LMFDB - Embedded newform 585.2.ca.a.58.11

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			58.11
Character	$\chi$	$=$	585.58
Dual form			585.2.ca.a.232.70

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.20453i q^{2} +(0.106040 + 1.72880i) q^{3} -2.85995 q^{4} +(-0.758370 + 2.10354i) q^{5} +(3.81119 - 0.233769i) q^{6} +(-0.828210 + 1.43450i) q^{7} +1.89577i q^{8} +(-2.97751 + 0.366645i) q^{9} +(4.63731 + 1.67185i) q^{10} +(-3.40253 - 3.40253i) q^{11} +(-0.303269 - 4.94428i) q^{12} +(0.195994 - 3.60022i) q^{13} +(3.16240 + 1.82581i) q^{14} +(-3.71702 - 1.08801i) q^{15} -1.54060 q^{16} +(0.0692009 - 0.258261i) q^{17} +(0.808280 + 6.56401i) q^{18} +(0.147606 - 0.550875i) q^{19} +(2.16890 - 6.01601i) q^{20} +(-2.56779 - 1.27970i) q^{21} +(-7.50098 + 7.50098i) q^{22} +(-7.18479 - 1.92516i) q^{23} +(-3.27742 + 0.201028i) q^{24} +(-3.84975 - 3.19052i) q^{25} +(-7.93679 - 0.432075i) q^{26} +(-0.949593 - 5.10865i) q^{27} +(2.36864 - 4.10260i) q^{28} +1.96366i q^{29} +(-2.39855 + 8.19427i) q^{30} +(0.861570 + 3.21542i) q^{31} +7.18785i q^{32} +(5.52150 - 6.24311i) q^{33} +(-0.569344 - 0.152555i) q^{34} +(-2.38944 - 2.83006i) q^{35} +(8.51552 - 1.04859i) q^{36} +(1.80663 - 3.12918i) q^{37} +(-1.21442 - 0.325403i) q^{38} +(6.24485 - 0.0429329i) q^{39} +(-3.98783 - 1.43770i) q^{40} +(-6.38147 - 1.70991i) q^{41} +(-2.82113 + 5.66077i) q^{42} +(3.27409 + 12.2191i) q^{43} +(9.73106 + 9.73106i) q^{44} +(1.48680 - 6.54136i) q^{45} +(-4.24407 + 15.8391i) q^{46} +(-4.97260 - 8.61279i) q^{47} +(-0.163366 - 2.66340i) q^{48} +(2.12814 + 3.68604i) q^{49} +(-7.03360 + 8.48688i) q^{50} +(0.453820 + 0.0922485i) q^{51} +(-0.560533 + 10.2964i) q^{52} +(0.587770 + 0.587770i) q^{53} +(-11.2622 + 2.09341i) q^{54} +(9.73774 - 4.57698i) q^{55} +(-2.71949 - 1.57010i) q^{56} +(0.968005 + 0.196767i) q^{57} +4.32894 q^{58} +(0.0234818 - 0.0234818i) q^{59} +(10.6305 + 3.11166i) q^{60} +(-1.95342 + 3.38343i) q^{61} +(7.08849 - 1.89935i) q^{62} +(1.94005 - 4.57491i) q^{63} +12.7646 q^{64} +(7.42457 + 3.14258i) q^{65} +(-13.7631 - 12.1723i) q^{66} +(-5.90548 + 3.40953i) q^{67} +(-0.197911 + 0.738613i) q^{68} +(2.56634 - 12.6252i) q^{69} +(-6.23894 + 5.26759i) q^{70} +(10.6224 + 2.84625i) q^{71} +(-0.695077 - 5.64469i) q^{72} -4.81106i q^{73} +(-6.89836 - 3.98277i) q^{74} +(5.10755 - 6.99378i) q^{75} +(-0.422146 + 1.57547i) q^{76} +(7.69895 - 2.06293i) q^{77} +(-0.0946469 - 13.7670i) q^{78} +(-8.01195 + 4.62570i) q^{79} +(1.16835 - 3.24072i) q^{80} +(8.73114 - 2.18338i) q^{81} +(-3.76955 + 14.0681i) q^{82} +(-3.58683 - 6.21257i) q^{83} +(7.34375 + 3.65986i) q^{84} +(0.490782 + 0.341424i) q^{85} +(26.9373 - 7.21782i) q^{86} +(-3.39477 + 0.208227i) q^{87} +(6.45043 - 6.45043i) q^{88} +(2.67869 + 9.99701i) q^{89} +(-14.4206 - 3.27770i) q^{90} +(5.00220 + 3.26289i) q^{91} +(20.5481 + 5.50585i) q^{92} +(-5.46747 + 1.83045i) q^{93} +(-18.9871 + 10.9622i) q^{94} +(1.04685 + 0.728263i) q^{95} +(-12.4264 + 0.762202i) q^{96} +(2.56517 + 1.48100i) q^{97} +(8.12598 - 4.69153i) q^{98} +(11.3786 + 8.88355i) 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 $

