LMFDB - Embedded newform 200.2.o.a.109.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,2,Mod(29,200)] 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("200.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.o (of order $10$, degree $4$, 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:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.18
Character	$\chi$	$=$	200.109
Dual form			200.2.o.a.189.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.345564 + 1.37134i) q^{2} +(0.615546 + 1.89446i) q^{3} +(-1.76117 + 0.947775i) q^{4} +(0.987308 + 2.00630i) q^{5} +(-2.38524 + 1.49878i) q^{6} -1.38088i q^{7} +(-1.90832 - 2.08765i) q^{8} +(-0.783019 + 0.568896i) q^{9} +(-2.41014 + 2.04724i) q^{10} +(3.04233 - 4.18740i) q^{11} +(-2.87960 - 2.75306i) q^{12} +(-2.49716 + 1.81429i) q^{13} +(1.89366 - 0.477183i) q^{14} +(-3.19311 + 3.10538i) q^{15} +(2.20344 - 3.33839i) q^{16} +(-3.63061 - 1.17966i) q^{17} +(-1.05074 - 0.877198i) q^{18} +(6.09071 + 1.97899i) q^{19} +(-3.64034 - 2.59768i) q^{20} +(2.61602 - 0.849997i) q^{21} +(6.79369 + 2.72506i) q^{22} +(-0.168832 + 0.232378i) q^{23} +(2.78031 - 4.90029i) q^{24} +(-3.05044 + 3.96166i) q^{25} +(-3.35095 - 2.79751i) q^{26} +(3.27483 + 2.37930i) q^{27} +(1.30877 + 2.43197i) q^{28} +(-8.75018 + 2.84311i) q^{29} +(-5.36197 - 3.30574i) q^{30} +(1.38826 - 4.27263i) q^{31} +(5.33951 + 1.86805i) q^{32} +(9.80555 + 3.18602i) q^{33} +(0.363107 - 5.38647i) q^{34} +(2.77046 - 1.36336i) q^{35} +(0.839843 - 1.74405i) q^{36} +(4.07603 - 2.96141i) q^{37} +(-0.609147 + 9.03633i) q^{38} +(-4.97421 - 3.61398i) q^{39} +(2.30435 - 5.88982i) q^{40} +(3.28522 - 2.38685i) q^{41} +(2.06964 + 3.29374i) q^{42} -7.54302 q^{43} +(-1.38934 + 10.2582i) q^{44} +(-1.91445 - 1.00929i) q^{45} +(-0.377013 - 0.151226i) q^{46} +(0.954360 - 0.310090i) q^{47} +(7.68075 + 2.11940i) q^{48} +5.09317 q^{49} +(-6.48693 - 2.81420i) q^{50} -7.60418i q^{51} +(2.67838 - 5.56202i) q^{52} +(1.02485 + 3.15418i) q^{53} +(-2.13118 + 5.31312i) q^{54} +(11.4049 + 1.96955i) q^{55} +(-2.88280 + 2.63517i) q^{56} +12.7567i q^{57} +(-6.92263 - 11.0170i) q^{58} +(-1.05228 - 1.44834i) q^{59} +(2.68040 - 8.49545i) q^{60} +(-1.30861 + 1.80115i) q^{61} +(6.33899 + 0.427317i) q^{62} +(0.785578 + 1.08126i) q^{63} +(-0.716599 + 7.96784i) q^{64} +(-6.10547 - 3.21877i) q^{65} +(-0.980677 + 14.5478i) q^{66} +(0.552275 - 1.69973i) q^{67} +(7.51218 - 1.36343i) q^{68} +(-0.544154 - 0.176806i) q^{69} +(2.82700 + 3.32812i) q^{70} +(-4.68658 - 14.4238i) q^{71} +(2.68191 + 0.549033i) q^{72} +(6.88021 - 9.46979i) q^{73} +(5.46964 + 4.56628i) q^{74} +(-9.38289 - 3.34035i) q^{75} +(-12.6024 + 2.28728i) q^{76} +(-5.78231 - 4.20109i) q^{77} +(3.23710 - 8.07022i) q^{78} +(-0.381800 - 1.17506i) q^{79} +(8.87327 + 1.12474i) q^{80} +(-3.38894 + 10.4301i) q^{81} +(4.40845 + 3.68036i) q^{82} +(-1.29836 + 3.99593i) q^{83} +(-3.80165 + 3.97639i) q^{84} +(-1.21779 - 8.44877i) q^{85} +(-2.60660 - 10.3441i) q^{86} +(-10.7723 - 14.8268i) q^{87} +(-14.5476 + 1.63960i) q^{88} +(-9.13763 - 6.63888i) q^{89} +(0.722518 - 2.97415i) q^{90} +(2.50532 + 3.44828i) q^{91} +(0.0771007 - 0.569272i) q^{92} +8.94886 q^{93} +(0.755034 + 1.20160i) q^{94} +(2.04297 + 14.1736i) q^{95} +(-0.252228 + 11.2653i) q^{96} +(-4.65397 + 1.51217i) q^{97} +(1.76002 + 6.98448i) q^{98} +5.00958i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28}+ \cdots + 90 q^{98}+O(q^{100}) $ 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.345564	+	1.37134i	0.244351	+	0.969687i
$2$	0.345564	+	1.37134i	0.244351	+	0.969687i
$3$	0.615546	+	1.89446i	0.355386	+	1.09377i	0.955785	+	0.294065i	$0.0950082\pi$
$3$	0.615546	+	1.89446i	0.355386	+	1.09377i	−0.600400	+	0.799700i	$0.704992\pi$
$4$	−1.76117	+	0.947775i	−0.880585	+	0.473888i
$5$	0.987308	+	2.00630i	0.441538	+	0.897243i
$5$	0.987308	+	2.00630i	0.441538	+	0.897243i
$6$	−2.38524	+	1.49878i	−0.973771	+	0.611875i
$7$		−	1.38088i		−	0.521924i	−0.965349	−	0.260962i	$-0.915960\pi$
$7$		−	1.38088i		−	0.521924i	0.965349	−	0.260962i	$-0.0840398\pi$
$8$	−1.90832	−	2.08765i	−0.674694	−	0.738097i
$9$	−0.783019	+	0.568896i	−0.261006	+	0.189632i
$10$	−2.41014	+	2.04724i	−0.762154	+	0.647395i
$11$	3.04233	−	4.18740i	0.917296	−	1.26255i	−0.0473169	−	0.998880i	$-0.515067\pi$
$11$	3.04233	−	4.18740i	0.917296	−	1.26255i	0.964613	−	0.263670i	$-0.0849330\pi$
$12$	−2.87960	−	2.75306i	−0.831269	−	0.794741i
$13$	−2.49716	+	1.81429i	−0.692587	+	0.503194i	−0.877510	−	0.479559i	$-0.840797\pi$
$13$	−2.49716	+	1.81429i	−0.692587	+	0.503194i	0.184923	+	0.982753i	$0.440797\pi$
$14$	1.89366	−	0.477183i	0.506103	−	0.127533i
$15$	−3.19311	+	3.10538i	−0.824457	+	0.801806i
$16$	2.20344	−	3.33839i	0.550861	−	0.834597i
$17$	−3.63061	−	1.17966i	−0.880553	−	0.286109i	−0.166366	−	0.986064i	$-0.553203\pi$
$17$	−3.63061	−	1.17966i	−0.880553	−	0.286109i	−0.714187	+	0.699955i	$0.753203\pi$
$18$	−1.05074	−	0.877198i	−0.247661	−	0.206758i
$19$	6.09071	+	1.97899i	1.39730	+	0.454012i	0.908318	−	0.418280i	$-0.137367\pi$
$19$	6.09071	+	1.97899i	1.39730	+	0.454012i	0.488986	+	0.872292i	$0.337367\pi$
$20$	−3.64034	−	2.59768i	−0.814004	−	0.580859i
$21$	2.61602	−	0.849997i	0.570863	−	0.185484i
$22$	6.79369	+	2.72506i	1.44842	+	0.580985i
$23$	−0.168832	+	0.232378i	−0.0352040	+	0.0484541i	−0.826256	−	0.563295i	$-0.809534\pi$
$23$	−0.168832	+	0.232378i	−0.0352040	+	0.0484541i	0.791052	+	0.611749i	$0.209534\pi$
$24$	2.78031	−	4.90029i	0.567528	−	1.00027i
$25$	−3.05044	+	3.96166i	−0.610089	+	0.792333i
$26$	−3.35095	−	2.79751i	−0.657175	−	0.548637i
$27$	3.27483	+	2.37930i	0.630241	+	0.457897i
$28$	1.30877	+	2.43197i	0.247333	+	0.459599i
$29$	−8.75018	+	2.84311i	−1.62487	+	0.527952i	−0.973084	−	0.230452i	$-0.925979\pi$
$29$	−8.75018	+	2.84311i	−1.62487	+	0.527952i	−0.651785	+	0.758404i	$0.725979\pi$
$30$	−5.36197	−	3.30574i	−0.978957	−	0.603543i
$31$	1.38826	−	4.27263i	0.249339	−	0.767388i	−0.745553	−	0.666446i	$-0.767815\pi$
$31$	1.38826	−	4.27263i	0.249339	−	0.767388i	0.994892	−	0.100941i	$-0.0321855\pi$
$32$	5.33951	+	1.86805i	0.943901	+	0.330228i
$33$	9.80555	+	3.18602i	1.70693	+	0.554614i
$34$	0.363107	−	5.38647i	0.0622723	−	0.923772i
$35$	2.77046	−	1.36336i	0.468293	−	0.230449i
$36$	0.839843	−	1.74405i	0.139974	−	0.290675i
$37$	4.07603	−	2.96141i	0.670095	−	0.486853i	−0.199962	−	0.979804i	$-0.564082\pi$
$37$	4.07603	−	2.96141i	0.670095	−	0.486853i	0.870057	+	0.492951i	$0.164082\pi$
$38$	−0.609147	+	9.03633i	−0.0988166	+	1.46589i
$39$	−4.97421	−	3.61398i	−0.796512	−	0.578700i
$40$	2.30435	−	5.88982i	0.364349	−	0.931262i
$41$	3.28522	−	2.38685i	0.513065	−	0.372764i	−0.300920	−	0.953649i	$-0.597294\pi$
$41$	3.28522	−	2.38685i	0.513065	−	0.372764i	0.813985	+	0.580886i	$0.197294\pi$
$42$	2.06964	+	3.29374i	0.319353	+	0.508235i
$43$	−7.54302			−1.15030			−0.575150	−	0.818048i	$-0.695056\pi$
$43$	−7.54302			−1.15030			−0.575150	+	0.818048i	$0.695056\pi$
$44$	−1.38934	+	10.2582i	−0.209451	+	1.54648i
$45$	−1.91445	−	1.00929i	−0.285390	−	0.150456i
$46$	−0.377013	−	0.151226i	−0.0555875	−	0.0222970i
$47$	0.954360	−	0.310090i	0.139208	−	0.0452313i	−0.238584	−	0.971122i	$-0.576683\pi$
$47$	0.954360	−	0.310090i	0.139208	−	0.0452313i	0.377792	+	0.925890i	$0.376683\pi$
$48$	7.68075	+	2.11940i	1.10862	+	0.305909i
$49$	5.09317			0.727595
$50$	−6.48693	−	2.81420i	−0.917391	−	0.397988i
$51$		−	7.60418i		−	1.06480i
$52$	2.67838	−	5.56202i	0.371425	−	0.771314i
$53$	1.02485	+	3.15418i	0.140775	+	0.433260i	0.996443	−	0.0842641i	$-0.0268539\pi$
$53$	1.02485	+	3.15418i	0.140775	+	0.433260i	−0.855669	+	0.517524i	$0.826854\pi$
$54$	−2.13118	+	5.31312i	−0.290017	+	0.723024i
$55$	11.4049	+	1.96955i	1.53783	+	0.265574i
$56$	−2.88280	+	2.63517i	−0.385231	+	0.352139i
$57$			12.7567i			1.68967i
$58$	−6.92263	−	11.0170i	−0.908986	−	1.44661i
$59$	−1.05228	−	1.44834i	−0.136996	−	0.188558i	0.735007	−	0.678060i	$-0.237179\pi$
$59$	−1.05228	−	1.44834i	−0.136996	−	0.188558i	−0.872003	+	0.489501i	$0.837179\pi$
$60$	2.68040	−	8.49545i	0.346038	−	1.09676i
$61$	−1.30861	+	1.80115i	−0.167550	+	0.230613i	−0.884533	−	0.466478i	$-0.845523\pi$
$61$	−1.30861	+	1.80115i	−0.167550	+	0.230613i	0.716983	+	0.697091i	$0.245523\pi$
$62$	6.33899	+	0.427317i	0.805052	+	0.0542693i
$63$	0.785578	+	1.08126i	0.0989736	+	0.136225i
$64$	−0.716599	+	7.96784i	−0.0895748	+	0.995980i
$65$	−6.10547	−	3.21877i	−0.757290	−	0.399239i
$66$	−0.980677	+	14.5478i	−0.120713	+	1.79071i
$67$	0.552275	−	1.69973i	0.0674711	−	0.207655i	−0.911637	−	0.410997i	$-0.865181\pi$
$67$	0.552275	−	1.69973i	0.0674711	−	0.207655i	0.979108	+	0.203343i	$0.0651805\pi$
$68$	7.51218	−	1.36343i	0.910986	−	0.165340i
$69$	−0.544154	−	0.176806i	−0.0655085	−	0.0212850i
$70$	2.82700	+	3.32812i	0.337891	+	0.397787i
$71$	−4.68658	−	14.4238i	−0.556194	−	1.71179i	−0.692768	−	0.721161i	$-0.743609\pi$
$71$	−4.68658	−	14.4238i	−0.556194	−	1.71179i	0.136574	−	0.990630i	$-0.456391\pi$
$72$	2.68191	+	0.549033i	0.316066	+	0.0647042i
$73$	6.88021	−	9.46979i	0.805267	−	1.10836i	−0.186769	−	0.982404i	$-0.559802\pi$
$73$	6.88021	−	9.46979i	0.805267	−	1.10836i	0.992036	−	0.125951i	$-0.0401983\pi$
$74$	5.46964	+	4.56628i	0.635833	+	0.530820i
$75$	−9.38289	−	3.34035i	−1.08344	−	0.385710i
$76$	−12.6024	+	2.28728i	−1.44560	+	0.262369i
