LMFDB - Embedded newform 456.2.bk.a.157.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("456.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			157.13
Character	$\chi$	$=$	456.157
Dual form			456.2.bk.a.61.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.783185 - 1.17755i) q^{2} +(-0.984808 - 0.173648i) q^{3} +(-0.773242 + 1.84448i) q^{4} +(-2.37243 + 2.82735i) q^{5} +(0.566808 + 1.29566i) q^{6} +(-1.53699 - 2.66215i) q^{7} +(2.77755 - 0.534038i) q^{8} +(0.939693 + 0.342020i) q^{9} +(5.18739 + 0.579311i) q^{10} +(2.74127 + 1.58267i) q^{11} +(1.08178 - 1.68218i) q^{12} +(-3.89235 + 0.686327i) q^{13} +(-1.93106 + 3.89484i) q^{14} +(2.82735 - 2.37243i) q^{15} +(-2.80419 - 2.85245i) q^{16} +(2.49527 - 0.908202i) q^{17} +(-0.333208 - 1.37440i) q^{18} +(2.78504 - 3.35314i) q^{19} +(-3.38052 - 6.56211i) q^{20} +(1.05136 + 2.88860i) q^{21} +(-0.283248 - 4.46751i) q^{22} +(3.24197 - 2.72033i) q^{23} +(-2.82809 + 0.0436073i) q^{24} +(-1.49725 - 8.49132i) q^{25} +(3.85661 + 4.04591i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(6.09873 - 0.776462i) q^{28} +(2.86316 - 7.86646i) q^{29} +(-5.00799 - 1.47129i) q^{30} +(-1.97221 - 3.41596i) q^{31} +(-1.16270 + 5.53608i) q^{32} +(-2.42480 - 2.03465i) q^{33} +(-3.02371 - 2.22701i) q^{34} +(11.1732 + 1.97014i) q^{35} +(-1.35746 + 1.46878i) q^{36} -5.95736i q^{37} +(-6.12969 - 0.653391i) q^{38} +3.95240 q^{39} +(-5.07963 + 9.12008i) q^{40} +(-1.49425 + 8.47431i) q^{41} +(2.57805 - 3.50034i) q^{42} +(-1.74646 + 2.08135i) q^{43} +(-5.03887 + 3.83243i) q^{44} +(-3.19636 + 1.84542i) q^{45} +(-5.74239 - 1.68705i) q^{46} +(8.24602 + 3.00130i) q^{47} +(2.26627 + 3.29606i) q^{48} +(-1.22468 + 2.12121i) q^{49} +(-8.82632 + 8.41336i) q^{50} +(-2.61506 + 0.461106i) q^{51} +(1.74381 - 7.71005i) q^{52} +(-7.44706 - 8.87506i) q^{53} +(0.0894840 + 1.41138i) q^{54} +(-10.9782 + 3.99575i) q^{55} +(-5.69076 - 6.57344i) q^{56} +(-3.32500 + 2.81858i) q^{57} +(-11.5055 + 2.78939i) q^{58} +(1.29016 + 3.54470i) q^{59} +(2.18966 + 7.04944i) q^{60} +(9.33185 + 11.1213i) q^{61} +(-2.47786 + 4.99770i) q^{62} +(-0.533791 - 3.02728i) q^{63} +(7.42961 - 2.96664i) q^{64} +(7.29384 - 12.6333i) q^{65} +(-0.496830 + 4.44882i) q^{66} +(4.61971 - 12.6926i) q^{67} +(-0.254285 + 5.30472i) q^{68} +(-3.66510 + 2.11604i) q^{69} +(-6.43076 - 14.7000i) q^{70} +(3.49678 + 2.93415i) q^{71} +(2.79270 + 0.448148i) q^{72} +(1.39681 - 7.92170i) q^{73} +(-7.01509 + 4.66572i) q^{74} +8.62231i q^{75} +(4.03128 + 7.72973i) q^{76} -9.73022i q^{77} +(-3.09546 - 4.65414i) q^{78} +(-0.609683 + 3.45768i) q^{79} +(14.7176 - 1.16120i) q^{80} +(0.766044 + 0.642788i) q^{81} +(11.1492 - 4.87741i) q^{82} +(3.13478 - 1.80986i) q^{83} +(-6.14091 - 0.294368i) q^{84} +(-3.35203 + 9.20963i) q^{85} +(3.81869 + 0.426459i) q^{86} +(-4.18566 + 7.24977i) q^{87} +(8.45924 + 2.93202i) q^{88} +(-0.688154 - 3.90272i) q^{89} +(4.67642 + 2.31857i) q^{90} +(7.80961 + 9.30713i) q^{91} +(2.51077 + 8.08321i) q^{92} +(1.34907 + 3.70654i) q^{93} +(-2.92398 - 12.0607i) q^{94} +(2.87319 + 15.8294i) q^{95} +(2.10637 - 5.25007i) q^{96} +(9.00340 - 3.27697i) q^{97} +(3.45698 - 0.219179i) q^{98} +(2.03465 + 2.42480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.783185	−	1.17755i	−0.553796	−	0.832653i
$2$	−0.783185	−	1.17755i	−0.553796	−	0.832653i
$3$	−0.984808	−	0.173648i	−0.568579	−	0.100256i
$3$	−0.984808	−	0.173648i	−0.568579	−	0.100256i
$4$	−0.773242	+	1.84448i	−0.386621	+	0.922239i
$5$	−2.37243	+	2.82735i	−1.06098	+	1.26443i	−0.0979068	+	0.995196i	$0.531215\pi$
$5$	−2.37243	+	2.82735i	−1.06098	+	1.26443i	−0.963075	+	0.269233i	$0.913230\pi$
$6$	0.566808	+	1.29566i	0.231398	+	0.528950i
$7$	−1.53699	−	2.66215i	−0.580928	−	1.00620i	−0.995370	−	0.0961208i	$-0.969356\pi$
$7$	−1.53699	−	2.66215i	−0.580928	−	1.00620i	0.414442	−	0.910076i	$-0.363977\pi$
$8$	2.77755	−	0.534038i	0.982013	−	0.188811i
$9$	0.939693	+	0.342020i	0.313231	+	0.114007i
$10$	5.18739	+	0.579311i	1.64040	+	0.183194i
$11$	2.74127	+	1.58267i	0.826525	+	0.477194i	0.852661	−	0.522464i	$-0.174987\pi$
$11$	2.74127	+	1.58267i	0.826525	+	0.477194i	−0.0261365	+	0.999658i	$0.508320\pi$
$12$	1.08178	−	1.68218i	0.312284	−	0.485605i
$13$	−3.89235	+	0.686327i	−1.07954	+	0.190353i	−0.685014	−	0.728530i	$-0.740204\pi$
$13$	−3.89235	+	0.686327i	−1.07954	+	0.190353i	−0.394530	+	0.918883i	$0.629093\pi$
$14$	−1.93106	+	3.89484i	−0.516097	+	1.04094i
$15$	2.82735	−	2.37243i	0.730018	−	0.612558i
$16$	−2.80419	−	2.85245i	−0.701049	−	0.713114i
$17$	2.49527	−	0.908202i	0.605191	−	0.220271i	−0.0212069	−	0.999775i	$-0.506751\pi$
$17$	2.49527	−	0.908202i	0.605191	−	0.220271i	0.626398	+	0.779504i	$0.284529\pi$
$18$	−0.333208	−	1.37440i	−0.0785379	−	0.323949i
$19$	2.78504	−	3.35314i	0.638932	−	0.769263i
$19$	2.78504	−	3.35314i	0.638932	−	0.769263i
$20$	−3.38052	−	6.56211i	−0.755908	−	1.46733i
$21$	1.05136	+	2.88860i	0.229426	+	0.630344i
$22$	−0.283248	−	4.46751i	−0.0603887	−	0.952476i
$23$	3.24197	−	2.72033i	0.675997	−	0.567229i	−0.238837	−	0.971060i	$-0.576766\pi$
$23$	3.24197	−	2.72033i	0.675997	−	0.567229i	0.914834	+	0.403831i	$0.132322\pi$
$24$	−2.82809	+	0.0436073i	−0.577282	+	0.00890131i
$25$	−1.49725	−	8.49132i	−0.299450	−	1.69826i
$26$	3.85661	+	4.04591i	0.756344	+	0.793469i
$27$	−0.866025	−	0.500000i	−0.166667	−	0.0962250i
$28$	6.09873	−	0.776462i	1.15255	−	0.146738i
$29$	2.86316	−	7.86646i	0.531675	−	1.46076i	−0.325402	−	0.945576i	$-0.605499\pi$
$29$	2.86316	−	7.86646i	0.531675	−	1.46076i	0.857077	−	0.515189i	$-0.172278\pi$
$30$	−5.00799	−	1.47129i	−0.914329	−	0.268620i
$31$	−1.97221	−	3.41596i	−0.354219	−	0.613525i	0.632765	−	0.774344i	$-0.281920\pi$
$31$	−1.97221	−	3.41596i	−0.354219	−	0.613525i	−0.986984	+	0.160819i	$0.948587\pi$
$32$	−1.16270	+	5.53608i	−0.205538	+	0.978649i
$33$	−2.42480	−	2.03465i	−0.422103	−	0.354187i
$34$	−3.02371	−	2.22701i	−0.518562	−	0.381928i
$35$	11.1732	+	1.97014i	1.88862	+	0.333014i
$36$	−1.35746	+	1.46878i	−0.226243	+	0.244796i
$37$		−	5.95736i		−	0.979385i	−0.871895	−	0.489692i	$-0.837109\pi$
$37$		−	5.95736i		−	0.979385i	0.871895	−	0.489692i	$-0.162891\pi$
$38$	−6.12969	−	0.653391i	−0.994367	−	0.105994i
$39$	3.95240			0.632890
$40$	−5.07963	+	9.12008i	−0.803161	+	1.44201i
$41$	−1.49425	+	8.47431i	−0.233363	+	1.32347i	0.612672	+	0.790337i	$0.290095\pi$
$41$	−1.49425	+	8.47431i	−0.233363	+	1.32347i	−0.846035	+	0.533128i	$0.821016\pi$
$42$	2.57805	−	3.50034i	0.397802	−	0.540114i
$43$	−1.74646	+	2.08135i	−0.266332	+	0.317403i	−0.882591	−	0.470141i	$-0.844203\pi$
$43$	−1.74646	+	2.08135i	−0.266332	+	0.317403i	0.616259	+	0.787544i	$0.288647\pi$
$44$	−5.03887	+	3.83243i	−0.759639	+	0.577760i
$45$	−3.19636	+	1.84542i	−0.476486	+	0.275099i
$46$	−5.74239	−	1.68705i	−0.846669	−	0.248742i
$47$	8.24602	+	3.00130i	1.20280	+	0.437785i	0.864202	−	0.503144i	$-0.167824\pi$
$47$	8.24602	+	3.00130i	1.20280	+	0.437785i	0.338603	+	0.940929i	$0.390046\pi$
$48$	2.26627	+	3.29606i	0.327108	+	0.475746i
$49$	−1.22468	+	2.12121i	−0.174955	+	0.303030i
$50$	−8.82632	+	8.41336i	−1.24823	+	1.18983i
$51$	−2.61506	+	0.461106i	−0.366182	+	0.0645678i
$52$	1.74381	−	7.71005i	0.241824	−	1.06919i
$53$	−7.44706	−	8.87506i	−1.02293	−	1.21908i	−0.975452	−	0.220211i	$-0.929325\pi$
$53$	−7.44706	−	8.87506i	−1.02293	−	1.21908i	−0.0474805	−	0.998872i	$-0.515119\pi$
$54$	0.0894840	+	1.41138i	0.0121772	+	0.192064i
$55$	−10.9782	+	3.99575i	−1.48031	+	0.538787i
$56$	−5.69076	−	6.57344i	−0.760460	−	0.878413i
$57$	−3.32500	+	2.81858i	−0.440407	+	0.373330i
$58$	−11.5055	+	2.78939i	−1.51075	+	0.366265i
$59$	1.29016	+	3.54470i	0.167965	+	0.461480i	0.994906	−	0.100809i	$-0.0321430\pi$
$59$	1.29016	+	3.54470i	0.167965	+	0.461480i	−0.826941	+	0.562289i	$0.809921\pi$
$60$	2.18966	+	7.04944i	0.282684	+	0.910079i
$61$	9.33185	+	11.1213i	1.19482	+	1.42393i	0.880127	+	0.474739i	$0.157458\pi$
$61$	9.33185	+	11.1213i	1.19482	+	1.42393i	0.314694	+	0.949193i	$0.398098\pi$
$62$	−2.47786	+	4.99770i	−0.314688	+	0.634709i
$63$	−0.533791	−	3.02728i	−0.0672514	−	0.381402i
$64$	7.42961	−	2.96664i	0.928701	−	0.370830i
$65$	7.29384	−	12.6333i	0.904689	−	1.56697i
$66$	−0.496830	+	4.44882i	−0.0611555	+	0.547612i
$67$	4.61971	−	12.6926i	0.564388	−	1.55064i	−0.248748	−	0.968568i	$-0.580019\pi$
$67$	4.61971	−	12.6926i	0.564388	−	1.55064i	0.813136	−	0.582074i	$-0.197759\pi$
$68$	−0.254285	+	5.30472i	−0.0308366	+	0.643292i
$69$	−3.66510	+	2.11604i	−0.441226	+	0.254742i
$70$	−6.43076	−	14.7000i	−0.768623	−	1.75698i
$71$	3.49678	+	2.93415i	0.414991	+	0.348219i	0.826254	−	0.563298i	$-0.190468\pi$
$71$	3.49678	+	2.93415i	0.414991	+	0.348219i	−0.411263	+	0.911517i	$0.634912\pi$
$72$	2.79270	+	0.448148i	0.329123	+	0.0528147i
$73$	1.39681	−	7.92170i	0.163484	−	0.927165i	−0.787129	−	0.616788i	$-0.788434\pi$
$73$	1.39681	−	7.92170i	0.163484	−	0.927165i	0.950614	−	0.310377i	$-0.100455\pi$
$74$	−7.01509	+	4.66572i	−0.815487	+	0.542379i
$75$			8.62231i			0.995619i
$76$	4.03128	+	7.72973i	0.462420	+	0.886661i
$77$		−	9.73022i		−	1.10886i
$78$	−3.09546	−	4.65414i	−0.350492	−	0.526978i
$79$	−0.609683	+	3.45768i	−0.0685947	+	0.389020i	0.931110	+	0.364737i	$0.118841\pi$
