LMFDB - Embedded newform 168.2.t.a.19.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,2,Mod(19,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.t (of order $6$, degree $2$, 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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	168.19
Dual form			168.2.t.a.115.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.647235 + 1.25741i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.16217 + 1.62768i) q^{4} +(-2.08776 + 3.61611i) q^{5} +(1.18923 + 0.765334i) q^{6} +(2.39694 - 1.12013i) q^{7} +(-2.79887 - 0.407838i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-5.89822 - 0.284706i) q^{10} +(-0.855485 - 1.48174i) q^{11} +(-0.192630 + 1.99070i) q^{12} +1.54062 q^{13} +(2.95984 + 2.28896i) q^{14} +4.17553i q^{15} +(-1.29871 - 3.78330i) q^{16} +(2.02094 - 1.16679i) q^{17} +(1.41257 + 0.0681843i) q^{18} +(6.09693 + 3.52006i) q^{19} +(-3.45954 - 7.60077i) q^{20} +(1.51575 - 2.16853i) q^{21} +(1.30946 - 2.03473i) q^{22} +(0.406066 + 0.234442i) q^{23} +(-2.62781 + 1.04624i) q^{24} +(-6.21752 - 10.7691i) q^{25} +(0.997145 + 1.93720i) q^{26} -1.00000i q^{27} +(-0.962447 + 5.20324i) q^{28} -3.33885i q^{29} +(-5.25036 + 2.70255i) q^{30} +(-1.58126 - 2.73883i) q^{31} +(3.91660 - 4.08169i) q^{32} +(-1.48174 - 0.855485i) q^{33} +(2.77516 + 1.78596i) q^{34} +(-0.953738 + 11.0062i) q^{35} +(0.828528 + 1.82031i) q^{36} +(-7.74648 - 4.47243i) q^{37} +(-0.480026 + 9.94467i) q^{38} +(1.33422 - 0.770311i) q^{39} +(7.31817 - 9.26956i) q^{40} +5.31411i q^{41} +(3.70778 + 0.502372i) q^{42} -3.42772 q^{43} +(3.40603 + 0.329584i) q^{44} +(2.08776 + 3.61611i) q^{45} +(-0.0319706 + 0.662331i) q^{46} +(2.95047 - 5.11037i) q^{47} +(-3.01636 - 2.62708i) q^{48} +(4.49063 - 5.36975i) q^{49} +(9.51696 - 14.7881i) q^{50} +(1.16679 - 2.02094i) q^{51} +(-1.79047 + 2.50765i) q^{52} +(1.35437 - 0.781947i) q^{53} +(1.25741 - 0.647235i) q^{54} +7.14421 q^{55} +(-7.16555 + 2.15753i) q^{56} +7.04013 q^{57} +(4.19831 - 2.16102i) q^{58} +(-5.26742 + 3.04114i) q^{59} +(-6.79644 - 4.85269i) q^{60} +(-4.55959 + 7.89744i) q^{61} +(2.42039 - 3.76097i) q^{62} +(0.228411 - 2.63587i) q^{63} +(7.66734 + 2.28297i) q^{64} +(-3.21646 + 5.57107i) q^{65} +(0.116661 - 2.41686i) q^{66} +(3.73658 + 6.47195i) q^{67} +(-0.449517 + 4.64545i) q^{68} +0.468884 q^{69} +(-14.4566 + 5.92433i) q^{70} +3.49263i q^{71} +(-1.75263 + 2.21997i) q^{72} +(-12.5811 + 7.26372i) q^{73} +(0.609899 - 12.6352i) q^{74} +(-10.7691 - 6.21752i) q^{75} +(-12.8152 + 5.83295i) q^{76} +(-3.71029 - 2.59340i) q^{77} +(1.83215 + 1.17909i) q^{78} +(1.46108 + 0.843557i) q^{79} +(16.3922 + 3.20237i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.68203 + 3.43948i) q^{82} -2.72601i q^{83} +(1.76812 + 4.98736i) q^{84} +9.74391i q^{85} +(-2.21854 - 4.31005i) q^{86} +(-1.66943 - 2.89153i) q^{87} +(1.79008 + 4.49611i) q^{88} +(1.83829 + 1.06134i) q^{89} +(-3.19567 + 4.96566i) q^{90} +(3.69278 - 1.72569i) q^{91} +(-0.853516 + 0.388484i) q^{92} +(-2.73883 - 1.58126i) q^{93} +(8.33550 + 0.402352i) q^{94} +(-25.4579 + 14.6981i) q^{95} +(1.35103 - 5.49315i) q^{96} +1.95202i q^{97} +(9.65849 + 2.17109i) q^{98} -1.71097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9} - 18 q^{10} + 8 q^{11} - 10 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{22} - 18 q^{24} - 16 q^{25} - 30 q^{26} - 14 q^{28} - 8 q^{30} - 12 q^{32} - 24 q^{35} - 4 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 16 * q^9 - 18 * q^10 + 8 * q^11 - 10 * q^14 + 6 * q^16 + 2 * q^18 - 20 * q^22 - 18 * q^24 - 16 * q^25 - 30 * q^26 - 14 * q^28 - 8 * q^30 - 12 * q^32 - 24 * q^35 - 4 * q^36 - 18 * q^38 - 30 * q^40 + 4 * q^42 - 16 * q^43 + 24 * q^44 + 8 * q^46 + 8 * q^49 + 76 * q^50 + 36 * q^52 + 16 * q^56 + 16 * q^57 - 6 * q^58 - 96 * q^59 - 2 * q^60 + 76 * q^64 - 36 * q^66 - 32 * q^67 + 96 * q^68 + 6 * q^70 + 8 * q^72 - 24 * q^73 - 34 * q^74 - 12 * q^78 + 36 * q^80 - 16 * q^81 - 36 * q^82 + 16 * q^84 + 50 * q^86 - 14 * q^88 + 56 * q^91 - 128 * q^92 + 36 * q^94 + 30 * q^96 + 60 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.647235	+	1.25741i	0.457664	+	0.889125i
$2$	0.647235	+	1.25741i	0.457664	+	0.889125i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−1.16217	+	1.62768i	−0.581087	+	0.813842i
$5$	−2.08776	+	3.61611i	−0.933677	+	1.61718i	−0.156700	+	0.987646i	$0.550085\pi$
$5$	−2.08776	+	3.61611i	−0.933677	+	1.61718i	−0.776977	+	0.629529i	$0.783248\pi$
$6$	1.18923	+	0.765334i	0.485500	+	0.312446i
$7$	2.39694	−	1.12013i	0.905958	−	0.423368i
$7$	2.39694	−	1.12013i	0.905958	−	0.423368i
$8$	−2.79887	−	0.407838i	−0.989550	−	0.144192i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−5.89822	−	0.284706i	−1.86518	−	0.0900318i
$11$	−0.855485	−	1.48174i	−0.257939	−	0.446763i	0.707751	−	0.706462i	$-0.249710\pi$
$11$	−0.855485	−	1.48174i	−0.257939	−	0.446763i	−0.965690	+	0.259699i	$0.916377\pi$
$12$	−0.192630	+	1.99070i	−0.0556075	+	0.574666i
$13$	1.54062			0.427292			0.213646	−	0.976911i	$-0.431466\pi$
$13$	1.54062			0.427292			0.213646	+	0.976911i	$0.431466\pi$
$14$	2.95984	+	2.28896i	0.791052	+	0.611749i
$15$			4.17553i			1.07812i
$16$	−1.29871	−	3.78330i	−0.324676	−	0.945825i
$17$	2.02094	−	1.16679i	0.490149	−	0.282988i	−0.234487	−	0.972119i	$-0.575341\pi$
$17$	2.02094	−	1.16679i	0.490149	−	0.282988i	0.724636	+	0.689132i	$0.242008\pi$
$18$	1.41257	+	0.0681843i	0.332946	+	0.0160712i
$19$	6.09693	+	3.52006i	1.39873	+	0.807558i	0.994260	−	0.106992i	$-0.0341221\pi$
$19$	6.09693	+	3.52006i	1.39873	+	0.807558i	0.404472	+	0.914551i	$0.367455\pi$
$20$	−3.45954	−	7.60077i	−0.773578	−	1.69958i
$21$	1.51575	−	2.16853i	0.330763	−	0.473212i
$22$	1.30946	−	2.03473i	0.279179	−	0.433807i
$23$	0.406066	+	0.234442i	0.0846705	+	0.0488846i	0.541737	−	0.840548i	$-0.317767\pi$
$23$	0.406066	+	0.234442i	0.0846705	+	0.0488846i	−0.457067	+	0.889432i	$0.651100\pi$
$24$	−2.62781	+	1.04624i	−0.536400	+	0.213562i
$25$	−6.21752	−	10.7691i	−1.24350	−	2.15381i
$26$	0.997145	+	1.93720i	0.195556	+	0.379916i
$27$		−	1.00000i		−	0.192450i
$28$	−0.962447	+	5.20324i	−0.181885	+	0.983320i
$29$		−	3.33885i		−	0.620009i	−0.950735	−	0.310005i	$-0.899669\pi$
$29$		−	3.33885i		−	0.620009i	0.950735	−	0.310005i	$-0.100331\pi$
$30$	−5.25036	+	2.70255i	−0.958581	+	0.493416i
$31$	−1.58126	−	2.73883i	−0.284003	−	0.491908i	0.688364	−	0.725366i	$-0.258329\pi$
$31$	−1.58126	−	2.73883i	−0.284003	−	0.491908i	−0.972367	+	0.233458i	$0.924996\pi$
$32$	3.91660	−	4.08169i	0.692364	−	0.721548i
$33$	−1.48174	−	0.855485i	−0.257939	−	0.148921i
$34$	2.77516	+	1.78596i	0.475935	+	0.306290i
$35$	−0.953738	+	11.0062i	−0.161211	+	1.86038i
$36$	0.828528	+	1.82031i	0.138088	+	0.303386i
$37$	−7.74648	−	4.47243i	−1.27351	−	0.735263i	−0.297865	−	0.954608i	$-0.596275\pi$
$37$	−7.74648	−	4.47243i	−1.27351	−	0.735263i	−0.975647	+	0.219345i	$0.929608\pi$
$38$	−0.480026	+	9.94467i	−0.0778705	+	1.61324i
$39$	1.33422	−	0.770311i	0.213646	−	0.123349i
$40$	7.31817	−	9.26956i	1.15710	−	1.46565i
$41$			5.31411i			0.829925i	0.909838	+	0.414963i	$0.136205\pi$
$41$			5.31411i			0.829925i	−0.909838	+	0.414963i	$0.863795\pi$
$42$	3.70778	+	0.502372i	0.572123	+	0.0775177i
$43$	−3.42772			−0.522722			−0.261361	−	0.965241i	$-0.584171\pi$
$43$	−3.42772			−0.522722			−0.261361	+	0.965241i	$0.584171\pi$
$44$	3.40603	+	0.329584i	0.513479	+	0.0496867i
$45$	2.08776	+	3.61611i	0.311226	+	0.539058i
$46$	−0.0319706	+	0.662331i	−0.00471380	+	0.0976554i
$47$	2.95047	−	5.11037i	0.430371	−	0.745424i	−0.566534	−	0.824038i	$-0.691716\pi$
$47$	2.95047	−	5.11037i	0.430371	−	0.745424i	0.996905	+	0.0786139i	$0.0250494\pi$
$48$	−3.01636	−	2.62708i	−0.435374	−	0.379187i
$49$	4.49063	−	5.36975i	0.641519	−	0.767107i
$50$	9.51696	−	14.7881i	1.34590	−	2.09135i
$51$	1.16679	−	2.02094i	0.163383	−	0.282988i
$52$	−1.79047	+	2.50765i	−0.248294	+	0.347748i
$53$	1.35437	−	0.781947i	0.186037	−	0.107409i	−0.404089	−	0.914720i	$-0.632411\pi$
$53$	1.35437	−	0.781947i	0.186037	−	0.107409i	0.590126	+	0.807311i	$0.299078\pi$
$54$	1.25741	−	0.647235i	0.171112	−	0.0880775i
$55$	7.14421			0.963325
$56$	−7.16555	+	2.15753i	−0.957537	+	0.288311i
$57$	7.04013			0.932488
$58$	4.19831	−	2.16102i	0.551266	−	0.283756i
$59$	−5.26742	+	3.04114i	−0.685759	+	0.395923i	−0.802021	−	0.597295i	$-0.796242\pi$
$59$	−5.26742	+	3.04114i	−0.685759	+	0.395923i	0.116262	+	0.993219i	$0.462909\pi$
$60$	−6.79644	−	4.85269i	−0.877416	−	0.626479i
$61$	−4.55959	+	7.89744i	−0.583795	+	1.01116i	0.411229	+	0.911532i	$0.365100\pi$
$61$	−4.55959	+	7.89744i	−0.583795	+	1.01116i	−0.995024	+	0.0996311i	$0.968234\pi$
$62$	2.42039	−	3.76097i	0.307390	−	0.477643i
$63$	0.228411	−	2.63587i	0.0287771	−	0.332089i
$64$	7.66734	+	2.28297i	0.958417	+	0.285371i
$65$	−3.21646	+	5.57107i	−0.398952	+	0.691006i
$66$	0.116661	−	2.41686i	0.0143600	−	0.297495i
$67$	3.73658	+	6.47195i	0.456496	+	0.790675i	0.998773	−	0.0495251i	$-0.0157708\pi$
$67$	3.73658	+	6.47195i	0.456496	+	0.790675i	−0.542276	+	0.840200i	$0.682437\pi$
$68$	−0.449517	+	4.64545i	−0.0545119	+	0.563344i
$69$	0.468884			0.0564470
$70$	−14.4566	+	5.92433i	−1.72789	+	0.708093i
$71$			3.49263i			0.414499i	0.978288	+	0.207249i	$0.0664512\pi$
$71$			3.49263i			0.414499i	−0.978288	+	0.207249i	$0.933549\pi$