$2$		−	2.20453i		−	1.55884i	−0.626504	−	0.779418i	$-0.715515\pi$
$2$		−	2.20453i		−	1.55884i	0.626504	−	0.779418i	$-0.284485\pi$
$3$	0.106040	+	1.72880i	0.0612224	+	0.998124i
$3$	0.106040	+	1.72880i	0.0612224	+	0.998124i
$4$	−2.85995			−1.42997
$5$	−0.758370	+	2.10354i	−0.339154	+	0.940731i
$5$	−0.758370	+	2.10354i	−0.339154	+	0.940731i
$6$	3.81119	−	0.233769i	1.55591	−	0.0954357i
$7$	−0.828210	+	1.43450i	−0.313034	+	0.542191i	−0.979018	−	0.203775i	$-0.934679\pi$
$7$	−0.828210	+	1.43450i	−0.313034	+	0.542191i	0.665984	+	0.745966i	$0.268012\pi$
$8$			1.89577i			0.670257i
$9$	−2.97751	+	0.366645i	−0.992504	+	0.122215i
$10$	4.63731	+	1.67185i	1.46645	+	0.528685i
$11$	−3.40253	−	3.40253i	−1.02590	−	1.02590i	−0.999656	−	0.0262464i	$-0.991645\pi$
$11$	−3.40253	−	3.40253i	−1.02590	−	1.02590i	−0.0262464	−	0.999656i	$-0.508355\pi$
$12$	−0.303269	−	4.94428i	−0.0875464	−	1.42729i
$13$	0.195994	−	3.60022i	0.0543591	−	0.998521i
$13$	0.195994	−	3.60022i	0.0543591	−	0.998521i
$14$	3.16240	+	1.82581i	0.845187	+	0.487969i
$15$	−3.71702	−	1.08801i	−0.959730	−	0.280924i
$16$	−1.54060			−0.385151
$17$	0.0692009	−	0.258261i	0.0167837	−	0.0626375i	−0.957026	−	0.290002i	$-0.906344\pi$
$17$	0.0692009	−	0.258261i	0.0167837	−	0.0626375i	0.973810	+	0.227364i	$0.0730108\pi$
$18$	0.808280	+	6.56401i	0.190513	+	1.54715i
$19$	0.147606	−	0.550875i	0.0338632	−	0.126379i	−0.946925	−	0.321454i	$-0.895828\pi$
$19$	0.147606	−	0.550875i	0.0338632	−	0.126379i	0.980788	+	0.195075i	$0.0624950\pi$
$20$	2.16890	−	6.01601i	0.484980	−	1.34522i
$21$	−2.56779	−	1.27970i	−0.560339	−	0.279253i
$22$	−7.50098	+	7.50098i	−1.59921	+	1.59921i
$23$	−7.18479	−	1.92516i	−1.49813	−	0.401423i	−0.585659	−	0.810558i	$-0.699164\pi$
$23$	−7.18479	−	1.92516i	−1.49813	−	0.401423i	−0.912474	+	0.409134i	$0.865831\pi$
$24$	−3.27742	+	0.201028i	−0.669000	+	0.0410348i
$25$	−3.84975	−	3.19052i	−0.769950	−	0.638104i
$26$	−7.93679	−	0.432075i	−1.55653	−	0.0847369i
$27$	−0.949593	−	5.10865i	−0.182749	−	0.983160i
$28$	2.36864	−	4.10260i	0.447630	−	0.775318i
$29$			1.96366i			0.364642i	0.983239	+	0.182321i	$0.0583610\pi$
$29$			1.96366i			0.364642i	−0.983239	+	0.182321i	$0.941639\pi$
$30$	−2.39855	+	8.19427i	−0.437914	+	1.49606i
$31$	0.861570	+	3.21542i	0.154742	+	0.577507i	0.999127	+	0.0417696i	$0.0132996\pi$
$31$	0.861570	+	3.21542i	0.154742	+	0.577507i	−0.844385	+	0.535737i	$0.820034\pi$
$32$			7.18785i			1.27064i
$33$	5.52150	−	6.24311i	0.961169	−	1.08679i
$34$	−0.569344	−	0.152555i	−0.0976417	−	0.0261630i
$35$	−2.38944	−	2.83006i	−0.403889	−	0.478367i
