LMFDB - Embedded newform 252.2.bj.b.103.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,2,Mod(103,252)] 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("252.103"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.19
Character	$\chi$	$=$	252.103
Dual form			252.2.bj.b.115.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.171292 - 1.40380i) q^{2} +(1.50942 - 0.849495i) q^{3} +(-1.94132 + 0.480920i) q^{4} +(3.50837 - 2.02556i) q^{5} +(-1.45107 - 1.97342i) q^{6} +(-2.35939 + 1.19719i) q^{7} +(1.00765 + 2.64285i) q^{8} +(1.55672 - 2.56450i) q^{9} +(-3.44444 - 4.57810i) q^{10} +(0.471017 + 0.271942i) q^{11} +(-2.52173 + 2.37505i) q^{12} +(1.01063 + 0.583488i) q^{13} +(2.08476 + 3.10705i) q^{14} +(3.57492 - 6.03778i) q^{15} +(3.53743 - 1.86724i) q^{16} +(-5.05773 + 2.92008i) q^{17} +(-3.86670 - 1.74604i) q^{18} +(-1.16501 + 2.01785i) q^{19} +(-5.83674 + 5.61950i) q^{20} +(-2.54431 + 3.81136i) q^{21} +(0.301071 - 0.707796i) q^{22} +(-1.39849 + 0.807417i) q^{23} +(3.76605 + 3.13318i) q^{24} +(5.70579 - 9.88272i) q^{25} +(0.645988 - 1.51867i) q^{26} +(0.171215 - 5.19333i) q^{27} +(4.00458 - 3.45881i) q^{28} +(2.40001 + 4.15694i) q^{29} +(-9.08819 - 3.98425i) q^{30} -4.49030 q^{31} +(-3.22716 - 4.64601i) q^{32} +(0.941977 + 0.0103485i) q^{33} +(4.96557 + 6.59987i) q^{34} +(-5.85265 + 8.97929i) q^{35} +(-1.78876 + 5.72716i) q^{36} +(-1.48498 + 2.57206i) q^{37} +(3.03222 + 1.28980i) q^{38} +(2.02114 + 0.0222040i) q^{39} +(8.88846 + 7.23105i) q^{40} +(-3.89836 - 2.25072i) q^{41} +(5.78621 + 2.91886i) q^{42} +(-2.89521 + 1.67155i) q^{43} +(-1.04518 - 0.301404i) q^{44} +(0.266999 - 12.1504i) q^{45} +(1.37300 + 1.82490i) q^{46} +8.58149 q^{47} +(3.75327 - 5.82348i) q^{48} +(4.13347 - 5.64928i) q^{49} +(-14.8507 - 6.31697i) q^{50} +(-5.15366 + 8.70416i) q^{51} +(-2.24257 - 0.646703i) q^{52} +(5.84343 + 10.1211i) q^{53} +(-7.31973 + 0.649223i) q^{54} +2.20334 q^{55} +(-5.54143 - 5.02917i) q^{56} +(-0.0443331 + 4.03546i) q^{57} +(5.42441 - 4.08118i) q^{58} +12.8781 q^{59} +(-4.03636 + 13.4405i) q^{60} +2.08317i q^{61} +(0.769151 + 6.30348i) q^{62} +(-0.602715 + 7.91434i) q^{63} +(-5.96929 + 5.32612i) q^{64} +4.72756 q^{65} +(-0.146826 - 1.32412i) q^{66} -7.09620i q^{67} +(8.41435 - 8.10118i) q^{68} +(-1.42501 + 2.40674i) q^{69} +(13.6076 + 6.67788i) q^{70} +5.17264i q^{71} +(8.34619 + 1.53005i) q^{72} +(5.58686 - 3.22558i) q^{73} +(3.86502 + 1.64404i) q^{74} +(0.217128 - 19.7643i) q^{75} +(1.29122 - 4.47756i) q^{76} +(-1.43688 - 0.0777206i) q^{77} +(-0.315035 - 2.84108i) q^{78} -4.02680i q^{79} +(8.62844 - 13.7162i) q^{80} +(-4.15327 - 7.98438i) q^{81} +(-2.49181 + 5.85806i) q^{82} +(2.76985 + 4.79753i) q^{83} +(3.10637 - 8.62267i) q^{84} +(-11.8296 + 20.4895i) q^{85} +(2.84245 + 3.77798i) q^{86} +(7.15393 + 4.23578i) q^{87} +(-0.244081 + 1.51885i) q^{88} +(-7.63381 - 4.40738i) q^{89} +(-17.1025 + 1.70646i) q^{90} +(-3.08302 - 0.166760i) q^{91} +(2.32661 - 2.24001i) q^{92} +(-6.77775 + 3.81448i) q^{93} +(-1.46994 - 12.0467i) q^{94} +9.43917i q^{95} +(-8.81792 - 4.27134i) q^{96} +(-13.8033 + 7.96935i) q^{97} +(-8.63851 - 4.83490i) q^{98} +(1.43063 - 0.784585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26}+ \cdots + 21 q^{98}+O(q^{100}) $ 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9 - 18 * q^10 - 6 * q^12 + 18 * q^13 + 14 * q^14 + 14 * q^16 + 6 * q^17 - 10 * q^18 - 24 * q^20 + 4 * q^21 + 6 * q^22 - 6 * q^24 + 16 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 11 * q^30 - 18 * q^32 - 18 * q^33 - 24 * q^34 - 38 * q^36 + 2 * q^37 + 33 * q^38 + 6 * q^40 + 6 * q^41 - 38 * q^42 - 13 * q^44 - 54 * q^45 + 10 * q^46 + 9 * q^48 - 28 * q^49 - 17 * q^50 - 27 * q^52 - 2 * q^53 - 39 * q^54 + 58 * q^56 + 6 * q^57 - 13 * q^58 - 31 * q^60 - 8 * q^64 - 100 * q^65 + 30 * q^66 - 18 * q^68 - 18 * q^69 - 19 * q^70 + 26 * q^72 + 30 * q^73 - 23 * q^74 - 2 * q^77 + 15 * q^78 + 3 * q^80 - 32 * q^81 - 18 * q^82 + 23 * q^84 - 50 * q^85 - 9 * q^86 + q^88 - 102 * q^89 - 39 * q^90 + 28 * q^92 - 36 * q^93 + 63 * q^96 + 6 * q^97 + 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.171292	−	1.40380i	−0.121122	−	0.992638i
$2$	−0.171292	−	1.40380i	−0.121122	−	0.992638i
$3$	1.50942	−	0.849495i	0.871466	−	0.490456i
$3$	1.50942	−	0.849495i	0.871466	−	0.490456i
$4$	−1.94132	+	0.480920i	−0.970659	+	0.240460i
$5$	3.50837	−	2.02556i	1.56899	−	0.905858i	0.572706	−	0.819761i	$-0.305894\pi$
$5$	3.50837	−	2.02556i	1.56899	−	0.905858i	0.996287	−	0.0860974i	$-0.0274396\pi$
$6$	−1.45107	−	1.97342i	−0.592399	−	0.805645i
$7$	−2.35939	+	1.19719i	−0.891767	+	0.452495i
$7$	−2.35939	+	1.19719i	−0.891767	+	0.452495i
$8$	1.00765	+	2.64285i	0.356257	+	0.934388i
$9$	1.55672	−	2.56450i	0.518905	−	0.854832i
$10$	−3.44444	−	4.57810i	−1.08923	−	1.44772i
$11$	0.471017	+	0.271942i	0.142017	+	0.0819935i	0.569325	−	0.822113i	$-0.307205\pi$
$11$	0.471017	+	0.271942i	0.142017	+	0.0819935i	−0.427308	+	0.904106i	$0.640538\pi$
$12$	−2.52173	+	2.37505i	−0.727961	+	0.685618i
$13$	1.01063	+	0.583488i	0.280298	+	0.161830i	0.633558	−	0.773695i	$-0.281594\pi$
$13$	1.01063	+	0.583488i	0.280298	+	0.161830i	−0.353260	+	0.935525i	$0.614927\pi$
$14$	2.08476	+	3.10705i	0.557176	+	0.830394i
$15$	3.57492	−	6.03778i	0.923039	−	1.55895i
$16$	3.53743	−	1.86724i	0.884358	−	0.466809i
$17$	−5.05773	+	2.92008i	−1.22668	+	0.708224i	−0.966334	−	0.257291i	$-0.917170\pi$
$17$	−5.05773	+	2.92008i	−1.22668	+	0.708224i	−0.260347	+	0.965515i	$0.583837\pi$
$18$	−3.86670	−	1.74604i	−0.911389	−	0.411546i
$19$	−1.16501	+	2.01785i	−0.267271	+	0.462927i	−0.968156	−	0.250347i	$-0.919455\pi$
$19$	−1.16501	+	2.01785i	−0.267271	+	0.462927i	0.700885	+	0.713274i	$0.252788\pi$
$20$	−5.83674	+	5.61950i	−1.30513	+	1.25656i
$21$	−2.54431	+	3.81136i	−0.555215	+	0.831707i
$22$	0.301071	−	0.707796i	0.0641885	−	0.150903i
$23$	−1.39849	+	0.807417i	−0.291605	+	0.168358i	−0.638665	−	0.769485i	$-0.720513\pi$
$23$	−1.39849	+	0.807417i	−0.291605	+	0.168358i	0.347061	+	0.937843i	$0.387180\pi$
$24$	3.76605	+	3.13318i	0.768743	+	0.639558i
$25$	5.70579	−	9.88272i	1.14116	−	1.97654i
$26$	0.645988	−	1.51867i	0.126689	−	0.297836i
$27$	0.171215	−	5.19333i	0.0329504	−	0.999457i
$28$	4.00458	−	3.45881i	0.756795	−	0.653653i
$29$	2.40001	+	4.15694i	0.445670	+	0.771924i	0.998099	−	0.0616368i	$-0.0196320\pi$
$29$	2.40001	+	4.15694i	0.445670	+	0.771924i	−0.552428	+	0.833560i	$0.686299\pi$
$30$	−9.08819	−	3.98425i	−1.65927	−	0.727421i
$31$	−4.49030			−0.806481			−0.403240	−	0.915094i	$-0.632116\pi$
$31$	−4.49030			−0.806481			−0.403240	+	0.915094i	$0.632116\pi$
$32$	−3.22716	−	4.64601i	−0.570487	−	0.821306i
$33$	0.941977	+	0.0103485i	0.163977	+	0.00180144i
$34$	4.96557	+	6.59987i	0.851588	+	1.13187i
$35$	−5.85265	+	8.97929i	−0.989279	+	1.51778i
$36$	−1.78876	+	5.72716i	−0.298127	+	0.954526i
$37$	−1.48498	+	2.57206i	−0.244129	+	0.422844i	−0.961886	−	0.273450i	$-0.911835\pi$
$37$	−1.48498	+	2.57206i	−0.244129	+	0.422844i	0.717757	+	0.696293i	$0.245169\pi$
$38$	3.03222	+	1.28980i	0.491891	+	0.209233i
$39$	2.02114	+	0.0222040i	0.323641	+	0.00355549i
$40$	8.88846	+	7.23105i	1.40539	+	1.14333i
$41$	−3.89836	−	2.25072i	−0.608822	−	0.351504i	0.163682	−	0.986513i	$-0.447663\pi$
$41$	−3.89836	−	2.25072i	−0.608822	−	0.351504i	−0.772504	+	0.635010i	$0.780996\pi$
$42$	5.78621	+	2.91886i	0.892832	+	0.450390i
$43$	−2.89521	+	1.67155i	−0.441515	+	0.254909i	−0.704240	−	0.709962i	$-0.748712\pi$
$43$	−2.89521	+	1.67155i	−0.441515	+	0.254909i	0.262725	+	0.964871i	$0.415379\pi$
$44$	−1.04518	−	0.301404i	−0.157566	−	0.0454384i
$45$	0.266999	−	12.1504i	0.0398019	−	1.81128i
$46$	1.37300	+	1.82490i	0.202438	+	0.269066i
$47$	8.58149			1.25174			0.625869	−	0.779928i	$-0.284744\pi$
$47$	8.58149			1.25174			0.625869	+	0.779928i	$0.284744\pi$
$48$	3.75327	−	5.82348i	0.541738	−	0.840547i
$49$	4.13347	−	5.64928i	0.590496	−	0.807041i
$50$	−14.8507	−	6.31697i	−2.10021	−	0.893355i
$51$	−5.15366	+	8.70416i	−0.721657	+	1.21883i
$52$	−2.24257	−	0.646703i	−0.310988	−	0.0896816i
$53$	5.84343	+	10.1211i	0.802658	+	1.39024i	0.917861	+	0.396902i	$0.129915\pi$
$53$	5.84343	+	10.1211i	0.802658	+	1.39024i	−0.115204	+	0.993342i	$0.536752\pi$
$54$	−7.31973	+	0.649223i	−0.996090	+	0.0883481i
$55$	2.20334			0.297098
$56$	−5.54143	−	5.02917i	−0.740505	−	0.672051i
$57$	−0.0443331	+	4.03546i	−0.00587207	+	0.534509i
$58$	5.42441	−	4.08118i	0.712260	−	0.535886i
$59$	12.8781			1.67658			0.838292	−	0.545222i	$-0.183555\pi$
$59$	12.8781			1.67658			0.838292	+	0.545222i	$0.183555\pi$
$60$	−4.03636	+	13.4405i	−0.521092	+	1.73516i
$61$			2.08317i			0.266722i	0.991067	+	0.133361i	$0.0425771\pi$
$61$			2.08317i			0.266722i	−0.991067	+	0.133361i	$0.957423\pi$
$62$	0.769151	+	6.30348i	0.0976823	+	0.800543i
$63$	−0.602715	+	7.91434i	−0.0759349	+	0.997113i
$64$	−5.96929	+	5.32612i	−0.746161	+	0.665765i
$65$	4.72756			0.586381
$66$	−0.146826	−	1.32412i	−0.0180730	−	0.162988i
$67$		−	7.09620i		−	0.866939i	−0.901168	−	0.433470i	$-0.857289\pi$
$67$		−	7.09620i		−	0.866939i	0.901168	−	0.433470i	$-0.142711\pi$
$68$	8.41435	−	8.10118i	1.02039	−	0.982412i
$69$	−1.42501	+	2.40674i	−0.171551	+	0.289738i
$70$	13.6076	+	6.67788i	1.62642	+	0.798160i
$71$			5.17264i			0.613879i	0.951729	+	0.306940i	$0.0993049\pi$
$71$			5.17264i			0.613879i	−0.951729	+	0.306940i	$0.900695\pi$
