LMFDB - Embedded newform 252.2.ba.a.155.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(155,252)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("252.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.22
Character	$\chi$	$=$	252.155
Dual form			252.2.ba.a.239.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.412980 + 1.35257i) q^{2} +(0.642722 - 1.60839i) q^{3} +(-1.65890 + 1.11717i) q^{4} +(2.51813 - 1.45385i) q^{5} +(2.44089 + 0.205095i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-2.19614 - 1.78241i) q^{8} +(-2.17382 - 2.06749i) q^{9} +O(q^{10})$	\(q+(0.412980 + 1.35257i) q^{2} +(0.642722 - 1.60839i) q^{3} +(-1.65890 + 1.11717i) q^{4} +(2.51813 - 1.45385i) q^{5} +(2.44089 + 0.205095i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-2.19614 - 1.78241i) q^{8} +(-2.17382 - 2.06749i) q^{9} +(3.00637 + 2.80555i) q^{10} +(1.18430 - 2.05127i) q^{11} +(0.730632 + 3.38617i) q^{12} +(-0.125913 - 0.218087i) q^{13} +(-0.318634 + 1.37785i) q^{14} +(-0.719887 - 4.98455i) q^{15} +(1.50387 - 3.70653i) q^{16} +7.60859i q^{17} +(1.89868 - 3.79407i) q^{18} -2.60920i q^{19} +(-2.55313 + 5.22496i) q^{20} +(1.36081 - 1.07154i) q^{21} +(3.26359 + 0.754720i) q^{22} +(4.51674 + 7.82323i) q^{23} +(-4.27830 + 2.38665i) q^{24} +(1.72733 - 2.99183i) q^{25} +(0.242979 - 0.260371i) q^{26} +(-4.72248 + 2.16752i) q^{27} +(-1.99523 + 0.138049i) q^{28} +(-5.53448 - 3.19533i) q^{29} +(6.44466 - 3.03222i) q^{30} +(-0.0905658 + 0.0522882i) q^{31} +(5.63441 + 0.503365i) q^{32} +(-2.53807 - 3.22322i) q^{33} +(-10.2912 + 3.14219i) q^{34} +2.90769 q^{35} +(5.91587 + 1.00123i) q^{36} -3.15261 q^{37} +(3.52912 - 1.07755i) q^{38} +(-0.431695 + 0.0623469i) q^{39} +(-8.12152 - 1.29549i) q^{40} +(-7.24183 + 4.18107i) q^{41} +(2.01132 + 1.39806i) q^{42} +(-7.18102 - 4.14596i) q^{43} +(0.326984 + 4.72592i) q^{44} +(-8.47978 - 2.04582i) q^{45} +(-8.71615 + 9.34005i) q^{46} +(0.248282 - 0.430036i) q^{47} +(-4.99497 - 4.80107i) q^{48} +(0.500000 + 0.866025i) q^{49} +(4.76001 + 1.10078i) q^{50} +(12.2376 + 4.89020i) q^{51} +(0.452516 + 0.221118i) q^{52} -2.38678i q^{53} +(-4.88201 - 5.49235i) q^{54} -6.88718i q^{55} +(-1.01071 - 2.64168i) q^{56} +(-4.19660 - 1.67699i) q^{57} +(2.03629 - 8.80538i) q^{58} +(3.99487 + 6.91932i) q^{59} +(6.76280 + 7.46462i) q^{60} +(3.69592 - 6.40151i) q^{61} +(-0.108125 - 0.100903i) q^{62} +(-0.848836 - 2.87741i) q^{63} +(1.64606 + 7.82882i) q^{64} +(-0.634129 - 0.366115i) q^{65} +(3.31146 - 4.76404i) q^{66} +(0.444103 - 0.256403i) q^{67} +(-8.50008 - 12.6219i) q^{68} +(15.4858 - 2.23651i) q^{69} +(1.20082 + 3.93286i) q^{70} +1.45233 q^{71} +(1.08890 + 8.41512i) q^{72} +4.06828 q^{73} +(-1.30196 - 4.26412i) q^{74} +(-3.70182 - 4.70113i) q^{75} +(2.91491 + 4.32839i) q^{76} +(2.05127 - 1.18430i) q^{77} +(-0.262610 - 0.558150i) q^{78} +(-10.0369 - 5.79482i) q^{79} +(-1.60178 - 11.5199i) q^{80} +(0.450966 + 8.98869i) q^{81} +(-8.64592 - 8.06839i) q^{82} +(-0.439593 + 0.761398i) q^{83} +(-1.06034 + 3.29783i) q^{84} +(11.0617 + 19.1594i) q^{85} +(2.64209 - 11.4250i) q^{86} +(-8.69646 + 6.84787i) q^{87} +(-6.25710 + 2.39398i) q^{88} +14.6787i q^{89} +(-0.734854 - 12.3144i) q^{90} -0.251825i q^{91} +(-16.2327 - 7.93195i) q^{92} +(0.0258910 + 0.179272i) q^{93} +(0.684190 + 0.158222i) q^{94} +(-3.79337 - 6.57031i) q^{95} +(4.43097 - 8.73880i) q^{96} +(2.88066 - 4.98945i) q^{97} +(-0.964871 + 1.03394i) q^{98} +(-6.81545 + 2.01056i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 72 * q + 6 * q^6 + 4 * q^9	$ 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) $ 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.412980	+	1.35257i	0.292021	+	0.956412i
$2$	0.412980	+	1.35257i	0.292021	+	0.956412i
$3$	0.642722	−	1.60839i	0.371076	−	0.928603i
$3$	0.642722	−	1.60839i	0.371076	−	0.928603i
$4$	−1.65890	+	1.11717i	−0.829448	+	0.558584i
$5$	2.51813	−	1.45385i	1.12614	−	0.650179i	0.183182	−	0.983079i	$-0.441360\pi$
$5$	2.51813	−	1.45385i	1.12614	−	0.650179i	0.942962	+	0.332900i	$0.108027\pi$
$6$	2.44089	+	0.205095i	0.996488	+	0.0837298i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$	−2.19614	−	1.78241i	−0.776453	−	0.630175i
$9$	−2.17382	−	2.06749i	−0.724606	−	0.689164i
$10$	3.00637	+	2.80555i	0.950697	+	0.887191i
$11$	1.18430	−	2.05127i	0.357081	−	0.618483i	−0.630391	−	0.776278i	$-0.717105\pi$
$11$	1.18430	−	2.05127i	0.357081	−	0.618483i	0.987472	+	0.157795i	$0.0504387\pi$
$12$	0.730632	+	3.38617i	0.210915	+	0.977504i
$13$	−0.125913	−	0.218087i	−0.0349219	−	0.0604864i	0.848036	−	0.529938i	$-0.177785\pi$
$13$	−0.125913	−	0.218087i	−0.0349219	−	0.0604864i	−0.882958	+	0.469452i	$0.844452\pi$
$14$	−0.318634	+	1.37785i	−0.0851586	+	0.368246i
$15$	−0.719887	−	4.98455i	−0.185874	−	1.28701i
$16$	1.50387	−	3.70653i	0.375967	−	0.926633i
$17$			7.60859i			1.84535i	0.385574	+	0.922677i	$0.374003\pi$
$17$			7.60859i			1.84535i	−0.385574	+	0.922677i	$0.625997\pi$
$18$	1.89868	−	3.79407i	0.447524	−	0.894272i
$19$		−	2.60920i		−	0.598591i	−0.954160	−	0.299295i	$-0.903248\pi$
$19$		−	2.60920i		−	0.598591i	0.954160	−	0.299295i	$-0.0967516\pi$
$20$	−2.55313	+	5.22496i	−0.570897	+	1.16834i
$21$	1.36081	−	1.07154i	0.296952	−	0.233830i
$22$	3.26359	+	0.754720i	0.695799	+	0.160907i
$23$	4.51674	+	7.82323i	0.941806	+	1.63126i	0.762024	+	0.647549i	$0.224206\pi$
$23$	4.51674	+	7.82323i	0.941806	+	1.63126i	0.179782	+	0.983706i	$0.442461\pi$
$24$	−4.27830	+	2.38665i	−0.873305	+	0.487173i
$25$	1.72733	−	2.99183i	0.345467	−	0.598366i
$26$	0.242979	−	0.260371i	0.0476520	−	0.0510630i
$27$	−4.72248	+	2.16752i	−0.908843	+	0.417139i
$28$	−1.99523	+	0.138049i	−0.377063	+	0.0260888i
$29$	−5.53448	−	3.19533i	−1.02773	−	0.593358i	−0.111394	−	0.993776i	$-0.535532\pi$
$29$	−5.53448	−	3.19533i	−1.02773	−	0.593358i	−0.916333	+	0.400418i	$0.868865\pi$
$30$	6.44466	−	3.03222i	1.17663	−	0.553605i
$31$	−0.0905658	+	0.0522882i	−0.0162661	+	0.00939124i	−0.508111	−	0.861292i	$-0.669656\pi$
$31$	−0.0905658	+	0.0522882i	−0.0162661	+	0.00939124i	0.491845	+	0.870683i	$0.336323\pi$
$32$	5.63441	+	0.503365i	0.996033	+	0.0889831i
$33$	−2.53807	−	3.22322i	−0.441820	−	0.561090i
$34$	−10.2912	+	3.14219i	−1.76492	+	0.538882i
$35$	2.90769			0.491489
$36$	5.91587	+	1.00123i	0.985979	+	0.166872i
$37$	−3.15261			−0.518285			−0.259143	−	0.965839i	$-0.583440\pi$
$37$	−3.15261			−0.518285			−0.259143	+	0.965839i	$0.583440\pi$
$38$	3.52912	−	1.07755i	0.572499	−	0.174801i
$39$	−0.431695	+	0.0623469i	−0.0691265	+	0.00998349i
$40$	−8.12152	−	1.29549i	−1.28412	−	0.204835i
$41$	−7.24183	+	4.18107i	−1.13098	+	0.652974i	−0.944182	−	0.329424i	$-0.893145\pi$
$41$	−7.24183	+	4.18107i	−1.13098	+	0.652974i	−0.186801	+	0.982398i	$0.559812\pi$
$42$	2.01132	+	1.39806i	0.310354	+	0.215726i
$43$	−7.18102	−	4.14596i	−1.09510	−	0.632254i	−0.160167	−	0.987090i	$-0.551203\pi$
$43$	−7.18102	−	4.14596i	−1.09510	−	0.632254i	−0.934928	+	0.354836i	$0.884537\pi$
$44$	0.326984	+	4.72592i	0.0492946	+	0.712459i
$45$	−8.47978	−	2.04582i	−1.26409	−	0.304973i
$46$	−8.71615	+	9.34005i	−1.28513	+	1.37712i
$47$	0.248282	−	0.430036i	0.0362156	−	0.0627273i	−0.847349	−	0.531036i	$-0.821803\pi$
$47$	0.248282	−	0.430036i	0.0362156	−	0.0627273i	0.883565	+	0.468308i	$0.155136\pi$
$48$	−4.99497	−	4.80107i	−0.720962	−	0.692975i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	4.76001	+	1.10078i	0.673167	+	0.155673i
$51$	12.2376	+	4.89020i	1.71360	+	0.684766i
$52$	0.452516	+	0.221118i	0.0627526	+	0.0306635i
$53$		−	2.38678i		−	0.327849i	−0.986473	−	0.163925i	$-0.947585\pi$
$53$		−	2.38678i		−	0.327849i	0.986473	−	0.163925i	$-0.0524154\pi$
$54$	−4.88201	−	5.49235i	−0.664358	−	0.747415i
$55$		−	6.88718i		−	0.928667i
$56$	−1.01071	−	2.64168i	−0.135062	−	0.353009i
$57$	−4.19660	−	1.67699i	−0.555853	−	0.222122i
$58$	2.03629	−	8.80538i	0.267377	−	1.15620i
$59$	3.99487	+	6.91932i	0.520088	+	0.900818i	0.999727	+	0.0233526i	$0.00743403\pi$
$59$	3.99487	+	6.91932i	0.520088	+	0.900818i	−0.479640	+	0.877466i	$0.659233\pi$
$60$	6.76280	+	7.46462i	0.873074	+	0.963678i
$61$	3.69592	−	6.40151i	0.473214	−	0.819630i	−0.526316	−	0.850289i	$-0.676427\pi$
$61$	3.69592	−	6.40151i	0.473214	−	0.819630i	0.999530	+	0.0306589i	$0.00976058\pi$
$62$	−0.108125	−	0.100903i	−0.0137319	−	0.0128147i
$63$	−0.848836	−	2.87741i	−0.106943	−	0.362519i
$64$	1.64606	+	7.82882i	0.205758	+	0.978603i
$65$	−0.634129	−	0.366115i	−0.0786541	−	0.0454109i
$66$	3.31146	−	4.76404i	0.407613	−	0.586412i
$67$	0.444103	−	0.256403i	0.0542559	−	0.0313246i	−0.472627	−	0.881263i	$-0.656694\pi$
$67$	0.444103	−	0.256403i	0.0542559	−	0.0313246i	0.526883	+	0.849938i	$0.323361\pi$
$68$	−8.50008	−	12.6219i	−1.03079	−	1.53062i
$69$	15.4858	−	2.23651i	1.86427	−	0.269244i
$70$	1.20082	+	3.93286i	0.143525	+	0.470066i
$71$	1.45233			0.172360			0.0861800	−	0.996280i	$-0.472534\pi$
$71$	1.45233			0.172360			0.0861800	+	0.996280i	$0.472534\pi$
$72$	1.08890	+	8.41512i	0.128328	+	0.991732i
$73$	4.06828			0.476157			0.238078	−	0.971246i	$-0.423483\pi$
$73$	4.06828			0.476157			0.238078	+	0.971246i	$0.423483\pi$
$74$	−1.30196	−	4.26412i	−0.151350	−	0.495694i