$72$	−1.75263	+	2.21997i	−0.206550	+	0.261626i
$73$	−12.5811	+	7.26372i	−1.47251	+	0.850154i	−0.999522	−	0.0309152i	$-0.990158\pi$
$73$	−12.5811	+	7.26372i	−1.47251	+	0.850154i	−0.472988	+	0.881069i	$0.656824\pi$
$74$	0.609899	−	12.6352i	0.0708993	−	1.46882i
$75$	−10.7691	−	6.21752i	−1.24350	−	0.717937i
$76$	−12.8152	+	5.83295i	−1.47001	+	0.669085i
$77$	−3.71029	−	2.59340i	−0.422826	−	0.295545i
$78$	1.83215	+	1.17909i	0.207450	+	0.133506i
$79$	1.46108	+	0.843557i	0.164385	+	0.0949075i	0.579935	−	0.814662i	$-0.303078\pi$
$79$	1.46108	+	0.843557i	0.164385	+	0.0949075i	−0.415551	+	0.909570i	$0.636411\pi$
$80$	16.3922	+	3.20237i	1.83271	+	0.358036i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.68203	+	3.43948i	−0.737907	+	0.379827i
$83$		−	2.72601i		−	0.299219i	−0.988745	−	0.149609i	$-0.952198\pi$
$83$		−	2.72601i		−	0.299219i	0.988745	−	0.149609i	$-0.0478016\pi$
$84$	1.76812	+	4.98736i	0.192917	+	0.544166i
$85$			9.74391i			1.05688i
$86$	−2.21854	−	4.31005i	−0.239231	−	0.464765i
$87$	−1.66943	−	2.89153i	−0.178981	−	0.310005i
$88$	1.79008	+	4.49611i	0.190823	+	0.479287i
$89$	1.83829	+	1.06134i	0.194858	+	0.112501i	0.594255	−	0.804277i	$-0.297447\pi$
$89$	1.83829	+	1.06134i	0.194858	+	0.112501i	−0.399397	+	0.916778i	$0.630780\pi$
$90$	−3.19567	+	4.96566i	−0.336854	+	0.523426i
$91$	3.69278	−	1.72569i	0.387108	−	0.180902i
$92$	−0.853516	+	0.388484i	−0.0889852	+	0.0405022i
$93$	−2.73883	−	1.58126i	−0.284003	−	0.163969i
$94$	8.33550	+	0.402352i	0.859741	+	0.0414995i
$95$	−25.4579	+	14.6981i	−2.61193	+	1.50800i
$96$	1.35103	−	5.49315i	0.137889	−	0.560642i
$97$			1.95202i			0.198198i	0.995078	+	0.0990990i	$0.0315960\pi$
$97$			1.95202i			0.198198i	−0.995078	+	0.0990990i	$0.968404\pi$
$98$	9.65849	+	2.17109i	0.975655	+	0.219313i
$99$	−1.71097			−0.171959
$100$	24.7545	+	2.39536i	2.47545	+	0.239536i
$101$	−6.89045	−	11.9346i	−0.685625	−	1.18754i	−0.973240	−	0.229792i	$-0.926196\pi$
$101$	−6.89045	−	11.9346i	−0.685625	−	1.18754i	0.287615	−	0.957746i	$-0.407138\pi$
$102$	3.29634	+	0.159113i	0.326386	+	0.0157546i
$103$	3.84129	−	6.65331i	0.378494	−	0.655570i	−0.612350	−	0.790587i	$-0.709776\pi$
$103$	3.84129	−	6.65331i	0.378494	−	0.655570i	0.990843	+	0.135017i	$0.0431089\pi$
$104$	−4.31200	−	0.628324i	−0.422826	−	0.0616123i
$105$	4.67712	+	10.0085i	0.456440	+	0.976728i
$106$	1.85983	+	1.19690i	0.180642	+	0.116253i
$107$	7.20414	−	12.4779i	0.696450	−	1.20629i	−0.273239	−	0.961946i	$-0.588095\pi$
$107$	7.20414	−	12.4779i	0.696450	−	1.20629i	0.969689	−	0.244341i	$-0.0785715\pi$
$108$	1.62768	+	1.16217i	0.156624	+	0.111830i
$109$	2.92380	−	1.68806i	0.280050	−	0.161687i	−0.353396	−	0.935474i	$-0.614973\pi$
$109$	2.92380	−	1.68806i	0.280050	−	0.161687i	0.633446	+	0.773787i	$0.281640\pi$
$110$	4.62398	+	8.98322i	0.440879	+	0.856516i
$111$	−8.94486			−0.849009
$112$	−7.35069	−	7.61363i	−0.694575	−	0.719420i
$113$	−10.7090			−1.00742			−0.503710	−	0.863873i	$-0.668032\pi$
$113$	−10.7090			−1.00742			−0.503710	+	0.863873i	$0.668032\pi$
$114$	4.55662	+	8.85235i	0.426766	+	0.829098i
$115$	−1.69554	+	0.978920i	−0.158110	+	0.0912847i
$116$	5.43459	+	3.88032i	0.504589	+	0.360279i
$117$	0.770311	−	1.33422i	0.0712153	−	0.123349i
$118$	−7.23323	−	4.65498i	−0.665873	−	0.428526i
$119$	3.53711	−	5.06042i	0.324246	−	0.463888i
$120$	1.70294	−	11.6868i	0.155456	−	1.06685i
$121$	4.03629	−	6.99106i	0.366935	−	0.635551i
$122$	−12.8815	−	0.621785i	−1.16623	−	0.0562937i
$123$	2.65706	+	4.60216i	0.239579	+	0.414963i
$124$	6.29565	+	0.609198i	0.565366	+	0.0547076i
$125$	31.0452			2.77677
$126$	3.46222	−	1.41882i	0.308439	−	0.126399i
$127$			9.49738i			0.842757i	0.906885	+	0.421378i	$0.138454\pi$
$127$			9.49738i			0.842757i	−0.906885	+	0.421378i	$0.861546\pi$
$128$	2.09193	+	11.1186i	0.184903	+	0.982757i
$129$	−2.96849	+	1.71386i	−0.261361	+	0.150897i
$130$	−9.08693	−	0.438624i	−0.796977	−	0.0384699i
$131$	−11.8364	−	6.83375i	−1.03415	−	0.597068i	−0.115981	−	0.993251i	$-0.537001\pi$
$131$	−11.8364	−	6.83375i	−1.03415	−	0.597068i	−0.918171	+	0.396184i	$0.870334\pi$
$132$	3.11450	−	1.41759i	0.271083	−	0.123385i
$133$	18.5569	+	1.60805i	1.60909	+	0.139435i
$134$	−5.71947	+	8.88730i	−0.494087	+	0.767746i
$135$	3.61611	+	2.08776i	0.311226	+	0.179686i
$136$	−6.13220	+	2.44147i	−0.525832	+	0.209355i
$137$	5.99460	+	10.3829i	0.512153	+	0.887075i	0.999901	+	0.0140902i	$0.00448520\pi$
$137$	5.99460	+	10.3829i	0.512153	+	0.887075i	−0.487748	+	0.872985i	$0.662181\pi$
$138$	0.303478	+	0.589581i	0.0258338	+	0.0501885i
$139$			6.64909i			0.563968i	0.959419	+	0.281984i	$0.0909925\pi$
$139$			6.64909i			0.563968i	−0.959419	+	0.281984i	$0.909007\pi$
$140$	−16.8061	−	14.3435i	−1.42038	−	1.21224i
$141$		−	5.90095i		−	0.496950i
$142$	−4.39168	+	2.26055i	−0.368541	+	0.189701i
$143$	−1.31798	−	2.28281i	−0.110215	−	0.190898i
$144$	−3.92579	−	0.766938i	−0.327149	−	0.0639115i
$145$	12.0737	+	6.97073i	1.00266	+	0.578888i
$146$	−17.2764	−	11.1183i	−1.42981	−	0.920160i
$147$	1.20413	−	6.89566i	0.0993147	−	0.568744i
$148$	16.2824	−	7.41107i	1.33841	−	0.609186i
$149$	−7.03123	−	4.05948i	−0.576021	−	0.332566i	0.183530	−	0.983014i	$-0.441248\pi$
$149$	−7.03123	−	4.05948i	−0.576021	−	0.332566i	−0.759550	+	0.650448i	$0.774581\pi$
$150$	0.847875	−	17.5653i	0.0692287	−	1.43420i
$151$	1.07044	−	0.618020i	0.0871113	−	0.0502937i	−0.455812	−	0.890076i	$-0.650651\pi$
$151$	1.07044	−	0.618020i	0.0871113	−	0.0502937i	0.542923	+	0.839783i	$0.317318\pi$
$152$	−15.6289	−	12.3388i	−1.26767	−	1.00081i
$153$		−	2.33358i		−	0.188658i
$154$	0.859544	−	6.34390i	0.0692640	−	0.511206i
$155$	13.2052			1.06067
$156$	−0.296770	+	3.06692i	−0.0237606	+	0.245550i
$157$	4.80286	+	8.31880i	0.383310	+	0.663913i	0.991533	−	0.129854i	$-0.0414507\pi$
$157$	4.80286	+	8.31880i	0.383310	+	0.663913i	−0.608223	+	0.793766i	$0.708117\pi$
$158$	−0.115035	+	2.38316i	−0.00915167	+	0.189594i
$159$	0.781947	−	1.35437i	0.0620124	−	0.107409i
$160$	6.58293	+	22.6845i	0.520426	+	1.79337i
$161$	1.23592	+	0.107099i	0.0974041	+	0.00844055i
$162$	0.765334	−	1.18923i	0.0601303	−	0.0934346i
$163$	9.70461	−	16.8089i	0.760123	−	1.31657i	−0.182663	−	0.983176i	$-0.558472\pi$
$163$	9.70461	−	16.8089i	0.760123	−	1.31657i	0.942787	−	0.333397i	$-0.108195\pi$
$164$	−8.64969	−	6.17592i	−0.675428	−	0.482258i
$165$	6.18706	−	3.57210i	0.481662	−	0.278088i
$166$	3.42773	−	1.76437i	0.266043	−	0.136942i
$167$	17.7482			1.37340			0.686699	−	0.726942i	$-0.259059\pi$
$167$	17.7482			1.37340			0.686699	+	0.726942i	$0.259059\pi$
$168$	−5.12678	+	5.45125i	−0.395540	+	0.420573i
$169$	−10.6265			−0.817422
$170$	−12.2521	+	6.30660i	−0.939695	+	0.483694i
$171$	6.09693	−	3.52006i	0.466244	−	0.269186i
$172$	3.98360	−	5.57924i	0.303747	−	0.425413i
$173$	−3.57075	+	6.18472i	−0.271479	+	0.470216i	−0.969241	−	0.246114i	$-0.920846\pi$
$173$	−3.57075	+	6.18472i	−0.271479	+	0.470216i	0.697762	+	0.716330i	$0.254179\pi$
$174$	2.55534	−	3.97066i	0.193719	−	0.301015i
$175$	−26.9657	−	18.8484i	−2.03842	−	1.42480i
$176$	−4.49486	+	5.16091i	−0.338813	+	0.389018i
$177$	−3.04114	+	5.26742i	−0.228586	+	0.395923i
$178$	−0.144733	+	2.99842i	−0.0108482	+	0.224741i
$179$	−11.9581	−	20.7121i	−0.893791	−	1.54809i	−0.835293	−	0.549805i	$-0.814702\pi$
$179$	−11.9581	−	20.7121i	−0.893791	−	1.54809i	−0.0584980	−	0.998288i	$-0.518631\pi$
$180$	−8.31223	−	0.804332i	−0.619557	−	0.0599514i
$181$	−20.5572			−1.52800			−0.764002	−	0.645214i	$-0.776768\pi$
$181$	−20.5572			−1.52800			−0.764002	+	0.645214i	$0.776768\pi$
$182$	4.56000	+	3.52642i	0.338010	+	0.261395i
$183$			9.11917i			0.674109i
$184$	−1.04091	−	0.821782i	−0.0767369	−	0.0605826i
$185$	32.3456	−	18.6748i	2.37810	−	1.37300i
$186$	0.215635	−	4.46729i	0.0158111	−	0.327557i
$187$	−3.45776	−	1.99634i	−0.252857	−	0.145987i
$188$	4.88910	+	10.7416i	0.356575	+	0.783410i
$189$	−1.12013	−	2.39694i	−0.0814772	−	0.174352i
$190$	−34.9589	−	22.4979i	−2.53618	−	1.63217i
$191$	1.74523	+	1.00761i	0.126280	+	0.0729079i	0.561809	−	0.827267i	$-0.310105\pi$
$191$	1.74523	+	1.00761i	0.126280	+	0.0729079i	−0.435529	+	0.900175i	$0.643439\pi$
$192$	7.78159	−	1.85656i	0.561588	−	0.133986i
$193$	1.78535	+	3.09232i	0.128512	+	0.222590i	0.923100	−	0.384559i	$-0.125646\pi$
$193$	1.78535	+	3.09232i	0.128512	+	0.222590i	−0.794588	+	0.607149i	$0.792313\pi$
$194$	−2.45450	+	1.26342i	−0.176223	+	0.0907081i
$195$			6.43291i			0.460671i
$196$	3.52136	+	13.5499i	0.251526	+	0.967851i
$197$			17.5393i			1.24962i	0.780775	+	0.624812i	$0.214824\pi$
$197$			17.5393i			1.24962i	−0.780775	+	0.624812i	$0.785176\pi$
$198$	−1.10740	−	2.15140i	−0.0786995	−	0.152893i
$199$	8.85336	+	15.3345i	0.627598	+	1.08703i	0.988032	+	0.154247i	$0.0492952\pi$
$199$	8.85336	+	15.3345i	0.627598	+	1.08703i	−0.360434	+	0.932785i	$0.617371\pi$
$200$	13.0100	+	32.6769i	0.919945	+	2.31061i
$201$	6.47195	+	3.73658i	0.456496	+	0.263558i
$202$	10.5470	−	16.3886i	0.742083	−	1.15310i
$203$	−3.73994	−	8.00302i	−0.262492	−	0.561702i
$204$	1.93343	+	4.24784i	0.135367	+	0.297408i
$205$	−19.2164	−	11.0946i	−1.34213	−	0.774882i
$206$	10.8522	+	0.523831i	0.756107	+	0.0364971i
$207$	0.406066	−	0.234442i	0.0282235	−	0.0162949i
$208$	−2.00082	−	5.82864i	−0.138732	−	0.404143i
$209$		−	12.0455i		−	0.833201i
