LMFDB - Embedded newform 544.2.bd.b.69.6

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			69.6
Character	$\chi$	$=$	544.69
Dual form			544.2.bd.b.205.6

$q$-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 $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

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

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	0.800719	+	0.599040i	$0.204451\pi$
$3$	1.13988	+	2.75191i	0.658110	+	1.58882i	−0.142609	+	0.989779i	$0.545549\pi$
$4$	1.12450	+	1.65393i	0.562252	+	0.826966i
$5$	−3.02227	−	1.25186i	−1.35160	−	0.559850i	−0.414861	−	0.909885i	$-0.636170\pi$
$5$	−3.02227	−	1.25186i	−1.35160	−	0.559850i	−0.936737	+	0.350034i	$0.886170\pi$
$6$	0.395998	−	4.19379i	0.161666	−	1.71211i
$7$	1.22449	+	1.22449i	0.462813	+	0.462813i	0.899576	−	0.436763i	$-0.143875\pi$
$7$	1.22449	+	1.22449i	0.462813	+	0.462813i	−0.436763	+	0.899576i	$0.643875\pi$
$8$	−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	−0.692919	−	0.721015i	$-0.743676\pi$
$11$	1.01782	−	2.45723i	0.306883	−	0.740882i	0.999803	−	0.0198666i	$-0.00632416\pi$
$12$	−3.26968	+	4.97982i	−0.943875	+	1.43755i
$13$	−5.68863	+	2.35631i	−1.57774	+	0.653522i	−0.988054	−	0.154109i	$-0.950749\pi$
$13$	−5.68863	+	2.35631i	−1.57774	+	0.653522i	−0.589688	+	0.807631i	$0.700749\pi$
$14$	−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	−0.426624	−	0.904429i	$-0.640297\pi$
$19$	−0.386916	+	0.160266i	−0.0887646	+	0.0367675i	0.337859	+	0.941197i	$0.390297\pi$
$20$	−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	−0.0438344	+	0.999039i	$0.513957\pi$
$23$	−5.00144	+	5.00144i	−1.04287	+	1.04287i	−0.999039	+	0.0438344i	$0.986043\pi$
$24$	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	−0.958179	−	0.286170i	$-0.907618\pi$
$29$	−2.60102	−	6.27941i	−0.482997	−	1.16606i	0.475182	−	0.879888i	$-0.342382\pi$
$30$	−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	0.189712	−	0.981840i	$-0.439245\pi$
$37$	−2.25310	−	0.933264i	−0.370407	−	0.153428i	−0.560119	+	0.828412i	$0.689245\pi$
$38$	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	−0.820176	−	0.572111i	$-0.806125\pi$
$41$	−1.58839	+	1.58839i	−0.248065	+	0.248065i	0.572111	+	0.820176i	$0.306125\pi$
$42$	5.62015	−	4.65036i	0.867207	−	0.717565i
$43$	1.74976	−	4.22430i	0.266836	−	0.644199i	−0.732495	−	0.680772i	$-0.761644\pi$
$43$	1.74976	−	4.22430i	0.266836	−	0.644199i	0.999331	+	0.0365733i	$0.0116442\pi$
$44$	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	$-0.768443\pi$
$47$		−	9.11765i		−	1.32995i	0.746868	−	0.664973i	$-0.231557\pi$
$48$	−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	0.674468	+	0.738304i	$0.264373\pi$
$53$	−2.36249	+	5.70355i	−0.324512	+	0.783442i	−0.998981	+	0.0451384i	$0.985627\pi$
$54$	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	0.381502	−	0.924368i	$-0.375407\pi$
$59$	−0.0181410	−	0.00751426i	−0.00236176	−	0.000978273i	−0.383864	+	0.923390i	$0.625407\pi$
$60$	16.1159	−	10.9572i	2.08055	−	1.41456i
$61$	−1.33410	−	3.22080i	−0.170814	−	0.412381i	0.815170	−	0.579222i	$-0.196643\pi$
$61$	−1.33410	−	3.22080i	−0.170814	−	0.412381i	−0.985984	+	0.166841i	$0.946643\pi$
$62$	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	0.938472	+	0.345357i	$0.112242\pi$
$67$	4.24882	+	10.2576i	0.519076	+	1.25316i	−0.419396	+	0.907804i	$0.637758\pi$
$68$	−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	0.821471	+	0.570250i	$0.193154\pi$
$71$	11.7269	+	11.7269i	1.39172	+	1.39172i	0.570250	+	0.821471i	$0.306846\pi$