$79$	−0.609683	+	3.45768i	−0.0685947	+	0.389020i	−0.999705	+	0.0242825i	$0.992270\pi$
$80$	14.7176	−	1.16120i	1.64548	−	0.129826i
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$	11.1492	−	4.87741i	1.23122	−	0.538619i
$83$	3.13478	−	1.80986i	0.344086	−	0.198658i	−0.317991	−	0.948094i	$-0.603008\pi$
$83$	3.13478	−	1.80986i	0.344086	−	0.198658i	0.662078	+	0.749435i	$0.269675\pi$
$84$	−6.14091	−	0.294368i	−0.670028	−	0.0321182i
$85$	−3.35203	+	9.20963i	−0.363579	+	0.998925i
$86$	3.81869	+	0.426459i	0.411780	+	0.0459862i
$87$	−4.18566	+	7.24977i	−0.448749	+	0.777257i
$88$	8.45924	+	2.93202i	0.901758	+	0.312554i
$89$	−0.688154	−	3.90272i	−0.0729442	−	0.413687i	−0.999313	−	0.0370688i	$-0.988198\pi$
$89$	−0.688154	−	3.90272i	−0.0729442	−	0.413687i	0.926369	−	0.376618i	$-0.122913\pi$
$90$	4.67642	+	2.31857i	0.492938	+	0.244398i
$91$	7.80961	+	9.30713i	0.818670	+	0.975652i
$92$	2.51077	+	8.08321i	0.261766	+	0.842733i
$93$	1.34907	+	3.70654i	0.139892	+	0.384350i
$94$	−2.92398	−	12.0607i	−0.301585	−	1.24396i
$95$	2.87319	+	15.8294i	0.294783	+	1.62406i
$96$	2.10637	−	5.25007i	0.214980	−	0.535833i
$97$	9.00340	−	3.27697i	0.914157	−	0.332726i	0.158246	−	0.987400i	$-0.449416\pi$
$97$	9.00340	−	3.27697i	0.914157	−	0.332726i	0.755911	+	0.654674i	$0.227194\pi$
$98$	3.45698	−	0.219179i	0.349208	−	0.0221404i
$99$	2.03465	+	2.42480i	0.204490	+	0.243701i
$100$	16.8198	+	3.80420i	1.68198	+	0.380420i
$101$	−10.0792	+	1.77724i	−1.00292	+	0.176842i	−0.650911	−	0.759154i	$-0.725613\pi$
$101$	−10.0792	+	1.77724i	−1.00292	+	0.176842i	−0.352010	+	0.935996i	$0.614502\pi$
$102$	2.59106	+	2.71823i	0.256553	+	0.269145i
$103$	5.63340	−	9.75733i	0.555075	−	0.961418i	−0.442823	−	0.896609i	$-0.646023\pi$
$103$	5.63340	−	9.75733i	0.555075	−	0.961418i	0.997898	−	0.0648090i	$-0.0206438\pi$
$104$	−10.4447	+	3.98497i	−1.02419	+	0.390759i
$105$	−10.6614	−	3.88042i	−1.04044	−	0.378690i
$106$	−4.61839	+	15.7201i	−0.448578	+	1.52687i
$107$	−0.913488	+	0.527402i	−0.0883102	+	0.0509859i	−0.543505	−	0.839406i	$-0.682903\pi$
$107$	−0.913488	+	0.527402i	−0.0883102	+	0.0509859i	0.455195	+	0.890392i	$0.349570\pi$
$108$	1.59189	−	1.21074i	0.153179	−	0.116504i
$109$	−1.51231	+	1.80230i	−0.144853	+	0.172629i	−0.833593	−	0.552380i	$-0.813720\pi$
$109$	−1.51231	+	1.80230i	−0.144853	+	0.172629i	0.688740	+	0.725009i	$0.258164\pi$
$110$	13.3032	+	9.79800i	1.26841	+	0.934203i
$111$	−1.03449	+	5.86686i	−0.0981890	+	0.556858i
$112$	−3.28363	+	11.8494i	−0.310274	+	1.11966i
$113$	−6.80497			−0.640158			−0.320079	−	0.947391i	$-0.603709\pi$
$113$	−6.80497			−0.640158			−0.320079	+	0.947391i	$0.603709\pi$
$114$	5.92310	+	1.70787i	0.554750	+	0.159957i
$115$			15.6200i			1.45657i
$116$	12.2956	+	11.3637i	1.14162	+	1.05509i
$117$	−3.89235	−	0.686327i	−0.359848	−	0.0634509i
$118$	3.16362	−	4.29539i	0.291235	−	0.395422i
$119$	−6.25297	−	5.24686i	−0.573209	−	0.480979i
$120$	6.58615	−	8.09945i	0.601230	−	0.739376i
$121$	−0.490284	−	0.849196i	−0.0445712	−	0.0771996i
$122$	5.78726	−	19.6987i	0.523954	−	1.78344i
$123$	2.94310	−	8.08610i	0.265370	−	0.729099i
$124$	7.82566	−	0.996326i	0.702765	−	0.0894728i
$125$	11.5782	+	6.68469i	1.03559	+	0.597897i
$126$	−3.14671	+	2.99949i	−0.280331	+	0.267216i
$127$	−1.32698	−	7.52566i	−0.117750	−	0.667794i	−0.985352	−	0.170534i	$-0.945451\pi$
$127$	−1.32698	−	7.52566i	−0.117750	−	0.667794i	0.867602	−	0.497260i	$-0.165660\pi$
$128$	−9.31212	−	6.42530i	−0.823083	−	0.567922i
$129$	2.08135	−	1.74646i	0.183252	−	0.153767i
$130$	−20.5887	+	1.30536i	−1.80575	+	0.114488i
$131$	−6.53932	−	17.9666i	−0.571343	−	1.56975i	−0.802385	−	0.596807i	$-0.796436\pi$
$131$	−6.53932	−	17.9666i	−0.571343	−	1.56975i	0.231042	−	0.972944i	$-0.425787\pi$
$132$	5.62782	−	2.89921i	0.489838	−	0.252344i
$133$	−13.2071	−	2.26044i	−1.14520	−	0.196005i
$134$	−18.5642	+	4.50068i	−1.60370	+	0.388800i
$135$	3.46826	−	1.26234i	0.298500	−	0.108645i
$136$	6.44572	−	3.85515i	0.552716	−	0.330576i
$137$	−11.6491	+	9.77473i	−0.995247	+	0.835112i	−0.986319	−	0.164848i	$-0.947287\pi$
$137$	−11.6491	+	9.77473i	−0.995247	+	0.835112i	−0.00892853	+	0.999960i	$0.502842\pi$
$138$	5.36219	+	2.65857i	0.456460	+	0.226313i
$139$	14.6449	−	2.58228i	1.24216	−	0.219027i	0.486320	−	0.873781i	$-0.338339\pi$
$139$	14.6449	−	2.58228i	1.24216	−	0.219027i	0.755842	+	0.654754i	$0.227228\pi$
$140$	−12.2735	+	19.0853i	−1.03730	+	1.61301i
$141$	−7.59957	−	4.38761i	−0.639999	−	0.369504i
$142$	0.716474	−	6.41561i	0.0601252	−	0.538386i
$143$	−11.7562	−	4.27892i	−0.983105	−	0.357821i
$144$	−1.65948	−	3.63952i	−0.138290	−	0.303293i
$145$	15.4486	+	26.7577i	1.28294	+	2.22211i
$146$	−10.4222	+	4.55935i	−0.862543	+	0.377334i
$147$	1.57442	−	1.87632i	0.129856	−	0.154756i
$148$	10.9882	+	4.60648i	0.903227	+	0.378651i
$149$	−7.21237	−	1.27173i	−0.590860	−	0.104185i	−0.129780	−	0.991543i	$-0.541427\pi$
$149$	−7.21237	−	1.27173i	−0.590860	−	0.104185i	−0.461081	+	0.887358i	$0.652538\pi$
$150$	10.1532	−	6.75287i	0.829005	−	0.551369i
$151$	0.713695			0.0580797			0.0290399	−	0.999578i	$-0.490755\pi$
$151$	0.713695			0.0580797			0.0290399	+	0.999578i	$0.490755\pi$
$152$	5.94490	−	10.8008i	0.482195	−	0.876064i
$153$	2.65541			0.214677
$154$	−11.4578	+	7.62057i	−0.923297	+	0.614083i
$155$	14.3370	+	2.52801i	1.15158	+	0.203054i
$156$	−3.05616	+	7.29011i	−0.244689	+	0.583676i
$157$	−6.50454	+	7.75181i	−0.519119	+	0.618662i	−0.960372	−	0.278721i	$-0.910090\pi$
$157$	−6.50454	+	7.75181i	−0.519119	+	0.618662i	0.441253	+	0.897383i	$0.354534\pi$
$158$	4.54909	−	1.99008i	0.361906	−	0.158322i
$159$	5.79279	+	10.0334i	0.459398	+	0.795700i
$160$	−12.8940	−	16.4213i	−1.01936	−	1.29822i
$161$	−12.2248	−	4.44946i	−0.963449	−	0.350667i
$162$	0.156959	−	1.40548i	0.0123319	−	0.110425i
$163$	−9.81921	−	5.66912i	−0.769100	−	0.444040i	0.0634534	−	0.997985i	$-0.479789\pi$
$163$	−9.81921	−	5.66912i	−0.769100	−	0.444040i	−0.832553	+	0.553945i	$0.813122\pi$
$164$	−14.4753	−	9.30880i	−1.13033	−	0.726895i
$165$	11.5053	−	2.02870i	0.895687	−	0.157934i
$166$	−4.58631	−	2.27389i	−0.355967	−	0.176488i
$167$	−8.82844	+	7.40794i	−0.683165	+	0.573243i	−0.916929	−	0.399050i	$-0.869340\pi$
$167$	−8.82844	+	7.40794i	−0.683165	+	0.573243i	0.233764	+	0.972293i	$0.424896\pi$
$168$	4.46284	+	7.46177i	0.344315	+	0.575688i
$169$	2.46335	−	0.896586i	0.189488	−	0.0689681i
$170$	13.4700	−	3.26567i	1.03311	−	0.250465i
$171$	3.76392	−	2.19838i	0.287834	−	0.168114i
$172$	−2.48857	−	4.83069i	−0.189751	−	0.368337i
$173$	6.31502	+	17.3504i	0.480122	+	1.31912i	0.909389	+	0.415946i	$0.136550\pi$
$173$	6.31502	+	17.3504i	0.480122	+	1.31912i	−0.429268	+	0.903177i	$0.641228\pi$
$174$	11.8151	−	0.749098i	0.895700	−	0.0567890i
$175$	−20.3039	+	17.0370i	−1.53483	+	1.28787i
$176$	−3.17255	−	12.2575i	−0.239140	−	0.923942i
$177$	−0.655034	−	3.71488i	−0.0492354	−	0.279228i
$178$	−4.05669	+	3.86688i	−0.304061	+	0.289835i
$179$	4.03652	+	2.33049i	0.301704	+	0.174189i	0.643208	−	0.765691i	$-0.277603\pi$
$179$	4.03652	+	2.33049i	0.301704	+	0.174189i	−0.341504	+	0.939880i	$0.610936\pi$
$180$	−0.932276	−	7.32258i	−0.0694878	−	0.545793i
$181$	0.794556	−	2.18303i	0.0590589	−	0.162263i	−0.906654	−	0.421875i	$-0.861372\pi$
$181$	0.794556	−	2.18303i	0.0590589	−	0.162263i	0.965713	+	0.259611i	$0.0835945\pi$
$182$	4.84323	−	16.4854i	0.359004	−	1.22198i
$183$	−7.25889	−	12.5728i	−0.536593	−	0.929406i
$184$	7.55198	−	9.28721i	0.556739	−	0.684662i
$185$	16.8435	+	14.1334i	1.23836	+	1.03911i
$186$	3.30806	−	4.49150i	0.242559	−	0.329333i
$187$	8.27759	+	1.45956i	0.605317	+	0.106734i
$188$	−11.9120	+	12.8889i	−0.868772	+	0.940016i
$189$			3.07398i			0.223599i
$190$	16.3896	−	15.7806i	1.18903	−	1.14485i
$191$	23.1852			1.67762			0.838810	−	0.544424i	$-0.183252\pi$
$191$	23.1852			1.67762			0.838810	+	0.544424i	$0.183252\pi$
$192$	−7.83189	+	1.63143i	−0.565218	+	0.117738i
$193$	−1.67736	+	9.51281i	−0.120739	+	0.684747i	0.863008	+	0.505190i	$0.168578\pi$
$193$	−1.67736	+	9.51281i	−0.120739	+	0.684747i	−0.983748	+	0.179557i	$0.942534\pi$
$194$	−10.9101	−	8.03547i	−0.783301	−	0.576913i
$195$	−9.37677	+	11.1748i	−0.671485	+	0.800244i
$196$	−2.96555	−	3.89911i	−0.211825	−	0.278508i
$197$	20.6251	−	11.9079i	1.46948	−	0.848404i	0.470064	−	0.882632i	$-0.344231\pi$
$197$	20.6251	−	11.9079i	1.46948	−	0.848404i	0.999414	+	0.0342283i	$0.0108973\pi$
$198$	1.26181	−	4.29496i	0.0896731	−	0.305230i
$199$	−4.07732	−	1.48402i	−0.289034	−	0.105200i	0.193434	−	0.981113i	$-0.438037\pi$
$199$	−4.07732	−	1.48402i	−0.289034	−	0.105200i	−0.482468	+	0.875914i	$0.660260\pi$
$200$	−8.69337	−	22.7855i	−0.614714	−	1.61118i
$201$	−6.75357	+	11.6975i	−0.476360	+	0.825079i
$202$	9.98669	+	10.4769i	0.702661	+	0.737150i
$203$	−25.3423	+	4.46853i	−1.77868	+	0.313630i
$204$	1.17158	−	5.17997i	0.0820268	−	0.362671i
$205$	−20.4148	−	24.3295i	−1.42583	−	1.69924i
$206$	−15.9017	+	1.00820i	−1.10793	+	0.0702444i
$207$	3.97686	−	1.44746i	0.276411	−	0.100605i
$208$	12.8726	+	9.17816i	0.892556	+	0.636391i
$209$	12.9415	−	4.78406i	0.895181	−	0.330920i
$210$	3.78044	+	15.5934i	0.260875	+	1.07604i
$211$	−8.39499	−	23.0651i	−0.577935	−	1.58786i	−0.791655	−	0.610969i	$-0.790780\pi$