$75$	−3.70182	−	4.70113i	−0.427450	−	0.542840i
$76$	2.91491	+	4.32839i	0.334364	+	0.496500i
$77$	2.05127	−	1.18430i	0.233764	−	0.134964i
$78$	−0.262610	−	0.558150i	−0.0297347	−	0.0631980i
$79$	−10.0369	−	5.79482i	−1.12924	−	0.651968i	−0.185498	−	0.982645i	$-0.559390\pi$
$79$	−10.0369	−	5.79482i	−1.12924	−	0.651968i	−0.943744	+	0.330677i	$0.892723\pi$
$80$	−1.60178	−	11.5199i	−0.179085	−	1.28797i
$81$	0.450966	+	8.98869i	0.0501073	+	0.998744i
$82$	−8.64592	−	8.06839i	−0.954782	−	0.891004i
$83$	−0.439593	+	0.761398i	−0.0482516	+	0.0835743i	−0.889142	−	0.457630i	$-0.848698\pi$
$83$	−0.439593	+	0.761398i	−0.0482516	+	0.0835743i	0.840891	+	0.541205i	$0.182032\pi$
$84$	−1.06034	+	3.29783i	−0.115693	+	0.359823i
$85$	11.0617	+	19.1594i	1.19981	+	2.07813i
$86$	2.64209	−	11.4250i	0.284904	−	1.23199i
$87$	−8.69646	+	6.84787i	−0.932359	+	0.734169i
$88$	−6.25710	+	2.39398i	−0.667009	+	0.255199i
$89$			14.6787i			1.55594i	0.628304	+	0.777968i	$0.283749\pi$
$89$			14.6787i			1.55594i	−0.628304	+	0.777968i	$0.716251\pi$
$90$	−0.734854	−	12.3144i	−0.0774605	−	1.29805i
$91$		−	0.251825i		−	0.0263984i
$92$	−16.2327	−	7.93195i	−1.69237	−	0.826963i
$93$	0.0258910	+	0.179272i	0.00268478	+	0.0185896i
$94$	0.684190	+	0.158222i	0.0705688	+	0.0163194i
$95$	−3.79337	−	6.57031i	−0.389191	−	0.674099i
$96$	4.43097	−	8.73880i	0.452234	−	0.891900i
$97$	2.88066	−	4.98945i	0.292487	−	0.506602i	−0.681910	−	0.731436i	$-0.738851\pi$
$97$	2.88066	−	4.98945i	0.292487	−	0.506602i	0.974397	+	0.224834i	$0.0721839\pi$
$98$	−0.964871	+	1.03394i	−0.0974667	+	0.104443i
$99$	−6.81545	+	2.01056i	−0.684979	+	0.202069i
$100$	0.476913	+	6.89285i	0.0476913	+	0.689285i
$101$	−12.4968	−	7.21504i	−1.24348	−	0.717923i	−0.273678	−	0.961821i	$-0.588240\pi$
$101$	−12.4968	−	7.21504i	−1.24348	−	0.717923i	−0.969801	+	0.243898i	$0.921574\pi$
$102$	−1.56049	+	18.5717i	−0.154511	+	1.83887i
$103$	−10.3804	+	5.99314i	−1.02281	+	0.590521i	−0.914918	−	0.403641i	$-0.867745\pi$
$103$	−10.3804	+	5.99314i	−1.02281	+	0.590521i	−0.107896	+	0.994162i	$0.534411\pi$
$104$	−0.112198	+	0.703377i	−0.0110019	+	0.0689718i
$105$	1.86884	−	4.67669i	0.182380	−	0.456398i
$106$	3.22829	−	0.985691i	0.313559	−	0.0957388i
$107$	6.10346			0.590043			0.295022	−	0.955491i	$-0.404673\pi$
$107$	6.10346			0.590043			0.295022	+	0.955491i	$0.404673\pi$
$108$	5.41262	−	8.87150i	0.520830	−	0.853660i
$109$	6.25509			0.599129			0.299564	−	0.954076i	$-0.403159\pi$
$109$	6.25509			0.599129			0.299564	+	0.954076i	$0.403159\pi$
$110$	9.31540	−	2.84427i	0.888188	−	0.271190i
$111$	−2.02625	+	5.07061i	−0.192323	+	0.481281i
$112$	3.15565	−	2.45802i	0.298181	−	0.232261i
$113$	15.8902	−	9.17418i	1.49482	−	0.863035i	0.494838	−	0.868985i	$-0.335228\pi$
$113$	15.8902	−	9.17418i	1.49482	−	0.863035i	0.999982	+	0.00595082i	$0.00189422\pi$
$114$	0.535134	−	6.36876i	0.0501199	−	0.596489i
$115$	22.7475	+	13.1333i	2.12122	+	1.22469i
$116$	12.7508	−	0.882224i	1.18389	−	0.0819125i
$117$	−0.177182	+	0.734404i	−0.0163805	+	0.0678957i
$118$	−7.70906	+	8.26088i	−0.709677	+	0.760476i
$119$	−3.80429	+	6.58923i	−0.348739	+	0.604034i
$120$	−7.30352	+	12.2299i	−0.666717	+	1.11643i
$121$	2.69485	+	4.66762i	0.244986	+	0.424329i
$122$	10.1848	+	2.35529i	0.922092	+	0.213238i
$123$	2.07030	+	14.3349i	0.186673	+	1.29254i
$124$	0.0918245	−	0.187918i	0.00824608	−	0.0168755i
$125$			4.49335i			0.401898i
$126$	3.54135	−	2.33642i	0.315488	−	0.208145i
$127$		−	13.5835i		−	1.20534i	−0.797989	−	0.602672i	$-0.794103\pi$
$127$		−	13.5835i		−	1.20534i	0.797989	−	0.602672i	$-0.205897\pi$
$128$	−9.90925	+	5.45956i	−0.875862	+	0.482562i
$129$	−11.2837	+	8.88516i	−0.993476	+	0.782295i
$130$	0.233314	−	1.00890i	0.0204629	−	0.0884866i
$131$	0.740508	+	1.28260i	0.0646985	+	0.112061i	0.896560	−	0.442922i	$-0.146058\pi$
$131$	0.740508	+	1.28260i	0.0646985	+	0.112061i	−0.831862	+	0.554983i	$0.812725\pi$
$132$	7.81126	+	2.51153i	0.679883	+	0.218601i
$133$	1.30460	−	2.25963i	0.113123	−	0.195935i
$134$	0.530209	+	0.494792i	0.0458031	+	0.0427435i
$135$	−8.74061	+	12.3239i	−0.752272	+	1.06067i
$136$	13.5616	−	16.7095i	1.16290	−	1.43283i
$137$	15.5721	+	8.99055i	1.33041	+	0.768115i	0.985363	−	0.170469i	$-0.0545284\pi$
$137$	15.5721	+	8.99055i	1.33041	+	0.768115i	0.345051	+	0.938584i	$0.387862\pi$
$138$	9.42036	+	20.0220i	0.801914	+	1.70438i
$139$	7.21297	−	4.16441i	0.611796	−	0.353221i	−0.161872	−	0.986812i	$-0.551753\pi$
$139$	7.21297	−	4.16441i	0.611796	−	0.353221i	0.773668	+	0.633591i	$0.218420\pi$
$140$	−4.82355	+	3.24838i	−0.407665	+	0.274538i
$141$	−0.532089	−	0.675727i	−0.0448100	−	0.0569064i
$142$	0.599783	+	1.96438i	0.0503327	+	0.164847i
$143$	−0.596475			−0.0498797
$144$	−10.9324	+	4.94809i	−0.911030	+	0.412341i
$145$	−18.5821			−1.54316
$146$	1.68012	+	5.50264i	0.139048	+	0.455402i
$147$	1.71426	−	0.247580i	0.141390	−	0.0204201i
$148$	5.22984	−	3.52199i	0.429890	−	0.289506i
$149$	−2.86752	+	1.65557i	−0.234917	+	0.135629i	−0.612838	−	0.790208i	$-0.709972\pi$
$149$	−2.86752	+	1.65557i	−0.234917	+	0.135629i	0.377921	+	0.925838i	$0.376639\pi$
$150$	4.82984	−	6.94845i	0.394355	−	0.567339i
$151$	5.39261	+	3.11343i	0.438845	+	0.253367i	0.703107	−	0.711084i	$-0.251795\pi$
$151$	5.39261	+	3.11343i	0.438845	+	0.253367i	−0.264263	+	0.964451i	$0.585129\pi$
$152$	−4.65065	+	5.73016i	−0.377217	+	0.464778i
$153$	15.7307	−	16.5397i	1.27175	−	1.33715i
$154$	2.44899	+	2.28540i	0.197345	+	0.184163i
$155$	−0.152038	+	0.263337i	−0.0122120	+	0.0211518i
$156$	0.646485	−	0.585703i	0.0517602	−	0.0468938i
$157$	1.48912	+	2.57922i	0.118844	+	0.205844i	0.919310	−	0.393534i	$-0.128748\pi$
$157$	1.48912	+	2.57922i	0.118844	+	0.205844i	−0.800466	+	0.599379i	$0.795414\pi$
$158$	3.69286	−	15.9688i	0.293788	−	1.27041i
$159$	−3.83886	−	1.53403i	−0.304442	−	0.121657i
$160$	14.9200	−	6.92403i	1.17953	−	0.547392i
$161$			9.03348i			0.711938i
$162$	−11.9716	+	4.32211i	−0.940578	+	0.339577i
$163$			8.29335i			0.649585i	0.945785	+	0.324793i	$0.105294\pi$
$163$			8.29335i			0.649585i	−0.945785	+	0.324793i	$0.894706\pi$
$164$	7.34247	−	15.0263i	0.573351	−	1.17336i
$165$	−11.0772	−	4.42654i	−0.862363	−	0.344606i
$166$	−1.21139	−	0.280139i	−0.0940219	−	0.0217430i
$167$	−9.34971	−	16.1942i	−0.723503	−	1.25314i	−0.959587	−	0.281411i	$-0.909198\pi$
$167$	−9.34971	−	16.1942i	−0.723503	−	1.25314i	0.236085	−	0.971732i	$-0.424136\pi$
$168$	−4.89845	−	0.0722504i	−0.377923	−	0.00557424i
$169$	6.46829	−	11.2034i	0.497561	−	0.861801i
$170$	−21.3462	+	22.8742i	−1.63718	+	1.75437i
$171$	−5.39449	+	5.67192i	−0.412527	+	0.433742i
$172$	16.5443	−	1.14469i	1.26149	−	0.0872819i
$173$	7.58848	+	4.38121i	0.576942	+	0.333097i	0.759917	−	0.650020i	$-0.225240\pi$
$173$	7.58848	+	4.38121i	0.576942	+	0.333097i	−0.182975	+	0.983118i	$0.558573\pi$
$174$	−12.8537	−	8.93455i	−0.974436	−	0.677326i
$175$	2.99183	−	1.72733i	0.226161	−	0.130574i
$176$	−5.82208	−	7.47451i	−0.438856	−	0.563412i
$177$	13.6965	−	1.97810i	1.02949	−	0.148683i
$178$	−19.8539	+	6.06199i	−1.48812	+	0.454365i
$179$	−2.87709			−0.215044			−0.107522	−	0.994203i	$-0.534292\pi$
$179$	−2.87709			−0.215044			−0.107522	+	0.994203i	$0.534292\pi$
$180$	16.3526	−	6.07953i	1.21885	−	0.453142i
$181$	−4.82998			−0.359010			−0.179505	−	0.983757i	$-0.557450\pi$
$181$	−4.82998			−0.359010			−0.179505	+	0.983757i	$0.557450\pi$
$182$	0.340611	−	0.103999i	0.0252478	−	0.00770890i
$183$	−7.92067	−	10.0589i	−0.585513	−	0.743572i
$184$	4.02476	−	25.2316i	0.296709	−	1.86010i
$185$	−7.93868	+	4.58340i	−0.583664	+	0.336978i
$186$	−0.231785	+	0.109055i	−0.0169953	+	0.00799630i
$187$	15.6073	+	9.01088i	1.14132	+	0.658941i
$188$	0.0685500	+	0.990758i	0.00499952	+	0.0722584i
$189$	−5.17355	−	0.484116i	−0.376320	−	0.0352143i
$190$	7.32022	−	7.84421i	0.531065	−	0.569078i
$191$	10.2584	−	17.7680i	0.742270	−	1.28565i	−0.209189	−	0.977875i	$-0.567082\pi$
$191$	10.2584	−	17.7680i	0.742270	−	1.28565i	0.951459	−	0.307775i	$-0.0995843\pi$
$192$	13.6497	+	2.38425i	0.985085	+	0.172068i
$193$	−9.29894	−	16.1062i	−0.669352	−	1.15935i	−0.978085	−	0.208204i	$-0.933238\pi$
$193$	−9.29894	−	16.1062i	−0.669352	−	1.15935i	0.308733	−	0.951149i	$-0.400095\pi$
$194$	7.93824	+	1.83576i	0.569932	+	0.131800i
$195$	−0.996423	+	0.784616i	−0.0713553	+	0.0561875i
$196$	−1.79694	−	0.878061i	−0.128353	−	0.0627187i
$197$		−	17.2523i		−	1.22917i	−0.788850	−	0.614586i	$-0.789323\pi$
$197$		−	17.2523i		−	1.22917i	0.788850	−	0.614586i	$-0.210677\pi$
$198$	−5.53407	−	8.38806i	−0.393289	−	0.596113i
$199$			1.17220i			0.0830948i	0.999137	+	0.0415474i	$0.0132288\pi$
$199$			1.17220i			0.0830948i	−0.999137	+	0.0415474i	$0.986771\pi$
$200$	−9.12612	+	3.49167i	−0.645314	+	0.246898i
$201$	−0.126961	−	0.879086i	−0.00895511	−	0.0620059i
$202$	4.59792	−	19.8825i	0.323508	−	1.39893i
$203$	−3.19533	−	5.53448i	−0.224268	−	0.388444i
$204$	−25.7640	+	5.55908i	−1.80384	+	0.389213i
$205$	−12.1573	+	21.0570i	−0.849100	+	1.47068i
$206$	−12.3930	−	11.5652i	−0.863464	−	0.805786i
$207$	6.35587	−	26.3446i	0.441764	−	1.83108i
$208$	−0.997702	+	0.138725i	−0.0691782	+	0.00961885i
$209$	−5.35218	−	3.09008i	−0.370218	−	0.213745i
