893381	+	0.257566i
$457$	14.4708	−	12.1424i	0.676914	−	0.567999i	−0.238189	−	0.971219i	$-0.576554\pi$
$457$	14.4708	−	12.1424i	0.676914	−	0.567999i	0.915103	+	0.403220i	$0.132109\pi$
$458$	9.88718	−	21.8621i	0.461998	−	1.02155i
$459$	−13.2726	+	20.6446i	−0.619510	+	0.963605i
$460$	15.8011	−	13.8962i	0.736729	−	0.647915i
$461$	19.7505	+	23.5377i	0.919873	+	1.09626i	0.995078	+	0.0990941i	$0.0315945\pi$
$461$	19.7505	+	23.5377i	0.919873	+	1.09626i	−0.0752048	+	0.997168i	$0.523961\pi$
$462$	−3.75181	−	5.40769i	−0.174550	−	0.251589i
$463$	−11.2430	−	1.98244i	−0.522506	−	0.0921319i	−0.0938266	−	0.995589i	$-0.529910\pi$
$463$	−11.2430	−	1.98244i	−0.522506	−	0.0921319i	−0.428679	+	0.903457i	$0.641021\pi$
$464$	−1.26036	+	0.283110i	−0.0585109	+	0.0131430i
$465$	−8.76492	−	10.7900i	−0.406463	−	0.500375i
$466$	0.954642	−	3.73567i	0.0442229	−	0.173052i
$467$	−0.126870	−	0.219745i	−0.00587084	−	0.0101686i	0.863075	−	0.505076i	$-0.168535\pi$
$467$	−0.126870	−	0.219745i	−0.00587084	−	0.0101686i	−0.868946	+	0.494907i	$0.835202\pi$
$468$	−8.91157	+	10.4360i	−0.411938	+	0.482404i
$469$	−6.68415	+	11.5773i	−0.308645	+	0.534590i
$470$	−27.7837	−	27.1461i	−1.28157	−	1.25216i
$471$	25.6729	−	29.6246i	1.18294	−	1.36503i
$472$	−3.80499	−	1.61551i	−0.175139	−	0.0743601i
$473$	18.9010	−	22.5254i	0.869070	−	1.03572i
$474$	0.217819	−	2.37167i	0.0100048	−	0.108935i
$475$	8.77223	−	24.1015i	0.402498	−	1.10585i
$476$	−9.26251	+	1.85587i	−0.424546	+	0.0850638i
$477$	−6.58462	−	4.08659i	−0.301489	−	0.187112i
$478$	−5.97087	+	0.592287i	−0.273101	+	0.0270906i
$479$	−6.66242	−	37.7844i	−0.304414	−	1.72642i	−0.626252	−	0.779621i	$-0.715412\pi$
$479$	−6.66242	−	37.7844i	−0.304414	−	1.72642i	0.321839	−	0.946795i	$-0.395699\pi$
$480$	20.0357	+	26.1938i	0.914501	+	1.19558i
$481$	−5.55272	+	2.02103i	−0.253182	+	0.0921508i
$482$	−15.1917	−	10.3767i	−0.691963	−	0.472645i
$483$	2.63210	+	4.73137i	0.119765	+	0.215285i
$484$	7.47387	+	1.13966i	0.339721	+	0.0518027i
$485$			21.8264i			0.991087i
$486$	−7.13987	+	20.8572i	−0.323871	+	0.946101i
$487$			21.1551i			0.958628i	0.877644	+	0.479314i	$0.159114\pi$
$487$			21.1551i			0.958628i	−0.877644	+	0.479314i	$0.840886\pi$
$488$	22.5819	−	34.7665i	1.02224	−	1.57380i
$489$	−15.3702	−	27.6290i	−0.695066	−	1.24942i
$490$	−2.68476	+	3.93055i	−0.121285	+	0.177564i
$491$	−15.4584	+	5.62638i	−0.697626	+	0.253915i	−0.666397	−	0.745597i	$-0.732164\pi$
$491$	−15.4584	+	5.62638i	−0.697626	+	0.253915i	−0.0312290	+	0.999512i	$0.509942\pi$
$492$	9.52872	+	25.5980i	0.429588	+	1.15405i
$493$	0.264875	+	1.50218i	0.0119294	+	0.0676547i
$494$	1.29402	+	13.0450i	0.0582205	+	0.586923i
$495$	23.0527	+	14.3071i	1.03614	+	0.643057i
$496$	5.78538	−	7.58339i	0.259771	−	0.340504i
$497$	0.775778	−	2.13143i	0.0347984	−	0.0956079i
$498$	−21.6580	−	1.98912i	−0.970519	−	0.0891345i
$499$	−5.22124	+	6.22243i	−0.233735	+	0.278554i	−0.870144	−	0.492797i	$-0.835974\pi$
$499$	−5.22124	+	6.22243i	−0.233735	+	0.278554i	0.636410	+	0.771351i	$0.280419\pi$
$500$	−8.94107	+	0.207582i	−0.399857	+	0.00928336i
$501$	22.6366	−	26.1209i	1.01133	−	1.16700i
$502$	−20.4452	+	20.9253i	−0.912512	+	0.933943i
$503$	−6.46211	+	11.1927i	−0.288131	+	0.499058i	−0.973364	−	0.229266i	$-0.926367\pi$
$503$	−6.46211	+	11.1927i	−0.288131	+	0.499058i	0.685232	+	0.728324i	$0.259701\pi$
$504$	−7.67960	+	3.60885i	−0.342076	+	0.160751i
$505$	−28.1291	−	48.7211i	−1.25173	−	2.16806i
$506$	11.5085	+	2.94097i	0.511615	+	0.130742i
$507$	−8.48399	−	10.4442i	−0.376787	−	0.463842i
$508$	1.15821	−	2.11814i	0.0513871	−	0.0939773i
$509$	−9.89056	−	1.74397i	−0.438392	−	0.0773003i	−0.0499035	−	0.998754i	$-0.515891\pi$
$509$	−9.89056	−	1.74397i	−0.438392	−	0.0773003i	−0.388488	+	0.921454i	$0.627003\pi$
$510$	31.9949	−	22.1978i	1.41676	−	0.982934i
$511$	9.45945	+	11.2733i	0.418461	+	0.498703i
$512$	−14.2445	+	17.5811i	−0.629525	+	0.776980i
$513$	9.64643	+	18.7195i	0.425900	+	0.826486i
$514$	14.6689	+	6.63406i	0.647018	+	0.292616i
$515$	2.01009	−	1.68667i	0.0885751	−	0.0743234i
$516$	−24.5785	−	28.8617i	−1.08201	−	1.27057i
$517$	3.80763	−	21.5941i	0.167459	−	0.949709i
$518$	−3.64323	−	0.276175i	−0.160074	−	0.0121344i
$519$	−5.99634	−	37.4885i	−0.263210	−	1.64556i
$520$	19.4016	−	9.88346i	0.850816	−	0.433418i
$521$	13.6405	−	7.87532i	0.597599	−	0.345024i	−0.170497	−	0.985358i	$-0.554537\pi$
$521$	13.6405	−	7.87532i	0.597599	−	0.345024i	0.768097	+	0.640334i	$0.221204\pi$
$522$	0.553786	+	1.25322i	0.0242386	+	0.0548521i
$523$	18.3147	+	10.5740i	0.800844	+	0.462368i	0.843766	−	0.536711i	$-0.180333\pi$
$523$	18.3147	+	10.5740i	0.800844	+	0.462368i	−0.0429220	+	0.999078i	$0.513667\pi$
$524$	10.0502	+	25.7376i	0.439045	+	1.12435i
$525$	2.07509	−	10.7632i	0.0905644	−	0.469745i
$526$	2.56897	−	1.23443i	0.112012	−	0.0538236i
$527$	−8.62797	−	7.23973i	−0.375840	−	0.315368i