$36$	8.51552	−	1.04859i	1.41925	−	0.174764i
$37$	1.80663	−	3.12918i	0.297008	−	0.514433i	−0.678442	−	0.734654i	$-0.737344\pi$
$37$	1.80663	−	3.12918i	0.297008	−	0.514433i	0.975450	+	0.220221i	$0.0706778\pi$
$38$	−1.21442	−	0.325403i	−0.197005	−	0.0527873i
$39$	6.24485	−	0.0429329i	0.999976	−	0.00687477i
$40$	−3.98783	−	1.43770i	−0.630532	−	0.227320i
$41$	−6.38147	−	1.70991i	−0.996619	−	0.267043i	−0.276590	−	0.960988i	$-0.589205\pi$
$41$	−6.38147	−	1.70991i	−0.996619	−	0.267043i	−0.720028	+	0.693945i	$0.755871\pi$
$42$	−2.82113	+	5.66077i	−0.435309	+	0.873477i
$43$	3.27409	+	12.2191i	0.499294	+	1.86339i	0.504513	+	0.863404i	$0.331672\pi$
$43$	3.27409	+	12.2191i	0.499294	+	1.86339i	−0.00521922	+	0.999986i	$0.501661\pi$
$44$	9.73106	+	9.73106i	1.46701	+	1.46701i
$45$	1.48680	−	6.54136i	0.221640	−	0.975129i
$46$	−4.24407	+	15.8391i	−0.625754	+	2.33534i
$47$	−4.97260	−	8.61279i	−0.725328	−	1.25630i	−0.958839	−	0.283950i	$-0.908355\pi$
$47$	−4.97260	−	8.61279i	−0.725328	−	1.25630i	0.233511	−	0.972354i	$-0.424978\pi$
$48$	−0.163366	−	2.66340i	−0.0235798	−	0.384428i
$49$	2.12814	+	3.68604i	0.304019	+	0.526577i
$50$	−7.03360	+	8.48688i	−0.994701	+	1.20023i
$51$	0.453820	+	0.0922485i	0.0635476	+	0.0129174i
$52$	−0.560533	+	10.2964i	−0.0777320	+	1.42786i
$53$	0.587770	+	0.587770i	0.0807365	+	0.0807365i	0.746322	−	0.665585i	$-0.231818\pi$
$53$	0.587770	+	0.587770i	0.0807365	+	0.0807365i	−0.665585	+	0.746322i	$0.731818\pi$
$54$	−11.2622	+	2.09341i	−1.53259	+	0.284876i
$55$	9.73774	−	4.57698i	1.31304	−	0.617160i
$56$	−2.71949	−	1.57010i	−0.363408	−	0.209813i
$57$	0.968005	+	0.196767i	0.128215	+	0.0260625i
$58$	4.32894			0.568418
$59$	0.0234818	−	0.0234818i	0.00305707	−	0.00305707i	−0.705577	−	0.708634i	$-0.749312\pi$
$59$	0.0234818	−	0.0234818i	0.00305707	−	0.00305707i	0.708634	+	0.705577i	$0.249312\pi$
$60$	10.6305	+	3.11166i	1.37239	+	0.401713i
$61$	−1.95342	+	3.38343i	−0.250110	+	0.433204i	−0.963556	−	0.267507i	$-0.913800\pi$
$61$	−1.95342	+	3.38343i	−0.250110	+	0.433204i	0.713446	+	0.700710i	$0.247134\pi$
$62$	7.08849	−	1.89935i	0.900239	−	0.241218i
$63$	1.94005	−	4.57491i	0.244424	−	0.576384i
$64$	12.7646			1.59558
$65$	7.42457	+	3.14258i	0.920904	+	0.389789i
$66$	−13.7631	−	12.1723i	−1.69412	−	1.49831i
$67$	−5.90548	+	3.40953i	−0.721469	+	0.416540i	−0.815293	−	0.579048i	$-0.803424\pi$
$67$	−5.90548	+	3.40953i	−0.721469	+	0.416540i	0.0938241	+	0.995589i	$0.470091\pi$
$68$	−0.197911	+	0.738613i	−0.0240002	+	0.0895699i
$69$	2.56634	−	12.6252i	0.308951	−	1.51990i
$70$	−6.23894	+	5.26759i	−0.745696	+	0.629598i
$71$	10.6224	+	2.84625i	1.26064	+	0.337788i	0.826438	−	0.563027i	$-0.190363\pi$
$71$	10.6224	+	2.84625i	1.26064	+	0.337788i	0.434203	+	0.900815i	$0.357030\pi$
$72$	−0.695077	−	5.64469i	−0.0819156	−	0.665233i
$73$		−	4.81106i		−	0.563092i	−0.959548	−	0.281546i	$-0.909153\pi$
