LMFDB - Embedded newform 228.2.w.b.79.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(67,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 17])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.w (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,3] 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:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			79.8
Character	$\chi$	$=$	228.79
Dual form			228.2.w.b.127.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.947134 - 1.05021i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.205875 - 1.98938i) q^{4} +(0.234529 - 1.33008i) q^{5} +(-0.530822 + 1.31081i) q^{6} +(1.38264 - 0.798268i) q^{7} +(-2.28425 - 1.66799i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-1.17473 - 1.50607i) q^{10} +(-2.03942 - 1.17746i) q^{11} +(0.873866 + 1.79899i) q^{12} +(0.358016 - 0.983642i) q^{13} +(0.471198 - 2.20813i) q^{14} +(0.234529 + 1.33008i) q^{15} +(-3.91523 + 0.819124i) q^{16} +(2.41328 + 2.02498i) q^{17} +(0.0504858 - 1.41331i) q^{18} +(2.22379 - 3.74897i) q^{19} +(-2.69431 - 0.192736i) q^{20} +(-1.02623 + 1.22302i) q^{21} +(-3.16818 + 1.02660i) q^{22} +(-3.00639 + 0.530108i) q^{23} +(2.71698 + 0.786142i) q^{24} +(2.98436 + 1.08622i) q^{25} +(-0.693939 - 1.30763i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(-1.87271 - 2.58625i) q^{28} +(1.87372 + 2.23302i) q^{29} +(1.61899 + 1.01346i) q^{30} +(5.06365 + 8.77049i) q^{31} +(-2.84800 + 4.88763i) q^{32} +(2.31914 + 0.408927i) q^{33} +(4.41235 - 0.616517i) q^{34} +(-0.737489 - 2.02624i) q^{35} +(-1.43646 - 1.39162i) q^{36} +5.03282i q^{37} +(-1.83097 - 5.88622i) q^{38} +1.04677i q^{39} +(-2.75428 + 2.64704i) q^{40} +(0.940545 + 2.58413i) q^{41} +(0.312442 + 2.23612i) q^{42} +(9.34512 + 1.64780i) q^{43} +(-1.92254 + 4.29958i) q^{44} +(-0.675298 - 1.16965i) q^{45} +(-2.29073 + 3.65942i) q^{46} +(-4.10313 - 4.88992i) q^{47} +(3.39896 - 2.10881i) q^{48} +(-2.22554 + 3.85474i) q^{49} +(3.96735 - 2.10541i) q^{50} +(-2.96033 - 1.07747i) q^{51} +(-2.03054 - 0.509722i) q^{52} +(-2.12715 + 0.375074i) q^{53} +(0.435940 + 1.34535i) q^{54} +(-2.04441 + 2.43644i) q^{55} +(-4.48980 - 0.482793i) q^{56} +(-0.807460 + 4.28346i) q^{57} +(4.11980 + 0.147166i) q^{58} +(-5.42410 - 4.55136i) q^{59} +(2.59774 - 0.740395i) q^{60} +(-1.92617 - 10.9238i) q^{61} +(14.0068 + 2.98895i) q^{62} +(0.546047 - 1.50025i) q^{63} +(2.43559 + 7.62023i) q^{64} +(-1.22435 - 0.706881i) q^{65} +(2.62600 - 2.04827i) q^{66} +(-2.47287 + 2.07498i) q^{67} +(3.53162 - 5.21781i) q^{68} +(2.64378 - 1.52638i) q^{69} +(-2.82647 - 1.14460i) q^{70} +(0.0247905 - 0.140594i) q^{71} +(-2.82200 + 0.190530i) q^{72} +(2.09404 - 0.762168i) q^{73} +(5.28551 + 4.76675i) q^{74} -3.17589 q^{75} +(-7.91592 - 3.65214i) q^{76} -3.75971 q^{77} +(1.09933 + 0.991431i) q^{78} +(7.69442 - 2.80054i) q^{79} +(0.171265 + 5.39967i) q^{80} +(0.173648 - 0.984808i) q^{81} +(3.60469 + 1.45974i) q^{82} +(6.01799 - 3.47449i) q^{83} +(2.64432 + 1.78978i) q^{84} +(3.25937 - 2.73493i) q^{85} +(10.5816 - 8.25364i) q^{86} +(-2.52446 - 1.45750i) q^{87} +(2.69455 + 6.09135i) q^{88} +(2.39122 - 6.56982i) q^{89} +(-1.86797 - 0.398612i) q^{90} +(-0.290202 - 1.64582i) q^{91} +(1.67352 + 5.87170i) q^{92} +(-7.75796 - 6.50970i) q^{93} +(-9.02165 - 0.322268i) q^{94} +(-4.46487 - 3.83706i) q^{95} +(1.00457 - 5.56694i) q^{96} +(-6.02952 + 7.18571i) q^{97} +(1.94040 + 5.98823i) q^{98} +(-2.31914 + 0.408927i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} + 21 q^{16} + 18 q^{19} + 30 q^{20} - 6 q^{21} - 12 q^{22} - 18 q^{24} - 30 q^{27} - 18 q^{28} - 12 q^{31} + 33 q^{32} - 15 q^{34}+ \cdots - 105 q^{98}+O(q^{100}) $ 60 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 + 21 * q^16 + 18 * q^19 + 30 * q^20 - 6 * q^21 - 12 * q^22 - 18 * q^24 - 30 * q^27 - 18 * q^28 - 12 * q^31 + 33 * q^32 - 15 * q^34 - 3 * q^36 - 84 * q^38 - 87 * q^40 - 12 * q^41 + 9 * q^42 - 18 * q^43 - 51 * q^44 - 21 * q^46 + 18 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 + 42 * q^56 - 36 * q^58 + 15 * q^60 + 105 * q^62 - 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 + 42 * q^67 - 15 * q^68 - 72 * q^69 - 96 * q^70 + 24 * q^71 + 18 * q^72 + 18 * q^73 + 69 * q^74 + 60 * q^75 + 54 * q^76 - 72 * q^77 + 57 * q^78 + 12 * q^79 - 12 * q^80 + 75 * q^82 + 39 * q^84 - 60 * q^85 + 21 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 - 84 * q^91 + 99 * q^92 - 12 * q^93 - 24 * q^95 + 12 * q^97 - 105 * q^98

Character values

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

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	0.947134	−	1.05021i	0.669725	−	0.742609i
$2$	0.947134	−	1.05021i	0.669725	−	0.742609i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$4$	−0.205875	−	1.98938i	−0.102937	−	0.994688i
$5$	0.234529	−	1.33008i	0.104884	−	0.594829i	−0.886382	−	0.462954i	$-0.846789\pi$
$5$	0.234529	−	1.33008i	0.104884	−	0.594829i	0.991266	−	0.131874i	$-0.0420995\pi$
$6$	−0.530822	+	1.31081i	−0.216707	+	0.535137i
$7$	1.38264	−	0.798268i	0.522589	−	0.301717i	−0.215404	−	0.976525i	$-0.569107\pi$
$7$	1.38264	−	0.798268i	0.522589	−	0.301717i	0.737993	+	0.674808i	$0.235774\pi$
$8$	−2.28425	−	1.66799i	−0.807604	−	0.589725i
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$	−1.17473	−	1.50607i	−0.371482	−	0.476260i
$11$	−2.03942	−	1.17746i	−0.614908	−	0.355017i	0.159976	−	0.987121i	$-0.448858\pi$
$11$	−2.03942	−	1.17746i	−0.614908	−	0.355017i	−0.774884	+	0.632104i	$0.782192\pi$
$12$	0.873866	+	1.79899i	0.252263	+	0.519323i
$13$	0.358016	−	0.983642i	0.0992959	−	0.272813i	−0.880092	−	0.474804i	$-0.842519\pi$
$13$	0.358016	−	0.983642i	0.0992959	−	0.272813i	0.979387	+	0.201991i	$0.0647411\pi$
$14$	0.471198	−	2.20813i	0.125933	−	0.590147i
$15$	0.234529	+	1.33008i	0.0605550	+	0.343425i
$16$	−3.91523	+	0.819124i	−0.978808	+	0.204781i
$17$	2.41328	+	2.02498i	0.585306	+	0.491130i	0.886685	−	0.462374i	$-0.153002\pi$
$17$	2.41328	+	2.02498i	0.585306	+	0.491130i	−0.301379	+	0.953505i	$0.597447\pi$
$18$	0.0504858	−	1.41331i	0.0118996	−	0.333121i
$19$	2.22379	−	3.74897i	0.510173	−	0.860072i
$19$	2.22379	−	3.74897i	0.510173	−	0.860072i
$20$	−2.69431	−	0.192736i	−0.602465	−	0.0430971i
$21$	−1.02623	+	1.22302i	−0.223943	+	0.266884i
$22$	−3.16818	+	1.02660i	−0.675458	+	0.218873i
$23$	−3.00639	+	0.530108i	−0.626876	+	0.110535i	−0.478056	−	0.878329i	$-0.658658\pi$
$23$	−3.00639	+	0.530108i	−0.626876	+	0.110535i	−0.148820	+	0.988864i	$0.547547\pi$
$24$	2.71698	+	0.786142i	0.554601	+	0.160471i
$25$	2.98436	+	1.08622i	0.596872	+	0.217244i
$26$	−0.693939	−	1.30763i	−0.136093	−	0.256448i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	−1.87271	−	2.58625i	−0.353908	−	0.488755i
$29$	1.87372	+	2.23302i	0.347942	+	0.414661i	0.911425	−	0.411467i	$-0.134983\pi$
$29$	1.87372	+	2.23302i	0.347942	+	0.414661i	−0.563483	+	0.826128i	$0.690539\pi$
$30$	1.61899	+	1.01346i	0.295585	+	0.185031i
$31$	5.06365	+	8.77049i	0.909458	+	1.57523i	0.814819	+	0.579715i	$0.196836\pi$
$31$	5.06365	+	8.77049i	0.909458	+	1.57523i	0.0946383	+	0.995512i	$0.469831\pi$
$32$	−2.84800	+	4.88763i	−0.503460	+	0.864019i
$33$	2.31914	+	0.408927i	0.403711	+	0.0711851i
$34$	4.41235	−	0.616517i	0.756712	−	0.105732i
$35$	−0.737489	−	2.02624i	−0.124658	−	0.342496i
$36$	−1.43646	−	1.39162i	−0.239409	−	0.231936i
$37$			5.03282i			0.827391i	0.910415	+	0.413695i	$0.135762\pi$
$37$			5.03282i			0.827391i	−0.910415	+	0.413695i	$0.864238\pi$
$38$	−1.83097	−	5.88622i	−0.297022	−	0.954871i
$39$			1.04677i			0.167617i
$40$	−2.75428	+	2.64704i	−0.435490	+	0.418533i
$41$	0.940545	+	2.58413i	0.146888	+	0.403573i	0.991216	−	0.132255i	$-0.0422218\pi$
$41$	0.940545	+	2.58413i	0.146888	+	0.403573i	−0.844327	+	0.535828i	$0.820000\pi$
$42$	0.312442	+	2.23612i	0.0482109	+	0.345041i
$43$	9.34512	+	1.64780i	1.42512	+	0.251287i	0.832423	−	0.554140i	$-0.186953\pi$
$43$	9.34512	+	1.64780i	1.42512	+	0.251287i	0.592695	+	0.805427i	$0.298064\pi$
$44$	−1.92254	+	4.29958i	−0.289834	+	0.648186i
$45$	−0.675298	−	1.16965i	−0.100667	−	0.174361i
$46$	−2.29073	+	3.65942i	−0.337750	+	0.539552i
$47$	−4.10313	−	4.88992i	−0.598503	−	0.713268i	0.378713	−	0.925514i	$-0.376367\pi$
$47$	−4.10313	−	4.88992i	−0.598503	−	0.713268i	−0.977216	+	0.212246i	$0.931922\pi$
$48$	3.39896	−	2.10881i	0.490597	−	0.304381i
$49$	−2.22554	+	3.85474i	−0.317934	+	0.550677i
$50$	3.96735	−	2.10541i	0.561067	−	0.297749i
$51$	−2.96033	−	1.07747i	−0.414529	−	0.150876i
$52$	−2.03054	−	0.509722i	−0.281585	−	0.0706857i
$53$	−2.12715	+	0.375074i	−0.292186	+	0.0515204i	−0.317820	−	0.948151i	$-0.602951\pi$
$53$	−2.12715	+	0.375074i	−0.292186	+	0.0515204i	0.0256336	+	0.999671i	$0.491840\pi$
$54$	0.435940	+	1.34535i	0.0593239	+	0.183078i
$55$	−2.04441	+	2.43644i	−0.275669	+	0.328529i
$56$	−4.48980	−	0.482793i	−0.599975	−	0.0645159i
$57$	−0.807460	+	4.28346i	−0.106951	+	0.567358i
$58$	4.11980	+	0.147166i	0.540956	+	0.0193238i
$59$	−5.42410	−	4.55136i	−0.706157	−	0.592536i	0.217361	−	0.976091i	$-0.430255\pi$
$59$	−5.42410	−	4.55136i	−0.706157	−	0.592536i	−0.923518	+	0.383555i	$0.874700\pi$
$60$	2.59774	−	0.740395i	0.335367	−	0.0955845i
$61$	−1.92617	−	10.9238i	−0.246621	−	1.39865i	−0.816699	−	0.577064i	$-0.804198\pi$
$61$	−1.92617	−	10.9238i	−0.246621	−	1.39865i	0.570078	−	0.821590i	$-0.306913\pi$
$62$	14.0068	+	2.98895i	1.77886	+	0.379597i
$63$	0.546047	−	1.50025i	0.0687955	−	0.189014i
$64$	2.43559	+	7.62023i	0.304449	+	0.952529i
$65$	−1.22435	−	0.706881i	−0.151863	−	0.0876779i
$66$	2.62600	−	2.04827i	0.323238	−	0.252125i
