LMFDB - Embedded newform 585.2.ca.a.58.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,2,Mod(58,585)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 9, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("585.58"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.ca (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$80$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			58.8
Character	$\chi$	$=$	585.58
Dual form			585.2.ca.a.232.73

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.37704i q^{2} +(1.71493 - 0.242904i) q^{3} -3.65031 q^{4} +(-1.07099 - 1.96290i) q^{5} +(-0.577391 - 4.07646i) q^{6} +(1.74707 - 3.02601i) q^{7} +3.92284i q^{8} +(2.88200 - 0.833127i) q^{9} +(-4.66589 + 2.54578i) q^{10} +(3.03601 + 3.03601i) q^{11} +(-6.26003 + 0.886672i) q^{12} +(1.70086 - 3.17916i) q^{13} +(-7.19293 - 4.15284i) q^{14} +(-2.31347 - 3.10610i) q^{15} +2.02412 q^{16} +(-0.739061 + 2.75821i) q^{17} +(-1.98037 - 6.85061i) q^{18} +(-0.433806 + 1.61899i) q^{19} +(3.90944 + 7.16519i) q^{20} +(2.26108 - 5.61377i) q^{21} +(7.21672 - 7.21672i) q^{22} +(-5.35140 - 1.43390i) q^{23} +(0.952871 + 6.72741i) q^{24} +(-2.70596 + 4.20449i) q^{25} +(-7.55699 - 4.04300i) q^{26} +(4.74006 - 2.12880i) q^{27} +(-6.37733 + 11.0459i) q^{28} +9.22139i q^{29} +(-7.38331 + 5.49921i) q^{30} +(1.71530 + 6.40158i) q^{31} +3.03427i q^{32} +(5.94402 + 4.46910i) q^{33} +(6.55638 + 1.75678i) q^{34} +(-7.81085 - 0.188496i) q^{35} +(-10.5202 + 3.04117i) q^{36} +(4.56675 - 7.90984i) q^{37} +(3.84839 + 1.03117i) q^{38} +(2.14463 - 5.86520i) q^{39} +(7.70014 - 4.20132i) q^{40} +(-5.01925 - 1.34490i) q^{41} +(-13.3441 - 5.37466i) q^{42} +(-0.520848 - 1.94383i) q^{43} +(-11.0824 - 11.0824i) q^{44} +(-4.72193 - 4.76480i) q^{45} +(-3.40844 + 12.7205i) q^{46} +(-2.13875 - 3.70442i) q^{47} +(3.47123 - 0.491666i) q^{48} +(-2.60448 - 4.51110i) q^{49} +(9.99424 + 6.43217i) q^{50} +(-0.597461 + 4.90967i) q^{51} +(-6.20865 + 11.6049i) q^{52} +(-2.09114 - 2.09114i) q^{53} +(-5.06025 - 11.2673i) q^{54} +(2.70786 - 9.21094i) q^{55} +(11.8705 + 6.85346i) q^{56} +(-0.350691 + 2.88183i) q^{57} +21.9196 q^{58} +(-1.97960 + 1.97960i) q^{59} +(8.44488 + 11.3382i) q^{60} +(-2.62118 + 4.54002i) q^{61} +(15.2168 - 4.07733i) q^{62} +(2.51399 - 10.1765i) q^{63} +11.2608 q^{64} +(-8.06199 + 0.0662388i) q^{65} +(10.6232 - 14.1292i) q^{66} +(10.5098 - 6.06786i) q^{67} +(2.69780 - 10.0683i) q^{68} +(-9.52559 - 1.15917i) q^{69} +(-0.448061 + 18.5667i) q^{70} +(5.32997 + 1.42816i) q^{71} +(3.26822 + 11.3056i) q^{72} +7.95506i q^{73} +(-18.8020 - 10.8553i) q^{74} +(-3.61926 + 7.86772i) q^{75} +(1.58352 - 5.90979i) q^{76} +(14.4911 - 3.88288i) q^{77} +(-13.9418 - 5.09786i) q^{78} +(12.3171 - 7.11130i) q^{79} +(-2.16781 - 3.97315i) q^{80} +(7.61180 - 4.80214i) q^{81} +(-3.19688 + 11.9309i) q^{82} +(4.14053 + 7.17160i) q^{83} +(-8.25362 + 20.4920i) q^{84} +(6.20563 - 1.50331i) q^{85} +(-4.62056 + 1.23808i) q^{86} +(2.23991 + 15.8141i) q^{87} +(-11.9098 + 11.9098i) q^{88} +(2.27358 + 8.48513i) q^{89} +(-11.3261 + 11.2242i) q^{90} +(-6.64867 - 10.7010i) q^{91} +(19.5342 + 5.23418i) q^{92} +(4.49659 + 10.5616i) q^{93} +(-8.80555 + 5.08388i) q^{94} +(3.64251 - 0.882399i) q^{95} +(0.737034 + 5.20357i) q^{96} +(-3.18891 - 1.84112i) q^{97} +(-10.7231 + 6.19096i) q^{98} +(11.2792 + 6.22039i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 2 q^{3} - 304 q^{4} - 2 q^{5} - 8 q^{6} + 2 q^{7} + 12 q^{9} - 16 q^{10} - 12 q^{11} - 14 q^{12} - 2 q^{13} + 48 q^{14} - 6 q^{15} + 264 q^{16} - 12 q^{17} + 4 q^{18} - 30 q^{20} - 16 q^{21} - 4 q^{22}+ \cdots - 20 q^{99}+O(q^{100}) $ 320 * q - 2 * q^3 - 304 * q^4 - 2 * q^5 - 8 * q^6 + 2 * q^7 + 12 * q^9 - 16 * q^10 - 12 * q^11 - 14 * q^12 - 2 * q^13 + 48 * q^14 - 6 * q^15 + 264 * q^16 - 12 * q^17 + 4 * q^18 - 30 * q^20 - 16 * q^21 - 4 * q^22 + 2 * q^23 + 56 * q^24 - 20 * q^27 - 24 * q^28 - 2 * q^30 - 4 * q^31 - 6 * q^33 + 8 * q^34 - 46 * q^35 - 60 * q^36 - 4 * q^37 - 40 * q^38 - 4 * q^39 + 28 * q^40 + 4 * q^41 + 22 * q^42 - 6 * q^43 + 8 * q^44 + 4 * q^45 - 16 * q^46 - 14 * q^47 + 2 * q^48 - 112 * q^49 + 56 * q^50 - 30 * q^52 - 16 * q^53 - 4 * q^55 - 108 * q^56 - 72 * q^57 + 28 * q^58 - 16 * q^59 + 10 * q^60 + 4 * q^61 - 28 * q^62 - 18 * q^63 - 192 * q^64 + 58 * q^65 - 6 * q^67 + 62 * q^68 + 24 * q^69 + 10 * q^70 - 2 * q^72 - 34 * q^75 - 20 * q^76 - 44 * q^77 - 42 * q^78 + 4 * q^80 + 8 * q^81 + 20 * q^82 + 8 * q^83 + 124 * q^84 - 16 * q^85 + 68 * q^86 + 38 * q^87 - 8 * q^88 + 64 * q^90 - 16 * q^91 - 32 * q^92 - 70 * q^93 + 48 * q^94 - 64 * q^96 - 6 * q^97 - 282 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{12}\right)$

Coefficient data

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

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

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

$2$		−	2.37704i		−	1.68082i	−0.541952	−	0.840410i	$-0.682314\pi$
$2$		−	2.37704i		−	1.68082i	0.541952	−	0.840410i	$-0.317686\pi$
$3$	1.71493	−	0.242904i	0.990117	−	0.140240i
$3$	1.71493	−	0.242904i	0.990117	−	0.140240i
$4$	−3.65031			−1.82515
$5$	−1.07099	−	1.96290i	−0.478961	−	0.877836i
$5$	−1.07099	−	1.96290i	−0.478961	−	0.877836i
$6$	−0.577391	−	4.07646i	−0.235719	−	1.66421i
$7$	1.74707	−	3.02601i	0.660329	−	1.14372i	−0.320200	−	0.947350i	$-0.603750\pi$
$7$	1.74707	−	3.02601i	0.660329	−	1.14372i	0.980529	−	0.196374i	$-0.0629166\pi$
$8$			3.92284i			1.38693i
$9$	2.88200	−	0.833127i	0.960665	−	0.277709i
$10$	−4.66589	+	2.54578i	−1.47548	+	0.805047i
$11$	3.03601	+	3.03601i	0.915393	+	0.915393i	0.996690	−	0.0812972i	$-0.0259063\pi$
$11$	3.03601	+	3.03601i	0.915393	+	0.915393i	−0.0812972	+	0.996690i	$0.525906\pi$
$12$	−6.26003	+	0.886672i	−1.80712	+	0.255960i
$13$	1.70086	−	3.17916i	0.471733	−	0.881742i
$13$	1.70086	−	3.17916i	0.471733	−	0.881742i
$14$	−7.19293	−	4.15284i	−1.92239	−	1.10989i
$15$	−2.31347	−	3.10610i	−0.597336	−	0.801991i
$16$	2.02412			0.506030
$17$	−0.739061	+	2.75821i	−0.179249	+	0.668965i	0.816540	+	0.577289i	$0.195889\pi$
$17$	−0.739061	+	2.75821i	−0.179249	+	0.668965i	−0.995789	+	0.0916764i	$0.970777\pi$
$18$	−1.98037	−	6.85061i	−0.466779	−	1.61470i
$19$	−0.433806	+	1.61899i	−0.0995219	+	0.371421i	−0.997666	−	0.0682800i	$-0.978249\pi$
$19$	−0.433806	+	1.61899i	−0.0995219	+	0.371421i	0.898144	+	0.439701i	$0.144916\pi$
$20$	3.90944	+	7.16519i	0.874177	+	1.60219i
$21$	2.26108	−	5.61377i	0.493407	−	1.22503i
$22$	7.21672	−	7.21672i	1.53861	−	1.53861i
$23$	−5.35140	−	1.43390i	−1.11584	−	0.298989i	−0.346643	−	0.937997i	$-0.612678\pi$
$23$	−5.35140	−	1.43390i	−1.11584	−	0.298989i	−0.769200	+	0.639008i	$0.779345\pi$
$24$	0.952871	+	6.72741i	0.194504	+	1.37323i
$25$	−2.70596	+	4.20449i	−0.541192	+	0.840899i
$26$	−7.55699	−	4.04300i	−1.48205	−	0.792897i
$27$	4.74006	−	2.12880i	0.912225	−	0.409689i
$28$	−6.37733	+	11.0459i	−1.20520	+	2.08747i
$29$			9.22139i			1.71237i	0.516669	+	0.856185i	$0.327172\pi$
$29$			9.22139i			1.71237i	−0.516669	+	0.856185i	$0.672828\pi$
$30$	−7.38331	+	5.49921i	−1.34800	+	1.00401i
$31$	1.71530	+	6.40158i	0.308077	+	1.14976i	0.930265	+	0.366890i	$0.119577\pi$
$31$	1.71530	+	6.40158i	0.308077	+	1.14976i	−0.622188	+	0.782868i	$0.713756\pi$
$32$			3.03427i			0.536388i
$33$	5.94402	+	4.46910i	1.03472	+	0.777971i
$34$	6.55638	+	1.75678i	1.12441	+	0.301285i
$35$	−7.81085	−	0.188496i	−1.32027	−	0.0318616i
$36$	−10.5202	+	3.04117i	−1.75336	+	0.506861i
$37$	4.56675	−	7.90984i	0.750769	−	1.30037i	−0.196682	−	0.980467i	$-0.563017\pi$
$37$	4.56675	−	7.90984i	0.750769	−	1.30037i	0.947451	−	0.319902i	$-0.103650\pi$
$38$	3.84839	+	1.03117i	0.624291	+	0.167278i
$39$	2.14463	−	5.86520i	0.343415	−	0.939184i
$40$	7.70014	−	4.20132i	1.21750	−	0.664287i
$41$	−5.01925	−	1.34490i	−0.783875	−	0.210039i	−0.155382	−	0.987854i	$-0.549661\pi$
$41$	−5.01925	−	1.34490i	−0.783875	−	0.210039i	−0.628492	+	0.777816i	$0.716328\pi$
$42$	−13.3441	−	5.37466i	−2.05905	−	0.829328i
$43$	−0.520848	−	1.94383i	−0.0794286	−	0.296432i	0.914772	−	0.403970i	$-0.132370\pi$
$43$	−0.520848	−	1.94383i	−0.0794286	−	0.296432i	−0.994201	+	0.107538i	$0.965703\pi$
$44$	−11.0824	−	11.0824i	−1.67073	−	1.67073i
$45$	−4.72193	−	4.76480i	−0.703904	−	0.710295i
$46$	−3.40844	+	12.7205i	−0.502547	+	1.87553i
$47$	−2.13875	−	3.70442i	−0.311968	−	0.540345i	0.666820	−	0.745219i	$-0.267655\pi$
$47$	−2.13875	−	3.70442i	−0.311968	−	0.540345i	−0.978788	+	0.204874i	$0.934322\pi$
$48$	3.47123	−	0.491666i	0.501029	−	0.0709659i
$49$	−2.60448	−	4.51110i	−0.372069	−	0.644443i
$50$	9.99424	+	6.43217i	1.41340	+	0.909647i
$51$	−0.597461	+	4.90967i	−0.0836612	+	0.687492i
$52$	−6.20865	+	11.6049i	−0.860984	+	1.60931i
$53$	−2.09114	−	2.09114i	−0.287240	−	0.287240i	0.548748	−	0.835988i	$-0.315105\pi$
$53$	−2.09114	−	2.09114i	−0.287240	−	0.287240i	−0.835988	+	0.548748i	$0.815105\pi$
$54$	−5.06025	−	11.2673i	−0.688613	−	1.53329i
$55$	2.70786	−	9.21094i	0.365127	−	1.24200i
$56$	11.8705	+	6.85346i	1.58627	+	0.915832i
$57$	−0.350691	+	2.88183i	−0.0464502	+	0.381707i
$58$	21.9196			2.87818
$59$	−1.97960	+	1.97960i	−0.257722	+	0.257722i	−0.824127	−	0.566405i	$-0.808334\pi$
$59$	−1.97960	+	1.97960i	−0.257722	+	0.257722i	0.566405	+	0.824127i	$0.308334\pi$
$60$	8.44488	+	11.3382i	1.09023	+	1.46376i
$61$	−2.62118	+	4.54002i	−0.335608	+	0.581290i	−0.983601	−	0.180356i	$-0.942275\pi$
$61$	−2.62118	+	4.54002i	−0.335608	+	0.581290i	0.647993	+	0.761646i	$0.275608\pi$
