LMFDB - Embedded newform 600.2.bg.a.11.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(11,600)] 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("600.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.bg (of order $10$, degree $4$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	600.11
Dual form			600.2.bg.a.491.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39814 + 0.212628i) q^{2} +(-1.71398 + 0.249524i) q^{3} +(1.90958 - 0.594567i) q^{4} +(2.23545 + 0.0525986i) q^{5} +(2.34333 - 0.713310i) q^{6} +5.07150i q^{7} +(-2.54343 + 1.23732i) q^{8} +(2.87548 - 0.855360i) q^{9} +(-3.13665 + 0.401779i) q^{10} +(1.39756 + 1.92358i) q^{11} +(-3.12463 + 1.49556i) q^{12} +(0.765213 - 1.05323i) q^{13} +(-1.07834 - 7.09066i) q^{14} +(-3.84465 + 0.467645i) q^{15} +(3.29298 - 2.27074i) q^{16} +(-4.82968 + 1.56926i) q^{17} +(-3.83844 + 1.80732i) q^{18} +(0.122705 + 0.377648i) q^{19} +(4.30004 - 1.22868i) q^{20} +(-1.26546 - 8.69247i) q^{21} +(-2.36299 - 2.39226i) q^{22} +(4.31687 - 3.13639i) q^{23} +(4.05066 - 2.75539i) q^{24} +(4.99447 + 0.235163i) q^{25} +(-0.845928 + 1.63526i) q^{26} +(-4.71508 + 2.18357i) q^{27} +(3.01535 + 9.68443i) q^{28} +(-0.355547 + 1.09426i) q^{29} +(5.27591 - 1.47131i) q^{30} +(-5.68581 + 1.84743i) q^{31} +(-4.12122 + 3.87499i) q^{32} +(-2.87537 - 2.94825i) q^{33} +(6.41889 - 3.22096i) q^{34} +(-0.266754 + 11.3371i) q^{35} +(4.98238 - 3.34304i) q^{36} +(6.34298 - 8.73037i) q^{37} +(-0.251858 - 0.501913i) q^{38} +(-1.04876 + 1.99615i) q^{39} +(-5.75079 + 2.63218i) q^{40} +(-3.88616 + 5.34884i) q^{41} +(3.61755 + 11.8842i) q^{42} +2.26245 q^{43} +(3.81245 + 2.84228i) q^{44} +(6.47297 - 1.76087i) q^{45} +(-5.36869 + 5.30299i) q^{46} +(-2.76067 + 8.49646i) q^{47} +(-5.07751 + 4.71370i) q^{48} -18.7201 q^{49} +(-7.03295 + 0.733174i) q^{50} +(7.88642 - 3.89480i) q^{51} +(0.835021 - 2.46619i) q^{52} +(-2.39342 + 7.36620i) q^{53} +(6.12805 - 4.05549i) q^{54} +(3.02300 + 4.37357i) q^{55} +(-6.27506 - 12.8990i) q^{56} +(-0.304547 - 0.616664i) q^{57} +(0.264433 - 1.60553i) q^{58} +(-1.41810 + 1.95185i) q^{59} +(-7.06361 + 3.17891i) q^{60} +(6.22363 + 8.56609i) q^{61} +(7.55674 - 3.79193i) q^{62} +(4.33796 + 14.5830i) q^{63} +(4.93809 - 6.29406i) q^{64} +(1.76599 - 2.31418i) q^{65} +(4.64705 + 3.51068i) q^{66} +(-1.03247 - 3.17761i) q^{67} +(-8.28962 + 5.86819i) q^{68} +(-6.61644 + 6.45288i) q^{69} +(-2.03763 - 15.9075i) q^{70} +(-0.261214 + 0.803935i) q^{71} +(-6.25523 + 5.73342i) q^{72} +(-11.0089 + 7.99842i) q^{73} +(-7.01204 + 13.5550i) q^{74} +(-8.61911 + 0.843174i) q^{75} +(0.458852 + 0.648192i) q^{76} +(-9.75543 + 7.08773i) q^{77} +(1.04187 - 3.01389i) q^{78} +(-3.90376 - 1.26841i) q^{79} +(7.48073 - 4.90293i) q^{80} +(7.53672 - 4.91913i) q^{81} +(4.29607 - 8.30472i) q^{82} +(3.46953 - 1.12732i) q^{83} +(-7.58475 - 15.8466i) q^{84} +(-10.8790 + 3.25396i) q^{85} +(-3.16322 + 0.481061i) q^{86} +(0.336357 - 1.96426i) q^{87} +(-5.93467 - 3.16326i) q^{88} +(0.453349 + 0.623981i) q^{89} +(-8.67569 + 3.83827i) q^{90} +(5.34144 + 3.88078i) q^{91} +(6.37861 - 8.55585i) q^{92} +(9.28441 - 4.58522i) q^{93} +(2.05321 - 12.4662i) q^{94} +(0.254438 + 0.850667i) q^{95} +(6.09679 - 7.67002i) q^{96} +(0.445166 - 1.37008i) q^{97} +(26.1733 - 3.98043i) q^{98} +(5.66400 + 4.33578i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q - 6 q^{3} - 6 q^{4} - 7 q^{6} - 6 q^{9} - 8 q^{10} + 3 q^{12} + 6 q^{16} + 2 q^{18} - 12 q^{19} - 22 q^{22} - 16 q^{25} - 6 q^{27} + 34 q^{28} + 3 q^{30} - 18 q^{33} - 30 q^{34} + 35 q^{36} + 4 q^{40}+ \cdots - 52 q^{99}+O(q^{100}) $ 464 * q - 6 * q^3 - 6 * q^4 - 7 * q^6 - 6 * q^9 - 8 * q^10 + 3 * q^12 + 6 * q^16 + 2 * q^18 - 12 * q^19 - 22 * q^22 - 16 * q^25 - 6 * q^27 + 34 * q^28 + 3 * q^30 - 18 * q^33 - 30 * q^34 + 35 * q^36 + 4 * q^40 + 43 * q^42 + 22 * q^46 - 50 * q^48 - 400 * q^49 - 28 * q^51 + 32 * q^54 - 4 * q^57 + 54 * q^58 - 76 * q^60 - 30 * q^64 - 58 * q^66 - 12 * q^67 + 48 * q^70 - 69 * q^72 - 12 * q^73 - 30 * q^75 + 48 * q^76 - 79 * q^78 - 6 * q^81 + 12 * q^82 - 22 * q^84 - 130 * q^88 - 48 * q^90 + 72 * q^91 - 72 * q^94 + 44 * q^96 - 36 * q^97 - 52 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.39814	+	0.212628i	−0.988633	+	0.150351i
$2$	−1.39814	+	0.212628i	−0.988633	+	0.150351i
$3$	−1.71398	+	0.249524i	−0.989569	+	0.144063i
$3$	−1.71398	+	0.249524i	−0.989569	+	0.144063i
$4$	1.90958	−	0.594567i	0.954789	−	0.297284i
$5$	2.23545	+	0.0525986i	0.999723	+	0.0235228i
$5$	2.23545	+	0.0525986i	0.999723	+	0.0235228i
$6$	2.34333	−	0.713310i	0.956660	−	0.291208i
$7$			5.07150i			1.91685i	0.285348	+	0.958424i	$0.407891\pi$
$7$			5.07150i			1.91685i	−0.285348	+	0.958424i	$0.592109\pi$
$8$	−2.54343	+	1.23732i	−0.899239	+	0.437458i
$9$	2.87548	−	0.855360i	0.958492	−	0.285120i
$10$	−3.13665	+	0.401779i	−0.991896	+	0.127054i
$11$	1.39756	+	1.92358i	0.421380	+	0.579980i	0.965948	−	0.258737i	$-0.0833062\pi$
$11$	1.39756	+	1.92358i	0.421380	+	0.579980i	−0.544568	+	0.838717i	$0.683306\pi$
$12$	−3.12463	+	1.49556i	−0.902002	+	0.431732i
$13$	0.765213	−	1.05323i	0.212232	−	0.292112i	−0.689608	−	0.724183i	$-0.742217\pi$
$13$	0.765213	−	1.05323i	0.212232	−	0.292112i	0.901840	+	0.432071i	$0.142217\pi$
$14$	−1.07834	−	7.09066i	−0.288200	−	1.89506i
$15$	−3.84465	+	0.467645i	−0.992683	+	0.120745i
$16$	3.29298	−	2.27074i	0.823245	−	0.567686i
$17$	−4.82968	+	1.56926i	−1.17137	+	0.380601i	−0.829154	−	0.559021i	$-0.811177\pi$
$17$	−4.82968	+	1.56926i	−1.17137	+	0.380601i	−0.342215	+	0.939622i	$0.611177\pi$
$18$	−3.83844	+	1.80732i	−0.904728	+	0.425989i
$19$	0.122705	+	0.377648i	0.0281505	+	0.0866384i	0.964145	−	0.265377i	$-0.0854964\pi$
$19$	0.122705	+	0.377648i	0.0281505	+	0.0866384i	−0.935994	+	0.352015i	$0.885496\pi$
$20$	4.30004	−	1.22868i	0.961518	−	0.274742i
$21$	−1.26546	−	8.69247i	−0.276146	−	1.89685i
$22$	−2.36299	−	2.39226i	−0.503791	−	0.510033i
$23$	4.31687	−	3.13639i	0.900130	−	0.653983i	−0.0383696	−	0.999264i	$-0.512216\pi$
$23$	4.31687	−	3.13639i	0.900130	−	0.653983i	0.938499	+	0.345281i	$0.112216\pi$
$24$	4.05066	−	2.75539i	0.826837	−	0.562441i
$25$	4.99447	+	0.235163i	0.998893	+	0.0470326i
$26$	−0.845928	+	1.63526i	−0.165900	+	0.320701i
$27$	−4.71508	+	2.18357i	−0.907418	+	0.420229i
$28$	3.01535	+	9.68443i	0.569847	+	1.83019i
$29$	−0.355547	+	1.09426i	−0.0660234	+	0.203199i	−0.978626	−	0.205649i	$-0.934069\pi$
$29$	−0.355547	+	1.09426i	−0.0660234	+	0.203199i	0.912602	+	0.408848i	$0.134069\pi$
$30$	5.27591	−	1.47131i	0.963245	−	0.268624i
$31$	−5.68581	+	1.84743i	−1.02120	+	0.331809i	−0.771306	−	0.636464i	$-0.780396\pi$
$31$	−5.68581	+	1.84743i	−1.02120	+	0.331809i	−0.249896	+	0.968273i	$0.580396\pi$
$32$	−4.12122	+	3.87499i	−0.728535	+	0.685009i
$33$	−2.87537	−	2.94825i	−0.500538	−	0.513225i
$34$	6.41889	−	3.22096i	1.10083	−	0.552391i
$35$	−0.266754	+	11.3371i	−0.0450896	+	1.91632i
$36$	4.98238	−	3.34304i	0.830396	−	0.557173i
$37$	6.34298	−	8.73037i	1.04278	−	1.43526i	0.147876	−	0.989006i	$-0.452756\pi$
$37$	6.34298	−	8.73037i	1.04278	−	1.43526i	0.894904	−	0.446258i	$-0.147244\pi$
$38$	−0.251858	−	0.501913i	−0.0408567	−	0.0814211i
$39$	−1.04876	+	1.99615i	−0.167936	+	0.319640i
$40$	−5.75079	+	2.63218i	−0.909280	+	0.416184i
$41$	−3.88616	+	5.34884i	−0.606916	+	0.835348i	−0.996319	−	0.0857190i	$-0.972681\pi$
$41$	−3.88616	+	5.34884i	−0.606916	+	0.835348i	0.389403	+	0.921067i	$0.372681\pi$
$42$	3.61755	+	11.8842i	0.558201	+	1.83377i
$43$	2.26245			0.345020			0.172510	−	0.985008i	$-0.444812\pi$
$43$	2.26245			0.345020			0.172510	+	0.985008i	$0.444812\pi$
$44$	3.81245	+	2.84228i	0.574748	+	0.428489i
$45$	6.47297	−	1.76087i	0.964933	−	0.262495i
$46$	−5.36869	+	5.30299i	−0.791571	+	0.781884i
$47$	−2.76067	+	8.49646i	−0.402685	+	1.23934i	0.520128	+	0.854088i	$0.325884\pi$
$47$	−2.76067	+	8.49646i	−0.402685	+	1.23934i	−0.922813	+	0.385248i	$0.874116\pi$
$48$	−5.07751	+	4.71370i	−0.732875	+	0.680363i
$49$	−18.7201			−2.67431
$50$	−7.03295	+	0.733174i	−0.994610	+	0.103687i
$51$	7.88642	−	3.89480i	1.10432	−	0.545381i
$52$	0.835021	−	2.46619i	0.115797	−	0.341999i
$53$	−2.39342	+	7.36620i	−0.328762	+	1.01182i	0.640952	+	0.767581i	$0.278540\pi$
$53$	−2.39342	+	7.36620i	−0.328762	+	1.01182i	−0.969714	+	0.244244i	$0.921460\pi$
$54$	6.12805	−	4.05549i	0.833922	−	0.551883i
$55$	3.02300	+	4.37357i	0.407621	+	0.589732i
$56$	−6.27506	−	12.8990i	−0.838540	−	1.72370i
$57$	−0.304547	−	0.616664i	−0.0403382	−	0.0816792i
$58$	0.264433	−	1.60553i	0.0347217	−	0.210816i
$59$	−1.41810	+	1.95185i	−0.184621	+	0.254109i	−0.891288	−	0.453437i	$-0.850198\pi$
$59$	−1.41810	+	1.95185i	−0.184621	+	0.254109i	0.706667	+	0.707546i	$0.250198\pi$
$60$	−7.06361	+	3.17891i	−0.911908	+	0.410395i
$61$	6.22363	+	8.56609i	0.796854	+	1.09678i	0.993221	+	0.116245i	$0.0370858\pi$
$61$	6.22363	+	8.56609i	0.796854	+	1.09678i	−0.196366	+	0.980531i	$0.562914\pi$
$62$	7.55674	−	3.79193i	0.959706	−	0.481576i
$63$	4.33796	+	14.5830i	0.546532	+	1.83728i
$64$	4.93809	−	6.29406i	0.617262	−	0.786758i
$65$	1.76599	−	2.31418i	0.219045	−	0.287039i
$66$	4.64705	+	3.51068i	0.572012	+	0.432135i
$67$	−1.03247	−	3.17761i	−0.126136	−	0.388207i	0.867970	−	0.496616i	$-0.165424\pi$
$67$	−1.03247	−	3.17761i	−0.126136	−	0.388207i	−0.994106	+	0.108409i	$0.965424\pi$
$68$	−8.28962	+	5.86819i	−1.00526	+	0.711622i
$69$	−6.61644	+	6.45288i	−0.796526	+	0.776836i
$70$	−2.03763	−	15.9075i	−0.243543	−	1.90131i
