LMFDB - Embedded newform 228.2.k.a.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			$-1.34963 - 0.422503i$ of defining polynomial
Character	$\chi$	$=$	228.103
Dual form			228.2.k.a.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+(1.04071 - 0.957560i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.166160 - 1.99309i) q^{4} +(0.984694 - 1.70554i) q^{5} +(0.308915 + 1.38006i) q^{6} -0.355075i q^{7} +(-1.73557 - 2.23333i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.608374 - 2.71788i) q^{10} +1.34327i q^{11} +(1.64298 + 1.14044i) q^{12} +(5.75562 - 3.32301i) q^{13} +(-0.340006 - 0.369531i) q^{14} +(0.984694 + 1.70554i) q^{15} +(-3.94478 - 0.662340i) q^{16} +(-1.91321 + 3.31378i) q^{17} +(-1.34963 - 0.422503i) q^{18} +(-2.96616 + 3.19404i) q^{19} +(-3.23567 - 2.24597i) q^{20} +(0.307504 + 0.177538i) q^{21} +(1.28626 + 1.39795i) q^{22} +(2.43262 - 1.40448i) q^{23} +(2.80191 - 0.386384i) q^{24} +(0.560757 + 0.971259i) q^{25} +(2.80796 - 8.96963i) q^{26} +1.00000 q^{27} +(-0.707695 - 0.0589991i) q^{28} +(-4.28481 + 2.47383i) q^{29} +(2.65794 + 0.832071i) q^{30} +1.76220 q^{31} +(-4.73961 + 3.08806i) q^{32} +(-1.16330 - 0.671634i) q^{33} +(1.18204 + 5.28071i) q^{34} +(-0.605595 - 0.349640i) q^{35} +(-1.80914 + 0.852645i) q^{36} +8.49598i q^{37} +(-0.0284229 + 6.16435i) q^{38} +6.64601i q^{39} +(-5.51805 + 0.760940i) q^{40} +(-5.63122 - 3.25119i) q^{41} +(0.490026 - 0.109688i) q^{42} +(4.14089 + 2.39074i) q^{43} +(2.67725 + 0.223197i) q^{44} -1.96939 q^{45} +(1.18679 - 3.79103i) q^{46} +(-6.83062 + 3.94366i) q^{47} +(2.54599 - 3.08511i) q^{48} +6.87392 q^{49} +(1.51362 + 0.473842i) q^{50} +(-1.91321 - 3.31378i) q^{51} +(-5.66669 - 12.0236i) q^{52} +(-2.89136 + 1.66933i) q^{53} +(1.04071 - 0.957560i) q^{54} +(2.29100 + 1.32271i) q^{55} +(-0.793001 + 0.616259i) q^{56} +(-1.28305 - 4.16579i) q^{57} +(-2.09040 + 6.67750i) q^{58} +(-1.83715 + 3.18204i) q^{59} +(3.56290 - 1.67919i) q^{60} +(1.98919 + 3.44537i) q^{61} +(1.83395 - 1.68742i) q^{62} +(-0.307504 + 0.177538i) q^{63} +(-1.97556 + 7.75223i) q^{64} -13.0886i q^{65} +(-1.85379 + 0.414956i) q^{66} +(1.05161 + 1.82144i) q^{67} +(6.28675 + 4.36381i) q^{68} +2.80895i q^{69} +(-0.965050 + 0.216018i) q^{70} +(7.80349 - 13.5160i) q^{71} +(-1.06634 + 2.61972i) q^{72} +(0.435445 - 0.754212i) q^{73} +(8.13541 + 8.84186i) q^{74} -1.12151 q^{75} +(5.87315 + 6.44252i) q^{76} +0.476961 q^{77} +(6.36395 + 6.91658i) q^{78} +(8.37212 - 14.5009i) q^{79} +(-5.01405 + 6.07578i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-8.97368 + 2.00868i) q^{82} -8.44752i q^{83} +(0.404942 - 0.583382i) q^{84} +(3.76786 + 6.52612i) q^{85} +(6.59875 - 1.47707i) q^{86} -4.94767i q^{87} +(2.99997 - 2.33134i) q^{88} +(1.83862 - 1.06153i) q^{89} +(-2.04956 + 1.88581i) q^{90} +(-1.17992 - 2.04368i) q^{91} +(-2.39504 - 5.08179i) q^{92} +(-0.881102 + 1.52611i) q^{93} +(-3.33241 + 10.6449i) q^{94} +(2.52682 + 8.20405i) q^{95} +(-0.304533 - 5.64865i) q^{96} +(-13.7139 - 7.91774i) q^{97} +(7.15377 - 6.58219i) q^{98} +(1.16330 - 0.671634i) 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} + 13 q^{16} + 2 q^{18} - 12 q^{19} - 14 q^{20} + 6 q^{21} - 8 q^{22} - 7 q^{24} - 10 q^{25} + 20 q^{27}+ \cdots - 12 q^{98}+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 + 13 * q^16 + 2 * q^18 - 12 * q^19 - 14 * q^20 + 6 * q^21 - 8 * q^22 - 7 * q^24 - 10 * q^25 + 20 * q^27 + 7 * q^28 - 12 * q^31 - 31 * q^32 - 30 * q^34 + q^36 - 11 * q^38 - 26 * q^40 + 12 * q^41 - 9 * q^42 + 18 * q^43 + 30 * q^44 + 32 * q^46 + 36 * q^47 - 11 * 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 + 10 * q^60 + 10 * q^61 + 29 * q^62 - 6 * q^63 - 14 * q^64 - 8 * q^66 - 14 * q^67 + 40 * q^68 + 46 * q^70 - 8 * q^71 + 11 * q^72 - 6 * q^73 + 3 * q^74 + 20 * q^75 + 3 * q^76 - 32 * q^77 + 33 * q^78 + 6 * q^79 + 40 * q^80 - 10 * q^81 - 60 * q^82 - 14 * q^84 + 8 * q^85 - 25 * q^86 - 44 * q^88 - 24 * q^89 - 6 * q^90 - 26 * q^91 + 36 * q^92 + 6 * q^93 + 52 * q^94 - 4 * q^95 + 2 * q^96 - 12 * q^97 - 12 * q^98

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 $

$2$	1.04071	−	0.957560i	0.735894	−	0.677097i
$2$	1.04071	−	0.957560i	0.735894	−	0.677097i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.166160	−	1.99309i	0.0830798	−	0.996543i
$5$	0.984694	−	1.70554i	0.440368	−	0.762740i	−0.557348	−	0.830279i	$-0.688181\pi$
$5$	0.984694	−	1.70554i	0.440368	−	0.762740i	0.997717	+	0.0675384i	$0.0215145\pi$
$6$	0.308915	+	1.38006i	0.126114	+	0.563408i
$7$		−	0.355075i		−	0.134206i	−0.997746	−	0.0671029i	$-0.978624\pi$
$7$		−	0.355075i		−	0.134206i	0.997746	−	0.0671029i	$-0.0213756\pi$
$8$	−1.73557	−	2.23333i	−0.613618	−	0.789603i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.608374	−	2.71788i	−0.192385	−	0.859468i
$11$			1.34327i			0.405011i	0.979281	+	0.202505i	$0.0649084\pi$
$11$			1.34327i			0.405011i	−0.979281	+	0.202505i	$0.935092\pi$
$12$	1.64298	+	1.14044i	0.474288	+	0.329217i
$13$	5.75562	−	3.32301i	1.59632	−	0.921636i	0.604133	−	0.796884i	$-0.293520\pi$
$13$	5.75562	−	3.32301i	1.59632	−	0.921636i	0.992188	−	0.124752i	$-0.0398137\pi$
$14$	−0.340006	−	0.369531i	−0.0908703	−	0.0987612i
$15$	0.984694	+	1.70554i	0.254247	+	0.440368i
$16$	−3.94478	−	0.662340i	−0.986196	−	0.165585i
$17$	−1.91321	+	3.31378i	−0.464022	+	0.803710i	−0.999157	−	0.0410566i	$-0.986928\pi$
$17$	−1.91321	+	3.31378i	−0.464022	+	0.803710i	0.535134	+	0.844767i	$0.320261\pi$
$18$	−1.34963	−	0.422503i	−0.318110	−	0.0995848i
$19$	−2.96616	+	3.19404i	−0.680483	+	0.732764i
$19$	−2.96616	+	3.19404i	−0.680483	+	0.732764i
$20$	−3.23567	−	2.24597i	−0.723518	−	0.502214i
$21$	0.307504	+	0.177538i	0.0671029	+	0.0387419i
$22$	1.28626	+	1.39795i	0.274231	+	0.298045i
$23$	2.43262	−	1.40448i	0.507237	−	0.292853i	−0.224460	−	0.974483i	$-0.572062\pi$
$23$	2.43262	−	1.40448i	0.507237	−	0.292853i	0.731697	+	0.681630i	$0.238729\pi$
$24$	2.80191	−	0.386384i	0.571938	−	0.0788703i
$25$	0.560757	+	0.971259i	0.112151	+	0.194252i
$26$	2.80796	−	8.96963i	0.550686	−	1.75909i
$27$	1.00000			0.192450
$28$	−0.707695	−	0.0589991i	−0.133742	−	0.0111498i
$29$	−4.28481	+	2.47383i	−0.795669	+	0.459380i	−0.841954	−	0.539549i	$-0.818595\pi$
$29$	−4.28481	+	2.47383i	−0.795669	+	0.459380i	0.0462857	+	0.998928i	$0.485262\pi$
$30$	2.65794	+	0.832071i	0.485271	+	0.151915i
$31$	1.76220			0.316501			0.158251	−	0.987399i	$-0.449415\pi$
$31$	1.76220			0.316501			0.158251	+	0.987399i	$0.449415\pi$
$32$	−4.73961	+	3.08806i	−0.837852	+	0.545897i
$33$	−1.16330	−	0.671634i	−0.202505	−	0.116917i
$34$	1.18204	+	5.28071i	0.202718	+	0.905634i
$35$	−0.605595	−	0.349640i	−0.102364	−	0.0591000i
$36$	−1.80914	+	0.852645i	−0.301524	+	0.142107i
$37$			8.49598i			1.39673i	0.715742	+	0.698365i	$0.246089\pi$
$37$			8.49598i			1.39673i	−0.715742	+	0.698365i	$0.753911\pi$
$38$	−0.0284229	+	6.16435i	−0.00461081	+	0.999989i
$39$			6.64601i			1.06421i
$40$	−5.51805	+	0.760940i	−0.872480	+	0.120315i
$41$	−5.63122	−	3.25119i	−0.879449	−	0.507750i	−0.00897225	−	0.999960i	$-0.502856\pi$
$41$	−5.63122	−	3.25119i	−0.879449	−	0.507750i	−0.870477	+	0.492210i	$0.836189\pi$
$42$	0.490026	−	0.109688i	0.0756126	−	0.0169252i
$43$	4.14089	+	2.39074i	0.631479	+	0.364585i	0.781325	−	0.624125i	$-0.214544\pi$
$43$	4.14089	+	2.39074i	0.631479	+	0.364585i	−0.149845	+	0.988709i	$0.547878\pi$
$44$	2.67725	+	0.223197i	0.403611	+	0.0336482i
$45$	−1.96939			−0.293579
$46$	1.18679	−	3.79103i	0.174982	−	0.558957i
$47$	−6.83062	+	3.94366i	−0.996348	+	0.575242i	−0.907166	−	0.420774i	$-0.861759\pi$
$47$	−6.83062	+	3.94366i	−0.996348	+	0.575242i	−0.0891820	+	0.996015i	$0.528425\pi$
$48$	2.54599	−	3.08511i	0.367483	−	0.445297i
$49$	6.87392			0.981989
$50$	1.51362	+	0.473842i	0.214059	+	0.0670114i
$51$	−1.91321	−	3.31378i	−0.267903	−	0.464022i
$52$	−5.66669	−	12.0236i	−0.785828	−	1.66737i
$53$	−2.89136	+	1.66933i	−0.397159	+	0.229300i	−0.685257	−	0.728301i	$-0.740310\pi$
$53$	−2.89136	+	1.66933i	−0.397159	+	0.229300i	0.288098	+	0.957601i	$0.406977\pi$
$54$	1.04071	−	0.957560i	0.141623	−	0.130307i
$55$	2.29100	+	1.32271i	0.308918	+	0.178354i
$56$	−0.793001	+	0.616259i	−0.105969	+	0.0823511i
$57$	−1.28305	−	4.16579i	−0.169944	−	0.551772i
$58$	−2.09040	+	6.67750i	−0.274483	+	0.876799i
$59$	−1.83715	+	3.18204i	−0.239177	+	0.414266i	−0.960478	−	0.278355i	$-0.910211\pi$
$59$	−1.83715	+	3.18204i	−0.239177	+	0.414266i	0.721302	+	0.692621i	$0.243544\pi$
$60$	3.56290	−	1.67919i	0.459969	−	0.216782i
$61$	1.98919	+	3.44537i	0.254689	+	0.441135i	0.964811	−	0.262944i	$-0.0846935\pi$
$61$	1.98919	+	3.44537i	0.254689	+	0.441135i	−0.710122	+	0.704079i	$0.751360\pi$
$62$	1.83395	−	1.68742i	0.232911	−	0.214302i
$63$	−0.307504	+	0.177538i	−0.0387419	+	0.0223676i
$64$	−1.97556	+	7.75223i	−0.246946	+	0.969029i
$65$		−	13.0886i		−	1.62344i
$66$	−1.85379	+	0.414956i	−0.228186	+	0.0510776i
$67$	1.05161	+	1.82144i	0.128475	+	0.222525i	0.923086	−	0.384594i	$-0.125659\pi$
$67$	1.05161	+	1.82144i	0.128475	+	0.222525i	−0.794611	+	0.607119i	$0.792325\pi$
$68$	6.28675	+	4.36381i	0.762381	+	0.529190i
$69$			2.80895i			0.338158i
$70$	−0.965050	+	0.216018i	−0.115346	+	0.0258191i