$67$	−2.47287	+	2.07498i	−0.302109	+	0.253499i	−0.781221	−	0.624254i	$-0.785403\pi$
$67$	−2.47287	+	2.07498i	−0.302109	+	0.253499i	0.479113	+	0.877753i	$0.340959\pi$
$68$	3.53162	−	5.21781i	0.428271	−	0.632753i
$69$	2.64378	−	1.52638i	0.318273	−	0.183755i
$70$	−2.82647	−	1.14460i	−0.337828	−	0.136806i
$71$	0.0247905	−	0.140594i	0.00294209	−	0.0166854i	−0.983301	−	0.181985i	$-0.941748\pi$
$71$	0.0247905	−	0.140594i	0.00294209	−	0.0166854i	0.986243	+	0.165299i	$0.0528590\pi$
$72$	−2.82200	+	0.190530i	−0.332576	+	0.0224542i
$73$	2.09404	−	0.762168i	0.245089	−	0.0892050i	−0.216555	−	0.976270i	$-0.569482\pi$
$73$	2.09404	−	0.762168i	0.245089	−	0.0892050i	0.461644	+	0.887065i	$0.347260\pi$
$74$	5.28551	+	4.76675i	0.614428	+	0.554124i
$75$	−3.17589			−0.366720
$76$	−7.91592	−	3.65214i	−0.908019	−	0.418929i
$77$	−3.75971			−0.428459
$78$	1.09933	+	0.991431i	0.124474	+	0.112257i
$79$	7.69442	−	2.80054i	0.865690	−	0.315085i	0.129269	−	0.991610i	$-0.458737\pi$
$79$	7.69442	−	2.80054i	0.865690	−	0.315085i	0.736420	+	0.676524i	$0.236515\pi$
$80$	0.171265	+	5.39967i	0.0191481	+	0.603701i
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$	3.60469	+	1.45974i	0.398072	+	0.161202i
$83$	6.01799	−	3.47449i	0.660560	−	0.381375i	−0.131930	−	0.991259i	$-0.542117\pi$
$83$	6.01799	−	3.47449i	0.660560	−	0.381375i	0.792490	+	0.609884i	$0.208784\pi$
$84$	2.64432	+	1.78978i	0.288519	+	0.195281i
$85$	3.25937	−	2.73493i	0.353528	−	0.296645i
$86$	10.5816	−	8.25364i	1.14104	−	0.890013i
$87$	−2.52446	−	1.45750i	−0.270651	−	0.156260i
$88$	2.69455	+	6.09135i	0.287240	+	0.649340i
$89$	2.39122	−	6.56982i	0.253469	−	0.696399i	−0.746065	−	0.665873i	$-0.768059\pi$
$89$	2.39122	−	6.56982i	0.253469	−	0.696399i	0.999534	−	0.0305266i	$-0.00971844\pi$
$90$	−1.86797	−	0.398612i	−0.196902	−	0.0420174i
$91$	−0.290202	−	1.64582i	−0.0304214	−	0.172528i
$92$	1.67352	+	5.87170i	0.174477	+	0.612168i
$93$	−7.75796	−	6.50970i	−0.804462	−	0.675024i
$94$	−9.02165	−	0.322268i	−0.930512	−	0.0332394i
$95$	−4.46487	−	3.83706i	−0.458086	−	0.393674i
$96$	1.00457	−	5.56694i	0.102529	−	0.568174i
$97$	−6.02952	+	7.18571i	−0.612205	+	0.729598i	−0.979709	−	0.200424i	$-0.935768\pi$
$97$	−6.02952	+	7.18571i	−0.612205	+	0.729598i	0.367504	+	0.930022i	$0.380212\pi$
$98$	1.94040	+	5.98823i	0.196010	+	0.604903i
$99$	−2.31914	+	0.408927i	−0.233082	+	0.0410987i
$100$	1.54649	−	6.16064i	0.154649	−	0.616064i
$101$	−17.8478	−	6.49608i	−1.77593	−	0.646385i	−0.999877	−	0.0157138i	$-0.994998\pi$
$101$	−17.8478	−	6.49608i	−1.77593	−	0.646385i	−0.776051	−	0.630671i	$-0.782780\pi$
$102$	−3.93539	+	2.08845i	−0.389662	+	0.206787i
$103$	−3.24316	+	5.61733i	−0.319559	+	0.553492i	−0.980396	−	0.197037i	$-0.936868\pi$
$103$	−3.24316	+	5.61733i	−0.319559	+	0.553492i	0.660837	+	0.750529i	$0.270201\pi$
$104$	−2.45851	+	1.64971i	−0.241076	+	0.161768i
$105$	1.38603	+	1.65180i	0.135262	+	0.161199i
$106$	−1.62079	+	2.58920i	−0.157425	+	0.251485i
$107$	9.83111	+	17.0280i	0.950409	+	1.64616i	0.744541	+	0.667577i	$0.232668\pi$
$107$	9.83111	+	17.0280i	0.950409	+	1.64616i	0.205868	+	0.978580i	$0.433998\pi$
$108$	1.82579	+	0.816395i	0.175686	+	0.0785577i
$109$	−12.6371	−	2.22826i	−1.21041	−	0.213429i	−0.468219	−	0.883612i	$-0.655104\pi$
$109$	−12.6371	−	2.22826i	−1.21041	−	0.213429i	−0.742195	+	0.670184i	$0.766215\pi$
$110$	0.622433	+	4.45469i	0.0593467	+	0.424738i
$111$	−1.72133	−	4.72930i	−0.163381	−	0.448886i
$112$	−4.75948	+	4.25796i	−0.449728	+	0.402339i
$113$		−	0.917903i		−	0.0863490i	−0.999068	−	0.0431745i	$-0.986253\pi$
$113$		−	0.917903i		−	0.0863490i	0.999068	−	0.0431745i	$-0.0137471\pi$
$114$	3.73375	+	4.90501i	0.349698	+	0.459396i
$115$			4.12306i			0.384477i
$116$	4.05656	−	4.18726i	0.376642	−	0.388778i
$117$	−0.358016	−	0.983642i	−0.0330986	−	0.0909377i
$118$	−9.91722	+	1.38569i	−0.912954	+	0.127563i
$119$	4.95318	+	0.873379i	0.454057	+	0.0800625i
$120$	1.68284	−	3.42942i	0.153621	−	0.313062i
$121$	−2.72718	−	4.72362i	−0.247926	−	0.429420i
$122$	−13.2966	−	8.32346i	−1.20382	−	0.753571i
$123$	−1.76765	−	2.10660i	−0.159383	−	0.189946i
$124$	16.4053	−	11.8791i	1.47324	−	1.06678i
$125$	5.52116	−	9.56293i	0.493828	−	0.855335i
$126$	−1.05840	−	1.99440i	−0.0942896	−	0.177676i
$127$	−7.79041	−	2.83548i	−0.691287	−	0.251608i	−0.0276007	−	0.999619i	$-0.508787\pi$
$127$	−7.79041	−	2.83548i	−0.691287	−	0.251608i	−0.663686	+	0.748011i	$0.731009\pi$
$128$	10.3097	+	4.65950i	0.911254	+	0.411845i
$129$	−9.34512	+	1.64780i	−0.822792	+	0.145080i
$130$	−1.90200	+	0.616316i	−0.166816	+	0.0540545i
$131$	−10.9712	+	13.0749i	−0.958556	+	1.14236i	0.0311888	+	0.999514i	$0.490071\pi$
$131$	−10.9712	+	13.0749i	−0.958556	+	1.14236i	−0.989745	+	0.142849i	$0.954374\pi$
$132$	0.336057	−	4.69783i	0.0292500	−	0.408894i
$133$	0.0820271	−	6.95866i	0.00711265	−	0.603392i
$134$	−0.162973	+	4.56231i	−0.0140787	+	0.394124i
$135$	1.03462	+	0.868146i	0.0890456	+	0.0747181i
$136$	−2.13488	−	8.65090i	−0.183064	−	0.741809i
$137$	1.72662	+	9.79216i	0.147515	+	0.836600i	0.965313	+	0.261095i	$0.0840836\pi$
$137$	1.72662	+	9.79216i	0.147515	+	0.836600i	−0.817798	+	0.575506i	$0.804805\pi$
$138$	0.900988	−	4.22221i	0.0766972	−	0.359418i
$139$	4.61239	−	12.6724i	0.391218	−	1.07486i	−0.575229	−	0.817993i	$-0.695087\pi$
$139$	4.61239	−	12.6724i	0.391218	−	1.07486i	0.966446	−	0.256869i	$-0.0826908\pi$
$140$	−3.87911	+	1.88429i	−0.327845	+	0.159252i
$141$	5.52813	+	3.19167i	0.465553	+	0.268787i
$142$	−0.124173	−	0.159196i	−0.0104203	−	0.0133594i
$143$	−1.88834	+	1.58451i	−0.157911	+	0.132503i
$144$	−2.47272	+	3.14415i	−0.206060	+	0.262012i
$145$	3.40953	−	1.96849i	0.283146	−	0.163474i
$146$	1.18290	−	2.92105i	0.0978975	−	0.241748i
$147$	0.772921	−	4.38345i	0.0637494	−	0.361541i
$148$	10.0122	−	1.03613i	0.822995	−	0.0851694i
$149$	−0.522585	+	0.190205i	−0.0428118	+	0.0155822i	−0.363337	−	0.931658i	$-0.618363\pi$
$149$	−0.522585	+	0.190205i	−0.0428118	+	0.0155822i	0.320525	+	0.947240i	$0.396141\pi$
$150$	−3.00799	+	3.33535i	−0.245602	+	0.272330i
$151$	17.5307			1.42663			0.713314	−	0.700844i	$-0.247193\pi$
$151$	17.5307			1.42663			0.713314	+	0.700844i	$0.247193\pi$
$152$	−11.3330	+	4.85430i	−0.919224	+	0.393736i
$153$	3.15031			0.254688
$154$	−3.56095	+	3.94848i	−0.286950	+	0.318178i
$155$	12.8530	−	4.67811i	1.03238	−	0.375755i
$156$	2.08242	−	0.215503i	0.166727	−	0.0172541i
$157$	0.251327	−	1.42535i	0.0200581	−	0.113755i	−0.973135	−	0.230236i	$-0.926050\pi$
$157$	0.251327	−	1.42535i	0.0200581	−	0.113755i	0.993193	+	0.116481i	$0.0371613\pi$
$158$	4.34650	−	10.7332i	0.345789	−	0.853890i
$159$	1.87058	−	1.07998i	0.148347	−	0.0856482i
$160$	5.83299	+	4.93434i	0.461138	+	0.390094i
$161$	−3.73359	+	3.13285i	−0.294248	+	0.246903i
$162$	−0.869785	−	1.11511i	−0.0683368	−	0.0876114i
$163$	−14.0156	−	8.09192i	−1.09779	−	0.633808i	−0.162148	−	0.986766i	$-0.551842\pi$
$163$	−14.0156	−	8.09192i	−1.09779	−	0.633808i	−0.935639	+	0.352959i	$0.885176\pi$
$164$	4.94716	−	2.40310i	0.386308	−	0.187651i
$165$	1.08781	−	2.98873i	0.0846859	−	0.232673i
$166$	2.05091	−	9.61095i	0.159181	−	0.745954i
$167$	0.432194	+	2.45110i	0.0334442	+	0.189672i	0.996953	−	0.0780054i	$-0.0248551\pi$
$167$	0.432194	+	2.45110i	0.0334442	+	0.189672i	−0.963509	+	0.267677i	$0.913744\pi$
$168$	4.38416	−	1.08193i	0.338245	−	0.0834724i
$169$	9.11920	+	7.65192i	0.701477	+	0.588609i
$170$	0.214807	−	6.01336i	0.0164749	−	0.461204i
$171$	−0.706265	−	4.30130i	−0.0540094	−	0.328929i
$172$	1.35416	−	18.9302i	0.103254	−	1.44341i
$173$	10.5582	−	12.5828i	0.802726	−	0.956652i	−0.196992	−	0.980405i	$-0.563117\pi$
$173$	10.5582	−	12.5828i	0.802726	−	0.956652i	0.999718	+	0.0237532i	$0.00756159\pi$
$174$	−3.92168	+	1.27076i	−0.297302	+	0.0963364i
$175$	4.99339	−	0.880470i	0.377465	−	0.0665573i
$176$	8.94928	+	2.93949i	0.674577	+	0.221572i
$177$	6.65364	+	2.42173i	0.500118	+	0.182028i
$178$	−4.63487	−	8.73378i	−0.347399	−	0.654624i
$179$	−10.9395	+	18.9478i	−0.817657	+	1.41622i	0.0897479	+	0.995965i	$0.471394\pi$
$179$	−10.9395	+	18.9478i	−0.817657	+	1.41622i	−0.907405	+	0.420258i	$0.861939\pi$
$180$	−2.18785	+	1.58422i	−0.163073	+	0.118081i
$181$	−5.82973	−	6.94760i	−0.433320	−	0.516411i	0.504557	−	0.863378i	$-0.331656\pi$
$181$	−5.82973	−	6.94760i	−0.433320	−	0.516411i	−0.937877	+	0.346968i	$0.887211\pi$
$182$	−2.00331	−	1.25404i	−0.148495	−	0.0929553i
$183$	5.54618	+	9.60627i	0.409985	+	0.710116i
$184$	7.75156	+	3.80374i	0.571453	+	0.280416i
$185$	6.69404	+	1.18034i	0.492156	+	0.0867803i
$186$	−14.1844	+	1.98191i	−1.04005	+	0.145321i
$187$	−2.53735	−	6.97132i	−0.185550	−	0.509794i
$188$	−8.88316	+	9.16938i	−0.647871	+	0.668746i
$189$			1.59654i			0.116131i
$190$	−8.25854	+	1.05484i	−0.599137	+	0.0765261i
$191$			9.57920i			0.693127i	0.938027	+	0.346563i	$0.112651\pi$
$191$			9.57920i			0.693127i	−0.938027	+	0.346563i	$0.887349\pi$
$192$	−4.89498	−	6.32765i	−0.353265	−	0.456659i
$193$	4.24932	+	11.6749i	0.305873	+	0.840379i	0.993450	+	0.114268i	$0.0364522\pi$
$193$	4.24932	+	11.6749i	0.305873	+	0.840379i	−0.687577	+	0.726112i	$0.741326\pi$
$194$	1.83572	+	13.1381i	0.131797	+	0.943259i
$195$	1.39228	+	0.245497i	0.0997036	+	0.0175804i
$196$	8.12671	+	3.63383i	0.580479	+	0.259560i
$197$	11.2357	+	19.4608i	0.800510	+	1.38652i	0.919281	+	0.393603i	$0.128771\pi$
$197$	11.2357	+	19.4608i	0.800510	+	1.38652i	−0.118770	+	0.992922i	$0.537895\pi$
$198$	−1.76708	+	2.82289i	−0.125581	+	0.200614i
$199$	−13.4735	−	16.0570i	−0.955108	−	1.13825i	−0.990310	−	0.138874i	$-0.955652\pi$
$199$	−13.4735	−	16.0570i	−0.955108	−	1.13825i	0.0352018	−	0.999380i	$-0.488793\pi$