$528$	−5.83061	+	17.6793i	−0.253745	+	0.769393i
$529$	12.4309	+	4.52449i	0.540475	+	0.196717i
$530$	7.16914	+	9.98978i	0.311407	+	0.433929i
$531$	−0.898474	+	4.29145i	−0.0389905	+	0.186233i
$532$	−2.59472	+	7.67901i	−0.112496	+	0.332927i
$533$	17.7603	−	3.13161i	0.769283	−	0.135645i
$534$	35.7865	+	9.75482i	1.54864	+	0.422132i
$535$	0.154121	+	0.423445i	0.00666325	+	0.0183071i
$536$	37.5298	−	4.60474i	1.62104	−	0.198895i
$537$	−0.391528	+	24.5837i	−0.0168957	+	1.06086i
$538$	−11.5114	+	3.22813i	−0.496293	+	0.139174i
$539$	−2.68698			−0.115736
$540$	23.1350	−	26.2347i	0.995571	−	1.12896i
$541$	−11.0755			−0.476174			−0.238087	−	0.971244i	$-0.576520\pi$
$541$	−11.0755			−0.476174			−0.238087	+	0.971244i	$0.576520\pi$
$542$	34.7840	−	9.75441i	1.49410	−	0.418988i
$543$	7.21883	+	4.32251i	0.309790	+	0.185497i
$544$	19.9572	+	17.7656i	0.855657	+	0.761695i
$545$	−16.7960	−	46.1467i	−0.719462	−	1.97671i
$546$	1.42664	+	5.41778i	0.0610546	+	0.231860i
$547$	35.4338	−	6.24793i	1.51504	−	0.267142i	0.646558	−	0.762865i	$-0.276208\pi$
$547$	35.4338	−	6.24793i	1.51504	−	0.267142i	0.868481	+	0.495722i	$0.165097\pi$
$548$	37.9936	+	12.8380i	1.62301	+	0.548411i
$549$	−40.8197	−	16.3473i	−1.74214	−	0.697685i
$550$	−14.0213	−	19.5379i	−0.597870	−	0.833098i
$551$	1.22988	+	0.447639i	0.0523946	+	0.0190701i
$552$	6.20850	−	13.9988i	0.264251	−	0.595827i
$553$	−0.744830	−	0.624986i	−0.0316734	−	0.0265771i
$554$	19.2029	−	9.22726i	0.815851	−	0.392029i
$555$	14.2333	−	4.92526i	0.604169	−	0.209066i
$556$	−21.8333	+	8.52561i	−0.925938	+	0.361566i
$557$	1.05774	+	0.610686i	0.0448179	+	0.0258756i	0.522242	−	0.852798i	$-0.325096\pi$
$557$	1.05774	+	0.610686i	0.0448179	+	0.0258756i	−0.477424	+	0.878673i	$0.658429\pi$
$558$	−9.08056	−	4.46029i	−0.384411	−	0.188819i
$559$	−21.6764	+	12.5149i	−0.916815	+	0.529324i
$560$	13.4487	−	0.624805i	0.568310	−	0.0264028i
$561$	20.5342	+	7.84634i	0.866953	+	0.331273i
$562$	22.6678	+	1.71833i	0.956183	+	0.0724833i
$563$	0.741064	−	4.20278i	0.0312321	−	0.177126i	−0.965201	−	0.261508i	$-0.915780\pi$
$563$	0.741064	−	4.20278i	0.0312321	−	0.177126i	0.996434	+	0.0843815i	$0.0268914\pi$
$564$	−26.6339	−	9.47472i	−1.12149	−	0.398958i
$565$	8.87506	−	7.44706i	0.373376	−	0.313300i
$566$	4.93093	+	2.23003i	0.207262	+	0.0937351i
$567$	5.33448	+	7.24868i	0.224027	+	0.304416i
$568$	−6.13535	+	1.87517i	−0.257433	+	0.0786806i
$569$	6.18453	+	7.37043i	0.259269	+	0.308985i	0.879938	−	0.475088i	$-0.157584\pi$
$569$	6.18453	+	7.37043i	0.259269	+	0.308985i	−0.620670	+	0.784072i	$0.713139\pi$
$570$	−2.76835	−	33.2981i	−0.115954	−	1.39470i
$571$	39.3258	+	6.93421i	1.64574	+	0.290188i	0.918269	−	0.395956i	$-0.129587\pi$
$571$	39.3258	+	6.93421i	1.64574	+	0.290188i	0.727466	+	0.686144i	$0.240698\pi$
$572$	10.7844	+	5.89694i	0.450918	+	0.246564i
$573$	2.89288	−	7.57078i	0.120852	−	0.316274i
$574$	10.8037	+	2.76086i	0.450937	+	0.115236i
$575$	9.89128	+	17.1322i	0.412495	+	0.714462i
$576$	21.2231	+	11.2062i	0.884297	+	0.466926i
$577$	−14.3536	+	24.8612i	−0.597548	+	1.03498i	0.395633	+	0.918409i	$0.370525\pi$
$577$	−14.3536	+	24.8612i	−0.597548	+	1.03498i	−0.993182	+	0.116576i	$0.962808\pi$
$578$	5.24760	−	5.37084i	0.218271	−	0.223398i
$579$	8.61828	+	24.9056i	0.358163	+	1.03504i
$580$	−0.0504576	−	2.17333i	−0.00209514	−	0.0902425i
$581$	−5.70735	+	6.80175i	−0.236781	+	0.282184i
$582$	6.65080	+	14.4250i	0.275685	+	0.597936i
$583$	−2.37399	+	6.52248i	−0.0983205	+	0.270133i
$584$	9.36691	−	40.5563i	0.387605	−	1.67823i
$585$	−14.2741	−	18.1554i	−0.590162	−	0.750632i
$586$	−0.377951	−	3.81014i	−0.0156130	−	0.157395i
$587$	0.708182	+	4.01630i	0.0292298	+	0.165770i	0.995928	−	0.0901469i	$-0.0287337\pi$
$587$	0.708182	+	4.01630i	0.0292298	+	0.165770i	−0.966699	+	0.255917i	$0.917623\pi$
$588$	−0.576658	+	3.41577i	−0.0237810	+	0.140864i
$589$	−9.08128	+	3.30531i	−0.374187	+	0.136193i
$590$	3.92377	−	5.74449i	0.161539	−	0.236497i
$591$	10.8102	−	18.0537i	0.444673	−	0.742629i
$592$	5.57686	+	8.70022i	0.229208	+	0.357577i
$593$			18.1547i			0.745523i	0.927927	+	0.372761i	$0.121589\pi$
$593$			18.1547i			0.745523i	−0.927927	+	0.372761i	$0.878411\pi$
$594$	19.5950	+	2.43107i	0.803991	+	0.0997479i
$595$		−	15.8977i		−	0.651741i
$596$	2.52904	−	16.5854i	0.103594	−	0.679364i
$597$	−21.4368	−	0.341409i	−0.877348	−	0.0139729i
$598$	−8.34921	−	5.70293i	−0.341425	−	0.233210i
$599$	−10.3032	+	3.75008i	−0.420979	+	0.153224i	−0.543819	−	0.839203i	$-0.683022\pi$
$599$	−10.3032	+	3.75008i	−0.420979	+	0.153224i	0.122840	+	0.992427i	$0.460800\pi$
$600$	−27.8462	+	13.6312i	−1.13682	+	0.556492i
$601$	4.26732	+	24.2012i	0.174068	+	0.987186i	0.939215	+	0.343330i	$0.111555\pi$
$601$	4.26732	+	24.2012i	0.174068	+	0.987186i	−0.765147	+	0.643855i	$0.777334\pi$
$602$	−15.4007	+	1.52770i	−0.627688	+	0.0622642i
$603$	−12.5096	−	38.1040i	−0.509431	−	1.55171i
