LMFDB - Embedded newform 228.2.k.b.31.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(31,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([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("228.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 3 x^{18} - 2 x^{17} + x^{16} + 3 x^{14} - 12 x^{13} + 28 x^{12} - 24 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 3x^18 - 2x^17 + x^16 + 3x^14 - 12x^13 + 28x^12 - 24x^11 + 40x^10 - 48x^9 + 112x^8 - 96x^7 + 48x^6 + 64x^4 - 256x^3 + 768x^2 - 1024x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.8
Root			$-0.237943 + 1.39405i$ of defining polynomial
Character	$\chi$	$=$	228.31
Dual form			228.2.k.b.103.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.08831 - 0.903091i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.368852 - 1.96569i) q^{4} +(1.43271 + 2.48152i) q^{5} +(1.32626 + 0.490961i) q^{6} +2.64551i q^{7} +(-1.37377 - 2.47240i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.80027 + 1.40681i) q^{10} -2.73265i q^{11} +(1.88677 - 0.663412i) q^{12} +(-1.86752 - 1.07822i) q^{13} +(2.38914 + 2.87915i) q^{14} +(-1.43271 + 2.48152i) q^{15} +(-3.72790 - 1.45010i) q^{16} +(-1.26747 - 2.19532i) q^{17} +(0.237943 + 1.39405i) q^{18} +(1.53443 - 4.07989i) q^{19} +(5.40636 - 1.90095i) q^{20} +(-2.29108 + 1.32276i) q^{21} +(-2.46783 - 2.97398i) q^{22} +(-3.37287 - 1.94733i) q^{23} +(1.45427 - 2.42592i) q^{24} +(-1.60529 + 2.78044i) q^{25} +(-3.00618 + 0.513109i) q^{26} -1.00000 q^{27} +(5.20027 + 0.975802i) q^{28} +(-2.79010 - 1.61086i) q^{29} +(0.681806 + 3.99453i) q^{30} +8.83425 q^{31} +(-5.36669 + 1.78847i) q^{32} +(2.36654 - 1.36632i) q^{33} +(-3.36199 - 1.24456i) q^{34} +(-6.56489 + 3.79024i) q^{35} +(1.51791 + 1.30228i) q^{36} +12.0463i q^{37} +(-2.01457 - 5.82593i) q^{38} -2.15643i q^{39} +(4.16708 - 6.95126i) q^{40} +(-4.75850 + 2.74732i) q^{41} +(-1.29884 + 3.50863i) q^{42} +(1.31272 - 0.757900i) q^{43} +(-5.37154 - 1.00794i) q^{44} -2.86541 q^{45} +(-5.42935 + 0.926708i) q^{46} +(-9.19542 - 5.30898i) q^{47} +(-0.608127 - 3.95350i) q^{48} +0.00125668 q^{49} +(0.763936 + 4.47571i) q^{50} +(1.26747 - 2.19532i) q^{51} +(-2.80828 + 3.27328i) q^{52} +(4.25386 + 2.45597i) q^{53} +(-1.08831 + 0.903091i) q^{54} +(6.78111 - 3.91508i) q^{55} +(6.54076 - 3.63434i) q^{56} +(4.30051 - 0.711086i) q^{57} +(-4.49126 + 0.766589i) q^{58} +(3.80546 + 6.59126i) q^{59} +(4.34945 + 3.73157i) q^{60} +(0.788072 - 1.36498i) q^{61} +(9.61444 - 7.97814i) q^{62} +(-2.29108 - 1.32276i) q^{63} +(-4.22549 + 6.79303i) q^{64} -6.17906i q^{65} +(1.34162 - 3.62419i) q^{66} +(-5.23140 + 9.06106i) q^{67} +(-4.78284 + 1.68171i) q^{68} -3.89465i q^{69} +(-3.72172 + 10.0537i) q^{70} +(-2.82329 - 4.89008i) q^{71} +(2.82805 + 0.0464748i) q^{72} +(-6.42096 - 11.1214i) q^{73} +(10.8789 + 13.1102i) q^{74} -3.21058 q^{75} +(-7.45383 - 4.52110i) q^{76} +7.22925 q^{77} +(-1.94746 - 2.34687i) q^{78} +(8.67850 + 15.0316i) q^{79} +(-1.74253 - 11.3284i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.69766 + 7.28730i) q^{82} +5.64965i q^{83} +(1.75506 + 4.99146i) q^{84} +(3.63183 - 6.29051i) q^{85} +(0.744199 - 2.01034i) q^{86} -3.22173i q^{87} +(-6.75619 + 3.75404i) q^{88} +(1.33617 + 0.771439i) q^{89} +(-3.11846 + 2.58773i) q^{90} +(2.85244 - 4.94056i) q^{91} +(-5.07194 + 5.91175i) q^{92} +(4.41713 + 7.65069i) q^{93} +(-14.8020 + 2.52647i) q^{94} +(12.3227 - 2.03755i) q^{95} +(-4.23221 - 3.75346i) q^{96} +(-2.09143 + 1.20749i) q^{97} +(0.00136766 - 0.00113490i) q^{98} +(2.36654 + 1.36632i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 10 q^{3} + q^{4} - q^{6} + 4 q^{8} - 10 q^{9} + 6 q^{10} + 2 q^{12} + 6 q^{13} + 9 q^{14} - 11 q^{16} - 2 q^{18} + 12 q^{19} - 14 q^{20} + 6 q^{21} + 8 q^{22} + 11 q^{24} - 10 q^{25} - 20 q^{27}+ \cdots - 12 q^{97}+O(q^{100}) $ 20 * q + q^2 + 10 * q^3 + q^4 - q^6 + 4 * q^8 - 10 * q^9 + 6 * q^10 + 2 * q^12 + 6 * q^13 + 9 * q^14 - 11 * q^16 - 2 * q^18 + 12 * q^19 - 14 * q^20 + 6 * q^21 + 8 * q^22 + 11 * q^24 - 10 * q^25 - 20 * q^27 + 7 * q^28 + 12 * q^31 - 29 * q^32 - 6 * q^34 + q^36 + 25 * q^38 - 46 * q^40 + 12 * q^41 + 9 * q^42 - 18 * q^43 - 12 * q^44 - 32 * q^46 - 36 * q^47 - 13 * q^48 - 24 * q^49 - 34 * q^50 + 3 * q^52 - 12 * q^53 - q^54 + 38 * q^56 + 6 * q^57 + 16 * q^58 - 4 * q^60 + 10 * q^61 - 55 * q^62 + 6 * q^63 - 14 * q^64 - 8 * q^66 + 14 * q^67 + 40 * q^68 + 26 * q^70 + 8 * q^71 + 7 * q^72 - 6 * q^73 + 45 * q^74 - 20 * q^75 - 69 * q^76 - 32 * q^77 + 33 * q^78 - 6 * q^79 + 22 * q^80 - 10 * q^81 + 24 * q^82 + 14 * q^84 + 8 * q^85 + 7 * q^86 + 44 * q^88 - 24 * q^89 - 6 * q^90 + 26 * q^91 - 18 * q^92 + 6 * q^93 - 52 * q^94 + 4 * q^95 + 2 * q^96 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.08831	−	0.903091i	0.769554	−	0.638582i
$2$	1.08831	−	0.903091i	0.769554	−	0.638582i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.368852	−	1.96569i	0.184426	−	0.982846i
$5$	1.43271	+	2.48152i	0.640725	+	1.10977i	0.985271	+	0.170999i	$0.0546995\pi$
$5$	1.43271	+	2.48152i	0.640725	+	1.10977i	−0.344546	+	0.938769i	$0.611967\pi$
$6$	1.32626	+	0.490961i	0.541442	+	0.200434i
$7$			2.64551i			0.999910i	0.866051	+	0.499955i	$0.166650\pi$
$7$			2.64551i			0.999910i	−0.866051	+	0.499955i	$0.833350\pi$
$8$	−1.37377	−	2.47240i	−0.485703	−	0.874124i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	3.80027	+	1.40681i	1.20175	+	0.444871i
$11$		−	2.73265i		−	0.823924i	−0.911201	−	0.411962i	$-0.864844\pi$
$11$		−	2.73265i		−	0.823924i	0.911201	−	0.411962i	$-0.135156\pi$
$12$	1.88677	−	0.663412i	0.544662	−	0.191510i
$13$	−1.86752	−	1.07822i	−0.517958	−	0.299043i	0.218141	−	0.975917i	$-0.430001\pi$
$13$	−1.86752	−	1.07822i	−0.517958	−	0.299043i	−0.736099	+	0.676874i	$0.763334\pi$
$14$	2.38914	+	2.87915i	0.638525	+	0.769485i
$15$	−1.43271	+	2.48152i	−0.369923	+	0.640725i
$16$	−3.72790	−	1.45010i	−0.931974	−	0.362525i
$17$	−1.26747	−	2.19532i	−0.307407	−	0.532445i	0.670387	−	0.742011i	$-0.266128\pi$
$17$	−1.26747	−	2.19532i	−0.307407	−	0.532445i	−0.977794	+	0.209567i	$0.932795\pi$
$18$	0.237943	+	1.39405i	0.0560838	+	0.328581i
$19$	1.53443	−	4.07989i	0.352024	−	0.935991i
$19$	1.53443	−	4.07989i	0.352024	−	0.935991i
$20$	5.40636	−	1.90095i	1.20890	−	0.425064i
$21$	−2.29108	+	1.32276i	−0.499955	+	0.288649i
$22$	−2.46783	−	2.97398i	−0.526143	−	0.634054i
$23$	−3.37287	−	1.94733i	−0.703292	−	0.406046i	0.105280	−	0.994443i	$-0.466426\pi$
$23$	−3.37287	−	1.94733i	−0.703292	−	0.406046i	−0.808572	+	0.588397i	$0.799759\pi$
$24$	1.45427	−	2.42592i	0.296852	−	0.495189i
$25$	−1.60529	+	2.78044i	−0.321058	+	0.556088i
$26$	−3.00618	+	0.513109i	−0.589560	+	0.100629i
$27$	−1.00000			−0.192450
$28$	5.20027	+	0.975802i	0.982758	+	0.184409i
$29$	−2.79010	−	1.61086i	−0.518108	−	0.299130i	0.218052	−	0.975937i	$-0.430030\pi$
$29$	−2.79010	−	1.61086i	−0.518108	−	0.299130i	−0.736160	+	0.676807i	$0.763363\pi$
$30$	0.681806	+	3.99453i	0.124480	+	0.729299i
$31$	8.83425			1.58668			0.793339	−	0.608780i	$-0.208341\pi$
$31$	8.83425			1.58668			0.793339	+	0.608780i	$0.208341\pi$
$32$	−5.36669	+	1.78847i	−0.948706	+	0.316160i
$33$	2.36654	−	1.36632i	0.411962	−	0.237846i
$34$	−3.36199	−	1.24456i	−0.576576	−	0.213440i
$35$	−6.56489	+	3.79024i	−1.10967	+	0.640668i
$36$	1.51791	+	1.30228i	0.252986	+	0.217047i
$37$			12.0463i			1.98040i	0.139656	+	0.990200i	$0.455400\pi$
$37$			12.0463i			1.98040i	−0.139656	+	0.990200i	$0.544600\pi$
$38$	−2.01457	−	5.82593i	−0.326806	−	0.945091i
$39$		−	2.15643i		−	0.345305i
$40$	4.16708	−	6.95126i	0.658874	−	1.09909i
$41$	−4.75850	+	2.74732i	−0.743153	+	0.429059i	−0.823214	−	0.567731i	$-0.807822\pi$
$41$	−4.75850	+	2.74732i	−0.743153	+	0.429059i	0.0800618	+	0.996790i	$0.474488\pi$
$42$	−1.29884	+	3.50863i	−0.200416	+	0.541393i
$43$	1.31272	−	0.757900i	0.200188	−	0.115579i	−0.396555	−	0.918011i	$-0.629794\pi$
$43$	1.31272	−	0.757900i	0.200188	−	0.115579i	0.596743	+	0.802432i	$0.296461\pi$
$44$	−5.37154	−	1.00794i	−0.809791	−	0.151953i
$45$	−2.86541			−0.427150
$46$	−5.42935	+	0.926708i	−0.800515	+	0.136636i
$47$	−9.19542	−	5.30898i	−1.34129	−	0.774394i	−0.354294	−	0.935134i	$-0.615279\pi$
$47$	−9.19542	−	5.30898i	−1.34129	−	0.774394i	−0.986997	+	0.160740i	$0.948612\pi$
$48$	−0.608127	−	3.95350i	−0.0877755	−	0.570639i
$49$	0.00125668			0.000179525
$50$	0.763936	+	4.47571i	0.108037	+	0.632961i
$51$	1.26747	−	2.19532i	0.177482	−	0.307407i
$52$	−2.80828	+	3.27328i	−0.389439	+	0.453922i
$53$	4.25386	+	2.45597i	0.584312	+	0.337353i	0.762845	−	0.646581i	$-0.223802\pi$
$53$	4.25386	+	2.45597i	0.584312	+	0.337353i	−0.178533	+	0.983934i	$0.557135\pi$
$54$	−1.08831	+	0.903091i	−0.148101	+	0.122895i
$55$	6.78111	−	3.91508i	0.914365	−	0.527909i
$56$	6.54076	−	3.63434i	0.874046	−	0.485659i
$57$	4.30051	−	0.711086i	0.569616	−	0.0941856i
$58$	−4.49126	+	0.766589i	−0.589731	+	0.100658i
$59$	3.80546	+	6.59126i	0.495429	+	0.858109i	0.999986	−	0.00526981i	$-0.00167744\pi$
$59$	3.80546	+	6.59126i	0.495429	+	0.858109i	−0.504557	+	0.863378i	$0.668344\pi$
$60$	4.34945	+	3.73157i	0.561511	+	0.481744i
$61$	0.788072	−	1.36498i	0.100902	−	0.174768i	−0.811154	−	0.584832i	$-0.801160\pi$
$61$	0.788072	−	1.36498i	0.100902	−	0.174768i	0.912057	+	0.410064i	$0.134494\pi$