$71$	7.80349	−	13.5160i	0.926104	−	1.60406i	0.136327	−	0.990664i	$-0.456470\pi$
$71$	7.80349	−	13.5160i	0.926104	−	1.60406i	0.789776	−	0.613395i	$-0.210197\pi$
$72$	−1.06634	+	2.61972i	−0.125669	+	0.308737i
$73$	0.435445	−	0.754212i	0.0509649	−	0.0882739i	−0.839417	−	0.543487i	$-0.817104\pi$
$73$	0.435445	−	0.754212i	0.0509649	−	0.0882739i	0.890382	+	0.455213i	$0.150437\pi$
$74$	8.13541	+	8.84186i	0.945722	+	1.02785i
$75$	−1.12151			−0.129501
$76$	5.87315	+	6.44252i	0.673697	+	0.739008i
$77$	0.476961			0.0543548
$78$	6.36395	+	6.91658i	0.720576	+	0.783148i
$79$	8.37212	−	14.5009i	0.941937	−	1.63148i	0.180165	−	0.983636i	$-0.442337\pi$
$79$	8.37212	−	14.5009i	0.941937	−	1.63148i	0.761771	−	0.647846i	$-0.224330\pi$
$80$	−5.01405	+	6.07578i	−0.560588	+	0.679293i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−8.97368	+	2.00868i	−0.990977	+	0.221822i
$83$		−	8.44752i		−	0.927235i	−0.886035	−	0.463618i	$-0.846551\pi$
$83$		−	8.44752i		−	0.927235i	0.886035	−	0.463618i	$-0.153449\pi$
$84$	0.404942	−	0.583382i	0.0441828	−	0.0636522i
$85$	3.76786	+	6.52612i	0.408682	+	0.707857i
$86$	6.59875	−	1.47707i	0.711561	−	0.159277i
$87$		−	4.94767i		−	0.530446i
$88$	2.99997	−	2.33134i	0.319798	−	0.248522i
$89$	1.83862	−	1.06153i	0.194894	−	0.112522i	−0.399378	−	0.916786i	$-0.630774\pi$
$89$	1.83862	−	1.06153i	0.194894	−	0.112522i	0.594271	+	0.804265i	$0.297440\pi$
$90$	−2.04956	+	1.88581i	−0.216043	+	0.198781i
$91$	−1.17992	−	2.04368i	−0.123689	−	0.214235i
$92$	−2.39504	−	5.08179i	−0.249700	−	0.529814i
$93$	−0.881102	+	1.52611i	−0.0913660	+	0.158251i
$94$	−3.33241	+	10.6449i	−0.343712	+	1.09794i
$95$	2.52682	+	8.20405i	0.259246	+	0.841718i
$96$	−0.304533	−	5.64865i	−0.0310812	−	0.576513i
$97$	−13.7139	−	7.91774i	−1.39244	−	0.803924i	−0.398853	−	0.917015i	$-0.630592\pi$
$97$	−13.7139	−	7.91774i	−1.39244	−	0.803924i	−0.993585	+	0.113090i	$0.963925\pi$
$98$	7.15377	−	6.58219i	0.722640	−	0.664902i
$99$	1.16330	−	0.671634i	0.116917	−	0.0675018i
$100$	2.02898	−	0.956252i	0.202898	−	0.0956252i
$101$	2.81400	+	4.87399i	0.280004	+	0.484980i	0.971385	−	0.237509i	$-0.0763310\pi$
$101$	2.81400	+	4.87399i	0.280004	+	0.484980i	−0.691382	+	0.722490i	$0.742998\pi$
$102$	−5.16425	−	1.61667i	−0.511337	−	0.160075i
$103$	−17.9755			−1.77118			−0.885590	−	0.464469i	$-0.846245\pi$
$103$	−17.9755			−1.77118			−0.885590	+	0.464469i	$0.846245\pi$
$104$	−17.4107	−	7.08689i	−1.70726	−	0.694927i
$105$	0.605595	−	0.349640i	0.0591000	−	0.0341214i
$106$	−1.41059	+	4.50594i	−0.137009	+	0.437655i
$107$	−10.4128			−1.00664			−0.503322	−	0.864099i	$-0.667889\pi$
$107$	−10.4128			−1.00664			−0.503322	+	0.864099i	$0.667889\pi$
$108$	0.166160	−	1.99309i	0.0159887	−	0.191785i
$109$	−0.0517777	−	0.0298939i	−0.00495940	−	0.00286331i	0.497518	−	0.867454i	$-0.334245\pi$
$109$	−0.0517777	−	0.0298939i	−0.00495940	−	0.00286331i	−0.502478	+	0.864590i	$0.667578\pi$
$110$	3.65084	−	0.817209i	0.348094	−	0.0779179i
$111$	−7.35773	−	4.24799i	−0.698365	−	0.403201i
$112$	−0.235181	+	1.40069i	−0.0222225	+	0.132353i
$113$			0.272476i			0.0256324i	0.999918	+	0.0128162i	$0.00407963\pi$
$113$			0.272476i			0.0256324i	−0.999918	+	0.0128162i	$0.995920\pi$
$114$	−5.32427	−	3.10679i	−0.498664	−	0.290977i
$115$		−	5.53191i		−	0.515853i
$116$	4.21860	+	8.95104i	0.391687	+	0.831083i
$117$	−5.75562	−	3.32301i	−0.532107	−	0.307212i
$118$	1.13505	+	5.07076i	0.104490	+	0.466802i
$119$	1.17664	+	0.679334i	0.107863	+	0.0622745i
$120$	2.10003	−	5.15924i	0.191706	−	0.470972i
$121$	9.19563			0.835966
$122$	5.36932	+	1.68087i	0.486115	+	0.152179i
$123$	5.63122	−	3.25119i	0.507750	−	0.293150i
$124$	0.292807	−	3.51222i	0.0262948	−	0.315407i
$125$	12.0556			1.07829
$126$	−0.150020	+	0.479219i	−0.0133649	+	0.0426922i
$127$	−6.44881	−	11.1697i	−0.572239	−	0.991148i	−0.996336	−	0.0855306i	$-0.972741\pi$
$127$	−6.44881	−	11.1697i	−0.572239	−	0.991148i	0.424096	−	0.905617i	$-0.360592\pi$
$128$	5.36723	+	9.95956i	0.474401	+	0.880309i
$129$	−4.14089	+	2.39074i	−0.364585	+	0.210493i
$130$	−12.5331	−	13.6214i	−1.09922	−	1.19468i
$131$	−9.18456	−	5.30271i	−0.802459	−	0.463300i	0.0418713	−	0.999123i	$-0.486668\pi$
$131$	−9.18456	−	5.30271i	−0.802459	−	0.463300i	−0.844330	+	0.535823i	$0.820001\pi$
$132$	−1.53192	+	2.20697i	−0.133336	+	0.192092i
$133$	1.13413	+	1.05321i	0.0983412	+	0.0913247i
$134$	2.83856	+	0.888617i	0.245215	+	0.0767648i
$135$	0.984694	−	1.70554i	0.0847489	−	0.146789i
$136$	10.7213	−	1.47847i	0.919345	−	0.126778i
$137$	−2.79679	−	4.84418i	−0.238946	−	0.413866i	0.721466	−	0.692449i	$-0.243468\pi$
$137$	−2.79679	−	4.84418i	−0.238946	−	0.413866i	−0.960412	+	0.278583i	$0.910135\pi$
$138$	2.68974	+	2.92331i	0.228966	+	0.248848i
$139$	9.39468	−	5.42402i	0.796846	−	0.460060i	−0.0455208	−	0.998963i	$-0.514495\pi$
$139$	9.39468	−	5.42402i	0.796846	−	0.460060i	0.842367	+	0.538904i	$0.181161\pi$
$140$	−0.797488	+	1.14891i	−0.0674001	+	0.0971003i
$141$		−	7.88732i		−	0.664232i
$142$	−4.82123	−	21.5386i	−0.404589	−	1.80748i
$143$	4.46369	+	7.73134i	0.373273	+	0.646527i
$144$	1.39879	+	3.74745i	0.116566	+	0.312288i
$145$			9.74388i			0.809185i
$146$	−0.269031	−	1.20188i	−0.0222652	−	0.0994684i
$147$	−3.43696	+	5.95299i	−0.283476	+	0.490994i
$148$	16.9332	+	1.41169i	1.39190	+	0.116040i
$149$	−9.13332	+	15.8194i	−0.748230	+	1.29597i	0.200440	+	0.979706i	$0.435763\pi$
$149$	−9.13332	+	15.8194i	−0.748230	+	1.29597i	−0.948670	+	0.316267i	$0.897570\pi$
$150$	−1.16717	+	1.07392i	−0.0952992	+	0.0876849i
$151$	1.59192			0.129549			0.0647743	−	0.997900i	$-0.479367\pi$
$151$	1.59192			0.129549			0.0647743	+	0.997900i	$0.479367\pi$
$152$	12.2814	+	1.08091i	0.996149	+	0.0876738i
$153$	3.82643			0.309348
$154$	0.496379	−	0.456719i	0.0399994	−	0.0368034i
$155$	1.73523	−	3.00551i	0.139377	−	0.241408i
$156$	13.2461	+	1.10430i	1.06053	+	0.0884146i
$157$	0.00391076	−	0.00677364i	0.000312113	−	0.000540595i	−0.865869	−	0.500270i	$-0.833234\pi$
$157$	0.00391076	−	0.00677364i	0.000312113	−	0.000540595i	0.866181	+	0.499730i	$0.166567\pi$
$158$	−5.17255	−	23.1081i	−0.411506	−	1.83838i
$159$		−	3.33866i		−	0.264773i
$160$	0.599742	+	11.1244i	0.0474138	+	0.879460i
$161$	−0.498694	−	0.863764i	−0.0393026	−	0.0680741i
$162$	0.308915	+	1.38006i	0.0242707	+	0.108428i
$163$			17.5559i			1.37509i	0.726143	+	0.687544i	$0.241311\pi$
$163$			17.5559i			1.37509i	−0.726143	+	0.687544i	$0.758689\pi$
$164$	−7.41558	+	10.6833i	−0.579059	+	0.834225i
$165$	−2.29100	+	1.32271i	−0.178354	+	0.102973i
$166$	−8.08900	−	8.79142i	−0.627828	−	0.682347i
$167$	11.2272	+	19.4461i	0.868787	+	1.50478i	0.863238	+	0.504798i	$0.168433\pi$
$167$	11.2272	+	19.4461i	0.868787	+	1.50478i	0.00554910	+	0.999985i	$0.498234\pi$
$168$	−0.137195	−	0.994889i	−0.0105849	−	0.0767574i
$169$	15.5847	−	26.9936i	1.19883	−	2.07643i
$170$	10.1704	+	3.18386i	0.780034	+	0.244191i
$171$	4.24920	+	0.971743i	0.324945	+	0.0743111i
$172$	5.45300	−	7.85590i	0.415788	−	0.599007i
$173$	−6.61142	−	3.81710i	−0.502657	−	0.290209i	0.227153	−	0.973859i	$-0.427058\pi$
$173$	−6.61142	−	3.81710i	−0.502657	−	0.290209i	−0.729810	+	0.683650i	$0.760391\pi$
$174$	−4.73769	−	5.14909i	−0.359163	−	0.390352i
$175$	0.344870	−	0.199111i	0.0260697	−	0.0150514i
$176$	0.889701	−	5.29890i	0.0670637	−	0.399420i
$177$	−1.83715	−	3.18204i	−0.138089	−	0.239177i
$178$	0.896998	−	2.86534i	0.0672329	−	0.214766i
$179$	12.2234			0.913619			0.456809	−	0.889565i	$-0.348992\pi$
$179$	12.2234			0.913619			0.456809	+	0.889565i	$0.348992\pi$
$180$	−0.327232	+	3.92516i	−0.0243905	+	0.292564i
$181$	−9.15093	+	5.28329i	−0.680183	+	0.392704i	−0.799924	−	0.600101i	$-0.795127\pi$
$181$	−9.15093	+	5.28329i	−0.680183	+	0.392704i	0.119741	+	0.992805i	$0.461794\pi$
$182$	−3.18489	−	0.997036i	−0.236080	−	0.0739052i
$183$	−3.97837			−0.294090
$184$	−7.35866	−	2.99529i	−0.542488	−	0.220816i
$185$	14.4902	+	8.36594i	1.06534	+	0.615076i
$186$	0.544372	+	2.43195i	0.0399153	+	0.178319i
$187$	−4.45130	−	2.56996i	−0.325511	−	0.187934i
$188$	6.72508	+	14.2693i	0.490477	+	1.04069i
$189$		−	0.355075i		−	0.0258279i
$190$	10.4856	+	6.11847i	0.760702	+	0.443881i
$191$			15.0979i			1.09244i	0.837641	+	0.546222i	$0.183934\pi$
$191$			15.0979i			1.09244i	−0.837641	+	0.546222i	$0.816066\pi$
$192$	−5.72585	−	5.58701i	−0.413228	−	0.403207i
$193$	−19.1330	−	11.0464i	−1.37722	−	0.795141i	−0.385400	−	0.922750i	$-0.625936\pi$
$193$	−19.1330	−	11.0464i	−1.37722	−	0.795141i	−0.991825	+	0.127609i	$0.959270\pi$
$194$	−21.8539	+	4.89182i	−1.56902	+	0.351212i
$195$	11.3350	+	6.54429i	0.811719	+	0.468646i
$196$	1.14217	−	13.7003i	0.0815834	−	0.978594i
$197$	11.7097			0.834278			0.417139	−	0.908843i	$-0.363033\pi$
$197$	11.7097			0.834278			0.417139	+	0.908843i	$0.363033\pi$
$198$	0.567534	−	1.81291i	0.0403329	−	0.128838i
$199$	0.153604	−	0.0886834i	0.0108887	−	0.00628660i	−0.494546	−	0.869152i	$-0.664666\pi$
$199$	0.153604	−	0.0886834i	0.0108887	−	0.00628660i	0.505434	+	0.862865i	$0.331332\pi$
$200$	1.19591	−	2.93805i	0.0845637	−	0.207751i
$201$	−2.10322			−0.148350
$202$	7.59570	+	2.37785i	0.534432	+	0.167305i
$203$	0.878397	+	1.52143i	0.0616514	+	0.106783i
$204$	−6.92255	+	3.26258i	−0.484676	+	0.228426i
