LMFDB - Embedded newform 228.2.k.b.103.8

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			103.8
Root			$-0.237943 - 1.39405i$ of defining polynomial
Character	$\chi$	$=$	228.103
Dual form			228.2.k.b.31.8

$q$-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 $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

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

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	−0.344546	−	0.938769i	$-0.611967\pi$
$5$	1.43271	−	2.48152i	0.640725	−	1.10977i	0.985271	−	0.170999i	$-0.0546995\pi$
$6$	1.32626	−	0.490961i	0.541442	−	0.200434i
$7$		−	2.64551i		−	0.999910i	−0.866051	−	0.499955i	$-0.833350\pi$
$7$		−	2.64551i		−	0.999910i	0.866051	−	0.499955i	$-0.166650\pi$
$8$	−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	$0.135156\pi$
$11$			2.73265i			0.823924i	−0.911201	+	0.411962i	$0.864844\pi$
$12$	1.88677	+	0.663412i	0.544662	+	0.191510i
$13$	−1.86752	+	1.07822i	−0.517958	+	0.299043i	−0.736099	−	0.676874i	$-0.763334\pi$
$13$	−1.86752	+	1.07822i	−0.517958	+	0.299043i	0.218141	+	0.975917i	$0.430001\pi$
$14$	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	−0.977794	−	0.209567i	$-0.932795\pi$
$17$	−1.26747	+	2.19532i	−0.307407	+	0.532445i	0.670387	+	0.742011i	$0.266128\pi$
$18$	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	−0.808572	−	0.588397i	$-0.799759\pi$
$23$	−3.37287	+	1.94733i	−0.703292	+	0.406046i	0.105280	+	0.994443i	$0.466426\pi$
$24$	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	−0.736160	−	0.676807i	$-0.763363\pi$
$29$	−2.79010	+	1.61086i	−0.518108	+	0.299130i	0.218052	+	0.975937i	$0.430030\pi$
$30$	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	$-0.544600\pi$
$37$		−	12.0463i		−	1.98040i	0.139656	−	0.990200i	$-0.455400\pi$
$38$	−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	0.0800618	−	0.996790i	$-0.474488\pi$
$41$	−4.75850	−	2.74732i	−0.743153	−	0.429059i	−0.823214	+	0.567731i	$0.807822\pi$
$42$	−1.29884	−	3.50863i	−0.200416	−	0.541393i
$43$	1.31272	+	0.757900i	0.200188	+	0.115579i	0.596743	−	0.802432i	$-0.296461\pi$
$43$	1.31272	+	0.757900i	0.200188	+	0.115579i	−0.396555	+	0.918011i	$0.629794\pi$
$44$	−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	−0.986997	−	0.160740i	$-0.948612\pi$
$47$	−9.19542	+	5.30898i	−1.34129	+	0.774394i	−0.354294	+	0.935134i	$0.615279\pi$
$48$	−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	−0.178533	−	0.983934i	$-0.557135\pi$
$53$	4.25386	−	2.45597i	0.584312	−	0.337353i	0.762845	+	0.646581i	$0.223802\pi$
$54$	−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	−0.504557	−	0.863378i	$-0.668344\pi$
$59$	3.80546	−	6.59126i	0.495429	−	0.858109i	0.999986	+	0.00526981i	$0.00167744\pi$
$60$	4.34945	−	3.73157i	0.561511	−	0.481744i
$61$	0.788072	+	1.36498i	0.100902	+	0.174768i	0.912057	−	0.410064i	$-0.134494\pi$
$61$	0.788072	+	1.36498i	0.100902	+	0.174768i	−0.811154	+	0.584832i	$0.801160\pi$
$62$	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	−0.985627	−	0.168938i	$-0.945966\pi$
$67$	−5.23140	−	9.06106i	−0.639118	−	1.10698i	0.346509	−	0.938047i	$-0.387367\pi$
$68$	−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	−0.983497	−	0.180925i	$-0.942091\pi$
