LMFDB - Embedded newform 544.2.bd.b.205.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(69,544)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("544.69"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.bd (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,0,0,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			205.6
Character	$\chi$	$=$	544.205
Dual form			544.2.bd.b.69.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24990 + 0.661625i) q^{2} +(1.13988 - 2.75191i) q^{3} +(1.12450 - 1.65393i) q^{4} +(-3.02227 + 1.25186i) q^{5} +(0.395998 + 4.19379i) q^{6} +(1.22449 - 1.22449i) q^{7} +(-0.311237 + 2.81125i) q^{8} +(-4.15239 - 4.15239i) q^{9} +(2.94927 - 3.56431i) q^{10} +(1.01782 + 2.45723i) q^{11} +(-3.26968 - 4.97982i) q^{12} +(-5.68863 - 2.35631i) q^{13} +(-0.720337 + 2.34064i) q^{14} +9.74399i q^{15} +(-1.47098 - 3.71971i) q^{16} -1.00000i q^{17} +(7.93739 + 2.44275i) q^{18} +(-0.386916 - 0.160266i) q^{19} +(-1.32805 + 6.40635i) q^{20} +(-1.97392 - 4.76546i) q^{21} +(-2.89793 - 2.39788i) q^{22} +(-5.00144 - 5.00144i) q^{23} +(7.38155 + 4.06099i) q^{24} +(4.03139 - 4.03139i) q^{25} +(8.66921 - 0.818589i) q^{26} +(-7.90449 + 3.27415i) q^{27} +(-0.648277 - 3.40216i) q^{28} +(-2.60102 + 6.27941i) q^{29} +(-6.44687 - 12.1790i) q^{30} -1.80647 q^{31} +(4.29963 + 3.67603i) q^{32} +7.92227 q^{33} +(0.661625 + 1.24990i) q^{34} +(-2.16784 + 5.23362i) q^{35} +(-11.5371 + 2.19839i) q^{36} +(-2.25310 + 0.933264i) q^{37} +(0.589642 - 0.0556769i) q^{38} +(-12.9687 + 12.9687i) q^{39} +(-2.57866 - 8.88597i) q^{40} +(-1.58839 - 1.58839i) q^{41} +(5.62015 + 4.65036i) q^{42} +(1.74976 + 4.22430i) q^{43} +(5.20862 + 1.07976i) q^{44} +(17.7478 + 7.35139i) q^{45} +(9.56039 + 2.94223i) q^{46} +9.11765i q^{47} +(-11.9131 - 0.192012i) q^{48} +4.00126i q^{49} +(-2.37157 + 7.70611i) q^{50} +(-2.75191 - 1.13988i) q^{51} +(-10.2941 + 6.75892i) q^{52} +(-2.36249 - 5.70355i) q^{53} +(7.71358 - 9.32217i) q^{54} +(-6.15222 - 6.15222i) q^{55} +(3.06124 + 3.82345i) q^{56} +(-0.882076 + 0.882076i) q^{57} +(-0.903602 - 9.56954i) q^{58} +(-0.0181410 + 0.00751426i) q^{59} +(16.1159 + 10.9572i) q^{60} +(-1.33410 + 3.22080i) q^{61} +(2.25791 - 1.19521i) q^{62} -10.1691 q^{63} +(-7.80626 - 1.74993i) q^{64} +20.1423 q^{65} +(-9.90205 + 5.24157i) q^{66} +(4.24882 - 10.2576i) q^{67} +(-1.65393 - 1.12450i) q^{68} +(-19.4646 + 8.06250i) q^{69} +(-0.753114 - 7.97580i) q^{70} +(11.7269 - 11.7269i) q^{71} +(12.9658 - 10.3810i) q^{72} +(-10.2149 - 10.2149i) q^{73} +(2.19868 - 2.65719i) q^{74} +(-6.49874 - 15.6893i) q^{75} +(-0.700157 + 0.459713i) q^{76} +(4.25515 + 1.76254i) q^{77} +(7.62918 - 24.7900i) q^{78} -13.3670i q^{79} +(9.10225 + 9.40048i) q^{80} +7.86755i q^{81} +(3.03625 + 0.934411i) q^{82} +(-8.52299 - 3.53034i) q^{83} +(-10.1014 - 2.09405i) q^{84} +(1.25186 + 3.02227i) q^{85} +(-4.98193 - 4.12227i) q^{86} +(14.3156 + 14.3156i) q^{87} +(-7.22466 + 2.09656i) q^{88} +(4.21014 - 4.21014i) q^{89} +(-27.0469 + 2.55390i) q^{90} +(-9.85093 + 4.08039i) q^{91} +(-13.8962 + 2.64790i) q^{92} +(-2.05916 + 4.97126i) q^{93} +(-6.03246 - 11.3962i) q^{94} +1.36999 q^{95} +(15.0172 - 7.64198i) q^{96} +1.25916 q^{97} +(-2.64733 - 5.00118i) q^{98} +(5.97699 - 14.4297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 20 q^{6} - 24 q^{8} - 16 q^{12} - 20 q^{16} - 20 q^{18} - 48 q^{22} - 8 q^{23} + 68 q^{24} + 20 q^{26} - 24 q^{27} + 20 q^{30} + 48 q^{31} - 24 q^{35} + 8 q^{36} + 68 q^{38} - 24 q^{39} - 36 q^{40}+ \cdots - 136 q^{99}+O(q^{100}) $ 128 * q + 20 * q^6 - 24 * q^8 - 16 * q^12 - 20 * q^16 - 20 * q^18 - 48 * q^22 - 8 * q^23 + 68 * q^24 + 20 * q^26 - 24 * q^27 + 20 * q^30 + 48 * q^31 - 24 * q^35 + 8 * q^36 + 68 * q^38 - 24 * q^39 - 36 * q^40 - 16 * q^42 - 8 * q^43 - 40 * q^44 - 80 * q^45 + 12 * q^50 + 56 * q^52 - 16 * q^53 - 136 * q^54 + 32 * q^55 + 128 * q^56 - 32 * q^58 + 20 * q^60 - 12 * q^62 - 80 * q^63 + 12 * q^64 - 8 * q^66 + 40 * q^67 - 4 * q^68 + 100 * q^70 - 44 * q^72 + 84 * q^74 + 32 * q^75 - 32 * q^76 - 16 * q^77 - 64 * q^78 + 44 * q^80 + 40 * q^82 + 84 * q^84 - 120 * q^86 - 56 * q^87 + 128 * q^88 - 68 * q^90 - 56 * q^91 - 40 * q^92 + 32 * q^95 - 72 * q^96 - 12 * q^98 - 136 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	−1.24990	+	0.661625i	−0.883813	+	0.467840i
$2$	−1.24990	+	0.661625i	−0.883813	+	0.467840i
$3$	1.13988	−	2.75191i	0.658110	−	1.58882i	−0.142609	−	0.989779i	$-0.545549\pi$
$3$	1.13988	−	2.75191i	0.658110	−	1.58882i	0.800719	−	0.599040i	$-0.204451\pi$
$4$	1.12450	−	1.65393i	0.562252	−	0.826966i
$5$	−3.02227	+	1.25186i	−1.35160	+	0.559850i	−0.936737	−	0.350034i	$-0.886170\pi$
$5$	−3.02227	+	1.25186i	−1.35160	+	0.559850i	−0.414861	+	0.909885i	$0.636170\pi$
$6$	0.395998	+	4.19379i	0.161666	+	1.71211i
$7$	1.22449	−	1.22449i	0.462813	−	0.462813i	−0.436763	−	0.899576i	$-0.643875\pi$
$7$	1.22449	−	1.22449i	0.462813	−	0.462813i	0.899576	+	0.436763i	$0.143875\pi$
$8$	−0.311237	+	2.81125i	−0.110039	+	0.993927i
$9$	−4.15239	−	4.15239i	−1.38413	−	1.38413i
$10$	2.94927	−	3.56431i	0.932640	−	1.12713i
$11$	1.01782	+	2.45723i	0.306883	+	0.740882i	0.999803	+	0.0198666i	$0.00632416\pi$
$11$	1.01782	+	2.45723i	0.306883	+	0.740882i	−0.692919	+	0.721015i	$0.743676\pi$
$12$	−3.26968	−	4.97982i	−0.943875	−	1.43755i
$13$	−5.68863	−	2.35631i	−1.57774	−	0.653522i	−0.589688	−	0.807631i	$-0.700749\pi$
$13$	−5.68863	−	2.35631i	−1.57774	−	0.653522i	−0.988054	+	0.154109i	$0.950749\pi$
$14$	−0.720337	+	2.34064i	−0.192518	+	0.625563i
$15$			9.74399i			2.51589i
$16$	−1.47098	−	3.71971i	−0.367745	−	0.929927i
$17$		−	1.00000i		−	0.242536i
$17$		−	1.00000i		−	0.242536i
$18$	7.93739	+	2.44275i	1.87086	+	0.575761i
$19$	−0.386916	−	0.160266i	−0.0887646	−	0.0367675i	0.337859	−	0.941197i	$-0.390297\pi$
$19$	−0.386916	−	0.160266i	−0.0887646	−	0.0367675i	−0.426624	+	0.904429i	$0.640297\pi$
$20$	−1.32805	+	6.40635i	−0.296962	+	1.43250i
$21$	−1.97392	−	4.76546i	−0.430744	−	1.03991i
$22$	−2.89793	−	2.39788i	−0.617841	−	0.511229i
$23$	−5.00144	−	5.00144i	−1.04287	−	1.04287i	−0.999039	−	0.0438344i	$-0.986043\pi$
$23$	−5.00144	−	5.00144i	−1.04287	−	1.04287i	−0.0438344	−	0.999039i	$-0.513957\pi$
$24$	7.38155	+	4.06099i	1.50675	+	0.828945i
$25$	4.03139	−	4.03139i	0.806278	−	0.806278i
$26$	8.66921	−	0.818589i	1.70017	−	0.160538i
$27$	−7.90449	+	3.27415i	−1.52122	+	0.630110i
$28$	−0.648277	−	3.40216i	−0.122513	−	0.642948i
$29$	−2.60102	+	6.27941i	−0.482997	+	1.16606i	0.475182	+	0.879888i	$0.342382\pi$
$29$	−2.60102	+	6.27941i	−0.482997	+	1.16606i	−0.958179	+	0.286170i	$0.907618\pi$
$30$	−6.44687	−	12.1790i	−1.17703	−	2.22357i
$31$	−1.80647			−0.324452			−0.162226	−	0.986754i	$-0.551867\pi$
$31$	−1.80647			−0.324452			−0.162226	+	0.986754i	$0.551867\pi$
$32$	4.29963	+	3.67603i	0.760074	+	0.649836i
$33$	7.92227			1.37909
$34$	0.661625	+	1.24990i	0.113468	+	0.214356i
$35$	−2.16784	+	5.23362i	−0.366431	+	0.884643i
$36$	−11.5371	+	2.19839i	−1.92286	+	0.366398i
$37$	−2.25310	+	0.933264i	−0.370407	+	0.153428i	−0.560119	−	0.828412i	$-0.689245\pi$
$37$	−2.25310	+	0.933264i	−0.370407	+	0.153428i	0.189712	+	0.981840i	$0.439245\pi$
$38$	0.589642	−	0.0556769i	0.0956526	−	0.00903198i
$39$	−12.9687	+	12.9687i	−2.07666	+	2.07666i
$40$	−2.57866	−	8.88597i	−0.407722	−	1.40500i
$41$	−1.58839	−	1.58839i	−0.248065	−	0.248065i	0.572111	−	0.820176i	$-0.306125\pi$
$41$	−1.58839	−	1.58839i	−0.248065	−	0.248065i	−0.820176	+	0.572111i	$0.806125\pi$
$42$	5.62015	+	4.65036i	0.867207	+	0.717565i
$43$	1.74976	+	4.22430i	0.266836	+	0.644199i	0.999331	−	0.0365733i	$-0.0116442\pi$
$43$	1.74976	+	4.22430i	0.266836	+	0.644199i	−0.732495	+	0.680772i	$0.761644\pi$
$44$	5.20862	+	1.07976i	0.785230	+	0.162780i
$45$	17.7478	+	7.35139i	2.64569	+	1.09588i
$46$	9.56039	+	2.94223i	1.40960	+	0.433808i
$47$			9.11765i			1.32995i	0.746868	+	0.664973i	$0.231557\pi$
$47$			9.11765i			1.32995i	−0.746868	+	0.664973i	$0.768443\pi$
$48$	−11.9131	−	0.192012i	−1.71950	−	0.0277145i
$49$			4.00126i			0.571608i
$50$	−2.37157	+	7.70611i	−0.335391	+	1.08981i
$51$	−2.75191	−	1.13988i	−0.385345	−	0.159615i
$52$	−10.2941	+	6.75892i	−1.42753	+	0.937294i
$53$	−2.36249	−	5.70355i	−0.324512	−	0.783442i	−0.998981	−	0.0451384i	$-0.985627\pi$
$53$	−2.36249	−	5.70355i	−0.324512	−	0.783442i	0.674468	−	0.738304i	$-0.264373\pi$
$54$	7.71358	−	9.32217i	1.04968	−	1.26859i
$55$	−6.15222	−	6.15222i	−0.829566	−	0.829566i
$56$	3.06124	+	3.82345i	0.409075	+	0.510930i
$57$	−0.882076	+	0.882076i	−0.116834	+	0.116834i
$58$	−0.903602	−	9.56954i	−0.118649	−	1.25654i
$59$	−0.0181410	+	0.00751426i	−0.00236176	+	0.000978273i	−0.383864	−	0.923390i	$-0.625407\pi$
$59$	−0.0181410	+	0.00751426i	−0.00236176	+	0.000978273i	0.381502	+	0.924368i	$0.375407\pi$
$60$	16.1159	+	10.9572i	2.08055	+	1.41456i
$61$	−1.33410	+	3.22080i	−0.170814	+	0.412381i	−0.985984	−	0.166841i	$-0.946643\pi$
$61$	−1.33410	+	3.22080i	−0.170814	+	0.412381i	0.815170	+	0.579222i	$0.196643\pi$
$62$	2.25791	−	1.19521i	0.286755	−	0.151792i
$63$	−10.1691			−1.28119
$64$	−7.80626	−	1.74993i	−0.975783	−	0.218741i
$65$	20.1423			2.49835
$66$	−9.90205	+	5.24157i	−1.21886	+	0.645193i