$72$	12.9658	+	10.3810i	1.52803	+	1.22342i
$73$	−10.2149	+	10.2149i	−1.19556	+	1.19556i	−0.220080	+	0.975482i	$0.570632\pi$
$73$	−10.2149	+	10.2149i	−1.19556	+	1.19556i	−0.975482	+	0.220080i	$0.929368\pi$
$74$	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	$0.270888\pi$
$79$			13.3670i			1.50390i	−0.659218	+	0.751952i	$0.729112\pi$
$80$	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	−0.797770	−	0.602962i	$-0.793987\pi$
$83$	−8.52299	+	3.53034i	−0.935520	+	0.387505i	−0.137750	+	0.990467i	$0.543987\pi$
$84$	−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	0.894114	−	0.447840i	$-0.147806\pi$
$89$	4.21014	+	4.21014i	0.446274	+	0.446274i	−0.447840	+	0.894114i	$0.647806\pi$
$90$	−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	−0.414059	−	0.910250i	$-0.635889\pi$
$101$	−13.5722	−	5.62180i	−1.35049	−	0.559390i	−0.936428	+	0.350860i	$0.885889\pi$
$102$	4.19379	+	0.395998i	0.415247	+	0.0392097i
$103$	3.10099	+	3.10099i	0.305550	+	0.305550i	0.843181	−	0.537631i	$-0.180680\pi$
$103$	3.10099	+	3.10099i	0.305550	+	0.305550i	−0.537631	+	0.843181i	$0.680680\pi$
$104$	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	−0.924778	−	0.380507i	$-0.875750\pi$
$107$	−0.0186441	+	0.0450107i	−0.00180239	+	0.00435135i	0.922976	+	0.384858i	$0.125750\pi$
$108$	−3.47342	−	16.7553i	−0.334230	−	1.61228i
$109$	17.0949	−	7.08094i	1.63740	−	0.678231i	0.641364	−	0.767237i	$-0.278369\pi$
$109$	17.0949	−	7.08094i	1.63740	−	0.678231i	0.996031	+	0.0890056i	$0.0283689\pi$
$110$	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	$0.290090\pi$
$113$			16.8026i			1.58066i	−0.612682	+	0.790329i	$0.709910\pi$
$114$	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	−0.998932	−	0.0462014i	$-0.985288\pi$
$131$	−3.72265	−	8.98728i	−0.325250	−	0.785222i	0.673682	−	0.739021i	$-0.264712\pi$
$132$	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	−0.705873	−	0.708339i	$-0.749445\pi$
$137$	0.0288605	−	0.0288605i	0.00246572	−	0.00246572i	0.708339	+	0.705873i	$0.249445\pi$
$138$	18.9945	+	22.9556i	1.61692	+	1.95411i
$139$	0.320931	−	0.774795i	0.0272210	−	0.0657173i	−0.909685	−	0.415300i	$-0.863677\pi$
$139$	0.320931	−	0.774795i	0.0272210	−	0.0657173i	0.936906	+	0.349583i	$0.113677\pi$
$140$	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	−0.999587	−	0.0287484i	$-0.990848\pi$
$149$	−3.32560	+	8.02872i	−0.272444	+	0.657738i	0.727143	+	0.686486i	$0.240848\pi$
$150$	18.5032	−	15.3104i	1.51078	−	1.25009i
$151$	−7.13146	+	7.13146i	−0.580350	+	0.580350i	−0.934999	−	0.354649i	$-0.884600\pi$
$151$	−7.13146	+	7.13146i	−0.580350	+	0.580350i	0.354649	+	0.934999i	$0.384600\pi$
$152$	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	0.991226	+	0.132178i	$0.0421972\pi$
$157$	4.80884	+	11.6096i	0.383788	+	0.926545i	−0.607438	+	0.794367i	$0.707803\pi$
$158$	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	0.820657	−	0.571421i	$-0.193608\pi$
$163$	−2.08987	−	5.04539i	−0.163691	−	0.395185i	−0.984348	+	0.176236i	$0.943608\pi$
$164$	−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	0.323064	−	0.946377i	$-0.395287\pi$
$167$	−8.05497	−	8.05497i	−0.623312	−	0.623312i	−0.946377	+	0.323064i	$0.895287\pi$
$168$	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	−0.798558	−	0.601918i	$-0.794403\pi$
$173$	−12.3322	+	5.10818i	−0.937603	+	0.388368i	−0.139045	+	0.990286i	$0.544403\pi$
$174$	−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	−0.999484	−	0.0321357i	$-0.989769\pi$