$77$	−5.78231	−	4.20109i	−0.658955	−	0.478759i
$78$	3.23710	−	8.07022i	0.366529	−	0.913773i
$79$	−0.381800	−	1.17506i	−0.0429559	−	0.132205i	0.927279	−	0.374372i	$-0.122142\pi$
$79$	−0.381800	−	1.17506i	−0.0429559	−	0.132205i	−0.970234	+	0.242167i	$0.922142\pi$
$80$	8.87327	+	1.12474i	0.992062	+	0.125750i
$81$	−3.38894	+	10.4301i	−0.376549	+	1.15890i
$82$	4.40845	+	3.68036i	0.486832	+	0.406428i
$83$	−1.29836	+	3.99593i	−0.142513	+	0.438610i	−0.996683	−	0.0813841i	$-0.974066\pi$
$83$	−1.29836	+	3.99593i	−0.142513	+	0.438610i	0.854170	+	0.519994i	$0.174066\pi$
$84$	−3.80165	+	3.97639i	−0.414794	+	0.433860i
$85$	−1.21779	−	8.44877i	−0.132088	−	0.916398i
$86$	−2.60660	−	10.3441i	−0.281077	−	1.11543i
$87$	−10.7723	−	14.8268i	−1.15491	−	1.58960i
$88$	−14.5476	+	1.63960i	−1.55078	+	0.174782i
$89$	−9.13763	−	6.63888i	−0.968587	−	0.703720i	−0.0134580	−	0.999909i	$-0.504284\pi$
$89$	−9.13763	−	6.63888i	−0.968587	−	0.703720i	−0.955129	+	0.296190i	$0.904284\pi$
$90$	0.722518	−	2.97415i	0.0761601	−	0.313503i
$91$	2.50532	+	3.44828i	0.262629	+	0.361478i
$92$	0.0771007	−	0.569272i	0.00803830	−	0.0593508i
$93$	8.94886			0.927954
$94$	0.755034	+	1.20160i	0.0778758	+	0.123936i
$95$	2.04297	+	14.1736i	0.209604	+	1.45418i
$96$	−0.252228	+	11.2653i	−0.0257429	+	1.14976i
$97$	−4.65397	+	1.51217i	−0.472539	+	0.153537i	−0.535599	−	0.844473i	$-0.679914\pi$
$97$	−4.65397	+	1.51217i	−0.472539	+	0.153537i	0.0630600	+	0.998010i	$0.479914\pi$
$98$	1.76002	+	6.98448i	0.177788	+	0.705539i
$99$			5.00958i			0.503482i
$100$	1.61758	−	9.86830i	0.161758	−	0.986830i
$101$			16.5698i			1.64876i	0.566039	+	0.824378i	$0.308475\pi$
$101$			16.5698i			1.64876i	−0.566039	+	0.824378i	$0.691525\pi$
$102$	10.4279	−	2.62773i	1.03252	−	0.260184i
$103$	−3.86872	+	1.25702i	−0.381196	+	0.123858i	−0.493346	−	0.869833i	$-0.664226\pi$
$103$	−3.86872	+	1.25702i	−0.381196	+	0.123858i	0.112150	+	0.993691i	$0.464226\pi$
$104$	8.55300	+	1.75095i	0.838691	+	0.171694i
$105$	4.28816	+	4.40930i	0.418482	+	0.430304i
$106$	−3.97131	+	2.49540i	−0.385728	+	0.242375i
$107$	−13.5206			−1.30709			−0.653545	−	0.756888i	$-0.726719\pi$
$107$	−13.5206			−1.30709			−0.653545	+	0.756888i	$0.726719\pi$
$108$	−8.02258	−	1.08656i	−0.771973	−	0.104554i
$109$	−5.89818	−	8.11815i	−0.564944	−	0.777578i	0.427001	−	0.904251i	$-0.359570\pi$
$109$	−5.89818	−	8.11815i	−0.564944	−	0.777578i	−0.991945	+	0.126673i	$0.959570\pi$
$110$	1.24019	+	16.3206i	0.118248	+	1.55611i
$111$	8.11925	+	5.89898i	0.770645	+	0.559906i
$112$	−4.60992	−	3.04270i	−0.435596	−	0.287508i
$113$	5.59149	+	7.69603i	0.526004	+	0.723982i	0.986515	−	0.163672i	$-0.0523339\pi$
$113$	5.59149	+	7.69603i	0.526004	+	0.723982i	−0.460511	+	0.887654i	$0.652334\pi$
$114$	−17.4939	+	4.40828i	−1.63845	+	0.412873i
$115$	−0.632909	−	0.109299i	−0.0590190	−	0.0101922i
$116$	12.7159	−	13.3004i	1.18065	−	1.23491i
$117$	0.923177	−	2.84125i	0.0853478	−	0.262673i
$118$	1.62255	−	1.94354i	0.149367	−	0.178917i
$119$	−1.62897	+	5.01345i	−0.149327	+	0.459582i
$120$	12.5764	+	0.740028i	1.14807	+	0.0675550i
$121$	−4.87941	−	15.0173i	−0.443583	−	1.36521i
$122$	−2.92220	−	1.17214i	−0.264564	−	0.106121i
$123$	6.54400	+	4.75449i	0.590052	+	0.428698i
$124$	1.60453	+	8.84060i	0.144091	+	0.793909i
$125$	−10.9600	−	2.20871i	−0.980292	−	0.197553i
$126$	−1.21131	+	1.45094i	−0.107912	+	0.129260i
$127$	−4.92287	+	6.77575i	−0.436834	+	0.601251i	−0.969505	−	0.245072i	$-0.921188\pi$
$127$	−4.92287	+	6.77575i	−0.436834	+	0.601251i	0.532671	+	0.846323i	$0.321188\pi$
$128$	−11.1743	+	1.77070i	−0.987677	+	0.156509i
$129$	−4.64308	−	14.2899i	−0.408800	−	1.25816i
$130$	2.30421	−	9.48499i	0.202093	−	0.831889i
$131$	−8.61583	−	2.79945i	−0.752769	−	0.244589i	−0.0925967	−	0.995704i	$-0.529517\pi$
$131$	−8.61583	−	2.79945i	−0.752769	−	0.244589i	−0.660172	+	0.751114i	$0.729517\pi$
$132$	−20.2889	+	3.68234i	−1.76592	+	0.320507i
$133$	2.73275	−	8.41055i	0.236960	−	0.729287i
$134$	2.52176	+	0.169994i	0.217847	+	0.0146852i
$135$	−1.54032	+	8.91938i	−0.132570	+	0.767658i
$136$	4.46567	+	9.83064i	0.382928	+	0.842970i
$137$	−0.409034	−	0.562988i	−0.0349462	−	0.0480993i	0.791186	−	0.611575i	$-0.209464\pi$
$137$	−0.409034	−	0.562988i	−0.0349462	−	0.0480993i	−0.826133	+	0.563476i	$0.809464\pi$
$138$	0.0544222	−	0.807321i	0.00463273	−	0.0687237i
$139$	6.25490	−	8.60913i	0.530533	−	0.730217i	−0.456678	−	0.889632i	$-0.650961\pi$
$139$	6.25490	−	8.60913i	0.530533	−	0.730217i	0.987212	+	0.159415i	$0.0509609\pi$
$140$	−3.58709	+	5.02687i	−0.303165	+	0.424848i
$141$	1.17491	+	1.61712i	0.0989449	+	0.136186i
$142$	18.1605	−	11.4113i	1.52399	−	0.957612i
$143$			15.9763i			1.33600i
$144$	0.173859	+	3.86755i	0.0144883	+	0.322296i
$145$	−14.3432	−	14.7484i	−1.19114	−	1.22479i
$146$	15.3639	+	6.16271i	1.27153	+	0.510029i
$147$	3.13508	+	9.64878i	0.258577	+	0.795818i
$148$	−4.37183	+	9.07871i	−0.359363	+	0.746265i
$149$		−	3.22211i		−	0.263966i	−0.991252	−	0.131983i	$-0.957866\pi$
$149$		−	3.22211i		−	0.263966i	0.991252	−	0.131983i	$-0.0421344\pi$
$150$	1.33837	−	14.0215i	0.109278	−	1.14485i
$151$	20.1976			1.64366			0.821828	−	0.569736i	$-0.192955\pi$
$151$	20.1976			1.64366			0.821828	+	0.569736i	$0.192955\pi$
$152$	−7.49160	−	16.4918i	−0.607649	−	1.33767i
$153$	3.51394	−	1.14175i	0.284085	−	0.0923049i
$154$	3.76299	−	9.38129i	0.303230	−	0.755966i
$155$	9.94281	−	1.43314i	0.798626	−	0.115113i
$156$	12.1857	+	1.65039i	0.975635	+	0.132137i
$157$	21.3717			1.70565			0.852824	−	0.522198i	$-0.174888\pi$
$157$	21.3717			1.70565			0.852824	+	0.522198i	$0.174888\pi$
$158$	1.47948	−	0.929638i	0.117701	−	0.0739581i
$159$	−5.34461	+	3.88309i	−0.423855	+	0.307949i
$160$	1.52388	+	12.5570i	0.120473	+	0.992717i
$161$	0.320886	+	0.233138i	0.0252894	+	0.0183738i
$162$	−15.4743	−	1.04314i	−1.21578	−	0.0819566i
$163$	10.2617	−	7.45556i	0.803759	−	0.583965i	−0.108256	−	0.994123i	$-0.534527\pi$
$163$	10.2617	−	7.45556i	0.803759	−	0.583965i	0.912014	+	0.410158i	$0.134527\pi$
$164$	−3.52363	+	7.31731i	−0.275150	+	0.571386i
$165$	3.28901	+	22.8184i	0.256049	+	1.77641i
$166$	−5.92846	−	0.399643i	−0.460138	−	0.0310183i
$167$	8.75032	+	2.84315i	0.677120	+	0.220010i	0.627334	−	0.778750i	$-0.284146\pi$
$167$	8.75032	+	2.84315i	0.677120	+	0.220010i	0.0497860	+	0.998760i	$0.484146\pi$
$168$	−6.76671	−	3.83928i	−0.522063	−	0.296207i
$169$	−1.07308	+	3.30259i	−0.0825444	+	0.254045i
$170$	11.1654	−	4.58961i	0.856343	−	0.352007i
$171$	−5.89498	+	1.91539i	−0.450800	+	0.146474i
$172$	13.2845	−	7.14909i	1.01294	−	0.545113i
$173$	−15.7758	−	11.4618i	−1.19941	−	0.871423i	−0.205184	−	0.978723i	$-0.565779\pi$
$173$	−15.7758	−	11.4618i	−1.19941	−	0.871423i	−0.994227	+	0.107301i	$0.965779\pi$
$174$	16.6101	−	19.8961i	1.25921	−	1.50832i
$175$	5.47059	+	4.21230i	0.413538	+	0.318420i
$176$	−7.27558	−	19.3832i	−0.548418	−	1.46106i
$177$	2.09609	−	2.88503i	0.157552	−	0.216852i
$178$	5.94655	−	14.8250i	0.445713	−	1.11118i
$179$	−3.15544	+	1.02527i	−0.235849	+	0.0766320i	−0.424557	−	0.905401i	$-0.639570\pi$
$179$	−3.15544	+	1.02527i	−0.235849	+	0.0766320i	0.188708	+	0.982033i	$0.439570\pi$
$180$	4.32826	−	0.0369401i	0.322610	−	0.00275335i
$181$	4.68953	+	1.52372i	0.348570	+	0.113257i	0.478069	−	0.878322i	$-0.341337\pi$
$181$	4.68953	+	1.52372i	0.348570	+	0.113257i	−0.129499	+	0.991580i	$0.541337\pi$
$182$	−3.86303	+	4.62726i	−0.286347	+	0.342995i
$183$	−4.21771	−	1.37042i	−0.311782	−	0.101304i
$184$	0.807312	−	0.0909887i	0.0595158	−	0.00670777i
$185$	9.96576	+	5.25390i	0.732697	+	0.386274i
$186$	3.09241	+	12.2720i	0.226746	+	0.899825i
$187$	−15.9852	+	11.6139i	−1.16896	+	0.849296i
$188$	−1.38690	+	1.45064i	−0.101150	+	0.105799i
$189$	3.28554	−	4.52215i	0.238988	−	0.328938i
$190$	−18.7310	+	7.69951i	−1.35889	+	0.558581i
$191$	−0.543712	+	0.395030i	−0.0393416	+	0.0285833i	−0.607282	−	0.794486i	$-0.707740\pi$
$191$	−0.543712	+	0.395030i	−0.0393416	+	0.0285833i	0.567941	+	0.823069i	$0.307740\pi$
$192$	−15.5358	+	3.54701i	−1.12120	+	0.255983i
$193$			4.75497i			0.342270i	0.985248	+	0.171135i	$0.0547434\pi$
$193$			4.75497i			0.342270i	−0.985248	+	0.171135i	$0.945257\pi$
$194$	−3.68194	−	5.85964i	−0.264348	−	0.420698i
$195$	2.33962	−	13.5479i	0.167544	−	0.970182i
$196$	−8.96993	+	4.82718i	−0.640710	+	0.344798i
$197$	1.73569	+	5.34192i	0.123663	+	0.380596i	0.993655	−	0.112470i	$-0.0358762\pi$
$197$	1.73569	+	5.34192i	0.123663	+	0.380596i	−0.869992	+	0.493066i	$0.835876\pi$
$198$	−6.86986	+	1.73113i	−0.488220	+	0.123026i
$199$	3.56353			0.252612			0.126306	−	0.991991i	$-0.459688\pi$
$199$	3.56353			0.252612			0.126306	+	0.991991i	$0.459688\pi$
$200$	14.0918	−	1.19187i	0.996442	−	0.0842778i
$201$	3.56001			0.251104
$202$	−22.7229	+	5.72593i	−1.59878	+	0.402875i
$203$	3.92599	+	12.0830i	0.275551	+	0.848058i
$204$	7.20705	+	13.3923i	0.504595	+	0.937645i
$205$	8.03226	+	4.23457i	0.560997	+	0.295755i
$206$	−3.06070	−	4.87096i	−0.213249	−	0.339376i
$207$		−	0.278004i		−	0.0193226i
$208$	0.554462	+	12.3342i	0.0384450	+	0.855221i
$209$	26.8168	−	19.4835i	1.85495	−	1.34770i
$210$	−4.56484	+	7.40425i	−0.315004	+	0.510942i
$211$	−16.5725	+	22.8101i	−1.14090	+	1.57031i	−0.375411	+	0.926859i	$0.622498\pi$
$211$	−16.5725	+	22.8101i	−1.14090	+	1.57031i	−0.765487	+	0.643452i	$0.777502\pi$
$212$	−4.79440	−	4.58371i	−0.329280	−	0.314811i