$205$	−11.0901	+	6.40285i	−0.774563	+	0.447194i
$206$	−18.7073	+	17.2126i	−1.30340	+	1.19926i
$207$	−2.43262	−	1.40448i	−0.169079	−	0.0976178i
$208$	−24.9056	+	9.29636i	−1.72689	+	0.644586i
$209$	−4.29046	−	3.98434i	−0.296777	−	0.275603i
$210$	0.295448	−	0.943767i	0.0203878	−	0.0651261i
$211$	6.51477	−	11.2839i	0.448495	−	0.776817i	−0.549793	−	0.835301i	$-0.685293\pi$
$211$	6.51477	−	11.2839i	0.448495	−	0.776817i	0.998288	+	0.0584842i	$0.0186267\pi$
$212$	2.84669	+	6.04010i	0.195511	+	0.414836i
$213$	7.80349	+	13.5160i	0.534686	+	0.926104i
$214$	−10.8367	+	9.97087i	−0.740783	+	0.681595i
$215$	8.15501	−	4.70830i	0.556167	−	0.321103i
$216$	−1.73557	−	2.23333i	−0.118091	−	0.151959i
$217$		−	0.625715i		−	0.0424763i
$218$	−0.0825108	+	0.0184693i	−0.00558834	+	0.00125090i
$219$	0.435445	+	0.754212i	0.0294246	+	0.0509649i
$220$	3.01694	−	4.34637i	0.203402	−	0.293032i
$221$			25.4305i			1.71064i
$222$	−11.7250	+	2.62454i	−0.786929	+	0.176147i
$223$	−2.15498	+	3.73253i	−0.144308	+	0.249949i	−0.929115	−	0.369792i	$-0.879429\pi$
$223$	−2.15498	+	3.73253i	−0.144308	+	0.249949i	0.784807	+	0.619741i	$0.212762\pi$
$224$	1.09649	+	1.68292i	0.0732625	+	0.112445i
$225$	0.560757	−	0.971259i	0.0373838	−	0.0647506i
$226$	0.260912	+	0.283569i	0.0173556	+	0.0188627i
$227$	−21.1194			−1.40175			−0.700873	−	0.713286i	$-0.747206\pi$
$227$	−21.1194			−1.40175			−0.700873	+	0.713286i	$0.747206\pi$
$228$	−8.51596	+	1.86504i	−0.563983	+	0.123515i
$229$	−4.17703			−0.276026			−0.138013	−	0.990430i	$-0.544072\pi$
$229$	−4.17703			−0.276026			−0.138013	+	0.990430i	$0.544072\pi$
$230$	−5.29713	−	5.75712i	−0.349283	−	0.379613i
$231$	−0.238481	+	0.413061i	−0.0156909	+	0.0271774i
$232$	12.9615	+	5.27588i	0.850964	+	0.346379i
$233$	14.2716	−	24.7192i	0.934964	−	1.61941i	0.160267	−	0.987074i	$-0.448764\pi$
$233$	14.2716	−	24.7192i	0.934964	−	1.61941i	0.774697	−	0.632332i	$-0.217902\pi$
$234$	−9.17191	+	2.05305i	−0.599587	+	0.134212i
$235$			15.5332i			1.01327i
$236$	6.03681	+	4.19032i	0.392963	+	0.272767i
$237$	8.37212	+	14.5009i	0.543827	+	0.941937i
$238$	1.87505	−	0.419714i	0.121541	−	0.0272060i
$239$			0.705254i			0.0456191i	0.999740	+	0.0228095i	$0.00726113\pi$
$239$			0.705254i			0.0456191i	−0.999740	+	0.0228095i	$0.992739\pi$
$240$	−2.75475	−	7.38018i	−0.177819	−	0.476389i
$241$	−4.95189	+	2.85897i	−0.318979	+	0.184163i	−0.650937	−	0.759131i	$-0.725624\pi$
$241$	−4.95189	+	2.85897i	−0.318979	+	0.184163i	0.331958	+	0.943294i	$0.392291\pi$
$242$	9.56999	−	8.80536i	0.615183	−	0.566030i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	7.19744	−	3.39214i	0.460769	−	0.217159i
$245$	6.76871	−	11.7237i	0.432437	−	0.749003i
$246$	2.74727	−	8.77578i	0.175160	−	0.559523i
$247$	−6.45822	+	28.2402i	−0.410927	+	1.79688i
$248$	−3.05844	−	3.93559i	−0.194211	−	0.249910i
$249$	7.31576	+	4.22376i	0.463618	+	0.267670i
$250$	12.5464	−	11.5440i	0.793506	−	0.730106i
$251$	−14.2589	+	8.23237i	−0.900013	+	0.519623i	−0.877204	−	0.480117i	$-0.840594\pi$
$251$	−14.2589	+	8.23237i	−0.900013	+	0.519623i	−0.0228086	+	0.999740i	$0.507261\pi$
$252$	0.302753	+	0.642382i	0.0190716	+	0.0404662i
$253$	1.88659	+	3.26767i	0.118609	+	0.205436i
$254$	−17.4070	−	5.44928i	−1.09221	−	0.341918i
$255$	−7.53572			−0.471905
$256$	15.1226	+	5.22558i	0.945163	+	0.326599i
$257$	−13.2604	+	7.65590i	−0.827161	+	0.477562i	−0.852880	−	0.522107i	$-0.825146\pi$
$257$	−13.2604	+	7.65590i	−0.827161	+	0.477562i	0.0257185	+	0.999669i	$0.491813\pi$
$258$	−2.02019	+	6.45322i	−0.125772	+	0.401760i
$259$	3.01671			0.187449
$260$	−26.0866	−	2.17479i	−1.61783	−	0.134875i
$261$	4.28481	+	2.47383i	0.265223	+	0.153127i
$262$	−14.6361	+	3.27618i	−0.904224	+	0.202403i
$263$	12.0977	+	6.98462i	0.745977	+	0.430690i	0.824238	−	0.566243i	$-0.191604\pi$
$263$	12.0977	+	6.98462i	0.745977	+	0.430690i	−0.0782616	+	0.996933i	$0.524937\pi$
$264$	0.519018	+	3.76372i	0.0319433	+	0.231641i
$265$			6.57511i			0.403905i
$266$	2.18881	+	0.0100923i	0.134204	+	0.000618797i
$267$			2.12306i			0.129929i
$268$	3.80503	−	1.79330i	0.232429	−	0.109543i
$269$	−17.7199	−	10.2306i	−1.08040	−	0.623770i	−0.149396	−	0.988777i	$-0.547733\pi$
$269$	−17.7199	−	10.2306i	−1.08040	−	0.623770i	−0.931004	+	0.365008i	$0.881066\pi$
$270$	−0.608374	−	2.71788i	−0.0370245	−	0.165405i
$271$	−7.40043	−	4.27264i	−0.449544	−	0.259544i	0.258094	−	0.966120i	$-0.416906\pi$
$271$	−7.40043	−	4.27264i	−0.449544	−	0.259544i	−0.707638	+	0.706576i	$0.750239\pi$
$272$	9.74206	−	11.8050i	0.590699	−	0.715780i
$273$	2.35983			0.142824
$274$	−7.54924	−	2.36330i	−0.456066	−	0.142772i
$275$	−1.30466	+	0.753247i	−0.0786741	+	0.0454225i
$276$	5.59848	+	0.466734i	0.336989	+	0.0280941i
$277$	−10.4223			−0.626213			−0.313107	−	0.949718i	$-0.601370\pi$
$277$	−10.4223			−0.626213			−0.313107	+	0.949718i	$0.601370\pi$
$278$	4.58333	−	14.6408i	0.274890	−	0.878097i
$279$	−0.881102	−	1.52611i	−0.0527502	−	0.0913660i
$280$	0.270191	+	1.95932i	0.0161470	+	0.117092i
$281$	12.0512	−	6.95777i	0.718915	−	0.415066i	−0.0954384	−	0.995435i	$-0.530425\pi$
$281$	12.0512	−	6.95777i	0.718915	−	0.415066i	0.814353	+	0.580370i	$0.197092\pi$
$282$	−7.55257	−	8.20842i	−0.449749	−	0.488804i
$283$	13.1484	+	7.59120i	0.781588	+	0.451250i	0.836993	−	0.547214i	$-0.184312\pi$
$283$	13.1484	+	7.59120i	0.781588	+	0.451250i	−0.0554045	+	0.998464i	$0.517645\pi$
$284$	−25.6420	−	17.7988i	−1.52157	−	1.05617i
$285$	−8.36832	−	1.91374i	−0.495697	−	0.113360i
$286$	12.0486	+	3.77184i	0.712450	+	0.223034i
$287$	−1.15442	+	1.99951i	−0.0681430	+	0.118027i
$288$	5.04414	+	2.56059i	0.297229	+	0.150884i
$289$	1.17923	+	2.04249i	0.0693665	+	0.120146i
$290$	9.33034	+	10.1406i	0.547897	+	0.595474i
$291$	13.7139	−	7.91774i	0.803924	−	0.464146i
$292$	−1.43086	−	0.993198i	−0.0837346	−	0.0581225i
$293$			15.3923i			0.899229i	0.893223	+	0.449614i	$0.148439\pi$
$293$			15.3923i			0.899229i	−0.893223	+	0.449614i	$0.851561\pi$
$294$	2.12346	+	9.48644i	0.123843	+	0.553260i
$295$	3.61806	+	6.26666i	0.210652	+	0.364859i
$296$	18.9744	−	14.7454i	1.10286	−	0.857059i
$297$			1.34327i			0.0779444i
$298$	5.64284	+	25.2091i	0.326881	+	1.46032i
$299$	9.33416	−	16.1672i	0.539808	−	0.934976i
$300$	−0.186350	+	2.23527i	−0.0107589	+	0.129054i
$301$	0.848893	−	1.47033i	0.0489294	−	0.0847482i
$302$	1.65673	−	1.52436i	0.0953341	−	0.0877170i
$303$	−5.62800			−0.323320
$304$	13.8164	−	10.6352i	0.792424	−	0.609971i
$305$	7.83496			0.448628
$306$	3.98220	−	3.66403i	0.227647	−	0.209459i
$307$	−16.2895	+	28.2143i	−0.929692	+	1.61027i	−0.145856	+	0.989306i	$0.546594\pi$
$307$	−16.2895	+	28.2143i	−0.929692	+	1.61027i	−0.783836	+	0.620968i	$0.786740\pi$
$308$	0.0792517	−	0.950625i	0.00451578	−	0.0541669i
$309$	8.98775	−	15.5672i	0.511295	−	0.885590i
$310$	−1.07208	−	4.78945i	−0.0608900	−	0.272023i
$311$		−	23.4521i		−	1.32984i	−0.746913	−	0.664922i	$-0.768465\pi$
$311$		−	23.4521i		−	1.32984i	0.746913	−	0.664922i	$-0.231535\pi$
$312$	14.8428	−	11.5346i	0.840306	−	0.653021i
$313$	0.505863	+	0.876180i	0.0285930	+	0.0495246i	0.879968	−	0.475033i	$-0.157564\pi$
$313$	0.505863	+	0.876180i	0.0285930	+	0.0495246i	−0.851375	+	0.524558i	$0.824231\pi$
$314$	−0.00241619	−	0.0107942i	−0.000136353	−	0.000609151i
$315$			0.699280i			0.0394000i
$316$	−27.5105	−	19.0958i	−1.54759	−	1.07422i
$317$	26.9491	−	15.5591i	1.51361	−	0.873885i	0.513740	−	0.857946i	$-0.328259\pi$
$317$	26.9491	−	15.5591i	1.51361	−	0.873885i	0.999873	−	0.0159394i	$-0.00507388\pi$
$318$	−3.19696	−	3.47458i	−0.179277	−	0.194845i
$319$	−3.32302	−	5.75565i	−0.186054	−	0.322254i
$320$	11.2764	+	11.0030i	0.630371	+	0.615085i
$321$	5.20640	−	9.01775i	0.290593	−	0.503322i
$322$	−1.34610	−	0.421399i	−0.0750153	−	0.0234837i
$323$	−4.90948	−	15.9401i	−0.273171	−	0.886930i
$324$	1.64298	+	1.14044i	0.0912768	+	0.0633578i
$325$	6.45500	+	3.72680i	0.358059	+	0.206725i
$326$	16.8109	+	18.2707i	0.931067	+	1.01192i
$327$	0.0517777	−	0.0298939i	0.00286331	−	0.00165313i
$328$	2.51241	+	18.2191i	0.138725	+	1.00598i
$329$	1.40029	+	2.42538i	0.0772007	+	0.133716i
$330$	−1.11770	+	3.57032i	−0.0615271	+	0.196540i
$331$	33.1040			1.81956			0.909781	−	0.415089i	$-0.136250\pi$
$331$	33.1040			1.81956			0.909781	+	0.415089i	$0.136250\pi$
$332$	−16.8366	−	1.40364i	−0.924030	−	0.0770345i
$333$	7.35773	−	4.24799i	0.403201	−	0.232788i
$334$	30.3050	+	9.48704i	1.65822	+	0.519108i
$335$	4.14206			0.226305
$336$	−1.09545	−	0.904019i	−0.0597615	−	0.0493183i
$337$	−26.3761	−	15.2282i	−1.43680	−	0.829535i	−0.439171	−	0.898404i	$-0.644728\pi$
$337$	−26.3761	−	15.2282i	−1.43680	−	0.829535i	−0.997626	+	0.0688690i	$0.978061\pi$
$338$	−9.62873	−	43.0158i	−0.523734	−	2.33975i
$339$	−0.235971	−	0.136238i	−0.0128162	−	0.00739943i
$340$	13.6332	−	6.42529i	0.739363	−	0.348460i
$341$			2.36711i			0.128186i
$342$	5.35269	−	3.05756i	0.289441	−	0.165334i
$343$		−	4.92628i		−	0.265994i
$344$	−1.84749	−	13.3973i	−0.0996100	−	0.722334i
$345$	4.79078	+	2.76596i	0.257927	+	0.148914i
$346$	−10.5357	+	2.35832i	−0.566402	+	0.126784i
$347$	0.161858	+	0.0934487i	0.00868898	+	0.00501659i	0.504338	−	0.863506i	$-0.331736\pi$