$604$	−5.95569	−	29.7244i	−0.242334	−	1.20947i
$605$	−4.35157	+	11.9558i	−0.176917	+	0.486074i
$606$	−33.4364	−	23.6283i	−1.35826	−	0.959833i
$607$	−11.8928	+	14.1733i	−0.482713	+	0.575275i	−0.951349	−	0.308117i	$-0.900301\pi$
$607$	−11.8928	+	14.1733i	−0.482713	+	0.575275i	0.468636	+	0.883392i	$0.344746\pi$
$608$	21.7633	−	7.20805i	0.882619	−	0.292325i
$609$	0.549238	+	0.105890i	0.0222562	+	0.00429088i
$610$	49.9021	+	48.7570i	2.02048	+	1.97411i
$611$	−9.33241	+	16.1642i	−0.377549	+	0.653934i
$612$	14.3814	−	24.4197i	0.581332	−	0.987107i
$613$	12.8298	+	22.2218i	0.518189	+	0.897530i	0.999777	+	0.0211319i	$0.00672698\pi$
$613$	12.8298	+	22.2218i	0.518189	+	0.897530i	−0.481588	+	0.876398i	$0.659940\pi$
$614$	11.3991	−	44.6066i	0.460030	−	1.80017i
$615$	−45.3896	+	7.26014i	−1.83029	+	0.292757i
$616$	4.57322	+	6.06998i	0.184260	+	0.244566i
$617$	−47.3199	−	8.34377i	−1.90503	−	0.335908i	−0.908408	−	0.418084i	$-0.862702\pi$
$617$	−47.3199	−	8.34377i	−1.90503	−	0.335908i	−0.996618	+	0.0821764i	$0.973813\pi$
$618$	0.814512	−	1.72721i	0.0327645	−	0.0694786i
$619$	−10.1380	−	12.0820i	−0.407481	−	0.485617i	0.522805	−	0.852453i	$-0.324886\pi$
$619$	−10.1380	−	12.0820i	−0.407481	−	0.485617i	−0.930286	+	0.366835i	$0.880441\pi$
$620$	10.6006	+	12.0537i	0.425730	+	0.484088i
$621$	−15.8430	−	3.58121i	−0.635756	−	0.143709i
$622$	15.2511	−	33.7226i	0.611515	−	1.35215i
$623$	11.6001	−	9.73363i	0.464748	−	0.389970i
$624$	9.81081	−	12.4439i	0.392747	−	0.498153i
$625$	−2.88116	+	16.3399i	−0.115247	+	0.653595i
$626$	−0.149597	+	1.97345i	−0.00597911	+	0.0788750i
$627$	14.6400	−	11.8923i	0.584666	−	0.474934i
$628$	−28.2833	+	35.3412i	−1.12863	+	1.41027i
$629$	10.5680	−	6.10143i	0.421373	−	0.243280i
$630$	−3.41594	−	13.8653i	−0.136094	−	0.552406i
$631$	−7.92332	−	4.57453i	−0.315423	−	0.182109i	0.333928	−	0.942599i	$-0.391626\pi$
$631$	−7.92332	−	4.57453i	−0.315423	−	0.182109i	−0.649350	+	0.760489i	$0.724959\pi$
$632$	−0.144170	+	2.74632i	−0.00573477	+	0.109243i
$633$	−22.1381	−	19.1850i	−0.879909	−	0.762536i
$634$	9.95636	+	20.7202i	0.395418	+	0.822904i
$635$	3.11222	+	2.61146i	0.123505	+	0.103633i
$636$	7.78207	+	4.41768i	0.308579	+	0.175172i
$637$	2.14926	+	0.782268i	0.0851570	+	0.0309946i
$638$	0.997001	−	0.715494i	0.0394716	−	0.0283267i
$639$	3.21295	+	5.99838i	0.127102	+	0.237292i
$640$	−24.3010	−	29.3176i	−0.960581	−	1.15888i
$641$	49.6595	−	8.75631i	1.96143	−	0.345853i	0.964902	−	0.262609i	$-0.0845828\pi$
$641$	49.6595	−	8.75631i	1.96143	−	0.345853i	0.996529	−	0.0832447i	$-0.0265283\pi$
$642$	0.230887	+	0.232890i	0.00911240	+	0.00919145i
$643$	−14.8271	−	40.7371i	−0.584724	−	1.60652i	−0.780009	−	0.625769i	$-0.784785\pi$
$643$	−14.8271	−	40.7371i	−0.584724	−	1.60652i	0.195285	−	0.980747i	$-0.437437\pi$
$644$	−3.25073	−	5.34022i	−0.128097	−	0.210434i
$645$	55.7509	−	31.0147i	2.19519	−	1.22120i
$646$	−7.30964	−	26.0660i	−0.287594	−	1.02555i
$647$	24.2771			0.954430			0.477215	−	0.878787i	$-0.341646\pi$
$647$	24.2771			0.954430			0.477215	+	0.878787i	$0.341646\pi$
$648$	7.29575	−	24.3879i	0.286604	−	0.958049i
$649$	3.92702			0.154149
$650$	5.52725	+	19.7100i	0.216796	+	0.773091i
$651$	−3.60928	+	2.00787i	−0.141459	+	0.0786948i
$652$	18.9827	+	31.1843i	0.743420	+	1.22127i
$653$	−2.74671	−	7.54652i	−0.107487	−	0.295318i	0.874275	−	0.485430i	$-0.161337\pi$
$653$	−2.74671	−	7.54652i	−0.107487	−	0.295318i	−0.981762	+	0.190112i	$0.939115\pi$
$654$	−25.1619	−	25.3802i	−0.983909	−	0.992444i
$655$	−45.7925	+	8.07446i	−1.78926	+	0.315495i
$656$	−12.1509	−	29.1048i	−0.474414	−	1.13635i
$657$	−44.1265	−	1.40590i	−1.72154	−	0.0548495i
$658$	−9.37618	+	6.72879i	−0.365522	+	0.262315i
$659$	−4.76384	−	1.73390i	−0.185573	−	0.0675430i	0.247562	−	0.968872i	$-0.420371\pi$
$659$	−4.76384	−	1.73390i	−0.185573	−	0.0675430i	−0.433135	+	0.901329i	$0.642593\pi$
$660$	−27.2449	−	15.4662i	−1.06051	−	0.602023i
$661$	−11.5525	−	9.69373i	−0.449341	−	0.377042i	0.389850	−	0.920878i	$-0.372527\pi$
$661$	−11.5525	−	9.69373i	−0.449341	−	0.377042i	−0.839191	+	0.543836i	$0.816971\pi$
$662$	7.93619	+	16.5160i	0.308449	+	0.641913i
$663$	−14.1406	−	12.2543i	−0.549174	−	0.475918i
$664$	25.0792	+	1.31655i	0.973263	+	0.0510922i
$665$	−11.8133	−	6.82040i	−0.458099	−	0.264484i
$666$	7.90594	−	7.59215i	0.306349	−	0.294190i
$667$	−0.874241	+	0.504743i	−0.0338507	+	0.0195437i
$668$	−24.9383	+	31.1615i	−0.964892	+	1.20568i
$669$	−10.9843	+	8.92273i	−0.424677	+	0.344973i
$670$	−4.80986	+	63.4505i	−0.185821	+	2.45131i
$671$	−6.83886	+	38.7851i	−0.264011	+	1.49728i
$672$	8.69779	−	4.51092i	0.335525	−	0.174012i
$673$	11.7618	−	9.86933i	0.453384	−	0.380435i	−0.387306	−	0.921951i	$-0.626594\pi$
$673$	11.7618	−	9.86933i	0.453384	−	0.380435i	0.840690	+	0.541517i	$0.182150\pi$
$674$	11.2194	−	24.8079i	0.432157	−	0.955564i
$675$	19.9105	+	26.1715i	0.766354	+	1.00734i