$210$	7.09735	+	0.596354i	0.489764	+	0.0411523i
$211$	−8.81152	+	5.08733i	−0.606610	+	0.350226i	−0.771637	−	0.636063i	$-0.780562\pi$
$211$	−8.81152	+	5.08733i	−0.606610	+	0.350226i	0.165028	+	0.986289i	$0.447229\pi$
$212$	2.66643	+	3.95942i	0.183131	+	0.271934i
$213$	0.933445	−	2.33591i	0.0639586	−	0.160054i
$214$	2.52060	+	8.25536i	0.172305	+	0.564325i
$215$	−24.1104			−1.64431
$216$	14.2346	+	3.65721i	0.968544	+	0.248841i
$217$	−0.104576			−0.00709911
$218$	2.58322	+	8.46045i	0.174958	+	0.573014i
$219$	2.61477	−	6.54337i	0.176690	−	0.442160i
$220$	7.69414	+	11.4251i	0.518739	+	0.770281i
$221$	1.65933	−	0.958017i	0.111619	−	0.0644432i
$222$	−7.69516	−	0.646585i	−0.516465	−	0.0433959i
$223$	5.28069	+	3.04881i	0.353621	+	0.204163i	0.666279	−	0.745703i	$-0.267886\pi$
$223$	5.28069	+	3.04881i	0.353621	+	0.204163i	−0.312658	+	0.949866i	$0.601219\pi$
$224$	4.62786	+	3.25313i	0.309212	+	0.217359i
$225$	−9.94048	+	2.93244i	−0.662699	+	0.195496i
$226$	18.9710	+	17.7038i	1.26194	+	1.17764i
$227$	−11.1581	+	19.3264i	−0.740589	+	1.28274i	0.211639	+	0.977348i	$0.432120\pi$
$227$	−11.1581	+	19.3264i	−0.740589	+	1.28274i	−0.952228	+	0.305390i	$0.901213\pi$
$228$	8.83520	−	1.90636i	0.585125	−	0.126252i
$229$	−2.70895	−	4.69204i	−0.179013	−	0.310059i	0.762530	−	0.646953i	$-0.223957\pi$
$229$	−2.70895	−	4.69204i	−0.179013	−	0.310059i	−0.941543	+	0.336894i	$0.890624\pi$
$230$	−8.36944	+	36.1914i	−0.551864	+	2.38639i
$231$	−0.586420	−	4.06042i	−0.0385836	−	0.267156i
$232$	6.45911	+	16.8821i	0.424062	+	1.10836i
$233$		−	6.08190i		−	0.398439i	−0.979955	−	0.199219i	$-0.936159\pi$
$233$		−	6.08190i		−	0.398439i	0.979955	−	0.199219i	$-0.0638406\pi$
$234$	−1.06651	+	0.0636432i	−0.0697197	+	0.00416049i
$235$		−	1.44385i		−	0.0941865i
$236$	−14.3571	−	7.01548i	−0.934568	−	0.456669i
$237$	−15.7713	+	12.4188i	−1.02445	+	0.806687i
$238$	−10.4835	−	2.42436i	−0.679544	−	0.157148i
$239$	−4.58910	−	7.94855i	−0.296844	−	0.514149i	0.678568	−	0.734538i	$-0.262601\pi$
$239$	−4.58910	−	7.94855i	−0.296844	−	0.514149i	−0.975412	+	0.220388i	$0.929268\pi$
$240$	−19.5580	−	4.82782i	−1.26246	−	0.311635i
$241$	−4.60034	+	7.96801i	−0.296334	+	0.513265i	−0.975294	−	0.220910i	$-0.929097\pi$
$241$	−4.60034	+	7.96801i	−0.296334	+	0.513265i	0.678961	+	0.734175i	$0.262431\pi$
$242$	−5.20036	+	5.57260i	−0.334292	+	0.358221i
$243$	14.7471	+	5.05190i	0.946030	+	0.324080i
$244$	1.02043	+	14.7484i	0.0653266	+	0.944170i
$245$	2.51813	+	1.45385i	0.160878	+	0.0928828i
$246$	−18.5340	+	8.72026i	−1.18169	+	0.555984i
$247$	−0.569032	+	0.328531i	−0.0362066	+	0.0209039i
$248$	0.292094	+	0.0465928i	0.0185480	+	0.00295864i
$249$	0.942087	+	1.19640i	0.0597023	+	0.0758190i
$250$	−6.07758	+	1.85566i	−0.384380	+	0.117363i
$251$	17.5771			1.10946			0.554729	−	0.832031i	$-0.312822\pi$
$251$	17.5771			1.10946			0.554729	+	0.832031i	$0.312822\pi$
$252$	4.62268	+	3.82503i	0.291202	+	0.240954i
$253$	21.3968			1.34520
$254$	18.3727	−	5.60972i	1.15280	−	0.351985i
$255$	37.9254	−	5.47732i	2.37498	−	0.343003i
$256$	−11.4768	−	11.1483i	−0.717298	−	0.696767i
$257$	−9.36418	+	5.40641i	−0.584122	+	0.337243i	−0.762770	−	0.646670i	$-0.776161\pi$
$257$	−9.36418	+	5.40641i	−0.584122	+	0.337243i	0.178648	+	0.983913i	$0.442828\pi$
$258$	−16.6778	−	11.5926i	−1.03831	−	0.721726i
$259$	−2.73024	−	1.57630i	−0.169649	−	0.0979467i
$260$	1.46097	−	0.101083i	0.0906053	−	0.00626893i
$261$	5.42463	+	18.3886i	0.335776	+	1.13822i
$262$	−1.42899	+	1.53128i	−0.0882833	+	0.0946026i
$263$	1.23346	−	2.13642i	0.0760585	−	0.131737i	−0.825488	−	0.564420i	$-0.809100\pi$
$263$	1.23346	−	2.13642i	0.0760585	−	0.131737i	0.901546	+	0.432683i	$0.142433\pi$
$264$	−0.171133	+	11.6025i	−0.0105325	+	0.714084i
$265$	−3.47001	−	6.01023i	−0.213161	−	0.369205i
$266$	3.59508	+	0.831380i	0.220429	+	0.0509752i
$267$	23.6090	+	9.43430i	1.44485	+	0.577370i
$268$	−0.450275	+	0.921484i	−0.0275049	+	0.0562886i
$269$		−	18.6417i		−	1.13661i	−0.822820	−	0.568303i	$-0.807600\pi$
$269$		−	18.6417i		−	1.13661i	0.822820	−	0.568303i	$-0.192400\pi$
$270$	−20.2786	−	6.73279i	−1.23412	−	0.409745i
$271$		−	11.9123i		−	0.723621i	−0.932252	−	0.361811i	$-0.882159\pi$
$271$		−	11.9123i		−	0.723621i	0.932252	−	0.361811i	$-0.117841\pi$
$272$	28.2015	+	11.4423i	1.70997	+	0.693792i
$273$	−0.405032	−	0.161853i	−0.0245137	−	0.00979582i
$274$	−5.72940	+	24.7753i	−0.346126	+	1.49673i
$275$	−4.09137	−	7.08647i	−0.246719	−	0.427330i
$276$	−23.1907	+	21.0104i	−1.39592	+	1.26468i
$277$	8.83024	−	15.2944i	0.530558	−	0.918953i	−0.468807	−	0.883301i	$-0.655316\pi$
$277$	8.83024	−	15.2944i	0.530558	−	0.918953i	0.999364	−	0.0356520i	$-0.0113508\pi$
$278$	8.61147	+	8.03624i	0.516482	+	0.481981i
$279$	0.304979	+	0.0735790i	0.0182586	+	0.00440506i
$280$	−6.38570	−	5.18268i	−0.381618	−	0.309725i
$281$	−16.5651	−	9.56389i	−0.988193	−	0.570534i	−0.0834596	−	0.996511i	$-0.526597\pi$
$281$	−16.5651	−	9.56389i	−0.988193	−	0.570534i	−0.904734	+	0.425977i	$0.859930\pi$
$282$	0.694226	−	0.998749i	0.0413406	−	0.0594747i
$283$	−2.81044	+	1.62261i	−0.167063	+	0.0964541i	−0.581200	−	0.813760i	$-0.697417\pi$
$283$	−2.81044	+	1.62261i	−0.167063	+	0.0964541i	0.414137	+	0.910215i	$0.364083\pi$
$284$	−2.40927	+	1.62250i	−0.142964	+	0.0962776i
$285$	−13.0057	+	1.87833i	−0.770390	+	0.111262i
$286$	−0.246332	−	0.806775i	−0.0145659	−	0.0477056i
$287$	−8.36214			−0.493602
$288$	−11.2075	−	12.7433i	−0.660407	−	0.750907i
$289$	−40.8906			−2.40533
$290$	−7.67402	−	25.1336i	−0.450634	−	1.47589i
$291$	−6.17351	−	7.84005i	−0.361897	−	0.459592i
$292$	−6.74886	+	4.54496i	−0.394947	+	0.265974i
$293$	11.1294	−	6.42555i	0.650185	−	0.375385i	−0.138342	−	0.990385i	$-0.544177\pi$
$293$	11.1294	−	6.42555i	0.650185	−	0.375385i	0.788527	+	0.615000i	$0.210844\pi$
$294$	1.04283	+	2.21642i	0.0608189	+	0.129264i
$295$	20.1192	+	11.6158i	1.17139	+	0.676300i
$296$	6.92356	+	5.61922i	0.402424	+	0.326611i
$297$	−1.14668	+	12.2541i	−0.0665372	+	0.711056i
$298$	−3.42350	−	3.19481i	−0.198318	−	0.185071i
$299$	1.13743	−	1.97009i	0.0657792	−	0.113933i
$300$	11.3929	+	3.66313i	0.657769	+	0.211491i
$301$	−4.14596	−	7.18102i	−0.238969	−	0.413907i
$302$	−1.98409	+	8.57967i	−0.114172	+	0.493705i
$303$	−19.6365	+	15.4624i	−1.12809	+	0.888294i
$304$	−9.67107	−	3.92389i	−0.554674	−	0.225050i
$305$		−	21.4932i		−	1.23069i
$306$	28.8675	+	14.4463i	1.65025	+	0.825840i
$307$		−	17.7017i		−	1.01029i	−0.863035	−	0.505144i	$-0.831439\pi$
$307$		−	17.7017i		−	1.01029i	0.863035	−	0.505144i	$-0.168561\pi$
$308$	−2.07978	+	4.25626i	−0.118507	+	0.242523i
$309$	2.96756	+	20.5477i	0.168819	+	1.16891i
$310$	−0.418971	−	0.0968890i	−0.0237960	−	0.00550293i
$311$	3.30345	+	5.72174i	0.187321	+	0.324450i	0.944356	−	0.328924i	$-0.106686\pi$
$311$	3.30345	+	5.72174i	0.187321	+	0.324450i	−0.757035	+	0.653374i	$0.773353\pi$
$312$	1.05919	+	0.632533i	0.0599648	+	0.0358101i
$313$	5.34114	−	9.25113i	0.301899	−	0.522905i	−0.674667	−	0.738122i	$-0.735713\pi$
$313$	5.34114	−	9.25113i	0.301899	−	0.522905i	0.976566	+	0.215217i	$0.0690460\pi$
$314$	−2.87361	+	3.07930i	−0.162167	+	0.173775i
$315$	−6.32079	−	6.01162i	−0.356136	−	0.338717i
$316$	23.1240	−	1.59994i	1.30083	−	0.0900034i
$317$	−22.1073	−	12.7636i	−1.24167	−	0.716878i	−0.272235	−	0.962231i	$-0.587763\pi$
$317$	−22.1073	−	12.7636i	−1.24167	−	0.716878i	−0.969434	+	0.245353i	$0.921096\pi$
$318$	0.489517	−	5.82586i	0.0274508	−	0.326698i
$319$	−13.1090	+	7.56849i	−0.733964	+	0.423754i
$320$	15.5269	+	17.3209i	0.867980	+	0.968268i
$321$	3.92282	−	9.81672i	0.218951	−	0.547916i
$322$	−12.2184	+	3.73065i	−0.680906	+	0.207901i
$323$	19.8523			1.10461
$324$	−10.7900	−	14.4075i	−0.599444	−	0.800417i
$325$	−0.869972			−0.0482573
$326$	−11.2173	+	3.42498i	−0.621271	+	0.189692i
$327$	4.02028	−	10.0606i	0.222322	−	0.556353i
$328$	23.3564	+	3.72565i	1.28964	+	0.205715i
$329$	0.430036	−	0.248282i	0.0237087	−	0.0136882i
$330$	1.41253	−	16.8108i	0.0777571	−	0.925406i
$331$	−23.0921	−	13.3322i	−1.26925	−	0.732804i	−0.294407	−	0.955680i	$-0.595122\pi$
$331$	−23.0921	−	13.3322i	−1.26925	−	0.732804i	−0.974847	+	0.222876i	$0.928456\pi$
$332$	−0.121371	−	1.75418i	−0.00666108	−	0.0962731i
$333$	6.85319	+	6.51798i	0.375553	+	0.357183i
$334$	18.0425	−	19.3340i	0.987243	−	1.05791i
$335$	0.745541	−	1.29132i	0.0407333	−	0.0705521i
$336$	−1.92524	−	6.65533i	−0.105030	−	0.363078i
$337$	3.17158	+	5.49333i	0.172767	+	0.299241i	0.939386	−	0.342861i	$-0.111396\pi$
$337$	3.17158	+	5.49333i	0.172767	+	0.299241i	−0.766619	+	0.642102i	$0.778063\pi$
$338$	17.8247	+	4.12204i	0.969535	+	0.224209i
$339$	−4.54269	−	31.4540i	−0.246725	−	1.70834i
$340$	−39.7546	−	19.4257i	−2.15599	−	1.05351i
$341$			0.247700i			0.0134137i
$342$	−9.89949	−	4.95404i	−0.535303	−	0.267884i
$343$			1.00000i			0.0539949i
$344$	8.38074	+	21.9046i	0.451859	+	1.18102i
$345$	35.7437	−	28.1458i	1.92438	−	1.51532i
$346$	−2.79201	+	12.0733i	−0.150099	+	0.649065i
$347$	2.10127	+	3.63950i	0.112802	+	0.195379i	0.916899	−	0.399119i	$-0.130684\pi$
$347$	2.10127	+	3.63950i	0.112802	+	0.195379i	−0.804097	+	0.594498i	$0.797351\pi$
$348$	6.77629	−	21.0753i	0.363247	−	1.12976i
