LMFDB - Embedded newform 756.2.cf.a.659.46

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)

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")

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);

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			659.46
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.46

$q$-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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$

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	0.361341	+	0.932434i	$0.382319\pi$
$5$	−1.15117	+	3.16281i	−0.514819	+	1.41445i	−0.876160	+	0.482020i	$0.839903\pi$
$6$	−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	−0.693351	−	0.720600i	$-0.743867\pi$
$11$	−2.52494	+	0.919002i	−0.761297	+	0.277089i	−0.0679456	+	0.997689i	$0.521644\pi$
$12$	−1.71014	−	3.01254i	−0.493676	−	0.869646i
$13$	1.75210	−	1.47018i	0.485944	−	0.407756i	−0.366626	−	0.930368i	$-0.619487\pi$
$13$	1.75210	−	1.47018i	0.485944	−	0.407756i	0.852570	+	0.522613i	$0.175043\pi$
$14$	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	−0.905899	−	0.423494i	$-0.860803\pi$
$17$	−4.09050	+	2.36165i	−0.992092	+	0.572784i	−0.0861929	+	0.996278i	$0.527470\pi$
$18$	−4.07501	+	1.18081i	−0.960489	+	0.278319i
$19$	−3.50980	−	2.02638i	−0.805204	−	0.464885i	0.0400839	−	0.999196i	$-0.487237\pi$
$19$	−3.50980	−	2.02638i	−0.805204	−	0.464885i	−0.845287	+	0.534312i	$0.820571\pi$
$20$	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	0.987634	+	0.156779i	$0.0501111\pi$
$23$	0.542808	+	3.07842i	0.113183	+	0.641894i	−0.874450	+	0.485115i	$0.838778\pi$
$24$	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	−0.784974	−	0.619529i	$-0.787324\pi$
$29$	−0.207583	+	0.247388i	−0.0385472	+	0.0459388i	0.746426	+	0.665468i	$0.231768\pi$
$30$	−3.51651	−	7.45692i	−0.642023	−	1.36144i
$31$	2.34834	−	0.414075i	0.421774	−	0.0743701i	0.0412669	−	0.999148i	$-0.486861\pi$
$31$	2.34834	−	0.414075i	0.421774	−	0.0743701i	0.380507	+	0.924778i	$0.375749\pi$
$32$	−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	0.740089	−	0.672509i	$-0.234784\pi$
$37$	−1.29177	−	2.23741i	−0.212366	−	0.367829i	−0.952455	+	0.304681i	$0.901450\pi$
$38$	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	0.999393	−	0.0348456i	$-0.0110939\pi$
$41$	5.06829	+	6.04015i	0.791534	+	0.943313i	−0.207859	+	0.978159i	$0.566649\pi$
$42$	2.00042	−	1.41362i	0.308671	−	0.218127i
$43$	−3.74287	−	10.2835i	−0.570782	−	1.56821i	−0.803272	−	0.595613i	$-0.796909\pi$
$43$	−3.74287	−	10.2835i	−0.570782	−	1.56821i	0.232490	−	0.972599i	$-0.425313\pi$
$44$	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	−0.688041	−	0.725671i	$-0.741529\pi$
$47$	1.41707	−	8.03658i	0.206700	−	1.17226i	0.894742	−	0.446584i	$-0.147360\pi$
$48$	−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	$0.0567740\pi$
$53$			2.58322i			0.354833i	−0.984136	+	0.177417i	$0.943226\pi$
$54$	−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	0.251071	−	0.967969i	$-0.419217\pi$
$59$	−1.37336	−	0.499862i	−0.178796	−	0.0650764i	−0.429867	+	0.902892i	$0.641440\pi$
$60$	11.4968	−	1.94091i	1.48423	−	0.250571i
$61$	−2.54518	+	14.4345i	−0.325877	+	1.84814i	0.177559	+	0.984110i	$0.443180\pi$
$61$	−2.54518	+	14.4345i	−0.325877	+	1.84814i	−0.503437	+	0.864032i	$0.667931\pi$
$62$	−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	0.967065	+	0.254531i	$0.0819211\pi$
$67$	8.59298	+	10.2407i	1.04980	+	1.25110i	0.0827351	+	0.996572i	$0.473634\pi$
$68$	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	0.790848	−	0.612013i	$-0.209640\pi$
$71$	−1.13411	−	1.96434i	−0.134594	−	0.233124i	−0.925442	+	0.378888i	$0.876306\pi$
$72$	8.18960	+	2.22048i	0.965153	+	0.261686i
$73$	−7.35814	+	12.7447i	−0.861205	+	1.49165i	0.00956070	+	0.999954i	$0.496957\pi$