$67$	4.24882	−	10.2576i	0.519076	−	1.25316i	−0.419396	−	0.907804i	$-0.637758\pi$
$67$	4.24882	−	10.2576i	0.519076	−	1.25316i	0.938472	−	0.345357i	$-0.112242\pi$
$68$	−1.65393	−	1.12450i	−0.200569	−	0.136366i
$69$	−19.4646	+	8.06250i	−2.34326	+	0.970611i
$70$	−0.753114	−	7.97580i	−0.0900143	−	0.953290i
$71$	11.7269	−	11.7269i	1.39172	−	1.39172i	0.570250	−	0.821471i	$-0.306846\pi$
$71$	11.7269	−	11.7269i	1.39172	−	1.39172i	0.821471	−	0.570250i	$-0.193154\pi$
$72$	12.9658	−	10.3810i	1.52803	−	1.22342i
$73$	−10.2149	−	10.2149i	−1.19556	−	1.19556i	−0.975482	−	0.220080i	$-0.929368\pi$
$73$	−10.2149	−	10.2149i	−1.19556	−	1.19556i	−0.220080	−	0.975482i	$-0.570632\pi$
$74$	2.19868	−	2.65719i	0.255591	−	0.308893i
$75$	−6.49874	−	15.6893i	−0.750410	−	1.81165i
$76$	−0.700157	+	0.459713i	−0.0803135	+	0.0527327i
$77$	4.25515	+	1.76254i	0.484919	+	0.200860i
$78$	7.62918	−	24.7900i	0.863834	−	2.80692i
$79$		−	13.3670i		−	1.50390i	−0.659218	−	0.751952i	$-0.729112\pi$
$79$		−	13.3670i		−	1.50390i	0.659218	−	0.751952i	$-0.270888\pi$
$80$	9.10225	+	9.40048i	1.01766	+	1.05101i
$81$			7.86755i			0.874172i
$82$	3.03625	+	0.934411i	0.335297	+	0.103188i
$83$	−8.52299	−	3.53034i	−0.935520	−	0.387505i	−0.137750	−	0.990467i	$-0.543987\pi$
$83$	−8.52299	−	3.53034i	−0.935520	−	0.387505i	−0.797770	+	0.602962i	$0.793987\pi$
$84$	−10.1014	−	2.09405i	−1.10216	−	0.228480i
$85$	1.25186	+	3.02227i	0.135784	+	0.327811i
$86$	−4.98193	−	4.12227i	−0.537215	−	0.444515i
$87$	14.3156	+	14.3156i	1.53479	+	1.53479i
$88$	−7.22466	+	2.09656i	−0.770152	+	0.223494i
$89$	4.21014	−	4.21014i	0.446274	−	0.446274i	−0.447840	−	0.894114i	$-0.647806\pi$
$89$	4.21014	−	4.21014i	0.446274	−	0.446274i	0.894114	+	0.447840i	$0.147806\pi$
$90$	−27.0469	+	2.55390i	−2.85099	+	0.269205i
$91$	−9.85093	+	4.08039i	−1.03266	+	0.427741i
$92$	−13.8962	+	2.64790i	−1.44878	+	0.276063i
$93$	−2.05916	+	4.97126i	−0.213525	+	0.515495i
$94$	−6.03246	−	11.3962i	−0.622201	−	1.17542i
$95$	1.36999			0.140558
$96$	15.0172	−	7.64198i	1.53268	−	0.779956i
$97$	1.25916			0.127849			0.0639244	−	0.997955i	$-0.479638\pi$
$97$	1.25916			0.127849			0.0639244	+	0.997955i	$0.479638\pi$
$98$	−2.64733	−	5.00118i	−0.267421	−	0.505195i
$99$	5.97699	−	14.4297i	0.600710	−	1.45024i
$100$	−2.13433	−	11.2010i	−0.213433	−	1.12010i
$101$	−13.5722	+	5.62180i	−1.35049	+	0.559390i	−0.936428	−	0.350860i	$-0.885889\pi$
$101$	−13.5722	+	5.62180i	−1.35049	+	0.559390i	−0.414059	+	0.910250i	$0.635889\pi$
$102$	4.19379	−	0.395998i	0.415247	−	0.0392097i
$103$	3.10099	−	3.10099i	0.305550	−	0.305550i	−0.537631	−	0.843181i	$-0.680680\pi$
$103$	3.10099	−	3.10099i	0.305550	−	0.305550i	0.843181	+	0.537631i	$0.180680\pi$
$104$	8.39468	−	15.2588i	0.823166	−	1.49625i
$105$	11.9314	+	11.9314i	1.16439	+	1.16439i
$106$	6.72648	+	5.56579i	0.653334	+	0.540597i
$107$	−0.0186441	−	0.0450107i	−0.00180239	−	0.00435135i	0.922976	−	0.384858i	$-0.125750\pi$
$107$	−0.0186441	−	0.0450107i	−0.00180239	−	0.00435135i	−0.924778	+	0.380507i	$0.875750\pi$
$108$	−3.47342	+	16.7553i	−0.334230	+	1.61228i
$109$	17.0949	+	7.08094i	1.63740	+	0.678231i	0.996031	−	0.0890056i	$-0.0283689\pi$
$109$	17.0949	+	7.08094i	1.63740	+	0.678231i	0.641364	+	0.767237i	$0.278369\pi$
$110$	11.7601	+	3.61920i	1.12128	+	0.345078i
$111$			7.26414i			0.689482i
$112$	−6.35593	−	2.75354i	−0.600579	−	0.260185i
$113$		−	16.8026i		−	1.58066i	−0.612682	−	0.790329i	$-0.709910\pi$
$113$		−	16.8026i		−	1.58066i	0.612682	−	0.790329i	$-0.290090\pi$
$114$	0.518904	−	1.68611i	0.0485998	−	0.157919i
$115$	21.3768	+	8.85457i	1.99340	+	0.825693i
$116$	7.46086	+	11.3631i	0.692724	+	1.05504i
$117$	13.8371	+	33.4057i	1.27924	+	3.08836i
$118$	0.0177029	−	0.0213946i	0.00162968	−	0.00196954i
$119$	−1.22449	−	1.22449i	−0.112249	−	0.112249i
$120$	−27.3928	−	3.03269i	−2.50061	−	0.276845i
$121$	2.77616	−	2.77616i	0.252378	−	0.252378i
$122$	−0.463470	−	4.90835i	−0.0419606	−	0.444381i
$123$	−6.18168	+	2.56054i	−0.557384	+	0.230876i
$124$	−2.03139	+	2.98778i	−0.182424	+	0.268311i
$125$	−0.877866	+	2.11936i	−0.0785187	+	0.189561i
$126$	12.7104	−	6.72813i	1.13233	−	0.599389i
$127$	−8.45928			−0.750640			−0.375320	−	0.926895i	$-0.622467\pi$
$127$	−8.45928			−0.750640			−0.375320	+	0.926895i	$0.622467\pi$
$128$	10.9149	−	2.97758i	0.964746	−	0.263184i
$129$	13.6194			1.19912
$130$	−25.1759	+	13.3267i	−2.20807	+	1.16883i
$131$	−3.72265	+	8.98728i	−0.325250	+	0.785222i	0.673682	+	0.739021i	$0.264712\pi$
$131$	−3.72265	+	8.98728i	−0.325250	+	0.785222i	−0.998932	+	0.0462014i	$0.985288\pi$
$132$	8.90862	−	13.1029i	0.775396	−	1.14046i
$133$	−0.670017	+	0.277530i	−0.0580979	+	0.0240649i
$134$	1.47605	+	15.6321i	0.127512	+	1.35040i
$135$	19.7907	−	19.7907i	1.70331	−	1.70331i
$136$	2.81125	+	0.311237i	0.241063	+	0.0266883i
$137$	0.0288605	+	0.0288605i	0.00246572	+	0.00246572i	0.708339	−	0.705873i	$-0.249445\pi$
$137$	0.0288605	+	0.0288605i	0.00246572	+	0.00246572i	−0.705873	+	0.708339i	$0.749445\pi$
$138$	18.9945	−	22.9556i	1.61692	−	1.95411i
$139$	0.320931	+	0.774795i	0.0272210	+	0.0657173i	0.936906	−	0.349583i	$-0.113677\pi$
$139$	0.320931	+	0.774795i	0.0272210	+	0.0657173i	−0.909685	+	0.415300i	$0.863677\pi$
$140$	6.21831	+	9.47068i	0.525543	+	0.800419i
$141$	25.0910	+	10.3930i	2.11304	+	0.875251i
$142$	−6.89862	+	22.4162i	−0.578920	+	1.88112i
$143$		−	16.3765i		−	1.36947i
$144$	−9.33759	+	21.5537i	−0.778132	+	1.79614i
$145$		−	22.2342i		−	1.84645i
$146$	19.5260	+	6.00917i	1.61598	+	0.497322i
$147$	11.0111	+	4.56095i	0.908182	+	0.376181i
$148$	−0.990065	+	4.77593i	−0.0813828	+	0.392579i
$149$	−3.32560	−	8.02872i	−0.272444	−	0.657738i	0.727143	−	0.686486i	$-0.240848\pi$
$149$	−3.32560	−	8.02872i	−0.272444	−	0.657738i	−0.999587	+	0.0287484i	$0.990848\pi$
$150$	18.5032	+	15.3104i	1.51078	+	1.25009i
$151$	−7.13146	−	7.13146i	−0.580350	−	0.580350i	0.354649	−	0.934999i	$-0.384600\pi$
$151$	−7.13146	−	7.13146i	−0.580350	−	0.580350i	−0.934999	+	0.354649i	$0.884600\pi$
$152$	0.570970	−	1.03784i	0.0463118	−	0.0841797i
$153$	−4.15239	+	4.15239i	−0.335701	+	0.335701i
$154$	−6.48466	+	0.612312i	−0.522548	+	0.0493415i
$155$	5.45964	−	2.26146i	0.438529	−	0.181645i
$156$	6.86599	+	36.0327i	0.549719	+	2.88493i
$157$	4.80884	−	11.6096i	0.383788	−	0.926545i	−0.607438	−	0.794367i	$-0.707803\pi$
$157$	4.80884	−	11.6096i	0.383788	−	0.926545i	0.991226	−	0.132178i	$-0.0421972\pi$
$158$	8.84394	+	16.7074i	0.703586	+	1.32917i
$159$	−18.3886			−1.45831
$160$	−17.5965	−	5.72738i	−1.39113	−	0.452789i
$161$	−12.2484			−0.965311
$162$	−5.20537	−	9.83365i	−0.408972	−	0.772605i
$163$	−2.08987	+	5.04539i	−0.163691	+	0.395185i	−0.984348	−	0.176236i	$-0.943608\pi$
$163$	−2.08987	+	5.04539i	−0.163691	+	0.395185i	0.820657	+	0.571421i	$0.193608\pi$
$164$	−4.41324	+	0.840936i	−0.344616	+	0.0656661i
$165$	−23.9432	+	9.91759i	−1.86397	+	0.772084i
$166$	12.9887	−	1.22645i	1.00811	−	0.0951911i
$167$	−8.05497	+	8.05497i	−0.623312	+	0.623312i	−0.946377	−	0.323064i	$-0.895287\pi$
$167$	−8.05497	+	8.05497i	−0.623312	+	0.623312i	0.323064	+	0.946377i	$0.395287\pi$
$168$	14.0113	−	4.06599i	1.08099	−	0.313698i
$169$	17.6159	+	17.6159i	1.35507	+	1.35507i
$170$	−3.56431	−	2.94927i	−0.273370	−	0.226199i
$171$	0.941139	+	2.27211i	0.0719707	+	0.173753i
$172$	8.95431	+	1.85626i	0.682760	+	0.141538i
$173$	−12.3322	−	5.10818i	−0.937603	−	0.388368i	−0.139045	−	0.990286i	$-0.544403\pi$
$173$	−12.3322	−	5.10818i	−0.937603	−	0.388368i	−0.798558	+	0.601918i	$0.794403\pi$
$174$	−27.3646	−	8.42150i	−2.07450	−	0.638432i
$175$		−	9.87278i		−	0.746312i
$176$	7.64298	−	7.40051i	0.576111	−	0.557834i
$177$			0.0584879i			0.00439622i
$178$	−2.47673	+	8.04780i	−0.185638	+	0.603208i
$179$	−22.5237	−	9.32963i	−1.68350	−	0.697329i	−0.684018	−	0.729465i	$-0.739769\pi$
$179$	−22.5237	−	9.32963i	−1.68350	−	0.697329i	−0.999484	+	0.0321357i	$0.989769\pi$
$180$	32.1162	−	21.0870i	2.39380	−	1.57173i
$181$	4.69553	+	11.3360i	0.349016	+	0.842599i	0.996737	+	0.0807214i	$0.0257224\pi$
$181$	4.69553	+	11.3360i	0.349016	+	0.842599i	−0.647721	+	0.761878i	$0.724278\pi$
$182$	9.61300	−	11.6177i	0.712563	−	0.861161i
$183$	7.34265	+	7.34265i	0.542784	+	0.542784i
$184$	15.6169	−	12.5037i	1.15130	−	0.921784i
$185$	5.64114	−	5.64114i	0.414745	−	0.414745i
$186$	−0.715360	−	7.57597i	−0.0524527	−	0.555497i
$187$	2.45723	−	1.01782i	0.179690	−	0.0744301i
$188$	15.0800	+	10.2528i	1.09982	+	0.747765i
$189$	−5.66980	+	13.6881i	−0.412417	+	0.995664i
$190$	−1.71236	+	0.906422i	−0.124227	+	0.0657587i
$191$	26.2696			1.90080			0.950399	−	0.311032i	$-0.100675\pi$
$191$	26.2696			1.90080			0.950399	+	0.311032i	$0.100675\pi$
$192$	−13.7139	+	19.4875i	−0.989713	+	1.40639i
$193$	21.7636			1.56658			0.783288	−	0.621660i	$-0.213541\pi$
$193$	21.7636			1.56658			0.783288	+	0.621660i	$0.213541\pi$
$194$	−1.57383	+	0.833094i	−0.112994	+	0.0598127i
$195$	22.9598	−	55.4299i	1.64419	−	3.96942i
$196$	6.61781	+	4.49943i	0.472700	+	0.321388i
$197$	17.1779	−	7.11530i	1.22387	−	0.506944i	0.325233	−	0.945634i	$-0.394557\pi$
$197$	17.1779	−	7.11530i	1.22387	−	0.506944i	0.898639	+	0.438690i	$0.144557\pi$
$198$	2.07643	+	21.9902i	0.147565	+	1.56278i
$199$	−1.42397	+	1.42397i	−0.100942	+	0.100942i	−0.755774	−	0.654832i	$-0.772739\pi$