$71$	−0.261214	+	0.803935i	−0.0310005	+	0.0954096i	−0.965360	−	0.260923i	$-0.915973\pi$
$71$	−0.261214	+	0.803935i	−0.0310005	+	0.0954096i	0.934359	+	0.356333i	$0.115973\pi$
$72$	−6.25523	+	5.73342i	−0.737185	+	0.675691i
$73$	−11.0089	+	7.99842i	−1.28849	+	0.936145i	−0.999774	−	0.0212691i	$-0.993229\pi$
$73$	−11.0089	+	7.99842i	−1.28849	+	0.936145i	−0.288719	+	0.957414i	$0.593229\pi$
$74$	−7.01204	+	13.5550i	−0.815133	+	1.57573i
$75$	−8.61911	+	0.843174i	−0.995249	+	0.0973614i
$76$	0.458852	+	0.648192i	0.0526340	+	0.0743527i
$77$	−9.75543	+	7.08773i	−1.11173	+	0.807722i
$78$	1.04187	−	3.01389i	0.117968	−	0.341256i
$79$	−3.90376	−	1.26841i	−0.439207	−	0.142707i	0.0810627	−	0.996709i	$-0.474169\pi$
$79$	−3.90376	−	1.26841i	−0.439207	−	0.142707i	−0.520270	+	0.854002i	$0.674169\pi$
$80$	7.48073	−	4.90293i	0.836371	−	0.548164i
$81$	7.53672	−	4.91913i	0.837413	−	0.546570i
$82$	4.29607	−	8.30472i	0.474422	−	0.917103i
$83$	3.46953	−	1.12732i	0.380831	−	0.123739i	−0.112345	−	0.993669i	$-0.535836\pi$
$83$	3.46953	−	1.12732i	0.380831	−	0.123739i	0.493175	+	0.869930i	$0.335836\pi$
$84$	−7.58475	−	15.8466i	−0.827565	−	1.72900i
$85$	−10.8790	+	3.25396i	−1.18000	+	0.352942i
$86$	−3.16322	+	0.481061i	−0.341098	+	0.0518741i
$87$	0.336357	−	1.96426i	0.0360612	−	0.210591i
$88$	−5.93467	−	3.16326i	−0.632638	−	0.337205i
$89$	0.453349	+	0.623981i	0.0480549	+	0.0661418i	0.832368	−	0.554223i	$-0.186985\pi$
$89$	0.453349	+	0.623981i	0.0480549	+	0.0661418i	−0.784313	+	0.620365i	$0.786985\pi$
$90$	−8.67569	+	3.83827i	−0.914498	+	0.404589i
$91$	5.34144	+	3.88078i	0.559935	+	0.406816i
$92$	6.37861	−	8.55585i	0.665016	−	0.892009i
$93$	9.28441	−	4.58522i	0.962749	−	0.475465i
$94$	2.05321	−	12.4662i	0.211772	−	1.28579i
$95$	0.254438	+	0.850667i	0.0261048	+	0.0872766i
$96$	6.09679	−	7.67002i	0.622251	−	0.782818i
$97$	0.445166	−	1.37008i	0.0451997	−	0.139110i	−0.925910	−	0.377745i	$-0.876700\pi$
$97$	0.445166	−	1.37008i	0.0451997	−	0.139110i	0.971110	+	0.238634i	$0.0766997\pi$
$98$	26.1733	−	3.98043i	2.64391	−	0.402084i
$99$	5.66400	+	4.33578i	0.569254	+	0.435762i
$100$	9.67715	−	2.52048i	0.967715	−	0.252048i
$101$	19.1934			1.90982			0.954908	−	0.296903i	$-0.0959539\pi$
$101$	19.1934			1.90982			0.954908	+	0.296903i	$0.0959539\pi$
$102$	−10.1982	+	7.12234i	−1.00977	+	0.705217i
$103$	9.87402	+	3.20826i	0.972916	+	0.316120i	0.751993	−	0.659172i	$-0.229093\pi$
$103$	9.87402	+	3.20826i	0.972916	+	0.316120i	0.220923	+	0.975291i	$0.429093\pi$
$104$	−0.643094	+	3.62562i	−0.0630606	+	0.355521i
$105$	−2.37166	−	19.4981i	−0.231451	−	1.90282i
$106$	1.78007	−	10.8079i	0.172896	−	1.04975i
$107$		−	6.83253i		−	0.660525i	−0.943889	−	0.330263i	$-0.892863\pi$
$107$		−	6.83253i		−	0.660525i	0.943889	−	0.330263i	$-0.107137\pi$
$108$	−7.70554	+	6.97314i	−0.741466	+	0.670990i
$109$	4.71117	−	6.48437i	0.451249	−	0.621090i	−0.521417	−	0.853302i	$-0.674596\pi$
$109$	4.71117	−	6.48437i	0.451249	−	0.621090i	0.972665	+	0.232212i	$0.0745963\pi$
$110$	−5.15651	−	5.47208i	−0.491654	−	0.521742i
$111$	−8.69333	+	16.5464i	−0.825134	+	1.57052i
$112$	11.5161	+	16.7004i	1.08817	+	1.57804i
$113$	7.18530	−	9.88972i	0.675937	−	0.930347i	−0.323940	−	0.946078i	$-0.605008\pi$
$113$	7.18530	−	9.88972i	0.675937	−	0.930347i	0.999876	+	0.0157309i	$0.00500751\pi$
$114$	0.556919	+	0.797427i	0.0521602	+	0.0746858i
$115$	9.81511	−	6.78418i	0.915264	−	0.632628i
$116$	−0.0283333	+	2.30097i	−0.00263068	+	0.213640i
$117$	1.29946	−	3.68306i	0.120136	−	0.340499i
$118$	1.56768	−	3.03048i	0.144317	−	0.278979i
$119$	−7.95849	−	24.4937i	−0.729554	−	2.24534i
$120$	9.19997	−	5.94647i	0.839839	−	0.542836i
$121$	1.65221	−	5.08499i	0.150201	−	0.462272i
$122$	−10.5229	−	10.6533i	−0.952697	−	0.964501i
$123$	5.32615	−	10.1375i	0.480243	−	0.914069i
$124$	−9.75909	+	6.90842i	−0.876392	+	0.620394i
$125$	11.1525	+	0.788396i	0.997511	+	0.0705163i
$126$	−9.16582	−	19.4666i	−0.816556	−	1.73423i
$127$	1.93591	+	2.66456i	0.171785	+	0.236441i	0.886225	−	0.463255i	$-0.153319\pi$
$127$	1.93591	+	2.66456i	0.171785	+	0.236441i	−0.714440	+	0.699696i	$0.753319\pi$
$128$	−5.56584	+	9.84995i	−0.491955	+	0.870620i
$129$	−3.87780	+	0.564536i	−0.341421	+	0.0497046i
$130$	−1.97704	+	3.61105i	−0.173398	+	0.316710i
$131$	−1.71932	+	0.558642i	−0.150218	+	0.0488088i	−0.383161	−	0.923682i	$-0.625164\pi$
$131$	−1.71932	+	0.558642i	−0.150218	+	0.0488088i	0.232943	+	0.972490i	$0.425164\pi$
$132$	−7.24369	−	3.92032i	−0.630482	−	0.341220i
$133$	−1.91524	+	0.622300i	−0.166073	+	0.0539603i
$134$	2.11918	+	4.22321i	0.183070	+	0.364830i
$135$	−10.6552	+	4.63326i	−0.917052	+	0.398767i
$136$	10.3423	−	9.96714i	0.886844	−	0.854675i
$137$	−9.40896	+	12.9503i	−0.803862	+	1.10642i	0.188380	+	0.982096i	$0.439676\pi$
$137$	−9.40896	+	12.9503i	−0.803862	+	1.10642i	−0.992242	+	0.124325i	$0.960324\pi$
$138$	7.87863	−	10.4289i	0.670673	−	0.887763i
$139$	−11.2881	+	8.20131i	−0.957448	+	0.695626i	−0.952557	−	0.304362i	$-0.901557\pi$
$139$	−11.2881	+	8.20131i	−0.957448	+	0.695626i	−0.00489105	+	0.999988i	$0.501557\pi$
$140$	6.23127	+	21.8077i	0.526639	+	1.84308i
$141$	2.61167	−	15.2516i	0.219942	−	1.28442i
$142$	0.194274	−	1.17955i	0.0163032	−	0.0989860i
$143$	3.09539			0.258850
$144$	7.52658	−	9.34615i	0.627215	−	0.778846i
$145$	−0.852363	+	2.42746i	−0.0707849	+	0.201590i
$146$	13.6913	−	13.5237i	1.13310	−	1.11923i
$147$	32.0860	−	4.67112i	2.64641	−	0.385268i
$148$	6.92164	−	20.4427i	0.568955	−	1.68038i
$149$	−5.99363			−0.491017			−0.245509	−	0.969394i	$-0.578955\pi$
$149$	−5.99363			−0.491017			−0.245509	+	0.969394i	$0.578955\pi$
$150$	11.8714	−	3.01154i	0.969297	−	0.245891i
$151$			5.49838i			0.447452i	0.974652	+	0.223726i	$0.0718220\pi$
$151$			5.49838i			0.447452i	−0.974652	+	0.223726i	$0.928178\pi$
$152$	−0.779363	−	0.808697i	−0.0632147	−	0.0655940i
$153$	−12.5453	+	8.64347i	−1.01423	+	0.698783i
$154$	12.1324	−	11.9839i	0.977655	−	0.965690i
$155$	−12.8075	+	3.83078i	−1.02872	+	0.307695i
$156$	−0.815840	+	4.43536i	−0.0653194	+	0.355113i
$157$		−	7.73070i		−	0.616977i	−0.951228	−	0.308489i	$-0.900177\pi$
$157$		−	7.73070i		−	0.616977i	0.951228	−	0.308489i	$-0.0998232\pi$
$158$	5.72769	+	0.943360i	0.455671	+	0.0750497i
$159$	2.26424	−	13.2228i	0.179566	−	1.04863i
$160$	−9.41659	+	8.44558i	−0.744447	+	0.667682i
$161$	15.9062	+	21.8930i	1.25358	+	1.72541i
$162$	−9.49143	+	8.48014i	−0.745717	+	0.666263i
$163$	−15.8256	−	11.4980i	−1.23956	−	0.900592i	−0.241990	−	0.970279i	$-0.577800\pi$
$163$	−15.8256	−	11.4980i	−1.23956	−	0.900592i	−0.997569	+	0.0696865i	$0.977800\pi$
$164$	−4.24068	+	12.5246i	−0.331142	+	0.978008i
$165$	−6.27268	−	6.74191i	−0.488327	−	0.524857i
$166$	−4.61118	+	2.31387i	−0.357897	+	0.179591i
$167$	−3.42956	−	10.5551i	−0.265387	−	0.816777i	−0.991604	−	0.129312i	$-0.958723\pi$
$167$	−3.42956	−	10.5551i	−0.265387	−	0.816777i	0.726217	−	0.687466i	$-0.241277\pi$
$168$	13.9740	+	20.5429i	1.07811	+	1.58492i
$169$	3.49349	+	10.7519i	0.268730	+	0.827065i
$170$	14.5185	−	6.86268i	1.11352	−	0.526343i
$171$	0.675861	+	0.980960i	0.0516844	+	0.0750159i
$172$	4.32033	−	1.34518i	0.329422	−	0.102569i
$173$	6.37695	−	4.63313i	0.484831	−	0.352250i	−0.318362	−	0.947969i	$-0.603133\pi$
$173$	6.37695	−	4.63313i	0.484831	−	0.352250i	0.803193	+	0.595719i	$0.203133\pi$
$174$	−0.0526159	+	2.81783i	−0.00398880	+	0.213619i
$175$	−1.19263	+	25.3295i	−0.0901543	+	1.91473i
$176$	8.97009	+	3.16080i	0.676146	+	0.238254i
$177$	1.94357	−	3.69929i	0.146088	−	0.278056i
$178$	−0.766520	−	0.776016i	−0.0574531	−	0.0581649i
$179$	−11.3768	−	3.69656i	−0.850344	−	0.276294i	−0.148754	−	0.988874i	$-0.547526\pi$
$179$	−11.3768	−	3.69656i	−0.850344	−	0.276294i	−0.701590	+	0.712581i	$0.747526\pi$
$180$	11.3137	−	7.21113i	0.843273	−	0.537486i
$181$	0.571867	−	0.185811i	0.0425066	−	0.0138112i	−0.287687	−	0.957725i	$-0.592886\pi$
$181$	0.571867	−	0.185811i	0.0425066	−	0.0138112i	0.330193	+	0.943913i	$0.392886\pi$
$182$	−8.29323	−	4.29013i	−0.614735	−	0.318005i
$183$	−12.8046	−	13.1292i	−0.946546	−	0.970538i
$184$	−7.09896	+	13.3185i	−0.523342	+	0.981855i
$185$	14.6386	−	19.1827i	1.07625	−	1.41034i
$186$	−12.0059	+	8.38489i	−0.880318	+	0.614810i
$187$	−9.76835	−	7.09712i	−0.714333	−	0.518993i
$188$	−0.219996	+	17.8661i	−0.0160448	+	1.30302i
$189$	−11.0740	−	23.9126i	−0.805515	−	1.73938i
$190$	−0.536615	−	1.13525i	−0.0389301	−	0.0823596i
$191$	1.33556	+	0.970340i	0.0966376	+	0.0702113i	0.635055	−	0.772467i	$-0.280978\pi$
$191$	1.33556	+	0.970340i	0.0966376	+	0.0702113i	−0.538417	+	0.842678i	$0.680978\pi$
$192$	−6.89329	+	12.0201i	−0.497480	+	0.867475i
$193$	4.58989			0.330387			0.165194	−	0.986261i	$-0.447175\pi$
$193$	4.58989			0.330387			0.165194	+	0.986261i	$0.447175\pi$
$194$	−0.331086	+	2.01021i	−0.0237706	+	0.144325i
$195$	−2.44944	+	4.40713i	−0.175408	+	0.315601i
$196$	−35.7476	+	11.1304i	−2.55340	+	0.795027i
$197$	−1.42676	+	4.39110i	−0.101652	+	0.312853i	−0.988930	−	0.148382i	$-0.952593\pi$
$197$	−1.42676	+	4.39110i	−0.101652	+	0.312853i	0.887278	+	0.461235i	$0.152593\pi$
$198$	−8.84096	−	4.85769i	−0.628300	−	0.345221i
$199$		−	4.85169i		−	0.343927i	−0.985103	−	0.171964i	$-0.944989\pi$
$199$		−	4.85169i		−	0.343927i	0.985103	−	0.171964i	$-0.0550111\pi$
$200$	−12.9941	+	5.58162i	−0.918819	+	0.394680i
$201$	2.56253	+	5.18875i	0.180747	+	0.365986i
$202$	−26.8350	+	4.08106i	−1.88811	+	0.287142i
$203$	−5.54954	−	1.80316i	−0.389502	−	0.126557i
$204$	12.7440	−	12.1264i	0.892259	−	0.849020i