$179$	−22.5237	+	9.32963i	−1.68350	+	0.697329i	−0.684018	+	0.729465i	$0.739769\pi$
$180$	32.1162	+	21.0870i	2.39380	+	1.57173i
$181$	4.69553	−	11.3360i	0.349016	−	0.842599i	−0.647721	−	0.761878i	$-0.724278\pi$
$181$	4.69553	−	11.3360i	0.349016	−	0.842599i	0.996737	−	0.0807214i	$-0.0257224\pi$
$182$	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	0.898639	−	0.438690i	$-0.144557\pi$
$197$	17.1779	+	7.11530i	1.22387	+	0.506944i	0.325233	+	0.945634i	$0.394557\pi$
$198$	2.07643	−	21.9902i	0.147565	−	1.56278i
$199$	−1.42397	−	1.42397i	−0.100942	−	0.100942i	0.654832	−	0.755774i	$-0.272739\pi$
$199$	−1.42397	−	1.42397i	−0.100942	−	0.100942i	−0.755774	+	0.654832i	$0.772739\pi$
$200$	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	−0.804654	−	0.593744i	$-0.797649\pi$
$211$	−13.8546	+	5.73876i	−0.953789	+	0.395072i	−0.149136	+	0.988817i	$0.547649\pi$
$212$	−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	0.767245	−	0.641354i	$-0.221627\pi$
$227$	−3.44699	−	8.32177i	−0.228785	−	0.552335i	−0.996030	+	0.0890186i	$0.971627\pi$
$228$	0.466995	−	2.45079i	0.0309275	−	0.162308i
$229$	5.87049	+	2.43164i	0.387933	+	0.160687i	0.568121	−	0.822945i	$-0.307671\pi$
$229$	5.87049	+	2.43164i	0.387933	+	0.160687i	−0.180188	+	0.983632i	$0.557671\pi$
$230$	−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	−0.351995	−	0.936002i	$-0.614497\pi$
$233$	8.91448	−	8.91448i	0.584007	−	0.584007i	0.936002	+	0.351995i	$0.114497\pi$
$234$	−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	$0.0181528\pi$
$239$			1.76233i			0.113995i	−0.998374	+	0.0569977i	$0.981847\pi$
$240$	36.2448	+	14.3332i	2.33959	+	0.925204i
$241$		−	15.1913i		−	0.978557i	−0.872128	−	0.489279i	$-0.837260\pi$
$241$		−	15.1913i		−	0.978557i	0.872128	−	0.489279i	$-0.162740\pi$
$242$	−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	−0.391063	−	0.920364i	$-0.627893\pi$
$251$	−20.8871	−	8.65172i	−1.31838	−	0.546092i	−0.927319	+	0.374272i	$0.877893\pi$
$252$	−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	0.598082	−	0.801435i	$-0.295930\pi$
$263$	−3.29782	−	3.29782i	−0.203352	−	0.203352i	−0.801435	+	0.598082i	$0.795930\pi$
$264$	−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	−0.521713	−	0.853121i	$-0.674707\pi$
$269$	−4.71325	+	1.95229i	−0.287372	+	0.119033i	0.234341	+	0.972154i	$0.424707\pi$
$270$	−11.6424	−	37.8304i	−0.708533	−	2.30229i
$271$			15.6962i			0.953477i	0.879045	+	0.476739i	$0.158181\pi$
$271$			15.6962i			0.953477i	−0.879045	+	0.476739i	$0.841819\pi$
$272$	−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	−0.989119	−	0.147120i	$-0.953000\pi$
$277$	−3.09027	+	7.46058i	−0.185677	+	0.448263i	0.803442	+	0.595383i	$0.203000\pi$
$278$	−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	0.379550	−	0.925171i	$-0.376079\pi$
$281$	−9.14627	−	9.14627i	−0.545621	−	0.545621i	−0.925171	+	0.379550i	$0.876079\pi$
$282$	−38.2375	−	3.61057i	−2.27701	−	0.215006i
$283$	17.8620	+	7.39867i	1.06178	+	0.439805i	0.844084	−	0.536210i	$-0.180145\pi$
$283$	17.8620	+	7.39867i	1.06178	+	0.439805i	0.217700	+	0.976016i	$0.430145\pi$
$284$	−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	0.999821	+	0.0189019i	$0.00601703\pi$
$293$	29.4445	+	12.1963i	1.72017	+	0.712517i	0.720346	+	0.693615i	$0.243983\pi$
$294$	−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	−0.0898434	−	0.995956i	$-0.528637\pi$
$307$	9.65211	−	3.99803i	0.550875	−	0.228180i	0.640718	+	0.767776i	$0.278637\pi$
