LMFDB - Embedded newform 378.2.z.a.41.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,2,Mod(41,378)] 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("378.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([17, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.15
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.984808 - 0.173648i) q^{2} +(-1.41919 + 0.992922i) q^{3} +(0.939693 - 0.342020i) q^{4} +(3.28093 + 2.75302i) q^{5} +(-1.22521 + 1.22428i) q^{6} +(-2.27542 - 1.34999i) q^{7} +(0.866025 - 0.500000i) q^{8} +(1.02821 - 2.81829i) q^{9} +(3.70914 + 2.14147i) q^{10} +(2.71017 + 3.22986i) q^{11} +(-0.994005 + 1.41843i) q^{12} +(-0.922962 - 0.162743i) q^{13} +(-2.47527 - 0.934353i) q^{14} +(-7.38980 - 0.649364i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-3.26843 + 5.66109i) q^{17} +(0.523198 - 2.95403i) q^{18} +(1.47194 - 0.849827i) q^{19} +(4.02465 + 1.46485i) q^{20} +(4.56969 - 0.343428i) q^{21} +(3.22986 + 2.71017i) q^{22} +(-0.996040 - 2.73660i) q^{23} +(-0.732595 + 1.56949i) q^{24} +(2.31710 + 13.1409i) q^{25} -0.937200 q^{26} +(1.33912 + 5.02063i) q^{27} +(-2.59992 - 0.490331i) q^{28} +(7.02413 - 1.23854i) q^{29} +(-7.39030 + 0.643727i) q^{30} +(-2.84339 - 7.81215i) q^{31} +(0.642788 - 0.766044i) q^{32} +(-7.05325 - 1.89280i) q^{33} +(-2.23574 + 6.14264i) q^{34} +(-3.74895 - 10.6935i) q^{35} +(0.00228814 - 3.00000i) q^{36} +(1.18098 - 2.04551i) q^{37} +(1.30201 - 1.09252i) q^{38} +(1.47145 - 0.685466i) q^{39} +(4.21788 + 0.743726i) q^{40} +(0.947038 - 5.37092i) q^{41} +(4.44063 - 1.13173i) q^{42} +(-3.40689 + 2.85872i) q^{43} +(3.65140 + 2.10814i) q^{44} +(11.1323 - 6.41593i) q^{45} +(-1.45611 - 2.52206i) q^{46} +(-0.161480 - 0.0587738i) q^{47} +(-0.448926 + 1.67286i) q^{48} +(3.35508 + 6.14357i) q^{49} +(4.56379 + 12.5389i) q^{50} +(-0.982491 - 11.2795i) q^{51} +(-0.922962 + 0.162743i) q^{52} -8.21598i q^{53} +(2.19060 + 4.71182i) q^{54} +18.0581i q^{55} +(-2.64556 - 0.0314111i) q^{56} +(-1.24516 + 2.66759i) q^{57} +(6.70235 - 2.43946i) q^{58} +(-6.04598 - 5.07318i) q^{59} +(-7.16624 + 1.91726i) q^{60} +(2.33237 - 6.40812i) q^{61} +(-4.15676 - 7.19972i) q^{62} +(-6.14427 + 5.02474i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-2.58014 - 3.07489i) q^{65} +(-7.27478 - 0.639256i) q^{66} +(0.519116 - 2.94405i) q^{67} +(-1.13511 + 6.43755i) q^{68} +(4.13080 + 2.89477i) q^{69} +(-5.54890 - 9.88003i) q^{70} +(-5.28304 - 3.05016i) q^{71} +(-0.518691 - 2.95482i) q^{72} +(-0.852614 + 0.492257i) q^{73} +(0.807835 - 2.21951i) q^{74} +(-16.3363 - 16.3488i) q^{75} +(1.09252 - 1.30201i) q^{76} +(-1.80652 - 11.0080i) q^{77} +(1.33007 - 0.930567i) q^{78} +(-0.885211 - 5.02028i) q^{79} +4.28295 q^{80} +(-6.88557 - 5.79560i) q^{81} -5.45377i q^{82} +(-0.395445 - 2.24268i) q^{83} +(4.17664 - 1.88564i) q^{84} +(-26.3086 + 9.57554i) q^{85} +(-2.85872 + 3.40689i) q^{86} +(-8.73882 + 8.73215i) q^{87} +(3.96201 + 1.44205i) q^{88} +(-1.22954 - 2.12963i) q^{89} +(9.84908 - 8.25156i) q^{90} +(1.88043 + 1.61629i) q^{91} +(-1.87194 - 2.23090i) q^{92} +(11.7922 + 8.26367i) q^{93} +(-0.169232 - 0.0298402i) q^{94} +(7.16894 + 1.26408i) q^{95} +(-0.151616 + 1.72540i) q^{96} +(-1.53146 - 1.82512i) q^{97} +(4.37093 + 5.46763i) q^{98} +(11.8893 - 4.31709i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57}+ \cdots + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$3$	−1.41919	+	0.992922i	−0.819371	+	0.573264i
$3$	−1.41919	+	0.992922i	−0.819371	+	0.573264i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	3.28093	+	2.75302i	1.46727	+	1.23119i	0.918621	+	0.395140i	$0.129304\pi$
$5$	3.28093	+	2.75302i	1.46727	+	1.23119i	0.548654	+	0.836049i	$0.315140\pi$
$6$	−1.22521	+	1.22428i	−0.500191	+	0.499809i
$7$	−2.27542	−	1.34999i	−0.860028	−	0.510246i
$7$	−2.27542	−	1.34999i	−0.860028	−	0.510246i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	1.02821	−	2.81829i	0.342737	−	0.939431i
$10$	3.70914	+	2.14147i	1.17293	+	0.677193i
$11$	2.71017	+	3.22986i	0.817147	+	0.973838i	0.999957	−	0.00930997i	$-0.00296350\pi$
$11$	2.71017	+	3.22986i	0.817147	+	0.973838i	−0.182809	+	0.983148i	$0.558519\pi$
$12$	−0.994005	+	1.41843i	−0.286944	+	0.409467i
$13$	−0.922962	−	0.162743i	−0.255984	−	0.0451368i	0.0441835	−	0.999023i	$-0.485931\pi$
$13$	−0.922962	−	0.162743i	−0.255984	−	0.0451368i	−0.300167	+	0.953887i	$0.597042\pi$
$14$	−2.47527	−	0.934353i	−0.661545	−	0.249716i
$15$	−7.38980	−	0.649364i	−1.90804	−	0.167665i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−3.26843	+	5.66109i	−0.792711	+	1.37302i	0.131572	+	0.991307i	$0.457998\pi$
$17$	−3.26843	+	5.66109i	−0.792711	+	1.37302i	−0.924283	+	0.381709i	$0.875336\pi$
$18$	0.523198	−	2.95403i	0.123319	−	0.696270i
$19$	1.47194	−	0.849827i	0.337687	−	0.194964i	−0.321562	−	0.946889i	$-0.604208\pi$
$19$	1.47194	−	0.849827i	0.337687	−	0.194964i	0.659249	+	0.751925i	$0.270874\pi$
$20$	4.02465	+	1.46485i	0.899940	+	0.327551i
$21$	4.56969	−	0.343428i	0.997188	−	0.0749422i
$22$	3.22986	+	2.71017i	0.688608	+	0.577811i
$23$	−0.996040	−	2.73660i	−0.207689	−	0.570620i	0.791488	−	0.611185i	$-0.209307\pi$
$23$	−0.996040	−	2.73660i	−0.207689	−	0.570620i	−0.999177	+	0.0405642i	$0.987084\pi$
$24$	−0.732595	+	1.56949i	−0.149540	+	0.320371i
$25$	2.31710	+	13.1409i	0.463419	+	2.62818i
$26$	−0.937200			−0.183800
$27$	1.33912	+	5.02063i	0.257714	+	0.966221i
$28$	−2.59992	−	0.490331i	−0.491338	−	0.0926639i
$29$	7.02413	−	1.23854i	1.30435	−	0.229992i	0.522061	−	0.852908i	$-0.325163\pi$
$29$	7.02413	−	1.23854i	1.30435	−	0.229992i	0.782288	+	0.622916i	$0.214052\pi$
$30$	−7.39030	+	0.643727i	−1.34928	+	0.117528i
$31$	−2.84339	−	7.81215i	−0.510688	−	1.40310i	−0.880522	−	0.474006i	$-0.842808\pi$
$31$	−2.84339	−	7.81215i	−0.510688	−	1.40310i	0.369834	−	0.929098i	$-0.379415\pi$
$32$	0.642788	−	0.766044i	0.113630	−	0.135419i
$33$	−7.05325	−	1.89280i	−1.22781	−	0.329493i
$34$	−2.23574	+	6.14264i	−0.383426	+	1.05345i
$35$	−3.74895	−	10.6935i	−0.633688	−	1.80753i
$36$	0.00228814	−	3.00000i	0.000381357	−	0.500000i
$37$	1.18098	−	2.04551i	0.194151	−	0.336280i	−0.752471	−	0.658626i	$-0.771138\pi$
$37$	1.18098	−	2.04551i	0.194151	−	0.336280i	0.946622	+	0.322346i	$0.104471\pi$
$38$	1.30201	−	1.09252i	0.211214	−	0.177230i
$39$	1.47145	−	0.685466i	0.235621	−	0.109762i
$40$	4.21788	+	0.743726i	0.666905	+	0.117593i
$41$	0.947038	−	5.37092i	0.147902	−	0.838796i	−0.817088	−	0.576513i	$-0.804413\pi$
$41$	0.947038	−	5.37092i	0.147902	−	0.838796i	0.964991	−	0.262284i	$-0.0844757\pi$
$42$	4.44063	−	1.13173i	0.685204	−	0.174630i
$43$	−3.40689	+	2.85872i	−0.519546	+	0.435950i	−0.864473	−	0.502679i	$-0.832348\pi$
$43$	−3.40689	+	2.85872i	−0.519546	+	0.435950i	0.344928	+	0.938629i	$0.387903\pi$
$44$	3.65140	+	2.10814i	0.550470	+	0.317814i
$45$	11.1323	−	6.41593i	1.65951	−	0.956430i
$46$	−1.45611	−	2.52206i	−0.214692	−	0.371858i
$47$	−0.161480	−	0.0587738i	−0.0235542	−	0.00857303i	0.330216	−	0.943905i	$-0.392878\pi$
$47$	−0.161480	−	0.0587738i	−0.0235542	−	0.00857303i	−0.353770	+	0.935332i	$0.615101\pi$
$48$	−0.448926	+	1.67286i	−0.0647968	+	0.241457i
$49$	3.35508	+	6.14357i	0.479297	+	0.877653i
$50$	4.56379	+	12.5389i	0.645417	+	1.77327i
$51$	−0.982491	−	11.2795i	−0.137576	−	1.57944i
$52$	−0.922962	+	0.162743i	−0.127992	+	0.0225684i
$53$		−	8.21598i		−	1.12855i	−0.825587	−	0.564276i	$-0.809156\pi$
$53$		−	8.21598i		−	1.12855i	0.825587	−	0.564276i	$-0.190844\pi$
$54$	2.19060	+	4.71182i	0.298103	+	0.641198i
$55$			18.0581i			2.43495i
$56$	−2.64556	−	0.0314111i	−0.353528	−	0.00419749i
$57$	−1.24516	+	2.66759i	−0.164925	+	0.353332i
$58$	6.70235	−	2.43946i	0.880062	−	0.320316i
$59$	−6.04598	−	5.07318i	−0.787119	−	0.660472i	0.157911	−	0.987453i	$-0.449524\pi$
$59$	−6.04598	−	5.07318i	−0.787119	−	0.660472i	−0.945031	+	0.326982i	$0.893968\pi$
$60$	−7.16624	+	1.91726i	−0.925157	+	0.247517i
$61$	2.33237	−	6.40812i	0.298629	−	0.820476i	−0.696101	−	0.717944i	$-0.745083\pi$
$61$	2.33237	−	6.40812i	0.298629	−	0.820476i	0.994730	−	0.102532i	$-0.0326944\pi$
$62$	−4.15676	−	7.19972i	−0.527909	−	0.914365i
$63$	−6.14427	+	5.02474i	−0.774105	+	0.633057i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−2.58014	−	3.07489i	−0.320026	−	0.381393i
$66$	−7.27478	−	0.639256i	−0.895463	−	0.0786870i
$67$	0.519116	−	2.94405i	0.0634201	−	0.359673i	−0.936538	−	0.350565i	$-0.885990\pi$
$67$	0.519116	−	2.94405i	0.0634201	−	0.359673i	0.999959	−	0.00910841i	$-0.00289934\pi$
$68$	−1.13511	+	6.43755i	−0.137653	+	0.780668i
$69$	4.13080	+	2.89477i	0.497290	+	0.348489i
$70$	−5.54890	−	9.88003i	−0.663220	−	1.18089i
$71$	−5.28304	−	3.05016i	−0.626981	−	0.361988i	0.152601	−	0.988288i	$-0.451235\pi$
$71$	−5.28304	−	3.05016i	−0.626981	−	0.361988i	−0.779582	+	0.626300i	$0.784568\pi$
$72$	−0.518691	−	2.95482i	−0.0611283	−	0.348229i
$73$	−0.852614	+	0.492257i	−0.0997909	+	0.0576143i	−0.549065	−	0.835780i	$-0.685016\pi$
$73$	−0.852614	+	0.492257i	−0.0997909	+	0.0576143i	0.449274	+	0.893394i	$0.351683\pi$
$74$	0.807835	−	2.21951i	0.0939089	−	0.258012i
$75$	−16.3363	−	16.3488i	−1.88635	−	1.88779i
$76$	1.09252	−	1.30201i	0.125320	−	0.149351i
$77$	−1.80652	−	11.0080i	−0.205872	−	1.25448i
$78$	1.33007	−	0.930567i	0.150600	−	0.105366i