$73$	−7.35814	+	12.7447i	−0.861205	+	1.49165i	−0.870766	+	0.491697i	$0.836377\pi$
$74$	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	−0.729739	−	0.683725i	$-0.760359\pi$
$79$	0.624986	−	0.744830i	0.0703165	−	0.0837999i	0.800056	+	0.599925i	$0.204803\pi$
$80$	−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	0.934599	−	0.355704i	$-0.115759\pi$
$83$	6.80175	+	5.70735i	0.746589	+	0.626463i	−0.188009	+	0.982167i	$0.560203\pi$
$84$	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	−0.396765	−	0.917920i	$-0.629867\pi$
$89$	−13.1141	−	7.57142i	−1.39009	−	0.802569i	−0.993325	+	0.115351i	$0.963201\pi$
$90$	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	−0.632315	−	0.774712i	$-0.717895\pi$
$97$	−6.09370	+	2.21792i	−0.618721	+	0.225196i	0.0135937	+	0.999908i	$0.495673\pi$
$98$	−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	0.915397	−	0.402552i	$-0.131877\pi$
$101$	16.4608	+	2.90248i	1.63791	+	0.288807i	0.722511	+	0.691359i	$0.242988\pi$
$102$	2.94616	−	11.1883i	0.291713	−	1.10780i
$103$	0.266640	−	0.732588i	0.0262728	−	0.0721840i	−0.925863	−	0.377860i	$-0.876660\pi$
$103$	0.266640	−	0.732588i	0.0262728	−	0.0721840i	0.952136	+	0.305676i	$0.0988824\pi$
$104$	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	−0.871920	−	0.489649i	$-0.837125\pi$
$113$	1.17728	−	3.23456i	0.110750	−	0.304282i	0.982669	+	0.185367i	$0.0593473\pi$
$114$	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	0.452903	−	0.891560i	$-0.350388\pi$
$127$	−1.04534	−	0.603529i	−0.0927592	−	0.0535546i	−0.545662	+	0.838005i	$0.683722\pi$
$128$	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	0.890036	+	0.455890i	$0.150679\pi$
$131$	2.39897	+	13.6053i	0.209599	+	1.18870i	−0.680437	+	0.732807i	$0.738210\pi$
$132$	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	−0.155304	+	0.987867i	$0.549636\pi$
$137$	−12.8892	+	15.3607i	−1.10119	+	1.31235i	−0.945890	+	0.324486i	$0.894809\pi$
$138$	−6.29105	−	4.36467i	−0.535530	−	0.371546i
$139$	11.5414	−	2.03506i	0.978927	−	0.172611i	0.338781	−	0.940865i	$-0.389985\pi$
$139$	11.5414	−	2.03506i	0.978927	−	0.172611i	0.640145	+	0.768254i	$0.278874\pi$
$140$	−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	0.498535	−	0.866870i	$-0.333872\pi$
$149$	−5.39206	−	6.42600i	−0.441735	−	0.526439i	−0.940270	+	0.340431i	$0.889427\pi$
$150$	15.4368	−	1.41775i	1.26041	−	0.115759i
$151$	−5.18420	−	14.2435i	−0.421884	−	1.15912i	−0.950627	−	0.310335i	$-0.899559\pi$
$151$	−5.18420	−	14.2435i	−0.421884	−	1.15912i	0.528743	−	0.848782i	$-0.322663\pi$
$152$	−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	0.995519	−	0.0945593i	$-0.0301442\pi$
$157$	21.2677	+	7.74082i	1.69735	+	0.617785i	0.701830	+	0.712344i	$0.252366\pi$
$158$	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	$0.253516\pi$
$163$			18.2538i			1.42975i	−0.699254	+	0.714874i	$0.746484\pi$
$164$	−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	0.942901	−	0.333074i	$-0.108086\pi$
$167$	18.7525	+	6.82534i	1.45111	+	0.528160i	0.508208	+	0.861234i	$0.330308\pi$
$168$	−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	0.804552	+	0.593882i	$0.202405\pi$
$173$	7.49678	+	20.5972i	0.569970	+	1.56598i	−0.234582	+	0.972096i	$0.575372\pi$
$174$	−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	−0.999367	−	0.0355829i	$-0.988671\pi$
$179$	−7.09759	−	12.2934i	−0.530499	−	0.918851i	0.468868	−	0.883268i	$-0.344662\pi$
$180$	19.0358	+	6.74285i	1.41885	+	0.502583i
$181$	2.42892	−	4.20701i	0.180540	−	0.312704i	−0.761525	−	0.648136i	$-0.775549\pi$
$181$	2.42892	−	4.20701i	0.180540	−	0.312704i	0.942065	+	0.335432i	$0.108882\pi$
$182$	−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	0.763193	−	0.646171i	$-0.223631\pi$