$211$	−8.39499	−	23.0651i	−0.577935	−	1.58786i	0.213720	−	0.976895i	$-0.431442\pi$
$212$	22.1282	−	6.87337i	1.51977	−	0.472065i
$213$	−2.93415	−	3.49678i	−0.201044	−	0.239595i
$214$	1.33647	+	0.662623i	0.0913594	+	0.0452959i
$215$	−1.74135	−	9.87569i	−0.118759	−	0.673517i
$216$	−2.67245	−	0.926287i	−0.181837	−	0.0630258i
$217$	−6.06253	+	10.5006i	−0.411551	+	0.712828i
$218$	3.30672	+	0.369283i	0.223959	+	0.0250110i
$219$	−2.75118	+	7.55880i	−0.185907	+	0.510776i
$220$	1.11876	−	23.3388i	0.0754267	−	1.57350i
$221$	−9.08913	+	5.24761i	−0.611401	+	0.352992i
$222$	7.71871	−	3.37668i	0.518046	−	0.226628i
$223$	−15.0233	−	12.6061i	−1.00604	−	0.844165i	−0.0182275	−	0.999834i	$-0.505802\pi$
$223$	−15.0233	−	12.6061i	−1.00604	−	0.844165i	−0.987809	+	0.155669i	$0.950247\pi$
$224$	16.5249	−	5.41362i	1.10412	−	0.361713i
$225$	1.49725	−	8.49132i	0.0998166	−	0.566088i
$226$	5.32955	+	8.01318i	0.354517	+	0.533029i
$227$		−	19.9663i		−	1.32521i	−0.748968	−	0.662606i	$-0.769450\pi$
$227$		−	19.9663i		−	1.32521i	0.748968	−	0.662606i	$-0.230550\pi$
$228$	−2.62778	−	8.31233i	−0.174029	−	0.550497i
$229$			4.78675i			0.316317i	0.987414	+	0.158159i	$0.0505557\pi$
$229$			4.78675i			0.316317i	−0.987414	+	0.158159i	$0.949444\pi$
$230$	18.3933	−	12.2333i	1.21282	−	0.806642i
$231$	−1.68964	+	9.58240i	−0.111170	+	0.630476i
$232$	3.75159	−	23.3785i	0.246304	−	1.53488i
$233$	3.23377	+	2.71345i	0.211851	+	0.177764i	0.742538	−	0.669804i	$-0.233622\pi$
$233$	3.23377	+	2.71345i	0.211851	+	0.177764i	−0.530687	+	0.847568i	$0.678066\pi$
$234$	2.24025	+	5.12095i	0.146450	+	0.334767i
$235$	−28.0488	+	16.1940i	−1.82970	+	1.05638i
$236$	−7.53573	−	0.361229i	−0.490534	−	0.0235140i
$237$	1.20084	−	3.29928i	0.0780030	−	0.214312i
$238$	−1.28120	+	11.4724i	−0.0830481	+	0.743648i
$239$	0.264464	−	0.458064i	0.0171067	−	0.0296297i	−0.857345	−	0.514742i	$-0.827888\pi$
$239$	0.264464	−	0.458064i	0.0171067	−	0.0296297i	0.874452	+	0.485112i	$0.161221\pi$
$240$	−14.6957	−	1.41214i	−0.948602	−	0.0911530i
$241$	−0.251247	−	1.42489i	−0.0161842	−	0.0917853i	0.975646	−	0.219352i	$-0.0703944\pi$
$241$	−0.251247	−	1.42489i	−0.0161842	−	0.0917853i	−0.991830	+	0.127567i	$0.959283\pi$
$242$	−0.615987	+	1.24241i	−0.0395971	+	0.0798652i
$243$	−0.642788	−	0.766044i	−0.0412348	−	0.0491418i
$244$	−27.7287	+	8.61296i	−1.77515	+	0.551388i
$245$	−3.09193	−	8.49502i	−0.197536	−	0.542727i
$246$	−11.8268	+	2.86727i	−0.754047	+	0.182810i
$247$	−8.53901	+	14.9630i	−0.543324	+	0.952076i
$248$	−7.30217	−	8.43479i	−0.463688	−	0.535610i
$249$	−3.40143	+	1.23802i	−0.215557	+	0.0784563i
$250$	−1.19635	−	18.8693i	−0.0756635	−	1.19340i
$251$	−6.24981	−	7.44823i	−0.394485	−	0.470128i	0.531845	−	0.846841i	$-0.321499\pi$
$251$	−6.24981	−	7.44823i	−0.394485	−	0.470128i	−0.926330	+	0.376713i	$0.877054\pi$
$252$	5.99650	+	1.35625i	0.377744	+	0.0854360i
$253$	13.1925	−	2.32620i	0.829407	−	0.146247i
$254$	−7.82256	+	7.45656i	−0.490831	+	0.467866i
$255$	4.90034	−	8.48764i	0.306871	−	0.531517i
$256$	−0.272989	+	15.9977i	−0.0170618	+	0.999854i
$257$	−1.86147	−	0.677520i	−0.116115	−	0.0422625i	0.283309	−	0.959029i	$-0.408568\pi$
$257$	−1.86147	−	0.677520i	−0.116115	−	0.0422625i	−0.399424	+	0.916766i	$0.630790\pi$
$258$	−3.68662	−	1.08309i	−0.229519	−	0.0674301i
$259$	−15.8594	+	9.15641i	−0.985454	+	0.568952i
$260$	17.6619	+	23.2219i	1.09535	+	1.44016i
$261$	5.38098	−	6.41280i	0.333074	−	0.396942i
$262$	−16.0351	+	21.7716i	−0.990650	+	1.34505i
$263$	0.752700	−	4.26877i	0.0464135	−	0.263224i	−0.952767	−	0.303702i	$-0.901777\pi$
$263$	0.752700	−	4.26877i	0.0464135	−	0.263224i	0.999180	+	0.0404786i	$0.0128883\pi$
$264$	−7.82158	−	4.35641i	−0.481385	−	0.268118i
$265$	42.7605			2.62676
$266$	7.68185	+	17.3224i	0.471005	+	1.06210i
$267$			3.96292i			0.242527i
$268$	19.8390	+	18.3354i	1.21186	+	1.12001i
$269$	−17.4029	−	3.06859i	−1.06107	−	0.187095i	−0.384239	−	0.923233i	$-0.625536\pi$
$269$	−17.4029	−	3.06859i	−1.06107	−	0.187095i	−0.676831	+	0.736138i	$0.736647\pi$
$270$	−4.20276	−	3.09539i	−0.255772	−	0.188380i
$271$	9.91919	+	8.32319i	0.602548	+	0.505598i	0.892264	−	0.451515i	$-0.149116\pi$
$271$	9.91919	+	8.32319i	0.602548	+	0.505598i	−0.289715	+	0.957113i	$0.593561\pi$
$272$	−9.58781	−	4.57085i	−0.581347	−	0.277149i
$273$	−6.07480	−	10.5219i	−0.367663	−	0.636812i
$274$	20.6336	+	6.06192i	1.24652	+	0.366214i
$275$	9.33463	−	25.6467i	0.562899	−	1.54655i
$276$	−1.06899	−	8.39640i	−0.0643457	−	0.505404i
$277$	−18.0559	−	10.4246i	−1.08487	−	0.626351i	−0.152665	−	0.988278i	$-0.548786\pi$
$277$	−18.0559	−	10.4246i	−1.08487	−	0.626351i	−0.932206	+	0.361927i	$0.882119\pi$
$278$	−14.5104	−	15.2226i	−0.870276	−	0.912993i
$279$	−0.684940	−	3.88449i	−0.0410063	−	0.232558i
$280$	32.0863	−	0.494750i	1.91753	−	0.0295670i
$281$	−1.75995	+	1.47677i	−0.104990	+	0.0880968i	−0.693771	−	0.720195i	$-0.744052\pi$
$281$	−1.75995	+	1.47677i	−0.104990	+	0.0880968i	0.588782	+	0.808292i	$0.299608\pi$
$282$	0.785242	+	12.3852i	0.0467605	+	0.737527i
$283$	1.40868	+	3.87031i	0.0837372	+	0.230066i	0.974494	−	0.224415i	$-0.0720470\pi$
$283$	1.40868	+	3.87031i	0.0837372	+	0.230066i	−0.890756	+	0.454481i	$0.849825\pi$
$284$	−8.11582	+	4.18093i	−0.481586	+	0.248092i
$285$	−0.0808004	−	16.0878i	−0.00478620	−	0.952959i
$286$	4.16867	+	17.1947i	0.246499	+	1.01674i
$287$	24.8565	−	9.04703i	1.46723	−	0.534029i
$288$	−2.98603	+	4.80454i	−0.175953	+	0.283110i
$289$	−7.62124	+	6.39498i	−0.448308	+	0.376175i
$290$	19.4094	−	39.1477i	1.13976	−	2.29883i
$291$	−9.43566	+	1.66376i	−0.553128	+	0.0975314i
$292$	13.5313	+	8.70178i	0.791861	+	0.509233i
$293$	16.8230	+	9.71275i	0.982809	+	0.567425i	0.903117	−	0.429395i	$-0.141273\pi$
$293$	16.8230	+	9.71275i	0.982809	+	0.567425i	0.0796918	+	0.996820i	$0.474606\pi$
$294$	−3.44252	−	0.384450i	−0.200772	−	0.0224216i
$295$	−13.0829	−	4.76179i	−0.761717	−	0.277242i
$296$	−3.18146	−	16.5469i	−0.184918	−	0.961769i
$297$	−1.58267	−	2.74127i	−0.0918361	−	0.159065i
$298$	4.15109	+	9.48892i	0.240466	+	0.549678i
$299$	−10.7518	+	12.8135i	−0.621795	+	0.741026i
$300$	−15.9037	−	6.66713i	−0.918198	−	0.384927i
$301$	8.22514	+	1.45031i	0.474089	+	0.0835948i
$302$	−0.558956	−	0.840411i	−0.0321643	−	0.0483602i
$303$	10.2347			0.587969
$304$	−17.3745	+	1.45866i	−0.996494	+	0.0836597i
$305$	−53.5828			−3.06814
$306$	−2.07967	−	3.12687i	−0.118887	−	0.178751i
$307$	4.85091	+	0.855347i	0.276856	+	0.0488172i	0.310352	−	0.950622i	$-0.399553\pi$
$307$	4.85091	+	0.855347i	0.276856	+	0.0488172i	−0.0334961	+	0.999439i	$0.510664\pi$
$308$	17.9472	+	7.52382i	1.02264	+	0.428709i
$309$	−7.24216	+	8.63086i	−0.411992	+	0.490993i
$310$	−8.25171	−	18.8625i	−0.468665	−	1.07132i
$311$	2.13799	+	3.70311i	0.121234	+	0.209984i	0.920255	−	0.391320i	$-0.127981\pi$
$311$	2.13799	+	3.70311i	0.121234	+	0.209984i	−0.799020	+	0.601304i	$0.794648\pi$
$312$	10.9780	−	2.11073i	0.621507	−	0.119496i
$313$	−14.6497	−	5.33206i	−0.828051	−	0.301386i	−0.106993	−	0.994260i	$-0.534122\pi$
$313$	−14.6497	−	5.33206i	−0.828051	−	0.301386i	−0.721059	+	0.692874i	$0.756344\pi$
$314$	14.2224	+	1.58831i	0.802616	+	0.0896335i
$315$	9.82556	+	5.67279i	0.553608	+	0.319625i
$316$	−5.90619	−	3.79817i	−0.332249	−	0.213664i
$317$	27.1491	−	4.78711i	1.52484	−	0.268871i	0.652509	−	0.757781i	$-0.273716\pi$
$317$	27.1491	−	4.78711i	1.52484	−	0.268871i	0.872335	+	0.488910i	$0.162605\pi$
$318$	7.27799	−	14.6793i	0.408130	−	0.823174i
$319$	20.2987	−	17.0327i	1.13651	−	0.953646i
$320$	−9.23849	+	28.0442i	−0.516447	+	1.56772i
$321$	0.991192	−	0.360765i	0.0553230	−	0.0201359i
$322$	4.33482	+	17.8801i	0.241570	+	0.996417i
$323$	3.90409	−	10.8964i	0.217229	−	0.606289i
$324$	−1.77794	+	0.915921i	−0.0987747	+	0.0508845i
$325$	11.6556	+	32.0236i	0.646538	+	1.77635i
$326$	1.01459	+	16.0026i	0.0561930	+	0.886301i
$327$	1.80230	−	1.51231i	0.0996675	−	0.0836309i
$328$	0.375243	+	24.3358i	0.0207193	+	1.34372i
$329$	−4.68414	−	26.5651i	−0.258245	−	1.46458i
$330$	−11.3997	−	11.9592i	−0.627532	−	0.658333i
$331$	12.2846	+	7.09252i	0.675223	+	0.389840i	0.798053	−	0.602588i	$-0.205864\pi$
$331$	12.2846	+	7.09252i	0.675223	+	0.389840i	−0.122830	+	0.992428i	$0.539197\pi$
$332$	0.914313	+	7.18149i	0.0501795	+	0.394135i
$333$	2.03754	−	5.59809i	0.111656	−	0.306774i
$334$	15.6375	+	4.59413i	0.855646	+	0.251379i
$335$	24.9263	+	43.1737i	1.36187	+	2.35883i
$336$	5.29136	−	11.0992i	0.288668	−	0.605509i
$337$	−11.0776	−	9.29520i	−0.603434	−	0.506342i	0.289113	−	0.957295i	$-0.406640\pi$
$337$	−11.0776	−	9.29520i	−0.603434	−	0.506342i	−0.892548	+	0.450953i	$0.851084\pi$
$338$	−2.98503	−	2.19852i	−0.162364	−	0.119584i
$339$	6.70159	+	1.18167i	0.363980	+	0.0641795i
$340$	−14.3950	−	13.3040i	−0.780680	−	0.721512i
$341$		−	12.4854i		−	0.676125i
$342$	−5.53655	−	2.71046i	−0.299382	−	0.146565i
$343$	−13.9886			−0.755312
$344$	−3.73936	+	6.71373i	−0.201613	+	0.361980i
$345$	2.71238	−	15.3827i	0.146030	−	0.828175i
$346$	15.4851	−	21.0248i	0.832482	−	1.13030i
$347$	−7.59757	+	9.05443i	−0.407859	+	0.486067i	−0.930399	−	0.366547i	$-0.880540\pi$
$347$	−7.59757	+	9.05443i	−0.407859	+	0.486067i	0.522541	+	0.852614i	$0.324984\pi$
$348$	−10.1355	−	13.3262i	−0.543320	−	0.714358i