$205$	−8.96865	+	11.7527i	−0.626398	+	0.820841i
$206$	−14.4874	−	2.38610i	−1.00939	−	0.166247i
$207$	9.73031	−	12.7111i	0.676303	−	0.883482i
$208$	0.128225	−	5.20586i	0.00889082	−	0.360961i
$209$	−0.554947	+	0.763819i	−0.0383865	+	0.0528345i
$210$	7.46177	+	26.7568i	0.514911	+	1.84639i
$211$	−2.34159	+	1.70126i	−0.161202	+	0.117120i	−0.665462	−	0.746432i	$-0.731765\pi$
$211$	−2.34159	+	1.70126i	−0.161202	+	0.117120i	0.504260	+	0.863552i	$0.331765\pi$
$212$	−0.190730	+	15.4894i	−0.0130994	+	1.06382i
$213$	0.247116	−	1.44311i	0.0169321	−	0.0988803i
$214$	1.45279	+	9.55281i	0.0993105	+	0.653017i
$215$	5.05759	+	0.119002i	0.344925	+	0.00811584i
$216$	9.29072	−	11.3878i	0.632154	−	0.774843i
$217$	−9.36926	−	28.8356i	−0.636027	−	1.95749i
$218$	−5.20811	+	10.0678i	−0.352738	+	0.681876i
$219$	16.8732	−	16.4561i	1.14019	−	1.11200i
$220$	8.37303	+	6.55430i	0.564510	+	0.441891i
$221$	−2.04295	+	6.28756i	−0.137424	+	0.422947i
$222$	8.63624	−	24.9826i	0.579626	−	1.67672i
$223$	3.22017	+	4.43219i	0.215639	+	0.296801i	0.903109	−	0.429411i	$-0.141279\pi$
$223$	3.22017	+	4.43219i	0.215639	+	0.296801i	−0.687470	+	0.726212i	$0.741279\pi$
$224$	−19.6520	−	20.9008i	−1.31306	−	1.39649i
$225$	14.5626	−	3.59586i	0.970841	−	0.239724i
$226$	−7.94321	+	15.3550i	−0.528375	+	1.02140i
$227$	−0.932775	−	1.28385i	−0.0619105	−	0.0852124i	0.776939	−	0.629576i	$-0.216771\pi$
$227$	−0.932775	−	1.28385i	−0.0619105	−	0.0852124i	−0.838850	+	0.544363i	$0.816771\pi$
$228$	−0.948205	−	0.996495i	−0.0627964	−	0.0659945i
$229$	8.46798	+	2.75141i	0.559580	+	0.181819i	0.575132	−	0.818061i	$-0.304951\pi$
$229$	8.46798	+	2.75141i	0.559580	+	0.181819i	−0.0155522	+	0.999879i	$0.504951\pi$
$230$	−12.2804	+	11.5722i	−0.809744	+	0.763047i
$231$	14.9521	−	14.5825i	0.983774	−	0.959456i
$232$	−0.449638	−	3.22310i	−0.0295202	−	0.211607i
$233$	17.1477	−	5.57161i	1.12338	−	0.365008i	0.312324	−	0.949976i	$-0.398893\pi$
$233$	17.1477	−	5.57161i	1.12338	−	0.365008i	0.811057	+	0.584967i	$0.198893\pi$
$234$	−1.03371	+	5.42572i	−0.0675757	+	0.354691i
$235$	−6.61823	+	18.8482i	−0.431726	+	1.22952i
$236$	−1.54747	+	4.57037i	−0.100732	+	0.297506i
$237$	7.00747	+	1.19995i	0.455184	+	0.0779450i
$238$	16.3351	+	32.5534i	1.05885	+	2.11012i
$239$	3.07126	−	2.23140i	0.198664	−	0.144337i	−0.484006	−	0.875065i	$-0.660819\pi$
$239$	3.07126	−	2.23140i	0.198664	−	0.144337i	0.682670	+	0.730727i	$0.260819\pi$
$240$	−11.5984	+	10.2702i	−0.748676	+	0.662936i
$241$	16.9906	+	12.3444i	1.09446	+	0.795172i	0.980147	−	0.198273i	$-0.0635332\pi$
$241$	16.9906	+	12.3444i	1.09446	+	0.795172i	0.114313	+	0.993445i	$0.463533\pi$
$242$	−1.22881	+	7.46083i	−0.0789909	+	0.479600i
$243$	−11.6904	+	10.3119i	−0.749937	+	0.661509i
$244$	16.9776	+	12.6573i	1.08688	+	0.810298i
$245$	−41.8479	−	0.984653i	−2.67357	−	0.0629071i
$246$	−5.29117	+	15.3061i	−0.337353	+	0.975883i
$247$	0.491644	+	0.159745i	0.0312826	+	0.0101643i
$248$	12.1756	−	11.7340i	0.773153	−	0.745108i
$249$	−5.66543	+	2.79794i	−0.359032	+	0.177312i
$250$	−15.7604	+	1.26905i	−0.996774	+	0.0802618i
$251$		−	24.3186i		−	1.53498i	−0.641063	−	0.767488i	$-0.721506\pi$
$251$		−	24.3186i		−	1.53498i	0.641063	−	0.767488i	$-0.278494\pi$
$252$	16.9542	+	25.2681i	1.06802	+	1.59174i
$253$	12.0662	+	3.92054i	0.758594	+	0.246482i
$254$	−3.27323	−	3.31379i	−0.205381	−	0.207926i
$255$	17.8345	−	8.29182i	1.11684	−	0.519254i
$256$	5.68744	−	14.9550i	0.355465	−	0.934690i
$257$		−	26.1051i		−	1.62839i	−0.580591	−	0.814195i	$-0.697179\pi$
$257$		−	26.1051i		−	1.62839i	0.580591	−	0.814195i	$-0.302821\pi$
$258$	5.30166	−	1.61383i	0.330067	−	0.100473i
$259$	44.2761	+	32.1685i	2.75118	+	1.99885i
$260$	1.99637	−	5.46912i	0.123809	−	0.339180i
$261$	−0.0863795	+	3.45064i	−0.00534676	+	0.213589i
$262$	2.28507	−	1.14663i	0.141172	−	0.0708393i
$263$	7.60253	+	5.52356i	0.468792	+	0.340597i	0.796970	−	0.604018i	$-0.206435\pi$
$263$	7.60253	+	5.52356i	0.468792	+	0.340597i	−0.328178	+	0.944616i	$0.606435\pi$
$264$	10.9612	+	3.94093i	0.674618	+	0.242548i
$265$	−5.73783	+	16.3409i	−0.352472	+	1.00381i
$266$	2.54546	−	1.27730i	0.156072	−	0.0783160i
$267$	−0.932730	−	0.956371i	−0.0570822	−	0.0585290i
$268$	−3.86088	−	5.45403i	−0.235841	−	0.333158i
$269$	−2.95820	−	9.10439i	−0.180364	−	0.555105i	0.819473	−	0.573117i	$-0.194266\pi$
$269$	−2.95820	−	9.10439i	−0.180364	−	0.555105i	−0.999838	+	0.0180127i	$0.994266\pi$
$270$	13.9123	−	8.74353i	0.846673	−	0.532114i
$271$	13.4394	+	4.36673i	0.816386	+	0.265260i	0.687300	−	0.726373i	$-0.258796\pi$
$271$	13.4394	+	4.36673i	0.816386	+	0.265260i	0.129086	+	0.991633i	$0.458796\pi$
$272$	−12.3406	+	16.1345i	−0.748262	+	0.978298i
$273$	−10.1235	−	5.31878i	−0.612701	−	0.321907i
$274$	10.4014	−	20.1069i	0.628373	−	1.21471i
$275$	6.52771	+	9.93589i	0.393636	+	0.599157i
$276$	−8.79794	+	16.2562i	−0.529574	+	0.978508i
$277$	−16.0379	−	22.0742i	−0.963621	−	1.32631i	−0.945204	−	0.326480i	$-0.894137\pi$
$277$	−16.0379	−	22.0742i	−0.963621	−	1.32631i	−0.0184170	−	0.999830i	$-0.505863\pi$
$278$	14.0385	−	13.8667i	0.841976	−	0.831672i
$279$	−14.7692	+	10.1757i	−0.884209	+	0.609201i
$280$	−13.3491	−	29.1652i	−0.797761	−	1.74295i
$281$	5.07493	−	1.64895i	0.302745	−	0.0983678i	−0.153705	−	0.988117i	$-0.549121\pi$
$281$	5.07493	−	1.64895i	0.302745	−	0.0983678i	0.456450	+	0.889749i	$0.349121\pi$
$282$	−0.408540	+	21.8792i	−0.0243282	+	1.30289i
$283$	−1.66015	−	5.10942i	−0.0986857	−	0.303723i	0.889511	−	0.456914i	$-0.151045\pi$
$283$	−1.66015	−	5.10942i	−0.0986857	−	0.303723i	−0.988197	+	0.153190i	$0.951045\pi$
$284$	−0.0208160	+	1.69049i	−0.00123520	+	0.100312i
$285$	−0.648364	−	1.39454i	−0.0384058	−	0.0826055i
$286$	−4.32778	+	0.658168i	−0.255907	+	0.0389183i
$287$	−27.1267	−	19.7087i	−1.60124	−	1.16337i
$288$	−8.53594	+	14.6676i	−0.502985	+	0.864295i
$289$	7.10993	−	5.16567i	0.418231	−	0.303863i
$290$	0.675574	−	3.57516i	0.0396711	−	0.209941i
$291$	−0.421139	+	2.45937i	−0.0246876	+	0.144171i
$292$	−16.2667	+	21.8191i	−0.951939	+	1.27687i
$293$	8.13380			0.475182			0.237591	−	0.971365i	$-0.423642\pi$
$293$	8.13380			0.475182			0.237591	+	0.971365i	$0.423642\pi$
$294$	−43.8674	+	13.3533i	−2.55840	+	0.778778i
$295$	−3.27276	+	4.28867i	−0.190547	+	0.249696i
$296$	−5.33072	+	30.0534i	−0.309842	+	1.74682i
$297$	−10.7899	−	6.01815i	−0.626093	−	0.349209i
$298$	8.37992	−	1.27441i	0.485436	−	0.0738248i
$299$		−	6.94665i		−	0.401735i
$300$	−15.9575	+	6.73475i	−0.921309	+	0.388831i
$301$			11.4740i			0.661352i
$302$	−1.16911	−	7.68749i	−0.0672747	−	0.442365i
$303$	−32.8972	+	4.78922i	−1.88989	+	0.275133i
$304$	1.26161	+	0.964955i	0.0723582	+	0.0553440i
$305$	13.4620	+	19.4764i	0.770834	+	1.11522i
$306$	15.7023	−	14.7523i	0.897639	−	0.843331i
$307$	18.8928			1.07827			0.539136	−	0.842219i	$-0.318751\pi$
$307$	18.8928			1.07827			0.539136	+	0.842219i	$0.318751\pi$
$308$	−14.4146	+	19.3348i	−0.821349	+	1.10170i
$309$	−17.7244	−	3.03510i	−1.00831	−	0.172661i
$310$	17.0922	−	8.07920i	0.970769	−	0.458867i
$311$	0.587788	−	0.427053i	0.0333304	−	0.0242159i	−0.570995	−	0.820953i	$-0.693443\pi$
$311$	0.587788	−	0.427053i	0.0333304	−	0.0242159i	0.604326	+	0.796737i	$0.293443\pi$
$312$	0.197573	−	6.37472i	0.0111854	−	0.360897i
$313$	−3.79043	−	2.75391i	−0.214248	−	0.155660i	0.475486	−	0.879723i	$-0.342272\pi$
$313$	−3.79043	−	2.75391i	−0.214248	−	0.155660i	−0.689733	+	0.724063i	$0.742272\pi$
$314$	1.64377	+	10.8086i	0.0927631	+	0.609964i
$315$	8.93025	+	32.8277i	0.503162	+	1.84963i
$316$	−8.20868	−	0.101079i	−0.461775	−	0.00568611i
$317$	8.26123	+	25.4254i	0.463997	+	1.42804i	0.860240	+	0.509890i	$0.170314\pi$
$317$	8.26123	+	25.4254i	0.463997	+	1.42804i	−0.396243	+	0.918146i	$0.629686\pi$
$318$	−0.354193	+	18.9687i	−0.0198621	+	1.06371i
$319$	−2.60179	+	0.845373i	−0.145672	+	0.0473318i
$320$	11.3699	−	13.8103i	0.635598	−	0.772020i
$321$	1.70488	+	11.7108i	0.0951571	+	0.653635i
$322$	−26.8941	−	27.2273i	−1.49875	−	1.51732i
$323$	−1.18525	−	1.63136i	−0.0659493	−	0.0907714i
$324$	11.4672	−	13.8746i	0.637067	−	0.770809i
$325$	4.06951	−	5.08035i	0.225736	−	0.281807i
$326$	24.5712	+	12.7108i	1.36087	+	0.703986i
$327$	−6.45686	+	12.2897i	−0.357065	+	0.679620i
$328$	3.26597	−	18.4128i	0.180333	−	1.01668i
$329$	−43.0898	−	14.0007i	−2.37562	−	0.771886i
$330$	10.2036	+	8.09237i	0.561689	+	0.445470i
$331$	−8.66742	−	26.6756i	−0.476405	−	1.46622i	−0.844054	−	0.536258i	$-0.819837\pi$
$331$	−8.66742	−	26.6756i	−0.476405	−	1.46622i	0.367649	−	0.929964i	$-0.380163\pi$
$332$	5.95508	−	4.21557i	0.326827	−	0.231360i
$333$	10.7715	−	30.5295i	0.590274	−	1.67301i
$334$	7.03930	+	14.0282i	0.385173	+	0.767592i
$335$	−2.14089	−	7.15770i	−0.116970	−	0.391067i
$336$	−23.9055	−	25.7506i	−1.30415	−	1.40481i
$337$	15.7729	+	11.4597i	0.859203	+	0.624247i	0.927668	−	0.373406i	$-0.121810\pi$
$337$	15.7729	+	11.4597i	0.859203	+	0.624247i	−0.0684651	+	0.997654i	$0.521810\pi$
$338$	−7.17052	−	14.2898i	−0.390025	−	0.777260i
$339$	−9.84777	+	18.7437i	−0.534857	+	1.01802i
$340$	−18.8397	+	12.6820i	−1.02173	+	0.687779i
$341$	−11.4999	−	8.35520i	−0.622757	−	0.452460i
$342$	−1.15353	−	1.22781i	−0.0623756	−	0.0663924i
$343$		−	59.4387i		−	3.20939i
$344$	−5.75439	+	2.79937i	−0.310256	+	0.150932i
$345$	−15.1301	+	14.0771i	−0.814578	+	0.757884i
$346$	−7.93073	+	7.83367i	−0.426358	+	0.421141i
$347$	20.4733	+	6.65218i	1.09907	+	0.357108i	0.801743	−	0.597669i	$-0.203906\pi$
$347$	20.4733	+	6.65218i	1.09907	+	0.357108i	0.297322	+	0.954777i	$0.403906\pi$