$73$		−	4.81106i		−	0.563092i	0.959548	−	0.281546i	$-0.0908472\pi$
$74$	−6.89836	−	3.98277i	−0.801918	−	0.462987i
$75$	5.10755	−	6.99378i	0.589769	−	0.807572i
$76$	−0.422146	+	1.57547i	−0.0484235	+	0.180719i
$77$	7.69895	−	2.06293i	0.877377	−	0.235092i
$78$	−0.0946469	−	13.7670i	−0.0107166	−	1.55880i
$79$	−8.01195	+	4.62570i	−0.901415	+	0.520432i	−0.877659	−	0.479286i	$-0.840896\pi$
$79$	−8.01195	+	4.62570i	−0.901415	+	0.520432i	−0.0237561	+	0.999718i	$0.507563\pi$
$80$	1.16835	−	3.24072i	0.130625	−	0.362323i
$81$	8.73114	−	2.18338i	0.970127	−	0.242598i
$82$	−3.76955	+	14.0681i	−0.416277	+	1.55357i
$83$	−3.58683	−	6.21257i	−0.393706	−	0.681919i	0.599229	−	0.800578i	$-0.295474\pi$
$83$	−3.58683	−	6.21257i	−0.393706	−	0.681919i	−0.992935	+	0.118659i	$0.962140\pi$
$84$	7.34375	+	3.65986i	0.801269	+	0.399324i
$85$	0.490782	+	0.341424i	0.0532328	+	0.0370327i
$86$	26.9373	−	7.21782i	2.90472	−	0.778318i
$87$	−3.39477	+	0.208227i	−0.363958	+	0.0223243i
$88$	6.45043	−	6.45043i	0.687618	−	0.687618i
$89$	2.67869	+	9.99701i	0.283941	+	1.05968i	0.949610	+	0.313434i	$0.101480\pi$
$89$	2.67869	+	9.99701i	0.283941	+	1.05968i	−0.665669	+	0.746247i	$0.731854\pi$
$90$	−14.4206	−	3.27770i	−1.52007	−	0.345500i
$91$	5.00220	+	3.26289i	0.524373	+	0.342044i
$92$	20.5481	+	5.50585i	2.14229	+	0.574025i
$93$	−5.46747	+	1.83045i	−0.566950	+	0.189809i
$94$	−18.9871	+	10.9622i	−1.95837	+	1.13067i
$95$	1.04685	+	0.728263i	0.107404	+	0.0747182i
$96$	−12.4264	+	0.762202i	−1.26826	+	0.0777919i
$97$	2.56517	+	1.48100i	0.260454	+	0.150373i	0.624541	−	0.780992i	$-0.285286\pi$
$97$	2.56517	+	1.48100i	0.260454	+	0.150373i	−0.364088	+	0.931365i	$0.618619\pi$
$98$	8.12598	−	4.69153i	0.820848	−	0.473917i
$99$	11.3786	+	8.88355i	1.14359	+	0.892831i
$100$	11.0101	+	9.12472i	1.10101	+	0.912472i
$101$			12.3662i			1.23048i	0.788341	+	0.615239i	$0.210941\pi$
$101$			12.3662i			1.23048i	−0.788341	+	0.615239i	$0.789059\pi$
$102$	0.203364	−	1.00046i	0.0201361	−	0.0990603i
$103$	0.892741	+	3.33175i	0.0879644	+	0.328287i	0.995859	−	0.0909109i	$-0.0289778\pi$
$103$	0.892741	+	3.33175i	0.0879644	+	0.328287i	−0.907895	+	0.419198i	$0.862311\pi$
$104$	6.82521	+	0.371561i	0.669266	+	0.0364346i
$105$	4.63923	−	4.43097i	0.452742	−	0.432418i
$106$	1.29576	−	1.29576i	0.125855	−	0.125855i
$107$	−4.91990	−	18.3613i	−0.475625	−	1.77506i	−0.619002	−	0.785389i	$-0.712463\pi$
$107$	−4.91990	−	18.3613i	−0.475625	−	1.77506i	0.143377	−	0.989668i	$-0.454204\pi$
$108$	2.71578	+	14.6105i	0.261327	+	1.40589i
$109$	3.96857	+	3.96857i	0.380120	+	0.380120i	0.871145	−	0.491025i	$-0.163378\pi$
$109$	3.96857	+	3.96857i	0.380120	+	0.380120i	−0.491025	+	0.871145i	$0.663378\pi$
$110$	−10.0901	−	21.4671i	−0.962051	−	2.04681i
$111$	5.60130	+	2.79149i	0.531652	+	0.264956i
$112$	1.27594	−	2.21000i	0.120565	−	0.208825i