$347$	0.161858	+	0.0934487i	0.00868898	+	0.00501659i	−0.495649	+	0.868523i	$0.665070\pi$
$348$	−9.86113	−	0.822102i	−0.528612	−	0.0440693i
$349$	5.01843			0.268631			0.134315	−	0.990939i	$-0.457116\pi$
$349$	5.01843			0.268631			0.134315	+	0.990939i	$0.457116\pi$
$350$	0.168250	−	0.537450i	0.00899332	−	0.0287279i
$351$	5.75562	−	3.32301i	0.307212	−	0.177369i
$352$	−4.14809	−	6.36657i	−0.221094	−	0.339339i
$353$	−29.7351			−1.58264			−0.791319	−	0.611404i	$-0.790605\pi$
$353$	−29.7351			−1.58264			−0.791319	+	0.611404i	$0.790605\pi$
$354$	−4.95893	−	1.55240i	−0.263564	−	0.0825092i
$355$	−15.3681	−	26.6183i	−0.815654	−	1.41275i
$356$	−1.81022	−	3.84092i	−0.0959412	−	0.203568i
$357$	−1.17664	+	0.679334i	−0.0622745	+	0.0359542i
$358$	12.7210	−	11.7046i	0.672327	−	0.618608i
$359$	−13.1403	−	7.58655i	−0.693518	−	0.400403i	0.111411	−	0.993774i	$-0.464463\pi$
$359$	−13.1403	−	7.58655i	−0.693518	−	0.400403i	−0.804929	+	0.593372i	$0.797796\pi$
$360$	3.41802	+	4.39830i	0.180145	+	0.231811i
$361$	−1.40385	−	18.9481i	−0.0738866	−	0.997267i
$362$	−4.46441	+	14.2609i	−0.234644	+	0.749538i
$363$	−4.59781	+	7.96365i	−0.241323	+	0.417983i
$364$	−4.26928	+	2.01210i	−0.223771	+	0.105463i
$365$	−0.857559	−	1.48534i	−0.0448867	−	0.0777461i
$366$	−4.14034	+	3.80953i	−0.216419	+	0.199127i
$367$	−12.4274	+	7.17495i	−0.648704	+	0.374530i	−0.787960	−	0.615727i	$-0.788862\pi$
$367$	−12.4274	+	7.17495i	−0.648704	+	0.374530i	0.139255	+	0.990257i	$0.455529\pi$
$368$	−10.5264	+	3.92912i	−0.548727	+	0.204820i
$369$			6.50237i			0.338500i
$370$	23.0910	−	5.16873i	1.20045	−	0.268710i
$371$	0.592737	+	1.02665i	0.0307734	+	0.0533010i
$372$	2.89527	+	2.00969i	0.150113	+	0.104198i
$373$			1.28645i			0.0666099i	0.999445	+	0.0333050i	$0.0106033\pi$
$373$			1.28645i			0.0666099i	−0.999445	+	0.0333050i	$0.989397\pi$
$374$	−7.09341	+	1.58780i	−0.366791	+	0.0821032i
$375$	−6.02782	+	10.4405i	−0.311275	+	0.539144i
$376$	20.6625	+	8.41054i	1.06559	+	0.433740i
$377$	−16.4411	+	28.4769i	−0.846762	+	1.46663i
$378$	−0.340006	−	0.369531i	−0.0174880	−	0.0190066i
$379$	1.85939			0.0955106			0.0477553	−	0.998859i	$-0.484793\pi$
$379$	1.85939			0.0955106			0.0477553	+	0.998859i	$0.484793\pi$
$380$	16.7712	−	3.67298i	0.860346	−	0.188420i
$381$	12.8976			0.660765
$382$	14.4571	+	15.7125i	0.739690	+	0.803922i
$383$	14.5822	−	25.2572i	0.745118	−	1.29058i	−0.205022	−	0.978757i	$-0.565727\pi$
$383$	14.5822	−	25.2572i	0.745118	−	1.29058i	0.950140	−	0.311824i	$-0.100940\pi$
$384$	−11.3088	−	0.331618i	−0.577102	−	0.0169228i
$385$	0.469661	−	0.813476i	0.0239361	−	0.0414586i
$386$	−30.4896	+	6.82483i	−1.55188	+	0.347375i
$387$		−	4.78149i		−	0.243057i
$388$	−18.0594	+	26.0174i	−0.916829	+	1.32083i
$389$	−2.67844	−	4.63919i	−0.135802	−	0.235216i	0.790101	−	0.612976i	$-0.210028\pi$
$389$	−2.67844	−	4.63919i	−0.135802	−	0.235216i	−0.925904	+	0.377760i	$0.876695\pi$
$390$	18.0630	−	4.04326i	0.914658	−	0.204738i
$391$			10.7482i			0.543562i
$392$	−11.9302	−	15.3518i	−0.602566	−	0.775381i
$393$	9.18456	−	5.30271i	0.463300	−	0.267486i
$394$	12.1864	−	11.2127i	0.613940	−	0.564887i
$395$	−16.4879	−	28.5580i	−0.829598	−	1.43691i
$396$	−1.14533	−	2.43016i	−0.0575550	−	0.122120i
$397$	13.0057	−	22.5266i	0.652738	−	1.13058i	−0.329718	−	0.944080i	$-0.606954\pi$
$397$	13.0057	−	22.5266i	0.652738	−	1.13058i	0.982456	−	0.186496i	$-0.0597131\pi$
$398$	0.0749380	−	0.239379i	0.00375630	−	0.0119990i
$399$	−1.47917	+	0.455578i	−0.0740510	+	0.0228074i
$400$	−1.56876	−	4.20282i	−0.0784379	−	0.210141i
$401$	19.4940	+	11.2548i	0.973482	+	0.562040i	0.900296	−	0.435278i	$-0.143350\pi$
$401$	19.4940	+	11.2548i	0.973482	+	0.562040i	0.0731860	+	0.997318i	$0.476683\pi$
$402$	−2.18885	+	2.01396i	−0.109170	+	0.100447i
$403$	10.1426	−	5.85582i	0.505237	−	0.291699i
$404$	10.1819	−	4.79869i	0.506566	−	0.238744i
$405$	0.984694	+	1.70554i	0.0489298	+	0.0847489i
$406$	2.37102	+	0.742250i	0.117672	+	0.0368372i
$407$	−11.4124			−0.565691
$408$	−4.08026	+	10.0242i	−0.202003	+	0.496270i
$409$	−17.7553	+	10.2510i	−0.877945	+	0.506882i	−0.869980	−	0.493087i	$-0.835869\pi$
$409$	−17.7553	+	10.2510i	−0.877945	+	0.506882i	−0.00796465	+	0.999968i	$0.502535\pi$
$410$	−5.41044	+	17.2829i	−0.267202	+	0.853542i
$411$	5.59357			0.275911
$412$	−2.98680	+	35.8267i	−0.147149	+	1.76506i
$413$	1.12986	+	0.652326i	0.0555969	+	0.0320989i
$414$	−3.87653	+	0.867728i	−0.190521	+	0.0426465i
$415$	−14.4076	−	8.31821i	−0.707240	−	0.408325i
$416$	−17.0177	+	33.5234i	−0.834363	+	1.64362i
$417$			10.8480i			0.531231i
$418$	−8.28038	−	0.0381796i	−0.405006	−	0.00186743i
$419$		−	12.8954i		−	0.629984i	−0.949094	−	0.314992i	$-0.897998\pi$
$419$		−	12.8954i		−	0.629984i	0.949094	−	0.314992i	$-0.102002\pi$
$420$	−0.596238	−	1.26510i	−0.0290934	−	0.0617305i
$421$	−16.5038	−	9.52845i	−0.804344	−	0.464388i	0.0406439	−	0.999174i	$-0.487059\pi$
$421$	−16.5038	−	9.52845i	−0.804344	−	0.464388i	−0.844988	+	0.534785i	$0.820392\pi$
$422$	−4.02502	−	17.9816i	−0.195935	−	0.875329i
$423$	6.83062	+	3.94366i	0.332116	+	0.191747i
$424$	8.74634	+	3.56013i	0.424760	+	0.172895i
$425$	−4.29139			−0.208163
$426$	21.0636	+	6.59399i	1.02053	+	0.319480i
$427$	1.22337	−	0.706310i	0.0592028	−	0.0341808i
$428$	−1.73019	+	20.7536i	−0.0836317	+	1.00316i
$429$	−8.92738			−0.431018
$430$	3.97854	−	12.7089i	0.191862	−	0.612877i
$431$	9.21153	+	15.9548i	0.443704	+	0.768517i	0.997961	−	0.0638282i	$-0.0203310\pi$
$431$	9.21153	+	15.9548i	0.443704	+	0.768517i	−0.554257	+	0.832345i	$0.686998\pi$
$432$	−3.94478	−	0.662340i	−0.189793	−	0.0318669i
$433$	−7.50721	+	4.33429i	−0.360774	+	0.208293i	−0.669420	−	0.742884i	$-0.733457\pi$
$433$	−7.50721	+	4.33429i	−0.360774	+	0.208293i	0.308646	+	0.951177i	$0.400124\pi$
$434$	−0.599159	−	0.651188i	−0.0287606	−	0.0312580i
$435$	−8.43844	−	4.87194i	−0.404592	−	0.233592i
$436$	−0.0681844	+	0.0982302i	−0.00326544	+	0.00470438i
$437$	−2.72958	+	11.9358i	−0.130573	+	0.570967i
$438$	1.17538	+	0.367953i	0.0561616	+	0.0175815i
$439$	15.6506	−	27.1077i	0.746963	−	1.29378i	−0.202309	−	0.979322i	$-0.564844\pi$
$439$	15.6506	−	27.1077i	0.746963	−	1.29378i	0.949272	−	0.314456i	$-0.101822\pi$
$440$	−1.02215	−	7.41222i	−0.0487289	−	0.353364i
$441$	−3.43696	−	5.95299i	−0.163665	−	0.283476i
$442$	24.3512	+	26.4658i	1.15827	+	1.25885i
$443$	2.99719	−	1.73043i	0.142401	−	0.0822152i	−0.427107	−	0.904201i	$-0.640467\pi$
$443$	2.99719	−	1.73043i	0.142401	−	0.0822152i	0.569508	+	0.821986i	$0.307134\pi$
$444$	−9.68917	+	13.9588i	−0.459827	+	0.662453i
$445$		−	4.18113i		−	0.198204i
$446$	1.33141	+	5.94801i	0.0630442	+	0.281646i
$447$	−9.13332	−	15.8194i	−0.431991	−	0.748230i
$448$	2.75263	+	0.701474i	0.130049	+	0.0331415i
$449$			17.3513i			0.818858i	0.912342	+	0.409429i	$0.134272\pi$
$449$			17.3513i			0.818858i	−0.912342	+	0.409429i	$0.865728\pi$
$450$	−0.346453	−	1.54776i	−0.0163319	−	0.0729620i
$451$	4.36722	−	7.56424i	0.205644	−	0.356186i
$452$	0.543068	+	0.0452745i	0.0255438	+	0.00212953i
$453$	−0.795961	+	1.37864i	−0.0373975	+	0.0647743i
$454$	−21.9792	+	20.2231i	−1.03154	+	0.949118i
$455$	−4.64743			−0.217875
$456$	−7.07678	+	10.0955i	−0.331400	+	0.472765i
$457$	−2.05680			−0.0962131			−0.0481065	−	0.998842i	$-0.515319\pi$
$457$	−2.05680			−0.0962131			−0.0481065	+	0.998842i	$0.515319\pi$
$458$	−4.34708	+	3.99976i	−0.203126	+	0.186896i
$459$	−1.91321	+	3.31378i	−0.0893011	+	0.154674i
$460$	−11.0256	−	0.919180i	−0.514070	−	0.0428570i
$461$	9.26074	−	16.0401i	0.431316	−	0.747061i	−0.565671	−	0.824631i	$-0.691383\pi$
$461$	9.26074	−	16.0401i	0.431316	−	0.747061i	0.996987	+	0.0775700i	$0.0247161\pi$
$462$	0.147341	+	0.658236i	0.00685491	+	0.0306239i
$463$			14.7319i			0.684649i	0.939582	+	0.342325i	$0.111214\pi$
$463$			14.7319i			0.684649i	−0.939582	+	0.342325i	$0.888786\pi$
$464$	18.5412	−	6.92074i	0.860751	−	0.321287i
$465$	1.73523	+	3.00551i	0.0804694	+	0.139377i
$466$	−8.81744	−	39.3914i	−0.408460	−	1.82477i
$467$			28.5370i			1.32054i	0.751030	+	0.660268i	$0.229557\pi$
$467$			28.5370i			1.32054i	−0.751030	+	0.660268i	$0.770443\pi$
$468$	−7.57939	+	10.9193i	−0.350357	+	0.504744i
$469$	0.646749	−	0.373401i	0.0298641	−	0.0172421i
$470$	14.8739	+	16.1656i	0.686084	+	0.745661i
$471$	0.00391076	+	0.00677364i	0.000180198	+	0.000312113i
$472$	10.2951	−	1.41969i	0.473869	−	0.0653466i
$473$	−3.21141	+	5.56232i	−0.147661	+	0.255756i
$474$	22.5985	+	7.07448i	1.03798	+	0.324942i
$475$	−4.76554	−	1.08982i	−0.218658	−	0.0500045i
$476$	1.54948	−	2.23227i	0.0710204	−	0.102316i
$477$	2.89136	+	1.66933i	0.132386	+	0.0764333i
$478$	0.675322	+	0.733966i	0.0308885	+	0.0335708i
$479$	−2.12263	+	1.22550i	−0.0969857	+	0.0559947i	−0.547708	−	0.836669i	$-0.684500\pi$
$479$	−2.12263	+	1.22550i	−0.0969857	+	0.0559947i	0.450723	+	0.892664i	$0.351166\pi$
$480$	−9.93387	−	5.04280i	−0.453417	−	0.230171i
$481$	28.2322	+	48.8996i	1.28728	+	2.22963i
$482$	−2.41585	+	7.71709i	−0.110039	+	0.351504i
$483$	0.997388			0.0453827
$484$	1.52794	−	18.3277i	0.0694519	−	0.833076i
$485$	−27.0080	+	15.5931i	−1.22637	+	0.708046i
$486$	−1.34963	−	0.422503i	−0.0612203	−	0.0191651i
$487$	−8.18323			−0.370817			−0.185409	−	0.982661i	$-0.559361\pi$