$191$	3.58450	+	3.00775i	0.259365	+	0.217633i	−0.503827	+	0.863804i	$0.668075\pi$
$192$	7.56245	−	11.6107i	0.545773	−	0.837933i
$193$	−2.64220	−	14.9847i	−0.190190	−	1.07862i	−0.919104	−	0.394014i	$-0.871086\pi$
$193$	−2.64220	−	14.9847i	−0.190190	−	1.07862i	0.728915	−	0.684605i	$-0.240025\pi$
$194$	−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	0.825555	−	0.564322i	$-0.190862\pi$
$197$	10.5214	+	6.07451i	0.749616	+	0.432791i	−0.0759393	+	0.997112i	$0.524196\pi$
$198$	9.20398	−	6.72640i	0.654098	−	0.478024i
$199$	−10.7197	+	6.18904i	−0.759902	+	0.438730i	−0.829261	−	0.558862i	$-0.811238\pi$
$199$	−10.7197	+	6.18904i	−0.759902	+	0.438730i	0.0693586	+	0.997592i	$0.477905\pi$
$200$	−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	0.564916	+	0.825148i	$0.308908\pi$
$211$	−5.78462	+	15.8931i	−0.398230	+	1.09413i	−0.963146	+	0.268979i	$0.913314\pi$
$212$	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	−0.102387	−	0.994745i	$-0.532648\pi$
$223$	−8.04634	−	1.41879i	−0.538823	−	0.0950090i	−0.436435	+	0.899736i	$0.643759\pi$
$224$	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	−0.259878	−	0.965641i	$-0.583682\pi$
$227$	2.43696	−	0.886979i	0.161746	−	0.0588709i	0.421624	+	0.906771i	$0.361460\pi$
$228$	−0.102311	+	14.0388i	−0.00677569	+	0.929744i
$229$	12.9969	−	10.9057i	0.858858	−	0.720668i	−0.102863	−	0.994695i	$-0.532800\pi$
$229$	12.9969	−	10.9057i	0.858858	−	0.720668i	0.961722	+	0.274028i	$0.0883560\pi$
$230$	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	−0.420660	−	0.907218i	$-0.638202\pi$
$233$	2.36114	−	1.36320i	0.154683	−	0.0893064i	0.575344	+	0.817912i	$0.304868\pi$
$234$	−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	0.999320	−	0.0368695i	$-0.0117386\pi$
$239$	0.736748	+	4.17831i	0.0476563	+	0.270272i	−0.951664	+	0.307142i	$0.900627\pi$
$240$	−21.6592	−	8.64006i	−1.39810	−	0.557714i
$241$	9.96540	+	8.36197i	0.641928	+	0.538642i	0.904610	−	0.426241i	$-0.140162\pi$
$241$	9.96540	+	8.36197i	0.641928	+	0.538642i	−0.262682	+	0.964883i	$0.584607\pi$
$242$	−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	0.329560	+	0.944135i	$0.393100\pi$
$251$	−10.3433	+	17.9151i	−0.652864	+	1.13079i	−0.982425	+	0.186660i	$0.940234\pi$
$252$	−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	0.487908	−	0.872895i	$-0.337760\pi$
$257$	−7.31745	−	8.72060i	−0.456450	−	0.543976i	−0.944358	+	0.328919i	$0.893316\pi$
$258$	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	−0.972115	−	0.234505i	$-0.924653\pi$
$263$	0.349965	−	1.98475i	0.0215797	−	0.122385i	0.993695	+	0.112120i	$0.0357642\pi$
$264$	−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	$0.0829708\pi$
$269$			8.45381i			0.515438i	−0.966220	+	0.257719i	$0.917029\pi$
$270$	13.4446	−	20.7602i	0.818213	−	1.26343i
$271$		−	25.5448i		−	1.55174i	−0.630895	−	0.775868i	$-0.717312\pi$
$271$		−	25.5448i		−	1.55174i	0.630895	−	0.775868i	$-0.282688\pi$
$272$	−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	−0.799590	−	0.600547i	$-0.794950\pi$
$277$	2.61596	−	14.8359i	0.157178	−	0.891400i	0.956768	−	0.290854i	$-0.0939393\pi$
$278$	−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	−0.988625	−	0.150404i	$-0.951943\pi$
$281$	−5.49781	−	15.1051i	−0.327972	−	0.901096i	0.660653	−	0.750692i	$-0.270280\pi$
$282$	11.5359	+	16.3245i	0.686955	+	0.972111i
$283$	−2.45975	−	2.93141i	−0.146217	−	0.174254i	0.687965	−	0.725744i	$-0.258504\pi$
$283$	−2.45975	−	2.93141i	−0.146217	−	0.174254i	−0.834182	+	0.551489i	$0.814060\pi$
$284$	−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	−0.0952219	−	0.995456i	$-0.530356\pi$
$293$	2.66626	−	0.470134i	0.155765	−	0.0274655i	0.250987	+	0.967991i	$0.419245\pi$
$294$	−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	0.619525	−	0.784977i	$-0.287325\pi$