$113$	−14.4637	−	14.4637i	−1.36063	−	1.36063i	−0.873111	−	0.487521i	$-0.837901\pi$
$113$	−14.4637	−	14.4637i	−1.36063	−	1.36063i	−0.487521	−	0.873111i	$-0.662099\pi$
$114$	0.433779	−	2.13400i	0.0406271	−	0.199867i
$115$	9.49838	−	13.6535i	0.885728	−	1.27320i
$116$		−	5.61595i		−	0.521428i
$117$	0.736428	+	10.7916i	0.0680828	+	0.997680i
$118$	−0.0517663	−	0.0517663i	−0.00476547	−	0.00476547i
$119$	0.313163	+	0.313163i	0.0287076	+	0.0287076i
$120$	2.06263	−	7.04663i	0.188291	−	0.643266i
$121$			12.1544i			1.10495i
$122$	7.45886	+	4.30638i	0.675294	+	0.389881i
$123$	2.27940	−	11.2136i	0.205527	−	1.01110i
$124$	−2.46404	−	9.19593i	−0.221278	−	0.825819i
$125$	9.63092	−	5.67850i	0.861416	−	0.507900i
$126$	−10.0855	−	4.27690i	−0.898489	−	0.381016i
$127$	−13.3973	+	3.58980i	−1.18882	+	0.318543i	−0.798419	−	0.602103i	$-0.794330\pi$
$127$	−13.3973	+	3.58980i	−1.18882	+	0.318543i	−0.390399	+	0.920646i	$0.627663\pi$
$128$		−	13.7643i		−	1.21660i
$129$	−20.7772	+	6.95597i	−1.82933	+	0.612439i
$130$	6.92791	−	16.3677i	0.607618	−	1.43554i
$131$	−8.34404	+	14.4523i	−0.729022	+	1.26270i	0.228275	+	0.973597i	$0.426692\pi$
$131$	−8.34404	+	14.4523i	−0.729022	+	1.26270i	−0.957297	+	0.289107i	$0.906642\pi$
$132$	−15.7912	+	17.8549i	−1.37445	+	1.55407i
$133$	0.667982	+	0.667982i	0.0579214	+	0.0579214i
$134$	7.51640	+	13.0188i	0.649318	+	1.12465i
$135$	11.4664	+	1.87674i	0.986869	+	0.161524i
$136$	0.489605	+	0.131189i	0.0419833	+	0.0112494i
$137$	−1.17643	+	2.03764i	−0.100509	+	0.174087i	−0.911895	−	0.410424i	$-0.865381\pi$
$137$	−1.17643	+	2.03764i	−0.100509	+	0.174087i	0.811385	+	0.584512i	$0.198714\pi$
$138$	−27.8327	−	5.65757i	−2.36927	−	0.481604i
$139$		−	1.13584i		−	0.0963406i	−0.998839	−	0.0481703i	$-0.984661\pi$
$139$		−	1.13584i		−	0.0963406i	0.998839	−	0.0481703i	$-0.0153390\pi$
$140$	6.83367	+	8.09381i	0.577551	+	0.684052i
$141$	14.3625	−	9.50994i	1.20954	−	0.800881i
$142$	6.27464	−	23.4173i	0.526556	−	1.96513i
$143$	−12.9167	+	11.5830i	−1.08015	+	0.968618i
$144$	4.58716	−	0.564855i	0.382263	−	0.0470712i
$145$	−4.13063	−	1.48918i	−0.343030	−	0.123670i
$146$	−10.6061			−0.877769
$147$	−6.14676	+	4.06999i	−0.506976	+	0.335687i
$148$	−5.16686	+	8.94927i	−0.424714	+	0.735625i
$149$	−1.90822	−	1.90822i	−0.156328	−	0.156328i	0.624610	−	0.780937i	$-0.285258\pi$
$149$	−1.90822	−	1.90822i	−0.156328	−	0.156328i	−0.780937	+	0.624610i	$0.785258\pi$
$150$	−15.4180	−	11.2597i	−1.25887	−	0.919354i
$151$	2.25535	−	8.41707i	0.183538	−	0.684971i	−0.811401	−	0.584489i	$-0.801295\pi$
$151$	2.25535	−	8.41707i	0.183538	−	0.684971i	0.994939	−	0.100482i	$-0.0320385\pi$
$152$	1.04433	+	0.279828i	0.0847067	+	0.0226971i
$153$	−0.111356	+	0.794347i	−0.00900260	+	0.0642192i
$154$	−4.54778	−	16.9726i	−0.366471	−	1.36769i
$155$	−7.41715	−	0.626135i	−0.595760	−	0.0502924i