$62$	9.61444	−	7.97814i	1.22103	−	1.01322i
$63$	−2.29108	−	1.32276i	−0.288649	−	0.166652i
$64$	−4.22549	+	6.79303i	−0.528186	+	0.849129i
$65$		−	6.17906i		−	0.766418i
$66$	1.34162	−	3.62419i	0.165142	−	0.446107i
$67$	−5.23140	+	9.06106i	−0.639118	+	1.10698i	0.346509	+	0.938047i	$0.387367\pi$
$67$	−5.23140	+	9.06106i	−0.639118	+	1.10698i	−0.985627	+	0.168938i	$0.945966\pi$
$68$	−4.78284	+	1.68171i	−0.580005	+	0.203937i
$69$		−	3.89465i		−	0.468861i
$70$	−3.72172	+	10.0537i	−0.444831	+	1.20164i
$71$	−2.82329	−	4.89008i	−0.335063	−	0.580346i	0.648434	−	0.761271i	$-0.275424\pi$
$71$	−2.82329	−	4.89008i	−0.335063	−	0.580346i	−0.983497	+	0.180925i	$0.942091\pi$
$72$	2.82805	+	0.0464748i	0.333288	+	0.00547711i
$73$	−6.42096	−	11.1214i	−0.751517	−	1.30167i	−0.947087	−	0.320976i	$-0.895989\pi$
$73$	−6.42096	−	11.1214i	−0.751517	−	1.30167i	0.195571	−	0.980690i	$-0.437344\pi$
$74$	10.8789	+	13.1102i	1.26465	+	1.52402i
$75$	−3.21058			−0.370725
$76$	−7.45383	−	4.52110i	−0.855013	−	0.518606i
$77$	7.22925			0.823850
$78$	−1.94746	−	2.34687i	−0.220506	−	0.265731i
$79$	8.67850	+	15.0316i	0.976408	+	1.69119i	0.675209	+	0.737626i	$0.264053\pi$
$79$	8.67850	+	15.0316i	0.976408	+	1.69119i	0.301198	+	0.953561i	$0.402613\pi$
$80$	−1.74253	−	11.3284i	−0.194821	−	1.26655i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.69766	+	7.28730i	−0.297906	+	0.804748i
$83$			5.64965i			0.620130i	0.950715	+	0.310065i	$0.100351\pi$
$83$			5.64965i			0.620130i	−0.950715	+	0.310065i	$0.899649\pi$
$84$	1.75506	+	4.99146i	0.191493	+	0.544613i
$85$	3.63183	−	6.29051i	0.393927	−	0.682301i
$86$	0.744199	−	2.01034i	0.0802490	−	0.216780i
$87$		−	3.22173i		−	0.345406i
$88$	−6.75619	+	3.75404i	−0.720212	+	0.400182i
$89$	1.33617	+	0.771439i	0.141634	+	0.0817724i	0.569142	−	0.822239i	$-0.307275\pi$
$89$	1.33617	+	0.771439i	0.141634	+	0.0817724i	−0.427509	+	0.904011i	$0.640609\pi$
$90$	−3.11846	+	2.58773i	−0.328715	+	0.272770i
$91$	2.85244	−	4.94056i	0.299016	−	0.517912i
$92$	−5.07194	+	5.91175i	−0.528786	+	0.616343i
$93$	4.41713	+	7.65069i	0.458035	+	0.793339i
$94$	−14.8020	+	2.52647i	−1.52671	+	0.260586i
$95$	12.3227	−	2.03755i	1.26428	−	0.209048i
$96$	−4.23221	−	3.75346i	−0.431948	−	0.383085i
$97$	−2.09143	+	1.20749i	−0.212353	+	0.122602i	−0.602404	−	0.798191i	$-0.705791\pi$
$97$	−2.09143	+	1.20749i	−0.212353	+	0.122602i	0.390052	+	0.920793i	$0.372457\pi$
$98$	0.00136766	−	0.00113490i	0.000138154	−	0.000114642i
$99$	2.36654	+	1.36632i	0.237846	+	0.137321i
$100$	4.87338	+	4.18107i	0.487338	+	0.418107i
$101$	3.32390	−	5.75717i	0.330741	−	0.572860i	−0.651916	−	0.758291i	$-0.726035\pi$
$101$	3.32390	−	5.75717i	0.330741	−	0.572860i	0.982657	+	0.185431i	$0.0593680\pi$
$102$	−0.603173	−	3.53384i	−0.0597230	−	0.349903i
$103$	9.22228			0.908698			0.454349	−	0.890824i	$-0.349872\pi$
$103$	9.22228			0.908698			0.454349	+	0.890824i	$0.349872\pi$
$104$	−0.100220	+	6.09849i	−0.00982737	+	0.598006i
$105$	−6.56489	−	3.79024i	−0.640668	−	0.369890i
$106$	6.84749	−	1.16876i	0.665087	−	0.113520i
$107$	−11.0441			−1.06767			−0.533836	−	0.845588i	$-0.679250\pi$
$107$	−11.0441			−1.06767			−0.533836	+	0.845588i	$0.679250\pi$
$108$	−0.368852	+	1.96569i	−0.0354928	+	0.189149i
$109$	8.11096	−	4.68287i	0.776889	−	0.448537i	−0.0584373	−	0.998291i	$-0.518612\pi$
$109$	8.11096	−	4.68287i	0.776889	−	0.448537i	0.835327	+	0.549754i	$0.185278\pi$
$110$	3.84430	−	10.3848i	0.366540	−	0.990151i
$111$	−10.4324	+	6.02315i	−0.990200	+	0.571692i
$112$	3.83625	−	9.86220i	0.362492	−	0.931891i
$113$		−	19.9991i		−	1.88136i	−0.339298	−	0.940679i	$-0.610189\pi$
$113$		−	19.9991i		−	1.88136i	0.339298	−	0.940679i	$-0.389811\pi$
$114$	4.03812	−	4.65763i	0.378205	−	0.436227i
$115$		−	11.1598i		−	1.04066i
$116$	−4.19560	+	4.89031i	−0.389551	+	0.454054i
$117$	1.86752	−	1.07822i	0.172653	−	0.0996811i
$118$	10.0940	+	3.73667i	0.929232	+	0.343988i
$119$	5.80776	−	3.35311i	0.532397	−	0.307379i
$120$	8.10351	+	0.133170i	0.739746	+	0.0121567i
$121$	3.53264			0.321149
$122$	−0.375033	−	2.19723i	−0.0339539	−	0.198928i
$123$	−4.75850	−	2.74732i	−0.429059	−	0.247718i
$124$	3.25853	−	17.3654i	0.292625	−	1.55946i
$125$	5.12743			0.458612
$126$	−3.68799	+	0.629483i	−0.328552	+	0.0560788i
$127$	0.531496	−	0.920577i	0.0471626	−	0.0816880i	−0.841480	−	0.540288i	$-0.818315\pi$
$127$	0.531496	−	0.920577i	0.0471626	−	0.0816880i	0.888643	+	0.458600i	$0.151649\pi$
$128$	1.53607	+	11.2089i	0.135771	+	0.990740i
$129$	1.31272	+	0.757900i	0.115579	+	0.0667293i
$130$	−5.58026	−	6.72476i	−0.489421	−	0.589800i
$131$	7.64858	−	4.41591i	0.668259	−	0.385820i	−0.127158	−	0.991883i	$-0.540585\pi$
$131$	7.64858	−	4.41591i	0.668259	−	0.385820i	0.795417	+	0.606063i	$0.207252\pi$
$132$	−1.81287	−	5.15586i	−0.157790	−	0.448760i
$133$	10.7934	+	4.05937i	0.935907	+	0.351992i
$134$	2.48956	+	14.5857i	0.215065	+	1.26001i
$135$	−1.43271	−	2.48152i	−0.123308	−	0.213575i
$136$	−3.68649	+	6.14957i	−0.316114	+	0.527322i
$137$	−10.2489	+	17.7515i	−0.875619	+	1.51662i	−0.0195162	+	0.999810i	$0.506213\pi$
$137$	−10.2489	+	17.7515i	−0.875619	+	1.51662i	−0.856102	+	0.516806i	$0.827121\pi$
$138$	−3.51723	−	4.23860i	−0.299406	−	0.360814i
$139$	−3.61248	−	2.08566i	−0.306406	−	0.176904i	0.338911	−	0.940818i	$-0.389941\pi$
$139$	−3.61248	−	2.08566i	−0.306406	−	0.176904i	−0.645317	+	0.763915i	$0.723275\pi$
$140$	5.02898	+	14.3026i	0.425026	+	1.20879i
$141$		−	10.6180i		−	0.894194i
$142$	−7.48882	−	2.77225i	−0.628448	−	0.232642i
$143$	−2.94638	+	5.10329i	−0.246389	+	0.426758i
$144$	3.11977	−	2.50340i	0.259981	−	0.208617i
$145$		−	9.23157i		−	0.766640i
$146$	−17.0317	−	6.30489i	−1.40955	−	0.521796i
$147$	0.000628339		0.00108832i	5.18245e−5		8.97627e-5i
$148$	23.6793	+	4.44330i	1.94643	+	0.365237i
$149$	8.11424	+	14.0543i	0.664744	+	1.15137i	0.979355	+	0.202150i	$0.0647928\pi$
$149$	8.11424	+	14.0543i	0.664744	+	1.15137i	−0.314610	+	0.949221i	$0.601874\pi$
$150$	−3.49411	+	2.89944i	−0.285293	+	0.236739i
$151$	−22.7285			−1.84962			−0.924809	−	0.380431i	$-0.875776\pi$
$151$	−22.7285			−1.84962			−0.924809	+	0.380431i	$0.875776\pi$
$152$	−12.1951	+	1.81112i	−0.989151	+	0.146901i
$153$	2.53494			0.204938
$154$	7.86769	−	6.52868i	0.633997	−	0.526096i
$155$	12.6569	+	21.9224i	1.01663	+	1.76085i
$156$	−4.23888	−	0.795404i	−0.339382	−	0.0636833i
$157$	4.24706	+	7.35612i	0.338952	+	0.587082i	0.984236	−	0.176861i	$-0.0565943\pi$
$157$	4.24706	+	7.35612i	0.338952	+	0.587082i	−0.645284	+	0.763943i	$0.723261\pi$
$158$	23.0198	+	8.52162i	1.83136	+	0.677943i
$159$			4.91193i			0.389542i
$160$	−12.1270	−	10.7552i	−0.958724	−	0.850272i
$161$	5.15168	−	8.92297i	0.406009	−	0.703229i
$162$	−1.32626	−	0.490961i	−0.104201	−	0.0385736i
$163$		−	0.960892i		−	0.0752629i	−0.999292	−	0.0376314i	$-0.988019\pi$
$163$		−	0.960892i		−	0.0752629i	0.999292	−	0.0376314i	$-0.0119813\pi$
$164$	3.64521	+	10.3671i	0.284643	+	0.809535i
$165$	6.78111	+	3.91508i	0.527909	+	0.304788i
$166$	5.10215	+	6.14859i	0.396004	+	0.477223i
$167$	8.88741	−	15.3934i	0.687728	−	1.19118i	−0.284843	−	0.958574i	$-0.591941\pi$
$167$	8.88741	−	15.3934i	0.687728	−	1.19118i	0.972571	−	0.232606i	$-0.0747253\pi$
$168$	6.41781	+	3.84729i	0.495145	+	0.296825i
$169$	−4.17490	−	7.23114i	−0.321146	−	0.556242i
$170$	−1.72834	−	10.1259i	−0.132558	−	0.776622i
$171$	2.76607	+	3.36881i	0.211527	+	0.257619i
$172$	−1.00560	−	2.85996i	−0.0766762	−	0.218070i
$173$	1.94298	−	1.12178i	0.147722	−	0.0852875i	−0.424317	−	0.905514i	$-0.639486\pi$
$173$	1.94298	−	1.12178i	0.147722	−	0.0852875i	0.572039	+	0.820226i	$0.306152\pi$
$174$	−2.90952	−	3.50625i	−0.220570	−	0.265808i
$175$	−7.35569	−	4.24681i	−0.556038	−	0.321029i
$176$	−3.96261	+	10.1870i	−0.298693	+	0.767876i
$177$	−3.80546	+	6.59126i	−0.286036	+	0.495429i
$178$	2.15085	−	0.367118i	0.161213	−	0.0275167i
$179$	2.69305			0.201288			0.100644	−	0.994922i	$-0.467910\pi$
$179$	2.69305			0.201288			0.100644	+	0.994922i	$0.467910\pi$
$180$	−1.05691	+	5.63252i	−0.0787775	+	0.419823i
$181$	7.51874	+	4.34095i	0.558864	+	0.322660i	0.752689	−	0.658376i	$-0.228756\pi$
$181$	7.51874	+	4.34095i	0.558864	+	0.322660i	−0.193825	+	0.981036i	$0.562090\pi$
$182$	−1.35744	−	7.95289i	−0.100620	−	0.589507i
$183$	1.57614			0.116512
$184$	−0.181003	+	11.0143i	−0.0133438	+	0.811982i
$185$	−29.8931	+	17.2588i	−2.19779	+	1.26889i
$186$	11.7165	+	4.33728i	0.859095	+	0.318025i
$187$	−5.99905	+	3.46355i	−0.438694	+	0.253280i
$188$	−13.8276	+	16.1172i	−1.00848	+	1.17546i
$189$		−	2.64551i		−	0.192433i
$190$	11.5709	−	13.3460i	0.839440	−	0.968223i
$191$			15.4264i			1.11622i	0.829768	+	0.558109i	$0.188473\pi$
$191$			15.4264i			1.11622i	−0.829768	+	0.558109i	$0.811527\pi$
$192$	−7.99568	−	0.262866i	−0.577039	−	0.0189707i
$193$	−13.1165	+	7.57281i	−0.944146	+	0.545103i	−0.891258	−	0.453497i	$-0.850176\pi$
$193$	−13.1165	+	7.57281i	−0.944146	+	0.545103i	−0.0528886	+	0.998600i	$0.516843\pi$
$194$	−1.18566	+	3.20288i	−0.0851255	+	0.229953i
$195$	5.35123	−	3.08953i	0.383209	−	0.221246i
$196$	0.000463528	−	0.00247024i	3.31091e−5	−	0.000176446i
$197$	1.69549			0.120799			0.0603994	−	0.998174i	$-0.480763\pi$
$197$	1.69549			0.120799			0.0603994	+	0.998174i	$0.480763\pi$