$487$	−8.18323			−0.370817			−0.185409	+	0.982661i	$0.559361\pi$
$488$	4.24229	−	10.4222i	0.192039	−	0.471791i
$489$	−15.2039	−	8.77797i	−0.687544	−	0.396954i
$490$	−4.18191	−	18.6825i	−0.188920	−	0.843988i
$491$	−0.994013	−	0.573893i	−0.0448592	−	0.0258994i	0.477403	−	0.878685i	$-0.341578\pi$
$491$	−0.994013	−	0.573893i	−0.0448592	−	0.0258994i	−0.522262	+	0.852785i	$0.674912\pi$
$492$	−5.54421	−	11.7637i	−0.249952	−	0.530350i
$493$		−	18.9319i		−	0.852649i
$494$	20.3206	+	35.5741i	0.914266	+	1.60055i
$495$		−	2.64542i		−	0.118903i
$496$	−6.95151	−	1.16718i	−0.312132	−	0.0524079i
$497$	−4.79921	−	2.77082i	−0.215274	−	0.124288i
$498$	11.6581	−	2.60957i	0.522412	−	0.116937i
$499$	−22.8813	−	13.2105i	−1.02431	−	0.591385i	−0.108959	−	0.994046i	$-0.534752\pi$
$499$	−22.8813	−	13.2105i	−1.02431	−	0.591385i	−0.915349	+	0.402662i	$0.868085\pi$
$500$	2.00316	−	24.0279i	0.0895840	−	1.07456i
$501$	−22.4544			−1.00319
$502$	−6.95640	+	22.2213i	−0.310479	+	0.991783i
$503$	33.7105	−	19.4628i	1.50308	−	0.867802i	0.503084	−	0.864238i	$-0.332199\pi$
$503$	33.7105	−	19.4628i	1.50308	−	0.867802i	0.999994	−	0.00356422i	$-0.00113453\pi$
$504$	0.930197	+	0.378630i	0.0414343	+	0.0168655i
$505$	11.0837			0.493219
$506$	5.09238	+	1.59418i	0.226384	+	0.0708698i
$507$	15.5847	+	26.9936i	0.692143	+	1.19883i
$508$	−23.3336	+	10.9971i	−1.03526	+	0.487917i
$509$	27.6426	−	15.9594i	1.22524	−	0.707390i	0.259206	−	0.965822i	$-0.416539\pi$
$509$	27.6426	−	15.9594i	1.22524	−	0.707390i	0.966029	+	0.258432i	$0.0832059\pi$
$510$	−7.84250	+	7.21590i	−0.347272	+	0.319525i
$511$	−0.267802	−	0.154616i	−0.0118469	−	0.00683979i
$512$	20.7421	−	9.04248i	0.916679	−	0.399625i
$513$	−2.96616	+	3.19404i	−0.130959	+	0.141021i
$514$	−6.46927	+	20.6652i	−0.285347	+	0.911503i
$515$	−17.7004	+	30.6579i	−0.779971	+	1.35095i
$516$	4.07691	+	8.65039i	0.179476	+	0.380812i
$517$	−5.29739	−	9.17535i	−0.232979	−	0.403531i
$518$	3.13952	−	2.88868i	0.137943	−	0.126921i
$519$	6.61142	−	3.81710i	0.290209	−	0.167552i
$520$	−29.2312	+	22.7162i	−1.28187	+	0.996171i
$521$		−	38.3269i		−	1.67913i	−0.543259	−	0.839565i	$-0.682810\pi$
$521$		−	38.3269i		−	1.67913i	0.543259	−	0.839565i	$-0.317190\pi$
$522$	6.82809	−	1.52841i	0.298857	−	0.0668967i
$523$	−12.2460	−	21.2106i	−0.535478	−	0.927475i	−0.999140	−	0.0414632i	$-0.986798\pi$
$523$	−12.2460	−	21.2106i	−0.535478	−	0.927475i	0.463662	−	0.886012i	$-0.346535\pi$
$524$	−12.0949	+	17.4245i	−0.528366	+	0.761194i
$525$			0.398222i			0.0173798i
$526$	19.2784	−	4.31531i	0.840579	−	0.188156i
$527$	−3.37147	+	5.83956i	−0.146864	+	0.254375i
$528$	4.14413	+	3.41995i	0.180350	+	0.148834i
$529$	−7.55490	+	13.0855i	−0.328474	+	0.568933i
$530$	6.29605	+	6.84279i	0.273483	+	0.297232i
$531$	3.67430			0.159451
$532$	2.28758	−	2.08541i	0.0991792	−	0.0904140i
$533$	−43.2149			−1.87184
$534$	2.03296	+	2.20949i	0.0879746	+	0.0956141i
$535$	−10.2534	+	17.7594i	−0.443294	+	0.767807i
$536$	2.24274	−	5.50985i	0.0968718	−	0.237989i
$537$	−6.11169	+	10.5858i	−0.263739	+	0.456809i
$538$	−28.2377	+	6.32077i	−1.21741	+	0.272508i
$539$			9.23352i			0.397716i
$540$	−3.23567	−	2.24597i	−0.139241	−	0.0966512i
$541$	15.0480	+	26.0639i	0.646964	+	1.12058i	0.983844	+	0.179027i	$0.0572951\pi$
$541$	15.0480	+	26.0639i	0.646964	+	1.12058i	−0.336880	+	0.941548i	$0.609372\pi$
$542$	−11.7930	+	2.63977i	−0.506553	+	0.113388i
$543$		−	10.5666i		−	0.453455i
$544$	−1.16527	−	21.6141i	−0.0499606	−	0.926699i
$545$	−0.101970	+	0.0588726i	−0.00436793	+	0.00252183i
$546$	2.45591	−	2.25968i	0.105103	−	0.0967054i
$547$	1.94265	+	3.36477i	0.0830619	+	0.143867i	0.904564	−	0.426339i	$-0.140197\pi$
$547$	1.94265	+	3.36477i	0.0830619	+	0.143867i	−0.821502	+	0.570206i	$0.806863\pi$
$548$	−10.1196	+	4.76933i	−0.432287	+	0.203736i
$549$	1.98919	−	3.44537i	0.0848964	−	0.147045i
$550$	−0.636498	+	2.03320i	−0.0271403	+	0.0866961i
$551$	4.80786	−	21.0236i	0.204822	−	0.895637i
$552$	6.27333	−	4.87514i	0.267010	−	0.207500i
$553$	−5.14892	−	2.97273i	−0.218954	−	0.126413i
$554$	−10.8466	+	9.97994i	−0.460827	+	0.424007i
$555$	−14.4902	+	8.36594i	−0.615076	+	0.355114i
$556$	−9.24952	−	19.6257i	−0.392267	−	0.832313i
$557$	9.25647	+	16.0327i	0.392209	+	0.679326i	0.992741	−	0.120275i	$-0.0383776\pi$
$557$	9.25647	+	16.0327i	0.392209	+	0.679326i	−0.600531	+	0.799601i	$0.705044\pi$
$558$	−2.37832	−	0.744536i	−0.100682	−	0.0315187i
$559$	31.7778			1.34406
$560$	2.15736	+	1.78036i	0.0911650	+	0.0752341i
$561$	4.45130	−	2.56996i	0.187934	−	0.108504i
$562$	5.87935	−	18.7808i	0.248005	−	0.792219i
$563$	37.3030			1.57213			0.786067	−	0.618141i	$-0.212114\pi$
$563$	37.3030			1.57213			0.786067	+	0.618141i	$0.212114\pi$
$564$	−15.7201	−	1.31055i	−0.661935	−	0.0551842i
$565$	0.464718	+	0.268305i	0.0195508	+	0.0112877i
$566$	20.9527	−	4.69008i	0.880706	−	0.197139i
$567$	0.307504	+	0.177538i	0.0129140	+	0.00745588i
$568$	−43.7294	+	6.03029i	−1.83484	+	0.253025i
$569$		−	35.1981i		−	1.47558i	−0.675030	−	0.737791i	$-0.735869\pi$
$569$		−	35.1981i		−	1.47558i	0.675030	−	0.737791i	$-0.264131\pi$
$570$	−10.5415	+	6.02152i	−0.441536	+	0.252214i
$571$		−	22.9289i		−	0.959544i	−0.877393	−	0.479772i	$-0.840719\pi$
$571$		−	22.9289i		−	0.959544i	0.877393	−	0.479772i	$-0.159281\pi$
$572$	16.1509	−	7.61188i	0.675303	−	0.318269i
$573$	−13.0751	−	7.54893i	−0.546222	−	0.315361i
$574$	0.713233	+	3.18633i	0.0297698	+	0.132995i
$575$	2.72822	+	1.57514i	0.113775	+	0.0656878i
$576$	7.70141	−	2.16523i	0.320892	−	0.0902178i
$577$	34.9147			1.45352			0.726759	−	0.686892i	$-0.241026\pi$
$577$	34.9147			1.45352			0.726759	+	0.686892i	$0.241026\pi$
$578$	3.18304	+	0.996456i	0.132397	+	0.0414471i
$579$	19.1330	−	11.0464i	0.795141	−	0.459075i
$580$	19.4204	+	1.61904i	0.806387	+	0.0672269i
$581$	−2.99950			−0.124440
$582$	6.69053	−	21.3720i	0.277331	−	0.885897i
$583$	−2.24236	−	3.88387i	−0.0928689	−	0.160854i
$584$	−2.44015	+	0.336498i	−0.100974	+	0.0139244i
$585$	−11.3350	+	6.54429i	−0.468646	+	0.270573i
$586$	14.7391	+	16.0190i	0.608865	+	0.661737i
$587$	−8.39604	−	4.84746i	−0.346542	−	0.200076i	0.316619	−	0.948553i	$-0.397452\pi$
$587$	−8.39604	−	4.84746i	−0.346542	−	0.200076i	−0.663161	+	0.748477i	$0.730786\pi$
$588$	11.2937	+	7.83930i	0.465746	+	0.323287i
$589$	−5.22697	+	5.62856i	−0.215374	+	0.231921i
$590$	9.76606	+	3.05728i	0.402062	+	0.125866i
$591$	−5.85483	+	10.1409i	−0.240835	+	0.417139i
$592$	5.62723	−	33.5148i	0.231278	−	1.37745i
$593$	−5.45069	−	9.44088i	−0.223833	−	0.387690i	0.732136	−	0.681159i	$-0.238524\pi$
$593$	−5.45069	−	9.44088i	−0.223833	−	0.387690i	−0.955969	+	0.293469i	$0.905190\pi$
$594$	1.28626	+	1.39795i	0.0527759	+	0.0573588i
$595$	2.31726	−	1.33787i	0.0949985	−	0.0548474i
$596$	30.0118	+	20.8320i	1.22933	+	0.853313i
$597$			0.177367i			0.00725914i
$598$	−5.76693	−	25.7634i	−0.235827	−	1.05355i
$599$	21.1928	+	36.7070i	0.865915	+	1.49981i	0.866136	+	0.499808i	$0.166596\pi$
$599$	21.1928	+	36.7070i	0.865915	+	1.49981i	−0.000221764		1.00000i	$0.500071\pi$
$600$	1.94647	+	2.50471i	0.0794643	+	0.102255i
$601$			5.82413i			0.237571i	0.992920	+	0.118786i	$0.0379001\pi$
$601$			5.82413i			0.237571i	−0.992920	+	0.118786i	$0.962100\pi$
$602$	−0.524472	−	2.34305i	−0.0213759	−	0.0954956i
$603$	1.05161	−	1.82144i	0.0428249	−	0.0741749i
$604$	0.264513	−	3.17284i	0.0107629	−	0.129101i
$605$	9.05488	−	15.6835i	0.368133	−	0.637625i
$606$	−5.85713	+	5.38915i	−0.237929	+	0.218919i
$607$	32.3172			1.31172			0.655858	−	0.754884i	$-0.272307\pi$
$607$	32.3172			1.31172			0.655858	+	0.754884i	$0.272307\pi$
$608$	4.19502	−	24.2982i	0.170131	−	0.985422i
$609$	−1.75679			−0.0711889
$610$	8.15393	−	7.50244i	0.330143	−	0.303765i
$611$	−26.2096	+	45.3964i	−1.06033	+	1.83654i
$612$	0.635797	−	7.62640i	0.0257006	−	0.308279i
$613$	−7.57118	+	13.1137i	−0.305797	+	0.529656i	−0.977438	−	0.211220i	$-0.932256\pi$
$613$	−7.57118	+	13.1137i	−0.305797	+	0.529656i	0.671641	+	0.740876i	$0.265590\pi$
$614$	10.0642	+	44.9611i	0.406157	+	1.81448i
$615$		−	12.8057i		−	0.516375i
$616$	−0.827802	−	1.06521i	−0.0333531	−	0.0429187i
$617$	17.9959	+	31.1699i	0.724489	+	1.25485i	0.959184	+	0.282782i	$0.0912573\pi$
$617$	17.9959	+	31.1699i	0.724489	+	1.25485i	−0.234696	+	0.972069i	$0.575409\pi$
$618$	−5.55291	−	24.8073i	−0.223371	−	0.997897i
$619$			18.3315i			0.736806i	0.929666	+	0.368403i	$0.120095\pi$
$619$			18.3315i			0.736806i	−0.929666	+	0.368403i	$0.879905\pi$
$620$	−5.70191	−	3.95786i	−0.228994	−	0.158951i
$621$	2.43262	−	1.40448i	0.0976178	−	0.0563597i
$622$	−22.4567	−	24.4068i	−0.900433	−	0.978624i
$623$	−0.376923	−	0.652850i	−0.0151011	−	0.0261559i
$624$	4.40192	−	26.2171i	0.176218	−	1.04952i
$625$	9.06732	−	15.7051i	0.362693	−	0.628202i
$626$	1.36545	+	0.427457i	0.0545744	+	0.0170846i
$627$	5.59577	−	1.72348i	0.223474	−	0.0688290i
$628$	−0.0128506	−	0.00891999i	−0.000512796	−	0.000355946i
$629$	−28.1538	−	16.2546i	−1.12257	−	0.648114i
$630$	0.669603	+	0.727749i	0.0266776	+	0.0289942i
$631$	−2.13172	+	1.23075i	−0.0848624	+	0.0489953i	−0.541831	−	0.840488i	$-0.682269\pi$
$631$	−2.13172	+	1.23075i	−0.0848624	+	0.0489953i	0.456968	+	0.889483i	$0.348935\pi$
$632$	−46.9159	+	6.46971i	−1.86621	+	0.257351i