$349$	2.84555	−	1.64288i	0.152319	−	0.0879414i	−0.421903	−	0.906641i	$-0.638638\pi$
$349$	2.84555	−	1.64288i	0.152319	−	0.0879414i	0.574222	+	0.818699i	$0.305305\pi$
$350$	35.9636	+	10.5657i	1.92233	+	0.564760i
$351$	3.71404	+	1.35180i	0.198241	+	0.0721537i
$352$	−11.9491	+	13.3357i	−0.636888	+	0.710796i
$353$	1.87007	−	3.23905i	0.0995337	−	0.172397i	−0.811958	−	0.583716i	$-0.801598\pi$
$353$	1.87007	−	3.23905i	0.0995337	−	0.172397i	0.911492	+	0.411318i	$0.134932\pi$
$354$	−3.86144	+	3.68077i	−0.205233	+	0.195631i
$355$	−16.5917	+	2.92557i	−0.880597	+	0.155273i
$356$	7.73058	+	1.74846i	0.409720	+	0.0926681i
$357$	5.24686	+	6.25297i	0.277693	+	0.330942i
$358$	−0.417083	−	6.57841i	−0.0220435	−	0.347680i
$359$	0.326452	−	0.118819i	0.0172295	−	0.00627101i	−0.333391	−	0.942789i	$-0.608193\pi$
$359$	0.326452	−	0.118819i	0.0172295	−	0.00627101i	0.350620	+	0.936518i	$0.385971\pi$
$360$	−7.89254	+	6.83273i	−0.415974	+	0.360117i
$361$	−3.48710	−	18.6773i	−0.183531	−	0.983014i
$362$	−3.19290	+	0.774085i	−0.167815	+	0.0406850i
$363$	0.335374	+	0.921432i	0.0176026	+	0.0483626i
$364$	−23.2055	+	7.20799i	−1.21630	+	0.377801i
$365$	19.0836	+	22.7429i	0.998881	+	1.19042i
$366$	−9.11999	+	18.3945i	−0.476709	+	0.961496i
$367$	0.254599	+	1.44390i	0.0132900	+	0.0753711i	0.990731	−	0.135835i	$-0.0433719\pi$
$367$	0.254599	+	1.44390i	0.0132900	+	0.0753711i	−0.977441	+	0.211207i	$0.932261\pi$
$368$	−16.8507	−	1.61922i	−0.878405	−	0.0844077i
$369$	−4.30252	+	7.45219i	−0.223980	+	0.387945i
$370$	3.45117	−	30.9032i	0.179418	−	1.60658i
$371$	−12.1806	+	33.4661i	−0.632388	+	1.73747i
$372$	−7.87978	−	0.377722i	−0.408548	−	0.0195840i
$373$	30.3011	−	17.4944i	1.56893	−	0.905824i	0.572640	−	0.819807i	$-0.305919\pi$
$373$	30.3011	−	17.4944i	1.56893	−	0.905824i	0.996294	−	0.0860175i	$-0.0274141\pi$
$374$	−4.76418	−	10.8904i	−0.246350	−	0.563128i
$375$	−10.2415	−	8.59367i	−0.528871	−	0.443775i
$376$	24.5066	+	3.93260i	1.26383	+	0.202808i
$377$	−5.74545	+	32.5841i	−0.295906	+	1.67817i
$378$	3.61976	−	2.40750i	0.186181	−	0.123828i
$379$		−	23.4433i		−	1.20420i	−0.798421	−	0.602100i	$-0.794331\pi$
$379$		−	23.4433i		−	1.20420i	0.798421	−	0.602100i	$-0.205669\pi$
$380$	−31.4186	−	6.94039i	−1.61174	−	0.356034i
$381$			7.64175i			0.391499i
$382$	−18.1583	−	27.3017i	−0.929058	−	1.39687i
$383$	0.511726	−	2.90215i	0.0261480	−	0.148293i	−0.968939	−	0.247302i	$-0.920456\pi$
$383$	0.511726	−	2.90215i	0.0261480	−	0.148293i	0.995087	+	0.0990090i	$0.0315673\pi$
$384$	8.05490	+	7.94472i	0.411050	+	0.405427i
$385$	27.5107	+	23.0842i	1.40208	+	1.17648i
$386$	12.5155	−	5.47511i	0.637021	−	0.278676i
$387$	−2.35300	+	1.35850i	−0.119610	+	0.0690566i
$388$	−0.917509	+	19.1405i	−0.0465794	+	0.971710i
$389$	−3.81438	+	10.4799i	−0.193397	+	0.531354i	−0.998052	−	0.0623889i	$-0.980128\pi$
$389$	−3.81438	+	10.4799i	−0.193397	+	0.531354i	0.804655	+	0.593743i	$0.202350\pi$
$390$	20.5026	+	2.28967i	1.03819	+	0.115942i
$391$	5.61896	−	9.73232i	0.284163	−	0.492185i
$392$	−2.26881	+	6.54580i	−0.114592	+	0.330613i
$393$	3.32010	+	18.8292i	0.167477	+	0.949808i
$394$	−30.1754	−	14.9610i	−1.52022	−	0.753723i
$395$	−8.32965	−	9.92689i	−0.419110	−	0.499476i
$396$	−6.04576	+	1.87791i	−0.303811	+	0.0943683i
$397$	8.20205	+	22.5349i	0.411649	+	1.13100i	0.956314	+	0.292343i	$0.0944347\pi$
$397$	8.20205	+	22.5349i	0.411649	+	1.13100i	−0.544665	+	0.838654i	$0.683343\pi$
$398$	1.44579	+	5.96351i	0.0724708	+	0.298924i
$399$	12.6140	+	4.51949i	0.631488	+	0.226258i
$400$	−20.0225	+	28.0821i	−1.00113	+	1.40411i
$401$	20.0321	−	7.29108i	1.00035	−	0.364099i	0.210633	−	0.977565i	$-0.432447\pi$
$401$	20.0321	−	7.29108i	1.00035	−	0.364099i	0.789721	+	0.613466i	$0.210225\pi$
$402$	19.0637	−	1.20867i	0.950810	−	0.0602831i
$403$	10.0210	+	11.9426i	0.499181	+	0.594901i
$404$	4.51560	−	19.9651i	0.224660	−	0.993303i
$405$	−3.63477	+	0.640908i	−0.180613	+	0.0318470i
$406$	25.1096	+	26.3421i	1.24617	+	1.30734i
$407$	9.42857	−	16.3308i	0.467357	−	0.809486i
$408$	−7.01723	+	2.67729i	−0.347405	+	0.132546i
$409$	−10.5359	−	3.83476i	−0.520967	−	0.189617i	0.0681334	−	0.997676i	$-0.478296\pi$
$409$	−10.5359	−	3.83476i	−0.520967	−	0.189617i	−0.589101	+	0.808060i	$0.700518\pi$
$410$	−12.6605	+	43.0939i	−0.625259	+	2.12826i
$411$	13.1695	−	7.60339i	0.649602	−	0.375048i
$412$	13.6412	+	17.9354i	0.672054	+	0.883616i
$413$	7.45353	−	8.88278i	0.366764	−	0.437093i
$414$	−4.81907	−	3.54932i	−0.236845	−	0.174440i
$415$	−2.31991	+	13.1569i	−0.113880	+	0.645846i
$416$	0.726082	−	22.3463i	0.0355991	−	1.09562i
$417$	−14.8708			−0.728225
$418$	−15.7690	−	11.4924i	−0.771289	−	0.562113i
$419$			19.7254i			0.963648i	0.876268	+	0.481824i	$0.160026\pi$
$419$			19.7254i			0.963648i	−0.876268	+	0.481824i	$0.839974\pi$
$420$	15.4011	−	16.6641i	0.751499	−	0.813126i
$421$	30.1972	+	5.32458i	1.47172	+	0.259504i	0.851264	−	0.524737i	$-0.175837\pi$
$421$	30.1972	+	5.32458i	1.47172	+	0.259504i	0.620456	+	0.784241i	$0.286948\pi$
$422$	−20.5854	+	27.9497i	−1.00208	+	1.36057i
$423$	6.72221	+	5.64061i	0.326845	+	0.274256i
$424$	−25.4242	−	20.6740i	−1.23471	−	1.00402i
$425$	−11.4479	−	19.8283i	−0.555303	−	0.961813i
$426$	−1.81965	+	6.19373i	−0.0881622	+	0.300087i
$427$	15.2635	−	41.9360i	0.738651	−	2.02943i
$428$	−0.266435	−	2.09272i	−0.0128786	−	0.101155i
$429$	10.8346	+	6.25536i	0.523099	+	0.302011i
$430$	−10.2653	+	9.78502i	−0.495037	+	0.471876i
$431$	−4.02769	−	22.8422i	−0.194007	−	1.10027i	−0.913826	−	0.406106i	$-0.866886\pi$
$431$	−4.02769	−	22.8422i	−0.194007	−	1.10027i	0.719819	−	0.694162i	$-0.244225\pi$
$432$	1.00228	+	3.87239i	0.0482220	+	0.186311i
$433$	11.8505	−	9.94373i	0.569498	−	0.477865i	−0.311981	−	0.950088i	$-0.600993\pi$
$433$	11.8505	−	9.94373i	0.569498	−	0.477865i	0.881479	+	0.472223i	$0.156548\pi$
$434$	17.1131	−	1.08500i	0.821453	−	0.0520816i
$435$	−10.5675	−	29.0339i	−0.506671	−	1.39207i
$436$	−2.15492	−	4.18304i	−0.103202	−	0.200331i
$437$	−0.0926494	−	18.4470i	−0.00443202	−	0.882440i
$438$	11.0555	−	2.68029i	0.528254	−	0.128069i
$439$	−8.16078	+	2.97028i	−0.389493	+	0.141764i	−0.529341	−	0.848409i	$-0.677561\pi$
$439$	−8.16078	+	2.97028i	−0.389493	+	0.141764i	0.139848	+	0.990173i	$0.455339\pi$
$440$	−28.3588	+	16.9612i	−1.35195	+	0.808594i
$441$	−1.87632	+	1.57442i	−0.0893486	+	0.0749724i
$442$	13.2978	+	6.59304i	0.632511	+	0.313599i
$443$	−0.109615	+	0.0193282i	−0.00520799	+	0.000918308i	−0.176252	−	0.984345i	$-0.556397\pi$
$443$	−0.109615	+	0.0193282i	−0.00520799	+	0.000918308i	0.171044	+	0.985263i	$0.445286\pi$
$444$	−10.0214	−	6.44459i	−0.475594	−	0.305847i
$445$	12.6669	+	7.31326i	0.600470	+	0.346682i
$446$	−3.07821	+	27.5636i	−0.145758	+	1.30517i
$447$	6.88196	+	2.50483i	0.325506	+	0.118474i
$448$	−19.3169	−	15.2190i	−0.912636	−	0.719031i
$449$	15.4231	+	26.7136i	0.727861	+	1.26069i	0.957785	+	0.287484i	$0.0928188\pi$
$449$	15.4231	+	26.7136i	0.727861	+	1.26069i	−0.229924	+	0.973209i	$0.573848\pi$
$450$	−11.1716	+	4.88719i	−0.526633	+	0.230385i
$451$	−17.5082	+	20.8655i	−0.824430	+	0.982518i
$452$	5.26189	−	12.5516i	0.247498	−	0.590378i
$453$	−0.702853	−	0.123932i	−0.0330229	−	0.00582283i
$454$	−23.5113	+	15.6373i	−1.10344	+	0.733897i
$455$	−44.8422			−2.10224
$456$	−7.73013	+	9.60443i	−0.361996	+	0.449769i
$457$	27.8279			1.30174			0.650868	−	0.759191i	$-0.274405\pi$
$457$	27.8279			1.30174			0.650868	+	0.759191i	$0.274405\pi$
$458$	5.63663	−	3.74891i	0.263382	−	0.175175i
$459$	−2.61506	−	0.461106i	−0.122061	−	0.0215226i
$460$	−28.8107	−	12.0780i	−1.34331	−	0.563140i
$461$	−5.11268	+	6.09306i	−0.238121	+	0.283782i	−0.871850	−	0.489774i	$-0.837079\pi$
$461$	−5.11268	+	6.09306i	−0.238121	+	0.283782i	0.633728	+	0.773556i	$0.281524\pi$
$462$	12.6070	−	5.51517i	0.586533	−	0.256589i
$463$	16.9811	+	29.4121i	0.789177	+	1.36689i	0.926472	+	0.376364i	$0.122826\pi$
$463$	16.9811	+	29.4121i	0.789177	+	1.36689i	−0.137295	+	0.990530i	$0.543841\pi$
$464$	−30.4676	+	13.8921i	−1.41442	+	0.644923i
$465$	−13.6802	−	4.97920i	−0.634406	−	0.230905i
$466$	0.662584	−	5.93305i	0.0306936	−	0.274843i
$467$	30.8324	+	17.8011i	1.42675	+	0.823735i	0.996863	−	0.0791465i	$-0.0252195\pi$
$467$	30.8324	+	17.8011i	1.42675	+	0.823735i	0.429889	+	0.902882i	$0.358553\pi$
$468$	4.27564	−	6.64866i	0.197642	−	0.307334i
$469$	−40.8899	+	7.20999i	−1.88812	+	0.332926i
$470$	41.0366	+	20.3459i	1.89288	+	0.938488i
$471$	7.75181	−	6.50454i	0.357184	−	0.299713i
$472$	5.47650	+	9.15659i	0.252077	+	0.421466i
$473$	−8.08162	+	2.94147i	−0.371593	+	0.135249i
$474$	−4.82555	+	1.16990i	−0.221645	+	0.0537354i
$475$	−32.6425	−	18.6282i	−1.49774	−	0.854720i
$476$	14.5128	−	7.47636i	0.665192	−	0.342679i
$477$	−3.96250	−	10.8869i	−0.181430	−	0.498476i
$478$	−0.746517	+	0.0473305i	−0.0341449	+	0.00216485i
$479$	12.7499	−	10.6985i	0.582559	−	0.488825i	−0.303227	−	0.952918i	$-0.598064\pi$
$479$	12.7499	−	10.6985i	0.582559	−	0.488825i	0.885786	+	0.464093i	$0.153620\pi$
$480$	9.84658	+	18.4108i	0.449433	+	0.840336i
$481$	4.08870	+	23.1882i	0.186429	+	1.05729i
$482$	−1.48111	+	1.41181i	−0.0674625	+	0.0643061i
$483$	11.2664	+	6.50468i	0.512641	+	0.295973i
$484$	1.94543	−	0.247683i	0.0884287	−	0.0112583i
$485$	−12.0948	+	33.2301i	−0.549196	+	1.50890i