$307$	28.1937	−	16.2776i	1.60910	−	0.929013i	0.989573	−	0.144035i	$-0.0460079\pi$
$308$	−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	0.137482	−	0.990504i	$-0.456099\pi$
$311$	20.0479	−	16.8222i	1.13681	−	0.953899i	0.999330	+	0.0366057i	$0.0116545\pi$
$312$	6.59915	−	9.05549i	0.373603	−	0.512666i
$313$	−1.31505	+	0.478638i	−0.0743309	+	0.0270542i	−0.378918	−	0.925430i	$-0.623704\pi$
$313$	−1.31505	+	0.478638i	−0.0743309	+	0.0270542i	0.304587	+	0.952484i	$0.401482\pi$
$314$	−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	−0.295053	−	0.955481i	$-0.595337\pi$
$317$	−16.0081	−	2.82267i	−0.899106	−	0.158537i	−0.604053	+	0.796944i	$0.706448\pi$
$318$	−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	−0.188412	−	0.982090i	$-0.560334\pi$
$331$	−12.7600	−	2.24994i	−0.701355	−	0.123668i	−0.512944	+	0.858422i	$0.671445\pi$
$332$	−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	−0.145635	−	0.989338i	$-0.546523\pi$
$337$	14.7482	−	12.3752i	0.803384	−	0.674119i	0.949019	+	0.315219i	$0.102078\pi$
$338$	−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	−0.935425	−	0.353524i	$-0.884983\pi$
$347$	−3.30321	−	18.7334i	−0.177325	−	1.00566i	0.758100	−	0.652138i	$-0.226128\pi$
$348$	1.10026	+	0.202284i	0.0589803	+	0.0108436i
$349$	−10.9659	−	9.20149i	−0.586992	−	0.492544i	0.300243	−	0.953863i	$-0.402932\pi$
$349$	−10.9659	−	9.20149i	−0.586992	−	0.492544i	−0.887235	+	0.461318i	$0.847377\pi$
$350$	−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	−0.477534	−	0.878613i	$-0.658469\pi$
$353$	8.84279	−	10.5384i	0.470654	−	0.560904i	0.948188	+	0.317709i	$0.102914\pi$
$354$	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	−0.897545	−	0.440923i	$-0.854651\pi$
$359$	−1.26798	+	2.19621i	−0.0669216	+	0.115912i	0.830623	+	0.556835i	$0.187984\pi$
$360$	−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	−0.934754	−	0.355295i	$-0.884380\pi$
$367$	−8.56463	−	23.5311i	−0.447070	−	1.22832i	0.487684	−	0.873020i	$-0.337842\pi$
$368$	−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	0.997412	−	0.0719028i	$-0.0229072\pi$
$373$	33.1271	+	12.0573i	1.71526	+	0.624302i	0.717843	+	0.696205i	$0.245129\pi$
$374$	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	$-0.827621\pi$
$379$		−	20.0699i		−	1.03092i	0.856913	−	0.515461i	$-0.172379\pi$
$380$	−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	0.407971	−	0.912995i	$-0.366237\pi$
$383$	2.61524	+	0.951871i	0.133633	+	0.0486383i	−0.274338	+	0.961633i	$0.588459\pi$
$384$	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	0.923822	−	0.382823i	$-0.125048\pi$
$389$	−0.590528	−	1.62246i	−0.0299409	−	0.0822621i	−0.953762	+	0.300561i	$0.902826\pi$
$390$	−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	−0.810343	−	0.585956i	$-0.800719\pi$
$397$	2.03793	−	3.52980i	0.102281	−	0.177155i	0.912624	+	0.408800i	$0.134053\pi$
$398$	−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	−0.639173	−	0.769063i	$-0.720723\pi$
$401$	−19.5597	+	3.44890i	−0.976765	+	0.172230i	−0.337592	+	0.941293i	$0.609612\pi$
$402$	−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	0.978672	+	0.205430i	$0.0658592\pi$
$409$	2.61457	+	14.8280i	0.129282	+	0.733196i	−0.849390	+	0.527766i	$0.823030\pi$
$410$	−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	−0.947879	−	0.318629i	$-0.896777\pi$
$419$	−16.3487	+	13.7182i	−0.798688	+	0.670179i	0.149191	+	0.988808i	$0.452333\pi$
$420$	−11.6591	−	0.0849683i	−0.568908	−	0.00414603i
$421$	2.17345	−	0.791071i	0.105927	−	0.0385545i	−0.288513	−	0.957476i	$-0.593161\pi$
$421$	2.17345	−	0.791071i	0.105927	−	0.0385545i	0.394440	+	0.918922i	$0.370939\pi$
$422$	−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	0.677786	−	0.735259i	$-0.262939\pi$