$72$	8.34619	+	1.53005i	0.983608	+	0.180319i
$73$	5.58686	−	3.22558i	0.653893	−	0.377525i	−0.136053	−	0.990702i	$-0.543442\pi$
$73$	5.58686	−	3.22558i	0.653893	−	0.377525i	0.789946	+	0.613176i	$0.210108\pi$
$74$	3.86502	+	1.64404i	0.449300	+	0.191116i
$75$	0.217128	−	19.7643i	0.0250718	−	2.28218i
$76$	1.29122	−	4.47756i	0.148114	−	0.513612i
$77$	−1.43688	−	0.0777206i	−0.163748	−	0.00885708i
$78$	−0.315035	−	2.84108i	−0.0356706	−	0.321689i
$79$		−	4.02680i		−	0.453050i	−0.974005	−	0.226525i	$-0.927264\pi$
$79$		−	4.02680i		−	0.453050i	0.974005	−	0.226525i	$-0.0727365\pi$
$80$	8.62844	−	13.7162i	0.964688	−	1.53352i
$81$	−4.15327	−	7.98438i	−0.461475	−	0.887153i
$82$	−2.49181	+	5.85806i	−0.275174	+	0.646914i
$83$	2.76985	+	4.79753i	0.304031	+	0.526597i	0.977045	−	0.213033i	$-0.0683340\pi$
$83$	2.76985	+	4.79753i	0.304031	+	0.526597i	−0.673014	+	0.739630i	$0.735001\pi$
$84$	3.10637	−	8.62267i	0.338932	−	0.940811i
$85$	−11.8296	+	20.4895i	−1.28310	+	2.22240i
$86$	2.84245	+	3.77798i	0.306509	+	0.407390i
$87$	7.15393	+	4.23578i	0.766981	+	0.454123i
$88$	−0.244081	+	1.51885i	−0.0260192	+	0.161910i
$89$	−7.63381	−	4.40738i	−0.809183	−	0.467182i	0.0374893	−	0.999297i	$-0.488064\pi$
$89$	−7.63381	−	4.40738i	−0.809183	−	0.467182i	−0.846672	+	0.532115i	$0.821397\pi$
$90$	−17.1025	+	1.70646i	−1.80276	+	0.179876i
$91$	−3.08302	−	0.166760i	−0.323188	−	0.0174812i
$92$	2.32661	−	2.24001i	0.242566	−	0.233538i
$93$	−6.77775	+	3.81448i	−0.702820	+	0.395544i
$94$	−1.46994	−	12.0467i	−0.151613	−	1.24252i
$95$			9.43917i			0.968438i
$96$	−8.81792	−	4.27134i	−0.899975	−	0.435941i
$97$	−13.8033	+	7.96935i	−1.40151	+	0.809165i	−0.994548	−	0.104278i	$-0.966747\pi$
$97$	−13.8033	+	7.96935i	−1.40151	+	0.809165i	−0.406966	+	0.913443i	$0.633413\pi$
$98$	−8.63851	−	4.83490i	−0.872621	−	0.488398i
$99$	1.43063	−	0.784585i	0.143784	−	0.0788537i
$100$	−6.32396	+	21.9295i	−0.632396	+	2.19295i
$101$	−6.41362	−	3.70290i	−0.638179	−	0.368453i	0.145734	−	0.989324i	$-0.453446\pi$
$101$	−6.41362	−	3.70290i	−0.638179	−	0.368453i	−0.783913	+	0.620871i	$0.786779\pi$
$102$	13.1017	+	5.74377i	1.29726	+	0.568718i
$103$	−3.23031	−	5.59507i	−0.318292	−	0.551298i	0.661840	−	0.749645i	$-0.269776\pi$
$103$	−3.23031	−	5.59507i	−0.318292	−	0.551298i	−0.980132	+	0.198347i	$0.936443\pi$
$104$	−0.523709	+	3.25889i	−0.0513539	+	0.319561i
$105$	−1.20627	+	18.5253i	−0.117720	+	1.80789i
$106$	13.2071	−	9.93669i	1.28279	−	0.965137i
$107$	−9.62572	−	5.55741i	−0.930553	−	0.537255i	−0.0435667	−	0.999051i	$-0.513872\pi$
$107$	−9.62572	−	5.55741i	−0.930553	−	0.537255i	−0.886987	+	0.461795i	$0.847205\pi$
$108$	2.16519	+	10.1642i	0.208346	+	0.978055i
$109$	−1.67348	−	2.89856i	−0.160291	−	0.277632i	0.774682	−	0.632351i	$-0.217910\pi$
$109$	−1.67348	−	2.89856i	−0.160291	−	0.277632i	−0.934973	+	0.354719i	$0.884576\pi$
$110$	−0.377414	−	3.09305i	−0.0359850	−	0.294911i
$111$	−0.0565093	+	5.14381i	−0.00536363	+	0.488228i
$112$	−6.11076	+	8.64052i	−0.577412	+	0.816453i
$113$	−1.36060	+	2.35662i	−0.127994	+	0.221692i	−0.922899	−	0.385041i	$-0.874187\pi$
$113$	−1.36060	+	2.35662i	−0.127994	+	0.221692i	0.794905	+	0.606734i	$0.207521\pi$
$114$	5.67258	−	0.629006i	0.531285	−	0.0589118i
$115$	−3.27095	+	5.66544i	−0.305017	+	0.528305i
$116$	−6.65833	−	6.91572i	−0.618211	−	0.642109i
$117$	3.06961	−	1.68343i	0.283786	−	0.155633i
$118$	−2.20591	−	18.0783i	−0.203071	−	1.66424i
$119$	8.43729	−	12.9447i	0.773445	−	1.18664i
$120$	19.5592	+	3.36401i	1.78550	+	0.307090i
$121$	−5.35210	−	9.27010i	−0.486554	−	0.842736i
$122$	2.92436	−	0.356830i	0.264759	−	0.0323059i
$123$	−7.79625	−	0.0856489i	−0.702965	−	0.00772270i
$124$	8.71709	−	2.15947i	0.782818	−	0.193926i
$125$		−	25.9741i		−	2.32320i
$126$	11.2134	−	0.509570i	0.998969	−	0.0453961i
$127$			14.2111i			1.26103i	0.776178	+	0.630513i	$0.217156\pi$
$127$			14.2111i			1.26103i	−0.776178	+	0.630513i	$0.782844\pi$
$128$	8.49931	+	7.46738i	0.751240	+	0.660029i
$129$	−2.95012	+	4.98254i	−0.259744	+	0.438688i
$130$	−0.809792	−	6.63655i	−0.0710235	−	0.582064i
$131$	−7.95497	−	13.7784i	−0.695029	−	1.20383i	−0.970171	−	0.242422i	$-0.922058\pi$
$131$	−7.95497	−	13.7784i	−0.695029	−	1.20383i	0.275142	−	0.961404i	$-0.411275\pi$
$132$	−1.83365	+	0.432926i	−0.159599	+	0.0376813i
$133$	0.332957	−	6.15564i	0.0288711	−	0.533761i
$134$	−9.96166	+	1.21552i	−0.860556	+	0.105005i
$135$	−9.91872	−	18.5670i	−0.853667	−	1.59799i
$136$	−12.8138	−	10.4244i	−1.09877	−	0.893885i
$137$	−6.27966	+	10.8767i	−0.536507	+	0.929258i	0.462581	+	0.886577i	$0.346923\pi$
$137$	−6.27966	+	10.8767i	−0.536507	+	0.929258i	−0.999089	+	0.0426811i	$0.986410\pi$
$138$	3.62268	+	1.58818i	0.308383	+	0.135195i
$139$	7.10577	−	12.3076i	0.602704	−	1.04391i	−0.389706	−	0.920939i	$-0.627423\pi$
$139$	7.10577	−	12.3076i	0.602704	−	1.04391i	0.992410	−	0.122974i	$-0.0392432\pi$
$140$	7.04354	−	20.2463i	0.595288	−	1.71113i
$141$	12.9531	−	7.28993i	1.09085	−	0.613923i
$142$	7.26136	−	0.886031i	0.609359	−	0.0743541i
$143$	0.317349	+	0.549665i	0.0265381	+	0.0459653i
$144$	0.718256	−	11.9785i	0.0598547	−	0.998207i
$145$	16.8403	+	9.72272i	1.39851	+	0.807428i
$146$	−5.48505	−	7.29033i	−0.453946	−	0.603352i
$147$	1.44012	−	12.0385i	0.118779	−	0.992921i
$148$	1.64586	−	5.70734i	0.135289	−	0.469140i
$149$	2.11648	+	3.66585i	0.173389	+	0.300318i	0.939603	−	0.342267i	$-0.111195\pi$
$149$	2.11648	+	3.66585i	0.173389	+	0.300318i	−0.766214	+	0.642586i	$0.777862\pi$
$150$	−27.7823	+	3.08065i	−2.26841	+	0.251534i
$151$	−7.54013	−	4.35330i	−0.613607	−	0.354266i	0.160769	−	0.986992i	$-0.448603\pi$
$151$	−7.54013	−	4.35330i	−0.613607	−	0.354266i	−0.774376	+	0.632726i	$0.781936\pi$
$152$	−6.50679	−	1.04565i	−0.527770	−	0.0848136i
$153$	−0.384911	+	17.5163i	−0.0311182	+	1.41611i
$154$	0.137022	+	2.03041i	0.0110415	+	0.163615i
$155$	−15.7536	+	9.09537i	−1.26536	+	0.730557i
$156$	−3.93435	+	0.928900i	−0.315000	+	0.0743715i
$157$			7.63781i			0.609563i	0.952422	+	0.304782i	$0.0985835\pi$
$157$			7.63781i			0.609563i	−0.952422	+	0.304782i	$0.901417\pi$
$158$	−5.65282	+	0.689758i	−0.449714	+	0.0548742i
$159$	17.4181	+	10.3131i	1.38134	+	0.817881i
$160$	−20.7329	−	9.76313i	−1.63908	−	0.771843i
$161$	2.33295	−	3.57927i	0.183862	−	0.282086i
$162$	−10.4971	+	7.19803i	−0.824727	+	0.565531i
$163$	−13.1093	−	7.56865i	−1.02680	−	0.592822i	−0.110732	−	0.993850i	$-0.535320\pi$
$163$	−13.1093	−	7.56865i	−1.02680	−	0.592822i	−0.916066	+	0.401028i	$0.868653\pi$
$164$	8.65038	+	2.49457i	0.675481	+	0.194793i
$165$	3.32577	−	1.87172i	0.258911	−	0.145714i
$166$	6.26032	−	4.71010i	0.485895	−	0.365575i
$167$	1.88524	−	3.26533i	0.145884	−	0.252679i	−0.783818	−	0.620990i	$-0.786731\pi$
$167$	1.88524	−	3.26533i	0.145884	−	0.252679i	0.929702	+	0.368311i	$0.120064\pi$
$168$	−12.6366	−	2.88373i	−0.974936	−	0.222484i
$169$	−5.81908	−	10.0790i	−0.447622	−	0.775304i
$170$	30.7895	+	13.0967i	2.36145	+	1.00447i
$171$	3.36118	+	6.12887i	0.257036	+	0.468687i
$172$	4.81664	−	4.63737i	0.367265	−	0.353596i
$173$		−	6.26492i		−	0.476313i	−0.971227	−	0.238157i	$-0.923457\pi$
$173$		−	6.26492i		−	0.476313i	0.971227	−	0.238157i	$-0.0765432\pi$
$174$	4.72078	−	10.7682i	0.357882	−	0.816339i
$175$	−1.63071	+	30.1481i	−0.123270	+	2.27899i
$176$	2.17397	+	0.0824755i	0.163869	+	0.00621682i
$177$	19.4385	−	10.9399i	1.46108	−	0.822291i
$178$	−4.87948	+	11.4713i	−0.365733	+	0.859811i
$179$	8.63863	−	4.98752i	0.645682	−	0.372785i	−0.141118	−	0.989993i	$-0.545070\pi$
$179$	8.63863	−	4.98752i	0.645682	−	0.372785i	0.786800	+	0.617208i	$0.211736\pi$
$180$	5.32505	+	23.7163i	0.396906	+	1.76771i
$181$		−	5.34622i		−	0.397382i	−0.980062	−	0.198691i	$-0.936331\pi$
$181$		−	5.34622i		−	0.397382i	0.980062	−	0.198691i	$-0.0636690\pi$
$182$	0.293998	+	4.35651i	0.0217926	+	0.322926i
$183$	1.76964	+	3.14438i	0.130816	+	0.232440i
$184$	−3.54306	−	2.88240i	−0.261198	−	0.212493i
$185$			12.0317i			0.884585i
$186$	6.51575	+	8.86123i	0.477758	+	0.649737i
$187$	−3.17637			−0.232279
$188$	−16.6594	+	4.12701i	−1.21501	+	0.300993i
$189$	5.81344	+	12.4581i	0.422866	+	0.906192i
$190$	13.2507	−	1.61685i	0.961308	−	0.117299i
$191$			22.0104i			1.59261i	0.604893	+	0.796307i	$0.293216\pi$
$191$			22.0104i			1.59261i	−0.604893	+	0.796307i	$0.706784\pi$
$192$	−4.48567	+	13.1103i	−0.323725	+	0.946151i
$193$	−5.83438			−0.419968			−0.209984	−	0.977705i	$-0.567341\pi$
$193$	−5.83438			−0.419968			−0.209984	+	0.977705i	$0.567341\pi$
$194$	13.5518	+	18.0120i	0.972961	+	1.29319i
$195$	7.13588	−	4.01604i	0.511011	−	0.287594i
$196$	−5.30753	+	12.9549i	−0.379109	+	0.925352i
$197$	14.2652			1.01636			0.508178	−	0.861252i	$-0.330319\pi$
$197$	14.2652			1.01636			0.508178	+	0.861252i	$0.330319\pi$
$198$	−1.34646	−	1.87393i	−0.0956885	−	0.133174i
$199$	2.14848	+	3.72128i	0.152302	+	0.263794i	0.932073	−	0.362270i	$-0.117998\pi$
$199$	2.14848	+	3.72128i	0.152302	+	0.263794i	−0.779771	+	0.626064i	$0.784665\pi$
$200$	31.8680	+	5.12124i	2.25341	+	0.362126i
$201$	−6.02819	−	10.7112i	−0.425196	−	0.755508i
$202$	−4.09954	+	9.63772i	−0.288443	+	0.678108i
$203$	−10.6392	−	6.93458i	−0.746726	−	0.486712i
$204$	5.81889	−	19.3760i	0.407404	−	1.35659i
$205$	−18.2359			−1.27365
$206$	−7.30104	+	5.49311i	−0.508687	+	0.382723i
$207$	−0.106430	+	4.84333i	−0.00739737	+	0.336635i