$213$	24.4405	−	17.7570i	1.67463	−	1.21669i
$214$	−4.67225	−	18.5415i	−0.319389	−	1.26747i
$215$	−7.44728	−	15.1335i	−0.507901	−	1.03210i
$216$	−1.28227	−	11.3772i	−0.0872478	−	0.774120i
$217$	−5.90000	−	1.91703i	−0.400518	−	0.130136i
$218$	9.09458	−	10.8938i	0.615963	−	0.737820i
$219$	22.1752	+	7.20516i	1.49846	+	0.486879i
$220$	−21.9526	+	7.34056i	−1.48005	+	0.494900i
$221$	11.2065	−	3.64120i	0.753828	−	0.244934i
$222$	−5.28381	+	13.1728i	−0.354626	+	0.884098i
$223$	9.72513	−	13.3855i	0.651243	−	0.896359i	−0.347909	−	0.937528i	$-0.613108\pi$
$223$	9.72513	−	13.3855i	0.651243	−	0.896359i	0.999152	+	0.0411689i	$0.0131082\pi$
$224$	2.57956	−	7.37323i	0.172354	−	0.492645i
$225$	0.134778	−	4.83744i	0.00898521	−	0.322496i
$226$	−8.62169	+	10.3273i	−0.573506	+	0.686964i
$227$	−9.97209	−	7.24515i	−0.661871	−	0.480878i	0.205423	−	0.978673i	$-0.434143\pi$
$227$	−9.97209	−	7.24515i	−0.661871	−	0.480878i	−0.867294	+	0.497796i	$0.834143\pi$
$228$	−12.0905	−	22.4668i	−0.800715	−	1.48790i
$229$	10.7797	−	3.50252i	0.712340	−	0.231453i	0.0696410	−	0.997572i	$-0.477815\pi$
$229$	10.7797	−	3.50252i	0.712340	−	0.231453i	0.642699	+	0.766119i	$0.277815\pi$
$230$	−0.0688239	−	0.905705i	−0.00453811	−	0.0597204i
$231$	4.39951	−	13.5403i	0.289467	−	0.890887i
$232$	22.6336	+	12.8418i	1.48597	+	0.843105i
$233$	−6.12514	−	1.99018i	−0.401271	−	0.130381i	0.101427	−	0.994843i	$-0.467659\pi$
$233$	−6.12514	−	1.99018i	−0.401271	−	0.130381i	−0.502698	+	0.864462i	$0.667659\pi$
$234$	4.21535	+	0.284160i	0.275566	+	0.0185761i
$235$	1.56438	+	1.60857i	0.102049	+	0.104932i
$236$	3.22595	+	1.55345i	0.209992	+	0.101121i
$237$	1.99109	−	1.44661i	0.129335	−	0.0939673i
$238$	−7.43808	−	0.501407i	−0.482139	−	0.0325014i
$239$	1.70418	+	1.23816i	0.110234	+	0.0800897i	0.641537	−	0.767092i	$-0.278297\pi$
$239$	1.70418	+	1.23816i	0.110234	+	0.0800897i	−0.531303	+	0.847182i	$0.678297\pi$
$240$	3.33114	+	17.5024i	0.215024	+	1.12977i
$241$	−17.2054	+	12.5005i	−1.10830	+	0.805227i	−0.982395	−	0.186816i	$-0.940183\pi$
$241$	−17.2054	+	12.5005i	−1.10830	+	0.805227i	−0.125904	+	0.992042i	$0.540183\pi$
$242$	18.9077	−	11.8808i	1.21543	−	0.763726i
$243$	−9.70164			−0.622360
$244$	0.597603	−	4.41240i	0.0382576	−	0.282475i
$245$	5.02853	+	10.2184i	0.321261	+	0.652829i
$246$	−4.25867	+	10.6171i	−0.271523	+	0.676919i
$247$	−18.7999	+	6.10847i	−1.19621	+	0.388672i
$248$	−11.5690	+	5.25536i	−0.734635	+	0.333716i
$249$	−8.36931			−0.530384
$250$	−0.758485	−	15.7932i	−0.0479708	−	0.998849i
$251$		−	17.4979i		−	1.10446i	−0.833693	−	0.552229i	$-0.813778\pi$
$251$		−	17.4979i		−	1.10446i	0.833693	−	0.552229i	$-0.186222\pi$
$252$	−2.40833	−	1.15972i	−0.151710	−	0.0730558i
$253$	0.459417	+	1.41394i	0.0288833	+	0.0888936i
$254$	−10.9931	−	4.40949i	−0.689766	−	0.276676i
$255$	15.2562	−	7.50767i	0.955382	−	0.470148i
$256$	−6.28967	−	14.7119i	−0.393104	−	0.919494i
$257$			28.7486i			1.79329i	0.442753	+	0.896644i	$0.354002\pi$
$257$			28.7486i			1.79329i	−0.442753	+	0.896644i	$0.645998\pi$
$258$	17.9919	−	11.3053i	1.12013	−	0.703840i
$259$	−4.08936	−	5.62852i	−0.254100	−	0.349739i
$260$	13.8034	−	0.117807i	0.856053	−	0.00730610i
$261$	5.23412	−	7.20415i	0.323984	−	0.445926i
$262$	0.861691	−	12.7827i	0.0532354	−	0.789716i
$263$	−12.3479	−	16.9955i	−0.761407	−	1.04799i	−0.997096	−	0.0761580i	$-0.975735\pi$
$263$	−12.3479	−	16.9955i	−0.761407	−	1.04799i	0.235689	−	0.971829i	$-0.424265\pi$
$264$	−12.0609	−	26.5505i	−0.742295	−	1.63407i
$265$	−5.31637	+	5.17031i	−0.326582	+	0.317609i
$266$	12.4781	+	0.841160i	0.765081	+	0.0515748i
$267$	6.95243	−	21.3974i	0.425482	−	1.30950i
$268$	0.638309	+	3.51694i	0.0389910	+	0.214831i
$269$	15.0792	+	4.89953i	0.919396	+	0.298730i	0.730219	−	0.683213i	$-0.239418\pi$
$269$	15.0792	+	4.89953i	0.919396	+	0.298730i	0.189177	+	0.981943i	$0.439418\pi$
$270$	−12.7638	+	0.969913i	−0.776782	+	0.0590270i
$271$	9.17886	+	28.2496i	0.557576	+	1.71604i	0.689041	+	0.724722i	$0.258032\pi$
$271$	9.17886	+	28.2496i	0.557576	+	1.71604i	−0.131465	+	0.991321i	$0.541968\pi$
$272$	−11.9380	+	9.52109i	−0.723848	+	0.577301i
$273$	−4.99048	+	6.86880i	−0.302037	+	0.415719i
$274$	0.630702	−	0.755475i	0.0381021	−	0.0456399i
$275$	7.30864	+	24.8261i	0.440728	+	1.49707i
$276$	1.12592	−	0.204350i	0.0677725	−	0.0123004i
$277$	−0.881062	−	0.640129i	−0.0529379	−	0.0384616i	0.561002	−	0.827815i	$-0.310416\pi$
$277$	−0.881062	−	0.640129i	−0.0529379	−	0.0384616i	−0.613940	+	0.789353i	$0.710416\pi$
$278$	13.9675	+	5.60261i	0.837718	+	0.336022i
$279$	1.34365	+	4.13533i	0.0804422	+	0.247576i
$280$	−8.13315	−	3.18203i	−0.486048	−	0.190163i
$281$	−7.85909	+	24.1878i	−0.468834	+	1.44292i	0.385261	+	0.922808i	$0.374111\pi$
$281$	−7.85909	+	24.1878i	−0.468834	+	1.44292i	−0.854096	+	0.520116i	$0.825889\pi$
$282$	−1.81162	+	2.17002i	−0.107881	+	0.129223i
$283$	−7.75392	+	23.8641i	−0.460923	+	1.41857i	0.403116	+	0.915149i	$0.367927\pi$
$283$	−7.75392	+	23.8641i	−0.460923	+	1.41857i	−0.864039	+	0.503425i	$0.832073\pi$
$284$	21.9244	+	20.9610i	1.30097	+	1.24380i
$285$	−25.5938	+	12.5948i	−1.51605	+	0.746054i
$286$	−21.9090	+	5.52083i	−1.29550	+	0.326454i
$287$	−3.29596	−	4.53650i	−0.194554	−	0.267781i
$288$	−5.24366	+	1.57491i	−0.308986	+	0.0928024i
$289$	−1.96352	−	1.42658i	−0.115501	−	0.0839166i
$290$	15.2687	−	24.7661i	0.896607	−	1.45431i
$291$	−5.72946	−	7.88593i	−0.335867	−	0.462281i
$292$	−3.14198	+	23.1988i	−0.183871	+	1.35761i
$293$	−31.6461			−1.84879			−0.924393	−	0.381440i	$-0.875428\pi$
$293$	−31.6461			−1.84879			−0.924393	+	0.381440i	$0.875428\pi$
$294$	−12.1484	+	7.63355i	−0.708511	+	0.445198i
$295$	1.86688	−	3.54115i	0.108694	−	0.206174i
$296$	−13.9608	−	2.85801i	−0.811454	−	0.166119i
$297$	19.9262	−	6.47442i	1.15624	−	0.375684i
$298$	4.41863	−	1.11345i	0.255964	−	0.0645003i
$299$		−	0.886596i		−	0.0512731i
$300$	19.6908	−	3.00995i	1.13685	−	0.173780i
$301$			10.4160i			0.600369i
$302$	6.97956	+	27.6978i	0.401629	+	1.59383i
$303$	−31.3908	+	10.1995i	−1.80335	+	0.585945i
$304$	20.0272	−	15.9726i	1.14864	−	0.916089i
$305$	−4.90564	−	0.847171i	−0.280896	−	0.0485089i
$306$	2.78002	+	4.42428i	0.158923	+	0.252919i
$307$	3.74062			0.213488			0.106744	−	0.994287i	$-0.465957\pi$
$307$	3.74062			0.213488			0.106744	+	0.994287i	$0.465957\pi$
$308$	14.1653	+	1.91851i	0.807144	+	0.109317i
$309$	−4.76275	−	6.55536i	−0.270943	−	0.372921i
$310$	5.40121	+	13.1398i	0.306768	+	0.746289i
$311$	−9.08998	−	6.60426i	−0.515446	−	0.374493i	0.299440	−	0.954115i	$-0.403200\pi$
$311$	−9.08998	−	6.60426i	−0.515446	−	0.374493i	−0.814885	+	0.579622i	$0.803200\pi$
$312$	1.94768	+	17.2811i	0.110265	+	0.978348i
$313$	−3.87093	−	5.32787i	−0.218798	−	0.301149i	0.685482	−	0.728089i	$-0.259591\pi$
$313$	−3.87093	−	5.32787i	−0.218798	−	0.301149i	−0.904280	+	0.426940i	$0.859591\pi$
$314$	7.38530	+	29.3080i	0.416777	+	1.65394i
$315$	−1.39371	+	2.64364i	−0.0785267	+	0.148952i
$316$	1.78611	+	1.70762i	0.100476	+	0.0960612i
$317$	−6.24885	+	19.2320i	−0.350970	+	1.08018i	0.607339	+	0.794443i	$0.292237\pi$
$317$	−6.24885	+	19.2320i	−0.350970	+	1.08018i	−0.958309	+	0.285733i	$0.907763\pi$
$318$	−7.17195	−	5.98744i	−0.402183	−	0.335759i
$319$	−14.7157	+	45.2902i	−0.823920	+	2.53577i
$320$	−16.6933	+	6.42901i	−0.933187	+	0.359392i
$321$	−8.32258	−	25.6143i	−0.464521	−	1.42965i
$322$	−0.208825	+	0.520610i	−0.0116374	+	0.0290125i
$323$	−19.7785	−	14.3699i	−1.10050	−	0.799563i
$324$	−3.91687	−	21.5811i	−0.217604	−	1.19895i
$325$	0.429827	−	15.4273i	0.0238425	−	0.855752i
$326$	13.7702	+	11.4960i	0.762662	+	0.636702i
$327$	11.7489	−	16.1710i	0.649715	−	0.894256i
$328$	−11.2522	−	2.30352i	−0.621298	−	0.127190i
$329$	−0.428198	−	1.31786i	−0.0236073	−	0.0726559i
$330$	−30.1553	+	12.3956i	−1.66000	+	0.682355i
$331$	20.2986	+	6.59541i	1.11571	+	0.362517i	0.808129	−	0.589005i	$-0.200480\pi$
$331$	20.2986	+	6.59541i	1.11571	+	0.362517i	0.307582	+	0.951522i	$0.400480\pi$
$332$	−1.50062	−	8.26806i	−0.0823570	−	0.453769i
$333$	−1.50687	+	4.63768i	−0.0825761	+	0.254143i
$334$	−0.875141	+	12.9822i	−0.0478856	+	0.710354i
$335$	3.95542	−	0.570128i	0.216108	−	0.0311494i
$336$	2.92664	−	10.6062i	0.159661	−	0.578616i
$337$	9.78712	+	13.4708i	0.533139	+	0.733802i	0.987605	−	0.156962i	$-0.0501700\pi$
$337$	9.78712	+	13.4708i	0.533139	+	0.733802i	−0.454466	+	0.890764i	$0.650170\pi$
$338$	−4.89981	−	0.330300i	−0.266514	−	0.0179660i
$339$	−11.1380	+	15.3301i	−0.604932	+	0.832617i
$340$	10.1523	+	13.7255i	0.550585	+	0.744372i
$341$	−13.6677	−	18.8120i	−0.740147	−	1.01873i
$342$	−4.66376	−	7.42215i	−0.252187	−	0.401344i
$343$		−	16.6992i		−	0.901674i
$344$	14.3945	+	15.7472i	0.776101	+	0.849033i
$345$	−0.182522	−	1.26630i	−0.00982666	−	0.0681751i
$346$	10.2665	−	25.5948i	0.551930	−	1.37599i
$347$	−4.90149	−	15.0852i	−0.263126	−	0.809818i	−0.992119	−	0.125297i	$-0.960012\pi$
$347$	−4.90149	−	15.0852i	−0.263126	−	0.809818i	0.728993	−	0.684521i	$-0.239988\pi$
$348$	33.0243	+	15.9028i	1.77029	+	0.852479i
$349$			11.9445i			0.639375i	0.947523	+	0.319688i	$0.103578\pi$
$349$			11.9445i			0.639375i	−0.947523	+	0.319688i	$0.896422\pi$
$350$	−3.88608	+	8.95768i	−0.207720	+	0.478808i
$351$	−12.4945			−0.666908
$352$	24.0668	−	16.6755i	1.28277	−	0.888805i
$353$	4.78471	−	1.55465i	0.254665	−	0.0827456i	−0.178903	−	0.983867i	$-0.557255\pi$