$71$	−2.82329	+	4.89008i	−0.335063	+	0.580346i	0.648434	+	0.761271i	$0.275424\pi$
$72$	2.82805	−	0.0464748i	0.333288	−	0.00547711i
$73$	−6.42096	+	11.1214i	−0.751517	+	1.30167i	0.195571	+	0.980690i	$0.437344\pi$
$73$	−6.42096	+	11.1214i	−0.751517	+	1.30167i	−0.947087	+	0.320976i	$0.895989\pi$
$74$	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	0.301198	−	0.953561i	$-0.402613\pi$
$79$	8.67850	−	15.0316i	0.976408	−	1.69119i	0.675209	−	0.737626i	$-0.264053\pi$
$80$	−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	$-0.899649\pi$
$83$		−	5.64965i		−	0.620130i	0.950715	−	0.310065i	$-0.100351\pi$
$84$	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	−0.427509	−	0.904011i	$-0.640609\pi$
$89$	1.33617	−	0.771439i	0.141634	−	0.0817724i	0.569142	+	0.822239i	$0.307275\pi$
$90$	−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	0.390052	−	0.920793i	$-0.372457\pi$
$97$	−2.09143	−	1.20749i	−0.212353	−	0.122602i	−0.602404	+	0.798191i	$0.705791\pi$
$98$	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	0.982657	−	0.185431i	$-0.0593680\pi$
$101$	3.32390	+	5.75717i	0.330741	+	0.572860i	−0.651916	+	0.758291i	$0.726035\pi$
$102$	−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	0.835327	−	0.549754i	$-0.185278\pi$
$109$	8.11096	+	4.68287i	0.776889	+	0.448537i	−0.0584373	+	0.998291i	$0.518612\pi$
$110$	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	$0.389811\pi$
$113$			19.9991i			1.88136i	−0.339298	+	0.940679i	$0.610189\pi$
$114$	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	0.888643	−	0.458600i	$-0.151649\pi$
$127$	0.531496	+	0.920577i	0.0471626	+	0.0816880i	−0.841480	+	0.540288i	$0.818315\pi$
$128$	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	0.795417	−	0.606063i	$-0.207252\pi$
$131$	7.64858	+	4.41591i	0.668259	+	0.385820i	−0.127158	+	0.991883i	$0.540585\pi$
$132$	−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	−0.856102	−	0.516806i	$-0.827121\pi$
$137$	−10.2489	−	17.7515i	−0.875619	−	1.51662i	−0.0195162	−	0.999810i	$-0.506213\pi$
$138$	−3.51723	+	4.23860i	−0.299406	+	0.360814i
$139$	−3.61248	+	2.08566i	−0.306406	+	0.176904i	−0.645317	−	0.763915i	$-0.723275\pi$
$139$	−3.61248	+	2.08566i	−0.306406	+	0.176904i	0.338911	+	0.940818i	$0.389941\pi$
$140$	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	−0.314610	−	0.949221i	$-0.601874\pi$
$149$	8.11424	−	14.0543i	0.664744	−	1.15137i	0.979355	−	0.202150i	$-0.0647928\pi$
$150$	−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	−0.645284	−	0.763943i	$-0.723261\pi$
$157$	4.24706	−	7.35612i	0.338952	−	0.587082i	0.984236	+	0.176861i	$0.0565943\pi$
$158$	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	$0.0119813\pi$
$163$			0.960892i			0.0752629i	−0.999292	+	0.0376314i	$0.988019\pi$
$164$	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	0.972571	+	0.232606i	$0.0747253\pi$
$167$	8.88741	+	15.3934i	0.687728	+	1.19118i	−0.284843	+	0.958574i	$0.591941\pi$
$168$	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	0.572039	−	0.820226i	$-0.306152\pi$
$173$	1.94298	+	1.12178i	0.147722	+	0.0852875i	−0.424317	+	0.905514i	$0.639486\pi$
$174$	−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	−0.193825	−	0.981036i	$-0.562090\pi$
$181$	7.51874	−	4.34095i	0.558864	−	0.322660i	0.752689	+	0.658376i	$0.228756\pi$