$200$	−5.00522	−	7.45909i	−0.353922	−	0.527437i
$201$	1.61405	−	2.79562i	0.113846	−	0.197188i
$202$	−23.7265	+	12.5913i	−1.66939	+	0.885920i
$203$	4.37323	+	1.59173i	0.306941	+	0.111717i
$204$	−1.53404	+	6.11102i	−0.107404	+	0.427857i
$205$	3.65767	−	0.644946i	0.255463	−	0.0450450i
$206$	2.82765	+	8.72636i	0.197012	+	0.607994i
$207$	−1.96228	+	2.33856i	−0.136388	+	0.162541i
$208$	−0.595992	+	4.14444i	−0.0413246	+	0.287366i
$209$	−8.94950	+	5.02729i	−0.619050	+	0.347745i
$210$	3.04749	+	0.108861i	0.210297	+	0.00751214i
$211$	−8.43419	−	7.07712i	−0.580634	−	0.487209i	0.304522	−	0.952505i	$-0.401503\pi$
$211$	−8.43419	−	7.07712i	−0.580634	−	0.487209i	−0.885155	+	0.465296i	$0.845948\pi$
$212$	1.18409	+	4.15448i	0.0813236	+	0.285331i
$213$	0.0247905	+	0.140594i	0.00169861	+	0.00963332i
$214$	27.1943	+	5.80306i	1.85896	+	0.396689i
$215$	4.38340	−	12.0433i	0.298945	−	0.821345i
$216$	2.58665	−	1.14422i	0.175999	−	0.0778544i
$217$	14.0024	+	8.08429i	0.950545	+	0.548798i
$218$	−14.3092	+	11.1611i	−0.969139	+	0.755927i
$219$	−1.70708	+	1.43241i	−0.115353	+	0.0967931i
$220$	5.26788	+	3.56551i	0.355161	+	0.240386i
$221$	2.85585	−	1.64883i	0.192105	−	0.110912i
$222$	−6.59708	−	2.67153i	−0.442767	−	0.179302i
$223$	−3.10354	+	17.6010i	−0.207828	+	1.17865i	0.685099	+	0.728450i	$0.259759\pi$
$223$	−3.10354	+	17.6010i	−0.207828	+	1.17865i	−0.892927	+	0.450202i	$0.851352\pi$
$224$	−0.0361193	+	9.03130i	−0.00241332	+	0.603429i
$225$	2.98436	−	1.08622i	0.198957	−	0.0724146i
$226$	−0.963989	−	0.869377i	−0.0641236	−	0.0578301i
$227$	27.8558			1.84885			0.924427	−	0.381360i	$-0.124544\pi$
$227$	27.8558			1.84885			0.924427	+	0.381360i	$0.124544\pi$
$228$	8.68764	+	0.724485i	0.575353	+	0.0479802i
$229$	−0.681640			−0.0450441			−0.0225220	−	0.999746i	$-0.507170\pi$
$229$	−0.681640			−0.0450441			−0.0225220	+	0.999746i	$0.507170\pi$
$230$	4.33007	+	3.90509i	0.285516	+	0.257494i
$231$	3.53297	−	1.28590i	0.232453	−	0.0846058i
$232$	−0.555394	−	8.22613i	−0.0364634	−	0.540072i
$233$	−3.08344	+	17.4871i	−0.202003	+	1.14561i	0.700084	+	0.714060i	$0.253146\pi$
$233$	−3.08344	+	17.4871i	−0.202003	+	1.14561i	−0.902087	+	0.431555i	$0.857965\pi$
$234$	−1.37212	−	0.555649i	−0.0896982	−	0.0363239i
$235$	−7.46628	+	4.31066i	−0.487046	+	0.281196i
$236$	−7.93768	+	11.7276i	−0.516699	+	0.763400i
$237$	−6.27255	+	5.26329i	−0.407446	+	0.341888i
$238$	5.60855	−	4.37466i	0.363548	−	0.283567i
$239$	−20.6481	−	11.9212i	−1.33562	−	0.771119i	−0.349463	−	0.936950i	$-0.613636\pi$
$239$	−20.6481	−	11.9212i	−1.33562	−	0.771119i	−0.986154	+	0.165831i	$0.946969\pi$
$240$	−2.00773	−	5.01545i	−0.129599	−	0.323746i
$241$	−4.95163	+	13.6045i	−0.318962	+	0.876342i	0.671800	+	0.740733i	$0.265521\pi$
$241$	−4.95163	+	13.6045i	−0.318962	+	0.876342i	−0.990762	+	0.135609i	$0.956701\pi$
$242$	−7.54379	−	1.60979i	−0.484933	−	0.103481i
$243$	0.173648	+	0.984808i	0.0111395	+	0.0631754i
$244$	−21.3351	+	6.08082i	−1.36584	+	0.389284i
$245$	4.60515	+	3.86418i	0.294212	+	0.246874i
$246$	−3.88656	−	0.138834i	−0.247798	−	0.00885176i
$247$	−2.89149	−	3.52961i	−0.183981	−	0.224583i
$248$	3.06249	−	28.4801i	0.194469	−	1.80849i
$249$	−4.46672	+	5.32323i	−0.283067	+	0.337346i
$250$	−4.81379	−	14.8557i	−0.304451	−	0.939560i
$251$	19.7457	−	3.48170i	1.24634	−	0.219763i	0.488707	−	0.872448i	$-0.337469\pi$
$251$	19.7457	−	3.48170i	1.24634	−	0.219763i	0.757629	+	0.652685i	$0.226358\pi$
$252$	−3.09698	−	0.777429i	−0.195092	−	0.0489734i
$253$	6.75547	+	2.45879i	0.424713	+	0.154583i
$254$	−10.3564	+	5.49597i	−0.649818	+	0.344848i
$255$	−2.12740	+	3.68477i	−0.133223	+	0.230749i
$256$	14.6581	−	6.41412i	0.916129	−	0.400883i
$257$	10.6605	+	12.7046i	0.664981	+	0.792494i	0.988091	−	0.153868i	$-0.0491729\pi$
$257$	10.6605	+	12.7046i	0.664981	+	0.792494i	−0.323110	+	0.946361i	$0.604728\pi$
$258$	−7.12055	+	11.3750i	−0.443306	+	0.708177i
$259$	4.01754	+	6.95858i	0.249638	+	0.432385i
$260$	−1.15419	+	2.58123i	−0.0715798	+	0.160081i
$261$	2.87071	+	0.506184i	0.177693	+	0.0313320i
$262$	3.34023	+	23.9057i	0.206360	+	1.47690i
$263$	−8.49910	−	23.3511i	−0.524077	−	1.43989i	−0.865944	−	0.500141i	$-0.833281\pi$
$263$	−8.49910	−	23.3511i	−0.524077	−	1.43989i	0.341867	−	0.939748i	$-0.388941\pi$
$264$	−4.61541	−	4.80241i	−0.284059	−	0.295568i
$265$			2.91724i			0.179205i
$266$	−7.23035	−	6.67692i	−0.443321	−	0.409388i
$267$			6.99146i			0.427870i
$268$	4.63702	+	4.49228i	0.283251	+	0.274410i
$269$	−6.24608	−	17.1610i	−0.380830	−	1.04632i	−0.971007	−	0.239049i	$-0.923164\pi$
$269$	−6.24608	−	17.1610i	−0.380830	−	1.04632i	0.590177	−	0.807274i	$-0.299058\pi$
$270$	1.89165	−	0.264312i	0.115122	−	0.0160855i
$271$	−4.86421	−	0.857691i	−0.295480	−	0.0521010i	0.0239432	−	0.999713i	$-0.492378\pi$
$271$	−4.86421	−	0.857691i	−0.295480	−	0.0521010i	−0.319423	+	0.947612i	$0.603489\pi$
$272$	−11.1073	−	5.95150i	−0.673477	−	0.360863i
$273$	0.835603	+	1.44731i	0.0505730	+	0.0875950i
$274$	11.9191	+	7.46117i	0.720062	+	0.450746i
$275$	−4.80738	−	5.72922i	−0.289896	−	0.345485i
$276$	−3.58084	−	4.94522i	−0.215541	−	0.297667i
$277$	−11.4284	+	19.7945i	−0.686663	+	1.18934i	0.286248	+	0.958156i	$0.407592\pi$
$277$	−11.4284	+	19.7945i	−0.686663	+	1.18934i	−0.972911	+	0.231180i	$0.925741\pi$
$278$	−8.94014	−	16.8465i	−0.536194	−	1.01038i
$279$	9.51654	+	3.46374i	0.569740	+	0.207369i
$280$	−1.69514	+	5.85856i	−0.101304	+	0.350116i
$281$	28.8824	−	5.09275i	1.72298	−	0.303808i	0.777354	−	0.629064i	$-0.216562\pi$
$281$	28.8824	−	5.09275i	1.72298	−	0.303808i	0.945626	+	0.325256i	$0.105450\pi$
$282$	8.58780	−	2.78275i	0.511396	−	0.165711i
$283$	−10.0992	+	12.0357i	−0.600333	+	0.715448i	−0.977556	−	0.210674i	$-0.932434\pi$
$283$	−10.0992	+	12.0357i	−0.600333	+	0.715448i	0.377224	+	0.926122i	$0.376879\pi$
$284$	−0.284797	−	0.0203729i	−0.0168996	−	0.00120891i
$285$	5.50796	+	2.07858i	0.326263	+	0.123124i
$286$	−0.124450	+	3.48389i	−0.00735891	+	0.206007i
$287$	3.36326	+	2.82211i	0.198527	+	0.166584i
$288$	0.960015	+	5.57480i	0.0565694	+	0.328498i
$289$	−1.22865	−	6.96803i	−0.0722737	−	0.409884i
$290$	1.16195	−	5.44514i	0.0682322	−	0.319750i
$291$	3.20824	−	8.81457i	0.188070	−	0.516719i
$292$	−1.94735	−	4.00892i	−0.113960	−	0.234604i
$293$	−15.3135	−	8.84126i	−0.894625	−	0.516512i	−0.0191724	−	0.999816i	$-0.506103\pi$
$293$	−15.3135	−	8.84126i	−0.894625	−	0.516512i	−0.875452	+	0.483304i	$0.839436\pi$
$294$	−3.87148	−	4.96344i	−0.225789	−	0.289474i
$295$	−7.32576	+	6.14705i	−0.426522	+	0.357895i
$296$	8.39471	−	11.4962i	0.487933	−	0.668204i
$297$	2.03942	−	1.17746i	0.118339	−	0.0683231i
$298$	−0.295203	+	0.728973i	−0.0171006	+	0.0422283i
$299$	−0.554901	+	3.14700i	−0.0320907	+	0.181996i
$300$	0.653836	+	6.31804i	0.0377492	+	0.364772i
$301$	14.2363	−	5.18160i	0.820568	−	0.298663i
$302$	16.6039	−	18.4109i	0.955449	−	1.05943i
$303$	18.9933			1.09114
$304$	−5.63579	+	16.4996i	−0.323235	+	0.946319i
$305$	−14.9813			−0.857827
$306$	2.98377	−	3.30848i	0.170571	−	0.189133i
$307$	−13.9831	+	5.08944i	−0.798058	+	0.290470i	−0.708682	−	0.705528i	$-0.750710\pi$
$307$	−13.9831	+	5.08944i	−0.798058	+	0.290470i	−0.0893768	+	0.995998i	$0.528488\pi$
$308$	0.774029	+	7.47948i	0.0441044	+	0.426183i
$309$	1.12634	−	6.38779i	0.0640752	−	0.363389i
$310$	7.26052	−	17.9291i	0.412370	−	1.01831i
$311$	4.05834	−	2.34308i	0.230127	−	0.132864i	−0.380503	−	0.924779i	$-0.624249\pi$
$311$	4.05834	−	2.34308i	0.230127	−	0.132864i	0.610631	+	0.791915i	$0.290916\pi$
$312$	1.74601	−	2.39108i	0.0988481	−	0.135368i
$313$	19.4812	−	16.3466i	1.10114	−	0.923967i	0.103639	−	0.994615i	$-0.466951\pi$
$313$	19.4812	−	16.3466i	1.10114	−	0.923967i	0.997501	+	0.0706484i	$0.0225068\pi$
$314$	−1.25887	−	1.61394i	−0.0710422	−	0.0910800i
$315$	−1.86739	−	1.07814i	−0.105215	−	0.0607462i
$316$	−7.15541	−	14.7305i	−0.402523	−	0.828657i
$317$	−0.868477	+	2.38612i	−0.0487785	+	0.134018i	−0.961690	−	0.274140i	$-0.911607\pi$
$317$	−0.868477	+	2.38612i	−0.0487785	+	0.134018i	0.912911	+	0.408158i	$0.133829\pi$
$318$	0.637487	−	2.98739i	0.0357485	−	0.167525i
$319$	−1.19202	−	6.76029i	−0.0667404	−	0.378504i
$320$	10.7067	−	1.45237i	0.598523	−	0.0811898i
$321$	−15.0621	−	12.6386i	−0.840686	−	0.705419i
$322$	−0.246061	+	6.88828i	−0.0137124	+	0.383869i
$323$	12.9582	−	4.54416i	0.721015	−	0.252844i
$324$	−1.99490	−	0.142704i	−0.110828	−	0.00792802i
$325$	2.13690	−	2.54666i	0.118534	−	0.141263i
$326$	−21.7729	+	7.05518i	−1.20589	+	0.390750i
$327$	12.6371	−	2.22826i	0.698833	−	0.123223i
$328$	2.16187	−	7.47161i	0.119369	−	0.412551i
$329$	−9.57663	−	3.48561i	−0.527976	−	0.192168i
$330$	−2.10849	−	3.97316i	−0.116069	−	0.218715i
$331$	−5.40685	+	9.36494i	−0.297187	+	0.514744i	−0.975491	−	0.220038i	$-0.929382\pi$
$331$	−5.40685	+	9.36494i	−0.297187	+	0.514744i	0.678304	+	0.734781i	$0.262715\pi$
$332$	−8.15101	−	11.2567i	−0.447345	−	0.617794i
$333$	3.23503	+	3.85536i	0.177279	+	0.211273i
$334$	2.98351	+	1.86762i	0.163250	+	0.102192i
$335$	2.17993	+	3.77575i	0.119102	+	0.206291i
$336$	3.01614	−	5.62901i	0.164544	−	0.307088i
$337$	4.15534	+	0.732698i	0.226356	+	0.0399126i	0.285675	−	0.958326i	$-0.407782\pi$
$337$	4.15534	+	0.732698i	0.226356	+	0.0399126i	−0.0593198	+	0.998239i	$0.518893\pi$
$338$	16.6732	−	2.32967i	0.906903	−	0.126717i
$339$	0.313941	+	0.862546i	0.0170509	+	0.0468471i
$340$	−6.11183	−	5.92105i	−0.331461	−	0.321114i
$341$		−	23.8489i		−	1.29149i
$342$	−5.18619	−	3.33218i	−0.280437	−	0.180184i
$343$			18.2820i			0.987138i
$344$	−18.5981	−	19.3516i	−1.00274	−	1.04337i
$345$	−1.41017	−	3.87441i	−0.0759209	−	0.208591i