$349$	−17.6897	+	30.6395i	−0.946908	+	1.64009i	−0.195023	+	0.980799i	$0.562478\pi$
$349$	−17.6897	+	30.6395i	−0.946908	+	1.64009i	−0.751885	+	0.659294i	$0.770855\pi$
$350$	3.57190	+	3.33331i	0.190926	+	0.178173i
$351$	1.06733	+	0.756994i	0.0569697	+	0.0404054i
$352$	7.70540	−	10.9616i	0.410699	−	0.584255i
$353$	25.9389	+	14.9758i	1.38059	+	0.797082i	0.992229	−	0.124426i	$-0.0397090\pi$
$353$	25.9389	+	14.9758i	1.38059	+	0.797082i	0.388358	+	0.921509i	$0.373042\pi$
$354$	8.33191	+	17.7086i	0.442836	+	0.941202i
$355$	3.65716	−	2.11146i	0.194102	−	0.112065i
$356$	−16.3985	−	24.3504i	−0.869121	−	1.29057i
$357$	8.15293	+	10.3538i	0.431499	+	0.547982i
$358$	−1.18818	−	3.89147i	−0.0627973	−	0.205670i
$359$	5.48093			0.289272			0.144636	−	0.989485i	$-0.453799\pi$
$359$	5.48093			0.289272			0.144636	+	0.989485i	$0.453799\pi$
$360$	14.9763	+	19.6073i	0.789320	+	1.03340i
$361$	12.1921			0.641689
$362$	−1.99468	−	6.53289i	−0.104838	−	0.343361i
$363$	9.23937	−	1.33438i	0.484941	−	0.0700369i
$364$	0.281331	+	0.417752i	0.0147458	+	0.0218961i
$365$	10.2445	−	5.91465i	0.536221	−	0.309587i
$366$	10.3342	−	14.8674i	0.540179	−	0.777130i
$367$	−14.7364	−	8.50804i	−0.769232	−	0.444116i	0.0633686	−	0.997990i	$-0.479816\pi$
$367$	−14.7364	−	8.50804i	−0.769232	−	0.444116i	−0.832601	+	0.553874i	$0.813149\pi$
$368$	35.7896	−	4.97635i	1.86566	−	0.259410i
$369$	24.3867	+	5.88352i	1.26952	+	0.306284i
$370$	−9.47789	−	8.84478i	−0.492732	−	0.459818i
$371$	1.19339	−	2.06701i	0.0619577	−	0.107314i
$372$	−0.243227	−	0.268468i	−0.0126107	−	0.0139194i
$373$	−0.570268	−	0.987733i	−0.0295274	−	0.0511429i	0.850884	−	0.525353i	$-0.176067\pi$
$373$	−0.570268	−	0.987733i	−0.0295274	−	0.0511429i	−0.880411	+	0.474211i	$0.842734\pi$
$374$	−5.74235	+	24.8313i	−0.296930	+	1.28400i
$375$	7.22705	+	2.88798i	0.373203	+	0.149134i
$376$	−1.31176	+	0.501882i	−0.0676489	+	0.0258826i
$377$			1.60933i			0.0828847i
$378$	−1.48177	−	7.19752i	−0.0762141	−	0.370201i
$379$			26.5456i			1.36356i	0.731559	+	0.681778i	$0.238793\pi$
$379$			26.5456i			1.36356i	−0.731559	+	0.681778i	$0.761207\pi$
$380$	13.6329	+	6.66162i	0.699355	+	0.341734i
$381$	−21.8476	−	8.73043i	−1.11928	−	0.447273i
$382$	28.2690	+	6.53735i	1.44637	+	0.334480i
$383$	17.3272	+	30.0116i	0.885380	+	1.53352i	0.845277	+	0.534328i	$0.179435\pi$
$383$	17.3272	+	30.0116i	0.885380	+	1.53352i	0.0401027	+	0.999196i	$0.487231\pi$
$384$	2.41220	+	19.4469i	0.123097	+	0.992395i
$385$	3.44359	−	5.96447i	0.175502	−	0.303978i
$386$	17.9446	−	19.2290i	0.913354	−	0.978732i
$387$	7.03849	+	23.8593i	0.357786	+	1.21283i
$388$	0.795344	+	11.4952i	0.0403775	+	0.583578i
$389$	10.2165	+	5.89849i	0.517996	+	0.299065i	0.736114	−	0.676857i	$-0.236659\pi$
$389$	10.2165	+	5.89849i	0.517996	+	0.299065i	−0.218118	+	0.975922i	$0.569992\pi$
$390$	−1.47275	−	1.02370i	−0.0745756	−	0.0518372i
$391$	−59.5237	+	34.3660i	−3.01024	+	1.73796i
$392$	0.445538	−	2.79312i	0.0225031	−	0.141074i
$393$	2.53885	−	0.366670i	0.128068	−	0.0184961i
$394$	23.3349	−	7.12483i	1.17559	−	0.358944i
$395$	−33.6991			−1.69558
$396$	9.05999	−	10.9493i	0.455281	−	0.550224i
$397$	−13.5577			−0.680441			−0.340221	−	0.940346i	$-0.610502\pi$
$397$	−13.5577			−0.680441			−0.340221	+	0.940346i	$0.610502\pi$
$398$	−1.58548	+	0.484094i	−0.0794729	+	0.0242654i
$399$	−2.79587	−	3.55061i	−0.139968	−	0.177753i
$400$	−8.49163	−	10.9017i	−0.424581	−	0.545086i
$401$	−5.39384	+	3.11414i	−0.269356	+	0.155513i	−0.628595	−	0.777733i	$-0.716370\pi$
$401$	−5.39384	+	3.11414i	−0.269356	+	0.155513i	0.359239	+	0.933246i	$0.383036\pi$
$402$	1.13659	−	0.534768i	0.0566881	−	0.0266718i
$403$	0.0228067	+	0.0131675i	0.00113609	+	0.000655919i
$404$	28.7913	−	1.99206i	1.43242	−	0.0991085i
$405$	14.2038	+	21.9791i	0.705791	+	1.09215i
$406$	6.16617	−	6.60754i	0.306022	−	0.327927i
$407$	−3.73364	+	6.46686i	−0.185070	+	0.320550i
$408$	−18.1591	−	32.5519i	−0.899007	−	1.61156i
$409$	−0.409311	−	0.708947i	−0.0202391	−	0.0350552i	0.855728	−	0.517425i	$-0.173109\pi$
$409$	−0.409311	−	0.708947i	−0.0202391	−	0.0350552i	−0.875968	+	0.482370i	$0.839776\pi$
$410$	−33.5018	−	7.74744i	−1.65453	−	0.382619i
$411$	24.4688	−	19.2675i	1.20696	−	0.950397i
$412$	10.5247	−	21.5387i	0.518514	−	1.06113i
$413$			7.98974i			0.393149i
$414$	38.2578	−	2.28301i	1.88027	−	0.112204i
$415$			2.55640i			0.125489i
$416$	−0.599666	−	1.29217i	−0.0294011	−	0.0633540i
$417$	−2.06205	−	14.2778i	−0.100979	−	0.699187i
$418$	1.96921	−	8.51534i	0.0963174	−	0.416499i
$419$	7.99122	+	13.8412i	0.390397	+	0.676187i	0.992502	−	0.122230i	$-0.0390045\pi$
$419$	7.99122	+	13.8412i	0.390397	+	0.676187i	−0.602105	+	0.798417i	$0.705671\pi$
$420$	2.12445	+	9.84595i	0.103663	+	0.480433i
$421$	−4.02490	+	6.97133i	−0.196161	+	0.339762i	−0.947281	−	0.320405i	$-0.896181\pi$
$421$	−4.02490	+	6.97133i	−0.196161	+	0.339762i	0.751119	+	0.660167i	$0.229514\pi$
$422$	−10.5200	−	9.81723i	−0.512103	−	0.477896i
$423$	−1.42882	+	0.421501i	−0.0694714	+	0.0204941i
$424$	−4.25421	+	5.24170i	−0.206603	+	0.254559i
$425$	22.7636	+	13.1426i	1.10420	+	0.637508i
$426$	3.54498	+	0.297866i	0.171755	+	0.0144317i
$427$	6.40151	−	3.69592i	0.309791	−	0.178858i
$428$	−10.1250	+	6.81859i	−0.489410	+	0.329589i
$429$	−0.383367	+	0.959362i	−0.0185092	+	0.0463185i
$430$	−9.95709	−	32.6110i	−0.480174	−	1.57264i
$431$	−32.4604			−1.56356			−0.781780	−	0.623554i	$-0.785688\pi$
$431$	−32.4604			−1.56356			−0.781780	+	0.623554i	$0.785688\pi$
$432$	0.931986	+	20.7637i	0.0448402	+	0.998994i
$433$	−18.4266			−0.885525			−0.442762	−	0.896639i	$-0.646001\pi$
$433$	−18.4266			−0.885525			−0.442762	+	0.896639i	$0.646001\pi$
$434$	−0.0431879	−	0.141447i	−0.00207309	−	0.00678967i
$435$	−11.9431	+	29.8872i	−0.572628	+	1.43298i
$436$	−10.3765	+	6.98799i	−0.496946	+	0.334664i
$437$	20.4123	−	11.7851i	0.976455	−	0.563756i
$438$	9.93023	+	0.834386i	0.474485	+	0.0398685i
$439$	31.5605	+	18.2214i	1.50630	+	0.869662i	0.999973	+	0.00731896i	$0.00232972\pi$
$439$	31.5605	+	18.2214i	1.50630	+	0.869662i	0.506325	+	0.862343i	$0.331004\pi$
$440$	−12.2757	+	15.1252i	−0.585223	+	0.721066i
$441$	0.703591	−	2.91633i	0.0335043	−	0.138873i
$442$	1.98106	+	1.84872i	0.0942293	+	0.0879349i
$443$	11.3610	−	19.6778i	0.539776	−	0.934919i	−0.459140	−	0.888364i	$-0.651842\pi$
$443$	11.3610	−	19.6778i	0.539776	−	0.934919i	0.998916	−	0.0465549i	$-0.0148243\pi$
$444$	−2.30339	−	10.6753i	−0.109314	−	0.506626i
$445$	21.3405	+	36.9628i	1.01164	+	1.75221i
$446$	−1.94291	+	8.40160i	−0.0919994	+	0.397827i
$447$	0.819770	+	5.67616i	0.0387738	+	0.268473i
$448$	−2.48888	+	7.60299i	−0.117589	+	0.359208i
$449$		−	9.26171i		−	0.437087i	−0.975827	−	0.218544i	$-0.929869\pi$
$449$		−	9.26171i		−	0.437087i	0.975827	−	0.218544i	$-0.0701306\pi$
$450$	−8.07156	−	12.2342i	−0.380497	−	0.576724i
$451$			19.8066i			0.932658i
$452$	−16.1110	+	32.9710i	−0.757797	+	1.55083i
$453$	8.47354	−	6.67234i	0.398122	−	0.313494i
$454$	−30.7484	−	7.11071i	−1.44309	−	0.333722i
$455$	−0.366115	−	0.634129i	−0.0171637	−	0.0297284i
$456$	6.22725	+	11.1629i	0.291618	+	0.522753i
$457$	5.90082	−	10.2205i	0.276029	−	0.478096i	−0.694365	−	0.719623i	$-0.744315\pi$
$457$	5.90082	−	10.2205i	0.276029	−	0.478096i	0.970394	+	0.241527i	$0.0776482\pi$
$458$	5.22758	−	5.60177i	0.244269	−	0.261753i
$459$	−16.4918	−	35.9314i	−0.769769	−	1.67714i
$460$	−52.4079	+	3.62607i	−2.44353	+	0.169066i
$461$	2.21744	+	1.28024i	0.103276	+	0.0596266i	0.550749	−	0.834671i	$-0.314342\pi$
$461$	2.21744	+	1.28024i	0.103276	+	0.0596266i	−0.447472	+	0.894298i	$0.647676\pi$
$462$	5.24983	−	2.47005i	0.244244	−	0.114917i
$463$	10.0234	−	5.78704i	0.465829	−	0.268947i	−0.248663	−	0.968590i	$-0.579991\pi$
$463$	10.0234	−	5.78704i	0.465829	−	0.268947i	0.714492	+	0.699643i	$0.246658\pi$
$464$	−20.1667	+	15.7084i	−0.936217	+	0.729243i
$465$	0.325830	+	0.413788i	0.0151100	+	0.0191890i
$466$	8.22620	−	2.51170i	0.381071	−	0.116352i
$467$	0.571766			0.0264582			0.0132291	−	0.999912i	$-0.495789\pi$
$467$	0.571766			0.0264582			0.0132291	+	0.999912i	$0.495789\pi$
$468$	−0.526527	−	1.41624i	−0.0243387	−	0.0654658i
$469$	0.512806			0.0236792
$470$	1.95291	−	0.596282i	0.0900811	−	0.0275044i
$471$	5.10548	−	0.737351i	0.235248	−	0.0339753i
$472$	3.55973	−	22.3163i	0.163850	−	1.02719i
$473$	−17.0090	+	9.82016i	−0.782076	+	0.451532i
$474$	−23.3105	−	16.2030i	−1.07069	−	0.744230i
$475$	−7.80627	−	4.50695i	−0.358176	−	0.206793i
$476$	−1.05036	−	15.1809i	−0.0481430	−	0.695815i
$477$	−4.93464	+	5.18842i	−0.225942	+	0.237562i
$478$	8.85578	−	9.48967i	0.405054	−	0.434048i
$479$	13.9036	−	24.0818i	0.635273	−	1.10033i	−0.351184	−	0.936306i	$-0.614221\pi$
$479$	13.9036	−	24.0818i	0.635273	−	1.10033i	0.986457	−	0.164019i	$-0.0524457\pi$
$480$	−1.54709	−	28.4474i	−0.0706147	−	1.29844i
$481$	0.396953	+	0.687542i	0.0180995	+	0.0313492i
$482$	−12.6771	−	2.93165i	−0.577428	−	0.133533i
$483$	14.5293	+	5.80602i	0.661108	+	0.264183i
$484$	−9.68499	−	4.73248i	−0.440227	−	0.215113i
$485$		−	16.7521i		−	0.760676i
$486$	−0.742783	+	22.0329i	−0.0336933	+	0.999432i
$487$		−	10.3286i		−	0.468031i	−0.972233	−	0.234016i	$-0.924813\pi$