$308$	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	0.0724563	−	0.997372i	$-0.476916\pi$
$311$	18.8666	−	18.8666i	1.06983	−	1.06983i	0.997372	−	0.0724563i	$-0.0230838\pi$
$312$	−32.4220	+	40.4946i	−1.83553	+	2.29256i
$313$	10.4916	+	10.4916i	0.593018	+	0.593018i	0.938445	−	0.345428i	$-0.112266\pi$
$313$	10.4916	+	10.4916i	0.593018	+	0.593018i	−0.345428	+	0.938445i	$0.612266\pi$
$314$	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	0.993768	+	0.111465i	$0.0355543\pi$
$317$	6.58563	+	15.8991i	0.369886	+	0.892983i	−0.623883	+	0.781518i	$0.714446\pi$
$318$	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	−0.989886	−	0.141864i	$-0.954690\pi$
$331$	−3.44980	+	8.32855i	−0.189618	+	0.457778i	0.800268	+	0.599642i	$0.204690\pi$
$332$	−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	$-0.814915\pi$
$337$		−	20.1656i		−	1.09849i	0.835661	−	0.549246i	$-0.185085\pi$
$338$	−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	0.914283	−	0.405075i	$-0.132755\pi$
$347$	23.7385	+	9.83279i	1.27435	+	0.527852i	0.360064	+	0.932928i	$0.382755\pi$
$348$	39.7749	+	7.57904i	2.13216	+	0.406279i
$349$	−5.57721	−	13.4646i	−0.298541	−	0.720742i	−0.999968	−	0.00800062i	$-0.997453\pi$
$349$	−5.57721	−	13.4646i	−0.298541	−	0.720742i	0.701427	−	0.712741i	$-0.252547\pi$
$350$	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	0.0379334	−	0.999280i	$-0.487923\pi$
$359$	−18.2149	−	18.2149i	−0.961347	−	0.961347i	−0.999280	+	0.0379334i	$0.987923\pi$
$360$	−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	$0.177882\pi$
$367$			20.3142i			1.06039i	−0.847874	+	0.530197i	$0.822118\pi$
$368$	−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	0.696052	+	0.717992i	$0.254938\pi$
$373$	−5.86789	+	14.1663i	−0.303828	+	0.733505i	−0.999880	+	0.0155137i	$0.995062\pi$
$374$	−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	0.380643	−	0.924722i	$-0.375703\pi$
$379$	−0.0793918	−	0.0328852i	−0.00407808	−	0.00168920i	−0.384722	+	0.923033i	$0.625703\pi$
$380$	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	0.0938540	−	0.995586i	$-0.470081\pi$
$389$	−10.7248	−	4.44234i	−0.543767	−	0.225236i	−0.637621	+	0.770350i	$0.720081\pi$
$390$	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	−0.257035	−	0.966402i	$-0.582746\pi$
$397$	4.87288	−	2.01841i	0.244563	−	0.101301i	0.501598	+	0.865101i	$0.332746\pi$
$398$	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	$0.0327021\pi$
$401$			4.10737i			0.205112i	−0.994727	+	0.102556i	$0.967298\pi$
$402$	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	0.178369	−	0.983964i	$-0.442918\pi$
$409$	−16.2922	−	16.2922i	−0.805595	−	0.805595i	−0.983964	+	0.178369i	$0.942918\pi$
$410$	−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	0.829894	−	0.557922i	$-0.188401\pi$
$419$	−3.09990	−	7.48382i	−0.151440	−	0.365608i	−0.981334	+	0.192313i	$0.938401\pi$
$420$	33.1506	+	6.31681i	1.61759	+	0.308229i
$421$	−18.4958	−	7.66122i	−0.901431	−	0.373385i	−0.116661	−	0.993172i	$-0.537219\pi$
$421$	−18.4958	−	7.66122i	−0.901431	−	0.373385i	−0.784770	+	0.619787i	$0.787219\pi$
$422$	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	$-0.837892\pi$
$431$		−	20.2434i		−	0.975090i	0.873098	−	0.487545i	$-0.162108\pi$
$432$	23.8062	−	24.5862i	1.14538	−	1.18290i
$433$		−	6.09154i		−	0.292741i	−0.989230	−	0.146370i	$-0.953241\pi$
$433$		−	6.09154i		−	0.292741i	0.989230	−	0.146370i	$-0.0467591\pi$
$434$	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	−0.516372	−	0.856364i	$-0.672718\pi$