$348$	−0.525585	−	3.95090i	−0.0281743	−	0.211790i
$349$			32.8526i			1.75856i	0.476306	+	0.879280i	$0.341975\pi$
$349$			32.8526i			1.75856i	−0.476306	+	0.879280i	$0.658025\pi$
$350$	−3.71830	−	35.6677i	−0.198751	−	1.90652i
$351$	−1.30825	+	6.63695i	−0.0698292	+	0.354254i
$352$	−13.2135	−	2.51194i	−0.704282	−	0.133887i
$353$	23.1133	+	7.50995i	1.23019	+	0.399714i	0.850785	−	0.525514i	$-0.176127\pi$
$353$	23.1133	+	7.50995i	1.23019	+	0.399714i	0.379410	+	0.925229i	$0.376127\pi$
$354$	−1.93080	+	5.58537i	−0.102621	+	0.296859i
$355$	−0.626218	+	1.78342i	−0.0332362	+	0.0946540i
$356$	1.23670	+	0.921994i	0.0655451	+	0.0488656i
$357$	19.7525	+	39.9960i	1.04541	+	2.11681i
$358$	16.6924	+	2.74926i	0.882219	+	0.145303i
$359$	11.8226	+	8.58965i	0.623975	+	0.453345i	0.854308	−	0.519767i	$-0.173981\pi$
$359$	11.8226	+	8.58965i	0.623975	+	0.453345i	−0.230333	+	0.973112i	$0.573981\pi$
$360$	−14.2848	+	12.4878i	−0.752876	+	0.658163i
$361$	15.2438	−	11.0752i	0.802303	−	0.582907i
$362$	−0.760041	+	0.381384i	−0.0399468	+	0.0200451i
$363$	−1.56304	+	9.12786i	−0.0820383	+	0.479088i
$364$	12.5073	+	4.23481i	0.655559	+	0.221965i
$365$	−25.0305	+	17.3010i	−1.31016	+	0.905577i
$366$	20.6943	+	15.6338i	1.08171	+	0.817191i
$367$	19.6235	−	6.37605i	1.02434	−	0.332827i	0.251787	−	0.967783i	$-0.418982\pi$
$367$	19.6235	−	6.37605i	1.02434	−	0.332827i	0.772549	+	0.634956i	$0.218982\pi$
$368$	7.09343	−	20.1306i	0.369770	−	1.04938i
$369$	−6.59937	+	18.7045i	−0.343550	+	0.973719i
$370$	−16.3880	+	29.9326i	−0.851974	+	1.55612i
$371$	−37.3577	−	12.1382i	−1.93951	−	0.630186i
$372$	15.0031	−	14.2760i	0.777874	−	0.740178i
$373$	−7.72971	−	10.6390i	−0.400229	−	0.550868i	0.560572	−	0.828105i	$-0.310581\pi$
$373$	−7.72971	−	10.6390i	−0.400229	−	0.550868i	−0.960801	+	0.277237i	$0.910581\pi$
$374$	15.1666	+	7.84573i	0.784244	+	0.405693i
$375$	−19.3119	+	1.43152i	−0.997264	+	0.0739234i
$376$	−3.49124	−	25.0260i	−0.180047	−	1.29062i
$377$	0.880434	+	1.21181i	0.0453446	+	0.0624116i
$378$	20.5675	+	31.0784i	1.05788	+	1.59850i
$379$	−2.64486	+	8.14005i	−0.135857	+	0.418126i	−0.995722	−	0.0923953i	$-0.970548\pi$
$379$	−2.64486	+	8.14005i	−0.135857	+	0.418126i	0.859865	+	0.510522i	$0.170548\pi$
$380$	0.991647	+	1.47314i	0.0508704	+	0.0755703i
$381$	−3.98300	−	4.08395i	−0.204055	−	0.209227i
$382$	−2.07362	−	1.07269i	−0.106095	−	0.0548837i
$383$	1.20167	+	3.69835i	0.0614022	+	0.188977i	0.977052	−	0.213000i	$-0.0683234\pi$
$383$	1.20167	+	3.69835i	0.0614022	+	0.188977i	−0.915650	+	0.401976i	$0.868323\pi$
$384$	7.08196	−	18.2714i	0.361400	−	0.932411i
$385$	−22.1806	+	15.3311i	−1.13043	+	0.781347i
$386$	−6.41729	+	0.975939i	−0.326632	+	0.0496740i
$387$	6.50562	−	1.93521i	0.330699	−	0.0983722i
$388$	0.0354750	−	2.88095i	0.00180097	−	0.146258i
$389$	16.3382	−	11.8704i	0.828378	−	0.601852i	−0.0907220	−	0.995876i	$-0.528917\pi$
$389$	16.3382	−	11.8704i	0.828378	−	0.601852i	0.919100	+	0.394024i	$0.128917\pi$
$390$	2.48757	−	6.68259i	0.125963	−	0.338386i
$391$	−15.9273	+	21.9220i	−0.805478	+	1.10864i
$392$	47.6134	−	23.1627i	2.40484	−	1.16990i
$393$	2.80750	−	1.38652i	0.141619	−	0.0699404i
$394$	1.06113	−	6.44273i	0.0534589	−	0.324580i
$395$	−8.65993	−	3.04079i	−0.435729	−	0.152999i
$396$	13.3938	+	4.91189i	0.673062	+	0.246832i
$397$	16.3467	+	5.31136i	0.820417	+	0.266570i	0.689004	−	0.724758i	$-0.258048\pi$
$397$	16.3467	+	5.31136i	0.820417	+	0.266570i	0.131414	+	0.991328i	$0.458048\pi$
$398$	1.03161	+	6.78333i	0.0517097	+	0.340018i
$399$	3.12742	−	1.54451i	0.156567	−	0.0773223i
$400$	16.9807	−	10.5668i	0.849034	−	0.528339i
$401$		−	4.74463i		−	0.236935i	−0.992958	−	0.118468i	$-0.962202\pi$
$401$		−	4.74463i		−	0.236935i	0.992958	−	0.118468i	$-0.0377982\pi$
$402$	−4.68604	−	6.70972i	−0.233718	−	0.334650i
$403$	−2.40510	+	7.40213i	−0.119806	+	0.368726i
$404$	36.6513	−	11.4118i	1.82347	−	0.567757i
$405$	17.1067	−	10.6001i	0.850038	−	0.526721i
$406$	8.14243	+	1.34107i	0.404102	+	0.0665562i
$407$	25.6582			1.27183
$408$	−15.2395	+	19.6642i	−0.754466	+	0.973521i
$409$	−29.5195	−	21.4472i	−1.45965	−	1.06050i	−0.983455	−	0.181154i	$-0.942017\pi$
$409$	−29.5195	−	21.4472i	−1.45965	−	1.06050i	−0.476192	−	0.879341i	$-0.657983\pi$
$410$	10.0405	−	18.3388i	0.495863	−	0.905690i
$411$	12.8954	−	24.5444i	0.636082	−	1.21069i
$412$	20.7627	+	0.255664i	1.02291	+	0.0125957i
$413$	−9.89881	−	7.19191i	−0.487089	−	0.353891i
$414$	−10.9016	+	19.8408i	−0.535784	+	0.975122i
$415$	7.81526	−	2.33757i	0.383636	−	0.114747i
$416$	0.927635	+	7.30577i	0.0454810	+	0.358195i
$417$	17.3013	−	16.8736i	0.847246	−	0.826303i
$418$	0.613483	−	1.18592i	0.0300064	−	0.0580053i
$419$	15.4834	−	5.03086i	0.756413	−	0.245774i	0.0946746	−	0.995508i	$-0.469819\pi$
$419$	15.4834	−	5.03086i	0.756413	−	0.245774i	0.661738	+	0.749735i	$0.269819\pi$
$420$	−16.1218	−	35.8231i	−0.786665	−	1.74799i
$421$	2.81876	+	0.915871i	0.137378	+	0.0446368i	0.376899	−	0.926254i	$-0.376990\pi$
$421$	2.81876	+	0.915871i	0.137378	+	0.0446368i	−0.239521	+	0.970891i	$0.576990\pi$
$422$	2.91213	−	2.87649i	0.141760	−	0.140025i
$423$	−0.670700	+	26.7927i	−0.0326106	+	1.30271i
$424$	−3.02681	−	21.6968i	−0.146995	−	1.05369i
$425$	−24.4907	+	6.70184i	−1.18797	+	0.325087i
$426$	−0.0386560	+	2.07021i	−0.00187289	+	0.100302i
$427$	−43.4430	+	31.5632i	−2.10235	+	1.52745i
$428$	−4.06240	−	13.0472i	−0.196363	−	0.630662i
$429$	−5.30545	+	0.772375i	−0.256150	+	0.0372906i
$430$	−7.09651	+	0.909006i	−0.342224	+	0.0438362i
$431$	−8.06770	−	24.8298i	−0.388607	−	1.19601i	−0.933829	−	0.357719i	$-0.883555\pi$
$431$	−8.06770	−	24.8298i	−0.388607	−	1.19601i	0.545222	−	0.838292i	$-0.316445\pi$
$432$	−10.5683	+	17.8972i	−0.508469	+	0.861080i
$433$	3.02851	+	9.32081i	0.145541	+	0.447929i	0.997080	−	0.0763617i	$-0.0243304\pi$
$433$	3.02851	+	9.32081i	0.145541	+	0.447929i	−0.851539	+	0.524291i	$0.824330\pi$
$434$	19.2308	+	38.3240i	0.923107	+	1.83961i
$435$	0.855226	−	4.37331i	0.0410049	−	0.209684i
$436$	5.14096	−	15.1835i	0.246207	−	0.727159i
$437$	1.71415	+	1.24541i	0.0819991	+	0.0595758i
$438$	−20.0921	+	26.5957i	−0.960037	+	1.27079i
$439$	3.90485	+	5.37456i	0.186368	+	0.256514i	0.891970	−	0.452095i	$-0.149323\pi$
$439$	3.90485	+	5.37456i	0.186368	+	0.256514i	−0.705602	+	0.708609i	$0.749323\pi$
$440$	−13.1003	−	7.38347i	−0.624531	−	0.351993i
$441$	−53.8293	+	16.0125i	−2.56330	+	0.762498i
$442$	1.51942	−	9.22526i	0.0722712	−	0.438801i
$443$			12.9747i			0.616447i	0.951314	+	0.308223i	$0.0997344\pi$
$443$			12.9747i			0.616447i	−0.951314	+	0.308223i	$0.900266\pi$
$444$	−6.76263	+	36.7655i	−0.320940	+	1.74481i
$445$	0.980617	+	1.41872i	0.0464857	+	0.0672539i
$446$	−5.44466	−	5.51211i	−0.257812	−	0.261006i
$447$	10.2730	−	1.49555i	0.485895	−	0.0707373i
$448$	31.9204	+	25.0436i	1.50810	+	1.18320i
$449$			13.8880i			0.655415i	0.944779	+	0.327707i	$0.106276\pi$
$449$			13.8880i			0.655415i	−0.944779	+	0.327707i	$0.893724\pi$
$450$	−19.5960	+	8.12393i	−0.923763	+	0.382966i
$451$	−15.7200			−0.740228
$452$	7.84080	−	23.1573i	0.368800	−	1.08923i
$453$	−1.37198	−	9.42413i	−0.0644611	−	0.442784i
$454$	1.57713	+	1.59667i	0.0740185	+	0.0749355i
$455$	11.7364	+	8.95624i	0.550210	+	0.419875i
$456$	1.53760	+	1.19162i	0.0720049	+	0.0558029i
$457$	4.73306			0.221403			0.110702	−	0.993854i	$-0.464690\pi$
$457$	4.73306			0.221403			0.110702	+	0.993854i	$0.464690\pi$
$458$	−12.4244	−	2.04632i	−0.580556	−	0.0956184i
$459$	19.3457	−	17.9451i	0.902982	−	0.837607i
$460$	14.7091	−	18.7907i	0.685814	−	0.876119i
$461$	−0.589650	+	0.428406i	−0.0274627	+	0.0199528i	−0.601432	−	0.798924i	$-0.705403\pi$
$461$	−0.589650	+	0.428406i	−0.0274627	+	0.0199528i	0.573969	+	0.818877i	$0.305403\pi$
$462$	−17.8044	+	23.5675i	−0.828336	+	1.09646i
$463$	8.49598	−	11.6937i	0.394841	−	0.543453i	−0.564598	−	0.825366i	$-0.690969\pi$
$463$	8.49598	−	11.6937i	0.394841	−	0.543453i	0.959440	+	0.281913i	$0.0909690\pi$
$464$	1.31398	+	4.41073i	0.0609999	+	0.204763i
$465$	20.9960	−	9.76167i	0.973666	−	0.452687i
$466$	−22.7901	+	11.4360i	−1.05573	+	0.529760i
$467$	21.8338	−	7.09423i	1.01035	−	0.328282i	0.243355	−	0.969937i	$-0.421752\pi$
$467$	21.8338	−	7.09423i	1.01035	−	0.328282i	0.766993	+	0.641655i	$0.221752\pi$
$468$	0.291606	−	7.80571i	0.0134795	−	0.360819i
$469$	16.1153	−	5.23617i	0.744134	−	0.241784i
$470$	5.24554	−	27.7596i	0.241959	−	1.28046i
$471$	1.92900	+	13.2503i	0.0888835	+	0.610541i
$472$	1.19179	−	6.71904i	0.0548566	−	0.309269i
$473$	3.16191	+	4.35200i	0.145385	+	0.200105i
$474$	−10.0526	−	0.187706i	−0.461729	−	0.00862164i
$475$	0.524039	+	1.91501i	0.0240445	+	0.0878665i
$476$	−29.7605	−	42.0408i	−1.36407	−	1.92694i
$477$	−0.581478	+	23.2286i	−0.0266241	+	1.06356i
$478$	−3.81959	+	3.77285i	−0.174704	+	0.172566i
$479$	−1.56404	+	4.81363i	−0.0714629	+	0.219940i	−0.980409	−	0.196974i	$-0.936888\pi$
$479$	−1.56404	+	4.81363i	−0.0714629	+	0.219940i	0.908946	+	0.416914i	$0.136888\pi$
$480$	14.0325	−	16.8253i	0.640493	−	0.767964i
$481$	−4.34131	−	13.3612i	−0.197947	−	0.609218i
$482$	−26.3800	−	13.6465i	−1.20157	−	0.621580i
$483$	−32.7258	−	33.5553i	−1.48908	−	1.52682i
$484$	0.131664	−	10.6925i	0.00598472	−	0.486025i
$485$	1.06721	−	3.03933i	0.0484595	−	0.138009i
$486$	14.1521	−	16.9032i	0.641954	−	0.766743i
$487$	−7.16134	+	9.85674i	−0.324511	+	0.446652i	−0.939838	−	0.341621i	$-0.889024\pi$
$487$	−7.16134	+	9.85674i	−0.324511	+	0.446652i	0.615327	+	0.788272i	$0.289024\pi$