$62$	15.2168	−	4.07733i	1.93253	−	0.517821i
$63$	2.51399	−	10.1765i	0.316733	−	1.28211i
$64$	11.2608			1.40760
$65$	−8.06199	+	0.0662388i	−0.999966	+	0.00821591i
$66$	10.6232	−	14.1292i	1.30763	−	1.73918i
$67$	10.5098	−	6.06786i	1.28398	−	0.741307i	0.306407	−	0.951901i	$-0.400873\pi$
$67$	10.5098	−	6.06786i	1.28398	−	0.741307i	0.977574	+	0.210594i	$0.0675398\pi$
$68$	2.69780	−	10.0683i	0.327156	−	1.22096i
$69$	−9.52559	−	1.15917i	−1.14675	−	0.139548i
$70$	−0.448061	+	18.5667i	−0.0535535	+	2.21914i
$71$	5.32997	+	1.42816i	0.632551	+	0.169492i	0.560827	−	0.827933i	$-0.310483\pi$
$71$	5.32997	+	1.42816i	0.632551	+	0.169492i	0.0717240	+	0.997425i	$0.477150\pi$
$72$	3.26822	+	11.3056i	0.385164	+	1.33238i
$73$			7.95506i			0.931070i	0.885030	+	0.465535i	$0.154138\pi$
$73$			7.95506i			0.931070i	−0.885030	+	0.465535i	$0.845862\pi$
$74$	−18.8020	−	10.8553i	−2.18569	−	1.26191i
$75$	−3.61926	+	7.86772i	−0.417916	+	0.908486i
$76$	1.58352	−	5.90979i	0.181643	−	0.677900i
$77$	14.4911	−	3.88288i	1.65142	−	0.442496i
$78$	−13.9418	−	5.09786i	−1.57860	−	0.577219i
$79$	12.3171	−	7.11130i	1.38579	−	0.800084i	0.392949	−	0.919560i	$-0.371455\pi$
$79$	12.3171	−	7.11130i	1.38579	−	0.800084i	0.992837	+	0.119476i	$0.0381215\pi$
$80$	−2.16781	−	3.97315i	−0.242369	−	0.444211i
$81$	7.61180	−	4.80214i	0.845755	−	0.533571i
$82$	−3.19688	+	11.9309i	−0.353037	+	1.31755i
$83$	4.14053	+	7.17160i	0.454482	+	0.787186i	0.998658	−	0.0517851i	$-0.0164911\pi$
$83$	4.14053	+	7.17160i	0.454482	+	0.787186i	−0.544176	+	0.838971i	$0.683158\pi$
$84$	−8.25362	+	20.4920i	−0.900543	+	2.23586i
$85$	6.20563	−	1.50331i	0.673095	−	0.163057i
$86$	−4.62056	+	1.23808i	−0.498248	+	0.133505i
$87$	2.23991	+	15.8141i	0.240144	+	1.69545i
$88$	−11.9098	+	11.9098i	−1.26959	+	1.26959i
$89$	2.27358	+	8.48513i	0.240999	+	0.899422i	0.975352	+	0.220654i	$0.0708191\pi$
$89$	2.27358	+	8.48513i	0.240999	+	0.899422i	−0.734353	+	0.678768i	$0.762514\pi$
$90$	−11.3261	+	11.2242i	−1.19388	+	1.18314i
$91$	−6.64867	−	10.7010i	−0.696970	−	1.12177i
$92$	19.5342	+	5.23418i	2.03658	+	0.545701i
$93$	4.49659	+	10.5616i	0.466275	+	1.09519i
$94$	−8.80555	+	5.08388i	−0.908223	+	0.524363i
$95$	3.64251	−	0.882399i	0.373714	−	0.0905322i
$96$	0.737034	+	5.20357i	0.0752233	+	0.531087i
$97$	−3.18891	−	1.84112i	−0.323785	−	0.186937i	0.329294	−	0.944228i	$-0.393189\pi$
$97$	−3.18891	−	1.84112i	−0.323785	−	0.186937i	−0.653078	+	0.757290i	$0.726523\pi$
$98$	−10.7231	+	6.19096i	−1.08319	+	0.625381i
$99$	11.2792	+	6.22039i	1.13360	+	0.625173i
$100$	9.87759	−	15.3477i	0.987759	−	1.53477i
$101$		−	12.2039i		−	1.21433i	−0.794574	−	0.607167i	$-0.792306\pi$
$101$		−	12.2039i		−	1.21433i	0.794574	−	0.607167i	$-0.207694\pi$
$102$	11.6705	+	1.42019i	1.15555	+	0.140619i
$103$	−1.76733	−	6.59575i	−0.174140	−	0.649898i	−0.996697	−	0.0812155i	$-0.974120\pi$
$103$	−1.76733	−	6.59575i	−0.174140	−	0.649898i	0.822557	−	0.568683i	$-0.192547\pi$
$104$	12.4713	+	6.67219i	1.22292	+	0.654262i
$105$	−13.4409	+	1.57403i	−1.31169	+	0.153609i
$106$	−4.97071	+	4.97071i	−0.482798	+	0.482798i
$107$	1.38026	+	5.15118i	0.133434	+	0.497984i	0.999999	−	0.00108042i	$-0.000343907\pi$
$107$	1.38026	+	5.15118i	0.133434	+	0.497984i	−0.866565	+	0.499064i	$0.833677\pi$
$108$	−17.3027	+	7.77079i	−1.66495	+	0.747744i
$109$	0.486216	+	0.486216i	0.0465710	+	0.0465710i	0.730009	−	0.683438i	$-0.239516\pi$
$109$	0.486216	+	0.486216i	0.0465710	+	0.0465710i	−0.683438	+	0.730009i	$0.739516\pi$
$110$	−21.8947	−	6.43667i	−2.08758	−	0.613713i
$111$	5.91034	−	14.6741i	0.560985	−	1.39281i
$112$	3.53627	−	6.12500i	0.334146	−	0.578759i
$113$	−5.69704	−	5.69704i	−0.535932	−	0.535932i	0.386399	−	0.922332i	$-0.373719\pi$
$113$	−5.69704	−	5.69704i	−0.535932	−	0.535932i	−0.922332	+	0.386399i	$0.873719\pi$
$114$	6.85021	+	0.833605i	0.641581	+	0.0780743i
$115$	2.91668	+	12.0400i	0.271982	+	1.12273i
$116$		−	33.6609i		−	3.12534i
$117$	2.25321	−	10.5794i	0.208310	−	0.978063i
$118$	4.70558	+	4.70558i	0.433184	+	0.433184i
$119$	7.05519	+	7.05519i	0.646748	+	0.646748i
$120$	12.1847	−	9.07538i	1.11231	−	0.828465i
$121$			7.43476i			0.675887i
$122$	10.7918	+	6.23065i	0.977044	+	0.564097i
$123$	−8.93436	−	1.08723i	−0.805584	−	0.0980319i
$124$	−6.26136	−	23.3677i	−0.562287	−	2.09848i
$125$	11.1511	+	0.808566i	0.997381	+	0.0723204i
$126$	−24.1899	−	5.97585i	−2.15500	−	0.532371i
$127$	−19.1201	+	5.12322i	−1.69664	+	0.454612i	−0.972089	−	0.234613i	$-0.924618\pi$
$127$	−19.1201	+	5.12322i	−1.69664	+	0.454612i	−0.724547	+	0.689225i	$0.757951\pi$
$128$		−	20.6988i		−	1.82953i
$129$	−1.36538	−	3.20703i	−0.120215	−	0.282363i
$130$	0.157452	+	19.1636i	0.0138095	+	1.68076i
$131$	7.25279	−	12.5622i	0.633679	−	1.09756i	−0.353115	−	0.935580i	$-0.614877\pi$
$131$	7.25279	−	12.5622i	0.633679	−	1.09756i	0.986793	−	0.161984i	$-0.0517892\pi$
$132$	−21.6975	−	16.3136i	−1.88852	−	1.41992i
$133$	4.14118	+	4.14118i	0.359086	+	0.359086i
$134$	−14.4235	−	24.9823i	−1.24600	−	2.15814i
$135$	−9.25519	−	7.02435i	−0.796560	−	0.604559i
$136$	−10.8200	−	2.89922i	−0.927809	−	0.248606i
$137$	−1.42726	+	2.47209i	−0.121939	+	0.211205i	−0.920532	−	0.390666i	$-0.872245\pi$
$137$	−1.42726	+	2.47209i	−0.121939	+	0.211205i	0.798593	+	0.601871i	$0.205578\pi$
$138$	−2.75540	+	22.6427i	−0.234555	+	1.92747i
$139$			0.00543496i			0.000460987i	1.00000		0.000230494i	$7.33684e-5\pi$
$139$			0.00543496i			0.000460987i	−1.00000		0.000230494i	$0.999927\pi$
$140$	28.5120	+	0.688066i	2.40970	+	0.0581522i
$141$	−4.56763	−	5.83333i	−0.384664	−	0.491255i
$142$	3.39479	−	12.6695i	0.284885	−	1.06320i
$143$	14.8158	−	4.48816i	1.23896	−	0.375319i
$144$	5.83351	−	1.68635i	0.486125	−	0.140529i
$145$	18.1007	−	9.87602i	1.50318	−	0.820159i
$146$	18.9095			1.56496
$147$	−5.56228	−	7.10360i	−0.458769	−	0.585895i
$148$	−16.6700	+	28.8733i	−1.37027	+	2.37337i
$149$	3.89787	+	3.89787i	0.319326	+	0.319326i	0.848508	−	0.529182i	$-0.177501\pi$
$149$	3.89787	+	3.89787i	0.319326	+	0.319326i	−0.529182	+	0.848508i	$0.677501\pi$
$150$	18.7019	+	8.60311i	1.52700	+	0.702441i
$151$	1.37709	−	5.13938i	0.112066	−	0.418237i	−0.886984	−	0.461799i	$-0.847204\pi$
$151$	1.37709	−	5.13938i	0.112066	−	0.418237i	0.999051	+	0.0435622i	$0.0138707\pi$
$152$	−6.35102	−	1.70175i	−0.515136	−	0.138030i
$153$	0.167972	+	8.56489i	0.0135797	+	0.692430i
$154$	−9.22976	−	34.4459i	−0.743755	−	2.77573i
$155$	10.7286	−	10.2230i	0.861742	−	0.821130i
$156$	−7.82854	+	21.4098i	−0.626785	+	1.71415i
$157$	5.40661	+	20.1777i	0.431495	+	1.61036i	0.749319	+	0.662210i	$0.230381\pi$
$157$	5.40661	+	20.1777i	0.431495	+	1.61036i	−0.317824	+	0.948150i	$0.602952\pi$
$158$	−16.9038	−	29.2783i	−1.34480	−	2.32926i
$159$	−4.09411	−	3.07822i	−0.324684	−	0.244118i
$160$	5.95597	−	3.24967i	0.470860	−	0.256909i
$161$	−13.6882	+	13.6882i	−1.07878	+	1.07878i
$162$	−11.4149	−	18.0935i	−0.896836	−	1.42156i
$163$	−19.7746	+	11.4169i	−1.54887	+	0.894240i	−0.550641	+	0.834742i	$0.685617\pi$
$163$	−19.7746	+	11.4169i	−1.54887	+	0.894240i	−0.998228	+	0.0594980i	$0.981050\pi$
$164$	18.3218	+	4.90931i	1.43069	+	0.383352i
$165$	2.40642	−	16.4539i	0.187340	−	1.28093i
$166$	17.0472	−	9.84219i	1.32312	−	0.763902i
$167$	−0.0719102	−	0.124552i	−0.00556458	−	0.00963814i	0.863230	−	0.504811i	$-0.168438\pi$
$167$	−0.0719102	−	0.124552i	−0.00556458	−	0.00963814i	−0.868794	+	0.495173i	$0.835105\pi$
$168$	22.0219	+	8.86983i	1.69903	+	0.684322i
$169$	−7.21417	−	10.8146i	−0.554936	−	0.831893i
$170$	−3.57343	−	14.7510i	−0.274070	−	1.13135i
$171$	0.0985941	+	5.02733i	0.00753968	+	0.384449i
$172$	1.90125	+	7.09558i	0.144969	+	0.541033i
$173$	−1.45880	−	5.44433i	−0.110911	−	0.413925i	0.888038	−	0.459771i	$-0.152068\pi$
$173$	−1.45880	−	5.44433i	−0.110911	−	0.413925i	−0.998949	+	0.0458459i	$0.985402\pi$
$174$	37.5907	−	5.32435i	2.84974	−	0.403638i
$175$	7.99534	+	15.5338i	0.604391	+	1.17424i
$176$	6.14526	+	6.14526i	0.463216	+	0.463216i
$177$	−2.91403	+	3.87573i	−0.219032	+	0.291318i
$178$	20.1695	−	5.40439i	1.51177	−	0.405076i
$179$	−9.25305	+	16.0268i	−0.691606	+	1.19790i	0.279706	+	0.960086i	$0.409763\pi$
$179$	−9.25305	+	16.0268i	−0.691606	+	1.19790i	−0.971312	+	0.237810i	$0.923570\pi$
$180$	17.2365	+	17.3930i	1.28473	+	1.29640i
$181$		−	6.20631i		−	0.461311i	−0.973035	−	0.230656i	$-0.925913\pi$
$181$		−	6.20631i		−	0.461311i	0.973035	−	0.230656i	$-0.0740871\pi$
$182$	−25.4367	+	15.8041i	−1.88550	+	1.17148i
$183$	−3.39237	+	8.42253i	−0.250771	+	0.622612i
$184$	5.62497	−	20.9927i	0.414678	−	1.54760i
$185$	−20.4172	−	0.492718i	−1.50110	−	0.0362253i
$186$	25.1054	−	10.6886i	1.84082	−	0.783723i
$187$	−10.6178	+	6.13017i	−0.776449	+	0.448283i
$188$	7.80708	+	13.5223i	0.569390	+	0.986213i
$189$	1.83942	−	18.0626i	0.133798	−	1.31386i
$190$	−2.09750	−	8.65838i	−0.152168	−	0.628145i
$191$	1.57772	−	2.73269i	0.114160	−	0.197730i	−0.803284	−	0.595596i	$-0.796916\pi$
$191$	1.57772	−	2.73269i	0.114160	−	0.197730i	0.917444	+	0.397866i	$0.130249\pi$
$192$	19.3115	−	2.73529i	1.39369	−	0.197403i
$193$	6.89997	−	3.98370i	0.496671	−	0.286753i	−0.230667	−	0.973033i	$-0.574091\pi$
$193$	6.89997	−	3.98370i	0.496671	−	0.286753i	0.727338	+	0.686280i	$0.240757\pi$
$194$	−4.37640	+	7.58015i	−0.314207	+	0.544223i
$195$	−13.8097	+	2.07188i	−0.988932	+	0.148370i
$196$	9.50717	+	16.4669i	0.679083	+	1.17621i
$197$	−19.6030	−	11.3178i	−1.39665	−	0.806359i	−0.402614	−	0.915370i	$-0.631898\pi$
$197$	−19.6030	−	11.3178i	−1.39665	−	0.806359i	−0.994041	+	0.109011i	$0.965232\pi$