$486$	−0.398633	+	1.35687i	−0.0180824	+	0.0615488i
$487$	−15.4827	−	26.8169i	−0.701590	−	1.21519i	−0.967908	−	0.251304i	$-0.919141\pi$
$487$	−15.4827	−	26.8169i	−0.701590	−	1.21519i	0.266318	−	0.963885i	$-0.414193\pi$
$488$	31.8589	+	25.9064i	1.44218	+	1.17273i
$489$	8.68560	+	7.28809i	0.392777	+	0.329579i
$490$	−7.58174	+	10.2941i	−0.342508	+	0.465039i
$491$	−9.47800	−	1.67123i	−0.427736	−	0.0754214i	−0.0443641	−	0.999015i	$-0.514126\pi$
$491$	−9.47800	−	1.67123i	−0.427736	−	0.0754214i	−0.383372	+	0.923594i	$0.625237\pi$
$492$	12.6389	+	11.6810i	0.569805	+	0.526620i
$493$		−	22.2292i		−	1.00115i
$494$	24.3073	−	1.66374i	1.09364	−	0.0748552i
$495$	−11.6828			−0.525103
$496$	−4.21343	+	15.2047i	−0.189188	+	0.682709i
$497$	2.43661	−	13.8187i	0.109297	−	0.619853i
$498$	4.12178	+	3.03575i	0.184701	+	0.136035i
$499$	1.13261	−	1.34980i	0.0507027	−	0.0604251i	−0.740097	−	0.672500i	$-0.765220\pi$
$499$	1.13261	−	1.34980i	0.0507027	−	0.0604251i	0.790800	+	0.612075i	$0.209665\pi$
$500$	−21.2825	+	16.1869i	−0.951784	+	0.723900i
$501$	9.98069	−	5.76235i	0.445904	−	0.257443i
$502$	−3.87590	+	13.1928i	−0.172990	+	0.588824i
$503$	−26.0278	−	9.47333i	−1.16052	−	0.422395i	−0.311237	−	0.950332i	$-0.600743\pi$
$503$	−26.0278	−	9.47333i	−1.16052	−	0.422395i	−0.849283	+	0.527938i	$0.822966\pi$
$504$	−3.09932	−	8.12337i	−0.138055	−	0.361844i
$505$	18.8874	−	32.7139i	0.840476	−	1.45575i
$506$	−13.0714	−	13.7130i	−0.581095	−	0.609617i
$507$	−2.58162	+	0.455208i	−0.114654	+	0.0202165i
$508$	14.9070	+	3.37157i	0.661390	+	0.149589i
$509$	7.12523	+	8.49152i	0.315820	+	0.376380i	0.900479	−	0.434899i	$-0.143216\pi$
$509$	7.12523	+	8.49152i	0.315820	+	0.376380i	−0.584659	+	0.811279i	$0.698772\pi$
$510$	−13.8325	+	0.877004i	−0.612513	+	0.0388344i
$511$	−23.2356	+	8.45707i	−1.02788	+	0.374119i
$512$	19.0518	−	12.2077i	0.841980	−	0.539508i
$513$	−4.08849	+	1.51138i	−0.180511	+	0.0667292i
$514$	0.660063	+	2.72259i	0.0291141	+	0.120089i
$515$	14.2225	+	39.0761i	0.626720	+	1.72190i
$516$	1.61192	+	5.18943i	0.0709607	+	0.228452i
$517$	17.8545	+	21.2781i	0.785239	+	0.935812i
$518$	23.2030	+	11.5040i	1.01948	+	0.505458i
$519$	−3.20622	−	18.1834i	−0.140737	−	0.798161i
$520$	13.5124	−	38.9848i	0.592556	−	1.70960i
$521$	5.57058	−	9.64853i	0.244051	−	0.422710i	−0.717813	−	0.696236i	$-0.754857\pi$
$521$	5.57058	−	9.64853i	0.244051	−	0.422710i	0.961865	+	0.273526i	$0.0881901\pi$
$522$	−11.7657	−	1.31395i	−0.514970	−	0.0575102i
$523$	−13.3420	+	36.6567i	−0.583403	+	1.60289i	0.198921	+	0.980015i	$0.436256\pi$
$523$	−13.3420	+	36.6567i	−0.583403	+	1.60289i	−0.782324	+	0.622871i	$0.785966\pi$
$524$	38.1955	+	1.83092i	1.66858	+	0.0799842i
$525$	22.9539	−	13.2524i	1.00179	−	0.578383i
$526$	−5.61619	+	2.45690i	−0.244878	+	0.107126i
$527$	−8.02357	−	6.73257i	−0.349512	−	0.293275i
$528$	0.995867	+	12.6222i	0.0433396	+	0.549309i
$529$	−0.883769	+	5.01210i	−0.0384247	+	0.217918i
$530$	−33.4894	−	50.3526i	−1.45469	−	2.18718i
$531$			3.77219i			0.163699i
$532$	14.3816	−	22.6124i	0.623523	−	0.980371i
$533$		−	34.0105i		−	1.47316i
$534$	4.66653	−	3.10370i	0.201941	−	0.134310i
$535$	0.676033	−	3.83397i	0.0292274	−	0.165757i
$536$	6.05319	−	37.7213i	0.261458	−	1.62931i
$537$	−3.57052	−	2.99602i	−0.154079	−	0.129288i
$538$	10.0162	+	22.8960i	0.431831	+	0.987116i
$539$	−6.71437	+	3.87654i	−0.289208	+	0.166975i
$540$	−0.353439	+	7.37322i	−0.0152096	+	0.317293i
$541$	−1.73142	+	4.75703i	−0.0744394	+	0.204521i	−0.971332	−	0.237729i	$-0.923597\pi$
$541$	−1.73142	+	4.75703i	−0.0744394	+	0.204521i	0.896892	+	0.442249i	$0.145819\pi$
$542$	2.03240	−	18.1989i	0.0872990	−	0.781711i
$543$	−1.16156	+	2.01189i	−0.0498475	+	0.0863384i
$544$	2.12663	+	14.8699i	0.0911786	+	0.637544i
$545$	−1.50789	−	8.55166i	−0.0645908	−	0.366313i
$546$	−7.63231	+	15.3939i	−0.326633	+	0.658800i
$547$	15.2691	+	18.1970i	0.652861	+	0.778050i	0.986343	−	0.164707i	$-0.0526679\pi$
$547$	15.2691	+	18.1970i	0.652861	+	0.778050i	−0.333481	+	0.942757i	$0.608223\pi$
$548$	−9.02172	−	29.0447i	−0.385389	−	1.24073i
$549$	4.96537	+	13.6423i	0.211917	+	0.582237i
$550$	−37.5110	+	9.09412i	−1.59947	+	0.387775i
$551$	−18.4033	−	31.5090i	−0.784008	−	1.34233i
$552$	−9.04995	+	7.83473i	−0.385192	+	0.333468i
$553$	10.1419	−	3.69136i	0.431279	−	0.156973i
$554$	1.86566	+	29.4260i	0.0792644	+	1.25019i
$555$	−14.1334	−	16.8435i	−0.599930	−	0.714969i
$556$	−6.56106	+	29.0089i	−0.278251	+	1.23025i
$557$	1.39336	−	0.245688i	0.0590388	−	0.0104101i	−0.144051	−	0.989570i	$-0.546013\pi$
$557$	1.39336	−	0.245688i	0.0590388	−	0.0104101i	0.203090	+	0.979160i	$0.434902\pi$
$558$	−4.03774	+	3.84883i	−0.170931	+	0.162934i
$559$	5.36935	−	9.29998i	0.227099	−	0.393347i
$560$	−25.7121	−	37.3957i	−1.08654	−	1.58026i
$561$	−7.89839	−	2.87478i	−0.333470	−	0.121373i
$562$	3.11733	+	0.915838i	0.131497	+	0.0386323i
$563$	−29.3376	+	16.9381i	−1.23643	+	0.713855i	−0.968363	−	0.249545i	$-0.919719\pi$
$563$	−29.3376	+	16.9381i	−1.23643	+	0.713855i	−0.268070	+	0.963400i	$0.586386\pi$
$564$	13.9692	−	10.6245i	0.588208	−	0.447374i
$565$	16.1443	−	19.2400i	0.679196	−	0.809434i
$566$	3.45423	−	4.68996i	0.145192	−	0.197134i
$567$	0.533791	−	3.02728i	0.0224171	−	0.127134i
$568$	11.2794	+	6.28234i	0.473275	+	0.263601i
$569$	−15.5776			−0.653046			−0.326523	−	0.945189i	$-0.605877\pi$
$569$	−15.5776			−0.653046			−0.326523	+	0.945189i	$0.605877\pi$
$570$	−18.8809	+	12.6949i	−0.790833	+	0.531730i
$571$		−	38.8421i		−	1.62549i	−0.582618	−	0.812746i	$-0.697971\pi$
$571$		−	38.8421i		−	1.62549i	0.582618	−	0.812746i	$-0.302029\pi$
$572$	16.9828	−	18.3755i	0.710085	−	0.768316i
$573$	−22.8329	−	4.02606i	−0.953859	−	0.168191i
$574$	−30.1206	−	22.1843i	−1.25721	−	0.925953i
$575$	−27.9533	−	23.4556i	−1.16573	−	0.978165i
$576$	7.99620	−	0.246651i	0.333175	−	0.0102771i
$577$	6.25930	+	10.8414i	0.260578	+	0.451334i	0.966396	−	0.257059i	$-0.0827536\pi$
$577$	6.25930	+	10.8414i	0.260578	+	0.451334i	−0.705818	+	0.708394i	$0.749420\pi$
$578$	13.4992	+	3.96593i	0.561494	+	0.164961i
$579$	3.30376	−	9.07702i	0.137300	−	0.377228i
$580$	−61.2996	+	7.80437i	−2.54533	+	0.324059i
$581$	−9.63624	−	5.56349i	−0.399779	−	0.230812i
$582$	9.34903	+	9.80792i	0.387530	+	0.406551i
$583$	−6.36809	−	36.1152i	−0.263739	−	1.49574i
$584$	−0.350773	−	22.7489i	−0.0145151	−	0.941356i
$585$	11.1748	−	9.37677i	0.462021	−	0.387682i
$586$	−1.73827	−	27.4168i	−0.0718073	−	1.13258i
$587$	−11.8741	−	32.6239i	−0.490098	−	1.34653i	−0.900590	−	0.434670i	$-0.856865\pi$
$587$	−11.8741	−	32.6239i	−0.490098	−	1.34653i	0.410492	−	0.911864i	$-0.365357\pi$
$588$	2.24342	+	4.35483i	0.0925173	+	0.179590i
$589$	−16.9469	−	2.90051i	−0.698284	−	0.119513i
$590$	4.63911	+	19.1351i	0.190989	+	0.787781i
$591$	−22.3796	+	8.14549i	−0.920572	+	0.335061i
$592$	−16.9931	+	16.7056i	−0.698413	+	0.686596i
$593$	−19.1155	+	16.0398i	−0.784979	+	0.658676i	−0.944497	−	0.328519i	$-0.893450\pi$
$593$	−19.1155	+	16.0398i	−0.784979	+	0.658676i	0.159518	+	0.987195i	$0.449006\pi$
$594$	−1.98845	+	4.01060i	−0.0815873	+	0.164557i
$595$	29.6694	−	5.23152i	1.21633	−	0.214471i
$596$	7.92259	−	12.3197i	0.324522	−	0.504634i
$597$	3.75768	+	2.16950i	0.153792	+	0.0887917i
$598$	23.5093	+	2.62544i	0.961365	+	0.107362i
$599$	18.6612	+	6.79213i	0.762477	+	0.277519i	0.693846	−	0.720123i	$-0.255915\pi$
$599$	18.6612	+	6.79213i	0.762477	+	0.277519i	0.0686308	+	0.997642i	$0.478137\pi$
$600$	4.60464	+	23.9489i	0.187984	+	0.977711i
$601$	−11.4205	−	19.7808i	−0.465850	−	0.806877i	0.533389	−	0.845870i	$-0.320918\pi$
$601$	−11.4205	−	19.7808i	−0.465850	−	0.806877i	−0.999239	+	0.0389935i	$0.987585\pi$
$602$	−4.73399	−	10.8214i	−0.192943	−	0.441046i
$603$	8.68222	−	10.3471i	0.353567	−	0.421365i
$604$	−0.551859	+	1.31640i	−0.0224548	+	0.0535634i
$605$	3.56414	+	0.628453i	0.144903	+	0.0255503i
$606$	−8.01568	−	12.0519i	−0.325615	−	0.489574i
$607$	31.4993			1.27852			0.639258	−	0.768992i	$-0.279241\pi$
$607$	31.4993			1.27852			0.639258	+	0.768992i	$0.279241\pi$
$608$	15.3251	+	19.3169i	0.621514	+	0.783403i
$609$	25.7333			1.04276
$610$	41.9653	+	63.0964i	1.69912	+	2.55470i
$611$	−34.1563	−	6.02267i	−1.38181	−	0.243651i
$612$	−2.05327	+	4.89784i	−0.0829986	+	0.197983i
$613$	−7.80162	+	9.29761i	−0.315104	+	0.375527i	−0.900229	−	0.435416i	$-0.856601\pi$
$613$	−7.80162	+	9.29761i	−0.315104	+	0.375527i	0.585125	+	0.810943i	$0.301046\pi$
$614$	−2.79195	−	6.38208i	−0.112674	−	0.257560i
$615$	15.8799	+	27.5048i	0.640340	+	1.10910i
$616$	−5.19631	−	27.0262i	−0.209365	−	1.08892i
$617$	45.6724	+	16.6234i	1.83870	+	0.669233i	0.990130	+	0.140152i	$0.0447592\pi$
$617$	45.6724	+	16.6234i	1.83870	+	0.669233i	0.848572	+	0.529080i	$0.177463\pi$
$618$	15.8352	+	1.76842i	0.636986	+	0.0711365i
$619$	−6.47558	−	3.73868i	−0.260275	−	0.150270i	0.364185	−	0.931327i	$-0.381348\pi$
$619$	−6.47558	−	3.73868i	−0.260275	−	0.150270i	−0.624460	+	0.781057i	$0.714681\pi$
$620$	−15.7488	+	24.4896i	−0.632489	+	0.983525i
$621$	−4.16779	+	0.734895i	−0.167248	+	0.0294903i
$622$	2.68615	−	5.41781i	0.107705	−	0.217234i
$623$	−9.33191	+	7.83041i	−0.373875	+	0.313719i
$624$	−11.0833	−	11.2740i	−0.443687	−	0.451322i
$625$	−5.85683	+	2.13171i	−0.234273	+	0.0852685i