$439$	22.2770	+	3.92804i	1.06322	+	0.187475i	0.385438	+	0.922734i	$0.374051\pi$
$440$	−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	−0.693631	−	0.720330i	$-0.743990\pi$
$443$	−16.0375	+	5.83717i	−0.761964	+	0.277332i	−0.0683331	+	0.997663i	$0.521768\pi$
$444$	−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	−0.0442693	−	0.999020i	$-0.514096\pi$
$449$	16.9257	−	9.77205i	0.798773	−	0.461172i	0.843042	+	0.537848i	$0.180763\pi$
$450$	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	0.915103	−	0.403220i	$-0.132109\pi$
$457$	14.4708	+	12.1424i	0.676914	+	0.567999i	−0.238189	+	0.971219i	$0.576554\pi$
$458$	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	−0.0752048	−	0.997168i	$-0.523961\pi$
$461$	19.7505	−	23.5377i	0.919873	−	1.09626i	0.995078	−	0.0990941i	$-0.0315945\pi$
$462$	−3.75181	+	5.40769i	−0.174550	+	0.251589i
$463$	−11.2430	+	1.98244i	−0.522506	+	0.0921319i	−0.428679	−	0.903457i	$-0.641021\pi$
$463$	−11.2430	+	1.98244i	−0.522506	+	0.0921319i	−0.0938266	+	0.995589i	$0.529910\pi$
$464$	−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	−0.868946	−	0.494907i	$-0.835202\pi$
$467$	−0.126870	+	0.219745i	−0.00587084	+	0.0101686i	0.863075	+	0.505076i	$0.168535\pi$
$468$	−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	0.321839	+	0.946795i	$0.395699\pi$
$479$	−6.66242	+	37.7844i	−0.304414	+	1.72642i	−0.626252	+	0.779621i	$0.715412\pi$
$480$	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	$-0.840886\pi$
$487$		−	21.1551i		−	0.958628i	0.877644	−	0.479314i	$-0.159114\pi$
$488$	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	−0.0312290	−	0.999512i	$-0.509942\pi$
$491$	−15.4584	−	5.62638i	−0.697626	−	0.253915i	−0.666397	+	0.745597i	$0.732164\pi$
$492$	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	0.636410	−	0.771351i	$-0.280419\pi$
$499$	−5.22124	−	6.22243i	−0.233735	−	0.278554i	−0.870144	+	0.492797i	$0.835974\pi$
$500$	−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	0.685232	−	0.728324i	$-0.259701\pi$
$503$	−6.46211	−	11.1927i	−0.288131	−	0.499058i	−0.973364	+	0.229266i	$0.926367\pi$
$504$	−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	−0.388488	−	0.921454i	$-0.627003\pi$
$509$	−9.89056	+	1.74397i	−0.438392	+	0.0773003i	−0.0499035	+	0.998754i	$0.515891\pi$
$510$	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	0.768097	−	0.640334i	$-0.221204\pi$
$521$	13.6405	+	7.87532i	0.597599	+	0.345024i	−0.170497	+	0.985358i	$0.554537\pi$
$522$	0.553786	−	1.25322i	0.0242386	−	0.0548521i
$523$	18.3147	−	10.5740i	0.800844	−	0.462368i	−0.0429220	−	0.999078i	$-0.513667\pi$
$523$	18.3147	−	10.5740i	0.800844	−	0.462368i	0.843766	+	0.536711i	$0.180333\pi$
$524$	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	0.868481	−	0.495722i	$-0.165097\pi$
$547$	35.4338	+	6.24793i	1.51504	+	0.267142i	0.646558	+	0.762865i	$0.276208\pi$
$548$	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	−0.477424	−	0.878673i	$-0.658429\pi$
$557$	1.05774	−	0.610686i	0.0448179	−	0.0258756i	0.522242	+	0.852798i	$0.325096\pi$
$558$	−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	0.996434	−	0.0843815i	$-0.0268914\pi$
$563$	0.741064	+	4.20278i	0.0312321	+	0.177126i	−0.965201	+	0.261508i	$0.915780\pi$
$564$	−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	−0.620670	−	0.784072i	$-0.713139\pi$
$569$	6.18453	−	7.37043i	0.259269	−	0.308985i	0.879938	+	0.475088i	$0.157584\pi$
$570$	−2.76835	+	33.2981i	−0.115954	+	1.39470i
$571$	39.3258	−	6.93421i	1.64574	−	0.290188i	0.727466	−	0.686144i	$-0.240698\pi$
$571$	39.3258	−	6.93421i	1.64574	−	0.290188i	0.918269	+	0.395956i	$0.129587\pi$
$572$	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	−0.993182	−	0.116576i	$-0.962808\pi$