$210$	−9.55760	+	12.3589i	−0.659537	+	0.852846i
$211$	−4.23050			−0.291240			−0.145620	−	0.989341i	$-0.546518\pi$
$211$	−4.23050			−0.291240			−0.145620	+	0.989341i	$0.546518\pi$
$212$	−0.301253	+	3.11325i	−0.0206901	+	0.213819i
$213$	1.74631	+	3.02471i	0.119656	+	0.207249i
$214$	20.3527	+	0.982418i	1.39128	+	0.0671567i
$215$	7.15626	−	12.3950i	0.488053	−	0.845333i
$216$	−0.407838	+	2.79887i	−0.0277499	+	0.190439i
$217$	−6.85803	−	4.79359i	−0.465553	−	0.325410i
$218$	4.01498	+	2.58386i	0.271928	+	0.175001i
$219$	−7.26372	+	12.5811i	−0.490837	+	0.850154i
$220$	−8.30281	+	11.6285i	−0.559775	+	0.783994i
$221$	3.11350	−	1.79758i	0.209437	−	0.120918i
$222$	−5.78943	−	11.2474i	−0.388561	−	0.754875i
$223$	1.43532			0.0961162			0.0480581	−	0.998845i	$-0.484697\pi$
$223$	1.43532			0.0961162			0.0480581	+	0.998845i	$0.484697\pi$
$224$	4.81584	−	14.1707i	0.321772	−	0.946817i
$225$	−12.4350			−0.829003
$226$	−6.93126	−	13.4657i	−0.461060	−	0.895723i
$227$	13.8688	−	8.00718i	0.920508	−	0.531455i	0.0367106	−	0.999326i	$-0.488312\pi$
$227$	13.8688	−	8.00718i	0.920508	−	0.531455i	0.883797	+	0.467871i	$0.154979\pi$
$228$	−8.18185	+	11.4591i	−0.541856	+	0.758897i
$229$	8.12499	−	14.0729i	0.536914	−	0.929963i	−0.462154	−	0.886800i	$-0.652923\pi$
$229$	8.12499	−	14.0729i	0.536914	−	0.929963i	0.999068	−	0.0431631i	$-0.0137435\pi$
$230$	−2.32832	−	1.49840i	−0.153525	−	0.0988016i
$231$	−4.50990	−	0.390805i	−0.296730	−	0.0257131i
$232$	−1.36171	+	9.34501i	−0.0894006	+	0.613530i
$233$	−5.93054	+	10.2720i	−0.388522	+	0.672941i	−0.992251	−	0.124249i	$-0.960348\pi$
$233$	−5.93054	+	10.2720i	−0.388522	+	0.672941i	0.603729	+	0.797190i	$0.293681\pi$
$234$	2.17624	+	0.105046i	0.142265	+	0.00686709i
$235$	12.3198	+	21.3385i	0.803654	+	1.39197i
$236$	1.17163	−	12.1080i	0.0762667	−	0.788165i
$237$	1.68711			0.109590
$238$	8.65238	+	1.17232i	0.560851	+	0.0759904i
$239$			0.846585i			0.0547610i	0.999625	+	0.0273805i	$0.00871657\pi$
$239$			0.846585i			0.0547610i	−0.999625	+	0.0273805i	$0.991283\pi$
$240$	15.7973	−	5.42278i	1.01971	−	0.350039i
$241$	−0.761425	+	0.439609i	−0.0490477	+	0.0283177i	−0.524323	−	0.851519i	$-0.675682\pi$
$241$	−0.761425	+	0.439609i	−0.0490477	+	0.0283177i	0.475276	+	0.879837i	$0.342348\pi$
$242$	11.4031	+	0.550423i	0.733017	+	0.0353825i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−7.55549	−	16.5998i	−0.483691	−	1.06269i
$245$	10.0422	+	27.4494i	0.641575	+	1.75368i
$246$	−4.06707	+	6.31969i	−0.259307	+	0.402929i
$247$	9.39307	+	5.42309i	0.597667	+	0.345063i
$248$	3.30875	+	8.31052i	0.210106	+	0.527719i
$249$	−1.36301	−	2.36080i	−0.0863771	−	0.149609i
$250$	20.0936	+	39.0367i	1.27083	+	2.46889i
$251$			18.1441i			1.14524i	0.819820	+	0.572622i	$0.194074\pi$
$251$			18.1441i			1.14524i	−0.819820	+	0.572622i	$0.805926\pi$
$252$	4.02491	+	3.43512i	0.253546	+	0.216392i
$253$		−	0.802247i		−	0.0504368i
$254$	−11.9421	+	6.14704i	−0.749316	+	0.385700i
$255$	4.87196	+	8.43848i	0.305094	+	0.528438i
$256$	−12.6267	+	9.82679i	−0.789170	+	0.614174i
$257$	15.8902	+	9.17421i	0.991203	+	0.572271i	0.905634	−	0.424061i	$-0.139396\pi$
$257$	15.8902	+	9.17421i	0.991203	+	0.572271i	0.0855695	+	0.996332i	$0.472729\pi$
$258$	−4.07634	−	2.62335i	−0.253782	−	0.163322i
$259$	−23.5775	−	2.04311i	−1.46504	−	0.126953i
$260$	−5.32985	−	11.7099i	−0.330543	−	0.726218i
$261$	−2.89153	−	1.66943i	−0.178981	−	0.103335i
$262$	0.931910	−	19.3063i	0.0575736	−	1.19275i
$263$	3.02044	−	1.74385i	0.186248	−	0.107531i	−0.403977	−	0.914769i	$-0.632372\pi$
$263$	3.02044	−	1.74385i	0.186248	−	0.107531i	0.590225	+	0.807239i	$0.299039\pi$
$264$	3.79831	+	2.99870i	0.233770	+	0.184557i
$265$			6.53008i			0.401140i
$266$	9.98869	+	24.3744i	0.612446	+	1.49449i
$267$	2.12267			0.129905
$268$	−14.8769	−	1.43956i	−0.908748	−	0.0879349i
$269$	−7.35605	−	12.7410i	−0.448506	−	0.776835i	0.549783	−	0.835308i	$-0.314710\pi$
$269$	−7.35605	−	12.7410i	−0.448506	−	0.776835i	−0.998289	+	0.0584722i	$0.981377\pi$
$270$	−0.284706	+	5.89822i	−0.0173266	+	0.358954i
$271$	−9.95139	+	17.2363i	−0.604504	+	1.04703i	0.387626	+	0.921817i	$0.373295\pi$
$271$	−9.95139	+	17.2363i	−0.604504	+	1.04703i	−0.992130	+	0.125215i	$0.960038\pi$
$272$	−7.03891	−	6.13049i	−0.426797	−	0.371716i
$273$	2.33519	−	3.34088i	0.141332	−	0.202199i
$274$	−9.17573	+	14.2579i	−0.554326	+	0.861350i
$275$	−10.6380	+	18.4255i	−0.641495	+	1.11110i
$276$	−0.544925	+	0.763195i	−0.0328006	+	0.0459389i
$277$	22.9034	−	13.2233i	1.37613	−	0.794510i	0.384440	−	0.923150i	$-0.374395\pi$
$277$	22.9034	−	13.2233i	1.37613	−	0.794510i	0.991691	+	0.128640i	$0.0410613\pi$
$278$	−8.36065	+	4.30352i	−0.501438	+	0.258108i
$279$	−3.16253			−0.189336
$280$	7.15812	−	30.4158i	0.427779	−	1.81769i
$281$	−20.2837			−1.21003			−0.605013	−	0.796216i	$-0.706832\pi$
$281$	−20.2837			−1.21003			−0.605013	+	0.796216i	$0.706832\pi$
$282$	7.41993	−	3.81930i	0.441850	−	0.227436i
$283$	5.70426	−	3.29336i	0.339083	−	0.195770i	−0.320783	−	0.947153i	$-0.603946\pi$
$283$	5.70426	−	3.29336i	0.339083	−	0.195770i	0.659866	+	0.751383i	$0.270613\pi$
$284$	−5.68489	−	4.05904i	−0.337336	−	0.240860i
$285$	−14.6981	+	25.4579i	−0.870642	+	1.50800i
$286$	2.01739	−	3.13476i	0.119291	−	0.185362i
$287$	5.95248	+	12.7376i	0.351364	+	0.751877i
$288$	−1.57655	−	5.43272i	−0.0928991	−	0.320126i
$289$	−5.77721	+	10.0064i	−0.339836	+	0.588613i
$290$	−0.950589	+	19.6933i	−0.0558205	+	1.15643i
$291$	0.976012	+	1.69050i	0.0572148	+	0.0990990i
$292$	2.79842	−	28.9198i	0.163765	−	1.69240i
$293$	−12.9438			−0.756187			−0.378094	−	0.925767i	$-0.623420\pi$
$293$	−12.9438			−0.756187			−0.378094	+	0.925767i	$0.623420\pi$
$294$	9.45004	−	2.94903i	0.551137	−	0.171991i
$295$		−	25.3968i		−	1.47866i
$296$	19.8573	+	15.6771i	1.15418	+	0.911210i
$297$	−1.48174	+	0.855485i	−0.0859795	+	0.0496403i
$298$	0.553586	−	11.4686i	0.0320684	−	0.664358i
$299$	0.625594	+	0.361187i	0.0361790	+	0.0208880i
$300$	22.6357	−	10.3028i	1.30687	−	0.594831i
$301$	−8.21603	+	3.83948i	−0.473564	+	0.221304i
$302$	1.46993	+	0.945983i	0.0845851	+	0.0544352i
$303$	−11.9346	−	6.89045i	−0.685625	−	0.395846i
$304$	5.39934	−	27.6380i	0.309674	−	1.58515i
$305$	−19.0387	−	32.9760i	−1.09015	−	1.88820i
$306$	2.93427	−	1.51037i	0.167741	−	0.0863422i
$307$			11.8773i			0.677871i	0.940810	+	0.338936i	$0.110067\pi$
$307$			11.8773i			0.677871i	−0.940810	+	0.338936i	$0.889933\pi$
$308$	8.53323	−	3.02519i	0.486226	−	0.172376i
$309$		−	7.68258i		−	0.437047i
$310$	8.54688	+	16.6044i	0.485430	+	0.943067i
$311$	−5.91849	−	10.2511i	−0.335607	−	0.581288i	0.647994	−	0.761645i	$-0.275608\pi$
$311$	−5.91849	−	10.2511i	−0.335607	−	0.581288i	−0.983601	+	0.180357i	$0.942275\pi$
$312$	−4.04846	+	1.61186i	−0.229199	+	0.0912534i
$313$	−12.8383	−	7.41217i	−0.725661	−	0.418961i	0.0911716	−	0.995835i	$-0.470939\pi$
$313$	−12.8383	−	7.41217i	−0.725661	−	0.418961i	−0.816833	+	0.576875i	$0.804272\pi$
$314$	−7.35159	+	11.4234i	−0.414874	+	0.644660i
$315$	9.05475	+	6.32904i	0.510177	+	0.356601i
$316$	−3.07107	+	1.39782i	−0.172761	+	0.0786336i
$317$	5.87478	+	3.39181i	0.329961	+	0.190503i	0.655824	−	0.754914i	$-0.272322\pi$
$317$	5.87478	+	3.39181i	0.329961	+	0.190503i	−0.325863	+	0.945417i	$0.605655\pi$
$318$	2.20911	+	0.106633i	0.123881	+	0.00597968i
$319$	−4.94732	+	2.85634i	−0.276997	+	0.159924i
$320$	−24.2631	+	22.9597i	−1.35635	+	1.28348i
$321$		−	14.4083i		−	0.804191i
$322$	0.665263	+	1.62338i	0.0370737	+	0.0904674i
$323$	16.4287			0.914116
$324$	1.99070	+	0.192630i	0.110595	+	0.0107017i
$325$	−9.57885	−	16.5911i	−0.531339	−	0.920306i
$326$	27.4168	+	1.32340i	1.51848	+	0.0732966i
$327$	1.68806	−	2.92380i	0.0933499	−	0.161687i
$328$	2.16730	−	14.8735i	0.119669	−	0.821252i
$329$	1.34784	−	15.5542i	0.0743090	−	0.857528i
$330$	8.49609	+	5.46770i	0.467695	+	0.300987i
$331$	2.37285	−	4.10989i	0.130424	−	0.225900i	−0.793416	−	0.608679i	$-0.791700\pi$
$331$	2.37285	−	4.10989i	0.130424	−	0.225900i	0.923840	+	0.382779i	$0.125033\pi$
$332$	4.43709	+	3.16810i	0.243517	+	0.173872i
$333$	−7.74648	+	4.47243i	−0.424504	+	0.245088i
$334$	11.4873	+	22.3168i	0.628555	+	1.22112i
$335$	−31.2044			−1.70488
$336$	−10.1727	−	2.91825i	−0.554966	−	0.159203i
$337$	16.5173			0.899754			0.449877	−	0.893090i	$-0.351468\pi$
$337$	16.5173			0.899754			0.449877	+	0.893090i	$0.351468\pi$
$338$	−6.87783	−	13.3619i	−0.374105	−	0.726790i
$339$	−9.27429	+	5.35451i	−0.503710	+	0.290817i
$340$	−15.8600	−	11.3241i	−0.860130	−	0.614137i
$341$	−2.70549	+	4.68605i	−0.146511	+	0.253764i
$342$	8.37232	+	5.38805i	0.452723	+	0.291352i
$343$	4.74897	−	17.9010i	0.256420	−	0.966565i
$344$	9.59373	+	1.39795i	0.517259	+	0.0753726i
$345$	−0.978920	+	1.69554i	−0.0527033	+	0.0912847i
$346$	−10.0879	−	0.486938i	−0.542327	−	0.0261780i
$347$	9.54986	+	16.5408i	0.512663	+	0.887959i	0.999892	+	0.0146846i	$0.00467441\pi$
$347$	9.54986	+	16.5408i	0.512663	+	0.887959i	−0.487229	+	0.873274i	$0.661992\pi$
$348$	6.64666	+	0.643163i	0.356298	+	0.0344772i
$349$	2.49767			0.133697			0.0668485	−	0.997763i	$-0.478706\pi$
$349$	2.49767			0.133697			0.0668485	+	0.997763i	$0.478706\pi$
$350$	6.24702	−	46.1064i	0.333917	−	2.46449i
$351$		−	1.54062i		−	0.0822323i
$352$	−9.39862	−	2.31157i	−0.500948	−	0.123207i