$79$	−0.885211	−	5.02028i	−0.0995940	−	0.564826i	−0.993242	−	0.116058i	$-0.962974\pi$
$79$	−0.885211	−	5.02028i	−0.0995940	−	0.564826i	0.893648	−	0.448768i	$-0.148137\pi$
$80$	4.28295			0.478848
$81$	−6.88557	−	5.79560i	−0.765063	−	0.643955i
$82$		−	5.45377i		−	0.602268i
$83$	−0.395445	−	2.24268i	−0.0434057	−	0.246166i	0.955383	−	0.295370i	$-0.0954428\pi$
$83$	−0.395445	−	2.24268i	−0.0434057	−	0.246166i	−0.998789	+	0.0492035i	$0.984332\pi$
$84$	4.17664	−	1.88564i	0.455709	−	0.205740i
$85$	−26.3086	+	9.57554i	−2.85357	+	1.03861i
$86$	−2.85872	+	3.40689i	−0.308264	+	0.367374i
$87$	−8.73882	+	8.73215i	−0.936899	+	0.936185i
$88$	3.96201	+	1.44205i	0.422351	+	0.153723i
$89$	−1.22954	−	2.12963i	−0.130331	−	0.225740i	0.793473	−	0.608605i	$-0.208271\pi$
$89$	−1.22954	−	2.12963i	−0.130331	−	0.225740i	−0.923804	+	0.382865i	$0.874937\pi$
$90$	9.84908	−	8.25156i	1.03818	−	0.869791i
$91$	1.88043	+	1.61629i	0.197122	+	0.169434i
$92$	−1.87194	−	2.23090i	−0.195164	−	0.232587i
$93$	11.7922	+	8.26367i	1.22279	+	0.856903i
$94$	−0.169232	−	0.0298402i	−0.0174550	−	0.00307778i
$95$	7.16894	+	1.26408i	0.735517	+	0.129692i
$96$	−0.151616	+	1.72540i	−0.0154743	+	0.176098i
$97$	−1.53146	−	1.82512i	−0.155496	−	0.185313i	0.682672	−	0.730725i	$-0.260818\pi$
$97$	−1.53146	−	1.82512i	−0.155496	−	0.185313i	−0.838168	+	0.545412i	$0.816373\pi$
$98$	4.37093	+	5.46763i	0.441530	+	0.552314i
$99$	11.8893	−	4.31709i	1.19492	−	0.433884i
$100$	6.67181	+	11.5559i	0.667181	+	1.15559i
$101$	8.69270	+	3.16388i	0.864956	+	0.314818i	0.736123	−	0.676848i	$-0.236655\pi$
$101$	8.69270	+	3.16388i	0.864956	+	0.314818i	0.128833	+	0.991666i	$0.458877\pi$
$102$	−2.92622	−	10.9375i	−0.289739	−	1.08297i
$103$	6.93337	−	8.26287i	0.683166	−	0.814165i	−0.307345	−	0.951598i	$-0.599441\pi$
$103$	6.93337	−	8.26287i	0.683166	−	0.814165i	0.990511	+	0.137433i	$0.0438852\pi$
$104$	−0.880680	+	0.320541i	−0.0863578	+	0.0314317i
$105$	15.9383	+	11.4537i	1.55542	+	1.11777i
$106$	−1.42669	−	8.09116i	−0.138572	−	0.785883i
$107$			10.3992i			1.00533i	0.864482	+	0.502663i	$0.167646\pi$
$107$			10.3992i			1.00533i	−0.864482	+	0.502663i	$0.832354\pi$
$108$	2.97552	+	4.25985i	0.286319	+	0.409904i
$109$	−7.17365			−0.687111			−0.343555	−	0.939132i	$-0.611631\pi$
$109$	−7.17365			−0.687111			−0.343555	+	0.939132i	$0.611631\pi$
$110$	3.13575	+	17.7837i	0.298982	+	1.69561i
$111$	0.355001	+	4.07559i	0.0336953	+	0.386838i
$112$	−2.61083	+	0.428464i	−0.246700	+	0.0404860i
$113$	8.56975	−	10.2130i	0.806174	−	0.960761i	−0.193620	−	0.981077i	$-0.562023\pi$
$113$	8.56975	−	10.2130i	0.806174	−	0.960761i	0.999794	+	0.0203160i	$0.00646723\pi$
$114$	−0.763019	+	2.84329i	−0.0714633	+	0.266298i
$115$	4.26599	−	11.7207i	0.397805	−	1.09296i
$116$	6.17692	−	3.56625i	0.573513	−	0.331118i
$117$	−1.40766	+	2.43385i	−0.130138	+	0.225009i
$118$	−6.83507	−	3.94623i	−0.629220	−	0.363280i
$119$	15.0794	−	8.46902i	1.38233	−	0.776354i
$120$	−6.72444	+	3.13254i	−0.613854	+	0.285960i
$121$	−1.17681	+	6.67405i	−0.106983	+	0.606731i
$122$	1.18417	−	6.71578i	0.107210	−	0.608018i
$123$	3.98888	+	8.56270i	0.359665	+	0.772072i
$124$	−5.34383	−	6.36852i	−0.479890	−	0.571910i
$125$	−17.8676	+	30.9476i	−1.59813	+	2.76804i
$126$	−5.17839	+	6.01534i	−0.461327	+	0.535889i
$127$	9.01001	+	15.6058i	0.799509	+	1.38479i	0.919936	+	0.392069i	$0.128240\pi$
$127$	9.01001	+	15.6058i	0.799509	+	1.38479i	−0.120427	+	0.992722i	$0.538426\pi$
$128$	0.342020	−	0.939693i	0.0302306	−	0.0830579i
$129$	1.99654	−	7.43984i	0.175786	−	0.655042i
$130$	−3.07489	−	2.58014i	−0.269685	−	0.226293i
$131$	3.97168	−	1.44557i	0.347007	−	0.126300i	−0.162636	−	0.986686i	$-0.552000\pi$
$131$	3.97168	−	1.44557i	0.347007	−	0.126300i	0.509643	+	0.860386i	$0.329777\pi$
$132$	−7.27526	+	0.633707i	−0.633230	+	0.0551571i
$133$	−4.49655	−	0.0533880i	−0.389900	−	0.00462933i
$134$		−	2.98947i		−	0.258251i
$135$	−9.42837	+	20.1590i	−0.811465	+	1.73501i
$136$			6.53686i			0.560531i
$137$	−16.0321	+	2.82690i	−1.36972	+	0.241518i	−0.809643	−	0.586923i	$-0.800339\pi$
$137$	−16.0321	+	2.82690i	−1.36972	+	0.241518i	−0.560076	+	0.828441i	$0.689228\pi$
$138$	4.57072	+	2.13348i	0.389085	+	0.181614i
$139$	3.13354	+	8.60932i	0.265783	+	0.730233i	0.998751	+	0.0499695i	$0.0159124\pi$
$139$	3.13354	+	8.60932i	0.265783	+	0.730233i	−0.732968	+	0.680263i	$0.761865\pi$
$140$	−7.18025	−	8.76638i	−0.606842	−	0.740894i
$141$	0.287528	−	0.0769255i	0.0242142	−	0.00647829i
$142$	−5.73243	−	2.08643i	−0.481055	−	0.175090i
$143$	−1.97575	−	3.42210i	−0.165220	−	0.286170i
$144$	−1.02391	−	2.81986i	−0.0853258	−	0.234988i
$145$	26.4554	+	15.2740i	2.19700	+	1.26844i
$146$	−0.754181	+	0.632833i	−0.0624165	+	0.0523737i
$147$	−10.8616	−	5.38757i	−0.895849	−	0.444359i
$148$	0.410148	−	2.32607i	0.0337140	−	0.191202i
$149$	4.12041	+	0.726540i	0.337557	+	0.0595205i	0.339858	−	0.940477i	$-0.389621\pi$
$149$	4.12041	+	0.726540i	0.337557	+	0.0595205i	−0.00230036	+	0.999997i	$0.500732\pi$
$150$	−18.9270	−	13.2636i	−1.54539	−	1.08297i
$151$	−4.88547	+	4.09940i	−0.397574	+	0.333604i	−0.819555	−	0.573000i	$-0.805779\pi$
$151$	−4.88547	+	4.09940i	−0.397574	+	0.333604i	0.421981	+	0.906605i	$0.361335\pi$
$152$	0.849827	−	1.47194i	0.0689301	−	0.119390i
$153$	12.5940	+	15.0322i	1.01816	+	1.21528i
$154$	−3.69059	−	10.5270i	−0.297396	−	0.848293i
$155$	12.1781	−	33.4590i	0.978167	−	2.68749i
$156$	1.14827	−	1.14739i	0.0919351	−	0.0918650i
$157$	−0.0375671	+	0.0447707i	−0.00299818	+	0.00357309i	−0.767541	−	0.640999i	$-0.778520\pi$
$157$	−0.0375671	+	0.0447707i	−0.00299818	+	0.00357309i	0.764543	+	0.644572i	$0.222965\pi$
$158$	−1.74353	−	4.79030i	−0.138707	−	0.381095i
$159$	8.15783	+	11.6600i	0.646958	+	0.924702i
$160$	4.21788	−	0.743726i	0.333453	−	0.0587967i
$161$	−1.42796	+	7.57155i	−0.112539	+	0.596722i
$162$	−7.78736	−	4.51188i	−0.611832	−	0.354487i
$163$	9.00382			0.705234			0.352617	−	0.935768i	$-0.385292\pi$
$163$	9.00382			0.705234			0.352617	+	0.935768i	$0.385292\pi$
$164$	−0.947038	−	5.37092i	−0.0739512	−	0.419398i
$165$	−17.9303	−	25.6279i	−1.39587	−	1.99513i
$166$	−0.778875	−	2.13994i	−0.0604524	−	0.166092i
$167$	4.82090	+	4.04521i	0.373052	+	0.313028i	0.809968	−	0.586475i	$-0.199485\pi$
$167$	4.82090	+	4.04521i	0.373052	+	0.313028i	−0.436915	+	0.899503i	$0.643929\pi$
$168$	3.78575	−	2.58226i	0.292077	−	0.199226i
$169$	−11.3906	−	4.14585i	−0.876202	−	0.318912i
$170$	−24.2461	+	13.9985i	−1.85959	+	1.07364i
$171$	−0.881596	−	5.02217i	−0.0674173	−	0.384055i
$172$	−2.22369	+	3.85154i	−0.169555	+	0.293677i
$173$	6.80187	−	5.70744i	0.517136	−	0.433929i	−0.346496	−	0.938052i	$-0.612628\pi$
$173$	6.80187	−	5.70744i	0.517136	−	0.433929i	0.863632	+	0.504123i	$0.168184\pi$
$174$	−7.08973	+	10.1170i	−0.537471	+	0.766966i
$175$	12.4677	−	33.0291i	0.942466	−	2.49677i
$176$	4.15222	+	0.732149i	0.312986	+	0.0551878i
$177$	13.6177	+	1.19663i	1.02357	+	0.0899439i
$178$	−1.58067	−	1.88376i	−0.118476	−	0.141194i
$179$	22.4768	+	12.9770i	1.67999	+	0.969945i	0.961659	+	0.274247i	$0.0884284\pi$
$179$	22.4768	+	12.9770i	1.67999	+	0.969945i	0.718334	+	0.695698i	$0.244905\pi$
$180$	8.26658	−	9.83648i	0.616154	−	0.733168i
$181$	−14.6761	+	8.47327i	−1.09087	+	0.629813i	−0.933808	−	0.357775i	$-0.883535\pi$
$181$	−14.6761	+	8.47327i	−1.09087	+	0.629813i	−0.157061	+	0.987589i	$0.550202\pi$
$182$	2.13253	+	1.26521i	0.158073	+	0.0937834i
$183$	3.05269	+	11.4102i	0.225662	+	0.843467i
$184$	−2.23090	−	1.87194i	−0.164464	−	0.138002i
$185$	9.50603	−	3.45991i	0.698897	−	0.254378i
$186$	13.0480	+	6.09044i	0.956726	+	0.446573i
$187$	−27.1425	+	4.78596i	−1.98486	+	0.349984i
$188$	−0.171843			−0.0125329
$189$	3.73072	−	13.2318i	0.271370	−	0.962475i
$190$	7.27953			0.528113
$191$	−15.8829	+	2.80059i	−1.14925	+	0.202643i	−0.715647	−	0.698462i	$-0.753868\pi$
$191$	−15.8829	+	2.80059i	−1.14925	+	0.202643i	−0.433601	+	0.901105i	$0.642757\pi$
$192$	0.150300	+	1.72552i	0.0108470	+	0.124528i
$193$	−3.29167	+	1.19807i	−0.236940	+	0.0862391i	−0.457761	−	0.889075i	$-0.651348\pi$
$193$	−3.29167	+	1.19807i	−0.236940	+	0.0862391i	0.220821	+	0.975314i	$0.429126\pi$
$194$	−1.82512	−	1.53146i	−0.131036	−	0.109952i
$195$	6.71483	+	1.80198i	0.480859	+	0.129042i
$196$	5.25397	+	4.62556i	0.375283	+	0.330397i
$197$	−10.5666	+	6.10064i	−0.752841	+	0.434653i	−0.826719	−	0.562614i	$-0.809796\pi$
$197$	−10.5666	+	6.10064i	−0.752841	+	0.434653i	0.0738786	+	0.997267i	$0.476462\pi$
$198$	10.9590	−	6.31606i	0.778825	−	0.448863i
$199$	−4.38581	−	2.53215i	−0.310902	−	0.179499i	0.336428	−	0.941709i	$-0.390781\pi$
$199$	−4.38581	−	2.53215i	−0.310902	−	0.179499i	−0.647330	+	0.762210i	$0.724114\pi$
$200$	8.57711	+	10.2218i	0.606493	+	0.722791i
$201$	2.18649	+	4.69362i	0.154223	+	0.331062i
$202$	9.11004	+	1.60635i	0.640980	+	0.113022i
$203$	−17.6549	−	6.66427i	−1.23913	−	0.467740i
$204$	−4.78104	−	10.2632i	−0.334740	−	0.718568i
$205$	17.8934	−	15.0144i	1.24973	−	1.04865i
$206$	5.39321	−	9.34131i	0.375763	−	0.650840i
$207$	−8.73668	−	0.00666360i	−0.607241	−	0.000463152i
$208$	−0.811639	+	0.468600i	−0.0562771	+	0.0324916i
$209$	6.73404	+	2.45099i	0.465803	+	0.169539i
$210$	17.6851	+	8.51204i	1.22038	+	0.587387i