$198$	14.7861	−	26.8110i	1.05080	−	1.90537i
$199$	1.29771	+	2.24771i	0.0919926	+	0.159336i	0.908349	−	0.418212i	$-0.137343\pi$
$199$	1.29771	+	2.24771i	0.0919926	+	0.159336i	−0.816357	+	0.577548i	$0.804010\pi$
$200$	−16.4935	−	10.6151i	−1.16627	−	0.750597i
$201$	16.5498	−	12.9588i	1.16733	−	0.914047i
$202$	−29.0091			−2.04107
$203$	27.9040	+	16.1104i	1.95848	+	1.13073i
$204$	2.18091	−	17.9218i	0.152695	−	1.25478i
$205$	2.73565	+	11.2927i	0.191066	+	0.788714i
$206$	−15.6783	+	4.20100i	−1.09236	+	0.292697i
$207$	−16.6173	+	0.325893i	−1.15498	+	0.0226511i
$208$	3.44274	−	6.43501i	0.238711	−	0.446188i
$209$	−6.23230	+	3.59822i	−0.431097	+	0.248894i
$210$	3.74152	+	31.9494i	0.258189	+	2.20472i
$211$	−9.98152	−	17.2885i	−0.687156	−	1.19019i	−0.972754	−	0.231840i	$-0.925526\pi$
$211$	−9.98152	−	17.2885i	−0.687156	−	1.19019i	0.285598	−	0.958350i	$-0.407808\pi$
$212$	7.63329	+	7.63329i	0.524256	+	0.524256i
$213$	9.48745	+	1.15453i	0.650069	+	0.0791073i
$214$	12.2446	−	3.28092i	0.837020	−	0.224279i
$215$	−3.25773	+	3.10420i	−0.222175	+	0.211704i
$216$	8.35096	+	18.5945i	0.568211	+	1.26520i
$217$	22.3680	+	5.99348i	1.51844	+	0.406864i
$218$	1.15575	−	1.15575i	0.0782775	−	0.0782775i
$219$	1.93231	+	13.6424i	0.130574	+	0.921868i
$220$	−9.88450	+	33.6227i	−0.666413	+	2.26684i
$221$	7.51178	+	7.04092i	0.505297	+	0.473624i
$222$	−34.8809	−	14.0491i	−2.34106	−	0.942914i
$223$	−2.62088			−0.175507			−0.0877537	−	0.996142i	$-0.527969\pi$
$223$	−2.62088			−0.175507			−0.0877537	+	0.996142i	$0.527969\pi$
$224$	9.18172	+	5.30107i	0.613479	+	0.354192i
$225$	−4.29569	+	14.3717i	−0.286380	+	0.958116i
$226$	−13.5421	+	13.5421i	−0.900805	+	0.900805i
$227$	16.1750	+	9.33863i	1.07357	+	0.619827i	0.929155	−	0.369691i	$-0.120536\pi$
$227$	16.1750	+	9.33863i	1.07357	+	0.619827i	0.144416	+	0.989517i	$0.453870\pi$
$228$	1.28013	−	10.5195i	0.0847786	−	0.696674i
$229$	−0.156206	−	0.582970i	−0.0103224	−	0.0385237i	0.960573	−	0.278029i	$-0.0896813\pi$
$229$	−0.156206	−	0.582970i	−0.0103224	−	0.0385237i	−0.970895	+	0.239506i	$0.923015\pi$
$230$	28.6194	−	6.93306i	1.88711	−	0.457152i
$231$	23.9081	−	10.1788i	1.57304	−	0.669718i
$232$	−36.1740			−2.37494
$233$	−5.19094	+	5.19094i	−0.340070	+	0.340070i	−0.856394	−	0.516324i	$-0.827300\pi$
$233$	−5.19094	+	5.19094i	−0.340070	+	0.340070i	0.516324	+	0.856394i	$0.327300\pi$
$234$	−25.1476	−	5.35597i	−1.64395	−	0.350131i
$235$	−4.98083	+	8.16555i	−0.324914	+	0.532662i
$236$	7.22614	−	7.22614i	0.470381	−	0.470381i
$237$	19.3957	−	15.1873i	1.25989	−	0.986520i
$238$	16.7704	−	16.7704i	1.08707	−	1.08707i
$239$	−3.48078	+	0.932671i	−0.225153	+	0.0603295i	−0.369632	−	0.929178i	$-0.620516\pi$
$239$	−3.48078	+	0.932671i	−0.225153	+	0.0603295i	0.144479	+	0.989508i	$0.453849\pi$
$240$	−4.68275	−	6.28712i	−0.302270	−	0.405832i
$241$	−7.32989	+	1.96404i	−0.472159	+	0.126515i	−0.487049	−	0.873374i	$-0.661927\pi$
$241$	−7.32989	+	1.96404i	−0.472159	+	0.126515i	0.0148900	+	0.999889i	$0.495260\pi$
$242$	17.6727			1.13604
$243$	11.8873	−	10.0843i	0.762569	−	0.646907i
$244$	9.56812	−	16.5725i	0.612536	−	1.06094i
$245$	−6.06547	+	9.94369i	−0.387508	+	0.635279i
$246$	−2.58438	+	21.2373i	−0.164774	+	1.35404i
$247$	4.40918	+	4.13280i	0.280549	+	0.262964i
$248$	−25.1124	+	6.72884i	−1.59464	+	0.427281i
$249$	8.84274	+	11.2931i	0.560386	+	0.715670i
$250$	1.92199	−	26.5065i	0.121557	−	1.67642i
$251$	−8.75098	+	5.05238i	−0.552357	+	0.318904i	−0.750072	−	0.661356i	$-0.769981\pi$
$251$	−8.75098	+	5.05238i	−0.552357	+	0.318904i	0.197715	+	0.980260i	$0.436648\pi$
$252$	−9.17683	+	37.1472i	−0.578086	+	2.34006i
$253$	−11.8936	−	20.6003i	−0.747742	−	1.29513i
$254$	12.1781	+	45.4492i	0.764121	+	2.85174i
$255$	10.2771	−	4.08545i	0.643576	−	0.255841i
$256$	−26.6803			−1.66752
$257$	−3.41795	+	12.7559i	−0.213206	+	0.795694i	0.773585	+	0.633693i	$0.218462\pi$
$257$	−3.41795	+	12.7559i	−0.213206	+	0.795694i	−0.986791	+	0.162002i	$0.948205\pi$
$258$	−7.62322	+	3.24557i	−0.474601	+	0.202060i
$259$	−15.9568	−	27.6380i	−0.991509	−	1.71734i
$260$	29.4287	−	0.241792i	1.82509	−	0.0149953i
$261$	7.68259	+	26.5760i	0.475541	+	1.64501i
$262$	−29.8608	−	17.2401i	−1.84481	−	1.06510i
$263$	−5.05889	−	5.05889i	−0.311945	−	0.311945i	0.533718	−	0.845663i	$-0.320794\pi$
$263$	−5.05889	−	5.05889i	−0.311945	−	0.311945i	−0.845663	+	0.533718i	$0.820794\pi$
$264$	−17.5316	+	23.3174i	−1.07899	+	1.43509i
$265$	−1.86511	+	6.34428i	−0.114573	+	0.389726i
$266$	9.84373	−	9.84373i	0.603558	−	0.603558i
$267$	5.96011	+	13.9992i	0.364753	+	0.856735i
$268$	−38.3641	+	22.1495i	−2.34346	+	1.35300i
$269$	−22.7156	+	13.1148i	−1.38499	+	0.799625i	−0.992745	−	0.120235i	$-0.961635\pi$
$269$	−22.7156	+	13.1148i	−1.38499	+	0.799625i	−0.392246	+	0.919860i	$0.628302\pi$
$270$	−16.6971	+	21.9999i	−1.01615	+	1.33887i
$271$	14.0813	−	3.77306i	0.855375	−	0.229197i	0.195622	−	0.980679i	$-0.437327\pi$
$271$	14.0813	−	3.77306i	0.855375	−	0.229197i	0.659753	+	0.751482i	$0.270661\pi$
$272$	−1.49595	+	5.58296i	−0.0907052	+	0.338516i
$273$	−14.0013	−	16.7366i	−0.847400	−	1.01294i
$274$	5.87626	+	3.39266i	0.354998	+	0.204958i
$275$	−20.9802	+	4.54956i	−1.26516	+	0.274349i
$276$	34.7713	+	4.23134i	2.09299	+	0.254697i
$277$	9.55946	−	2.56145i	0.574372	−	0.153903i	0.0400712	−	0.999197i	$-0.487242\pi$
$277$	9.55946	−	2.56145i	0.574372	−	0.153903i	0.534301	+	0.845294i	$0.320575\pi$
$278$	0.0129191			0.000774836
$279$	10.2768	+	17.0203i	0.615256	+	1.01898i
$280$	0.739437	−	30.6407i	0.0441898	−	1.83113i
$281$	−2.02667	+	7.56363i	−0.120901	+	0.451208i	−0.999660	−	0.0260564i	$-0.991705\pi$
$281$	−2.02667	+	7.56363i	−0.120901	+	0.451208i	0.878760	+	0.477265i	$0.158372\pi$
$282$	−13.8660	+	10.8574i	−0.825710	+	0.646550i
$283$	−27.2179	−	7.29301i	−1.61793	−	0.433524i	−0.667541	−	0.744573i	$-0.732653\pi$
$283$	−27.2179	−	7.29301i	−1.61793	−	0.433524i	−0.950394	+	0.311049i	$0.899320\pi$
$284$	−19.4560	−	5.21323i	−1.15450	−	0.309348i
$285$	6.03233	−	2.39803i	0.357324	−	0.142047i
$286$	−10.6685	−	35.2177i	−0.630843	−	2.08247i
$287$	−12.8386	+	12.8386i	−0.757841	+	0.757841i
$288$	2.52793	+	8.74474i	0.148960	+	0.515289i
$289$	7.66090	+	4.42302i	0.450641	+	0.260178i
$290$	−23.4757	−	43.0260i	−1.37854	−	2.52657i
$291$	−5.91598	−	2.38280i	−0.346801	−	0.139682i
$292$		−	29.0384i		−	1.69934i
$293$		−	17.6333i		−	1.03015i	−0.857145	−	0.515074i	$-0.827764\pi$
$293$		−	17.6333i		−	1.03015i	0.857145	−	0.515074i	$-0.172236\pi$
$294$	−16.8855	+	13.2217i	−0.984783	+	0.771108i
$295$	6.00588	+	1.76563i	0.349676	+	0.102799i
$296$	31.0290	+	17.9146i	1.80352	+	1.04127i
$297$	20.8540	+	7.92781i	1.21007	+	0.460018i
$298$	9.26539	−	9.26539i	0.536730	−	0.536730i
$299$	−13.6606	+	14.5741i	−0.790011	+	0.842842i
$300$	13.2114	−	28.7196i	0.762761	−	1.65813i
$301$	−6.79201	−	1.81991i	−0.391485	−	0.104898i
$302$	−12.2165	−	3.27340i	−0.702981	−	0.188363i
$303$	−2.96437	−	20.9289i	−0.170299	−	1.20233i
$304$	−0.878075	+	3.27702i	−0.0503611	+	0.187950i
$305$	11.7189	+	0.282806i	0.671021	+	0.0161934i
$306$	20.3591	−	0.399275i	1.16385	−	0.0228250i
$307$	19.9489			1.13855			0.569273	−	0.822149i	$-0.307225\pi$
$307$	19.9489			1.13855			0.569273	+	0.822149i	$0.307225\pi$
$308$	−52.8970	+	14.1737i	−3.01409	+	0.807622i
$309$	−4.63298	−	10.8820i	−0.263561	−	0.619054i
$310$	−24.3004	−	25.5023i	−1.38017	−	1.44843i
$311$	12.8921	+	7.44326i	0.731044	+	0.422069i	0.818804	−	0.574073i	$-0.194637\pi$
$311$	12.8921	+	7.44326i	0.731044	+	0.422069i	−0.0877599	+	0.996142i	$0.527971\pi$
$312$	23.0082	+	8.41302i	1.30258	+	0.476294i
$313$	−5.63662	+	21.0362i	−0.318601	+	1.18903i	0.601989	+	0.798504i	$0.294375\pi$
$313$	−5.63662	+	21.0362i	−0.318601	+	1.18903i	−0.920590	+	0.390530i	$0.872292\pi$
$314$	47.9633	−	12.8517i	2.70672	−	0.725264i
$315$	−22.6679	+	5.96418i	−1.27719	+	0.336044i
$316$	−44.9613	+	25.9584i	−2.52927	+	1.46028i
$317$	13.6581	−	7.88551i	0.767116	−	0.442895i	−0.0647289	−	0.997903i	$-0.520618\pi$
$317$	13.6581	−	7.88551i	0.767116	−	0.442895i	0.831845	+	0.555008i	$0.187285\pi$
$318$	−7.31703	+	9.73184i	−0.410319	+	0.545735i
$319$	−27.9963	+	27.9963i	−1.56749	+	1.56749i
$320$	−12.0602	−	22.1038i	−0.674186	−	1.23564i
$321$	3.61829	+	8.49867i	0.201953	+	0.474349i
$322$	32.5375	+	32.5375i	1.81324	+	1.81324i
$323$	−4.14490	−	2.39306i	−0.230628	−	0.133153i
$324$	−27.7854	+	17.5293i	−1.54363	+	0.973848i
$325$	8.76432	+	15.7539i	0.486157	+	0.873871i
$326$	27.1384	+	47.0051i	1.50306	+	2.60337i
$327$	0.951932	+	0.715725i	0.0526420	+	0.0395797i
$328$	5.27584	−	19.6897i	0.291309	−	1.08718i
$329$	−14.9461			−0.824008
$330$	−39.1115	−	5.72016i	−2.15302	−	0.314884i
$331$	−5.75088	−	21.4626i	−0.316097	−	1.17969i	−0.922964	−	0.384886i	$-0.874241\pi$
$331$	−5.75088	−	21.4626i	−0.316097	−	1.17969i	0.606867	−	0.794803i	$-0.292426\pi$
$332$	−15.1142	−	26.1785i	−0.829499	−	1.43673i
$333$	6.57144	−	26.6008i	0.360113	−	1.45771i
$334$	−0.296065	+	0.170933i	−0.0162000	+	0.00935306i
$335$	−23.1665	−	14.1312i	−1.26572	−	0.772067i
$336$	4.57669	−	11.3630i	0.249679	−	0.619900i
$337$	26.0761	−	6.98706i	1.42045	−	0.380609i	0.534809	−	0.844973i	$-0.320383\pi$
$337$	26.0761	−	6.98706i	1.42045	−	0.380609i	0.885645	+	0.464363i	$0.153717\pi$
$338$	−25.7067	+	17.1484i	−1.39826	+	0.932748i
$339$	−11.1539	−	8.38621i	−0.605795	−	0.455476i
$340$	−22.6524	+	5.48756i	−1.22850	+	0.297605i
$341$	−14.2276	+	24.6429i	−0.770468	+	1.33449i