$353$	−22.3071	+	12.8790i	−1.18729	+	0.685481i	−0.957689	−	0.287805i	$-0.907075\pi$
$353$	−22.3071	+	12.8790i	−1.18729	+	0.685481i	−0.229599	+	0.973285i	$0.573741\pi$
$354$	−8.59165	−	0.414717i	−0.456641	−	0.0220419i
$355$	−12.6297	−	7.29179i	−0.670317	−	0.387008i
$356$	−3.86393	+	1.75869i	−0.204788	+	0.0932105i
$357$	0.533015	−	6.15101i	0.0282102	−	0.325546i
$358$	18.3039	−	28.4419i	0.967391	−	1.50320i
$359$	28.7697	+	16.6102i	1.51840	+	0.876651i	0.999765	+	0.0216582i	$0.00689457\pi$
$359$	28.7697	+	16.6102i	1.51840	+	0.876651i	0.518639	+	0.854993i	$0.326439\pi$
$360$	−4.36859	−	10.9725i	−0.230245	−	0.578301i
$361$	15.2817	+	26.4687i	0.804300	+	1.39309i
$362$	−13.3053	−	25.8489i	−0.699313	−	1.35859i
$363$		−	8.07258i		−	0.423701i
$364$	−1.48277	+	8.01623i	−0.0777182	+	0.420164i
$365$		−	60.6597i		−	3.17507i
$366$	−11.4666	+	5.90225i	−0.599367	+	0.308516i
$367$	2.17584	+	3.76866i	0.113578	+	0.196722i	0.917210	−	0.398403i	$-0.130436\pi$
$367$	2.17584	+	3.76866i	0.113578	+	0.196722i	−0.803633	+	0.595126i	$0.797102\pi$
$368$	0.359605	−	1.84074i	0.0187457	−	0.0959552i
$369$	4.60216	+	2.65706i	0.239579	+	0.138321i
$370$	44.4171	+	28.5849i	2.30914	+	1.48606i
$371$	2.37047	−	3.39135i	0.123068	−	0.176070i
$372$	5.75679	−	2.62024i	0.298476	−	0.135853i
$373$	11.0943	+	6.40533i	0.574444	+	0.331655i	0.758922	−	0.651181i	$-0.225726\pi$
$373$	11.0943	+	6.40533i	0.574444	+	0.331655i	−0.184479	+	0.982837i	$0.559060\pi$
$374$	0.272238	−	5.63994i	0.0140771	−	0.291634i
$375$	26.8859	−	15.5226i	1.38838	−	0.801584i
$376$	−10.3422	+	13.0999i	−0.533358	+	0.675578i
$377$		−	5.14391i		−	0.264925i
$378$	2.28896	−	2.95984i	0.117731	−	0.152238i
$379$	−24.0807			−1.23694			−0.618472	−	0.785807i	$-0.712248\pi$
$379$	−24.0807			−1.23694			−0.618472	+	0.785807i	$0.712248\pi$
$380$	5.66260	−	58.5192i	0.290485	−	3.00197i
$381$	4.74869	+	8.22498i	0.243283	+	0.421378i
$382$	−0.137406	+	2.84663i	−0.00703030	+	0.145646i
$383$	8.78233	−	15.2114i	0.448756	−	0.777268i	−0.549549	−	0.835461i	$-0.685201\pi$
$383$	8.78233	−	15.2114i	0.448756	−	0.777268i	0.998305	+	0.0581930i	$0.0185339\pi$
$384$	7.37098	+	8.58304i	0.376149	+	0.438002i
$385$	17.1242	−	8.00242i	0.872731	−	0.407841i
$386$	−2.73278	+	4.24638i	−0.139095	+	0.216135i
$387$	−1.71386	+	2.96849i	−0.0871203	+	0.150897i
$388$	−3.17728	−	2.26859i	−0.161302	−	0.115170i
$389$	−23.9022	+	13.7999i	−1.21189	+	0.699685i	−0.963171	−	0.268890i	$-0.913343\pi$
$389$	−23.9022	+	13.7999i	−1.21189	+	0.699685i	−0.248719	+	0.968576i	$0.580010\pi$
$390$	−8.08883	+	4.16361i	−0.409594	+	0.210832i
$391$	1.09418			0.0553349
$392$	−14.7587	+	13.1978i	−0.745426	+	0.666588i
$393$	−13.6675			−0.689435
$394$	−22.0541	+	11.3521i	−1.11107	+	0.571908i
$395$	−6.10079	+	3.52229i	−0.306964	+	0.177226i
$396$	1.98844	−	2.78492i	0.0999231	−	0.139947i
$397$	−8.65850	+	14.9970i	−0.434558	+	0.752676i	−0.997259	−	0.0739841i	$-0.976429\pi$
$397$	−8.65850	+	14.9970i	−0.434558	+	0.752676i	0.562702	+	0.826660i	$0.309762\pi$
$398$	−13.5516	+	21.0573i	−0.679278	+	1.05551i
$399$	16.8748	−	7.88583i	0.844794	−	0.394786i
$400$	−32.6679	+	37.5086i	−1.63339	+	1.87543i
$401$	−3.87616	+	6.71371i	−0.193566	+	0.335266i	−0.946430	−	0.322910i	$-0.895339\pi$
$401$	−3.87616	+	6.71371i	−0.193566	+	0.335266i	0.752863	+	0.658177i	$0.228672\pi$
$402$	−0.509553	+	10.5564i	−0.0254142	+	0.526504i
$403$	−2.43613	−	4.21950i	−0.121352	−	0.210188i
$404$	27.4337	+	2.65462i	1.36488	+	0.132072i
$405$	4.17553			0.207484
$406$	7.64248	−	9.88248i	0.379290	−	0.490459i
$407$			15.3044i			0.758611i
$408$	−4.08990	+	5.18048i	−0.202480	+	0.256472i
$409$	−4.01694	+	2.31918i	−0.198625	+	0.114676i	−0.596014	−	0.802974i	$-0.703250\pi$
$409$	−4.01694	+	2.31918i	−0.198625	+	0.114676i	0.397389	+	0.917650i	$0.369916\pi$
$410$	1.51296	−	31.3438i	0.0747196	−	1.54796i
$411$	10.3829	+	5.99460i	0.512153	+	0.295692i
$412$	6.36524	+	13.9847i	0.313593	+	0.688977i
$413$	−9.21921	+	13.1896i	−0.453648	+	0.649018i
$414$	0.557610	+	0.358853i	0.0274051	+	0.0176367i
$415$	9.85758	+	5.69128i	0.483889	+	0.279374i
$416$	6.03401	−	6.28835i	0.295841	−	0.308312i
$417$	3.32454	+	5.75828i	0.162804	+	0.281984i
$418$	15.1461	−	7.79624i	0.740820	−	0.381327i
$419$			14.2419i			0.695760i	0.937539	+	0.347880i	$0.113098\pi$
$419$			14.2419i			0.695760i	−0.937539	+	0.347880i	$0.886902\pi$
$420$	−21.7263	−	4.01873i	−1.06013	−	0.196094i
$421$			20.0126i			0.975356i	0.873024	+	0.487678i	$0.162156\pi$
$421$			20.0126i			0.975356i	−0.873024	+	0.487678i	$0.837844\pi$
$422$	−2.73813	−	5.31948i	−0.133290	−	0.258948i
$423$	−2.95047	−	5.11037i	−0.143457	−	0.248475i
$424$	−4.10962	+	1.63620i	−0.199581	+	0.0794610i
$425$	−25.1304	−	14.5091i	−1.21900	−	0.703793i
$426$	−2.67303	+	4.15353i	−0.129509	+	0.201239i
$427$	−2.08292	+	24.0370i	−0.100800	+	1.16323i
$428$	11.9377	+	26.2276i	0.577029	+	1.26776i
$429$	−2.28281	−	1.31798i	−0.110215	−	0.0636327i
$430$	20.2174	+	0.975890i	0.974971	+	0.0470616i
$431$	12.1099	−	6.99165i	0.583313	−	0.336776i	−0.179136	−	0.983824i	$-0.557330\pi$
$431$	12.1099	−	6.99165i	0.583313	−	0.336776i	0.762449	+	0.647049i	$0.223997\pi$
$432$	−3.78330	+	1.29871i	−0.182024	+	0.0624840i
$433$			0.984888i			0.0473307i	0.999720	+	0.0236653i	$0.00753362\pi$
$433$			0.984888i			0.0473307i	−0.999720	+	0.0236653i	$0.992466\pi$
$434$	1.58876	−	11.7259i	0.0762632	−	0.562864i
$435$	13.9415			0.668442
$436$	−0.650342	+	6.72084i	−0.0311457	+	0.321870i
$437$	1.65050	+	2.85875i	0.0789542	+	0.136753i
$438$	−20.5210	−	0.990543i	−0.980531	−	0.0473300i
$439$	3.43693	−	5.95294i	0.164036	−	0.284118i	−0.772277	−	0.635286i	$-0.780882\pi$
$439$	3.43693	−	5.95294i	0.164036	−	0.284118i	0.936312	+	0.351168i	$0.114215\pi$
$440$	−19.9957	−	2.91368i	−0.953258	−	0.138904i
$441$	−2.40502	−	6.57388i	−0.114525	−	0.313042i
$442$	4.27547	+	2.75150i	0.203363	+	0.130875i
$443$	−1.70483	+	2.95285i	−0.0809989	+	0.140294i	−0.903679	−	0.428210i	$-0.859144\pi$
$443$	−1.70483	+	2.95285i	−0.0809989	+	0.140294i	0.822680	+	0.568504i	$0.192478\pi$
$444$	10.3955	−	14.5594i	0.493348	−	0.690959i
$445$	−7.67582	+	4.43164i	−0.363869	+	0.210080i
$446$	0.928990	+	1.80479i	0.0439890	+	0.0854593i
$447$	−8.11897			−0.384014
$448$	20.9354	−	3.11625i	0.989102	−	0.147229i
$449$	32.9924			1.55701			0.778503	−	0.627641i	$-0.215979\pi$
$449$	32.9924			1.55701			0.778503	+	0.627641i	$0.215979\pi$
$450$	−8.04839	−	15.6360i	−0.379405	−	0.737087i
$451$	7.87416	−	4.54615i	0.370780	−	0.214070i
$452$	12.4457	−	17.4309i	0.585399	−	0.819881i
$453$	0.618020	−	1.07044i	0.0290371	−	0.0502937i
$454$	19.0447	+	12.2563i	0.893814	+	0.575218i
$455$	−1.46935	+	16.9563i	−0.0688842	+	0.794926i
$456$	−19.7044	−	2.87123i	−0.922743	−	0.134458i
$457$	11.4224	−	19.7842i	0.534319	−	0.925467i	−0.464877	−	0.885375i	$-0.653902\pi$
$457$	11.4224	−	19.7842i	0.534319	−	0.925467i	0.999196	−	0.0400919i	$-0.0127651\pi$
$458$	22.9542	+	1.10799i	1.07258	+	0.0517731i
$459$	−1.16679	−	2.02094i	−0.0544610	−	0.0943292i
$460$	0.377139	−	3.89747i	0.0175842	−	0.181721i
$461$	15.8743			0.739338			0.369669	−	0.929164i	$-0.379471\pi$
$461$	15.8743			0.739338			0.369669	+	0.929164i	$0.379471\pi$
$462$	−2.42756	−	5.92375i	−0.112940	−	0.275598i
$463$		−	2.72059i		−	0.126436i	−0.998000	−	0.0632182i	$-0.979864\pi$
$463$		−	2.72059i		−	0.126436i	0.998000	−	0.0632182i	$-0.0201364\pi$
$464$	−12.6319	+	4.33619i	−0.586420	+	0.201302i
$465$	11.4361	−	6.60261i	0.530334	−	0.306189i
$466$	−16.7546	−	0.808739i	−0.776141	−	0.0374641i
$467$	20.7726	+	11.9931i	0.961240	+	0.554972i	0.896555	−	0.442933i	$-0.146062\pi$
$467$	20.7726	+	11.9931i	0.961240	+	0.554972i	0.0646858	+	0.997906i	$0.479395\pi$
$468$	1.27645	+	2.80442i	0.0590039	+	0.129634i
$469$	16.2058	+	11.3274i	0.748313	+	0.523052i
$470$	−18.8575	+	29.3021i	−0.869832	+	1.35160i
$471$	8.31880	+	4.80286i	0.383310	+	0.221304i
$472$	15.9831	−	6.36351i	0.735682	−	0.292904i
$473$	2.93236	+	5.07900i	0.134830	+	0.233533i
$474$	1.09196	+	2.12140i	0.0501553	+	0.0974390i
$475$		−	87.5443i		−	4.01681i
$476$	4.12603	+	11.6384i	0.189116	+	0.533445i
$477$		−	1.56389i		−	0.0716058i
$478$	−1.06451	+	0.547939i	−0.0486894	+	0.0250622i
$479$	−9.87511	−	17.1042i	−0.451205	−	0.781511i	0.547256	−	0.836965i	$-0.315672\pi$
$479$	−9.87511	−	17.1042i	−0.451205	−	0.781511i	−0.998461	+	0.0554547i	$0.982339\pi$
$480$	17.0432	+	16.3539i	0.777913	+	0.746449i
$481$	−11.9344	−	6.89033i	−0.544162	−	0.314172i
$482$	−1.04559	−	0.672895i	−0.0476253	−	0.0306495i
$483$	1.12389	−	0.525210i	0.0511386	−	0.0238979i
$484$	6.68836	+	14.6946i	0.304016	+	0.667937i
$485$	−7.05874	−	4.07536i	−0.320521	−	0.185053i
$486$	0.0681843	−	1.41257i	0.00309290	−	0.0640754i
$487$	−32.1435	+	18.5581i	−1.45656	+	0.840946i	−0.998840	−	0.0481495i	$-0.984668\pi$
$487$	−32.1435	+	18.5581i	−1.45656	+	0.840946i	−0.457721	+	0.889096i	$0.651334\pi$
$488$	15.9826	−	20.2443i	0.723497	−	0.916417i
$489$		−	19.4092i		−	0.877715i
$490$	−28.0155	+	30.3935i	−1.26561	+	1.37304i
$491$	−20.5746			−0.928517			−0.464259	−	0.885700i	$-0.653679\pi$
$491$	−20.5746			−0.928517			−0.464259	+	0.885700i	$0.653679\pi$
$492$	−10.5788	−	1.02366i	−0.476930	−	0.0461501i
$493$	−3.89573	−	6.74761i	−0.175455	−	0.303897i
$494$	−0.739539	+	15.3210i	−0.0332734	+	0.689323i
$495$	3.57210	−	6.18706i	0.160554	−	0.278088i