$676$	10.2608	+	11.6673i	0.394648	+	0.448744i
$677$	19.8324	+	23.6353i	0.762220	+	0.908378i	0.997986	−	0.0634317i	$-0.0202045\pi$
$677$	19.8324	+	23.6353i	0.762220	+	0.908378i	−0.235767	+	0.971810i	$0.575760\pi$
$678$	3.59628	−	7.62608i	0.138114	−	0.292878i
$679$	6.38626	+	1.12607i	0.245082	+	0.0432146i
$680$	−35.9133	+	27.0577i	−1.37721	+	1.03762i
$681$	4.43544	−	0.709455i	0.169966	−	0.0271864i
$682$	−2.24349	+	8.77914i	−0.0859076	+	0.336171i
$683$	0.0142495	+	0.0246808i	0.000545242	+	0.000944386i	0.866298	−	0.499528i	$-0.166493\pi$
$683$	0.0142495	+	0.0246808i	0.000545242	+	0.000944386i	−0.865753	+	0.500472i	$0.833160\pi$
$684$	−11.9760	−	21.1630i	−0.457912	−	0.809189i
$685$	−33.7454	+	58.4488i	−1.28935	+	2.23321i
$686$	1.01154	+	0.988327i	0.0386207	+	0.0377345i
$687$	28.8550	+	5.56309i	1.10089	+	0.212245i
$688$	29.6631	+	32.1907i	1.13089	+	1.22726i
$689$	3.79781	−	4.52606i	0.144685	−	0.172429i
$690$	21.0467	+	14.8729i	0.801235	+	0.566203i
$691$	−4.12900	+	11.3443i	−0.157075	+	0.431559i	−0.993120	−	0.117102i	$-0.962640\pi$
$691$	−4.12900	+	11.3443i	−0.157075	+	0.431559i	0.836045	+	0.548660i	$0.184862\pi$
$692$	8.61243	+	42.9839i	0.327395	+	1.63400i
$693$	5.37549	−	6.00691i	0.204198	−	0.228184i
$694$	26.7704	−	2.65552i	1.01619	−	0.100802i
$695$	−6.84958	−	38.8459i	−0.259819	−	1.47351i
$696$	−0.695589	−	1.42097i	−0.0263662	−	0.0538617i
$697$	−34.9966	+	12.7377i	−1.32559	+	0.482475i
$698$	16.7169	+	11.4185i	0.632745	+	0.432196i
$699$	4.72167	+	0.0751990i	0.178590	+	0.00284429i
$700$	−1.90799	+	12.5125i	−0.0721151	+	0.472929i
$701$		−	31.9466i		−	1.20661i	−0.797511	−	0.603304i	$-0.793851\pi$
$701$		−	31.9466i		−	1.20661i	0.797511	−	0.603304i	$-0.206149\pi$
$702$	−14.9659	−	7.64930i	−0.564851	−	0.288704i
$703$		−	10.4705i		−	0.394903i
$704$	5.92869	−	20.6621i	0.223446	−	0.778732i
$705$	24.4400	−	40.8161i	0.920463	−	1.53722i
$706$	10.9734	−	16.0653i	0.412988	−	0.604624i
$707$	−15.7067	+	5.71677i	−0.590711	+	0.215001i
$708$	0.842784	−	4.99214i	0.0316738	−	0.187616i
$709$	−4.63618	−	26.2931i	−0.174115	−	0.987458i	−0.939160	−	0.343480i	$-0.888394\pi$
$709$	−4.63618	−	26.2931i	−0.174115	−	0.987458i	0.765044	−	0.643977i	$-0.222717\pi$
$710$	−1.06576	−	10.7439i	−0.0399971	−	0.403212i
$711$	2.88728	−	0.414784i	0.108281	−	0.0155556i
$712$	−41.7318	−	9.63841i	−1.56397	−	0.361215i
$713$	2.54939	−	7.00440i	0.0954755	−	0.262317i
$714$	−4.84423	−	10.5067i	−0.181291	−	0.393204i
$715$	−13.2961	+	15.8457i	−0.497246	+	0.592594i
$716$	−0.658954	−	28.3827i	−0.0246263	−	1.06071i
$717$	−2.40311	−	6.94465i	−0.0897459	−	0.259353i
$718$	−2.50636	+	2.56523i	−0.0935367	+	0.0957335i
$719$	−1.34291	+	2.32598i	−0.0500819	+	0.0867444i	−0.889980	−	0.456000i	$-0.849282\pi$
$719$	−1.34291	+	2.32598i	−0.0500819	+	0.0867444i	0.839898	+	0.542745i	$0.182615\pi$
$720$	−25.5082	+	31.3153i	−0.950635	+	1.16705i
$721$	−0.389802	−	0.675156i	−0.0145170	−	0.0251441i
$722$	3.52830	+	0.901649i	0.131310	+	0.0335559i
$723$	8.04262	−	21.0478i	0.299108	−	0.782777i
$724$	−8.52450	−	4.66123i	−0.316811	−	0.173233i
$725$	2.01272	+	0.354896i	0.0747504	+	0.0131805i
$726$	0.767165	+	9.22755i	0.0284722	+	0.342467i
$727$	−15.5274	−	18.5049i	−0.575881	−	0.686308i	0.396946	−	0.917842i	$-0.370070\pi$
$727$	−15.5274	−	18.5049i	−0.575881	−	0.686308i	−0.972827	+	0.231534i	$0.925626\pi$
$728$	−1.89086	−	6.18667i	−0.0700800	−	0.229293i
$729$	−26.8768	−	2.57592i	−0.995439	−	0.0954046i
$730$	63.8251	+	28.8651i	2.36227	+	1.06835i
$731$	39.5961	−	33.2251i	1.46452	−	1.22887i
$732$	47.8370	+	17.0175i	1.76811	+	0.628985i
$733$	0.351729	−	1.99475i	0.0129914	−	0.0736779i	−0.977623	−	0.210366i	$-0.932535\pi$
$733$	0.351729	−	1.99475i	0.0129914	−	0.0736779i	0.990614	+	0.136688i	$0.0436457\pi$
$734$	35.3124	+	2.67686i	1.30341	+	0.0988045i
$735$	−5.44571	−	2.08087i	−0.200868	−	0.0767540i
$736$	−6.53100	+	16.4325i	−0.240736	+	0.605710i
$737$	−31.1080	+	17.9602i	−1.14588	+	0.661572i
$738$	−27.7856	+	18.6290i	−1.02280	+	0.685743i
$739$	−13.7088	−	7.91475i	−0.504285	−	0.291149i	0.226197	−	0.974082i	$-0.427371\pi$
$739$	−13.7088	−	7.91475i	−0.504285	−	0.291149i	−0.730481	+	0.682933i	$0.760704\pi$
$740$	−16.2001	+	6.32591i	−0.595527	+	0.232545i
$741$	−15.1725	+	5.25027i	−0.557376	+	0.192873i
$742$	3.29281	−	1.58224i	0.120883	−	0.0580860i
$743$	−39.1393	−	32.8418i	−1.43588	−	1.20485i	−0.942131	−	0.335246i	$-0.891181\pi$
$743$	−39.1393	−	32.8418i	−1.43588	−	1.20485i	−0.493752	−	0.869603i	$-0.664375\pi$
$744$	10.6788	+	4.73609i	0.391504	+	0.173634i
$745$	26.5314	+	9.65665i	0.972036	+	0.353792i
$746$	−29.0679	−	40.5045i	−1.06425	−	1.48298i
$747$	−3.78779	−	26.3665i	−0.138588	−	0.964699i
$748$	−24.0471	−	8.12549i	−0.879251	−	0.297097i
$749$	0.131848	−	0.0232484i	0.00481763	−	0.000849479i
$750$	−2.78925	−	10.5924i	−0.101849	−	0.386779i
$751$	−14.7164	−	40.4329i	−0.537008	−	1.47542i	−0.850576	−	0.525852i	$-0.823747\pi$