$439$	7.12362	−	7.12362i	0.339992	−	0.339992i	0.856364	+	0.516372i	$0.172718\pi$
$440$	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	0.411922	−	0.911219i	$-0.364858\pi$
$443$	1.23897	+	0.513196i	0.0588650	+	0.0243827i	−0.353057	+	0.935602i	$0.614858\pi$
$444$	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	−0.840072	−	0.542475i	$-0.817487\pi$
$457$	−6.36191	+	6.36191i	−0.297597	+	0.297597i	0.542475	+	0.840072i	$0.317487\pi$
$458$	−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	−0.455044	−	0.890469i	$-0.650376\pi$
$461$	−3.15947	+	1.30869i	−0.147151	+	0.0609520i	0.307892	+	0.951421i	$0.400376\pi$
$462$	−5.70670	−	18.5432i	−0.265500	−	0.862707i
$463$		−	23.7666i		−	1.10453i	−0.833669	−	0.552264i	$-0.813764\pi$
$463$		−	23.7666i		−	1.10453i	0.833669	−	0.552264i	$-0.186236\pi$
$464$	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	−0.928313	−	0.371801i	$-0.878740\pi$
$467$	−28.5649	+	11.8320i	−1.32183	+	0.547518i	−0.393513	+	0.919319i	$0.628740\pi$
$468$	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	−0.977904	−	0.209054i	$-0.932962\pi$
$487$	−26.1939	−	26.1939i	−1.18696	−	1.18696i	−0.209054	−	0.977904i	$-0.567038\pi$
$488$	−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	−0.826177	−	0.563410i	$-0.809489\pi$
$491$	3.46580	−	8.36717i	0.156409	−	0.377605i	0.982587	+	0.185805i	$0.0594892\pi$
$492$	−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	−0.398881	−	0.917003i	$-0.630601\pi$
$499$	−0.726291	+	0.300839i	−0.0325132	+	0.0134674i	0.366368	+	0.930470i	$0.380601\pi$
$500$	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	0.305774	−	0.952104i	$-0.401085\pi$
$503$	28.2113	−	28.2113i	1.25788	−	1.25788i	0.952104	−	0.305774i	$-0.0989151\pi$
$504$	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	0.994819	−	0.101662i	$-0.0324159\pi$
$509$	4.95192	+	11.9550i	0.219490	+	0.529896i	−0.775329	+	0.631558i	$0.782416\pi$
$510$	−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	−0.999631	−	0.0271637i	$-0.991352\pi$
$521$	−22.1970	+	22.1970i	−0.972467	+	0.972467i	0.0271637	+	0.999631i	$0.491352\pi$
$522$	−35.9843	−	43.4886i	−1.57499	−	1.90344i
$523$	6.24803	−	15.0841i	0.273207	−	0.659581i	−0.726409	−	0.687262i	$-0.758812\pi$
$523$	6.24803	−	15.0841i	0.273207	−	0.659581i	0.999617	+	0.0276813i	$0.00881236\pi$
$524$	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	0.970078	+	0.242792i	$0.0780632\pi$
$541$	10.6019	+	25.5951i	0.455809	+	1.10042i	−0.514269	+	0.857629i	$0.671937\pi$
$542$	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	−0.998888	−	0.0471445i	$-0.984988\pi$
$547$	−7.62225	−	18.4017i	−0.325904	−	0.786801i	0.672984	−	0.739657i	$-0.265012\pi$
$548$	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	−0.795865	−	0.605474i	$-0.792983\pi$
$557$	−21.9604	+	9.09629i	−0.930492	+	0.385422i	−0.134627	+	0.990896i	$0.542983\pi$
$558$	−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	−0.664847	−	0.746979i	$-0.731503\pi$
$563$	−14.3972	+	5.96353i	−0.606772	+	0.251333i	0.0580759	+	0.998312i	$0.481503\pi$
$564$	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	0.986910	+	0.161273i	$0.0515598\pi$
$569$	27.3884	+	27.3884i	1.14818	+	1.14818i	0.161273	+	0.986910i	$0.448440\pi$
$570$	0.542515	−	5.74547i	0.0227234	−	0.240651i
$571$	2.79633	+	1.15828i	0.117023	+	0.0484724i	0.440427	−	0.897789i	$-0.354827\pi$
$571$	2.79633	+	1.15828i	0.117023	+	0.0484724i	−0.323404	+	0.946261i	$0.604827\pi$