$342$	11.9501	−	0.234362i	0.646190	−	0.0126728i
$343$	6.25810			0.337906
$344$	7.62534	−	2.04320i	0.411131	−	0.110162i
$345$	7.92646	+	19.9393i	0.426746	+	1.07349i
$346$	−12.9414	+	3.46763i	−0.695733	+	0.186421i
$347$	−23.2182	+	23.2182i	−1.24642	+	1.24642i	−0.289128	+	0.957291i	$0.593365\pi$
$347$	−23.2182	+	23.2182i	−1.24642	+	1.24642i	−0.957291	+	0.289128i	$0.906635\pi$
$348$	−8.17636	−	57.7262i	−0.438299	−	3.09445i
$349$	−3.57385	+	3.57385i	−0.191304	+	0.191304i	−0.796259	−	0.604955i	$-0.793191\pi$
$349$	−3.57385	+	3.57385i	−0.191304	+	0.191304i	0.604955	+	0.796259i	$0.293191\pi$
$350$	36.9244	−	19.0052i	1.97369	−	1.01587i
$351$	1.29435	−	18.6902i	0.0690871	−	0.997611i
$352$	−9.21208	+	9.21208i	−0.491005	+	0.491005i
$353$	15.9718			0.850092			0.425046	−	0.905172i	$-0.360258\pi$
$353$	15.9718			0.850092			0.425046	+	0.905172i	$0.360258\pi$
$354$	9.21276	+	6.92675i	0.489652	+	0.368153i
$355$	−2.90500	−	11.9918i	−0.154182	−	0.636456i
$356$	−8.29927	−	30.9733i	−0.439861	−	1.64158i
$357$	13.8129	+	10.3854i	0.731057	+	0.549656i
$358$	38.0962	+	21.9949i	2.01345	+	1.16246i
$359$	6.95162	−	6.95162i	0.366892	−	0.366892i	−0.499450	−	0.866343i	$-0.666465\pi$
$359$	6.95162	−	6.95162i	0.366892	−	0.366892i	0.866343	+	0.499450i	$0.166465\pi$
$360$	18.6915	−	18.5234i	0.985131	−	0.976268i
$361$	14.0216	+	8.09535i	0.737977	+	0.426071i
$362$	−14.7526			−0.775381
$363$	1.80593	+	12.7501i	0.0947868	+	0.669208i
$364$	24.2697	+	39.0620i	1.27208	+	2.04740i
$365$	15.6150	−	8.51979i	0.817327	−	0.445946i
$366$	20.0207	+	8.06378i	1.04650	+	0.421501i
$367$	−21.7412	+	21.7412i	−1.13488	+	1.13488i	−0.145525	+	0.989355i	$0.546487\pi$
$367$	−21.7412	+	21.7412i	−1.13488	+	1.13488i	−0.989355	+	0.145525i	$0.953513\pi$
$368$	−10.8319	−	2.90239i	−0.564650	−	0.151298i
$369$	−15.5859	+	0.305666i	−0.811371	+	0.0159123i
$370$	−1.17121	+	48.5324i	−0.0608883	+	2.52308i
$371$	−9.98115	+	2.67444i	−0.518196	+	0.138850i
$372$	−16.4139	−	38.5532i	−0.851022	−	1.99889i
$373$	25.3916	+	25.3916i	1.31473	+	1.31473i	0.917887	+	0.396842i	$0.129894\pi$
$373$	25.3916	+	25.3916i	1.31473	+	1.31473i	0.396842	+	0.917887i	$0.370106\pi$
$374$	14.5717	+	25.2388i	0.753482	+	1.30507i
$375$	19.3197	−	1.32200i	0.997667	−	0.0682676i
$376$	14.5318	−	8.38996i	0.749422	−	0.432679i
$377$	29.3163	+	15.6843i	1.50987	+	0.807781i
$378$	−42.9355	−	4.37238i	−2.20837	−	0.224891i
$379$	−14.6841	+	3.93459i	−0.754270	+	0.202106i	−0.615411	−	0.788206i	$-0.711010\pi$
$379$	−14.6841	+	3.93459i	−0.754270	+	0.202106i	−0.138859	+	0.990312i	$0.544343\pi$
$380$	−13.2963	+	3.22103i	−0.682085	+	0.165235i
$381$	−31.5453	+	13.4303i	−1.61611	+	0.688056i
$382$	−6.49570	−	3.75030i	−0.332349	−	0.191882i
$383$	−1.48890			−0.0760793			−0.0380397	−	0.999276i	$-0.512111\pi$
$383$	−1.48890			−0.0760793			−0.0380397	+	0.999276i	$0.512111\pi$
$384$	−5.02782	−	35.4971i	−0.256575	−	1.81145i
$385$	−23.1416	−	24.2861i	−1.17940	−	1.23773i
$386$	−9.46941	−	16.4015i	−0.481980	−	0.834814i
$387$	−3.12054	−	5.16818i	−0.158626	−	0.262713i
$388$	11.6405	+	6.72064i	0.590956	+	0.341189i
$389$	−7.08135	−	12.2653i	−0.359039	−	0.621873i	0.628762	−	0.777598i	$-0.283562\pi$
$389$	−7.08135	−	12.2653i	−0.359039	−	0.621873i	−0.987801	+	0.155725i	$0.950229\pi$
$390$	4.92494	+	32.8261i	0.249384	+	1.66222i
$391$	7.91002	−	13.7006i	0.400027	−	0.692867i
$392$	17.6963	−	10.2170i	0.893799	−	0.516035i
$393$	9.38664	−	23.3051i	0.473494	−	1.17558i
$394$	−26.9028	+	46.5970i	−1.35534	+	2.34752i
$395$	−27.1503	−	16.5612i	−1.36608	−	0.833284i
$396$	−41.1724	−	22.7063i	−2.06899	−	1.14104i
$397$	3.62721	+	6.28251i	0.182044	+	0.315310i	0.942577	−	0.333990i	$-0.108395\pi$
$397$	3.62721	+	6.28251i	0.182044	+	0.315310i	−0.760532	+	0.649300i	$0.775062\pi$
$398$	5.34288	−	3.08472i	0.267815	−	0.154623i
$399$	8.10775	+	6.09594i	0.405895	+	0.305179i
$400$	−5.47719	+	8.51040i	−0.273860	+	0.425520i
$401$	5.41739	−	20.2180i	0.270532	−	1.00964i	−0.688245	−	0.725478i	$-0.741619\pi$
$401$	5.41739	−	20.2180i	0.270532	−	1.00964i	0.958777	−	0.284160i	$-0.0917146\pi$
$402$	−30.8037	−	39.3394i	−1.53635	−	1.96207i
$403$	23.2691	+	5.43495i	1.15912	+	0.270734i
$404$			44.5480i			2.21634i
$405$	−17.5783	−	9.79817i	−0.873472	−	0.486875i
$406$	38.2950	−	66.3289i	1.90055	−	3.29185i
$407$	37.8791	−	10.1497i	1.87760	−	0.503100i
$408$	−19.2599	−	2.34374i	−0.953505	−	0.116033i
$409$	13.8798	+	13.8798i	0.686314	+	0.686314i	0.961415	−	0.275101i	$-0.0887114\pi$
$409$	13.8798	+	13.8798i	0.686314	+	0.686314i	−0.275101	+	0.961415i	$0.588711\pi$
$410$	26.8431	−	6.50274i	1.32569	−	0.321147i
$411$	−1.84718	+	4.58616i	−0.0911148	+	0.226219i
$412$	6.45128	+	24.0765i	0.317832	+	1.18616i
$413$	2.53179	+	9.44877i	0.124581	+	0.464944i
$414$	0.774660	+	39.5000i	0.0380725	+	1.94132i
$415$	9.64269	−	15.8082i	0.473341	−	0.775992i
$416$	9.64643	+	5.16085i	0.472955	+	0.253032i
$417$	0.00132017	+	0.00932060i	6.46491e−5	+	0.000456432i
$418$	8.55311	+	14.8144i	0.418346	+	0.724597i
$419$	3.30548	−	1.90842i	0.161483	−	0.0932324i	−0.417081	−	0.908870i	$-0.636947\pi$
$419$	3.30548	−	1.90842i	0.161483	−	0.0932324i	0.578564	+	0.815637i	$0.303613\pi$
$420$	49.0633	−	5.74567i	2.39404	−	0.280360i
$421$	8.75470	+	2.34582i	0.426678	+	0.114328i	0.465766	−	0.884908i	$-0.345779\pi$
$421$	8.75470	+	2.34582i	0.426678	+	0.114328i	−0.0390883	+	0.999236i	$0.512445\pi$
$422$	−41.0954	+	23.7264i	−2.00049	+	1.15498i
$423$	−9.25012	−	8.89427i	−0.449756	−	0.432454i
$424$	8.20319	−	8.20319i	0.398382	−	0.398382i
$425$	−9.59702	−	10.5710i	−0.465524	−	0.512769i
$426$	2.74437	−	22.5520i	0.132965	−	1.09265i
$427$	9.15876	+	15.8634i	0.443224	+	0.767686i
$428$	−5.03835	−	18.8034i	−0.243538	−	0.908896i
$429$	24.3179	−	11.2957i	1.17408	−	0.545362i
$430$	7.37879	+	7.74374i	0.355837	+	0.373436i
$431$	3.86455	+	14.4227i	0.186149	+	0.694717i	0.994382	+	0.105854i	$0.0337577\pi$
$431$	3.86455	+	14.4227i	0.186149	+	0.694717i	−0.808233	+	0.588863i	$0.799576\pi$
$432$	9.59446	−	4.30896i	0.461613	−	0.207315i
$433$	4.14442	+	1.11049i	0.199168	+	0.0533670i	0.357024	−	0.934095i	$-0.383791\pi$
$433$	4.14442	+	1.11049i	0.199168	+	0.0533670i	−0.157856	+	0.987462i	$0.550458\pi$
$434$	14.2467	−	53.1695i	0.683865	−	2.55222i
$435$	28.6426	−	21.3334i	1.37331	−	1.02286i
$436$	−1.77484	−	1.77484i	−0.0849993	−	0.0849993i
$437$	4.64293	−	8.04180i	0.222102	−	0.384691i
$438$	32.4285	−	4.59318i	1.54949	−	0.219471i
$439$	−9.30765			−0.444230			−0.222115	−	0.975020i	$-0.571296\pi$
$439$	−9.30765			−0.444230			−0.222115	+	0.975020i	$0.571296\pi$
$440$	36.1330	+	10.6225i	1.72257	+	0.506407i
$441$	−11.2644	−	10.8311i	−0.536402	−	0.515767i
$442$	16.7365	−	17.8558i	0.796076	−	0.849312i
$443$	2.81190	−	10.4942i	0.133598	−	0.498593i	−0.866402	−	0.499347i	$-0.833573\pi$
$443$	2.81190	−	10.4942i	0.133598	−	0.498593i	1.00000		0.000754026i	$0.000240014\pi$
$444$	−21.5745	+	53.5650i	−1.02388	+	2.54208i
$445$	14.2205	−	13.5503i	0.674116	−	0.642346i
$446$			6.22994i			0.294996i
$447$	7.63140	+	5.73779i	0.360953	+	0.271388i
$448$	19.6734	−	34.0753i	0.929480	−	1.60991i
$449$	6.44259	+	1.72629i	0.304045	+	0.0814685i	0.407616	−	0.913154i	$-0.366360\pi$
$449$	6.44259	+	1.72629i	0.304045	+	0.0814685i	−0.103571	+	0.994622i	$0.533027\pi$
$450$	34.1622	+	10.2110i	1.61042	+	0.481352i
$451$	−11.1554	−	19.3216i	−0.525285	−	0.909821i
$452$	20.7959	+	20.7959i	0.978158	+	0.978158i
$453$	1.11325	−	9.14820i	0.0523050	−	0.429820i
$454$	22.1983	−	38.4485i	1.04182	−	1.80448i
$455$	−13.8844	+	24.5114i	−0.650910	+	1.14911i
$456$	−11.3049	−	1.37570i	−0.529402	−	0.0644232i
$457$		−	7.39168i		−	0.345768i	−0.984942	−	0.172884i	$-0.944691\pi$
$457$		−	7.39168i		−	0.345768i	0.984942	−	0.172884i	$-0.0553086\pi$
$458$	−1.38574	+	0.371308i	−0.0647514	+	0.0173501i
$459$	2.36850	+	14.6474i	0.110552	+	0.683683i
$460$	−10.6468	−	43.9495i	−0.496409	−	2.04916i
$461$	1.51222	+	5.64368i	0.0704310	+	0.262852i	0.992159	−	0.124986i	$-0.0398886\pi$
$461$	1.51222	+	5.64368i	0.0704310	+	0.262852i	−0.921727	+	0.387838i	$0.873222\pi$
$462$	−24.1955	−	56.8306i	−1.12568	−	2.64400i
$463$	−14.1016	−	8.14157i	−0.655358	−	0.378371i	0.135148	−	0.990825i	$-0.456849\pi$
$463$	−14.1016	−	8.14157i	−0.655358	−	0.378371i	−0.790506	+	0.612454i	$0.790182\pi$
$464$			18.6652i			0.866511i
$465$	15.9156	−	20.1378i	0.738070	−	0.933866i
$466$	12.3391	+	12.3391i	0.571596	+	0.571596i
$467$	−13.4543	−	13.4543i	−0.622592	−	0.622592i	0.323601	−	0.946194i	$-0.395106\pi$
$467$	−13.4543	−	13.4543i	−0.622592	−	0.622592i	−0.946194	+	0.323601i	$0.895106\pi$
$468$	−8.22492	+	38.6179i	−0.380197	+	1.78511i
$469$		−	42.4038i		−	1.95803i
$470$	19.4098	+	11.8396i	0.895308	+	0.546121i
$471$	14.1732	+	33.2902i	0.653068	+	1.53393i
$472$	−7.76564	−	7.76564i	−0.357443	−	0.357443i
$473$	4.32020	−	7.48280i	0.198643	−	0.344060i
$474$	−36.1007	−	46.1043i	−1.65816	−	2.11764i
$475$	−5.63315	−	6.20485i	−0.258467	−	0.284698i
$476$	−25.7536	−	25.7536i	−1.18041	−	1.18041i
$477$	−7.76883	−	4.28446i	−0.355710	−	0.196172i
$478$	2.21699	+	8.27394i	0.101403	+	0.378441i
$479$	−2.54150	+	2.54150i	−0.116124	+	0.116124i	−0.762781	−	0.646657i	$-0.776167\pi$
$479$	−2.54150	+	2.54150i	−0.116124	+	0.116124i	0.646657	+	0.762781i	$0.276167\pi$
$480$	9.42473	−	7.01969i	0.430178	−	0.320404i
$481$	−17.3793	−	27.9719i	−0.792428	−	1.27541i
$482$	4.66859	+	17.4234i	0.212648	+	0.793615i
$483$	−20.1495	+	26.7994i	−0.916835	+	1.21941i
$484$		−	27.1392i		−	1.23360i