$353$	4.78471	−	1.55465i	0.254665	−	0.0827456i	0.433567	+	0.901121i	$0.357255\pi$
$354$	4.68070	+	1.87751i	0.248776	+	0.0997883i
$355$	24.3113	−	23.6434i	1.29031	−	1.25486i
$356$	22.3851	+	3.03178i	1.18641	+	0.160684i
$357$	−10.5005			−0.555744
$358$	−2.49640	−	3.97291i	−0.131939	−	0.209975i
$359$	4.41690	−	3.20906i	0.233115	−	0.169368i	−0.465096	−	0.885260i	$-0.653980\pi$
$359$	4.41690	−	3.20906i	0.233115	−	0.169368i	0.698210	+	0.715893i	$0.253980\pi$
$360$	1.54635	+	5.92277i	0.0814998	+	0.312158i
$361$	17.8090	+	12.9390i	0.937315	+	0.681000i
$362$	−0.469011	+	6.95750i	−0.0246507	+	0.365678i
$363$	25.4461	−	18.4877i	1.33557	−	0.970351i
$364$	−7.68049	−	3.69853i	−0.402567	−	0.193855i
$365$	25.7921	+	4.45412i	1.35002	+	0.233139i
$366$	0.421823	−	6.25749i	0.0220491	−	0.327084i
$367$	14.3846	+	4.67384i	0.750871	+	0.243973i	0.659356	−	0.751831i	$-0.270829\pi$
$367$	14.3846	+	4.67384i	0.750871	+	0.243973i	0.0915149	+	0.995804i	$0.470829\pi$
$368$	0.403755	+	1.07566i	0.0210472	+	0.0560727i
$369$	−1.21452	+	3.73790i	−0.0632253	+	0.194587i
$370$	−3.76109	+	15.4821i	−0.195530	+	0.804874i
$371$	4.35555	−	1.41520i	0.226129	−	0.0734737i
$372$	−15.7605	+	8.48151i	−0.817142	+	0.439746i
$373$	−26.1912	−	19.0290i	−1.35613	−	0.985284i	−0.998681	−	0.0513509i	$-0.983647\pi$
$373$	−26.1912	−	19.0290i	−1.35613	−	0.985284i	−0.357447	−	0.933933i	$-0.616353\pi$
$374$	−21.4506	−	17.9079i	−1.10919	−	0.925994i
$375$	−2.56209	−	22.1228i	−0.132306	−	1.14242i
$376$	−2.46859	−	1.40062i	−0.127308	−	0.0722315i
$377$	16.6924	−	22.9751i	0.859701	−	1.18328i
$378$	7.33679	+	2.94291i	0.377364	+	0.151367i
$379$	−12.3752	+	4.02096i	−0.635674	+	0.206543i	−0.609087	−	0.793104i	$-0.708464\pi$
$379$	−12.3752	+	4.02096i	−0.635674	+	0.206543i	−0.0265869	+	0.999647i	$0.508464\pi$
$380$	−17.0314	−	23.0259i	−0.873694	−	1.18120i
$381$	−15.8666	−	5.15538i	−0.812872	−	0.264118i
$382$	−0.729609	−	0.609108i	−0.0373300	−	0.0311647i
$383$	13.4131	+	4.35817i	0.685376	+	0.222692i	0.630948	−	0.775825i	$-0.282666\pi$
$383$	13.4131	+	4.35817i	0.685376	+	0.222692i	0.0544287	+	0.998518i	$0.482666\pi$
$384$	−10.2328	−	20.0793i	−0.522190	−	1.02467i
$385$	2.71971	−	15.7488i	0.138609	−	0.802633i
$386$	−6.52070	+	1.64315i	−0.331895	+	0.0836340i
$387$	5.90632	−	4.29119i	0.300235	−	0.218134i
$388$	6.76324	−	7.07410i	0.343351	−	0.359133i
$389$	−11.6423	+	16.0243i	−0.590290	+	0.812465i	−0.994776	−	0.102080i	$-0.967450\pi$
$389$	−11.6423	+	16.0243i	−0.590290	+	0.812465i	0.404486	+	0.914544i	$0.367450\pi$
$390$	19.3873	−	1.47322i	0.981712	−	0.0745995i
$391$	0.887092	−	0.644510i	0.0448622	−	0.0325943i
$392$	−9.71941	−	10.6328i	−0.490904	−	0.537036i
$393$		−	18.0455i		−	0.910276i
$394$	−6.72582	+	4.22621i	−0.338842	+	0.212913i
$395$	1.98056	−	1.92615i	0.0996530	−	0.0969152i
$396$	−4.74796	−	8.82273i	−0.238594	−	0.443359i
$397$	−3.25515	−	10.0183i	−0.163371	−	0.502805i	0.835541	−	0.549428i	$-0.185154\pi$
$397$	−3.25515	−	10.0183i	−0.163371	−	0.502805i	−0.998913	+	0.0466224i	$0.985154\pi$
$398$	1.23143	+	4.88682i	0.0617259	+	0.244954i
$399$	17.6156			0.881881
$400$	6.50409	+	18.9129i	0.325205	+	0.945644i
$401$	−14.5328			−0.725732			−0.362866	−	0.931841i	$-0.618202\pi$
$401$	−14.5328			−0.725732			−0.362866	+	0.931841i	$0.618202\pi$
$402$	1.23021	+	4.88200i	0.0613574	+	0.243492i
$403$	4.28509	+	13.1882i	0.213456	+	0.656949i
$404$	−15.7044	−	29.1822i	−0.781325	−	1.45187i
$405$	−24.2717	+	3.49849i	−1.20607	+	0.173841i
$406$	−15.2132	+	9.55933i	−0.755020	+	0.474422i
$407$		−	26.0776i		−	1.29262i
$408$	−15.8749	+	14.5112i	−0.785924	+	0.718413i
$409$	−20.3026	+	14.7507i	−1.00390	+	0.729375i	−0.962920	−	0.269785i	$-0.913047\pi$
$409$	−20.3026	+	14.7507i	−1.00390	+	0.729375i	−0.0409776	+	0.999160i	$0.513047\pi$
$410$	−3.03138	+	12.4783i	−0.149709	+	0.616260i
$411$	0.814776	−	1.12144i	0.0401899	−	0.0553167i
$412$	5.62209	−	5.88050i	0.276981	−	0.289712i
$413$	−1.99999	+	1.45308i	−0.0984131	+	0.0715013i
$414$	0.381240	−	0.0960684i	0.0187369	−	0.00472150i
$415$	−9.29889	+	1.34033i	−0.456465	+	0.0657941i
$416$	−16.7228	+	5.02261i	−0.819902	+	0.246254i
$417$	20.1598	+	6.55032i	0.987230	+	0.320770i
$418$	35.9855	+	30.0422i	1.76011	+	1.46941i
$419$	0.728039	+	0.236554i	0.0355671	+	0.0115564i	0.326746	−	0.945112i	$-0.394048\pi$
$419$	0.728039	+	0.236554i	0.0355671	+	0.0115564i	−0.291179	+	0.956668i	$0.594048\pi$
$420$	−11.7312	−	3.70132i	−0.572425	−	0.180606i
$421$	−11.1284	+	3.61584i	−0.542366	+	0.176225i	−0.567371	−	0.823462i	$-0.692040\pi$
$421$	−11.1284	+	3.61584i	−0.542366	+	0.176225i	0.0250056	+	0.999687i	$0.492040\pi$
$422$	−37.0073	−	14.8442i	−1.80149	−	0.722606i
$423$	−0.570872	+	0.785739i	−0.0277568	+	0.0382039i
$424$	4.62908	−	8.15874i	0.224808	−	0.396223i
$425$	15.7484	−	10.7848i	0.763909	−	0.523139i
$426$	32.7968	+	27.3801i	1.58901	+	1.32657i
$427$	2.48717	+	1.80704i	0.120363	+	0.0874486i
$428$	23.8122	−	12.8145i	1.15100	−	0.619414i
$429$	−30.2664	+	9.83414i	−1.46127	+	0.474797i
$430$	18.1798	−	15.4424i	0.876706	−	0.744698i
$431$	6.71966	−	20.6810i	0.323675	−	0.996169i	−0.648360	−	0.761334i	$-0.724545\pi$
$431$	6.71966	−	20.6810i	0.323675	−	0.996169i	0.972035	−	0.234835i	$-0.0754550\pi$
$432$	15.1589	−	5.68999i	0.729335	−	0.273760i
$433$	−3.49647	−	1.13607i	−0.168030	−	0.0545962i	0.223794	−	0.974636i	$-0.428156\pi$
$433$	−3.49647	−	1.13607i	−0.168030	−	0.0545962i	−0.391824	+	0.920040i	$0.628156\pi$
$434$	0.590074	−	8.75339i	0.0283245	−	0.420176i
$435$	19.1113	−	36.2510i	0.916319	−	1.73810i
$436$	18.0819	+	8.70730i	0.865966	+	0.417004i
$437$	−1.48818	+	1.08123i	−0.0711894	+	0.0517222i
$438$	−2.21780	+	32.8997i	−0.105970	+	1.57201i
$439$	−1.89736	−	1.37851i	−0.0905559	−	0.0657927i	0.541586	−	0.840645i	$-0.317824\pi$
$439$	−1.89736	−	1.37851i	−0.0905559	−	0.0657927i	−0.632142	+	0.774853i	$0.717824\pi$
$440$	−17.6525	−	27.5680i	−0.841549	−	1.31425i
$441$	−3.98804	+	2.89748i	−0.189907	+	0.137975i
$442$	8.86589	+	14.1096i	0.421707	+	0.671127i
$443$	0.969245			0.0460502			0.0230251	−	0.999735i	$-0.492670\pi$
$443$	0.969245			0.0460502			0.0230251	+	0.999735i	$0.492670\pi$
$444$	−19.8903	−	2.69389i	−0.943951	−	0.127846i
$445$	4.29789	−	24.8874i	0.203740	−	1.17978i
$446$	21.7168	+	8.71096i	1.02832	+	0.412476i
$447$	6.10416	−	1.98336i	0.288717	−	0.0938098i
$448$	11.0026	+	0.989538i	0.519826	+	0.0467513i
$449$	34.3240			1.61985			0.809925	−	0.586533i	$-0.199508\pi$
$449$	34.3240			1.61985			0.809925	+	0.586533i	$0.199508\pi$
$450$	6.68038	−	1.48682i	0.314916	−	0.0700894i
$451$		−	21.0181i		−	0.989705i
$452$	−17.1417	−	8.25455i	−0.806277	−	0.388261i
$453$	12.4325	+	38.2634i	0.584132	+	1.79777i
$454$	6.48960	−	16.1788i	0.304572	−	0.759311i
$455$	−4.44474	+	8.43093i	−0.208373	+	0.395248i
$456$	26.6317	−	24.3440i	1.24714	−	1.14001i
$457$		−	34.4324i		−	1.61068i	−0.592812	−	0.805341i	$-0.701982\pi$
$457$		−	34.4324i		−	1.61068i	0.592812	−	0.805341i	$-0.298018\pi$
$458$	8.52823	+	13.5723i	0.398498	+	0.634191i
$459$	−9.08288	−	12.5015i	−0.423953	−	0.583521i
$460$	1.21825	−	0.407361i	0.0568012	−	0.0189933i
$461$	21.8458	−	30.0682i	1.01746	−	1.40041i	0.103491	−	0.994630i	$-0.466999\pi$
$461$	21.8458	−	30.0682i	1.01746	−	1.40041i	0.913969	−	0.405783i	$-0.133001\pi$
$462$	20.0887	+	1.35420i	0.934612	+	0.0630031i
$463$	−8.48120	−	11.6734i	−0.394155	−	0.542507i	0.565110	−	0.825015i	$-0.308834\pi$
$463$	−8.48120	−	11.6734i	−0.394155	−	0.542507i	−0.959265	+	0.282508i	$0.908834\pi$
$464$	−9.78914	+	35.4761i	−0.454450	+	1.64694i
$465$	8.83529	+	17.9541i	0.409727	+	0.832600i
$466$	0.612591	−	9.08741i	0.0283777	−	0.420966i
$467$	−3.46409	+	10.6614i	−0.160299	+	0.493349i	−0.998659	−	0.0517673i	$-0.983515\pi$
$467$	−3.46409	+	10.6614i	−0.160299	+	0.493349i	0.838360	+	0.545116i	$0.183515\pi$
$468$	1.06699	+	5.87889i	0.0493217	+	0.271752i
$469$	−2.34712	−	0.762626i	−0.108380	−	0.0352148i
$470$	−1.66531	+	2.70117i	−0.0768152	+	0.124596i
$471$	13.1553	+	40.4878i	0.606163	+	1.86558i
$472$	−1.01554	+	4.96071i	−0.0467441	+	0.228335i
$473$	−22.9483	+	31.5857i	−1.05517	+	1.45231i
$474$	2.67185	+	2.23057i	0.122722	+	0.102453i
$475$	−26.4195	+	18.0925i	−1.21221	+	0.830143i
$476$	−1.88273	−	10.3734i	−0.0862949	−	0.475466i
$477$	−2.59688	−	1.88674i	−0.118903	−	0.0863881i
$478$	−1.10904	+	2.76488i	−0.0507262	+	0.126462i
$479$	1.46974	+	4.52340i	0.0671543	+	0.206680i	0.979003	−	0.203848i	$-0.0653447\pi$
$479$	1.46974	+	4.52340i	0.0671543	+	0.206680i	−0.911848	+	0.410527i	$0.865345\pi$
$480$	−22.8506	+	10.6163i	−1.04298	+	0.484567i
$481$	−4.80563	+	14.7902i	−0.219118	+	0.674376i
$482$	−23.0880	−	19.2749i	−1.05163	−	0.877946i
$483$	−0.244149	+	0.751413i	−0.0111092	+	0.0341905i
$484$	22.8265	+	21.8234i	1.03757	+	0.991973i
$485$	−7.62875	−	7.84426i	−0.346404	−	0.356189i
$486$	−3.35254	−	13.3043i	−0.152074	−	0.603495i
$487$	7.81977	+	10.7630i	0.354348	+	0.487718i	0.948563	−	0.316588i	$-0.102537\pi$
$487$	7.81977	+	10.7630i	0.354348	+	0.487718i	−0.594215	+	0.804306i	$0.702537\pi$
$488$	6.25742	−	0.705248i	0.283260	−	0.0319251i
$489$	20.4408	+	14.8511i	0.924365	+	0.671590i
$490$	−12.2753	+	10.4270i	−0.554540	+	0.471042i
$491$	10.4364	+	14.3645i	0.470990	+	0.648262i	0.976742	−	0.214417i	$-0.0687851\pi$