$633$	6.51477	+	11.2839i	0.258939	+	0.448495i
$634$	13.1475	−	41.9979i	0.522154	−	1.66795i
$635$	−25.4004			−1.00798
$636$	−6.65423	−	0.554749i	−0.263857	−	0.0219972i
$637$	39.5637	−	22.8421i	1.56757	−	0.905036i
$638$	−8.96968	−	2.80797i	−0.355113	−	0.111169i
$639$	−15.6070			−0.617402
$640$	22.2715	+	0.653084i	0.880358	+	0.0258154i
$641$	36.7475	+	21.2162i	1.45144	+	0.837988i	0.998563	−	0.0535862i	$-0.0170652\pi$
$641$	36.7475	+	21.2162i	1.45144	+	0.837988i	0.452875	+	0.891574i	$0.350399\pi$
$642$	−3.21667	−	14.3703i	−0.126952	−	0.567151i
$643$	18.1691	+	10.4899i	0.716519	+	0.413682i	0.813470	−	0.581607i	$-0.197576\pi$
$643$	18.1691	+	10.4899i	0.716519	+	0.413682i	−0.0969511	+	0.995289i	$0.530909\pi$
$644$	−1.80442	+	0.850418i	−0.0711040	+	0.0335112i
$645$			9.41660i			0.370778i
$646$	−20.3729	−	11.8879i	−0.801562	−	0.467723i
$647$			41.3586i			1.62597i	0.582282	+	0.812987i	$0.302160\pi$
$647$			41.3586i			1.62597i	−0.582282	+	0.812987i	$0.697840\pi$
$648$	2.80191	−	0.386384i	0.110069	−	0.0151786i
$649$	−4.27433	−	2.46779i	−0.167782	−	0.0968691i
$650$	10.2864	−	2.30253i	0.403467	−	0.0903126i
$651$	0.541885	+	0.312857i	0.0212381	+	0.0122618i
$652$	34.9905	+	2.91709i	1.37033	+	0.114242i
$653$	21.1062			0.825950			0.412975	−	0.910742i	$-0.364490\pi$
$653$	21.1062			0.825950			0.412975	+	0.910742i	$0.364490\pi$
$654$	0.0252605	−	0.0806911i	0.000987763	−	0.00315527i
$655$	−18.0880	+	10.4431i	−0.706755	+	0.408045i
$656$	20.0605	+	16.5550i	0.783233	+	0.646364i
$657$	−0.870889			−0.0339766
$658$	3.77975	+	1.18326i	0.147350	+	0.0461281i
$659$	−10.9192	−	18.9126i	−0.425351	−	0.736730i	0.571102	−	0.820879i	$-0.306516\pi$
$659$	−10.9192	−	18.9126i	−0.425351	−	0.736730i	−0.996453	+	0.0841494i	$0.973183\pi$
$660$	2.25560	+	4.78594i	0.0877991	+	0.186292i
$661$	−7.76653	+	4.48401i	−0.302083	+	0.174408i	−0.643378	−	0.765548i	$-0.722468\pi$
$661$	−7.76653	+	4.48401i	−0.302083	+	0.174408i	0.341295	+	0.939956i	$0.389134\pi$
$662$	34.4517	−	31.6991i	1.33900	−	1.23202i
$663$	−22.0234	−	12.7152i	−0.855320	−	0.493819i
$664$	−18.8661	+	14.6613i	−0.732148	+	0.568968i
$665$	2.91305	−	0.897209i	0.112963	−	0.0347923i
$666$	3.58957	−	11.4664i	0.139093	−	0.444314i
$667$	−6.94888	+	12.0358i	−0.269062	+	0.466028i
$668$	40.6232	−	19.1456i	1.57176	−	0.740766i
$669$	−2.15498	−	3.73253i	−0.0833163	−	0.144308i
$670$	4.31069	−	3.96627i	0.166536	−	0.153230i
$671$	−4.62806	+	2.67201i	−0.178664	+	0.103152i
$672$	−2.00570	+	0.108132i	−0.0773714	+	0.00417128i
$673$			3.65151i			0.140756i	0.997520	+	0.0703778i	$0.0224205\pi$
$673$			3.65151i			0.140756i	−0.997520	+	0.0703778i	$0.977580\pi$
$674$	−42.0318	+	9.40847i	−1.61901	+	0.362401i
$675$	0.560757	+	0.971259i	0.0215835	+	0.0373838i
$676$	−51.2109	−	35.5470i	−1.96965	−	1.36719i
$677$		−	12.3206i		−	0.473520i	−0.971568	−	0.236760i	$-0.923915\pi$
$677$		−	12.3206i		−	0.473520i	0.971568	−	0.236760i	$-0.0760855\pi$
$678$	−0.376034	+	0.0841719i	−0.0144415	+	0.00323260i
$679$	−2.81139	+	4.86947i	−0.107891	+	0.186873i
$680$	8.03561	−	19.7415i	0.308152	−	0.757050i
$681$	10.5597	−	18.2900i	0.404649	−	0.700873i
$682$	2.26665	+	2.46348i	0.0867946	+	0.0943316i
$683$	−34.1567			−1.30697			−0.653486	−	0.756939i	$-0.726694\pi$
$683$	−34.1567			−1.30697			−0.653486	+	0.756939i	$0.726694\pi$
$684$	2.64281	−	8.30756i	0.101050	−	0.317647i
$685$	−11.0159			−0.420896
$686$	−4.71721	−	5.12684i	−0.180104	−	0.195744i
$687$	2.08852	−	3.61741i	0.0796818	−	0.138013i
$688$	−14.7514	−	12.1736i	−0.562392	−	0.464116i
$689$	−11.0944	+	19.2160i	−0.422662	+	0.732072i
$690$	7.63438	−	1.70889i	0.290636	−	0.0650564i
$691$		−	10.5938i		−	0.403008i	−0.979488	−	0.201504i	$-0.935417\pi$
$691$		−	10.5938i		−	0.403008i	0.979488	−	0.201504i	$-0.0645830\pi$
$692$	−8.70636	+	12.5429i	−0.330966	+	0.476808i
$693$	−0.238481	−	0.413061i	−0.00905913	−	0.0156909i
$694$	0.257930	−	0.0577354i	0.00979088	−	0.00219161i
$695$		−	21.3640i		−	0.810383i
$696$	−11.0498	+	8.58705i	−0.418842	+	0.325491i
$697$	21.5475	−	12.4404i	0.816168	−	0.471215i
$698$	5.22274	−	4.80545i	0.197684	−	0.181889i
$699$	14.2716	+	24.7192i	0.539802	+	0.934964i
$700$	−0.339541	−	0.720440i	−0.0128335	−	0.0272301i
$701$	5.91254	−	10.2408i	0.223314	−	0.386791i	−0.732498	−	0.680769i	$-0.761646\pi$
$701$	5.91254	−	10.2408i	0.223314	−	0.386791i	0.955812	+	0.293978i	$0.0949792\pi$
$702$	2.80796	−	8.96963i	0.105980	−	0.338537i
$703$	−27.1365	−	25.2004i	−1.02347	−	0.950451i
$704$	−10.4133	−	2.65371i	−0.392467	−	0.100016i
$705$	−13.4521	−	7.76659i	−0.506636	−	0.292507i
$706$	−30.9456	+	28.4731i	−1.16465	+	1.07160i
$707$	1.73063	−	0.999182i	0.0650872	−	0.0375781i
$708$	−6.64733	+	3.13287i	−0.249822	+	0.117741i
$709$	−3.70068	−	6.40977i	−0.138982	−	0.240724i	0.788130	−	0.615509i	$-0.211050\pi$
$709$	−3.70068	−	6.40977i	−0.138982	−	0.240724i	−0.927112	+	0.374786i	$0.877716\pi$
$710$	−41.4824	−	12.9861i	−1.55681	−	0.487360i
$711$	−16.7442			−0.627958
$712$	−5.56182	−	2.26390i	−0.208438	−	0.0848432i
$713$	4.28678	−	2.47497i	0.160541	−	0.0926884i
$714$	−0.574041	+	1.83370i	−0.0214829	+	0.0686243i
$715$	17.5815			0.657510
$716$	2.03103	−	24.3623i	0.0759032	−	0.910460i
$717$	−0.610768	−	0.352627i	−0.0228095	−	0.0131691i
$718$	−20.9398	+	4.68720i	−0.781467	+	0.174925i
$719$	28.7145	+	16.5783i	1.07087	+	0.618268i	0.928419	−	0.371534i	$-0.121168\pi$
$719$	28.7145	+	16.5783i	1.07087	+	0.618268i	0.142452	+	0.989802i	$0.454501\pi$
$720$	7.76880	+	1.30440i	0.289526	+	0.0486123i
$721$			6.38265i			0.237702i
$722$	−19.6049	−	18.3752i	−0.729619	−	0.683854i
$723$		−	5.71795i		−	0.212653i
$724$	9.00954	+	19.1164i	0.334837	+	0.710457i
$725$	−4.80547	−	2.77444i	−0.178471	−	0.103040i
$726$	2.84067	+	12.6905i	0.105427	+	0.470990i
$727$	−30.3035	−	17.4957i	−1.12390	−	0.648881i	−0.181503	−	0.983390i	$-0.558096\pi$
$727$	−30.3035	−	17.4957i	−1.12390	−	0.648881i	−0.942393	+	0.334509i	$0.891430\pi$
$728$	−2.51638	+	6.18210i	−0.0932632	+	0.229124i
$729$	1.00000			0.0370370
$730$	−2.31477	−	0.724642i	−0.0856735	−	0.0268202i
$731$	−15.8448	+	9.14800i	−0.586041	+	0.338351i
$732$	−0.661044	+	7.92924i	−0.0244329	+	0.293073i
$733$	4.06091			0.149993			0.0749966	−	0.997184i	$-0.476105\pi$
$733$	4.06091			0.149993			0.0749966	+	0.997184i	$0.476105\pi$
$734$	−6.06287	+	19.3670i	−0.223785	+	0.714850i
$735$	6.76871	+	11.7237i	0.249668	+	0.432437i
$736$	−7.19258	+	14.1687i	−0.265122	+	0.522267i
$737$	−2.44669	+	1.41260i	−0.0901249	+	0.0520336i
$738$	6.22641	+	6.76709i	0.229197	+	0.249100i
$739$	37.7065	+	21.7699i	1.38706	+	0.800817i	0.992982	−	0.118261i	$-0.0377321\pi$
$739$	37.7065	+	21.7699i	1.38706	+	0.800817i	0.394074	+	0.919079i	$0.371065\pi$
$740$	19.0817	−	27.4902i	0.701458	−	1.01056i
$741$	−21.2277	−	19.7131i	−0.779818	−	0.724179i
$742$	1.59995	+	0.500866i	0.0587359	+	0.0183874i
$743$	1.52131	−	2.63499i	0.0558115	−	0.0966683i	−0.836770	−	0.547555i	$-0.815559\pi$
$743$	1.52131	−	2.63499i	0.0558115	−	0.0966683i	0.892581	+	0.450887i	$0.148892\pi$
$744$	4.93754	−	0.680888i	0.181019	−	0.0249626i
$745$	17.9870	+	31.1545i	0.658994	+	1.14141i
$746$	1.23185	+	1.33882i	0.0451014	+	0.0490178i
$747$	−7.31576	+	4.22376i	−0.267670	+	0.154539i
$748$	−5.86178	+	8.44480i	−0.214328	+	0.308772i
$749$			3.69733i			0.135097i
$750$	3.72417	+	16.6375i	0.135987	+	0.607516i
$751$	13.9706	+	24.1977i	0.509794	+	0.882988i	0.999936	+	0.0113458i	$0.00361156\pi$
$751$	13.9706	+	24.1977i	0.509794	+	0.882988i	−0.490142	+	0.871643i	$0.663055\pi$
$752$	29.5573	−	11.0327i	1.07785	−	0.402320i
$753$		−	16.4647i		−	0.600009i
$754$	10.1578	+	45.3796i	0.369927	+	1.65263i
$755$	1.56755	−	2.71508i	0.0570492	−	0.0988120i
$756$	−0.707695	−	0.0589991i	−0.0257386	−	0.00214578i
$757$	6.64342	−	11.5067i	0.241459	−	0.418219i	−0.719671	−	0.694315i	$-0.755707\pi$
$757$	6.64342	−	11.5067i	0.241459	−	0.418219i	0.961130	+	0.276096i	$0.0890407\pi$
$758$	1.93509	−	1.78048i	0.0702857	−	0.0646699i
$759$	−3.77318			−0.136958
$760$	13.9369	−	19.8820i	0.505545	−	0.721195i
$761$	0.108264			0.00392458			0.00196229	−	0.999998i	$-0.499375\pi$
$761$	0.108264			0.00392458			0.00196229	+	0.999998i	$0.499375\pi$
$762$	13.4227	−	12.3502i	0.486253	−	0.447402i
$763$	−0.0106146	+	0.0183850i	−0.000384273	+	0.000665581i
$764$	30.0913	+	2.50865i	1.08867	+	0.0907599i
$765$	3.76786	−	6.52612i	0.136227	−	0.235952i
$766$	−9.00935	−	40.2488i	−0.325521	−	1.45425i
$767$			24.4194i			0.881735i
$768$	−12.0868	+	10.4838i	−0.436144	+	0.378301i
$769$	16.3034	+	28.2383i	0.587916	+	1.01830i	0.994505	+	0.104689i	$0.0333847\pi$
$769$	16.3034	+	28.2383i	0.587916	+	1.01830i	−0.406589	+	0.913611i	$0.633282\pi$
$770$	−0.290171	−	1.29632i	−0.0104570	−	0.0467162i
$771$		−	15.3118i		−	0.551441i
$772$	−25.1957	+	36.2983i	−0.906811	+	1.30640i
$773$	23.4972	−	13.5661i	0.845135	−	0.487939i	−0.0138713	−	0.999904i	$-0.504416\pi$
$773$	23.4972	−	13.5661i	0.845135	−	0.487939i	0.859006	+	0.511965i	$0.171082\pi$
$774$	−4.57856	−	4.97615i	−0.164573	−	0.178864i
$775$	0.988168	+	1.71156i	0.0354960	+	0.0614809i
$776$	6.11858	+	44.3696i	0.219644	+	1.59278i
$777$	−1.50836	+	2.61255i	−0.0541119	+	0.0937246i
$778$	−7.22979	−	2.26329i	−0.259200	−	0.0811431i