$208$	4.66454	+	0.176962i	0.323428	+	0.0122701i
$209$	−1.09748	+	0.633628i	−0.0759139	+	0.0438289i
$210$	26.2125	−	1.47988i	1.80884	−	0.102122i
$211$	−0.0869189	−	0.0501826i	−0.00598374	−	0.00345472i	0.497005	−	0.867748i	$-0.334433\pi$
$211$	−0.0869189	−	0.0501826i	−0.00598374	−	0.00345472i	−0.502989	+	0.864293i	$0.667766\pi$
$212$	−16.2114	−	16.8381i	−1.11340	−	1.15645i
$213$	4.39413	+	7.80770i	0.301081	+	0.534975i
$214$	−6.15269	+	14.4645i	−0.420590	+	0.988775i
$215$	−6.77165	+	11.7288i	−0.461823	+	0.799901i
$216$	13.8977	−	4.78055i	0.945619	−	0.325275i
$217$	10.5944	−	5.37574i	0.719193	−	0.364929i
$218$	−3.78235	+	2.84574i	−0.256173	+	0.192738i
$219$	5.69283	−	9.61477i	0.384686	−	0.649706i
$220$	−4.27738	+	1.05963i	−0.288381	+	0.0714401i
$221$	−6.81533			−0.458449
$222$	7.23056	−	0.801764i	0.485284	−	0.0538109i
$223$	6.41092	+	11.1040i	0.429307	+	0.743582i	0.996812	−	0.0797885i	$-0.0254245\pi$
$223$	6.41092	+	11.1040i	0.429307	+	0.743582i	−0.567505	+	0.823370i	$0.692091\pi$
$224$	13.1763	+	7.09824i	0.880379	+	0.474271i
$225$	−16.4619	−	30.0171i	−1.09746	−	2.00114i
$226$	3.54129	+	1.50634i	0.235563	+	0.100200i
$227$	9.39256	−	16.2684i	0.623406	−	1.07977i	−0.365440	−	0.930835i	$-0.619082\pi$
$227$	9.39256	−	16.2684i	0.623406	−	1.07977i	0.988847	−	0.148937i	$-0.0475850\pi$
$228$	−1.85467	−	7.85543i	−0.122828	−	0.520238i
$229$	−15.6660	+	9.04474i	−1.03524	+	0.597693i	−0.918480	−	0.395467i	$-0.870583\pi$
$229$	−15.6660	+	9.04474i	−1.03524	+	0.597693i	−0.116755	+	0.993161i	$0.537249\pi$
$230$	8.51345	+	3.62131i	0.561360	+	0.238782i
$231$	−2.23488	+	1.10331i	−0.147044	+	0.0725924i
$232$	−8.56779	+	10.5316i	−0.562503	+	0.691432i
$233$	−5.88363	+	10.1908i	−0.385450	+	0.667618i	−0.991831	−	0.127555i	$-0.959287\pi$
$233$	−5.88363	+	10.1908i	−0.385450	+	0.667618i	0.606382	+	0.795174i	$0.292620\pi$
$234$	−2.88900	−	4.02077i	−0.188860	−	0.262846i
$235$	30.1071	−	17.3823i	1.96397	−	1.13390i
$236$	−25.0005	+	6.19332i	−1.62739	+	0.403151i
$237$	−3.42074	−	6.07814i	−0.222201	−	0.394817i
$238$	−19.6170	−	9.62696i	−1.27158	−	0.624023i
$239$	1.69786	+	0.980260i	0.109825	+	0.0634077i	0.553907	−	0.832579i	$-0.313136\pi$
$239$	1.69786	+	0.980260i	0.109825	+	0.0634077i	−0.444081	+	0.895987i	$0.646470\pi$
$240$	1.37207	−	28.0334i	0.0885667	−	1.80955i
$241$	−5.93725	−	3.42787i	−0.382452	−	0.220809i	0.296433	−	0.955054i	$-0.404203\pi$
$241$	−5.93725	−	3.42787i	−0.382452	−	0.220809i	−0.678885	+	0.734245i	$0.737536\pi$
$242$	−12.0966	+	9.10117i	−0.777600	+	0.585046i
$243$	−13.0517	−	8.52362i	−0.837269	−	0.546790i
$244$	−1.00184	−	4.04409i	−0.0641361	−	0.258897i
$245$	3.05879	−	28.1924i	0.195419	−	1.80115i
$246$	1.21520	+	10.9591i	0.0774784	+	0.698725i
$247$	−2.35478	+	1.35953i	−0.149831	+	0.0865051i
$248$	−4.52464	−	11.8672i	−0.287315	−	0.753566i
$249$	8.25636	+	4.88852i	0.523225	+	0.309797i
$250$	−36.4625	+	4.44916i	−2.30609	+	0.281389i
$251$	17.0335			1.07515			0.537574	−	0.843217i	$-0.319341\pi$
$251$	17.0335			1.07515			0.537574	+	0.843217i	$0.319341\pi$
$252$	−2.63610	−	15.6541i	−0.166059	−	0.986116i
$253$	−0.878282			−0.0552171
$254$	19.9495	−	2.43424i	1.25174	−	0.152738i
$255$	−0.450164	+	40.9765i	−0.0281904	+	2.56605i
$256$	9.02686	−	13.2104i	0.564178	−	0.825653i
$257$	17.9980	−	10.3911i	1.12268	−	0.648182i	0.180599	−	0.983557i	$-0.442196\pi$
$257$	17.9980	−	10.3911i	1.12268	−	0.648182i	0.942085	+	0.335375i	$0.108863\pi$
$258$	7.49983	+	3.28792i	0.466919	+	0.204697i
$259$	0.424405	−	7.84630i	0.0263712	−	0.487545i
$260$	−9.17769	+	2.27358i	−0.569176	+	0.141001i
$261$	14.3966	+	0.316357i	0.891126	+	0.0195820i
$262$	−17.9795	+	13.5273i	−1.11078	+	0.835721i
$263$	8.50377	+	4.90965i	0.524365	+	0.302742i	0.738719	−	0.674014i	$-0.235431\pi$
$263$	8.50377	+	4.90965i	0.524365	+	0.302742i	−0.214354	+	0.976756i	$0.568765\pi$
$264$	0.921832	+	2.49993i	0.0567348	+	0.153860i
$265$	41.0019	+	23.6725i	2.51873	+	1.45419i
$266$	−8.69833	+	0.587005i	−0.533329	+	0.0359916i
$267$	−15.2667	−	0.167719i	−0.934307	−	0.0102642i
$268$	3.41270	+	13.7760i	0.208464	+	0.841502i
$269$	4.88843	−	2.82234i	0.298053	−	0.172081i	−0.343515	−	0.939147i	$-0.611618\pi$
$269$	4.88843	−	2.82234i	0.298053	−	0.172081i	0.641568	+	0.767066i	$0.278284\pi$
$270$	−24.3653	+	17.1043i	−1.48283	+	1.04093i
$271$	11.3288	−	19.6221i	0.688177	−	1.19196i	−0.284251	−	0.958750i	$-0.591745\pi$
$271$	11.3288	−	19.6221i	0.688177	−	1.19196i	0.972427	−	0.233207i	$-0.0749219\pi$
$272$	−12.4389	+	19.7736i	−0.754219	+	1.19895i
$273$	−4.79524	+	2.36730i	−0.290221	+	0.143275i
$274$	16.3444	+	6.95230i	0.987399	+	0.420004i
$275$	5.37505	−	3.10329i	0.324128	−	0.187135i
$276$	1.60895	−	5.35757i	0.0968475	−	0.322488i
$277$	−5.76634	+	9.98759i	−0.346466	+	0.600096i	−0.985619	−	0.168983i	$-0.945952\pi$
$277$	−5.76634	+	9.98759i	−0.346466	+	0.600096i	0.639153	+	0.769079i	$0.279285\pi$
$278$	−18.4945	−	7.86691i	−1.10923	−	0.471826i
$279$	−6.99011	+	11.5153i	−0.418487	+	0.689405i
$280$	−29.6283	−	6.41971i	−1.77063	−	0.383651i
$281$	0.625840	+	1.08399i	0.0373345	+	0.0646652i	0.884089	−	0.467319i	$-0.154780\pi$
$281$	0.625840	+	1.08399i	0.0373345	+	0.0646652i	−0.846754	+	0.531984i	$0.821447\pi$
$282$	−12.4524	−	16.9349i	−0.741529	−	1.00846i
$283$	−0.951483			−0.0565598			−0.0282799	−	0.999600i	$-0.509003\pi$
$283$	−0.951483			−0.0565598			−0.0282799	+	0.999600i	$0.509003\pi$
$284$	−2.48762	−	10.0417i	−0.147613	−	0.595867i
$285$	8.01853	+	14.2477i	0.474977	+	0.843961i
$286$	0.717261	−	0.539648i	0.0424125	−	0.0319101i
$287$	11.8923	+	0.643253i	0.701981	+	0.0379700i
$288$	−16.9384	+	1.04353i	−0.998108	+	0.0614905i
$289$	8.55378	−	14.8156i	0.503164	−	0.871505i
$290$	10.7642	−	25.3058i	0.632094	−	1.48601i
$291$	−14.0651	+	23.7550i	−0.824512	+	1.39254i
$292$	−9.29463	+	8.94870i	−0.543927	+	0.523683i
$293$	14.3254	+	8.27078i	0.836900	+	0.483184i	0.856209	−	0.516629i	$-0.172813\pi$
$293$	14.3254	+	8.27078i	0.836900	+	0.483184i	−0.0193095	+	0.999814i	$0.506147\pi$
$294$	−17.1464	+	0.0404652i	−0.999997	+	0.00235998i
$295$	45.1811	−	26.0853i	2.63055	−	1.51875i
$296$	−8.29389	−	1.33284i	−0.482073	−	0.0774699i
$297$	1.49293	−	2.39959i	0.0866285	−	0.139238i
$298$	4.78360	−	3.59905i	0.277106	−	0.208487i
$299$	−1.88447			−0.108982
$300$	9.08351	+	38.4731i	0.524436	+	2.22125i
$301$	4.82977	−	7.40996i	0.278384	−	0.427103i
$302$	−4.81960	+	11.3305i	−0.277337	+	0.651999i
$303$	−12.8265	−	0.140910i	−0.736861	−	0.00809508i
$304$	−0.353328	+	9.31335i	−0.0202647	+	0.534157i
$305$	4.21959	+	7.30854i	0.241613	+	0.418486i
$306$	24.6553	−	2.46006i	1.40945	−	0.140632i
$307$	−27.1061			−1.54702			−0.773512	−	0.633781i	$-0.781502\pi$
$307$	−27.1061			−1.54702			−0.773512	+	0.633781i	$0.781502\pi$
$308$	2.82682	−	0.540143i	0.161073	−	0.0307775i
$309$	−9.62889	−	5.70118i	−0.547768	−	0.324329i
$310$	15.4666	+	20.5570i	0.878442	+	1.16756i
$311$	−12.4603			−0.706561			−0.353281	−	0.935517i	$-0.614934\pi$
$311$	−12.4603			−0.706561			−0.353281	+	0.935517i	$0.614934\pi$
$312$	1.97791	+	5.36393i	0.111977	+	0.303673i
$313$		−	19.0083i		−	1.07441i	−0.843451	−	0.537206i	$-0.819480\pi$
$313$		−	19.0083i		−	1.07441i	0.843451	−	0.537206i	$-0.180520\pi$
$314$	10.7220	−	1.30829i	0.605075	−	0.0738313i
$315$	13.9164	+	28.9873i	0.784102	+	1.63325i
$316$	1.93657	+	7.81729i	0.108940	+	0.439757i
$317$	−20.5387			−1.15357			−0.576784	−	0.816897i	$-0.695692\pi$
$317$	−20.5387			−1.15357			−0.576784	+	0.816897i	$0.695692\pi$
$318$	11.4940	−	26.2181i	0.644549	−	1.47024i
$319$			2.61065i			0.146168i
$320$	−10.1541	+	30.7772i	−0.567633	+	1.72050i
$321$	−19.2503	−	0.211482i	−1.07445	−	0.0118038i
$322$	−5.42420	−	2.66190i	−0.302279	−	0.148342i
$323$		−	13.6077i		−	0.757151i
$324$	11.9027	+	13.5028i	0.661260	+	0.750157i
$325$	11.5329	−	6.65852i	0.639730	−	0.369348i
$326$	−8.37937	+	19.6993i	−0.464090	+	1.09104i
$327$	−4.98831	−	2.95353i	−0.275854	−	0.163331i
$328$	2.02013	−	12.5707i	0.111543	−	0.694102i
$329$	−20.2471	+	10.2737i	−1.11626	+	0.566406i
$330$	−3.19721	−	4.34811i	−0.176000	−	0.239355i
$331$			11.4735i			0.630638i	0.948986	+	0.315319i	$0.102112\pi$
$331$			11.4735i			0.630638i	−0.948986	+	0.315319i	$0.897888\pi$
$332$	−7.68439	−	7.98145i	−0.421736	−	0.438039i
$333$	4.28434	+	7.81218i	0.234780	+	0.428105i
$334$	−4.90680	−	2.08718i	−0.268488	−	0.114205i
$335$	−14.3738	−	24.8961i	−0.785324	−	1.36022i
$336$	−1.88363	+	18.2333i	−0.102760	+	0.994706i
$337$	−4.74216	+	8.21367i	−0.258322	+	0.447427i	−0.965793	−	0.259316i	$-0.916503\pi$
$337$	−4.74216	+	8.21367i	−0.258322	+	0.447427i	0.707470	+	0.706743i	$0.249836\pi$
$338$	−13.1521	+	9.89528i	−0.715379	+	0.538232i
$339$	−0.0517761	+	4.71296i	−0.00281209	+	0.255973i
$340$	13.1112	−	45.4657i	0.711057	−	2.46573i
$341$	−2.11500	−	1.22110i	−0.114534	−	0.0661262i
$342$	8.02798	−	5.76826i	0.434103	−	0.311912i
$343$	−2.98921	+	18.2774i	−0.161402	+	0.986889i
$344$	−7.33500	−	5.96726i	−0.395477	−	0.321733i
$345$	−0.124472	+	11.3302i	−0.00670137	+	0.609998i
$346$	−8.79471	+	1.07313i	−0.472807	+	0.0576919i
$347$			2.29103i			0.122989i	0.998107	+	0.0614943i	$0.0195866\pi$
$347$			2.29103i			0.122989i	−0.998107	+	0.0614943i	$0.980413\pi$
$348$	−15.9251	−	4.78253i	−0.853676	−	0.256371i
$349$	28.3807	−	16.3856i	1.51918	−	0.877100i	0.519437	−	0.854509i	$-0.326142\pi$