$198$	3.80945	−	0.650215i	0.270726	−	0.0462088i
$199$	−13.3077	−	7.68321i	−0.943358	−	0.544648i	−0.0523468	−	0.998629i	$-0.516670\pi$
$199$	−13.3077	−	7.68321i	−0.943358	−	0.544648i	−0.891011	+	0.453981i	$0.850003\pi$
$200$	9.07965	+	0.149211i	0.642028	+	0.0105508i
$201$	−10.4628			−0.737989
$202$	−1.58180	−	9.26740i	−0.111295	−	0.652052i
$203$	4.26156	−	7.38124i	0.299103	−	0.518062i
$204$	−3.84783	−	3.30121i	−0.269402	−	0.231131i
$205$	−13.6351	−	7.87220i	−0.952313	−	0.549818i
$206$	10.0367	−	8.32856i	0.699292	−	0.580279i
$207$	3.37287	−	1.94733i	0.234431	−	0.135349i
$208$	5.39842	+	6.72757i	0.374313	+	0.466473i
$209$	−11.1489	−	4.19307i	−0.771185	−	0.290041i
$210$	−10.5676	+	1.80373i	−0.729233	+	0.124469i
$211$	2.98218	+	5.16529i	0.205302	+	0.355593i	0.950229	−	0.311553i	$-0.100849\pi$
$211$	2.98218	+	5.16529i	0.205302	+	0.355593i	−0.744927	+	0.667146i	$0.767516\pi$
$212$	6.39672	−	7.45589i	0.439328	−	0.512073i
$213$	2.82329	−	4.89008i	0.193449	−	0.335063i
$214$	−12.0194	+	9.97382i	−0.821631	+	0.681797i
$215$	3.76148	+	2.17169i	0.256531	+	0.148108i
$216$	1.37377	+	2.47240i	0.0934735	+	0.168225i
$217$			23.3711i			1.58654i
$218$	4.59821	−	12.4214i	0.311430	−	0.841281i
$219$	6.42096	−	11.1214i	0.433888	−	0.751517i
$220$	−5.19461	−	14.7737i	−0.350221	−	0.996040i
$221$			5.46643i			0.367712i
$222$	−5.91427	+	15.9765i	−0.396940	+	1.07227i
$223$	5.15998	+	8.93736i	0.345538	+	0.598490i	0.985451	−	0.169958i	$-0.0543631\pi$
$223$	5.15998	+	8.93736i	0.345538	+	0.598490i	−0.639913	+	0.768447i	$0.721030\pi$
$224$	−4.73142	−	14.1977i	−0.316132	−	0.948621i
$225$	−1.60529	−	2.78044i	−0.107019	−	0.185363i
$226$	−18.0610	−	21.7653i	−1.20140	−	1.44781i
$227$	−7.97639			−0.529411			−0.264706	−	0.964329i	$-0.585275\pi$
$227$	−7.97639			−0.529411			−0.264706	+	0.964329i	$0.585275\pi$
$228$	0.188473	−	8.71576i	0.0124819	−	0.577215i
$229$	−5.24797			−0.346796			−0.173398	−	0.984852i	$-0.555475\pi$
$229$	−5.24797			−0.346796			−0.173398	+	0.984852i	$0.555475\pi$
$230$	−10.0783	−	12.1453i	−0.664544	−	0.800840i
$231$	3.61463	+	6.26072i	0.237825	+	0.411925i
$232$	−0.149729	+	9.11119i	−0.00983021	+	0.598179i
$233$	−6.29168	−	10.8975i	−0.412181	−	0.713919i	0.582947	−	0.812510i	$-0.301900\pi$
$233$	−6.29168	−	10.8975i	−0.412181	−	0.713919i	−0.995128	+	0.0985913i	$0.968566\pi$
$234$	1.05872	−	2.85998i	0.0692110	−	0.186963i
$235$		−	30.4248i		−	1.98470i
$236$	14.3600	−	5.04918i	0.934759	−	0.328673i
$237$	−8.67850	+	15.0316i	−0.563729	+	0.976408i
$238$	3.29250	−	8.89418i	0.213421	−	0.576524i
$239$		−	10.3998i		−	0.672707i	−0.941736	−	0.336354i	$-0.890806\pi$
$239$		−	10.3998i		−	0.672707i	0.941736	−	0.336354i	$-0.109194\pi$
$240$	8.93942	−	7.17328i	0.577037	−	0.463033i
$241$	−13.6723	−	7.89370i	−0.880710	−	0.508478i	−0.00981747	−	0.999952i	$-0.503125\pi$
$241$	−13.6723	−	7.89370i	−0.880710	−	0.508478i	−0.870892	+	0.491474i	$0.836458\pi$
$242$	3.84462	−	3.19030i	0.247142	−	0.205080i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.39245	−	2.05258i	−0.153161	−	0.131403i
$245$	0.00180045	+	0.00311847i	0.000115026	+	0.000199232i
$246$	−7.65982	+	1.30741i	−0.488372	+	0.0833577i
$247$	−7.26460	+	5.96485i	−0.462235	+	0.379534i
$248$	−12.1363	−	21.8418i	−0.770654	−	1.38695i
$249$	−4.89274	+	2.82482i	−0.310065	+	0.179016i
$250$	5.58026	−	4.63054i	0.352926	−	0.292861i
$251$	3.72142	+	2.14856i	0.234894	+	0.135616i	0.612828	−	0.790216i	$-0.290032\pi$
$251$	3.72142	+	2.14856i	0.234894	+	0.135616i	−0.377934	+	0.925833i	$0.623365\pi$
$252$	−3.44520	+	4.01566i	−0.217027	+	0.252963i
$253$	−5.32136	+	9.21686i	−0.334551	+	0.579459i
$254$	−0.252932	−	1.48187i	−0.0158704	−	0.0929805i
$255$	7.26365			0.454867
$256$	11.7944	+	10.8116i	0.737152	+	0.675727i
$257$	24.0830	+	13.9043i	1.50226	+	0.867328i	0.999997	+	0.00261095i	$0.000831091\pi$
$257$	24.0830	+	13.9043i	1.50226	+	0.867328i	0.502259	+	0.864717i	$0.332502\pi$
$258$	2.11310	−	0.360675i	0.131556	−	0.0224546i
$259$	−31.8687			−1.98022
$260$	−12.1461	−	2.27916i	−0.753272	−	0.141347i
$261$	2.79010	−	1.61086i	0.172703	−	0.0997100i
$262$	4.33608	−	11.7133i	0.267884	−	0.723647i
$263$	−19.9939	+	11.5435i	−1.23288	+	0.711803i	−0.967629	−	0.252376i	$-0.918788\pi$
$263$	−19.9939	+	11.5435i	−1.23288	+	0.711803i	−0.265250	+	0.964180i	$0.585455\pi$
$264$	−6.62919	−	3.97401i	−0.407998	−	0.244583i
$265$			14.0747i			0.864602i
$266$	15.4126	−	5.32957i	0.945007	−	0.326777i
$267$			1.54288i			0.0944226i
$268$	15.8816	+	13.6255i	0.970126	+	0.832311i
$269$	−23.3260	+	13.4673i	−1.42221	+	0.821113i	−0.996488	−	0.0837405i	$-0.973313\pi$
$269$	−23.3260	+	13.4673i	−1.42221	+	0.821113i	−0.425722	+	0.904854i	$0.639980\pi$
$270$	−3.80027	−	1.40681i	−0.231277	−	0.0856154i
$271$	15.9754	−	9.22339i	0.970435	−	0.560281i	0.0710661	−	0.997472i	$-0.477360\pi$
$271$	15.9754	−	9.22339i	0.970435	−	0.560281i	0.899369	+	0.437191i	$0.144027\pi$
$272$	1.54157	+	10.0219i	0.0934712	+	0.607667i
$273$	5.70487			0.345274
$274$	4.87730	+	28.5749i	0.294648	+	1.72627i
$275$	7.59796	+	4.38668i	0.458174	+	0.264527i
$276$	−7.65570	−	1.43655i	−0.460819	−	0.0864701i
$277$	4.74769			0.285261			0.142631	−	0.989776i	$-0.454444\pi$
$277$	4.74769			0.285261			0.142631	+	0.989776i	$0.454444\pi$
$278$	−5.81505	+	0.992541i	−0.348764	+	0.0595286i
$279$	−4.41713	+	7.65069i	−0.264446	+	0.458035i
$280$	18.3897	+	11.0241i	1.09899	+	0.658815i
$281$	0.594707	+	0.343354i	0.0354773	+	0.0204828i	0.517634	−	0.855602i	$-0.326813\pi$
$281$	0.594707	+	0.343354i	0.0354773	+	0.0204828i	−0.482156	+	0.876085i	$0.660146\pi$
$282$	−9.58899	−	11.5557i	−0.571016	−	0.688130i
$283$	12.0092	−	6.93350i	0.713871	−	0.412154i	−0.0986215	−	0.995125i	$-0.531443\pi$
$283$	12.0092	−	6.93350i	0.713871	−	0.412154i	0.812493	+	0.582971i	$0.198110\pi$
$284$	−10.6538	+	3.74601i	−0.632186	+	0.222285i
$285$	7.92593	+	9.65301i	0.469492	+	0.571795i
$286$	1.40215	+	8.21483i	0.0829106	+	0.485753i
$287$	−7.26807	−	12.5887i	−0.429021	−	0.743086i
$288$	1.13448	−	5.54193i	0.0668501	−	0.326561i
$289$	5.28703	−	9.15741i	0.311002	−	0.538671i
$290$	−8.33695	−	10.0468i	−0.489563	−	0.589971i
$291$	−2.09143	−	1.20749i	−0.122602	−	0.0707843i
$292$	−24.2297	+	8.51948i	−1.41794	+	0.498565i
$293$			12.9508i			0.756594i	0.925684	+	0.378297i	$0.123490\pi$
$293$			12.9508i			0.756594i	−0.925684	+	0.378297i	$0.876510\pi$
$294$	0.00166668		0.000616980i	9.72026e−5		3.59830e-5i
$295$	−10.9042	+	18.8867i	−0.634868	+	1.09962i
$296$	29.7832	−	16.5489i	1.73112	−	0.961885i
$297$			2.73265i			0.158564i
$298$	21.5231	+	7.96755i	1.24680	+	0.461548i
$299$	4.19928	+	7.27337i	0.242851	+	0.420630i
$300$	−1.18423	+	6.31101i	−0.0683713	+	0.364366i
$301$	2.00503	+	3.47282i	0.115568	+	0.200170i
$302$	−24.7357	+	20.5259i	−1.42338	+	1.18113i
$303$	6.64781			0.381907
$304$	−11.6365	+	12.9843i	−0.667397	+	0.744702i
$305$	4.51630			0.258603
$306$	2.75881	−	2.28929i	0.157711	−	0.130870i
$307$	15.3302	+	26.5527i	0.874940	+	1.51544i	0.856826	+	0.515605i	$0.172433\pi$
$307$	15.3302	+	26.5527i	0.874940	+	1.51544i	0.0181139	+	0.999836i	$0.494234\pi$
$308$	2.66652	−	14.2105i	0.151939	−	0.809718i
$309$	4.61114	+	7.98673i	0.262319	+	0.454349i
$310$	33.5725	+	12.4281i	1.90679	+	0.705867i
$311$		−	16.5211i		−	0.936826i	−0.883510	−	0.468413i	$-0.844826\pi$
$311$		−	16.5211i		−	0.936826i	0.883510	−	0.468413i	$-0.155174\pi$
$312$	−5.33156	+	2.96245i	−0.301840	+	0.167716i
$313$	11.5598	−	20.0221i	0.653397	−	1.13172i	−0.328897	−	0.944366i	$-0.606677\pi$
$313$	11.5598	−	20.0221i	0.653397	−	1.13172i	0.982293	−	0.187350i	$-0.0599899\pi$
$314$	11.2654	+	4.17028i	0.635742	+	0.235342i
$315$		−	7.58048i		−	0.427112i
$316$	32.7486	−	11.5148i	1.84225	−	0.647760i
$317$	9.01160	+	5.20285i	0.506142	+	0.292221i	0.731246	−	0.682114i	$-0.238939\pi$
$317$	9.01160	+	5.20285i	0.506142	+	0.292221i	−0.225104	+	0.974335i	$0.572272\pi$
$318$	4.43592	+	5.34572i	0.248754	+	0.299773i
$319$	−4.40192	+	7.62435i	−0.246460	+	0.426882i
$320$	−22.9109	−	0.753219i	−1.28076	−	0.0421062i
$321$	−5.52204	−	9.56446i	−0.308210	−	0.533836i
$322$	−2.45162	−	14.3634i	−0.136623	−	0.800443i
$323$	−10.9015	+	1.80256i	−0.606578	+	0.100297i
$324$	−1.88677	+	0.663412i	−0.104820	+	0.0368562i
$325$	5.99583	−	3.46169i	0.332589	−	0.192020i
$326$	−0.867773	−	1.04575i	−0.0480615	−	0.0579188i
$327$	8.11096	+	4.68287i	0.448537	+	0.258963i
$328$	13.3296	+	7.99070i	0.736002	+	0.441212i
$329$	14.0450	−	24.3266i	0.774325	−	1.34117i
$330$	10.9156	−	1.86313i	0.600887	−	0.102562i
$331$	−2.96358			−0.162893			−0.0814465	−	0.996678i	$-0.525954\pi$
$331$	−2.96358			−0.162893			−0.0814465	+	0.996678i	$0.525954\pi$
$332$	11.1055	+	2.08388i	0.609492	+	0.114368i
$333$	−10.4324	−	6.02315i	−0.571692	−	0.330067i
$334$	−4.22940	−	24.7790i	−0.231423	−	1.35585i
$335$	−29.9802			−1.63800
$336$	10.4590	−	1.60881i	0.570588	−	0.0877676i
$337$	17.9284	−	10.3510i	0.976625	−	0.563854i	0.0753752	−	0.997155i	$-0.475985\pi$
$337$	17.9284	−	10.3510i	0.976625	−	0.563854i	0.901249	+	0.433301i	$0.142651\pi$
$338$	−11.0740	−	4.09943i	−0.602345	−	0.222980i
$339$	17.3197	−	9.99956i	0.940679	−	0.543101i
$340$	−11.0256	−	9.45932i	−0.597947	−	0.513004i
$341$		−	24.1409i		−	1.30730i