$779$	27.0875	−	8.34285i	0.970511	−	0.298914i
$780$	14.9267	−	21.5043i	0.534463	−	0.769978i
$781$	18.1557	+	10.4822i	0.649661	+	0.375082i
$782$	10.2921	+	11.1858i	0.368044	+	0.400004i
$783$	−4.28481	+	2.47383i	−0.153127	+	0.0884076i
$784$	−27.1161	−	4.55288i	−0.968433	−	0.162603i
$785$	−0.00770181	−	0.0133399i	−0.000274889	−	0.000476122i
$786$	4.48082	−	14.3134i	0.159825	−	0.510540i
$787$	−21.3735			−0.761882			−0.380941	−	0.924599i	$-0.624400\pi$
$787$	−21.3735			−0.761882			−0.380941	+	0.924599i	$0.624400\pi$
$788$	1.94567	−	23.3383i	0.0693117	−	0.831394i
$789$	−12.0977	+	6.98462i	−0.430690	+	0.248659i
$790$	−44.5051	−	13.9324i	−1.58342	−	0.495692i
$791$	0.0967494			0.00344001
$792$	−3.51899	−	1.43238i	−0.125042	−	0.0508973i
$793$	22.8980	+	13.2202i	0.813131	+	0.469461i
$794$	−8.03533	−	35.8974i	−0.285163	−	1.27395i
$795$	−5.69421	−	3.28755i	−0.201953	−	0.116597i
$796$	−0.151231	−	0.320882i	−0.00536024	−	0.0113734i
$797$			16.8176i			0.595709i	0.954611	+	0.297854i	$0.0962710\pi$
$797$			16.8176i			0.595709i	−0.954611	+	0.297854i	$0.903729\pi$
$798$	−1.10314	+	1.89052i	−0.0390509	+	0.0669235i
$799$		−	30.1802i		−	1.06770i
$800$	−5.65707	−	2.87174i	−0.200008	−	0.101531i
$801$	−1.83862	−	1.06153i	−0.0649646	−	0.0375073i
$802$	31.0648	−	6.95359i	1.09694	−	0.245540i
$803$	1.01311	+	0.584919i	0.0357519	+	0.0206414i
$804$	−0.349470	+	4.19190i	−0.0123249	+	0.147837i
$805$	−1.96424			−0.0692305
$806$	4.94819	−	15.8063i	0.174293	−	0.556754i
$807$	17.7199	−	10.2306i	0.623770	−	0.360134i
$808$	6.00135	−	14.7438i	0.211127	−	0.518684i
$809$	2.57747			0.0906191			0.0453095	−	0.998973i	$-0.485573\pi$
$809$	2.57747			0.0906191			0.0453095	+	0.998973i	$0.485573\pi$
$810$	2.65794	+	0.832071i	0.0933904	+	0.0292360i
$811$	3.04330	+	5.27116i	0.106865	+	0.185095i	0.914499	−	0.404589i	$-0.132585\pi$
$811$	3.04330	+	5.27116i	0.106865	+	0.185095i	−0.807634	+	0.589684i	$0.799252\pi$
$812$	3.17829	−	1.49792i	0.111536	−	0.0525667i
$813$	7.40043	−	4.27264i	0.259544	−	0.149848i
$814$	−11.8770	+	10.9280i	−0.416288	+	0.383027i
$815$	29.9424	+	17.2872i	1.04883	+	0.605545i
$816$	5.35236	+	14.3393i	0.187370	+	0.501978i
$817$	−19.9187	+	6.13487i	−0.696866	+	0.214632i
$818$	−8.66219	+	27.6702i	−0.302866	+	0.967465i
$819$	−1.17992	+	2.04368i	−0.0412296	+	0.0714118i
$820$	10.9187	+	23.1673i	0.381298	+	0.809038i
$821$	−8.28986	−	14.3585i	−0.289318	−	0.501114i	0.684329	−	0.729173i	$-0.260095\pi$
$821$	−8.28986	−	14.3585i	−0.289318	−	0.501114i	−0.973647	+	0.228060i	$0.926762\pi$
$822$	5.82129	−	5.35618i	0.203041	−	0.186818i
$823$	0.808864	−	0.466998i	0.0281952	−	0.0162785i	−0.485836	−	0.874050i	$-0.661485\pi$
$823$	0.808864	−	0.466998i	0.0281952	−	0.0162785i	0.514031	+	0.857771i	$0.328151\pi$
$824$	31.1978	+	40.1453i	1.08683	+	1.39853i
$825$		−	1.50649i		−	0.0524494i
$826$	1.80050	−	0.403027i	0.0626475	−	0.0140231i
$827$	−23.7237	−	41.0907i	−0.824954	−	1.42886i	−0.901954	−	0.431831i	$-0.857868\pi$
$827$	−23.7237	−	41.0907i	−0.824954	−	1.42886i	0.0770002	−	0.997031i	$-0.475466\pi$
$828$	−3.20344	+	4.61506i	−0.111327	+	0.160384i
$829$		−	47.7375i		−	1.65799i	−0.559254	−	0.828997i	$-0.688912\pi$
$829$		−	47.7375i		−	1.65799i	0.559254	−	0.828997i	$-0.311088\pi$
$830$	−22.9593	+	5.13925i	−0.796929	+	0.178386i
$831$	5.21113	−	9.02595i	0.180772	−	0.313107i
$832$	14.3901	+	51.1837i	0.498888	+	1.77448i
$833$	−13.1513	+	22.7787i	−0.455665	+	0.789235i
$834$	10.3876	+	11.2897i	0.359695	+	0.390930i
$835$	44.2214			1.53034
$836$	−8.65404	+	7.88922i	−0.299306	+	0.272854i
$837$	1.76220			0.0609107
$838$	−12.3482	−	13.4204i	−0.426560	−	0.463601i
$839$	−7.37906	+	12.7809i	−0.254754	+	0.441246i	−0.964829	−	0.262880i	$-0.915328\pi$
$839$	−7.37906	+	12.7809i	−0.254754	+	0.441246i	0.710075	+	0.704126i	$0.248661\pi$
$840$	−1.83192	−	0.745669i	−0.0632072	−	0.0257280i
$841$	−2.26029	+	3.91493i	−0.0779409	+	0.134998i
$842$	−26.2997	+	5.88697i	−0.906348	+	0.202878i
$843$			13.9155i			0.479276i
$844$	−21.4073	−	14.8594i	−0.736870	−	0.511483i
$845$	−30.6924	−	53.1608i	−1.05585	−	1.82879i
$846$	10.8850	−	2.43651i	0.374233	−	0.0837690i
$847$		−	3.26514i		−	0.112192i
$848$	12.5114	−	4.67007i	0.429645	−	0.160371i
$849$	−13.1484	+	7.59120i	−0.451250	+	0.260529i
$850$	−4.46610	+	4.10926i	−0.153186	+	0.140946i
$851$	11.9324	+	20.6675i	0.409037	+	0.708473i
$852$	28.2352	−	13.3072i	0.967324	−	0.455897i
$853$	−17.8909	+	30.9879i	−0.612573	+	1.06101i	0.378232	+	0.925711i	$0.376532\pi$
$853$	−17.8909	+	30.9879i	−0.612573	+	1.06101i	−0.990805	+	0.135296i	$0.956801\pi$
$854$	0.596836	−	1.90651i	0.0204233	−	0.0652394i
$855$	5.84151	−	6.29031i	0.199775	−	0.215124i
$856$	18.0722	+	23.2553i	0.617695	+	0.794848i
$857$	−11.1696	−	6.44877i	−0.381546	−	0.220286i	0.296945	−	0.954895i	$-0.404032\pi$
$857$	−11.1696	−	6.44877i	−0.381546	−	0.220286i	−0.678491	+	0.734609i	$0.737366\pi$
$858$	−9.29082	+	8.54850i	−0.317184	+	0.291841i
$859$	24.0984	−	13.9132i	0.822225	−	0.474712i	−0.0289579	−	0.999581i	$-0.509219\pi$
$859$	24.0984	−	13.9132i	0.822225	−	0.474712i	0.851183	+	0.524869i	$0.175886\pi$
$860$	−8.02901	−	17.0360i	−0.273787	−	0.580922i
$861$	−1.15442	−	1.99951i	−0.0393424	−	0.0681430i
$862$	24.8642	+	7.78379i	0.846879	+	0.265117i
$863$	13.5990			0.462917			0.231458	−	0.972845i	$-0.425650\pi$
$863$	13.5990			0.462917			0.231458	+	0.972845i	$0.425650\pi$
$864$	−4.73961	+	3.08806i	−0.161245	+	0.105058i
$865$	−13.0204	+	7.51735i	−0.442708	+	0.255598i
$866$	−3.66250	+	11.6993i	−0.124457	+	0.397560i
$867$	−2.35846			−0.0800975
$868$	−1.24710	−	0.103968i	−0.0423294	−	0.00352892i
$869$	19.4786	+	11.2460i	0.660768	+	0.381494i
$870$	−13.4472	+	3.01003i	−0.455901	+	0.102050i
$871$	12.1053	+	6.98902i	0.410174	+	0.236814i
$872$	0.0231010	+	0.167520i	0.000782300	+	0.00567294i
$873$			15.8355i			0.535950i
$874$	8.58853	+	15.0355i	0.290511	+	0.508582i
$875$		−	4.28065i		−	0.144713i
$876$	1.57556	−	0.742559i	0.0532333	−	0.0250887i
$877$	0.579383	+	0.334507i	0.0195644	+	0.0112955i	0.509750	−	0.860322i	$-0.329738\pi$
$877$	0.579383	+	0.334507i	0.0195644	+	0.0112955i	−0.490186	+	0.871618i	$0.663071\pi$
$878$	−9.66943	−	43.1976i	−0.326327	−	1.45785i
$879$	−13.3301	−	7.69616i	−0.449614	−	0.259585i
$880$	−8.16140	−	6.73522i	−0.275121	−	0.227044i
$881$	−44.4036			−1.49600			−0.747998	−	0.663701i	$-0.768985\pi$
$881$	−44.4036			−1.49600			−0.747998	+	0.663701i	$0.768985\pi$
$882$	−9.27723	−	2.90425i	−0.312380	−	0.0977912i
$883$	−37.7133	+	21.7738i	−1.26915	+	0.732747i	−0.974828	−	0.222958i	$-0.928429\pi$
$883$	−37.7133	+	21.7738i	−1.26915	+	0.732747i	−0.294326	+	0.955705i	$0.595095\pi$
$884$	50.6851	+	4.22552i	1.70473	+	0.142120i
$885$	−7.23612			−0.243240
$886$	1.46222	−	4.67087i	0.0491243	−	0.156921i
$887$	−6.59049	−	11.4151i	−0.221287	−	0.383280i	0.733912	−	0.679245i	$-0.237692\pi$
$887$	−6.59049	−	11.4151i	−0.221287	−	0.383280i	−0.955199	+	0.295964i	$0.904359\pi$
$888$	3.28271	+	23.8050i	0.110161	+	0.798843i
$889$	−3.96607	+	2.28981i	−0.133018	+	0.0767978i
$890$	−4.00368	−	4.35135i	−0.134204	−	0.145857i
$891$	−1.16330	−	0.671634i	−0.0389722	−	0.0225006i
$892$	7.08119	+	4.91525i	0.237096	+	0.164575i
$893$	7.66445	−	33.5148i	0.256481	−	1.12153i
$894$	−24.6531	−	7.71770i	−0.824524	−	0.258118i
$895$	12.0363	−	20.8475i	0.402329	−	0.696854i
$896$	3.53639	−	1.90577i	0.118143	−	0.0636674i
$897$	9.33416	+	16.1672i	0.311659	+	0.539808i
$898$	16.6149	+	18.0577i	0.554446	+	0.602593i
$899$	−7.55070	+	4.35940i	−0.251830	+	0.145394i
$900$	−1.84263	−	1.27902i	−0.0614209	−	0.0426340i
$901$		−	12.7751i		−	0.425601i
$902$	−2.69820	−	12.0541i	−0.0898402	−	0.401356i
$903$	0.848893	+	1.47033i	0.0282494	+	0.0489294i
$904$	0.608530	−	0.472902i	0.0202394	−	0.0157285i
$905$			20.8097i			0.691737i
$906$	0.491769	+	2.19695i	0.0163379	+	0.0729888i
$907$	−26.1929	+	45.3674i	−0.869720	+	1.50640i	−0.00743704	+	0.999972i	$0.502367\pi$
$907$	−26.1929	+	45.3674i	−0.869720	+	1.50640i	−0.862283	+	0.506427i	$0.830966\pi$
$908$	−3.50920	+	42.0928i	−0.116457	+	1.39690i
$909$	2.81400	−	4.87399i	0.0933345	−	0.161660i
$910$	−4.83663	+	4.45019i	−0.160333	+	0.147522i
$911$	19.4053			0.642925			0.321462	−	0.946922i	$-0.395826\pi$
$911$	19.4053			0.642925			0.321462	+	0.946922i	$0.395826\pi$
$912$	2.30217	+	17.2829i	0.0762324	+	0.572295i
$913$	11.3473			0.375540
$914$	−2.14054	+	1.96951i	−0.0708026	+	0.0651456i
$915$	−3.91748	+	6.78527i	−0.129508	+	0.224314i
$916$	−0.694053	+	8.32518i	−0.0229322	+	0.275072i
$917$	−1.88286	+	3.26121i	−0.0621775	+	0.107695i
$918$	1.18204	+	5.28071i	0.0390132	+	0.174289i
$919$		−	16.2385i		−	0.535660i	−0.963466	−	0.267830i	$-0.913693\pi$
$919$		−	16.2385i		−	0.535660i	0.963466	−	0.267830i	$-0.0863065\pi$
$920$	−12.3546	+	9.60104i	−0.407319	+	0.316537i
$921$	−16.2895	−	28.2143i	−0.536758	−	0.929692i
$922$	−5.72157	−	25.5608i	−0.188430	−	0.841800i
$923$		−	103.724i		−	3.41412i
$924$	0.783639	+	0.543946i	0.0257798	+	0.0178945i
$925$	−8.25180	+	4.76418i	−0.271317	+	0.156645i
$926$	14.1067	+	15.3317i	0.463574	+	0.503829i
$927$	8.98775	+	15.5672i	0.295197	+	0.511295i
$928$	12.6690	−	24.9567i	0.415879	−	0.819245i