$349$	28.3807	−	16.3856i	1.51918	−	0.877100i	0.999745	−	0.0225916i	$-0.00719173\pi$
$350$	42.6013	−	2.87494i	2.27714	−	0.153672i
$351$	3.20328	−	5.14863i	0.170978	−	0.274814i
$352$	−0.256604	−	3.06595i	−0.0136770	−	0.163416i
$353$	18.2716	+	10.5491i	0.972501	+	0.561474i	0.899998	−	0.435894i	$-0.143568\pi$
$353$	18.2716	+	10.5491i	0.972501	+	0.561474i	0.0725034	+	0.997368i	$0.476901\pi$
$354$	−18.6871	−	25.4138i	−0.993206	−	1.35073i
$355$	10.4775	+	18.1475i	0.556087	+	0.963172i
$356$	16.9393	+	4.88488i	0.897779	+	0.258898i
$357$	1.73898	−	26.7065i	0.0920364	−	1.41346i
$358$	−8.48121	−	11.2726i	−0.448246	−	0.595776i
$359$	−25.9102	−	14.9593i	−1.36749	−	0.789519i	−0.376881	−	0.926262i	$-0.623003\pi$
$359$	−25.9102	−	14.9593i	−1.36749	−	0.789519i	−0.990607	+	0.136742i	$0.956337\pi$
$360$	32.3808	−	11.5377i	1.70662	−	0.608091i
$361$	6.78552	+	11.7529i	0.357133	+	0.618572i
$362$	−7.50504	+	0.915765i	−0.394456	+	0.0481315i
$363$	−15.9535	−	9.44592i	−0.837341	−	0.495782i
$364$	6.06532	−	1.15895i	0.317909	−	0.0607455i
$365$	13.0672	−	22.6331i	0.683969	−	1.18467i
$366$	4.11097	−	3.02283i	0.214884	−	0.158006i
$367$	10.0638	−	17.4310i	0.525325	−	0.909890i	−0.474239	−	0.880396i	$-0.657277\pi$
$367$	10.0638	−	17.4310i	0.525325	−	0.909890i	0.999565	−	0.0294945i	$-0.00938976\pi$
$368$	−3.43942	+	5.46749i	−0.179292	+	0.285013i
$369$	−11.8406	+	6.49360i	−0.616397	+	0.338043i
$370$	16.8901	−	2.06093i	0.878072	−	0.107142i
$371$	−25.9039	−	16.8840i	−1.34486	−	0.876574i
$372$	11.3233	−	10.6647i	0.587087	−	0.552938i
$373$	5.47058	+	9.47532i	0.283256	+	0.490613i	0.972185	−	0.234216i	$-0.0752522\pi$
$373$	5.47058	+	9.47532i	0.283256	+	0.490613i	−0.688929	+	0.724829i	$0.741919\pi$
$374$	0.544087	+	4.45899i	0.0281340	+	0.230569i
$375$	−22.0649	−	39.2059i	−1.13943	−	2.02459i
$376$	8.64712	+	22.6796i	0.445941	+	1.16961i
$377$			5.60150i			0.288492i
$378$	16.4929	−	10.2949i	0.848303	−	0.529512i
$379$			15.9358i			0.818566i	0.912407	+	0.409283i	$0.134221\pi$
$379$			15.9358i			0.818566i	−0.912407	+	0.409283i	$0.865779\pi$
$380$	−4.53948	−	18.3244i	−0.232870	−	0.940023i
$381$	12.0722	+	21.4505i	0.618479	+	1.09894i
$382$	30.8982	−	3.77020i	1.58089	−	0.192900i
$383$	−11.7448	−	20.3425i	−0.600130	−	1.03946i	−0.992801	−	0.119777i	$-0.961782\pi$
$383$	−11.7448	−	20.3425i	−0.600130	−	1.03946i	0.392671	−	0.919679i	$-0.371551\pi$
$384$	19.1726	+	4.05131i	0.978395	+	0.206743i
$385$	−5.19854	+	2.63781i	−0.264942	+	0.134435i
$386$	0.999382	+	8.19031i	0.0508672	+	0.416876i
$387$	−0.220335	+	10.0269i	−0.0112003	+	0.509695i
$388$	22.9640	−	22.1093i	1.16582	−	1.12243i
$389$	4.06677	−	7.04385i	0.206193	−	0.357138i	−0.744319	−	0.667824i	$-0.767226\pi$
$389$	4.06677	−	7.04385i	0.206193	−	0.357138i	0.950512	+	0.310687i	$0.100559\pi$
$390$	−6.86004	−	9.32945i	−0.347372	−	0.472415i
$391$	4.71545	−	8.16740i	0.238471	−	0.413043i
$392$	19.0953	+	5.23164i	0.964458	+	0.264238i
$393$	−23.7121	−	14.0397i	−1.19612	−	0.708211i
$394$	−2.44352	−	20.0256i	−0.123103	−	1.00887i
$395$	−8.15652	−	14.1275i	−0.410399	−	0.710832i
$396$	−2.39999	+	2.21115i	−0.120604	+	0.111114i
$397$	−23.7199	−	13.6947i	−1.19047	−	0.687318i	−0.232057	−	0.972702i	$-0.574545\pi$
$397$	−23.7199	−	13.6947i	−1.19047	−	0.687318i	−0.958413	+	0.285384i	$0.907879\pi$
$398$	4.85592	−	3.65347i	0.243405	−	0.183132i
$399$	−4.72661	−	9.57431i	−0.236627	−	0.479315i
$400$	1.73047	−	45.6135i	0.0865237	−	2.28068i
$401$	−9.42465	−	16.3240i	−0.470644	−	0.815180i	0.528792	−	0.848752i	$-0.322645\pi$
$401$	−9.42465	−	16.3240i	−0.470644	−	0.815180i	−0.999436	+	0.0335714i	$0.989312\pi$
$402$	−14.0038	+	10.2971i	−0.698445	+	0.513574i
$403$	−4.53803	−	2.62003i	−0.226055	−	0.130513i
$404$	14.2317	+	4.10408i	0.708052	+	0.204186i
$405$	−30.7441	−	19.5995i	−1.52769	−	0.973906i
$406$	−7.91236	+	16.1232i	−0.392684	+	0.800180i
$407$	−1.39890	+	0.807655i	−0.0693409	+	0.0400340i
$408$	−28.1969	−	4.84961i	−1.39595	−	0.240092i
$409$		−	19.0825i		−	0.943567i	−0.881714	−	0.471784i	$-0.843610\pi$
$409$		−	19.0825i		−	0.943567i	0.881714	−	0.471784i	$-0.156390\pi$
$410$	3.12366	+	25.5996i	0.154267	+	1.26427i
$411$	−0.238966	+	21.7521i	−0.0117873	+	1.07295i
$412$	8.96184	+	9.30828i	0.441518	+	0.458586i
$413$	−30.3845	+	15.4175i	−1.49512	+	0.758646i
$414$	6.81731	−	0.680218i	0.335053	−	0.0334309i
$415$	19.4354	+	11.2210i	0.954045	+	0.550818i
$416$	−0.550579	−	6.57841i	−0.0269944	−	0.322533i
$417$	0.270403	−	24.6136i	0.0132417	−	1.20533i
$418$	1.07748	+	1.43210i	0.0527011	+	0.0700464i
$419$	−12.7212	+	22.0338i	−0.621473	+	1.07642i	0.367739	+	0.929929i	$0.380132\pi$
$419$	−12.7212	+	22.0338i	−0.621473	+	1.07642i	−0.989212	+	0.146493i	$0.953201\pi$
$420$	−6.56745	−	36.5437i	−0.320459	−	1.78315i
$421$	10.2492	+	17.7521i	0.499514	+	0.865183i	1.00000		0.000561434i	$-0.000178710\pi$
$421$	10.2492	+	17.7521i	0.499514	+	0.865183i	−0.500486	+	0.865745i	$0.666845\pi$
$422$	−0.0555580	+	0.130613i	−0.00270452	+	0.00635813i
$423$	13.3589	−	22.0072i	0.649534	−	1.07003i
$424$	−20.8605	+	25.6418i	−1.01307	+	1.24528i
$425$			66.6456i			3.23279i
$426$	10.2078	−	7.50588i	0.494568	−	0.363661i
$427$	−2.49395	−	4.91501i	−0.120691	−	0.237854i
$428$	21.3592	+	6.15950i	1.03244	+	0.297731i
$429$	0.945952	+	0.560090i	0.0456710	+	0.0270414i
$430$	17.6249	+	7.49700i	0.849948	+	0.361537i
$431$	15.2031	−	8.77752i	0.732308	−	0.422798i	−0.0869578	−	0.996212i	$-0.527715\pi$
$431$	15.2031	−	8.77752i	0.732308	−	0.422798i	0.819266	+	0.573414i	$0.194381\pi$
$432$	−9.09151	−	18.6908i	−0.437416	−	0.899259i
$433$			15.2009i			0.730507i	0.930908	+	0.365254i	$0.119018\pi$
$433$			15.2009i			0.730507i	−0.930908	+	0.365254i	$0.880982\pi$
$434$	−9.36120	−	13.9516i	−0.449352	−	0.669697i
$435$	33.6785	+	0.369988i	1.61476	+	0.0177396i
$436$	4.64274	+	4.82221i	0.222347	+	0.230942i
$437$		−	3.76259i		−	0.179989i
$438$	−14.4724	−	6.34467i	−0.691517	−	0.303160i
$439$	14.5691			0.695345			0.347673	−	0.937616i	$-0.386972\pi$
$439$	14.5691			0.695345			0.347673	+	0.937616i	$0.386972\pi$
$440$	2.22019	+	5.82309i	0.105843	+	0.277605i
$441$	−8.05293	−	19.3946i	−0.383473	−	0.923552i
$442$	1.16741	+	9.56737i	0.0555281	+	0.455074i
$443$			24.0275i			1.14158i	0.821095	+	0.570791i	$0.193363\pi$
$443$			24.0275i			1.14158i	−0.821095	+	0.570791i	$0.806637\pi$
$444$	−2.36406	−	10.0129i	−0.112193	−	0.475193i
$445$	−35.7097			−1.69280
$446$	14.4897	−	10.9017i	0.686109	−	0.516210i
$447$	6.30879	+	3.73538i	0.298396	+	0.176678i
$448$	7.70752	−	19.7128i	0.364146	−	0.931342i
$449$	36.1930			1.70806			0.854028	−	0.520228i	$-0.174153\pi$
$449$	36.1930			1.70806			0.854028	+	0.520228i	$0.174153\pi$
$450$	−39.3182	+	28.2509i	−1.85348	+	1.33176i
$451$	−1.22413	−	2.12025i	−0.0576420	−	0.0998389i
$452$	1.50800	−	5.22929i	0.0709305	−	0.245965i
$453$	−15.0793	−	0.165660i	−0.708490	−	0.00778340i
$454$	−24.4465	−	10.3986i	−1.14733	−	0.488033i
$455$	−11.1542	+	5.65979i	−0.522915	+	0.265335i
$456$	−10.7098	+	3.94916i	−0.501531	+	0.184936i
$457$	20.5719			0.962312			0.481156	−	0.876635i	$-0.340217\pi$
$457$	20.5719			0.962312			0.481156	+	0.876635i	$0.340217\pi$
$458$	15.3805	+	20.4426i	0.718682	+	0.955220i
$459$	14.2990	+	26.7665i	0.667420	+	1.24935i
$460$	3.62532	−	12.5715i	0.169032	−	0.586149i
$461$	20.0785	−	11.5923i	0.935149	−	0.539908i	0.0467125	−	0.998908i	$-0.485126\pi$
$461$	20.0785	−	11.5923i	0.935149	−	0.539908i	0.888436	+	0.459000i	$0.151792\pi$
$462$	1.93164	+	2.94834i	0.0898682	+	0.137169i
$463$	−11.0442	−	6.37637i	−0.513268	−	0.296335i	0.220908	−	0.975295i	$-0.429098\pi$
$463$	−11.0442	−	6.37637i	−0.513268	−	0.296335i	−0.734176	+	0.678959i	$0.762431\pi$
$464$	16.2518	+	10.2235i	0.754473	+	0.474614i
$465$	−16.0524	+	27.1114i	−0.744414	+	1.25726i
$466$	15.3136	+	6.51386i	0.709389	+	0.301749i
$467$	10.3847	−	17.9868i	0.480545	−	0.832329i	−0.519206	−	0.854649i	$-0.673772\pi$
$467$	10.3847	−	17.9868i	0.480545	−	0.832329i	0.999751	+	0.0223206i	$0.00710547\pi$
$468$	−5.14950	+	4.74432i	−0.238036	+	0.219306i
$469$	8.49550	+	16.7427i	0.392286	+	0.773108i
$470$	−29.5584	−	39.2869i	−1.36343	−	1.81217i
$471$	6.48828	+	11.5287i	0.298964	+	0.531214i
$472$	12.9766	+	34.0348i	0.597295	+	1.56658i
$473$	−1.81826			−0.0836035
$474$	−7.94655	+	5.84318i	−0.364997	+	0.268386i
$475$	13.2946	+	23.0269i	0.609997	+	1.05655i
$476$	−10.1541	+	29.1874i	−0.465412	+	1.33780i
$477$	35.0521	+	0.770252i	1.60493	+	0.0352674i
$478$	1.08526	−	2.55137i	0.0496387	−	0.116697i
$479$	−9.11736	+	15.7917i	−0.416583	+	0.721543i	−0.995593	−	0.0937776i	$-0.970106\pi$
$479$	−9.11736	+	15.7917i	−0.416583	+	0.721543i	0.579010	+	0.815320i	$0.303439\pi$
$480$	−39.5884	+	2.87579i	−1.80696	+	0.131261i
$481$	−3.00153	+	1.73293i	−0.136858	+	0.0790149i
$482$	−3.79505	+	8.92189i	−0.172860	+	0.406381i
$483$	0.480835	−	7.38446i	0.0218788	−	0.336005i
$484$	14.8483	+	15.4223i	0.674923	+	0.701013i
$485$	−32.2848	+	55.9189i	−1.46598	+	2.53915i
$486$	−9.72981	+	19.7821i	−0.441353	+	0.897333i
$487$	−8.32199	+	4.80470i	−0.377105	+	0.217722i	−0.676558	−	0.736389i	$-0.736529\pi$
$487$	−8.32199	+	4.80470i	−0.377105	+	0.217722i	0.299453	+	0.954111i	$0.403196\pi$
$488$	−5.50550	+	2.09910i	−0.249222	+	0.0950219i
$489$	−26.2170	−	0.288017i	−1.18557	−	0.0130246i
$490$	−40.1005	+	0.535190i	−1.81156	+	0.0241774i