$485$	−0.198643	+	8.23133i	−0.00901991	+	0.373765i
$486$	−23.9707	−	28.2565i	−1.08733	−	1.28174i
$487$	−20.8530	+	12.0395i	−0.944938	+	0.545560i	−0.891505	−	0.453011i	$-0.850350\pi$
$487$	−20.8530	+	12.0395i	−0.944938	+	0.545560i	−0.0534335	+	0.998571i	$0.517017\pi$
$488$	−17.8098	−	10.2825i	−0.806210	−	0.465466i
$489$	−31.1390	+	24.3825i	−1.40815	+	1.10262i
$490$	23.6365	+	14.4178i	1.06779	+	0.651332i
$491$	−12.7063	+	7.33599i	−0.573428	+	0.331069i	−0.758517	−	0.651653i	$-0.774076\pi$
$491$	−12.7063	+	7.33599i	−0.573428	+	0.331069i	0.185089	+	0.982722i	$0.440743\pi$
$492$	32.6131	+	3.96871i	1.47031	+	0.178923i
$493$	−25.4346	−	6.81517i	−1.14552	−	0.306940i
$494$	9.82383	−	10.4808i	0.441995	−	0.471553i
$495$	0.130148	−	28.8019i	0.00584974	−	1.29455i
$496$	3.47197	+	12.9576i	0.155896	+	0.581812i
$497$	13.6334	−	13.6334i	0.611543	−	0.611543i
$498$	26.8441	−	21.0195i	1.20291	−	0.941907i
$499$	2.98340	−	0.799400i	0.133555	−	0.0357861i	−0.191422	−	0.981508i	$-0.561310\pi$
$499$	2.98340	−	0.799400i	0.133555	−	0.0357861i	0.324978	+	0.945722i	$0.394643\pi$
$500$	−40.7048	−	2.95151i	−1.82037	−	0.131996i
$501$	−0.153575	−	0.196132i	−0.00686125	−	0.00876251i
$502$	12.0097	+	20.8014i	0.536019	+	0.928412i
$503$	−5.88063	+	21.9468i	−0.262204	+	0.978559i	0.701735	+	0.712438i	$0.252409\pi$
$503$	−5.88063	+	21.9468i	−0.262204	+	0.978559i	−0.963940	+	0.266121i	$0.914258\pi$
$504$	39.9207	+	9.86197i	1.77821	+	0.439287i
$505$	−23.9550	+	13.0703i	−1.06599	+	0.581619i
$506$	−48.9676	+	28.2714i	−2.17687	+	1.25682i
$507$	−14.9987	−	16.7940i	−0.666117	−	0.745847i
$508$	69.7943	−	18.7013i	3.09662	−	0.829737i
$509$	−0.799160	+	2.98250i	−0.0354221	+	0.132197i	−0.981373	−	0.192114i	$-0.938466\pi$
$509$	−0.799160	+	2.98250i	−0.0354221	+	0.132197i	0.945951	+	0.324311i	$0.105132\pi$
$510$	−9.71127	−	24.4290i	−0.430022	−	1.08173i
$511$	24.0721	+	13.8980i	1.06489	+	0.614813i
$512$			22.0223i			0.973258i
$513$	1.39024	+	8.59758i	0.0613805	+	0.379592i
$514$	30.3214	+	8.12459i	1.33742	+	0.358360i
$515$	−11.0540	+	10.5331i	−0.487098	+	0.464142i
$516$	4.98407	+	11.7066i	0.219411	+	0.515356i
$517$	4.75340	−	17.7399i	0.209054	−	0.780202i
$518$	−65.6966	+	37.9300i	−2.88654	+	1.66655i
$519$	−3.82420	−	8.98232i	−0.167864	−	0.394280i
$520$	−0.259844	−	31.6259i	−0.0113949	−	1.38689i
$521$	20.9639			0.918445			0.459222	−	0.888321i	$-0.348128\pi$
$521$	20.9639			0.918445			0.459222	+	0.888321i	$0.348128\pi$
$522$	63.1722	−	18.2618i	2.76497	−	0.799298i
$523$	−33.0825	+	8.86442i	−1.44660	+	0.387614i	−0.894838	−	0.446391i	$-0.852709\pi$
$523$	−33.0825	+	8.86442i	−1.44660	+	0.387614i	−0.551757	+	0.834005i	$0.686042\pi$
$524$	−26.4749	+	45.8558i	−1.15656	+	2.00322i
$525$	17.4847	+	24.6973i	0.763094	+	1.07788i
$526$	−12.0252	+	12.0252i	−0.524323	+	0.524323i
$527$	−18.9246			−0.824370
$528$	12.0314	+	9.04600i	0.523600	+	0.393677i
$529$	6.66278	+	3.84676i	0.289686	+	0.167250i
$530$	15.0806	+	4.43343i	0.655059	+	0.192576i
$531$	−4.05594	+	7.35445i	−0.176013	+	0.319156i
$532$	−15.1166	−	15.1166i	−0.655386	−	0.655386i
$533$	−12.8127	+	13.6695i	−0.554979	+	0.592093i
$534$	33.2766	−	14.1674i	1.44002	−	0.613084i
$535$	8.63302	−	8.22617i	0.373238	−	0.355648i
$536$	23.8032	+	41.2284i	1.02814	+	1.78079i
$537$	−11.9754	+	29.7324i	−0.516777	+	1.28305i
$538$	31.1744	+	53.9957i	1.34403	+	2.32792i
$539$	5.78851	−	21.6030i	0.249329	−	0.930508i
$540$	33.7843	+	25.6410i	1.45384	+	1.10341i
$541$	20.8225	+	20.8225i	0.895228	+	0.895228i	0.995009	−	0.0997815i	$-0.0318144\pi$
$541$	20.8225	+	20.8225i	0.895228	+	0.895228i	−0.0997815	+	0.995009i	$0.531814\pi$
$542$	−8.96871	−	33.4717i	−0.385239	−	1.43773i
$543$	−1.50753	−	10.6434i	−0.0646945	−	0.456752i
$544$	−8.36916	−	2.24251i	−0.358825	−	0.0961468i
$545$	0.433662	−	1.47513i	0.0185760	−	0.0631875i
$546$	−39.7834	+	33.2817i	−1.70257	+	1.42433i
$547$	0.349941	+	0.0937665i	0.0149624	+	0.00400917i	0.266292	−	0.963892i	$-0.414201\pi$
$547$	0.349941	+	0.0937665i	0.0149624	+	0.00400917i	−0.251330	+	0.967901i	$0.580868\pi$
$548$	5.20995	−	9.02390i	0.222558	−	0.385482i
$549$	−3.77182	+	15.2681i	−0.160977	+	0.651627i
$550$	10.8145	+	49.8708i	0.461131	+	2.12650i
$551$	−14.9293	−	4.00030i	−0.636010	−	0.170418i
$552$	4.54725	−	37.3673i	0.193544	−	1.59046i
$553$		−	49.6957i		−	2.11328i
$554$	−6.08866	−	22.7232i	−0.258682	−	0.965416i
$555$	−35.1338	+	4.11442i	−1.49135	+	0.174648i
$556$		−	0.0198393i		−	0.000841372i
$557$	3.52383	−	6.10345i	0.149309	−	0.258611i	−0.781663	−	0.623701i	$-0.785628\pi$
$557$	3.52383	−	6.10345i	0.149309	−	0.258611i	0.930972	+	0.365090i	$0.118962\pi$
$558$	40.4578	−	24.4284i	1.71271	−	1.03413i
$559$	−7.06565	−	1.65032i	−0.298845	−	0.0698010i
$560$	−15.8101	−	0.381538i	−0.668098	−	0.0161229i
$561$	−16.7197	+	13.0919i	−0.705908	+	0.552742i
$562$	17.9790	+	4.81747i	0.758400	+	0.203213i
$563$	−5.81004	+	5.81004i	−0.244864	+	0.244864i	−0.818859	−	0.573995i	$-0.805393\pi$
$563$	−5.81004	+	5.81004i	−0.244864	+	0.244864i	0.573995	+	0.818859i	$0.305393\pi$
$564$	16.6732	+	21.2934i	0.702070	+	0.896615i
$565$	−5.08125	+	17.2842i	−0.213770	+	0.727151i
$566$	−17.3357	+	64.6979i	−0.728676	+	2.71946i
$567$	−1.23299	−	31.4230i	−0.0517807	−	1.31964i
$568$	−5.60245	+	20.9086i	−0.235073	+	0.877306i
$569$	43.4165			1.82011			0.910057	−	0.414484i	$-0.136038\pi$
$569$	43.4165			1.82011			0.910057	+	0.414484i	$0.136038\pi$
$570$	−5.70022	−	14.3391i	−0.238756	−	0.600597i
$571$	13.4302	+	7.75393i	0.562037	+	0.324492i	0.753963	−	0.656917i	$-0.228140\pi$
$571$	13.4302	+	7.75393i	0.562037	+	0.324492i	−0.191926	+	0.981409i	$0.561473\pi$
$572$	−54.0822	+	16.3832i	−2.26129	+	0.685015i
$573$	2.04190	−	5.06961i	0.0853017	−	0.211786i
$574$	30.5179	+	30.5179i	1.27379	+	1.27379i
$575$	20.5095	−	18.6198i	0.855306	−	0.776500i
$576$	32.4536	−	9.38168i	1.35223	−	0.390903i
$577$		−	27.5632i		−	1.14747i	−0.819040	−	0.573736i	$-0.805493\pi$
$577$		−	27.5632i		−	1.14747i	0.819040	−	0.573736i	$-0.194507\pi$
$578$	10.5137	−	18.2102i	0.437312	−	0.757447i
$579$	10.8653	−	8.50781i	0.451548	−	0.353573i
$580$	−66.0730	+	36.0505i	−2.74353	+	1.49691i
$581$	28.9351			1.20043
$582$	−5.66400	+	14.0625i	−0.234780	+	0.582910i
$583$		−	12.6974i		−	0.525874i
$584$	−31.2064			−1.29133
$585$	−23.1794	+	6.90756i	−0.958351	+	0.285592i
$586$	−41.9150			−1.73149
$587$			28.4313i			1.17349i	0.809773	+	0.586744i	$0.199590\pi$
$587$			28.4313i			1.17349i	−0.809773	+	0.586744i	$0.800410\pi$
$588$	20.3040	+	25.9303i	0.837324	+	1.06935i
$589$	−11.1082			−0.457704
$590$	4.19696	−	14.2762i	0.172786	−	0.587742i
$591$	−36.3669	−	14.6476i	−1.49594	−	0.602522i
$592$	9.24364	−	16.0105i	0.379911	−	0.658026i
$593$		−	38.9286i		−	1.59861i	−0.600927	−	0.799304i	$-0.705202\pi$
$593$		−	38.9286i		−	1.59861i	0.600927	−	0.799304i	$-0.294798\pi$
$594$	18.8447	−	49.5707i	0.773208	−	2.03391i
$595$	6.29260	−	21.4047i	0.257972	−	0.877506i
$596$	−14.2284	−	14.2284i	−0.582819	−	0.582819i
$597$	2.77147	+	3.53945i	0.113429	+	0.144860i
$598$	34.6432	+	32.4717i	1.41667	+	1.32787i
$599$	−33.8868	−	19.5646i	−1.38458	−	0.799387i	−0.391881	−	0.920016i	$-0.628176\pi$
$599$	−33.8868	−	19.5646i	−1.38458	−	0.799387i	−0.992698	+	0.120629i	$0.961509\pi$
$600$	−30.8638	−	14.1978i	−1.26001	−	0.579621i
$601$	−2.35751			−0.0961646			−0.0480823	−	0.998843i	$-0.515311\pi$
$601$	−2.35751			−0.0961646			−0.0480823	+	0.998843i	$0.515311\pi$
$602$	−4.32600	+	16.1449i	−0.176315	+	0.658015i
$603$	25.2340	−	26.2436i	1.02761	−	1.06872i
$604$	−5.02681	+	18.7603i	−0.204538	+	0.763347i
$605$	14.5937	−	7.96255i	0.593318	−	0.323724i
$606$	−49.7487	+	7.04642i	−2.02090	+	0.286241i
$607$	−5.60450	+	5.60450i	−0.227480	+	0.227480i	−0.811639	−	0.584159i	$-0.801424\pi$
$607$	−5.60450	+	5.60450i	−0.227480	+	0.227480i	0.584159	+	0.811639i	$0.301424\pi$
$608$	−4.91243	−	1.31628i	−0.199226	−	0.0533823i
$609$	51.7668	+	20.8503i	2.09770	+	0.844896i
$610$	0.672241	−	27.8562i	0.0272182	−	1.12786i
$611$	−15.4147	+	0.498744i	−0.623611	+	0.0201770i
$612$	−0.613148	−	31.2645i	−0.0247850	−	1.26379i
$613$	−3.55141	+	6.15122i	−0.143440	+	0.248445i	−0.928790	−	0.370607i	$-0.879150\pi$
$613$	−3.55141	+	6.15122i	−0.143440	+	0.248445i	0.785350	+	0.619052i	$0.212483\pi$
$614$		−	47.4193i		−	1.91369i
$615$	7.43449	+	18.7017i	0.299787	+	0.754124i
$616$	15.2319	+	56.8463i	0.613712	+	2.29040i
$617$		−	26.4906i		−	1.06647i	−0.845967	−	0.533235i	$-0.820976\pi$
$617$		−	26.4906i		−	1.06647i	0.845967	−	0.533235i	$-0.179024\pi$
$618$	−25.8669	+	11.0128i	−1.04052	+	0.442998i
$619$	−23.4572	−	6.28535i	−0.942826	−	0.252629i	−0.245511	−	0.969394i	$-0.578956\pi$
$619$	−23.4572	−	6.28535i	−0.942826	−	0.252629i	−0.697315	+	0.716764i	$0.745622\pi$
$620$	−39.1627	+	37.3170i	−1.57281	+	1.49869i
$621$	−28.4184	+	4.59529i	−1.14039	+	0.184403i
$622$	17.6929	−	30.6450i	0.709421	−	1.22875i
$623$	29.6482	+	7.94420i	1.18783	+	0.318278i
$624$	4.34098	−	11.8719i	0.173778	−	0.475255i
$625$	−10.3555	−	22.7544i	−0.414222	−	0.910176i
$626$	50.0037	+	13.3985i	1.99855	+	0.535510i
$627$	−9.81397	+	7.68456i	−0.391932	+	0.306892i
$628$	−19.7358	−	73.6549i	−0.787543	−	2.93915i
$629$	18.4419	+	18.4419i	0.735327	+	0.735327i
$630$	14.1771	+	53.8824i	0.564829	+	2.14672i
$631$	−6.33767	+	23.6525i	−0.252299	+	0.941591i	0.717275	+	0.696790i	$0.245389\pi$
$631$	−6.33767	+	23.6525i	−0.252299	+	0.941591i	−0.969573	+	0.244801i	$0.921277\pi$
$632$	27.8965	+	48.3181i	1.10966	+	1.92199i