$929$	−14.8773	+	25.7682i	−0.488108	+	0.845429i	−0.999906	−	0.0136771i	$-0.995646\pi$
$929$	−14.8773	+	25.7682i	−0.488108	+	0.845429i	0.511798	+	0.859106i	$0.328980\pi$
$930$	4.68383	+	1.46628i	0.153589	+	0.0480812i
$931$	−20.3891	+	21.9556i	−0.668226	+	0.719566i
$932$	−46.8960	−	32.5519i	−1.53613	−	1.06627i
$933$	20.3101	+	11.7260i	0.664922	+	0.383893i
$934$	27.3259	+	29.6988i	0.894131	+	0.971775i
$935$	−8.76633	+	5.06125i	−0.286690	+	0.165520i
$936$	2.56791	+	18.6215i	0.0839349	+	0.608664i
$937$	−5.96068	−	10.3242i	−0.194727	−	0.337277i	0.752084	−	0.659067i	$-0.229049\pi$
$937$	−5.96068	−	10.3242i	−0.194727	−	0.337277i	−0.946811	+	0.321790i	$0.895715\pi$
$938$	0.315526	−	1.00790i	0.0103023	−	0.0329092i
$939$	−1.01173			−0.0330164
$940$	30.9590	+	2.58099i	1.00977	+	0.0841825i
$941$	−39.8041	+	22.9809i	−1.29758	+	0.749156i	−0.979985	−	0.199071i	$-0.936207\pi$
$941$	−39.8041	+	22.9809i	−1.29758	+	0.749156i	−0.317592	+	0.948228i	$0.602874\pi$
$942$	0.0105561	+	0.00330461i	0.000343938	+	0.000107670i
$943$	−18.2648			−0.594785
$944$	9.35475	−	11.3356i	0.304471	−	0.368943i
$945$	−0.605595	−	0.349640i	−0.0197000	−	0.0113738i
$946$	1.98411	+	8.86389i	0.0645089	+	0.288190i
$947$	−12.3615	−	7.13691i	−0.401695	−	0.231918i	0.285520	−	0.958373i	$-0.407834\pi$
$947$	−12.3615	−	7.13691i	−0.401695	−	0.231918i	−0.687215	+	0.726454i	$0.741167\pi$
$948$	30.2927	−	14.2769i	0.983861	−	0.463691i
$949$		−	5.78794i		−	0.187885i
$950$	−6.00312	+	3.42909i	−0.194767	+	0.111255i
$951$			31.1182i			1.00908i
$952$	−0.524968	−	3.80687i	−0.0170143	−	0.123381i
$953$	42.9569	+	24.8012i	1.39151	+	0.803389i	0.993483	−	0.113985i	$-0.0363615\pi$
$953$	42.9569	+	24.8012i	1.39151	+	0.803389i	0.398028	+	0.917373i	$0.369695\pi$
$954$	4.60755	−	1.03136i	0.149175	−	0.0333916i
$955$	25.7500	+	14.8668i	0.833251	+	0.481078i
$956$	1.40563	+	0.117185i	0.0454614	+	0.00379002i
$957$	6.64605			0.214836
$958$	−1.03556	+	3.30794i	−0.0334573	+	0.106875i
$959$	−1.72005	+	0.993069i	−0.0555432	+	0.0320679i
$960$	−15.1671	+	4.26417i	−0.489515	+	0.137626i
$961$	−27.8946			−0.899827
$962$	76.2058	+	23.8563i	2.45697	+	0.769160i
$963$	5.20640	+	9.01775i	0.167774	+	0.290593i
$964$	4.87538	+	10.3446i	0.157025	+	0.333176i
$965$	−37.6803	+	21.7547i	−1.21297	+	0.700310i
$966$	1.03799	−	0.955059i	0.0333969	−	0.0307285i
$967$	−33.2407	−	19.1915i	−1.06895	−	0.617157i	−0.141054	−	0.990002i	$-0.545049\pi$
$967$	−33.2407	−	19.1915i	−1.06895	−	0.617157i	−0.927894	+	0.372845i	$0.878382\pi$
$968$	−15.9597	−	20.5369i	−0.512964	−	0.660081i
$969$	16.2593	+	3.71830i	0.522323	+	0.119449i
$970$	−13.1762	+	42.0897i	−0.423064	+	1.35142i
$971$	−2.90903	+	5.03859i	−0.0933552	+	0.161696i	−0.908921	−	0.416968i	$-0.863093\pi$
$971$	−2.90903	+	5.03859i	−0.0933552	+	0.161696i	0.815566	+	0.578664i	$0.196426\pi$
$972$	−1.80914	+	0.852645i	−0.0580283	+	0.0273486i
$973$	−1.92594	−	3.33582i	−0.0617426	−	0.106941i
$974$	−8.51638	+	7.83593i	−0.272882	+	0.251079i
$975$	−6.45500	+	3.72680i	−0.206725	+	0.119353i
$976$	−5.56490	−	14.9088i	−0.178128	−	0.477218i
$977$			44.4183i			1.42107i	0.703663	+	0.710533i	$0.251546\pi$
$977$			44.4183i			1.42107i	−0.703663	+	0.710533i	$0.748454\pi$
$978$	−24.2283	+	5.42330i	−0.774735	+	0.173418i
$979$	1.42592	+	2.46977i	0.0455726	+	0.0789341i
$980$	−22.2417	−	15.4386i	−0.710486	−	0.493169i
$981$			0.0597877i			0.00190888i
$982$	−1.58402	+	0.354569i	−0.0505480	+	0.0113147i
$983$	−4.00137	+	6.93057i	−0.127624	+	0.221051i	−0.922755	−	0.385386i	$-0.874068\pi$
$983$	−4.00137	+	6.93057i	−0.127624	+	0.221051i	0.795132	+	0.606437i	$0.207402\pi$
$984$	−17.0344	−	6.93372i	−0.543036	−	0.221039i
$985$	11.5304	−	19.9713i	0.367390	−	0.636338i
$986$	−18.1284	−	19.7026i	−0.577326	−	0.627460i
$987$	−2.80059			−0.0891437
$988$	55.2121	+	17.5642i	1.75653	+	0.558791i
$989$	13.4310			0.427080
$990$	−2.53314	−	2.75311i	−0.0805086	−	0.0874997i
$991$	9.93799	−	17.2131i	0.315691	−	0.546792i	−0.663893	−	0.747827i	$-0.731097\pi$
$991$	9.93799	−	17.2131i	0.315691	−	0.546792i	0.979584	+	0.201035i	$0.0644305\pi$
$992$	−8.35216	+	5.44179i	−0.265181	+	0.172777i
$993$	−16.5520	+	28.6689i	−0.525262	+	0.909781i
$994$	−7.64782	+	1.71190i	−0.242574	+	0.0542982i
$995$		−	0.349304i		−	0.0110737i
$996$	9.63390	−	13.8791i	0.305262	−	0.439777i
$997$	−1.78001	−	3.08307i	−0.0563736	−	0.0976419i	0.836461	−	0.548026i	$-0.184620\pi$
$997$	−1.78001	−	3.08307i	−0.0563736	−	0.0976419i	−0.892835	+	0.450384i	$0.851287\pi$
$998$	−36.4627	+	8.16187i	−1.15421	+	0.258359i
$999$			8.49598i			0.268801i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.k.a.103.8	yes	20
3.2	odd	2		684.2.r.c.559.3		20
4.3	odd	2		228.2.k.b.103.5	yes	20
12.11	even	2		684.2.r.b.559.6		20
19.12	odd	6		228.2.k.b.31.5	yes	20
57.50	even	6		684.2.r.b.487.6		20
76.31	even	6	inner	228.2.k.a.31.8	✓	20
228.107	odd	6		684.2.r.c.487.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.k.a.31.8	✓	20	76.31	even	6	inner
228.2.k.a.103.8	yes	20	1.1	even	1	trivial
228.2.k.b.31.5	yes	20	19.12	odd	6
228.2.k.b.103.5	yes	20	4.3	odd	2
684.2.r.b.487.6		20	57.50	even	6
684.2.r.b.559.6		20	12.11	even	2
684.2.r.c.487.3		20	228.107	odd	6
684.2.r.c.559.3		20	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(1.04071 - 0.957560i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.166160 - 1.99309i) q^{4} +(0.984694 - 1.70554i) q^{5} +(0.308915 + 1.38006i) q^{6} -0.355075i q^{7} +(-1.73557 - 2.23333i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.608374 - 2.71788i) q^{10} +1.34327i q^{11} +(1.64298 + 1.14044i) q^{12} +(5.75562 - 3.32301i) q^{13} +(-0.340006 - 0.369531i) q^{14} +(0.984694 + 1.70554i) q^{15} +(-3.94478 - 0.662340i) q^{16} +(-1.91321 + 3.31378i) q^{17} +(-1.34963 - 0.422503i) q^{18} +(-2.96616 + 3.19404i) q^{19} +(-3.23567 - 2.24597i) q^{20} +(0.307504 + 0.177538i) q^{21} +(1.28626 + 1.39795i) q^{22} +(2.43262 - 1.40448i) q^{23} +(2.80191 - 0.386384i) q^{24} +(0.560757 + 0.971259i) q^{25} +(2.80796 - 8.96963i) q^{26} +1.00000 q^{27} +(-0.707695 - 0.0589991i) q^{28} +(-4.28481 + 2.47383i) q^{29} +(2.65794 + 0.832071i) q^{30} +1.76220 q^{31} +(-4.73961 + 3.08806i) q^{32} +(-1.16330 - 0.671634i) q^{33} +(1.18204 + 5.28071i) q^{34} +(-0.605595 - 0.349640i) q^{35} +(-1.80914 + 0.852645i) q^{36} +8.49598i q^{37} +(-0.0284229 + 6.16435i) q^{38} +6.64601i q^{39} +(-5.51805 + 0.760940i) q^{40} +(-5.63122 - 3.25119i) q^{41} +(0.490026 - 0.109688i) q^{42} +(4.14089 + 2.39074i) q^{43} +(2.67725 + 0.223197i) q^{44} -1.96939 q^{45} +(1.18679 - 3.79103i) q^{46} +(-6.83062 + 3.94366i) q^{47} +(2.54599 - 3.08511i) q^{48} +6.87392 q^{49} +(1.51362 + 0.473842i) q^{50} +(-1.91321 - 3.31378i) q^{51} +(-5.66669 - 12.0236i) q^{52} +(-2.89136 + 1.66933i) q^{53} +(1.04071 - 0.957560i) q^{54} +(2.29100 + 1.32271i) q^{55} +(-0.793001 + 0.616259i) q^{56} +(-1.28305 - 4.16579i) q^{57} +(-2.09040 + 6.67750i) q^{58} +(-1.83715 + 3.18204i) q^{59} +(3.56290 - 1.67919i) q^{60} +(1.98919 + 3.44537i) q^{61} +(1.83395 - 1.68742i) q^{62} +(-0.307504 + 0.177538i) q^{63} +(-1.97556 + 7.75223i) q^{64} -13.0886i q^{65} +(-1.85379 + 0.414956i) q^{66} +(1.05161 + 1.82144i) q^{67} +(6.28675 + 4.36381i) q^{68} +2.80895i q^{69} +(-0.965050 + 0.216018i) q^{70} +(7.80349 - 13.5160i) q^{71} +(-1.06634 + 2.61972i) q^{72} +(0.435445 - 0.754212i) q^{73} +(8.13541 + 8.84186i) q^{74} -1.12151 q^{75} +(5.87315 + 6.44252i) q^{76} +0.476961 q^{77} +(6.36395 + 6.91658i) q^{78} +(8.37212 - 14.5009i) q^{79} +(-5.01405 + 6.07578i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-8.97368 + 2.00868i) q^{82} -8.44752i q^{83} +(0.404942 - 0.583382i) q^{84} +(3.76786 + 6.52612i) q^{85} +(6.59875 - 1.47707i) q^{86} -4.94767i q^{87} +(2.99997 - 2.33134i) q^{88} +(1.83862 - 1.06153i) q^{89} +(-2.04956 + 1.88581i) q^{90} +(-1.17992 - 2.04368i) q^{91} +(-2.39504 - 5.08179i) q^{92} +(-0.881102 + 1.52611i) q^{93} +(-3.33241 + 10.6449i) q^{94} +(2.52682 + 8.20405i) q^{95} +(-0.304533 - 5.64865i) q^{96} +(-13.7139 - 7.91774i) q^{97} +(7.15377 - 6.58219i) q^{98} +(1.16330 - 0.671634i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} - 10 q^{3} + q^{4} - q^{6} - 4 q^{8} - 10 q^{9} + 6 q^{10} - 2 q^{12} + 6 q^{13} + 9 q^{14} + 13 q^{16} + 2 q^{18} - 12 q^{19} - 14 q^{20} + 6 q^{21} - 8 q^{22} - 7 q^{24} - 10 q^{25} + 20 q^{27}+ \cdots - 12 q^{98}+O(q^{100}) \) 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 + 13 * q^16 + 2 * q^18 - 12 * q^19 - 14 * q^20 + 6 * q^21 - 8 * q^22 - 7 * q^24 - 10 * q^25 + 20 * q^27 + 7 * q^28 - 12 * q^31 - 31 * q^32 - 30 * q^34 + q^36 - 11 * q^38 - 26 * q^40 + 12 * q^41 - 9 * q^42 + 18 * q^43 + 30 * q^44 + 32 * q^46 + 36 * q^47 - 11 * 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 + 10 * q^60 + 10 * q^61 + 29 * q^62 - 6 * q^63 - 14 * q^64 - 8 * q^66 - 14 * q^67 + 40 * q^68 + 46 * q^70 - 8 * q^71 + 11 * q^72 - 6 * q^73 + 3 * q^74 + 20 * q^75 + 3 * q^76 - 32 * q^77 + 33 * q^78 + 6 * q^79 + 40 * q^80 - 10 * q^81 - 60 * q^82 - 14 * q^84 + 8 * q^85 - 25 * q^86 - 44 * q^88 - 24 * q^89 - 6 * q^90 - 26 * q^91 + 36 * q^92 + 6 * q^93 + 52 * q^94 - 4 * q^95 + 2 * q^96 - 12 * q^97 - 12 * q^98

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