$182$	−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	$-0.811527\pi$
$191$		−	15.4264i		−	1.11622i	0.829768	−	0.558109i	$-0.188473\pi$
$192$	−7.99568	+	0.262866i	−0.577039	+	0.0189707i
$193$	−13.1165	−	7.57281i	−0.944146	−	0.545103i	−0.0528886	−	0.998600i	$-0.516843\pi$
$193$	−13.1165	−	7.57281i	−0.944146	−	0.545103i	−0.891258	+	0.453497i	$0.850176\pi$
$194$	−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	−0.891011	−	0.453981i	$-0.850003\pi$
$199$	−13.3077	+	7.68321i	−0.943358	+	0.544648i	−0.0523468	+	0.998629i	$0.516670\pi$
$200$	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	−0.744927	−	0.667146i	$-0.767516\pi$
$211$	2.98218	−	5.16529i	0.205302	−	0.355593i	0.950229	+	0.311553i	$0.100849\pi$
$212$	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	−0.639913	−	0.768447i	$-0.721030\pi$
$223$	5.15998	−	8.93736i	0.345538	−	0.598490i	0.985451	+	0.169958i	$0.0543631\pi$
$224$	−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	−0.995128	−	0.0985913i	$-0.968566\pi$
$233$	−6.29168	+	10.8975i	−0.412181	+	0.713919i	0.582947	+	0.812510i	$0.301900\pi$
$234$	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	$0.109194\pi$
$239$			10.3998i			0.672707i	−0.941736	+	0.336354i	$0.890806\pi$
$240$	8.93942	+	7.17328i	0.577037	+	0.463033i
$241$	−13.6723	+	7.89370i	−0.880710	+	0.508478i	−0.870892	−	0.491474i	$-0.836458\pi$
$241$	−13.6723	+	7.89370i	−0.880710	+	0.508478i	−0.00981747	+	0.999952i	$0.503125\pi$
$242$	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	−0.377934	−	0.925833i	$-0.623365\pi$
$251$	3.72142	−	2.14856i	0.234894	−	0.135616i	0.612828	+	0.790216i	$0.290032\pi$
$252$	−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	0.502259	−	0.864717i	$-0.332502\pi$
$257$	24.0830	−	13.9043i	1.50226	−	0.867328i	0.999997	−	0.00261095i	$-0.000831091\pi$
$258$	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	−0.265250	−	0.964180i	$-0.585455\pi$
$263$	−19.9939	−	11.5435i	−1.23288	−	0.711803i	−0.967629	+	0.252376i	$0.918788\pi$
$264$	−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	−0.425722	−	0.904854i	$-0.639980\pi$
$269$	−23.3260	−	13.4673i	−1.42221	−	0.821113i	−0.996488	+	0.0837405i	$0.973313\pi$
$270$	−3.80027	+	1.40681i	−0.231277	+	0.0856154i
$271$	15.9754	+	9.22339i	0.970435	+	0.560281i	0.899369	−	0.437191i	$-0.144027\pi$
$271$	15.9754	+	9.22339i	0.970435	+	0.560281i	0.0710661	+	0.997472i	$0.477360\pi$
$272$	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	−0.482156	−	0.876085i	$-0.660146\pi$
$281$	0.594707	−	0.343354i	0.0354773	−	0.0204828i	0.517634	+	0.855602i	$0.326813\pi$
$282$	−9.58899	+	11.5557i	−0.571016	+	0.688130i
$283$	12.0092	+	6.93350i	0.713871	+	0.412154i	0.812493	−	0.582971i	$-0.198110\pi$
$283$	12.0092	+	6.93350i	0.713871	+	0.412154i	−0.0986215	+	0.995125i	$0.531443\pi$
$284$	−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	$-0.876510\pi$
$293$		−	12.9508i		−	0.756594i	0.925684	−	0.378297i	$-0.123490\pi$
$294$	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	0.0181139	−	0.999836i	$-0.494234\pi$
$307$	15.3302	−	26.5527i	0.874940	−	1.51544i	0.856826	−	0.515605i	$-0.172433\pi$
$308$	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	$0.155174\pi$