$342$	6.05269	+	1.16830i	0.327292	+	0.0631744i
$343$			18.5219i			1.00009i
$344$	−3.67721	−	2.20438i	−0.198262	−	0.118852i
$345$	9.66466	−	5.57989i	0.520328	−	0.300411i
$346$	1.10150	−	2.97554i	0.0592172	−	0.159966i
$347$	23.9465	−	13.8255i	1.28552	−	0.742192i	0.307664	−	0.951495i	$-0.400453\pi$
$347$	23.9465	−	13.8255i	1.28552	−	0.742192i	0.977851	+	0.209303i	$0.0671193\pi$
$348$	−6.33293	−	1.18834i	−0.339481	−	0.0637017i
$349$	−20.6404			−1.10486			−0.552428	−	0.833560i	$-0.686299\pi$
$349$	−20.6404			−1.10486			−0.552428	+	0.833560i	$0.686299\pi$
$350$	−11.8406	+	2.02100i	−0.632904	+	0.108027i
$351$	1.86752	+	1.07822i	0.0996811	+	0.0575509i
$352$	4.88726	+	14.6653i	0.260492	+	0.781661i
$353$	7.25841			0.386326			0.193163	−	0.981167i	$-0.438125\pi$
$353$	7.25841			0.386326			0.193163	+	0.981167i	$0.438125\pi$
$354$	1.81097	+	10.6100i	0.0962520	+	0.563917i
$355$	8.08989	−	14.0121i	0.429367	−	0.743685i
$356$	2.00926	−	2.34196i	0.106491	−	0.124123i
$357$	5.80776	+	3.35311i	0.307379	+	0.177466i
$358$	2.93089	−	2.43207i	0.154902	−	0.128539i
$359$	31.4803	−	18.1752i	1.66147	−	0.959249i	0.689453	−	0.724330i	$-0.257851\pi$
$359$	31.4803	−	18.1752i	1.66147	−	0.959249i	0.972015	−	0.234919i	$-0.0754825\pi$
$360$	3.93643	+	7.08443i	0.207468	+	0.373382i
$361$	−14.2910	−	12.5207i	−0.752159	−	0.658982i
$362$	12.1030	−	2.06580i	0.636121	−	0.108576i
$363$	1.76632	+	3.05936i	0.0927079	+	0.160575i
$364$	−8.65950	−	7.42935i	−0.453881	−	0.389404i
$365$	18.3987	−	31.8675i	0.963031	−	1.66802i
$366$	1.71534	−	1.42340i	0.0896622	−	0.0744024i
$367$	−24.0822	−	13.9038i	−1.25708	−	0.725774i	−0.284573	−	0.958654i	$-0.591852\pi$
$367$	−24.0822	−	13.9038i	−1.25708	−	0.725774i	−0.972505	+	0.232880i	$0.925185\pi$
$368$	9.74990	+	12.1504i	0.508248	+	0.633385i
$369$		−	5.49464i		−	0.286040i
$370$	−16.9468	+	45.7792i	−0.881022	+	2.37995i
$371$	−6.49729	+	11.2536i	−0.337323	+	0.584260i
$372$	16.6682	−	5.86075i	0.864204	−	0.303866i
$373$		−	14.1662i		−	0.733496i	−0.930320	−	0.366748i	$-0.880471\pi$
$373$		−	14.1662i		−	0.733496i	0.930320	−	0.366748i	$-0.119529\pi$
$374$	−3.40094	+	9.18712i	−0.175858	+	0.475054i
$375$	2.56372	+	4.44049i	0.132390	+	0.229306i
$376$	−0.493468	+	30.0281i	−0.0254487	+	1.54858i
$377$	3.47372	+	6.01666i	0.178906	+	0.309874i
$378$	−2.38914	−	2.87915i	−0.122884	−	0.148087i
$379$	8.17116			0.419724			0.209862	−	0.977731i	$-0.432699\pi$
$379$	8.17116			0.419724			0.209862	+	0.977731i	$0.432699\pi$
$380$	0.540052	−	24.9742i	0.0277041	−	1.28115i
$381$	1.06299			0.0544587
$382$	13.9315	+	16.7888i	0.712797	+	0.858990i
$383$	−5.41972	−	9.38723i	−0.276935	−	0.479665i	0.693687	−	0.720277i	$-0.255985\pi$
$383$	−5.41972	−	9.38723i	−0.276935	−	0.479665i	−0.970621	+	0.240612i	$0.922652\pi$
$384$	−8.93920	+	6.93475i	−0.456176	+	0.353887i
$385$	10.3574	+	17.9395i	0.527861	+	0.914283i
$386$	−7.43592	+	20.0870i	−0.378478	+	1.02240i
$387$			1.51580i			0.0770524i
$388$	1.60212	+	4.55650i	0.0813355	+	0.231321i
$389$	1.89844	−	3.28819i	0.0962545	−	0.166718i	−0.813877	−	0.581037i	$-0.802647\pi$
$389$	1.89844	−	3.28819i	0.0962545	−	0.166718i	0.910132	+	0.414319i	$0.135980\pi$
$390$	3.03368	−	8.19502i	0.153616	−	0.414971i
$391$			9.87273i			0.499285i
$392$	−0.00172639	−	0.00310701i	−8.71960e−5	−	0.000156928i
$393$	7.64858	+	4.41591i	0.385820	+	0.222753i
$394$	1.84523	−	1.53118i	0.0929612	−	0.0771400i
$395$	−24.8675	+	43.0717i	−1.25122	+	2.16717i
$396$	3.55867	−	4.14792i	0.178830	−	0.208441i
$397$	14.4380	+	25.0074i	0.724625	+	1.25509i	0.959128	+	0.282971i	$0.0913202\pi$
$397$	14.4380	+	25.0074i	0.724625	+	1.25509i	−0.234504	+	0.972115i	$0.575347\pi$
$398$	−21.4216	+	3.65634i	−1.07377	+	0.183276i
$399$	1.88119	+	11.3770i	0.0941772	+	0.569565i
$400$	10.0163	−	8.03737i	0.500813	−	0.401868i
$401$	5.26528	−	3.03991i	0.262936	−	0.151806i	−0.362737	−	0.931891i	$-0.618158\pi$
$401$	5.26528	−	3.03991i	0.262936	−	0.151806i	0.625673	+	0.780085i	$0.284824\pi$
$402$	−11.3868	+	9.44887i	−0.567923	+	0.471267i
$403$	−16.4982	−	9.52523i	−0.821833	−	0.474486i
$404$	−10.0908	−	8.65732i	−0.502036	−	0.430718i
$405$	1.43271	−	2.48152i	0.0711917	−	0.123308i
$406$	−2.02802	−	11.8817i	−0.100649	−	0.589678i
$407$	32.9183			1.63170
$408$	−7.16893	−	0.117811i	−0.354915	−	0.00583252i
$409$	−10.5135	−	6.06998i	−0.519860	−	0.300141i	0.217017	−	0.976168i	$-0.430367\pi$
$409$	−10.5135	−	6.06998i	−0.519860	−	0.300141i	−0.736877	+	0.676026i	$0.763701\pi$
$410$	−21.9485	+	3.74628i	−1.08396	+	0.185015i
$411$	−20.4977			−1.01108
$412$	3.40165	−	18.1282i	0.167587	−	0.893111i
$413$	−17.4373	+	10.0674i	−0.858032	+	0.495385i
$414$	1.91212	−	5.16531i	0.0939758	−	0.253861i
$415$	−14.0197	+	8.09428i	−0.688200	+	0.397333i
$416$	11.9508	+	2.44644i	0.585936	+	0.119947i
$417$		−	4.17133i		−	0.204271i
$418$	−15.9202	+	5.50510i	−0.778683	+	0.269263i
$419$		−	29.9456i		−	1.46294i	−0.681875	−	0.731468i	$-0.738835\pi$
$419$		−	29.9456i		−	1.46294i	0.681875	−	0.731468i	$-0.261165\pi$
$420$	−9.87192	+	11.5065i	−0.481700	+	0.561461i
$421$	25.1779	−	14.5365i	1.22710	−	0.708465i	0.260676	−	0.965426i	$-0.416055\pi$
$421$	25.1779	−	14.5365i	1.22710	−	0.708465i	0.966422	+	0.256962i	$0.0827214\pi$
$422$	7.91028	+	2.92827i	0.385066	+	0.142546i
$423$	9.19542	−	5.30898i	0.447097	−	0.258131i
$424$	0.228281	−	13.8912i	0.0110863	−	0.674615i
$425$	8.13863			0.394781
$426$	−1.34357	−	7.87163i	−0.0650961	−	0.381382i
$427$	3.61108	+	2.08486i	0.174752	+	0.100893i
$428$	−4.07363	+	21.7093i	−0.196906	+	1.04936i
$429$	−5.89277			−0.284505
$430$	6.05491	−	1.03348i	0.291994	−	0.0498389i
$431$	13.2187	−	22.8955i	0.636724	−	1.10284i	−0.349423	−	0.936965i	$-0.613622\pi$
$431$	13.2187	−	22.8955i	0.636724	−	1.10284i	0.986147	−	0.165873i	$-0.0530443\pi$
$432$	3.72790	+	1.45010i	0.179359	+	0.0697679i
$433$	7.80644	+	4.50705i	0.375154	+	0.216595i	0.675708	−	0.737170i	$-0.263838\pi$
$433$	7.80644	+	4.50705i	0.375154	+	0.216595i	−0.300554	+	0.953765i	$0.597172\pi$
$434$	21.1063	+	25.4351i	1.01313	+	1.22092i
$435$	7.99478	−	4.61579i	0.383320	−	0.221310i
$436$	−6.21334	−	17.6709i	−0.297565	−	0.846285i
$437$	−13.1203	+	10.7729i	−0.627631	+	0.515337i
$438$	−3.05565	−	17.9023i	−0.146005	−	0.855406i
$439$	−1.79046	−	3.10116i	−0.0854539	−	0.148011i	0.820131	−	0.572176i	$-0.193901\pi$
$439$	−1.79046	−	3.10116i	−0.0854539	−	0.148011i	−0.905585	+	0.424166i	$0.860567\pi$
$440$	−18.9953	−	11.3872i	−0.905567	−	0.542862i
$441$	−0.000628339		0.00108832i	−2.99209e−5		5.18245e-5i
$442$	4.93669	+	5.94919i	0.234814	+	0.282974i
$443$	−24.9361	−	14.3969i	−1.18475	−	0.684015i	−0.227641	−	0.973745i	$-0.573101\pi$
$443$	−24.9361	−	14.3969i	−1.18475	−	0.684015i	−0.957108	+	0.289730i	$0.906434\pi$
$444$	7.99166	+	22.7286i	0.379267	+	1.07865i
$445$			4.42098i			0.209575i
$446$	13.6869	+	5.06671i	0.648095	+	0.239915i
$447$	−8.11424	+	14.0543i	−0.383790	+	0.664744i
$448$	−17.9711	−	11.1786i	−0.849052	−	0.528139i
$449$			6.55031i			0.309128i	0.987983	+	0.154564i	$0.0493973\pi$
$449$			6.55031i			0.309128i	−0.987983	+	0.154564i	$0.950603\pi$
$450$	−4.25805	−	1.57627i	−0.200726	−	0.0743060i
$451$	7.50746	+	13.0033i	0.353512	+	0.612301i
$452$	−39.3121	−	7.37671i	−1.84909	−	0.346971i
$453$	−11.3642	−	19.6835i	−0.533939	−	0.924809i
$454$	−8.68081	+	7.20341i	−0.407410	+	0.338073i
$455$	16.3468			0.766350
$456$	−7.66601	−	9.65569i	−0.358994	−	0.452169i
$457$	−22.7229			−1.06293			−0.531467	−	0.847079i	$-0.678359\pi$
$457$	−22.7229			−1.06293			−0.531467	+	0.847079i	$0.678359\pi$
$458$	−5.71144	+	4.73940i	−0.266878	+	0.221458i
$459$	1.26747	+	2.19532i	0.0591605	+	0.102469i
$460$	−21.9367	−	4.11631i	−1.02280	−	0.191924i
$461$	−2.15879	−	3.73913i	−0.100545	−	0.174149i	0.811364	−	0.584541i	$-0.198725\pi$
$461$	−2.15879	−	3.73913i	−0.100545	−	0.174149i	−0.911909	+	0.410392i	$0.865392\pi$
$462$	9.58785	+	3.54928i	0.446067	+	0.165128i
$463$		−	4.45527i		−	0.207054i	−0.994627	−	0.103527i	$-0.966987\pi$
$463$		−	4.45527i		−	0.207054i	0.994627	−	0.103527i	$-0.0330128\pi$
$464$	8.06529	+	10.0511i	0.374422	+	0.466608i
$465$	−12.6569	+	21.9224i	−0.586949	+	1.01663i
$466$	−16.6888	−	6.17794i	−0.773092	−	0.286187i
$467$			29.6919i			1.37398i	0.726669	+	0.686988i	$0.241067\pi$
$467$			29.6919i			1.37398i	−0.726669	+	0.686988i	$0.758933\pi$
$468$	−1.43060	−	4.06868i	−0.0661296	−	0.188075i
$469$	−23.9711	−	13.8397i	−1.10688	−	0.639060i
$470$	−27.4764	−	33.1117i	−1.26739	−	1.52733i
$471$	−4.24706	+	7.35612i	−0.195694	+	0.338952i
$472$	11.0684	−	18.4635i	0.509462	−	0.849852i
$473$	−2.07107	−	3.58720i	−0.0952280	−	0.164940i
$474$	4.12999	+	24.1966i	0.189697	+	1.11139i
$475$	8.88068	+	10.8158i	0.407474	+	0.496263i
$476$	−4.44899	−	12.6531i	−0.203919	−	0.579953i
$477$	−4.25386	+	2.45597i	−0.194771	+	0.112451i
$478$	−9.39197	−	11.3182i	−0.429579	−	0.517684i
$479$	−0.612140	−	0.353419i	−0.0279694	−	0.0161481i	0.485950	−	0.873987i	$-0.338474\pi$
$479$	−0.612140	−	0.353419i	−0.0279694	−	0.0161481i	−0.513920	+	0.857838i	$0.671807\pi$
$480$	3.25076	−	15.8799i	0.148376	−	0.724815i
$481$	12.9885	−	22.4968i	0.592225	−	1.02576i
$482$	−22.0085	+	3.75651i	−1.00246	+	0.171104i
$483$	10.3034			0.468819
$484$	1.30302	−	6.94409i	0.0592283	−	0.315641i