$496$	−8.30821	+	9.53933i	−0.373050	+	0.428328i
$497$	3.91219	+	8.37162i	0.175486	+	0.375518i
$498$	2.08631	−	3.24185i	0.0934898	−	0.145271i
$499$	−0.517579	+	0.896473i	−0.0231700	+	0.0401316i	−0.877378	−	0.479800i	$-0.840709\pi$
$499$	−0.517579	+	0.896473i	−0.0231700	+	0.0401316i	0.854208	+	0.519932i	$0.174043\pi$
$500$	−36.0799	+	50.5318i	−1.61354	+	2.25985i
$501$	15.3704	−	8.87410i	0.686699	−	0.396466i
$502$	−22.8146	+	11.7435i	−1.01826	+	0.524137i
$503$	−19.7898			−0.882382			−0.441191	−	0.897413i	$-0.645444\pi$
$503$	−19.7898			−0.882382			−0.441191	+	0.897413i	$0.645444\pi$
$504$	−1.71430	+	7.28431i	−0.0763611	+	0.324469i
$505$	57.5425			2.56061
$506$	1.00876	−	0.519243i	0.0448447	−	0.0230831i
$507$	−9.20280	+	5.31324i	−0.408711	+	0.235969i
$508$	−15.4587	−	11.0376i	−0.685870	−	0.489715i
$509$	2.11849	−	3.66933i	0.0939004	−	0.162640i	−0.815249	−	0.579111i	$-0.803400\pi$
$509$	2.11849	−	3.66933i	0.0939004	−	0.162640i	0.909149	+	0.416471i	$0.136733\pi$
$510$	−7.45735	+	11.5877i	−0.330217	+	0.513114i
$511$	−22.0199	+	31.5031i	−0.974104	+	1.39362i
$512$	−20.5288	−	9.51676i	−0.907253	−	0.420586i
$513$	3.52006	−	6.09693i	0.155415	−	0.269186i
$514$	−1.25107	+	25.9184i	−0.0551825	+	1.14321i
$515$	16.0394	+	27.7811i	0.706781	+	1.22418i
$516$	0.660281	−	6.82356i	0.0290673	−	0.300391i
$517$	−10.0963			−0.444037
$518$	−12.6912	−	30.9690i	−0.557618	−	1.36070i
$519$			7.14150i			0.313477i
$520$	11.2745	−	14.2809i	0.494421	−	0.626259i
$521$	−33.6570	+	19.4319i	−1.47454	+	0.851326i	−0.999588	−	0.0286855i	$-0.990868\pi$
$521$	−33.6570	+	19.4319i	−1.47454	+	0.851326i	−0.474952	+	0.880012i	$0.657535\pi$
$522$	0.227657	−	4.71636i	0.00996429	−	0.206429i
$523$	14.8181	+	8.55526i	0.647952	+	0.374095i	0.787671	−	0.616096i	$-0.211287\pi$
$523$	14.8181	+	8.55526i	0.647952	+	0.374095i	−0.139719	+	0.990191i	$0.544620\pi$
$524$	24.8791	−	11.3239i	1.08685	−	0.494688i
$525$	−32.7772	−	2.84030i	−1.43051	−	0.123961i
$526$	4.14768	+	2.66926i	0.180847	+	0.116385i
$527$	−6.39126	−	3.69000i	−0.278408	−	0.160739i
$528$	−1.31221	+	6.71691i	−0.0571065	+	0.292316i
$529$	−11.3901	−	19.7282i	−0.495221	−	0.857747i
$530$	−8.21101	+	4.22650i	−0.356663	+	0.183587i
$531$			6.08229i			0.263949i
$532$	−24.1837	+	28.3359i	−1.04850	+	1.22852i
$533$			8.18704i			0.354620i
$534$	1.37387	+	2.66907i	0.0594530	+	0.115502i
$535$	30.0811	+	52.1019i	1.30052	+	2.25256i
$536$	−7.81870	−	19.6381i	−0.337717	−	0.848236i
$537$	−20.7121	−	11.9581i	−0.893791	−	0.516031i
$538$	11.2597	−	17.4960i	0.485439	−	0.754308i
$539$	−11.7983	−	2.06023i	−0.508187	−	0.0887402i
$540$	−7.60077	+	3.45954i	−0.327085	+	0.148875i
$541$	37.6652	+	21.7460i	1.61935	+	0.934935i	0.987087	+	0.160185i	$0.0512092\pi$
$541$	37.6652	+	21.7460i	1.61935	+	0.934935i	0.632268	+	0.774750i	$0.282124\pi$
$542$	−28.1140	−	1.35706i	−1.20760	−	0.0582906i
$543$	−17.8030	+	10.2786i	−0.764002	+	0.441097i
$544$	3.15273	−	12.8187i	0.135172	−	0.549597i
$545$			14.0971i			0.603852i
$546$	5.71229	+	0.773966i	0.244463	+	0.0331227i
$547$	10.8290			0.463016			0.231508	−	0.972833i	$-0.425634\pi$
$547$	10.8290			0.463016			0.231508	+	0.972833i	$0.425634\pi$
$548$	−23.8669	−	2.30948i	−1.01954	−	0.0986560i
$549$	4.55959	+	7.89744i	0.194598	+	0.337054i
$550$	−30.0538	−	1.45069i	−1.28150	−	0.0618576i
$551$	11.7530	−	20.3567i	0.500693	−	0.867226i
$552$	−1.31235	−	0.191229i	−0.0558571	−	0.00813924i
$553$	4.44702	+	0.385356i	0.189106	+	0.0163870i
$554$	31.4510	+	20.2404i	1.33622	+	0.859934i
$555$	18.6748	−	32.3456i	0.792699	−	1.37300i
$556$	−10.8226	−	7.72739i	−0.458981	−	0.327714i
$557$	−7.04197	+	4.06568i	−0.298378	+	0.172269i	−0.641714	−	0.766944i	$-0.721776\pi$
$557$	−7.04197	+	4.06568i	−0.298378	+	0.172269i	0.343336	+	0.939213i	$0.388443\pi$
$558$	−2.04690	−	3.97660i	−0.0866521	−	0.168343i
$559$	−5.28082			−0.223355
$560$	42.8783	−	10.6855i	1.81194	−	0.451544i
$561$	−3.99268			−0.168571
$562$	−13.1283	−	25.5050i	−0.553786	−	1.07586i
$563$	19.6081	−	11.3207i	0.826381	−	0.477111i	−0.0262311	−	0.999656i	$-0.508351\pi$
$563$	19.6081	−	11.3207i	0.826381	−	0.477111i	0.852612	+	0.522545i	$0.175017\pi$
$564$	9.60488	+	6.85793i	0.404438	+	0.288771i
$565$	22.3579	−	38.7251i	0.940605	−	1.62918i
$566$	7.83310	+	5.04103i	0.329250	+	0.211890i
$567$	−2.16853	−	1.51575i	−0.0910696	−	0.0636554i
$568$	1.42443	−	9.77541i	0.0597676	−	0.410167i
$569$	10.1485	−	17.5778i	0.425449	−	0.736900i	−0.571013	−	0.820941i	$-0.693449\pi$
$569$	10.1485	−	17.5778i	0.425449	−	0.736900i	0.996462	+	0.0840413i	$0.0267828\pi$
$570$	−41.5242	−	2.00436i	−1.73926	−	0.0839535i
$571$	−18.3819	−	31.8383i	−0.769257	−	1.33239i	−0.937967	−	0.346726i	$-0.887293\pi$
$571$	−18.3819	−	31.8383i	−0.769257	−	1.33239i	0.168710	−	0.985666i	$-0.446040\pi$
$572$	5.24741	+	0.507765i	0.219405	+	0.0212307i
$573$	2.01521			0.0841868
$574$	−12.1638	+	15.7289i	−0.507706	+	0.656514i
$575$		−	5.83059i		−	0.243153i
$576$	5.81078	−	5.49862i	0.242116	−	0.229109i
$577$	1.39915	−	0.807801i	0.0582475	−	0.0336292i	−0.470593	−	0.882350i	$-0.655960\pi$
$577$	1.39915	−	0.807801i	0.0582475	−	0.0336292i	0.528841	+	0.848721i	$0.322627\pi$
$578$	−16.3214	−	0.787830i	−0.678881	−	0.0327694i
$579$	3.09232	+	1.78535i	0.128512	+	0.0741967i
$580$	−25.3778	+	11.5509i	−1.05376	+	0.479625i
$581$	−3.05348	−	6.53409i	−0.126680	−	0.271080i
$582$	−1.49395	+	2.32140i	−0.0619262	+	0.0962252i
$583$	−2.31729	−	1.33789i	−0.0959723	−	0.0554097i
$584$	38.1753	−	15.1991i	1.57971	−	0.628945i
$585$	3.21646	+	5.57107i	0.132984	+	0.230335i
$586$	−8.37771	−	16.2758i	−0.346080	−	0.672345i
$587$		−	3.68747i		−	0.152198i	−0.997100	−	0.0760991i	$-0.975753\pi$
$587$		−	3.68747i		−	0.152198i	0.997100	−	0.0760991i	$-0.0242465\pi$
$588$	9.82454	+	9.97389i	0.405157	+	0.411316i
$589$		−	22.2646i		−	0.917396i
$590$	31.9342	−	16.4377i	1.31471	−	0.676729i
$591$	8.76965	+	15.1895i	0.360735	+	0.624812i
$592$	−6.86015	+	35.1156i	−0.281951	+	1.44324i
$593$	32.3781	+	18.6935i	1.32961	+	0.767650i	0.985239	−	0.171184i	$-0.0547591\pi$
$593$	32.3781	+	18.6935i	1.32961	+	0.767650i	0.344370	+	0.938834i	$0.388092\pi$
$594$	−2.03473	−	1.30946i	−0.0834862	−	0.0537279i
$595$	10.9144	+	23.3556i	0.447447	+	0.957485i
$596$	14.7791	−	6.72679i	0.605374	−	0.275540i
$597$	15.3345	+	8.85336i	0.627598	+	0.362344i
$598$	−0.0492546	+	1.02040i	−0.00201417	+	0.0417274i
$599$	8.61435	−	4.97350i	0.351973	−	0.203212i	−0.313581	−	0.949561i	$-0.601529\pi$
$599$	8.61435	−	4.97350i	0.351973	−	0.203212i	0.665554	+	0.746350i	$0.268195\pi$
$600$	27.6054	+	21.7941i	1.12699	+	0.889739i
$601$			35.9296i			1.46560i	0.680445	+	0.732799i	$0.261786\pi$
$601$			35.9296i			1.46560i	−0.680445	+	0.732799i	$0.738214\pi$
$602$	−10.1455	−	7.84589i	−0.413500	−	0.319775i
$603$	7.47317			0.304331
$604$	−0.238098	+	2.46059i	−0.00968808	+	0.100120i
$605$	16.8536	+	29.1914i	0.685198	+	1.18680i
$606$	0.939641	−	19.4665i	0.0381703	−	0.790771i
$607$	−14.9355	+	25.8690i	−0.606212	+	1.04999i	0.385646	+	0.922647i	$0.373978\pi$
$607$	−14.9355	+	25.8690i	−0.606212	+	1.04999i	−0.991859	+	0.127344i	$0.959355\pi$
$608$	38.2471	−	11.0991i	1.55112	−	0.450128i
$609$	−7.24039	−	5.06085i	−0.293395	−	0.205076i
$610$	29.1419	−	45.2827i	1.17992	−	1.83344i
$611$	4.54557	−	7.87315i	0.183894	−	0.318514i
$612$	3.79832	+	2.71202i	0.153538	+	0.109627i
$613$	32.8160	−	18.9463i	1.32542	−	0.765234i	0.340836	−	0.940123i	$-0.389290\pi$
$613$	32.8160	−	18.9463i	1.32542	−	0.765234i	0.984588	+	0.174889i	$0.0559566\pi$
$614$	−14.9346	+	7.68738i	−0.602712	+	0.310238i
$615$	−22.1892			−0.894756
$616$	9.32692	+	8.77178i	0.375792	+	0.353425i
$617$	39.0332			1.57142			0.785709	−	0.618597i	$-0.212298\pi$
$617$	39.0332			1.57142			0.785709	+	0.618597i	$0.212298\pi$
$618$	9.66017	−	4.97244i	0.388589	−	0.200021i
$619$	−21.5338	+	12.4325i	−0.865517	+	0.499706i	−0.865856	−	0.500294i	$-0.833225\pi$
$619$	−21.5338	+	12.4325i	−0.865517	+	0.499706i	0.000339137		1.00000i	$0.499892\pi$
$620$	−15.3468	+	21.4939i	−0.616341	+	0.863216i
$621$	0.234442	−	0.406066i	0.00940784	−	0.0162949i
$622$	9.05924	−	14.0769i	0.363242	−	0.564431i
$623$	5.59509	+	0.484842i	0.224163	+	0.0194248i
$624$	−4.64708	−	4.04734i	−0.186032	−	0.162023i
$625$	−33.7275	+	58.4177i	−1.34910	+	2.33671i
$626$	1.01079	−	20.9404i	0.0403992	−	0.836947i
$627$	−6.02273	−	10.4317i	−0.240525	−	0.416601i
$628$	−19.1221	−	1.85035i	−0.763056	−	0.0738371i
$629$	−20.8735			−0.832281
$630$	−2.09767	+	15.4819i	−0.0835731	+	0.616815i
$631$		−	43.3823i		−	1.72702i	−0.504330	−	0.863511i	$-0.668260\pi$
$631$		−	43.3823i		−	1.72702i	0.504330	−	0.863511i	$-0.331740\pi$
$632$	−3.74535	−	2.95689i	−0.148982	−	0.117619i
$633$	−3.66372	+	2.11525i	−0.145620	+	0.0840736i
$634$	−0.462536	+	9.58232i	−0.0183696	+	0.380563i
$635$	−34.3436	−	19.8283i	−1.36289	−	0.786862i
$636$	1.29573	+	2.84678i	0.0513790	+	0.112882i
$637$	6.91837	−	8.27276i	0.274116	−	0.327779i
$638$	−6.79368	−	4.37210i	−0.268964	−	0.173093i
$639$	3.02471	+	1.74631i	0.119656	+	0.0690831i
$640$	−44.5737	−	15.6484i	−1.76193	−	0.618557i
$641$	−3.32559	−	5.76010i	−0.131353	−	0.227510i	0.792845	−	0.609423i	$-0.208599\pi$
$641$	−3.32559	−	5.76010i	−0.131353	−	0.227510i	−0.924198	+	0.381913i	$0.875265\pi$
$642$	18.1171	−	9.32554i	0.715027	−	0.368050i