$487$		−	10.3286i		−	0.468031i	0.972233	−	0.234016i	$-0.0751867\pi$
$488$	−19.5268	+	7.47100i	−0.883939	+	0.338196i
$489$	13.3389	+	5.33031i	0.603206	+	0.241045i
$490$	−0.926490	+	4.00636i	−0.0418546	+	0.180989i
$491$	−16.9157	−	29.2988i	−0.763394	−	1.32224i	−0.941091	−	0.338153i	$-0.890198\pi$
$491$	−16.9157	−	29.2988i	−0.763394	−	1.32224i	0.177697	−	0.984085i	$-0.443135\pi$
$492$	−19.4489	−	21.4673i	−0.876826	−	0.967819i
$493$	24.3120	−	42.1096i	1.09496	−	1.89652i
$494$	−0.679360	−	0.633979i	−0.0305658	−	0.0285241i
$495$	−14.2392	+	14.9715i	−0.640003	+	0.672918i
$496$	0.0576089	+	0.414320i	0.00258672	+	0.0186035i
$497$	1.25776	+	0.726166i	0.0564181	+	0.0325730i
$498$	−1.22916	+	1.76833i	−0.0550799	+	0.0792407i
$499$	−5.27446	+	3.04521i	−0.236117	+	0.136322i	−0.613391	−	0.789779i	$-0.710195\pi$
$499$	−5.27446	+	3.04521i	−0.236117	+	0.136322i	0.377274	+	0.926102i	$0.376862\pi$
$500$	−5.01984	−	7.45400i	−0.224494	−	0.333353i
$501$	−32.0558	+	4.62961i	−1.43215	+	0.206836i
$502$	7.25900	+	23.7743i	0.323985	+	1.06110i
$503$	21.4710			0.957345			0.478673	−	0.877993i	$-0.341118\pi$
$503$	21.4710			0.957345			0.478673	+	0.877993i	$0.341118\pi$
$504$	−3.26454	+	7.83216i	−0.145414	+	0.348872i
$505$	−41.9582			−1.86712
$506$	8.83644	+	28.9407i	0.392828	+	1.28657i
$507$	−13.8621	−	17.6042i	−0.615638	−	0.781830i
$508$	15.1751	+	22.5337i	0.673286	+	0.999769i
$509$	−18.4897	+	10.6750i	−0.819540	+	0.473161i	−0.850258	−	0.526367i	$-0.823554\pi$
$509$	−18.4897	+	10.6750i	−0.819540	+	0.473161i	0.0307180	+	0.999528i	$0.490221\pi$
$510$	23.0709	+	49.0348i	1.02160	+	2.17130i
$511$	3.52324	+	2.03414i	0.155859	+	0.0899851i
$512$	10.3392	−	20.1271i	0.456930	−	0.889503i
$513$	5.65548	+	12.3219i	0.249696	+	0.544025i
$514$	−11.1798	−	10.4330i	−0.493119	−	0.460179i
$515$	−17.4262	+	30.1830i	−0.767890	+	1.33002i
$516$	8.79228	−	27.3454i	0.387058	−	1.20381i
$517$	−0.588082	−	1.01859i	−0.0258638	−	0.0447974i
$518$	1.00453	−	4.34382i	0.0441365	−	0.190856i
$519$	11.9240	−	9.38932i	0.523404	−	0.412145i
$520$	0.740072	+	1.93431i	0.0324543	+	0.0848253i
$521$			30.4799i			1.33535i	0.744453	+	0.667675i	$0.232710\pi$
$521$			30.4799i			1.33535i	−0.744453	+	0.667675i	$0.767290\pi$
$522$	−22.6316	+	14.9313i	−0.990557	+	0.653525i
$523$			28.4494i			1.24401i	0.783014	+	0.622004i	$0.213681\pi$
$523$			28.4494i			1.24401i	−0.783014	+	0.622004i	$0.786319\pi$
$524$	−2.66130	−	1.30042i	−0.116260	−	0.0568092i
$525$	−0.855307	−	5.92221i	−0.0373286	−	0.258467i
$526$	3.39905	+	0.786046i	0.148206	+	0.0342733i
$527$	−0.397839	−	0.689078i	−0.0173302	−	0.0300167i
$528$	−15.7639	+	4.56013i	−0.686035	+	0.198454i
$529$	−29.3019	+	50.7524i	−1.27400	+	2.20663i
$530$	6.69622	−	7.17553i	0.290865	−	0.311685i
$531$	5.62150	−	23.3007i	0.243952	−	1.01116i
$532$	0.360197	+	5.20595i	0.0156165	+	0.225706i
$533$	1.82367	+	1.05290i	0.0789921	+	0.0456061i
$534$	−3.01052	+	35.8290i	−0.130278	+	1.55047i
$535$	15.3693	−	8.87348i	0.664474	−	0.383634i
$536$	−1.43233	−	0.228475i	−0.0618671	−	0.00986861i
$537$	−1.84917	+	4.62747i	−0.0797975	+	0.199690i
$538$	25.2142	−	7.69865i	1.08706	−	0.331912i
$539$	2.36861			0.102023
$540$	0.731924	−	30.2087i	0.0314970	−	1.29998i
$541$	28.9747			1.24572			0.622861	−	0.782333i	$-0.285970\pi$
$541$	28.9747			1.24572			0.622861	+	0.782333i	$0.285970\pi$
$542$	16.1122	−	4.91954i	0.692080	−	0.211312i
$543$	−3.10433	+	7.76848i	−0.133220	+	0.333377i
$544$	−3.82989	+	42.8699i	−0.164205	+	1.83803i
$545$	15.7512	−	9.09393i	0.674705	−	0.389541i
$546$	0.0516481	−	0.614677i	0.00221034	−	0.0263057i
$547$	−32.0274	−	18.4910i	−1.36939	−	0.790619i	−0.378541	−	0.925584i	$-0.623574\pi$
$547$	−32.0274	−	18.4910i	−1.36939	−	0.790619i	−0.990850	+	0.134966i	$0.956908\pi$
$548$	−35.8764	+	2.48227i	−1.53257	+	0.106037i
$549$	−21.2693	+	6.27445i	−0.907752	+	0.267787i
$550$	7.89529	−	8.46044i	0.336656	−	0.360754i
$551$	−8.33725	+	14.4405i	−0.355179	+	0.615188i
$552$	−37.9953	−	22.6903i	−1.61719	−	0.965761i
$553$	−5.79482	−	10.0369i	−0.246421	−	0.426813i
$554$	24.3335	+	5.62724i	1.03383	+	0.239078i
$555$	2.26952	+	15.7143i	0.0963357	+	0.667036i
$556$	−7.31321	+	14.9664i	−0.310149	+	0.634718i
$557$			4.29428i			0.181955i	0.995853	+	0.0909773i	$0.0289991\pi$
$557$			4.29428i			0.181955i	−0.995853	+	0.0909773i	$0.971001\pi$
$558$	0.0264294	+	0.442892i	0.00111884	+	0.0187491i
$559$			2.08812i			0.0883179i
$560$	4.37278	−	10.7774i	0.184784	−	0.455430i
$561$	24.5241	−	19.3111i	1.03541	−	0.815315i
$562$	6.09477	−	26.3552i	0.257092	−	1.11173i
$563$	2.78657	+	4.82649i	0.117440	+	0.203412i	0.918753	−	0.394834i	$-0.129198\pi$
$563$	2.78657	+	4.82649i	0.117440	+	0.203412i	−0.801312	+	0.598246i	$0.795865\pi$
$564$	1.63758	+	0.526527i	0.0689546	+	0.0221708i
$565$	26.6757	−	46.2037i	1.12225	−	1.94380i
$566$	−3.35535	−	3.13122i	−0.141036	−	0.131615i
$567$	−4.10380	+	8.00992i	−0.172343	+	0.336385i
$568$	−3.18952	−	2.58864i	−0.133829	−	0.108617i
$569$	−5.72734	−	3.30668i	−0.240103	−	0.138623i	0.375121	−	0.926976i	$-0.377601\pi$
$569$	−5.72734	−	3.30668i	−0.240103	−	0.138623i	−0.615224	+	0.788352i	$0.710934\pi$
$570$	−7.91165	−	16.8154i	−0.331383	−	0.704319i
$571$	28.7640	−	16.6069i	1.20374	−	0.694978i	0.242353	−	0.970188i	$-0.422081\pi$
$571$	28.7640	−	16.6069i	1.20374	−	0.694978i	0.961384	+	0.275211i	$0.0887476\pi$
$572$	0.989489	−	0.666363i	0.0413726	−	0.0278620i
$573$	−21.9846	−	27.9193i	−0.918420	−	1.16635i
$574$	−3.45340	−	11.3104i	−0.144142	−	0.472087i
$575$	31.2077			1.30145
$576$	12.6078	−	20.4217i	0.525324	−	0.850902i
$577$	27.6524			1.15119			0.575593	−	0.817736i	$-0.304771\pi$
$577$	27.6524			1.15119			0.575593	+	0.817736i	$0.304771\pi$
$578$	−16.8870	−	55.3074i	−0.702406	−	2.30049i
$579$	−31.8817	+	4.60447i	−1.32496	+	0.191355i
$580$	30.8257	−	20.7593i	1.27997	−	0.861984i
$581$	−0.761398	+	0.439593i	−0.0315881	+	0.0182374i
$582$	8.05468	−	11.5879i	0.333877	−	0.480333i
$583$	−4.89594	−	2.82667i	−0.202769	−	0.117069i
$584$	−8.93452	−	7.25133i	−0.369713	−	0.300062i
$585$	0.621543	+	2.10692i	0.0256976	+	0.0871106i
$586$	13.2872	+	12.3996i	0.548890	+	0.512225i
$587$	−12.0238	+	20.8258i	−0.496274	+	0.859571i	−0.999991	−	0.00429733i	$-0.998632\pi$
$587$	−12.0238	+	20.8258i	−0.496274	+	0.859571i	0.503717	+	0.863869i	$0.331965\pi$
$588$	−2.56720	+	2.32583i	−0.105869	+	0.0959157i
$589$	0.136430	+	0.236304i	0.00562151	+	0.00973674i
$590$	−7.40241	+	32.0098i	−0.304753	+	1.31782i
$591$	−27.7483	−	11.0884i	−1.14141	−	0.456116i
$592$	−4.74110	+	11.6852i	−0.194858	+	0.480260i
$593$			7.02971i			0.288675i	0.989528	+	0.144338i	$0.0461052\pi$
$593$			7.02971i			0.288675i	−0.989528	+	0.144338i	$0.953895\pi$
$594$	−17.0481	+	3.50973i	−0.699492	+	0.144006i
$595$			22.1234i			0.906972i
$596$	2.90738	−	5.94992i	0.119091	−	0.243718i
$597$	1.88535	+	0.753396i	0.0771621	+	0.0308345i
$598$	3.13441	+	0.724848i	0.128176	+	0.0296412i
$599$	14.7689	+	25.5804i	0.603439	+	1.04519i	0.992296	+	0.123889i	$0.0395366\pi$
$599$	14.7689	+	25.5804i	0.603439	+	1.04519i	−0.388857	+	0.921298i	$0.627130\pi$
$600$	−0.249601	+	16.9225i	−0.0101899	+	0.690858i
$601$	−11.2326	+	19.4555i	−0.458188	+	0.793605i	−0.998865	−	0.0476250i	$-0.984835\pi$
$601$	−11.2326	+	19.4555i	−0.458188	+	0.793605i	0.540677	+	0.841230i	$0.318168\pi$
$602$	8.00064	−	8.57333i	0.326082	−	0.349423i
$603$	−1.49551	−	0.360806i	−0.0609019	−	0.0146931i
$604$	−12.4240	+	0.859610i	−0.505526	+	0.0349770i
$605$	13.5720	+	7.83579i	0.551780	+	0.318570i
$606$	−29.0236	−	20.1741i	−1.17900	−	0.819518i
$607$	31.5236	−	18.2002i	1.27950	−	0.738722i	0.302748	−	0.953071i	$-0.402096\pi$
$607$	31.5236	−	18.2002i	1.27950	−	0.738722i	0.976757	+	0.214348i	$0.0687628\pi$
$608$	1.31338	−	14.7013i	0.0532645	−	0.596216i
$609$	−10.9553	+	1.58220i	−0.443931	+	0.0641141i
$610$	29.0710	−	8.87624i	1.17705	−	0.359388i
$611$	−0.125047			−0.00505886
$612$	−7.61794	+	45.0114i	−0.307937	+	1.81948i
$613$	12.8571			0.519293			0.259646	−	0.965704i	$-0.416394\pi$
$613$	12.8571			0.519293			0.259646	+	0.965704i	$0.416394\pi$
$614$	23.9428	−	7.31043i	0.966251	−	0.295025i
$615$	26.0541	+	33.0874i	1.05060	+	1.33421i
$616$	−6.61580	−	1.05531i	−0.266558	−	0.0425195i
$617$	−37.5894	+	21.7022i	−1.51329	+	0.873699i	−0.513412	+	0.858142i	$0.671619\pi$
$617$	−37.5894	+	21.7022i	−1.51329	+	0.873699i	−0.999879	+	0.0155564i	$0.995048\pi$
$618$	−26.5666	+	12.4996i	−1.06867	+	0.502808i
$619$	−0.893596	−	0.515918i	−0.0359167	−	0.0207365i	0.481934	−	0.876207i	$-0.339934\pi$
$619$	−0.893596	−	0.515918i	−0.0359167	−	0.0207365i	−0.517851	+	0.855471i	$0.673268\pi$
$620$	−0.0419773	−	0.606701i	−0.00168585	−	0.0243657i
$621$	−38.2872	−	27.1549i	−1.53641	−	1.08969i
$622$	−6.37480	+	6.83111i	−0.255606	+	0.273903i
$623$	−7.33933	+	12.7121i	−0.294044	+	0.509299i
$624$	−0.418121	+	1.69385i	−0.0167382	+	0.0678084i
$625$	15.1693	+	26.2740i	0.606772	+	1.05096i
$626$	14.7186	+	3.40374i	0.588274	+	0.136041i
$627$	−8.41001	+	6.62231i	−0.335863	+	0.264470i
$628$	−5.35172	−	2.61507i	−0.213557	−	0.104353i
$629$		−	23.9869i		−	0.956420i
$630$	5.52079	−	11.0320i	0.219953	−	0.439525i