$577$	−14.3536	−	24.8612i	−0.597548	−	1.03498i	0.395633	−	0.918409i	$-0.370525\pi$
$578$	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	−0.966699	−	0.255917i	$-0.917623\pi$
$587$	0.708182	−	4.01630i	0.0292298	−	0.165770i	0.995928	+	0.0901469i	$0.0287337\pi$
$588$	−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	$-0.878411\pi$
$593$		−	18.1547i		−	0.745523i	0.927927	−	0.372761i	$-0.121589\pi$
$594$	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	0.122840	−	0.992427i	$-0.460800\pi$
$599$	−10.3032	−	3.75008i	−0.420979	−	0.153224i	−0.543819	+	0.839203i	$0.683022\pi$
$600$	−27.8462	−	13.6312i	−1.13682	−	0.556492i
$601$	4.26732	−	24.2012i	0.174068	−	0.987186i	−0.765147	−	0.643855i	$-0.777334\pi$
$601$	4.26732	−	24.2012i	0.174068	−	0.987186i	0.939215	−	0.343330i	$-0.111555\pi$
$602$	−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	0.468636	−	0.883392i	$-0.344746\pi$
$607$	−11.8928	−	14.1733i	−0.482713	−	0.575275i	−0.951349	+	0.308117i	$0.900301\pi$
$608$	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	−0.481588	−	0.876398i	$-0.659940\pi$
$613$	12.8298	−	22.2218i	0.518189	−	0.897530i	0.999777	−	0.0211319i	$-0.00672698\pi$
$614$	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	−0.996618	−	0.0821764i	$-0.973813\pi$
$617$	−47.3199	+	8.34377i	−1.90503	+	0.335908i	−0.908408	+	0.418084i	$0.862702\pi$
$618$	0.814512	+	1.72721i	0.0327645	+	0.0694786i
$619$	−10.1380	+	12.0820i	−0.407481	+	0.485617i	−0.930286	−	0.366835i	$-0.880441\pi$
$619$	−10.1380	+	12.0820i	−0.407481	+	0.485617i	0.522805	+	0.852453i	$0.324886\pi$
$620$	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	−0.649350	−	0.760489i	$-0.724959\pi$
$631$	−7.92332	+	4.57453i	−0.315423	+	0.182109i	0.333928	+	0.942599i	$0.391626\pi$
$632$	−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	0.996529	+	0.0832447i	$0.0265283\pi$
$641$	49.6595	+	8.75631i	1.96143	+	0.345853i	0.964902	+	0.262609i	$0.0845828\pi$
$642$	0.230887	−	0.232890i	0.00911240	−	0.00919145i
$643$	−14.8271	+	40.7371i	−0.584724	+	1.60652i	0.195285	+	0.980747i	$0.437437\pi$
$643$	−14.8271	+	40.7371i	−0.584724	+	1.60652i	−0.780009	+	0.625769i	$0.784785\pi$
$644$	−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	−0.981762	−	0.190112i	$-0.939115\pi$
$653$	−2.74671	+	7.54652i	−0.107487	+	0.295318i	0.874275	+	0.485430i	$0.161337\pi$
$654$	−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	−0.433135	−	0.901329i	$-0.642593\pi$
$659$	−4.76384	+	1.73390i	−0.185573	+	0.0675430i	0.247562	+	0.968872i	$0.420371\pi$
$660$	−27.2449	+	15.4662i	−1.06051	+	0.602023i
$661$	−11.5525	+	9.69373i	−0.449341	+	0.377042i	−0.839191	−	0.543836i	$-0.816971\pi$
$661$	−11.5525	+	9.69373i	−0.449341	+	0.377042i	0.389850	+	0.920878i	$0.372527\pi$
$662$	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	0.840690	−	0.541517i	$-0.182150\pi$
$673$	11.7618	+	9.86933i	0.453384	+	0.380435i	−0.387306	+	0.921951i	$0.626594\pi$
$674$	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	−0.235767	−	0.971810i	$-0.575760\pi$
$677$	19.8324	−	23.6353i	0.762220	−	0.908378i	0.997986	+	0.0634317i	$0.0202045\pi$
$678$	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	−0.865753	−	0.500472i	$-0.833160\pi$
$683$	0.0142495	−	0.0246808i	0.000545242	−	0.000944386i	0.866298	+	0.499528i	$0.166493\pi$
$684$	−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	0.836045	−	0.548660i	$-0.184862\pi$
$691$	−4.12900	−	11.3443i	−0.157075	−	0.431559i	−0.993120	+	0.117102i	$0.962640\pi$
$692$	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	$0.206149\pi$
$701$			31.9466i			1.20661i	−0.797511	+	0.603304i	$0.793851\pi$
$702$	−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	0.765044	+	0.643977i	$0.222717\pi$
$709$	−4.63618	+	26.2931i	−0.174115	+	0.987458i	−0.939160	+	0.343480i	$0.888394\pi$