$311$			16.5211i			0.936826i	−0.883510	+	0.468413i	$0.844826\pi$
$312$	−5.33156	−	2.96245i	−0.301840	−	0.167716i
$313$	11.5598	+	20.0221i	0.653397	+	1.13172i	0.982293	+	0.187350i	$0.0599899\pi$
$313$	11.5598	+	20.0221i	0.653397	+	1.13172i	−0.328897	+	0.944366i	$0.606677\pi$
$314$	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	−0.225104	−	0.974335i	$-0.572272\pi$
$317$	9.01160	−	5.20285i	0.506142	−	0.292221i	0.731246	+	0.682114i	$0.238939\pi$
$318$	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	0.901249	−	0.433301i	$-0.142651\pi$
$337$	17.9284	+	10.3510i	0.976625	+	0.563854i	0.0753752	+	0.997155i	$0.475985\pi$
$338$	−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	0.977851	−	0.209303i	$-0.0671193\pi$
$347$	23.9465	+	13.8255i	1.28552	+	0.742192i	0.307664	+	0.951495i	$0.400453\pi$
$348$	−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	0.972015	+	0.234919i	$0.0754825\pi$
$359$	31.4803	+	18.1752i	1.66147	+	0.959249i	0.689453	+	0.724330i	$0.257851\pi$
$360$	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	−0.972505	−	0.232880i	$-0.925185\pi$
$367$	−24.0822	+	13.9038i	−1.25708	+	0.725774i	−0.284573	+	0.958654i	$0.591852\pi$
$368$	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	$0.119529\pi$
$373$			14.1662i			0.733496i	−0.930320	+	0.366748i	$0.880471\pi$
$374$	−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	−0.970621	−	0.240612i	$-0.922652\pi$
$383$	−5.41972	+	9.38723i	−0.276935	+	0.479665i	0.693687	+	0.720277i	$0.255985\pi$
$384$	−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	0.910132	−	0.414319i	$-0.135980\pi$
$389$	1.89844	+	3.28819i	0.0962545	+	0.166718i	−0.813877	+	0.581037i	$0.802647\pi$
$390$	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	−0.234504	−	0.972115i	$-0.575347\pi$
$397$	14.4380	−	25.0074i	0.724625	−	1.25509i	0.959128	−	0.282971i	$-0.0913202\pi$
$398$	−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	0.625673	−	0.780085i	$-0.284824\pi$
$401$	5.26528	+	3.03991i	0.262936	+	0.151806i	−0.362737	+	0.931891i	$0.618158\pi$
$402$	−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	−0.736877	−	0.676026i	$-0.763701\pi$
$409$	−10.5135	+	6.06998i	−0.519860	+	0.300141i	0.217017	+	0.976168i	$0.430367\pi$
$410$	−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	$0.261165\pi$
$419$			29.9456i			1.46294i	−0.681875	+	0.731468i	$0.738835\pi$
$420$	−9.87192	−	11.5065i	−0.481700	−	0.561461i
$421$	25.1779	+	14.5365i	1.22710	+	0.708465i	0.966422	−	0.256962i	$-0.0827214\pi$
$421$	25.1779	+	14.5365i	1.22710	+	0.708465i	0.260676	+	0.965426i	$0.416055\pi$
$422$	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	0.986147	+	0.165873i	$0.0530443\pi$
$431$	13.2187	+	22.8955i	0.636724	+	1.10284i	−0.349423	+	0.936965i	$0.613622\pi$
$432$	3.72790	−	1.45010i	0.179359	−	0.0697679i
$433$	7.80644	−	4.50705i	0.375154	−	0.216595i	−0.300554	−	0.953765i	$-0.597172\pi$
$433$	7.80644	−	4.50705i	0.375154	−	0.216595i	0.675708	+	0.737170i	$0.263838\pi$
$434$	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	−0.905585	−	0.424166i	$-0.860567\pi$
$439$	−1.79046	+	3.10116i	−0.0854539	+	0.148011i	0.820131	+	0.572176i	$0.193901\pi$
$440$	−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	−0.957108	−	0.289730i	$-0.906434\pi$