$346$	−3.21451	−	23.0059i	−0.172813	−	1.23681i
$347$	−14.0334	−	2.47446i	−0.753351	−	0.132836i	−0.216231	−	0.976342i	$-0.569377\pi$
$347$	−14.0334	−	2.47446i	−0.753351	−	0.132836i	−0.537120	+	0.843506i	$0.680488\pi$
$348$	−2.37979	+	5.32217i	−0.127570	+	0.285298i
$349$	−17.7239	−	30.6987i	−0.948739	−	1.64326i	−0.748086	−	0.663602i	$-0.769027\pi$
$349$	−17.7239	−	30.6987i	−0.948739	−	1.64326i	−0.200653	−	0.979662i	$-0.564307\pi$
$350$	3.80473	−	6.07802i	0.203372	−	0.324884i
$351$	0.672851	+	0.801872i	0.0359141	+	0.0428008i
$352$	11.5632	−	6.61452i	0.616323	−	0.352555i
$353$	8.48081	−	14.6892i	0.451388	−	0.781827i	−0.547085	−	0.837077i	$-0.684262\pi$
$353$	8.48081	−	14.6892i	0.451388	−	0.781827i	0.998473	+	0.0552505i	$0.0175957\pi$
$354$	8.84521	−	4.69401i	0.470117	−	0.249484i
$355$	−0.181186	−	0.0659465i	−0.00961638	−	0.00350008i
$356$	−13.5621	−	3.40447i	−0.718791	−	0.180437i
$357$	−4.95318	+	0.873379i	−0.262150	+	0.0462241i
$358$	9.53793	+	29.4348i	0.504095	+	1.55568i
$359$	6.71587	−	8.00366i	0.354450	−	0.422417i	−0.559127	−	0.829082i	$-0.688864\pi$
$359$	6.71587	−	8.00366i	0.354450	−	0.422417i	0.913578	+	0.406664i	$0.133308\pi$
$360$	−0.408420	+	3.79817i	−0.0215256	+	0.200181i
$361$	−9.10949	−	16.6738i	−0.479447	−	0.877571i
$362$	−12.8180	−	0.457878i	−0.673697	−	0.0240655i
$363$	4.17828	+	3.50600i	0.219303	+	0.184017i
$364$	−3.21440	+	0.916152i	−0.168480	+	0.0480194i
$365$	−0.522630	−	2.96398i	−0.0273557	−	0.155142i
$366$	15.3416	+	3.27378i	0.801916	+	0.171123i
$367$	0.364940	−	1.00267i	0.0190497	−	0.0523387i	−0.929803	−	0.368057i	$-0.880023\pi$
$367$	0.364940	−	1.00267i	0.0190497	−	0.0523387i	0.948853	+	0.315718i	$0.102245\pi$
$368$	11.3365	−	4.53810i	0.590955	−	0.236565i
$369$	2.38154	+	1.37498i	0.123978	+	0.0715788i
$370$	7.57976	−	5.91220i	0.394053	−	0.307360i
$371$	−2.64167	+	2.21663i	−0.137149	+	0.115082i
$372$	−11.3531	+	16.7737i	−0.588629	+	0.869674i
$373$	−20.6495	+	11.9220i	−1.06919	+	0.617297i	−0.927960	−	0.372680i	$-0.878439\pi$
$373$	−20.6495	+	11.9220i	−1.06919	+	0.617297i	−0.141229	+	0.989977i	$0.545106\pi$
$374$	−9.72456	−	3.93803i	−0.502845	−	0.203631i
$375$	−1.91748	+	10.8746i	−0.0990182	+	0.561560i
$376$	1.21622	+	18.0138i	0.0627216	+	0.928991i
$377$	2.86731	−	1.04362i	0.147674	−	0.0537490i
$378$	1.67670	+	1.51213i	0.0862399	+	0.0777757i
$379$	8.89400			0.456854			0.228427	−	0.973561i	$-0.426642\pi$
$379$	8.89400			0.456854			0.228427	+	0.973561i	$0.426642\pi$
$380$	−6.71414	+	9.67226i	−0.344428	+	0.496176i
$381$	8.29038			0.424729
$382$	10.0602	+	9.07279i	0.514722	+	0.464204i
$383$	−19.4046	+	7.06270i	−0.991530	+	0.360887i	−0.786312	−	0.617829i	$-0.788012\pi$
$383$	−19.4046	+	7.06270i	−0.991530	+	0.360887i	−0.205217	+	0.978716i	$0.565790\pi$
$384$	−11.2816	−	0.852383i	−0.575709	−	0.0434980i
$385$	−0.881759	+	5.00071i	−0.0449386	+	0.254860i
$386$	16.2858	+	6.59504i	0.828924	+	0.335679i
$387$	8.21796	−	4.74464i	0.417743	−	0.241184i
$388$	15.5364	+	10.5156i	0.788741	+	0.533850i
$389$	−25.9541	+	21.7781i	−1.31593	+	1.10419i	−0.328775	+	0.944408i	$0.606636\pi$
$389$	−25.9541	+	21.7781i	−1.31593	+	1.10419i	−0.987152	+	0.159786i	$0.948920\pi$
$390$	1.57650	−	1.22967i	0.0798294	−	0.0622668i
$391$	−8.32872	−	4.80859i	−0.421202	−	0.243181i
$392$	11.5134	−	5.09301i	0.581513	−	0.257236i
$393$	5.83764	−	16.0388i	0.294470	−	0.809049i
$394$	31.0796	+	6.63216i	1.56577	+	0.334123i
$395$	−1.92037	−	10.8910i	−0.0966245	−	0.547985i
$396$	1.29096	+	4.52946i	0.0648733	+	0.227614i
$397$	23.6944	+	19.8820i	1.18919	+	0.997849i	0.999873	+	0.0159330i	$0.00507186\pi$
$397$	23.6944	+	19.8820i	1.18919	+	0.997849i	0.189317	+	0.981916i	$0.439373\pi$
$398$	−29.6244	−	1.05823i	−1.48494	−	0.0530444i
$399$	2.30292	+	6.56705i	0.115290	+	0.328764i
$400$	−12.5742	−	1.80823i	−0.628711	−	0.0904117i
$401$	1.13248	−	1.34964i	0.0565534	−	0.0673977i	−0.737026	−	0.675864i	$-0.763771\pi$
$401$	1.13248	−	1.34964i	0.0565534	−	0.0673977i	0.793580	+	0.608467i	$0.208215\pi$
$402$	−1.40726	−	4.34291i	−0.0701877	−	0.216605i
$403$	10.4399	−	1.84083i	0.520048	−	0.0916985i
$404$	−9.24873	+	36.8435i	−0.460142	+	1.83303i
$405$	−1.26915	−	0.461931i	−0.0630643	−	0.0229535i
$406$	5.81368	−	3.08523i	0.288528	−	0.153117i
$407$	5.92594	−	10.2640i	0.293738	−	0.508769i
$408$	4.96491	+	7.39902i	0.245800	+	0.366306i
$409$	−23.8485	−	28.4215i	−1.17923	−	1.40535i	−0.894688	−	0.446691i	$-0.852602\pi$
$409$	−23.8485	−	28.4215i	−1.17923	−	1.40535i	−0.284544	−	0.958663i	$-0.591842\pi$
$410$	2.78698	−	4.45217i	0.137639	−	0.219877i
$411$	−4.97161	−	8.61108i	−0.245231	−	0.424753i
$412$	11.8427	+	5.29541i	0.583446	+	0.260886i
$413$	−11.1328	−	1.96301i	−0.547808	−	0.0965934i
$414$	0.597428	+	4.27573i	0.0293620	+	0.210141i
$415$	−3.20995	−	8.81926i	−0.157570	−	0.432920i
$416$	3.78805	+	4.55126i	0.185724	+	0.223144i
$417$			13.4857i			0.660398i
$418$	−3.19668	+	14.1604i	−0.156355	+	0.692605i
$419$			38.1001i			1.86131i	0.365898	+	0.930655i	$0.380762\pi$
$419$			38.1001i			1.86131i	−0.365898	+	0.930655i	$0.619238\pi$
$420$	3.00071	−	3.09739i	0.146420	−	0.151137i
$421$	0.712497	+	1.95757i	0.0347250	+	0.0954061i	0.955844	−	0.293876i	$-0.0949453\pi$
$421$	0.712497	+	1.95757i	0.0347250	+	0.0954061i	−0.921119	+	0.389282i	$0.872723\pi$
$422$	−15.4208	+	2.15467i	−0.750671	+	0.104888i
$423$	−6.28636	−	1.10846i	−0.305653	−	0.0538949i
$424$	5.48456	+	2.69131i	0.266354	+	0.130702i
$425$	5.00252	+	8.66463i	0.242658	+	0.420296i
$426$	0.171133	+	0.107126i	0.00829140	+	0.00519027i
$427$	−11.3834	−	13.5662i	−0.550879	−	0.656512i
$428$	31.8511	−	23.0634i	1.53958	−	1.11481i
$429$	1.23253	−	2.13480i	0.0595070	−	0.103069i
$430$	−8.49629	−	16.0101i	−0.409728	−	0.772075i
$431$	−30.3760	−	11.0560i	−1.46316	−	0.532547i	−0.516926	−	0.856030i	$-0.672924\pi$
$431$	−30.3760	−	11.0560i	−1.46316	−	0.532547i	−0.946234	+	0.323483i	$0.895146\pi$
$432$	1.24823	−	3.80025i	0.0600556	−	0.182840i
$433$	−30.2622	+	5.33604i	−1.45431	+	0.256434i	−0.844262	−	0.535931i	$-0.819961\pi$
$433$	−30.2622	+	5.33604i	−1.45431	+	0.256434i	−0.610047	+	0.792365i	$0.708850\pi$
$434$	21.7523	−	7.04853i	1.04415	−	0.338340i
$435$	−2.53064	+	3.01590i	−0.121335	+	0.144602i
$436$	−1.83119	+	25.5987i	−0.0876981	+	1.22595i
$437$	−4.69823	+	12.4497i	−0.224747	+	0.595550i
$438$	−0.112504	+	3.14947i	−0.00537565	+	0.150487i
$439$	5.78473	+	4.85396i	0.276090	+	0.231667i	0.770310	−	0.637670i	$-0.220102\pi$
$439$	5.78473	+	4.85396i	0.276090	+	0.231667i	−0.494220	+	0.869337i	$0.664546\pi$
$440$	8.73391	−	2.15536i	0.416373	−	0.102753i
$441$	0.772921	+	4.38345i	0.0368057	+	0.208736i
$442$	0.973262	−	4.56090i	0.0462934	−	0.216940i
$443$	6.45550	−	17.7363i	0.306710	−	0.842679i	−0.686583	−	0.727052i	$-0.740890\pi$
$443$	6.45550	−	17.7363i	0.306710	−	0.842679i	0.993293	−	0.115627i	$-0.0368878\pi$
$444$	−9.05399	+	4.39801i	−0.429683	+	0.208720i
$445$	−8.17756	−	4.72132i	−0.387653	−	0.223812i
$446$	15.5453	+	19.9299i	0.736090	+	0.943707i
$447$	0.426015	−	0.357469i	0.0201498	−	0.0169077i
$448$	9.45053	+	8.59178i	0.446496	+	0.405924i
$449$	−3.15250	+	1.82010i	−0.148776	+	0.0858957i	−0.572540	−	0.819877i	$-0.694042\pi$
$449$	−3.15250	+	1.82010i	−0.148776	+	0.0858957i	0.423764	+	0.905773i	$0.360709\pi$
$450$	1.68583	−	4.16299i	0.0794710	−	0.196245i
$451$	1.12454	−	6.37757i	0.0529524	−	0.300308i
$452$	−1.82605	+	0.188973i	−0.0858903	+	0.00888854i
$453$	−16.4735	+	5.99585i	−0.773991	+	0.281710i
$454$	26.3832	−	29.2544i	1.23822	−	1.37298i
$455$	−2.25712			−0.105816
$456$	8.98922	−	8.43765i	0.420959	−	0.395129i
$457$	12.4021			0.580146			0.290073	−	0.957005i	$-0.406320\pi$
$457$	12.4021			0.580146			0.290073	+	0.957005i	$0.406320\pi$
$458$	−0.645605	+	0.715864i	−0.0301671	+	0.0334501i
$459$	−2.96033	+	1.07747i	−0.138176	+	0.0502920i
$460$	8.20231	−	0.848833i	0.382435	−	0.0395771i
$461$	−0.138586	+	0.785963i	−0.00645461	+	0.0366059i	−0.987865	−	0.155315i	$-0.950361\pi$
$461$	−0.138586	+	0.785963i	−0.00645461	+	0.0366059i	0.981410	+	0.191921i	$0.0614718\pi$
$462$	1.99574	−	4.92827i	0.0928502	−	0.229284i
$463$	15.5749	−	8.99215i	0.723825	−	0.417901i	−0.0923339	−	0.995728i	$-0.529433\pi$
$463$	15.5749	−	8.99215i	0.723825	−	0.417901i	0.816159	+	0.577828i	$0.196099\pi$
$464$	−9.16518	−	7.20797i	−0.425483	−	0.334621i
$465$	−10.4779	+	8.79197i	−0.485899	+	0.407718i
$466$	15.4446	+	19.8008i	0.715458	+	0.917256i
$467$	13.2268	+	7.63648i	0.612062	+	0.353374i	0.773772	−	0.633464i	$-0.218368\pi$
$467$	13.2268	+	7.63648i	0.612062	+	0.353374i	−0.161710	+	0.986838i	$0.551701\pi$
$468$	−1.88313	+	0.914736i	−0.0870476	+	0.0422837i
$469$	−1.76270	+	4.84297i	−0.0813937	+	0.223627i
$470$	−2.54448	+	11.9239i	−0.117368	+	0.550009i
$471$	0.251327	+	1.42535i	0.0115805	+	0.0656765i
$472$	4.79836	+	19.4438i	0.220862	+	0.894973i
$473$	−17.1184	−	14.3640i	−0.787105	−	0.660460i
$474$	−0.413390	+	11.5725i	−0.0189876	+	0.531544i
$475$	10.7088	−	8.77274i	0.491353	−	0.402521i
$476$	0.717745	−	10.0335i	0.0328978	−	0.459886i
$477$	−1.38840	+	1.65463i	−0.0635704	+	0.0757602i
$478$	−32.0763	+	10.3939i	−1.46714	+	0.475404i
$479$	20.0338	−	3.53249i	0.915366	−	0.161404i	0.303927	−	0.952695i	$-0.401702\pi$
$479$	20.0338	−	3.53249i	0.915366	−	0.161404i	0.611439	+	0.791292i	$0.290591\pi$
$480$	−7.16886	−	2.64177i	−0.327212	−	0.120580i
$481$	4.95049	+	1.80183i	0.225723	+	0.0821565i
$482$	9.59769	+	18.0855i	0.437163	+	0.823773i
$483$	2.43693	−	4.22088i	0.110884	−	0.192057i
$484$	−8.83559	+	6.39786i	−0.401618	+	0.290812i
$485$	8.14345	+	9.70498i	0.369775	+	0.440681i
$486$	1.19872	+	0.750378i	0.0543751	+	0.0340378i