$710$	−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	0.839898	−	0.542745i	$-0.182615\pi$
$719$	−1.34291	−	2.32598i	−0.0500819	−	0.0867444i	−0.889980	+	0.456000i	$0.849282\pi$
$720$	−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	−0.972827	−	0.231534i	$-0.925626\pi$
$727$	−15.5274	+	18.5049i	−0.575881	+	0.686308i	0.396946	+	0.917842i	$0.370070\pi$
$728$	−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	0.990614	−	0.136688i	$-0.0436457\pi$
$733$	0.351729	+	1.99475i	0.0129914	+	0.0736779i	−0.977623	+	0.210366i	$0.932535\pi$
$734$	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	−0.730481	−	0.682933i	$-0.760704\pi$
$739$	−13.7088	+	7.91475i	−0.504285	+	0.291149i	0.226197	+	0.974082i	$0.427371\pi$
$740$	−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	−0.493752	+	0.869603i	$0.664375\pi$
$743$	−39.1393	+	32.8418i	−1.43588	+	1.20485i	−0.942131	+	0.335246i	$0.891181\pi$
$744$	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	0.313568	+	0.949566i	$0.398476\pi$
$751$	−14.7164	+	40.4329i	−0.537008	+	1.47542i	−0.850576	+	0.525852i	$0.823747\pi$
$752$	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	−0.972526	−	0.232795i	$-0.925213\pi$
$761$	−2.14870	+	5.90351i	−0.0778904	+	0.214002i	0.894636	+	0.446797i	$0.147435\pi$
$762$	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	−0.0258652	−	0.999665i	$-0.508234\pi$
$769$	26.4586	−	22.2014i	0.954122	−	0.800603i	0.979987	+	0.199062i	$0.0637896\pi$
$770$	−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	0.184338	−	0.982863i	$-0.440986\pi$
$773$	31.3530	−	18.1017i	1.12769	−	0.651072i	0.943353	+	0.331791i	$0.107653\pi$
$774$	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	0.739752	−	0.672879i	$-0.234943\pi$
$787$	46.7100	−	8.23623i	1.66503	−	0.293590i	0.925278	+	0.379290i	$0.123832\pi$
$788$	−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	0.999996	+	0.00283592i	$0.000902704\pi$
$797$	23.4076	+	27.8961i	0.829141	+	0.988132i	−0.170855	+	0.985296i	$0.554653\pi$
$798$	−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	$-0.983625\pi$
$809$		−	2.92521i		−	0.102845i	0.998677	−	0.0514224i	$-0.0163755\pi$
$810$	37.8305	−	20.1019i	1.32923	−	0.706309i
$811$			41.5184i			1.45791i	0.684563	+	0.728954i	$0.259993\pi$
$811$			41.5184i			1.45791i	−0.684563	+	0.728954i	$0.740007\pi$
$812$	−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	−0.959439	−	0.281917i	$-0.909030\pi$
$821$	−11.6240	−	31.9365i	−0.405679	−	1.11459i	0.553760	−	0.832676i	$-0.313192\pi$
$822$	−4.49211	−	48.9112i	−0.156680	−	1.70598i
$823$	18.5624	+	22.1218i	0.647046	+	0.771119i	0.985465	−	0.169876i	$-0.0543368\pi$
$823$	18.5624	+	22.1218i	0.647046	+	0.771119i	−0.338420	+	0.940995i	$0.609892\pi$
$824$	−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	−0.914535	−	0.404506i	$-0.867443\pi$
$827$	−23.2241	−	40.2253i	−0.807580	−	1.39877i	0.106955	−	0.994264i	$-0.465890\pi$
$828$	18.4417	−	3.41626i	0.640893	−	0.118723i
$829$	−9.10298	+	15.7668i	−0.316160	+	0.547605i	−0.979683	−	0.200551i	$-0.935727\pi$
$829$	−9.10298	+	15.7668i	−0.316160	+	0.547605i	0.663524	+	0.748155i	$0.269060\pi$
$830$	−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	0.487808	−	0.872951i	$-0.337797\pi$
$839$	−8.31813	−	6.97974i	−0.287174	−	0.240967i	−0.774982	+	0.631984i	$0.782241\pi$
$840$	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	−0.558659	−	0.829397i	$-0.688684\pi$
$853$	−13.2447	+	4.82069i	−0.453491	+	0.165057i	0.105168	+	0.994454i	$0.466462\pi$
$854$	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	0.712712	−	0.701457i	$-0.247467\pi$
$857$	33.4471	+	5.89762i	1.14253	+	0.201459i	0.429818	+	0.902916i	$0.358578\pi$
$858$	−3.95896	−	14.5238i	−0.135157	−	0.495836i