$199$	−1.42397	+	1.42397i	−0.100942	+	0.100942i	0.654832	+	0.755774i	$0.272739\pi$
$200$	10.0785	+	12.5880i	0.712660	+	0.890104i
$201$	−23.3848	−	23.3848i	−1.64943	−	1.64943i
$202$	13.2444	−	16.0064i	0.931873	−	1.12621i
$203$	4.50415	+	10.8740i	0.316129	+	0.763204i
$204$	−4.97982	+	3.26968i	−0.348657	+	0.228923i
$205$	6.78898	+	2.81209i	0.474163	+	0.196405i
$206$	−1.82424	+	5.92763i	−0.127101	+	0.412998i
$207$			41.5359i			2.88694i
$208$	−0.396918	+	24.6261i	−0.0275213	+	1.70751i
$209$		−	1.11386i		−	0.0770474i
$210$	−22.8072	−	7.01895i	−1.57384	−	0.484354i
$211$	−13.8546	−	5.73876i	−0.953789	−	0.395072i	−0.149136	−	0.988817i	$-0.547649\pi$
$211$	−13.8546	−	5.73876i	−0.953789	−	0.395072i	−0.804654	+	0.593744i	$0.797649\pi$
$212$	−12.0899	−	2.50627i	−0.830338	−	0.172132i
$213$	−18.9041	−	45.6385i	−1.29529	−	3.12710i
$214$	0.0530835	+	0.0439236i	0.00362871	+	0.00300256i
$215$	−10.5765	−	10.5765i	−0.721310	−	0.721310i
$216$	−6.74429	−	23.2406i	−0.458890	−	1.58132i
$217$	−2.21200	+	2.21200i	−0.150161	+	0.150161i
$218$	−26.0519	+	2.45994i	−1.76446	+	0.166608i
$219$	−39.7542	+	16.4667i	−2.68634	+	1.11272i
$220$	−17.0936	+	3.25715i	−1.15245	+	0.219597i
$221$	−2.35631	+	5.68863i	−0.158502	+	0.382659i
$222$	−4.80614	−	9.07946i	−0.322567	−	0.609373i
$223$	2.35926			0.157988			0.0789940	−	0.996875i	$-0.474829\pi$
$223$	2.35926			0.157988			0.0789940	+	0.996875i	$0.474829\pi$
$224$	9.76610	−	0.763592i	0.652525	−	0.0510197i
$225$	−33.4798			−2.23199
$226$	11.1170	+	21.0016i	0.739495	+	1.39701i
$227$	−3.44699	+	8.32177i	−0.228785	+	0.552335i	−0.996030	−	0.0890186i	$-0.971627\pi$
$227$	−3.44699	+	8.32177i	−0.228785	+	0.552335i	0.767245	+	0.641354i	$0.221627\pi$
$228$	0.466995	+	2.45079i	0.0309275	+	0.162308i
$229$	5.87049	−	2.43164i	0.387933	−	0.160687i	−0.180188	−	0.983632i	$-0.557671\pi$
$229$	5.87049	−	2.43164i	0.387933	−	0.160687i	0.568121	+	0.822945i	$0.307671\pi$
$230$	−32.5773	+	3.07611i	−2.14808	+	0.202832i
$231$	9.70072	−	9.70072i	0.638261	−	0.638261i
$232$	−16.8435	−	9.26650i	−1.10583	−	0.608375i
$233$	8.91448	+	8.91448i	0.584007	+	0.584007i	0.936002	−	0.351995i	$-0.114497\pi$
$233$	8.91448	+	8.91448i	0.584007	+	0.584007i	−0.351995	+	0.936002i	$0.614497\pi$
$234$	−39.3970	−	32.5988i	−2.57546	−	2.13105i
$235$	−11.4140	−	27.5559i	−0.744570	−	1.79755i
$236$	−0.00797159	+	0.0384538i	−0.000518906	+	0.00250313i
$237$	−36.7848	−	15.2368i	−2.38943	−	0.989735i
$238$	2.34064	+	0.720337i	0.151721	+	0.0466925i
$239$		−	1.76233i		−	0.113995i	−0.998374	−	0.0569977i	$-0.981847\pi$
$239$		−	1.76233i		−	0.113995i	0.998374	−	0.0569977i	$-0.0181528\pi$
$240$	36.2448	−	14.3332i	2.33959	−	0.925204i
$241$			15.1913i			0.978557i	0.872128	+	0.489279i	$0.162740\pi$
$241$			15.1913i			0.978557i	−0.872128	+	0.489279i	$0.837260\pi$
$242$	−1.63315	+	5.30671i	−0.104983	+	0.341128i
$243$	−2.06267	−	0.854385i	−0.132320	−	0.0548088i
$244$	3.82678	+	5.82831i	0.244984	+	0.373119i
$245$	−5.00903	−	12.0929i	−0.320015	−	0.772585i
$246$	6.03238	−	7.29037i	0.384610	−	0.464817i
$247$	1.82338	+	1.82338i	0.116019	+	0.116019i
$248$	0.562240	−	5.07845i	0.0357023	−	0.322482i
$249$	−19.4304	+	19.4304i	−1.23135	+	1.23135i
$250$	−0.304973	−	3.22980i	−0.0192882	−	0.204271i
$251$	−20.8871	+	8.65172i	−1.31838	+	0.546092i	−0.927319	−	0.374272i	$-0.877893\pi$
$251$	−20.8871	+	8.65172i	−1.31838	+	0.546092i	−0.391063	+	0.920364i	$0.627893\pi$
$252$	−11.4352	+	16.8190i	−0.720350	+	1.05950i
$253$	7.19913	−	17.3802i	0.452605	−	1.09269i
$254$	10.5733	−	5.59687i	0.663425	−	0.351179i
$255$	9.74399			0.610192
$256$	−11.6724	+	10.9432i	−0.729528	+	0.683951i
$257$	−16.6477			−1.03846			−0.519228	−	0.854636i	$-0.673780\pi$
$257$	−16.6477			−1.03846			−0.519228	+	0.854636i	$0.673780\pi$
$258$	−17.0229	+	9.01095i	−1.05980	+	0.560997i
$259$	−1.61612	+	3.90166i	−0.100421	+	0.242438i
$260$	22.6501	−	33.3140i	1.40470	−	2.06605i
$261$	36.8750	−	15.2741i	2.28250	−	0.945444i
$262$	−1.29326	−	13.6962i	−0.0798980	−	0.846155i
$263$	−3.29782	+	3.29782i	−0.203352	+	0.203352i	−0.801435	−	0.598082i	$-0.795930\pi$
$263$	−3.29782	+	3.29782i	−0.203352	+	0.203352i	0.598082	+	0.801435i	$0.295930\pi$
$264$	−2.46570	+	22.2715i	−0.151753	+	1.37071i
$265$	14.2801	+	14.2801i	0.877221	+	0.877221i
$266$	0.653834	−	0.790186i	0.0400892	−	0.0484494i
$267$	−6.78690	−	16.3850i	−0.415351	−	1.00275i
$268$	−12.1875	−	18.5619i	−0.744469	−	1.13385i
$269$	−4.71325	−	1.95229i	−0.287372	−	0.119033i	0.234341	−	0.972154i	$-0.424707\pi$
$269$	−4.71325	−	1.95229i	−0.287372	−	0.119033i	−0.521713	+	0.853121i	$0.674707\pi$
$270$	−11.6424	+	37.8304i	−0.708533	+	2.30229i
$271$		−	15.6962i		−	0.953477i	−0.879045	−	0.476739i	$-0.841819\pi$
$271$		−	15.6962i		−	0.953477i	0.879045	−	0.476739i	$-0.158181\pi$
$272$	−3.71971	+	1.47098i	−0.225540	+	0.0891912i
$273$			31.7601i			1.92221i
$274$	−0.0551677	−	0.0169780i	−0.00333280	−	0.00102568i
$275$	14.0093	+	5.80282i	0.844790	+	0.349923i
$276$	−8.55320	+	41.2594i	−0.514842	+	2.48353i
$277$	−3.09027	−	7.46058i	−0.185677	−	0.448263i	0.803442	−	0.595383i	$-0.203000\pi$
$277$	−3.09027	−	7.46058i	−0.185677	−	0.448263i	−0.989119	+	0.147120i	$0.953000\pi$
$278$	−0.913755	−	0.756081i	−0.0548034	−	0.0453467i
$279$	7.50117	+	7.50117i	0.449083	+	0.449083i
$280$	−14.0383	−	7.72323i	−0.838949	−	0.461551i
$281$	−9.14627	+	9.14627i	−0.545621	+	0.545621i	−0.925171	−	0.379550i	$-0.876079\pi$
$281$	−9.14627	+	9.14627i	−0.545621	+	0.545621i	0.379550	+	0.925171i	$0.376079\pi$
$282$	−38.2375	+	3.61057i	−2.27701	+	0.215006i
$283$	17.8620	−	7.39867i	1.06178	−	0.439805i	0.217700	−	0.976016i	$-0.430145\pi$
$283$	17.8620	−	7.39867i	1.06178	−	0.439805i	0.844084	+	0.536210i	$0.180145\pi$
$284$	−6.20851	−	32.5823i	−0.368407	−	1.93340i
$285$	1.56163	−	3.77010i	0.0925029	−	0.223322i
$286$	10.8351	+	20.4690i	0.640694	+	1.21036i
$287$	−3.88993			−0.229615
$288$	−2.58943	−	33.1180i	−0.152584	−	1.95150i
$289$	−1.00000			−0.0588235
$290$	14.7107	+	27.7905i	0.863841	+	1.63191i
$291$	1.43530	−	3.46511i	0.0841385	−	0.203128i
$292$	−28.3814	+	5.40804i	−1.66090	+	0.316481i
$293$	29.4445	−	12.1963i	1.72017	−	0.712517i	0.720346	−	0.693615i	$-0.243983\pi$
$293$	29.4445	−	12.1963i	1.72017	−	0.712517i	0.999821	−	0.0189019i	$-0.00601703\pi$
$294$	−16.7805	+	1.58449i	−0.978656	+	0.0924094i
$295$	0.0454201	−	0.0454201i	0.00264446	−	0.00264446i
$296$	−1.92239	−	6.62449i	−0.111737	−	0.385041i
$297$	−16.0906	−	16.0906i	−0.933674	−	0.933674i
$298$	9.46867	+	7.83480i	0.548505	+	0.453858i
$299$	16.6664	+	40.2363i	0.963844	+	2.32692i
$300$	−33.2570	−	6.89427i	−1.92009	−	0.398041i
$301$	7.31516	+	3.03004i	0.421639	+	0.174649i
$302$	13.6320	+	4.19527i	0.784432	+	0.241410i
$303$			43.7578i			2.51382i
$304$	−0.0269966	+	1.67496i	−0.00154836	+	0.0960656i
$305$		−	11.4042i		−	0.653003i
$306$	2.44275	−	7.93739i	0.139643	−	0.453751i
$307$	9.65211	+	3.99803i	0.550875	+	0.228180i	0.640718	−	0.767776i	$-0.278637\pi$
$307$	9.65211	+	3.99803i	0.550875	+	0.228180i	−0.0898434	+	0.995956i	$0.528637\pi$
$308$	7.70006	−	5.05574i	0.438751	−	0.288078i
$309$	−4.99891	−	12.0684i	−0.284378	−	0.686549i
$310$	−5.32777	+	6.43883i	−0.302597	+	0.365701i
$311$	18.8666	+	18.8666i	1.06983	+	1.06983i	0.997372	+	0.0724563i	$0.0230838\pi$
$311$	18.8666	+	18.8666i	1.06983	+	1.06983i	0.0724563	+	0.997372i	$0.476916\pi$
$312$	−32.4220	−	40.4946i	−1.83553	−	2.29256i
$313$	10.4916	−	10.4916i	0.593018	−	0.593018i	−0.345428	−	0.938445i	$-0.612266\pi$
$313$	10.4916	−	10.4916i	0.593018	−	0.593018i	0.938445	+	0.345428i	$0.112266\pi$
$314$	1.67061	+	17.6925i	0.0942779	+	0.998444i
$315$	30.7337	−	12.7303i	1.73165	−	0.717272i
$316$	−22.1081	−	15.0312i	−1.24368	−	0.845574i
$317$	6.58563	−	15.8991i	0.369886	−	0.892983i	−0.623883	−	0.781518i	$-0.714446\pi$
$317$	6.58563	−	15.8991i	0.369886	−	0.892983i	0.993768	−	0.111465i	$-0.0355543\pi$
$318$	22.9840	−	12.1664i	1.28888	−	0.682256i
$319$	−18.0773			−1.01213
$320$	25.7833	−	4.48363i	1.44133	−	0.250642i
$321$	−0.145118			−0.00809968
$322$	15.3093	−	8.10386i	0.853154	−	0.451611i
$323$	−0.160266	+	0.386916i	−0.00891743	+	0.0215286i
$324$	13.0124	+	8.84709i	0.722910	+	0.491505i
$325$	−32.4323	+	13.4339i	−1.79902	+	0.745178i
$326$	−0.726027	−	7.68894i	−0.0402109	−	0.425851i
$327$	38.9723	−	38.9723i	2.15517	−	2.15517i
$328$	4.95972	−	3.97099i	0.273855	−	0.219261i
$329$	11.1645	+	11.1645i	0.615516	+	0.615516i
$330$	23.3649	−	28.2374i	1.28619	−	1.55442i
$331$	−3.44980	−	8.32855i	−0.189618	−	0.457778i	0.800268	−	0.599642i	$-0.204690\pi$
$331$	−3.44980	−	8.32855i	−0.189618	−	0.457778i	−0.989886	+	0.141864i	$0.954690\pi$
$332$	−15.4231	+	10.1266i	−0.846451	+	0.555767i
$333$	13.2310	+	5.48046i	0.725055	+	0.300328i
$334$	4.73855	−	15.3973i	0.259282	−	0.842502i
$335$			36.3200i			1.98437i
$336$	−14.8225	+	14.3523i	−0.808634	+	0.782981i
$337$			20.1656i			1.09849i	0.835661	+	0.549246i	$0.185085\pi$
$337$			20.1656i			1.09849i	−0.835661	+	0.549246i	$0.814915\pi$
$338$	−33.6733	−	10.3630i	−1.83159	−	0.563674i
$339$	−46.2394	−	19.1530i	−2.51138	−	1.04025i
$340$	6.40635	+	1.32805i	0.347433	+	0.0720239i
$341$	−1.83866	−	4.43891i	−0.0995689	−	0.240381i