$491$	−1.55447	−	0.897475i	−0.0701524	−	0.0405025i	0.464514	−	0.885566i	$-0.346229\pi$
$491$	−1.55447	−	0.897475i	−0.0701524	−	0.0405025i	−0.534666	+	0.845064i	$0.679563\pi$
$492$	15.1762	−	3.58310i	0.684196	−	0.161539i
$493$	−24.2772	−	14.0165i	−1.09339	−	0.631269i
$494$	2.31187	+	3.07277i	0.104016	+	0.138250i
$495$	3.42997	−	5.65045i	0.154166	−	0.253969i
$496$	−15.8841	+	8.38444i	−0.713218	+	0.376473i
$497$	−6.19263	−	12.2043i	−0.277777	−	0.547437i
$498$	5.44827	−	12.4277i	0.244143	−	0.556897i
$499$	38.0844	−	21.9881i	1.70489	−	0.984321i	0.764254	−	0.644915i	$-0.223107\pi$
$499$	38.0844	−	21.9881i	1.70489	−	0.984321i	0.940640	−	0.339406i	$-0.110226\pi$
$500$	12.4915	+	50.4240i	0.558635	+	2.25503i
$501$	0.0717409	−	6.53027i	0.00320515	−	0.291751i
$502$	−2.91771	−	23.9117i	−0.130224	−	1.06723i
$503$	18.3538			0.818355			0.409178	−	0.912455i	$-0.365816\pi$
$503$	18.3538			0.818355			0.409178	+	0.912455i	$0.365816\pi$
$504$	−21.5237	+	6.38198i	−0.958742	+	0.284276i
$505$	−30.0018			−1.33506
$506$	0.150443	+	1.23293i	0.00668799	+	0.0548106i
$507$	−17.3455	−	10.2701i	−0.770340	−	0.456112i
$508$	−6.83438	−	27.5882i	−0.303226	−	1.22403i
$509$	−13.1711	+	7.60431i	−0.583797	+	0.337055i	−0.762641	−	0.646822i	$-0.776098\pi$
$509$	−13.1711	+	7.60431i	−0.583797	+	0.337055i	0.178844	+	0.983877i	$0.442764\pi$
$510$	57.6000	−	6.38701i	2.55057	−	0.282821i
$511$	−9.31998	+	14.2989i	−0.412291	+	0.632548i
$512$	−20.0911	−	10.4091i	−0.887908	−	0.460020i
$513$	10.2799	+	6.39575i	0.453869	+	0.282379i
$514$	−17.6700	−	23.4857i	−0.779391	−	1.03591i
$515$	−22.6663	−	13.0864i	−0.998796	−	0.576655i
$516$	3.33092	−	11.0915i	0.146636	−	0.488275i
$517$	4.04203	+	2.33366i	0.177768	+	0.102634i
$518$	−11.0873	+	0.748227i	−0.487150	+	0.0328752i
$519$	−5.32202	−	9.45642i	−0.233611	−	0.415091i
$520$	4.76371	+	12.4942i	0.208903	+	0.547908i
$521$	14.2730	−	8.24049i	0.625309	−	0.361023i	−0.153624	−	0.988129i	$-0.549094\pi$
$521$	14.2730	−	8.24049i	0.625309	−	0.361023i	0.778933	+	0.627107i	$0.215761\pi$
$522$	−2.02191	−	20.2641i	−0.0884968	−	0.886937i
$523$	−7.92785	+	13.7314i	−0.346661	+	0.600434i	−0.985654	−	0.168778i	$-0.946018\pi$
$523$	−7.92785	+	13.7314i	−0.346661	+	0.600434i	0.638993	+	0.769212i	$0.279351\pi$
$524$	22.0694	+	22.9226i	0.964108	+	1.00138i
$525$	23.1493	+	46.8916i	1.01032	+	2.04652i
$526$	5.43555	−	12.7786i	0.237001	−	0.557173i
$527$	22.7107	−	13.1120i	0.989295	−	0.571169i
$528$	3.35150	−	1.72229i	0.145855	−	0.0749529i
$529$	−10.1962	+	17.6603i	−0.443311	+	0.767837i
$530$	26.2081	−	61.6135i	1.13841	−	2.67632i
$531$	20.0475	−	33.0258i	0.869988	−	1.43320i
$532$	2.31399	+	12.1102i	0.100324	+	0.525043i
$533$	−2.62653	−	4.54929i	−0.113768	−	0.197052i
$534$	2.37962	+	21.4602i	0.102976	+	0.928672i
$535$	−45.0275			−1.94671
$536$	18.7542	−	7.15048i	0.810057	−	0.308853i
$537$	8.80248	−	14.8668i	0.379855	−	0.641548i
$538$	−4.79935	−	6.37895i	−0.206915	−	0.275016i
$539$	3.48321	−	1.53684i	0.150032	−	0.0661966i
$540$	28.1846	+	31.2743i	1.21287	+	1.34583i
$541$	16.3113	−	28.2520i	0.701278	−	1.21465i	−0.266740	−	0.963768i	$-0.585947\pi$
$541$	16.3113	−	28.2520i	0.701278	−	1.21465i	0.968018	−	0.250880i	$-0.0807201\pi$
$542$	−29.4861	−	12.5423i	−1.26653	−	0.538738i
$543$	−4.54159	−	8.06971i	−0.194898	−	0.346305i
$544$	29.8889	+	14.0747i	1.28148	+	0.603448i
$545$	−11.7424	−	6.77949i	−0.502990	−	0.290401i
$546$	4.14460	+	6.32607i	0.177373	+	0.270731i
$547$	−30.4408	+	17.5750i	−1.30155	+	0.751453i	−0.980671	−	0.195666i	$-0.937313\pi$
$547$	−30.4408	+	17.5750i	−1.30155	+	0.751453i	−0.320884	+	0.947119i	$0.603980\pi$
$548$	6.96000	−	24.1351i	0.297316	−	1.03100i
$549$	5.34228	+	3.24290i	0.228003	+	0.138404i
$550$	−5.27710	−	7.01393i	−0.225016	−	0.299075i
$551$	−11.1841			−0.476459
$552$	−7.79657	−	1.34094i	−0.331844	−	0.0570742i
$553$	4.82084	+	9.50079i	0.205003	+	0.404015i
$554$	15.0083	+	6.38400i	0.637642	+	0.271230i
$555$	10.2208	+	18.1609i	0.433850	+	0.770885i
$556$	−7.87561	+	27.3102i	−0.334000	+	1.15821i
$557$	−21.0919	−	36.5322i	−0.893692	−	1.54792i	−0.835415	−	0.549620i	$-0.814773\pi$
$557$	−21.0919	−	36.5322i	−0.893692	−	1.54792i	−0.0582771	−	0.998300i	$-0.518561\pi$
$558$	17.3626	+	7.84025i	0.735018	+	0.331904i
$559$	−3.90131			−0.165008
$560$	−3.93691	+	42.6919i	−0.166365	+	1.80406i
$561$	−4.79449	+	2.69831i	−0.202423	+	0.113923i
$562$	1.41450	−	1.06423i	0.0596671	−	0.0448919i
$563$	32.4344			1.36695			0.683473	−	0.729976i	$-0.260469\pi$
$563$	32.4344			1.36695			0.683473	+	0.729976i	$0.260469\pi$
$564$	−21.6402	+	20.3815i	−0.911217	+	0.858215i
$565$			11.0239i			0.463778i
$566$	0.162981	+	1.33569i	0.00685062	+	0.0561434i
$567$	19.3580	+	13.8660i	0.812961	+	0.582319i
$568$	−13.6705	+	5.21220i	−0.573601	+	0.218699i
$569$	19.4904			0.817080			0.408540	−	0.912740i	$-0.366038\pi$
$569$	19.4904			0.817080			0.408540	+	0.912740i	$0.366038\pi$
$570$	18.6274	−	13.6969i	0.780217	−	0.573702i
$571$			30.1571i			1.26203i	0.775769	+	0.631017i	$0.217362\pi$
$571$			30.1571i			1.26203i	−0.775769	+	0.631017i	$0.782638\pi$
$572$	−0.880420	−	0.914455i	−0.0368122	−	0.0382353i
$573$	18.6977	+	33.2229i	0.781107	+	1.38791i
$574$	−1.13406	−	16.8046i	−0.0473346	−	0.701412i
$575$			18.4278i			0.768493i
$576$	4.36633	+	23.5995i	0.181930	+	0.983311i
$577$	−14.9496	+	8.63117i	−0.622361	+	0.359320i	−0.777788	−	0.628527i	$-0.783658\pi$
$577$	−14.9496	+	8.63117i	−0.622361	+	0.359320i	0.155426	+	0.987847i	$0.450325\pi$
$578$	−22.2633	−	9.47003i	−0.926033	−	0.393901i
$579$	−8.80655	+	4.95628i	−0.365988	+	0.205976i
$580$	−37.3681	−	10.7761i	−1.55163	−	0.447453i
$581$	−12.2787	−	8.00321i	−0.509407	−	0.332029i
$582$	35.7565	+	15.6756i	1.48215	+	0.649775i
$583$			6.35629i			0.263251i
$584$	14.1543	+	11.5150i	0.585709	+	0.476493i
$585$	7.35946	−	12.1238i	0.304276	−	0.501257i
$586$	9.15671	−	21.5268i	0.378260	−	0.889262i
$587$	17.3621	+	30.0720i	0.716611	+	1.24121i	0.962335	+	0.271866i	$0.0876409\pi$
$587$	17.3621	+	30.0720i	0.716611	+	1.24121i	−0.245724	+	0.969340i	$0.579026\pi$
$588$	2.99384	+	24.0632i	0.123464	+	0.992349i
$589$	5.23122	−	9.06074i	0.215549	−	0.373341i
$590$	−44.3578	−	58.9571i	−1.82618	−	2.42723i
$591$	21.5323	−	12.1182i	0.885719	−	0.498478i
$592$	−0.450370	+	11.8713i	−0.0185101	+	0.487907i
$593$	15.7360	+	9.08520i	0.646201	+	0.373085i	0.786999	−	0.616954i	$-0.211633\pi$
$593$	15.7360	+	9.08520i	0.646201	+	0.373085i	−0.140798	+	0.990038i	$0.544967\pi$
$594$	−3.62427	−	1.68475i	−0.148706	−	0.0691260i
$595$	3.38089	−	62.5051i	0.138603	−	2.56246i
$596$	−5.87175	−	6.09873i	−0.240516	−	0.249814i
$597$	6.40418	+	3.79186i	0.262105	+	0.155190i
$598$	0.322795	+	2.64542i	0.0132001	+	0.108179i
$599$			28.3339i			1.15769i	0.815438	+	0.578845i	$0.196496\pi$
$599$			28.3339i			1.15769i	−0.815438	+	0.578845i	$0.803504\pi$
$600$	52.4527	−	19.3416i	2.14137	−	0.789617i
$601$	16.3852	−	9.46002i	0.668368	−	0.385882i	−0.127090	−	0.991891i	$-0.540564\pi$
$601$	16.3852	−	9.46002i	0.668368	−	0.385882i	0.795458	+	0.606009i	$0.207230\pi$
$602$	−11.2294	−	5.51078i	−0.457677	−	0.224603i
$603$	−18.1982	−	11.0468i	−0.741087	−	0.449859i
$604$	16.7314	+	4.82493i	0.680790	+	0.196324i
$605$	−37.5543	−	21.6820i	−1.52680	−	0.881498i
$606$	1.99926	+	18.0299i	0.0812144	+	0.732416i
$607$	3.02327	+	5.23646i	0.122711	+	0.212542i	0.920836	−	0.389950i	$-0.127508\pi$
$607$	3.02327	+	5.23646i	0.122711	+	0.212542i	−0.798125	+	0.602492i	$0.794175\pi$
$608$	13.1346	−	1.09930i	0.532679	−	0.0445825i
$609$	−21.9500	−	1.42926i	−0.889457	−	0.0579165i
$610$	9.53696	−	7.17535i	0.386140	−	0.290522i
$611$	8.67271	+	5.00719i	0.350860	+	0.202569i
$612$	−7.67669	−	34.1898i	−0.310312	−	1.38204i
$613$	−0.0235058	−	0.0407133i	−0.000949392	−	0.00164439i	0.865550	−	0.500822i	$-0.166969\pi$
$613$	−0.0235058	−	0.0407133i	−0.000949392	−	0.00164439i	−0.866500	+	0.499178i	$0.833636\pi$
$614$	4.64305	+	38.0515i	0.187378	+	1.53564i
$615$	−27.5257	+	15.4913i	−1.10994	+	0.624669i
$616$	−1.24247	−	3.87577i	−0.0500604	−	0.156159i
$617$	−10.4917	+	18.1721i	−0.422379	+	0.731582i	−0.996172	−	0.0874187i	$-0.972138\pi$
$617$	−10.4917	+	18.1721i	−0.422379	+	0.731582i	0.573793	+	0.819001i	$0.305472\pi$
$618$	−6.35398	+	14.4936i	−0.255595	+	0.583019i
$619$	2.67167	−	4.62746i	0.107383	−	0.185993i	−0.807326	−	0.590106i	$-0.799086\pi$
$619$	2.67167	−	4.62746i	0.107383	−	0.185993i	0.914709	+	0.404112i	$0.132419\pi$
$620$	26.2087	−	25.2332i	1.05257	−	1.01339i
$621$	3.95374	+	7.40105i	0.158658	+	0.296994i
$622$	2.13436	+	17.4919i	0.0855799	+	0.701359i
$623$	23.2876	+	1.25963i	0.933000	+	0.0504658i
$624$	7.19110	−	3.69540i	0.287874	−	0.147934i
$625$	−24.0832	−	41.7133i	−0.963327	−	1.66853i
$626$	−26.6838	+	3.25596i	−1.06650	+	0.130135i
$627$	−1.11829	+	1.88871i	−0.0446602	+	0.0754279i
$628$	−3.67317	−	14.8274i	−0.146576	−	0.591678i
$629$		−	17.3450i		−	0.691592i
$630$	38.3086	−	24.5012i	1.52625	−	0.976151i
$631$		−	23.1548i		−	0.921776i	−0.887458	−	0.460888i	$-0.847531\pi$
$631$		−	23.1548i		−	0.921776i	0.887458	−	0.460888i	$-0.152469\pi$
$632$	10.6422	−	4.05759i	0.423324	−	0.161402i
$633$	−0.173827	−	0.00190965i	−0.00690901	−	7.59017e-5i
$634$	3.51811	+	28.8322i	0.139722	+	1.14507i
$635$	28.7853	+	49.8577i	1.14231	+	1.97854i
$636$	−38.7738	−	11.6443i	−1.53748	−	0.461726i
$637$	7.47370	−	3.29751i	0.296119	−	0.130652i