$631$		−	25.4447i		−	1.01294i	−0.862258	−	0.506469i	$-0.830951\pi$
$631$		−	25.4447i		−	1.01294i	0.862258	−	0.506469i	$-0.169049\pi$
$632$	11.7138	+	30.6161i	0.465949	+	1.21784i
$633$	2.51904	+	17.4421i	0.100123	+	0.693260i
$634$	8.13387	−	35.1728i	0.323037	−	1.39689i
$635$	−19.7483	−	34.2051i	−0.783689	−	1.35739i
$636$	8.08205	−	1.74386i	0.320474	−	0.0691484i
$637$	0.125913	−	0.218087i	0.00498884	−	0.00864092i
$638$	−15.6507	−	14.6052i	−0.619616	−	0.578227i
$639$	−3.15710	−	3.00268i	−0.124893	−	0.118784i
$640$	−17.0155	+	28.1544i	−0.672595	+	1.11290i
$641$	−24.3065	−	14.0334i	−0.960049	−	0.554284i	−0.0638607	−	0.997959i	$-0.520341\pi$
$641$	−24.3065	−	14.0334i	−0.960049	−	0.554284i	−0.896188	+	0.443674i	$0.853675\pi$
$642$	14.8979	+	1.25179i	0.587972	+	0.0494042i
$643$	11.1062	−	6.41216i	0.437985	−	0.252871i	−0.264757	−	0.964315i	$-0.585292\pi$
$643$	11.1062	−	6.41216i	0.437985	−	0.252871i	0.702743	+	0.711444i	$0.251959\pi$
$644$	−10.0919	−	14.9856i	−0.397678	−	0.590516i
$645$	−15.4963	+	38.7788i	−0.610164	+	1.52691i
$646$	8.19860	+	26.8516i	0.322570	+	1.05646i
$647$	−39.1711			−1.53998			−0.769988	−	0.638058i	$-0.779738\pi$
$647$	−39.1711			−1.53998			−0.769988	+	0.638058i	$0.779738\pi$
$648$	15.0311	−	20.5442i	0.590478	−	0.807054i
$649$	18.9246			0.742854
$650$	−0.359281	−	1.17670i	−0.0140921	−	0.0461539i
$651$	−0.0672135	+	0.168199i	−0.00263431	+	0.00659225i
$652$	−9.26507	−	13.7578i	−0.362848	−	0.538797i
$653$	5.09574	−	2.94203i	0.199412	−	0.115130i	−0.396969	−	0.917832i	$-0.629938\pi$
$653$	5.09574	−	2.94203i	0.199412	−	0.115130i	0.596381	+	0.802701i	$0.296605\pi$
$654$	15.2680	+	1.28289i	0.597025	+	0.0501649i
$655$	3.72940	+	2.15317i	0.145720	+	0.0841313i
$656$	4.60652	+	33.1298i	0.179855	+	1.29350i
$657$	−8.84371	−	8.41114i	−0.345026	−	0.328150i
$658$	0.513415	+	0.479119i	0.0200150	+	0.0186780i
$659$	−12.9730	+	22.4699i	−0.505357	+	0.875304i	0.494624	+	0.869107i	$0.335306\pi$
$659$	−12.9730	+	22.4699i	−0.505357	+	0.875304i	−0.999981	+	0.00619658i	$0.998028\pi$
$660$	23.3212	−	5.03199i	0.907776	−	0.195870i
$661$	−19.8403	−	34.3644i	−0.771699	−	1.33662i	−0.936631	−	0.350316i	$-0.886074\pi$
$661$	−19.8403	−	34.3644i	−0.771699	−	1.33662i	0.164933	−	0.986305i	$-0.447259\pi$
$662$	8.49620	−	36.7396i	0.330214	−	1.42792i
$663$	−0.474372	−	3.28459i	−0.0184231	−	0.127563i
$664$	2.32253	−	0.888603i	0.0901316	−	0.0344845i
$665$		−	7.58674i		−	0.294201i
$666$	−5.98580	+	11.9612i	−0.231945	+	0.463488i
$667$		−	57.7300i		−	2.23531i
$668$	33.6018	+	16.4192i	1.30009	+	0.635279i
$669$	8.29767	−	6.53386i	0.320807	−	0.252613i
$670$	2.05449	+	0.475110i	0.0793718	+	0.0183551i
$671$	−8.75417	−	15.1627i	−0.337951	−	0.585349i
$672$	8.20673	−	5.35254i	0.316581	−	0.206479i
$673$	5.16943	−	8.95371i	0.199267	−	0.345140i	−0.749024	−	0.662543i	$-0.769477\pi$
$673$	5.16943	−	8.95371i	0.199267	−	0.345140i	0.948291	+	0.317403i	$0.102811\pi$
$674$	−6.12032	+	6.55842i	−0.235746	+	0.252621i
$675$	−1.67246	+	17.8729i	−0.0643730	+	0.687928i
$676$	1.78588	+	25.8115i	0.0686877	+	0.992748i
$677$	−4.67459	−	2.69887i	−0.179659	−	0.103726i	0.407473	−	0.913217i	$-0.366410\pi$
$677$	−4.67459	−	2.69887i	−0.179659	−	0.103726i	−0.587132	+	0.809491i	$0.699743\pi$
$678$	40.6677	−	19.1342i	1.56183	−	0.734843i
$679$	4.98945	−	2.88066i	0.191478	−	0.110550i
$680$	9.85683	−	61.7933i	0.377992	−	2.36966i
$681$	23.9128	+	30.3680i	0.916339	+	1.16371i
$682$	−0.335032	+	0.102295i	−0.0128291	+	0.00391709i
$683$	39.2840			1.50316			0.751581	−	0.659641i	$-0.229292\pi$
$683$	39.2840			1.50316			0.751581	+	0.659641i	$0.229292\pi$
$684$	2.61241	−	15.4357i	0.0998878	−	0.590198i
$685$	52.2835			1.99765
$686$	−1.35257	+	0.412980i	−0.0516414	+	0.0157676i
$687$	−9.28772	+	1.34137i	−0.354349	+	0.0511763i
$688$	−26.1665	+	20.3817i	−0.997587	+	0.777045i
$689$	−0.520525	+	0.300525i	−0.0198304	+	0.0114491i
$690$	52.8306	+	36.7223i	2.01123	+	1.39799i
$691$	−15.8640	−	9.15909i	−0.603495	−	0.348428i	0.166920	−	0.985970i	$-0.446618\pi$
$691$	−15.8640	−	9.15909i	−0.603495	−	0.348428i	−0.770415	+	0.637542i	$0.779951\pi$
$692$	−17.4831	+	1.20964i	−0.664606	+	0.0459837i
$693$	−6.90763	−	1.66653i	−0.262399	−	0.0633062i
$694$	−4.05490	+	4.34515i	−0.153922	+	0.164940i
$695$	12.1088	−	20.9731i	0.459314	−	0.795555i
$696$	31.3043	+	0.461728i	1.18659	+	0.0175018i
$697$	−31.8120	−	55.1001i	−1.20497	−	2.08706i
$698$	−48.7475	−	11.2731i	−1.84512	−	0.426693i
$699$	−9.78205	−	3.90897i	−0.369991	−	0.147851i
$700$	−3.03341	+	6.20784i	−0.114652	+	0.234634i
$701$			14.7290i			0.556306i	0.960537	+	0.278153i	$0.0897222\pi$
$701$			14.7290i			0.556306i	−0.960537	+	0.278153i	$0.910278\pi$
$702$	−0.583104	+	1.75626i	−0.0220078	+	0.0662857i
$703$			8.22577i			0.310241i
$704$	18.0085	+	5.89518i	0.678721	+	0.222183i
$705$	−2.32227	−	0.927995i	−0.0874619	−	0.0349503i
$706$	−9.54362	+	41.2689i	−0.359179	+	1.55317i
$707$	−7.21504	−	12.4968i	−0.271349	−	0.469991i
$708$	−20.5112	+	18.5828i	−0.770859	+	0.698384i
$709$	−0.246081	+	0.426224i	−0.00924175	+	0.0160072i	−0.870609	−	0.491975i	$-0.836275\pi$
$709$	−0.246081	+	0.426224i	−0.00924175	+	0.0160072i	0.861368	+	0.507982i	$0.169608\pi$
$710$	4.36624	+	4.07458i	0.163862	+	0.152916i
$711$	9.83770	+	33.3481i	0.368943	+	1.25065i
$712$	26.1633	−	32.2364i	0.980512	−	1.20811i
$713$	−0.818125	−	0.472345i	−0.0306390	−	0.0176894i
$714$	−10.6373	+	15.3033i	−0.398090	+	0.572713i
$715$	−1.50200	+	0.867182i	−0.0561718	+	0.0324308i
$716$	4.77279	−	3.21419i	0.178368	−	0.120120i
$717$	−15.7339	+	2.27234i	−0.587592	+	0.0848621i
$718$	2.26351	+	7.41334i	0.0844736	+	0.276664i
$719$	−7.89549			−0.294452			−0.147226	−	0.989103i	$-0.547034\pi$
$719$	−7.89549			−0.294452			−0.147226	+	0.989103i	$0.547034\pi$
$720$	−20.3354	+	28.3539i	−0.757855	+	1.05669i
$721$	−11.9863			−0.446392
$722$	5.03509	+	16.4907i	0.187387	+	0.613719i
$723$	9.85892	+	12.5203i	0.366657	+	0.465636i
$724$	8.01243	−	5.39590i	0.297780	−	0.200537i
$725$	−19.1198	+	11.0388i	−0.710091	+	0.409971i
$726$	5.62052	+	11.9458i	0.208597	+	0.443351i
$727$	9.22490	+	5.32600i	0.342133	+	0.197530i	0.661215	−	0.750197i	$-0.270041\pi$
$727$	9.22490	+	5.32600i	0.342133	+	0.197530i	−0.319082	+	0.947727i	$0.603375\pi$
$728$	−0.448854	+	0.553043i	−0.0166357	+	0.0204971i
$729$	17.6037	−	20.4721i	0.651990	−	0.758228i
$730$	12.2308	+	11.4138i	0.452681	+	0.422442i
$731$	31.5449	−	54.6374i	1.16673	−	2.02084i
$732$	24.3770	+	7.83787i	0.901000	+	0.289696i
$733$	26.0962	+	45.1999i	0.963885	+	1.66950i	0.712581	+	0.701590i	$0.247526\pi$
$733$	26.0962	+	45.1999i	0.963885	+	1.66950i	0.251304	+	0.967908i	$0.419141\pi$
$734$	5.42191	−	23.4456i	0.200126	−	0.865394i
$735$	3.95681	−	3.11572i	0.145949	−	0.114925i
$736$	21.5113	+	46.3529i	0.792916	+	1.70859i
$737$		−	1.21464i		−	0.0447417i
$738$	2.11335	+	35.4146i	0.0777934	+	1.30363i
$739$			34.1328i			1.25560i	0.778376	+	0.627798i	$0.216044\pi$
$739$			34.1328i			1.25560i	−0.778376	+	0.627798i	$0.783956\pi$
$740$	8.04901	−	16.4722i	0.295888	−	0.605531i
$741$	0.162675	+	1.12638i	0.00597603	+	0.0413785i
$742$	3.28862	+	0.760510i	0.120729	+	0.0279192i
$743$	7.11347	+	12.3209i	0.260968	+	0.452009i	0.966499	−	0.256669i	$-0.0826250\pi$
$743$	7.11347	+	12.3209i	0.260968	+	0.452009i	−0.705532	+	0.708678i	$0.749292\pi$
$744$	0.262674	−	0.439854i	0.00963011	−	0.0161258i
$745$	−4.81387	+	8.33787i	−0.176367	+	0.305476i
$746$	1.10047	−	1.17924i	0.0402911	−	0.0431751i
$747$	2.52978	−	0.746285i	0.0925598	−	0.0273052i
$748$	−35.9576	+	2.48788i	−1.31474	+	0.0909660i
$749$	5.28575	+	3.05173i	0.193137	+	0.111508i
$750$	−0.921566	+	10.9678i	−0.0336508	+	0.400487i
$751$	27.8733	−	16.0926i	1.01711	−	0.587228i	0.103844	−	0.994594i	$-0.466886\pi$
$751$	27.8733	−	16.0926i	1.01711	−	0.587228i	0.913265	+	0.407365i	$0.133552\pi$
$752$	−1.22056	−	1.56698i	−0.0445093	−	0.0571419i
$753$	11.2972	−	28.2708i	0.411693	−	1.03025i
$754$	−2.17673	+	0.664621i	−0.0792719	+	0.0242041i
$755$	18.1058			0.658936
$756$	9.12322	−	4.97663i	0.331808	−	0.180998i
$757$	−33.8024			−1.22857			−0.614284	−	0.789085i	$-0.710555\pi$
$757$	−33.8024			−1.22857			−0.614284	+	0.789085i	$0.710555\pi$
$758$	−35.9048	+	10.9628i	−1.30412	+	0.398187i
$759$	13.7522	−	34.4143i	0.499172	−	1.24916i
$760$	−3.38018	+	21.1906i	−0.122612	+	0.768665i
$761$	7.39633	−	4.27027i	0.268117	−	0.154797i	−0.359915	−	0.932985i	$-0.617194\pi$
$761$	7.39633	−	4.27027i	0.268117	−	0.154797i	0.628031	+	0.778188i	$0.283861\pi$
$762$	2.78592	−	33.1559i	0.100923	−	1.20111i
$763$	5.41707	+	3.12754i	0.196111	+	0.113225i
$764$	2.83232	+	40.9357i	0.102470	+	1.48100i
$765$	15.5658	−	64.5191i	0.562784	−	2.33269i
$766$	−33.4371	+	35.8305i	−1.20813	+	1.29461i
$767$	1.00601	−	1.74246i	0.0363249	−	0.0629165i
$768$	−25.3071	+	11.2938i	−0.913191	+	0.407531i
$769$	−13.0938	−	22.6792i	−0.472176	−	0.817833i	0.527317	−	0.849669i	$-0.323198\pi$
$769$	−13.0938	−	22.6792i	−0.472176	−	0.817833i	−0.999493	+	0.0318354i	$0.989865\pi$
$770$	9.48950	+	2.19449i	0.341978	+	0.0790840i
$771$	2.67704	+	18.5360i	0.0964113	+	0.667559i
$772$	33.4194	+	16.3301i	1.20279	+	0.587732i