$485$	−5.99281	−	3.45995i	−0.272120	−	0.157108i
$486$	−0.237943	−	1.39405i	−0.0107933	−	0.0632355i
$487$	2.51995			0.114190			0.0570950	−	0.998369i	$-0.481816\pi$
$487$	2.51995			0.114190			0.0570950	+	0.998369i	$0.481816\pi$
$488$	−4.45741	−	0.0732511i	−0.201777	−	0.00331592i
$489$	0.832157	−	0.480446i	0.0376314	−	0.0217265i
$490$	0.00477572	+	0.00176790i	0.000215745	+	7.98657e-5i
$491$	−1.58171	+	0.913203i	−0.0713817	+	0.0412123i	−0.535266	−	0.844684i	$-0.679789\pi$
$491$	−1.58171	+	0.913203i	−0.0713817	+	0.0412123i	0.463884	+	0.885896i	$0.346455\pi$
$492$	−7.15557	+	8.34039i	−0.322598	+	0.376014i
$493$			8.16690i			0.367819i
$494$	−2.51936	+	13.0522i	−0.113351	+	0.587247i
$495$			7.83015i			0.351939i
$496$	−32.9332	−	12.8105i	−1.47874	−	0.575210i
$497$	12.9368	−	7.46906i	0.580294	−	0.335033i
$498$	−2.77376	+	7.49289i	−0.124295	+	0.335764i
$499$	−1.45988	+	0.842864i	−0.0653534	+	0.0377318i	−0.532321	−	0.846543i	$-0.678680\pi$
$499$	−1.45988	+	0.842864i	−0.0653534	+	0.0377318i	0.466967	+	0.884275i	$0.345347\pi$
$500$	1.89126	−	10.0790i	0.0845798	−	0.450745i
$501$	17.7748			0.794120
$502$	5.99042	−	1.02247i	0.267366	−	0.0456352i
$503$	−0.506143	−	0.292222i	−0.0225678	−	0.0130295i	0.488674	−	0.872467i	$-0.337481\pi$
$503$	−0.506143	−	0.292222i	−0.0225678	−	0.0130295i	−0.511241	+	0.859437i	$0.670814\pi$
$504$	−0.122950	+	7.48163i	−0.00547662	+	0.333258i
$505$	19.0487			0.847656
$506$	2.53236	+	14.8365i	0.112577	+	0.659563i
$507$	4.17490	−	7.23114i	0.185414	−	0.321146i
$508$	−1.61353	−	1.38431i	−0.0715888	−	0.0614190i
$509$	−27.4296	−	15.8365i	−1.21579	−	0.701939i	−0.251778	−	0.967785i	$-0.581015\pi$
$509$	−27.4296	−	15.8365i	−1.21579	−	0.701939i	−0.964015	+	0.265846i	$0.914349\pi$
$510$	7.90513	−	6.55974i	0.350045	−	0.290470i
$511$	29.4219	−	16.9867i	1.30155	−	0.751449i
$512$	22.5999	+	1.11499i	0.998785	+	0.0492763i
$513$	−1.53443	+	4.07989i	−0.0677470	+	0.180132i
$514$	38.7667	−	6.61689i	1.70993	−	0.291858i
$515$	13.2128	+	22.8853i	0.582226	+	1.00845i
$516$	1.97400	−	2.30085i	0.0869004	−	0.101289i
$517$	−14.5076	+	25.1278i	−0.638042	+	1.10512i
$518$	−34.6831	+	28.7803i	−1.52389	+	1.26453i
$519$	1.94298	+	1.12178i	0.0852875	+	0.0492408i
$520$	−15.2771	+	8.48864i	−0.669945	+	0.372251i
$521$		−	9.96539i		−	0.436592i	−0.975883	−	0.218296i	$-0.929950\pi$
$521$		−	9.96539i		−	0.436592i	0.975883	−	0.218296i	$-0.0700498\pi$
$522$	1.58174	−	4.27284i	0.0692310	−	0.187017i
$523$	6.71352	−	11.6282i	0.293562	−	0.508464i	−0.681088	−	0.732202i	$-0.738493\pi$
$523$	6.71352	−	11.6282i	0.293562	−	0.508464i	0.974649	+	0.223738i	$0.0718261\pi$
$524$	−5.85913	−	16.6636i	−0.255957	−	0.727951i
$525$		−	8.49362i		−	0.370692i
$526$	−11.3348	+	30.6193i	−0.494222	+	1.33507i
$527$	−11.1972	−	19.3941i	−0.487756	−	0.844818i
$528$	−10.8035	+	1.66179i	−0.470163	+	0.0723203i
$529$	−3.91583	−	6.78242i	−0.170254	−	0.294888i
$530$	12.7107	+	15.3177i	0.552119	+	0.665358i
$531$	−7.61093			−0.330286
$532$	11.9606	−	19.7192i	0.518559	−	0.854937i
$533$	11.8488			0.513229
$534$	1.39336	+	1.67914i	0.0602966	+	0.0726633i
$535$	−15.8229	−	27.4061i	−0.684085	−	1.18487i
$536$	29.5893	+	0.486257i	1.27806	+	0.0210031i
$537$	1.34653	+	2.33225i	0.0581069	+	0.100644i
$538$	−13.2238	+	35.7221i	−0.570119	+	1.54009i
$539$		−	0.00343406i		−	0.000147915i
$540$	−5.40636	+	1.90095i	−0.232653	+	0.0818037i
$541$	−8.23202	+	14.2583i	−0.353922	+	0.613011i	−0.986933	−	0.161132i	$-0.948486\pi$
$541$	−8.23202	+	14.2583i	−0.353922	+	0.613011i	0.633011	+	0.774143i	$0.281819\pi$
$542$	9.05665	−	24.4652i	0.389016	−	1.05087i
$543$			8.68190i			0.372576i
$544$	10.7284	+	9.51480i	0.459976	+	0.407943i
$545$	23.2412	+	13.4183i	0.995545	+	0.574778i
$546$	6.20869	−	5.15202i	0.265707	−	0.220486i
$547$	−3.77873	+	6.54495i	−0.161567	+	0.279842i	−0.935431	−	0.353510i	$-0.884988\pi$
$547$	−3.77873	+	6.54495i	−0.161567	+	0.279842i	0.773864	+	0.633352i	$0.218321\pi$
$548$	31.1138	+	26.6938i	1.32911	+	1.14030i
$549$	0.788072	+	1.36498i	0.0336341	+	0.0582560i
$550$	12.2305	−	2.08757i	0.521512	−	0.0890141i
$551$	−10.8534	+	8.91153i	−0.462369	+	0.379644i
$552$	−9.62913	+	5.35038i	−0.409843	+	0.227727i
$553$	−39.7663	+	22.9591i	−1.69104	+	0.976320i
$554$	5.16698	−	4.28760i	0.219524	−	0.182163i
$555$	−29.8931	−	17.2588i	−1.26889	−	0.732595i
$556$	−5.43224	+	6.33172i	−0.230378	+	0.268525i
$557$	−16.7655	+	29.0386i	−0.710376	+	1.23041i	0.254340	+	0.967115i	$0.418142\pi$
$557$	−16.7655	+	29.0386i	−0.710376	+	1.23041i	−0.964716	+	0.263292i	$0.915192\pi$
$558$	2.10205	+	12.3154i	0.0889870	+	0.521353i
$559$	−3.26872			−0.138252
$560$	29.9695	−	4.60989i	1.26644	−	0.194804i
$561$	−5.99905	−	3.46355i	−0.253280	−	0.146231i
$562$	0.957308	−	0.163398i	0.0403816	−	0.00689252i
$563$	−8.75511			−0.368984			−0.184492	−	0.982834i	$-0.559064\pi$
$563$	−8.75511			−0.368984			−0.184492	+	0.982834i	$0.559064\pi$
$564$	−20.8716	−	3.91645i	−0.878855	−	0.164912i
$565$	49.6282	−	28.6528i	2.08787	−	1.20543i
$566$	6.80816	−	18.3912i	0.286168	−	0.773040i
$567$	2.29108	−	1.32276i	0.0962164	−	0.0555506i
$568$	−8.21166	+	13.6982i	−0.344554	+	0.574762i
$569$			6.32953i			0.265348i	0.991160	+	0.132674i	$0.0423563\pi$
$569$			6.32953i			0.265348i	−0.991160	+	0.132674i	$0.957644\pi$
$570$	17.3434	+	3.34766i	0.726437	+	0.140218i
$571$		−	20.2768i		−	0.848559i	−0.905531	−	0.424279i	$-0.860527\pi$
$571$		−	20.2768i		−	0.848559i	0.905531	−	0.424279i	$-0.139473\pi$
$572$	8.94471	+	7.67404i	0.373997	+	0.320868i
$573$	−13.3597	+	7.71322i	−0.558109	+	0.322224i
$574$	−19.2787	−	7.13669i	−0.804676	−	0.297879i
$575$	10.8289	−	6.25204i	0.451594	−	0.260728i
$576$	−3.77019	−	7.05590i	−0.157091	−	0.293996i
$577$	11.2386			0.467870			0.233935	−	0.972252i	$-0.424840\pi$
$577$	11.2386			0.467870			0.233935	+	0.972252i	$0.424840\pi$
$578$	−2.51603	−	14.7408i	−0.104653	−	0.613137i
$579$	−13.1165	−	7.57281i	−0.545103	−	0.314715i
$580$	−18.1464	−	3.40508i	−0.753490	−	0.141388i
$581$	−14.9462			−0.620074
$582$	−3.36661	+	0.574628i	−0.139550	+	0.0238191i
$583$	6.71129	−	11.6243i	0.277953	−	0.481429i
$584$	−18.6756	+	31.1535i	−0.772803	+	1.28914i
$585$	5.35123	+	3.08953i	0.221246	+	0.127736i
$586$	11.6958	+	14.0945i	0.483147	+	0.582240i
$587$	−18.7495	+	10.8250i	−0.773874	+	0.446797i	−0.834255	−	0.551379i	$-0.814102\pi$
$587$	−18.7495	+	10.8250i	−0.773874	+	0.446797i	0.0603806	+	0.998175i	$0.480769\pi$
$588$	0.00237106		0.000833695i	9.77808e−5		3.43810e-5i
$589$	13.5556	−	36.0428i	0.558548	−	1.48512i
$590$	5.18917	+	30.4021i	0.213635	+	1.25163i
$591$	0.847746	+	1.46834i	0.0348716	+	0.0603994i
$592$	17.4683	−	44.9074i	0.717944	−	1.84568i
$593$	10.8984	−	18.8765i	0.447542	−	0.775166i	−0.550683	−	0.834714i	$-0.685633\pi$
$593$	10.8984	−	18.8765i	0.447542	−	0.775166i	0.998225	+	0.0595485i	$0.0189661\pi$
$594$	2.46783	+	2.97398i	0.101256	+	0.122024i
$595$	16.6416	+	9.60804i	0.682240	+	0.393891i
$596$	30.6193	−	10.7662i	1.25422	−	0.440999i
$597$		−	15.3664i		−	0.628906i
$598$	11.1386	+	4.12337i	0.455493	+	0.168617i
$599$	−12.9904	+	22.5000i	−0.530773	+	0.919326i	0.468582	+	0.883420i	$0.344765\pi$
$599$	−12.9904	+	22.5000i	−0.530773	+	0.919326i	−0.999355	+	0.0359059i	$0.988568\pi$
$600$	4.41061	+	7.93782i	0.180062	+	0.324060i
$601$			5.80590i			0.236828i	0.992964	+	0.118414i	$0.0377809\pi$
$601$			5.80590i			0.236828i	−0.992964	+	0.118414i	$0.962219\pi$
$602$	5.31838	+	1.96879i	0.216761	+	0.0802418i
$603$	−5.23140	−	9.06106i	−0.213039	−	0.368995i
$604$	−8.38344	+	44.6772i	−0.341117	+	1.81789i
$605$	5.06124	+	8.76632i	0.205769	+	0.356402i
$606$	7.23490	−	6.00358i	0.293898	−	0.243879i
$607$	−16.2119			−0.658022			−0.329011	−	0.944326i	$-0.606715\pi$
$607$	−16.2119			−0.658022			−0.329011	+	0.944326i	$0.606715\pi$
$608$	−0.938073	+	24.6398i	−0.0380439	+	0.999276i
$609$	8.52313			0.345375
$610$	4.91515	−	4.07863i	0.199009	−	0.165139i
$611$	11.4485	+	19.8293i	0.463155	+	0.802208i
$612$	0.935018	−	4.98292i	0.0377959	−	0.201423i
$613$	−11.3947	−	19.7362i	−0.460227	−	0.797136i	0.538745	−	0.842469i	$-0.318899\pi$
$613$	−11.3947	−	19.7362i	−0.460227	−	0.797136i	−0.998972	+	0.0453327i	$0.985565\pi$
$614$	40.6635	+	15.0531i	1.64105	+	0.607492i
$615$		−	15.7444i		−	0.634876i
$616$	−9.93136	−	17.8736i	−0.400146	−	0.720147i
$617$	−16.2450	+	28.1372i	−0.653999	+	1.13276i	0.328144	+	0.944628i	$0.393577\pi$
$617$	−16.2450	+	28.1372i	−0.653999	+	1.13276i	−0.982144	+	0.188132i	$0.939757\pi$
$618$	12.2311	+	4.52778i	0.492008	+	0.182134i
$619$		−	6.61987i		−	0.266075i	−0.991111	−	0.133037i	$-0.957527\pi$
$619$		−	6.61987i		−	0.266075i	0.991111	−	0.133037i	$-0.0424731\pi$
$620$	47.7611	−	16.7934i	1.91813	−	0.674441i
$621$	3.37287	+	1.94733i	0.135349	+	0.0781436i
$622$	−14.9201	−	17.9801i	−0.598241	−	0.720938i
$623$	−2.04085	+	3.53486i	−0.0817651	+	0.141621i
$624$	−3.12704	+	8.03896i	−0.125182	+	0.321816i
$625$	15.3725	+	26.6260i	0.614902	+	1.06504i
$626$	−5.50114	−	32.2298i	−0.219870	−	1.28816i
$627$	−1.94315	−	11.7518i	−0.0776018	−	0.469320i
$628$	16.0264	−	5.63509i	0.639523	−	0.224865i
$629$	26.4456	−	15.2683i	1.05445	−	0.608789i
$630$	−6.84587	−	8.24994i	−0.272746	−	0.328685i
$631$	6.62256	+	3.82354i	0.263640	+	0.152213i	0.625994	−	0.779828i	$-0.284693\pi$