$211$	2.94533	+	2.47142i	0.202765	+	0.170140i	0.738516	−	0.674236i	$-0.235527\pi$
$211$	2.94533	+	2.47142i	0.202765	+	0.170140i	−0.535751	+	0.844376i	$0.679971\pi$
$212$	−2.81003	−	7.72049i	−0.192994	−	0.530246i
$213$	10.5262	−	0.916880i	0.721245	−	0.0628236i
$214$	1.80580	+	10.2412i	0.123442	+	0.700073i
$215$	−19.0479			−1.29905
$216$	3.67003	+	3.67844i	0.249714	+	0.250286i
$217$	−4.07638	+	21.6145i	−0.276723	+	1.46729i
$218$	−7.06466	+	1.24569i	−0.478479	+	0.0843688i
$219$	0.721250	−	1.54519i	0.0487375	−	0.104414i
$220$	6.17623	+	16.9691i	0.416401	+	1.14405i
$221$	3.93794	−	4.69306i	0.264895	−	0.315689i
$222$	1.05733	+	3.95202i	0.0709631	+	0.265242i
$223$	1.13390	−	3.11537i	0.0759317	−	0.208621i	−0.895919	−	0.444217i	$-0.853482\pi$
$223$	1.13390	−	3.11537i	0.0759317	−	0.208621i	0.971851	+	0.235596i	$0.0757043\pi$
$224$	−2.49676	+	0.875320i	−0.166822	+	0.0584848i
$225$	39.4174	+	6.98135i	2.62783	+	0.465423i
$226$	6.66608	−	11.5460i	0.443421	−	0.768028i
$227$	−20.8175	+	17.4680i	−1.38171	+	1.15939i	−0.413130	+	0.910672i	$0.635564\pi$
$227$	−20.8175	+	17.4680i	−1.38171	+	1.15939i	−0.968576	+	0.248717i	$0.919991\pi$
$228$	−0.257695	+	2.93259i	−0.0170663	+	0.194215i
$229$	−18.9625	−	3.34360i	−1.25308	−	0.220951i	−0.492565	−	0.870276i	$-0.663941\pi$
$229$	−18.9625	−	3.34360i	−1.25308	−	0.220951i	−0.760511	+	0.649325i	$0.775052\pi$
$230$	2.16590	−	12.2834i	0.142815	−	0.809945i
$231$	13.4939	+	13.8287i	0.887831	+	0.909861i
$232$	5.46381	−	4.58468i	0.358716	−	0.300999i
$233$	−24.1282	−	13.9304i	−1.58069	−	0.912612i	−0.994759	−	0.102251i	$-0.967396\pi$
$233$	−24.1282	−	13.9304i	−1.58069	−	0.912612i	−0.585931	−	0.810361i	$-0.699271\pi$
$234$	−0.963639	+	2.64131i	−0.0629951	+	0.172668i
$235$	−0.367997	−	0.637390i	−0.0240055	−	0.0415787i
$236$	−7.41649	−	2.69938i	−0.482772	−	0.175715i
$237$	6.24103	+	6.24579i	0.405399	+	0.405708i
$238$	13.3797	−	10.9589i	0.867278	−	0.710358i
$239$	5.15973	+	14.1762i	0.333755	+	0.916984i	0.987126	+	0.159946i	$0.0511321\pi$
$239$	5.15973	+	14.1762i	0.333755	+	0.916984i	−0.653371	+	0.757038i	$0.726646\pi$
$240$	−6.07832	+	4.25263i	−0.392354	+	0.274506i
$241$	3.06738	−	0.540862i	0.197587	−	0.0348400i	−0.0739785	−	0.997260i	$-0.523570\pi$
$241$	3.06738	−	0.540862i	0.197587	−	0.0348400i	0.271566	+	0.962420i	$0.412459\pi$
$242$			6.77700i			0.435642i
$243$	15.5265	+	1.38823i	0.996027	+	0.0890551i
$244$		−	6.81938i		−	0.436566i
$245$	−5.90562	+	29.3932i	−0.377296	+	1.87786i
$246$	5.41517	+	7.73995i	0.345259	+	0.493481i
$247$	−1.49685	+	0.544810i	−0.0952425	+	0.0346654i
$248$	−6.36852	−	5.34383i	−0.404402	−	0.339333i
$249$	2.78802	+	2.79015i	0.176684	+	0.176818i
$250$	−12.2222	+	33.5802i	−0.772999	+	2.12380i
$251$	9.77652	+	16.9334i	0.617088	+	1.06883i	0.990014	+	0.140967i	$0.0450212\pi$
$251$	9.77652	+	16.9334i	0.617088	+	1.06883i	−0.372926	+	0.927861i	$0.621645\pi$
$252$	−4.05516	+	6.82317i	−0.255451	+	0.429819i
$253$	6.13938	−	10.6337i	0.385980	−	0.668536i
$254$	11.5830	+	13.8041i	0.726785	+	0.866149i
$255$	27.8292	−	39.7119i	1.74273	−	2.48686i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	2.88017	−	16.3342i	0.179660	−	1.01890i	−0.752966	−	0.658059i	$-0.771378\pi$
$257$	2.88017	−	16.3342i	0.179660	−	1.01890i	0.932626	−	0.360843i	$-0.117511\pi$
$258$	0.674294	−	7.67351i	0.0419797	−	0.477732i
$259$	−5.44862	+	3.06009i	−0.338561	+	0.190145i
$260$	−3.47621	−	2.00699i	−0.215585	−	0.124468i
$261$	3.73170	−	21.0696i	0.230987	−	1.30417i
$262$	3.66032	−	2.11329i	0.226135	−	0.130559i
$263$	−4.43602	+	12.1879i	−0.273537	+	0.751536i	0.724522	+	0.689252i	$0.242061\pi$
$263$	−4.43602	+	12.1879i	−0.273537	+	0.751536i	−0.998058	+	0.0622842i	$0.980161\pi$
$264$	−7.05469	+	1.88742i	−0.434186	+	0.116162i
$265$	22.6188	−	26.9560i	1.38946	−	1.65589i
$266$	−4.43751	+	0.728240i	−0.272081	+	0.0446513i
$267$	3.85951	+	1.80151i	0.236198	+	0.110251i
$268$	−0.519116	−	2.94405i	−0.0317101	−	0.179837i
$269$	−6.74975			−0.411540			−0.205770	−	0.978600i	$-0.565970\pi$
$269$	−6.74975			−0.411540			−0.205770	+	0.978600i	$0.565970\pi$
$270$	−5.78457	+	21.4899i	−0.352037	+	1.30783i
$271$		−	3.05291i		−	0.185451i	−0.995692	−	0.0927254i	$-0.970442\pi$
$271$		−	3.05291i		−	0.185451i	0.995692	−	0.0927254i	$-0.0295579\pi$
$272$	1.13511	+	6.43755i	0.0688264	+	0.390334i
$273$	−4.27354	−	0.426714i	−0.258646	−	0.0258259i
$274$	−15.2977	+	5.56791i	−0.924168	+	0.336369i
$275$	−36.1635	+	43.0980i	−2.18074	+	2.59891i
$276$	4.87175	+	1.30737i	0.293245	+	0.0786947i
$277$	6.03800	+	2.19765i	0.362788	+	0.132044i	0.516982	−	0.855997i	$-0.327056\pi$
$277$	6.03800	+	2.19765i	0.362788	+	0.132044i	−0.154193	+	0.988041i	$0.549278\pi$
$278$	4.58092	+	7.93439i	0.274746	+	0.475873i
$279$	−24.9405	−	0.0190225i	−1.49315	−	0.00113885i
$280$	−8.59343	−	7.38636i	−0.513556	−	0.441420i
$281$	8.20909	+	9.78322i	0.489714	+	0.583618i	0.953145	−	0.302515i	$-0.0978263\pi$
$281$	8.20909	+	9.78322i	0.489714	+	0.583618i	−0.463431	+	0.886133i	$0.653382\pi$
$282$	0.269802	−	0.125686i	0.0160665	−	0.00748446i
$283$	−12.3371	−	2.17537i	−0.733365	−	0.129312i	−0.205520	−	0.978653i	$-0.565889\pi$
$283$	−12.3371	−	2.17537i	−0.733365	−	0.129312i	−0.527845	+	0.849341i	$0.677000\pi$
$284$	−6.00765	−	1.05931i	−0.356488	−	0.0628585i
$285$	−11.4292	+	5.32423i	−0.677009	+	0.315380i
$286$	−2.53997	−	3.02702i	−0.150192	−	0.178992i
$287$	−9.40557	+	10.9426i	−0.555193	+	0.645922i
$288$	−1.49802	−	2.59922i	−0.0882716	−	0.153160i
$289$	−12.8653	−	22.2833i	−0.756781	−	1.31078i
$290$	28.7058	+	10.4481i	1.68566	+	0.613531i
$291$	3.98563	+	1.06958i	0.233642	+	0.0626996i
$292$	−0.632833	+	0.754181i	−0.0370338	+	0.0441351i
$293$	6.81576	−	2.48073i	0.398181	−	0.144926i	−0.135165	−	0.990823i	$-0.543157\pi$
$293$	6.81576	−	2.48073i	0.398181	−	0.144926i	0.533346	+	0.845897i	$0.320934\pi$
$294$	−11.6321	−	3.41962i	−0.678399	−	0.199437i
$295$	−5.86983	−	33.2894i	−0.341755	−	1.93819i
$296$		−	2.36195i		−	0.137286i
$297$	−12.5867	+	17.9319i	−0.730353	+	1.04052i
$298$	4.18398			0.242371
$299$	0.473945	+	2.68788i	0.0274090	+	0.155444i
$300$	−20.9427	−	9.77547i	−1.20913	−	0.564387i
$301$	11.6113	−	1.90554i	0.669266	−	0.109833i
$302$	−4.09940	+	4.88547i	−0.235894	+	0.281127i
$303$	−15.4781	+	4.14102i	−0.889194	+	0.237895i
$304$	0.581316	−	1.59715i	0.0333408	−	0.0916030i
$305$	25.2940	−	14.6035i	1.44833	−	0.836195i
$306$	15.0130	+	12.6169i	0.858234	+	0.721260i
$307$	−17.2164	−	9.93987i	−0.982589	−	0.567298i	−0.0795384	−	0.996832i	$-0.525345\pi$
$307$	−17.2164	−	9.93987i	−0.982589	−	0.567298i	−0.903051	+	0.429534i	$0.858678\pi$
$308$	−5.46252	−	9.72625i	−0.311256	−	0.554204i
$309$	−1.63540	+	18.6109i	−0.0930344	+	1.05874i
$310$	6.18298	−	35.0654i	0.351169	−	1.99158i
$311$	0.232541	−	1.31880i	0.0131862	−	0.0747825i	−0.977505	−	0.210914i	$-0.932356\pi$
$311$	0.232541	−	1.31880i	0.0131862	−	0.0747825i	0.990691	+	0.136132i	$0.0434670\pi$
$312$	0.931581	−	1.32936i	0.0527404	−	0.0752600i
$313$	15.0793	+	17.9708i	0.852333	+	1.01577i	0.999644	+	0.0266804i	$0.00849363\pi$
$313$	15.0793	+	17.9708i	0.852333	+	1.01577i	−0.147311	+	0.989090i	$0.547062\pi$
$314$	−0.0292220	+	0.0506140i	−0.00164909	+	0.00285631i
$315$	−33.9921	−	0.429523i	−1.91524	−	0.0242009i
$316$	−2.54886	−	4.41476i	−0.143385	−	0.248350i
$317$	0.895561	−	2.46053i	0.0502997	−	0.138197i	−0.911999	−	0.410193i	$-0.865461\pi$
$317$	0.895561	−	2.46053i	0.0502997	−	0.138197i	0.962299	+	0.271996i	$0.0876836\pi$
$318$	10.0586	+	10.0663i	0.564060	+	0.564491i
$319$	23.0369	+	19.3303i	1.28982	+	1.08229i
$320$	4.02465	−	1.46485i	0.224985	−	0.0818878i
$321$	−10.3256	−	14.7584i	−0.576317	−	0.823735i
$322$	−0.0914763	+	7.70449i	−0.00509777	+	0.429354i
$323$			11.1104i			0.618200i
$324$	−8.45253	−	3.09108i	−0.469585	−	0.171727i
$325$		−	12.5056i		−	0.693688i
$326$	8.86704	−	1.56350i	0.491100	−	0.0865941i
$327$	10.1808	−	7.12288i	0.562998	−	0.393896i
$328$	−1.86530	−	5.12487i	−0.102994	−	0.282974i
$329$	0.288090	+	0.351730i	0.0158829	+	0.0193915i
$330$	−22.1081	−	22.1250i	−1.21701	−	1.21794i
$331$	9.48568	+	3.45250i	0.521380	+	0.189767i	0.589285	−	0.807925i	$-0.299409\pi$
$331$	9.48568	+	3.45250i	0.521380	+	0.189767i	−0.0679054	+	0.997692i	$0.521632\pi$
$332$	−1.13864	−	1.97218i	−0.0624909	−	0.108237i
$333$	−4.55056	−	5.43155i	−0.249369	−	0.297647i
$334$	5.45010	+	3.14662i	0.298216	+	0.172175i
$335$	9.80823	−	8.23009i	0.535881	−	0.449658i
$336$	3.27983	−	3.20042i	0.178930	−	0.174597i
$337$	0.261659	−	1.48394i	0.0142535	−	0.0808354i	−0.976851	−	0.213920i	$-0.931377\pi$
$337$	0.261659	−	1.48394i	0.0142535	−	0.0808354i	0.991105	+	0.133084i	$0.0424881\pi$
$338$	−11.9375	−	2.10490i	−0.649314	−	0.114492i
$339$	−2.02137	+	23.0033i	−0.109786	+	1.24937i
$340$	−21.4470	+	17.9961i	−1.16312	+	0.975977i
$341$	17.5261	−	30.3560i	0.949089	−	1.64387i
$342$	−1.74029	−	4.79279i	−0.0941043	−	0.259164i
$343$	0.659509	−	18.5085i	0.0356102	−	0.999366i
$344$	−1.52109	+	4.17917i	−0.0820118	+	0.225326i
$345$	5.58349	+	20.8697i	0.300605	+	1.12359i
$346$	5.70744	−	6.80187i	0.306834	−	0.365671i
$347$	−2.41952	−	6.64759i	−0.129887	−	0.356861i	0.857653	−	0.514228i	$-0.171922\pi$
$347$	−2.41952	−	6.64759i	−0.129887	−	0.356861i	−0.987540	+	0.157367i	$0.949699\pi$