$626$	5.19468	+	21.4268i	0.207621	+	0.856385i
$627$	−13.5756	+	2.46411i	−0.542158	+	0.0984072i
$628$	−9.26845	−	17.9915i	−0.369852	−	0.717939i
$629$	−5.41049	−	14.8652i	−0.215730	−	0.592715i
$630$	−1.01525	−	16.0129i	−0.0404484	−	0.637970i
$631$	14.9776	−	12.5677i	0.596249	−	0.500312i	−0.293988	−	0.955809i	$-0.594983\pi$
$631$	14.9776	−	12.5677i	0.596249	−	0.500312i	0.890238	+	0.455497i	$0.150538\pi$
$632$	0.153106	+	9.92950i	0.00609024	+	0.394974i
$633$	4.26225	+	24.1724i	0.169409	+	0.960767i
$634$	−26.8998	−	28.2202i	−1.06833	−	1.12077i
$635$	24.4258	+	14.1022i	0.969309	+	0.559631i
$636$	−22.9856	+	2.92642i	−0.911438	+	0.116040i
$637$	3.31105	−	9.09703i	0.131188	−	0.360437i
$638$	−35.9545	−	10.5630i	−1.42345	−	0.418194i
$639$	2.28236	+	3.95316i	0.0902888	+	0.156385i
$640$	40.2589	−	11.0851i	1.59137	−	0.438175i
$641$	−28.3051	−	23.7508i	−1.11798	−	0.938099i	−0.119482	−	0.992836i	$-0.538123\pi$
$641$	−28.3051	−	23.7508i	−1.11798	−	0.938099i	−0.998501	+	0.0547378i	$0.982568\pi$
$642$	−1.20111	−	0.884632i	−0.0474038	−	0.0349136i
$643$	14.6955	+	2.59121i	0.579533	+	0.102187i	0.455728	−	0.890119i	$-0.349379\pi$
$643$	14.6955	+	2.59121i	0.579533	+	0.102187i	0.123805	+	0.992307i	$0.460490\pi$
$644$	17.6597	−	19.1079i	0.695888	−	0.752955i
$645$			10.0280i			0.394854i
$646$	−15.8886	+	3.93661i	−0.625129	+	0.154884i
$647$	42.5242			1.67180			0.835900	−	0.548882i	$-0.184946\pi$
$647$	42.5242			1.67180			0.835900	+	0.548882i	$0.184946\pi$
$648$	2.47100	+	1.37628i	0.0970701	+	0.0540654i
$649$	−2.07341	+	11.7589i	−0.0813885	+	0.461577i
$650$	28.5808	−	38.8055i	1.12103	−	1.52208i
$651$	7.79384	−	9.28833i	0.305465	−	0.364039i
$652$	18.0492	−	13.7277i	0.706861	−	0.537619i
$653$	−32.0017	+	18.4762i	−1.25232	+	0.723030i	−0.971571	−	0.236750i	$-0.923918\pi$
$653$	−32.0017	+	18.4762i	−1.25232	+	0.723030i	−0.280753	+	0.959780i	$0.590584\pi$
$654$	−3.19235	−	0.937878i	−0.124831	−	0.0366739i
$655$	66.3120	+	24.1356i	2.59102	+	0.943055i
$656$	28.3628	−	19.5013i	1.10738	−	0.761399i
$657$	4.02195	−	6.96623i	0.156911	−	0.271778i
$658$	−27.6131	+	26.3212i	−1.07647	+	1.02611i
$659$	−7.48553	+	1.31990i	−0.291595	+	0.0514161i	−0.317532	−	0.948248i	$-0.602854\pi$
$659$	−7.48553	+	1.31990i	−0.291595	+	0.0514161i	0.0259371	+	0.999664i	$0.491743\pi$
$660$	−5.15450	+	22.7900i	−0.200639	+	0.887098i
$661$	20.6518	+	24.6119i	0.803262	+	0.957291i	0.999730	−	0.0232194i	$-0.00739163\pi$
$661$	20.6518	+	24.6119i	0.803262	+	0.957291i	−0.196468	+	0.980510i	$0.562947\pi$
$662$	−1.26933	−	20.0205i	−0.0493340	−	0.778118i
$663$	9.86228	−	3.58958i	0.383019	−	0.139408i
$664$	7.74047	−	6.70108i	0.300389	−	0.260052i
$665$	37.7240	−	31.9784i	1.46287	−	1.24007i
$666$	−8.18780	+	1.98504i	−0.317271	+	0.0769188i
$667$	−12.1171	−	33.2916i	−0.469177	−	1.28905i
$668$	−6.83726	−	22.0120i	−0.264541	−	0.851669i
$669$	12.6061	+	15.0233i	0.487379	+	0.580836i
$670$	31.3172	−	63.1650i	1.20989	−	2.44028i
$671$	7.97980	+	45.2557i	0.308057	+	1.74708i
$672$	−17.2139	+	2.46186i	−0.664041	+	0.0949681i
$673$	−15.7636	+	27.3033i	−0.607641	+	1.05247i	0.383987	+	0.923339i	$0.374551\pi$
$673$	−15.7636	+	27.3033i	−0.607641	+	1.05247i	−0.991628	+	0.129127i	$0.958782\pi$
$674$	−2.26975	+	20.3243i	−0.0874274	+	0.782861i
$675$	−2.94900	+	8.10232i	−0.113507	+	0.311859i
$676$	−0.251032	+	5.23687i	−0.00965509	+	0.201418i
$677$	9.05163	−	5.22596i	0.347883	−	0.200850i	−0.315870	−	0.948803i	$-0.602296\pi$
$677$	9.05163	−	5.22596i	0.347883	−	0.200850i	0.663752	+	0.747952i	$0.268963\pi$
$678$	−3.85711	−	8.81691i	−0.148131	−	0.338612i
$679$	−22.5619	−	18.9317i	−0.865847	−	0.726532i
$680$	−4.39216	+	27.3704i	−0.168432	+	1.04961i
$681$	−3.46712	+	19.6630i	−0.132860	+	0.753488i
$682$	−14.7022	+	9.77842i	−0.562977	+	0.374435i
$683$			9.89520i			0.378629i	0.981916	+	0.189315i	$0.0606266\pi$
$683$			9.89520i			0.378629i	−0.981916	+	0.189315i	$0.939373\pi$
$684$	1.14444	+	8.64235i	0.0437588	+	0.330449i
$685$		−	56.1258i		−	2.14446i
$686$	10.9556	+	16.4722i	0.418288	+	0.628913i
$687$	0.831210	−	4.71403i	0.0317126	−	0.179851i
$688$	10.8344	−	0.854812i	0.413056	−	0.0325894i
$689$	35.0778	+	29.4337i	1.33636	+	1.12134i
$690$	−20.2381	+	8.85352i	−0.770453	+	0.337048i
$691$	17.2003	−	9.93060i	0.654330	−	0.377778i	−0.135783	−	0.990739i	$-0.543355\pi$
$691$	17.2003	−	9.93060i	0.654330	−	0.377778i	0.790113	+	0.612961i	$0.210022\pi$
$692$	−36.8854	−	1.76812i	−1.40217	−	0.0672139i
$693$	3.32793	−	9.14342i	0.126418	−	0.347330i
$694$	16.6123	+	1.85521i	0.630596	+	0.0704228i
$695$	−27.4429	+	47.5324i	−1.04097	+	1.80301i
$696$	−7.75423	+	22.3719i	−0.293923	+	0.848005i
$697$	3.96784	+	22.5027i	0.150293	+	0.852352i
$698$	−4.16317	−	2.06410i	−0.157578	−	0.0781273i
$699$	−2.71345	−	3.23377i	−0.102632	−	0.122312i
$700$	−15.7245	−	50.6237i	−0.594331	−	1.91340i
$701$	7.69407	+	21.1393i	0.290601	+	0.798420i	0.995979	+	0.0895884i	$0.0285552\pi$
$701$	7.69407	+	21.1393i	0.290601	+	0.798420i	−0.705378	+	0.708832i	$0.749223\pi$
$702$	−1.31697	−	5.43217i	−0.0497058	−	0.205024i
$703$	−19.9759	−	16.5915i	−0.753405	−	0.625760i
$704$	25.0618	+	3.62629i	0.944552	+	0.136671i
$705$	30.4347	−	11.0773i	1.14624	−	0.417197i
$706$	−5.27875	+	0.334682i	−0.198669	+	0.0125959i
$707$	20.2230	+	24.1008i	0.760562	+	0.906403i
$708$	7.35851	+	1.66431i	0.276550	+	0.0625485i
$709$	23.3995	−	4.12597i	0.878788	−	0.154954i	0.283988	−	0.958828i	$-0.408342\pi$
$709$	23.3995	−	4.12597i	0.878788	−	0.154954i	0.594800	+	0.803874i	$0.297231\pi$
$710$	16.4394	+	17.2463i	0.616959	+	0.647242i
$711$	−1.75551	+	3.04064i	−0.0658369	+	0.114033i
$712$	−3.99558	−	10.4725i	−0.149741	−	0.392474i
$713$	−15.6864	−	5.70938i	−0.587460	−	0.213818i
$714$	3.25391	−	11.0757i	0.121774	−	0.414496i
$715$	39.9888	−	23.0875i	1.49550	−	0.863425i
$716$	−7.41974	+	5.64325i	−0.277289	+	0.210898i
$717$	−0.339988	+	0.405182i	−0.0126971	+	0.0151318i
$718$	−0.395587	−	0.291356i	−0.0147632	−	0.0108733i
$719$	−1.59826	+	9.06417i	−0.0596049	+	0.338036i	−0.999998	−	0.00205343i	$-0.999346\pi$
$719$	−1.59826	+	9.06417i	−0.0596049	+	0.338036i	0.940393	+	0.340090i	$0.110457\pi$
$720$	14.2272	+	3.94256i	0.530216	+	0.146931i
$721$	−34.6339			−1.28983
$722$	−19.2623	+	18.7340i	−0.716870	+	0.697207i
$723$			1.44687i			0.0538098i
$724$	3.41216	+	3.15355i	0.126812	+	0.117201i
$725$	−71.0835	−	12.5339i	−2.63997	−	0.465499i
$726$	0.822371	−	1.11657i	0.0305210	−	0.0414398i
$727$	−29.1599	−	24.4681i	−1.08148	−	0.907471i	−0.0854393	−	0.996343i	$-0.527229\pi$
$727$	−29.1599	−	24.4681i	−1.08148	−	0.907471i	−0.996043	+	0.0888719i	$0.971674\pi$
$728$	26.6620	+	21.6804i	0.988158	+	0.803530i
$729$	0.500000	+	0.866025i	0.0185185	+	0.0320750i
$730$	11.8349	−	40.2838i	0.438030	−	1.49097i
$731$	−2.46759	+	6.77965i	−0.0912672	+	0.250755i
$732$	28.8031	−	3.66707i	1.06459	−	0.135539i
$733$	−14.4568	−	8.34664i	−0.533974	−	0.308290i	0.208659	−	0.977988i	$-0.433090\pi$
$733$	−14.4568	−	8.34664i	−0.533974	−	0.308290i	−0.742633	+	0.669698i	$0.766423\pi$
$734$	1.50087	−	1.43065i	0.0553980	−	0.0528061i
$735$	1.56982	+	8.90287i	0.0579035	+	0.328387i
$736$	11.2905	+	21.1107i	0.416175	+	0.778151i
$737$	32.7521	−	27.4822i	1.20644	−	1.01232i
$738$	12.1450	−	0.770013i	0.447063	−	0.0283446i
$739$	8.53630	+	23.4533i	0.314013	+	0.862743i	0.991836	+	0.127518i	$0.0407011\pi$
$739$	8.53630	+	23.4533i	0.314013	+	0.862743i	−0.677824	+	0.735225i	$0.737077\pi$
$740$	−39.0929	+	20.1390i	−1.43708	+	0.740324i
$741$	11.0076	−	13.2529i	0.404374	−	0.486859i
$742$	48.9476	−	11.8668i	1.79692	−	0.435644i
$743$	−6.91003	+	2.51504i	−0.253504	+	0.0922680i	−0.465647	−	0.884971i	$-0.654178\pi$
$743$	−6.91003	+	2.51504i	−0.253504	+	0.0922680i	0.212142	+	0.977239i	$0.431956\pi$
$744$	5.72654	+	9.57465i	0.209945	+	0.351024i
$745$	20.7065	−	17.3748i	0.758626	−	0.636563i
$746$	−44.3319	−	21.9797i	−1.62311	−	0.804735i
$747$	3.56474	−	0.628559i	0.130427	−	0.0229978i
$748$	−9.09271	+	14.1392i	−0.332462	+	0.516982i
$749$	2.80804	+	1.62123i	0.102604	+	0.0592383i
$750$	−2.09845	+	18.7904i	−0.0766244	+	0.686127i
$751$	30.9023	+	11.2475i	1.12764	+	0.410427i	0.837435	−	0.546537i	$-0.184054\pi$
$751$	30.9023	+	11.2475i	1.12764	+	0.410427i	0.290205	+	0.956964i	$0.406276\pi$
$752$	−14.5623	−	31.9376i	−0.531034	−	1.16465i
$753$	4.86149	+	8.42035i	0.177163	+	0.306854i
$754$	42.8691	−	18.7538i	1.56120	−	0.682974i
$755$	−1.69319	+	2.01787i	−0.0616215	+	0.0734377i
$756$	−5.66989	−	2.37693i	−0.206212	−	0.0864481i
$757$	−41.5055	−	7.31854i	−1.50854	−	0.265997i	−0.642624	−	0.766182i	$-0.722154\pi$
$757$	−41.5055	−	7.31854i	−1.50854	−	0.265997i	−0.865919	+	0.500185i	$0.833265\pi$
$758$	−27.6056	+	18.3604i	−1.00268	+	0.666881i
$759$	−13.3960			−0.486245
$760$	16.4339	+	42.4325i	0.596121	+	1.53919i
$761$	−47.5168			−1.72248			−0.861241	−	0.508197i	$-0.830312\pi$
$761$	−47.5168			−1.72248			−0.861241	+	0.508197i	$0.830312\pi$
$762$	8.99853	−	5.98491i	0.325983	−	0.216810i
$763$	7.12239	+	1.25587i	0.257848	+	0.0454656i
$764$	−17.9277	+	42.7645i	−0.648603	+	1.54717i
$765$	−6.29976	+	7.50776i	−0.227768	+	0.271444i
$766$	−3.81819	+	1.67033i	−0.137957	+	0.0603516i
$767$	−7.45459	−	12.9117i	−0.269170	−	0.466216i