$638$	3.66483	−	0.447183i	0.145092	−	0.0177041i
$639$	13.2652	+	8.05232i	0.524763	+	0.318545i
$640$	44.9444	+	8.98249i	1.77658	+	0.355064i
$641$	8.19831	−	14.1999i	0.323814	−	0.560862i	−0.657458	−	0.753491i	$-0.728368\pi$
$641$	8.19831	−	14.1999i	0.323814	−	0.560862i	0.981272	+	0.192629i	$0.0617015\pi$
$642$	3.00054	+	27.0598i	0.118422	+	1.06796i
$643$	−4.77787	+	8.27551i	−0.188421	+	0.326354i	−0.944724	−	0.327867i	$-0.893670\pi$
$643$	−4.77787	+	8.27551i	−0.188421	+	0.326354i	0.756303	+	0.654221i	$0.227004\pi$
$644$	−2.80766	+	8.07047i	−0.110637	+	0.318021i
$645$	−0.257688	+	23.4563i	−0.0101465	+	0.923590i
$646$	−19.1025	+	2.33088i	−0.751577	+	0.0917074i
$647$	10.7329	+	18.5900i	0.421956	+	0.730849i	0.996131	−	0.0878838i	$-0.0280104\pi$
$647$	10.7329	+	18.5900i	0.421956	+	0.730849i	−0.574175	+	0.818733i	$0.694677\pi$
$648$	16.9165	−	19.0219i	0.664541	−	0.747251i
$649$	6.06579	+	3.50209i	0.238103	+	0.137469i
$650$	−11.3227	−	15.0493i	−0.444114	−	0.590284i
$651$	11.4247	−	17.1141i	0.447770	−	0.670756i
$652$	29.0892	+	8.38864i	1.13922	+	0.328525i
$653$	1.57618	+	2.73003i	0.0616808	+	0.106834i	0.895217	−	0.445631i	$-0.147021\pi$
$653$	1.57618	+	2.73003i	0.0616808	+	0.106834i	−0.833536	+	0.552465i	$0.813687\pi$
$654$	−3.29172	+	7.50851i	−0.128716	+	0.293606i
$655$	−55.8180	−	32.2265i	−2.18099	−	1.25920i
$656$	−17.9928	−	0.682607i	−0.702502	−	0.0266513i
$657$	0.425179	−	19.3488i	0.0165878	−	0.754868i
$658$	17.8904	+	26.6631i	0.697439	+	1.03944i
$659$	−9.56754	+	5.52382i	−0.372698	+	0.215178i	−0.674637	−	0.738150i	$-0.735700\pi$
$659$	−9.56754	+	5.52382i	−0.372698	+	0.215178i	0.301938	+	0.953327i	$0.402366\pi$
$660$	−5.55622	+	5.23304i	−0.216276	+	0.203696i
$661$		−	28.3829i		−	1.10397i	−0.833855	−	0.551983i	$-0.813871\pi$
$661$		−	28.3829i		−	1.10397i	0.833855	−	0.551983i	$-0.186129\pi$
$662$	16.1065	−	1.96531i	0.625995	−	0.0763840i
$663$	−10.2872	+	5.78959i	−0.399522	+	0.224849i
$664$	−9.88810	+	12.1545i	−0.383733	+	0.471687i
$665$	−11.3005	−	22.2707i	−0.438214	−	0.863621i
$666$	10.2329	−	7.35253i	0.396516	−	0.284905i
$667$	−6.71276	−	3.87562i	−0.259919	−	0.150064i
$668$	−2.08949	+	7.24570i	−0.0808447	+	0.280344i
$669$	19.1096	+	11.3146i	0.738821	+	0.437450i
$670$	−32.4871	+	24.4425i	−1.25509	+	0.944295i
$671$	−0.566500	+	0.981208i	−0.0218695	+	0.0378791i
$672$	25.9185	−	0.478967i	0.999829	−	0.0184766i
$673$	14.8049	+	25.6429i	0.570688	+	0.988461i	0.996495	+	0.0836470i	$0.0266568\pi$
$673$	14.8049	+	25.6429i	0.570688	+	0.988461i	−0.425807	+	0.904814i	$0.640010\pi$
$674$	12.3427	+	5.25012i	0.475421	+	0.202227i
$675$	−50.3473	−	31.3241i	−1.93787	−	1.20567i
$676$	16.1439	+	16.7679i	0.620918	+	0.644921i
$677$		−	19.6587i		−	0.755545i	−0.925898	−	0.377772i	$-0.876690\pi$
$677$		−	19.6587i		−	0.755545i	0.925898	−	0.377772i	$-0.123310\pi$
$678$	6.62493	−	0.734608i	0.254429	−	0.0282125i
$679$	23.0266	−	35.3280i	0.883681	−	1.35576i
$680$	−66.0707	−	10.6177i	−2.53370	−	0.407169i
$681$	0.357424	−	32.5348i	0.0136965	−	1.24674i
$682$	−1.35190	+	3.17821i	−0.0517668	+	0.121700i
$683$	−4.93427	+	2.84880i	−0.188804	+	0.109006i	−0.591423	−	0.806362i	$-0.701434\pi$
$683$	−4.93427	+	2.84880i	−0.188804	+	0.109006i	0.402618	+	0.915368i	$0.368100\pi$
$684$	−9.47263	−	10.2816i	−0.362195	−	0.393128i
$685$			50.8793i			1.94400i
$686$	26.1699	+	1.06549i	0.999172	+	0.0406805i
$687$	−15.9631	+	26.9605i	−0.609030	+	1.02861i
$688$	−7.12043	+	11.3190i	−0.271464	+	0.431534i
$689$			13.6383i			0.519577i
$690$	15.9267	−	1.76604i	0.606318	−	0.0672319i
$691$	−17.8054			−0.677347			−0.338674	−	0.940904i	$-0.609978\pi$
$691$	−17.8054			−0.677347			−0.338674	+	0.940904i	$0.609978\pi$
$692$	3.01293	+	12.1622i	0.114534	+	0.462338i
$693$	−2.43613	+	3.56388i	−0.0925408	+	0.135381i
$694$	3.21614	−	0.392434i	0.122083	−	0.0148966i
$695$		−	57.5727i		−	2.18386i
$696$	−3.98588	+	23.1749i	−0.151084	+	0.878443i
$697$	26.2892			0.995774
$698$	−27.8635	−	37.0341i	−1.05465	−	1.40176i
$699$	−0.223896	+	20.3803i	−0.00846851	+	0.770853i
$700$	−11.3331	−	59.3114i	−0.428352	−	2.24176i
$701$	9.77794			0.369308			0.184654	−	0.982804i	$-0.440884\pi$
$701$	9.77794			0.369308			0.184654	+	0.982804i	$0.440884\pi$
$702$	−7.77636	−	3.61485i	−0.293500	−	0.136434i
$703$	−3.46002	−	5.99293i	−0.130497	−	0.226028i
$704$	−4.26003	+	0.885394i	−0.160556	+	0.0333695i
$705$	30.6781	−	51.8131i	1.15540	−	1.95139i
$706$	11.6791	−	27.4567i	0.439549	−	1.03335i
$707$	19.5653	+	1.05829i	0.735830	+	0.0398009i
$708$	−32.4751	+	30.5861i	−1.22049	+	1.14950i
$709$	−13.0588			−0.490432			−0.245216	−	0.969468i	$-0.578859\pi$
$709$	−13.0588			−0.490432			−0.245216	+	0.969468i	$0.578859\pi$
$710$	23.6808	−	17.8168i	0.888726	−	0.668654i
$711$	−10.3267	−	6.26857i	−0.387281	−	0.235090i
$712$	3.95585	−	24.6161i	0.148252	−	0.922527i
$713$	6.27962	−	3.62554i	0.235174	−	0.135778i
$714$	−37.7884	+	2.13342i	−1.41420	+	0.0798414i
$715$	2.22676	+	1.28562i	0.0832761	+	0.0480795i
$716$	−14.3717	+	13.8368i	−0.537097	+	0.517107i
$717$	3.39551	+	0.0373028i	0.126808	+	0.00139310i
$718$	−16.5616	+	38.9352i	−0.618074	+	1.45305i
$719$	−15.4289	+	26.7237i	−0.575401	+	0.996624i	0.420597	+	0.907248i	$0.361821\pi$
$719$	−15.4289	+	26.7237i	−0.575401	+	0.996624i	−0.995998	+	0.0893766i	$0.971513\pi$
$720$	−21.7432	−	43.4799i	−0.810323	−	1.62040i
$721$	14.3199	+	9.33366i	0.533302	+	0.347604i
$722$	15.3364	−	11.5387i	0.570761	−	0.429426i
$723$	−11.8738	−	0.130444i	−0.441591	−	0.00485127i
$724$	2.57111	+	10.3787i	0.0955544	+	0.385722i
$725$	54.7758			2.03432
$726$	−10.5275	+	24.0135i	−0.390712	+	0.891226i
$727$	1.75480	+	3.03940i	0.0650819	+	0.112725i	0.896730	−	0.442577i	$-0.145936\pi$
$727$	1.75480	+	3.03940i	0.0650819	+	0.112725i	−0.831648	+	0.555303i	$0.812602\pi$
$728$	−2.66588	−	8.31599i	−0.0988040	−	0.308211i
$729$	−26.9414	−	1.77836i	−0.997829	−	0.0658650i
$730$	−34.0106	−	14.4669i	−1.25879	−	0.535444i
$731$	9.76213	−	16.9085i	0.361066	−	0.625384i
$732$	−4.94764	−	5.25319i	−0.182870	−	0.194164i
$733$	−2.19882	+	1.26949i	−0.0812153	+	0.0468897i	−0.540058	−	0.841628i	$-0.681598\pi$
$733$	−2.19882	+	1.26949i	−0.0812153	+	0.0468897i	0.458842	+	0.888518i	$0.348264\pi$
$734$	−26.1935	−	11.1418i	−0.966820	−	0.411250i
$735$	−19.3323	−	45.1527i	−0.713083	−	1.66548i
$736$	8.26442	+	3.89172i	0.304631	+	0.143451i
$737$	1.92975	−	3.34243i	0.0710834	−	0.123120i
$738$	11.1439	+	15.5096i	0.410214	+	0.570915i
$739$	7.43557	−	4.29293i	0.273522	−	0.157918i	−0.356965	−	0.934118i	$-0.616188\pi$
$739$	7.43557	−	4.29293i	0.273522	−	0.157918i	0.630487	+	0.776200i	$0.282855\pi$
$740$	−5.78626	−	23.3573i	−0.212707	−	0.858630i
$741$	−2.39944	+	4.05249i	−0.0881458	+	0.148872i
$742$	−19.2647	+	39.2560i	−0.707229	+	1.44113i
$743$	0.852403	+	0.492135i	0.0312716	+	0.0180547i	0.515554	−	0.856857i	$-0.327586\pi$
$743$	0.852403	+	0.492135i	0.0312716	+	0.0180547i	−0.484283	+	0.874912i	$0.660919\pi$
$744$	−16.9107	−	14.0689i	−0.619976	−	0.515792i
$745$	14.8508	+	8.57412i	0.544092	+	0.314132i
$746$	12.3644	−	9.30265i	0.452693	−	0.340594i
$747$	16.6151	+	0.365108i	0.607915	+	0.0133586i
$748$	6.16635	−	1.52758i	0.225464	−	0.0558538i
$749$	29.3641	+	1.58830i	1.07294	+	0.0580353i
$750$	−51.2578	+	37.6904i	−1.87167	+	1.37626i
$751$	4.18189	−	2.41442i	0.152599	−	0.0881033i	−0.421756	−	0.906709i	$-0.638586\pi$
$751$	4.18189	−	2.41442i	0.152599	−	0.0881033i	0.574355	+	0.818606i	$0.305253\pi$
$752$	30.3564	−	16.0237i	1.10699	−	0.584323i
$753$	25.7108	−	14.4699i	0.936954	−	0.527313i
$754$	7.86339	−	0.959492i	0.286368	−	0.0349426i
$755$	−35.2715			−1.28366
$756$	−17.2771	−	21.3893i	−0.628361	−	0.777922i
$757$	−39.8457			−1.44822			−0.724109	−	0.689686i	$-0.757749\pi$
$757$	−39.8457			−1.44822			−0.724109	+	0.689686i	$0.757749\pi$
$758$	22.3707	−	2.72967i	0.812540	−	0.0991461i
$759$	−1.32570	+	0.746096i	−0.0481198	+	0.0270816i
$760$	−24.9463	+	9.51136i	−0.904897	+	0.345013i
$761$	20.4850	−	11.8270i	0.742582	−	0.428730i	−0.0804252	−	0.996761i	$-0.525628\pi$
$761$	20.4850	−	11.8270i	0.742582	−	0.428730i	0.823007	+	0.568031i	$0.192294\pi$
$762$	28.0444	−	20.6213i	1.01594	−	0.747031i
$763$	7.41853	+	4.83536i	0.268569	+	0.175052i
$764$	−10.5852	−	42.7291i	−0.382960	−	1.54588i
$765$	34.1299	+	62.2333i	1.23397	+	2.25005i
$766$	−26.5451	+	19.9719i	−0.959114	+	0.721612i
$767$	13.0150	+	7.51420i	0.469944	+	0.271322i
$768$	2.40313	−	27.6084i	0.0867155	−	0.996233i
$769$	−1.86343	−	1.07585i	−0.0671971	−	0.0387963i	0.466025	−	0.884772i	$-0.345686\pi$
$769$	−1.86343	−	1.07585i	−0.0671971	−	0.0387963i	−0.533222	+	0.845975i	$0.679019\pi$
$770$	4.59344	+	6.84588i	0.165536	+	0.246708i
$771$	18.3394	−	30.9738i	0.660476	−	1.11550i
$772$	11.3264	−	2.80587i	0.407646	−	0.100985i
$773$	24.9256	−	14.3908i	0.896513	−	0.517602i	0.0204456	−	0.999791i	$-0.493491\pi$
$773$	24.9256	−	14.3908i	0.896513	−	0.517602i	0.876067	+	0.482189i	$0.160158\pi$
$774$	14.1135	−	1.40822i	0.507299	−	0.0506173i
$775$	−25.6207	+	44.3763i	−0.920323	+	1.59405i
$776$	−34.9707	−	28.4498i	−1.25537	−	1.02129i
$777$	−6.02479	−	12.2039i	−0.216138	−	0.437813i
$778$	−10.5848	−	4.50238i	−0.379483	−	0.161418i
$779$	9.08324	−	5.24421i	0.325441	−	0.187893i
$780$	−11.9216	+	11.2282i	−0.426863	+	0.402034i
$781$	−1.40666	+	2.43640i	−0.0503341	+	0.0871812i
$782$	−12.2731	−	5.22055i	−0.438886	−	0.186687i