$572$	−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	−0.773241	−	0.634112i	$-0.781366\pi$
$587$	5.37640	−	12.9798i	0.221908	−	0.535733i	0.995149	+	0.0983792i	$0.0313658\pi$
$588$	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	$0.178495\pi$
$593$			25.9018i			1.06366i	−0.846852	+	0.531829i	$0.821505\pi$
$594$	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	−0.473547	−	0.880769i	$-0.657027\pi$
$599$	9.96654	−	9.96654i	0.407222	−	0.407222i	0.880769	+	0.473547i	$0.157027\pi$
$600$	46.1293	+	13.3865i	1.88322	+	0.546501i
$601$	18.3118	+	18.3118i	0.746955	+	0.746955i	0.973906	−	0.226951i	$-0.0728757\pi$
$601$	18.3118	+	18.3118i	0.746955	+	0.746955i	−0.226951	+	0.973906i	$0.572876\pi$
$602$	−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	0.704530	−	0.709674i	$-0.251158\pi$
$613$	17.3533	+	7.18796i	0.700892	+	0.290319i	−0.00363774	+	0.999993i	$0.501158\pi$
$614$	−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	−0.125208	−	0.992131i	$-0.539960\pi$
$617$	21.5339	−	21.5339i	0.866923	−	0.866923i	0.992131	+	0.125208i	$0.0399597\pi$
$618$	14.2329	−	11.7769i	0.572532	−	0.473738i
$619$	−1.11728	+	2.69735i	−0.0449073	+	0.108416i	−0.944742	−	0.327816i	$-0.893687\pi$
$619$	−1.11728	+	2.69735i	−0.0449073	+	0.108416i	0.899834	+	0.436232i	$0.143687\pi$
$620$	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	−0.665054	−	0.746796i	$-0.731591\pi$
$631$	2.05334	−	2.05334i	0.0817421	−	0.0817421i	0.746796	+	0.665054i	$0.231591\pi$
$632$	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	0.997774	−	0.0666883i	$-0.0212433\pi$
$643$	6.21474	+	15.0037i	0.245085	+	0.591689i	−0.752688	+	0.658377i	$0.771243\pi$
$644$	−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	0.816850	−	0.576851i	$-0.195719\pi$
$647$	6.10466	+	6.10466i	0.239999	+	0.239999i	−0.576851	+	0.816850i	$0.695719\pi$
$648$	−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	−0.965490	−	0.260439i	$-0.916133\pi$
$653$	−37.4118	+	15.4965i	−1.46404	+	0.606424i	−0.498547	+	0.866863i	$0.666133\pi$
$654$	−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	−0.185712	−	0.982604i	$-0.559459\pi$
$659$	9.69787	−	4.01699i	0.377775	−	0.156480i	0.563488	+	0.826124i	$0.309459\pi$
$660$	−10.5212	−	50.7528i	−0.409537	−	1.97555i
$661$	9.36267	−	22.6035i	0.364166	−	0.879174i	−0.630516	−	0.776176i	$-0.717157\pi$
$661$	9.36267	−	22.6035i	0.364166	−	0.879174i	0.994682	−	0.102997i	$-0.0328433\pi$
$662$	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	0.637450	−	0.770491i	$-0.279989\pi$
$677$	14.1382	+	5.85624i	0.543376	+	0.225074i	−0.0940743	+	0.995565i	$0.529989\pi$
$678$	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	−0.739530	−	0.673123i	$-0.764952\pi$
$683$	6.77836	−	16.3644i	0.259367	−	0.626167i	0.998897	+	0.0469567i	$0.0149523\pi$
$684$	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	0.225330	−	0.974282i	$-0.427654\pi$
$691$	28.2212	−	11.6896i	1.07358	−	0.444693i	0.848254	+	0.529589i	$0.177654\pi$
$692$	−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	−0.997329	−	0.0730465i	$-0.976728\pi$
$701$	−9.10159	−	21.9732i	−0.343762	−	0.829916i	0.653566	−	0.756869i	$-0.273272\pi$
$702$	−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	0.389008	−	0.921234i	$-0.372818\pi$
$709$	0.337277	+	0.139705i	0.0126667	+	0.00524672i	−0.376341	+	0.926481i	$0.622818\pi$
$710$	−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	$0.258063\pi$
$719$			38.8693i			1.44958i	−0.688970	+	0.724790i	$0.741937\pi$