$342$	−2.67961	−	2.21723i	−0.144897	−	0.119894i
$343$	13.4709	+	13.4709i	0.727361	+	0.727361i
$344$	−12.4201	+	3.60426i	−0.669650	+	0.194329i
$345$	48.7340	−	48.7340i	2.62375	−	2.62375i
$346$	18.7938	−	1.77460i	1.01036	−	0.0954030i
$347$	23.7385	−	9.83279i	1.27435	−	0.527852i	0.360064	−	0.932928i	$-0.382755\pi$
$347$	23.7385	−	9.83279i	1.27435	−	0.527852i	0.914283	+	0.405075i	$0.132755\pi$
$348$	39.7749	−	7.57904i	2.13216	−	0.406279i
$349$	−5.57721	+	13.4646i	−0.298541	+	0.720742i	0.701427	+	0.712741i	$0.252547\pi$
$349$	−5.57721	+	13.4646i	−0.298541	+	0.720742i	−0.999968	+	0.00800062i	$0.997453\pi$
$350$	6.53208	+	12.3400i	0.349154	+	0.659601i
$351$	52.6806			2.81188
$352$	−4.65660	+	14.3067i	−0.248198	+	0.762549i
$353$	−15.1403			−0.805836			−0.402918	−	0.915236i	$-0.632004\pi$
$353$	−15.1403			−0.805836			−0.402918	+	0.915236i	$0.632004\pi$
$354$	−0.0386971	−	0.0731041i	−0.00205673	−	0.00388544i
$355$	−20.7612	+	50.1221i	−1.10189	+	2.66020i
$356$	−2.22896	−	11.6976i	−0.118135	−	0.619972i
$357$	−4.76546	+	1.97392i	−0.252215	+	0.104471i
$358$	34.3251	−	3.24114i	1.81414	−	0.171300i
$359$	−18.2149	+	18.2149i	−0.961347	+	0.961347i	−0.999280	−	0.0379334i	$-0.987923\pi$
$359$	−18.2149	+	18.2149i	−0.961347	+	0.961347i	0.0379334	+	0.999280i	$0.487923\pi$
$360$	−26.1904	+	47.6056i	−1.38035	+	2.50903i
$361$	−13.3110	−	13.3110i	−0.700579	−	0.700579i
$362$	−13.3691	−	11.0622i	−0.702666	−	0.581417i
$363$	−4.47527	−	10.8043i	−0.234891	−	0.567076i
$364$	−4.32873	+	20.8812i	−0.226887	+	1.09447i
$365$	43.6597	+	18.0844i	2.28525	+	0.946583i
$366$	−14.0357	−	4.31950i	−0.733656	−	0.225784i
$367$		−	20.3142i		−	1.06039i	−0.847874	−	0.530197i	$-0.822118\pi$
$367$		−	20.3142i		−	1.06039i	0.847874	−	0.530197i	$-0.177882\pi$
$368$	−11.2469	+	25.9609i	−0.586285	+	1.35331i
$369$			13.1912i			0.686707i
$370$	−3.31855	+	10.7832i	−0.172523	+	0.560591i
$371$	−9.87676	−	4.09109i	−0.512776	−	0.212399i
$372$	5.90658	+	8.99592i	0.306242	+	0.466417i
$373$	−5.86789	−	14.1663i	−0.303828	−	0.733505i	−0.999880	−	0.0155137i	$-0.995062\pi$
$373$	−5.86789	−	14.1663i	−0.303828	−	0.733505i	0.696052	−	0.717992i	$-0.254938\pi$
$374$	−2.39788	+	2.89793i	−0.123991	+	0.149849i
$375$	4.83162	+	4.83162i	0.249504	+	0.249504i
$376$	−25.6320	−	2.83775i	−1.32187	−	0.146346i
$377$	29.5924	−	29.5924i	1.52409	−	1.52409i
$378$	−1.96971	−	20.8601i	−0.101311	−	1.07293i
$379$	−0.0793918	+	0.0328852i	−0.00407808	+	0.00168920i	−0.384722	−	0.923033i	$-0.625703\pi$
$379$	−0.0793918	+	0.0328852i	−0.00407808	+	0.00168920i	0.380643	+	0.924722i	$0.375703\pi$
$380$	1.54056	−	2.26587i	0.0790292	−	0.116237i
$381$	−9.64257	+	23.2792i	−0.494004	+	1.19263i
$382$	−32.8343	+	17.3806i	−1.67995	+	0.889269i
$383$	−20.2805			−1.03628			−0.518142	−	0.855295i	$-0.673376\pi$
$383$	−20.2805			−1.03628			−0.518142	+	0.855295i	$0.673376\pi$
$384$	4.24757	−	33.4308i	0.216758	−	1.70601i
$385$	−15.0666			−0.767867
$386$	−27.2023	+	14.3993i	−1.38456	+	0.732906i
$387$	10.2752	−	24.8066i	0.522319	−	1.26099i
$388$	1.41594	−	2.08257i	0.0718832	−	0.105727i
$389$	−10.7248	+	4.44234i	−0.543767	+	0.225236i	−0.637621	−	0.770350i	$-0.720081\pi$
$389$	−10.7248	+	4.44234i	−0.543767	+	0.225236i	0.0938540	+	0.995586i	$0.470081\pi$
$390$	7.97632	+	84.4727i	0.403897	+	4.27744i
$391$	−5.00144	+	5.00144i	−0.252934	+	0.252934i
$392$	−11.2485	−	1.24534i	−0.568137	−	0.0628991i
$393$	20.4888	+	20.4888i	1.03353	+	1.03353i
$394$	−16.7630	+	20.2587i	−0.844506	+	1.02062i
$395$	16.7336	+	40.3986i	0.841961	+	2.03267i
$396$	−17.1446	−	26.1118i	−0.861550	−	1.31217i
$397$	4.87288	+	2.01841i	0.244563	+	0.101301i	0.501598	−	0.865101i	$-0.332746\pi$
$397$	4.87288	+	2.01841i	0.244563	+	0.101301i	−0.257035	+	0.966402i	$0.582746\pi$
$398$	0.837685	−	2.72195i	0.0419893	−	0.136439i
$399$			2.16018i			0.108144i
$400$	−20.9257	−	9.06550i	−1.04628	−	0.453275i
$401$		−	4.10737i		−	0.205112i	−0.994727	−	0.102556i	$-0.967298\pi$
$401$		−	4.10737i		−	0.205112i	0.994727	−	0.102556i	$-0.0327021\pi$
$402$	44.7006	+	13.7567i	2.22946	+	0.686122i
$403$	10.2763	+	4.25660i	0.511901	+	0.212037i
$404$	−5.96395	+	28.7693i	−0.296718	+	1.43132i
$405$	−9.84909	−	23.7778i	−0.489405	−	1.18153i
$406$	−12.8242	−	10.6113i	−0.636456	−	0.526632i
$407$	−4.58648	−	4.58648i	−0.227343	−	0.227343i
$408$	4.06099	−	7.38155i	0.201049	−	0.365441i
$409$	−16.2922	+	16.2922i	−0.805595	+	0.805595i	−0.983964	−	0.178369i	$-0.942918\pi$
$409$	−16.2922	+	16.2922i	−0.805595	+	0.805595i	0.178369	+	0.983964i	$0.442918\pi$
$410$	−10.3461	+	0.976928i	−0.510957	+	0.0482470i
$411$	0.112319	−	0.0465242i	0.00554030	−	0.00229487i
$412$	−1.64175	−	8.61591i	−0.0808832	−	0.424476i
$413$	−0.0130123	+	0.0314146i	−0.000640296	+	0.00154581i
$414$	−27.4812	−	51.9157i	−1.35063	−	2.55152i
$415$	30.1782			1.48139
$416$	−15.7971	−	31.0428i	−0.774519	−	1.52200i
$417$	2.49799			0.122327
$418$	0.736958	+	1.39222i	0.0360458	+	0.0680955i
$419$	−3.09990	+	7.48382i	−0.151440	+	0.365608i	−0.981334	−	0.192313i	$-0.938401\pi$
$419$	−3.09990	+	7.48382i	−0.151440	+	0.365608i	0.829894	+	0.557922i	$0.188401\pi$
$420$	33.1506	−	6.31681i	1.61759	−	0.308229i
$421$	−18.4958	+	7.66122i	−0.901431	+	0.373385i	−0.784770	−	0.619787i	$-0.787219\pi$
$421$	−18.4958	+	7.66122i	−0.901431	+	0.373385i	−0.116661	+	0.993172i	$0.537219\pi$
$422$	21.1138	−	1.99366i	1.02780	−	0.0970501i
$423$	37.8600	−	37.8600i	1.84082	−	1.84082i
$424$	16.7694	−	4.86639i	0.814394	−	0.236333i
$425$	−4.03139	−	4.03139i	−0.195551	−	0.195551i
$426$	53.8238	+	44.5362i	2.60777	+	2.15779i
$427$	2.31024	+	5.57742i	0.111800	+	0.269910i
$428$	−0.0954100	−	0.0197788i	−0.00461182	−	0.000956044i
$429$	−45.0668	−	18.6673i	−2.17585	−	0.901265i
$430$	20.2172	+	6.22189i	0.974961	+	0.300046i
$431$			20.2434i			0.975090i	0.873098	+	0.487545i	$0.162108\pi$
$431$			20.2434i			0.975090i	−0.873098	+	0.487545i	$0.837892\pi$
$432$	23.8062	+	24.5862i	1.14538	+	1.18290i
$433$			6.09154i			0.292741i	0.989230	+	0.146370i	$0.0467591\pi$
$433$			6.09154i			0.292741i	−0.989230	+	0.146370i	$0.953241\pi$
$434$	1.30127	−	4.22830i	0.0624629	−	0.202965i
$435$	−61.1865	−	25.3443i	−2.93367	−	1.21517i
$436$	30.9347	−	20.3113i	1.48150	−	0.972733i
$437$	1.13358	+	2.73670i	0.0542264	+	0.130914i
$438$	38.7940	−	46.8842i	1.85365	−	2.24021i
$439$	7.12362	+	7.12362i	0.339992	+	0.339992i	0.856364	−	0.516372i	$-0.172718\pi$
$439$	7.12362	+	7.12362i	0.339992	+	0.339992i	−0.516372	+	0.856364i	$0.672718\pi$
$440$	19.2102	−	15.3806i	0.915812	−	0.733243i
$441$	16.6148	−	16.6148i	0.791179	−	0.791179i
$442$	−0.818589	−	8.66921i	−0.0389363	−	0.412352i
$443$	1.23897	−	0.513196i	0.0588650	−	0.0243827i	−0.353057	−	0.935602i	$-0.614858\pi$
$443$	1.23897	−	0.513196i	0.0588650	−	0.0243827i	0.411922	+	0.911219i	$0.364858\pi$
$444$	12.0144	+	8.16856i	0.570178	+	0.387663i
$445$	−7.45365	+	17.9947i	−0.353337	+	0.853030i
$446$	−2.94885	+	1.56095i	−0.139632	+	0.0739131i
$447$	−25.8851			−1.22432
$448$	−11.7014	+	7.41591i	−0.552841	+	0.350369i
$449$	13.7050			0.646778			0.323389	−	0.946266i	$-0.395178\pi$
$449$	13.7050			0.646778			0.323389	+	0.946266i	$0.395178\pi$
$450$	41.8464	−	22.1511i	1.97266	−	1.04421i
$451$	2.28634	−	5.51972i	0.107660	−	0.259913i
$452$	−27.7904	−	18.8946i	−1.30715	−	0.888729i
$453$	−27.7542	+	11.4962i	−1.30401	+	0.540137i
$454$	−1.19750	−	12.6820i	−0.0562013	−	0.595196i
$455$	24.6640	−	24.6640i	1.15627	−	1.15627i
$456$	−2.20520	−	2.75427i	−0.103268	−	0.128980i
$457$	−6.36191	−	6.36191i	−0.297597	−	0.297597i	0.542475	−	0.840072i	$-0.317487\pi$
$457$	−6.36191	−	6.36191i	−0.297597	−	0.297597i	−0.840072	+	0.542475i	$0.817487\pi$
$458$	−5.72870	+	6.92337i	−0.267684	+	0.323508i
$459$	3.27415	+	7.90449i	0.152824	+	0.368950i
$460$	38.6832	−	25.3988i	1.80361	−	1.18422i
$461$	−3.15947	−	1.30869i	−0.147151	−	0.0609520i	0.307892	−	0.951421i	$-0.400376\pi$
$461$	−3.15947	−	1.30869i	−0.147151	−	0.0609520i	−0.455044	+	0.890469i	$0.650376\pi$
$462$	−5.70670	+	18.5432i	−0.265500	+	0.862707i
$463$			23.7666i			1.10453i	0.833669	+	0.552264i	$0.186236\pi$
$463$			23.7666i			1.10453i	−0.833669	+	0.552264i	$0.813764\pi$
$464$	27.1836	+	0.438139i	1.26197	+	0.0203401i
$465$		−	17.6022i		−	0.816285i
$466$	−17.0403	−	5.24417i	−0.789375	−	0.242932i
$467$	−28.5649	−	11.8320i	−1.32183	−	0.547518i	−0.393513	−	0.919319i	$-0.628740\pi$
$467$	−28.5649	−	11.8320i	−1.32183	−	0.547518i	−0.928313	+	0.371801i	$0.878740\pi$
$468$	70.8106	+	14.6792i	3.27322	+	0.678548i
$469$	−7.35763	−	17.7629i	−0.339744	−	0.820214i
$470$	32.4981	+	26.8904i	1.49903	+	1.24036i
$471$	−26.4671	−	26.4671i	−1.21954	−	1.21954i
$472$	−0.0154783	−	0.0533377i	−0.000712447	−	0.00245507i
$473$	−8.59912	+	8.59912i	−0.395388	+	0.395388i
$474$	56.0584	−	5.29331i	2.57485	−	0.243130i
$475$	−2.20590	+	0.913715i	−0.101214	+	0.0419241i
$476$	−3.40216	+	0.648277i	−0.155938	+	0.0297137i
$477$	−13.8734	+	33.4933i	−0.635218	+	1.53355i
$478$	1.16600	+	2.20273i	0.0533316	+	0.100751i
$479$	−7.29958			−0.333526			−0.166763	−	0.985997i	$-0.553332\pi$
$479$	−7.29958			−0.333526			−0.166763	+	0.985997i	$0.553332\pi$
$480$	−35.8192	+	41.8955i	−1.63491	+	1.91226i
$481$	15.0161			0.684675
$482$	−10.0509	−	18.9876i	−0.457808	−	0.864862i