$491$	10.4364	+	14.3645i	0.470990	+	0.648262i	−0.505752	+	0.862679i	$0.668785\pi$
$492$	−16.0313	−	2.17123i	−0.722746	−	0.0978867i
$493$	35.1224			1.58184
$494$	−14.8734	−	23.6703i	−0.669186	−	1.06498i
$495$	−10.0507	+	4.94600i	−0.451746	+	0.222306i
$496$	−11.2048	−	14.0491i	−0.503108	−	0.630822i
$497$	−19.9176	+	6.47161i	−0.893425	+	0.290291i
$498$	−2.89214	−	11.4772i	−0.129600	−	0.514306i
$499$			15.6179i			0.699151i	0.936908	+	0.349576i	$0.113674\pi$
$499$			15.6179i			0.699151i	−0.936908	+	0.349576i	$0.886326\pi$
$500$	21.3958	−	6.49771i	0.956849	−	0.290586i
$501$			18.3272i			0.818799i
$502$	23.9956	−	6.04665i	1.07098	−	0.269875i
$503$	0.0298452	−	0.00969730i	0.00133073	−	0.000432381i	−0.308352	−	0.951272i	$-0.599777\pi$
$503$	0.0298452	−	0.00969730i	0.00133073	−	0.000432381i	0.309682	+	0.950840i	$0.399777\pi$
$504$	0.758150	−	3.70340i	0.0337707	−	0.164963i
$505$	−33.2439	+	16.3595i	−1.47933	+	0.727988i
$506$	−1.78024	+	1.11863i	−0.0791413	+	0.0497290i
$507$	−6.91715			−0.307201
$508$	2.24813	−	16.5990i	0.0997445	−	0.736463i
$509$	−6.00479	−	8.26488i	−0.266157	−	0.366334i	0.654930	−	0.755689i	$-0.272698\pi$
$509$	−6.00479	−	8.26488i	−0.266157	−	0.366334i	−0.921088	+	0.389355i	$0.872698\pi$
$510$	15.5676	+	18.3272i	0.689345	+	0.811540i
$511$	−13.0767	−	9.50075i	−0.578477	−	0.420288i
$512$	18.0016	−	13.7092i	0.795566	−	0.605867i
$513$	15.2374	+	20.9725i	0.672748	+	0.925959i
$514$	−39.4242	+	9.93448i	−1.73893	+	0.438191i
$515$	−6.34157	−	6.52072i	−0.279443	−	0.287337i
$516$	21.7209	+	20.7664i	0.956209	+	0.914189i
$517$	1.60500	−	4.93969i	0.0705879	−	0.217247i
$518$	6.30550	−	7.55293i	0.277048	−	0.331857i
$519$	12.0031	−	36.9418i	0.526878	−	1.62156i
$520$	4.93153	+	18.8886i	0.216262	+	0.828318i
$521$	6.03139	+	18.5627i	0.264240	+	0.813248i	0.991867	+	0.127275i	$0.0406231\pi$
$521$	6.03139	+	18.5627i	0.264240	+	0.813248i	−0.727627	+	0.685973i	$0.759377\pi$
$522$	11.6881	+	4.68829i	0.511574	+	0.205201i
$523$	7.08464	+	5.14729i	0.309789	+	0.225075i	0.731806	−	0.681513i	$-0.238678\pi$
$523$	7.08464	+	5.14729i	0.309789	+	0.225075i	−0.422017	+	0.906588i	$0.638678\pi$
$524$	17.8272	−	3.23556i	0.778785	−	0.141346i
$525$	−4.61262	+	12.9567i	−0.201311	+	0.565475i
$526$	19.0397	−	22.8063i	0.830168	−	0.994403i
$527$	−10.0805	+	13.8746i	−0.439113	+	0.604388i
$528$	32.2421	−	25.7145i	1.40316	−	1.11908i
$529$	7.08190	+	21.7958i	0.307909	+	0.947645i
$530$	−8.92742	−	5.50389i	−0.387782	−	0.239074i
$531$	1.64791	+	0.535440i	0.0715134	+	0.0232361i
$532$	3.15847	+	17.4024i	0.136937	+	0.754492i
$533$	−3.87327	+	11.9207i	−0.167770	+	0.516343i
$534$	31.7457	+	2.14001i	1.37377	+	0.0926071i
$535$	−13.3490	−	27.1264i	−0.577129	−	1.17278i
$536$	−4.60236	+	2.09067i	−0.198792	+	0.0903033i
$537$	−3.88464	−	5.34675i	−0.167635	−	0.230729i
$538$	−1.50811	+	22.3719i	−0.0650192	+	0.964521i
$539$	15.4951	−	21.3271i	0.667420	−	0.918625i
$540$	−5.74081	−	17.1684i	−0.247045	−	0.738812i
$541$	15.5336	+	21.3802i	0.667843	+	0.919208i	0.999709	−	0.0241190i	$-0.00767806\pi$
$541$	15.5336	+	21.3802i	0.667843	+	0.919208i	−0.331866	+	0.943327i	$0.607678\pi$
$542$	−35.5681	+	22.3494i	−1.52778	+	0.959991i
$543$			9.82203i			0.421504i
$544$	−17.1820	−	13.0810i	−0.736674	−	0.560842i
$545$	10.4641	−	19.8486i	0.448232	−	0.850221i
$546$	−11.1440	−	4.47005i	−0.476920	−	0.191300i
$547$	8.93390	+	27.4957i	0.381986	+	1.17563i	0.938643	+	0.344890i	$0.112084\pi$
$547$	8.93390	+	27.4957i	0.381986	+	1.17563i	−0.556657	+	0.830742i	$0.687916\pi$
$548$	1.25397	+	0.603844i	0.0535667	+	0.0257950i
$549$		−	2.15480i		−	0.0919644i
$550$	−31.5196	+	18.6017i	−1.34400	+	0.793179i
$551$	−58.9213			−2.51013
$552$	0.669312	+	1.47341i	0.0284878	+	0.0627125i
$553$	−1.62262	+	0.527221i	−0.0690008	+	0.0224197i
$554$	0.573374	−	1.42944i	0.0243603	−	0.0607313i
$555$	−3.81889	+	22.1137i	−0.162103	+	0.938675i
$556$	−2.85642	+	21.0904i	−0.121139	+	0.894431i
$557$	33.1381			1.40411			0.702053	−	0.712125i	$-0.252267\pi$
$557$	33.1381			1.40411			0.702053	+	0.712125i	$0.252267\pi$
$558$	−5.20664	+	3.27163i	−0.220415	+	0.138499i
$559$	18.8361	−	13.6852i	0.796682	−	0.578824i
$560$	1.55313	−	12.2529i	0.0656319	−	0.517781i
$561$	−31.8418	−	23.1344i	−1.34436	−	0.976735i
$562$	−35.8856	−	2.41908i	−1.51374	−	0.102043i
$563$	25.4540	−	18.4934i	1.07276	−	0.779404i	0.0963518	−	0.995347i	$-0.469283\pi$
$563$	25.4540	−	18.4934i	1.07276	−	0.779404i	0.976406	+	0.215943i	$0.0692826\pi$
$564$	−3.60188	−	1.73448i	−0.151666	−	0.0730346i
$565$	−9.91999	+	18.8165i	−0.417337	+	0.791618i
$566$	−35.4054	−	2.38671i	−1.48820	−	0.100321i
$567$	14.4027	+	4.67972i	0.604857	+	0.196530i
$568$	−21.1684	+	37.3092i	−0.888206	+	1.56546i
$569$	−5.66167	+	17.4248i	−0.237350	+	0.730487i	0.759451	+	0.650564i	$0.225467\pi$
$569$	−5.66167	+	17.4248i	−0.237350	+	0.730487i	−0.996801	+	0.0799229i	$0.974533\pi$
$570$	−26.1162	−	30.7456i	−1.09389	−	1.28779i
$571$	−4.90965	+	1.59524i	−0.205462	+	0.0667588i	−0.409940	−	0.912112i	$-0.634450\pi$
$571$	−4.90965	+	1.59524i	−0.205462	+	0.0667588i	0.204478	+	0.978871i	$0.434450\pi$
$572$	−15.1419	−	28.1369i	−0.633115	−	1.17646i
$573$	−1.08305	−	0.786879i	−0.0452449	−	0.0328723i
$574$	5.08214	−	6.08755i	0.212124	−	0.254089i
$575$	−0.405590	−	1.37771i	−0.0169143	−	0.0574546i
$576$	−3.97176	−	6.64664i	−0.165490	−	0.276943i
$577$	0.868662	−	1.19561i	0.0361629	−	0.0497739i	−0.790553	−	0.612394i	$-0.790207\pi$
$577$	0.868662	−	1.19561i	0.0361629	−	0.0497739i	0.826716	+	0.562620i	$0.190207\pi$
$578$	1.27781	−	3.18564i	0.0531500	−	0.132505i
$579$	−9.00808	+	2.92690i	−0.374363	+	0.121638i
$580$	39.2391	+	12.3803i	1.62931	+	0.514065i
$581$	5.51790	+	1.79288i	0.228921	+	0.0743810i
$582$	8.83443	−	10.5822i	0.366199	−	0.438645i
$583$	16.3258	+	5.30456i	0.676144	+	0.219692i
$584$	−32.8993	+	3.70794i	−1.36138	+	0.153436i
$585$	6.61184	−	0.953021i	0.273366	−	0.0394026i
$586$	−10.9358	−	43.3977i	−0.451753	−	1.79274i
$587$	6.19025	−	4.49748i	0.255499	−	0.185631i	−0.452662	−	0.891682i	$-0.649525\pi$
$587$	6.19025	−	4.49748i	0.255499	−	0.185631i	0.708160	+	0.706052i	$0.249525\pi$
$588$	−14.6663	−	14.0218i	−0.604828	−	0.578249i
$589$	16.9110	−	23.2760i	0.696806	−	0.959071i
$590$	5.50126	+	1.33644i	0.226483	+	0.0550202i
$591$	−9.05163	+	6.57640i	−0.372334	+	0.270517i
$592$	−0.905030	−	20.1327i	−0.0371965	−	0.827448i
$593$		−	31.1703i		−	1.28001i	−0.768370	−	0.640006i	$-0.778932\pi$
$593$		−	31.1703i		−	1.28001i	0.768370	−	0.640006i	$-0.221068\pi$
$594$	15.7644	+	25.0884i	0.646823	+	1.02939i
$595$	−11.6668	+	1.68163i	−0.478290	+	0.0689400i
$596$	3.05384	+	5.67469i	0.125090	+	0.232445i
$597$	2.19352	+	6.75095i	0.0897747	+	0.276298i
$598$	1.21583	−	0.306376i	0.0497189	−	0.0125286i
$599$	−30.2376			−1.23547			−0.617737	−	0.786385i	$-0.711950\pi$
$599$	−30.2376			−1.23547			−0.617737	+	0.786385i	$0.711950\pi$
$600$	10.9321	+	25.9627i	0.446302	+	1.05992i
$601$	47.2925			1.92910			0.964551	−	0.263895i	$-0.0850073\pi$
$601$	47.2925			1.92910			0.964551	+	0.263895i	$0.0850073\pi$
$602$	−14.2839	+	3.59940i	−0.582170	+	0.146701i
$603$	0.534527	+	1.64511i	0.0217676	+	0.0669939i
$604$	−35.5714	+	19.1428i	−1.44738	+	0.778908i
$605$	25.3116	−	24.6162i	1.02906	−	1.00079i
$606$	−24.8345	−	39.5230i	−1.00883	−	1.60551i
$607$		−	13.6800i		−	0.555252i	−0.960689	−	0.277626i	$-0.910452\pi$
$607$		−	13.6800i		−	0.555252i	0.960689	−	0.277626i	$-0.0895477\pi$
$608$	28.8245	+	21.9446i	1.16899	+	0.889971i
$609$	−20.4740	+	14.8753i	−0.829650	+	0.602776i
$610$	−0.533450	−	7.02007i	−0.0215987	−	0.284234i
$611$	−1.82059	+	2.50583i	−0.0736533	+	0.101375i
$612$	−5.10653	+	5.34124i	−0.206419	+	0.215907i
$613$	12.8625	−	9.34518i	0.519513	−	0.377448i	−0.296907	−	0.954906i	$-0.595955\pi$
$613$	12.8625	−	9.34518i	0.519513	−	0.377448i	0.816420	+	0.577458i	$0.195955\pi$
$614$	1.29262	+	5.12968i	0.0521661	+	0.207017i
$615$	−3.07797	+	17.8233i	−0.124116	+	0.718706i
$616$	2.26409	+	20.0885i	0.0912228	+	0.809389i
$617$	−10.0312	−	3.25933i	−0.403840	−	0.131216i	0.100052	−	0.994982i	$-0.468099\pi$
$617$	−10.0312	−	3.25933i	−0.403840	−	0.131216i	−0.503892	+	0.863767i	$0.668099\pi$
$618$	7.34382	−	8.79667i	0.295412	−	0.353854i
$619$	−25.5938	−	8.31591i	−1.02870	−	0.334245i	−0.254424	−	0.967093i	$-0.581886\pi$
$619$	−25.5938	−	8.31591i	−1.02870	−	0.334245i	−0.774276	+	0.632848i	$0.781886\pi$
$620$	−16.1527	+	11.9476i	−0.648708	+	0.479825i
$621$	−1.10580	+	0.359295i	−0.0443740	+	0.0144180i
$622$	5.91554	−	14.7477i	0.237192	−	0.591329i
$623$	−9.16751	+	12.6180i	−0.367288	+	0.505529i
$624$	−23.0253	+	8.64266i	−0.921748	+	0.345983i
$625$	−6.38958	−	24.1697i	−0.255583	−	0.966787i
$626$	5.96869	−	7.14949i	0.238557	−	0.285751i
$627$	53.4176	+	38.8102i	2.13330	+	1.54993i
$628$	−37.6392	+	20.2556i	−1.50197	+	0.808286i
$629$	−18.2919	+	5.94341i	−0.729348	+	0.236979i
$630$	−4.10695	−	0.997711i	−0.163625	−	0.0397498i
$631$	0.0360428	−	0.110928i	0.00143484	−	0.00441599i	−0.950337	−	0.311224i	$-0.899261\pi$
$631$	0.0360428	−	0.110928i	0.00143484	−	0.00441599i	0.951771	+	0.306808i	$0.0992610\pi$
$632$	−1.72452	+	3.03946i	−0.0685978	+	0.120903i
$633$	−53.4138	−	17.3552i	−2.12301	−	0.689808i
$634$	−28.5330	−	1.92344i	−1.13319	−	0.0763895i
$635$	−18.4545	−	3.18698i	−0.732346	−	0.126471i
$636$	5.73247	−	11.9043i	0.227307	−	0.472035i