$156$	−17.8599	+	0.122786i	−1.42994	+	0.00983073i
$157$	0.158745	+	0.592443i	0.0126692	+	0.0472821i	0.971971	−	0.235100i	$-0.0755419\pi$
$157$	0.158745	+	0.592443i	0.0126692	+	0.0472821i	−0.959302	+	0.282383i	$0.908875\pi$
$158$	10.1975	+	17.6626i	0.811269	+	1.40516i
$159$	−0.953811	+	1.07847i	−0.0756422	+	0.0855279i
$160$	−15.1199	−	5.45105i	−1.19533	−	0.430944i
$161$	8.71216	−	8.71216i	0.686615	−	0.686615i
$162$	−4.81333	−	19.2481i	−0.378171	−	1.51227i
$163$	−4.39178	+	2.53560i	−0.343991	+	0.198603i	−0.662035	−	0.749473i	$-0.730307\pi$
$163$	−4.39178	+	2.53560i	−0.343991	+	0.198603i	0.318045	+	0.948076i	$0.396974\pi$
$164$	18.2507	+	4.89025i	1.42514	+	0.381864i
$165$	8.94528	+	16.3493i	0.696389	+	1.27279i
$166$	−13.6958	+	7.90727i	−1.06300	+	0.613723i
$167$	−9.70001	−	16.8009i	−0.750609	−	1.30009i	−0.947528	−	0.319674i	$-0.896427\pi$
$167$	−9.70001	−	16.8009i	−0.750609	−	1.30009i	0.196918	−	0.980420i	$-0.436907\pi$
$168$	2.42602	−	4.86796i	0.187171	−	0.375571i
$169$	−12.9232	−	1.41125i	−0.994090	−	0.108557i
$170$	0.752679	−	1.08194i	0.0577279	−	0.0829813i
$171$	−0.237524	+	1.69435i	−0.0181639	+	0.129571i
$172$	−9.36372	−	34.9459i	−0.713977	−	2.66460i
$173$	−1.07888	−	4.02642i	−0.0820254	−	0.306123i	0.912709	−	0.408610i	$-0.133987\pi$
$173$	−1.07888	−	4.02642i	−0.0820254	−	0.306123i	−0.994734	+	0.102487i	$0.967320\pi$
$174$	0.459042	+	7.48388i	0.0347999	+	0.567351i
$175$	7.76521	−	2.88005i	0.586995	−	0.217711i
$176$	5.24195	+	5.24195i	0.395127	+	0.395127i
$177$	0.0430854	+	0.0381054i	0.00323850	+	0.00286417i
$178$	22.0387	−	5.90525i	1.65187	−	0.442617i
$179$	0.920848	−	1.59496i	0.0688274	−	0.119213i	−0.829558	−	0.558421i	$-0.811408\pi$
$179$	0.920848	−	1.59496i	0.0688274	−	0.119213i	0.898385	+	0.439208i	$0.144741\pi$
$180$	−4.25218	+	18.7079i	−0.316939	+	1.39441i
$181$		−	10.0912i		−	0.750072i	−0.927010	−	0.375036i	$-0.877630\pi$
$181$		−	10.0912i		−	0.750072i	0.927010	−	0.375036i	$-0.122370\pi$
$182$	7.19314	−	11.0275i	0.533191	−	0.817412i
$183$	−6.05642	−	3.01830i	−0.447703	−	0.223119i
$184$	3.64967	−	13.6207i	0.269057	−	1.00413i
$185$	5.21225	+	6.17339i	0.383212	+	0.453877i
$186$	4.03527	+	12.0532i	0.295881	+	0.883782i
$187$	−1.11420	+	0.643283i	−0.0814783	+	0.0470415i
$188$	14.2214	+	24.6321i	1.03720	+	1.79648i
$189$	8.11483	+	2.86884i	0.590267	+	0.208677i
$190$	1.60548	−	2.30780i	0.116473	−	0.167425i
$191$	−8.31473	+	14.4015i	−0.601632	+	1.04206i	0.390942	+	0.920415i	$0.372149\pi$
$191$	−8.31473	+	14.4015i	−0.601632	+	1.04206i	−0.992574	+	0.121642i	$0.961184\pi$
$192$	1.35356	+	22.0675i	0.0976851	+	1.59258i
$193$	22.7720	−	13.1474i	1.63917	−	0.946374i	0.658047	−	0.752977i	$-0.271383\pi$
$193$	22.7720	−	13.1474i	1.63917	−	0.946374i	0.981121	−	0.193397i	$-0.0619505\pi$
$194$	3.26491	−	5.65499i	0.234407	−	0.406005i
$195$	−4.64560	+	13.1688i	−0.332678	+	0.943040i