$631$	6.62256	+	3.82354i	0.263640	+	0.152213i	−0.362354	+	0.932041i	$0.618027\pi$
$632$	25.2418	−	42.1067i	1.00406	−	1.67492i
$633$	−2.98218	+	5.16529i	−0.118531	+	0.205302i
$634$	14.5061	−	2.47597i	0.576111	−	0.0983333i
$635$	3.04591			0.120873
$636$	9.65535	+	1.81177i	0.382860	+	0.0718415i
$637$	−0.00234688	−	0.00135497i	−9.29867e−5	−	5.36859e-5i
$638$	2.09482	+	12.2730i	0.0829346	+	0.485894i
$639$	5.64658			0.223375
$640$	−25.6145	+	19.8709i	−1.01250	+	0.785466i
$641$	−34.0636	+	19.6666i	−1.34543	+	0.776785i	−0.987598	−	0.157001i	$-0.949817\pi$
$641$	−34.0636	+	19.6666i	−1.34543	+	0.776785i	−0.357833	+	0.933786i	$0.616484\pi$
$642$	−14.6473	−	5.42222i	−0.578083	−	0.213998i
$643$	26.2592	−	15.1608i	1.03556	−	0.597882i	0.116989	−	0.993133i	$-0.462676\pi$
$643$	26.2592	−	15.1608i	1.03556	−	0.597882i	0.918573	+	0.395251i	$0.129342\pi$
$644$	−15.6396	−	13.4179i	−0.616287	−	0.528738i
$645$			4.34339i			0.171021i
$646$	−10.2364	+	11.8068i	−0.402746	+	0.464534i
$647$			16.9422i			0.666068i	0.942915	+	0.333034i	$0.108072\pi$
$647$			16.9422i			0.666068i	−0.942915	+	0.333034i	$0.891928\pi$
$648$	−1.45427	+	2.42592i	−0.0571292	+	0.0952992i
$649$	18.0116	−	10.3990i	0.707016	−	0.408196i
$650$	3.39912	−	9.18219i	0.133324	−	0.360155i
$651$	−20.2400	+	11.6856i	−0.793268	+	0.457994i
$652$	−1.88882	−	0.354427i	−0.0739718	−	0.0138804i
$653$	−20.3739			−0.797293			−0.398647	−	0.917105i	$-0.630520\pi$
$653$	−20.3739			−0.797293			−0.398647	+	0.917105i	$0.630520\pi$
$654$	13.0563	−	2.22852i	0.510543	−	0.0871419i
$655$	21.9163	+	12.6534i	0.856341	+	0.494409i
$656$	21.7231	−	3.34144i	0.848144	−	0.130461i
$657$	12.8419			0.501011
$658$	−6.68382	−	39.1589i	−0.260563	−	1.52657i
$659$	−9.33757	+	16.1732i	−0.363740	+	0.630017i	−0.988573	−	0.150742i	$-0.951834\pi$
$659$	−9.33757	+	16.1732i	−0.363740	+	0.630017i	0.624833	+	0.780758i	$0.285167\pi$
$660$	10.1971	−	11.8855i	0.396920	−	0.462642i
$661$	−4.59355	−	2.65209i	−0.178668	−	0.103154i	0.407999	−	0.912983i	$-0.366227\pi$
$661$	−4.59355	−	2.65209i	−0.178668	−	0.103154i	−0.586667	+	0.809828i	$0.699560\pi$
$662$	−3.22530	+	2.67638i	−0.125355	+	0.104020i
$663$	−4.73407	+	2.73322i	−0.183856	+	0.106149i
$664$	13.9682	−	7.76134i	0.542070	−	0.301198i
$665$	5.39037	+	32.5999i	0.209030	+	1.26417i
$666$	−16.7932	+	2.86634i	−0.650723	+	0.111068i
$667$	6.27376	+	10.8665i	0.242921	+	0.420751i
$668$	−26.9806	−	23.1478i	−1.04391	−	0.895616i
$669$	−5.15998	+	8.93736i	−0.199497	+	0.345538i
$670$	−32.6279	+	27.0749i	−1.26053	+	1.04599i
$671$	−3.73001	−	2.15352i	−0.143995	−	0.0831358i
$672$	9.92982	−	11.1964i	0.383051	−	0.431909i
$673$			46.2022i			1.78096i	0.455018	+	0.890482i	$0.349633\pi$
$673$			46.2022i			1.78096i	−0.455018	+	0.890482i	$0.650367\pi$
$674$	10.1639	−	27.4561i	0.391498	−	1.05757i
$675$	1.60529	−	2.78044i	0.0617876	−	0.107019i
$676$	−15.7541	+	5.53935i	−0.605928	+	0.213052i
$677$		−	6.63900i		−	0.255157i	−0.991828	−	0.127579i	$-0.959279\pi$
$677$		−	6.63900i		−	0.255157i	0.991828	−	0.127579i	$-0.0407205\pi$
$678$	9.81879	−	26.5240i	0.377088	−	1.01865i
$679$	−3.19443	−	5.53291i	−0.122591	−	0.212334i
$680$	−20.5419	−	0.337577i	−0.787747	−	0.0129455i
$681$	−3.98819	−	6.90775i	−0.152828	−	0.264706i
$682$	−21.8014	−	26.2729i	−0.834820	−	1.00604i
$683$	17.9771			0.687875			0.343938	−	0.938992i	$-0.388239\pi$
$683$	17.9771			0.687875			0.343938	+	0.938992i	$0.388239\pi$
$684$	7.64231	−	4.19466i	0.292211	−	0.160387i
$685$	−58.7343			−2.24412
$686$	16.7270	+	20.1577i	0.638639	+	0.769623i
$687$	−2.62399	−	4.54488i	−0.100111	−	0.173398i
$688$	−5.99272	+	0.921798i	−0.228470	+	0.0351432i
$689$	−5.29612	−	9.17316i	−0.201766	−	0.349469i
$690$	5.47902	−	14.8007i	0.208583	−	0.563455i
$691$			5.97635i			0.227351i	0.993518	+	0.113675i	$0.0362624\pi$
$691$			5.97635i			0.227351i	−0.993518	+	0.113675i	$0.963738\pi$
$692$	−1.48841	−	4.23308i	−0.0565807	−	0.160918i
$693$	−3.61463	+	6.26072i	−0.137308	+	0.237825i
$694$	13.5756	−	36.6724i	0.515322	−	1.39206i
$695$		−	11.9526i		−	0.453387i
$696$	−7.96539	+	4.42593i	−0.301927	+	0.167764i
$697$	12.0625	+	6.96430i	0.456901	+	0.263792i
$698$	−22.4633	+	18.6402i	−0.850247	+	0.705542i
$699$	6.29168	−	10.8975i	0.237973	−	0.412181i
$700$	−11.0611	+	12.8926i	−0.418070	+	0.487294i
$701$	10.7697	+	18.6537i	0.406766	+	0.704540i	0.994525	−	0.104496i	$-0.0333230\pi$
$701$	10.7697	+	18.6537i	0.406766	+	0.704540i	−0.587759	+	0.809036i	$0.699990\pi$
$702$	3.00618	−	0.513109i	0.113461	−	0.0193661i
$703$	49.1476	+	18.4843i	1.85364	+	0.697147i
$704$	18.5629	+	11.5468i	0.699617	+	0.435185i
$705$	26.3487	−	15.2124i	0.992348	−	0.572932i
$706$	7.89942	−	6.55501i	0.297299	−	0.246701i
$707$	15.2307	+	8.79344i	0.572809	+	0.330711i
$708$	11.5527	+	9.91157i	0.434178	+	0.372500i
$709$	−13.0879	+	22.6689i	−0.491526	+	0.851348i	−0.999952	−	0.00975743i	$-0.996894\pi$
$709$	−13.0879	+	22.6689i	−0.491526	+	0.851348i	0.508426	+	0.861105i	$0.330227\pi$
$710$	−3.84987	−	22.5555i	−0.144483	−	0.846491i
$711$	−17.3570			−0.650938
$712$	0.0717050	−	4.36333i	0.00268726	−	0.163523i
$713$	−29.7968	−	17.2032i	−1.11590	−	0.644264i
$714$	9.34883	−	1.59570i	0.349871	−	0.0597177i
$715$	−16.8852			−0.631470
$716$	0.993338	−	5.29372i	0.0371228	−	0.197836i
$717$	9.00649	−	5.19990i	0.336354	−	0.194194i
$718$	17.8466	−	48.2099i	0.666030	−	1.79918i
$719$	8.14319	−	4.70147i	0.303690	−	0.175335i	−0.340409	−	0.940277i	$-0.610566\pi$
$719$	8.14319	−	4.70147i	0.303690	−	0.175335i	0.644099	+	0.764942i	$0.277232\pi$
$720$	10.6820	+	4.15513i	0.398093	+	0.154852i
$721$			24.3977i			0.908617i
$722$	−26.8604	−	0.720297i	−0.999641	−	0.0268067i
$723$		−	15.7874i		−	0.587140i
$724$	11.3063	−	13.1784i	0.420194	−	0.489770i
$725$	8.95782	−	5.17180i	0.332685	−	0.192076i
$726$	4.68519	+	1.73439i	0.173884	+	0.0643693i
$727$	−9.47912	+	5.47277i	−0.351561	+	0.202974i	−0.665373	−	0.746511i	$-0.731727\pi$
$727$	−9.47912	+	5.47277i	−0.351561	+	0.202974i	0.313811	+	0.949485i	$0.398394\pi$
$728$	−16.1336	−	0.265133i	−0.597952	−	0.00982648i
$729$	1.00000			0.0370370
$730$	−8.75570	−	51.2975i	−0.324063	−	1.89861i
$731$	−3.32767	−	1.92123i	−0.123078	−	0.0710593i
$732$	0.581363	−	3.09822i	0.0214878	−	0.114513i
$733$	7.49814			0.276950			0.138475	−	0.990366i	$-0.455780\pi$
$733$	7.49814			0.276950			0.138475	+	0.990366i	$0.455780\pi$
$734$	−38.7654	+	6.61665i	−1.43086	+	0.244225i
$735$	−0.00180045	+	0.00311847i	−6.64106e−5	+	0.000115026i
$736$	21.5839	+	4.41843i	0.795593	+	0.162865i
$737$	24.7607	+	14.2956i	0.912071	+	0.526584i
$738$	−4.96216	−	5.97989i	−0.182660	−	0.220123i
$739$	−25.4925	+	14.7181i	−0.937758	+	0.541415i	−0.889257	−	0.457409i	$-0.848778\pi$
$739$	−25.4925	+	14.7181i	−0.937758	+	0.541415i	−0.0485009	+	0.998823i	$0.515444\pi$
$740$	22.8994	+	65.1266i	0.841798	+	2.39410i
$741$	−8.79801	−	3.30890i	−0.323203	−	0.121556i
$742$	3.09198	+	18.1151i	0.113510	+	0.665027i
$743$	−10.1494	−	17.5793i	−0.372345	−	0.644921i	0.617581	−	0.786508i	$-0.288113\pi$
$743$	−10.1494	−	17.5793i	−0.372345	−	0.644921i	−0.989926	+	0.141587i	$0.954780\pi$
$744$	12.8474	−	21.4312i	0.471009	−	0.785706i
$745$	−23.2506	+	40.2713i	−0.851837	+	1.47542i
$746$	−12.7933	−	15.4172i	−0.468398	−	0.564465i
$747$	−4.89274	−	2.82482i	−0.179016	−	0.103355i
$748$	4.59552	+	13.0698i	0.168029	+	0.477880i
$749$		−	29.2173i		−	1.06758i
$750$	6.80029	+	2.51737i	0.248312	+	0.0919214i
$751$	4.68855	−	8.12080i	0.171087	−	0.296332i	−0.767713	−	0.640794i	$-0.778605\pi$
$751$	4.68855	−	8.12080i	0.171087	−	0.296332i	0.938800	+	0.344462i	$0.111939\pi$
$752$	26.5810	+	33.1256i	0.969311	+	1.20797i
$753$			4.29713i			0.156596i
$754$	9.21409	+	3.41092i	0.335557	+	0.124218i
$755$	−32.5632	−	56.4012i	−1.18510	−	2.05265i
$756$	−5.20027	−	0.975802i	−0.189132	−	0.0354896i
$757$	−11.3062	−	19.5829i	−0.410930	−	0.711752i	0.584062	−	0.811709i	$-0.301463\pi$
$757$	−11.3062	−	19.5829i	−0.410930	−	0.711752i	−0.994992	+	0.0999576i	$0.968129\pi$
$758$	8.89278	−	7.37930i	0.323000	−	0.268028i
$759$	−10.6427			−0.386306
$760$	−21.9663	−	27.6675i	−0.796800	−	1.00361i
$761$	22.6617			0.821484			0.410742	−	0.911752i	$-0.365270\pi$
$761$	22.6617			0.821484			0.410742	+	0.911752i	$0.365270\pi$
$762$	1.15687	−	0.959978i	0.0419089	−	0.0347763i
$763$	12.3886	+	21.4577i	0.448497	+	0.776820i
$764$	30.3236	+	5.69007i	1.09707	+	0.205859i
$765$	3.63183	+	6.29051i	0.131309	+	0.227434i
$766$	−14.3759	−	5.32174i	−0.519422	−	0.192282i
$767$		−	16.4125i		−	0.592619i
$768$	−3.46593	+	15.6201i	−0.125066	+	0.563642i
$769$	23.0145	−	39.8622i	0.829923	−	1.43747i	−0.0681747	−	0.997673i	$-0.521718\pi$
$769$	23.0145	−	39.8622i	0.829923	−	1.43747i	0.898098	−	0.439796i	$-0.144949\pi$
$770$	27.4731	+	10.1702i	0.990062	+	0.366507i
$771$			27.8086i			1.00150i
$772$	10.0478	+	28.5763i	0.361628	+	1.02848i
$773$	0.612546	+	0.353654i	0.0220318	+	0.0127200i	0.510975	−	0.859595i	$-0.329284\pi$
$773$	0.612546	+	0.353654i	0.0220318	+	0.0127200i	−0.488944	+	0.872315i	$0.662618\pi$
$774$	1.36891	+	1.64966i	0.0492043	+	0.0592960i
$775$	−14.1815	+	24.5631i	−0.509415	+	0.882333i
$776$	5.85855	+	3.51203i	0.210310	+	0.126075i
$777$	−15.9343	−	27.5991i	−0.571641	−	0.990111i
$778$	−0.903441	−	5.29304i	−0.0323899	−	0.189765i