$488$	−26.4283	−	14.0867i	−1.19636	−	0.637674i
$489$	29.9939	+	15.7585i	1.35637	+	0.712623i
$490$	58.7185	−	7.52137i	2.65263	−	0.339781i
$491$	13.0008	−	17.8940i	0.586716	−	0.807545i	−0.407696	−	0.913118i	$-0.633668\pi$
$491$	13.0008	−	17.8940i	0.586716	−	0.807545i	0.994412	+	0.105573i	$0.0336675\pi$
$492$	4.14327	−	22.5251i	0.186793	−	1.01551i
$493$		−	5.84287i		−	0.263150i
$494$	−0.721353	−	0.118808i	−0.0324552	−	0.00534542i
$495$	12.4335	+	9.99034i	0.558846	+	0.449032i
$496$	−14.5282	+	18.9946i	−0.652337	+	0.852883i
$497$	−4.07716	−	1.32475i	−0.182886	−	0.0594232i
$498$	7.32613	−	5.11653i	0.328292	−	0.229277i
$499$	−4.46835			−0.200031			−0.100015	−	0.994986i	$-0.531889\pi$
$499$	−4.46835			−0.200031			−0.100015	+	0.994986i	$0.531889\pi$
$500$	21.7653	−	5.12541i	0.973376	−	0.229215i
$501$	8.51195	+	17.2355i	0.380286	+	0.770025i
$502$	5.17082	+	34.0008i	0.230785	+	1.51753i
$503$	−6.76611	+	20.8239i	−0.301686	+	0.928493i	0.679207	+	0.733946i	$0.262324\pi$
$503$	−6.76611	+	20.8239i	−0.301686	+	0.928493i	−0.980893	+	0.194547i	$0.937676\pi$
$504$	−29.0771	−	31.7234i	−1.29520	−	1.41307i
$505$	42.9059	+	1.00955i	1.90929	+	0.0449242i
$506$	−17.7038	−	2.91584i	−0.787029	−	0.129625i
$507$	−8.67062	−	17.5568i	−0.385076	−	0.779724i
$508$	5.28104	+	3.93715i	0.234308	+	0.174683i
$509$	21.7657	+	15.8137i	0.964750	+	0.700932i	0.954249	−	0.299013i	$-0.0966575\pi$
$509$	21.7657	+	15.8137i	0.964750	+	0.700932i	0.0105007	+	0.999945i	$0.496657\pi$
$510$	−23.1721	+	15.3852i	−1.02608	+	0.681269i
$511$	−40.5640	−	55.8316i	−1.79445	−	2.46984i
$512$	−4.77196	+	22.1185i	−0.210893	+	0.977509i
$513$	−1.40319	−	1.51271i	−0.0619522	−	0.0667876i
$514$	5.55068	+	36.4985i	0.244830	+	1.60988i
$515$	21.9041	+	7.69127i	0.965211	+	0.338918i
$516$	−7.06931	+	3.38364i	−0.311209	+	0.148956i
$517$	−20.2018	+	6.56396i	−0.888474	+	0.288683i
$518$	−68.7440	−	35.5616i	−3.02044	−	1.56249i
$519$	−9.77391	+	9.53230i	−0.429027	+	0.418422i
$520$	−1.62831	+	8.07106i	−0.0714060	+	0.353939i
$521$	29.3622	+	9.54035i	1.28638	+	0.417970i	0.870823	−	0.491597i	$-0.163587\pi$
$521$	29.3622	+	9.54035i	1.28638	+	0.417970i	0.415557	+	0.909567i	$0.363587\pi$
$522$	−0.612933	−	4.84283i	−0.0268273	−	0.211965i
$523$	−6.38799	+	4.64115i	−0.279327	+	0.202943i	−0.718624	−	0.695399i	$-0.755228\pi$
$523$	−6.38799	+	4.64115i	−0.279327	+	0.202943i	0.439297	+	0.898342i	$0.355228\pi$
$524$	−2.95103	+	2.08902i	−0.128916	+	0.0912594i
$525$	−4.27616	−	43.7118i	−0.186627	−	1.90774i
$526$	−11.8038	−	6.10619i	−0.514672	−	0.266242i
$527$	24.5616	−	17.8450i	1.06992	−	0.777341i
$528$	−16.1633	−	3.17930i	−0.703416	−	0.138361i
$529$	1.69104	−	5.20448i	0.0735234	−	0.226282i
$530$	4.54774	−	24.0668i	0.197541	−	1.04540i
$531$	−2.40818	+	6.82549i	−0.104506	+	0.296201i
$532$	−3.28731	+	2.32707i	−0.142523	+	0.100891i
$533$	2.65979	+	8.18601i	0.115208	+	0.354575i
$534$	1.50744	+	1.13881i	0.0652332	+	0.0492813i
$535$	0.359381	−	15.2738i	0.0155374	−	0.660343i
$536$	6.55773	+	6.80455i	0.283251	+	0.293912i
$537$	20.4221	+	3.49704i	0.881277	+	0.150908i
$538$	6.07182	+	12.1002i	0.261775	+	0.521677i
$539$	−26.1625	−	36.0096i	−1.12690	−	1.55104i
$540$	−17.5921	+	15.1828i	−0.757044	+	0.653363i
$541$	−12.2199	+	16.8193i	−0.525376	+	0.723118i	−0.986417	−	0.164261i	$-0.947476\pi$
$541$	−12.2199	+	16.8193i	−0.525376	+	0.723118i	0.461041	+	0.887379i	$0.347476\pi$
$542$	−19.7186	−	3.24769i	−0.846988	−	0.139500i
$543$	−0.933806	+	0.461171i	−0.0400735	+	0.0197908i
$544$	13.8233	−	25.1822i	0.592668	−	1.07968i
$545$	10.8727	−	14.2477i	0.465733	−	0.610304i
$546$	15.2849	+	5.28384i	0.654135	+	0.226128i
$547$	4.82933	−	14.8632i	0.206487	−	0.635503i	−0.793162	−	0.609011i	$-0.791566\pi$
$547$	4.82933	−	14.8632i	0.206487	−	0.635503i	0.999649	−	0.0264917i	$-0.00843357\pi$
$548$	−10.2673	+	30.3239i	−0.438598	+	1.29537i
$549$	25.2230	+	19.3081i	1.07649	+	0.824051i
$550$	−11.2393	−	12.5038i	−0.479245	−	0.533163i
$551$	−0.456873			−0.0194634
$552$	8.84420	−	24.5991i	0.376434	−	1.04701i
$553$	6.43273	−	19.7979i	0.273548	−	0.841893i
$554$	27.1167	+	27.4527i	1.15208	+	1.16635i
$555$	−20.3038	+	36.5314i	−0.861849	+	1.55067i
$556$	−16.6794	+	22.3726i	−0.707362	+	0.948810i
$557$	−32.3028			−1.36871			−0.684356	−	0.729148i	$-0.739917\pi$
$557$	−32.3028			−1.36871			−0.684356	+	0.729148i	$0.739917\pi$
$558$	18.4857	−	17.3673i	0.782564	−	0.735218i
$559$	1.73126	−	2.38287i	0.0732244	−	0.100785i
$560$	24.8652	+	37.9385i	1.05075	+	1.60320i
$561$	18.5137	+	9.72691i	0.781649	+	0.410671i
$562$	−6.74484	+	3.38453i	−0.284514	+	0.142768i
$563$	8.92839	−	12.2889i	0.376287	−	0.517915i	−0.578309	−	0.815818i	$-0.696287\pi$
$563$	8.92839	−	12.2889i	0.376287	−	0.517915i	0.954596	+	0.297903i	$0.0962872\pi$
$564$	−4.08094	−	30.6770i	−0.171839	−	1.29174i
$565$	16.5826	−	21.7300i	0.697634	−	0.914189i
$566$	3.40753	+	6.79068i	0.143229	+	0.285433i
$567$	24.9474	+	38.2225i	1.04769	+	1.60519i
$568$	−0.330342	−	2.36796i	−0.0138608	−	0.0993574i
$569$	−26.2390	+	8.52555i	−1.09999	+	0.357410i	−0.802100	−	0.597189i	$-0.796284\pi$
$569$	−26.2390	+	8.52555i	−1.09999	+	0.357410i	−0.297894	+	0.954599i	$0.596284\pi$
$570$	1.20302	+	1.81190i	0.0503890	+	0.0758921i
$571$	11.7518	−	36.1682i	0.491796	−	1.51359i	−0.330094	−	0.943948i	$-0.607080\pi$
$571$	11.7518	−	36.1682i	0.491796	−	1.51359i	0.821890	−	0.569646i	$-0.192920\pi$
$572$	5.91089	−	1.84042i	0.247147	−	0.0769517i
$573$	−2.53125	−	1.32989i	−0.105744	−	0.0555571i
$574$	42.1174	+	21.7875i	1.75795	+	0.909394i
$575$	22.2980	−	14.6494i	0.929892	−	0.610923i
$576$	8.81568	−	22.3223i	0.367320	−	0.930095i
$577$	19.0916	−	13.8708i	0.794793	−	0.577451i	−0.114589	−	0.993413i	$-0.536555\pi$
$577$	19.0916	−	13.8708i	0.794793	−	0.577451i	0.909382	+	0.415962i	$0.136555\pi$
$578$	−8.84229	+	8.73408i	−0.367791	+	0.363290i
$579$	−7.86699	+	1.14529i	−0.326941	+	0.0475965i
$580$	−0.184365	+	5.14222i	−0.00765536	+	0.213519i
$581$	5.71720	+	17.5957i	0.237190	+	0.729994i
$582$	0.0658782	−	3.52809i	0.00273074	−	0.146244i
$583$	−17.5144	+	5.69077i	−0.725372	+	0.235688i
$584$	18.1038	−	33.9649i	0.749139	−	1.40548i
$585$	3.09861	−	8.16494i	0.128112	−	0.337579i
$586$	−11.3722	+	1.72947i	−0.469780	+	0.0714439i
$587$	−8.06528	+	11.1009i	−0.332890	+	0.458183i	−0.942348	−	0.334635i	$-0.891387\pi$
$587$	−8.06528	+	11.1009i	−0.332890	+	0.458183i	0.609458	+	0.792818i	$0.291387\pi$
$588$	58.4934	−	27.9972i	2.41223	−	1.15458i
$589$	−1.39536	−	1.92055i	−0.0574948	−	0.0791348i
$590$	3.66388	−	6.69204i	0.150839	−	0.275507i
$591$	1.34975	−	7.88228i	0.0555213	−	0.324234i
$592$	1.06288	−	43.1522i	0.0436841	−	1.77355i
$593$		−	9.44437i		−	0.387834i	−0.981018	−	0.193917i	$-0.937881\pi$
$593$		−	9.44437i		−	0.387834i	0.981018	−	0.193917i	$-0.0621192\pi$
$594$	16.3654	+	6.11997i	0.671479	+	0.251105i
$595$	−16.5025	−	55.1731i	−0.676535	−	2.26188i
$596$	−11.4453	+	3.56361i	−0.468818	+	0.145971i
$597$	1.21061	+	8.31571i	0.0495471	+	0.340339i
$598$	1.47705	+	9.71237i	0.0604012	+	0.397168i
$599$	33.3150			1.36121			0.680607	−	0.732648i	$-0.261716\pi$
$599$	33.3150			1.36121			0.680607	+	0.732648i	$0.261716\pi$
$600$	20.8788	−	12.8091i	0.852375	−	0.522930i
$601$	−31.2444			−1.27448			−0.637242	−	0.770664i	$-0.719925\pi$
$601$	−31.2444			−1.27448			−0.637242	+	0.770664i	$0.719925\pi$
$602$	−2.43970	−	16.0423i	−0.0994348	−	0.653834i
$603$	−5.68684	−	8.25402i	−0.231586	−	0.336129i
$604$	3.26915	+	10.4996i	0.133020	+	0.427222i
$605$	3.96090	−	11.2803i	0.161034	−	0.458611i
$606$	44.9765	−	13.6908i	1.82704	−	0.556153i
$607$			3.42894i			0.139176i	0.997576	+	0.0695882i	$0.0221685\pi$
$607$			3.42894i			0.139176i	−0.997576	+	0.0695882i	$0.977831\pi$
$608$	−1.96908	−	1.08089i	−0.0798567	−	0.0438357i
$609$	9.96175	+	1.70583i	0.403671	+	0.0691239i
$610$	−22.9630	−	24.3683i	−0.929746	−	0.986644i
$611$	6.83619	+	9.40921i	0.276563	+	0.380656i
$612$	−18.8172	+	23.9644i	−0.760640	+	0.968705i
$613$	−0.884634	+	1.21759i	−0.0357300	+	0.0491782i	−0.826508	−	0.562925i	$-0.809676\pi$
$613$	−0.884634	+	1.21759i	−0.0357300	+	0.0491782i	0.790778	+	0.612103i	$0.209676\pi$
$614$	−26.4148	+	4.01715i	−1.06601	+	0.162119i
$615$	12.4396	−	22.3817i	0.501611	−	0.902519i
$616$	16.0425	−	30.0977i	0.646370	−	1.21267i
$617$	−32.8511	+	10.6740i	−1.32253	+	0.429717i	−0.883364	−	0.468687i	$-0.844727\pi$
$617$	−32.8511	+	10.6740i	−1.32253	+	0.429717i	−0.439169	+	0.898404i	$0.644727\pi$
$618$	25.4266	+	0.474778i	1.02281	+	0.0190984i
$619$	−8.70997	−	26.8065i	−0.350083	−	1.07745i	−0.958806	−	0.284062i	$-0.908318\pi$
$619$	−8.70997	−	26.8065i	−0.350083	−	1.07745i	0.608723	−	0.793383i	$-0.291682\pi$
$620$	−22.1793	+	14.9301i	−0.890743	+	0.599607i
$621$	−13.5059	+	24.2145i	−0.541972	+	0.971696i
$622$	−0.731005	+	0.722059i	−0.0293106	+	0.0289519i
$623$	−3.16452	+	2.29916i	−0.126784	+	0.0921139i
$624$	1.07921	+	8.95474i	0.0432030	+	0.358477i
$625$	24.8894	+	2.34903i	0.995576	+	0.0939610i
$626$	5.88510	+	3.04439i	0.235216	+	0.121678i
$627$	0.760578	−	1.44765i	0.0303746	−	0.0578134i
$628$	−4.59642	−	14.7624i	−0.183417	−	0.589083i
$629$	−16.9344	+	52.1186i	−0.675218	+	2.07811i
$630$	−19.4658	−	43.9988i	−0.775536	−	1.75295i
$631$	13.4765	−	4.37879i	0.536492	−	0.174317i	−0.0282246	−	0.999602i	$-0.508985\pi$
$631$	13.4765	−	4.37879i	0.536492	−	0.174317i	0.564717	+	0.825285i	$0.308985\pi$
$632$	11.4984	−	1.60408i	0.457380	−	0.0638067i
$633$	3.58894	−	3.50022i	0.142647	−	0.139121i
$634$	−16.9565	−	33.7917i	−0.673429	−	1.34204i