$720$	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	−0.424295	−	0.905524i	$-0.639478\pi$
$727$	12.9754	−	12.9754i	0.481230	−	0.481230i	0.905524	+	0.424295i	$0.139478\pi$
$728$	−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	−0.949704	−	0.313149i	$-0.898616\pi$
$733$	−13.5259	−	32.6545i	−0.499591	−	1.20612i	0.450113	−	0.892972i	$-0.351384\pi$
$734$	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	0.964314	−	0.264762i	$-0.0852933\pi$
$739$	2.58868	+	6.24963i	0.0952263	+	0.229897i	−0.869088	+	0.494658i	$0.835293\pi$
$740$	−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	0.846832	−	0.531860i	$-0.178507\pi$
$743$	8.58553	+	8.58553i	0.314972	+	0.314972i	−0.531860	+	0.846832i	$0.678507\pi$
$744$	−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	$0.0557941\pi$
$751$			9.55789i			0.348773i	−0.984677	+	0.174386i	$0.944206\pi$
$752$	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	0.653177	+	0.757205i	$0.273436\pi$
$757$	−9.46781	+	22.8573i	−0.344114	+	0.830764i	−0.997291	+	0.0735587i	$0.976564\pi$
$758$	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	0.746733	−	0.665124i	$-0.231621\pi$
$761$	2.25131	+	2.25131i	0.0816098	+	0.0816098i	−0.665124	+	0.746733i	$0.731621\pi$
$762$	−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	0.406838	−	0.913500i	$-0.366631\pi$
$773$	1.35047	+	0.559382i	0.0485729	+	0.0201196i	−0.358265	+	0.933620i	$0.616631\pi$
$774$	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	−0.555388	−	0.831592i	$-0.687430\pi$
$787$	−10.1016	+	4.18421i	−0.360082	+	0.149151i	0.195306	+	0.980742i	$0.437430\pi$
$788$	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	0.711432	−	0.702755i	$-0.248047\pi$
$797$	−8.14609	−	19.6664i	−0.288549	−	0.696620i	−0.999981	+	0.00613546i	$0.998047\pi$
$798$	−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	−0.539265	−	0.842136i	$-0.681298\pi$
$809$	8.61454	−	8.61454i	0.302871	−	0.302871i	0.842136	+	0.539265i	$0.181298\pi$
$810$	28.0424	−	23.2035i	0.985309	−	0.815288i
$811$	8.05711	−	19.4516i	0.282923	−	0.683038i	−0.716978	−	0.697096i	$-0.754475\pi$
$811$	8.05711	−	19.4516i	0.282923	−	0.683038i	0.999901	+	0.0140584i	$0.00447507\pi$
$812$	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	−0.999701	−	0.0244668i	$-0.992211\pi$
$821$	−7.89407	+	19.0580i	−0.275505	+	0.665128i	0.724196	+	0.689594i	$0.242211\pi$
$822$	−0.109606	−	0.132464i	−0.00382296	−	0.00462021i
$823$	−4.03863	+	4.03863i	−0.140778	+	0.140778i	−0.773983	−	0.633206i	$-0.781739\pi$
$823$	−4.03863	+	4.03863i	−0.140778	+	0.140778i	0.633206	+	0.773983i	$0.281739\pi$
$824$	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	0.174322	−	0.984689i	$-0.444227\pi$
$827$	−11.4655	−	4.74915i	−0.398693	−	0.165144i	−0.573016	+	0.819545i	$0.694227\pi$
$828$	68.6975	−	46.7073i	2.38740	−	1.62319i
$829$	9.19286	+	22.1935i	0.319281	+	0.770813i	0.999292	+	0.0376112i	$0.0119748\pi$
$829$	9.19286	+	22.1935i	0.319281	+	0.770813i	−0.680011	+	0.733202i	$0.738025\pi$
$830$	−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	0.135897	−	0.990723i	$-0.456608\pi$
$839$	−24.7605	−	24.7605i	−0.854826	−	0.854826i	−0.990723	+	0.135897i	$0.956608\pi$
$840$	−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	−0.958663	−	0.284543i	$-0.908158\pi$
$853$	−2.32433	+	5.61143i	−0.0795835	+	0.192132i	0.879080	+	0.476675i	$0.158158\pi$
$854$	−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	0.569971	−	0.821665i	$-0.306954\pi$
$857$	−7.36821	−	7.36821i	−0.251693	−	0.251693i	−0.821665	+	0.569971i	$0.806954\pi$