$643$		−	18.1066i		−	0.714055i	−0.934094	−	0.357027i	$-0.883790\pi$
$643$		−	18.1066i		−	0.714055i	0.934094	−	0.357027i	$-0.116210\pi$
$644$	−1.61068	+	1.88722i	−0.0634695	+	0.0743668i
$645$		−	14.3125i		−	0.563555i
$646$	10.6332	+	20.6576i	0.418358	+	0.812763i
$647$	−24.6421	−	42.6815i	−0.968783	−	1.67798i	−0.699089	−	0.715035i	$-0.746411\pi$
$647$	−24.6421	−	42.6815i	−0.968783	−	1.67798i	−0.269694	−	0.962946i	$-0.586923\pi$
$648$	1.04624	+	2.62781i	0.0411001	+	0.103230i
$649$	9.01239	+	5.20331i	0.353767	+	0.204248i
$650$	14.6620	−	22.7829i	0.575092	−	0.893618i
$651$	−8.33602	−	0.722357i	−0.326714	−	0.0283114i
$652$	16.0811	+	35.3308i	0.629784	+	1.38366i
$653$	22.1087	+	12.7645i	0.865181	+	0.499512i	0.865744	−	0.500488i	$-0.166846\pi$
$653$	22.1087	+	12.7645i	0.865181	+	0.499512i	−0.000563051		1.00000i	$0.500179\pi$
$654$	4.76900	+	0.230198i	0.186483	+	0.00900147i
$655$	49.4233	−	28.5345i	1.93113	−	1.11494i
$656$	20.1049	−	6.90147i	0.784964	−	0.269457i
$657$			14.5274i			0.566769i
$658$	20.4304	−	8.37240i	0.796458	−	0.326390i
$659$	−12.0942			−0.471125			−0.235562	−	0.971859i	$-0.575693\pi$
$659$	−12.0942			−0.471125			−0.235562	+	0.971859i	$0.575693\pi$
$660$	−1.37619	+	14.2220i	−0.0535681	+	0.553590i
$661$	5.42541	+	9.39708i	0.211024	+	0.365504i	0.952035	−	0.305988i	$-0.0989869\pi$
$661$	5.42541	+	9.39708i	0.211024	+	0.365504i	−0.741011	+	0.671493i	$0.765654\pi$
$662$	6.70362	+	0.323582i	0.260544	+	0.0125764i
$663$	1.79758	−	3.11350i	0.0698122	−	0.120918i
$664$	−1.11177	+	7.62976i	−0.0431451	+	0.296092i
$665$	−44.5573	+	63.7466i	−1.72786	+	2.47199i
$666$	−10.6375	−	6.84580i	−0.412194	−	0.265270i
$667$	0.782767	−	1.35579i	0.0303089	−	0.0524965i
$668$	−20.6265	+	28.8885i	−0.798063	+	1.11773i
$669$	1.24302	−	0.717661i	0.0480581	−	0.0277464i
$670$	−20.1966	−	39.2368i	−0.780263	−	1.51585i
$671$	15.6026			0.602333
$672$	−2.91469	−	14.6801i	−0.112437	−	0.566296i
$673$	−48.1931			−1.85771			−0.928854	−	0.370446i	$-0.879205\pi$
$673$	−48.1931			−1.85771			−0.928854	+	0.370446i	$0.879205\pi$
$674$	10.6906	+	20.7691i	0.411785	+	0.799994i
$675$	−10.7691	+	6.21752i	−0.414501	+	0.239312i
$676$	12.3498	−	17.2965i	0.474993	−	0.665252i
$677$	−2.56093	+	4.43567i	−0.0984246	+	0.170476i	−0.911033	−	0.412334i	$-0.864714\pi$
$677$	−2.56093	+	4.43567i	−0.0984246	+	0.170476i	0.812608	+	0.582810i	$0.198047\pi$
$678$	−12.7355	−	8.19598i	−0.489103	−	0.314765i
$679$	2.18651	+	4.67888i	0.0839107	+	0.179559i
$680$	3.97394	−	27.2719i	0.152394	−	1.04583i
$681$	8.00718	−	13.8688i	0.306836	−	0.531455i
$682$	−7.64340	−	0.368945i	−0.292681	−	0.0141276i
$683$	−11.7191	−	20.2980i	−0.448418	−	0.776682i	0.549866	−	0.835253i	$-0.314679\pi$
$683$	−11.7191	−	20.2980i	−0.448418	−	0.776682i	−0.998283	+	0.0585709i	$0.981346\pi$
$684$	−1.35614	+	14.0148i	−0.0518533	+	0.535869i
$685$	−50.0612			−1.91274
$686$	25.5827	−	5.61476i	0.976752	−	0.214373i
$687$		−	16.2500i		−	0.619975i
$688$	4.45160	+	12.9681i	0.169715	+	0.494404i
$689$	2.08658	−	1.20468i	0.0794922	−	0.0458948i
$690$	−2.76558	−	0.133494i	−0.105284	−	0.00508203i
$691$	11.9534	+	6.90129i	0.454728	+	0.262537i	0.709825	−	0.704378i	$-0.248774\pi$
$691$	11.9534	+	6.90129i	0.454728	+	0.262537i	−0.255097	+	0.966915i	$0.582107\pi$
$692$	−5.91694	−	12.9998i	−0.224928	−	0.494177i
$693$	−4.10109	+	1.91650i	−0.155788	+	0.0728020i
$694$	−14.6177	+	22.7139i	−0.554879	+	0.862209i
$695$	−24.0439	−	13.8817i	−0.912035	−	0.526564i
$696$	3.49323	+	8.77387i	0.132410	+	0.332573i
$697$	6.20044	+	10.7395i	0.234859	+	0.406787i
$698$	1.61658	+	3.14060i	0.0611884	+	0.118873i
$699$			11.8611i			0.448627i
$700$	62.0180	−	21.9866i	2.34406	−	0.831015i
$701$		−	11.8718i		−	0.448393i	−0.974544	−	0.224196i	$-0.928024\pi$
$701$		−	11.8718i		−	0.448393i	0.974544	−	0.224196i	$-0.0719757\pi$
$702$	1.93720	−	0.997145i	0.0731148	−	0.0376348i
$703$	−31.4865	−	54.5362i	−1.18754	−	2.05687i
$704$	−3.17652	−	13.3141i	−0.119719	−	0.501793i
$705$	21.3385	+	12.3198i	0.803654	+	0.463990i
$706$	−30.6322	−	19.7135i	−1.15286	−	0.741927i
$707$	−29.8843	−	20.8883i	−1.12391	−	0.785587i
$708$	−5.03935	−	11.0717i	−0.189390	−	0.416099i
$709$	−27.1241	−	15.6601i	−1.01867	−	0.588127i	−0.104949	−	0.994478i	$-0.533468\pi$
$709$	−27.1241	−	15.6601i	−1.01867	−	0.588127i	−0.913717	+	0.406350i	$0.866801\pi$
$710$	0.994371	−	20.6003i	0.0373181	−	0.773116i
$711$	1.46108	−	0.843557i	0.0547949	−	0.0316358i
$712$	−4.71227	−	3.72026i	−0.176600	−	0.139423i
$713$		−	1.48286i		−	0.0555335i
$714$	8.07935	−	3.31093i	0.302362	−	0.123908i
$715$	11.0065			0.411621
$716$	47.6101	+	4.60698i	1.77927	+	0.172171i
$717$	0.423292	+	0.733164i	0.0158081	+	0.0273805i
$718$	−2.26511	+	46.9260i	−0.0845330	+	1.75126i
$719$	−12.6273	+	21.8712i	−0.470920	+	0.815657i	−0.999447	−	0.0332594i	$-0.989411\pi$
$719$	−12.6273	+	21.8712i	−0.470920	+	0.815657i	0.528527	+	0.848917i	$0.322745\pi$
$720$	10.9695	−	12.5949i	0.408807	−	0.469385i
$721$	1.75479	−	20.2503i	0.0653518	−	0.754161i
$722$	−23.3912	+	36.3469i	−0.870530	+	1.35269i
$723$	−0.439609	+	0.761425i	−0.0163492	+	0.0283177i
$724$	23.8910	−	33.4606i	0.887903	−	1.24355i
$725$	−35.9563	+	20.7594i	−1.33538	+	0.770984i
$726$	10.1506	−	5.22486i	0.376723	−	0.193913i
$727$	−17.9342			−0.665144			−0.332572	−	0.943078i	$-0.607916\pi$
$727$	−17.9342			−0.665144			−0.332572	+	0.943078i	$0.607916\pi$
$728$	−11.0394	+	3.32393i	−0.409148	+	0.123193i
$729$	−1.00000			−0.0370370
$730$	76.2743	−	39.2611i	2.82304	−	1.45312i
$731$	−6.92720	+	3.99942i	−0.256212	+	0.147924i
$732$	−14.8431	−	10.5981i	−0.548618	−	0.391716i
$733$	6.16779	−	10.6829i	0.227813	−	0.394583i	−0.729347	−	0.684144i	$-0.760176\pi$
$733$	6.16779	−	10.6829i	0.227813	−	0.394583i	0.957160	+	0.289561i	$0.0935093\pi$
$734$	−3.33048	+	5.17513i	−0.122930	+	0.191018i
$735$	22.4215	+	18.7508i	0.827031	+	0.691632i
$736$	2.54732	−	0.739219i	0.0938954	−	0.0272480i
$737$	6.39319	−	11.0733i	0.235496	−	0.407891i
$738$	−0.362339	+	7.50655i	−0.0133379	+	0.276320i
$739$	−21.7463	−	37.6656i	−0.799949	−	1.38555i	−0.919648	−	0.392743i	$-0.871526\pi$
$739$	−21.7463	−	37.6656i	−0.799949	−	1.38555i	0.119699	−	0.992810i	$-0.461807\pi$
$740$	−7.19464	+	74.3518i	−0.264480	+	2.73322i
$741$	10.8462			0.398444
$742$	5.79857	+	0.785656i	0.212872	+	0.0288424i
$743$			32.8397i			1.20477i	0.798205	+	0.602386i	$0.205783\pi$
$743$			32.8397i			1.20477i	−0.798205	+	0.602386i	$0.794217\pi$
$744$	7.02072	+	5.54275i	0.257392	+	0.203207i
$745$	29.3591	−	16.9505i	1.07563	−	0.621018i
$746$	−0.873485	+	18.0959i	−0.0319806	+	0.662539i
$747$	−2.36080	−	1.36301i	−0.0863771	−	0.0498698i
$748$	7.26793	−	3.30805i	0.265742	−	0.120954i
$749$	3.29101	−	37.9784i	0.120251	−	1.38770i
$750$	36.9199	+	23.7600i	1.34812	+	0.867591i
$751$	−7.62670	−	4.40328i	−0.278302	−	0.160678i	0.354352	−	0.935112i	$-0.384701\pi$
$751$	−7.62670	−	4.40328i	−0.278302	−	0.160678i	−0.632655	+	0.774434i	$0.718035\pi$
$752$	−23.1659	−	4.52566i	−0.844772	−	0.165034i
$753$	9.07203	+	15.7132i	0.330603	+	0.572622i
$754$	6.46802	−	3.32932i	0.235551	−	0.121247i
$755$			5.16112i			0.187832i
$756$	5.20324	+	0.962447i	0.189240	+	0.0350039i
$757$			16.9328i			0.615433i	0.951478	+	0.307717i	$0.0995649\pi$
$757$			16.9328i			0.615433i	−0.951478	+	0.307717i	$0.900435\pi$
$758$	−15.5859	−	30.2794i	−0.566105	−	1.09980i
$759$	−0.401124	−	0.694766i	−0.0145599	−	0.0252184i
$760$	77.2478	−	30.7554i	2.80207	−	1.11562i
$761$	10.9108	+	6.29937i	0.395517	+	0.228352i	0.684548	−	0.728968i	$-0.260000\pi$
$761$	10.9108	+	6.29937i	0.395517	+	0.228352i	−0.289031	+	0.957320i	$0.593333\pi$
$762$	−7.26867	+	11.2946i	−0.263316	+	0.409159i
$763$	5.11734	−	7.32121i	0.185260	−	0.265045i
$764$	−3.66832	+	1.66966i	−0.132715	+	0.0604063i
$765$	8.43848	+	4.87196i	0.305094	+	0.176146i
$766$	24.8113	+	1.19763i	0.896468	+	0.0432723i
$767$	−8.11510	+	4.68526i	−0.293019	+	0.169175i
$768$	−6.02167	+	14.8236i	−0.217288	+	0.534901i
$769$		−	16.0445i		−	0.578581i	−0.957241	−	0.289291i	$-0.906581\pi$
$769$		−	16.0445i		−	0.578581i	0.957241	−	0.289291i	$-0.0934194\pi$
$770$	21.1457	+	16.3528i	0.762040	+	0.589313i
$771$	18.3484			0.660802
$772$	−7.10820	−	0.687825i	−0.255830	−	0.0247554i
$773$	9.15671	+	15.8599i	0.329344	+	0.570440i	0.982382	−	0.186885i	$-0.0598391\pi$
$773$	9.15671	+	15.8599i	0.329344	+	0.570440i	−0.653038	+	0.757325i	$0.726506\pi$
$774$	−4.84189	−	0.233717i	−0.174038	−	0.00840077i
$775$	−19.6631	+	34.0574i	−0.706318	+	1.22338i
$776$	0.796109	−	5.46346i	0.0285787	−	0.196127i
$777$	−21.4403	+	10.0194i	−0.769166	+	0.359443i
$778$	−32.8226	−	21.1231i	−1.17675	−	0.757301i
$779$	−18.7060	+	32.3998i	−0.670213	+	1.16084i
$780$	−10.4707	−	7.47616i	−0.374913	−	0.267690i
$781$	5.17518	−	2.98789i	0.185183	−	0.106915i
$782$	0.708190	+	1.37583i	0.0253248	+	0.0491997i
$783$	−3.33885			−0.119321
$784$	−26.1474	−	10.0157i	−0.933835	−	0.357703i
$785$	−40.1090			−1.43155
$786$	−8.84609	−	17.1857i	−0.315530	−	0.612994i
$787$	3.88976	−	2.24576i	0.138655	−	0.0800526i	−0.429068	−	0.903272i	$-0.641158\pi$
$787$	3.88976	−	2.24576i	0.138655	−	0.0800526i	0.567723	+	0.823220i	$0.307825\pi$
$788$	−28.5484	−	20.3837i	−1.01700	−	0.726140i
$789$	1.74385	−	3.02044i	0.0620828	−	0.107531i
$790$	−8.37763	−	5.39146i	−0.298063	−	0.191820i