$773$			3.16655i			0.113893i	0.998377	+	0.0569464i	$0.0181364\pi$
$773$			3.16655i			0.113893i	−0.998377	+	0.0569464i	$0.981864\pi$
$774$	−29.3646	+	19.3734i	−1.05549	+	0.696364i
$775$			0.361277i			0.0129774i
$776$	−15.2196	+	5.82303i	−0.546350	+	0.209035i
$777$	−4.29009	+	3.37815i	−0.153906	+	0.121191i
$778$	−3.75892	+	16.2545i	−0.134764	+	0.582751i
$779$	10.9092	+	18.8954i	0.390864	+	0.676996i
$780$	0.776413	−	2.41477i	0.0278001	−	0.0864626i
$781$	1.72000	−	2.97913i	0.0615465	−	0.106602i
$782$	−71.0646	−	66.3176i	−2.54126	−	2.37151i
$783$	33.0624	+	3.09382i	1.18156	+	0.110564i
$784$	3.96189	−	0.550878i	0.141496	−	0.0196742i
$785$	7.49959	+	4.32989i	0.267672	+	0.154540i
$786$	1.54444	+	3.28255i	0.0550885	+	0.117085i
$787$	6.34026	−	3.66055i	0.226006	−	0.130485i	−0.382722	−	0.923863i	$-0.625013\pi$
$787$	6.34026	−	3.66055i	0.226006	−	0.130485i	0.608728	+	0.793379i	$0.291680\pi$
$788$	19.2737	+	28.6197i	0.686596	+	1.01953i
$789$	−2.64341	−	3.35701i	−0.0941080	−	0.119513i
$790$	−13.9170	−	45.5804i	−0.495146	−	1.62168i
$791$	18.3484			0.652393
$792$	18.5513	+	7.73243i	0.659192	+	0.274760i
$793$	−1.86145			−0.0661020
$794$	−5.59905	−	18.3377i	−0.198703	−	0.650782i
$795$	−11.8970	+	1.71821i	−0.421944	+	0.0609386i
$796$	−1.30954	−	1.94455i	−0.0464155	−	0.0689228i
$797$	−10.8713	+	6.27653i	−0.385080	+	0.222326i	−0.680026	−	0.733188i	$-0.738032\pi$
$797$	−10.8713	+	6.27653i	−0.385080	+	0.222326i	0.294946	+	0.955514i	$0.404698\pi$
$798$	3.64782	−	5.24794i	0.129131	−	0.185775i
$799$	3.27197	+	1.88907i	0.115754	+	0.0668306i
$800$	11.2385	−	15.9877i	0.397341	−	0.565251i
$801$	30.3480	−	31.9087i	1.07229	−	1.12744i
$802$	−6.43964	−	6.00948i	−0.227392	−	0.212202i
$803$	4.81808	−	8.34517i	0.170026	−	0.294494i
$804$	1.19270	+	1.31647i	0.0420633	+	0.0464285i
$805$	13.1333	+	22.7475i	0.462888	+	0.801745i
$806$	−0.00839123	+	0.0362856i	−0.000295568	+	0.00127811i
$807$	−29.9831	−	11.9814i	−1.05545	−	0.421766i
$808$	14.5846	+	38.1196i	0.513085	+	1.34104i
$809$			42.4323i			1.49184i	0.666036	+	0.745920i	$0.267990\pi$
$809$			42.4323i			1.49184i	−0.666036	+	0.745920i	$0.732010\pi$
$810$	−23.8624	+	28.2885i	−0.838440	+	0.993957i
$811$		−	52.0205i		−	1.82669i	−0.407192	−	0.913343i	$-0.633492\pi$
$811$		−	52.0205i		−	1.82669i	0.407192	−	0.913343i	$-0.366508\pi$
$812$	11.4837	+	5.61140i	0.402998	+	0.196921i
$813$	−19.1596	−	7.65630i	−0.671956	−	0.268518i
$814$	−10.2888	−	2.37933i	−0.360622	−	0.0833956i
$815$	12.0572	+	20.8838i	0.422347	+	0.731526i
$816$	36.5294	−	38.0047i	1.27878	−	1.33043i
$817$	−10.8176	+	18.7367i	−0.378461	+	0.655514i
$818$	0.789864	−	0.846402i	0.0276169	−	0.0295938i
$819$	−0.520646	+	0.547422i	−0.0181928	+	0.0191285i
$820$	−3.35659	−	48.5131i	−0.117217	−	1.69415i
$821$	2.93634	+	1.69530i	0.102479	+	0.0591663i	0.550364	−	0.834925i	$-0.314489\pi$
$821$	2.93634	+	1.69530i	0.102479	+	0.0591663i	−0.447885	+	0.894091i	$0.647822\pi$
$822$	36.1658	+	25.1387i	1.26143	+	0.876813i
$823$	16.1029	−	9.29699i	0.561311	−	0.324073i	−0.192361	−	0.981324i	$-0.561614\pi$
$823$	16.1029	−	9.29699i	0.561311	−	0.324073i	0.753671	+	0.657251i	$0.228281\pi$
$824$	33.4791	+	5.34034i	1.16630	+	0.186040i
$825$	−14.0274	+	2.02589i	−0.488371	+	0.0705323i
$826$	−10.8067	+	3.29960i	−0.376013	+	0.114808i
$827$	−22.2626			−0.774145			−0.387072	−	0.922049i	$-0.626514\pi$
$827$	−22.2626			−0.774145			−0.387072	+	0.922049i	$0.626514\pi$
$828$	18.8876	+	50.8035i	0.656390	+	1.76554i
$829$	17.1771			0.596586			0.298293	−	0.954474i	$-0.403583\pi$
$829$	17.1771			0.596586			0.298293	+	0.954474i	$0.403583\pi$
$830$	−3.45772	+	1.05574i	−0.120019	+	0.0366454i
$831$	−18.9240	−	24.0325i	−0.656465	−	0.833678i
$832$	1.50010	−	1.34473i	0.0520068	−	0.0466202i
$833$	−6.58923	+	3.80429i	−0.228303	+	0.131811i
$834$	18.4602	−	8.68551i	0.639223	−	0.300755i
$835$	−47.0877	−	27.1861i	−1.62954	−	0.940813i
$836$	12.3308	−	0.853165i	0.426471	−	0.0295073i
$837$	0.314360	−	0.443233i	0.0108659	−	0.0153204i
$838$	−15.4210	+	16.5248i	−0.532709	+	0.570841i
$839$	21.6662	−	37.5270i	0.748000	−	1.29557i	−0.200780	−	0.979636i	$-0.564348\pi$
$839$	21.6662	−	37.5270i	0.748000	−	1.29557i	0.948780	−	0.315938i	$-0.102319\pi$
$840$	−12.4400	+	6.93965i	−0.429220	+	0.239441i
$841$	5.92031	+	10.2543i	0.204149	+	0.353596i
$842$	−11.0914	−	2.56494i	−0.382235	−	0.0883937i
$843$	−26.0292	+	20.4962i	−0.896494	+	0.705928i
$844$	8.93398	−	18.2833i	0.307520	−	0.629337i
$845$		−	37.6156i		−	1.29402i
$846$	−1.16018	−	1.75850i	−0.0398879	−	0.0604586i
$847$			5.38970i			0.185192i
$848$	−8.84667	−	3.58940i	−0.303796	−	0.123260i
$849$	0.803452	+	5.56317i	0.0275744	+	0.190927i
$850$	−8.37535	+	36.2170i	−0.287272	+	1.24223i
$851$	−14.2395	−	24.6636i	−0.488124	−	0.845456i
$852$	1.06112	+	4.91785i	0.0363533	+	0.168483i
$853$	−4.55011	+	7.88103i	−0.155793	+	0.269841i	−0.933347	−	0.358974i	$-0.883127\pi$
$853$	−4.55011	+	7.88103i	−0.155793	+	0.269841i	0.777555	+	0.628816i	$0.216460\pi$
$854$	7.64268	+	7.13216i	0.261527	+	0.244058i
$855$	−5.33796	+	22.1254i	−0.182554	+	0.756673i
$856$	−13.4040	−	10.8788i	−0.458141	−	0.371831i
$857$	12.1291	+	7.00275i	0.414323	+	0.239209i	0.692645	−	0.721278i	$-0.256445\pi$
$857$	12.1291	+	7.00275i	0.414323	+	0.239209i	−0.278323	+	0.960488i	$0.589778\pi$
$858$	−1.45593	−	0.122334i	−0.0497046	−	0.00417642i
$859$	15.1108	−	8.72425i	0.515575	−	0.297668i	−0.219547	−	0.975602i	$-0.570458\pi$
$859$	15.1108	−	8.72425i	0.515575	−	0.297668i	0.735122	+	0.677934i	$0.237125\pi$
$860$	39.9966	−	26.9353i	1.36387	−	0.918488i
$861$	−5.37453	+	13.4496i	−0.183164	+	0.458360i
$862$	−13.4055	−	43.9049i	−0.456592	−	1.49541i
$863$	−4.26940			−0.145332			−0.0726660	−	0.997356i	$-0.523151\pi$
$863$	−4.26940			−0.145332			−0.0726660	+	0.997356i	$0.523151\pi$
$864$	−27.6995	+	9.83557i	−0.942356	+	0.334613i
$865$	25.4784			0.866293
$866$	−7.60980	−	24.9232i	−0.258592	−	0.846926i
$867$	−26.2813	+	65.7679i	−0.892559	+	2.23360i
$868$	0.173481	−	0.116829i	0.00588834	−	0.00396545i
$869$	−23.7735	+	13.7256i	−0.806462	+	0.465611i
$870$	−45.3568	−	3.81110i	−1.53774	−	0.129208i
$871$	−0.111836	−	0.0645688i	−0.00378943	−	0.00218783i
$872$	−13.7370	−	11.1491i	−0.465195	−	0.377556i
$873$	−16.5777	+	4.89042i	−0.561069	+	0.165516i
$874$	24.3700	+	22.7421i	0.824329	+	0.769264i
$875$	−2.24668	+	3.89136i	−0.0759516	+	0.131552i
$876$	2.97242	+	13.7759i	0.100429	+	0.465445i
$877$	5.31547	+	9.20667i	0.179491	+	0.310887i	0.941706	−	0.336436i	$-0.109222\pi$
$877$	5.31547	+	9.20667i	0.179491	+	0.310887i	−0.762216	+	0.647323i	$0.775888\pi$
$878$	−11.6120	+	50.2128i	−0.391884	+	1.69460i
$879$	−3.18168	−	22.0302i	−0.107315	−	0.743060i
$880$	−25.5276	−	10.3574i	−0.860534	−	0.349148i
$881$			5.53762i			0.186567i	0.995640	+	0.0932837i	$0.0297363\pi$
$881$			5.53762i			0.186567i	−0.995640	+	0.0932837i	$0.970264\pi$
$882$	4.23511	−	0.252728i	0.142603	−	0.00850979i
$883$			14.0261i			0.472017i	0.971751	+	0.236009i	$0.0758393\pi$
$883$			14.0261i			0.472017i	−0.971751	+	0.236009i	$0.924161\pi$
$884$	−1.68239	+	3.44301i	−0.0565851	+	0.115801i
$885$	31.6138	−	24.8938i	1.06269	−	0.836794i
$886$	31.3074	+	7.23999i	1.05179	+	0.243232i
$887$	−0.0103232	−	0.0178804i	−0.000346621	−	0.000600365i	0.865852	−	0.500300i	$-0.166777\pi$
$887$	−0.0103232	−	0.0178804i	−0.000346621	−	0.000600365i	−0.866199	+	0.499700i	$0.833444\pi$
$888$	13.4878	−	7.52418i	0.452621	−	0.252495i
$889$	6.79176	−	11.7637i	0.227788	−	0.394541i
$890$	−41.1817	+	44.1295i	−1.38041	+	1.47922i
$891$	18.9724	+	9.72029i	0.635598	+	0.325642i
$892$	−12.1661	+	0.841769i	−0.407353	+	0.0281845i
$893$	−1.12205	−	0.647816i	−0.0375480	−	0.0216783i
$894$	−7.33885	+	3.45293i	−0.245448	+	0.115483i
$895$	−7.24490	+	4.18284i	−0.242170	+	0.139817i
$896$	−11.3114	−	0.226504i	−0.377889	−	0.00756696i
$897$	−2.43761	−	3.09564i	−0.0813894	−	0.103361i
$898$	12.5271	−	3.82490i	0.418035	−	0.127639i
$899$	0.668313			0.0222895
$900$	13.2142	−	15.9698i	0.440473	−	0.532327i
$901$	18.1600			0.604998
$902$	−26.7899	+	8.17974i	−0.892005	+	0.272356i
$903$	−14.2146	+	2.05292i	−0.473031	+	0.0683168i
$904$	−51.2491	−	8.17490i	−1.70452	−	0.271893i
$905$	−12.1625	+	7.02205i	−0.404297	+	0.233421i
$906$	12.5242	+	8.70553i	0.416089	+	0.289222i
$907$	40.9665	+	23.6520i	1.36027	+	0.785353i	0.989660	−	0.143436i	$-0.0458150\pi$
$907$	40.9665	+	23.6520i	1.36027	+	0.785353i	0.370611	+	0.928788i	$0.379148\pi$
$908$	−3.08072	−	44.5259i	−0.102237	−	1.47765i
$909$	12.2488	+	41.5212i	0.406266	+	1.37717i
$910$	0.706507	−	0.757079i	0.0234205	−	0.0250969i
$911$	14.3035	−	24.7744i	0.473897	−	0.820813i	−0.525657	−	0.850697i	$-0.676180\pi$
$911$	14.3035	−	24.7744i	0.473897	−	0.820813i	0.999553	+	0.0298838i	$0.00951371\pi$
$912$	−12.5269	+	13.0329i	−0.414808	+	0.431561i
$913$	1.04122	+	1.80345i	0.0344595	+	0.0596856i
$914$	16.2609	+	3.76041i	0.537863	+	0.124383i
$915$	−34.5693	−	13.8141i	−1.14283	−	0.456681i
$916$	9.73567	+	4.75725i	0.321676	+	0.157184i
$917$			1.48102i			0.0489075i
$918$	41.7891	−	37.1452i	1.37924	−	1.22598i
$919$			42.1651i			1.39090i	0.718575	+	0.695449i	$0.244795\pi$
$919$			42.1651i			1.39090i	−0.718575	+	0.695449i	$0.755205\pi$