$348$	−5.22523	+	11.1944i	−0.280102	+	0.600082i
$349$	4.74497	−	0.836667i	0.253993	−	0.0447857i	−0.0452020	−	0.998978i	$-0.514393\pi$
$349$	4.74497	−	0.836667i	0.253993	−	0.0447857i	0.299195	+	0.954192i	$0.403282\pi$
$350$	6.54280	−	34.6923i	0.349727	−	1.85438i
$351$	−0.418884	−	4.85179i	−0.0223584	−	0.258969i
$352$	4.21628			0.224728
$353$	−5.48436	−	31.1034i	−0.291903	−	1.65547i	−0.679529	−	0.733648i	$-0.737816\pi$
$353$	−5.48436	−	31.1034i	−0.291903	−	1.65547i	0.387626	−	0.921817i	$-0.373295\pi$
$354$	13.6186	−	1.18624i	0.723820	−	0.0630479i
$355$	−8.93608	−	24.5517i	−0.474278	−	1.30307i
$356$	−1.88376	−	1.58067i	−0.0998393	−	0.0837751i
$357$	−12.9915	+	26.9919i	−0.687585	+	1.42856i
$358$	24.3887	+	8.87677i	1.28898	+	0.469152i
$359$	22.5683	−	13.0298i	1.19111	−	0.687686i	0.232550	−	0.972585i	$-0.425293\pi$
$359$	22.5683	−	13.0298i	1.19111	−	0.687686i	0.958558	+	0.284898i	$0.0919599\pi$
$360$	6.43290	−	11.1225i	0.339044	−	0.586208i
$361$	−8.05559	+	13.9527i	−0.423978	+	0.734352i
$362$	−12.9818	+	10.8930i	−0.682309	+	0.572525i
$363$	−4.95668	−	10.6402i	−0.260158	−	0.558468i
$364$	2.31983	+	0.875676i	0.121592	+	0.0458979i
$365$	−4.15256	−	0.732208i	−0.217355	−	0.0383255i
$366$	4.98768	+	10.7068i	0.260710	+	0.559652i
$367$	−7.50882	−	8.94866i	−0.391957	−	0.467116i	0.533593	−	0.845741i	$-0.320841\pi$
$367$	−7.50882	−	8.94866i	−0.391957	−	0.467116i	−0.925550	+	0.378625i	$0.876397\pi$
$368$	−2.52206	−	1.45611i	−0.131472	−	0.0759052i
$369$	−14.1631	−	8.19146i	−0.737300	−	0.426431i
$370$	8.76080	−	5.05805i	0.455452	−	0.262956i
$371$	−11.0914	+	18.6948i	−0.575839	+	0.970586i
$372$	13.9074	+	3.73215i	0.721063	+	0.193503i
$373$	19.6733	+	16.5078i	1.01864	+	0.854742i	0.989456	−	0.144832i	$-0.0462640\pi$
$373$	19.6733	+	16.5078i	1.01864	+	0.854742i	0.0291861	+	0.999574i	$0.490708\pi$
$374$	−25.8991	+	9.42649i	−1.33921	+	0.487432i
$375$	−5.37102	−	61.6618i	−0.277358	−	3.18420i
$376$	−0.169232	+	0.0298402i	−0.00872749	+	0.00153889i
$377$	−6.68458			−0.344273
$378$	1.37636	−	13.6787i	0.0707921	−	0.703554i
$379$	−8.63096			−0.443343			−0.221671	−	0.975121i	$-0.571151\pi$
$379$	−8.63096			−0.443343			−0.221671	+	0.975121i	$0.571151\pi$
$380$	7.16894	−	1.26408i	0.367759	−	0.0648458i
$381$	−28.2823	−	13.2014i	−1.44895	−	0.676327i
$382$	−15.1553	+	5.51608i	−0.775413	+	0.282227i
$383$	23.7246	+	19.9073i	1.21227	+	1.01721i	0.999193	+	0.0401784i	$0.0127926\pi$
$383$	23.7246	+	19.9073i	1.21227	+	1.01721i	0.213076	+	0.977036i	$0.431652\pi$
$384$	0.447650	+	1.67320i	0.0228440	+	0.0853853i
$385$	24.3782	−	41.0898i	1.24243	−	2.09413i
$386$	−3.03362	+	1.75146i	−0.154407	+	0.0891471i
$387$	4.55371	+	12.5410i	0.231478	+	0.637494i
$388$	−2.06332	−	1.19126i	−0.104749	−	0.0604771i
$389$	10.0823	+	12.0156i	0.511191	+	0.609213i	0.958474	−	0.285179i	$-0.0920530\pi$
$389$	10.0823	+	12.0156i	0.511191	+	0.609213i	−0.447284	+	0.894392i	$0.647609\pi$
$390$	6.92573	+	0.608584i	0.350698	+	0.0308169i
$391$	18.7476	+	3.30571i	0.948108	+	0.167177i
$392$	5.97737	+	3.64295i	0.301903	+	0.183997i
$393$	−4.20123	+	5.99511i	−0.211924	+	0.302413i
$394$	−9.34673	+	7.84284i	−0.470881	+	0.395116i
$395$	10.9166	−	18.9082i	0.549276	−	0.951374i
$396$	9.69577	−	8.12312i	0.487231	−	0.408202i
$397$	−29.0034	+	16.7451i	−1.45564	+	0.840413i	−0.998792	−	0.0491327i	$-0.984354\pi$
$397$	−29.0034	+	16.7451i	−1.45564	+	0.840413i	−0.456846	+	0.889546i	$0.651021\pi$
$398$	−4.75888	−	1.73209i	−0.238541	−	0.0868219i
$399$	6.43447	−	4.38895i	0.322127	−	0.219723i
$400$	10.2218	+	8.57711i	0.511090	+	0.428856i
$401$	−0.346612	−	0.952308i	−0.0173090	−	0.0475560i	0.930737	−	0.365689i	$-0.119166\pi$
$401$	−0.346612	−	0.952308i	−0.0173090	−	0.0475560i	−0.948046	+	0.318133i	$0.896944\pi$
$402$	2.96831	+	4.24263i	0.148046	+	0.211603i
$403$	1.35297	+	7.67306i	0.0673961	+	0.382223i
$404$	9.25058			0.460234
$405$	−6.63562	−	37.9711i	−0.329726	−	1.88680i
$406$	−18.5439	−	3.49729i	−0.920318	−	0.173567i
$407$	9.80735	−	1.72930i	0.486132	−	0.0857182i
$408$	−6.49060	−	9.27706i	−0.321332	−	0.459283i
$409$	1.04409	+	2.86860i	0.0516267	+	0.141843i	0.962826	−	0.270123i	$-0.0870644\pi$
$409$	1.04409	+	2.86860i	0.0516267	+	0.141843i	−0.911199	+	0.411966i	$0.864842\pi$
$410$	15.0144	−	17.8934i	0.741507	−	0.883693i
$411$	19.9458	−	19.9306i	0.983854	−	0.983103i
$412$	3.68917	−	10.1359i	0.181752	−	0.499361i
$413$	6.90843	+	19.7056i	0.339942	+	0.969649i
$414$	−8.60511	+	1.51055i	−0.422918	+	0.0742393i
$415$	4.87673	−	8.44674i	0.239389	−	0.414634i
$416$	−0.717937	+	0.602421i	−0.0351998	+	0.0295361i
$417$	−12.9955	−	9.10692i	−0.636391	−	0.445968i
$418$	7.05735	+	1.24440i	0.345186	+	0.0608656i
$419$	0.989706	−	5.61290i	0.0483503	−	0.274208i	−0.951042	−	0.309061i	$-0.899985\pi$
$419$	0.989706	−	5.61290i	0.0483503	−	0.274208i	0.999392	+	0.0348530i	$0.0110963\pi$
$420$	18.8945	+	5.31175i	0.921956	+	0.259187i
$421$	−21.7564	+	18.2558i	−1.06034	+	0.889735i	−0.994143	−	0.108072i	$-0.965532\pi$
$421$	−21.7564	+	18.2558i	−1.06034	+	0.889735i	−0.0662013	+	0.997806i	$0.521088\pi$
$422$	3.32974	+	1.92243i	0.162089	+	0.0935822i
$423$	−0.331677	+	0.394665i	−0.0161267	+	0.0191893i
$424$	−4.10799	−	7.11524i	−0.199502	−	0.345547i
$425$	−81.9650	−	29.8328i	−3.97589	−	1.44711i
$426$	10.2071	−	2.73081i	0.494535	−	0.132308i
$427$	−13.9580	+	11.4325i	−0.675474	+	0.553258i
$428$	3.55673	+	9.77203i	0.171921	+	0.472349i
$429$	6.20184	+	2.89485i	0.299428	+	0.139765i
$430$	−18.7585	+	3.30763i	−0.904615	+	0.159508i
$431$			18.2402i			0.878597i	0.898341	+	0.439299i	$0.144773\pi$
$431$			18.2402i			0.878597i	−0.898341	+	0.439299i	$0.855227\pi$
$432$	4.25303	+	2.98526i	0.204624	+	0.143628i
$433$		−	2.65984i		−	0.127824i	−0.997956	−	0.0639119i	$-0.979642\pi$
$433$		−	2.65984i		−	0.127824i	0.997956	−	0.0639119i	$-0.0203576\pi$
$434$	−0.261137	+	21.9940i	−0.0125350	+	1.05574i
$435$	−52.7112	+	4.59138i	−2.52731	+	0.220140i
$436$	−6.74102	+	2.45353i	−0.322836	+	0.117503i
$437$	−3.79175	−	3.18166i	−0.181384	−	0.152199i
$438$	0.441974	−	1.64696i	0.0211183	−	0.0786946i
$439$	−6.16869	+	16.9483i	−0.294416	+	0.808900i	0.700992	+	0.713169i	$0.252741\pi$
$439$	−6.16869	+	16.9483i	−0.294416	+	0.808900i	−0.995407	+	0.0957306i	$0.969481\pi$
$440$	9.02904	+	15.6388i	0.430443	+	0.745549i
$441$	20.7641	−	3.13872i	0.988767	−	0.149463i
$442$	3.06317	−	5.30557i	0.145700	−	0.252360i
$443$	−14.1761	−	16.8944i	−0.673526	−	0.802678i	0.315733	−	0.948848i	$-0.397750\pi$
$443$	−14.1761	−	16.8944i	−0.673526	−	0.802678i	−0.989259	+	0.146171i	$0.953305\pi$
$444$	1.72752	+	3.70838i	0.0819847	+	0.175992i
$445$	1.82888	−	10.3721i	0.0866973	−	0.491685i
$446$	0.575697	−	3.26494i	0.0272600	−	0.154599i
$447$	−6.56905	+	3.06015i	−0.310705	+	0.144740i
$448$	−2.30683	+	1.29558i	−0.108988	+	0.0612104i
$449$	−26.7178	−	15.4255i	−1.26089	−	0.727975i	−0.287643	−	0.957738i	$-0.592872\pi$
$449$	−26.7178	−	15.4255i	−1.26089	−	0.727975i	−0.973247	+	0.229763i	$0.926205\pi$
$450$	40.0308	+	0.0305321i	1.88707	+	0.00143930i
$451$	19.9139	−	11.4973i	0.937710	−	0.541387i
$452$	4.55987	−	12.5281i	0.214478	−	0.589274i
$453$	2.86304	−	10.6687i	0.134517	−	0.501261i
$454$	−17.4680	+	20.8175i	−0.819812	+	0.977014i
$455$	1.71984	+	10.4798i	0.0806275	+	0.491301i
$456$	0.255458	+	2.93278i	0.0119629	+	0.137340i
$457$	0.828717	+	4.69989i	0.0387658	+	0.219852i	0.998036	−	0.0626373i	$-0.0199511\pi$
$457$	0.828717	+	4.69989i	0.0387658	+	0.219852i	−0.959271	+	0.282489i	$0.908840\pi$
$458$	−19.2550			−0.899727
$459$	−32.7991	−	8.82871i	−1.53093	−	0.412089i
$460$		−	12.4729i		−	0.581552i
$461$	−5.02400	−	28.4925i	−0.233991	−	1.32703i	−0.844728	−	0.535195i	$-0.820238\pi$
$461$	−5.02400	−	28.4925i	−0.233991	−	1.32703i	0.610738	−	0.791833i	$-0.290873\pi$
$462$	15.6902	+	11.2754i	0.729974	+	0.524580i
$463$	8.54385	−	3.10971i	0.397066	−	0.144520i	−0.135767	−	0.990741i	$-0.543350\pi$
$463$	8.54385	−	3.10971i	0.397066	−	0.144520i	0.532833	+	0.846221i	$0.321127\pi$
$464$	4.58468	−	5.46381i	0.212838	−	0.253651i
$465$	15.9392	+	59.5767i	0.739161	+	2.76280i
$466$	−26.1806	−	9.52896i	−1.21279	−	0.441421i
$467$	−2.99174	−	5.18185i	−0.138441	−	0.239787i	0.788465	−	0.615079i	$-0.210876\pi$
$467$	−2.99174	−	5.18185i	−0.138441	−	0.239787i	−0.926907	+	0.375292i	$0.877543\pi$
$468$	−0.490341	+	2.76851i	−0.0226660	+	0.127975i
$469$	−5.15564	+	5.99816i	−0.238065	+	0.276969i
$470$	−0.473088	−	0.563804i	−0.0218219	−	0.0260063i
$471$	0.00886105	−	0.100839i	0.000408296	−	0.00464643i
$472$	−7.77256	−	1.37051i	−0.357761	−	0.0630829i
$473$	−18.4665	−	3.25614i	−0.849091	−	0.149718i
$474$	7.23079	+	5.06716i	0.332121	+	0.232743i
$475$	14.5781	+	17.3735i	0.668891	+	0.797153i
$476$	11.2735	−	13.1158i	0.516718	−	0.601159i
$477$	−23.1550	−	8.44775i	−1.06020	−	0.386796i
$478$	7.54302	+	13.0649i	0.345010	+	0.597574i
$479$	29.6142	+	10.7787i	1.35311	+	0.492491i	0.913917	−	0.405902i	$-0.133043\pi$
$479$	29.6142	+	10.7787i	1.35311	+	0.492491i	0.439192	+	0.898393i	$0.355265\pi$
$480$	−5.24752	+	5.24351i	−0.239515	+	0.239333i
$481$	−1.42289	+	1.69573i	−0.0648781	+	0.0773187i
$482$	2.92686	−	1.06529i	0.133315	−	0.0485226i
$483$	−5.49142	−	12.1633i	−0.249868	−	0.553451i
$484$	1.17681	+	6.67405i	0.0534916	+	0.303366i