$859$	−14.1686	+	38.9280i	−0.483427	+	1.32821i	0.423109	+	0.906079i	$0.360939\pi$
$859$	−14.1686	+	38.9280i	−0.483427	+	1.32821i	−0.906537	+	0.422127i	$0.861284\pi$
$860$	−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	−0.377818	−	0.925880i	$-0.623326\pi$
$877$	13.8709	−	11.6391i	0.468388	−	0.393024i	0.846206	+	0.532856i	$0.178881\pi$
$878$	−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	−0.952403	−	0.304841i	$-0.901397\pi$
$881$	−34.5674	+	19.9575i	−1.16460	+	0.672385i	−0.212202	+	0.977226i	$0.568063\pi$
$882$	−4.23312	−	0.284141i	−0.142536	−	0.00956751i
$883$	3.33190	+	1.92367i	0.112127	+	0.0647367i	0.555015	−	0.831840i	$-0.312713\pi$
$883$	3.33190	+	1.92367i	0.112127	+	0.0647367i	−0.442888	+	0.896577i	$0.646046\pi$
$884$	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	0.791782	+	0.610803i	$0.209153\pi$
$887$	7.64391	+	43.3508i	0.256657	+	1.45558i	−0.535125	+	0.844773i	$0.679736\pi$
$888$	−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	0.957392	−	0.288792i	$-0.0932536\pi$
$907$	1.15512	+	3.17368i	0.0383553	+	0.105380i	−0.919037	+	0.394172i	$0.871031\pi$
$908$	−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	−0.893641	−	0.448783i	$-0.851858\pi$
$911$	3.00619	−	17.0490i	0.0995995	−	0.564857i	0.993241	−	0.116074i	$-0.0370311\pi$
$912$	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	$-0.898038\pi$
$919$		−	19.0908i		−	0.629749i	0.949133	−	0.314874i	$-0.101962\pi$
$920$	−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	−0.987561	−	0.157233i	$-0.949743\pi$
$929$	−10.1226	−	27.8117i	−0.332113	−	0.912473i	0.655448	−	0.755240i	$-0.272480\pi$
$930$	−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	−0.700497	−	0.713655i	$-0.747038\pi$
$937$	8.19732	−	14.1982i	0.267795	−	0.463834i	0.968292	+	0.249821i	$0.0803718\pi$
$938$	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	−0.0345704	−	0.999402i	$-0.511006\pi$
$941$	8.42845	−	1.48616i	0.274760	−	0.0484476i	0.309330	+	0.950955i	$0.399895\pi$
$942$	−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	0.801349	−	0.598198i	$-0.204116\pi$
$947$	10.8135	+	9.07361i	0.351392	+	0.294853i	−0.449957	+	0.893050i	$0.648561\pi$
$948$	−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	0.649887	−	0.760031i	$-0.274816\pi$
$953$	9.77443	+	5.64327i	0.316625	+	0.182804i	−0.333262	+	0.942834i	$0.608149\pi$
$954$	−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	−0.685201	−	0.728354i	$-0.740285\pi$
$967$	9.57374	−	26.3036i	0.307871	−	0.845868i	0.993071	−	0.117513i	$-0.0374923\pi$
$968$	−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	−0.790628	−	0.612297i	$-0.790246\pi$
$977$	6.52036	−	17.9145i	0.208605	−	0.573137i	0.999233	+	0.0391596i	$0.0124681\pi$
$978$	−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	−0.0694088	−	0.997588i	$-0.522111\pi$
$983$	16.2614	−	5.91867i	0.518658	−	0.188776i	0.588067	+	0.808812i	$0.299889\pi$
$984$	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	0.991371	+	0.131088i	$0.0418471\pi$
$991$	50.3866	+	29.0907i	1.60058	+	0.924096i	0.609211	+	0.793008i	$0.291486\pi$
$992$	−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	0.831427	−	0.555634i	$-0.187525\pi$
$997$	13.5335	+	11.3559i	0.428610	+	0.359646i	−0.402817	+	0.915280i	$0.631969\pi$
$998$	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.659.46	yes	648
4.3	odd	2	inner	756.2.cf.a.659.15	yes	648
27.5	odd	18	inner	756.2.cf.a.491.15	✓	648
108.59	even	18	inner	756.2.cf.a.491.46	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.15	✓	648	27.5	odd	18	inner
756.2.cf.a.491.46	yes	648	108.59	even	18	inner
756.2.cf.a.659.15	yes	648	4.3	odd	2	inner
756.2.cf.a.659.46	yes	648	1.1	even	1	trivial

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

Related objects

Downloads

Learn more