$637$	−12.7184	+	9.24049i	−0.503923	+	0.366121i
$638$	−67.1937	−	4.52959i	−2.66022	−	0.179328i
$639$	11.8753	+	8.62793i	0.469781	+	0.341316i
$640$	−14.5850	−	20.6707i	−0.576523	−	0.817081i
$641$	8.56388	−	6.22202i	0.338253	−	0.245755i	−0.405672	−	0.914019i	$-0.632962\pi$
$641$	8.56388	−	6.22202i	0.338253	−	0.245755i	0.743924	+	0.668264i	$0.232962\pi$
$642$	32.2500	−	20.2645i	1.27281	−	0.799776i
$643$	−7.74220			−0.305323			−0.152661	−	0.988279i	$-0.548784\pi$
$643$	−7.74220			−0.305323			−0.152661	+	0.988279i	$0.548784\pi$
$644$	−0.786098	−	0.106467i	−0.0309766	−	0.00419538i
$645$	24.0857	−	23.4239i	0.948372	−	0.922317i
$646$	12.8714	−	32.0888i	0.506417	−	1.26252i
$647$	21.5750	−	7.01014i	0.848200	−	0.275597i	0.147508	−	0.989061i	$-0.452875\pi$
$647$	21.5750	−	7.01014i	0.848200	−	0.275597i	0.700692	+	0.713464i	$0.252875\pi$
$648$	28.2416	−	12.8290i	1.10943	−	0.503972i
$649$	−9.26619			−0.363730
$650$	21.3047	−	4.74168i	0.835638	−	0.185984i
$651$		−	12.3573i		−	0.484322i
$652$	−11.0064	+	22.8563i	−0.431044	+	0.895122i
$653$	9.55959	+	29.4214i	0.374096	+	1.15135i	0.944087	+	0.329697i	$0.106947\pi$
$653$	9.55959	+	29.4214i	0.374096	+	1.15135i	−0.569991	+	0.821651i	$0.693053\pi$
$654$	26.2359	+	10.5237i	1.02591	+	0.411508i
$655$	−2.88995	−	20.0498i	−0.112920	−	0.783412i
$656$	−0.729441	−	16.2266i	−0.0284799	−	0.633544i
$657$			11.3291i			0.441992i
$658$	1.65927	−	1.04261i	0.0646850	−	0.0406453i
$659$	13.3643	+	18.3944i	0.520601	+	0.716545i	0.985662	−	0.168733i	$-0.0539676\pi$
$659$	13.3643	+	18.3944i	0.520601	+	0.716545i	−0.465061	+	0.885279i	$0.653968\pi$
$660$	−27.4192	−	37.0699i	−1.06729	−	1.44294i
$661$	−9.06815	+	12.4812i	−0.352710	+	0.485464i	−0.948100	−	0.317973i	$-0.896998\pi$
$661$	−9.06815	+	12.4812i	−0.352710	+	0.485464i	0.595389	+	0.803437i	$0.296998\pi$
$662$	−2.03011	+	30.1155i	−0.0789025	+	1.17047i
$663$	13.7962	+	18.9888i	0.535800	+	0.737465i
$664$	10.8198	−	4.91501i	0.419890	−	0.190739i
$665$	19.5721	−	2.82109i	0.758974	−	0.109397i
$666$	−6.88057	−	0.463826i	−0.266617	−	0.0179729i
$667$	0.816640	−	2.51336i	0.0316204	−	0.0973176i
$668$	−18.1055	+	3.28606i	−0.700522	+	0.127142i
$669$	31.3445	+	10.1845i	1.21185	+	0.393754i
$670$	2.14869	+	5.22723i	0.0830113	+	0.201945i
$671$	3.56091	+	10.9594i	0.137467	+	0.423081i
$672$	15.5561	+	0.348297i	0.600090	+	0.0134359i
$673$	13.5949	−	18.7118i	0.524046	−	0.721288i	−0.462162	−	0.886795i	$-0.652926\pi$
$673$	13.5949	−	18.7118i	0.524046	−	0.721288i	0.986209	+	0.165507i	$0.0529262\pi$
$674$	−15.0910	+	18.0765i	−0.581286	+	0.696283i
$675$	−19.4157	+	5.71585i	−0.747310	+	0.220003i
$676$	−1.24024	−	6.83346i	−0.0477017	−	0.262825i
$677$	−2.66645	−	1.93729i	−0.102480	−	0.0744561i	0.535365	−	0.844621i	$-0.320174\pi$
$677$	−2.66645	−	1.93729i	−0.102480	−	0.0744561i	−0.637845	+	0.770165i	$0.720174\pi$
$678$	−24.8717	−	9.97646i	−0.955194	−	0.383144i
$679$	2.08812	+	6.42658i	0.0801348	+	0.246629i
$680$	−15.3142	+	18.6653i	−0.587272	+	0.715783i
$681$	7.58734	−	23.3514i	0.290747	−	0.894829i
$682$	21.0746	−	25.2439i	0.806989	−	0.966637i
$683$	−4.53666	+	13.9624i	−0.173591	+	0.534257i	−0.999566	−	0.0294489i	$-0.990625\pi$
$683$	−4.53666	+	13.9624i	−0.173591	+	0.534257i	0.825976	+	0.563706i	$0.190625\pi$
$684$	8.56670	−	8.96045i	0.327556	−	0.342611i
$685$	0.725676	−	1.37649i	0.0277267	−	0.0525928i
$686$	22.9004	−	5.77066i	0.874341	−	0.220325i
$687$	13.2708	+	18.2656i	0.506311	+	0.696877i
$688$	−16.6206	+	25.1815i	−0.633655	+	0.960036i
$689$	−8.28182	−	6.01710i	−0.315512	−	0.229233i
$690$	1.67346	−	0.687887i	0.0637074	−	0.0261874i
$691$	−0.529926	−	0.729380i	−0.0201593	−	0.0277469i	0.798818	−	0.601572i	$-0.205459\pi$
$691$	−0.529926	−	0.729380i	−0.0201593	−	0.0277469i	−0.818978	+	0.573825i	$0.805459\pi$
$692$	38.6470	+	5.23425i	1.46914	+	0.198976i
$693$	6.91764			0.262779
$694$	18.9933	−	11.9346i	0.720975	−	0.453029i
$695$	23.4480	+	4.04931i	0.889432	+	0.153599i
$696$	−10.3962	+	50.7831i	−0.394066	+	1.92493i
$697$	−14.7430	+	4.79030i	−0.558433	+	0.181446i
$698$	−16.3800	+	4.12760i	−0.619994	+	0.156232i
$699$		−	12.8289i		−	0.485232i
$700$	−13.6270	−	2.23369i	−0.515051	−	0.0844257i
$701$			25.3479i			0.957379i	0.877984	+	0.478689i	$0.158888\pi$
$701$			25.3479i			0.957379i	−0.877984	+	0.478689i	$0.841112\pi$
$702$	−4.31766	−	17.1343i	−0.162960	−	0.646692i
$703$	30.6865	−	9.97065i	1.15736	−	0.376050i
$704$	31.1844	+	27.2415i	1.17531	+	1.02670i
$705$	−2.08442	+	3.95380i	−0.0785040	+	0.148909i
$706$	3.78538	+	6.02426i	0.142465	+	0.226726i
$707$	22.8809			0.860526
$708$	−0.957223	+	7.06765i	−0.0359746	+	0.265619i
$709$	3.03019	+	4.17070i	0.113801	+	0.156634i	0.862118	−	0.506708i	$-0.169138\pi$
$709$	3.03019	+	4.17070i	0.113801	+	0.156634i	−0.748317	+	0.663342i	$0.769138\pi$
$710$	40.8244	+	25.1689i	1.53211	+	0.944571i
$711$	0.967444	+	0.702889i	0.0362820	+	0.0263604i
$712$	3.57788	+	31.7453i	0.134087	+	1.18971i
$713$	0.758482	+	1.04396i	0.0284054	+	0.0390966i
$714$	−3.62859	−	14.3998i	−0.135796	−	0.538897i
$715$	−32.0531	+	15.7735i	−1.19872	+	0.589896i
$716$	4.58555	−	4.79632i	0.171370	−	0.179247i
$717$	−1.29663	+	3.99063i	−0.0484237	+	0.149033i
$718$	5.92705	+	4.94815i	0.221196	+	0.184663i
$719$	5.09933	−	15.6941i	0.190173	−	0.585292i	−0.809826	−	0.586670i	$-0.800439\pi$
$719$	5.09933	−	15.6941i	0.190173	−	0.585292i	0.999999	+	0.00137806i	$0.000438650\pi$
$720$	−7.58780	+	4.16728i	−0.282781	+	0.155305i
$721$	1.73580	+	5.34224i	0.0646445	+	0.198955i
$722$	−11.5897	+	28.8935i	−0.431322	+	1.07531i
$723$	−34.2724	−	24.9003i	−1.27460	−	0.926053i
$724$	−9.70320	+	1.76109i	−0.360617	+	0.0654503i
$725$	15.4285	−	43.3380i	0.573001	−	1.60953i
$726$	34.1462	+	28.5067i	1.26729	+	1.05798i
$727$	−13.5429	+	18.6402i	−0.502278	+	0.691326i	−0.982593	−	0.185770i	$-0.940522\pi$
$727$	−13.5429	+	18.6402i	−0.502278	+	0.691326i	0.480315	+	0.877096i	$0.340522\pi$
$728$	2.41785	−	11.8107i	0.0896114	−	0.437733i
$729$	4.19500	+	12.9109i	0.155370	+	0.478181i
$730$	2.80469	+	36.9090i	0.103806	+	1.36606i
$731$	27.3858	+	8.89818i	1.01290	+	0.329111i
$732$	8.72695	−	1.58390i	0.322557	−	0.0585427i
$733$	11.8423	−	36.4467i	0.437404	−	1.34619i	−0.453200	−	0.891409i	$-0.649718\pi$
$733$	11.8423	−	36.4467i	0.437404	−	1.34619i	0.890603	−	0.454781i	$-0.150282\pi$
$734$	−1.43864	+	21.3414i	−0.0531012	+	0.787724i
$735$	−16.2630	+	15.8162i	−0.599871	+	0.583390i
$736$	−1.33558	+	0.925397i	−0.0492300	+	0.0341106i
$737$	−5.43724	−	7.48373i	−0.200283	−	0.275667i
$738$	−5.54564	−	0.373837i	−0.204138	−	0.0137611i
$739$	5.15085	−	7.08954i	0.189477	−	0.260793i	−0.703701	−	0.710497i	$-0.748470\pi$
$739$	5.15085	−	7.08954i	0.189477	−	0.260793i	0.893178	+	0.449704i	$0.148470\pi$
$740$	−22.5309	+	0.192293i	−0.828253	+	0.00706883i
$741$	−23.1444	−	31.8556i	−0.850233	−	1.17024i
$742$	3.44585	+	5.48391i	0.126501	+	0.201321i
$743$			7.97007i			0.292393i	0.989256	+	0.146197i	$0.0467032\pi$
$743$			7.97007i			0.292393i	−0.989256	+	0.146197i	$0.953297\pi$
$744$	−17.0773	−	18.6821i	−0.626085	−	0.684920i
$745$	6.46451	−	3.18122i	0.236841	−	0.116551i
$746$	17.0446	−	42.4929i	0.624046	−	1.55577i
$747$	−1.25663	−	3.86752i	−0.0459778	−	0.141505i
$748$	17.1453	−	35.6045i	0.626894	−	1.30183i
$749$			18.6704i			0.682202i
$750$	29.4526	−	11.1584i	1.07546	−	0.407446i
$751$	1.54105			0.0562339			0.0281169	−	0.999605i	$-0.491049\pi$
$751$	1.54105			0.0562339			0.0281169	+	0.999605i	$0.491049\pi$
$752$	1.06768	−	3.86929i	0.0389342	−	0.141099i
$753$	33.1490	−	10.7708i	1.20802	−	0.392508i
$754$	37.2750	+	14.9516i	1.35748	+	0.544506i
$755$	19.9412	+	40.5223i	0.725736	+	1.47476i
$756$	−1.50041	+	11.0782i	−0.0545692	+	0.402911i
$757$	−20.8270			−0.756971			−0.378485	−	0.925607i	$-0.623555\pi$
$757$	−20.8270			−0.756971			−0.378485	+	0.925607i	$0.623555\pi$
$758$	−9.79056	−	15.5812i	−0.355609	−	0.565935i
$759$	−2.39585	+	1.74069i	−0.0869640	+	0.0631831i
$760$	25.6910	−	31.3129i	0.931911	−	1.13584i
$761$	−7.81874	−	5.68064i	−0.283429	−	0.205923i	0.436983	−	0.899470i	$-0.356047\pi$
$761$	−7.81874	−	5.68064i	−0.283429	−	0.205923i	−0.720412	+	0.693547i	$0.756047\pi$
$762$	1.58686	−	23.5401i	0.0574859	−	0.852768i
$763$	−11.2102	+	8.14469i	−0.405837	+	0.294858i
$764$	0.583170	−	1.21103i	0.0210983	−	0.0438136i
$765$	5.76003	+	5.92275i	0.208254	+	0.214137i
$766$	−1.34148	+	19.9000i	−0.0484695	+	0.719015i
$767$	5.25543	+	1.70759i	0.189763	+	0.0616576i
$768$	23.9995	−	20.9714i	0.866007	−	0.756739i
$769$	−1.06128	+	3.26628i	−0.0382706	+	0.117785i	−0.968367	−	0.249532i	$-0.919723\pi$
$769$	−1.06128	+	3.26628i	−0.0382706	+	0.117785i	0.930096	+	0.367316i	$0.119723\pi$
$770$	22.5369	−	1.71256i	0.812172	−	0.0617163i
$771$	−54.4630	+	17.6961i	−1.96144	+	0.637309i
$772$	−4.50664	−	8.37431i	−0.162198	−	0.301398i
$773$	5.52497	+	4.01412i	0.198719	+	0.144378i	0.682695	−	0.730703i	$-0.260808\pi$
$773$	5.52497	+	4.01412i	0.198719	+	0.144378i	−0.483976	+	0.875081i	$0.660808\pi$
$774$	7.92572	+	6.61672i	0.284884	+	0.237833i
$775$	12.6919	+	18.5333i	0.455907	+	0.665735i
$776$	12.0382	+	6.83017i	0.432145	+	0.245189i
$777$	8.14579	−	11.2117i	0.292229	−	0.402218i
$778$	−25.9980	−	10.4282i	−0.932074	−	0.373870i
$779$	24.7329	−	8.03620i	0.886147	−	0.287927i
$780$	8.71984	+	26.0775i	0.312220	+	0.933725i
$781$	−74.6564	−	24.2573i	−2.67142	−	0.867996i