$858$	68.6798	+	6.48508i	2.34469	+	0.221397i
$859$	−33.2157	−	13.7584i	−1.13331	−	0.469431i	−0.264403	−	0.964412i	$-0.585175\pi$
$859$	−33.2157	−	13.7584i	−1.13331	−	0.469431i	−0.868903	+	0.494982i	$0.835175\pi$
$860$	−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	−0.0861977	−	0.996278i	$-0.527472\pi$
$877$	16.5048	−	6.83650i	0.557326	−	0.230852i	0.643524	+	0.765426i	$0.277472\pi$
$878$	−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	$-0.986837\pi$
$881$		−	2.45411i		−	0.0826810i	0.999145	−	0.0413405i	$-0.0131628\pi$
$882$	−9.77407	−	31.7596i	−0.329110	−	1.06940i
$883$	−39.3368	+	16.2938i	−1.32379	+	0.548332i	−0.928877	−	0.370387i	$-0.879225\pi$
$883$	−39.3368	+	16.2938i	−1.32379	+	0.548332i	−0.394912	+	0.918719i	$0.629225\pi$
$884$	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	−0.983255	−	0.182233i	$-0.941668\pi$
$887$	−23.8565	+	23.8565i	−0.801023	+	0.801023i	0.182233	+	0.983255i	$0.441668\pi$
$888$	−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	−0.946467	−	0.322802i	$-0.895375\pi$
$907$	−1.47445	+	3.55963i	−0.0489582	+	0.118196i	0.897508	+	0.440997i	$0.145375\pi$
$908$	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	$0.182570\pi$
$911$			32.7559i			1.08525i	−0.839974	+	0.542626i	$0.817430\pi$
$912$	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	−0.705174	−	0.709035i	$-0.749131\pi$
$919$	0.117040	−	0.117040i	0.00386081	−	0.00386081i	0.709035	+	0.705174i	$0.249131\pi$
$920$	−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	−0.0705150	+	0.997511i	$0.522464\pi$
$937$	−32.6928	+	32.6928i	−1.06803	+	1.06803i	−0.997511	+	0.0705150i	$0.977536\pi$
$938$	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	−0.439478	−	0.898253i	$-0.644837\pi$
$941$	−3.53001	+	1.46218i	−0.115075	+	0.0476656i	0.324403	+	0.945919i	$0.394837\pi$
$942$	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	−0.514921	−	0.857237i	$-0.672179\pi$
$947$	−8.39705	+	3.47817i	−0.272868	+	0.113025i	0.242054	+	0.970263i	$0.422179\pi$
$948$	−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	0.971297	+	0.237870i	$0.0764492\pi$
$953$	37.3278	+	37.3278i	1.20917	+	1.20917i	0.237870	+	0.971297i	$0.423551\pi$
$954$	−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	0.664734	−	0.747080i	$-0.268545\pi$
$967$	−2.56068	−	2.56068i	−0.0823459	−	0.0823459i	−0.747080	+	0.664734i	$0.768545\pi$
$968$	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	−0.716465	−	0.697623i	$-0.754241\pi$
$971$	8.83244	−	21.3234i	0.283447	−	0.684301i	0.999911	+	0.0133228i	$0.00424090\pi$
$972$	−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	$0.0293739\pi$
$977$			5.76065i			0.184300i	−0.995745	+	0.0921498i	$0.970626\pi$
$978$	−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	−0.935379	−	0.353647i	$-0.884941\pi$
$983$	−18.2389	+	18.2389i	−0.581732	+	0.581732i	0.353647	+	0.935379i	$0.384941\pi$
$984$	−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	0.181484	−	0.983394i	$-0.441910\pi$
$997$	−12.1739	−	5.04261i	−0.385553	−	0.159701i	−0.567036	+	0.823693i	$0.691910\pi$
$998$	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.69.6	✓	128
32.13	even	8	inner	544.2.bd.b.205.6	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.bd.b.69.6	✓	128	1.1	even	1	trivial
544.2.bd.b.205.6	yes	128	32.13	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
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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