$751$	−14.7164	−	40.4329i	−0.537008	−	1.47542i	0.313568	−	0.949566i	$-0.398476\pi$
$752$	31.1587	+	9.72875i	1.13624	+	0.354771i
$753$	−30.7407	−	18.4070i	−1.12025	−	0.670789i
$754$	−1.00579	+	0.282051i	−0.0366286	+	0.0102717i
$755$	51.0173			1.85671
$756$	−6.48251	−	8.12263i	−0.235767	−	0.295417i
$757$	−18.5843			−0.675456			−0.337728	−	0.941244i	$-0.609658\pi$
$757$	−18.5843			−0.675456			−0.337728	+	0.941244i	$0.609658\pi$
$758$	27.3289	−	7.66379i	0.992630	−	0.278361i
$759$	−0.231666	+	14.5461i	−0.00840894	+	0.527989i
$760$	4.69860	+	38.2948i	0.170436	+	1.38910i
$761$	−2.14870	−	5.90351i	−0.0778904	−	0.214002i	0.894636	−	0.446797i	$-0.147435\pi$
$761$	−2.14870	−	5.90351i	−0.0778904	−	0.214002i	−0.972526	+	0.232795i	$0.925213\pi$
$762$	2.85260	+	0.777571i	0.103339	+	0.0281684i
$763$	−14.3687	+	2.53359i	−0.520183	+	0.0917223i
$764$	−2.99580	+	8.86600i	−0.108384	+	0.320760i
$765$	35.5402	+	31.8044i	1.28496	+	1.14989i
$766$	−2.29479	−	3.19766i	−0.0829142	−	0.115536i
$767$	−3.14115	−	1.14328i	−0.113420	−	0.0412816i
$768$	−24.9939	−	11.9710i	−0.901889	−	0.431968i
$769$	26.4586	+	22.2014i	0.954122	+	0.800603i	0.979987	−	0.199062i	$-0.0637896\pi$
$769$	26.4586	+	22.2014i	0.954122	+	0.800603i	−0.0258652	+	0.999665i	$0.508234\pi$
$770$	−11.5281	+	5.53942i	−0.415443	+	0.199627i
$771$	−3.73270	+	19.3610i	−0.134430	+	0.697270i
$772$	−11.0692	−	28.3471i	−0.398388	−	1.02023i
$773$	31.3530	+	18.1017i	1.12769	+	0.651072i	0.943353	−	0.331791i	$-0.107653\pi$
$773$	31.3530	+	18.1017i	1.12769	+	0.651072i	0.184338	+	0.982863i	$0.440986\pi$
$774$	27.3950	−	37.4856i	0.984692	−	1.34739i
$775$	−13.0691	+	7.54546i	−0.469457	+	0.271041i
$776$	−8.32553	−	16.3433i	−0.298869	−	0.586691i
$777$	−0.706771	−	4.41866i	−0.0253553	−	0.158519i
$778$	2.43478	+	0.184568i	0.0872910	+	0.00661709i
$779$	−5.54902	+	31.4700i	−0.198814	+	1.12753i
$780$	17.2900	+	20.3030i	0.619080	+	0.726965i
$781$	4.66879	−	3.91758i	0.167063	−	0.140182i
$782$	19.0251	+	8.60417i	0.680337	+	0.307684i
$783$	−1.33551	+	1.01601i	−0.0477273	+	0.0363093i
$784$	0.511031	−	3.96722i	0.0182511	−	0.141686i
$785$	−48.9655	−	58.3549i	−1.74766	−	2.08277i
$786$	−27.8037	+	19.2900i	−0.991725	+	0.688050i
$787$	46.7100	+	8.23623i	1.66503	+	0.293590i	0.925278	−	0.379290i	$-0.123832\pi$
$787$	46.7100	+	8.23623i	1.66503	+	0.293590i	0.739752	+	0.672879i	$0.234943\pi$
$788$	−11.6573	+	21.3190i	−0.415275	+	0.759459i
$789$	2.20092	+	2.70944i	0.0783549	+	0.0964585i
$790$	−4.48404	−	1.14588i	−0.159535	−	0.0407687i
$791$	−1.72107	−	2.98099i	−0.0611943	−	0.105992i
$792$	−22.7188	−	1.91969i	−0.807279	−	0.0682133i
$793$	16.7619	−	29.0324i	0.595232	−	1.03097i
$794$	4.02828	−	4.12289i	0.142958	−	0.146316i
$795$	−9.86254	+	11.3806i	−0.349788	+	0.403629i
$796$	24.7495	−	0.574602i	0.877223	−	0.0203662i
$797$	23.4076	−	27.8961i	0.829141	−	0.988132i	−0.170855	−	0.985296i	$-0.554653\pi$
$797$	23.4076	−	27.8961i	0.829141	−	0.988132i	0.999996	−	0.00283592i	$-0.000902704\pi$
$798$	−9.88561	−	0.907915i	−0.349947	−	0.0321399i
$799$	13.1831	−	36.2202i	0.466384	−	1.28138i
$800$	31.5136	−	16.9860i	1.11417	−	0.600547i
$801$	−1.44665	+	45.4055i	−0.0511150	+	1.60432i
$802$	2.77265	+	27.9511i	0.0979055	+	0.986989i
$803$	6.86646	+	38.9417i	0.242312	+	1.37422i
$804$	16.1554	+	43.3998i	0.569756	+	1.53059i
$805$	9.88666	−	3.59845i	0.348459	−	0.126829i
$806$	4.35042	−	6.36911i	0.153237	−	0.224342i
$807$	−7.11835	−	12.7957i	−0.250578	−	0.450430i
$808$	39.6470	+	25.7520i	1.39478	+	0.905953i
$809$			2.92521i			0.102845i	0.998677	+	0.0514224i	$0.0163755\pi$
$809$			2.92521i			0.102845i	−0.998677	+	0.0514224i	$0.983625\pi$
$810$	37.8305	+	20.1019i	1.32923	+	0.706309i
$811$		−	41.5184i		−	1.45791i	−0.684563	−	0.728954i	$-0.740007\pi$
$811$		−	41.5184i		−	1.45791i	0.684563	−	0.728954i	$-0.259993\pi$
$812$	−0.638503	−	0.0973629i	−0.0224071	−	0.00341677i
$813$	21.5095	+	38.6646i	0.754370	+	1.35603i
$814$	−8.10674	−	5.53730i	−0.284141	−	0.194082i
$815$	−57.7333	+	21.0132i	−2.02231	+	0.736061i
$816$	−15.4902	+	28.8256i	−0.542264	+	1.00910i
$817$	−7.70150	−	43.6774i	−0.269441	−	1.52808i
$818$	−21.1894	+	2.10191i	−0.740871	+	0.0734915i
$819$	−6.04856	+	3.23983i	−0.211354	+	0.113209i
$820$	52.0433	−	10.4276i	1.81743	−	0.364147i
$821$	−11.6240	+	31.9365i	−0.405679	+	1.11459i	0.553760	+	0.832676i	$0.313192\pi$
$821$	−11.6240	+	31.9365i	−0.405679	+	1.11459i	−0.959439	+	0.281917i	$0.909030\pi$
$822$	−4.49211	+	48.9112i	−0.156680	+	1.70598i
$823$	18.5624	−	22.1218i	0.647046	−	0.771119i	−0.338420	−	0.940995i	$-0.609892\pi$
$823$	18.5624	−	22.1218i	0.647046	−	0.771119i	0.985465	+	0.169876i	$0.0543368\pi$
$824$	−0.861760	+	2.02968i	−0.0300208	+	0.0707074i
$825$	19.2890	−	22.2581i	0.671557	−	0.774927i
$826$	−1.47836	−	1.44444i	−0.0514388	−	0.0502584i
$827$	−23.2241	+	40.2253i	−0.807580	+	1.39877i	0.106955	+	0.994264i	$0.465890\pi$