$633$	−21.3171	−	27.2241i	−0.847278	−	1.08206i
$634$	−18.7442	−	32.4658i	−0.744426	−	1.28938i
$635$	30.5338	+	32.0440i	1.21170	+	1.27163i
$636$	14.9447	+	11.2364i	0.592597	+	0.445553i
$637$	−18.7714	+	0.607351i	−0.743749	+	0.0240641i
$638$	66.5482	+	66.5482i	2.63467	+	2.63467i
$639$	16.5508	−	0.324588i	0.654739	−	0.0128405i
$640$	−40.6297	+	22.1682i	−1.60603	+	0.876276i
$641$	−40.3903	−	23.3193i	−1.59532	−	0.921059i	−0.992372	−	0.123278i	$-0.960659\pi$
$641$	−40.3903	−	23.3193i	−1.59532	−	0.921059i	−0.602948	−	0.797780i	$-0.706007\pi$
$642$	20.2017	−	8.60080i	0.797296	−	0.339447i
$643$	−37.4221			−1.47578			−0.737891	−	0.674920i	$-0.764178\pi$
$643$	−37.4221			−1.47578			−0.737891	+	0.674920i	$0.764178\pi$
$644$	49.9663	−	49.9663i	1.96895	−	1.96895i
$645$	−4.83276	+	6.11481i	−0.190290	+	0.240770i
$646$	−5.68839	+	9.85258i	−0.223807	+	0.387645i
$647$	41.9998	−	11.2538i	1.65118	−	0.442433i	0.691240	−	0.722626i	$-0.257065\pi$
$647$	41.9998	−	11.2538i	1.65118	−	0.442433i	0.959944	+	0.280192i	$0.0903982\pi$
$648$	18.8380	+	29.8599i	0.740027	+	1.17301i
$649$	−12.0202			−0.471833
$650$	37.4477	−	20.8331i	1.46882	−	0.817142i
$651$	39.8154	+	4.84516i	1.56049	+	0.189897i
$652$	72.1835	−	41.6752i	2.82692	−	1.63213i
$653$	−9.96233	+	37.1799i	−0.389856	+	1.45496i	0.440512	+	0.897747i	$0.354797\pi$
$653$	−9.96233	+	37.1799i	−0.389856	+	1.45496i	−0.830368	+	0.557216i	$0.811870\pi$
$654$	1.70130	−	2.26278i	0.0665263	−	0.0884816i
$655$	−32.4260	−	0.782522i	−1.26699	−	0.0305756i
$656$	−10.1596	−	2.72225i	−0.396664	−	0.106286i
$657$	6.62758	+	22.9265i	0.258566	+	0.894446i
$658$			35.5275i			1.38501i
$659$	−15.8067	−	9.12601i	−0.615742	−	0.355499i	0.159467	−	0.987203i	$-0.449022\pi$
$659$	−15.8067	−	9.12601i	−0.615742	−	0.355499i	−0.775209	+	0.631704i	$0.782356\pi$
$660$	−8.78418	+	60.0617i	−0.341924	+	2.33790i
$661$	−6.37354	+	23.7864i	−0.247902	+	0.925183i	0.724000	+	0.689800i	$0.242301\pi$
$661$	−6.37354	+	23.7864i	−0.247902	+	0.925183i	−0.971903	+	0.235384i	$0.924365\pi$
$662$	−51.0173	+	13.6701i	−1.98285	+	0.531302i
$663$	14.5925	+	10.2501i	0.566724	+	0.398080i
$664$	−28.1330	+	16.2426i	−1.09177	+	0.630336i
$665$	3.69356	−	12.5639i	0.143230	−	0.487206i
$666$	−63.2311	−	15.6206i	−2.45015	−	0.605285i
$667$	13.2226	−	49.3473i	0.511980	−	1.91074i
$668$	0.262494	+	0.454654i	0.0101562	+	0.0175911i
$669$	−4.49464	+	0.636622i	−0.173773	+	0.0246132i
$670$	−33.5903	+	55.0677i	−1.29771	+	2.12745i
$671$	−21.7415	+	5.82562i	−0.839322	+	0.224896i
$672$	17.0337	+	6.86071i	0.657089	+	0.264658i
$673$	8.64401	−	8.64401i	0.333202	−	0.333202i	−0.520599	−	0.853801i	$-0.674291\pi$
$673$	8.64401	−	8.64401i	0.333202	−	0.333202i	0.853801	+	0.520599i	$0.174291\pi$
$674$	−16.6085	−	61.9838i	−0.639736	−	2.38753i
$675$	−3.87588	+	25.6900i	−0.149183	+	0.988810i
$676$	26.3339	+	39.4766i	1.01284	+	1.51833i
$677$	−25.5435	−	6.84435i	−0.981715	−	0.263050i	−0.267948	−	0.963433i	$-0.586346\pi$
$677$	−25.5435	−	6.84435i	−0.981715	−	0.263050i	−0.713767	+	0.700384i	$0.753012\pi$
$678$	−19.9343	+	26.5132i	−0.765574	+	1.01823i
$679$	−11.1425	+	6.43311i	−0.427609	+	0.246880i
$680$	5.89726	+	24.3437i	0.226150	+	0.933537i
$681$	30.0074	+	12.0862i	1.14989	+	0.463143i
$682$	58.5772	+	33.8196i	2.24304	+	1.29502i
$683$	14.7577	−	8.52038i	0.564689	−	0.326023i	−0.190337	−	0.981719i	$-0.560958\pi$
$683$	14.7577	−	8.52038i	0.564689	−	0.326023i	0.755025	+	0.655696i	$0.227625\pi$
$684$	−0.359899	−	18.3513i	−0.0137611	−	0.701678i
$685$	6.38106	+	0.153991i	0.243808	+	0.00588370i
$686$		−	14.8757i		−	0.567958i
$687$	−0.409489	−	0.961811i	−0.0156230	−	0.0366954i
$688$	−1.05426	−	3.93455i	−0.0401933	−	0.150003i
$689$	−10.2048	+	3.09134i	−0.388772	+	0.117771i
$690$	47.3963	−	18.8415i	1.80435	−	0.717284i
$691$	−3.85708	+	3.85708i	−0.146730	+	0.146730i	−0.776656	−	0.629925i	$-0.783085\pi$
$691$	−3.85708	+	3.85708i	−0.146730	+	0.146730i	0.629925	+	0.776656i	$0.283085\pi$
$692$	5.32508	+	19.8735i	0.202429	+	0.755476i
$693$	38.5284	−	23.2634i	1.46357	−	0.883704i
$694$	55.1905	+	55.1905i	2.09500	+	2.09500i
$695$	0.0106683	−	0.00582079i	0.000404671	−	0.000220795i
$696$	−62.0361	+	8.78680i	−2.35147	+	0.333063i
$697$	7.41906	−	12.8502i	0.281017	−	0.486736i
$698$	8.49518	+	8.49518i	0.321547	+	0.321547i
$699$	−7.64123	+	10.1630i	−0.289018	+	0.384401i
$700$	−29.1854	−	56.7031i	−1.10311	−	2.14318i
$701$			1.06862i			0.0403614i	0.999796	+	0.0201807i	$0.00642415\pi$
$701$			1.06862i			0.0403614i	−0.999796	+	0.0201807i	$0.993576\pi$
$702$	−44.4274	−	3.07671i	−1.67680	−	0.116123i
$703$	10.8248	+	10.8248i	0.408266	+	0.408266i
$704$	34.1880	+	34.1880i	1.28851	+	1.28851i
$705$	−6.55836	+	15.2132i	−0.247002	+	0.572964i
$706$		−	37.9655i		−	1.42885i
$707$	−36.9291	−	21.3210i	−1.38886	−	0.801860i
$708$	10.6371	−	14.1476i	0.399766	−	0.531699i
$709$	−3.70163	−	13.8147i	−0.139018	−	0.518821i	−0.999949	−	0.0100998i	$-0.996785\pi$
$709$	−3.70163	−	13.8147i	−0.139018	−	0.518821i	0.860931	−	0.508721i	$-0.169882\pi$
$710$	−28.5048	+	6.90530i	−1.06977	+	0.259151i
$711$	29.5733	−	30.7565i	1.10909	−	1.15346i
$712$	−33.2858	+	8.91890i	−1.24744	+	0.334250i
$713$		−	36.7170i		−	1.37506i
$714$	24.6866	−	32.8338i	0.923873	−	1.22877i
$715$	−24.6774	−	24.2752i	−0.922883	−	0.907841i
$716$	33.7765	−	58.5026i	1.26229	−	2.18634i
$717$	−5.74275	+	2.44496i	−0.214467	+	0.0913088i
$718$	−16.5242	−	16.5242i	−0.616679	−	0.616679i
$719$	−2.52443	−	4.37244i	−0.0941452	−	0.163064i	0.815106	−	0.579311i	$-0.196678\pi$
$719$	−2.52443	−	4.37244i	−0.0941452	−	0.163064i	−0.909252	+	0.416247i	$0.863345\pi$
$720$	−9.55776	−	9.64453i	−0.356197	−	0.359430i
$721$	−23.0464	−	6.17527i	−0.858294	−	0.229979i
$722$	19.2429	−	33.3298i	0.716148	−	1.24041i
$723$	−12.0932	+	5.14865i	−0.449751	+	0.191480i
$724$			22.6549i			0.841964i
$725$	−38.7713	−	24.9527i	−1.43993	−	0.926722i
$726$	30.3075	−	4.29276i	1.12482	−	0.159319i
$727$	−7.66579	+	28.6091i	−0.284309	+	1.06105i	0.665035	+	0.746813i	$0.268417\pi$
$727$	−7.66579	+	28.6091i	−0.284309	+	1.06105i	−0.949343	+	0.314241i	$0.898250\pi$
$728$	41.9784	−	26.0816i	1.55582	−	0.966650i
$729$	17.9364	−	20.1813i	0.664310	−	0.747457i
$730$	−20.2519	−	37.1174i	−0.749555	−	1.37378i
$731$	5.74644			0.212540
$732$	12.3832	−	30.7448i	0.457695	−	1.13636i
$733$	−9.09683	+	15.7562i	−0.335999	+	0.581967i	−0.983676	−	0.179947i	$-0.942407\pi$
$733$	−9.09683	+	15.7562i	−0.335999	+	0.581967i	0.647677	+	0.761915i	$0.275741\pi$
$734$	51.6796	+	51.6796i	1.90753	+	1.90753i
$735$	−7.98652	+	18.5261i	−0.294587	+	0.683345i
$736$	4.35084	−	16.2376i	0.160374	−	0.598525i
$737$	50.3301	+	13.4859i	1.85393	+	0.496760i
$738$	0.726578	+	37.0483i	0.0267457	+	1.36377i
$739$	3.41695	+	12.7522i	0.125695	+	0.469099i	0.999863	−	0.0165235i	$-0.00525983\pi$
$739$	3.41695	+	12.7522i	0.125695	+	0.469099i	−0.874169	+	0.485622i	$0.838593\pi$
$740$	74.5289	+	1.79857i	2.73974	+	0.0661168i
$741$	8.56532	+	6.01648i	0.314655	+	0.221021i
$742$	6.35725	+	23.7256i	0.233382	+	0.870993i
$743$	−8.07469	−	13.9858i	−0.296232	−	0.513089i	0.679039	−	0.734102i	$-0.262397\pi$
$743$	−8.07469	−	13.9858i	−0.296232	−	0.513089i	−0.975271	+	0.221014i	$0.929063\pi$
$744$	−41.4316	+	17.6394i	−1.51895	+	0.646691i
$745$	3.47656	−	11.8257i	0.127371	−	0.433261i
$746$	60.3568	−	60.3568i	2.20982	−	2.20982i
$747$	17.9078	+	17.2189i	0.655214	+	0.630008i
$748$	38.7581	−	22.3770i	1.41714	−	0.818185i
$749$	17.9989	+	4.82280i	0.657666	+	0.176221i
$750$	−3.14243	−	45.9237i	−0.114745	−	1.67690i
$751$	8.99601	−	5.19385i	0.328269	−	0.189526i	−0.326803	−	0.945092i	$-0.605971\pi$
$751$	8.99601	−	5.19385i	0.328269	−	0.189526i	0.655072	+	0.755566i	$0.272638\pi$
$752$	−4.32908	−	7.49819i	−0.157865	−	0.273431i
$753$	−13.7801	+	10.7901i	−0.502175	+	0.393215i
$754$	37.2821	−	69.6860i	1.35773	−	2.53781i
$755$	−11.5630	+	2.80113i	−0.420819	+	0.101943i
$756$	−6.71446	+	65.9341i	−0.244202	+	2.39800i
$757$	7.47159	+	27.8844i	0.271560	+	1.01347i	0.958112	+	0.286394i	$0.0924565\pi$
$757$	7.47159	+	27.8844i	0.271560	+	1.01347i	−0.686552	+	0.727080i	$0.740877\pi$
$758$	9.35266	+	34.9046i	0.339704	+	1.26779i
$759$	−25.4006	−	32.4391i	−0.921982	−	1.17746i
$760$	3.46151	+	14.2890i	0.125562	+	0.518316i
$761$	−13.0009	−	13.0009i	−0.471284	−	0.471284i	0.431046	−	0.902330i	$-0.358145\pi$
$761$	−13.0009	−	13.0009i	−0.471284	−	0.471284i	−0.902330	+	0.431046i	$0.858145\pi$
$762$	31.9244	+	74.9843i	1.15650	+	2.71639i
$763$	2.32075	−	0.621842i	0.0840166	−	0.0225122i
$764$	−5.75916	+	9.97515i	−0.208359	+	0.360888i
$765$	16.6321	−	9.50262i	0.601336	−	0.343568i
$766$			3.53917i			0.127876i
$767$	2.92645	+	9.66048i	0.105668	+	0.348820i
$768$	−45.7549	+	6.48073i	−1.65104	+	0.233853i
$769$	−2.85945	+	10.6716i	−0.103114	+	0.384828i	−0.998124	−	0.0612182i	$-0.980501\pi$
$769$	−2.85945	+	10.6716i	−0.103114	+	0.384828i	0.895010	+	0.446046i	$0.147168\pi$
$770$	−57.7290	+	55.0084i	−2.08041	+	1.98236i
$771$	−2.76309	+	22.7058i	−0.0995101	+	0.817731i
$772$	−25.1870	+	14.5417i	−0.906500	+	0.523368i
$773$	11.1093	+	19.2419i	0.399573	+	0.692081i	0.993673	−	0.112310i	$-0.0358250\pi$
$773$	11.1093	+	19.2419i	0.399573	+	0.692081i	−0.594100	+	0.804391i	$0.702492\pi$
$774$	−12.2850	+	7.41764i	−0.441574	+	0.266622i
$775$	−31.5569	−	10.1105i	−1.13356	−	0.363179i
$776$	7.22240	−	12.5096i	0.259269	−	0.449067i
$777$	−34.0783	−	43.5214i	−1.22255	−	1.56132i
$778$	−29.1550	+	16.8326i	−1.04526	+	0.603479i
$779$	4.35476	−	7.54266i	0.156025	−	0.270244i