$783$	21.9993	−	11.7523i	0.786190	−	0.419993i
$784$	4.07332	−	27.7021i	0.145476	−	0.989362i
$785$	15.4708	+	26.7963i	0.552178	+	0.956400i
$786$	−15.6473	+	35.6920i	−0.558121	+	1.27309i
$787$	11.1297			0.396731			0.198365	−	0.980128i	$-0.436437\pi$
$787$	11.1297			0.396731			0.198365	+	0.980128i	$0.436437\pi$
$788$	−27.6934	+	6.86043i	−0.986535	+	0.244393i
$789$	17.0065	+	0.186832i	0.605448	+	0.00665139i
$790$	−18.4351	+	13.8701i	−0.655890	+	0.493475i
$791$	0.388857	−	7.18909i	0.0138262	−	0.255615i
$792$	3.51511	+	2.99036i	0.124904	+	0.106258i
$793$	−1.21550	+	2.10531i	−0.0431638	+	0.0747619i
$794$	−15.1616	+	35.6439i	−0.538066	+	1.26495i
$795$	81.9989	+	0.900831i	2.90820	+	0.0319492i
$796$	−5.96052	−	6.19094i	−0.211265	−	0.219432i
$797$	−25.2083	−	14.5540i	−0.892923	−	0.515529i	−0.0180253	−	0.999838i	$-0.505738\pi$
$797$	−25.2083	−	14.5540i	−0.892923	−	0.515529i	−0.874897	+	0.484308i	$0.839071\pi$
$798$	−12.6308	+	8.27523i	−0.447125	+	0.292940i
$799$	−43.4029	+	25.0587i	−1.53548	+	0.886512i
$800$	−64.3288	+	5.38399i	−2.27437	+	0.190353i
$801$	−23.1864	+	12.7158i	−0.819251	+	0.449292i
$802$	−21.3012	+	16.0265i	−0.752173	+	0.565915i
$803$	3.50867			0.123818
$804$	16.8539	+	17.8947i	0.594389	+	0.631098i
$805$	0.934832	−	17.2830i	0.0329485	−	0.609144i
$806$	−2.90068	+	6.81928i	−0.102172	+	0.240199i
$807$	4.98115	−	8.41280i	0.175345	−	0.296145i
$808$	3.32354	−	20.6814i	0.116922	−	0.727571i
$809$	11.9462	+	20.6915i	0.420007	+	0.727474i	0.995940	−	0.0900232i	$-0.0286941\pi$
$809$	11.9462	+	20.6915i	0.420007	+	0.727474i	−0.575932	+	0.817497i	$0.695361\pi$
$810$	−22.2476	+	46.5158i	−0.781700	+	1.63440i
$811$	−20.7873			−0.729940			−0.364970	−	0.931019i	$-0.618921\pi$
$811$	−20.7873			−0.729940			−0.364970	+	0.931019i	$0.618921\pi$
$812$	23.9891	+	8.34562i	0.841851	+	0.292874i
$813$	0.431107	−	39.2418i	0.0151196	−	1.37627i
$814$	1.37341	+	1.82543i	0.0481379	+	0.0639814i
$815$	−61.3230			−2.14805
$816$	−1.97800	+	40.4135i	−0.0692438	+	1.41476i
$817$		−	7.78947i		−	0.272519i
$818$	−26.7880	+	3.26867i	−0.936621	+	0.114286i
$819$	−5.22704	+	7.64679i	−0.182648	+	0.267200i
$820$	35.4017	−	8.77000i	1.23628	−	0.306262i
$821$	−5.78113			−0.201763			−0.100881	−	0.994898i	$-0.532166\pi$
$821$	−5.78113			−0.201763			−0.100881	+	0.994898i	$0.532166\pi$
$822$	30.5765	−	3.39049i	1.06648	−	0.118257i
$823$			19.0746i			0.664899i	0.943121	+	0.332449i	$0.107875\pi$
$823$			19.0746i			0.664899i	−0.943121	+	0.332449i	$0.892125\pi$
$824$	11.5319	−	14.1751i	0.401732	−	0.493812i
$825$	5.47699	−	9.25025i	0.190684	−	0.322052i
$826$	26.8477	+	40.0129i	0.934152	+	1.39223i
$827$		−	14.6270i		−	0.508631i	−0.967121	−	0.254315i	$-0.918150\pi$
$827$		−	14.6270i		−	0.508631i	0.967121	−	0.254315i	$-0.0818501\pi$
$828$	−2.12264	−	9.45364i	−0.0737669	−	0.328537i
$829$	3.92858	−	2.26817i	0.136445	−	0.0787767i	−0.430223	−	0.902722i	$-0.641565\pi$
$829$	3.92858	−	2.26817i	0.136445	−	0.0787767i	0.566669	+	0.823946i	$0.308232\pi$
$830$	12.4230	−	29.2055i	0.431207	−	1.01374i
$831$	−0.219432	+	19.9740i	−0.00761201	+	0.692889i
$832$	−9.14047	+	1.89973i	−0.316889	+	0.0658613i
$833$	−4.40961	+	40.6427i	−0.152784	+	1.40818i
$834$	−34.5990	+	3.83652i	−1.19806	+	0.132848i
$835$		−	15.2747i		−	0.528602i
$836$	1.82582	−	1.75787i	0.0631475	−	0.0607972i
$837$	−0.768807	+	23.3196i	−0.0265739	+	0.806043i
$838$	33.1101	+	14.0839i	1.14377	+	0.486519i
$839$	−12.4814	−	21.6184i	−0.430906	−	0.746351i	0.566046	−	0.824374i	$-0.308473\pi$
$839$	−12.4814	−	21.6184i	−0.430906	−	0.746351i	−0.996952	+	0.0780231i	$0.975139\pi$
$840$	−50.1751	+	15.4790i	−1.73121	+	0.534078i
$841$	2.97992	−	5.16138i	0.102756	−	0.177978i
$842$	23.1648	−	17.4286i	0.798311	−	0.600629i
$843$	1.86550	+	1.10455i	0.0642511	+	0.0380426i
$844$	0.192871	+	0.0556195i	0.00663889	+	0.00191450i
$845$	−40.8311	−	23.5738i	−1.40463	−	0.810964i
$846$	−33.1820	−	14.9836i	−1.14082	−	0.515148i
$847$	23.7258	+	15.4643i	0.815227	+	0.531361i
$848$	39.5693	+	24.8917i	1.35882	+	0.854785i
$849$	−1.43619	+	0.808281i	−0.0492899	+	0.0277401i
$850$	93.5572	−	11.4159i	3.20898	−	0.391560i
$851$		−	4.79599i		−	0.164404i
$852$	−12.2853	−	13.0440i	−0.420887	−	0.446880i
$853$	−13.2403	+	7.64427i	−0.453338	+	0.261735i	−0.709239	−	0.704968i	$-0.750961\pi$
$853$	−13.2403	+	7.64427i	−0.453338	+	0.261735i	0.255901	+	0.966703i	$0.417628\pi$
$854$	−6.47251	+	4.34291i	−0.221485	+	0.148611i
$855$	24.2067	+	14.6941i	0.827852	+	0.502527i
$856$	4.98806	−	31.0392i	0.170488	−	1.06090i
$857$	−42.0171	−	24.2586i	−1.43528	−	0.828658i	−0.437761	−	0.899091i	$-0.644228\pi$
$857$	−42.0171	−	24.2586i	−1.43528	−	0.828658i	−0.997516	+	0.0704337i	$0.977562\pi$
$858$	0.624222	−	1.42387i	0.0213106	−	0.0486100i
$859$	−25.8723	−	44.8121i	−0.882751	−	1.52897i	−0.848270	−	0.529563i	$-0.822356\pi$
$859$	−25.8723	−	44.8121i	−0.882751	−	1.52897i	−0.0344802	−	0.999405i	$-0.510978\pi$
$860$	7.50530	−	26.0260i	0.255928	−	0.887481i
$861$	18.4970	−	9.13152i	0.630375	−	0.311201i
$862$	−14.9261	−	19.8386i	−0.508384	−	0.675707i
$863$	38.8024	+	22.4026i	1.32085	+	0.762592i	0.983864	−	0.178919i	$-0.0572599\pi$
$863$	38.8024	+	22.4026i	1.32085	+	0.762592i	0.336984	+	0.941510i	$0.390593\pi$
$864$	−24.6808	+	15.9643i	−0.839658	+	0.543115i
$865$	−12.6900	−	21.9797i	−0.431472	−	0.747332i
$866$	21.3390	−	2.60379i	0.725129	−	0.0884803i
$867$	0.325506	−	29.6294i	0.0110547	−	1.00627i
$868$	−17.9817	+	15.5311i	−0.610340	+	0.527159i
$869$	1.09505	−	1.89669i	0.0371471	−	0.0643407i
$870$	−5.24946	−	47.3413i	−0.177973	−	1.60502i
$871$	4.14055	−	7.17164i	0.140297	−	0.243002i
$872$	5.97417	−	7.34349i	0.202311	−	0.248682i
$873$	−1.05048	+	47.8045i	−0.0355533	+	1.61794i
$874$	−5.28192	+	0.644501i	−0.178664	+	0.0218006i
$875$	31.0960	+	61.2831i	1.05124	+	2.07175i
$876$	−6.42765	+	21.4031i	−0.217170	+	0.723145i
$877$	18.4097	+	31.8865i	0.621651	+	1.07673i	0.989178	+	0.146718i	$0.0468710\pi$
$877$	18.4097	+	31.8865i	0.621651	+	1.07673i	−0.367527	+	0.930013i	$0.619796\pi$
$878$	−2.49557	−	20.4521i	−0.0842214	−	0.690226i
$879$	28.6491	+	0.314736i	0.966310	+	0.0106158i
$880$	7.79416	−	4.11415i	0.262741	−	0.138688i
$881$		−	50.8325i		−	1.71259i	−0.516486	−	0.856295i	$-0.672760\pi$
$881$		−	50.8325i		−	1.71259i	0.516486	−	0.856295i	$-0.327240\pi$
$882$	−25.8468	+	14.6268i	−0.870306	+	0.492512i
$883$			28.5456i			0.960635i	0.877095	+	0.480317i	$0.159479\pi$
$883$			28.5456i			0.960635i	−0.877095	+	0.480317i	$0.840521\pi$
$884$	13.2307	−	3.27763i	0.444997	−	0.110239i
$885$	46.0381	−	77.7550i	1.54755	−	2.61370i
$886$	33.7299	−	4.11572i	1.13318	−	0.138270i
$887$	0.916708	+	1.58779i	0.0307800	+	0.0533126i	0.881005	−	0.473107i	$-0.156868\pi$
$887$	0.916708	+	1.58779i	0.0307800	+	0.0533126i	−0.850225	+	0.526419i	$0.823534\pi$
$888$	−13.6512	+	5.03380i	−0.458106	+	0.168923i
$889$	−17.0133	−	33.5295i	−0.570609	−	1.12454i
$890$	6.11678	+	50.1293i	0.205035	+	1.68034i
$891$	0.215024	−	4.89022i	0.00720357	−	0.163829i
$892$	−17.7858	−	18.4733i	−0.595512	−	0.618533i
$893$	−9.99749	+	17.3162i	−0.334553	+	0.579463i
$894$	4.16309	−	9.49613i	0.139235	−	0.317598i
$895$	20.2050	−	34.9962i	0.675380	−	1.16979i
$896$	−28.9931	−	7.44319i	−0.968591	−	0.248660i
$897$	−2.84447	+	1.60085i	−0.0949739	+	0.0534508i
$898$	−6.19958	−	50.8078i	−0.206883	−	1.69548i
$899$	−10.7767	−	18.6659i	−0.359425	−	0.622542i
$900$	46.3936	+	50.3558i	1.54645	+	1.67853i
$901$	−59.1091	−	34.1266i	−1.96921	−	1.13692i
$902$	−2.76673	+	2.08162i	−0.0921221	+	0.0693103i
$903$	0.995446	−	15.2876i	0.0331264	−	0.508741i
$904$	−7.59920	−	1.22120i	−0.252745	−	0.0406166i
$905$	−10.8291	−	18.7566i	−0.359972	−	0.623489i
$906$	2.35042	+	21.1968i	0.0780874	+	0.704216i
$907$	29.5577	+	17.0652i	0.981448	+	0.566640i	0.902707	−	0.430256i	$-0.141577\pi$
$907$	29.5577	+	17.0652i	0.981448	+	0.566640i	0.0787413	+	0.996895i	$0.474910\pi$
$908$	−10.4102	+	36.0992i	−0.345473	+	1.19799i
$909$	−19.4803	+	10.6833i	−0.646119	+	0.354344i
$910$	9.85584	+	14.6888i	0.326718	+	0.486928i
$911$	46.1098	−	26.6215i	1.52769	−	0.882010i	0.528228	−	0.849103i	$-0.322857\pi$
$911$	46.1098	−	26.6215i	1.52769	−	0.882010i	0.999458	−	0.0329076i	$-0.0104767\pi$
$912$	7.37833	+	14.3579i	0.244321	+	0.475439i
$913$			3.01295i			0.0997143i
$914$	−3.52380	−	28.8788i	−0.116557	−	0.955227i
$915$	12.5777	+	7.44716i	0.415806	+	0.246195i
$916$	26.0628	−	25.0928i	0.861139	−	0.829089i
$917$	35.2643	+	22.9851i	1.16453	+	0.759034i
$918$	35.1255	−	24.6578i	1.15931	−	0.813830i
$919$	13.4852	+	7.78568i	0.444836	+	0.256826i	0.705647	−	0.708564i	$-0.250657\pi$
$919$	13.4852	+	7.78568i	0.444836	+	0.256826i	−0.260811	+	0.965390i	$0.583990\pi$
$920$	−18.2689	−	2.93584i	−0.602307	−	0.0967917i
$921$	−40.9145	+	23.0265i	−1.34818	+	0.758748i
$922$	−19.7126	−	26.2006i	−0.649200	−	0.862869i
$923$	−3.01817	+	5.22762i	−0.0993442	+	0.172069i
$924$	3.80801	−	3.21667i	0.125274	−	0.105821i
$925$	16.9460	+	29.3513i	0.557180	+	0.965063i
$926$	−7.05938	+	16.5961i	−0.231986	+	0.545381i
$927$	−19.3772	−	0.425803i	−0.636431	−	0.0139852i
$928$	11.5680	−	24.5656i	0.379737	−	0.806405i
$929$		−	6.16139i		−	0.202149i	−0.994879	−	0.101074i	$-0.967772\pi$
$929$		−	6.16139i		−	0.202149i	0.994879	−	0.101074i	$-0.0322280\pi$
$930$	40.8087	+	17.8905i	1.33817	+	0.586651i
$931$	6.58389	+	14.9222i	0.215778	+	0.489055i