$635$	4.18749	+	6.05831i	0.166175	+	0.240417i
$636$	−3.53806	−	26.5961i	−0.140293	−	1.05461i
$637$	−14.3249	+	19.7165i	−0.567573	+	0.781197i
$638$	3.45791	−	1.73516i	0.136900	−	0.0686957i
$639$	−0.0634617	+	2.53513i	−0.00251050	+	0.100288i
$640$	−12.9602	+	21.7263i	−0.512299	+	0.858807i
$641$	11.7879	−	16.2246i	0.465594	−	0.640835i	−0.510063	−	0.860137i	$-0.670378\pi$
$641$	11.7879	−	16.2246i	0.465594	−	0.640835i	0.975657	+	0.219302i	$0.0703780\pi$
$642$	−4.87371	−	16.0109i	−0.192350	−	0.631898i
$643$	−19.1870			−0.756661			−0.378331	−	0.925670i	$-0.623502\pi$
$643$	−19.1870			−0.756661			−0.378331	+	0.925670i	$0.623502\pi$
$644$	43.3910	+	32.3491i	1.70985	+	1.27473i
$645$	−8.69832	+	1.05802i	−0.342496	+	0.0416597i
$646$	2.00402	+	2.02885i	0.0788472	+	0.0798241i
$647$	11.8451	−	36.4553i	0.465677	−	1.43321i	−0.392452	−	0.919772i	$-0.628373\pi$
$647$	11.8451	−	36.4553i	0.465677	−	1.43321i	0.858129	−	0.513434i	$-0.171627\pi$
$648$	−13.0826	+	21.8368i	−0.513933	+	0.857830i
$649$	−5.73642			−0.225174
$650$	−4.60951	+	7.96832i	−0.180800	+	0.312543i
$651$	23.2539	+	47.0859i	0.911394	+	1.84544i
$652$	−37.0566	−	12.5469i	−1.45125	−	0.491375i
$653$	0.237484	−	0.730900i	0.00929345	−	0.0286023i	−0.946302	−	0.323283i	$-0.895213\pi$
$653$	0.237484	−	0.730900i	0.00929345	−	0.0286023i	0.955596	+	0.294681i	$0.0952134\pi$
$654$	6.41446	−	18.5555i	0.250825	−	0.725579i
$655$	−3.87284	+	1.15838i	−0.151325	+	0.0452617i
$656$	−0.651196	+	26.4381i	−0.0254249	+	1.03223i
$657$	−24.8143	+	32.4158i	−0.968096	+	1.26466i
$658$	63.2225	+	10.4128i	2.46467	+	0.405935i
$659$	4.14345	−	5.70296i	0.161406	−	0.222156i	−0.720652	−	0.693297i	$-0.756158\pi$
$659$	4.14345	−	5.70296i	0.161406	−	0.222156i	0.882058	+	0.471141i	$0.156158\pi$
$660$	−15.9867	−	9.14468i	−0.622281	−	0.355956i
$661$	−2.20910	−	3.04057i	−0.0859241	−	0.118264i	0.763891	−	0.645345i	$-0.223286\pi$
$661$	−2.20910	−	3.04057i	−0.0859241	−	0.118264i	−0.849815	+	0.527081i	$0.823286\pi$
$662$	17.7902	+	35.4532i	0.691437	+	1.37793i
$663$	1.93269	−	11.2865i	0.0750593	−	0.438333i
$664$	−7.42967	+	7.16017i	−0.288327	+	0.277869i
$665$	−4.31416	+	1.29038i	−0.167296	+	0.0500388i
$666$	−8.56859	+	44.9748i	−0.332026	+	1.74274i
$667$	1.89718	+	5.83891i	0.0734590	+	0.226084i
$668$	−12.8247	−	18.1167i	−0.496203	−	0.700955i
$669$	−6.62526	−	6.79319i	−0.256147	−	0.262640i
$670$	4.51519	+	9.55223i	0.174437	+	0.369035i
$671$	−7.77964	+	23.9433i	−0.300330	+	0.924319i
$672$	38.8985	+	30.9199i	1.50054	+	1.19276i
$673$	−11.5382	+	8.38300i	−0.444765	+	0.323141i	−0.787526	−	0.616282i	$-0.788638\pi$
$673$	−11.5382	+	8.38300i	−0.444765	+	0.323141i	0.342760	+	0.939423i	$0.388638\pi$
$674$	−24.4893	−	12.6684i	−0.943292	−	0.487970i
$675$	−24.0628	+	9.79697i	−0.926178	+	0.377085i
$676$	13.0638	+	18.4544i	0.502453	+	0.709784i
$677$	15.6471	−	11.3683i	0.601368	−	0.436919i	−0.244996	−	0.969524i	$-0.578787\pi$
$677$	15.6471	−	11.3683i	0.601368	−	0.436919i	0.846364	+	0.532605i	$0.178787\pi$
$678$	9.78309	−	28.3002i	0.375717	−	1.08686i
$679$	6.94836	+	2.25766i	0.266654	+	0.0866410i
$680$	23.6439	−	21.7370i	0.906703	−	0.833578i
$681$	1.91911	+	1.96776i	0.0735406	+	0.0754046i
$682$	17.8551	+	9.23651i	0.683706	+	0.353684i
$683$	−24.6219	+	8.00013i	−0.942130	+	0.306117i	−0.739514	−	0.673142i	$-0.764944\pi$
$683$	−24.6219	+	8.00013i	−0.942130	+	0.306117i	−0.202616	+	0.979258i	$0.564944\pi$
$684$	1.87386	+	1.47138i	0.0716487	+	0.0562595i
$685$	−21.7144	+	28.4549i	−0.829666	+	1.08721i
$686$	12.6383	+	83.1035i	0.482534	+	3.17291i
$687$	−15.2005	−	2.60291i	−0.579936	−	0.0993073i
$688$	7.45020	−	5.13745i	0.284036	−	0.195863i
$689$	5.92679	+	8.15752i	0.225793	+	0.310777i
$690$	18.1608	−	22.8988i	0.691370	−	0.871742i
$691$	30.8044	+	22.3807i	1.17185	+	0.851402i	0.991230	−	0.132150i	$-0.0421880\pi$
$691$	30.8044	+	22.3807i	1.17185	+	0.851402i	0.180625	+	0.983552i	$0.442188\pi$
$692$	9.42259	−	12.6388i	0.358193	−	0.480457i
$693$	−21.9889	+	28.7250i	−0.835290	+	1.09117i
$694$	−30.0390	−	4.94747i	−1.14026	−	0.187803i
$695$	−25.6654	+	17.7399i	−0.973546	+	0.672912i
$696$	1.57491	+	5.41214i	0.0596969	+	0.205147i
$697$	10.3752	−	31.9316i	0.392988	−	1.20949i
$698$	−6.98539	−	45.9325i	−0.264401	−	1.73857i
$699$	−28.0005	+	13.8284i	−1.05908	+	0.523038i
$700$	12.7826	+	49.0777i	0.483138	+	1.85496i
$701$	−6.54275			−0.247116			−0.123558	−	0.992337i	$-0.539431\pi$
$701$	−6.54275			−0.247116			−0.123558	+	0.992337i	$0.539431\pi$
$702$	0.417911	−	9.55753i	0.0157730	−	0.360726i
$703$	4.07532	+	1.32415i	0.153704	+	0.0499414i
$704$	19.0084	+	0.702470i	0.716406	+	0.0264753i
$705$	6.64046	−	33.9569i	0.250094	−	1.27889i
$706$	−33.9123	−	5.58542i	−1.27631	−	0.210210i
$707$			97.3394i			3.66082i
$708$	1.51192	−	8.21966i	0.0568216	−	0.308914i
$709$	−15.7919	+	21.7356i	−0.593076	+	0.816299i	−0.995052	−	0.0993513i	$-0.968323\pi$
$709$	−15.7919	+	21.7356i	−0.593076	+	0.816299i	0.401977	+	0.915650i	$0.368323\pi$
$710$	0.496334	−	2.62661i	0.0186271	−	0.0985751i
$711$	−12.3101	−	0.308158i	−0.461665	−	0.0115568i
$712$	−1.92512	−	1.02612i	−0.0721471	−	0.0384554i
$713$	−18.7507	+	25.8081i	−0.702218	+	0.966520i
$714$	−36.1210	−	51.7200i	−1.35179	−	1.93557i
$715$	6.91959	+	0.162813i	0.258778	+	0.00608887i
$716$	−23.9228	−	0.294576i	−0.894037	−	0.0110088i
$717$	−4.70730	+	4.59094i	−0.175798	+	0.171452i
$718$	−18.3561	−	9.49569i	−0.685043	−	0.354376i
$719$	−6.01074	−	18.4991i	−0.224163	−	0.689902i	−0.998376	−	0.0569763i	$-0.981854\pi$
$719$	−6.01074	−	18.4991i	−0.224163	−	0.689902i	0.774213	−	0.632925i	$-0.218146\pi$
$720$	17.3169	−	20.4970i	0.645362	−	0.763877i
$721$	−16.2707	+	50.0761i	−0.605953	+	1.86493i
$722$	−18.9580	+	18.7260i	−0.705543	+	0.696908i
$723$	−32.2018	−	16.9185i	−1.19760	−	0.629206i
$724$	0.981548	−	0.694834i	0.0364790	−	0.0258233i
$725$	−2.03310	+	5.38163i	−0.0755073	+	0.199869i
$726$	0.244504	−	13.0943i	0.00907441	−	0.485977i
$727$	−18.2820	−	25.1630i	−0.678041	−	0.933243i	0.321867	−	0.946785i	$-0.395690\pi$
$727$	−18.2820	−	25.1630i	−0.678041	−	0.933243i	−0.999908	+	0.0135414i	$0.995690\pi$
$728$	−18.3873	−	3.26145i	−0.681480	−	0.120877i
$729$	17.4640	−	20.5915i	0.646816	−	0.762646i
$730$	31.3174	−	29.5114i	1.15911	−	1.09227i
$731$	−10.9269	+	3.55037i	−0.404146	+	0.131315i
$732$	−32.2577	−	17.4580i	−1.19228	−	0.645266i
$733$	−7.27269	+	2.36304i	−0.268623	+	0.0872809i	−0.440231	−	0.897884i	$-0.645104\pi$
$733$	−7.27269	+	2.36304i	−0.268623	+	0.0872809i	0.171608	+	0.985165i	$0.445104\pi$
$734$	−26.0806	+	13.0871i	−0.962651	+	0.483053i
$735$	71.9723	−	8.75438i	2.65474	−	0.322910i
$736$	−5.63726	+	29.6536i	−0.207792	+	1.09305i
$737$	4.66944	−	6.42694i	0.172001	−	0.236739i
$738$	5.24972	−	27.5547i	0.193245	−	1.01430i
$739$	30.6104	−	22.2398i	1.12602	−	0.818103i	0.140911	−	0.990022i	$-0.454997\pi$
$739$	30.6104	−	22.2398i	1.12602	−	0.818103i	0.985111	+	0.171920i	$0.0549970\pi$
$740$	16.5482	−	45.3344i	0.608325	−	1.66653i
$741$	−0.882530	−	0.151123i	−0.0324206	−	0.00555164i
$742$	54.8121	+	9.02765i	2.01222	+	0.331415i
$743$	0.891938			0.0327220			0.0163610	−	0.999866i	$-0.494792\pi$
$743$	0.891938			0.0327220			0.0163610	+	0.999866i	$0.494792\pi$
$744$	−17.9409	+	23.1499i	−0.657745	+	0.848718i
$745$	−13.3985	−	0.315256i	−0.490881	−	0.0115501i
$746$	13.0694	+	13.2313i	0.478503	+	0.484431i
$747$	9.01229	−	6.20928i	0.329743	−	0.227186i
$748$	−22.8732	−	7.74457i	−0.836325	−	0.283170i
$749$	34.6512			1.26613
$750$	26.6964	−	6.10772i	0.974813	−	0.223023i
$751$		−	7.62241i		−	0.278146i	−0.990282	−	0.139073i	$-0.955588\pi$
$751$		−	7.62241i		−	0.278146i	0.990282	−	0.139073i	$-0.0444122\pi$
$752$	10.2025	+	34.2475i	0.372046	+	1.24888i
$753$	6.06808	+	41.6817i	0.221133	+	1.51896i
$754$	−1.48863	−	1.50708i	−0.0542128	−	0.0548845i
$755$	−0.289207	+	12.2913i	−0.0105253	+	0.447328i
$756$	−35.3643	−	39.0787i	−1.28619	−	1.42128i
$757$		−	32.3412i		−	1.17546i	−0.809057	−	0.587730i	$-0.800022\pi$
$757$		−	32.3412i		−	1.17546i	0.809057	−	0.587730i	$-0.199978\pi$
$758$	1.96708	−	11.9433i	0.0714475	−	0.433800i
$759$	−21.6595	−	3.70893i	−0.786190	−	0.134626i
$760$	−1.69969	−	1.84879i	−0.0616542	−	0.0670628i
$761$	−20.6507	−	28.4232i	−0.748587	−	1.03034i	−0.998078	−	0.0619643i	$-0.980263\pi$
$761$	−20.6507	−	28.4232i	−0.748587	−	1.03034i	0.249492	−	0.968377i	$-0.419737\pi$
$762$	6.43714	+	4.86303i	0.233193	+	0.176169i
$763$	32.8855	+	23.8927i	1.19054	+	0.864975i
$764$	3.12729	+	1.05886i	0.113141	+	0.0383083i
$765$	−28.4991	+	18.6622i	−1.03039	+	0.674733i
$766$	−2.46647	−	4.91529i	−0.0891171	−	0.177597i
$767$	0.970588	+	2.98716i	0.0350459	+	0.107860i
$768$	−6.01653	+	27.0518i	−0.217103	+	0.976149i
$769$	7.31490	+	22.5130i	0.263782	+	0.811838i	0.991971	+	0.126462i	$0.0403622\pi$
$769$	7.31490	+	22.5130i	0.263782	+	0.811838i	−0.728189	+	0.685376i	$0.759638\pi$
$770$	27.7516	−	26.1513i	1.00010	−	0.942426i
$771$	6.51384	+	44.7437i	0.234590	+	1.61140i
$772$	8.76475	−	2.72900i	0.315450	−	0.0982187i
$773$	−24.3961	+	17.7248i	−0.877466	+	0.637517i	−0.932580	−	0.360963i	$-0.882448\pi$
$773$	−24.3961	+	17.7248i	−0.877466	+	0.637517i	0.0551136	+	0.998480i	$0.482448\pi$
$774$	−8.68427	+	4.08897i	−0.312150	+	0.146975i
$775$	−28.8321	+	7.88985i	−1.03568	+	0.283412i
$776$	0.562973	+	4.03551i	0.0202096	+	0.144867i
$777$	−83.9153	−	44.0882i	−3.01044	−	1.58166i
$778$	−20.3190	+	20.0704i	−0.728473	+	0.719558i
$779$	−2.49683	−	0.811270i	−0.0894583	−	0.0290668i