$443$	−24.9361	+	14.3969i	−1.18475	+	0.684015i	−0.227641	+	0.973745i	$0.573101\pi$
$444$	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	$-0.950603\pi$
$449$		−	6.55031i		−	0.309128i	0.987983	−	0.154564i	$-0.0493973\pi$
$450$	−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	−0.911909	−	0.410392i	$-0.865392\pi$
$461$	−2.15879	+	3.73913i	−0.100545	+	0.174149i	0.811364	+	0.584541i	$0.198725\pi$
$462$	9.58785	−	3.54928i	0.446067	−	0.165128i
$463$			4.45527i			0.207054i	0.994627	+	0.103527i	$0.0330128\pi$
$463$			4.45527i			0.207054i	−0.994627	+	0.103527i	$0.966987\pi$
$464$	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	$-0.758933\pi$
$467$		−	29.6919i		−	1.37398i	0.726669	−	0.686988i	$-0.241067\pi$
$468$	−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	−0.513920	−	0.857838i	$-0.671807\pi$
$479$	−0.612140	+	0.353419i	−0.0279694	+	0.0161481i	0.485950	+	0.873987i	$0.338474\pi$
$480$	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	0.463884	−	0.885896i	$-0.346455\pi$
$491$	−1.58171	−	0.913203i	−0.0713817	−	0.0412123i	−0.535266	+	0.844684i	$0.679789\pi$
$492$	−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	0.466967	−	0.884275i	$-0.345347\pi$
$499$	−1.45988	−	0.842864i	−0.0653534	−	0.0377318i	−0.532321	+	0.846543i	$0.678680\pi$
$500$	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	−0.511241	−	0.859437i	$-0.670814\pi$
$503$	−0.506143	+	0.292222i	−0.0225678	+	0.0130295i	0.488674	+	0.872467i	$0.337481\pi$
$504$	−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	−0.964015	−	0.265846i	$-0.914349\pi$
$509$	−27.4296	+	15.8365i	−1.21579	+	0.701939i	−0.251778	+	0.967785i	$0.581015\pi$
$510$	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	$0.0700498\pi$
$521$			9.96539i			0.436592i	−0.975883	+	0.218296i	$0.929950\pi$
$522$	1.58174	+	4.27284i	0.0692310	+	0.187017i
$523$	6.71352	+	11.6282i	0.293562	+	0.508464i	0.974649	−	0.223738i	$-0.0718261\pi$
$523$	6.71352	+	11.6282i	0.293562	+	0.508464i	−0.681088	+	0.732202i	$0.738493\pi$
$524$	−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	0.633011	−	0.774143i	$-0.281819\pi$
$541$	−8.23202	−	14.2583i	−0.353922	−	0.613011i	−0.986933	+	0.161132i	$0.948486\pi$
$542$	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	0.773864	−	0.633352i	$-0.218321\pi$
$547$	−3.77873	−	6.54495i	−0.161567	−	0.279842i	−0.935431	+	0.353510i	$0.884988\pi$
$548$	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	−0.964716	−	0.263292i	$-0.915192\pi$
$557$	−16.7655	−	29.0386i	−0.710376	−	1.23041i	0.254340	−	0.967115i	$-0.418142\pi$
$558$	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	$-0.957644\pi$
$569$		−	6.32953i		−	0.265348i	0.991160	−	0.132674i	$-0.0423563\pi$
$570$	17.3434	−	3.34766i	0.726437	−	0.140218i
$571$			20.2768i			0.848559i	0.905531	+	0.424279i	$0.139473\pi$
$571$			20.2768i			0.848559i	−0.905531	+	0.424279i	$0.860527\pi$
$572$	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	0.0603806	−	0.998175i	$-0.480769\pi$
$587$	−18.7495	−	10.8250i	−0.773874	−	0.446797i	−0.834255	+	0.551379i	$0.814102\pi$
$588$	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	0.998225	−	0.0595485i	$-0.0189661\pi$
$593$	10.8984	+	18.8765i	0.447542	+	0.775166i	−0.550683	+	0.834714i	$0.685633\pi$