$483$	−13.9617	+	33.7066i	−0.635281	+	1.53370i
$484$	−1.46978	−	7.71339i	−0.0668080	−	0.350609i
$485$	−3.80553	+	1.57630i	−0.172800	+	0.0715761i
$486$	3.14341	−	0.296816i	0.142588	−	0.0134639i
$487$	−26.1939	+	26.1939i	−1.18696	+	1.18696i	−0.209054	+	0.977904i	$0.567038\pi$
$487$	−26.1939	+	26.1939i	−1.18696	+	1.18696i	−0.977904	+	0.209054i	$0.932962\pi$
$488$	−8.63925	−	4.75291i	−0.391081	−	0.215154i
$489$	11.5023	+	11.5023i	0.520151	+	0.520151i
$490$	14.2617	+	11.8008i	0.644279	+	0.533105i
$491$	3.46580	+	8.36717i	0.156409	+	0.377605i	0.982587	−	0.185805i	$-0.0594892\pi$
$491$	3.46580	+	8.36717i	0.156409	+	0.377605i	−0.826177	+	0.563410i	$0.809489\pi$
$492$	−2.71638	+	13.1034i	−0.122464	+	0.590748i
$493$	6.27941	+	2.60102i	0.282811	+	0.117144i
$494$	−3.48545	−	1.07265i	−0.156818	−	0.0482609i
$495$			51.0928i			2.29645i
$496$	2.65728	+	6.71955i	0.119316	+	0.301717i
$497$		−	28.7188i		−	1.28821i
$498$	11.4304	−	37.1417i	0.512209	−	1.66436i
$499$	−0.726291	−	0.300839i	−0.0325132	−	0.0134674i	0.366368	−	0.930470i	$-0.380601\pi$
$499$	−0.726291	−	0.300839i	−0.0325132	−	0.0134674i	−0.398881	+	0.917003i	$0.630601\pi$
$500$	2.51810	+	3.83515i	0.112613	+	0.171513i
$501$	12.9849	+	31.3483i	0.580122	+	1.40054i
$502$	20.3826	−	24.6332i	0.909720	−	1.09943i
$503$	28.2113	+	28.2113i	1.25788	+	1.25788i	0.952104	+	0.305774i	$0.0989151\pi$
$503$	28.2113	+	28.2113i	1.25788	+	1.25788i	0.305774	+	0.952104i	$0.401085\pi$
$504$	3.16500	−	28.5879i	0.140980	−	1.27341i
$505$	33.9811	−	33.9811i	1.51214	−	1.51214i
$506$	2.50100	+	26.4867i	0.111183	+	1.17748i
$507$	68.5575	−	28.3975i	3.04475	−	1.26118i
$508$	−9.51250	+	13.9911i	−0.422049	+	0.620753i
$509$	4.95192	−	11.9550i	0.219490	−	0.529896i	−0.775329	−	0.631558i	$-0.782416\pi$
$509$	4.95192	−	11.9550i	0.219490	−	0.529896i	0.994819	+	0.101662i	$0.0324159\pi$
$510$	−12.1790	+	6.44687i	−0.539296	+	0.285472i
$511$	−25.0160			−1.10664
$512$	7.34908	−	21.4007i	0.324787	−	0.945787i
$513$	3.58311			0.158198
$514$	20.8080	−	11.0145i	0.917801	−	0.485831i
$515$	−5.49001	+	13.2540i	−0.241919	+	0.584043i
$516$	15.3151	−	22.5256i	0.674210	−	0.991634i
$517$	−22.4041	+	9.28009i	−0.985332	+	0.408138i
$518$	−0.561446	−	5.94596i	−0.0246685	−	0.261250i
$519$	−28.1146	+	28.1146i	−1.23409	+	1.23409i
$520$	−6.26903	+	56.6251i	−0.274915	+	2.48317i
$521$	−22.1970	−	22.1970i	−0.972467	−	0.972467i	0.0271637	−	0.999631i	$-0.491352\pi$
$521$	−22.1970	−	22.1970i	−0.972467	−	0.972467i	−0.999631	+	0.0271637i	$0.991352\pi$
$522$	−35.9843	+	43.4886i	−1.57499	+	1.90344i
$523$	6.24803	+	15.0841i	0.273207	+	0.659581i	0.999617	−	0.0276813i	$-0.00881236\pi$
$523$	6.24803	+	15.0841i	0.273207	+	0.659581i	−0.726409	+	0.687262i	$0.758812\pi$
$524$	10.6782	+	16.2633i	0.466480	+	0.710463i
$525$	−27.1690	−	11.2538i	−1.18575	−	0.491156i
$526$	1.94003	−	6.30386i	0.0845891	−	0.274861i
$527$			1.80647i			0.0786912i
$528$	−11.6535	−	29.4685i	−0.507153	−	1.28245i
$529$			27.0289i			1.17517i
$530$	−27.2968	−	8.40065i	−1.18570	−	0.364901i
$531$	0.106531	+	0.0441264i	0.00462304	+	0.00191492i
$532$	−0.294421	+	1.42025i	−0.0127648	+	0.0615755i
$533$	5.29302	+	12.7785i	0.229266	+	0.553498i
$534$	19.3237	+	15.9893i	0.836218	+	0.691923i
$535$	0.112695	+	0.112695i	0.00487221	+	0.00487221i
$536$	27.5142	+	15.1370i	1.18843	+	0.653820i
$537$	−51.3487	+	51.3487i	−2.21586	+	2.21586i
$538$	7.18278	−	0.678233i	0.309672	−	0.0292407i
$539$	−9.83200	+	4.07255i	−0.423494	+	0.175417i
$540$	−10.4777	−	54.9872i	−0.450890	−	2.36627i
$541$	10.6019	−	25.5951i	0.455809	−	1.10042i	−0.514269	−	0.857629i	$-0.671937\pi$
$541$	10.6019	−	25.5951i	0.455809	−	1.10042i	0.970078	−	0.242792i	$-0.0780632\pi$
$542$	10.3850	+	19.6187i	0.446074	+	0.842696i
$543$	36.5481			1.56843
$544$	3.67603	−	4.29963i	0.157608	−	0.184345i
$545$	−60.5297			−2.59281
$546$	−21.0133	−	39.6969i	−0.899284	−	1.69887i
$547$	−7.62225	+	18.4017i	−0.325904	+	0.786801i	0.672984	+	0.739657i	$0.265012\pi$
$547$	−7.62225	+	18.4017i	−0.325904	+	0.786801i	−0.998888	+	0.0471445i	$0.984988\pi$
$548$	0.0801872	−	0.0152795i	0.00342543	−	0.000652710i
$549$	18.9137	−	7.83431i	0.807217	−	0.334360i
$550$	−21.3495	+	2.01592i	−0.910345	+	0.0859591i
$551$	2.01275	−	2.01275i	0.0857460	−	0.0857460i
$552$	−16.6076	−	57.2292i	−0.706867	−	2.43584i
$553$	−16.3677	−	16.3677i	−0.696027	−	0.696027i
$554$	8.79864	+	7.28038i	0.373818	+	0.309314i
$555$	−9.09371	−	21.9542i	−0.386007	−	0.931903i
$556$	1.64235	+	0.340463i	0.0696510	+	0.0144389i
$557$	−21.9604	−	9.09629i	−0.930492	−	0.385422i	−0.134627	−	0.990896i	$-0.542983\pi$
$557$	−21.9604	−	9.09629i	−0.930492	−	0.385422i	−0.795865	+	0.605474i	$0.792983\pi$
$558$	−14.3387	−	4.41276i	−0.607005	−	0.186807i
$559$		−	28.1534i		−	1.19076i
$560$	22.6564	+	0.365170i	0.957406	+	0.0154312i
$561$		−	7.92227i		−	0.334478i
$562$	5.38053	−	17.4833i	0.226964	−	0.737490i
$563$	−14.3972	−	5.96353i	−0.606772	−	0.251333i	0.0580759	−	0.998312i	$-0.481503\pi$
$563$	−14.3972	−	5.96353i	−0.606772	−	0.251333i	−0.664847	+	0.746979i	$0.731503\pi$
$564$	45.4043	−	29.8118i	1.91187	−	1.25530i
$565$	21.0346	+	50.7820i	0.884932	+	2.13641i
$566$	−17.4306	+	21.0655i	−0.732661	+	0.885451i
$567$	9.63372	+	9.63372i	0.404578	+	0.404578i
$568$	29.3173	+	36.6169i	1.23013	+	1.53641i
$569$	27.3884	−	27.3884i	1.14818	−	1.14818i	0.161273	−	0.986910i	$-0.448440\pi$
$569$	27.3884	−	27.3884i	1.14818	−	1.14818i	0.986910	−	0.161273i	$-0.0515598\pi$
$570$	0.542515	+	5.74547i	0.0227234	+	0.240651i
$571$	2.79633	−	1.15828i	0.117023	−	0.0484724i	−0.323404	−	0.946261i	$-0.604827\pi$
$571$	2.79633	−	1.15828i	0.117023	−	0.0484724i	0.440427	+	0.897789i	$0.354827\pi$
$572$	−27.0857	−	18.4155i	−1.13251	−	0.769990i
$573$	29.9442	−	72.2916i	1.25094	−	3.02002i
$574$	4.86202	−	2.57367i	0.202937	−	0.107423i
$575$	−40.3256			−1.68169
$576$	25.1482	+	39.6810i	1.04784	+	1.65338i
$577$	1.55473			0.0647242			0.0323621	−	0.999476i	$-0.489697\pi$
$577$	1.55473			0.0647242			0.0323621	+	0.999476i	$0.489697\pi$
$578$	1.24990	−	0.661625i	0.0519890	−	0.0275200i
$579$	24.8078	−	59.8914i	1.03098	−	2.48900i
$580$	−36.7738	−	25.0024i	−1.52695	−	1.03817i
$581$	−14.7592	+	6.11344i	−0.612313	+	0.253628i
$582$	0.498627	+	5.28067i	0.0206687	+	0.218891i
$583$	11.6103	−	11.6103i	0.480851	−	0.480851i
$584$	31.8958	−	25.5374i	1.31986	−	1.05674i
$585$	−83.6387	−	83.6387i	−3.45803	−	3.45803i
$586$	−28.7333	+	34.7254i	−1.18696	+	1.43449i
$587$	5.37640	+	12.9798i	0.221908	+	0.535733i	0.995149	−	0.0983792i	$-0.0313658\pi$
$587$	5.37640	+	12.9798i	0.221908	+	0.535733i	−0.773241	+	0.634112i	$0.781366\pi$
$588$	19.9256	−	13.0828i	0.821716	−	0.539527i
$589$	0.698953	+	0.289516i	0.0287998	+	0.0119293i
$590$	−0.0267196	+	0.0868218i	−0.00110003	+	0.00357440i
$591$		−	55.3826i		−	2.27814i
$592$	6.78573	+	7.00805i	0.278892	+	0.288029i
$593$		−	25.9018i		−	1.06366i	−0.846852	−	0.531829i	$-0.821505\pi$
$593$		−	25.9018i		−	1.06366i	0.846852	−	0.531829i	$-0.178495\pi$
$594$	30.7577	+	9.46574i	1.26200	+	0.388384i
$595$	5.23362	+	2.16784i	0.214557	+	0.0888726i
$596$	−17.0186	−	3.52801i	−0.697109	−	0.144513i
$597$	2.29548	+	5.54178i	0.0939478	+	0.226810i
$598$	−47.4527	−	39.2645i	−1.94049	−	1.60564i
$599$	9.96654	+	9.96654i	0.407222	+	0.407222i	0.880769	−	0.473547i	$-0.157027\pi$
$599$	9.96654	+	9.96654i	0.407222	+	0.407222i	−0.473547	+	0.880769i	$0.657027\pi$
$600$	46.1293	−	13.3865i	1.88322	−	0.546501i
$601$	18.3118	−	18.3118i	0.746955	−	0.746955i	−0.226951	−	0.973906i	$-0.572876\pi$
$601$	18.3118	−	18.3118i	0.746955	−	0.746955i	0.973906	+	0.226951i	$0.0728757\pi$
$602$	−11.1480	+	1.05265i	−0.454358	+	0.0429026i
$603$	−60.2361	+	24.9506i	−2.45300	+	1.01607i
$604$	−19.8143	+	3.77559i	−0.806233	+	0.153627i
$605$	−4.91492	+	11.8657i	−0.199820	+	0.482408i
$606$	−28.9512	−	54.6929i	−1.17606	−	2.22175i
$607$	21.5927			0.876422			0.438211	−	0.898872i	$-0.355612\pi$
$607$	21.5927			0.876422			0.438211	+	0.898872i	$0.355612\pi$
$608$	−1.07445	−	2.11140i	−0.0435748	−	0.0856285i
$609$	35.0585			1.42064
$610$	7.54531	+	14.2541i	0.305501	+	0.577133i
$611$	21.4840	−	51.8669i	0.869149	−	2.09831i
$612$	2.19839	+	11.5371i	0.0888645	+	0.466361i
$613$	17.3533	−	7.18796i	0.700892	−	0.290319i	−0.00363774	−	0.999993i	$-0.501158\pi$
$613$	17.3533	−	7.18796i	0.700892	−	0.290319i	0.704530	+	0.709674i	$0.251158\pi$
$614$	−14.7094	+	1.38893i	−0.593622	+	0.0560527i
$615$	15.4772	−	15.4772i	0.624103	−	0.624103i
$616$	−6.27930	+	11.4137i	−0.253000	+	0.459872i
$617$	21.5339	+	21.5339i	0.866923	+	0.866923i	0.992131	−	0.125208i	$-0.0399597\pi$
$617$	21.5339	+	21.5339i	0.866923	+	0.866923i	−0.125208	+	0.992131i	$0.539960\pi$
$618$	14.2329	+	11.7769i	0.572532	+	0.473738i
$619$	−1.11728	−	2.69735i	−0.0449073	−	0.108416i	0.899834	−	0.436232i	$-0.143687\pi$
$619$	−1.11728	−	2.69735i	−0.0449073	−	0.108416i	−0.944742	+	0.327816i	$0.893687\pi$
$620$	2.39909	−	11.5729i	0.0963499	−	0.464778i
$621$	55.9094	+	23.1584i	2.24357	+	0.929315i
$622$	−36.0640	−	11.0988i	−1.44604	−	0.445020i
$623$		−	10.3105i		−	0.413083i
$624$	67.3165	+	29.1631i	2.69482	+	1.16746i
$625$			21.0020i			0.840081i
$626$	−6.17193	+	20.0549i	−0.246680	+	0.801554i