$196$	−6.08635	−	10.5419i	−0.434739	−	0.752991i
$197$	18.8909	+	10.9067i	1.34592	+	0.777070i	0.987669	−	0.156554i	$-0.0500386\pi$
$197$	18.8909	+	10.9067i	1.34592	+	0.777070i	0.358255	+	0.933624i	$0.383372\pi$
$198$	19.5840	−	25.0844i	1.39178	−	1.78267i
$199$	−0.0984258	−	0.170478i	−0.00697722	−	0.0120849i	0.862516	−	0.506030i	$-0.168888\pi$
$199$	−0.0984258	−	0.170478i	−0.00697722	−	0.0120849i	−0.869493	+	0.493945i	$0.835554\pi$
$200$	6.04851	−	7.29826i	0.427694	−	0.516065i
$201$	−6.52062	−	9.84785i	−0.459929	−	0.694614i
$202$	27.2615			1.91812
$203$	−2.81687	−	1.62632i	−0.197706	−	0.114145i
$204$	−1.29790	−	0.263826i	−0.0908713	−	0.0184715i
$205$	8.43638	−	12.1269i	0.589222	−	0.846981i
$206$	7.34495	−	1.96807i	0.511747	−	0.137122i
$207$	22.0986	+	3.09791i	1.53596	+	0.215320i
$208$	−0.301950	+	5.54651i	−0.0209364	+	0.384581i
$209$	−2.37660	+	1.37213i	−0.164393	+	0.0949124i
$210$	−9.76820	−	10.2273i	−0.674070	−	0.705752i
$211$	−9.25914	−	16.0373i	−0.637425	−	1.10405i	−0.985996	−	0.166770i	$-0.946666\pi$
$211$	−9.25914	−	16.0373i	−0.637425	−	1.10405i	0.348571	−	0.937283i	$-0.386667\pi$
$212$	−1.68099	−	1.68099i	−0.115451	−	0.115451i
$213$	−3.79421	+	18.6658i	−0.259975	+	1.27896i
$214$	−40.4781	+	10.8461i	−2.76702	+	0.741422i
$215$	−28.1863	−	2.37941i	−1.92229	−	0.162274i
$216$	9.68484	−	1.80021i	0.658970	−	0.122489i
$217$	−5.32609	−	1.42712i	−0.361559	−	0.0968794i
$218$	8.74883	−	8.74883i	0.592545	−	0.592545i
$219$	8.31737	−	0.510166i	0.562036	−	0.0344738i
$220$	−27.8494	+	13.0899i	−1.87761	+	0.882521i
$221$	−0.916234	−	0.299756i	−0.0616326	−	0.0201638i
$222$	6.15391	−	12.3482i	0.413023	−	0.828758i
$223$	26.7905			1.79403			0.897013	−	0.442004i	$-0.145732\pi$
$223$	26.7905			1.79403			0.897013	+	0.442004i	$0.145732\pi$
$224$	−10.3110	−	5.95305i	−0.688932	−	0.397755i
$225$	12.6325	+	8.08832i	0.842164	+	0.539222i
$226$	−31.8857	+	31.8857i	−2.12100	+	2.12100i
$227$	−3.06658	−	1.77049i	−0.203536	−	0.117512i	0.394768	−	0.918781i	$-0.370825\pi$
$227$	−3.06658	−	1.77049i	−0.203536	−	0.117512i	−0.598304	+	0.801269i	$0.704158\pi$
$228$	−2.76844	−	0.562744i	−0.183345	−	0.0372686i
$229$	−5.83721	−	21.7848i	−0.385734	−	1.43958i	−0.837007	−	0.547192i	$-0.815697\pi$
$229$	−5.83721	−	21.7848i	−0.385734	−	1.43958i	0.451273	−	0.892386i	$-0.350970\pi$
$230$	−30.0995	−	20.9394i	−1.98470	−	1.38071i
$231$	4.38279	+	13.0912i	0.288367	+	0.861338i
$232$	−3.72265			−0.244404
$233$	−6.98913	+	6.98913i	−0.457873	+	0.457873i	−0.897957	−	0.440084i	$-0.854949\pi$
$233$	−6.98913	+	6.98913i	−0.457873	+	0.457873i	0.440084	+	0.897957i	$0.354949\pi$
$234$	23.7903	−	1.62348i	1.55522	−	0.106130i
$235$	21.8884	−	3.92836i	1.42784	−	0.256258i
$236$	−0.0671567	+	0.0671567i	−0.00437153	+	0.00437153i
$237$	−8.84651	−	13.3606i	−0.574643	−	0.867862i
$238$	0.690377	−	0.690377i	0.0447505	−	0.0447505i