$920$	−26.5479	−	69.3879i	−0.875259	−	2.28765i
$921$	−28.4711	−	11.3772i	−0.938156	−	0.374893i
$922$	−0.815855	+	3.52795i	−0.0268688	+	0.116187i
$923$	−0.182867	−	0.316734i	−0.00601913	−	0.0104254i
$924$	5.50899	+	6.08068i	0.181232	+	0.200040i
$925$	−5.44560	+	9.43206i	−0.179050	+	0.310124i
$926$	11.9669	+	11.1675i	0.393256	+	0.366987i
$927$	34.9559	+	8.43343i	1.14810	+	0.276990i
$928$	−29.5751	−	20.7897i	−0.970851	−	0.682455i
$929$	5.09749	+	2.94304i	0.167243	+	0.0965579i	0.581285	−	0.813700i	$-0.302550\pi$
$929$	5.09749	+	2.94304i	0.167243	+	0.0965579i	−0.414042	+	0.910258i	$0.635883\pi$
$930$	−0.425117	+	0.611595i	−0.0139401	+	0.0200550i
$931$	2.25963	−	1.30460i	0.0740564	−	0.0427565i
$932$	6.79451	+	10.0892i	0.222562	+	0.330484i
$933$	11.3260	−	1.63574i	0.370796	−	0.0535516i
$934$	0.236128	+	0.773353i	0.00772633	+	0.0253049i
$935$	52.4017			1.71372
$936$	1.69812	−	1.29704i	0.0555049	−	0.0423952i
$937$	10.0029			0.326781			0.163391	−	0.986561i	$-0.447757\pi$
$937$	10.0029			0.326781			0.163391	+	0.986561i	$0.447757\pi$
$938$	0.211779	+	0.693607i	0.00691482	+	0.0226471i
$939$	−11.4465	−	14.5365i	−0.373544	−	0.474382i
$940$	1.61303	+	2.39520i	0.0526111	+	0.0781228i
$941$	24.7724	−	14.3023i	0.807557	−	0.466243i	−0.0385499	−	0.999257i	$-0.512274\pi$
$941$	24.7724	−	14.3023i	0.807557	−	0.466243i	0.846107	+	0.533014i	$0.178941\pi$
$942$	3.10578	+	6.60101i	0.101192	+	0.215072i
$943$	−65.4189	−	37.7696i	−2.13033	−	1.22995i
$944$	31.6544	−	4.40137i	1.03026	−	0.143253i
$945$	−13.7315	+	6.30247i	−0.446687	+	0.205020i
$946$	−20.3068	−	18.9504i	−0.660233	−	0.616130i
$947$	−1.45936	+	2.52769i	−0.0474228	+	0.0821387i	−0.888762	−	0.458368i	$-0.848434\pi$
$947$	−1.45936	+	2.52769i	−0.0474228	+	0.0821387i	0.841340	+	0.540507i	$0.181767\pi$
$948$	12.2890	−	38.2206i	0.399127	−	1.24135i
$949$	−0.512248	−	0.887239i	−0.0166283	−	0.0288010i
$950$	2.87214	−	12.4198i	0.0931845	−	0.402952i
$951$	−34.7377	+	27.3536i	−1.12645	+	0.887001i
$952$	20.0994	−	7.69008i	0.651427	−	0.249237i
$953$			24.4516i			0.792065i	0.918236	+	0.396032i	$0.129613\pi$
$953$			24.4516i			0.792065i	−0.918236	+	0.396032i	$0.870387\pi$
$954$	−9.05562	−	4.53174i	−0.293186	−	0.146721i
$955$		−	59.6564i		−	1.93044i
$956$	16.4927	+	8.05902i	0.533412	+	0.260647i
$957$	3.74762	+	25.9488i	0.121143	+	0.838805i
$958$	38.3142	+	8.86035i	1.23788	+	0.286265i
$959$	8.99055	+	15.5721i	0.290320	+	0.502849i
$960$	37.8382	−	13.8408i	1.22122	−	0.446708i
$961$	−15.4945	+	26.8373i	−0.499824	+	0.865720i
$962$	−0.766016	+	0.820848i	−0.0246973	+	0.0264652i
$963$	−13.2678	−	12.6188i	−0.427549	−	0.406636i
$964$	−1.27014	−	18.3575i	−0.0409085	−	0.591254i
$965$	−46.8320	−	27.0384i	−1.50757	−	0.870398i
$966$	−1.85273	+	22.0497i	−0.0596105	+	0.709438i
$967$	0.983735	−	0.567960i	0.0316348	−	0.0182644i	−0.484099	−	0.875013i	$-0.660853\pi$
$967$	0.983735	−	0.567960i	0.0316348	−	0.0182644i	0.515734	+	0.856749i	$0.327519\pi$
$968$	2.40132	−	15.0540i	0.0771812	−	0.483855i
$969$	12.7595	−	31.9302i	0.409894	−	1.02575i
$970$	22.6585	−	6.91830i	0.727519	−	0.222133i
$971$	7.03338			0.225712			0.112856	−	0.993611i	$-0.464000\pi$
$971$	7.03338			0.225712			0.112856	+	0.993611i	$0.464000\pi$
$972$	−30.1078	+	8.09447i	−0.965708	+	0.259630i
$973$	8.32882			0.267010
$974$	13.9701	−	4.26548i	0.447631	−	0.136675i
$975$	−0.559150	+	1.39925i	−0.0179071	+	0.0448119i
$976$	−18.1692	−	23.3261i	−0.581584	−	0.746649i
$977$	21.1140	−	12.1901i	0.675495	−	0.389997i	−0.122660	−	0.992449i	$-0.539143\pi$
$977$	21.1140	−	12.1901i	0.675495	−	0.389997i	0.798156	+	0.602451i	$0.205809\pi$
$978$	−1.70093	+	20.2431i	−0.0543896	+	0.647304i
$979$	30.1100	+	17.3840i	0.962319	+	0.555595i
$980$	−5.80151	+	0.401403i	−0.185322	+	0.0128224i
$981$	−13.5974	−	12.9323i	−0.434132	−	0.412898i
$982$	32.6429	−	34.9795i	1.04168	−	1.11624i
$983$	−21.0741	+	36.5015i	−0.672161	+	1.16422i	0.305130	+	0.952311i	$0.401300\pi$
$983$	−21.0741	+	36.5015i	−0.672161	+	1.16422i	−0.977290	+	0.211905i	$0.932033\pi$
$984$	21.0040	−	35.1716i	0.669582	−	1.12123i
$985$	−25.0821	−	43.4435i	−0.799182	−	1.38422i
$986$	66.9965	+	15.4933i	2.13360	+	0.493406i
$987$	−0.122939	−	0.851241i	−0.00391320	−	0.0270953i
$988$	0.576940	−	1.18070i	0.0183549	−	0.0375632i
$989$		−	74.9050i		−	2.38184i
$990$	−26.1305	−	13.0766i	−0.830481	−	0.415601i
$991$			9.26522i			0.294320i	0.989113	+	0.147160i	$0.0470131\pi$
$991$			9.26522i			0.294320i	−0.989113	+	0.147160i	$0.952987\pi$
$992$	−0.536605	+	0.249026i	−0.0170372	+	0.00790658i
$993$	−36.2851	+	28.5721i	−1.15147	+	0.906707i
$994$	−0.462763	+	2.00110i	−0.0146779	+	0.0634709i
$995$	1.70419	+	2.95175i	0.0540266	+	0.0935767i
$996$	−2.89941	−	0.932238i	−0.0918712	−	0.0295391i
$997$	−15.8531	+	27.4584i	−0.502073	+	0.869615i	0.497924	+	0.867220i	$0.334096\pi$
$997$	−15.8531	+	27.4584i	−0.502073	+	0.869615i	−0.999997	+	0.00239501i	$0.999238\pi$
$998$	−6.29711	−	5.87647i	−0.199332	−	0.186016i
$999$	14.8881	−	6.83333i	0.471040	−	0.216197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.ba.a.155.22	✓	72
3.2	odd	2		756.2.ba.a.575.15		72
4.3	odd	2	inner	252.2.ba.a.155.34	yes	72
9.4	even	3		756.2.ba.a.71.3		72
9.5	odd	6	inner	252.2.ba.a.239.34	yes	72
12.11	even	2		756.2.ba.a.575.3		72
36.23	even	6	inner	252.2.ba.a.239.22	yes	72
36.31	odd	6		756.2.ba.a.71.15		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.22	✓	72	1.1	even	1	trivial
252.2.ba.a.155.34	yes	72	4.3	odd	2	inner
252.2.ba.a.239.22	yes	72	36.23	even	6	inner
252.2.ba.a.239.34	yes	72	9.5	odd	6	inner
756.2.ba.a.71.3		72	9.4	even	3
756.2.ba.a.71.15		72	36.31	odd	6
756.2.ba.a.575.3		72	12.11	even	2
756.2.ba.a.575.15		72	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.412980 + 1.35257i) q^{2} +(0.642722 - 1.60839i) q^{3} +(-1.65890 + 1.11717i) q^{4} +(2.51813 - 1.45385i) q^{5} +(2.44089 + 0.205095i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-2.19614 - 1.78241i) q^{8} +(-2.17382 - 2.06749i) q^{9} +O(q^{10})\)	\(q+(0.412980 + 1.35257i) q^{2} +(0.642722 - 1.60839i) q^{3} +(-1.65890 + 1.11717i) q^{4} +(2.51813 - 1.45385i) q^{5} +(2.44089 + 0.205095i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-2.19614 - 1.78241i) q^{8} +(-2.17382 - 2.06749i) q^{9} +(3.00637 + 2.80555i) q^{10} +(1.18430 - 2.05127i) q^{11} +(0.730632 + 3.38617i) q^{12} +(-0.125913 - 0.218087i) q^{13} +(-0.318634 + 1.37785i) q^{14} +(-0.719887 - 4.98455i) q^{15} +(1.50387 - 3.70653i) q^{16} +7.60859i q^{17} +(1.89868 - 3.79407i) q^{18} -2.60920i q^{19} +(-2.55313 + 5.22496i) q^{20} +(1.36081 - 1.07154i) q^{21} +(3.26359 + 0.754720i) q^{22} +(4.51674 + 7.82323i) q^{23} +(-4.27830 + 2.38665i) q^{24} +(1.72733 - 2.99183i) q^{25} +(0.242979 - 0.260371i) q^{26} +(-4.72248 + 2.16752i) q^{27} +(-1.99523 + 0.138049i) q^{28} +(-5.53448 - 3.19533i) q^{29} +(6.44466 - 3.03222i) q^{30} +(-0.0905658 + 0.0522882i) q^{31} +(5.63441 + 0.503365i) q^{32} +(-2.53807 - 3.22322i) q^{33} +(-10.2912 + 3.14219i) q^{34} +2.90769 q^{35} +(5.91587 + 1.00123i) q^{36} -3.15261 q^{37} +(3.52912 - 1.07755i) q^{38} +(-0.431695 + 0.0623469i) q^{39} +(-8.12152 - 1.29549i) q^{40} +(-7.24183 + 4.18107i) q^{41} +(2.01132 + 1.39806i) q^{42} +(-7.18102 - 4.14596i) q^{43} +(0.326984 + 4.72592i) q^{44} +(-8.47978 - 2.04582i) q^{45} +(-8.71615 + 9.34005i) q^{46} +(0.248282 - 0.430036i) q^{47} +(-4.99497 - 4.80107i) q^{48} +(0.500000 + 0.866025i) q^{49} +(4.76001 + 1.10078i) q^{50} +(12.2376 + 4.89020i) q^{51} +(0.452516 + 0.221118i) q^{52} -2.38678i q^{53} +(-4.88201 - 5.49235i) q^{54} -6.88718i q^{55} +(-1.01071 - 2.64168i) q^{56} +(-4.19660 - 1.67699i) q^{57} +(2.03629 - 8.80538i) q^{58} +(3.99487 + 6.91932i) q^{59} +(6.76280 + 7.46462i) q^{60} +(3.69592 - 6.40151i) q^{61} +(-0.108125 - 0.100903i) q^{62} +(-0.848836 - 2.87741i) q^{63} +(1.64606 + 7.82882i) q^{64} +(-0.634129 - 0.366115i) q^{65} +(3.31146 - 4.76404i) q^{66} +(0.444103 - 0.256403i) q^{67} +(-8.50008 - 12.6219i) q^{68} +(15.4858 - 2.23651i) q^{69} +(1.20082 + 3.93286i) q^{70} +1.45233 q^{71} +(1.08890 + 8.41512i) q^{72} +4.06828 q^{73} +(-1.30196 - 4.26412i) q^{74} +(-3.70182 - 4.70113i) q^{75} +(2.91491 + 4.32839i) q^{76} +(2.05127 - 1.18430i) q^{77} +(-0.262610 - 0.558150i) q^{78} +(-10.0369 - 5.79482i) q^{79} +(-1.60178 - 11.5199i) q^{80} +(0.450966 + 8.98869i) q^{81} +(-8.64592 - 8.06839i) q^{82} +(-0.439593 + 0.761398i) q^{83} +(-1.06034 + 3.29783i) q^{84} +(11.0617 + 19.1594i) q^{85} +(2.64209 - 11.4250i) q^{86} +(-8.69646 + 6.84787i) q^{87} +(-6.25710 + 2.39398i) q^{88} +14.6787i q^{89} +(-0.734854 - 12.3144i) q^{90} -0.251825i q^{91} +(-16.2327 - 7.93195i) q^{92} +(0.0258910 + 0.179272i) q^{93} +(0.684190 + 0.158222i) q^{94} +(-3.79337 - 6.57031i) q^{95} +(4.43097 - 8.73880i) q^{96} +(2.88066 - 4.98945i) q^{97} +(-0.964871 + 1.03394i) q^{98} +(-6.81545 + 2.01056i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 72 * q + 6 * q^6 + 4 * q^9	\( 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) \) 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

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