$627$	−3.06525	−	1.26967i	−0.122414	−	0.0507057i
$628$	−13.7939	−	21.0085i	−0.550436	−	0.838331i
$629$	0.933264	+	2.25310i	0.0372117	+	0.0898369i
$630$	−29.9914	+	36.2458i	−1.19489	+	1.44407i
$631$	2.05334	+	2.05334i	0.0817421	+	0.0817421i	0.746796	−	0.665054i	$-0.231591\pi$
$631$	2.05334	+	2.05334i	0.0817421	+	0.0817421i	−0.665054	+	0.746796i	$0.731591\pi$
$632$	37.5780	+	4.16030i	1.49477	+	0.165488i
$633$	−31.5852	+	31.5852i	−1.25540	+	1.25540i
$634$	2.28787	+	24.2295i	0.0908629	+	0.962277i
$635$	25.5662	−	10.5899i	1.01456	−	0.420246i
$636$	−20.6781	+	30.4135i	−0.819939	+	1.20597i
$637$	9.42819	−	22.7617i	0.373558	−	0.901850i
$638$	22.5948	−	11.9604i	0.894538	−	0.473517i
$639$	−97.3888			−3.85264
$640$	−29.2601	+	22.6629i	−1.15661	+	0.895832i
$641$	−43.5078			−1.71846			−0.859228	−	0.511593i	$-0.829056\pi$
$641$	−43.5078			−1.71846			−0.859228	+	0.511593i	$0.829056\pi$
$642$	0.181383	−	0.0960135i	0.00715861	−	0.00378935i
$643$	6.21474	−	15.0037i	0.245085	−	0.591689i	−0.752688	−	0.658377i	$-0.771243\pi$
$643$	6.21474	−	15.0037i	0.245085	−	0.591689i	0.997774	+	0.0666883i	$0.0212433\pi$
$644$	−13.7734	+	20.2580i	−0.542748	+	0.798279i
$645$	−41.1615	+	17.0497i	−1.62073	+	0.671329i
$646$	−0.0556769	−	0.589642i	−0.00219058	−	0.0231992i
$647$	6.10466	−	6.10466i	0.239999	−	0.239999i	−0.576851	−	0.816850i	$-0.695719\pi$
$647$	6.10466	−	6.10466i	0.239999	−	0.239999i	0.816850	+	0.576851i	$0.195719\pi$
$648$	−22.1176	−	2.44867i	−0.868863	−	0.0961928i
$649$	−0.0369285	−	0.0369285i	−0.00144957	−	0.00144957i
$650$	31.6489	−	38.2490i	1.24137	−	1.50025i
$651$	3.56583	+	8.60867i	0.139756	+	0.337400i
$652$	5.99466	+	9.13006i	0.234769	+	0.357561i
$653$	−37.4118	−	15.4965i	−1.46404	−	0.606424i	−0.498547	−	0.866863i	$-0.666133\pi$
$653$	−37.4118	−	15.4965i	−1.46404	−	0.606424i	−0.965490	+	0.260439i	$0.916133\pi$
$654$	−22.9265	+	74.4966i	−0.896495	+	2.91305i
$655$		−	31.8222i		−	1.24340i
$656$	−3.57185	+	8.24483i	−0.139457	+	0.321906i
$657$			84.8323i			3.30962i
$658$	−21.3411	−	6.56778i	−0.831964	−	0.256039i
$659$	9.69787	+	4.01699i	0.377775	+	0.156480i	0.563488	−	0.826124i	$-0.309459\pi$
$659$	9.69787	+	4.01699i	0.377775	+	0.156480i	−0.185712	+	0.982604i	$0.559459\pi$
$660$	−10.5212	+	50.7528i	−0.409537	+	1.97555i
$661$	9.36267	+	22.6035i	0.364166	+	0.879174i	0.994682	+	0.102997i	$0.0328433\pi$
$661$	9.36267	+	22.6035i	0.364166	+	0.879174i	−0.630516	+	0.776176i	$0.717157\pi$
$662$	9.82228	+	8.12739i	0.381754	+	0.315880i
$663$	12.9687	+	12.9687i	0.503663	+	0.503663i
$664$	12.5773	−	22.8615i	0.488095	−	0.887198i
$665$	1.67754	−	1.67754i	0.0650522	−	0.0650522i
$666$	−20.1635	+	1.90393i	−0.781318	+	0.0737758i
$667$	44.4150	−	18.3973i	1.71976	−	0.712346i
$668$	4.26452	+	22.3802i	0.164999	+	0.865917i
$669$	2.68928	−	6.49249i	0.103974	−	0.251014i
$670$	−24.0302	−	45.3964i	−0.928368	−	1.75382i
$671$	−9.27210			−0.357945
$672$	9.03084	−	27.7459i	0.348372	−	1.07032i
$673$	38.7005			1.49179			0.745896	−	0.666062i	$-0.232021\pi$
$673$	38.7005			1.49179			0.745896	+	0.666062i	$0.232021\pi$
$674$	−13.3421	−	25.2051i	−0.513918	−	0.970862i
$675$	−18.6667	+	45.0655i	−0.718483	+	1.73457i
$676$	48.9447	−	9.32634i	1.88249	−	0.358705i
$677$	14.1382	−	5.85624i	0.543376	−	0.225074i	−0.0940743	−	0.995565i	$-0.529989\pi$
$677$	14.1382	−	5.85624i	0.543376	−	0.225074i	0.637450	+	0.770491i	$0.279989\pi$
$678$	70.4668	−	6.65381i	2.70626	−	0.255538i
$679$	1.54183	−	1.54183i	0.0591700	−	0.0591700i
$680$	−8.88597	+	2.57866i	−0.340761	+	0.0988872i
$681$	18.9716	+	18.9716i	0.726995	+	0.726995i
$682$	5.23504	+	4.33170i	0.200460	+	0.165869i
$683$	6.77836	+	16.3644i	0.259367	+	0.626167i	0.998897	−	0.0469567i	$-0.0149523\pi$
$683$	6.77836	+	16.3644i	0.259367	+	0.626167i	−0.739530	+	0.673123i	$0.764952\pi$
$684$	4.81623	+	0.998419i	0.184153	+	0.0381755i
$685$	−0.123354	−	0.0510947i	−0.00471310	−	0.00195223i
$686$	−25.7500	−	7.92461i	−0.983139	−	0.302563i
$687$		−	18.9269i		−	0.722105i
$688$	13.1393	−	12.7225i	0.500931	−	0.485039i
$689$			38.0121i			1.44815i
$690$	−28.6690	+	93.1564i	−1.09141	+	3.54640i
$691$	28.2212	+	11.6896i	1.07358	+	0.444693i	0.848254	−	0.529589i	$-0.177654\pi$
$691$	28.2212	+	11.6896i	1.07358	+	0.444693i	0.225330	+	0.974282i	$0.427654\pi$
$692$	−22.3162	+	14.6525i	−0.848336	+	0.557005i
$693$	−10.3503	−	24.9878i	−0.393174	−	0.949207i
$694$	−23.1651	+	27.9960i	−0.879335	+	1.06271i
$695$	−1.93987	−	1.93987i	−0.0735836	−	0.0735836i
$696$	−44.7002	+	35.7891i	−1.69436	+	1.35658i
$697$	−1.58839	+	1.58839i	−0.0601645	+	0.0601645i
$698$	−1.93754	−	20.5194i	−0.0733370	−	0.776671i
$699$	34.6933	−	14.3704i	1.31222	−	0.543540i
$700$	−16.3289	−	11.1020i	−0.617175	−	0.419616i
$701$	−9.10159	+	21.9732i	−0.343762	+	0.829916i	0.653566	+	0.756869i	$0.273272\pi$
$701$	−9.10159	+	21.9732i	−0.343762	+	0.829916i	−0.997329	+	0.0730465i	$0.976728\pi$
$702$	−65.8456	+	34.8548i	−2.48518	+	1.31551i
$703$	1.02133			0.0385202
$704$	−3.64537	−	20.9629i	−0.137390	−	0.790068i
$705$	−88.8423			−3.34599
$706$	18.9238	−	10.0172i	0.712208	−	0.377002i
$707$	−9.73520	+	23.5029i	−0.366130	+	0.883916i
$708$	0.0967350	+	0.0657699i	0.00363552	+	0.00247178i
$709$	0.337277	−	0.139705i	0.0126667	−	0.00524672i	−0.376341	−	0.926481i	$-0.622818\pi$
$709$	0.337277	−	0.139705i	0.0126667	−	0.00524672i	0.389008	+	0.921234i	$0.372818\pi$
$710$	−7.21252	−	76.3838i	−0.270681	−	2.86663i
$711$	−55.5049	+	55.5049i	−2.08160	+	2.08160i
$712$	10.5254	+	13.1461i	0.394457	+	0.492672i
$713$	9.03497	+	9.03497i	0.338362	+	0.338362i
$714$	4.65036	−	5.62015i	0.174035	−	0.210329i
$715$	20.5012	+	49.4942i	0.766701	+	1.85098i
$716$	−40.7586	+	26.7615i	−1.52322	+	1.00012i
$717$	−4.84978	−	2.00884i	−0.181118	−	0.0750216i
$718$	10.7154	−	34.8183i	0.399895	−	1.29941i
$719$		−	38.8693i		−	1.44958i	−0.688970	−	0.724790i	$-0.741937\pi$
$719$		−	38.8693i		−	1.44958i	0.688970	−	0.724790i	$-0.258063\pi$
$720$	1.23834	−	76.8305i	0.0461500	−	2.86330i
$721$		−	7.59426i		−	0.282825i
$722$	25.4443	+	7.83055i	0.946940	+	0.291423i
$723$	41.8051	+	17.3163i	1.55475	+	0.643998i
$724$	24.0291	+	4.98131i	0.893036	+	0.185129i
$725$	14.8290	+	35.8005i	0.550737	+	1.32960i
$726$	12.7420	+	10.5433i	0.472900	+	0.391299i
$727$	12.9754	+	12.9754i	0.481230	+	0.481230i	0.905524	−	0.424295i	$-0.139478\pi$
$727$	12.9754	+	12.9754i	0.481230	+	0.481230i	−0.424295	+	0.905524i	$0.639478\pi$
$728$	−8.40502	−	28.9634i	−0.311511	−	1.07345i
$729$	−21.3920	+	21.3920i	−0.792295	+	0.792295i
$730$	−66.5355	+	6.28260i	−2.46259	+	0.232529i
$731$	4.22430	−	1.74976i	0.156241	−	0.0647172i
$732$	20.4011	−	3.88740i	0.754046	−	0.143682i
$733$	−13.5259	+	32.6545i	−0.499591	+	1.20612i	0.450113	+	0.892972i	$0.351384\pi$
$733$	−13.5259	+	32.6545i	−0.499591	+	1.20612i	−0.949704	+	0.313149i	$0.898616\pi$
$734$	13.4404	+	25.3908i	0.496094	+	0.937191i
$735$	−38.9882			−1.43810
$736$	−3.11891	−	39.8898i	−0.114964	−	1.47036i
$737$	29.5297			1.08774
$738$	−8.72763	−	16.4877i	−0.321269	−	0.606921i
$739$	2.58868	−	6.24963i	0.0952263	−	0.229897i	−0.869088	−	0.494658i	$-0.835293\pi$
$739$	2.58868	−	6.24963i	0.0952263	−	0.229897i	0.964314	+	0.264762i	$0.0852933\pi$
$740$	−2.98657	−	15.6736i	−0.109789	−	0.576171i
$741$	7.09624	−	2.93936i	0.260687	−	0.107980i
$742$	15.0517	−	1.42126i	0.552567	−	0.0521760i
$743$	8.58553	−	8.58553i	0.314972	−	0.314972i	−0.531860	−	0.846832i	$-0.678507\pi$
$743$	8.58553	−	8.58553i	0.314972	−	0.314972i	0.846832	+	0.531860i	$0.178507\pi$
$744$	−13.3346	−	7.33606i	−0.488869	−	0.268953i
$745$	20.1017	+	20.1017i	0.736469	+	0.736469i
$746$	16.7071	+	13.8242i	0.611690	+	0.506139i
$747$	20.7314	+	50.0501i	0.758523	+	1.83124i
$748$	1.07976	−	5.20862i	0.0394801	−	0.190446i
$749$	−0.0779446	−	0.0322857i	−0.00284803	−	0.00117969i
$750$	−9.23577	−	2.84233i	−0.337243	−	0.103787i
$751$		−	9.55789i		−	0.348773i	−0.984677	−	0.174386i	$-0.944206\pi$
$751$		−	9.55789i		−	0.348773i	0.984677	−	0.174386i	$-0.0557941\pi$
$752$	33.9150	−	13.4119i	1.23675	−	0.489081i
$753$			67.3414i			2.45406i
$754$	−17.4085	+	56.5667i	−0.633981	+	2.06004i
$755$	30.4808	+	12.6256i	1.10931	+	0.459491i
$756$	16.2635	+	24.7698i	0.591497	+	0.900869i
$757$	−9.46781	−	22.8573i	−0.344114	−	0.830764i	−0.997291	−	0.0735587i	$-0.976564\pi$
$757$	−9.46781	−	22.8573i	−0.344114	−	0.830764i	0.653177	−	0.757205i	$-0.273436\pi$
$758$	0.0774743	−	0.0936308i	0.00281399	−	0.00340082i
$759$	−39.6228	−	39.6228i	−1.43822	−	1.43822i
$760$	−0.426392	+	3.85139i	−0.0154669	+	0.139705i
$761$	2.25131	−	2.25131i	0.0816098	−	0.0816098i	−0.665124	−	0.746733i	$-0.731621\pi$
$761$	2.25131	−	2.25131i	0.0816098	−	0.0816098i	0.746733	+	0.665124i	$0.231621\pi$
$762$	−3.34986	−	35.4765i	−0.121353	−	1.28518i
$763$	29.6030	−	12.2620i	1.07170	−	0.443913i
$764$	29.5402	−	43.4481i	1.06873	−	1.57190i
$765$	7.35139	−	17.7478i	0.265790	−	0.641674i
$766$	25.3486	−	13.4181i	0.915881	−	0.484815i
$767$	0.120903			0.00436557
$768$	16.8096	+	44.5955i	0.606565	+	1.60920i
$769$	−42.2200			−1.52249			−0.761246	−	0.648463i	$-0.775412\pi$
$769$	−42.2200			−1.52249			−0.761246	+	0.648463i	$0.775412\pi$
$770$	18.8318	−	9.96847i	0.678652	−	0.359239i
$771$	−18.9764	+	45.8131i	−0.683419	+	1.64992i