$791$	−25.6689	+	11.9955i	−0.912680	+	0.426510i
$792$	4.78878	+	0.697799i	0.170162	+	0.0247952i
$793$	−7.02460	+	12.1670i	−0.249451	+	0.432062i
$794$	−24.4615	−	1.18075i	−0.868104	−	0.0419032i
$795$	3.26504	+	5.65522i	0.115799	+	0.200570i
$796$	−35.2488	−	3.41085i	−1.24936	−	0.120894i
$797$	31.7698			1.12534			0.562672	−	0.826680i	$-0.309773\pi$
$797$	31.7698			1.12534			0.562672	+	0.826680i	$0.309773\pi$
$798$	20.8377	+	16.1145i	0.737646	+	0.570449i
$799$		−	13.7703i		−	0.487159i
$800$	−68.3076	−	16.8001i	−2.41504	−	0.593974i
$801$	1.83829	−	1.06134i	0.0649527	−	0.0375004i
$802$	−10.9507	−	0.528587i	−0.386682	−	0.0186650i
$803$	21.5259	+	12.4280i	0.759634	+	0.438575i
$804$	−13.6035	+	6.19173i	−0.479759	+	0.218366i
$805$	−2.96759	+	4.24563i	−0.104594	+	0.149639i
$806$	3.72890	−	5.79423i	0.131345	−	0.204093i
$807$	−12.7410	−	7.35605i	−0.448506	−	0.258945i
$808$	14.4181	+	36.2136i	0.507226	+	1.27399i
$809$	−12.5784	−	21.7864i	−0.442232	−	0.765969i	0.555623	−	0.831435i	$-0.312480\pi$
$809$	−12.5784	−	21.7864i	−0.442232	−	0.765969i	−0.997855	+	0.0654659i	$0.979147\pi$
$810$	2.70255	+	5.25036i	0.0949579	+	0.184479i
$811$			48.0042i			1.68565i	0.538184	+	0.842827i	$0.319110\pi$
$811$			48.0042i			1.68565i	−0.538184	+	0.842827i	$0.680890\pi$
$812$	17.3728	+	3.21347i	0.609667	+	0.112771i
$813$			19.9028i			0.698021i
$814$	−19.2439	+	9.90554i	−0.674500	+	0.347189i
$815$	40.5219	+	70.1859i	1.41942	+	2.45851i
$816$	−9.16112	−	1.78971i	−0.320703	−	0.0626523i
$817$	−20.8985	−	12.0658i	−0.731148	−	0.422128i
$818$	−5.51607	−	3.54989i	−0.192865	−	0.124119i
$819$	0.351896	−	4.06089i	0.0122962	−	0.141899i
$820$	40.3914	−	18.3844i	1.41053	−	0.642011i
$821$	14.5854	+	8.42089i	0.509034	+	0.293891i	0.732437	−	0.680835i	$-0.238383\pi$
$821$	14.5854	+	8.42089i	0.509034	+	0.293891i	−0.223402	+	0.974726i	$0.571716\pi$
$822$	−0.817475	+	16.9356i	−0.0285127	+	0.590695i
$823$	−17.1163	+	9.88209i	−0.596636	+	0.344468i	−0.767717	−	0.640789i	$-0.778607\pi$
$823$	−17.1163	+	9.88209i	−0.596636	+	0.344468i	0.171081	+	0.985257i	$0.445274\pi$
$824$	−13.4647	+	17.0551i	−0.469066	+	0.594143i
$825$			21.2760i			0.740735i
$826$	−22.5518	−	3.05557i	−0.784677	−	0.106317i
$827$	49.1702			1.70981			0.854907	−	0.518781i	$-0.173614\pi$
$827$	49.1702			1.70981			0.854907	+	0.518781i	$0.173614\pi$
$828$	−0.0903212	+	0.933409i	−0.00313888	+	0.0324382i
$829$	7.96007	+	13.7872i	0.276465	+	0.478851i	0.970504	−	0.241087i	$-0.0775038\pi$
$829$	7.96007	+	13.7872i	0.276465	+	0.478851i	−0.694039	+	0.719937i	$0.744171\pi$
$830$	−0.776111	+	16.0786i	−0.0269392	+	0.558098i
$831$	13.2233	−	22.9034i	0.458710	−	0.794510i
$832$	11.8125	+	3.51719i	0.409524	+	0.121937i
$833$	2.80992	−	16.0915i	0.0973580	−	0.557539i
$834$	−5.08877	+	7.90728i	−0.176210	+	0.273807i
$835$	−37.0541	+	64.1795i	−1.28231	+	2.22102i
$836$	19.6062	+	13.9989i	0.678094	+	0.484162i
$837$	−2.73883	+	1.58126i	−0.0946678	+	0.0546565i
$838$	−17.9079	+	9.21783i	−0.618618	+	0.318425i
$839$	38.3305			1.32332			0.661658	−	0.749806i	$-0.269853\pi$
$839$	38.3305			1.32332			0.661658	+	0.749806i	$0.269853\pi$
$840$	−9.00881	−	29.9200i	−0.310833	−	1.03234i
$841$	17.8521			0.615589
$842$	−25.1641	+	12.9529i	−0.867213	+	0.446385i
$843$	−17.5662	+	10.1419i	−0.605013	+	0.349304i
$844$	4.91657	−	6.88591i	0.169235	−	0.237023i
$845$	22.1856	−	38.4266i	0.763207	−	1.32191i
$846$	4.51620	−	7.01758i	0.155270	−	0.241269i
$847$	1.84387	−	21.2783i	0.0633561	−	0.731131i
$848$	−4.71727	−	4.10848i	−0.161992	−	0.141086i
$849$	3.29336	−	5.70426i	0.113028	−	0.195770i
$850$	1.97858	−	40.9901i	0.0678647	−	1.40595i
$851$	−2.09705	−	3.63220i	−0.0718860	−	0.124510i
$852$	−6.95278	−	0.672785i	−0.238198	−	0.0230493i
$853$	−22.5158			−0.770927			−0.385463	−	0.922723i	$-0.625958\pi$
$853$	−22.5158			−0.770927			−0.385463	+	0.922723i	$0.625958\pi$
$854$	−31.5726	+	12.9385i	−1.08039	+	0.442746i
$855$			29.3963i			1.00533i
$856$	−25.2524	+	31.9860i	−0.863109	+	1.09326i
$857$	−11.1913	+	6.46129i	−0.382287	+	0.220713i	−0.678813	−	0.734311i	$-0.737505\pi$
$857$	−11.1913	+	6.46129i	−0.382287	+	0.220713i	0.296526	+	0.955025i	$0.404172\pi$
$858$	0.179731	−	3.72347i	0.00613592	−	0.127117i
$859$	20.1418	+	11.6289i	0.687229	+	0.396772i	0.802573	−	0.596554i	$-0.203464\pi$
$859$	20.1418	+	11.6289i	0.687229	+	0.396772i	−0.115344	+	0.993326i	$0.536797\pi$
$860$	11.8583	+	26.0533i	0.404366	+	0.888410i
$861$	11.5238	+	8.05485i	0.392730	+	0.274509i
$862$	16.6293	+	10.7019i	0.566397	+	0.364508i
$863$	−7.69412	−	4.44220i	−0.261911	−	0.151214i	0.363295	−	0.931674i	$-0.381652\pi$
$863$	−7.69412	−	4.44220i	−0.261911	−	0.151214i	−0.625206	+	0.780460i	$0.714985\pi$
$864$	−4.08169	−	3.91660i	−0.138862	−	0.133246i
$865$	−14.9098	−	25.8245i	−0.506947	−	0.878059i
$866$	−1.23841	+	0.637454i	−0.0420829	+	0.0216616i
$867$			11.5544i			0.392409i
$868$	15.7727	−	5.59171i	0.535359	−	0.189795i
$869$		−	2.88660i		−	0.0979212i
$870$	9.02341	+	17.5302i	0.305922	+	0.594329i
$871$	5.75667	+	9.97084i	0.195057	+	0.337849i
$872$	−8.87180	+	3.53222i	−0.300437	+	0.119616i
$873$	1.69050	+	0.976012i	0.0572148	+	0.0330330i
$874$	−2.52637	+	3.92565i	−0.0854558	+	0.132787i
$875$	74.4135	−	34.7746i	2.51564	−	1.17560i
$876$	−12.0364	−	26.4445i	−0.406672	−	0.893476i
$877$	−40.2134	−	23.2172i	−1.35791	−	0.783990i	−0.368569	−	0.929600i	$-0.620152\pi$
$877$	−40.2134	−	23.2172i	−1.35791	−	0.783990i	−0.989342	+	0.145610i	$0.953485\pi$
$878$	9.70981	+	0.468690i	0.327690	+	0.0158175i
$879$	−11.2097	+	6.47192i	−0.378094	+	0.218292i
$880$	−9.27822	−	27.0287i	−0.312769	−	0.911137i
$881$		−	27.1901i		−	0.916058i	−0.888937	−	0.458029i	$-0.848556\pi$
$881$		−	27.1901i		−	0.916058i	0.888937	−	0.458029i	$-0.151444\pi$
$882$	6.70946	−	7.27895i	0.225919	−	0.245095i
$883$	−21.7975			−0.733543			−0.366772	−	0.930311i	$-0.619537\pi$
$883$	−21.7975			−0.733543			−0.366772	+	0.930311i	$0.619537\pi$
$884$	−0.692536	+	7.15689i	−0.0232925	+	0.240712i
$885$	−12.6984	−	21.9942i	−0.426852	−	0.739329i
$886$	−4.81638	−	0.232485i	−0.161809	−	0.00781049i
$887$	−21.1661	+	36.6607i	−0.710688	+	1.23095i	0.253911	+	0.967227i	$0.418283\pi$
$887$	−21.1661	+	36.6607i	−0.710688	+	1.23095i	−0.964599	+	0.263720i	$0.915051\pi$
$888$	25.0355	+	3.64805i	0.840136	+	0.122421i
$889$	10.6383	+	22.7646i	0.356796	+	0.763502i
$890$	−10.5405	−	6.78336i	−0.353317	−	0.227379i
$891$	−0.855485	+	1.48174i	−0.0286598	+	0.0496403i
$892$	−1.66809	+	2.33625i	−0.0558519	+	0.0782234i
$893$	35.9777	−	20.7717i	1.20395	−	0.695099i
$894$	−5.25488	−	10.2089i	−0.175749	−	0.341436i
$895$	99.8629			3.33805
$896$	17.4685	+	24.3074i	0.583582	+	0.812054i
$897$	0.722374			0.0241194
$898$	21.3538	+	41.4850i	0.712586	+	1.38437i
$899$	−9.14454	+	5.27960i	−0.304987	+	0.176085i
$900$	14.4517	−	20.2403i	0.481722	−	0.674677i
$901$	1.82473	−	3.16053i	0.0607906	−	0.105292i
$902$	10.8128	+	6.95864i	0.360027	+	0.231697i
$903$	−5.19555	+	7.43310i	−0.172897	+	0.247358i
$904$	29.9732	+	4.36755i	0.996892	+	0.145262i
$905$	42.9186	−	74.3371i	1.42666	−	2.47105i
$906$	1.74599	+	0.0842785i	0.0580066	+	0.00279996i
$907$	22.5605	+	39.0760i	0.749109	+	1.29750i	0.948250	+	0.317525i	$0.102852\pi$
$907$	22.5605	+	39.0760i	0.749109	+	1.29750i	−0.199141	+	0.979971i	$0.563815\pi$
$908$	−3.08485	+	31.8798i	−0.102374	+	1.05797i
$909$	−13.7809			−0.457083
$910$	−22.2721	+	9.12716i	−0.738314	+	0.302562i
$911$		−	36.2714i		−	1.20173i	−0.799352	−	0.600863i	$-0.794824\pi$
$911$		−	36.2714i		−	1.20173i	0.799352	−	0.600863i	$-0.205176\pi$
$912$	−9.14305	−	26.6349i	−0.302757	−	0.881970i
$913$	−4.03926	+	2.33207i	−0.133680	+	0.0771801i
$914$	32.2699	+	1.55766i	1.06739	+	0.0515228i
$915$	−32.9760	−	19.0387i	−1.09015	−	0.629400i
$916$	13.4636	+	29.5801i	0.444849	+	0.977352i
$917$	−36.0258	−	3.12181i	−1.18968	−	0.103091i
$918$	1.78596	−	2.77516i	0.0589456	−	0.0915938i
$919$	−37.7905	−	21.8183i	−1.24659	−	0.719721i	−0.276164	−	0.961110i	$-0.589063\pi$
$919$	−37.7905	−	21.8183i	−1.24659	−	0.719721i	−0.970428	+	0.241390i	$0.922397\pi$
$920$	5.14483	−	2.04836i	0.169620	−	0.0675325i
$921$	5.93863	+	10.2860i	0.195685	+	0.338936i
$922$	10.2744	+	19.9605i	0.338369	+	0.657364i
$923$			5.38082i			0.177112i
$924$	5.87740	−	6.88651i	0.193352	−	0.226549i
$925$			111.230i			3.65721i
$926$	3.42090	−	1.76086i	0.112418	−	0.0578654i
$927$	−3.84129	−	6.65331i	−0.126165	−	0.218523i
$928$	−13.6282	−	13.0770i	−0.447367	−	0.429272i
$929$	10.2075	+	5.89332i	0.334898	+	0.193354i	0.658014	−	0.753006i	$-0.271397\pi$
$929$	10.2075	+	5.89332i	0.334898	+	0.193354i	−0.323115	+	0.946360i	$0.604730\pi$
$930$	15.7040	+	10.1064i	0.514955	+	0.331402i
$931$	46.2809	−	16.9317i	1.51680	−	0.554913i
$932$	−9.82724	−	21.5909i	−0.321902	−	0.707233i
$933$	−10.2511	−	5.91849i	−0.335607	−	0.193763i
$934$	−1.63548	+	33.8820i	−0.0535144	+	1.10865i
$935$	14.4380	−	8.33578i	0.472173	−	0.272609i
$936$	−2.70015	+	3.42014i	−0.0882570	+	0.111791i
$937$		−	35.0529i		−	1.14513i	−0.819860	−	0.572565i	$-0.805949\pi$
$937$		−	35.0529i		−	1.14513i	0.819860	−	0.572565i	$-0.194051\pi$
$938$	−3.75431	+	27.7089i	−0.122583	+	0.904726i
$939$	−14.8243			−0.483774
$940$	−49.0501	−	4.74632i	−1.59984	−	0.154808i
$941$	−14.2985	−	24.7658i	−0.466119	−	0.807342i	0.533132	−	0.846032i	$-0.321015\pi$