$780$	−2.05706	+	9.87211i	−0.0736546	+	0.353478i
$781$	−1.91149	+	0.621082i	−0.0683987	+	0.0222241i
$782$	17.6073	−	34.0366i	0.629636	−	1.21715i
$783$	−0.712964	−	5.93589i	−0.0254793	−	0.212131i
$784$	−61.6450	+	42.5087i	−2.20161	+	1.51817i
$785$	0.406624	−	17.2816i	0.0145130	−	0.616807i
$786$	−3.63045	+	2.53549i	−0.129494	+	0.0904380i
$787$	28.8668	+	20.9730i	1.02899	+	0.747606i	0.968107	−	0.250538i	$-0.0806076\pi$
$787$	28.8668	+	20.9730i	1.02899	+	0.747606i	0.0608853	+	0.998145i	$0.480608\pi$
$788$	−0.113697	+	9.23346i	−0.00405030	+	0.328928i
$789$	−14.4089	−	7.57027i	−0.512969	−	0.269509i
$790$	12.7543	+	2.41010i	0.453779	+	0.0857476i
$791$	50.1558	+	36.4403i	1.78333	+	1.29567i
$792$	−19.7707	−	4.01960i	−0.702523	−	0.142830i
$793$	13.7844			0.489499
$794$	−23.9843	−	3.95025i	−0.851170	−	0.140189i
$795$	5.75710	−	29.4397i	0.204183	−	1.04412i
$796$	−2.88465	−	9.26468i	−0.102244	−	0.328378i
$797$	14.0374	−	43.2026i	0.497230	−	1.53032i	−0.316223	−	0.948685i	$-0.602415\pi$
$797$	14.0374	−	43.2026i	0.497230	−	1.53032i	0.813453	−	0.581631i	$-0.197585\pi$
$798$	−4.04415	+	2.82442i	−0.143161	+	0.0999832i
$799$		−	45.3674i		−	1.60498i
$800$	−21.4945	+	18.3844i	−0.759946	+	0.649986i
$801$	1.83732	+	1.40647i	0.0649185	+	0.0496950i
$802$	1.00884	+	6.63364i	0.0356234	+	0.234242i
$803$	−30.7712	−	9.99816i	−1.08589	−	0.352827i
$804$	7.97840	+	8.38473i	0.281377	+	0.295707i
$805$	34.4060	+	49.7774i	1.21265	+	1.75442i
$806$	1.78876	−	10.8606i	0.0630062	−	0.382548i
$807$	7.34206	+	14.8666i	0.258453	+	0.523330i
$808$	−48.8171	+	23.7483i	−1.71738	+	0.835463i
$809$	−20.4537	+	28.1521i	−0.719113	+	0.989774i	0.280440	+	0.959872i	$0.409520\pi$
$809$	−20.4537	+	28.1521i	−0.719113	+	0.989774i	−0.999553	+	0.0299028i	$0.990480\pi$
$810$	−21.6636	+	18.4577i	−0.761183	+	0.648537i
$811$	13.4055	−	9.73964i	0.470729	−	0.342005i	−0.326996	−	0.945026i	$-0.606036\pi$
$811$	13.4055	−	9.73964i	0.470729	−	0.342005i	0.797725	+	0.603021i	$0.206036\pi$
$812$	−11.6694	−	0.143692i	−0.409515	−	0.00504261i
$813$	−24.1245	−	4.13105i	−0.846084	−	0.144882i
$814$	−35.8738	+	5.45566i	−1.25737	+	0.191221i
$815$	−34.7726	−	26.5356i	−1.21803	−	0.929501i
$816$	17.1257	−	30.7335i	0.599520	−	1.07589i
$817$	0.277615	+	0.854410i	0.00971251	+	0.0298920i
$818$	45.8327	+	23.7094i	1.60250	+	0.828981i
$819$	18.6786	+	6.59024i	0.652684	+	0.230282i
$820$	−10.1386	+	27.7751i	−0.354056	+	0.969948i
$821$	3.51019	−	10.8033i	0.122507	−	0.377036i	−0.870932	−	0.491404i	$-0.836484\pi$
$821$	3.51019	−	10.8033i	0.122507	−	0.377036i	0.993439	+	0.114367i	$0.0364840\pi$
$822$	−12.8107	+	37.0584i	−0.446824	+	1.29256i
$823$	27.8924	+	38.3906i	0.972269	+	1.33821i	0.940892	+	0.338706i	$0.109989\pi$
$823$	27.8924	+	38.3906i	0.972269	+	1.33821i	0.0313768	+	0.999508i	$0.490011\pi$
$824$	−29.0835	+	4.05729i	−1.01317	+	0.141342i
$825$	−13.6676	−	15.4011i	−0.475846	−	0.536199i
$826$	15.3691	+	7.95051i	0.534760	+	0.276634i
$827$	−20.4376	−	28.1300i	−0.710685	−	0.978174i	−0.999782	−	0.0208744i	$-0.993355\pi$
$827$	−20.4376	−	28.1300i	−0.710685	−	0.978174i	0.289097	−	0.957300i	$-0.406645\pi$
$828$	11.0232	−	30.0581i	0.383083	−	1.04459i
$829$	−46.0831	−	14.9733i	−1.60053	−	0.520044i	−0.633292	−	0.773913i	$-0.718297\pi$
$829$	−46.0831	−	14.9733i	−1.60053	−	0.520044i	−0.967239	+	0.253869i	$0.918297\pi$
$830$	−10.4298	+	4.92999i	−0.362023	+	0.171123i
$831$	32.9966	+	33.8330i	1.14464	+	1.17365i
$832$	−2.85037	−	10.0172i	−0.0988189	−	0.347285i
$833$	90.4122	−	29.3767i	3.13260	−	1.01784i
$834$	−20.6017	+	27.2703i	−0.713380	+	0.944294i
$835$	−7.11142	−	23.7758i	−0.246101	−	0.822794i
$836$	−0.605573	+	1.78853i	−0.0209442	+	0.0618574i
$837$	22.7751	−	21.1262i	0.787222	−	0.730228i
$838$	−20.5782	+	10.3260i	−0.710862	+	0.356707i
$839$	−13.0064	+	9.44968i	−0.449029	+	0.326239i	−0.789212	−	0.614120i	$-0.789511\pi$
$839$	−13.0064	+	9.44968i	−0.449029	+	0.326239i	0.340183	+	0.940359i	$0.389511\pi$
$840$	30.1575	+	46.6577i	1.04053	+	1.60984i
$841$	22.3905	+	16.2677i	0.772086	+	0.560953i
$842$	−4.13576	−	0.681166i	−0.142528	−	0.0234745i
$843$	−8.28690	+	4.09258i	−0.285416	+	0.140956i
$844$	−3.45993	+	4.64093i	−0.119096	+	0.159747i
$845$	7.24398	+	24.2190i	0.249201	+	0.833158i
$846$	−4.75916	−	37.6025i	−0.163623	−	1.29280i
$847$	25.7886	+	8.37921i	0.886105	+	0.287913i
$848$	8.84526	+	29.6916i	0.303747	+	1.01961i
$849$	4.12039	+	8.34321i	0.141412	+	0.286338i
$850$	32.8164	−	14.5775i	1.12559	−	0.500005i
$851$		−	57.5819i		−	1.97388i
$852$	−0.386139	−	2.90266i	−0.0132289	−	0.0994435i
$853$	29.0720	+	9.44606i	0.995406	+	0.323427i	0.761028	−	0.648719i	$-0.224695\pi$
$853$	29.0720	+	9.44606i	0.995406	+	0.323427i	0.234378	+	0.972146i	$0.424695\pi$
$854$	54.0280	−	53.3668i	1.84880	−	1.82618i
$855$	1.45926	+	2.22844i	0.0499055	+	0.0762109i
$856$	8.45400	+	17.3781i	0.288952	+	0.593970i
$857$			27.8244i			0.950463i	0.879861	+	0.475231i	$0.157636\pi$
$857$			27.8244i			0.950463i	−0.879861	+	0.475231i	$0.842364\pi$
$858$	7.25352	−	2.20797i	0.247631	−	0.0753790i
$859$	−21.3813	−	15.5345i	−0.729522	−	0.530029i	0.159890	−	0.987135i	$-0.448886\pi$
$859$	−21.3813	−	15.5345i	−0.729522	−	0.530029i	−0.889412	+	0.457106i	$0.848886\pi$
$860$	9.72862	−	2.77983i	0.331743	−	0.0947916i
$861$	51.4124	+	27.0116i	1.75213	+	0.920552i
$862$	16.5593	+	33.0001i	0.564011	+	1.12399i
$863$	32.7379	+	23.7855i	1.11441	+	0.809667i	0.983353	−	0.181708i	$-0.0581625\pi$
$863$	32.7379	+	23.7855i	1.11441	+	0.809667i	0.131058	+	0.991375i	$0.458163\pi$
$864$	10.9705	−	27.2699i	0.373225	−	0.927741i
$865$	14.4991	−	10.0217i	0.492983	−	0.340748i
$866$	−6.21615	−	12.3878i	−0.211233	−	0.420955i
$867$	−10.8973	+	10.6280i	−0.370093	+	0.360945i
$868$	−35.0361	−	49.4932i	−1.18920	−	1.67991i
$869$	−3.01586	−	9.28185i	−0.102306	−	0.314865i
$870$	−0.265834	+	6.29634i	−0.00901261	+	0.213466i
$871$	−4.13680	−	1.34413i	−0.140170	−	0.0455441i
$872$	−3.95932	+	22.3218i	−0.134080	+	0.755911i
$873$	0.108152	−	4.32041i	0.00366040	−	0.146224i
$874$	−2.66143	−	1.37677i	−0.0900243	−	0.0465700i
$875$	−3.99835	+	56.5600i	−0.135169	+	1.91208i
$876$	22.4365	−	41.4566i	0.758059	−	1.40069i
$877$	−0.675843	−	0.930219i	−0.0228216	−	0.0314112i	0.797454	−	0.603380i	$-0.206180\pi$
$877$	−0.675843	−	0.930219i	−0.0228216	−	0.0314112i	−0.820275	+	0.571969i	$0.806180\pi$
$878$	−6.60230	−	6.68410i	−0.222817	−	0.225577i
$879$	−13.9412	+	2.02958i	−0.470225	+	0.0684560i
$880$	19.8859	+	7.53762i	0.670355	+	0.254093i
$881$	−26.4272	+	8.58673i	−0.890356	+	0.289294i	−0.718251	−	0.695784i	$-0.755057\pi$
$881$	−26.4272	+	8.58673i	−0.890356	+	0.289294i	−0.172105	+	0.985079i	$0.555057\pi$
$882$	71.8561	−	33.8332i	2.41952	−	1.13922i
$883$	16.4434	+	50.6076i	0.553364	+	1.70308i	0.700224	+	0.713923i	$0.253083\pi$
$883$	16.4434	+	50.6076i	0.553364	+	1.70308i	−0.146860	+	0.989157i	$0.546917\pi$
$884$	−0.162801	+	13.2213i	−0.00547560	+	0.444679i
$885$	4.53933	−	8.16734i	0.152588	−	0.274542i
$886$	−2.75879	−	18.1404i	−0.0926833	−	0.609440i
$887$	38.2902	+	27.8194i	1.28566	+	0.934086i	0.999708	−	0.0241590i	$-0.00769078\pi$
$887$	38.2902	+	27.8194i	1.28566	+	0.934086i	0.285950	+	0.958244i	$0.407691\pi$
$888$	1.63772	−	52.8411i	0.0549582	−	1.77323i
$889$	−13.5133	+	9.81799i	−0.453222	+	0.329285i
$890$	−1.67270	−	1.77506i	−0.0560690	−	0.0595003i
$891$	19.9953	+	7.62267i	0.669869	+	0.255369i
$892$	8.78441	+	6.54900i	0.294124	+	0.219277i
$893$	−3.54742			−0.118710
$894$	−14.0450	+	4.27532i	−0.469736	+	0.142988i
$895$	−25.2379	−	8.86187i	−0.843610	−	0.296220i
$896$	−49.9540	−	28.2272i	−1.66885	−	0.943004i
$897$	1.73335	+	11.9064i	0.0578750	+	0.397544i
$898$	−2.95298	−	19.4173i	−0.0985422	−	0.647965i
$899$		−	6.87861i		−	0.229414i
$900$	25.6705	−	15.5250i	0.855683	−	0.517501i
$901$		−	39.3323i		−	1.31035i
$902$	21.9788	−	3.34253i	0.731814	−	0.111294i
$903$	−2.86304	−	19.6663i	−0.0952761	−	0.654453i
$904$	−6.03861	+	34.0443i	−0.200841	+	1.13230i
$905$	1.28815	−	0.385292i	0.0428197	−	0.0128075i
$906$	3.92205	+	12.8845i	0.130301	+	0.428059i
$907$	−37.8387			−1.25641			−0.628206	−	0.778047i	$-0.716211\pi$
$907$	−37.8387			−1.25641			−0.628206	+	0.778047i	$0.716211\pi$
$908$	−2.54455	−	1.89702i	−0.0844437	−	0.0629550i
$909$	55.1902	−	16.4173i	1.83054	−	0.544526i
$910$	−18.3134	−	10.0266i	−0.607084	−	0.332378i
$911$	−42.4842	+	30.8666i	−1.40756	+	1.02266i	−0.413894	+	0.910325i	$0.635832\pi$
$911$	−42.4842	+	30.8666i	−1.40756	+	1.02266i	−0.993671	+	0.112330i	$0.964168\pi$
$912$	−2.40315	−	1.33911i	−0.0795764	−	0.0443425i
$913$	7.01737	+	5.09842i	0.232241	+	0.168733i
$914$	−6.61747	+	1.00638i	−0.218886	+	0.0332881i
$915$	−27.9335	−	30.0231i	−0.923455	−	0.992535i
$916$	17.8062	+	0.219258i	0.588333	+	0.00724450i
$917$	−2.83315	−	8.71955i	−0.0935590	−	0.287945i
$918$	−23.2324	+	29.2032i	−0.766783	+	0.963850i
$919$	38.9715	−	12.6626i	1.28555	−	0.417701i	0.415020	−	0.909812i	$-0.363775\pi$
$919$	38.9715	−	12.6626i	1.28555	−	0.417701i	0.870533	+	0.492111i	$0.163775\pi$
$920$	−16.5699	+	29.3995i	−0.546293	+	0.969273i
$921$	−32.3820	+	4.71422i	−1.06702	+	0.155339i
$922$	0.733321	−	0.724346i	0.0241506	−	0.0238551i
$923$	0.646841	+	0.890300i	0.0212910	+	0.0293046i
$924$	19.8819	−	36.7364i	0.654067	−	1.20854i
$925$	33.7329	−	42.1119i	1.10913	−	1.38463i
$926$	−9.39213	+	18.1559i	−0.308645	+	0.596640i
$927$	31.1367	+	0.779443i	1.02266	+	0.0256003i
$928$	−2.77497	−	5.88742i	−0.0910928	−	0.193264i
$929$	33.3588	+	10.8389i	1.09447	+	0.355613i	0.799970	−	0.600039i	$-0.204848\pi$