$487$	6.29349	+	10.9006i	0.285185	+	0.493955i	0.972654	−	0.232259i	$-0.0746116\pi$
$487$	6.29349	+	10.9006i	0.285185	+	0.493955i	−0.687469	+	0.726214i	$0.741278\pi$
$488$	−13.8211	+	28.1656i	−0.625650	+	1.27500i
$489$	15.9380	+	2.81029i	0.720740	+	0.127086i
$490$	8.41989	−	1.17647i	0.380372	−	0.0531476i
$491$	4.03224	+	11.0785i	0.181973	+	0.499966i	0.996818	−	0.0797129i	$-0.0254004\pi$
$491$	4.03224	+	11.0785i	0.181973	+	0.499966i	−0.814845	+	0.579679i	$0.803178\pi$
$492$	−3.82690	+	3.95021i	−0.172530	+	0.178089i
$493$			9.18315i			0.413588i
$494$	−6.44545	−	0.306348i	−0.289994	−	0.0137833i
$495$			3.18054i			0.142955i
$496$	−27.0095	−	30.1907i	−1.21276	−	1.35560i
$497$	−0.0779551	−	0.214180i	−0.00349677	−	0.00960729i
$498$	1.35992	+	9.73279i	0.0609393	+	0.436137i
$499$	−25.9271	−	4.57164i	−1.16065	−	0.204655i	−0.440032	−	0.897982i	$-0.645033\pi$
$499$	−25.9271	−	4.57164i	−1.16065	−	0.204655i	−0.720623	+	0.693327i	$0.756144\pi$
$500$	−20.1609	−	9.01490i	−0.901624	−	0.403159i
$501$	−1.24445	−	2.15546i	−0.0555981	−	0.0962988i
$502$	15.0453	−	24.0347i	0.671505	−	1.07272i
$503$	−13.4375	−	16.0142i	−0.599150	−	0.714039i	0.378187	−	0.925729i	$-0.376548\pi$
$503$	−13.4375	−	16.0142i	−0.599150	−	0.714039i	−0.977337	+	0.211690i	$0.932103\pi$
$504$	−3.74972	+	2.51615i	−0.167026	+	0.112078i
$505$	−12.8261	+	22.2155i	−0.570755	+	0.988577i
$506$	8.98058	−	4.76585i	0.399235	−	0.211868i
$507$	−11.1864	−	4.07150i	−0.496804	−	0.180822i
$508$	−4.03698	+	16.0818i	−0.179112	+	0.713514i
$509$	22.0661	−	3.89085i	0.978064	−	0.172459i	0.338307	−	0.941036i	$-0.390146\pi$
$509$	22.0661	−	3.89085i	0.978064	−	0.172459i	0.639757	+	0.768577i	$0.279035\pi$
$510$	1.85484	+	5.72418i	0.0821336	+	0.253471i
$511$	2.28689	−	2.72541i	0.101166	−	0.120565i
$512$	7.14699	−	21.4691i	0.315855	−	0.948807i
$513$	2.13480	+	3.80034i	0.0942539	+	0.167789i
$514$	23.4394	+	0.837294i	1.03387	+	0.0369314i
$515$	6.71086	+	5.63108i	0.295716	+	0.248135i
$516$	5.20201	+	18.2517i	0.229006	+	0.803487i
$517$	2.61032	+	14.8039i	0.114802	+	0.651073i
$518$	11.1131	+	2.37146i	0.488282	+	0.104196i
$519$	−5.61791	+	15.4351i	−0.246599	+	0.677525i
$520$	1.61766	+	3.65691i	0.0709390	+	0.160366i
$521$	−13.6596	−	7.88639i	−0.598439	−	0.345509i	0.169988	−	0.985446i	$-0.445627\pi$
$521$	−13.6596	−	7.88639i	−0.598439	−	0.345509i	−0.768427	+	0.639937i	$0.778960\pi$
$522$	3.25055	−	2.53542i	0.142273	−	0.110972i
$523$	−17.5057	+	14.6890i	−0.765472	+	0.642307i	−0.939545	−	0.342426i	$-0.888751\pi$
$523$	−17.5057	+	14.6890i	−0.765472	+	0.642307i	0.174073	+	0.984733i	$0.444307\pi$
$524$	28.2696	+	19.1340i	1.23497	+	0.835872i
$525$	−4.39112	+	2.53521i	−0.191644	+	0.110646i
$526$	−32.5733	−	13.1908i	−1.42026	−	0.575145i
$527$	−5.54010	+	31.4194i	−0.241330	+	1.36865i
$528$	−9.41494	+	0.298621i	−0.409733	+	0.0129958i
$529$	−12.8556	+	4.67904i	−0.558937	+	0.203437i
$530$	3.06371	+	2.76302i	0.133079	+	0.120018i
$531$	−7.08066			−0.307274
$532$	−13.8603	+	1.26943i	−0.600919	+	0.0550367i
$533$	2.87858			0.124685
$534$	7.34248	+	6.62184i	0.317740	+	0.286555i
$535$	24.9542	−	9.08259i	1.07886	−	0.392674i
$536$	9.10971	−	0.615050i	0.393479	−	0.0265661i
$537$	3.79925	−	21.5466i	0.163950	−	0.929805i
$538$	−23.9385	−	9.69405i	−1.03206	−	0.417940i
$539$	9.07760	−	5.24096i	0.391000	−	0.225744i
$540$	1.51407	−	2.23697i	0.0651551	−	0.0962639i
$541$	13.5128	−	11.3386i	0.580961	−	0.487484i	−0.304302	−	0.952576i	$-0.598423\pi$
$541$	13.5128	−	11.3386i	0.580961	−	0.487484i	0.885262	+	0.465092i	$0.153979\pi$
$542$	−5.50781	+	4.29608i	−0.236581	+	0.184533i
$543$	7.85437	+	4.53472i	0.337063	+	0.194604i
$544$	−16.7704	+	6.02807i	−0.719024	+	0.258451i
$545$	−5.92752	+	16.2857i	−0.253907	+	0.697604i
$546$	2.31140	+	0.493236i	0.0989188	+	0.0211086i
$547$	−2.96069	−	16.7909i	−0.126590	−	0.717927i	−0.980351	−	0.197262i	$-0.936795\pi$
$547$	−2.96069	−	16.7909i	−0.126590	−	0.717927i	0.853761	−	0.520665i	$-0.174316\pi$
$548$	19.1248	−	5.45086i	0.816971	−	0.232849i
$549$	−8.49724	−	7.13003i	−0.362653	−	0.304302i
$550$	−10.5701	−	0.377581i	−0.450711	−	0.0161001i
$551$	12.5383	−	2.05876i	0.534149	−	0.0877061i
$552$	−8.58504	−	0.923158i	−0.365404	−	0.0392922i
$553$	8.40304	−	10.0143i	0.357333	−	0.425853i
$554$	9.96416	+	30.7502i	0.423336	+	1.30645i
$555$	−6.69404	+	1.18034i	−0.284146	+	0.0501026i
$556$	−26.1598	−	6.56684i	−1.10942	−	0.278496i
$557$	25.0787	+	9.12791i	1.06262	+	0.386762i	0.813412	−	0.581688i	$-0.197608\pi$
$557$	25.0787	+	9.12791i	1.06262	+	0.386762i	0.249207	+	0.968450i	$0.419830\pi$
$558$	12.6511	−	6.71373i	0.535563	−	0.284215i
$559$	4.96655	−	8.60232i	0.210063	−	0.363839i
$560$	4.54718	+	7.32909i	0.192153	+	0.309710i
$561$	4.76867	+	5.68308i	0.201333	+	0.239940i
$562$	22.0071	−	35.1560i	0.928312	−	1.48297i
$563$	2.21876	+	3.84300i	0.0935096	+	0.161963i	0.908986	−	0.416828i	$-0.136858\pi$
$563$	2.21876	+	3.84300i	0.0935096	+	0.161963i	−0.815476	+	0.578791i	$0.803525\pi$
$564$	5.21133	−	11.6546i	0.219436	−	0.490748i
$565$	−1.22088	−	0.215274i	−0.0513629	−	0.00905666i
$566$	3.07474	+	22.0056i	0.129241	+	0.924966i
$567$	−0.546047	−	1.50025i	−0.0229318	−	0.0630047i
$568$	−0.291137	+	0.279801i	−0.0122158	+	0.0117402i
$569$		−	32.6770i		−	1.36989i	−0.728594	−	0.684946i	$-0.759826\pi$
$569$		−	32.6770i		−	1.36989i	0.728594	−	0.684946i	$-0.240174\pi$
$570$	7.39971	−	3.81581i	0.309940	−	0.159827i
$571$			26.4624i			1.10742i	0.832711	+	0.553708i	$0.186788\pi$
$571$			26.4624i			1.10742i	−0.832711	+	0.553708i	$0.813212\pi$
$572$	3.54094	+	3.43041i	0.148054	+	0.143433i
$573$	−3.27628	−	9.00151i	−0.136869	−	0.376043i
$574$	6.14926	−	0.859207i	0.256665	−	0.0358626i
$575$	−9.54797	−	1.68356i	−0.398178	−	0.0702095i
$576$	6.76396	+	4.27186i	0.281832	+	0.177994i
$577$	−6.67973	−	11.5696i	−0.278081	−	0.481650i	0.692827	−	0.721104i	$-0.256365\pi$
$577$	−6.67973	−	11.5696i	−0.278081	−	0.481650i	−0.970908	+	0.239454i	$0.923032\pi$
$578$	−8.48158	−	5.30932i	−0.352787	−	0.220839i
$579$	−7.98612	−	9.51748i	−0.331892	−	0.395533i
$580$	−4.61801	−	6.37757i	−0.191752	−	0.264814i
$581$	5.54715	−	9.60794i	0.230134	−	0.398604i
$582$	−6.21850	−	11.7179i	−0.257765	−	0.485723i
$583$	4.77978	+	1.73970i	0.197958	+	0.0720510i
$584$	−6.05460	−	1.75186i	−0.250541	−	0.0724926i
$585$	−1.39228	+	0.245497i	−0.0575639	+	0.0101501i
$586$	−23.7891	+	7.70852i	−0.982719	+	0.318436i
$587$	11.7750	−	14.0329i	0.486005	−	0.579198i	−0.466192	−	0.884684i	$-0.654374\pi$
$587$	11.7750	−	14.0329i	0.486005	−	0.579198i	0.952197	+	0.305486i	$0.0988188\pi$
$588$	−8.87946	−	0.635188i	−0.366183	−	0.0261947i
$589$	44.1408	+	0.520322i	1.81879	+	0.0214395i
$590$	−0.482801	+	13.5157i	−0.0198766	+	0.556431i
$591$	−17.2141	−	14.4443i	−0.708093	−	0.594161i
$592$	−4.12251	−	19.7047i	−0.169434	−	0.809856i
$593$	2.70931	+	15.3652i	0.111258	+	0.630975i	0.988535	+	0.150991i	$0.0482464\pi$
$593$	2.70931	+	15.3652i	0.111258	+	0.630975i	−0.877277	+	0.479984i	$0.840643\pi$
$594$	0.695026	−	3.25703i	0.0285172	−	0.133637i
$595$	2.32332	−	6.38328i	0.0952469	−	0.261689i
$596$	0.485977	+	1.00046i	0.0199064	+	0.0409804i
$597$	18.1527	+	10.4805i	0.742942	+	0.428938i
$598$	2.77944	+	3.56339i	0.113660	+	0.145718i
$599$	−27.8423	+	23.3625i	−1.13761	+	0.954565i	−0.999358	−	0.0358322i	$-0.988592\pi$
$599$	−27.8423	+	23.3625i	−1.13761	+	0.954565i	−0.138249	+	0.990398i	$0.544147\pi$
$600$	7.25453	+	5.29737i	0.296165	+	0.216264i
$601$	28.9950	−	16.7402i	1.18273	−	0.682849i	0.226085	−	0.974108i	$-0.427407\pi$
$601$	28.9950	−	16.7402i	1.18273	−	0.682849i	0.956644	+	0.291259i	$0.0940741\pi$
$602$	8.04195	−	19.8588i	0.327765	−	0.809384i
$603$	−0.560554	+	3.17906i	−0.0228275	+	0.129461i
$604$	−3.60913	−	34.8752i	−0.146853	−	1.41905i
$605$	−6.92238	+	2.51954i	−0.281435	+	0.102434i
$606$	17.9892	−	19.9469i	0.730760	−	0.810287i
$607$	21.9579			0.891245			0.445622	−	0.895221i	$-0.352982\pi$
$607$	21.9579			0.891245			0.445622	+	0.895221i	$0.352982\pi$
$608$	11.9902	+	21.5461i	0.486267	+	0.873810i
$609$	−4.65390			−0.188585
$610$	−14.1893	+	15.7335i	−0.574508	+	0.637030i
$611$	−6.27892	+	2.28534i	−0.254018	+	0.0924550i
$612$	−0.648570	−	6.26716i	−0.0262169	−	0.253335i
$613$	0.720275	−	4.08488i	0.0290916	−	0.164987i	−0.966801	−	0.255531i	$-0.917750\pi$
$613$	0.720275	−	4.08488i	0.0290916	−	0.164987i	0.995892	+	0.0905444i	$0.0288607\pi$
$614$	−7.89891	+	19.5056i	−0.318774	+	0.787180i
$615$	−3.21650	+	1.85705i	−0.129702	+	0.0748834i
$616$	8.58812	+	6.27117i	0.346025	+	0.252673i
$617$	11.5688	−	9.70734i	0.465741	−	0.390803i	−0.379497	−	0.925193i	$-0.623903\pi$
$617$	11.5688	−	9.70734i	0.465741	−	0.390803i	0.845238	+	0.534390i	$0.179459\pi$
$618$	−5.64171	−	7.23298i	−0.226943	−	0.290953i
$619$	19.2689	+	11.1249i	0.774482	+	0.447147i	0.834471	−	0.551052i	$-0.185773\pi$
$619$	19.2689	+	11.1249i	0.774482	+	0.447147i	−0.0599891	+	0.998199i	$0.519107\pi$
$620$	−11.9526	−	24.6063i	−0.480029	−	0.988215i
$621$	1.04411	−	2.86866i	0.0418986	−	0.115116i
$622$	1.38307	−	6.48132i	0.0554559	−	0.259877i
$623$	−1.93828	−	10.9925i	−0.0776556	−	0.440407i
$624$	−0.857435	−	4.09835i	−0.0343249	−	0.164065i
$625$	0.739795	+	0.620761i	0.0295918	+	0.0248305i
$626$	1.28390	−	35.9417i	0.0513149	−	1.43652i
$627$	6.69034	−	7.78501i	0.267187	−	0.310903i
$628$	−2.88729	−	0.206541i	−0.115216	−	0.00824189i
$629$	−10.1914	+	12.1456i	−0.406357	+	0.484277i
$630$	−2.90094	+	0.940007i	−0.115576	+	0.0374508i
$631$	21.9990	−	3.87902i	0.875767	−	0.154421i	0.282345	−	0.959313i	$-0.408888\pi$
$631$	21.9990	−	3.87902i	0.875767	−	0.154421i	0.593422	+	0.804892i	$0.297777\pi$