$772$	24.4732	−	35.9954i	0.880810	−	1.29550i
$773$	1.35047	−	0.559382i	0.0485729	−	0.0201196i	−0.358265	−	0.933620i	$-0.616631\pi$
$773$	1.35047	−	0.559382i	0.0485729	−	0.0201196i	0.406838	+	0.913500i	$0.366631\pi$
$774$	3.56965	+	37.8041i	0.128308	+	1.35884i
$775$	−7.28260	+	7.28260i	−0.261599	+	0.261599i
$776$	−0.391898	+	3.53983i	−0.0140683	+	0.127072i
$777$	8.89486	+	8.89486i	0.319101	+	0.319101i
$778$	10.4657	−	12.6483i	0.375214	−	0.453462i
$779$	0.360008	+	0.869137i	0.0128986	+	0.0311401i
$780$	−65.8589	−	100.305i	−2.35813	−	3.59150i
$781$	40.7513	+	16.8797i	1.45820	+	0.604005i
$782$	2.94223	−	9.56039i	0.105214	−	0.341879i
$783$		−	58.1517i		−	2.07817i
$784$	14.8835	−	5.88577i	0.531554	−	0.210206i
$785$			41.1072i			1.46718i
$786$	−39.1650	−	12.0531i	−1.39697	−	0.429920i
$787$	−10.1016	−	4.18421i	−0.360082	−	0.149151i	0.195306	−	0.980742i	$-0.437430\pi$
$787$	−10.1016	−	4.18421i	−0.360082	−	0.149151i	−0.555388	+	0.831592i	$0.687430\pi$
$788$	7.54836	−	36.4122i	0.268899	−	1.29713i
$789$	5.31619	+	12.8344i	0.189261	+	0.456918i
$790$	−47.6441	−	39.4228i	−1.69510	−	1.40260i
$791$	−20.5746	−	20.5746i	−0.731549	−	0.731549i
$792$	38.7053	+	21.2939i	1.37533	+	0.756645i
$793$	15.1784	−	15.1784i	0.539000	−	0.539000i
$794$	−7.42604	+	0.701203i	−0.263540	+	0.0248848i
$795$	55.5753	−	23.0200i	1.97105	−	0.816437i
$796$	0.753886	+	3.95640i	0.0267208	+	0.140231i
$797$	−8.14609	+	19.6664i	−0.288549	+	0.696620i	−0.999981	−	0.00613546i	$-0.998047\pi$
$797$	−8.14609	+	19.6664i	−0.288549	+	0.696620i	0.711432	+	0.702755i	$0.248047\pi$
$798$	−1.42923	−	2.70001i	−0.0505942	−	0.0955794i
$799$	9.11765			0.322559
$800$	32.1530	−	2.51398i	1.13678	−	0.0888826i
$801$	−34.9643			−1.23540
$802$	2.71754	+	5.13381i	0.0959597	+	0.181281i
$803$	14.7034	−	35.4972i	0.518872	−	1.25267i
$804$	−64.9731	+	12.3805i	−2.29142	+	0.436628i
$805$	37.0180	−	15.3333i	1.30471	−	0.540429i
$806$	−15.6607	+	1.47876i	−0.551624	+	0.0520870i
$807$	−10.7451	+	10.7451i	−0.378245	+	0.378245i
$808$	−11.5801	−	39.9046i	−0.407387	−	1.40384i
$809$	8.61454	+	8.61454i	0.302871	+	0.302871i	0.842136	−	0.539265i	$-0.181298\pi$
$809$	8.61454	+	8.61454i	0.302871	+	0.302871i	−0.539265	+	0.842136i	$0.681298\pi$
$810$	28.0424	+	23.2035i	0.985309	+	0.815288i
$811$	8.05711	+	19.4516i	0.282923	+	0.683038i	0.999901	−	0.0140584i	$-0.00447507\pi$
$811$	8.05711	+	19.4516i	0.282923	+	0.683038i	−0.716978	+	0.697096i	$0.754475\pi$
$812$	23.0498	+	4.77829i	0.808888	+	0.167685i
$813$	−43.1946	−	17.8918i	−1.51490	−	0.627493i
$814$	8.76718	+	2.69812i	0.307289	+	0.0945689i
$815$		−	17.8647i		−	0.625774i
$816$	−0.192012	+	11.9131i	−0.00672176	+	0.417040i
$817$		−	1.91487i		−	0.0669930i
$818$	9.58428	−	31.1429i	0.335107	−	1.08889i
$819$	57.8482	+	23.9615i	2.02138	+	0.837283i
$820$	12.2852	−	8.06630i	0.429019	−	0.281687i
$821$	−7.89407	−	19.0580i	−0.275505	−	0.665128i	0.724196	−	0.689594i	$-0.242211\pi$
$821$	−7.89407	−	19.0580i	−0.275505	−	0.665128i	−0.999701	+	0.0244668i	$0.992211\pi$
$822$	−0.109606	+	0.132464i	−0.00382296	+	0.00462021i
$823$	−4.03863	−	4.03863i	−0.140778	−	0.140778i	0.633206	−	0.773983i	$-0.281739\pi$
$823$	−4.03863	−	4.03863i	−0.140778	−	0.140778i	−0.773983	+	0.633206i	$0.781739\pi$
$824$	7.75253	+	9.68281i	0.270072	+	0.337317i
$825$	31.9378	−	31.9378i	1.11193	−	1.11193i
$826$	−0.00452053	−	0.0478744i	−0.000157289	−	0.00166576i
$827$	−11.4655	+	4.74915i	−0.398693	+	0.165144i	−0.573016	−	0.819545i	$-0.694227\pi$
$827$	−11.4655	+	4.74915i	−0.398693	+	0.165144i	0.174322	+	0.984689i	$0.444227\pi$
$828$	68.6975	+	46.7073i	2.38740	+	1.62319i
$829$	9.19286	−	22.1935i	0.319281	−	0.770813i	−0.680011	−	0.733202i	$-0.738025\pi$
$829$	9.19286	−	22.1935i	0.319281	−	0.770813i	0.999292	−	0.0376112i	$-0.0119748\pi$
$830$	−37.7198	+	19.9667i	−1.30927	+	0.693053i
$831$	−24.0534			−0.834404
$832$	40.2836	+	28.3486i	1.39658	+	0.982812i
$833$	4.00126			0.138635
$834$	−3.12224	+	1.65273i	−0.108114	+	0.0572295i
$835$	14.2605	−	34.4280i	0.493506	−	1.19143i
$836$	−1.84225	−	1.25254i	−0.0637155	−	0.0433201i
$837$	14.2793	−	5.91466i	0.493563	−	0.204441i
$838$	−1.07692	−	11.4050i	−0.0372014	−	0.393979i
$839$	−24.7605	+	24.7605i	−0.854826	+	0.854826i	−0.990723	−	0.135897i	$-0.956608\pi$
$839$	−24.7605	+	24.7605i	−0.854826	+	0.854826i	0.135897	+	0.990723i	$0.456608\pi$
$840$	−37.2556	+	29.8287i	−1.28544	+	1.02919i
$841$	−12.1596	−	12.1596i	−0.419298	−	0.419298i
$842$	18.0491	−	21.8131i	0.622013	−	0.751728i
$843$	14.7441	+	35.5954i	0.507814	+	1.22597i
$844$	−25.0711	+	16.4613i	−0.862982	+	0.566621i
$845$	−75.2927	−	31.1873i	−2.59015	−	1.07287i
$846$	−22.2721	+	72.3704i	−0.765731	+	2.48814i
$847$		−	6.79876i		−	0.233608i
$848$	−17.7403	+	17.1776i	−0.609206	+	0.589880i
$849$		−	57.5882i		−	1.97642i
$850$	7.70611	+	2.37157i	0.264317	+	0.0813442i
$851$	15.9364	+	6.60108i	0.546293	+	0.226282i
$852$	−96.7407	−	20.0546i	−3.31428	−	0.687061i
$853$	−2.32433	−	5.61143i	−0.0795835	−	0.192132i	0.879080	−	0.476675i	$-0.158158\pi$
$853$	−2.32433	−	5.61143i	−0.0795835	−	0.192132i	−0.958663	+	0.284543i	$0.908158\pi$
$854$	−6.57773	−	5.44270i	−0.225085	−	0.186245i
$855$	−5.68874	−	5.68874i	−0.194551	−	0.194551i
$856$	0.132339	−	0.0384041i	0.00452326	−	0.00131263i
$857$	−7.36821	+	7.36821i	−0.251693	+	0.251693i	−0.821665	−	0.569971i	$-0.806954\pi$
$857$	−7.36821	+	7.36821i	−0.251693	+	0.251693i	0.569971	+	0.821665i	$0.306954\pi$
$858$	68.6798	−	6.48508i	2.34469	−	0.221397i
$859$	−33.2157	+	13.7584i	−1.13331	+	0.469431i	−0.868903	−	0.494982i	$-0.835175\pi$
$859$	−33.2157	+	13.7584i	−1.13331	+	0.469431i	−0.264403	+	0.964412i	$0.585175\pi$
$860$	−29.3861	+	5.59948i	−1.00206	+	0.190941i
$861$	−4.43405	+	10.7047i	−0.151112	+	0.364817i
$862$	−13.3935	−	25.3022i	−0.456186	−	0.861798i
$863$	−6.23881			−0.212372			−0.106186	−	0.994346i	$-0.533864\pi$
$863$	−6.23881			−0.212372			−0.106186	+	0.994346i	$0.533864\pi$
$864$	−46.0223	−	14.9795i	−1.56571	−	0.509614i
$865$	43.6660			1.48469
$866$	−4.03032	−	7.61382i	−0.136956	−	0.258728i
$867$	−1.13988	+	2.75191i	−0.0387124	+	0.0934599i
$868$	1.17109	+	6.14591i	0.0397495	+	0.208606i
$869$	32.8457	−	13.6051i	1.11422	−	0.461523i
$870$	93.2455	−	8.80469i	3.16132	−	0.298507i
$871$	−48.3399	+	48.3399i	−1.63794	+	1.63794i
$872$	−25.2269	+	45.8542i	−0.854289	+	1.55282i
$873$	−5.22853	−	5.22853i	−0.176959	−	0.176959i
$874$	−3.22753	−	2.67060i	−0.109173	−	0.0903343i
$875$	1.52019	+	3.67006i	0.0513918	+	0.124071i
$876$	−17.4689	+	84.2677i	−0.590221	+	2.84714i
$877$	16.5048	+	6.83650i	0.557326	+	0.230852i	0.643524	−	0.765426i	$-0.277472\pi$
$877$	16.5048	+	6.83650i	0.557326	+	0.230852i	−0.0861977	+	0.996278i	$0.527472\pi$
$878$	−13.6170	−	4.19065i	−0.459551	−	0.141428i
$879$		−	94.9312i		−	3.20195i
$880$	−13.8347	+	31.9343i	−0.466367	+	1.07650i
$881$			2.45411i			0.0826810i	0.999145	+	0.0413405i	$0.0131628\pi$
$881$			2.45411i			0.0826810i	−0.999145	+	0.0413405i	$0.986837\pi$
$882$	−9.77407	+	31.7596i	−0.329110	+	1.06940i
$883$	−39.3368	−	16.2938i	−1.32379	−	0.548332i	−0.394912	−	0.918719i	$-0.629225\pi$
$883$	−39.3368	−	16.2938i	−1.32379	−	0.548332i	−0.928877	+	0.370387i	$0.879225\pi$
$884$	6.75892	+	10.2941i	0.227327	+	0.346227i
$885$	−0.0732188	−	0.176766i	−0.00246122	−	0.00594192i
$886$	−1.20904	+	1.46118i	−0.0406185	+	0.0490891i
$887$	−23.8565	−	23.8565i	−0.801023	−	0.801023i	0.182233	−	0.983255i	$-0.441668\pi$
$887$	−23.8565	−	23.8565i	−0.801023	−	0.801023i	−0.983255	+	0.182233i	$0.941668\pi$
$888$	−20.4213	−	2.26087i	−0.685295	−	0.0758697i
$889$	−10.3583	+	10.3583i	−0.347406	+	0.347406i
$890$	−2.58942	−	27.4231i	−0.0867976	−	0.919225i
$891$	−19.3323	+	8.00772i	−0.647658	+	0.268269i
$892$	2.65300	−	3.90206i	0.0888291	−	0.130651i
$893$	1.46125	−	3.52776i	0.0488988	−	0.118052i
$894$	32.3538	−	17.1262i	1.08207	−	0.572787i
$895$	79.7521			2.66582
$896$	9.71909	−	17.0111i	0.324692	−	0.568302i
$897$	129.725			4.33138
$898$	−17.1299	+	9.06756i	−0.571631	+	0.302589i
$899$	4.69867	−	11.3436i	0.156709	−	0.378330i
$900$	−37.6482	+	55.3733i	−1.25494	+	1.84578i
$901$	−5.70355	+	2.36249i	−0.190013	+	0.0787058i
$902$	0.794283	+	8.41180i	0.0264467	+	0.280082i
$903$	16.6768	−	16.6768i	0.554970	−	0.554970i
$904$	47.2364	+	5.22959i	1.57106	+	0.173934i
$905$	−28.3823	−	28.3823i	−0.943459	−	0.943459i
$906$	27.0838	−	32.7319i	0.899800	−	1.08745i
$907$	−1.47445	−	3.55963i	−0.0489582	−	0.118196i	0.897508	−	0.440997i	$-0.145375\pi$
$907$	−1.47445	−	3.55963i	−0.0489582	−	0.118196i	−0.946467	+	0.322802i	$0.895375\pi$
$908$	9.88748	+	15.0590i	0.328128	+	0.499749i
$909$	79.7010	+	33.0132i	2.64352	+	1.09498i
$910$	−14.5092	+	47.1459i	−0.480977	+	1.56287i
$911$		−	32.7559i		−	1.08525i	−0.839974	−	0.542626i	$-0.817430\pi$
$911$		−	32.7559i		−	1.08525i	0.839974	−	0.542626i	$-0.182570\pi$
$912$	4.57858	+	1.98355i	0.151612	+	0.0656818i
$913$		−	24.5361i		−	0.812028i
$914$	12.1610	+	3.74256i	0.402249	+	0.123793i
$915$	−31.3834	−	12.9994i	−1.03750	−	0.429748i
$916$	2.57963	−	12.4438i	0.0852334	−	0.411154i
$917$	6.44647	+	15.5632i	0.212881	+	0.513941i
$918$	−9.32217	−	7.71358i	−0.307678	−	0.254586i
$919$	0.117040	+	0.117040i	0.00386081	+	0.00386081i	0.709035	−	0.705174i	$-0.249131\pi$