$485$		−	10.2042i		−	0.463349i
$486$	15.5317	−	1.32901i	0.704532	−	0.0602851i
$487$	−6.21420			−0.281592			−0.140796	−	0.990039i	$-0.544966\pi$
$487$	−6.21420			−0.281592			−0.140796	+	0.990039i	$0.544966\pi$
$488$	−1.18417	−	6.71578i	−0.0536050	−	0.304009i
$489$	−12.7782	+	8.94010i	−0.577848	+	0.404285i
$490$	−0.711827	+	29.9722i	−0.0321570	+	1.35400i
$491$	9.93046	−	11.8347i	0.448156	−	0.534091i	−0.493913	−	0.869511i	$-0.664434\pi$
$491$	9.93046	−	11.8347i	0.448156	−	0.534091i	0.942069	+	0.335420i	$0.108878\pi$
$492$	6.67693	+	6.68203i	0.301019	+	0.301249i
$493$	−15.9464	+	43.8123i	−0.718189	+	1.97321i
$494$	−1.37951	+	0.796459i	−0.0620669	+	0.0358344i
$495$	50.8930	+	18.5675i	2.28747	+	0.834548i
$496$	−7.19972	−	4.15676i	−0.323277	−	0.186644i
$497$	7.90346	+	14.0724i	0.354519	+	0.631235i
$498$	3.23017	+	2.26362i	0.144747	+	0.101435i
$499$	5.22149	−	29.6125i	0.233746	−	1.32564i	−0.611493	−	0.791250i	$-0.709431\pi$
$499$	5.22149	−	29.6125i	0.233746	−	1.32564i	0.845239	−	0.534389i	$-0.179458\pi$
$500$	−6.20536	+	35.1924i	−0.277512	+	1.57385i
$501$	−10.8584	−	0.954156i	−0.485116	−	0.0426285i
$502$	12.5684	+	14.9785i	0.560957	+	0.668523i
$503$	2.00906	−	3.47979i	0.0895795	−	0.155156i	−0.817754	−	0.575568i	$-0.804781\pi$
$503$	2.00906	−	3.47979i	0.0895795	−	0.155156i	0.907333	+	0.420412i	$0.138114\pi$
$504$	−2.80872	+	7.42368i	−0.125110	+	0.330677i
$505$	19.8099	+	34.3117i	0.881527	+	1.52685i
$506$	4.19958	−	11.5383i	0.186694	−	0.512938i
$507$	20.2820	−	5.42626i	0.900755	−	0.240988i
$508$	13.8041	+	11.5830i	0.612460	+	0.513915i
$509$	18.7699	−	6.83170i	0.831962	−	0.302810i	0.109298	−	0.994009i	$-0.465140\pi$
$509$	18.7699	−	6.83170i	0.831962	−	0.302810i	0.722664	+	0.691199i	$0.242917\pi$
$510$	20.5105	−	43.9411i	0.908219	−	1.94574i
$511$	2.60460	+	0.0309247i	0.115221	+	0.00136803i
$512$		−	1.00000i		−	0.0441942i
$513$	6.23778	+	6.25207i	0.275405	+	0.276036i
$514$		−	16.5862i		−	0.731587i
$515$	45.4958	−	8.02213i	2.00478	−	0.353497i
$516$	−0.668441	−	7.67402i	−0.0294265	−	0.337830i
$517$	−0.247807	−	0.680843i	−0.0108985	−	0.0299434i
$518$	−4.83447	+	3.95975i	−0.212414	+	0.173981i
$519$	−3.98610	+	14.8537i	−0.174971	+	0.652004i
$520$	−3.77191	−	1.37286i	−0.165409	−	0.0602040i
$521$	16.5672	+	28.6953i	0.725823	+	1.25716i	0.958634	+	0.284640i	$0.0918741\pi$
$521$	16.5672	+	28.6953i	0.725823	+	1.25716i	−0.232812	+	0.972522i	$0.574793\pi$
$522$	0.0163202	−	21.3975i	0.000714315	−	0.936542i
$523$	−10.6704	−	6.16053i	−0.466582	−	0.269381i	0.248226	−	0.968702i	$-0.420152\pi$
$523$	−10.6704	−	6.16053i	−0.466582	−	0.269381i	−0.714808	+	0.699321i	$0.753486\pi$
$524$	3.23774	−	2.71679i	0.141441	−	0.118683i
$525$	15.1014	+	59.2541i	0.659077	+	2.58606i
$526$	−2.25223	+	12.7730i	−0.0982018	+	0.556930i
$527$	53.5187	+	9.43679i	2.33131	+	0.411073i
$528$	−6.61977	+	3.08378i	−0.288088	+	0.134204i
$529$	11.1221	−	9.33259i	0.483572	−	0.405765i
$530$	17.5943	−	30.4742i	0.764247	−	1.32371i
$531$	−20.5142	+	11.8231i	−0.890242	+	0.513077i
$532$	−4.24363	+	1.48774i	−0.183985	+	0.0645018i
$533$	−1.74816	+	4.80303i	−0.0757212	+	0.208042i
$534$	4.11370	+	1.10394i	0.178017	+	0.0477723i
$535$	−28.6292	+	34.1189i	−1.23775	+	1.47509i
$536$	−1.02246	−	2.80918i	−0.0441635	−	0.121338i
$537$	−44.7840	+	3.90088i	−1.93257	+	0.168336i
$538$	−6.64721	+	1.17208i	−0.286581	+	0.0505320i
$539$	−10.7500	+	27.4866i	−0.463036	+	1.18393i
$540$	−1.96500	+	22.1679i	−0.0845601	+	0.953955i
$541$	0.560016			0.0240770			0.0120385	−	0.999928i	$-0.496168\pi$
$541$	0.560016			0.0240770			0.0120385	+	0.999928i	$0.496168\pi$
$542$	−0.530132	−	3.00653i	−0.0227711	−	0.129141i
$543$	12.4150	−	26.5975i	0.532777	−	1.14141i
$544$	2.23574	+	6.14264i	0.0958565	+	0.263363i
$545$	−23.5362	−	19.7492i	−1.00818	−	0.845964i
$546$	−4.28271	+	0.321861i	−0.183283	+	0.0137744i
$547$	−20.1773	−	7.34395i	−0.862721	−	0.314005i	−0.127505	−	0.991838i	$-0.540697\pi$
$547$	−20.1773	−	7.34395i	−0.862721	−	0.314005i	−0.735216	+	0.677833i	$0.762919\pi$
$548$	−14.0984	+	8.13973i	−0.602255	+	0.347712i
$549$	−15.6618	−	13.1622i	−0.668430	−	0.561749i
$550$	−28.1302	+	48.7229i	−1.19948	+	2.07755i
$551$	9.28659	−	7.79237i	0.395622	−	0.331966i
$552$	5.02476	+	0.441541i	0.213868	+	0.0187932i
$553$	−4.76308	+	12.6183i	−0.202547	+	0.536584i
$554$	6.32789	+	1.11578i	0.268846	+	0.0474049i
$555$	−10.0555	+	14.3490i	−0.426830	+	0.609082i
$556$	5.88912	+	7.01838i	0.249754	+	0.297646i
$557$	17.8318	+	10.2952i	0.755559	+	0.436222i	0.827699	−	0.561172i	$-0.189649\pi$
$557$	17.8318	+	10.2952i	0.755559	+	0.436222i	−0.0721397	+	0.997395i	$0.522983\pi$
$558$	−24.5649	+	4.31215i	−1.03992	+	0.182548i
$559$	3.60967	−	2.08404i	0.152673	−	0.0881456i
$560$	−9.74550	−	5.78191i	−0.411823	−	0.244330i
$561$	33.7683	−	33.7426i	1.42570	−	1.42461i
$562$	9.78322	+	8.20909i	0.412680	+	0.346280i
$563$	−19.4745	+	7.08813i	−0.820752	+	0.298729i	−0.718057	−	0.695984i	$-0.754968\pi$
$563$	−19.4745	+	7.08813i	−0.820752	+	0.298729i	−0.102694	+	0.994713i	$0.532746\pi$
$564$	0.243878	−	0.170627i	0.0102691	−	0.00718468i
$565$	56.2334	−	9.91547i	2.36576	−	0.417147i
$566$	−12.5274			−0.526567
$567$	7.84359	+	22.4828i	0.329400	+	0.944191i
$568$	−6.10033			−0.255964
$569$	−30.0743	+	5.30292i	−1.26078	+	0.222310i	−0.763801	−	0.645452i	$-0.776669\pi$
$569$	−30.0743	+	5.30292i	−1.26078	+	0.222310i	−0.496981	+	0.867762i	$0.665558\pi$
$570$	−10.3310	+	7.22801i	−0.432720	+	0.302748i
$571$	−28.8754	+	10.5098i	−1.20840	+	0.439820i	−0.866147	−	0.499789i	$-0.833411\pi$
$571$	−28.8754	+	10.5098i	−1.20840	+	0.439820i	−0.342249	+	0.939609i	$0.611189\pi$
$572$	−3.02702	−	2.53997i	−0.126566	−	0.106202i
$573$	19.7602	−	19.7451i	0.825492	−	0.824863i
$574$	−7.36251	+	12.4096i	−0.307305	+	0.517968i
$575$	33.6534	−	19.4298i	1.40345	−	0.810280i
$576$	−1.92661	−	2.29960i	−0.0802754	−	0.0958168i
$577$	38.1505	+	22.0262i	1.58823	+	0.916963i	0.993599	+	0.112962i	$0.0360339\pi$
$577$	38.1505	+	22.0262i	1.58823	+	0.916963i	0.594628	+	0.804001i	$0.297299\pi$
$578$	−16.5393	−	19.7107i	−0.687943	−	0.819859i
$579$	3.48192	−	4.96867i	0.144704	−	0.206491i
$580$	30.0840	+	5.30462i	1.24917	+	0.220262i
$581$	−2.12778	+	5.63689i	−0.0882753	+	0.233858i
$582$	4.11081	+	0.361229i	0.170398	+	0.0149734i
$583$	26.5364	−	22.2667i	1.09903	−	0.922193i
$584$	−0.492257	+	0.852614i	−0.0203697	+	0.0352814i
$585$	−11.3189	+	4.10995i	−0.467977	+	0.169926i
$586$	6.28144	−	3.62659i	0.259484	−	0.149813i
$587$	11.4367	+	4.16262i	0.472044	+	0.171810i	0.567078	−	0.823664i	$-0.308074\pi$
$587$	11.4367	+	4.16262i	0.472044	+	0.171810i	−0.0950342	+	0.995474i	$0.530296\pi$
$588$	−12.0492	−	1.34778i	−0.496901	−	0.0555814i
$589$	−10.8243	−	9.08266i	−0.446007	−	0.374245i
$590$	−11.5613	−	31.7644i	−0.475971	−	1.30772i
$591$	8.93860	−	19.1498i	0.367685	−	0.787718i
$592$	−0.410148	−	2.32607i	−0.0168570	−	0.0956008i
$593$	29.6667			1.21826			0.609132	−	0.793069i	$-0.291518\pi$
$593$	29.6667			1.21826			0.609132	+	0.793069i	$0.291518\pi$
$594$	−9.28161	+	19.8452i	−0.380829	+	0.814257i
$595$	72.7900	+	13.7278i	2.98410	+	0.562786i
$596$	4.12041	−	0.726540i	0.168779	−	0.0297602i
$597$	8.73853	−	0.761165i	0.357644	−	0.0311524i
$598$	0.933490	+	2.56474i	0.0381732	+	0.104880i
$599$	21.8012	−	25.9816i	0.890772	−	1.06158i	−0.106960	−	0.994263i	$-0.534112\pi$
$599$	21.8012	−	25.9816i	0.890772	−	1.06158i	0.997732	−	0.0673173i	$-0.0214440\pi$
$600$	−22.3220	−	5.99029i	−0.911293	−	0.244553i
$601$	1.40098	−	3.84917i	0.0571472	−	0.157011i	−0.907834	−	0.419330i	$-0.862265\pi$
$601$	1.40098	−	3.84917i	0.0571472	−	0.157011i	0.964981	+	0.262319i	$0.0844873\pi$
$602$	11.1040	−	3.89288i	0.452567	−	0.158662i
$603$	−7.76345	−	4.49013i	−0.316152	−	0.182852i
$604$	−3.18877	+	5.52311i	−0.129749	+	0.224732i
$605$	−22.2349	+	18.6573i	−0.903975	+	0.758525i
$606$	−14.5239	+	6.76585i	−0.589992	+	0.274844i
$607$	−40.2011	−	7.08854i	−1.63171	−	0.287715i	−0.718600	−	0.695423i	$-0.755217\pi$
$607$	−40.2011	−	7.08854i	−1.63171	−	0.287715i	−0.913112	+	0.407708i	$0.866328\pi$
$608$	0.295142	−	1.67383i	0.0119696	−	0.0678829i
$609$	31.6728	−	8.07205i	1.28344	−	0.327096i
$610$	22.3739	−	18.7739i	0.905892	−	0.760134i
$611$	0.139475	+	0.0805257i	0.00564254	+	0.00325772i
$612$	16.9758	+	9.81824i	0.686205	+	0.396879i
$613$	7.18869	+	12.4512i	0.290348	+	0.502898i	0.973892	−	0.227012i	$-0.0728955\pi$
$613$	7.18869	+	12.4512i	0.290348	+	0.502898i	−0.683544	+	0.729910i	$0.739562\pi$
$614$	−18.6808	−	6.79927i	−0.753897	−	0.274396i
$615$	−10.4861	+	39.0751i	−0.422840	+	1.57566i
$616$	−7.06848	−	8.62992i	−0.284797	−	0.347710i
$617$	−11.9082	−	32.7175i	−0.479406	−	1.31716i	−0.909999	−	0.414611i	$-0.863918\pi$
$617$	−11.9082	−	32.7175i	−0.479406	−	1.31716i	0.430593	−	0.902546i	$-0.358305\pi$
$618$	1.62120	+	18.6121i	0.0652142	+	0.748690i
$619$	10.4750	−	1.84703i	0.421027	−	0.0742384i	0.0408789	−	0.999164i	$-0.486984\pi$
$619$	10.4750	−	1.84703i	0.421027	−	0.0742384i	0.380148	+	0.924926i	$0.375873\pi$
$620$		−	35.6063i		−	1.42999i
$621$	12.4056	−	8.66539i	0.497821	−	0.347730i
$622$		−	1.33915i		−	0.0536949i
$623$	−0.0772424	+	6.50566i	−0.00309465	+	0.260644i
$624$	0.686588	−	1.47093i	0.0274855	−	0.0588843i