$827$	−23.2241	+	40.2253i	−0.807580	+	1.39877i	−0.914535	+	0.404506i	$0.867443\pi$
$828$	18.4417	+	3.41626i	0.640893	+	0.118723i
$829$	−9.10298	−	15.7668i	−0.316160	−	0.547605i	0.663524	−	0.748155i	$-0.269060\pi$
$829$	−9.10298	−	15.7668i	−0.316160	−	0.547605i	−0.979683	+	0.200551i	$0.935727\pi$
$830$	−10.4642	+	40.9480i	−0.363217	+	1.42133i
$831$	16.4517	+	20.2529i	0.570705	+	0.702564i
$832$	−10.7577	+	14.8012i	−0.372955	+	0.513139i
$833$	−4.65154	−	0.820193i	−0.161166	−	0.0284180i
$834$	−16.3637	−	23.5860i	−0.566629	−	0.816715i
$835$	−43.1745	−	51.4534i	−1.49412	−	1.78062i
$836$	−16.3546	+	14.3830i	−0.565635	+	0.497447i
$837$	2.73189	−	12.0856i	0.0944279	−	0.417741i
$838$	−12.4371	+	27.5002i	−0.429631	+	0.949979i
$839$	−8.31813	+	6.97974i	−0.287174	+	0.240967i	−0.774982	−	0.631984i	$-0.782241\pi$
$839$	−8.31813	+	6.97974i	−0.287174	+	0.240967i	0.487808	+	0.872951i	$0.337797\pi$
$840$	4.56780	+	15.8436i	0.157604	+	0.546658i
$841$	5.01769	−	28.4567i	0.173024	−	0.981266i
$842$	0.247247	−	3.26163i	0.00852071	−	0.112403i
$843$	4.39746	+	27.4924i	0.151456	+	0.946890i
$844$	26.4101	+	21.1358i	0.909072	+	0.727523i
$845$	−22.6448	+	13.0740i	−0.779003	+	0.449758i
$846$	3.71508	−	34.4224i	0.127727	−	1.18347i
$847$	3.27369	+	1.89007i	0.112485	+	0.0649434i
$848$	−9.17868	−	4.74559i	−0.315197	−	0.162964i
$849$	−1.25474	+	6.50817i	−0.0430626	+	0.223360i
$850$	−18.3090	−	38.1028i	−0.627992	−	1.30691i
$851$	6.18651	+	5.19110i	0.212071	+	0.177949i
$852$	−3.97816	−	6.77586i	−0.136290	−	0.232137i
$853$	−13.2447	−	4.82069i	−0.453491	−	0.165057i	0.105168	−	0.994454i	$-0.466462\pi$
$853$	−13.2447	−	4.82069i	−0.453491	−	0.165057i	−0.558659	+	0.829397i	$0.688684\pi$
$854$	16.8405	−	12.0855i	0.576270	−	0.413558i
$855$	38.8807	−	12.7646i	1.32969	−	0.436541i
$856$	−0.276924	−	0.258281i	−0.00946506	−	0.00882786i
$857$	33.4471	−	5.89762i	1.14253	−	0.201459i	0.429818	−	0.902916i	$-0.358578\pi$
$857$	33.4471	−	5.89762i	1.14253	−	0.201459i	0.712712	+	0.701457i	$0.247467\pi$
$858$	−3.95896	+	14.5238i	−0.135157	+	0.495836i
$859$	−14.1686	−	38.9280i	−0.483427	−	1.32821i	−0.906537	−	0.422127i	$-0.861284\pi$
$859$	−14.1686	−	38.9280i	−0.483427	−	1.32821i	0.423109	−	0.906079i	$-0.360939\pi$
$860$	−62.9251	+	38.3042i	−2.14573	+	1.30616i
$861$	−0.217478	+	13.6552i	−0.00741163	+	0.465369i
$862$	13.3230	+	47.5094i	0.453783	+	1.61818i
$863$	−41.7747			−1.42203			−0.711013	−	0.703178i	$-0.751763\pi$
$863$	−41.7747			−1.42203			−0.711013	+	0.703178i	$0.751763\pi$
$864$	−7.31610	+	28.4688i	−0.248899	+	0.968530i
$865$	−73.7753			−2.50843
$866$	−11.8597	−	42.2915i	−0.403010	−	1.43712i
$867$	7.89013	+	4.72447i	0.267963	+	0.160452i
$868$	4.07373	−	2.47979i	0.138271	−	0.0841694i
$869$	−0.893551	−	2.45501i	−0.0303117	−	0.0832806i
$870$	2.57472	−	0.677990i	0.0872912	−	0.0229860i
$871$	30.1115	−	5.30946i	1.02029	−	0.179904i
$872$	30.1789	+	28.1473i	1.02199	+	0.953186i
$873$	−15.2935	+	12.0241i	−0.517608	+	0.406954i
$874$	14.5557	−	10.4459i	0.492355	−	0.353337i
$875$	−4.20206	−	1.52942i	−0.142056	−	0.0517040i
$876$	50.9774	−	0.371507i	1.72237	−	0.0125521i
$877$	13.8709	+	11.6391i	0.468388	+	0.393024i	0.846206	−	0.532856i	$-0.178881\pi$
$877$	13.8709	+	11.6391i	0.468388	+	0.393024i	−0.377818	+	0.925880i	$0.623326\pi$
$878$	−13.8553	−	28.8343i	−0.467595	−	0.973112i
$879$	4.43153	−	1.53348i	0.149472	−	0.0517229i
$880$	32.1344	+	16.6143i	1.08325	+	0.560066i
$881$	−34.5674	−	19.9575i	−1.16460	−	0.672385i	−0.212202	−	0.977226i	$-0.568063\pi$
$881$	−34.5674	−	19.9575i	−1.16460	−	0.672385i	−0.952403	+	0.304841i	$0.901397\pi$
$882$	−4.23312	+	0.284141i	−0.142536	+	0.00956751i
$883$	3.33190	−	1.92367i	0.112127	−	0.0647367i	−0.442888	−	0.896577i	$-0.646046\pi$
$883$	3.33190	−	1.92367i	0.112127	−	0.0647367i	0.555015	+	0.831840i	$0.312713\pi$
$884$	16.8693	+	13.5003i	0.567374	+	0.454065i
$885$	7.95889	+	3.04118i	0.267535	+	0.102228i
$886$	−1.82439	+	24.0670i	−0.0612917	+	0.808546i
$887$	7.64391	−	43.3508i	0.256657	−	1.45558i	−0.535125	−	0.844773i	$-0.679736\pi$
$887$	7.64391	−	43.3508i	0.256657	−	1.45558i	0.791782	−	0.610803i	$-0.209153\pi$
$888$	−8.77898	+	9.11715i	−0.294603	+	0.305951i
$889$	0.924660	−	0.775882i	0.0310121	−	0.0260223i
$890$	29.7018	−	65.6751i	0.995606	−	2.20143i
$891$	2.67477	+	24.0345i	0.0896082	+	0.805185i
$892$	12.2707	−	10.7915i	0.410854	−	0.361325i
$893$	−21.2588	−	25.3353i	−0.711399	−	0.847813i
$894$	20.4770	−	1.70243i	0.684854	−	0.0569378i
$895$	47.0522	+	8.29658i	1.57278	+	0.277324i
$896$	−9.83185	+	5.59774i	−0.328459	+	0.187007i
$897$	4.42015	−	11.5677i	0.147584	−	0.386234i
$898$	6.84330	−	26.7790i	0.228364	−	0.893626i
$899$	−0.385038	−	0.666906i	−0.0128417	−	0.0222425i
$900$	−24.1555	−	29.2976i	−0.805182	−	0.976586i
$901$	−6.10067	+	10.5667i	−0.203243	+	0.352027i
$902$	21.4309	+	20.9392i	0.713572	+	0.697197i