$632$	−22.2473	−	6.43711i	−0.884948	−	0.256055i
$633$	10.3461	+	3.76566i	0.411219	+	0.149672i
$634$	1.68336	+	3.17206i	0.0668548	+	0.125978i
$635$	−5.59847	+	9.69684i	−0.222169	+	0.384807i
$636$	−2.53360	−	3.49895i	−0.100464	−	0.138743i
$637$	2.99491	+	3.56919i	0.118663	+	0.141417i
$638$	−8.22872	−	5.15103i	−0.325778	−	0.203931i
$639$	−0.0713813	−	0.123636i	−0.00282380	−	0.00489097i
$640$	8.61540	−	12.6199i	0.340554	−	0.498844i
$641$	0.604719	+	0.106628i	0.0238850	+	0.00421156i	0.185578	−	0.982630i	$-0.440584\pi$
$641$	0.604719	+	0.106628i	0.0238850	+	0.00421156i	−0.161693	+	0.986841i	$0.551695\pi$
$642$	−27.5390	+	3.84790i	−1.08688	+	0.151864i
$643$	−7.00943	−	19.2583i	−0.276425	−	0.759471i	−0.997761	−	0.0668858i	$-0.978694\pi$
$643$	−7.00943	−	19.2583i	−0.276425	−	0.759471i	0.721336	−	0.692586i	$-0.243529\pi$
$644$	7.00108	+	6.78254i	0.275881	+	0.267269i
$645$			12.8162i			0.504637i
$646$	7.50086	−	17.9128i	0.295117	−	0.704768i
$647$		−	4.56862i		−	0.179611i	−0.995959	−	0.0898055i	$-0.971375\pi$
$647$		−	4.56862i		−	0.179611i	0.995959	−	0.0898055i	$-0.0286245\pi$
$648$	−2.03931	+	1.95990i	−0.0801116	+	0.0769922i
$649$	5.70297	+	15.6688i	0.223861	+	0.615053i
$650$	−0.650591	−	4.65622i	−0.0255183	−	0.182632i
$651$	−15.9229	−	2.80765i	−0.624070	−	0.110040i
$652$	−13.2124	+	29.5482i	−0.517438	+	1.15720i
$653$	14.1643	+	24.5334i	0.554293	+	0.960064i	0.997958	+	0.0638715i	$0.0203448\pi$
$653$	14.1643	+	24.5334i	0.554293	+	0.960064i	−0.443665	+	0.896193i	$0.646322\pi$
$654$	9.62889	−	15.3820i	0.376519	−	0.601486i
$655$	14.8176	+	17.6590i	0.578972	+	0.689992i
$656$	−5.79917	−	9.34702i	−0.226420	−	0.364940i
$657$	1.11421	−	1.92988i	0.0434697	−	0.0752916i
$658$	−12.7310	+	6.75611i	−0.496304	+	0.263381i
$659$	23.7644	+	8.64953i	0.925729	+	0.336938i	0.760515	−	0.649320i	$-0.224946\pi$
$659$	23.7644	+	8.64953i	0.925729	+	0.336938i	0.165214	+	0.986258i	$0.447169\pi$
$660$	−6.16966	−	1.54876i	−0.240154	−	0.0602853i
$661$	−21.0762	+	3.71629i	−0.819767	+	0.144547i	−0.567777	−	0.823183i	$-0.692196\pi$
$661$	−21.0762	+	3.71629i	−0.819767	+	0.144547i	−0.251991	+	0.967730i	$0.581085\pi$
$662$	4.71413	+	14.5482i	0.183220	+	0.565431i
$663$	−2.11969	+	2.52615i	−0.0823219	+	0.0981075i
$664$	−19.5420	−	2.10137i	−0.758377	−	0.0815490i
$665$	−9.23631	−	1.74111i	−0.358169	−	0.0675172i
$666$	7.11295	+	0.254086i	0.275621	+	0.00984563i
$667$	−6.81689	−	5.72005i	−0.263951	−	0.221481i
$668$	4.78717	−	1.36442i	0.185221	−	0.0527908i
$669$	−3.10354	−	17.6010i	−0.119990	−	0.680495i
$670$	6.03001	+	1.28676i	0.232960	+	0.0497119i
$671$	−8.93411	+	24.5463i	−0.344898	+	0.947598i
$672$	−3.05495	−	8.49900i	−0.117847	−	0.327856i
$673$	−16.7079	−	9.64634i	−0.644044	−	0.371839i	0.142127	−	0.989848i	$-0.454606\pi$
$673$	−16.7079	−	9.64634i	−0.644044	−	0.371839i	−0.786171	+	0.618010i	$0.787939\pi$
$674$	4.70515	−	3.67001i	0.181235	−	0.141363i
$675$	−2.43287	+	2.04142i	−0.0936413	+	0.0785744i
$676$	13.3451	−	19.7169i	0.513274	−	0.758341i
$677$	7.48210	−	4.31979i	0.287560	−	0.166023i	−0.349281	−	0.937018i	$-0.613574\pi$
$677$	7.48210	−	4.31979i	0.287560	−	0.166023i	0.636841	+	0.770995i	$0.280241\pi$
$678$	1.20320	+	0.487243i	0.0462085	+	0.0187125i
$679$	−2.60054	+	14.7484i	−0.0997998	+	0.565993i
$680$	−12.0071	+	0.810667i	−0.460450	+	0.0310877i
$681$	−26.1759	+	9.52724i	−1.00306	+	0.365085i
$682$	−25.0464	−	22.5881i	−0.959074	−	0.864945i
$683$	3.31152			0.126712			0.0633558	−	0.997991i	$-0.479820\pi$
$683$	3.31152			0.126712			0.0633558	+	0.997991i	$0.479820\pi$
$684$	−8.41150	+	2.29055i	−0.321622	+	0.0875816i
$685$	13.4293			0.513106
$686$	19.2000	+	17.3155i	0.733058	+	0.661111i
$687$	0.640532	−	0.233135i	0.0244378	−	0.00889464i
$688$	−37.9381	+	1.20331i	−1.44638	+	0.0458758i
$689$	−0.392616	+	2.22664i	−0.0149575	+	0.0848281i
$690$	−5.40455	−	2.18861i	−0.205748	−	0.0833190i
$691$	23.7593	−	13.7175i	0.903848	−	0.521837i	0.0254013	−	0.999677i	$-0.491914\pi$
$691$	23.7593	−	13.7175i	0.903848	−	0.521837i	0.878447	+	0.477841i	$0.158580\pi$
$692$	−27.2056	−	18.4138i	−1.03420	−	0.699987i
$693$	−2.88011	+	2.41670i	−0.109406	+	0.0918027i
$694$	−15.8902	+	12.3943i	−0.603183	+	0.470482i
$695$	−15.7736	−	9.10688i	−0.598326	−	0.345444i
$696$	3.33540	+	7.54008i	0.126428	+	0.285806i
$697$	−2.96301	+	8.14080i	−0.112232	+	0.308355i
$698$	−49.0270	−	10.4620i	−1.85570	−	0.395992i
$699$	−3.08344	−	17.4871i	−0.116626	−	0.661421i
$700$	−2.77960	−	9.75247i	−0.105059	−	0.368609i
$701$	1.31167	+	1.10062i	0.0495410	+	0.0415698i	0.667222	−	0.744859i	$-0.267483\pi$
$701$	1.31167	+	1.10062i	0.0495410	+	0.0415698i	−0.617681	+	0.786429i	$0.711928\pi$
$702$	1.47941	+	0.0528470i	0.0558368	+	0.00199458i
$703$	18.8679	+	11.1920i	0.711615	+	0.422112i
$704$	4.00531	−	18.4086i	0.150956	−	0.693802i
$705$	5.54167	−	6.60431i	0.208712	−	0.248733i
$706$	−7.39425	−	22.8192i	−0.278286	−	0.858814i
$707$	−29.8628	+	5.26561i	−1.12311	+	0.198034i
$708$	3.44791	−	13.7352i	0.129580	−	0.516199i
$709$	−8.27549	−	3.01203i	−0.310793	−	0.113119i	0.181915	−	0.983314i	$-0.441770\pi$
$709$	−8.27549	−	3.01203i	−0.310793	−	0.113119i	−0.492707	+	0.870195i	$0.663993\pi$
$710$	−0.240865	+	0.127823i	−0.00903952	+	0.00479712i
$711$	4.09412	−	7.09122i	0.153541	−	0.265941i
$712$	−16.4206	+	11.0186i	−0.615386	+	0.412938i
$713$	−19.8726	−	23.6832i	−0.744235	−	0.886945i
$714$	−3.77409	+	6.02907i	−0.141242	+	0.225632i
$715$	1.66465	+	2.88325i	0.0622543	+	0.107828i
$716$	39.9464	+	17.8619i	1.49287	+	0.667531i
$717$	23.4802	+	4.14019i	0.876884	+	0.154618i
$718$	−2.04468	−	14.6336i	−0.0763069	−	0.546121i
$719$	−6.68071	−	18.3551i	−0.249149	−	0.684530i	−0.999718	−	0.0237388i	$-0.992443\pi$
$719$	−6.68071	−	18.3551i	−0.249149	−	0.684530i	0.750570	−	0.660791i	$-0.229779\pi$
$720$	3.60204	+	4.02630i	0.134240	+	0.150051i
$721$			10.3557i			0.385665i
$722$	−26.1389	−	6.22550i	−0.972790	−	0.231689i
$723$		−	14.4776i		−	0.538428i
$724$	−12.6212	+	13.0278i	−0.469063	+	0.484176i
$725$	3.16632	+	8.69940i	0.117594	+	0.323088i
$726$	7.63942	−	1.06742i	0.283525	−	0.0396157i
$727$	−37.4214	−	6.59840i	−1.38788	−	0.244721i	−0.570728	−	0.821139i	$-0.693339\pi$
$727$	−37.4214	−	6.59840i	−1.38788	−	0.244721i	−0.817155	+	0.576418i	$0.804450\pi$
$728$	−2.08232	+	4.24351i	−0.0771758	+	0.157275i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−3.60780	−	2.25842i	−0.133531	−	0.0835878i
$731$	19.2156	+	22.9003i	0.710716	+	0.846998i
$732$	17.9687	−	13.0111i	0.664141	−	0.480905i
$733$	−8.23163	+	14.2576i	−0.304042	+	0.526616i	−0.977048	−	0.213021i	$-0.931670\pi$
$733$	−8.23163	+	14.2576i	−0.304042	+	0.526616i	0.673005	+	0.739637i	$0.265003\pi$
$734$	−0.707360	−	1.33292i	−0.0261091	−	0.0491990i
$735$	−5.64906	−	2.05609i	−0.208369	−	0.0758400i
$736$	5.97122	−	16.2039i	0.220102	−	0.597282i
$737$	7.48642	−	1.32006i	0.275766	−	0.0486250i
$738$	3.69966	−	1.19882i	0.136186	−	0.0441292i
$739$	14.4234	−	17.1891i	0.530572	−	0.632311i	−0.432474	−	0.901646i	$-0.642359\pi$
$739$	14.4234	−	17.1891i	0.530572	−	0.632311i	0.963047	+	0.269335i	$0.0868038\pi$
$740$	0.970006	−	13.5600i	0.0356581	−	0.498474i
$741$	3.92430	+	2.32780i	0.144163	+	0.0855138i
$742$	−0.174098	+	4.87375i	−0.00639135	+	0.178921i
$743$	−4.76260	−	3.99629i	−0.174723	−	0.146610i	0.551233	−	0.834352i	$-0.314158\pi$
$743$	−4.76260	−	3.99629i	−0.174723	−	0.146610i	−0.725955	+	0.687742i	$0.758602\pi$
$744$	6.86297	+	27.8100i	0.251609	+	1.01956i
$745$	0.130427	+	0.739687i	0.00477847	+	0.0271000i
$746$	−7.03726	+	32.9780i	−0.257652	+	1.20741i
$747$	2.37669	−	6.52990i	0.0869585	−	0.238917i
$748$	−13.3462	+	6.48297i	−0.487986	+	0.237041i
$749$	27.1858	+	15.6957i	0.993347	+	0.573509i
$750$	9.60445	+	12.3134i	0.350705	+	0.449623i
$751$	−1.47193	+	1.23509i	−0.0537114	+	0.0450692i	−0.669248	−	0.743039i	$-0.733384\pi$
$751$	−1.47193	+	1.23509i	−0.0537114	+	0.0450692i	0.615537	+	0.788108i	$0.288939\pi$
$752$	20.0702	+	15.7842i	0.731884	+	0.575591i
$753$	−17.3641	+	10.0251i	−0.632782	+	0.365337i
$754$	1.61971	−	3.99972i	0.0589865	−	0.145661i
$755$	4.11145	−	23.3172i	0.149631	−	0.848600i
$756$	3.17611	−	0.328686i	0.115514	−	0.0119542i
$757$	20.5410	−	7.47633i	0.746577	−	0.271732i	0.0594123	−	0.998234i	$-0.481077\pi$
$757$	20.5410	−	7.47633i	0.746577	−	0.271732i	0.687165	+	0.726502i	$0.258855\pi$
$758$	8.42381	−	9.34055i	0.305967	−	0.339264i
$759$	−7.18902			−0.260945
$760$	3.79870	+	16.2122i	0.137793	+	0.588077i
$761$	26.9658			0.977511			0.488755	−	0.872421i	$-0.337451\pi$
$761$	26.9658			0.977511			0.488755	+	0.872421i	$0.337451\pi$
$762$	7.85210	−	8.70662i	0.284451	−	0.315408i
$763$	−19.2513	+	7.00691i	−0.696944	+	0.253667i
$764$	19.0566	−	1.97212i	0.689445	−	0.0713486i
$765$	0.738838	−	4.19016i	0.0267128	−	0.151496i
$766$	−10.9615	+	27.0682i	−0.396054	+	0.978014i
$767$	−6.41882	+	3.70591i	−0.231770	+	0.133813i
$768$	−11.5803	+	11.0407i	−0.417869	+	0.398395i
$769$	−0.753733	+	0.632457i	−0.0271803	+	0.0228070i	−0.656277	−	0.754520i	$-0.727870\pi$
$769$	−0.753733	+	0.632457i	−0.0271803	+	0.0228070i	0.629096	+	0.777327i	$0.283425\pi$
$770$	4.41664	+	5.66237i	0.159165	+	0.204058i
$771$	−14.3628	−	8.29237i	−0.517264	−	0.298642i
$772$	22.3510	−	10.8571i	0.804429	−	0.390755i
$773$	−2.33280	+	6.40932i	−0.0839050	+	0.230527i	−0.974549	−	0.224174i	$-0.928032\pi$
$773$	−2.33280	+	6.40932i	−0.0839050	+	0.230527i	0.890644	+	0.454701i	$0.150254\pi$
$774$	2.80065	−	13.1244i	0.100667	−	0.471746i
$775$	5.58508	+	31.6745i	0.200622	+	1.13778i
$776$	25.7586	−	6.35674i	0.924682	−	0.228194i
$777$	−6.15523	−	5.16485i	−0.220818	−	0.185288i