$779$	3.90716	+	23.6297i	0.139989	+	0.846623i
$780$	−4.09926	−	11.6584i	−0.146777	−	0.417439i
$781$	−13.3629	+	7.71506i	−0.478161	+	0.276066i
$782$	8.91598	+	10.7446i	0.318835	+	0.384227i
$783$	2.79010	+	1.61086i	0.0997100	+	0.0575676i
$784$	−0.00468477	−	0.00182231i	−0.000167313	−	6.50824e-5i
$785$	−12.1696	+	21.0783i	−0.434350	+	0.752316i
$786$	12.3120	−	2.10147i	0.439155	−	0.0749570i
$787$	−18.5369			−0.660769			−0.330385	−	0.943846i	$-0.607178\pi$
$787$	−18.5369			−0.660769			−0.330385	+	0.943846i	$0.607178\pi$
$788$	0.625385	−	3.33282i	0.0222784	−	0.118727i
$789$	−19.9939	−	11.5435i	−0.711803	−	0.410960i
$790$	11.8341	+	69.3331i	0.421039	+	2.46676i
$791$	52.9079			1.88119
$792$	0.126999	−	7.72805i	0.00451272	−	0.274604i
$793$	−2.94349	+	1.69942i	−0.104526	+	0.0603483i
$794$	38.2971	+	14.1770i	1.35911	+	0.503124i
$795$	−12.1890	+	7.03735i	−0.432301	+	0.249589i
$796$	−20.0114	+	23.3249i	−0.709285	+	0.826729i
$797$		−	9.45153i		−	0.334790i	−0.985890	−	0.167395i	$-0.946464\pi$
$797$		−	9.45153i		−	0.334790i	0.985890	−	0.167395i	$-0.0535356\pi$
$798$	12.3218	+	10.6829i	0.436188	+	0.378171i
$799$			26.9159i			0.952217i
$800$	3.64235	−	17.7928i	0.128776	−	0.629070i
$801$	−1.33617	+	0.771439i	−0.0472113	+	0.0272575i
$802$	2.98496	−	8.06341i	0.105402	−	0.284729i
$803$	−30.3909	+	17.5462i	−1.07247	+	0.619193i
$804$	−3.85922	+	20.5667i	−0.136104	+	0.725330i
$805$	29.5234			1.04056
$806$	−26.5574	+	4.53293i	−0.935443	+	0.159666i
$807$	−23.3260	−	13.4673i	−0.821113	−	0.474070i
$808$	−18.8003	−	0.308956i	−0.661393	−	0.0108690i
$809$	−43.4906			−1.52905			−0.764524	−	0.644596i	$-0.777026\pi$
$809$	−43.4906			−1.52905			−0.764524	+	0.644596i	$0.777026\pi$
$810$	−0.681806	−	3.99453i	−0.0239562	−	0.140354i
$811$	26.7843	−	46.3918i	0.940525	−	1.62904i	0.176053	−	0.984381i	$-0.443667\pi$
$811$	26.7843	−	46.3918i	0.940525	−	1.62904i	0.764472	−	0.644657i	$-0.223000\pi$
$812$	−12.9374	−	11.0995i	−0.454013	−	0.389516i
$813$	15.9754	+	9.22339i	0.560281	+	0.323478i
$814$	35.8254	−	29.7282i	1.25568	−	1.04197i
$815$	2.38447	−	1.37667i	0.0835244	−	0.0482228i
$816$	−7.90844	+	6.34599i	−0.276851	+	0.222154i
$817$	−1.07786	−	6.51870i	−0.0377097	−	0.228061i
$818$	−16.9238	+	2.88863i	−0.591725	+	0.100998i
$819$	2.85244	+	4.94056i	0.0996722	+	0.172637i
$820$	−20.5036	+	23.8986i	−0.716018	+	0.834577i
$821$	8.34812	−	14.4594i	0.291351	−	0.504635i	−0.682778	−	0.730626i	$-0.739228\pi$
$821$	8.34812	−	14.4594i	0.291351	−	0.504635i	0.974130	+	0.225990i	$0.0725618\pi$
$822$	−22.3079	+	18.5113i	−0.778078	+	0.645656i
$823$	−0.302319	−	0.174544i	−0.0105382	−	0.00608423i	0.494722	−	0.869051i	$-0.335270\pi$
$823$	−0.302319	−	0.174544i	−0.0105382	−	0.00608423i	−0.505260	+	0.862967i	$0.668603\pi$
$824$	−12.6693	−	22.8011i	−0.441357	−	0.794315i
$825$			8.77337i			0.305449i
$826$	−9.88541	+	26.7039i	−0.343958	+	0.929149i
$827$	0.101413	−	0.175653i	0.00352648	−	0.00610804i	−0.864257	−	0.503051i	$-0.832211\pi$
$827$	0.101413	−	0.175653i	0.00352648	−	0.00610804i	0.867783	+	0.496943i	$0.165544\pi$
$828$	−2.58376	−	7.34830i	−0.0897918	−	0.255371i
$829$			44.0142i			1.52868i	0.644815	+	0.764339i	$0.276934\pi$
$829$			44.0142i			1.52868i	−0.644815	+	0.764339i	$0.723066\pi$
$830$	−7.94796	+	21.4702i	−0.275878	+	0.745241i
$831$	2.37385	+	4.11162i	0.0823478	+	0.142631i
$832$	15.2156	−	8.13016i	0.527505	−	0.281863i
$833$	−0.00159280	−	0.00275882i	−5.51874e−5	−	9.55873e-5i
$834$	−3.76709	−	4.53971i	−0.130444	−	0.157197i
$835$	50.9321			1.76258
$836$	−12.3546	+	20.3687i	−0.427292	+	0.704466i
$837$	−8.83425			−0.305356
$838$	−27.0436	−	32.5902i	−0.934205	−	1.12581i
$839$	−3.76071	−	6.51373i	−0.129834	−	0.224879i	0.793778	−	0.608207i	$-0.208111\pi$
$839$	−3.76071	−	6.51373i	−0.129834	−	0.224879i	−0.923612	+	0.383328i	$0.874778\pi$
$840$	−0.352302	+	21.4379i	−0.0121556	+	0.739679i
$841$	−9.31023	−	16.1258i	−0.321043	−	0.556062i
$842$	14.2737	−	38.5582i	0.491904	−	1.32880i
$843$			0.686709i			0.0236515i
$844$	11.2534	−	3.95683i	0.387357	−	0.136200i
$845$	11.9628	−	20.7202i	0.411533	−	0.712796i
$846$	5.21301	−	14.0821i	0.179227	−	0.484154i
$847$			9.34566i			0.321121i
$848$	−12.2966	−	15.3241i	−0.422265	−	0.526232i
$849$	12.0092	+	6.93350i	0.412154	+	0.237957i
$850$	8.85738	−	7.34992i	0.303805	−	0.252100i
$851$	23.4581	−	40.6306i	0.804133	−	1.39280i
$852$	−8.57103	−	7.35344i	−0.293639	−	0.251925i
$853$	−14.0714	−	24.3724i	−0.481797	−	0.834497i	0.517985	−	0.855390i	$-0.326682\pi$
$853$	−14.0714	−	24.3724i	−0.481797	−	0.834497i	−0.999782	+	0.0208932i	$0.993349\pi$
$854$	5.81280	−	0.992156i	0.198910	−	0.0339509i
$855$	−4.39679	+	11.6906i	−0.150367	+	0.399809i
$856$	15.1721	+	27.3054i	0.518571	+	0.933278i
$857$	36.3583	−	20.9915i	1.24197	−	0.717054i	0.272479	−	0.962162i	$-0.412157\pi$
$857$	36.3583	−	20.9915i	1.24197	−	0.717054i	0.969496	+	0.245108i	$0.0788233\pi$
$858$	−6.41318	+	5.32171i	−0.218942	+	0.181680i
$859$	34.5524	+	19.9488i	1.17891	+	0.680645i	0.955763	−	0.294139i	$-0.0950329\pi$
$859$	34.5524	+	19.9488i	1.17891	+	0.680645i	0.223149	+	0.974784i	$0.428366\pi$
$860$	5.65631	−	6.59289i	0.192879	−	0.224816i
$861$	7.26807	−	12.5887i	0.247695	−	0.429021i
$862$	−6.29062	−	36.8552i	−0.214259	−	1.25529i
$863$	−29.5216			−1.00493			−0.502463	−	0.864598i	$-0.667573\pi$
$863$	−29.5216			−1.00493			−0.502463	+	0.864598i	$0.667573\pi$
$864$	5.36669	−	1.78847i	0.182579	−	0.0608450i
$865$	5.56745	+	3.21437i	0.189299	+	0.109292i
$866$	12.5661	−	2.14485i	0.427015	−	0.0728849i
$867$	10.5741			0.359114
$868$	45.9405	+	8.62048i	1.55932	+	0.292598i
$869$	41.0761	−	23.7153i	1.39341	−	0.804486i
$870$	4.53234	−	12.2434i	0.153661	−	0.415091i
$871$	19.5396	−	11.2812i	0.662072	−	0.382248i
$872$	−22.7205	−	13.6203i	−0.769414	−	0.461242i
$873$		−	2.41498i		−	0.0817346i
$874$	−4.55012	+	23.5731i	−0.153910	+	0.797374i
$875$			13.5647i			0.458571i
$876$	−19.4929	−	16.7238i	−0.658605	−	0.565045i
$877$	−23.1449	+	13.3627i	−0.781549	+	0.451227i	−0.836979	−	0.547235i	$-0.815680\pi$
$877$	−23.1449	+	13.3627i	−0.781549	+	0.451227i	0.0554303	+	0.998463i	$0.482347\pi$
$878$	−4.74921	−	1.75809i	−0.160278	−	0.0593327i
$879$	−11.2157	+	6.47540i	−0.378297	+	0.218410i
$880$	−30.9565	+	4.76172i	−1.04354	+	0.160518i
$881$	−16.4961			−0.555767			−0.277883	−	0.960615i	$-0.589633\pi$
$881$	−16.4961			−0.555767			−0.277883	+	0.960615i	$0.589633\pi$
$882$	0.000299018		0.00175188i	1.00685e−5		5.89887e-5i
$883$	−20.0563	−	11.5795i	−0.674950	−	0.389682i	0.123000	−	0.992407i	$-0.460749\pi$
$883$	−20.0563	−	11.5795i	−0.674950	−	0.389682i	−0.797949	+	0.602724i	$0.794082\pi$
$884$	10.7453	+	2.01630i	0.361404	+	0.0678156i
$885$	−21.8084			−0.733082
$886$	−40.1399	+	6.85128i	−1.34853	+	0.230173i
$887$	6.35899	−	11.0141i	0.213514	−	0.369817i	−0.739298	−	0.673379i	$-0.764842\pi$
$887$	6.35899	−	11.0141i	0.213514	−	0.369817i	0.952812	+	0.303561i	$0.0981757\pi$
$888$	29.2234	+	17.5186i	0.980673	+	0.587885i
$889$	2.43540	+	1.40608i	0.0816807	+	0.0471584i
$890$	3.99255	+	4.81141i	0.133831	+	0.161279i
$891$	−2.36654	+	1.36632i	−0.0792821	+	0.0457735i
$892$	19.4714	−	6.84639i	0.651950	−	0.229234i
$893$	−35.7698	+	29.3700i	−1.19699	+	0.982831i
$894$	3.86146	+	22.6233i	0.129147	+	0.756638i
$895$	3.85835	+	6.68286i	0.128970	+	0.223383i
$896$	−29.6534	+	4.06370i	−0.990651	+	0.135759i
$897$	−4.19928	+	7.27337i	−0.140210	+	0.242851i
$898$	5.91553	+	7.12879i	0.197404	+	0.237891i
$899$	−24.6484	−	14.2308i	−0.822071	−	0.474623i
$900$	−6.05760	+	2.12993i	−0.201920	+	0.0709978i
$901$		−	12.4515i		−	0.414818i
$902$	19.9136	+	7.37174i	0.663051	+	0.245452i
$903$	−2.00503	+	3.47282i	−0.0667233	+	0.115568i
$904$	−49.4457	+	27.4743i	−1.64454	+	0.913780i
$905$			24.8772i			0.826946i
$906$	−30.1438	−	11.1588i	−1.00146	−	0.370727i
$907$	−22.0367	−	38.1687i	−0.731717	−	1.26737i	−0.956149	−	0.292881i	$-0.905386\pi$
$907$	−22.0367	−	38.1687i	−0.731717	−	1.26737i	0.224432	−	0.974490i	$-0.427947\pi$
$908$	−2.94210	+	15.6791i	−0.0976371	+	0.520330i
$909$	3.32390	+	5.75717i	0.110247	+	0.190953i
$910$	17.7904	−	14.7627i	0.589747	−	0.489377i
$911$	−25.3618			−0.840273			−0.420136	−	0.907461i	$-0.638018\pi$
$911$	−25.3618			−0.840273			−0.420136	+	0.907461i	$0.638018\pi$
$912$	−17.0630	−	3.58530i	−0.565012	−	0.118721i
$913$	15.4385			0.510940
$914$	−24.7297	+	20.5209i	−0.817985	+	0.678771i
$915$	2.25815	+	3.91123i	0.0746521	+	0.129301i
$916$	−1.93572	+	10.3159i	−0.0639581	+	0.340847i
$917$	11.6823	+	20.2344i	0.385785	+	0.668199i
$918$	3.36199	+	1.24456i	0.110962	+	0.0410766i
$919$		−	0.0795611i		−	0.00262448i	−0.999999	−	0.00131224i	$-0.999582\pi$
$919$		−	0.0795611i		−	0.00262448i	0.999999	−	0.00131224i	$-0.000417699\pi$
$920$	−27.5914	+	15.3310i	−0.909662	+	0.505449i
$921$	−15.3302	+	26.5527i	−0.505147	+	0.874940i
$922$	−5.72621	−	2.11976i	−0.188583	−	0.0698106i
$923$			12.1765i			0.400793i
$924$	13.6399	−	4.79597i	0.448720	−	0.157776i
$925$	−33.4940	−	19.3378i	−1.10128	−	0.635823i
$926$	−4.02352	−	4.84873i	−0.132221	−	0.159339i
$927$	−4.61114	+	7.98673i	−0.151450	+	0.262319i
$928$	17.8546	+	3.65500i	0.586105	+	0.119981i
$929$	3.96340	+	6.86481i	0.130035	+	0.225227i	0.923690	−	0.383141i	$-0.125158\pi$