$594$	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	−0.999355	−	0.0359059i	$-0.988568\pi$
$599$	−12.9904	−	22.5000i	−0.530773	−	0.919326i	0.468582	−	0.883420i	$-0.344765\pi$
$600$	4.41061	−	7.93782i	0.180062	−	0.324060i
$601$		−	5.80590i		−	0.236828i	−0.992964	−	0.118414i	$-0.962219\pi$
$601$		−	5.80590i		−	0.236828i	0.992964	−	0.118414i	$-0.0377809\pi$
$602$	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	−0.998972	−	0.0453327i	$-0.985565\pi$
$613$	−11.3947	+	19.7362i	−0.460227	+	0.797136i	0.538745	+	0.842469i	$0.318899\pi$
$614$	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	−0.982144	−	0.188132i	$-0.939757\pi$
$617$	−16.2450	−	28.1372i	−0.653999	−	1.13276i	0.328144	−	0.944628i	$-0.393577\pi$
$618$	12.2311	−	4.52778i	0.492008	−	0.182134i
$619$			6.61987i			0.266075i	0.991111	+	0.133037i	$0.0424731\pi$
$619$			6.61987i			0.266075i	−0.991111	+	0.133037i	$0.957527\pi$
$620$	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	−0.362354	−	0.932041i	$-0.618027\pi$
$631$	6.62256	−	3.82354i	0.263640	−	0.152213i	0.625994	+	0.779828i	$0.284693\pi$
$632$	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	−0.357833	−	0.933786i	$-0.616484\pi$
$641$	−34.0636	−	19.6666i	−1.34543	−	0.776785i	−0.987598	+	0.157001i	$0.949817\pi$
$642$	−14.6473	+	5.42222i	−0.578083	+	0.213998i
$643$	26.2592	+	15.1608i	1.03556	+	0.597882i	0.918573	−	0.395251i	$-0.129342\pi$
$643$	26.2592	+	15.1608i	1.03556	+	0.597882i	0.116989	+	0.993133i	$0.462676\pi$
$644$	−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	$-0.891928\pi$
$647$		−	16.9422i		−	0.666068i	0.942915	−	0.333034i	$-0.108072\pi$
$648$	−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	0.624833	−	0.780758i	$-0.285167\pi$
$659$	−9.33757	−	16.1732i	−0.363740	−	0.630017i	−0.988573	+	0.150742i	$0.951834\pi$
$660$	10.1971	+	11.8855i	0.396920	+	0.462642i
$661$	−4.59355	+	2.65209i	−0.178668	+	0.103154i	−0.586667	−	0.809828i	$-0.699560\pi$
$661$	−4.59355	+	2.65209i	−0.178668	+	0.103154i	0.407999	+	0.912983i	$0.366227\pi$
$662$	−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	$-0.650367\pi$
$673$		−	46.2022i		−	1.78096i	0.455018	−	0.890482i	$-0.349633\pi$
$674$	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	$0.0407205\pi$
$677$			6.63900i			0.255157i	−0.991828	+	0.127579i	$0.959279\pi$
$678$	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	$-0.963738\pi$
$691$		−	5.97635i		−	0.227351i	0.993518	−	0.113675i	$-0.0362624\pi$
$692$	−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	−0.587759	−	0.809036i	$-0.699990\pi$
$701$	10.7697	−	18.6537i	0.406766	−	0.704540i	0.994525	+	0.104496i	$0.0333230\pi$
$702$	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	0.508426	−	0.861105i	$-0.330227\pi$
$709$	−13.0879	−	22.6689i	−0.491526	−	0.851348i	−0.999952	+	0.00975743i	$0.996894\pi$
$710$	−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	0.644099	−	0.764942i	$-0.277232\pi$
$719$	8.14319	+	4.70147i	0.303690	+	0.175335i	−0.340409	+	0.940277i	$0.610566\pi$
$720$	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	0.313811	−	0.949485i	$-0.398394\pi$
$727$	−9.47912	−	5.47277i	−0.351561	−	0.202974i	−0.665373	+	0.746511i	$0.731727\pi$