$778$	−1.71050	+	47.8840i	−0.0613242	+	1.71673i
$779$	11.7794	+	2.22049i	0.422040	+	0.0795573i
$780$	0.201750	−	2.82032i	0.00722382	−	0.100984i
$781$	−0.216101	+	0.257540i	−0.00773272	+	0.00921549i
$782$	−12.9384	+	4.19251i	−0.462677	+	0.149924i
$783$	−2.87071	+	0.506184i	−0.102591	+	0.0180895i
$784$	5.55598	−	16.9152i	0.198428	−	0.604114i
$785$	−1.83688	−	0.668569i	−0.0655610	−	0.0238623i
$786$	−11.3150	−	21.3216i	−0.403594	−	0.760517i
$787$	4.06236	−	7.03621i	0.144807	−	0.250814i	−0.784494	−	0.620137i	$-0.787077\pi$
$787$	4.06236	−	7.03621i	0.144807	−	0.250814i	0.929301	+	0.369323i	$0.120410\pi$
$788$	36.4017	−	26.3585i	1.29676	−	0.938983i
$789$	15.9731	+	19.0360i	0.568657	+	0.677699i
$790$	−13.2566	−	8.29842i	−0.471650	−	0.295245i
$791$	−0.732732	−	1.26913i	−0.0260530	−	0.0451251i
$792$	5.97959	+	2.93422i	0.212475	+	0.104263i
$793$	−11.4347	−	2.01625i	−0.406060	−	0.0715993i
$794$	43.3221	−	6.05319i	1.53744	−	0.214820i
$795$	−0.997755	−	2.74131i	−0.0353867	−	0.0972242i
$796$	−29.1697	+	30.1095i	−1.03389	+	1.06720i
$797$		−	17.7711i		−	0.629485i	−0.949177	−	0.314743i	$-0.898082\pi$
$797$		−	17.7711i		−	0.629485i	0.949177	−	0.314743i	$-0.101918\pi$
$798$	9.07795	+	3.80133i	0.321356	+	0.134566i
$799$		−	20.1095i		−	0.711424i
$800$	−13.8085	+	11.4929i	−0.488204	+	0.406335i
$801$	−2.39122	−	6.56982i	−0.0844896	−	0.232133i
$802$	−0.344790	−	2.46763i	−0.0121750	−	0.0871350i
$803$	−5.16804	−	0.911265i	−0.182376	−	0.0321579i
$804$	−5.89382	−	2.63541i	−0.207859	−	0.0929436i
$805$	3.29130	+	5.70071i	0.116003	+	0.200924i
$806$	7.95471	−	12.7076i	0.280193	−	0.447605i
$807$	11.7388	+	13.9898i	0.413225	+	0.492463i
$808$	29.9335	+	44.6088i	1.05306	+	1.56933i
$809$	22.3975	−	38.7936i	0.787454	−	1.36391i	−0.140069	−	0.990142i	$-0.544732\pi$
$809$	22.3975	−	38.7936i	0.787454	−	1.36391i	0.927522	−	0.373768i	$-0.121934\pi$
$810$	−1.68717	+	0.895356i	−0.0592813	+	0.0314596i
$811$	31.5176	+	11.4715i	1.10673	+	0.402818i	0.829795	−	0.558069i	$-0.188458\pi$
$811$	31.5176	+	11.4715i	1.10673	+	0.402818i	0.276940	+	0.960887i	$0.410680\pi$
$812$	2.26620	−	9.02770i	0.0795282	−	0.316810i
$813$	4.86421	−	0.857691i	0.170595	−	0.0300805i
$814$	−5.16671	−	15.9449i	−0.181093	−	0.558868i
$815$	−14.0499	+	16.7441i	−0.492148	+	0.586519i
$816$	12.4729	+	1.79367i	0.436640	+	0.0627911i
$817$	26.9592	−	31.3702i	0.943181	−	1.09750i
$818$	−52.4362	−	1.87311i	−1.83339	−	0.0654917i
$819$	−1.28022	−	1.07423i	−0.0447344	−	0.0375366i
$820$	−2.03606	−	7.14370i	−0.0711024	−	0.249469i
$821$	3.72543	+	21.1280i	0.130018	+	0.737371i	0.978200	+	0.207665i	$0.0665865\pi$
$821$	3.72543	+	21.1280i	0.130018	+	0.737371i	−0.848182	+	0.529706i	$0.822302\pi$
$822$	−13.7522	−	2.93462i	−0.479663	−	0.102357i
$823$	−9.29160	+	25.5285i	−0.323885	+	0.889866i	0.665739	+	0.746184i	$0.268116\pi$
$823$	−9.29160	+	25.5285i	−0.323885	+	0.889866i	−0.989624	+	0.143682i	$0.954106\pi$
$824$	16.7779	−	7.42180i	0.584485	−	0.258551i
$825$	6.47697	+	3.73948i	0.225499	+	0.130192i
$826$	−12.6058	+	9.83250i	−0.438612	+	0.342117i
$827$	−14.7153	+	12.3476i	−0.511702	+	0.429369i	−0.861728	−	0.507371i	$-0.830617\pi$
$827$	−14.7153	+	12.3476i	−0.511702	+	0.429369i	0.350026	+	0.936740i	$0.386173\pi$
$828$	5.05625	+	3.42227i	0.175717	+	0.118932i
$829$	−4.34612	+	2.50924i	−0.150947	+	0.0871493i	−0.573571	−	0.819156i	$-0.694442\pi$
$829$	−4.34612	+	2.50924i	−0.150947	+	0.0871493i	0.422624	+	0.906305i	$0.361109\pi$
$830$	−12.3023	−	4.98191i	−0.427019	−	0.172924i
$831$	3.96903	−	22.5095i	0.137684	−	0.780845i
$832$	8.36756	+	0.332415i	0.290093	+	0.0115244i
$833$	−13.1766	+	4.79590i	−0.456543	+	0.166168i
$834$	14.1628	+	12.7728i	0.490418	+	0.442285i
$835$	3.36151			0.116330
$836$	11.8436	+	16.7689i	0.409621	+	0.579965i
$837$	−10.1273			−0.350050
$838$	40.0130	+	36.0859i	1.38223	+	1.24657i
$839$	37.4539	−	13.6321i	1.29305	−	0.470632i	0.398324	−	0.917245i	$-0.369592\pi$
$839$	37.4539	−	13.6321i	1.29305	−	0.470632i	0.894728	+	0.446612i	$0.147370\pi$
$840$	−0.410835	−	6.08501i	−0.0141752	−	0.209953i
$841$	3.56027	−	20.1913i	0.122768	−	0.696252i
$842$	2.73068	+	1.10581i	0.0941056	+	0.0381087i
$843$	−25.3988	+	14.6640i	−0.874780	+	0.505054i
$844$	−12.3427	+	18.2358i	−0.424852	+	0.627701i
$845$	12.3164	−	10.3347i	0.423696	−	0.355523i
$846$	−7.11814	+	5.55213i	−0.244727	+	0.190886i
$847$	−7.54142	−	4.35404i	−0.259126	−	0.149607i
$848$	8.02105	−	3.21090i	0.275444	−	0.110263i
$849$	5.37365	−	14.7640i	0.184423	−	0.506698i
$850$	13.8377	+	2.95287i	0.474630	+	0.101283i
$851$	−2.66794	−	15.1306i	−0.0914557	−	0.518671i
$852$	0.274590	−	0.0782622i	0.00940730	−	0.00268122i
$853$	18.6833	+	15.6772i	0.639705	+	0.536776i	0.903928	−	0.427686i	$-0.140671\pi$
$853$	18.6833	+	15.6772i	0.639705	+	0.536776i	−0.264223	+	0.964462i	$0.585115\pi$
$854$	−25.0288	−	0.894071i	−0.856469	−	0.0305945i
$855$	−5.88670	−	0.0693911i	−0.201321	−	0.00237313i
$856$	5.94586	−	55.2944i	0.203225	−	1.88992i
$857$	−27.2495	+	32.4746i	−0.930824	+	1.10931i	0.0629633	+	0.998016i	$0.479945\pi$
$857$	−27.2495	+	32.4746i	−0.930824	+	1.10931i	−0.993787	+	0.111297i	$0.964500\pi$
$858$	−1.07462	−	3.31635i	−0.0366868	−	0.113218i
$859$	−21.3591	+	3.76619i	−0.728764	+	0.128501i	−0.525706	−	0.850666i	$-0.676199\pi$
$859$	−21.3591	+	3.76619i	−0.728764	+	0.128501i	−0.203058	+	0.979167i	$0.565088\pi$
$860$	−24.8610	−	6.24081i	−0.847754	−	0.212810i
$861$	−4.12565	−	1.50161i	−0.140602	−	0.0511748i
$862$	−40.3812	+	21.4297i	−1.37539	+	0.729897i
$863$	22.4408	−	38.8686i	0.763894	−	1.32310i	−0.176936	−	0.984222i	$-0.556619\pi$
$863$	22.4408	−	38.8686i	0.763894	−	1.32310i	0.940830	−	0.338880i	$-0.110048\pi$
$864$	−2.80881	−	4.91025i	−0.0955577	−	0.167050i
$865$	−14.2599	−	16.9943i	−0.484851	−	0.577822i
$866$	−23.0584	+	36.8356i	−0.783556	+	1.25172i
$867$	3.53776	+	6.12759i	0.120149	+	0.208104i
$868$	13.2000	−	29.5204i	0.448036	−	1.00199i
$869$	−18.9897	−	3.34839i	−0.644180	−	0.113586i
$870$	0.770469	+	5.51417i	0.0261213	+	0.186948i
$871$	1.15571	+	3.17529i	0.0391598	+	0.107591i
$872$	25.1496	+	26.1685i	0.851672	+	0.886178i
$873$			9.38027i			0.317474i
$874$	8.62493	+	16.7257i	0.291743	+	0.565754i
$875$		−	17.6295i		−	0.595985i
$876$	3.20104	+	3.10112i	0.108153	+	0.104777i
$877$	9.52062	+	26.1577i	0.321489	+	0.883282i	0.990187	+	0.139749i	$0.0446295\pi$
$877$	9.52062	+	26.1577i	0.321489	+	0.883282i	−0.668698	+	0.743534i	$0.733148\pi$
$878$	10.5766	−	1.47782i	0.356942	−	0.0498739i
$879$	17.4139	+	3.07054i	0.587356	+	0.103567i
$880$	6.00861	−	11.2138i	0.202550	−	0.378019i
$881$	−0.394509	−	0.683309i	−0.0132913	−	0.0230213i	0.859303	−	0.511466i	$-0.170898\pi$
$881$	−0.394509	−	0.683309i	−0.0132913	−	0.0230213i	−0.872595	+	0.488445i	$0.837564\pi$
$882$	5.33560	+	3.33999i	0.179659	+	0.112463i
$883$	11.2709	+	13.4322i	0.379297	+	0.452028i	0.921592	−	0.388160i	$-0.126889\pi$
$883$	11.2709	+	13.4322i	0.379297	+	0.452028i	−0.542296	+	0.840188i	$0.682445\pi$
$884$	−3.86808	−	5.34191i	−0.130098	−	0.179668i
$885$	4.78155	−	8.28189i	0.160730	−	0.278393i
$886$	−12.5126	−	23.5783i	−0.420370	−	0.792129i
$887$	−0.173935	−	0.0633073i	−0.00584017	−	0.00212565i	0.339098	−	0.940751i	$-0.389878\pi$
$887$	−0.173935	−	0.0633073i	−0.00584017	−	0.00212565i	−0.344939	+	0.938625i	$0.612100\pi$
$888$	−3.95651	+	13.6741i	−0.132772	+	0.458872i
$889$	−13.0348	+	2.29839i	−0.437173	+	0.0770854i
$890$	−12.7036	+	4.11642i	−0.425826	+	0.137983i
$891$	−1.51371	+	1.80397i	−0.0507113	+	0.0604353i
$892$	35.6540	+	2.55049i	1.19378	+	0.0853968i
$893$	−27.4567	+	4.50833i	−0.918802	+	0.150865i
$894$	0.0280764	−	0.785976i	0.000939014	−	0.0262870i
$895$	22.6364	+	18.9942i	0.756651	+	0.634905i
$896$	17.9741	−	1.78746i	0.600472	−	0.0597149i
$897$	−0.554901	−	3.14700i	−0.0185276	−	0.105075i
$898$	−1.07436	+	5.03466i	−0.0358518	+	0.168009i
$899$	−10.0968	+	27.7407i	−0.336747	+	0.925204i
$900$	−2.77530	−	5.71339i	−0.0925100	−	0.190446i
$901$	−5.89293	−	3.40228i	−0.196322	−	0.113346i
$902$	−5.63269	−	7.22141i	−0.187548	−	0.240447i
$903$	−11.6056	+	9.73822i	−0.386209	+	0.324068i
$904$	−1.53106	+	2.09672i	−0.0509222	+	0.0697358i
$905$	−10.6081	+	6.12458i	−0.352624	+	0.203588i
$906$	−9.30569	+	22.9795i	−0.309161	+	0.763441i
$907$	6.63698	−	37.6402i	0.220377	−	1.24982i	−0.650950	−	0.759120i	$-0.725629\pi$
$907$	6.63698	−	37.6402i	0.220377	−	1.24982i	0.871328	−	0.490702i	$-0.163259\pi$
$908$	−5.73480	−	55.4156i	−0.190316	−	1.83903i
$909$	−17.8478	+	6.49608i	−0.591976	+	0.215462i
$910$	−2.13780	+	2.37045i	−0.0708673	+	0.0785796i
$911$	−15.1371			−0.501514			−0.250757	−	0.968050i	$-0.580680\pi$
$911$	−15.1371			−0.501514			−0.250757	+	0.968050i	$0.580680\pi$
$912$	−0.347292	−	17.4321i	−0.0115000	−	0.577236i
$913$	−16.3643			−0.541578
$914$	11.7465	−	13.0248i	0.388538	−	0.430822i
$915$	14.0778	−	5.12391i	0.465398	−	0.169391i
$916$	0.140333	+	1.35604i	0.00463672	+	0.0448048i
$917$	−4.73189	+	26.8359i	−0.156261	+	0.886199i
$918$	−1.67226	+	4.12947i	−0.0551927	+	0.136293i
$919$	−3.21723	+	1.85747i	−0.106126	+	0.0612722i	−0.552124	−	0.833762i	$-0.686182\pi$
$919$	−3.21723	+	1.85747i	−0.106126	+	0.0612722i	0.445997	+	0.895034i	$0.352849\pi$
$920$	6.87723	−	9.41809i	0.226736	−	0.310505i
$921$	11.3991	−	9.56501i	0.375614	−	0.315178i
$922$	0.694165	+	0.889957i	0.0228611	+	0.0293092i
$923$	−0.129418	−	0.0747198i	−0.00425986	−	0.00245943i
$924$	−3.28548	−	6.76368i	−0.108084	−	0.222509i
$925$	−5.46674	+	15.0198i	−0.179745	+	0.493846i
$926$	5.30785	−	24.8736i	0.174427	−	0.817398i
$927$	1.12634	+	6.38779i	0.0369938	+	0.209802i