$625$	−81.1275	+	29.5280i	−3.24510	+	1.18112i
$626$	17.9708	+	15.0793i	0.718258	+	0.602690i
$627$	−11.9905	+	3.20796i	−0.478856	+	0.128113i
$628$	−0.0199890	+	0.0549194i	−0.000797649	+	0.00219152i
$629$	7.71987	+	13.3712i	0.307811	+	0.533145i
$630$	−33.5503	+	5.47967i	−1.33668	+	0.218315i
$631$	−9.26818	+	16.0530i	−0.368960	+	0.639058i	−0.989403	−	0.145194i	$-0.953620\pi$
$631$	−9.26818	+	16.0530i	−0.368960	+	0.639058i	0.620443	+	0.784252i	$0.286953\pi$
$632$	−3.27676	−	3.90509i	−0.130342	−	0.155336i
$633$	−6.63391	−	0.582942i	−0.263674	−	0.0231698i
$634$	0.454688	−	2.57866i	0.0180580	−	0.102412i
$635$	−13.4020	+	76.0063i	−0.531840	+	3.01622i
$636$	11.6538	+	8.16672i	0.462104	+	0.323831i
$637$	−2.09679	−	6.21630i	−0.0830778	−	0.246299i
$638$	26.0436	+	15.0363i	1.03108	+	0.595292i
$639$	−14.0283	+	11.7529i	−0.554952	+	0.464939i
$640$	3.70914	−	2.14147i	0.146617	−	0.0846491i
$641$	8.39421	−	23.0629i	0.331551	−	0.910930i	−0.656157	−	0.754624i	$-0.727819\pi$
$641$	8.39421	−	23.0629i	0.331551	−	0.910930i	0.987709	−	0.156306i	$-0.0499585\pi$
$642$	−12.7315	−	12.7412i	−0.502471	−	0.502855i
$643$	9.57118	−	11.4065i	0.377450	−	0.449828i	−0.543557	−	0.839372i	$-0.682923\pi$
$643$	9.57118	−	11.4065i	0.377450	−	0.449828i	0.921008	+	0.389544i	$0.127367\pi$
$644$	1.24778	+	7.60332i	0.0491696	+	0.299613i
$645$	27.0326	−	18.9131i	1.06441	−	0.744701i
$646$	1.92930	+	10.9416i	0.0759074	+	0.430492i
$647$	33.0416			1.29900			0.649500	−	0.760361i	$-0.274978\pi$
$647$	33.0416			1.29900			0.649500	+	0.760361i	$0.274978\pi$
$648$	−8.86088	−	1.57635i	−0.348088	−	0.0619250i
$649$		−	33.2768i		−	1.30623i
$650$	−2.17158	−	12.3157i	−0.0851765	−	0.483060i
$651$	−15.6763	−	34.7226i	−0.614404	−	1.36089i
$652$	8.46083	−	3.07949i	0.331352	−	0.120602i
$653$	30.6634	−	36.5433i	1.19995	−	1.43005i	0.325087	−	0.945684i	$-0.394606\pi$
$653$	30.6634	−	36.5433i	1.19995	−	1.43005i	0.874866	−	0.484365i	$-0.160949\pi$
$654$	8.78924	−	8.78254i	0.343686	−	0.343424i
$655$	17.0105	+	6.19131i	0.664654	+	0.241914i
$656$	−2.72689	−	4.72311i	−0.106467	−	0.184406i
$657$	0.510658	+	2.90906i	0.0199227	+	0.113493i
$658$	0.344791	+	0.296360i	0.0134413	+	0.0115533i
$659$	−13.0065	−	15.5005i	−0.506660	−	0.603814i	0.450713	−	0.892669i	$-0.351170\pi$
$659$	−13.0065	−	15.5005i	−0.506660	−	0.603814i	−0.957373	+	0.288855i	$0.906725\pi$
$660$	−25.6142	−	17.9498i	−0.997032	−	0.698696i
$661$	24.5339	+	4.32600i	0.954260	+	0.168262i	0.629037	−	0.777376i	$-0.283450\pi$
$661$	24.5339	+	4.32600i	0.954260	+	0.168262i	0.325223	+	0.945637i	$0.394561\pi$
$662$	9.94109	+	1.75288i	0.386371	+	0.0681277i
$663$	−0.928854	+	10.5704i	−0.0360737	+	0.410521i
$664$	−1.46381	−	1.74450i	−0.0568067	−	0.0676996i
$665$	−14.6059	−	12.5543i	−0.566391	−	0.486834i
$666$	−5.42460	−	4.55884i	−0.210199	−	0.176651i
$667$	−10.3857	−	17.9886i	−0.402137	−	0.696521i
$668$	5.91370	+	2.15241i	0.228808	+	0.0832793i
$669$	1.48410	+	5.54718i	0.0573785	+	0.214466i
$670$	8.23009	−	9.80823i	0.317956	−	0.378925i
$671$	27.0184	−	9.83390i	1.04303	−	0.379634i
$672$	2.67426	−	3.72134i	0.103162	−	0.143554i
$673$	8.26627	+	46.8804i	0.318641	+	1.80711i	0.551033	+	0.834483i	$0.314234\pi$
$673$	8.26627	+	46.8804i	0.318641	+	1.80711i	−0.232392	+	0.972622i	$0.574655\pi$
$674$		−	1.50683i		−	0.0580410i
$675$	−62.8728	+	29.2305i	−2.41997	+	1.12508i
$676$	−12.1217			−0.466218
$677$	3.98108	+	22.5778i	0.153005	+	0.867736i	0.960587	+	0.277980i	$0.0896650\pi$
$677$	3.98108	+	22.5778i	0.153005	+	0.867736i	−0.807581	+	0.589756i	$0.799224\pi$
$678$	2.00383	+	23.0049i	0.0769565	+	0.883497i
$679$	1.02082	+	6.22035i	0.0391756	+	0.238715i
$680$	−17.9961	+	21.4470i	−0.690120	+	0.822453i
$681$	12.1997	−	45.4605i	0.467493	−	1.74205i
$682$	11.9885	−	32.9382i	0.459064	−	1.26127i
$683$	−32.2456	+	18.6170i	−1.23384	+	0.712359i	−0.967829	−	0.251610i	$-0.919040\pi$
$683$	−32.2456	+	18.6170i	−1.23384	+	0.712359i	−0.266014	+	0.963969i	$0.585707\pi$
$684$	−2.54611	−	4.41778i	−0.0973531	−	0.168918i
$685$	−60.3828	−	34.8620i	−2.30711	−	1.33201i
$686$	−2.56448	−	18.3418i	−0.0979123	−	0.700295i
$687$	30.2313	−	14.0831i	1.15340	−	0.537303i
$688$	−0.772279	+	4.37981i	−0.0294429	+	0.166979i
$689$	−1.33709	+	7.58304i	−0.0509392	+	0.288891i
$690$	9.12266	+	19.5831i	0.347294	+	0.745516i
$691$	−9.24229	−	11.0145i	−0.351593	−	0.419013i	0.561042	−	0.827787i	$-0.310401\pi$
$691$	−9.24229	−	11.0145i	−0.351593	−	0.419013i	−0.912635	+	0.408775i	$0.865956\pi$
$692$	4.43960	−	7.68962i	0.168768	−	0.292315i
$693$	−32.8812	−	6.22720i	−1.24905	−	0.236552i
$694$	−3.53711	−	6.12645i	−0.134267	−	0.232557i
$695$	−13.4208	+	36.8732i	−0.509079	+	1.39868i
$696$	−3.20196	+	11.9317i	−0.121370	+	0.452269i
$697$	27.3099	+	22.9157i	1.03444	+	0.867995i
$698$	4.52760	−	1.64791i	0.171372	−	0.0623744i
$699$	48.0743	−	4.18749i	1.81834	−	0.158385i
$700$	0.419138	−	35.3014i	0.0158419	−	1.33427i
$701$			9.05570i			0.342029i	0.985269	+	0.171015i	$0.0547045\pi$
$701$			9.05570i			0.342029i	−0.985269	+	0.171015i	$0.945295\pi$
$702$	−1.25502	−	4.70534i	−0.0473678	−	0.177592i
$703$		−	4.01450i		−	0.151410i
$704$	4.15222	−	0.732149i	0.156493	−	0.0275939i
$705$	1.15514	+	0.539185i	0.0435050	+	0.0203069i
$706$	−10.8021	−	29.6785i	−0.406542	−	1.11696i
$707$	−15.5084	−	18.9342i	−0.583252	−	0.712093i
$708$	13.2057	−	3.53306i	0.496301	−	0.132780i
$709$	−17.6092	−	6.40922i	−0.661327	−	0.240703i	−0.0105181	−	0.999945i	$-0.503348\pi$
$709$	−17.6092	−	6.40922i	−0.661327	−	0.240703i	−0.650809	+	0.759241i	$0.725570\pi$
$710$	−13.0637	−	22.6270i	−0.490271	−	0.849175i
$711$	−15.0588	−	2.66712i	−0.564750	−	0.100025i
$712$	−2.12963	−	1.22954i	−0.0798111	−	0.0460790i
$713$	−18.5466	+	15.5624i	−0.694575	+	0.582818i
$714$	−8.10707	+	28.8378i	−0.303399	+	1.07923i
$715$	2.93883	−	16.6669i	0.109906	−	0.623308i
$716$	25.5597	+	4.50686i	0.955209	+	0.168429i
$717$	−21.3985	−	14.9956i	−0.799143	−	0.560020i
$718$	19.9628	−	16.7508i	0.745005	−	0.625133i
$719$	−7.42325	+	12.8574i	−0.276840	+	0.479502i	−0.970598	−	0.240707i	$-0.922621\pi$
$719$	−7.42325	+	12.8574i	−0.276840	+	0.479502i	0.693757	+	0.720209i	$0.255954\pi$
$720$	4.40377	−	12.0706i	0.164119	−	0.449845i
$721$	−26.9311	+	9.44156i	−1.00297	+	0.351622i
$722$	−5.51035	+	15.1396i	−0.205074	+	0.563436i
$723$	−3.81617	+	3.81326i	−0.141925	+	0.141817i
$724$	−10.8930	+	12.9818i	−0.404836	+	0.482465i
$725$	32.5512	+	89.4336i	1.20892	+	3.32148i
$726$	−6.72904	−	9.61787i	−0.249738	−	0.356953i
$727$	31.7970	−	5.60667i	1.17929	−	0.207940i	0.450560	−	0.892746i	$-0.351224\pi$
$727$	31.7970	−	5.60667i	1.17929	−	0.207940i	0.728725	+	0.684806i	$0.240113\pi$
$728$	2.43664	+	0.459539i	0.0903081	+	0.0170316i
$729$	−23.4135	+	13.4465i	−0.867167	+	0.498017i
$730$	−4.21662			−0.156064
$731$	−5.04828	−	28.6302i	−0.186717	−	1.05893i
$732$	6.77112	+	9.67801i	0.250268	+	0.357710i
$733$	−12.9816	−	35.6667i	−0.479486	−	1.31738i	−0.909931	−	0.414761i	$-0.863865\pi$
$733$	−12.9816	−	35.6667i	−0.479486	−	1.31738i	0.430444	−	0.902617i	$-0.358357\pi$
$734$	−8.94866	−	7.50882i	−0.330301	−	0.277156i
$735$	−20.8040	−	47.5784i	−0.767366	−	1.75496i
$736$	−2.73660	−	0.996040i	−0.100872	−	0.0367145i
$737$	10.9158	−	6.30222i	0.402087	−	0.232145i
$738$	−15.3703	−	5.60763i	−0.565790	−	0.206420i
$739$	−0.127925	+	0.221572i	−0.00470579	+	0.00815067i	−0.868369	−	0.495919i	$-0.834831\pi$
$739$	−0.127925	+	0.221572i	−0.00470579	+	0.00815067i	0.863663	+	0.504070i	$0.168165\pi$
$740$	7.74939	−	6.50251i	0.284873	−	0.239037i
$741$	1.58337	−	2.25945i	0.0581664	−	0.0830029i
$742$	−7.67662	+	20.3368i	−0.281818	+	0.746587i
$743$	−9.20379	−	1.62288i	−0.337654	−	0.0595376i	0.00225037	−	0.999997i	$-0.499284\pi$
$743$	−9.20379	−	1.62288i	−0.337654	−	0.0595376i	−0.339905	+	0.940460i	$0.610395\pi$
$744$	14.3442	+	1.26046i	0.525882	+	0.0462108i
$745$	11.5186	+	13.7273i	0.422008	+	0.502930i
$746$	22.2409	+	12.8408i	0.814298	+	0.470135i
$747$	−6.72714	−	1.19147i	−0.246133	−	0.0435935i
$748$	−23.8687	+	13.7806i	−0.872727	+	0.503869i
$749$	14.0387	−	23.6625i	0.512964	−	0.864609i
$750$	−15.9969	−	59.7924i	−0.584123	−	2.18331i
$751$	10.0962	+	8.47175i	0.368417	+	0.309139i	0.808135	−	0.588997i	$-0.200477\pi$
$751$	10.0962	+	8.47175i	0.368417	+	0.309139i	−0.439718	+	0.898136i	$0.644922\pi$
$752$	−0.161480	+	0.0587738i	−0.00588855	+	0.00214326i
$753$	−30.6883	−	14.3245i	−1.11834	−	0.522012i
$754$	−6.58302	+	1.16076i	−0.239740	+	0.0422725i
$755$	−27.3146			−0.994081
$756$	−1.01983	−	13.7098i	−0.0370908	−	0.498622i
$757$	−27.5811			−1.00245			−0.501226	−	0.865316i	$-0.667118\pi$
$757$	−27.5811			−1.00245			−0.501226	+	0.865316i	$0.667118\pi$
$758$	−8.49984	+	1.49875i	−0.308728	+	0.0544371i
$759$	1.84550	+	21.1872i	0.0669874	+	0.769047i
$760$	6.84052	−	2.48975i	0.248132	−	0.0903126i
$761$	33.2251	+	27.8792i	1.20441	+	1.01062i	0.999493	+	0.0318404i	$0.0101368\pi$
$761$	33.2251	+	27.8792i	1.20441	+	1.01062i	0.204917	+	0.978779i	$0.434308\pi$
$762$	−30.1450	−	8.08965i	−1.09204	−	0.293057i
$763$	16.3231	+	9.68432i	0.590935	+	0.350596i
$764$	−13.9672	+	8.06397i	−0.505316	+	0.291744i
$765$	−0.0640612	+	83.9910i	−0.00231614	+	3.03670i
$766$	26.8210	+	15.4851i	0.969082	+	0.559500i
$767$	4.75458	+	5.66629i	0.171678	+	0.204598i