$728$	−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	−0.0485009	−	0.998823i	$-0.515444\pi$
$739$	−25.4925	−	14.7181i	−0.937758	−	0.541415i	−0.889257	+	0.457409i	$0.848778\pi$
$740$	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	−0.989926	−	0.141587i	$-0.954780\pi$
$743$	−10.1494	+	17.5793i	−0.372345	+	0.644921i	0.617581	+	0.786508i	$0.288113\pi$
$744$	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	0.938800	−	0.344462i	$-0.111939\pi$
$751$	4.68855	+	8.12080i	0.171087	+	0.296332i	−0.767713	+	0.640794i	$0.778605\pi$
$752$	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	−0.994992	−	0.0999576i	$-0.968129\pi$
$757$	−11.3062	+	19.5829i	−0.410930	+	0.711752i	0.584062	+	0.811709i	$0.301463\pi$
$758$	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	0.898098	+	0.439796i	$0.144949\pi$
$769$	23.0145	+	39.8622i	0.829923	+	1.43747i	−0.0681747	+	0.997673i	$0.521718\pi$
$770$	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	−0.488944	−	0.872315i	$-0.662618\pi$
$773$	0.612546	−	0.353654i	0.0220318	−	0.0127200i	0.510975	+	0.859595i	$0.329284\pi$
$774$	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	$0.0535356\pi$
$797$			9.45153i			0.334790i	−0.985890	+	0.167395i	$0.946464\pi$
$798$	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	0.764472	+	0.644657i	$0.223000\pi$
$811$	26.7843	+	46.3918i	0.940525	+	1.62904i	0.176053	+	0.984381i	$0.443667\pi$
$812$	−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	0.974130	−	0.225990i	$-0.0725618\pi$
$821$	8.34812	+	14.4594i	0.291351	+	0.504635i	−0.682778	+	0.730626i	$0.739228\pi$
$822$	−22.3079	−	18.5113i	−0.778078	−	0.645656i
$823$	−0.302319	+	0.174544i	−0.0105382	+	0.00608423i	−0.505260	−	0.862967i	$-0.668603\pi$
$823$	−0.302319	+	0.174544i	−0.0105382	+	0.00608423i	0.494722	+	0.869051i	$0.335270\pi$
$824$	−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	0.867783	−	0.496943i	$-0.165544\pi$
$827$	0.101413	+	0.175653i	0.00352648	+	0.00610804i	−0.864257	+	0.503051i	$0.832211\pi$
$828$	−2.58376	+	7.34830i	−0.0897918	+	0.255371i
$829$		−	44.0142i		−	1.52868i	−0.644815	−	0.764339i	$-0.723066\pi$
$829$		−	44.0142i		−	1.52868i	0.644815	−	0.764339i	$-0.276934\pi$
$830$	−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	−0.923612	−	0.383328i	$-0.874778\pi$
$839$	−3.76071	+	6.51373i	−0.129834	+	0.224879i	0.793778	+	0.608207i	$0.208111\pi$
$840$	−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	−0.999782	−	0.0208932i	$-0.993349\pi$
$853$	−14.0714	+	24.3724i	−0.481797	+	0.834497i	0.517985	+	0.855390i	$0.326682\pi$
$854$	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	0.969496	−	0.245108i	$-0.0788233\pi$
$857$	36.3583	+	20.9915i	1.24197	+	0.717054i	0.272479	+	0.962162i	$0.412157\pi$
$858$	−6.41318	−	5.32171i	−0.218942	−	0.181680i
$859$	34.5524	−	19.9488i	1.17891	−	0.680645i	0.223149	−	0.974784i	$-0.428366\pi$
$859$	34.5524	−	19.9488i	1.17891	−	0.680645i	0.955763	+	0.294139i	$0.0950329\pi$
$860$	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	0.0554303	−	0.998463i	$-0.482347\pi$
$877$	−23.1449	−	13.3627i	−0.781549	−	0.451227i	−0.836979	+	0.547235i	$0.815680\pi$
$878$	−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	−0.797949	−	0.602724i	$-0.794082\pi$