$929$	3.96340	+	6.86481i	0.130035	+	0.225227i	−0.793655	+	0.608368i	$0.791824\pi$
$930$	6.02324	+	35.2887i	0.197510	+	1.15716i
$931$	0.00192829	−	0.00512711i	6.31972e−5	−	0.000168034i
$932$	−23.7418	+	8.34794i	−0.777690	+	0.273446i
$933$	14.3077	−	8.26056i	0.468413	−	0.270438i
$934$	26.8145	+	32.3140i	0.877396	+	1.05735i
$935$	−17.1897	−	9.92450i	−0.562164	−	0.324566i
$936$	−5.23134	−	3.13604i	−0.170992	−	0.102505i
$937$	20.9870	−	36.3506i	0.685616	−	1.18752i	−0.287627	−	0.957742i	$-0.592866\pi$
$937$	20.9870	−	36.3506i	0.685616	−	1.18752i	0.973243	−	0.229779i	$-0.0738002\pi$
$938$	−38.5867	+	6.58616i	−1.25990	+	0.215046i
$939$	23.1195			0.754477
$940$	−59.8058	−	11.2222i	−1.95065	−	0.366029i
$941$	17.0598	+	9.84946i	0.556132	+	0.321083i	0.751592	−	0.659629i	$-0.229286\pi$
$941$	17.0598	+	9.84946i	0.556132	+	0.321083i	−0.195459	+	0.980712i	$0.562620\pi$
$942$	2.02112	+	11.8412i	0.0658516	+	0.385808i
$943$	21.3997			0.696871
$944$	−4.62841	−	30.0898i	−0.150642	−	0.979340i
$945$	6.56489	−	3.79024i	0.213556	−	0.123297i
$946$	−5.49355	−	2.03363i	−0.178611	−	0.0661191i
$947$	4.89713	−	2.82736i	0.159135	−	0.0918768i	−0.418318	−	0.908301i	$-0.637380\pi$
$947$	4.89713	−	2.82736i	0.159135	−	0.0918768i	0.577453	+	0.816424i	$0.304047\pi$
$948$	26.3464	+	22.6037i	0.855693	+	0.734134i
$949$			27.6927i			0.898944i
$950$	19.4326	+	3.75091i	0.630478	+	0.121696i
$951$			10.4057i			0.337428i
$952$	−16.2688	−	9.75267i	−0.527274	−	0.316086i
$953$	7.89881	−	4.56038i	0.255868	−	0.147725i	−0.366580	−	0.930386i	$-0.619472\pi$
$953$	7.89881	−	4.56038i	0.255868	−	0.147725i	0.622448	+	0.782661i	$0.286138\pi$
$954$	−2.41157	+	6.51448i	−0.0780774	+	0.210914i
$955$	−38.2810	+	22.1015i	−1.23874	+	0.715189i
$956$	−20.4428	−	3.83598i	−0.661168	−	0.124065i
$957$	−8.80384			−0.284588
$958$	−0.985370	+	0.168188i	−0.0318359	+	0.00543389i
$959$	−46.9619	−	27.1135i	−1.51648	−	0.875540i
$960$	−10.8031	−	20.2180i	−0.348670	−	0.652534i
$961$	47.0440			1.51755
$962$	−6.18107	−	36.2134i	−0.199286	−	1.16757i
$963$	5.52204	−	9.56446i	0.177945	−	0.308210i
$964$	−20.5596	+	23.9639i	−0.662182	+	0.771826i
$965$	−37.5841	−	21.6992i	−1.20988	−	0.698523i
$966$	11.2133	−	9.30488i	0.360782	−	0.299380i
$967$	−20.6723	+	11.9351i	−0.664775	+	0.383808i	−0.794094	−	0.607795i	$-0.792054\pi$
$967$	−20.6723	+	11.9351i	−0.664775	+	0.383808i	0.129319	+	0.991603i	$0.458721\pi$
$968$	−4.85306	−	8.73410i	−0.155983	−	0.280724i
$969$	−7.01183	−	8.53973i	−0.225253	−	0.274336i
$970$	−9.64671	+	1.64655i	−0.309737	+	0.0528674i
$971$	28.0027	+	48.5022i	0.898651	+	1.55651i	0.829220	+	0.558922i	$0.188785\pi$
$971$	28.0027	+	48.5022i	0.898651	+	1.55651i	0.0694307	+	0.997587i	$0.477882\pi$
$972$	−1.51791	−	1.30228i	−0.0486871	−	0.0417707i
$973$	5.51766	−	9.55686i	0.176888	−	0.306379i
$974$	2.74250	−	2.27575i	0.0878753	−	0.0729197i
$975$	5.99583	+	3.46169i	0.192020	+	0.110863i
$976$	−4.91721	+	3.94573i	−0.157396	+	0.126300i
$977$			7.94428i			0.254160i	0.991892	+	0.127080i	$0.0405605\pi$
$977$			7.94428i			0.254160i	−0.991892	+	0.127080i	$0.959439\pi$
$978$	0.471761	−	1.27439i	0.0150852	−	0.0407505i
$979$	2.10807	−	3.65129i	0.0673742	−	0.116696i
$980$	0.00679405	−	0.00238888i	0.000217028	−	7.63099e-5i
$981$			9.36573i			0.299025i
$982$	−0.896694	+	2.42228i	−0.0286147	+	0.0772981i
$983$	19.4039	+	33.6085i	0.618887	+	1.07194i	0.989689	+	0.143232i	$0.0457494\pi$
$983$	19.4039	+	33.6085i	0.618887	+	1.07194i	−0.370802	+	0.928712i	$0.620917\pi$
$984$	−0.255363	+	15.5391i	−0.00814066	+	0.495368i
$985$	2.42914	+	4.20740i	0.0773989	+	0.134059i
$986$	7.37545	+	8.88814i	0.234882	+	0.283056i
$987$	28.0900			0.894113
$988$	9.04550	+	16.4801i	0.287776	+	0.524302i
$989$	−5.90351			−0.187721
$990$	7.07134	+	8.52166i	0.224742	+	0.270836i
$991$	−10.7169	−	18.5622i	−0.340433	−	0.589648i	0.644080	−	0.764958i	$-0.277240\pi$
$991$	−10.7169	−	18.5622i	−0.340433	−	0.589648i	−0.984513	+	0.175310i	$0.943907\pi$
$992$	−47.4107	+	15.7998i	−1.50529	+	0.501644i
$993$	−1.48179	−	2.56653i	−0.0470231	−	0.0814465i
$994$	7.33403	−	19.8118i	0.232621	−	0.628391i
$995$		−	44.0311i		−	1.39588i
$996$	3.74804	+	10.6596i	0.118761	+	0.337761i
$997$	17.7924	−	30.8174i	0.563492	−	0.975997i	−0.433696	−	0.901059i	$-0.642791\pi$
$997$	17.7924	−	30.8174i	0.563492	−	0.975997i	0.997188	−	0.0749376i	$-0.0238758\pi$
$998$	−0.827627	+	2.23571i	−0.0261981	+	0.0707701i
$999$		−	12.0463i		−	0.381128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.k.b.31.8	yes	20
3.2	odd	2		684.2.r.b.487.3		20
4.3	odd	2		228.2.k.a.31.10	✓	20
12.11	even	2		684.2.r.c.487.1		20
19.8	odd	6		228.2.k.a.103.10	yes	20
57.8	even	6		684.2.r.c.559.1		20
76.27	even	6	inner	228.2.k.b.103.8	yes	20
228.179	odd	6		684.2.r.b.559.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.k.a.31.10	✓	20	4.3	odd	2
228.2.k.a.103.10	yes	20	19.8	odd	6
228.2.k.b.31.8	yes	20	1.1	even	1	trivial
228.2.k.b.103.8	yes	20	76.27	even	6	inner
684.2.r.b.487.3		20	3.2	odd	2
684.2.r.b.559.3		20	228.179	odd	6
684.2.r.c.487.1		20	12.11	even	2
684.2.r.c.559.1		20	57.8	even	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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.08831 - 0.903091i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.368852 - 1.96569i) q^{4} +(1.43271 + 2.48152i) q^{5} +(1.32626 + 0.490961i) q^{6} +2.64551i q^{7} +(-1.37377 - 2.47240i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.80027 + 1.40681i) q^{10} -2.73265i q^{11} +(1.88677 - 0.663412i) q^{12} +(-1.86752 - 1.07822i) q^{13} +(2.38914 + 2.87915i) q^{14} +(-1.43271 + 2.48152i) q^{15} +(-3.72790 - 1.45010i) q^{16} +(-1.26747 - 2.19532i) q^{17} +(0.237943 + 1.39405i) q^{18} +(1.53443 - 4.07989i) q^{19} +(5.40636 - 1.90095i) q^{20} +(-2.29108 + 1.32276i) q^{21} +(-2.46783 - 2.97398i) q^{22} +(-3.37287 - 1.94733i) q^{23} +(1.45427 - 2.42592i) q^{24} +(-1.60529 + 2.78044i) q^{25} +(-3.00618 + 0.513109i) q^{26} -1.00000 q^{27} +(5.20027 + 0.975802i) q^{28} +(-2.79010 - 1.61086i) q^{29} +(0.681806 + 3.99453i) q^{30} +8.83425 q^{31} +(-5.36669 + 1.78847i) q^{32} +(2.36654 - 1.36632i) q^{33} +(-3.36199 - 1.24456i) q^{34} +(-6.56489 + 3.79024i) q^{35} +(1.51791 + 1.30228i) q^{36} +12.0463i q^{37} +(-2.01457 - 5.82593i) q^{38} -2.15643i q^{39} +(4.16708 - 6.95126i) q^{40} +(-4.75850 + 2.74732i) q^{41} +(-1.29884 + 3.50863i) q^{42} +(1.31272 - 0.757900i) q^{43} +(-5.37154 - 1.00794i) q^{44} -2.86541 q^{45} +(-5.42935 + 0.926708i) q^{46} +(-9.19542 - 5.30898i) q^{47} +(-0.608127 - 3.95350i) q^{48} +0.00125668 q^{49} +(0.763936 + 4.47571i) q^{50} +(1.26747 - 2.19532i) q^{51} +(-2.80828 + 3.27328i) q^{52} +(4.25386 + 2.45597i) q^{53} +(-1.08831 + 0.903091i) q^{54} +(6.78111 - 3.91508i) q^{55} +(6.54076 - 3.63434i) q^{56} +(4.30051 - 0.711086i) q^{57} +(-4.49126 + 0.766589i) q^{58} +(3.80546 + 6.59126i) q^{59} +(4.34945 + 3.73157i) q^{60} +(0.788072 - 1.36498i) q^{61} +(9.61444 - 7.97814i) q^{62} +(-2.29108 - 1.32276i) q^{63} +(-4.22549 + 6.79303i) q^{64} -6.17906i q^{65} +(1.34162 - 3.62419i) q^{66} +(-5.23140 + 9.06106i) q^{67} +(-4.78284 + 1.68171i) q^{68} -3.89465i q^{69} +(-3.72172 + 10.0537i) q^{70} +(-2.82329 - 4.89008i) q^{71} +(2.82805 + 0.0464748i) q^{72} +(-6.42096 - 11.1214i) q^{73} +(10.8789 + 13.1102i) q^{74} -3.21058 q^{75} +(-7.45383 - 4.52110i) q^{76} +7.22925 q^{77} +(-1.94746 - 2.34687i) q^{78} +(8.67850 + 15.0316i) q^{79} +(-1.74253 - 11.3284i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.69766 + 7.28730i) q^{82} +5.64965i q^{83} +(1.75506 + 4.99146i) q^{84} +(3.63183 - 6.29051i) q^{85} +(0.744199 - 2.01034i) q^{86} -3.22173i q^{87} +(-6.75619 + 3.75404i) q^{88} +(1.33617 + 0.771439i) q^{89} +(-3.11846 + 2.58773i) q^{90} +(2.85244 - 4.94056i) q^{91} +(-5.07194 + 5.91175i) q^{92} +(4.41713 + 7.65069i) q^{93} +(-14.8020 + 2.52647i) q^{94} +(12.3227 - 2.03755i) q^{95} +(-4.23221 - 3.75346i) q^{96} +(-2.09143 + 1.20749i) q^{97} +(0.00136766 - 0.00113490i) q^{98} +(2.36654 + 1.36632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 10 q^{3} + q^{4} - q^{6} + 4 q^{8} - 10 q^{9} + 6 q^{10} + 2 q^{12} + 6 q^{13} + 9 q^{14} - 11 q^{16} - 2 q^{18} + 12 q^{19} - 14 q^{20} + 6 q^{21} + 8 q^{22} + 11 q^{24} - 10 q^{25} - 20 q^{27}+ \cdots - 12 q^{97}+O(q^{100}) \) 20 * q + q^2 + 10 * q^3 + q^4 - q^6 + 4 * q^8 - 10 * q^9 + 6 * q^10 + 2 * q^12 + 6 * q^13 + 9 * q^14 - 11 * q^16 - 2 * q^18 + 12 * q^19 - 14 * q^20 + 6 * q^21 + 8 * q^22 + 11 * q^24 - 10 * q^25 - 20 * q^27 + 7 * q^28 + 12 * q^31 - 29 * q^32 - 6 * q^34 + q^36 + 25 * q^38 - 46 * q^40 + 12 * q^41 + 9 * q^42 - 18 * q^43 - 12 * q^44 - 32 * q^46 - 36 * q^47 - 13 * q^48 - 24 * q^49 - 34 * q^50 + 3 * q^52 - 12 * q^53 - q^54 + 38 * q^56 + 6 * q^57 + 16 * q^58 - 4 * q^60 + 10 * q^61 - 55 * q^62 + 6 * q^63 - 14 * q^64 - 8 * q^66 + 14 * q^67 + 40 * q^68 + 26 * q^70 + 8 * q^71 + 7 * q^72 - 6 * q^73 + 45 * q^74 - 20 * q^75 - 69 * q^76 - 32 * q^77 + 33 * q^78 - 6 * q^79 + 22 * q^80 - 10 * q^81 + 24 * q^82 + 14 * q^84 + 8 * q^85 + 7 * q^86 + 44 * q^88 - 24 * q^89 - 6 * q^90 + 26 * q^91 - 18 * q^92 + 6 * q^93 - 52 * q^94 + 4 * q^95 + 2 * q^96 - 12 * q^97

Introduction

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