$768$	0.731398	+	1.57005i	0.0263920	+	0.0566543i
$769$	−49.2137	−	8.67771i	−1.77469	−	0.312926i	−0.812027	−	0.583620i	$-0.801636\pi$
$769$	−49.2137	−	8.67771i	−1.77469	−	0.312926i	−0.962666	+	0.270694i	$0.912747\pi$
$770$	16.8726	−	44.6987i	0.608048	−	1.61083i
$771$	12.1311	+	26.0412i	0.436892	+	0.937851i
$772$	−2.68340	+	2.25164i	−0.0965776	+	0.0810382i
$773$	7.07838	−	12.2601i	0.254591	−	0.440965i	−0.710193	−	0.704007i	$-0.751392\pi$
$773$	7.07838	−	12.2601i	0.254591	−	0.440965i	0.964784	+	0.263042i	$0.0847257\pi$
$774$	6.66225	+	11.5597i	0.239470	+	0.415505i
$775$	96.0703	−	55.4662i	3.45095	−	1.99241i
$776$	−2.23884	−	0.814870i	−0.0803696	−	0.0292521i
$777$	4.69420	−	9.75292i	0.168404	−	0.349884i
$778$	12.0156	+	10.0823i	0.430779	+	0.361466i
$779$	−3.17037	−	8.71051i	−0.113590	−	0.312086i
$780$	6.92619	−	0.603301i	0.247997	−	0.0216017i
$781$	−4.46635	−	25.3299i	−0.159819	−	0.906376i
$782$	19.0368			0.680755
$783$	15.6244	+	33.6070i	0.558372	+	1.20102i
$784$	6.51915	+	2.54964i	0.232827	+	0.0910587i
$785$	−0.246510	+	0.0434663i	−0.00879830	+	0.00155138i
$786$	−3.09636	+	6.63357i	−0.110444	+	0.236612i
$787$	12.2983	+	33.7893i	0.438387	+	1.20446i	0.940541	+	0.339680i	$0.110319\pi$
$787$	12.2983	+	33.7893i	0.438387	+	1.20446i	−0.502154	+	0.864778i	$0.667459\pi$
$788$	−7.84284	+	9.34673i	−0.279389	+	0.332963i
$789$	−5.80604	−	21.7016i	−0.206701	−	0.772596i
$790$	7.46742	−	20.5166i	0.265679	−	0.729947i
$791$	−33.2872	+	11.6699i	−1.18356	+	0.414934i
$792$	8.13790	−	9.68337i	0.289168	−	0.344083i
$793$	−3.19556	+	5.53488i	−0.113478	+	0.196549i
$794$	−25.6550	+	21.5271i	−0.910462	+	0.763968i
$795$	−5.33516	+	60.7144i	−0.189219	+	2.15332i
$796$	−4.98736	−	0.879406i	−0.176772	−	0.0311697i
$797$	5.20379	−	29.5121i	0.184328	−	1.04537i	−0.742489	−	0.669859i	$-0.766355\pi$
$797$	5.20379	−	29.5121i	0.184328	−	1.04537i	0.926816	−	0.375515i	$-0.122534\pi$
$798$	5.57458	−	5.43961i	0.197338	−	0.192560i
$799$	0.860508	−	0.722052i	0.0304426	−	0.0255444i
$800$	11.5559	+	6.67181i	0.408563	+	0.235884i
$801$	−7.26614	+	1.27550i	−0.256736	+	0.0450677i
$802$	−0.506712	−	0.877651i	−0.0178926	−	0.0309909i
$803$	−3.90065	−	1.41972i	−0.137651	−	0.0501008i
$804$	3.65994	+	3.66274i	0.129076	+	0.129175i
$805$	−25.5297	+	20.9105i	−0.899803	+	0.736999i
$806$	2.66483	+	7.32155i	0.0938645	+	0.257891i
$807$	9.57919	−	6.70198i	0.337203	−	0.235921i
$808$	9.11004	−	1.60635i	0.320490	−	0.0565111i
$809$			27.0141i			0.949765i	0.880049	+	0.474883i	$0.157510\pi$
$809$			27.0141i			0.949765i	−0.880049	+	0.474883i	$0.842490\pi$
$810$	−13.1284	−	36.2419i	−0.461285	−	1.27341i
$811$		−	7.44427i		−	0.261404i	−0.991422	−	0.130702i	$-0.958277\pi$
$811$		−	7.44427i		−	0.261404i	0.991422	−	0.130702i	$-0.0417231\pi$
$812$	−18.8695	−	0.224040i	−0.662189	−	0.00786225i
$813$	3.03130	+	4.33266i	0.106312	+	0.151953i
$814$	9.35806	−	3.40606i	0.328000	−	0.119382i
$815$	29.5409	+	24.7877i	1.03477	+	0.868277i
$816$	−8.00293	−	8.00904i	−0.280159	−	0.280372i
$817$	−2.58533	+	7.10314i	−0.0904493	+	0.248507i
$818$	1.52635	+	2.64372i	0.0533676	+	0.0924354i
$819$	6.48867	−	3.63771i	0.226732	−	0.127112i
$820$	11.6791	−	20.2288i	0.407852	−	0.706420i
$821$	−4.85476	−	5.78568i	−0.169432	−	0.201922i	0.674646	−	0.738141i	$-0.264296\pi$
$821$	−4.85476	−	5.78568i	−0.169432	−	0.201922i	−0.844078	+	0.536220i	$0.819852\pi$
$822$	16.1819	−	23.0913i	0.564407	−	0.805403i
$823$	−1.65832	+	9.40480i	−0.0578054	+	0.327831i	−0.999973	−	0.00731067i	$-0.997673\pi$
$823$	−1.65832	+	9.40480i	−0.0578054	+	0.327831i	0.942168	+	0.335141i	$0.108784\pi$
$824$	1.87304	−	10.6225i	0.0652505	−	0.370054i
$825$	8.52999	−	97.0718i	0.296976	−	3.37961i
$826$	10.2253	+	18.2066i	0.355784	+	0.633488i
$827$	17.5247	+	10.1179i	0.609395	+	0.351834i	0.772729	−	0.634737i	$-0.218891\pi$
$827$	17.5247	+	10.1179i	0.609395	+	0.351834i	−0.163334	+	0.986571i	$0.552225\pi$
$828$	−8.21207	+	2.98186i	−0.285389	+	0.103627i
$829$	−30.3693	+	17.5337i	−1.05477	+	0.608971i	−0.923981	−	0.382439i	$-0.875084\pi$
$829$	−30.3693	+	17.5337i	−1.05477	+	0.608971i	−0.130788	+	0.991410i	$0.541751\pi$
$830$	3.33588	−	9.16525i	0.115790	−	0.318131i
$831$	−10.7512	+	2.87638i	−0.372954	+	0.0997804i
$832$	−0.602421	+	0.717937i	−0.0208852	+	0.0248900i
$833$	−45.7451	−	1.08643i	−1.58497	−	0.0376425i
$834$	−14.3794	−	6.71192i	−0.497919	−	0.232415i
$835$	4.68044	+	26.5441i	0.161973	+	0.918596i
$836$	7.16622			0.247849
$837$	35.4143	−	24.7370i	1.22410	−	0.855037i
$838$		−	5.69949i		−	0.196886i
$839$	−8.80329	−	49.9259i	−0.303923	−	1.72363i	−0.628530	−	0.777785i	$-0.716343\pi$
$839$	−8.80329	−	49.9259i	−0.303923	−	1.72363i	0.324607	−	0.945849i	$-0.394768\pi$
$840$	19.5298	+	1.95006i	0.673842	+	0.0672833i
$841$	20.5534	−	7.48082i	0.708738	−	0.257959i
$842$	−18.2558	+	21.7564i	−0.629137	+	0.749777i
$843$	−21.3643	−	5.73327i	−0.735824	−	0.197464i
$844$	3.61298	+	1.31502i	0.124364	+	0.0452647i
$845$	−25.9582	−	44.9609i	−0.892989	−	1.54670i
$846$	−0.258105	+	0.446264i	−0.00887383	+	0.0153429i
$847$	11.6876	−	13.5976i	0.401591	−	0.467218i
$848$	−5.28113	−	6.29380i	−0.181355	−	0.216130i
$849$	19.6687	−	9.16254i	0.675028	−	0.314457i
$850$	−85.9002	−	15.1465i	−2.94635	−	0.519522i
$851$	−6.77404	−	1.19445i	−0.232211	−	0.0409451i
$852$	9.57782	−	4.46176i	0.328131	−	0.152858i
$853$	−21.5890	−	25.7287i	−0.739192	−	0.880935i	0.257151	−	0.966371i	$-0.417216\pi$
$853$	−21.5890	−	25.7287i	−0.739192	−	0.880935i	−0.996344	+	0.0854361i	$0.972772\pi$
$854$	−11.7607	+	13.6826i	−0.402443	+	0.468209i
$855$	10.9337	−	18.9044i	0.373925	−	0.646518i
$856$	5.19959	+	9.00595i	0.177718	+	0.307817i
$857$	9.20743	+	3.35123i	0.314520	+	0.114476i	0.494457	−	0.869202i	$-0.335367\pi$
$857$	9.20743	+	3.35123i	0.314520	+	0.114476i	−0.179937	+	0.983678i	$0.557589\pi$
$858$	6.61031	+	1.77393i	0.225672	+	0.0605609i
$859$	−6.65503	+	7.93115i	−0.227067	+	0.270607i	−0.867534	−	0.497378i	$-0.834296\pi$
$859$	−6.65503	+	7.93115i	−0.227067	+	0.270607i	0.640467	+	0.767985i	$0.278741\pi$
$860$	−17.8991	+	6.51475i	−0.610356	+	0.222151i
$861$	2.48314	−	24.8687i	0.0846253	−	0.847522i
$862$	3.16737	+	17.9630i	0.107881	+	0.611824i
$863$		−	11.1328i		−	0.378963i	−0.981884	−	0.189482i	$-0.939319\pi$
$863$		−	11.1328i		−	0.378963i	0.981884	−	0.189482i	$-0.0606807\pi$
$864$	4.70680	+	2.20138i	0.160129	+	0.0748923i
$865$	38.0292			1.29303
$866$	−0.461876	−	2.61943i	−0.0156952	−	0.0890119i
$867$	40.3839	+	18.8501i	1.37151	+	0.640182i
$868$	3.56204	+	21.7052i	0.120904	+	0.736721i
$869$	13.8157	−	16.4649i	0.468666	−	0.558534i
$870$	−51.1131	+	13.6748i	−1.73290	+	0.463620i
$871$	−0.958249	+	2.63277i	−0.0324690	+	0.0892080i
$872$	−6.21256	+	3.58682i	−0.210384	+	0.121465i
$873$	−6.71838	+	2.43949i	−0.227383	+	0.0825642i
$874$	−4.28664	−	2.47489i	−0.144998	−	0.0837144i
$875$	82.4352	−	46.2979i	2.78682	−	1.56515i
$876$	0.149268	−	1.69868i	0.00504331	−	0.0573932i
$877$	5.19854	−	29.4824i	0.175542	−	0.995550i	−0.761974	−	0.647608i	$-0.775769\pi$
$877$	5.19854	−	29.4824i	0.175542	−	0.995550i	0.937516	−	0.347942i	$-0.113119\pi$
$878$	−3.13193	+	17.7620i	−0.105697	+	0.599440i
$879$	−7.20970	+	10.2882i	−0.243177	+	0.347011i
$880$	11.6075	+	13.8333i	0.391289	+	0.466320i
$881$	−1.71292	+	2.96686i	−0.0577097	+	0.0999561i	−0.893437	−	0.449189i	$-0.851713\pi$
$881$	−1.71292	+	2.96686i	−0.0577097	+	0.0999561i	0.835727	+	0.549145i	$0.185046\pi$
$882$	19.9036	−	6.69669i	0.670190	−	0.225489i
$883$	−10.2067	−	17.6786i	−0.343484	−	0.594931i	0.641593	−	0.767045i	$-0.278274\pi$
$883$	−10.2067	−	17.6786i	−0.343484	−	0.594931i	−0.985077	+	0.172114i	$0.944940\pi$
$884$	2.09533	−	5.75688i	0.0704737	−	0.193625i
$885$	41.3842	+	41.4158i	1.39112	+	1.39218i
$886$	−16.8944	−	14.1761i	−0.567579	−	0.476255i
$887$	−37.9425	+	13.8099i	−1.27398	+	0.463692i	−0.888438	−	0.458996i	$-0.848209\pi$
$887$	−37.9425	+	13.8099i	−1.27398	+	0.463692i	−0.385546	+	0.922688i	$0.625987\pi$
$888$	2.34523	+	3.35206i	0.0787009	+	0.112488i
$889$	0.566029	−	47.6731i	0.0189840	−	1.59891i
$890$		−	10.5321i		−	0.353037i
$891$	0.0578847	−	37.9465i	0.00193921	−	1.27125i
$892$		−	3.31531i		−	0.111005i
$893$	−0.287636	+	0.0507181i	−0.00962539	+	0.00169722i
$894$	−5.93786	+	4.15436i	−0.198592	+	0.138943i
$895$	38.0187	+	104.456i	1.27083	+	3.49157i
$896$	−2.04681	+	1.67647i	−0.0683792	+	0.0560071i
$897$	−3.34147	−	3.34402i	−0.111568	−	0.111654i
$898$	−28.9905	−	10.5517i	−0.967425	−	0.352114i
$899$	−29.6481	−	51.3519i	−0.988818	−	1.71268i
$900$	39.4280	−	6.92122i	1.31427	−	0.230707i
$901$	46.5114	+	26.8533i	1.54952	+	0.894615i
$902$	17.6149	−	14.7807i	0.586512	−	0.492142i
$903$	−14.5867	+	14.2335i	−0.485413	+	0.473660i
$904$	2.31511	−	13.1296i	0.0769992	−	0.436684i
$905$	−71.4785	−	12.6036i	−2.37602	−	0.418957i
$906$	0.966937	−	11.0038i	0.0321243	−	0.365577i
$907$	−15.1135	+	12.6817i	−0.501835	+	0.421089i	−0.858245	−	0.513240i	$-0.828445\pi$
$907$	−15.1135	+	12.6817i	−0.501835	+	0.421089i	0.356410	+	0.934330i	$0.384001\pi$
$908$	−13.5877	+	23.5345i	−0.450922	+	0.781020i
$909$	17.8547	−	21.2455i	0.592202	−	0.704667i
$910$	3.51351	+	10.0219i	0.116472	+	0.332224i
$911$	−18.9862	+	52.1643i	−0.629042	+	1.72828i	0.0546461	+	0.998506i	$0.482597\pi$