$941$	−14.2985	−	24.7658i	−0.466119	−	0.807342i	−0.999251	+	0.0386903i	$0.987681\pi$
$942$	−0.654960	+	13.5687i	−0.0213397	+	0.442094i
$943$	−1.24585	+	2.15788i	−0.0405705	+	0.0702702i
$944$	18.3464	+	15.9787i	0.597124	+	0.520061i
$945$	11.0062	+	0.953738i	0.358031	+	0.0310251i
$946$	−4.48847	+	6.97449i	−0.145933	+	0.226760i
$947$	25.7444	−	44.5906i	0.836580	−	1.44900i	−0.0561576	−	0.998422i	$-0.517885\pi$
$947$	25.7444	−	44.5906i	0.836580	−	1.44900i	0.892738	−	0.450577i	$-0.148782\pi$
$948$	−1.96072	+	2.74609i	−0.0636812	+	0.0891887i
$949$	−19.3828	+	11.1906i	−0.629191	+	0.363264i
$950$	110.079	−	56.6617i	3.57144	−	1.83835i
$951$	6.78361			0.219974
$952$	−11.9637	+	12.7209i	−0.387747	+	0.412287i
$953$	−11.8761			−0.384706			−0.192353	−	0.981326i	$-0.561612\pi$
$953$	−11.8761			−0.384706			−0.192353	+	0.981326i	$0.561612\pi$
$954$	1.96646	−	1.01221i	0.0636665	−	0.0327714i
$955$	−7.28724	+	4.20729i	−0.235810	+	0.136145i
$956$	−1.37797	−	0.983878i	−0.0445668	−	0.0318209i
$957$	−2.85634	+	4.94732i	−0.0923323	+	0.159924i
$958$	15.1155	−	23.4875i	0.488360	−	0.758848i
$959$	25.9989	+	18.1726i	0.839548	+	0.586823i
$960$	−9.53261	+	32.0152i	−0.307664	+	1.03329i
$961$	10.4992	−	18.1852i	0.338684	−	0.586618i
$962$	0.939624	−	19.4661i	0.0302947	−	0.627613i
$963$	−7.20414	−	12.4779i	−0.232150	−	0.402096i
$964$	0.169364	−	1.75026i	0.00545484	−	0.0563721i
$965$	−14.9096			−0.479956
$966$	1.38782	+	1.07326i	0.0446525	+	0.0345314i
$967$		−	59.2193i		−	1.90437i	−0.305530	−	0.952183i	$-0.598833\pi$
$967$		−	59.2193i		−	1.90437i	0.305530	−	0.952183i	$-0.401167\pi$
$968$	−14.1483	+	17.9209i	−0.454742	+	0.576000i
$969$	14.2276	−	8.21434i	0.457058	−	0.263883i
$970$	0.555752	−	11.5135i	0.0178441	−	0.369675i
$971$	−4.53638	−	2.61908i	−0.145579	−	0.0840503i	0.425441	−	0.904986i	$-0.360119\pi$
$971$	−4.53638	−	2.61908i	−0.145579	−	0.0840503i	−0.571020	+	0.820936i	$0.693452\pi$
$972$	1.82031	−	0.828528i	0.0583866	−	0.0265751i
$973$	7.44782	+	15.9375i	0.238766	+	0.510931i
$974$	−44.1396	−	28.4062i	−1.41432	−	0.910194i
$975$	−16.5911	−	9.57885i	−0.531339	−	0.306769i
$976$	35.7999	+	6.99384i	1.14593	+	0.223867i
$977$	26.6049	+	46.0810i	0.851165	+	1.47426i	0.880158	+	0.474682i	$0.157437\pi$
$977$	26.6049	+	46.0810i	0.851165	+	1.47426i	−0.0289924	+	0.999580i	$0.509230\pi$
$978$	24.4054	−	12.5623i	0.780398	−	0.401699i
$979$		−	3.63183i		−	0.116074i
$980$	−56.3498	−	15.5554i	−1.80003	−	0.496899i
$981$		−	3.37612i		−	0.107791i
$982$	−13.3166	−	25.8707i	−0.424949	−	0.825568i
$983$	−13.9737	−	24.2032i	−0.445693	−	0.771963i	0.552407	−	0.833574i	$-0.313709\pi$
$983$	−13.9737	−	24.2032i	−0.445693	−	0.771963i	−0.998100	+	0.0616113i	$0.980376\pi$
$984$	−5.55982	−	13.9645i	−0.177241	−	0.445171i
$985$	−63.4241	−	36.6179i	−2.02086	−	1.16674i
$986$	5.96307	−	9.26583i	0.189903	−	0.295084i
$987$	−6.60981	−	14.1442i	−0.210393	−	0.450215i
$988$	−19.7434	+	8.98637i	−0.628123	+	0.285894i
$989$	−1.39188	−	0.803601i	−0.0442592	−	0.0255530i
$990$	10.0917	+	0.487123i	0.320735	+	0.0154818i
$991$	18.7980	−	10.8530i	0.597139	−	0.344758i	−0.170776	−	0.985310i	$-0.554628\pi$
$991$	18.7980	−	10.8530i	0.597139	−	0.344758i	0.767915	+	0.640552i	$0.221294\pi$
$992$	−17.3722	−	4.27267i	−0.551569	−	0.135657i
$993$		−	4.74570i		−	0.150600i
$994$	−7.99448	+	10.3376i	−0.253569	+	0.327890i
$995$	−73.9349			−2.34389
$996$	5.42668	+	0.525112i	0.171951	+	0.0166388i
$997$	−16.8274	−	29.1458i	−0.532928	−	0.923058i	−0.999261	−	0.0384485i	$-0.987758\pi$
$997$	−16.8274	−	29.1458i	−0.532928	−	0.923058i	0.466333	−	0.884609i	$-0.345575\pi$
$998$	−1.46223	−	0.0705815i	−0.0462861	−	0.00223422i
$999$	−4.47243	+	7.74648i	−0.141501	+	0.245088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.t.a.19.12	yes	32
3.2	odd	2		504.2.bk.c.19.5		32
4.3	odd	2		672.2.bb.a.271.1		32
7.2	even	3		1176.2.p.a.979.17		32
7.3	odd	6	inner	168.2.t.a.115.1	yes	32
7.5	odd	6		1176.2.p.a.979.18		32
8.3	odd	2	inner	168.2.t.a.19.1	✓	32
8.5	even	2		672.2.bb.a.271.8		32
12.11	even	2		2016.2.bs.c.271.16		32
21.17	even	6		504.2.bk.c.451.16		32
24.5	odd	2		2016.2.bs.c.271.1		32
24.11	even	2		504.2.bk.c.19.16		32
28.3	even	6		672.2.bb.a.367.8		32
28.19	even	6		4704.2.p.a.3919.6		32
28.23	odd	6		4704.2.p.a.3919.23		32
56.3	even	6	inner	168.2.t.a.115.12	yes	32
56.5	odd	6		4704.2.p.a.3919.24		32
56.19	even	6		1176.2.p.a.979.19		32
56.37	even	6		4704.2.p.a.3919.5		32
56.45	odd	6		672.2.bb.a.367.1		32
56.51	odd	6		1176.2.p.a.979.20		32
84.59	odd	6		2016.2.bs.c.1711.1		32
168.59	odd	6		504.2.bk.c.451.5		32
168.101	even	6		2016.2.bs.c.1711.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.1	✓	32	8.3	odd	2	inner
168.2.t.a.19.12	yes	32	1.1	even	1	trivial
168.2.t.a.115.1	yes	32	7.3	odd	6	inner
168.2.t.a.115.12	yes	32	56.3	even	6	inner
504.2.bk.c.19.5		32	3.2	odd	2
504.2.bk.c.19.16		32	24.11	even	2
504.2.bk.c.451.5		32	168.59	odd	6
504.2.bk.c.451.16		32	21.17	even	6
672.2.bb.a.271.1		32	4.3	odd	2
672.2.bb.a.271.8		32	8.5	even	2
672.2.bb.a.367.1		32	56.45	odd	6
672.2.bb.a.367.8		32	28.3	even	6
1176.2.p.a.979.17		32	7.2	even	3
1176.2.p.a.979.18		32	7.5	odd	6
1176.2.p.a.979.19		32	56.19	even	6
1176.2.p.a.979.20		32	56.51	odd	6
2016.2.bs.c.271.1		32	24.5	odd	2
2016.2.bs.c.271.16		32	12.11	even	2
2016.2.bs.c.1711.1		32	84.59	odd	6
2016.2.bs.c.1711.16		32	168.101	even	6
4704.2.p.a.3919.5		32	56.37	even	6
4704.2.p.a.3919.6		32	28.19	even	6
4704.2.p.a.3919.23		32	28.23	odd	6
4704.2.p.a.3919.24		32	56.5	odd	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.647235 + 1.25741i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.16217 + 1.62768i) q^{4} +(-2.08776 + 3.61611i) q^{5} +(1.18923 + 0.765334i) q^{6} +(2.39694 - 1.12013i) q^{7} +(-2.79887 - 0.407838i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-5.89822 - 0.284706i) q^{10} +(-0.855485 - 1.48174i) q^{11} +(-0.192630 + 1.99070i) q^{12} +1.54062 q^{13} +(2.95984 + 2.28896i) q^{14} +4.17553i q^{15} +(-1.29871 - 3.78330i) q^{16} +(2.02094 - 1.16679i) q^{17} +(1.41257 + 0.0681843i) q^{18} +(6.09693 + 3.52006i) q^{19} +(-3.45954 - 7.60077i) q^{20} +(1.51575 - 2.16853i) q^{21} +(1.30946 - 2.03473i) q^{22} +(0.406066 + 0.234442i) q^{23} +(-2.62781 + 1.04624i) q^{24} +(-6.21752 - 10.7691i) q^{25} +(0.997145 + 1.93720i) q^{26} -1.00000i q^{27} +(-0.962447 + 5.20324i) q^{28} -3.33885i q^{29} +(-5.25036 + 2.70255i) q^{30} +(-1.58126 - 2.73883i) q^{31} +(3.91660 - 4.08169i) q^{32} +(-1.48174 - 0.855485i) q^{33} +(2.77516 + 1.78596i) q^{34} +(-0.953738 + 11.0062i) q^{35} +(0.828528 + 1.82031i) q^{36} +(-7.74648 - 4.47243i) q^{37} +(-0.480026 + 9.94467i) q^{38} +(1.33422 - 0.770311i) q^{39} +(7.31817 - 9.26956i) q^{40} +5.31411i q^{41} +(3.70778 + 0.502372i) q^{42} -3.42772 q^{43} +(3.40603 + 0.329584i) q^{44} +(2.08776 + 3.61611i) q^{45} +(-0.0319706 + 0.662331i) q^{46} +(2.95047 - 5.11037i) q^{47} +(-3.01636 - 2.62708i) q^{48} +(4.49063 - 5.36975i) q^{49} +(9.51696 - 14.7881i) q^{50} +(1.16679 - 2.02094i) q^{51} +(-1.79047 + 2.50765i) q^{52} +(1.35437 - 0.781947i) q^{53} +(1.25741 - 0.647235i) q^{54} +7.14421 q^{55} +(-7.16555 + 2.15753i) q^{56} +7.04013 q^{57} +(4.19831 - 2.16102i) q^{58} +(-5.26742 + 3.04114i) q^{59} +(-6.79644 - 4.85269i) q^{60} +(-4.55959 + 7.89744i) q^{61} +(2.42039 - 3.76097i) q^{62} +(0.228411 - 2.63587i) q^{63} +(7.66734 + 2.28297i) q^{64} +(-3.21646 + 5.57107i) q^{65} +(0.116661 - 2.41686i) q^{66} +(3.73658 + 6.47195i) q^{67} +(-0.449517 + 4.64545i) q^{68} +0.468884 q^{69} +(-14.4566 + 5.92433i) q^{70} +3.49263i q^{71} +(-1.75263 + 2.21997i) q^{72} +(-12.5811 + 7.26372i) q^{73} +(0.609899 - 12.6352i) q^{74} +(-10.7691 - 6.21752i) q^{75} +(-12.8152 + 5.83295i) q^{76} +(-3.71029 - 2.59340i) q^{77} +(1.83215 + 1.17909i) q^{78} +(1.46108 + 0.843557i) q^{79} +(16.3922 + 3.20237i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.68203 + 3.43948i) q^{82} -2.72601i q^{83} +(1.76812 + 4.98736i) q^{84} +9.74391i q^{85} +(-2.21854 - 4.31005i) q^{86} +(-1.66943 - 2.89153i) q^{87} +(1.79008 + 4.49611i) q^{88} +(1.83829 + 1.06134i) q^{89} +(-3.19567 + 4.96566i) q^{90} +(3.69278 - 1.72569i) q^{91} +(-0.853516 + 0.388484i) q^{92} +(-2.73883 - 1.58126i) q^{93} +(8.33550 + 0.402352i) q^{94} +(-25.4579 + 14.6981i) q^{95} +(1.35103 - 5.49315i) q^{96} +1.95202i q^{97} +(9.65849 + 2.17109i) q^{98} -1.71097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9} - 18 q^{10} + 8 q^{11} - 10 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{22} - 18 q^{24} - 16 q^{25} - 30 q^{26} - 14 q^{28} - 8 q^{30} - 12 q^{32} - 24 q^{35} - 4 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 16 * q^9 - 18 * q^10 + 8 * q^11 - 10 * q^14 + 6 * q^16 + 2 * q^18 - 20 * q^22 - 18 * q^24 - 16 * q^25 - 30 * q^26 - 14 * q^28 - 8 * q^30 - 12 * q^32 - 24 * q^35 - 4 * q^36 - 18 * q^38 - 30 * q^40 + 4 * q^42 - 16 * q^43 + 24 * q^44 + 8 * q^46 + 8 * q^49 + 76 * q^50 + 36 * q^52 + 16 * q^56 + 16 * q^57 - 6 * q^58 - 96 * q^59 - 2 * q^60 + 76 * q^64 - 36 * q^66 - 32 * q^67 + 96 * q^68 + 6 * q^70 + 8 * q^72 - 24 * q^73 - 34 * q^74 - 12 * q^78 + 36 * q^80 - 16 * q^81 - 36 * q^82 + 16 * q^84 + 50 * q^86 - 14 * q^88 + 56 * q^91 - 128 * q^92 + 36 * q^94 + 30 * q^96 + 60 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more