$782$	1.19039	+	0.993789i	0.0425684	+	0.0355378i
$783$	−35.4200	−	11.5086i	−1.26581	−	0.411286i
$784$	11.2225	−	17.0030i	0.400804	−	0.607249i
$785$	21.1005	+	42.8780i	0.753108	+	1.53038i
$786$	24.7466	−	6.23589i	0.882683	−	0.222427i
$787$	−3.59275	+	2.61029i	−0.128068	+	0.0930467i	−0.649975	−	0.759956i	$-0.725221\pi$
$787$	−3.59275	+	2.61029i	−0.128068	+	0.0930467i	0.521907	+	0.853002i	$0.325221\pi$
$788$	−8.11979	−	7.76298i	−0.289256	−	0.276545i
$789$	24.5965	−	33.8542i	0.875658	−	1.20524i
$790$	3.32583	+	2.05043i	0.118328	+	0.0729509i
$791$	10.6273	−	7.72119i	0.377864	−	0.274534i
$792$	10.4583	−	9.55991i	0.371619	−	0.339697i
$793$		−	6.87195i		−	0.244030i
$794$	12.6137	−	7.92591i	0.447644	−	0.281280i
$795$	−13.0674	−	6.88906i	−0.463453	−	0.244330i
$796$	−6.27598	+	3.37742i	−0.222446	+	0.119710i
$797$	−4.56123	−	14.0380i	−0.161567	−	0.497252i	0.837200	−	0.546897i	$-0.184191\pi$
$797$	−4.56123	−	14.0380i	−0.161567	−	0.497252i	−0.998767	+	0.0496450i	$0.984191\pi$
$798$	6.08731	+	24.1570i	0.215488	+	0.855148i
$799$	−3.83071			−0.135521
$800$	−23.6885	+	15.4550i	−0.837514	+	0.546416i
$801$	10.9318			0.386255
$802$	−5.02201	−	19.9294i	−0.177333	−	0.703733i
$803$	−18.7220	−	57.6204i	−0.660685	−	2.03338i
$804$	−6.26979	+	3.37409i	−0.221118	+	0.118995i
$805$	−0.150929	+	0.873972i	−0.00531955	+	0.0308035i
$806$	−16.6047	+	10.4337i	−0.584877	+	0.367511i
$807$			31.5828i			1.11177i
$808$	34.5920	−	31.6205i	1.21694	−	1.11241i
$809$	14.9496	−	10.8616i	0.525601	−	0.381872i	−0.293108	−	0.956079i	$-0.594690\pi$
$809$	14.9496	−	10.8616i	0.525601	−	0.381872i	0.818710	+	0.574207i	$0.194690\pi$
$810$	−13.1851	−	32.0760i	−0.463277	−	1.12703i
$811$	15.6070	−	21.4812i	0.548036	−	0.754307i	−0.441708	−	0.897159i	$-0.645627\pi$
$811$	15.6070	−	21.4812i	0.548036	−	0.754307i	0.989744	+	0.142852i	$0.0456274\pi$
$812$	−18.3663	−	17.5592i	−0.644530	−	0.616207i
$813$	−47.8677	+	34.7779i	−1.67879	+	1.21971i
$814$	35.7613	−	9.01148i	1.25343	−	0.315852i
$815$	25.0895	+	13.2271i	0.878848	+	0.463324i
$816$	−25.3857	−	16.7554i	−0.888677	−	0.586555i
$817$	−45.9423	−	14.9276i	−1.60732	−	0.522249i
$818$	−27.2441	−	22.7445i	−0.952568	−	0.795243i
$819$	−3.92343	−	1.27480i	−0.137096	−	0.0445451i
$820$	−18.1596	+	0.154985i	−0.634161	+	0.00541232i
$821$	41.8393	−	13.5944i	1.46020	−	0.474448i	0.532070	−	0.846700i	$-0.321414\pi$
$821$	41.8393	−	13.5944i	1.46020	−	0.474448i	0.928132	+	0.372252i	$0.121414\pi$
$822$	1.81944	+	0.729808i	0.0634603	+	0.0254550i
$823$	14.3603	−	19.7653i	0.500569	−	0.688975i	−0.481724	−	0.876323i	$-0.659989\pi$
$823$	14.3603	−	19.7653i	0.500569	−	0.688975i	0.982294	+	0.187348i	$0.0599893\pi$
$824$	10.0070	+	5.67774i	0.348610	+	0.197793i
$825$	−42.5332	+	29.1275i	−1.48082	+	1.01409i
$826$	−2.68380	−	2.24054i	−0.0933812	−	0.0779585i
$827$	−38.6082	−	28.0505i	−1.34254	−	0.975412i	−0.999347	−	0.0361465i	$-0.988492\pi$
$827$	−38.6082	−	28.0505i	−1.34254	−	0.975412i	−0.343192	−	0.939265i	$-0.611508\pi$
$828$	0.263486	+	0.489613i	0.00915676	+	0.0170152i
$829$	22.8468	−	7.42337i	0.793502	−	0.257824i	0.115907	−	0.993260i	$-0.463022\pi$
$829$	22.8468	−	7.42337i	0.793502	−	0.257824i	0.677595	+	0.735436i	$0.263022\pi$
$830$	−5.05142	−	12.2888i	−0.175337	−	0.426551i
$831$	0.670362	−	2.06316i	0.0232546	−	0.0715703i
$832$	−12.6665	−	21.1971i	−0.439133	−	0.734876i
$833$	−18.4913	−	6.00819i	−0.640686	−	0.208172i
$834$	−2.01623	+	29.9096i	−0.0698164	+	1.03568i
$835$	2.93506	+	20.3628i	0.101572	+	0.704684i
$836$	−28.7629	+	59.7301i	−0.994785	+	2.06581i
$837$	14.7122	−	10.6891i	0.508529	−	0.369468i
$838$	−0.0728130	+	1.08014i	−0.00251528	+	0.0373127i
$839$	13.1474	+	9.55211i	0.453897	+	0.329776i	0.791132	−	0.611645i	$-0.209492\pi$
$839$	13.1474	+	9.55211i	0.453897	+	0.329776i	−0.337235	+	0.941420i	$0.609492\pi$
$840$	1.02189	−	17.3666i	0.0352586	−	0.599204i
$841$	45.0210	−	32.7096i	1.55245	−	1.12792i
$842$	−8.80415	−	14.0114i	−0.303411	−	0.482864i
$843$	−50.6604			−1.74484
$844$	7.56816	−	55.8794i	0.260507	−	1.92345i
$845$	−7.68543	+	1.10777i	−0.264387	+	0.0381083i
$846$	−1.27479	−	0.511340i	−0.0438282	−	0.0175802i
$847$	−20.7371	+	6.73789i	−0.712535	+	0.231517i
$848$	12.7881	+	3.52869i	0.439144	+	0.121176i
$849$	−49.9824			−1.71539
$850$	20.2318	+	17.8696i	0.693943	+	0.612923i
$851$			1.44716i			0.0496081i
$852$	−26.2141	+	54.4372i	−0.898082	+	1.86499i
$853$	14.3719	+	44.2323i	0.492086	+	1.51449i	0.821449	+	0.570282i	$0.193166\pi$
$853$	14.3719	+	44.2323i	0.492086	+	1.51449i	−0.329363	+	0.944203i	$0.606834\pi$
$854$	−1.61859	+	4.03522i	−0.0553870	+	0.138082i
$855$	−9.66301	−	9.93598i	−0.330468	−	0.339803i
$856$	25.8018	+	28.2264i	0.881886	+	0.964759i
$857$		−	34.8114i		−	1.18913i	−0.804046	−	0.594567i	$-0.797323\pi$
$857$		−	34.8114i		−	1.18913i	0.804046	−	0.594567i	$-0.202677\pi$
$858$	−23.9450	−	38.1073i	−0.817468	−	1.30096i
$859$	−23.5563	−	32.4224i	−0.803730	−	1.10624i	−0.992261	−	0.124172i	$-0.960373\pi$
$859$	−23.5563	−	32.4224i	−0.803730	−	1.10624i	0.188531	−	0.982067i	$-0.439627\pi$
$860$	27.4591	+	19.5944i	0.936348	+	0.668162i
$861$	6.56539	−	9.03648i	0.223748	−	0.307963i
$862$	30.6828	+	2.06836i	1.04506	+	0.0704485i
$863$	30.0211	+	41.3205i	1.02193	+	1.40657i	0.910842	+	0.412755i	$0.135433\pi$
$863$	30.0211	+	41.3205i	1.02193	+	1.40657i	0.111087	+	0.993811i	$0.464567\pi$
$864$	13.0413	+	18.8219i	0.443675	+	0.640333i
$865$	7.42015	−	42.9672i	0.252293	−	1.46093i
$866$	0.349691	−	5.18745i	0.0118830	−	0.176277i
$867$	1.49396	−	4.59793i	0.0507375	−	0.156154i
$868$	12.2078	−	2.21567i	0.414360	−	0.0752046i
$869$	−6.08201	−	1.97617i	−0.206318	−	0.0670368i
$870$	56.3168	+	13.6812i	1.90932	+	0.463835i
$871$	1.70468	+	5.24648i	0.0577610	+	0.177770i
$872$	−5.69225	+	27.8054i	−0.192764	+	0.941611i
$873$	2.78388	−	3.83168i	0.0942200	−	0.129683i
$874$	−1.99700	−	1.66718i	−0.0675495	−	0.0563931i
$875$	−3.04996	+	15.1345i	−0.103108	+	0.511638i
$876$	−45.8832	+	8.32759i	−1.55025	+	0.281363i
$877$	−14.2117	−	10.3254i	−0.479894	−	0.348664i	0.321390	−	0.946947i	$-0.395850\pi$
$877$	−14.2117	−	10.3254i	−0.479894	−	0.348664i	−0.801285	+	0.598283i	$0.795850\pi$
$878$	1.23475	−	3.07829i	0.0416709	−	0.103887i
$879$	−19.4797	−	59.9522i	−0.657033	−	2.02214i
$880$	31.7051	−	33.7341i	1.06878	−	1.13718i
$881$	2.27227	−	6.99332i	0.0765546	−	0.235611i	−0.905455	−	0.424443i	$-0.860470\pi$
$881$	2.27227	−	6.99332i	0.0765546	−	0.235611i	0.982009	+	0.188832i	$0.0604701\pi$
$882$	−5.35157	−	4.46771i	−0.180197	−	0.150436i
$883$	13.8280	−	42.5583i	0.465350	−	1.43220i	−0.393191	−	0.919457i	$-0.628629\pi$
$883$	13.8280	−	42.5583i	0.465350	−	1.43220i	0.858541	−	0.512745i	$-0.171371\pi$
$884$	−16.2854	+	17.0340i	−0.547739	+	0.572915i
$885$	7.85771	+	1.35697i	0.264134	+	0.0456142i
$886$	0.334936	+	1.32917i	0.0112524	+	0.0446543i
$887$	22.0394	+	30.3347i	0.740012	+	1.01854i	0.998618	+	0.0525565i	$0.0167370\pi$
$887$	22.0394	+	30.3347i	0.740012	+	1.01854i	−0.258606	+	0.965983i	$0.583263\pi$
$888$	−3.17913	−	28.2073i	−0.106685	−	0.946577i
$889$	9.35651	+	6.79790i	0.313807	+	0.227994i
$890$	35.6144	−	2.70631i	1.19380	−	0.0907158i
$891$	33.3647	+	45.9226i	1.11776	+	1.53846i
$892$	−4.44118	+	32.7914i	−0.148702	+	1.09794i
$893$	6.42640			0.215051
$894$	4.82925	+	7.68552i	0.161514	+	0.257042i
$895$	−5.17238	−	5.31850i	−0.172894	−	0.177778i
$896$	2.44512	+	15.4304i	0.0816859	+	0.515492i
$897$	1.67962	−	0.545741i	0.0560808	−	0.0182218i
$898$	11.8612	+	47.0700i	0.395812	+	1.57075i
$899$			41.3333i			1.37854i
$900$	4.34744	+	8.64730i	0.144915	+	0.288243i
$901$		−	12.6606i		−	0.421785i
$902$	28.8231	−	7.26312i	0.959704	−	0.241835i
$903$	−19.7327	+	6.41154i	−0.656663	+	0.213363i
$904$	5.39627	−	26.3596i	0.179477	−	0.876708i
$905$	1.57298	+	10.9130i	0.0522875	+	0.362759i
$906$	−48.1761	+	30.2718i	−1.60054	+	1.00571i
$907$	−9.10715			−0.302398			−0.151199	−	0.988503i	$-0.548313\pi$
$907$	−9.10715			−0.302398			−0.151199	+	0.988503i	$0.548313\pi$
$908$	24.4293	+	3.30864i	0.810716	+	0.109801i
$909$	−9.42650	−	12.9745i	−0.312657	−	0.430336i
$910$	−13.0977	−	3.18184i	−0.434183	−	0.105477i
$911$	4.83681	+	3.51415i	0.160251	+	0.116429i	0.665021	−	0.746825i	$-0.268423\pi$
$911$	4.83681	+	3.51415i	0.160251	+	0.116429i	−0.504770	+	0.863254i	$0.668423\pi$
$912$	42.5870	+	28.1088i	1.41020	+	0.930774i
$913$	12.7825	+	17.5937i	0.423040	+	0.582265i
$914$	47.2187	−	11.8986i	1.56186	−	0.393571i
$915$	−1.41472	−	9.81499i	−0.0467691	−	0.324473i
$916$	−15.6652	+	16.3852i	−0.517593	+	0.541384i
$917$	−3.86572	+	11.8974i	−0.127657	+	0.392888i
$918$	14.0052	−	16.7758i	0.462239	−	0.553685i
$919$	5.41966	−	16.6800i	0.178778	−	0.550222i	−0.821008	−	0.570917i	$-0.806588\pi$
$919$	5.41966	−	16.6800i	0.178778	−	0.550222i	0.999786	+	0.0206948i	$0.00658785\pi$
$920$	0.979616	+	1.52987i	0.0322970	+	0.0504384i
$921$	2.30252	+	7.08644i	0.0758708	+	0.233506i
$922$	48.7829	+	19.5676i	1.60658	+	0.644425i
$923$	37.8721	+	27.5157i	1.24658	+	0.905690i
$924$	5.08488	+	28.0165i	0.167280	+	0.921676i
$925$	−0.701592	+	25.1815i	−0.0230682	+	0.827962i
$926$	13.0774	−	15.6645i	0.429750	−	0.514769i
$927$	2.31416	−	3.18517i	0.0760070	−	0.104615i
$928$	−52.0328	−	1.16500i	−1.70806	−	0.0382430i
$929$	−8.23207	−	25.3357i	−0.270085	−	0.831237i	−0.990478	−	0.137671i	$-0.956038\pi$