$768$	3.04681	−	15.7072i	0.109942	−	0.566786i
$769$	−31.0875	−	11.3149i	−1.12105	−	0.408027i	−0.286012	−	0.958226i	$-0.592330\pi$
$769$	−31.0875	−	11.3149i	−1.12105	−	0.408027i	−0.835034	+	0.550199i	$0.814552\pi$
$770$	5.63682	−	50.4745i	0.203137	−	1.81897i
$771$	1.71554	+	0.990467i	0.0617837	+	0.0356708i
$772$	−16.2492	−	10.4496i	−0.584820	−	0.376088i
$773$	−47.9733	+	8.45898i	−1.72548	+	0.304248i	−0.946476	−	0.322773i	$-0.895385\pi$
$773$	−47.9733	+	8.45898i	−1.72548	+	0.304248i	−0.779002	+	0.627022i	$0.784274\pi$
$774$	3.44254	+	1.70681i	0.123739	+	0.0613500i
$775$	−26.0532	+	21.8612i	−0.935857	+	0.785277i
$776$	23.2574	−	13.9101i	0.834892	−	0.499344i
$777$	17.2084	−	6.26336i	0.617349	−	0.224697i
$778$	15.3280	−	3.71611i	0.549536	−	0.133229i
$779$	24.2540	+	28.6117i	0.868990	+	1.02512i
$780$	−13.3612	−	25.9361i	−0.478406	−	0.928660i
$781$	4.94183	+	13.5776i	0.176832	+	0.485843i
$782$	−15.8610	+	1.00561i	−0.567187	+	0.0359607i
$783$	−6.41280	+	5.38098i	−0.229175	+	0.192300i
$784$	9.48490	−	2.45494i	0.338746	−	0.0876764i
$785$	−6.48552	−	36.7812i	−0.231478	−	1.31278i
$786$	19.5721	−	18.6563i	0.698112	−	0.665450i
$787$	−29.4854	−	17.0234i	−1.05104	−	0.606819i	−0.128101	−	0.991761i	$-0.540888\pi$
$787$	−29.4854	−	17.0234i	−1.05104	−	0.606819i	−0.922941	+	0.384942i	$0.874222\pi$
$788$	6.01568	+	47.2503i	0.214300	+	1.68322i
$789$	−1.48253	+	4.07321i	−0.0527794	+	0.145010i
$790$	−5.16574	+	17.5832i	−0.183789	+	0.625581i
$791$	10.4592	+	18.1158i	0.371886	+	0.644125i
$792$	6.94627	+	5.64843i	0.246825	+	0.200708i
$793$	−43.9557	−	36.8832i	−1.56091	−	1.30976i
$794$	20.1123	−	27.3073i	0.713758	−	0.969102i
$795$	−42.1109	−	7.42529i	−1.49352	−	0.263348i
$796$	5.89001	−	6.37302i	0.208766	−	0.225886i
$797$			20.3773i			0.721799i	0.932605	+	0.360900i	$0.117530\pi$
$797$			20.3773i			0.721799i	−0.932605	+	0.360900i	$0.882470\pi$
$798$	−4.55715	−	18.3932i	−0.161321	−	0.651111i
$799$	23.3018			0.824358
$800$	48.7494	+	1.58398i	1.72355	+	0.0560020i
$801$	0.688154	−	3.90272i	0.0243147	−	0.137896i
$802$	−24.2744	−	17.8785i	−0.857160	−	0.631311i
$803$	16.3665	−	19.5049i	0.577562	−	0.688311i
$804$	−16.3537	−	21.5018i	−0.576749	−	0.758310i
$805$	41.5826	−	24.0078i	1.46560	−	0.846162i
$806$	6.21464	−	21.1534i	0.218901	−	0.745098i
$807$	16.6056	+	6.04395i	0.584545	+	0.212757i
$808$	−27.0465	+	10.3191i	−0.951492	+	0.363023i
$809$	2.01021	−	3.48179i	0.0706753	−	0.122413i	−0.828522	−	0.559956i	$-0.810818\pi$
$809$	2.01021	−	3.48179i	0.0706753	−	0.122413i	0.899197	+	0.437543i	$0.144151\pi$
$810$	3.60140	+	3.77817i	0.126540	+	0.132751i
$811$	16.6933	−	2.94348i	0.586182	−	0.103360i	0.127311	−	0.991863i	$-0.459365\pi$
$811$	16.6933	−	2.94348i	0.586182	−	0.103360i	0.458871	+	0.888503i	$0.348254\pi$
$812$	11.3536	−	50.1986i	0.398434	−	1.76162i
$813$	−8.32319	−	9.91919i	−0.291907	−	0.347881i
$814$	−26.6146	+	1.68741i	−0.932841	+	0.0591437i
$815$	39.3240	−	14.3128i	1.37746	−	0.501354i
$816$	8.64843	+	6.16632i	0.302756	+	0.215864i
$817$	2.11509	+	11.6528i	0.0739978	+	0.407678i
$818$	3.73596	+	15.4099i	0.130625	+	0.538794i
$819$	4.15541	+	11.4169i	0.145202	+	0.398938i
$820$	60.6607	−	18.8422i	2.11837	−	0.657997i
$821$	8.23815	+	9.81785i	0.287514	+	0.342645i	0.890398	−	0.455183i	$-0.150426\pi$
$821$	8.23815	+	9.81785i	0.287514	+	0.342645i	−0.602884	+	0.797829i	$0.705982\pi$
$822$	−19.2675	−	9.55282i	−0.672031	−	0.333193i
$823$	7.26342	+	41.1929i	0.253187	+	1.43589i	0.800684	+	0.599086i	$0.204469\pi$
$823$	7.26342	+	41.1929i	0.253187	+	1.43589i	−0.547498	+	0.836807i	$0.684420\pi$
$824$	10.4363	−	30.1100i	0.363565	−	1.04893i
$825$	−13.6463	+	23.6361i	−0.475104	+	0.822904i
$826$	−16.2974	−	1.82004i	−0.567059	−	0.0633273i
$827$	3.79069	−	10.4148i	0.131815	−	0.362159i	−0.856173	−	0.516689i	$-0.827164\pi$
$827$	3.79069	−	10.4148i	0.131815	−	0.362159i	0.987988	+	0.154530i	$0.0493864\pi$
$828$	−0.405270	+	8.45447i	−0.0140841	+	0.293813i
$829$	−11.5995	+	6.69695i	−0.402866	+	0.232595i	−0.687720	−	0.725976i	$-0.741388\pi$
$829$	−11.5995	+	6.69695i	−0.402866	+	0.232595i	0.284854	+	0.958571i	$0.408055\pi$
$830$	17.3098	−	7.57246i	0.600831	−	0.262844i
$831$	15.9714	+	13.4016i	0.554040	+	0.464895i
$832$	−26.8826	+	16.6463i	−0.931985	+	0.577108i
$833$	−1.12942	+	6.40524i	−0.0391320	+	0.221928i
$834$	11.6466	+	17.5111i	0.403288	+	0.606359i
$835$		−	42.5359i		−	1.47201i
$836$	−1.18281	+	27.5695i	−0.0409083	+	0.953511i
$837$			3.94441i			0.136339i
$838$	23.2276	−	15.4486i	0.802384	−	0.533664i
$839$	6.28608	−	35.6501i	0.217019	−	1.23078i	−0.660348	−	0.750960i	$-0.729591\pi$
$839$	6.28608	−	35.6501i	0.217019	−	1.23078i	0.877368	−	0.479819i	$-0.159298\pi$
$840$	−31.6848	−	5.08450i	−1.09323	−	0.175432i
$841$	−31.4682	−	26.4050i	−1.08511	−	0.910517i
$842$	−17.3800	−	39.7288i	−0.598955	−	1.36914i
$843$	1.98965	−	1.14872i	0.0685271	−	0.0395641i
$844$	49.0343	+	2.35049i	1.68783	+	0.0809071i
$845$	−3.30916	+	9.09183i	−0.113838	+	0.312768i
$846$	1.37735	−	12.3334i	0.0473543	−	0.424030i
$847$	−1.50712	+	2.61041i	−0.0517853	+	0.0896948i
$848$	−4.43270	+	46.1298i	−0.152220	+	1.58410i
$849$	−0.715205	−	4.05613i	−0.0245458	−	0.139206i
$850$	−14.3830	+	29.0097i	−0.493332	+	0.995023i
$851$	−16.2060	−	19.3136i	−0.555535	−	0.662061i
$852$	8.71854	−	2.70811i	0.298692	−	0.0927784i
$853$	−14.5195	−	39.8921i	−0.497139	−	1.36588i	−0.894027	−	0.448012i	$-0.852132\pi$
$853$	−14.5195	−	39.8921i	−0.497139	−	1.36588i	0.396888	−	0.917867i	$-0.370090\pi$
$854$	−61.3358	+	14.8702i	−2.09887	+	0.508848i
$855$	−2.71404	+	15.8574i	−0.0928184	+	0.542312i
$856$	−2.25561	+	1.95273i	−0.0770951	+	0.0667428i
$857$	−49.5214	+	18.0243i	−1.69162	+	0.615698i	−0.994828	−	0.101577i	$-0.967611\pi$
$857$	−49.5214	+	18.0243i	−1.69162	+	0.615698i	−0.696789	+	0.717276i	$0.745389\pi$
$858$	−1.11951	−	17.6574i	−0.0382194	−	0.602813i
$859$	27.7566	+	33.0790i	0.947042	+	1.12864i	0.991562	+	0.129632i	$0.0413797\pi$
$859$	27.7566	+	33.0790i	0.947042	+	1.12864i	−0.0445201	+	0.999008i	$0.514176\pi$
$860$	19.5620	+	4.42442i	0.667058	+	0.150871i
$861$	−26.0499	+	4.59330i	−0.887778	+	0.156539i
$862$	−23.7433	+	22.6325i	−0.808701	+	0.770864i
$863$	−6.87326	+	11.9048i	−0.233968	+	0.405245i	−0.958972	−	0.283500i	$-0.908505\pi$
$863$	−6.87326	+	11.9048i	−0.233968	+	0.405245i	0.725004	+	0.688745i	$0.241838\pi$
$864$	3.77497	−	4.21303i	0.128427	−	0.143330i
$865$	−64.0374	−	23.3077i	−2.17734	−	0.792486i
$866$	−20.9904	−	6.16673i	−0.713281	−	0.209554i
$867$	8.61593	−	4.97441i	0.292612	−	0.168940i
$868$	−14.6803	−	19.3017i	−0.498283	−	0.655143i
$869$	−7.14370	+	8.51352i	−0.242333	+	0.288802i
$870$	−25.9125	+	35.1826i	−0.878516	+	1.19280i
$871$	−9.27030	+	52.5745i	−0.314112	+	1.78142i
$872$	−3.23803	+	5.81362i	−0.109653	+	0.196874i
$873$	9.58122			0.324275
$874$	−21.6497	+	14.5565i	−0.732312	+	0.492382i
$875$		−	41.0972i		−	1.38934i
$876$	−11.8147	−	10.9193i	−0.399182	−	0.368928i
$877$	21.0968	+	3.71993i	0.712387	+	0.125613i	0.518085	−	0.855329i	$-0.326645\pi$
$877$	21.0968	+	3.71993i	0.712387	+	0.125613i	0.194301	+	0.980942i	$0.437756\pi$
$878$	9.88906	+	7.28344i	0.333739	+	0.245804i
$879$	−14.8808	−	12.4865i	−0.501917	−	0.421158i
$880$	42.1828	+	20.1101i	1.42198	+	0.677910i
$881$	16.2960	+	28.2255i	0.549026	+	0.950941i	0.998342	+	0.0575679i	$0.0183346\pi$
$881$	16.2960	+	28.2255i	0.549026	+	0.950941i	−0.449316	+	0.893373i	$0.648332\pi$
$882$	3.32346	+	0.976397i	0.111907	+	0.0328770i
$883$	−10.7327	+	29.4879i	−0.361185	+	0.992346i	0.617427	+	0.786628i	$0.288175\pi$
$883$	−10.7327	+	29.4879i	−0.361185	+	0.992346i	−0.978611	+	0.205718i	$0.934047\pi$
$884$	−2.65101	−	20.8224i	−0.0891629	−	0.700332i
$885$	12.0573	+	6.96128i	0.405301	+	0.234001i
$886$	0.108609	+	0.113940i	0.00364879	+	0.00382789i
$887$	0.999168	+	5.66656i	0.0335488	+	0.190264i	0.996976	−	0.0777038i	$-0.0247589\pi$
$887$	0.999168	+	5.66656i	0.0335488	+	0.190264i	−0.963428	+	0.267968i	$0.913648\pi$
$888$	0.259785	+	16.8480i	0.00871780	+	0.565381i
$889$	−17.9948	+	15.0995i	−0.603528	+	0.506420i
$890$	−1.30884	−	20.6436i	−0.0438724	−	0.691974i
$891$	1.08261	+	2.97445i	0.0362689	+	0.0996480i
$892$	34.8683	−	17.9627i	1.16748	−	0.601434i
$893$	33.0293	−	19.2913i	1.10528	−	0.645558i
$894$	−2.44029	−	10.0656i	−0.0816156	−	0.336644i
$895$	−16.1655	+	5.88375i	−0.540352	+	0.196672i
$896$	−2.79245	+	34.6658i	−0.0932890	+	1.15810i
$897$	12.8135	−	10.7518i	0.427832	−	0.358994i
$898$	19.3774	−	39.0831i	0.646633	−	1.30422i
$899$	−32.5183	+	5.73385i	−1.08455	+	0.191235i
$900$	14.5043	+	9.32749i	0.483477	+	0.310916i
$901$	−26.6427	−	15.3822i	−0.887599	−	0.512455i
$902$	38.2823	+	4.27524i	1.27466	+	0.142350i
$903$	−7.84834	−	2.85656i	−0.261176	−	0.0950604i
$904$	−18.9012	+	3.63411i	−0.628644	+	0.120869i
$905$	4.28715	+	7.42556i	0.142510	+	0.246834i
$906$	0.404528	+	0.924705i	0.0134395	+	0.0307213i
$907$	−19.0924	+	22.7534i	−0.633953	+	0.755515i	−0.983402	−	0.181440i	$-0.941924\pi$
$907$	−19.0924	+	22.7534i	−0.633953	+	0.755515i	0.349449	+	0.936955i	$0.386369\pi$
$908$	36.8274	+	15.4388i	1.22216	+	0.512355i
$909$	−10.0792	−	1.77724i	−0.334307	−	0.0589473i
$910$	35.1198	+	52.8039i	1.16421	+	1.75043i
$911$	−41.5054			−1.37513			−0.687567	−	0.726121i	$-0.741321\pi$