$780$	50.4096	−	7.56300i	1.80495	−	0.270799i
$781$	11.8459	+	20.5178i	0.423881	+	0.734184i
$782$	−32.5667	−	18.8024i	−1.16458	−	0.672373i
$783$	19.6305	+	43.7100i	0.701539	+	1.56207i
$784$	−5.27179	−	9.13101i	−0.188278	−	0.326107i
$785$	33.8165	−	32.2228i	1.20696	−	1.15008i
$786$	−55.3970	−	22.3124i	−1.97594	−	0.795857i
$787$	−17.1065			−0.609781			−0.304890	−	0.952387i	$-0.598620\pi$
$787$	−17.1065			−0.609781			−0.304890	+	0.952387i	$0.598620\pi$
$788$	71.5569	+	41.3134i	2.54911	+	1.47173i
$789$	−9.90449	−	7.44684i	−0.352609	−	0.265115i
$790$	−39.3666	+	64.5373i	−1.40060	+	2.29613i
$791$	−27.1924	+	7.28618i	−0.966850	+	0.259067i
$792$	−24.4016	+	44.2463i	−0.867073	+	1.57223i
$793$	9.97522	+	16.0551i	0.354230	+	0.570133i
$794$	14.9338	−	8.62201i	0.529979	−	0.305984i
$795$	−1.65749	+	11.3331i	−0.0587851	+	0.401942i
$796$	−4.73706	−	8.20482i	−0.167900	−	0.290812i
$797$	9.90210	+	9.90210i	0.350750	+	0.350750i	0.860389	−	0.509638i	$-0.170221\pi$
$797$	9.90210	+	9.90210i	0.350750	+	0.350750i	−0.509638	+	0.860389i	$0.670221\pi$
$798$	14.4903	−	19.2724i	0.512950	−	0.682236i
$799$	11.7982	−	3.16133i	0.417392	−	0.111840i
$800$	−12.7576	−	8.21061i	−0.451048	−	0.290289i
$801$	13.6216	+	22.5599i	0.481297	+	0.797116i
$802$	−48.0589	−	12.8773i	−1.69702	−	0.454715i
$803$	−24.1517	+	24.1517i	−0.852294	+	0.852294i
$804$	−60.4117	+	47.3038i	−2.13056	+	1.66827i
$805$	41.5286	+	12.2087i	1.46369	+	0.430300i
$806$	12.9191	−	55.3116i	0.455055	−	1.94827i
$807$	−35.7700	+	28.0088i	−1.25916	+	0.985955i
$808$	47.8739			1.68420
$809$	14.0728	+	8.12494i	0.494774	+	0.285658i	0.726553	−	0.687111i	$-0.241121\pi$
$809$	14.0728	+	8.12494i	0.494774	+	0.285658i	−0.231779	+	0.972768i	$0.574455\pi$
$810$	−23.2906	+	41.7842i	−0.818349	+	1.46815i
$811$	−9.45176	+	9.45176i	−0.331896	+	0.331896i	−0.853306	−	0.521410i	$-0.825406\pi$
$811$	−9.45176	+	9.45176i	−0.331896	+	0.331896i	0.521410	+	0.853306i	$0.325406\pi$
$812$	−101.858	−	58.8079i	−3.57452	−	2.06375i
$813$	23.2319	−	9.89094i	0.814779	−	0.346890i
$814$	−24.1261	−	90.0400i	−0.845621	−	3.15590i
$815$	43.5887	+	26.5883i	1.52684	+	0.931347i
$816$	−1.20933	+	9.93777i	−0.0423351	+	0.347892i
$817$	3.37298			0.118006
$818$	32.9929	−	32.9929i	1.15357	−	1.15357i
$819$	−28.0767	−	25.3011i	−0.981081	−	0.884092i
$820$	−9.98596	−	41.2217i	−0.348725	−	1.43952i
$821$	24.5389	−	24.5389i	0.856412	−	0.856412i	−0.134502	−	0.990913i	$-0.542943\pi$
$821$	24.5389	−	24.5389i	0.856412	−	0.856412i	0.990913	+	0.134502i	$0.0429433\pi$
$822$	10.9015	+	4.39082i	0.380233	+	0.153147i
$823$	−21.0790	+	21.0790i	−0.734767	+	0.734767i	−0.971560	−	0.236793i	$-0.923904\pi$
$823$	−21.0790	+	21.0790i	−0.734767	+	0.734767i	0.236793	+	0.971560i	$0.423904\pi$
$824$	25.8741	−	6.93293i	0.901365	−	0.241520i
$825$	−34.8746	+	12.8984i	−1.21418	+	0.449064i
$826$	22.4601	−	6.01816i	0.781486	−	0.209399i
$827$	12.3929			0.430943			0.215472	−	0.976510i	$-0.430871\pi$
$827$	12.3929			0.430943			0.215472	+	0.976510i	$0.430871\pi$
$828$	60.6583	−	1.18961i	2.10802	−	0.0413418i
$829$	10.7008	−	18.5343i	0.371654	−	0.643723i	−0.618166	−	0.786047i	$-0.712124\pi$
$829$	10.7008	−	18.5343i	0.371654	−	0.643723i	0.989820	+	0.142324i	$0.0454576\pi$
$830$	−37.5766	−	22.9210i	−1.30430	−	0.795600i
$831$	15.7717	−	6.71474i	0.547113	−	0.232932i
$832$	19.1530	−	35.8000i	0.664011	−	1.24114i
$833$	14.3674	−	3.84975i	0.497803	−	0.133386i
$834$	0.0221554	−	0.00313810i	0.000767179	−	0.000108663i
$835$	−0.167469	+	0.274547i	−0.00579549	+	0.00950108i
$836$	22.7498	−	13.1346i	0.786819	−	0.454270i
$837$	21.7583	+	26.6923i	0.752078	+	0.922622i
$838$	−4.53638	−	7.85725i	−0.156707	−	0.271424i
$839$	−7.31463	−	27.2986i	−0.252529	−	0.942451i	−0.969448	−	0.245295i	$-0.921115\pi$
$839$	−7.31463	−	27.2986i	−0.252529	−	0.942451i	0.716919	−	0.697156i	$-0.245552\pi$
$840$	−6.17465	−	52.7264i	−0.213046	−	1.81923i
$841$	−56.0341			−1.93221
$842$	5.57609	−	20.8103i	0.192165	−	0.717169i
$843$	−1.63837	+	13.4634i	−0.0564284	+	0.463704i
$844$	36.4356	+	63.1083i	1.25416	+	2.17228i
$845$	−13.5017	+	25.7430i	−0.464473	+	0.885588i
$846$	−21.1420	+	21.9879i	−0.726878	+	0.755959i
$847$	22.4977	+	12.9890i	0.773028	+	0.446308i
$848$	−4.23271	−	4.23271i	−0.145352	−	0.145352i
$849$	−48.4484	−	5.89571i	−1.66274	−	0.202340i
$850$	−25.1277	+	22.8125i	−0.861871	+	0.782461i
$851$	−35.7804	+	35.7804i	−1.22654	+	1.22654i
$852$	−34.6321	−	4.21440i	−1.18648	−	0.144383i
$853$	17.3607	−	10.0232i	0.594419	−	0.343188i	−0.172424	−	0.985023i	$-0.555160\pi$
$853$	17.3607	−	10.0232i	0.594419	−	0.343188i	0.766843	+	0.641835i	$0.221827\pi$
$854$	37.7080	−	21.7707i	1.29034	−	0.744979i
$855$	9.76255	−	5.57774i	0.333872	−	0.190755i
$856$	−20.2073	+	5.41452i	−0.690670	+	0.185064i
$857$	13.4987	−	50.3777i	0.461106	−	1.72087i	−0.208383	−	0.978047i	$-0.566820\pi$
$857$	13.4987	−	50.3777i	0.461106	−	1.72087i	0.669488	−	0.742822i	$-0.266513\pi$
$858$	−26.8503	−	57.8047i	−0.916655	−	1.97342i
$859$	−2.21126	−	1.27667i	−0.0754472	−	0.0435594i	0.461802	−	0.886983i	$-0.347203\pi$
$859$	−2.21126	−	1.27667i	−0.0754472	−	0.0435594i	−0.537249	+	0.843424i	$0.680536\pi$
$860$	11.8917	−	11.3313i	0.405503	−	0.386393i
$861$	−18.8989	+	25.1360i	−0.644072	+	0.856632i
$862$	34.2833	−	9.18619i	1.16769	−	0.312883i
$863$	−16.8073			−0.572126			−0.286063	−	0.958211i	$-0.592347\pi$
$863$	−16.8073			−0.572126			−0.286063	+	0.958211i	$0.592347\pi$
$864$	6.45936	+	14.3826i	0.219752	+	0.489306i
$865$	−9.12432	+	8.69431i	−0.310236	+	0.295615i
$866$	2.63969	−	9.85145i	0.0897002	−	0.334766i
$867$	14.2123	+	5.72433i	0.482675	+	0.194409i
$868$	−81.6499	−	21.8780i	−2.77138	−	0.742589i
$869$	58.9850	+	15.8050i	2.00093	+	0.536147i
$870$	−50.7104	−	68.0844i	−1.71924	−	2.30828i
$871$	−1.41499	−	43.7330i	−0.0479451	−	1.48184i
$872$	−1.90735	+	1.90735i	−0.0645909	+	0.0645909i
$873$	−10.7243	−	2.64933i	−0.362963	−	0.0896661i
$874$	−19.1157	−	11.0364i	−0.646597	−	0.373313i
$875$	21.9284	−	32.3306i	0.741315	−	1.09297i
$876$	−7.05353	−	49.7990i	−0.238317	−	1.68255i
$877$		−	38.7069i		−	1.30704i	−0.756910	−	0.653519i	$-0.773292\pi$
$877$		−	38.7069i		−	1.30704i	0.756910	−	0.653519i	$-0.226708\pi$
$878$			22.1246i			0.746670i
$879$	−4.28319	−	30.2400i	−0.144469	−	1.01997i
$880$	5.48103	−	18.6440i	0.184765	−	0.628490i
$881$	−22.5601	−	13.0251i	−0.760068	−	0.438825i	0.0692522	−	0.997599i	$-0.477939\pi$
$881$	−22.5601	−	13.0251i	−0.760068	−	0.438825i	−0.829320	+	0.558774i	$0.811272\pi$
$882$	−25.7459	+	26.7760i	−0.866911	+	0.901594i
$883$	16.1740	−	16.1740i	0.544298	−	0.544298i	−0.380488	−	0.924786i	$-0.624244\pi$
$883$	16.1740	−	16.1740i	0.544298	−	0.544298i	0.924786	+	0.380488i	$0.124244\pi$
$884$	−27.4203	−	25.7015i	−0.922244	−	0.864436i
$885$	10.7286	+	1.56908i	0.360637	+	0.0527441i
$886$	−24.9450	−	6.68400i	−0.838044	−	0.224553i
$887$	−21.6808	−	5.80934i	−0.727968	−	0.195059i	−0.124244	−	0.992252i	$-0.539651\pi$
$887$	−21.6808	−	5.80934i	−0.727968	−	0.195059i	−0.603724	+	0.797193i	$0.706317\pi$
$888$	57.5642	+	23.1853i	1.93173	+	0.778048i
$889$	−17.9012	+	66.8082i	−0.600387	+	2.24068i
$890$	−32.2096	−	33.8026i	−1.07967	−	1.13307i
$891$	37.6889	+	8.53017i	1.26263	+	0.285771i
$892$	9.56703			0.320328
$893$	6.92521	−	1.85560i	0.231743	−	0.0620954i
$894$	13.6389	−	18.1401i	0.456154	−	0.606697i
$895$	41.3689	+	0.998336i	1.38281	+	0.0333707i
$896$	−62.6348	−	36.1622i	−2.09248	−	1.20809i
$897$	−19.8869	+	28.3118i	−0.664003	+	0.945304i
$898$	4.10345	−	15.3143i	0.136934	−	0.511044i
$899$	−59.0315	+	15.8174i	−1.96881	+	0.527541i
$900$	15.6806	−	52.4613i	0.522686	−	1.74871i
$901$	7.31328	−	4.22232i	0.243641	−	0.140666i
$902$	−45.9283	+	26.5167i	−1.52924	+	0.882909i
$903$	−12.0899	−	1.47123i	−0.402327	−	0.0489594i
$904$	22.3486	−	22.3486i	0.743302	−	0.743302i
$905$	−12.1824	+	6.64689i	−0.404956	+	0.220950i
$906$	−21.7456	−	2.64624i	−0.722450	−	0.0879153i
$907$	−33.5660	−	33.5660i	−1.11454	−	1.11454i	−0.992529	−	0.122012i	$-0.961065\pi$
$907$	−33.5660	−	33.5660i	−1.11454	−	1.11454i	−0.122012	−	0.992529i	$-0.538935\pi$
$908$	−59.0436	−	34.0888i	−1.95943	−	1.13128i
$909$	−10.1674	−	35.1716i	−0.337231	−	1.16657i
$910$	58.2644	+	33.0037i	1.93145	+	1.09406i
$911$	5.60158	+	9.70223i	0.185589	+	0.321449i	0.943775	−	0.330589i	$-0.107247\pi$
$911$	5.60158	+	9.70223i	0.185589	+	0.321449i	−0.758186	+	0.652038i	$0.773914\pi$
$912$	−0.709841	+	5.83316i	−0.0235052	+	0.193155i
$913$	−9.20239	+	34.3438i	−0.304555	+	1.13661i
$914$	−17.5703			−0.581174
$915$	20.1658	−	2.36156i	0.666660	−	0.0780709i
$916$	0.570201	+	2.12802i	0.0188400	+	0.0703117i
$917$	−25.3422	−	43.8940i	−0.836873	−	1.44951i
$918$	34.8175	−	5.63002i	1.14915	−	0.185818i
$919$	−30.9935	+	17.8941i	−1.02238	+	0.590273i	−0.914793	−	0.403923i	$-0.867646\pi$
$919$	−30.9935	+	17.8941i	−1.02238	+	0.590273i	−0.107589	+	0.994195i	$0.534313\pi$
$920$	−47.2308	+	11.4417i	−1.55715	+	0.377221i
$921$	34.2111	−	4.84567i	1.12729	−	0.159670i
$922$	13.4152	−	3.59460i	0.441807	−	0.118382i
$923$	13.6059	−	14.5158i	0.447843	−	0.477792i
$924$	−87.2721	+	37.1559i	−2.87104	+	1.22234i
$925$	20.8994	+	40.6046i	0.687169	+	1.33507i
$926$	−19.3528	+	33.5201i	−0.635973	+	1.10154i
$927$	−10.5885	−	17.5365i	−0.347773	−	0.575975i
$928$	−27.9802			−0.918494
$929$	9.35036	−	2.50542i	0.306775	−	0.0822002i	−0.102147	−	0.994769i	$-0.532571\pi$
$929$	9.35036	−	2.50542i	0.306775	−	0.0822002i	0.408923	+	0.912569i	$0.365905\pi$