$919$	0.117040	+	0.117040i	0.00386081	+	0.00386081i	−0.705174	+	0.709035i	$0.749131\pi$
$920$	−31.5457	+	57.3397i	−1.04003	+	1.89043i
$921$	22.0045	−	22.0045i	0.725073	−	0.725073i
$922$	4.81489	−	0.454645i	0.158570	−	0.0149729i
$923$	−94.3418	+	39.0776i	−3.10530	+	1.28626i
$924$	−5.13582	−	26.9528i	−0.168956	−	0.886683i
$925$	−5.32077	+	12.8455i	−0.174946	+	0.422356i
$926$	−15.7246	−	29.7059i	−0.516742	−	0.976197i
$927$	−25.7531			−0.845841
$928$	−34.2667	+	17.4377i	−1.12486	+	0.572422i
$929$	3.61288			0.118535			0.0592674	−	0.998242i	$-0.481124\pi$
$929$	3.61288			0.118535			0.0592674	+	0.998242i	$0.481124\pi$
$930$	11.6461	+	22.0011i	0.381890	+	0.721443i
$931$	0.641265	−	1.54815i	0.0210166	−	0.0507386i
$932$	24.7683	−	4.71957i	0.811313	−	0.154595i
$933$	73.4250	−	30.4136i	2.40383	−	0.995698i
$934$	43.5316	−	4.11047i	1.42440	−	0.134499i
$935$	−6.15222	+	6.15222i	−0.201199	+	0.201199i
$936$	−98.2184	+	28.5024i	−3.21037	+	0.931632i
$937$	−32.6928	−	32.6928i	−1.06803	−	1.06803i	−0.997511	−	0.0705150i	$-0.977536\pi$
$937$	−32.6928	−	32.6928i	−1.06803	−	1.06803i	−0.0705150	−	0.997511i	$-0.522464\pi$
$938$	20.9487	+	17.3339i	0.683999	+	0.565970i
$939$	−16.9127	−	40.8310i	−0.551927	−	1.33247i
$940$	−58.4108	−	12.1087i	−1.90515	−	0.394943i
$941$	−3.53001	−	1.46218i	−0.115075	−	0.0476656i	0.324403	−	0.945919i	$-0.394837\pi$
$941$	−3.53001	−	1.46218i	−0.115075	−	0.0476656i	−0.439478	+	0.898253i	$0.644837\pi$
$942$	50.5925	+	15.5699i	1.64839	+	0.507296i
$943$			15.8885i			0.517400i
$944$	0.0546359	+	0.0564260i	0.00177825	+	0.00183651i
$945$		−	48.4669i		−	1.57663i
$946$	5.05865	−	16.4374i	0.164471	−	0.534427i
$947$	−8.39705	−	3.47817i	−0.272868	−	0.113025i	0.242054	−	0.970263i	$-0.422179\pi$
$947$	−8.39705	−	3.47817i	−0.272868	−	0.113025i	−0.514921	+	0.857237i	$0.672179\pi$
$948$	−66.5653	+	43.7058i	−2.16194	+	1.41950i
$949$	34.0393	+	82.1781i	1.10496	+	2.66761i
$950$	2.15262	−	2.60153i	0.0698403	−	0.0844049i
$951$	−36.2462	−	36.2462i	−1.17536	−	1.17536i
$952$	3.82345	−	3.06124i	0.123919	−	0.0992153i
$953$	37.3278	−	37.3278i	1.20917	−	1.20917i	0.237870	−	0.971297i	$-0.423551\pi$
$953$	37.3278	−	37.3278i	1.20917	−	1.20917i	0.971297	−	0.237870i	$-0.0764492\pi$
$954$	−4.81966	−	51.0422i	−0.156042	−	1.65255i
$955$	−79.3936	+	32.8859i	−2.56912	+	1.06416i
$956$	−2.91477	−	1.98175i	−0.0942704	−	0.0640942i
$957$	−20.6060	+	49.7472i	−0.666096	+	1.60810i
$958$	9.12376	−	4.82959i	0.294775	−	0.156037i
$959$	0.0706788			0.00228234
$960$	17.0513	−	76.0642i	0.550328	−	2.45496i
$961$	−27.7367			−0.894731
$962$	−18.7686	+	9.93502i	−0.605125	+	0.320318i
$963$	−0.109485	+	0.264319i	−0.00352809	+	0.00851757i
$964$	25.1254	+	17.0827i	0.809233	+	0.550196i
$965$	−65.7752	+	27.2450i	−2.11738	+	0.877047i
$966$	−4.85035	−	51.3673i	−0.156058	−	1.65272i
$967$	−2.56068	+	2.56068i	−0.0823459	+	0.0823459i	−0.747080	−	0.664734i	$-0.768545\pi$
$967$	−2.56068	+	2.56068i	−0.0823459	+	0.0823459i	0.664734	+	0.747080i	$0.268545\pi$
$968$	6.94045	+	8.66853i	0.223074	+	0.278617i
$969$	0.882076	+	0.882076i	0.0283363	+	0.0283363i
$970$	3.71361	−	4.48805i	0.119237	−	0.144103i
$971$	8.83244	+	21.3234i	0.283447	+	0.684301i	0.999911	−	0.0133228i	$-0.00424090\pi$
$971$	8.83244	+	21.3234i	0.283447	+	0.684301i	−0.716465	+	0.697623i	$0.754241\pi$
$972$	−3.73257	+	2.45075i	−0.119722	+	0.0786079i
$973$	1.34170	+	0.555752i	0.0430130	+	0.0178166i
$974$	15.4092	−	50.0703i	0.493743	−	1.60436i
$975$			104.564i			3.34872i
$976$	13.9429	+	0.224728i	0.446300	+	0.00719335i
$977$		−	5.76065i		−	0.184300i	−0.995745	−	0.0921498i	$-0.970626\pi$
$977$		−	5.76065i		−	0.184300i	0.995745	−	0.0921498i	$-0.0293739\pi$
$978$	−21.9869	−	6.76651i	−0.703063	−	0.216369i
$979$	14.6304	+	6.06012i	0.467591	+	0.193682i
$980$	−25.6334	−	5.31389i	−0.818830	−	0.169746i
$981$	−41.5819	−	100.387i	−1.32761	−	3.20513i
$982$	−9.86783	−	8.16508i	−0.314895	−	0.260558i
$983$	−18.2389	−	18.2389i	−0.581732	−	0.581732i	0.353647	−	0.935379i	$-0.384941\pi$
$983$	−18.2389	−	18.2389i	−0.581732	−	0.581732i	−0.935379	+	0.353647i	$0.884941\pi$
$984$	−5.27435	−	18.1752i	−0.168140	−	0.579404i
$985$	−43.0087	+	43.0087i	−1.37037	+	1.37037i
$986$	−9.56954	+	0.903602i	−0.304756	+	0.0287766i
$987$	43.4498	−	17.9975i	1.38302	−	0.572866i
$988$	5.06616	−	0.965349i	0.161176	−	0.0307118i
$989$	12.3763	−	29.8789i	0.393542	−	0.950094i
$990$	−33.8043	−	63.8610i	−1.07437	−	2.02963i
$991$	32.1599			1.02159			0.510797	−	0.859701i	$-0.329350\pi$
$991$	32.1599			1.02159			0.510797	+	0.859701i	$0.329350\pi$
$992$	−7.76716	−	6.64064i	−0.246608	−	0.210841i
$993$	−26.8518			−0.852116
$994$	19.0011	+	35.8956i	0.602677	+	1.13854i
$995$	2.52099	−	6.08621i	0.0799208	−	0.192946i
$996$	10.2870	+	53.9861i	0.325955	+	1.71061i
$997$	−12.1739	+	5.04261i	−0.385553	+	0.159701i	−0.567036	−	0.823693i	$-0.691910\pi$
$997$	−12.1739	+	5.04261i	−0.385553	+	0.159701i	0.181484	+	0.983394i	$0.441910\pi$
$998$	1.10683	−	0.104513i	0.0350362	−	0.00330829i
$999$	14.7540	−	14.7540i	0.466795	−	0.466795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.bd.b.205.6	yes	128
32.5	even	8	inner	544.2.bd.b.69.6	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.bd.b.69.6	✓	128	32.5	even	8	inner
544.2.bd.b.205.6	yes	128	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24990 + 0.661625i) q^{2} +(1.13988 - 2.75191i) q^{3} +(1.12450 - 1.65393i) q^{4} +(-3.02227 + 1.25186i) q^{5} +(0.395998 + 4.19379i) q^{6} +(1.22449 - 1.22449i) q^{7} +(-0.311237 + 2.81125i) q^{8} +(-4.15239 - 4.15239i) q^{9} +(2.94927 - 3.56431i) q^{10} +(1.01782 + 2.45723i) q^{11} +(-3.26968 - 4.97982i) q^{12} +(-5.68863 - 2.35631i) q^{13} +(-0.720337 + 2.34064i) q^{14} +9.74399i q^{15} +(-1.47098 - 3.71971i) q^{16} -1.00000i q^{17} +(7.93739 + 2.44275i) q^{18} +(-0.386916 - 0.160266i) q^{19} +(-1.32805 + 6.40635i) q^{20} +(-1.97392 - 4.76546i) q^{21} +(-2.89793 - 2.39788i) q^{22} +(-5.00144 - 5.00144i) q^{23} +(7.38155 + 4.06099i) q^{24} +(4.03139 - 4.03139i) q^{25} +(8.66921 - 0.818589i) q^{26} +(-7.90449 + 3.27415i) q^{27} +(-0.648277 - 3.40216i) q^{28} +(-2.60102 + 6.27941i) q^{29} +(-6.44687 - 12.1790i) q^{30} -1.80647 q^{31} +(4.29963 + 3.67603i) q^{32} +7.92227 q^{33} +(0.661625 + 1.24990i) q^{34} +(-2.16784 + 5.23362i) q^{35} +(-11.5371 + 2.19839i) q^{36} +(-2.25310 + 0.933264i) q^{37} +(0.589642 - 0.0556769i) q^{38} +(-12.9687 + 12.9687i) q^{39} +(-2.57866 - 8.88597i) q^{40} +(-1.58839 - 1.58839i) q^{41} +(5.62015 + 4.65036i) q^{42} +(1.74976 + 4.22430i) q^{43} +(5.20862 + 1.07976i) q^{44} +(17.7478 + 7.35139i) q^{45} +(9.56039 + 2.94223i) q^{46} +9.11765i q^{47} +(-11.9131 - 0.192012i) q^{48} +4.00126i q^{49} +(-2.37157 + 7.70611i) q^{50} +(-2.75191 - 1.13988i) q^{51} +(-10.2941 + 6.75892i) q^{52} +(-2.36249 - 5.70355i) q^{53} +(7.71358 - 9.32217i) q^{54} +(-6.15222 - 6.15222i) q^{55} +(3.06124 + 3.82345i) q^{56} +(-0.882076 + 0.882076i) q^{57} +(-0.903602 - 9.56954i) q^{58} +(-0.0181410 + 0.00751426i) q^{59} +(16.1159 + 10.9572i) q^{60} +(-1.33410 + 3.22080i) q^{61} +(2.25791 - 1.19521i) q^{62} -10.1691 q^{63} +(-7.80626 - 1.74993i) q^{64} +20.1423 q^{65} +(-9.90205 + 5.24157i) q^{66} +(4.24882 - 10.2576i) q^{67} +(-1.65393 - 1.12450i) q^{68} +(-19.4646 + 8.06250i) q^{69} +(-0.753114 - 7.97580i) q^{70} +(11.7269 - 11.7269i) q^{71} +(12.9658 - 10.3810i) q^{72} +(-10.2149 - 10.2149i) q^{73} +(2.19868 - 2.65719i) q^{74} +(-6.49874 - 15.6893i) q^{75} +(-0.700157 + 0.459713i) q^{76} +(4.25515 + 1.76254i) q^{77} +(7.62918 - 24.7900i) q^{78} -13.3670i q^{79} +(9.10225 + 9.40048i) q^{80} +7.86755i q^{81} +(3.03625 + 0.934411i) q^{82} +(-8.52299 - 3.53034i) q^{83} +(-10.1014 - 2.09405i) q^{84} +(1.25186 + 3.02227i) q^{85} +(-4.98193 - 4.12227i) q^{86} +(14.3156 + 14.3156i) q^{87} +(-7.22466 + 2.09656i) q^{88} +(4.21014 - 4.21014i) q^{89} +(-27.0469 + 2.55390i) q^{90} +(-9.85093 + 4.08039i) q^{91} +(-13.8962 + 2.64790i) q^{92} +(-2.05916 + 4.97126i) q^{93} +(-6.03246 - 11.3962i) q^{94} +1.36999 q^{95} +(15.0172 - 7.64198i) q^{96} +1.25916 q^{97} +(-2.64733 - 5.00118i) q^{98} +(5.97699 - 14.4297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 20 q^{6} - 24 q^{8} - 16 q^{12} - 20 q^{16} - 20 q^{18} - 48 q^{22} - 8 q^{23} + 68 q^{24} + 20 q^{26} - 24 q^{27} + 20 q^{30} + 48 q^{31} - 24 q^{35} + 8 q^{36} + 68 q^{38} - 24 q^{39} - 36 q^{40}+ \cdots - 136 q^{99}+O(q^{100}) \) 128 * q + 20 * q^6 - 24 * q^8 - 16 * q^12 - 20 * q^16 - 20 * q^18 - 48 * q^22 - 8 * q^23 + 68 * q^24 + 20 * q^26 - 24 * q^27 + 20 * q^30 + 48 * q^31 - 24 * q^35 + 8 * q^36 + 68 * q^38 - 24 * q^39 - 36 * q^40 - 16 * q^42 - 8 * q^43 - 40 * q^44 - 80 * q^45 + 12 * q^50 + 56 * q^52 - 16 * q^53 - 136 * q^54 + 32 * q^55 + 128 * q^56 - 32 * q^58 + 20 * q^60 - 12 * q^62 - 80 * q^63 + 12 * q^64 - 8 * q^66 + 40 * q^67 - 4 * q^68 + 100 * q^70 - 44 * q^72 + 84 * q^74 + 32 * q^75 - 32 * q^76 - 16 * q^77 - 64 * q^78 + 44 * q^80 + 40 * q^82 + 84 * q^84 - 120 * q^86 - 56 * q^87 + 128 * q^88 - 68 * q^90 - 56 * q^91 - 40 * q^92 + 32 * q^95 - 72 * q^96 - 12 * q^98 - 136 * q^99

Introduction

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