$932$	6.52107	−	22.6130i	0.213605	−	0.740715i
$933$	−18.8079	+	10.5850i	−0.615744	+	0.346537i
$934$	−27.0287	−	11.4970i	−0.884405	−	0.376194i
$935$	−11.1439	+	6.43393i	−0.364444	+	0.210412i
$936$	7.54215	+	6.41622i	0.246523	+	0.209721i
$937$		−	20.3159i		−	0.663692i	−0.943334	−	0.331846i	$-0.892329\pi$
$937$		−	20.3159i		−	0.663692i	0.943334	−	0.331846i	$-0.107671\pi$
$938$	22.0483	−	14.7939i	0.719901	−	0.483038i
$939$	−16.1474	−	28.6915i	−0.526952	−	0.936313i
$940$	−50.0879	+	48.2237i	−1.63369	+	1.57288i
$941$			38.3234i			1.24931i	0.780902	+	0.624654i	$0.214760\pi$
$941$			38.3234i			1.24931i	−0.780902	+	0.624654i	$0.785240\pi$
$942$	15.0726	−	11.0830i	0.491092	−	0.361105i
$943$	7.26908			0.236714
$944$	45.5553	−	24.0464i	1.48270	−	0.782644i
$945$	45.6303	+	31.9322i	1.48435	+	1.03875i
$946$	0.311453	+	2.55247i	0.0101262	+	0.0829880i
$947$			13.2141i			0.429401i	0.976680	+	0.214700i	$0.0688775\pi$
$947$			13.2141i			0.429401i	−0.976680	+	0.214700i	$0.931123\pi$
$948$	9.56385	+	10.1545i	0.310619	+	0.329803i
$949$	7.52834			0.244380
$950$	30.0479	−	22.6073i	0.974883	−	0.733476i
$951$	−31.0016	+	17.4475i	−1.00529	+	0.565774i
$952$	42.7127	+	9.25477i	1.38433	+	0.299949i
$953$	11.6066			0.375976			0.187988	−	0.982171i	$-0.439803\pi$
$953$	11.6066			0.375976			0.187988	+	0.982171i	$0.439803\pi$
$954$	−4.92287	−	49.3382i	−0.159384	−	1.59738i
$955$	44.5833	+	77.2206i	1.44268	+	2.49880i
$956$	−3.76751	−	1.08646i	−0.121850	−	0.0351387i
$957$	2.21773	+	3.94057i	0.0716892	+	0.127381i
$958$	23.7302	+	10.0940i	0.766688	+	0.326121i
$959$	1.79472	−	33.1803i	0.0579545	−	1.07145i
$960$	10.8182	+	55.0817i	0.349156	+	1.77775i
$961$	−10.8372			−0.349589
$962$	2.94683	+	3.91671i	0.0950097	+	0.126280i
$963$	−29.2365	+	16.0338i	−0.942132	+	0.516682i
$964$	13.1746	+	3.79925i	0.424326	+	0.122366i
$965$	−20.4692	+	11.8179i	−0.658926	+	0.380431i
$966$	−10.4487	+	0.589902i	−0.336181	+	0.0189798i
$967$	−40.7431	−	23.5230i	−1.31021	−	0.756449i	−0.328078	−	0.944651i	$-0.606401\pi$
$967$	−40.7431	−	23.5230i	−1.31021	−	0.756449i	−0.982130	+	0.188201i	$0.939734\pi$
$968$	19.1064	−	23.4858i	0.614104	−	0.754861i
$969$	−11.5597	−	20.5397i	−0.371349	−	0.659831i
$970$	84.0292	+	35.7430i	2.69801	+	1.14764i
$971$	−17.2692	+	29.9112i	−0.554195	+	0.959895i	0.443770	+	0.896141i	$0.353641\pi$
$971$	−17.2692	+	29.9112i	−0.554195	+	0.959895i	−0.997966	+	0.0637540i	$0.979693\pi$
$972$	29.4368	+	10.2702i	0.944184	+	0.329417i
$973$	−2.03082	+	37.5453i	−0.0651051	+	1.20365i
$974$	8.17034	+	10.8594i	0.261795	+	0.347958i
$975$	11.7516	−	19.8477i	0.376353	−	0.635634i
$976$	3.88977	+	7.36907i	0.124508	+	0.235878i
$977$	−27.3080			−0.873659			−0.436830	−	0.899544i	$-0.643899\pi$
$977$	−27.3080			−0.873659			−0.436830	+	0.899544i	$0.643899\pi$
$978$	4.08644	+	36.8528i	0.130670	+	1.17842i
$979$	−2.39710	−	4.15190i	−0.0766117	−	0.132695i
$980$	7.62019	+	56.2015i	0.243418	+	1.79529i
$981$	−10.0385	−	0.220590i	−0.320504	−	0.00704290i
$982$	−0.993609	+	2.33590i	−0.0317073	+	0.0745416i
$983$	−9.56607	+	16.5689i	−0.305110	+	0.528467i	−0.977286	−	0.211925i	$-0.932027\pi$
$983$	−9.56607	+	16.5689i	−0.305110	+	0.528467i	0.672176	+	0.740392i	$0.265360\pi$
$984$	−7.62952	−	20.6906i	−0.243220	−	0.659593i
$985$	50.0478	−	28.8951i	1.59465	−	0.920674i
$986$	−15.5178	+	36.4813i	−0.494188	+	1.16180i
$987$	−21.8340	+	32.7071i	−0.694984	+	1.04108i
$988$	3.91755	−	3.77175i	0.124634	−	0.119995i
$989$	2.69928	−	4.67528i	0.0858320	−	0.148665i
$990$	−8.51964	−	3.84712i	−0.270772	−	0.122270i
$991$	19.9326	−	11.5081i	0.633179	−	0.365566i	−0.148803	−	0.988867i	$-0.547542\pi$
$991$	19.9326	−	11.5081i	0.633179	−	0.365566i	0.781982	+	0.623301i	$0.214209\pi$
$992$	14.4909	+	20.8620i	0.460087	+	0.662368i
$993$	9.74665	+	17.3183i	0.309300	+	0.549580i
$994$	−16.0716	+	10.7837i	−0.509762	+	0.342039i
$995$	15.0754	+	8.70376i	0.477921	+	0.275928i
$996$	−18.3792	−	5.51953i	−0.582367	−	0.174893i
$997$	52.8055	+	30.4872i	1.67237	+	0.965541i	0.966309	+	0.257385i	$0.0828609\pi$
$997$	52.8055	+	30.4872i	1.67237	+	0.965541i	0.706056	+	0.708156i	$0.250472\pi$
$998$	−37.3904	−	49.6966i	−1.18357	−	1.57312i
$999$	13.1033	+	8.15236i	0.414570	+	0.257929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bj.b.103.19	yes	84
3.2	odd	2		756.2.bj.b.523.24		84
4.3	odd	2	inner	252.2.bj.b.103.20	yes	84
7.3	odd	6		252.2.n.b.31.38	yes	84
9.2	odd	6		756.2.n.b.19.33		84
9.7	even	3		252.2.n.b.187.10	yes	84
12.11	even	2		756.2.bj.b.523.23		84
21.17	even	6		756.2.n.b.199.5		84
28.3	even	6		252.2.n.b.31.10	✓	84
36.7	odd	6		252.2.n.b.187.38	yes	84
36.11	even	6		756.2.n.b.19.5		84
63.38	even	6		756.2.bj.b.451.24		84
63.52	odd	6	inner	252.2.bj.b.115.19	yes	84
84.59	odd	6		756.2.n.b.199.33		84
252.115	even	6	inner	252.2.bj.b.115.20	yes	84
252.227	odd	6		756.2.bj.b.451.23		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.10	✓	84	28.3	even	6
252.2.n.b.31.38	yes	84	7.3	odd	6
252.2.n.b.187.10	yes	84	9.7	even	3
252.2.n.b.187.38	yes	84	36.7	odd	6
252.2.bj.b.103.19	yes	84	1.1	even	1	trivial
252.2.bj.b.103.20	yes	84	4.3	odd	2	inner
252.2.bj.b.115.19	yes	84	63.52	odd	6	inner
252.2.bj.b.115.20	yes	84	252.115	even	6	inner
756.2.n.b.19.5		84	36.11	even	6
756.2.n.b.19.33		84	9.2	odd	6
756.2.n.b.199.5		84	21.17	even	6
756.2.n.b.199.33		84	84.59	odd	6
756.2.bj.b.451.23		84	252.227	odd	6
756.2.bj.b.451.24		84	63.38	even	6
756.2.bj.b.523.23		84	12.11	even	2
756.2.bj.b.523.24		84	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.171292 - 1.40380i) q^{2} +(1.50942 - 0.849495i) q^{3} +(-1.94132 + 0.480920i) q^{4} +(3.50837 - 2.02556i) q^{5} +(-1.45107 - 1.97342i) q^{6} +(-2.35939 + 1.19719i) q^{7} +(1.00765 + 2.64285i) q^{8} +(1.55672 - 2.56450i) q^{9} +(-3.44444 - 4.57810i) q^{10} +(0.471017 + 0.271942i) q^{11} +(-2.52173 + 2.37505i) q^{12} +(1.01063 + 0.583488i) q^{13} +(2.08476 + 3.10705i) q^{14} +(3.57492 - 6.03778i) q^{15} +(3.53743 - 1.86724i) q^{16} +(-5.05773 + 2.92008i) q^{17} +(-3.86670 - 1.74604i) q^{18} +(-1.16501 + 2.01785i) q^{19} +(-5.83674 + 5.61950i) q^{20} +(-2.54431 + 3.81136i) q^{21} +(0.301071 - 0.707796i) q^{22} +(-1.39849 + 0.807417i) q^{23} +(3.76605 + 3.13318i) q^{24} +(5.70579 - 9.88272i) q^{25} +(0.645988 - 1.51867i) q^{26} +(0.171215 - 5.19333i) q^{27} +(4.00458 - 3.45881i) q^{28} +(2.40001 + 4.15694i) q^{29} +(-9.08819 - 3.98425i) q^{30} -4.49030 q^{31} +(-3.22716 - 4.64601i) q^{32} +(0.941977 + 0.0103485i) q^{33} +(4.96557 + 6.59987i) q^{34} +(-5.85265 + 8.97929i) q^{35} +(-1.78876 + 5.72716i) q^{36} +(-1.48498 + 2.57206i) q^{37} +(3.03222 + 1.28980i) q^{38} +(2.02114 + 0.0222040i) q^{39} +(8.88846 + 7.23105i) q^{40} +(-3.89836 - 2.25072i) q^{41} +(5.78621 + 2.91886i) q^{42} +(-2.89521 + 1.67155i) q^{43} +(-1.04518 - 0.301404i) q^{44} +(0.266999 - 12.1504i) q^{45} +(1.37300 + 1.82490i) q^{46} +8.58149 q^{47} +(3.75327 - 5.82348i) q^{48} +(4.13347 - 5.64928i) q^{49} +(-14.8507 - 6.31697i) q^{50} +(-5.15366 + 8.70416i) q^{51} +(-2.24257 - 0.646703i) q^{52} +(5.84343 + 10.1211i) q^{53} +(-7.31973 + 0.649223i) q^{54} +2.20334 q^{55} +(-5.54143 - 5.02917i) q^{56} +(-0.0443331 + 4.03546i) q^{57} +(5.42441 - 4.08118i) q^{58} +12.8781 q^{59} +(-4.03636 + 13.4405i) q^{60} +2.08317i q^{61} +(0.769151 + 6.30348i) q^{62} +(-0.602715 + 7.91434i) q^{63} +(-5.96929 + 5.32612i) q^{64} +4.72756 q^{65} +(-0.146826 - 1.32412i) q^{66} -7.09620i q^{67} +(8.41435 - 8.10118i) q^{68} +(-1.42501 + 2.40674i) q^{69} +(13.6076 + 6.67788i) q^{70} +5.17264i q^{71} +(8.34619 + 1.53005i) q^{72} +(5.58686 - 3.22558i) q^{73} +(3.86502 + 1.64404i) q^{74} +(0.217128 - 19.7643i) q^{75} +(1.29122 - 4.47756i) q^{76} +(-1.43688 - 0.0777206i) q^{77} +(-0.315035 - 2.84108i) q^{78} -4.02680i q^{79} +(8.62844 - 13.7162i) q^{80} +(-4.15327 - 7.98438i) q^{81} +(-2.49181 + 5.85806i) q^{82} +(2.76985 + 4.79753i) q^{83} +(3.10637 - 8.62267i) q^{84} +(-11.8296 + 20.4895i) q^{85} +(2.84245 + 3.77798i) q^{86} +(7.15393 + 4.23578i) q^{87} +(-0.244081 + 1.51885i) q^{88} +(-7.63381 - 4.40738i) q^{89} +(-17.1025 + 1.70646i) q^{90} +(-3.08302 - 0.166760i) q^{91} +(2.32661 - 2.24001i) q^{92} +(-6.77775 + 3.81448i) q^{93} +(-1.46994 - 12.0467i) q^{94} +9.43917i q^{95} +(-8.81792 - 4.27134i) q^{96} +(-13.8033 + 7.96935i) q^{97} +(-8.63851 - 4.83490i) q^{98} +(1.43063 - 0.784585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26}+ \cdots + 21 q^{98}+O(q^{100}) \) 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9 - 18 * q^10 - 6 * q^12 + 18 * q^13 + 14 * q^14 + 14 * q^16 + 6 * q^17 - 10 * q^18 - 24 * q^20 + 4 * q^21 + 6 * q^22 - 6 * q^24 + 16 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 11 * q^30 - 18 * q^32 - 18 * q^33 - 24 * q^34 - 38 * q^36 + 2 * q^37 + 33 * q^38 + 6 * q^40 + 6 * q^41 - 38 * q^42 - 13 * q^44 - 54 * q^45 + 10 * q^46 + 9 * q^48 - 28 * q^49 - 17 * q^50 - 27 * q^52 - 2 * q^53 - 39 * q^54 + 58 * q^56 + 6 * q^57 - 13 * q^58 - 31 * q^60 - 8 * q^64 - 100 * q^65 + 30 * q^66 - 18 * q^68 - 18 * q^69 - 19 * q^70 + 26 * q^72 + 30 * q^73 - 23 * q^74 - 2 * q^77 + 15 * q^78 + 3 * q^80 - 32 * q^81 - 18 * q^82 + 23 * q^84 - 50 * q^85 - 9 * q^86 + q^88 - 102 * q^89 - 39 * q^90 + 28 * q^92 - 36 * q^93 + 63 * q^96 + 6 * q^97 + 21 * q^98

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