$930$	−47.8682	−	37.8321i	−1.56966	−	1.24056i
$931$	8.43325	−	2.25968i	0.276389	−	0.0740581i
$932$	18.9485	−	18.9485i	0.620680	−	0.620680i
$933$	23.9171	+	9.63316i	0.783011	+	0.315375i
$934$	−31.9815	+	31.9815i	−1.04647	+	1.04647i
$935$	23.4045	+	14.2763i	0.765407	+	0.466884i
$936$	41.5011	+	8.83899i	1.35651	+	0.288911i
$937$	−11.8784	+	11.8784i	−0.388051	+	0.388051i	−0.873992	−	0.485941i	$-0.838477\pi$
$937$	−11.8784	+	11.8784i	−0.388051	+	0.388051i	0.485941	+	0.873992i	$0.338477\pi$
$938$	−100.795			−3.29109
$939$	−4.55668	+	37.4448i	−0.148702	+	1.22196i
$940$	18.1816	−	29.8067i	0.593017	−	0.972189i
$941$	−12.8068	−	47.7955i	−0.417489	−	1.55809i	−0.779798	−	0.626031i	$-0.784678\pi$
$941$	−12.8068	−	47.7955i	−0.417489	−	1.55809i	0.362309	−	0.932058i	$-0.381988\pi$
$942$	79.1321	−	33.6903i	2.57826	−	1.09769i
$943$	24.9315	+	14.3942i	0.811882	+	0.468740i
$944$	−4.00694	+	4.00694i	−0.130415	+	0.130415i
$945$	−37.4252	+	15.7343i	−1.21744	+	0.511836i
$946$	−17.7869	−	10.2693i	−0.578302	−	0.333883i
$947$	52.6619			1.71128			0.855641	−	0.517570i	$-0.173163\pi$
$947$	52.6619			1.71128			0.855641	+	0.517570i	$0.173163\pi$
$948$	−70.8003	+	55.4382i	−2.29949	+	1.80055i
$949$	25.2905	+	13.5304i	0.820963	+	0.439216i
$950$	−14.7492	+	13.3902i	−0.478526	+	0.434436i
$951$	21.5073	−	16.8407i	0.697423	−	0.546098i
$952$	−27.6764	+	27.6764i	−0.896996	+	0.896996i
$953$	−2.19138	−	0.587179i	−0.0709859	−	0.0190206i	0.223151	−	0.974784i	$-0.428366\pi$
$953$	−2.19138	−	0.587179i	−0.0709859	−	0.0190206i	−0.294137	+	0.955763i	$0.595032\pi$
$954$	−10.1843	+	18.4668i	−0.329730	+	0.597885i
$955$	−7.05372	−	0.170224i	−0.228253	−	0.00550832i
$956$	12.7059	−	3.40454i	0.410938	−	0.110111i
$957$	−41.2114	+	54.8122i	−1.33217	+	1.77183i
$958$	6.04124	+	6.04124i	0.195184	+	0.195184i
$959$	4.98705	+	8.63782i	0.161040	+	0.278930i
$960$	−26.0516	−	34.9772i	−0.840811	−	1.12888i
$961$	−11.1912	+	6.46123i	−0.361006	+	0.208427i
$962$	−66.4903	+	41.3112i	−2.14373	+	1.33193i
$963$	8.26948	+	13.6958i	0.266480	+	0.441340i
$964$	26.7563	−	7.16934i	0.861763	−	0.230909i
$965$	−15.2094	−	9.27746i	−0.489608	−	0.298652i
$966$	63.7031	+	47.8961i	2.04961	+	1.54103i
$967$	5.74765	+	3.31841i	0.184832	+	0.106713i	0.589561	−	0.807724i	$-0.299301\pi$
$967$	5.74765	+	3.31841i	0.184832	+	0.106713i	−0.404729	+	0.914437i	$0.632634\pi$
$968$	−29.1654			−0.937410
$969$	−7.68951	−	3.09713i	−0.247023	−	0.0994940i
$970$	19.5662	+	0.472181i	0.628232	+	0.0151608i
$971$	12.8246	+	22.2128i	0.411560	+	0.712842i	0.995061	−	0.0992702i	$-0.0316508\pi$
$971$	12.8246	+	22.2128i	0.411560	+	0.712842i	−0.583501	+	0.812113i	$0.698317\pi$
$972$	−43.3922	+	36.8107i	−1.39180	+	1.18070i
$973$	0.0164462	+	0.00949524i	0.000527242	+	0.000304403i
$974$	28.6183	+	49.5683i	0.916988	+	1.58827i
$975$	18.8569	+	24.8881i	0.603905	+	0.797056i
$976$	−5.30559	+	9.18955i	−0.169828	+	0.294150i
$977$	45.7227	−	26.3980i	1.46280	−	0.844548i	0.463660	−	0.886013i	$-0.346536\pi$
$977$	45.7227	−	26.3980i	1.46280	−	0.844548i	0.999140	+	0.0414653i	$0.0132026\pi$
$978$	57.9582	+	74.0185i	1.85330	+	2.36685i
$979$	−18.8583	+	32.6636i	−0.602715	+	1.04393i
$980$	22.1408	−	36.2975i	0.707262	−	1.15948i
$981$	1.80635	+	0.996193i	0.0576724	+	0.0318060i
$982$	17.4379	+	30.2034i	0.556467	+	0.963829i
$983$	14.4090	−	8.31906i	0.459577	−	0.265337i	−0.252289	−	0.967652i	$-0.581184\pi$
$983$	14.4090	−	8.31906i	0.459577	−	0.265337i	0.711866	+	0.702315i	$0.247850\pi$
$984$	4.26501	−	35.0480i	0.135964	−	1.11729i
$985$	−1.22110	+	50.5999i	−0.0389076	+	1.61225i
$986$	−16.1999	+	60.4589i	−0.515911	+	1.92540i
$987$	−25.6316	+	3.63047i	−0.815864	+	0.115559i
$988$	−16.0949	−	15.0860i	−0.512046	−	0.479949i
$989$			11.1491i			0.354519i
$990$	−68.4631	−	0.309368i	−2.17590	−	0.00983235i
$991$	18.4690	−	31.9892i	0.586686	−	1.01617i	−0.407976	−	0.912992i	$-0.633765\pi$
$991$	18.4690	−	31.9892i	0.586686	−	1.01617i	0.994663	−	0.103178i	$-0.0329012\pi$
$992$	−19.4241	+	5.20467i	−0.616716	+	0.165248i
$993$	−15.0757	−	35.4100i	−0.478413	−	1.12370i
$994$	−32.4072	−	32.4072i	−1.02789	−	1.02789i
$995$	3.02219	−	4.95456i	0.0958098	−	0.157070i
$996$	−32.2787	−	41.2232i	−1.02279	−	1.30621i
$997$	−14.2117	−	53.0390i	−0.450091	−	1.67976i	−0.702134	−	0.712045i	$-0.747769\pi$
$997$	−14.2117	−	53.0390i	−0.450091	−	1.67976i	0.252043	−	0.967716i	$-0.418897\pi$
$998$	−1.90020	−	7.09166i	−0.0601499	−	0.224483i
$999$	4.80816	−	47.2148i	0.152124	−	1.49381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.ca.a.58.8	✓	320
5.2	odd	4		585.2.dv.a.292.73	yes	320
9.7	even	3		585.2.dt.a.448.8	yes	320
13.11	odd	12		585.2.cc.a.193.8	yes	320
45.7	odd	12		585.2.cc.a.97.8	yes	320
65.37	even	12		585.2.dt.a.427.8	yes	320
117.115	odd	12		585.2.dv.a.583.73	yes	320
585.232	even	12	inner	585.2.ca.a.232.73	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.ca.a.58.8	✓	320	1.1	even	1	trivial
585.2.ca.a.232.73	yes	320	585.232	even	12	inner
585.2.cc.a.97.8	yes	320	45.7	odd	12
585.2.cc.a.193.8	yes	320	13.11	odd	12
585.2.dt.a.427.8	yes	320	65.37	even	12
585.2.dt.a.448.8	yes	320	9.7	even	3
585.2.dv.a.292.73	yes	320	5.2	odd	4
585.2.dv.a.583.73	yes	320	117.115	odd	12

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.ca (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-2.37704i q^{2} +(1.71493 - 0.242904i) q^{3} -3.65031 q^{4} +(-1.07099 - 1.96290i) q^{5} +(-0.577391 - 4.07646i) q^{6} +(1.74707 - 3.02601i) q^{7} +3.92284i q^{8} +(2.88200 - 0.833127i) q^{9} +(-4.66589 + 2.54578i) q^{10} +(3.03601 + 3.03601i) q^{11} +(-6.26003 + 0.886672i) q^{12} +(1.70086 - 3.17916i) q^{13} +(-7.19293 - 4.15284i) q^{14} +(-2.31347 - 3.10610i) q^{15} +2.02412 q^{16} +(-0.739061 + 2.75821i) q^{17} +(-1.98037 - 6.85061i) q^{18} +(-0.433806 + 1.61899i) q^{19} +(3.90944 + 7.16519i) q^{20} +(2.26108 - 5.61377i) q^{21} +(7.21672 - 7.21672i) q^{22} +(-5.35140 - 1.43390i) q^{23} +(0.952871 + 6.72741i) q^{24} +(-2.70596 + 4.20449i) q^{25} +(-7.55699 - 4.04300i) q^{26} +(4.74006 - 2.12880i) q^{27} +(-6.37733 + 11.0459i) q^{28} +9.22139i q^{29} +(-7.38331 + 5.49921i) q^{30} +(1.71530 + 6.40158i) q^{31} +3.03427i q^{32} +(5.94402 + 4.46910i) q^{33} +(6.55638 + 1.75678i) q^{34} +(-7.81085 - 0.188496i) q^{35} +(-10.5202 + 3.04117i) q^{36} +(4.56675 - 7.90984i) q^{37} +(3.84839 + 1.03117i) q^{38} +(2.14463 - 5.86520i) q^{39} +(7.70014 - 4.20132i) q^{40} +(-5.01925 - 1.34490i) q^{41} +(-13.3441 - 5.37466i) q^{42} +(-0.520848 - 1.94383i) q^{43} +(-11.0824 - 11.0824i) q^{44} +(-4.72193 - 4.76480i) q^{45} +(-3.40844 + 12.7205i) q^{46} +(-2.13875 - 3.70442i) q^{47} +(3.47123 - 0.491666i) q^{48} +(-2.60448 - 4.51110i) q^{49} +(9.99424 + 6.43217i) q^{50} +(-0.597461 + 4.90967i) q^{51} +(-6.20865 + 11.6049i) q^{52} +(-2.09114 - 2.09114i) q^{53} +(-5.06025 - 11.2673i) q^{54} +(2.70786 - 9.21094i) q^{55} +(11.8705 + 6.85346i) q^{56} +(-0.350691 + 2.88183i) q^{57} +21.9196 q^{58} +(-1.97960 + 1.97960i) q^{59} +(8.44488 + 11.3382i) q^{60} +(-2.62118 + 4.54002i) q^{61} +(15.2168 - 4.07733i) q^{62} +(2.51399 - 10.1765i) q^{63} +11.2608 q^{64} +(-8.06199 + 0.0662388i) q^{65} +(10.6232 - 14.1292i) q^{66} +(10.5098 - 6.06786i) q^{67} +(2.69780 - 10.0683i) q^{68} +(-9.52559 - 1.15917i) q^{69} +(-0.448061 + 18.5667i) q^{70} +(5.32997 + 1.42816i) q^{71} +(3.26822 + 11.3056i) q^{72} +7.95506i q^{73} +(-18.8020 - 10.8553i) q^{74} +(-3.61926 + 7.86772i) q^{75} +(1.58352 - 5.90979i) q^{76} +(14.4911 - 3.88288i) q^{77} +(-13.9418 - 5.09786i) q^{78} +(12.3171 - 7.11130i) q^{79} +(-2.16781 - 3.97315i) q^{80} +(7.61180 - 4.80214i) q^{81} +(-3.19688 + 11.9309i) q^{82} +(4.14053 + 7.17160i) q^{83} +(-8.25362 + 20.4920i) q^{84} +(6.20563 - 1.50331i) q^{85} +(-4.62056 + 1.23808i) q^{86} +(2.23991 + 15.8141i) q^{87} +(-11.9098 + 11.9098i) q^{88} +(2.27358 + 8.48513i) q^{89} +(-11.3261 + 11.2242i) q^{90} +(-6.64867 - 10.7010i) q^{91} +(19.5342 + 5.23418i) q^{92} +(4.49659 + 10.5616i) q^{93} +(-8.80555 + 5.08388i) q^{94} +(3.64251 - 0.882399i) q^{95} +(0.737034 + 5.20357i) q^{96} +(-3.18891 - 1.84112i) q^{97} +(-10.7231 + 6.19096i) q^{98} +(11.2792 + 6.22039i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 2 q^{3} - 304 q^{4} - 2 q^{5} - 8 q^{6} + 2 q^{7} + 12 q^{9} - 16 q^{10} - 12 q^{11} - 14 q^{12} - 2 q^{13} + 48 q^{14} - 6 q^{15} + 264 q^{16} - 12 q^{17} + 4 q^{18} - 30 q^{20} - 16 q^{21} - 4 q^{22}+ \cdots - 20 q^{99}+O(q^{100}) \) 320 * q - 2 * q^3 - 304 * q^4 - 2 * q^5 - 8 * q^6 + 2 * q^7 + 12 * q^9 - 16 * q^10 - 12 * q^11 - 14 * q^12 - 2 * q^13 + 48 * q^14 - 6 * q^15 + 264 * q^16 - 12 * q^17 + 4 * q^18 - 30 * q^20 - 16 * q^21 - 4 * q^22 + 2 * q^23 + 56 * q^24 - 20 * q^27 - 24 * q^28 - 2 * q^30 - 4 * q^31 - 6 * q^33 + 8 * q^34 - 46 * q^35 - 60 * q^36 - 4 * q^37 - 40 * q^38 - 4 * q^39 + 28 * q^40 + 4 * q^41 + 22 * q^42 - 6 * q^43 + 8 * q^44 + 4 * q^45 - 16 * q^46 - 14 * q^47 + 2 * q^48 - 112 * q^49 + 56 * q^50 - 30 * q^52 - 16 * q^53 - 4 * q^55 - 108 * q^56 - 72 * q^57 + 28 * q^58 - 16 * q^59 + 10 * q^60 + 4 * q^61 - 28 * q^62 - 18 * q^63 - 192 * q^64 + 58 * q^65 - 6 * q^67 + 62 * q^68 + 24 * q^69 + 10 * q^70 - 2 * q^72 - 34 * q^75 - 20 * q^76 - 44 * q^77 - 42 * q^78 + 4 * q^80 + 8 * q^81 + 20 * q^82 + 8 * q^83 + 124 * q^84 - 16 * q^85 + 68 * q^86 + 38 * q^87 - 8 * q^88 + 64 * q^90 - 16 * q^91 - 32 * q^92 - 70 * q^93 + 48 * q^94 - 64 * q^96 - 6 * q^97 - 282 * q^98 - 20 * q^99

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