$928$	−16.2505	+	2.79844i	−0.533450	+	0.0918633i
$929$	−8.75785	−	7.34871i	−0.287336	−	0.241103i	0.487714	−	0.873003i	$-0.337831\pi$
$929$	−8.75785	−	7.34871i	−0.287336	−	0.241103i	−0.775050	+	0.631900i	$0.782275\pi$
$930$	−0.690539	+	19.3311i	−0.0226437	+	0.633892i
$931$	9.50217	+	16.9156i	0.311421	+	0.554387i
$932$	35.4231	+	2.53398i	1.16032	+	0.0830032i
$933$	−3.01221	+	3.58981i	−0.0986153	+	0.117525i
$934$	20.5474	−	6.65809i	0.672332	−	0.217859i
$935$	−9.86748	+	1.73990i	−0.322701	+	0.0569009i
$936$	−0.822910	+	2.84405i	−0.0268976	+	0.0929608i
$937$	−15.2965	−	5.56747i	−0.499715	−	0.181881i	0.0798510	−	0.996807i	$-0.474556\pi$
$937$	−15.2965	−	5.56747i	−0.499715	−	0.181881i	−0.579566	+	0.814926i	$0.696778\pi$
$938$	3.41661	+	6.43814i	0.111556	+	0.210213i
$939$	−12.7154	+	22.0238i	−0.414952	+	0.718718i
$940$	10.1126	+	13.9658i	0.329838	+	0.455513i
$941$	25.9392	+	30.9131i	0.845594	+	1.00774i	0.999806	+	0.0197020i	$0.00627174\pi$
$941$	25.9392	+	30.9131i	0.845594	+	1.00774i	−0.154212	+	0.988038i	$0.549284\pi$
$942$	1.73495	+	1.08605i	0.0565278	+	0.0353854i
$943$	−4.19751	−	7.27030i	−0.136690	−	0.236754i
$944$	24.9647	+	13.3766i	0.812532	+	0.435372i
$945$	2.12352	+	0.374433i	0.0690780	+	0.0121803i
$946$	−31.2987	+	4.37321i	−1.01761	+	0.142185i
$947$	9.10710	+	25.0216i	0.295941	+	0.813091i	0.995168	+	0.0981911i	$0.0313056\pi$
$947$	9.10710	+	25.0216i	0.295941	+	0.813091i	−0.699227	+	0.714900i	$0.746472\pi$
$948$	11.7620	+	11.3949i	0.382013	+	0.370088i
$949$		−	2.33265i		−	0.0757211i
$950$	0.929458	−	19.5554i	0.0301556	−	0.634462i
$951$		−	2.53926i		−	0.0823410i
$952$	−9.85750	−	10.2569i	−0.319484	−	0.332428i
$953$	−8.70111	−	23.9061i	−0.281857	−	0.774395i	−0.997141	−	0.0755614i	$-0.975925\pi$
$953$	−8.70111	−	23.9061i	−0.281857	−	0.774395i	0.715285	−	0.698833i	$-0.246297\pi$
$954$	0.422706	+	3.02526i	0.0136856	+	0.0979465i
$955$	12.7411	+	2.24660i	0.412292	+	0.0726981i
$956$	−19.4648	+	43.5312i	−0.629538	+	1.40790i
$957$	3.43229	+	5.94490i	0.110950	+	0.192171i
$958$	15.2648	−	24.3854i	0.493183	−	0.787855i
$959$	10.2041	+	12.1607i	0.329506	+	0.392690i
$960$	−9.56428	+	5.02669i	−0.308686	+	0.162236i
$961$	−35.7810	+	61.9745i	−1.15423	+	1.99918i
$962$	6.58108	−	3.49247i	0.212182	−	0.112602i
$963$	18.4764	+	6.72487i	0.595395	+	0.216706i
$964$	28.0839	+	7.04983i	0.904520	+	0.227060i
$965$	16.5251	−	2.91383i	0.531963	−	0.0937994i
$966$	−2.12471	−	6.55702i	−0.0683614	−	0.210969i
$967$	12.5451	−	14.9507i	0.403423	−	0.480781i	−0.525637	−	0.850709i	$-0.676173\pi$
$967$	12.5451	−	14.9507i	0.403423	−	0.480781i	0.929061	+	0.369928i	$0.120618\pi$
$968$	−1.64940	+	15.3388i	−0.0530137	+	0.493009i
$969$	−10.6226	+	8.70209i	−0.341246	+	0.279551i
$970$	17.9052	+	0.639603i	0.574901	+	0.0205364i
$971$	−14.2819	−	11.9839i	−0.458328	−	0.384583i	0.384187	−	0.923255i	$-0.374482\pi$
$971$	−14.2819	−	11.9839i	−0.458328	−	0.384583i	−0.842515	+	0.538672i	$0.818926\pi$
$972$	1.92340	−	0.548198i	0.0616932	−	0.0175835i
$973$	−3.73872	−	21.2033i	−0.119858	−	0.679748i
$974$	17.4087	+	3.71489i	0.557811	+	0.119033i
$975$	−1.13702	+	3.12394i	−0.0364138	+	0.100046i
$976$	16.4894	+	41.1916i	0.527812	+	1.31851i
$977$	−49.9788	−	28.8553i	−1.59896	−	0.923163i	−0.991687	−	0.128673i	$-0.958928\pi$
$977$	−49.9788	−	28.8553i	−1.59896	−	0.923163i	−0.607278	−	0.794490i	$-0.707738\pi$
$978$	18.0468	−	14.0765i	0.577072	−	0.450115i
$979$	−12.6124	+	10.5831i	−0.403094	+	0.338236i
$980$	6.73923	−	9.95692i	0.215277	−	0.318062i
$981$	−11.1129	+	6.41602i	−0.354807	+	0.204848i
$982$	15.4538	+	6.25813i	0.493151	+	0.199705i
$983$	4.83315	−	27.4102i	0.154154	−	0.874249i	−0.805402	−	0.592729i	$-0.798050\pi$
$983$	4.83315	−	27.4102i	0.154154	−	0.874249i	0.959555	−	0.281520i	$-0.0908384\pi$
$984$	0.523952	+	7.76042i	0.0167030	+	0.247393i
$985$	28.5195	−	10.3802i	0.908706	−	0.330742i
$986$	9.64423	+	8.69768i	0.307135	+	0.276990i
$987$	10.1912			0.324390
$988$	−6.42643	+	6.47891i	−0.204452	+	0.206122i
$989$	−28.9686			−0.921148
$990$	3.34023	+	3.01240i	0.106160	+	0.0957403i
$991$	36.8595	−	13.4157i	1.17088	−	0.426165i	0.317907	−	0.948122i	$-0.397020\pi$
$991$	36.8595	−	13.4157i	1.17088	−	0.426165i	0.852972	+	0.521956i	$0.174798\pi$
$992$	−57.2882	−	0.229115i	−1.81890	−	0.00727441i
$993$	1.87778	−	10.6494i	0.0595895	−	0.337949i
$994$	−0.298768	−	0.120988i	−0.00947633	−	0.00383751i
$995$	−24.5170	+	14.1549i	−0.777242	+	0.448741i
$996$	11.5095	+	7.79006i	0.364692	+	0.246837i
$997$	−15.1089	+	12.6779i	−0.478505	+	0.401513i	−0.849885	−	0.526968i	$-0.823329\pi$
$997$	−15.1089	+	12.6779i	−0.478505	+	0.401513i	0.371381	+	0.928481i	$0.378884\pi$
$998$	−29.3576	+	22.8989i	−0.929298	+	0.724851i
$999$	−4.35855	−	2.51641i	−0.137898	−	0.0796157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.w.b.79.8	yes	60
3.2	odd	2		684.2.cf.b.307.3		60
4.3	odd	2		228.2.w.a.79.7	✓	60
12.11	even	2		684.2.cf.c.307.4		60
19.13	odd	18		228.2.w.a.127.7	yes	60
57.32	even	18		684.2.cf.c.127.4		60
76.51	even	18	inner	228.2.w.b.127.8	yes	60
228.203	odd	18		684.2.cf.b.127.3		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.79.7	✓	60	4.3	odd	2
228.2.w.a.127.7	yes	60	19.13	odd	18
228.2.w.b.79.8	yes	60	1.1	even	1	trivial
228.2.w.b.127.8	yes	60	76.51	even	18	inner
684.2.cf.b.127.3		60	228.203	odd	18
684.2.cf.b.307.3		60	3.2	odd	2
684.2.cf.c.127.4		60	57.32	even	18
684.2.cf.c.307.4		60	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.w (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.947134 - 1.05021i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.205875 - 1.98938i) q^{4} +(0.234529 - 1.33008i) q^{5} +(-0.530822 + 1.31081i) q^{6} +(1.38264 - 0.798268i) q^{7} +(-2.28425 - 1.66799i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-1.17473 - 1.50607i) q^{10} +(-2.03942 - 1.17746i) q^{11} +(0.873866 + 1.79899i) q^{12} +(0.358016 - 0.983642i) q^{13} +(0.471198 - 2.20813i) q^{14} +(0.234529 + 1.33008i) q^{15} +(-3.91523 + 0.819124i) q^{16} +(2.41328 + 2.02498i) q^{17} +(0.0504858 - 1.41331i) q^{18} +(2.22379 - 3.74897i) q^{19} +(-2.69431 - 0.192736i) q^{20} +(-1.02623 + 1.22302i) q^{21} +(-3.16818 + 1.02660i) q^{22} +(-3.00639 + 0.530108i) q^{23} +(2.71698 + 0.786142i) q^{24} +(2.98436 + 1.08622i) q^{25} +(-0.693939 - 1.30763i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(-1.87271 - 2.58625i) q^{28} +(1.87372 + 2.23302i) q^{29} +(1.61899 + 1.01346i) q^{30} +(5.06365 + 8.77049i) q^{31} +(-2.84800 + 4.88763i) q^{32} +(2.31914 + 0.408927i) q^{33} +(4.41235 - 0.616517i) q^{34} +(-0.737489 - 2.02624i) q^{35} +(-1.43646 - 1.39162i) q^{36} +5.03282i q^{37} +(-1.83097 - 5.88622i) q^{38} +1.04677i q^{39} +(-2.75428 + 2.64704i) q^{40} +(0.940545 + 2.58413i) q^{41} +(0.312442 + 2.23612i) q^{42} +(9.34512 + 1.64780i) q^{43} +(-1.92254 + 4.29958i) q^{44} +(-0.675298 - 1.16965i) q^{45} +(-2.29073 + 3.65942i) q^{46} +(-4.10313 - 4.88992i) q^{47} +(3.39896 - 2.10881i) q^{48} +(-2.22554 + 3.85474i) q^{49} +(3.96735 - 2.10541i) q^{50} +(-2.96033 - 1.07747i) q^{51} +(-2.03054 - 0.509722i) q^{52} +(-2.12715 + 0.375074i) q^{53} +(0.435940 + 1.34535i) q^{54} +(-2.04441 + 2.43644i) q^{55} +(-4.48980 - 0.482793i) q^{56} +(-0.807460 + 4.28346i) q^{57} +(4.11980 + 0.147166i) q^{58} +(-5.42410 - 4.55136i) q^{59} +(2.59774 - 0.740395i) q^{60} +(-1.92617 - 10.9238i) q^{61} +(14.0068 + 2.98895i) q^{62} +(0.546047 - 1.50025i) q^{63} +(2.43559 + 7.62023i) q^{64} +(-1.22435 - 0.706881i) q^{65} +(2.62600 - 2.04827i) q^{66} +(-2.47287 + 2.07498i) q^{67} +(3.53162 - 5.21781i) q^{68} +(2.64378 - 1.52638i) q^{69} +(-2.82647 - 1.14460i) q^{70} +(0.0247905 - 0.140594i) q^{71} +(-2.82200 + 0.190530i) q^{72} +(2.09404 - 0.762168i) q^{73} +(5.28551 + 4.76675i) q^{74} -3.17589 q^{75} +(-7.91592 - 3.65214i) q^{76} -3.75971 q^{77} +(1.09933 + 0.991431i) q^{78} +(7.69442 - 2.80054i) q^{79} +(0.171265 + 5.39967i) q^{80} +(0.173648 - 0.984808i) q^{81} +(3.60469 + 1.45974i) q^{82} +(6.01799 - 3.47449i) q^{83} +(2.64432 + 1.78978i) q^{84} +(3.25937 - 2.73493i) q^{85} +(10.5816 - 8.25364i) q^{86} +(-2.52446 - 1.45750i) q^{87} +(2.69455 + 6.09135i) q^{88} +(2.39122 - 6.56982i) q^{89} +(-1.86797 - 0.398612i) q^{90} +(-0.290202 - 1.64582i) q^{91} +(1.67352 + 5.87170i) q^{92} +(-7.75796 - 6.50970i) q^{93} +(-9.02165 - 0.322268i) q^{94} +(-4.46487 - 3.83706i) q^{95} +(1.00457 - 5.56694i) q^{96} +(-6.02952 + 7.18571i) q^{97} +(1.94040 + 5.98823i) q^{98} +(-2.31914 + 0.408927i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} + 21 q^{16} + 18 q^{19} + 30 q^{20} - 6 q^{21} - 12 q^{22} - 18 q^{24} - 30 q^{27} - 18 q^{28} - 12 q^{31} + 33 q^{32} - 15 q^{34}+ \cdots - 105 q^{98}+O(q^{100}) \) 60 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 + 21 * q^16 + 18 * q^19 + 30 * q^20 - 6 * q^21 - 12 * q^22 - 18 * q^24 - 30 * q^27 - 18 * q^28 - 12 * q^31 + 33 * q^32 - 15 * q^34 - 3 * q^36 - 84 * q^38 - 87 * q^40 - 12 * q^41 + 9 * q^42 - 18 * q^43 - 51 * q^44 - 21 * q^46 + 18 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 + 42 * q^56 - 36 * q^58 + 15 * q^60 + 105 * q^62 - 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 + 42 * q^67 - 15 * q^68 - 72 * q^69 - 96 * q^70 + 24 * q^71 + 18 * q^72 + 18 * q^73 + 69 * q^74 + 60 * q^75 + 54 * q^76 - 72 * q^77 + 57 * q^78 + 12 * q^79 - 12 * q^80 + 75 * q^82 + 39 * q^84 - 60 * q^85 + 21 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 - 84 * q^91 + 99 * q^92 - 12 * q^93 - 24 * q^95 + 12 * q^97 - 105 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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