$929$	33.3588	+	10.8389i	1.09447	+	0.355613i	0.294495	+	0.955653i	$0.404848\pi$
$930$	−27.2797	+	18.1125i	−0.894537	+	0.593932i
$931$	−2.29706	−	7.06962i	−0.0752831	−	0.231698i
$932$	29.4321	−	20.8349i	0.964081	−	0.682469i
$933$	−0.900898	+	0.878628i	−0.0294941	+	0.0287650i
$934$	−29.0182	+	14.5612i	−0.949506	+	0.476457i
$935$	−21.4634	−	16.3791i	−0.701927	−	0.535653i
$936$	1.25201	+	10.9755i	0.0409232	+	0.358744i
$937$	32.4932	+	23.6077i	1.06151	+	0.771230i	0.974367	−	0.224966i	$-0.0722270\pi$
$937$	32.4932	+	23.6077i	1.06151	+	0.771230i	0.0871407	+	0.996196i	$0.472227\pi$
$938$	−21.4180	+	10.7474i	−0.699323	+	0.350917i
$939$	7.18389	+	3.77435i	0.234438	+	0.123171i
$940$	−1.43152	+	39.9271i	−0.0466910	+	1.30228i
$941$	10.8108	+	7.85448i	0.352421	+	0.256049i	0.749884	−	0.661569i	$-0.230109\pi$
$941$	10.8108	+	7.85448i	0.352421	+	0.256049i	−0.397463	+	0.917618i	$0.630109\pi$
$942$	−5.51439	−	18.1156i	−0.179669	−	0.590238i
$943$			35.2788i			1.14883i
$944$	−0.237629	+	9.64755i	−0.00773415	+	0.314001i
$945$	−23.4976	−	54.0378i	−0.764377	−	1.75785i
$946$	−5.34614	−	5.41238i	−0.173818	−	0.175972i
$947$	−8.44500	−	2.74395i	−0.274426	−	0.0891663i	0.168571	−	0.985689i	$-0.446085\pi$
$947$	−8.44500	−	2.74395i	−0.274426	−	0.0891663i	−0.442997	+	0.896523i	$0.646085\pi$
$948$	14.0948	−	1.87502i	0.457777	−	0.0608977i
$949$			17.7153i			0.575064i
$950$	−1.13986	−	2.56602i	−0.0369820	−	0.0832526i
$951$	−20.5039	−	41.5174i	−0.664883	−	1.34629i
$952$	50.5484	+	52.4509i	1.63828	+	1.69994i
$953$	−20.8350	−	6.76970i	−0.674912	−	0.219292i	−0.0485455	−	0.998821i	$-0.515459\pi$
$953$	−20.8350	−	6.76970i	−0.674912	−	0.219292i	−0.626366	+	0.779529i	$0.715459\pi$
$954$	−4.12606	−	32.6004i	−0.133586	−	1.05548i
$955$	2.93453	+	2.23939i	0.0949593	+	0.0724651i
$956$	4.53810	−	6.08711i	0.146773	−	0.196871i
$957$	4.24849	−	2.09816i	0.137334	−	0.0678240i
$958$	1.16323	−	7.06267i	0.0375824	−	0.228185i
$959$	−65.6776	−	47.7176i	−2.12084	−	1.54088i
$960$	−16.0418	+	26.5077i	−0.517748	+	0.855533i
$961$	3.83595	−	2.78698i	0.123740	−	0.0899027i
$962$	8.91072	+	17.7577i	0.287293	+	0.572531i
$963$	−5.84427	−	19.6468i	−0.188329	−	0.633108i
$964$	39.7844	+	13.4705i	1.28137	+	0.433857i
$965$	10.2605	+	0.241422i	0.330296	+	0.00777163i
$966$	52.8900	+	39.9565i	1.70171	+	1.28558i
$967$	−39.9824	+	12.9911i	−1.28575	+	0.417765i	−0.870601	−	0.491990i	$-0.836270\pi$
$967$	−39.9824	+	12.9911i	−1.28575	+	0.417765i	−0.415147	+	0.909754i	$0.636270\pi$
$968$	2.08945	+	14.9776i	0.0671575	+	0.481400i
$969$	2.43857	+	2.50038i	0.0783381	+	0.0803237i
$970$	−0.845859	+	4.47632i	−0.0271589	+	0.143726i
$971$	9.32941	+	3.03131i	0.299395	+	0.0972793i	0.454863	−	0.890562i	$-0.349688\pi$
$971$	9.32941	+	3.03131i	0.299395	+	0.0972793i	−0.155468	+	0.987841i	$0.549688\pi$
$972$	−16.1926	+	26.6421i	−0.519376	+	0.854546i
$973$	−41.5930	−	57.2478i	−1.33341	−	1.83528i
$974$	7.91672	−	15.3038i	0.253668	−	0.490365i
$975$	−5.70740	+	9.72308i	−0.182783	+	0.311388i
$976$	39.9457	+	14.0757i	1.27863	+	0.450552i
$977$	−0.247391	−	0.340505i	−0.00791475	−	0.0108937i	0.805041	−	0.593219i	$-0.202143\pi$
$977$	−0.247391	−	0.340505i	−0.00791475	−	0.0108937i	−0.812956	+	0.582325i	$0.802143\pi$
$978$	−45.2863	−	15.6550i	−1.44810	−	0.500591i
$979$	−0.566693	+	1.74410i	−0.0181116	+	0.0557417i
$980$	−80.4973	+	23.0011i	−2.57139	+	0.734744i
$981$	8.00039	−	22.6754i	0.255433	−	0.723970i
$982$	−14.3721	+	27.7826i	−0.458632	+	0.886579i
$983$	−14.6380	−	45.0510i	−0.466878	−	1.43690i	−0.856605	−	0.515973i	$-0.827430\pi$
$983$	−14.6380	−	45.0510i	−0.466878	−	1.43690i	0.389726	−	0.920931i	$-0.372570\pi$
$984$	−1.00338	+	32.3742i	−0.0319866	+	1.03205i
$985$	−3.42041	+	9.74104i	−0.108983	+	0.310375i
$986$	1.24236	+	8.16913i	0.0395648	+	0.260158i
$987$	77.3488	+	13.2451i	2.46204	+	0.421595i
$988$	1.03381	+	0.0127300i	0.0328900	+	0.000404994i
$989$	9.76670	−	7.09593i	0.310563	−	0.225637i
$990$	−19.5080	−	11.3241i	−0.620005	−	0.359905i
$991$	−19.8578	+	27.3320i	−0.630805	+	0.868228i	−0.998083	−	0.0618828i	$-0.980290\pi$
$991$	−19.8578	+	27.3320i	−0.630805	+	0.868228i	0.367279	+	0.930111i	$0.380290\pi$
$992$	16.2737	−	29.6462i	0.516690	−	0.941267i
$993$	21.5120	+	43.5588i	0.682663	+	1.38230i
$994$	5.98211	+	0.985263i	0.189741	+	0.0312507i
$995$	0.255192	−	10.8457i	0.00809012	−	0.343832i
$996$	−9.15501	+	8.71136i	−0.290088	+	0.276030i
$997$	−15.0666	−	4.89545i	−0.477165	−	0.155040i	0.0605530	−	0.998165i	$-0.480714\pi$
$997$	−15.0666	−	4.89545i	−0.477165	−	0.155040i	−0.537718	+	0.843125i	$0.680714\pi$
$998$	6.24737	−	0.950097i	0.197757	−	0.0300748i
$999$	−10.8443	+	55.0148i	−0.343099	+	1.74059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bg.a.11.6	✓	464
3.2	odd	2	inner	600.2.bg.a.11.111	yes	464
8.3	odd	2	inner	600.2.bg.a.11.75	yes	464
24.11	even	2	inner	600.2.bg.a.11.42	yes	464
25.16	even	5	inner	600.2.bg.a.491.42	yes	464
75.41	odd	10	inner	600.2.bg.a.491.75	yes	464
200.91	odd	10	inner	600.2.bg.a.491.111	yes	464
600.491	even	10	inner	600.2.bg.a.491.6	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bg.a.11.6	✓	464	1.1	even	1	trivial
600.2.bg.a.11.42	yes	464	24.11	even	2	inner
600.2.bg.a.11.75	yes	464	8.3	odd	2	inner
600.2.bg.a.11.111	yes	464	3.2	odd	2	inner
600.2.bg.a.491.6	yes	464	600.491	even	10	inner
600.2.bg.a.491.42	yes	464	25.16	even	5	inner
600.2.bg.a.491.75	yes	464	75.41	odd	10	inner
600.2.bg.a.491.111	yes	464	200.91	odd	10	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bg (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39814 + 0.212628i) q^{2} +(-1.71398 + 0.249524i) q^{3} +(1.90958 - 0.594567i) q^{4} +(2.23545 + 0.0525986i) q^{5} +(2.34333 - 0.713310i) q^{6} +5.07150i q^{7} +(-2.54343 + 1.23732i) q^{8} +(2.87548 - 0.855360i) q^{9} +(-3.13665 + 0.401779i) q^{10} +(1.39756 + 1.92358i) q^{11} +(-3.12463 + 1.49556i) q^{12} +(0.765213 - 1.05323i) q^{13} +(-1.07834 - 7.09066i) q^{14} +(-3.84465 + 0.467645i) q^{15} +(3.29298 - 2.27074i) q^{16} +(-4.82968 + 1.56926i) q^{17} +(-3.83844 + 1.80732i) q^{18} +(0.122705 + 0.377648i) q^{19} +(4.30004 - 1.22868i) q^{20} +(-1.26546 - 8.69247i) q^{21} +(-2.36299 - 2.39226i) q^{22} +(4.31687 - 3.13639i) q^{23} +(4.05066 - 2.75539i) q^{24} +(4.99447 + 0.235163i) q^{25} +(-0.845928 + 1.63526i) q^{26} +(-4.71508 + 2.18357i) q^{27} +(3.01535 + 9.68443i) q^{28} +(-0.355547 + 1.09426i) q^{29} +(5.27591 - 1.47131i) q^{30} +(-5.68581 + 1.84743i) q^{31} +(-4.12122 + 3.87499i) q^{32} +(-2.87537 - 2.94825i) q^{33} +(6.41889 - 3.22096i) q^{34} +(-0.266754 + 11.3371i) q^{35} +(4.98238 - 3.34304i) q^{36} +(6.34298 - 8.73037i) q^{37} +(-0.251858 - 0.501913i) q^{38} +(-1.04876 + 1.99615i) q^{39} +(-5.75079 + 2.63218i) q^{40} +(-3.88616 + 5.34884i) q^{41} +(3.61755 + 11.8842i) q^{42} +2.26245 q^{43} +(3.81245 + 2.84228i) q^{44} +(6.47297 - 1.76087i) q^{45} +(-5.36869 + 5.30299i) q^{46} +(-2.76067 + 8.49646i) q^{47} +(-5.07751 + 4.71370i) q^{48} -18.7201 q^{49} +(-7.03295 + 0.733174i) q^{50} +(7.88642 - 3.89480i) q^{51} +(0.835021 - 2.46619i) q^{52} +(-2.39342 + 7.36620i) q^{53} +(6.12805 - 4.05549i) q^{54} +(3.02300 + 4.37357i) q^{55} +(-6.27506 - 12.8990i) q^{56} +(-0.304547 - 0.616664i) q^{57} +(0.264433 - 1.60553i) q^{58} +(-1.41810 + 1.95185i) q^{59} +(-7.06361 + 3.17891i) q^{60} +(6.22363 + 8.56609i) q^{61} +(7.55674 - 3.79193i) q^{62} +(4.33796 + 14.5830i) q^{63} +(4.93809 - 6.29406i) q^{64} +(1.76599 - 2.31418i) q^{65} +(4.64705 + 3.51068i) q^{66} +(-1.03247 - 3.17761i) q^{67} +(-8.28962 + 5.86819i) q^{68} +(-6.61644 + 6.45288i) q^{69} +(-2.03763 - 15.9075i) q^{70} +(-0.261214 + 0.803935i) q^{71} +(-6.25523 + 5.73342i) q^{72} +(-11.0089 + 7.99842i) q^{73} +(-7.01204 + 13.5550i) q^{74} +(-8.61911 + 0.843174i) q^{75} +(0.458852 + 0.648192i) q^{76} +(-9.75543 + 7.08773i) q^{77} +(1.04187 - 3.01389i) q^{78} +(-3.90376 - 1.26841i) q^{79} +(7.48073 - 4.90293i) q^{80} +(7.53672 - 4.91913i) q^{81} +(4.29607 - 8.30472i) q^{82} +(3.46953 - 1.12732i) q^{83} +(-7.58475 - 15.8466i) q^{84} +(-10.8790 + 3.25396i) q^{85} +(-3.16322 + 0.481061i) q^{86} +(0.336357 - 1.96426i) q^{87} +(-5.93467 - 3.16326i) q^{88} +(0.453349 + 0.623981i) q^{89} +(-8.67569 + 3.83827i) q^{90} +(5.34144 + 3.88078i) q^{91} +(6.37861 - 8.55585i) q^{92} +(9.28441 - 4.58522i) q^{93} +(2.05321 - 12.4662i) q^{94} +(0.254438 + 0.850667i) q^{95} +(6.09679 - 7.67002i) q^{96} +(0.445166 - 1.37008i) q^{97} +(26.1733 - 3.98043i) q^{98} +(5.66400 + 4.33578i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q - 6 q^{3} - 6 q^{4} - 7 q^{6} - 6 q^{9} - 8 q^{10} + 3 q^{12} + 6 q^{16} + 2 q^{18} - 12 q^{19} - 22 q^{22} - 16 q^{25} - 6 q^{27} + 34 q^{28} + 3 q^{30} - 18 q^{33} - 30 q^{34} + 35 q^{36} + 4 q^{40}+ \cdots - 52 q^{99}+O(q^{100}) \) 464 * q - 6 * q^3 - 6 * q^4 - 7 * q^6 - 6 * q^9 - 8 * q^10 + 3 * q^12 + 6 * q^16 + 2 * q^18 - 12 * q^19 - 22 * q^22 - 16 * q^25 - 6 * q^27 + 34 * q^28 + 3 * q^30 - 18 * q^33 - 30 * q^34 + 35 * q^36 + 4 * q^40 + 43 * q^42 + 22 * q^46 - 50 * q^48 - 400 * q^49 - 28 * q^51 + 32 * q^54 - 4 * q^57 + 54 * q^58 - 76 * q^60 - 30 * q^64 - 58 * q^66 - 12 * q^67 + 48 * q^70 - 69 * q^72 - 12 * q^73 - 30 * q^75 + 48 * q^76 - 79 * q^78 - 6 * q^81 + 12 * q^82 - 22 * q^84 - 130 * q^88 - 48 * q^90 + 72 * q^91 - 72 * q^94 + 44 * q^96 - 36 * q^97 - 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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