$903$	−6.19838	−	17.9124i	−0.206269	−	0.596089i
$904$	−3.80489	+	8.96157i	−0.126549	+	0.298057i
$905$	10.5099	−	12.5252i	0.349360	−	0.416351i
$906$	33.7171	−	15.5456i	1.12018	−	0.516469i
$907$	1.15512	−	3.17368i	0.0383553	−	0.105380i	−0.919037	−	0.394172i	$-0.871031\pi$
$907$	1.15512	−	3.17368i	0.0383553	−	0.105380i	0.957392	+	0.288792i	$0.0932536\pi$
$908$	−5.08563	+	1.01898i	−0.168773	+	0.0338159i
$909$	18.6421	−	46.5500i	0.618320	−	1.54397i
$910$	10.8338	−	1.07467i	0.359137	−	0.0356250i
$911$	3.00619	+	17.0490i	0.0995995	+	0.564857i	0.993241	+	0.116074i	$0.0370311\pi$
$911$	3.00619	+	17.0490i	0.0995995	+	0.564857i	−0.893641	+	0.448783i	$0.851858\pi$
$912$	14.7742	+	23.8772i	0.489223	+	0.790652i
$913$	−22.4191	+	8.15987i	−0.741963	+	0.270052i
$914$	−22.0599	−	15.0680i	−0.729676	−	0.498405i
$915$	−43.8965	+	73.3096i	−1.45117	+	2.42354i
$916$	−33.5447	−	5.11510i	−1.10835	−	0.169008i
$917$			13.8151i			0.456216i
$918$	33.1796	+	10.1898i	1.09509	+	0.336314i
$919$			19.0908i			0.629749i	0.949133	+	0.314874i	$0.101962\pi$
$919$			19.0908i			0.629749i	−0.949133	+	0.314874i	$0.898038\pi$
$920$	−24.9560	−	16.2097i	−0.822776	−	0.534419i
$921$	56.3802	+	0.897930i	1.85779	+	0.0295878i
$922$	24.5092	−	35.8820i	0.807167	−	1.18171i
$923$	−4.87502	+	1.77436i	−0.160463	+	0.0584038i
$924$	−5.93093	+	7.17374i	−0.195113	+	0.235999i
$925$	−2.83918	−	16.1018i	−0.0933516	−	0.529423i
$926$	1.59373	+	16.0664i	0.0523731	+	0.527975i
$927$	2.28918	+	0.479271i	0.0751864	+	0.0157413i
$928$	0.866782	+	1.60811i	0.0284535	+	0.0527888i
$929$	−10.1226	+	27.8117i	−0.332113	+	0.912473i	0.655448	+	0.755240i	$0.272480\pi$
$929$	−10.1226	+	27.8117i	−0.332113	+	0.912473i	−0.987561	+	0.157233i	$0.949743\pi$
$930$	−11.3457	+	16.0553i	−0.372039	+	0.526473i
$931$	−2.60507	+	3.10460i	−0.0853777	+	0.101749i
$932$	−5.45134	+	0.126562i	−0.178565	+	0.00414569i
$933$	44.5093	+	8.58116i	1.45717	+	0.280934i
$934$	−0.250778	+	0.256667i	−0.00820570	+	0.00839842i
$935$	21.3584	−	36.9938i	0.698493	−	1.20983i
$936$	17.6135	+	8.14972i	0.575714	+	0.266382i
$937$	8.19732	+	14.1982i	0.267795	+	0.463834i	0.968292	−	0.249821i	$-0.0803718\pi$
$937$	8.19732	+	14.1982i	0.267795	+	0.463834i	−0.700497	+	0.713655i	$0.747038\pi$
$938$	18.3170	+	4.68087i	0.598071	+	0.152836i
$939$	−2.39349	+	0.382841i	−0.0781084	+	0.0124936i
$940$	−26.3552	+	48.1985i	−0.859610	+	1.57206i
$941$	8.42845	+	1.48616i	0.274760	+	0.0484476i	0.309330	−	0.950955i	$-0.399895\pi$
$941$	8.42845	+	1.48616i	0.274760	+	0.0484476i	−0.0345704	+	0.999402i	$0.511006\pi$
$942$	−50.1426	−	23.6461i	−1.63374	−	0.770430i
$943$	−15.8430	−	18.8809i	−0.515919	−	0.614848i
$944$	−0.746870	+	5.79808i	−0.0243086	+	0.188712i
$945$	15.5464	−	8.01129i	0.505725	−	0.260607i
$946$	−37.8899	−	17.1358i	−1.23191	−	0.557134i
$947$	10.8135	−	9.07361i	0.351392	−	0.294853i	−0.449957	−	0.893050i	$-0.648561\pi$
$947$	10.8135	−	9.07361i	0.351392	−	0.294853i	0.801349	+	0.598198i	$0.204116\pi$
$948$	−3.31265	+	0.609033i	−0.107590	+	0.0197805i
$949$	5.84484	−	33.1477i	0.189732	−	1.07602i
$950$	−36.1684	−	2.74174i	−1.17346	−	0.0889538i
$951$	−21.8532	+	17.7517i	−0.708637	+	0.575638i
$952$	6.06405	+	11.9039i	0.196537	+	0.385809i
$953$	9.77443	−	5.64327i	0.316625	−	0.182804i	−0.333262	−	0.942834i	$-0.608149\pi$
$953$	9.77443	−	5.64327i	0.316625	−	0.182804i	0.649887	+	0.760031i	$0.274816\pi$
$954$	−3.05029	+	10.5267i	−0.0987567	+	0.340813i
$955$	−13.6393	−	7.87467i	−0.441358	−	0.254818i
$956$	3.08651	+	7.90428i	0.0998250	+	0.255643i
$957$	1.13581	+	0.984301i	0.0367155	+	0.0318179i
$958$	−48.9064	+	23.5003i	−1.58010	+	0.759260i
$959$	15.3607	+	12.8892i	0.496023	+	0.416213i
$960$	28.0169	−	37.2846i	0.904243	−	1.20335i
$961$	−23.7872	−	8.65785i	−0.767330	−	0.279285i
$962$	4.87233	+	6.78932i	0.157090	+	0.218896i
$963$	−0.211798	+	0.341265i	−0.00682511	+	0.0109971i
$964$	−8.32875	+	24.6487i	−0.268251	+	0.793881i
$965$	50.4353	−	8.89310i	1.62357	−	0.286279i
$966$	5.43756	−	5.39079i	0.174951	−	0.173446i
$967$	9.57374	+	26.3036i	0.307871	+	0.845868i	0.993071	+	0.117513i	$0.0374923\pi$
$967$	9.57374	+	26.3036i	0.307871	+	0.845868i	−0.685201	+	0.728354i	$0.740285\pi$
$968$	−1.30207	−	10.6122i	−0.0418502	−	0.341090i
$969$	28.9740	−	16.1185i	0.930780	−	0.517801i
$970$	29.7207	−	8.33453i	0.954275	−	0.267606i
$971$	32.2404			1.03464			0.517321	−	0.855791i	$-0.326929\pi$
$971$	32.2404			1.03464			0.517321	+	0.855791i	$0.326929\pi$
$972$	31.1273	+	1.75783i	0.998409	+	0.0563825i
$973$	−11.7194			−0.375707
$974$	28.8066	−	8.07817i	0.923021	−	0.258841i
$975$	−21.9090	+	12.1881i	−0.701648	+	0.390333i
$976$	−55.9640	−	17.4738i	−1.79136	−	0.559321i
$977$	6.52036	+	17.9145i	0.208605	+	0.573137i	0.999233	−	0.0391596i	$-0.0124681\pi$
$977$	6.52036	+	17.9145i	0.208605	+	0.573137i	−0.790628	+	0.612297i	$0.790246\pi$
$978$	−31.7527	+	31.4797i	−1.01534	+	1.00661i