$911$	−41.5054			−1.37513			−0.687567	+	0.726121i	$0.741321\pi$
$912$	17.3638	+	1.58055i	0.574973	+	0.0523372i
$913$	11.4577			0.379195
$914$	−21.7944	−	32.7687i	−0.720896	−	1.08389i
$915$	52.7688	+	9.30456i	1.74448	+	0.307599i
$916$	−8.82905	−	3.70131i	−0.291720	−	0.122295i
$917$	−37.7789	+	45.0232i	−1.24757	+	1.48680i
$918$	1.50510	+	3.44050i	0.0496759	+	0.113553i
$919$	17.2431	+	29.8658i	0.568796	+	0.985183i	0.996685	+	0.0813522i	$0.0259239\pi$
$919$	17.2431	+	29.8658i	0.568796	+	0.985183i	−0.427890	+	0.903831i	$0.640743\pi$
$920$	8.34165	+	43.3853i	0.275016	+	1.43037i
$921$	−4.62869	−	1.68470i	−0.152520	−	0.0555129i
$922$	11.1790	+	1.24844i	0.368162	+	0.0411152i
$923$	−15.6245	−	9.02080i	−0.514286	−	0.296923i
$924$	−16.3680	−	10.5260i	−0.538468	−	0.346280i
$925$	−50.5859	+	8.91966i	−1.66325	+	0.293277i
$926$	21.3348	−	43.0311i	0.701105	−	1.41409i
$927$	8.63086	−	7.24216i	0.283475	−	0.237864i
$928$	40.2203	+	24.9970i	1.32030	+	0.820566i
$929$	11.3453	−	4.12936i	0.372228	−	0.135480i	−0.149131	−	0.988817i	$-0.547648\pi$
$929$	11.3453	−	4.12936i	0.372228	−	0.135480i	0.521359	+	0.853338i	$0.325425\pi$
$930$	4.85091	+	20.0088i	0.159068	+	0.656114i
$931$	3.70193	+	10.0142i	0.121326	+	0.328202i
$932$	−7.50538	+	3.86645i	−0.245847	+	0.126650i
$933$	−1.46247	−	4.01811i	−0.0478792	−	0.131547i
$934$	−3.18582	−	50.2481i	−0.104243	−	1.64417i
$935$	−23.7647	+	19.9409i	−0.777188	+	0.652138i
$936$	−11.1777	+	0.172353i	−0.365356	+	0.00563355i
$937$	5.36896	+	30.4489i	0.175396	+	0.994721i	0.937686	+	0.347485i	$0.112964\pi$
$937$	5.36896	+	30.4489i	0.175396	+	0.994721i	−0.762290	+	0.647236i	$0.775925\pi$
$938$	40.5145	+	42.5031i	1.32284	+	1.38777i
$939$	13.5013	+	7.79496i	0.440597	+	0.254379i
$940$	−8.18093	−	64.2573i	−0.266833	−	2.09584i
$941$	0.0709935	−	0.195053i	0.00231432	−	0.00635854i	−0.938530	−	0.345197i	$-0.887812\pi$
$941$	0.0709935	−	0.195053i	0.00231432	−	0.00635854i	0.940844	+	0.338839i	$0.110034\pi$
$942$	−13.7305	−	4.03387i	−0.447364	−	0.131431i
$943$	18.2087	+	31.5383i	0.592955	+	1.02703i
$944$	6.49322	−	13.6202i	0.211336	−	0.443298i
$945$	−8.69122	−	7.29280i	−0.282725	−	0.237235i
$946$	9.79312	+	7.21278i	0.318402	+	0.234508i
$947$	27.3102	+	4.81553i	0.887463	+	0.156484i	0.598754	−	0.800933i	$-0.295663\pi$
$947$	27.3102	+	4.81553i	0.887463	+	0.156484i	0.288709	+	0.957417i	$0.406774\pi$
$948$	5.15691	+	4.76607i	0.167489	+	0.154795i
$949$			31.7927i			1.03204i
$950$	3.62952	+	53.0274i	0.117757	+	1.72044i
$951$	−27.5679			−0.893950
$952$	−20.1700	−	11.2341i	−0.653713	−	0.364100i
$953$	−4.18432	+	23.7304i	−0.135543	+	0.768704i	0.838937	+	0.544229i	$0.183178\pi$
$953$	−4.18432	+	23.7304i	−0.135543	+	0.768704i	−0.974480	+	0.224475i	$0.927933\pi$
$954$	−9.71646	+	13.1925i	−0.314582	+	0.427122i
$955$	−55.0051	+	65.5526i	−1.77992	+	2.12123i
$956$	0.640395	+	0.841992i	0.0207119	+	0.0272320i
$957$	−22.9480	+	13.2491i	−0.741805	+	0.428281i
$958$	−22.5835	−	6.63478i	−0.729640	−	0.214360i
$959$	43.9263	+	15.9879i	1.41845	+	0.516275i
$960$	13.9680	−	26.0139i	0.450814	−	0.839596i
$961$	7.72080	−	13.3728i	0.249058	−	0.431381i
$962$	24.1030	−	22.9753i	0.777111	−	0.740752i
$963$	−1.03878	+	0.183165i	−0.0334742	+	0.00590241i
$964$	2.82245	+	0.638366i	0.0909051	+	0.0205604i
$965$	−22.9166	−	27.3109i	−0.737712	−	0.879170i
$966$	−1.16413	−	18.3612i	−0.0374553	−	0.590760i
$967$	−21.2195	+	7.72326i	−0.682372	+	0.248363i	−0.659866	−	0.751383i	$-0.729387\pi$
$967$	−21.2195	+	7.72326i	−0.682372	+	0.248363i	−0.0225065	+	0.999747i	$0.507165\pi$
$968$	−1.81529	−	2.09686i	−0.0583457	−	0.0673956i
$969$	−5.73691	+	10.0529i	−0.184296	+	0.322945i
$970$	48.6026	−	11.7832i	1.56053	−	0.378334i
$971$	−13.7047	−	37.6535i	−0.439806	−	1.20836i	−0.939619	−	0.342223i	$-0.888820\pi$
$971$	−13.7047	−	37.6535i	−0.439806	−	1.20836i	0.499813	−	0.866134i	$-0.333402\pi$
$972$	1.90998	−	0.593270i	0.0612627	−	0.0190291i
$973$	−29.3834	−	35.0178i	−0.941990	−	1.12262i
$974$	−19.4523	+	39.2343i	−0.623293	+	1.25715i
$975$	−5.91772	−	33.5611i	−0.189519	−	1.07481i
$976$	5.55458	−	57.8049i	0.177798	−	1.85029i
$977$	−19.4299	+	33.6537i	−0.621619	+	1.07668i	0.367565	+	0.929998i	$0.380191\pi$
$977$	−19.4299	+	33.6537i	−0.621619	+	1.07668i	−0.989184	+	0.146678i	$0.953142\pi$
$978$	1.77964	−	15.9356i	0.0569066	−	0.509566i
$979$	4.29031	−	11.7875i	0.137119	−	0.376731i
$980$	18.0597	+	0.865701i	0.576895	+	0.0276538i
$981$	−2.03753	+	1.17637i	−0.0650533	+	0.0375585i
$982$	5.45508	+	12.4697i	0.174079	+	0.397924i
$983$	−10.9317	−	9.17281i	−0.348668	−	0.292567i	0.451587	−	0.892227i	$-0.350858\pi$
$983$	−10.9317	−	9.17281i	−0.348668	−	0.292567i	−0.800255	+	0.599660i	$0.795303\pi$
$984$	3.85633	−	24.0313i	0.122935	−	0.766090i
$985$	−15.2638	+	86.5651i	−0.486344	+	2.75819i
$986$	−26.1760	+	17.4096i	−0.833614	+	0.554435i
$987$			26.9749i			0.858620i
$988$	−20.9963	−	27.3201i	−0.667981	−	0.869167i
$989$			11.4986i			0.365635i
$990$	9.14980	+	13.7571i	0.290800	+	0.437228i
$991$	8.91672	−	50.5692i	0.283249	−	1.60638i	−0.428225	−	0.903672i	$-0.640861\pi$
$991$	8.91672	−	50.5692i	0.283249	−	1.60638i	0.711474	−	0.702712i	$-0.248028\pi$
$992$	21.2041	−	6.94655i	0.673231	−	0.220553i
$993$	−10.8664	−	9.11797i	−0.344834	−	0.289350i
$994$	−18.1805	+	7.95337i	−0.576651	+	0.252266i
$995$	13.8690	−	8.00728i	0.439677	−	0.253848i
$996$	0.346629	−	7.23115i	0.0109834	−	0.229128i
$997$	7.80462	−	21.4430i	0.247175	−	0.679107i	−0.752612	−	0.658464i	$-0.771206\pi$
$997$	7.80462	−	21.4430i	0.247175	−	0.679107i	0.999787	−	0.0206429i	$-0.00657131\pi$
$998$	−2.47649	−	0.276567i	−0.0783921	−	0.00875457i
$999$	−2.97868	+	5.15923i	−0.0942413	+	0.163231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.157.13	yes	240
8.5	even	2	inner	456.2.bk.a.157.21	yes	240
19.4	even	9	inner	456.2.bk.a.61.21	yes	240
152.61	even	18	inner	456.2.bk.a.61.13	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.61.13	✓	240	152.61	even	18	inner
456.2.bk.a.61.21	yes	240	19.4	even	9	inner
456.2.bk.a.157.13	yes	240	1.1	even	1	trivial
456.2.bk.a.157.21	yes	240	8.5	even	2	inner

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.783185 - 1.17755i) q^{2} +(-0.984808 - 0.173648i) q^{3} +(-0.773242 + 1.84448i) q^{4} +(-2.37243 + 2.82735i) q^{5} +(0.566808 + 1.29566i) q^{6} +(-1.53699 - 2.66215i) q^{7} +(2.77755 - 0.534038i) q^{8} +(0.939693 + 0.342020i) q^{9} +(5.18739 + 0.579311i) q^{10} +(2.74127 + 1.58267i) q^{11} +(1.08178 - 1.68218i) q^{12} +(-3.89235 + 0.686327i) q^{13} +(-1.93106 + 3.89484i) q^{14} +(2.82735 - 2.37243i) q^{15} +(-2.80419 - 2.85245i) q^{16} +(2.49527 - 0.908202i) q^{17} +(-0.333208 - 1.37440i) q^{18} +(2.78504 - 3.35314i) q^{19} +(-3.38052 - 6.56211i) q^{20} +(1.05136 + 2.88860i) q^{21} +(-0.283248 - 4.46751i) q^{22} +(3.24197 - 2.72033i) q^{23} +(-2.82809 + 0.0436073i) q^{24} +(-1.49725 - 8.49132i) q^{25} +(3.85661 + 4.04591i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(6.09873 - 0.776462i) q^{28} +(2.86316 - 7.86646i) q^{29} +(-5.00799 - 1.47129i) q^{30} +(-1.97221 - 3.41596i) q^{31} +(-1.16270 + 5.53608i) q^{32} +(-2.42480 - 2.03465i) q^{33} +(-3.02371 - 2.22701i) q^{34} +(11.1732 + 1.97014i) q^{35} +(-1.35746 + 1.46878i) q^{36} -5.95736i q^{37} +(-6.12969 - 0.653391i) q^{38} +3.95240 q^{39} +(-5.07963 + 9.12008i) q^{40} +(-1.49425 + 8.47431i) q^{41} +(2.57805 - 3.50034i) q^{42} +(-1.74646 + 2.08135i) q^{43} +(-5.03887 + 3.83243i) q^{44} +(-3.19636 + 1.84542i) q^{45} +(-5.74239 - 1.68705i) q^{46} +(8.24602 + 3.00130i) q^{47} +(2.26627 + 3.29606i) q^{48} +(-1.22468 + 2.12121i) q^{49} +(-8.82632 + 8.41336i) q^{50} +(-2.61506 + 0.461106i) q^{51} +(1.74381 - 7.71005i) q^{52} +(-7.44706 - 8.87506i) q^{53} +(0.0894840 + 1.41138i) q^{54} +(-10.9782 + 3.99575i) q^{55} +(-5.69076 - 6.57344i) q^{56} +(-3.32500 + 2.81858i) q^{57} +(-11.5055 + 2.78939i) q^{58} +(1.29016 + 3.54470i) q^{59} +(2.18966 + 7.04944i) q^{60} +(9.33185 + 11.1213i) q^{61} +(-2.47786 + 4.99770i) q^{62} +(-0.533791 - 3.02728i) q^{63} +(7.42961 - 2.96664i) q^{64} +(7.29384 - 12.6333i) q^{65} +(-0.496830 + 4.44882i) q^{66} +(4.61971 - 12.6926i) q^{67} +(-0.254285 + 5.30472i) q^{68} +(-3.66510 + 2.11604i) q^{69} +(-6.43076 - 14.7000i) q^{70} +(3.49678 + 2.93415i) q^{71} +(2.79270 + 0.448148i) q^{72} +(1.39681 - 7.92170i) q^{73} +(-7.01509 + 4.66572i) q^{74} +8.62231i q^{75} +(4.03128 + 7.72973i) q^{76} -9.73022i q^{77} +(-3.09546 - 4.65414i) q^{78} +(-0.609683 + 3.45768i) q^{79} +(14.7176 - 1.16120i) q^{80} +(0.766044 + 0.642788i) q^{81} +(11.1492 - 4.87741i) q^{82} +(3.13478 - 1.80986i) q^{83} +(-6.14091 - 0.294368i) q^{84} +(-3.35203 + 9.20963i) q^{85} +(3.81869 + 0.426459i) q^{86} +(-4.18566 + 7.24977i) q^{87} +(8.45924 + 2.93202i) q^{88} +(-0.688154 - 3.90272i) q^{89} +(4.67642 + 2.31857i) q^{90} +(7.80961 + 9.30713i) q^{91} +(2.51077 + 8.08321i) q^{92} +(1.34907 + 3.70654i) q^{93} +(-2.92398 - 12.0607i) q^{94} +(2.87319 + 15.8294i) q^{95} +(2.10637 - 5.25007i) q^{96} +(9.00340 - 3.27697i) q^{97} +(3.45698 - 0.219179i) q^{98} +(2.03465 + 2.42480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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