$911$	−18.9862	+	52.1643i	−0.629042	+	1.72828i	−0.683688	+	0.729774i	$0.739625\pi$
$912$	0.760850	+	2.84387i	0.0251943	+	0.0941699i
$913$	6.17181	−	7.35528i	0.204257	−	0.243424i
$914$	1.63225	+	4.48458i	0.0539902	+	0.148337i
$915$	−21.3969	+	45.8402i	−0.707361	+	1.51543i
$916$	−18.9625	+	3.34360i	−0.626538	+	0.110476i
$917$	−10.9887	−	2.07242i	−0.362880	−	0.0684374i
$918$	−33.8339	−	2.99909i	−1.11668	−	0.0989847i
$919$	−45.3817			−1.49701			−0.748503	−	0.663132i	$-0.769227\pi$
$919$	−45.3817			−1.49701			−0.748503	+	0.663132i	$0.769227\pi$
$920$	−2.16590	−	12.2834i	−0.0714076	−	0.404972i
$921$	34.3028	−	2.98793i	1.13032	−	0.0984555i
$922$	−9.89534	−	27.1872i	−0.325886	−	0.895364i
$923$	4.37965	+	3.67496i	0.144158	+	0.120963i
$924$	17.4098	+	8.37954i	0.572740	+	0.275667i
$925$	29.6163	+	10.7794i	0.973777	+	0.354426i
$926$	7.87405	−	4.54609i	0.258757	−	0.149394i
$927$	−16.1582	−	28.0363i	−0.530706	−	0.920832i
$928$	3.56625	−	6.17692i	0.117068	−	0.202767i
$929$	5.26558	−	4.41834i	0.172758	−	0.144961i	−0.552309	−	0.833639i	$-0.686253\pi$
$929$	5.26558	−	4.41834i	0.172758	−	0.144961i	0.725067	+	0.688678i	$0.241809\pi$
$930$	26.0424	+	55.9037i	0.853964	+	1.83316i
$931$	10.1595	+	6.19175i	0.332963	+	0.202926i
$932$	−27.4376	−	4.83798i	−0.898747	−	0.158473i
$933$	0.979449	+	2.10253i	0.0320657	+	0.0688337i
$934$	−3.84611	−	4.58361i	−0.125849	−	0.149980i
$935$	−102.228	−	59.0216i	−3.34323	−	1.93021i
$936$	−0.00214445	+	2.81160i	−7.00936e−5	+	0.0919000i
$937$	−34.4015	+	19.8617i	−1.12385	+	0.648854i	−0.942381	−	0.334543i	$-0.891418\pi$
$937$	−34.4015	+	19.8617i	−1.12385	+	0.648854i	−0.181468	+	0.983397i	$0.558085\pi$
$938$	−4.03574	+	6.80230i	−0.131772	+	0.222103i
$939$	−39.2440	−	10.5315i	−1.28068	−	0.343681i
$940$	−0.563804	−	0.473088i	−0.0183893	−	0.0154304i
$941$	−16.2107	+	5.90020i	−0.528453	+	0.192341i	−0.592447	−	0.805609i	$-0.701838\pi$
$941$	−16.2107	+	5.90020i	−0.528453	+	0.192341i	0.0639947	+	0.997950i	$0.479616\pi$
$942$	−0.00878414	−	0.100846i	−0.000286203	−	0.00328574i
$943$	−15.6413	+	2.75799i	−0.509352	+	0.0898125i
$944$	−7.89246			−0.256878
$945$	48.6678	−	33.1420i	1.58316	−	1.07811i
$946$	−18.7514			−0.609660
$947$	39.1762	−	6.90782i	1.27306	−	0.224474i	0.504026	−	0.863688i	$-0.331851\pi$
$947$	39.1762	−	6.90782i	1.27306	−	0.224474i	0.769029	+	0.639214i	$0.220740\pi$
$948$	8.00084	+	3.73457i	0.259855	+	0.121293i
$949$	0.867042	−	0.315577i	0.0281454	−	0.0102441i
$950$	17.3735	+	14.5781i	0.563672	+	0.472977i
$951$	1.17215	+	4.38119i	0.0380094	+	0.142070i
$952$	8.82467	−	14.8741i	0.286009	−	0.482073i
$953$	32.9295	−	19.0118i	1.06669	−	0.615854i	0.139415	−	0.990234i	$-0.455478\pi$
$953$	32.9295	−	19.0118i	1.06669	−	0.615854i	0.927275	+	0.374380i	$0.122144\pi$
$954$	−24.2702	−	4.29858i	−0.785777	−	0.139172i
$955$	−59.8208	−	34.5376i	−1.93576	−	1.11761i
$956$	9.69712	+	11.5566i	0.313627	+	0.373766i
$957$	−51.8873	−	4.55949i	−1.67728	−	0.147387i
$958$	31.0360	+	5.47249i	1.00273	+	0.176808i
$959$	40.2961	+	15.2108i	1.30123	+	0.491181i
$960$	−4.25727	+	6.07508i	−0.137403	+	0.196072i
$961$	−29.1975	+	24.4996i	−0.941854	+	0.790309i
$962$	−1.10681	+	1.91705i	−0.0356850	+	0.0618082i
$963$	29.3079	+	10.6925i	0.944435	+	0.344562i
$964$	2.69741	−	1.55735i	0.0868777	−	0.0501589i
$965$	−14.0981	−	5.13127i	−0.453833	−	0.165182i
$966$	−7.52014	−	11.0250i	−0.241956	−	0.354723i
$967$	37.7038	+	31.6373i	1.21247	+	1.01739i	0.999184	+	0.0403976i	$0.0128624\pi$
$967$	37.7038	+	31.6373i	1.21247	+	1.01739i	0.213290	+	0.976989i	$0.431582\pi$
$968$	2.31787	+	6.36830i	0.0744992	+	0.204685i
$969$	−11.0318	−	15.7678i	−0.354392	−	0.506535i
$970$	−1.77194	−	10.0492i	−0.0568936	−	0.322660i
$971$	44.9939			1.44392			0.721961	−	0.691934i	$-0.243241\pi$
$971$	44.9939			1.44392			0.721961	+	0.691934i	$0.243241\pi$
$972$	15.0650	−	4.00587i	0.483209	−	0.128488i
$973$	4.49234	−	23.8201i	0.144018	−	0.763636i
$974$	−6.11979	+	1.07908i	−0.196091	+	0.0345761i
$975$	12.4171	+	17.7479i	0.397667	+	0.568388i
$976$	−2.33237	−	6.40812i	−0.0746572	−	0.205119i
$977$	−17.8488	+	21.2714i	−0.571034	+	0.680532i	−0.971843	−	0.235630i	$-0.924285\pi$
$977$	−17.8488	+	21.2714i	−0.571034	+	0.680532i	0.400809	+	0.916162i	$0.368729\pi$
$978$	−11.0316	+	11.0232i	−0.352751	+	0.352482i
$979$	3.54612	−	9.74289i	0.113335	−	0.311384i
$980$	4.50360	+	29.6404i	0.143862	+	0.946829i
$981$	−7.37602	+	20.2175i	−0.235498	+	0.645494i
$982$	7.72453	−	13.3793i	0.246500	−	0.426950i
$983$	−37.9165	+	31.8157i	−1.20935	+	1.01476i	−0.210035	+	0.977694i	$0.567358\pi$
$983$	−37.9165	+	31.8157i	−1.20935	+	1.01476i	−0.999313	+	0.0370694i	$0.988198\pi$
$984$	7.73582	+	5.42108i	0.246609	+	0.172818i
$985$	−51.4635	−	9.07441i	−1.63976	−	0.289135i
$986$	−8.09619	+	45.9158i	−0.257835	+	1.46226i
$987$	−0.758096	−	0.213121i	−0.0241305	−	0.00678372i
$988$	−1.22025	+	1.02391i	−0.0388212	+	0.0325748i
$989$	11.2166	+	6.47589i	0.356666	+	0.205921i
$990$	53.3440	+	9.44795i	1.69539	+	0.300276i
$991$	−20.7930	−	36.0145i	−0.660511	−	1.14404i	−0.980481	−	0.196611i	$-0.937006\pi$
$991$	−20.7930	−	36.0145i	−0.660511	−	1.14404i	0.319970	−	0.947428i	$-0.396327\pi$
$992$	−7.81215	−	2.84339i	−0.248036	−	0.0902777i
$993$	−16.8901	+	4.51877i	−0.535990	+	0.143399i
$994$	10.2270	+	12.4862i	0.324382	+	0.396039i
$995$	−7.41845	−	20.3820i	−0.235181	−	0.646154i
$996$	3.57417	+	1.66832i	0.113252	+	0.0528628i
$997$	32.5808	−	5.74488i	1.03185	−	0.181942i	0.368011	−	0.929822i	$-0.380039\pi$
$997$	32.5808	−	5.74488i	1.03185	−	0.181942i	0.663835	+	0.747879i	$0.268928\pi$
$998$		−	30.0694i		−	0.951829i
$999$	11.8512	+	3.19006i	0.374956	+	0.100929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.41.15	✓	144
7.6	odd	2	inner	378.2.z.a.41.22	yes	144
27.2	odd	18	inner	378.2.z.a.83.22	yes	144
189.83	even	18	inner	378.2.z.a.83.15	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.15	✓	144	1.1	even	1	trivial
378.2.z.a.41.22	yes	144	7.6	odd	2	inner
378.2.z.a.83.15	yes	144	189.83	even	18	inner
378.2.z.a.83.22	yes	144	27.2	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 - 0.173648i) q^{2} +(-1.41919 + 0.992922i) q^{3} +(0.939693 - 0.342020i) q^{4} +(3.28093 + 2.75302i) q^{5} +(-1.22521 + 1.22428i) q^{6} +(-2.27542 - 1.34999i) q^{7} +(0.866025 - 0.500000i) q^{8} +(1.02821 - 2.81829i) q^{9} +(3.70914 + 2.14147i) q^{10} +(2.71017 + 3.22986i) q^{11} +(-0.994005 + 1.41843i) q^{12} +(-0.922962 - 0.162743i) q^{13} +(-2.47527 - 0.934353i) q^{14} +(-7.38980 - 0.649364i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-3.26843 + 5.66109i) q^{17} +(0.523198 - 2.95403i) q^{18} +(1.47194 - 0.849827i) q^{19} +(4.02465 + 1.46485i) q^{20} +(4.56969 - 0.343428i) q^{21} +(3.22986 + 2.71017i) q^{22} +(-0.996040 - 2.73660i) q^{23} +(-0.732595 + 1.56949i) q^{24} +(2.31710 + 13.1409i) q^{25} -0.937200 q^{26} +(1.33912 + 5.02063i) q^{27} +(-2.59992 - 0.490331i) q^{28} +(7.02413 - 1.23854i) q^{29} +(-7.39030 + 0.643727i) q^{30} +(-2.84339 - 7.81215i) q^{31} +(0.642788 - 0.766044i) q^{32} +(-7.05325 - 1.89280i) q^{33} +(-2.23574 + 6.14264i) q^{34} +(-3.74895 - 10.6935i) q^{35} +(0.00228814 - 3.00000i) q^{36} +(1.18098 - 2.04551i) q^{37} +(1.30201 - 1.09252i) q^{38} +(1.47145 - 0.685466i) q^{39} +(4.21788 + 0.743726i) q^{40} +(0.947038 - 5.37092i) q^{41} +(4.44063 - 1.13173i) q^{42} +(-3.40689 + 2.85872i) q^{43} +(3.65140 + 2.10814i) q^{44} +(11.1323 - 6.41593i) q^{45} +(-1.45611 - 2.52206i) q^{46} +(-0.161480 - 0.0587738i) q^{47} +(-0.448926 + 1.67286i) q^{48} +(3.35508 + 6.14357i) q^{49} +(4.56379 + 12.5389i) q^{50} +(-0.982491 - 11.2795i) q^{51} +(-0.922962 + 0.162743i) q^{52} -8.21598i q^{53} +(2.19060 + 4.71182i) q^{54} +18.0581i q^{55} +(-2.64556 - 0.0314111i) q^{56} +(-1.24516 + 2.66759i) q^{57} +(6.70235 - 2.43946i) q^{58} +(-6.04598 - 5.07318i) q^{59} +(-7.16624 + 1.91726i) q^{60} +(2.33237 - 6.40812i) q^{61} +(-4.15676 - 7.19972i) q^{62} +(-6.14427 + 5.02474i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-2.58014 - 3.07489i) q^{65} +(-7.27478 - 0.639256i) q^{66} +(0.519116 - 2.94405i) q^{67} +(-1.13511 + 6.43755i) q^{68} +(4.13080 + 2.89477i) q^{69} +(-5.54890 - 9.88003i) q^{70} +(-5.28304 - 3.05016i) q^{71} +(-0.518691 - 2.95482i) q^{72} +(-0.852614 + 0.492257i) q^{73} +(0.807835 - 2.21951i) q^{74} +(-16.3363 - 16.3488i) q^{75} +(1.09252 - 1.30201i) q^{76} +(-1.80652 - 11.0080i) q^{77} +(1.33007 - 0.930567i) q^{78} +(-0.885211 - 5.02028i) q^{79} +4.28295 q^{80} +(-6.88557 - 5.79560i) q^{81} -5.45377i q^{82} +(-0.395445 - 2.24268i) q^{83} +(4.17664 - 1.88564i) q^{84} +(-26.3086 + 9.57554i) q^{85} +(-2.85872 + 3.40689i) q^{86} +(-8.73882 + 8.73215i) q^{87} +(3.96201 + 1.44205i) q^{88} +(-1.22954 - 2.12963i) q^{89} +(9.84908 - 8.25156i) q^{90} +(1.88043 + 1.61629i) q^{91} +(-1.87194 - 2.23090i) q^{92} +(11.7922 + 8.26367i) q^{93} +(-0.169232 - 0.0298402i) q^{94} +(7.16894 + 1.26408i) q^{95} +(-0.151616 + 1.72540i) q^{96} +(-1.53146 - 1.82512i) q^{97} +(4.37093 + 5.46763i) q^{98} +(11.8893 - 4.31709i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57}+ \cdots + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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