$979$	40.0704	−	7.06549i	1.28065	−	0.225814i
$980$	6.37736	+	2.15490i	0.203717	+	0.0688357i
$981$	23.0816	−	37.1908i	0.736939	−	1.18741i
$982$	13.5642	+	18.9010i	0.432851	+	0.603154i
$983$	16.2614	+	5.91867i	0.518658	+	0.188776i	0.588067	−	0.808812i	$-0.299889\pi$
$983$	16.2614	+	5.91867i	0.518658	+	0.188776i	−0.0694088	+	0.997588i	$0.522111\pi$
$984$	31.2178	−	22.7498i	0.995186	−	0.725238i
$985$	−31.3244	−	26.2843i	−0.998079	−	0.837488i
$986$	1.94435	−	0.934290i	0.0619208	−	0.0297539i
$987$	−10.6816	−	9.25675i	−0.339999	−	0.294646i
$988$	17.2691	−	6.74335i	0.549403	−	0.214534i
$989$	29.6251	+	17.1040i	0.942023	+	0.543877i
$990$	10.6790	−	36.8537i	0.339401	−	1.17129i
$991$	50.3866	−	29.0907i	1.60058	−	0.924096i	0.609211	−	0.793008i	$-0.291486\pi$
$991$	50.3866	−	29.0907i	1.60058	−	0.924096i	0.991371	−	0.131088i	$-0.0418471\pi$
$992$	−12.5354	−	4.98211i	−0.397998	−	0.158182i
$993$	−17.4191	+	14.1498i	−0.552778	+	0.449031i
$994$	−3.19858	−	0.242468i	−0.101453	−	0.00769061i
$995$	−7.23455	+	41.0292i	−0.229351	+	1.30071i
$996$	5.56166	+	30.2509i	0.176228	+	0.958538i
$997$	13.5335	−	11.3559i	0.428610	−	0.359646i	−0.402817	−	0.915280i	$-0.631969\pi$
$997$	13.5335	−	11.3559i	0.428610	−	0.359646i	0.831427	+	0.555634i	$0.187525\pi$
$998$	10.4667	+	4.73362i	0.331319	+	0.149840i
$999$	11.2921	+	7.25980i	0.357267	+	0.229690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.491.46	yes	648
4.3	odd	2	inner	756.2.cf.a.491.15	✓	648
27.11	odd	18	inner	756.2.cf.a.659.15	yes	648
108.11	even	18	inner	756.2.cf.a.659.46	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.15	✓	648	4.3	odd	2	inner
756.2.cf.a.491.46	yes	648	1.1	even	1	trivial
756.2.cf.a.659.15	yes	648	27.11	odd	18	inner
756.2.cf.a.659.46	yes	648	108.11	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.381855 - 1.36169i) q^{2} +(1.51360 - 0.842029i) q^{3} +(-1.70837 + 1.03993i) q^{4} +(-1.15117 - 3.16281i) q^{5} +(-1.72455 - 1.73951i) q^{6} +(-0.984808 + 0.173648i) q^{7} +(2.06841 + 1.92916i) q^{8} +(1.58197 - 2.54899i) q^{9} +(-3.86718 + 2.77527i) q^{10} +(-2.52494 - 0.919002i) q^{11} +(-1.71014 + 3.01254i) q^{12} +(1.75210 + 1.47018i) q^{13} +(0.612508 + 1.27469i) q^{14} +(-4.40559 - 3.81792i) q^{15} +(1.83708 - 3.55319i) q^{16} +(-4.09050 - 2.36165i) q^{17} +(-4.07501 - 1.18081i) q^{18} +(-3.50980 + 2.02638i) q^{19} +(5.25574 + 4.20613i) q^{20} +(-1.34439 + 1.09207i) q^{21} +(-0.287232 + 3.78909i) q^{22} +(0.542808 - 3.07842i) q^{23} +(4.75516 + 1.17832i) q^{24} +(-4.84798 + 4.06793i) q^{25} +(1.33288 - 2.94720i) q^{26} +(0.248152 - 5.19022i) q^{27} +(1.50184 - 1.32079i) q^{28} +(-0.207583 - 0.247388i) q^{29} +(-3.51651 + 7.45692i) q^{30} +(2.34834 + 0.414075i) q^{31} +(-5.53982 - 1.14473i) q^{32} +(-4.59557 + 0.735068i) q^{33} +(-1.65385 + 6.47178i) q^{34} +(1.68290 + 2.91486i) q^{35} +(-0.0518239 + 5.99978i) q^{36} +(-1.29177 + 2.23741i) q^{37} +(4.09953 + 4.00546i) q^{38} +(3.88991 + 0.749955i) q^{39} +(3.72049 - 8.76280i) q^{40} +(5.06829 - 6.04015i) q^{41} +(2.00042 + 1.41362i) q^{42} +(-3.74287 + 10.2835i) q^{43} +(5.26924 - 1.05576i) q^{44} +(-9.88311 - 2.06917i) q^{45} +(-4.39911 + 0.436375i) q^{46} +(1.41707 + 8.03658i) q^{47} +(-0.211278 - 6.92498i) q^{48} +(0.939693 - 0.342020i) q^{49} +(7.39047 + 5.04806i) q^{50} +(-8.17996 - 0.130277i) q^{51} +(-4.52213 - 0.689561i) q^{52} -2.58322i q^{53} +(-7.16221 + 1.64401i) q^{54} +9.04383i q^{55} +(-2.37198 - 1.54068i) q^{56} +(-3.60616 + 6.02249i) q^{57} +(-0.257598 + 0.377129i) q^{58} +(-1.37336 + 0.499862i) q^{59} +(11.4968 + 1.94091i) q^{60} +(-2.54518 - 14.4345i) q^{61} +(-0.332884 - 3.35581i) q^{62} +(-1.11531 + 2.78497i) q^{63} +(0.556651 + 7.98061i) q^{64} +(2.63296 - 7.23399i) q^{65} +(2.75577 + 5.97703i) q^{66} +(8.59298 - 10.2407i) q^{67} +(9.44406 - 0.219260i) q^{68} +(-1.77052 - 5.11655i) q^{69} +(3.32651 - 3.40463i) q^{70} +(-1.13411 + 1.96434i) q^{71} +(8.18960 - 2.22048i) q^{72} +(-7.35814 - 12.7447i) q^{73} +(3.53992 + 0.904619i) q^{74} +(-3.91258 + 10.2394i) q^{75} +(3.88875 - 7.11178i) q^{76} +(2.64616 + 0.466589i) q^{77} +(-0.464180 - 5.58321i) q^{78} +(0.624986 + 0.744830i) q^{79} +(-13.3529 - 1.72003i) q^{80} +(-3.99472 - 8.06488i) q^{81} +(-10.1601 - 4.59495i) q^{82} +(6.80175 - 5.70735i) q^{83} +(1.16104 - 3.26374i) q^{84} +(-2.76060 + 15.6561i) q^{85} +(15.4321 + 1.16983i) q^{86} +(-0.522506 - 0.199656i) q^{87} +(-3.44970 - 6.77189i) q^{88} +(-13.1141 + 7.57142i) q^{89} +(0.956359 + 14.2478i) q^{90} +(-1.98077 - 1.14360i) q^{91} +(2.27403 + 5.82357i) q^{92} +(3.90311 - 1.35062i) q^{93} +(10.4022 - 4.99840i) q^{94} +(10.4495 + 8.76813i) q^{95} +(-9.34897 + 2.93203i) q^{96} +(-6.09370 - 2.21792i) q^{97} +(-0.824550 - 1.14896i) q^{98} +(-6.33691 + 4.98221i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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