$929$	−8.23207	−	25.3357i	−0.270085	−	0.831237i	0.720393	−	0.693566i	$-0.243962\pi$
$930$	−21.5680	+	18.3205i	−0.707244	+	0.600753i
$931$	31.0210	+	10.0793i	1.01667	+	0.330337i
$932$	12.6737	−	2.30021i	0.415140	−	0.0753460i
$933$	6.91618	−	21.2858i	0.226425	−	0.696866i
$934$	−15.8175	−	1.06627i	−0.517563	−	0.0348894i
$935$	−39.0833	−	20.6045i	−1.27816	−	0.673840i
$936$	−7.69326	+	3.49475i	−0.251462	+	0.114229i
$937$	5.75045	+	7.91482i	0.187859	+	0.258566i	0.892550	−	0.450949i	$-0.148914\pi$
$937$	5.75045	+	7.91482i	0.187859	+	0.258566i	−0.704691	+	0.709515i	$0.748914\pi$
$938$	0.234742	−	3.48225i	0.00766458	−	0.113699i
$939$	7.71069	−	10.6129i	0.251629	−	0.346337i
$940$	−4.27971	−	1.35029i	−0.139589	−	0.0440417i
$941$	0.184526	+	0.253979i	0.00601539	+	0.00827947i	0.812014	−	0.583638i	$-0.198371\pi$
$941$	0.184526	+	0.253979i	0.00601539	+	0.00827947i	−0.805999	+	0.591917i	$0.798371\pi$
$942$	−50.9767	+	32.0316i	−1.66091	+	1.04364i
$943$			1.16639i			0.0379829i
$944$	−7.15378	+	0.321586i	−0.232836	+	0.0104667i
$945$	12.3166	+	2.12700i	0.400659	+	0.0691913i
$946$	−51.2449	−	20.5552i	−1.66612	−	0.668306i
$947$	−14.4398	−	44.4410i	−0.469229	−	1.44414i	−0.853585	−	0.520954i	$-0.825576\pi$
$947$	−14.4398	−	44.4410i	−0.469229	−	1.44414i	0.384356	−	0.923185i	$-0.374424\pi$
$948$	−2.13558	+	4.43483i	−0.0693605	+	0.144036i
$949$			36.1303i			1.17284i
$950$	−33.9407	−	29.9780i	−1.10118	−	0.972616i
$951$	−40.2806			−1.30619
$952$	13.5749	−	6.16656i	0.439967	−	0.199859i
$953$	−31.6721	+	10.2909i	−1.02596	+	0.333354i	−0.773191	−	0.634173i	$-0.781341\pi$
$953$	−31.6721	+	10.2909i	−1.02596	+	0.333354i	−0.252768	+	0.967527i	$0.581341\pi$
$954$	1.68999	−	4.21321i	0.0547153	−	0.136408i
$955$	−1.32936	−	0.700830i	−0.0430170	−	0.0226783i
$956$	−4.17484	−	0.565429i	−0.135024	−	0.0182873i
$957$	−94.8585			−3.06634
$958$	−5.69525	+	3.57865i	−0.184005	+	0.115621i
$959$	−0.777419	+	0.564828i	−0.0251042	+	0.0182393i
$960$	−22.4550	−	27.6675i	−0.724732	−	0.892964i
$961$	8.75140	+	6.35826i	0.282303	+	0.205105i
$962$	−21.9431	−	1.47921i	−0.707475	−	0.0476915i
$963$	10.5869	−	7.69184i	0.341159	−	0.247866i
$964$	18.4541	−	38.3224i	0.594365	−	1.23428i
$965$	−9.53987	+	4.69462i	−0.307099	+	0.151125i
$966$	−1.11481	−	0.0751506i	−0.0358686	−	0.00241793i
$967$	−28.5494	−	9.27626i	−0.918087	−	0.298304i	−0.188405	−	0.982091i	$-0.560332\pi$
$967$	−28.5494	−	9.27626i	−0.918087	−	0.298304i	−0.729682	+	0.683787i	$0.760332\pi$
$968$	−22.0394	+	38.8444i	−0.708373	+	1.24851i
$969$	15.0486	−	46.3148i	0.483431	−	1.48785i
$970$	8.12096	−	13.1723i	0.260748	−	0.422938i
$971$	−12.0721	+	3.92245i	−0.387411	+	0.125878i	−0.496245	−	0.868182i	$-0.665288\pi$
$971$	−12.0721	+	3.92245i	−0.387411	+	0.125878i	0.108834	+	0.994060i	$0.465288\pi$
$972$	17.0862	−	9.19498i	0.548042	−	0.294929i
$973$	−11.8882	−	8.63727i	−0.381118	−	0.276898i
$974$	−12.0575	+	14.4429i	−0.386348	+	0.462781i
$975$	29.4909	−	8.68193i	0.944466	−	0.278044i
$976$	3.12948	+	8.33737i	0.100172	+	0.266873i
$977$	−29.7939	+	41.0078i	−0.953191	+	1.31196i	−0.00309631	+	0.999995i	$0.500986\pi$
$977$	−29.7939	+	41.0078i	−0.953191	+	1.31196i	−0.950095	+	0.311960i	$0.899014\pi$
$978$	−13.3024	+	33.1634i	−0.425363	+	1.06045i
$979$	−55.5993	+	18.0653i	−1.77696	+	0.577370i
$980$	−18.5408	−	13.2304i	−0.592265	−	0.422630i
$981$	9.23677	+	3.00121i	0.294907	+	0.0958213i
$982$	−16.0922	+	19.2758i	−0.513524	+	0.615116i
$983$	50.4346	+	16.3872i	1.60862	+	0.522671i	0.969218	−	0.246206i	$-0.0791839\pi$
$983$	50.4346	+	16.3872i	1.60862	+	0.522671i	0.639397	+	0.768876i	$0.279184\pi$
$984$	−2.56233	−	22.7347i	−0.0816842	−	0.724756i
$985$	−9.00380	+	8.75644i	−0.286885	+	0.279003i
$986$	12.1371	+	48.1650i	0.386523	+	1.53388i
$987$	2.23305	−	1.62241i	0.0710788	−	0.0516418i
$988$	27.3204	−	28.5762i	0.869178	−	0.909129i
$989$	1.27351	−	1.75283i	0.0404951	−	0.0557368i
$990$	−10.2558	−	12.0738i	−0.325952	−	0.383731i
$991$	1.47581	−	1.07224i	0.0468808	−	0.0340609i	−0.564098	−	0.825708i	$-0.690776\pi$
$991$	1.47581	−	1.07224i	0.0468808	−	0.0340609i	0.610979	+	0.791647i	$0.290776\pi$
$992$	15.3942	−	20.2204i	0.488765	−	0.641999i
$993$			42.5146i			1.34916i
$994$	−15.7576	−	25.0775i	−0.499801	−	0.795409i
$995$	3.51830	+	7.14949i	0.111538	+	0.226654i
$996$	14.7398	−	7.93223i	0.467048	−	0.251342i
$997$	−5.04048	−	15.5130i	−0.159634	−	0.491302i	0.838967	−	0.544182i	$-0.183160\pi$
$997$	−5.04048	−	15.5130i	−0.159634	−	0.491302i	−0.998601	+	0.0528802i	$0.983160\pi$
$998$	−21.4175	+	5.39697i	−0.677958	+	0.170838i
$999$	20.3944			0.645250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.o.a.109.18	yes	112
4.3	odd	2		800.2.be.a.209.7		112
5.2	odd	4		1000.2.t.b.701.5		224
5.3	odd	4		1000.2.t.b.701.52		224
5.4	even	2		1000.2.o.a.549.11		112
8.3	odd	2		800.2.be.a.209.22		112
8.5	even	2	inner	200.2.o.a.109.1	✓	112
25.2	odd	20		1000.2.t.b.301.27		224
25.11	even	5		1000.2.o.a.949.28		112
25.14	even	10	inner	200.2.o.a.189.1	yes	112
25.23	odd	20		1000.2.t.b.301.30		224
40.13	odd	4		1000.2.t.b.701.30		224
40.29	even	2		1000.2.o.a.549.28		112
40.37	odd	4		1000.2.t.b.701.27		224
100.39	odd	10		800.2.be.a.689.22		112
200.61	even	10		1000.2.o.a.949.11		112
200.77	odd	20		1000.2.t.b.301.5		224
200.139	odd	10		800.2.be.a.689.7		112
200.173	odd	20		1000.2.t.b.301.52		224
200.189	even	10	inner	200.2.o.a.189.18	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.1	✓	112	8.5	even	2	inner
200.2.o.a.109.18	yes	112	1.1	even	1	trivial
200.2.o.a.189.1	yes	112	25.14	even	10	inner
200.2.o.a.189.18	yes	112	200.189	even	10	inner
800.2.be.a.209.7		112	4.3	odd	2
800.2.be.a.209.22		112	8.3	odd	2
800.2.be.a.689.7		112	200.139	odd	10
800.2.be.a.689.22		112	100.39	odd	10
1000.2.o.a.549.11		112	5.4	even	2
1000.2.o.a.549.28		112	40.29	even	2
1000.2.o.a.949.11		112	200.61	even	10
1000.2.o.a.949.28		112	25.11	even	5
1000.2.t.b.301.5		224	200.77	odd	20
1000.2.t.b.301.27		224	25.2	odd	20
1000.2.t.b.301.30		224	25.23	odd	20
1000.2.t.b.301.52		224	200.173	odd	20
1000.2.t.b.701.5		224	5.2	odd	4
1000.2.t.b.701.27		224	40.37	odd	4
1000.2.t.b.701.30		224	40.13	odd	4
1000.2.t.b.701.52		224	5.3	odd	4

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.345564 + 1.37134i) q^{2} +(0.615546 + 1.89446i) q^{3} +(-1.76117 + 0.947775i) q^{4} +(0.987308 + 2.00630i) q^{5} +(-2.38524 + 1.49878i) q^{6} -1.38088i q^{7} +(-1.90832 - 2.08765i) q^{8} +(-0.783019 + 0.568896i) q^{9} +(-2.41014 + 2.04724i) q^{10} +(3.04233 - 4.18740i) q^{11} +(-2.87960 - 2.75306i) q^{12} +(-2.49716 + 1.81429i) q^{13} +(1.89366 - 0.477183i) q^{14} +(-3.19311 + 3.10538i) q^{15} +(2.20344 - 3.33839i) q^{16} +(-3.63061 - 1.17966i) q^{17} +(-1.05074 - 0.877198i) q^{18} +(6.09071 + 1.97899i) q^{19} +(-3.64034 - 2.59768i) q^{20} +(2.61602 - 0.849997i) q^{21} +(6.79369 + 2.72506i) q^{22} +(-0.168832 + 0.232378i) q^{23} +(2.78031 - 4.90029i) q^{24} +(-3.05044 + 3.96166i) q^{25} +(-3.35095 - 2.79751i) q^{26} +(3.27483 + 2.37930i) q^{27} +(1.30877 + 2.43197i) q^{28} +(-8.75018 + 2.84311i) q^{29} +(-5.36197 - 3.30574i) q^{30} +(1.38826 - 4.27263i) q^{31} +(5.33951 + 1.86805i) q^{32} +(9.80555 + 3.18602i) q^{33} +(0.363107 - 5.38647i) q^{34} +(2.77046 - 1.36336i) q^{35} +(0.839843 - 1.74405i) q^{36} +(4.07603 - 2.96141i) q^{37} +(-0.609147 + 9.03633i) q^{38} +(-4.97421 - 3.61398i) q^{39} +(2.30435 - 5.88982i) q^{40} +(3.28522 - 2.38685i) q^{41} +(2.06964 + 3.29374i) q^{42} -7.54302 q^{43} +(-1.38934 + 10.2582i) q^{44} +(-1.91445 - 1.00929i) q^{45} +(-0.377013 - 0.151226i) q^{46} +(0.954360 - 0.310090i) q^{47} +(7.68075 + 2.11940i) q^{48} +5.09317 q^{49} +(-6.48693 - 2.81420i) q^{50} -7.60418i q^{51} +(2.67838 - 5.56202i) q^{52} +(1.02485 + 3.15418i) q^{53} +(-2.13118 + 5.31312i) q^{54} +(11.4049 + 1.96955i) q^{55} +(-2.88280 + 2.63517i) q^{56} +12.7567i q^{57} +(-6.92263 - 11.0170i) q^{58} +(-1.05228 - 1.44834i) q^{59} +(2.68040 - 8.49545i) q^{60} +(-1.30861 + 1.80115i) q^{61} +(6.33899 + 0.427317i) q^{62} +(0.785578 + 1.08126i) q^{63} +(-0.716599 + 7.96784i) q^{64} +(-6.10547 - 3.21877i) q^{65} +(-0.980677 + 14.5478i) q^{66} +(0.552275 - 1.69973i) q^{67} +(7.51218 - 1.36343i) q^{68} +(-0.544154 - 0.176806i) q^{69} +(2.82700 + 3.32812i) q^{70} +(-4.68658 - 14.4238i) q^{71} +(2.68191 + 0.549033i) q^{72} +(6.88021 - 9.46979i) q^{73} +(5.46964 + 4.56628i) q^{74} +(-9.38289 - 3.34035i) q^{75} +(-12.6024 + 2.28728i) q^{76} +(-5.78231 - 4.20109i) q^{77} +(3.23710 - 8.07022i) q^{78} +(-0.381800 - 1.17506i) q^{79} +(8.87327 + 1.12474i) q^{80} +(-3.38894 + 10.4301i) q^{81} +(4.40845 + 3.68036i) q^{82} +(-1.29836 + 3.99593i) q^{83} +(-3.80165 + 3.97639i) q^{84} +(-1.21779 - 8.44877i) q^{85} +(-2.60660 - 10.3441i) q^{86} +(-10.7723 - 14.8268i) q^{87} +(-14.5476 + 1.63960i) q^{88} +(-9.13763 - 6.63888i) q^{89} +(0.722518 - 2.97415i) q^{90} +(2.50532 + 3.44828i) q^{91} +(0.0771007 - 0.569272i) q^{92} +8.94886 q^{93} +(0.755034 + 1.20160i) q^{94} +(2.04297 + 14.1736i) q^{95} +(-0.252228 + 11.2653i) q^{96} +(-4.65397 + 1.51217i) q^{97} +(1.76002 + 6.98448i) q^{98} +5.00958i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28}+ \cdots + 90 q^{98}+O(q^{100}) \) 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

Introduction

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