$883$	−20.0563	+	11.5795i	−0.674950	+	0.389682i	0.123000	+	0.992407i	$0.460749\pi$
$884$	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	0.952812	−	0.303561i	$-0.0981757\pi$
$887$	6.35899	+	11.0141i	0.213514	+	0.369817i	−0.739298	+	0.673379i	$0.764842\pi$
$888$	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	0.224432	+	0.974490i	$0.427947\pi$
$907$	−22.0367	+	38.1687i	−0.731717	+	1.26737i	−0.956149	+	0.292881i	$0.905386\pi$
$908$	−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	$0.000417699\pi$
$919$			0.0795611i			0.00262448i	−0.999999	+	0.00131224i	$0.999582\pi$
$920$	−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	−0.793655	−	0.608368i	$-0.791824\pi$
$929$	3.96340	−	6.86481i	0.130035	−	0.225227i	0.923690	+	0.383141i	$0.125158\pi$
$930$	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	0.973243	+	0.229779i	$0.0738002\pi$
$937$	20.9870	+	36.3506i	0.685616	+	1.18752i	−0.287627	+	0.957742i	$0.592866\pi$
$938$	−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	−0.195459	−	0.980712i	$-0.562620\pi$
$941$	17.0598	−	9.84946i	0.556132	−	0.321083i	0.751592	+	0.659629i	$0.229286\pi$
$942$	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	0.577453	−	0.816424i	$-0.304047\pi$
$947$	4.89713	+	2.82736i	0.159135	+	0.0918768i	−0.418318	+	0.908301i	$0.637380\pi$
$948$	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	0.622448	−	0.782661i	$-0.286138\pi$
$953$	7.89881	+	4.56038i	0.255868	+	0.147725i	−0.366580	+	0.930386i	$0.619472\pi$
$954$	−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	0.129319	−	0.991603i	$-0.458721\pi$
$967$	−20.6723	−	11.9351i	−0.664775	−	0.383808i	−0.794094	+	0.607795i	$0.792054\pi$
$968$	−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	0.0694307	−	0.997587i	$-0.477882\pi$
$971$	28.0027	−	48.5022i	0.898651	−	1.55651i	0.829220	−	0.558922i	$-0.188785\pi$
$972$	−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	$-0.959439\pi$
$977$		−	7.94428i		−	0.254160i	0.991892	−	0.127080i	$-0.0405605\pi$
$978$	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	−0.370802	−	0.928712i	$-0.620917\pi$
$983$	19.4039	−	33.6085i	0.618887	−	1.07194i	0.989689	−	0.143232i	$-0.0457494\pi$
$984$	−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	−0.984513	−	0.175310i	$-0.943907\pi$
$991$	−10.7169	+	18.5622i	−0.340433	+	0.589648i	0.644080	+	0.764958i	$0.277240\pi$
$992$	−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	0.997188	+	0.0749376i	$0.0238758\pi$
$997$	17.7924	+	30.8174i	0.563492	+	0.975997i	−0.433696	+	0.901059i	$0.642791\pi$
$998$	−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.103.8	yes	20
3.2	odd	2		684.2.r.b.559.3		20
4.3	odd	2		228.2.k.a.103.10	yes	20
12.11	even	2		684.2.r.c.559.1		20
19.12	odd	6		228.2.k.a.31.10	✓	20
57.50	even	6		684.2.r.c.487.1		20
76.31	even	6	inner	228.2.k.b.31.8	yes	20
228.107	odd	6		684.2.r.b.487.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.k.a.31.10	✓	20	19.12	odd	6
228.2.k.a.103.10	yes	20	4.3	odd	2
228.2.k.b.31.8	yes	20	76.31	even	6	inner
228.2.k.b.103.8	yes	20	1.1	even	1	trivial
684.2.r.b.487.3		20	228.107	odd	6
684.2.r.b.559.3		20	3.2	odd	2
684.2.r.c.487.1		20	57.50	even	6
684.2.r.c.559.1		20	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more