$239$	21.0066	−	5.62870i	1.35880	−	0.364091i	0.495427	−	0.868649i	$-0.335011\pi$
$239$	21.0066	−	5.62870i	1.35880	−	0.364091i	0.863377	+	0.504559i	$0.168345\pi$
$240$	5.72645	+	1.67619i	0.369641	+	0.108198i
$241$	6.99344	−	1.87389i	0.450487	−	0.120708i	−0.0264401	−	0.999650i	$-0.508417\pi$
$241$	6.99344	−	1.87389i	0.450487	−	0.120708i	0.476927	+	0.878943i	$0.341750\pi$
$242$	26.7948			1.72244
$243$	4.70049	+	14.8629i	0.301536	+	0.953455i
$244$	5.58668	−	9.67642i	0.357651	−	0.619469i
$245$	−9.36764	+	1.68123i	−0.598476	+	0.107410i
$246$	−24.7207	−	5.02501i	−1.57614	−	0.320383i
$247$	−1.95434	−	0.639384i	−0.124352	−	0.0406830i
$248$	−6.09571	+	1.63334i	−0.387078	+	0.103717i
$249$	10.3600	−	6.85970i	0.656536	−	0.434716i
$250$	−12.5184	−	21.2316i	−0.791734	−	1.34281i
$251$	−21.4587	+	12.3892i	−1.35446	+	0.781999i	−0.988871	−	0.148777i	$-0.952466\pi$
$251$	−21.4587	+	12.3892i	−1.35446	+	0.781999i	−0.365590	+	0.930776i	$0.619133\pi$
$252$	−5.54844	+	13.0840i	−0.349519	+	0.824213i
$253$	17.8961	+	30.9969i	1.12512	+	1.94876i
$254$	7.91381	+	29.5347i	0.496556	+	1.85317i
$255$	−0.538212	+	0.884670i	−0.0337041	+	0.0554002i
$256$	−4.81447			−0.300904
$257$	6.11414	−	22.8183i	0.381390	−	1.42337i	−0.462390	−	0.886676i	$-0.653008\pi$
$257$	6.11414	−	22.8183i	0.381390	−	1.42337i	0.843780	−	0.536689i	$-0.180325\pi$
$258$	15.3346	+	45.8038i	0.954692	+	2.85162i
$259$	2.99254	+	5.18323i	0.185947	+	0.322070i
$260$	−21.2339	−	8.98761i	−1.31687	−	0.557388i
$261$	−0.719966	−	5.84681i	−0.0445648	−	0.361909i
$262$	31.8605	+	18.3947i	1.96835	+	1.13643i
$263$	7.12321	+	7.12321i	0.439236	+	0.439236i	0.891755	−	0.452519i	$-0.149475\pi$
$263$	7.12321	+	7.12321i	0.439236	+	0.439236i	−0.452519	+	0.891755i	$0.649475\pi$
$264$	11.8355	+	10.4675i	0.728426	+	0.644231i
$265$	−1.68215	+	0.790650i	−0.103333	+	0.0485693i
$266$	1.47258	−	1.47258i	0.0902900	−	0.0902900i
$267$	−16.9988	+	5.69101i	−1.04031	+	0.348284i
$268$	16.8893	−	9.75107i	1.03168	−	0.595641i
$269$	12.8231	−	7.40344i	0.781841	−	0.451396i	−0.0552417	−	0.998473i	$-0.517593\pi$
$269$	12.8231	−	7.40344i	0.781841	−	0.451396i	0.837082	+	0.547077i	$0.184260\pi$
$270$	4.13733	−	25.2780i	0.251790	−	1.53837i
$271$	−15.9258	+	4.26732i	−0.967426	+	0.259221i	−0.707741	−	0.706472i	$-0.750286\pi$
$271$	−15.9258	+	4.26732i	−0.967426	+	0.259221i	−0.259685	+	0.965693i	$0.583619\pi$
$272$	−0.106611	+	0.397878i	−0.00646424	+	0.0241249i
$273$	−5.11046	+	8.99381i	−0.309299	+	0.544330i
$274$	4.49204	+	2.59348i	0.271374	+	0.156678i
$275$	2.24304	+	23.9547i	0.135260	+	1.44453i
$276$	−7.33960	+	36.1075i	−0.441792	+	2.17341i
$277$	−15.4780	+	4.14731i	−0.929982	+	0.249188i	−0.691847	−	0.722044i	$-0.743203\pi$
$277$	−15.4780	+	4.14731i	−0.929982	+	0.249188i	−0.238135	+	0.971232i	$0.576536\pi$
$278$	−2.50399			−0.150179
$279$	−3.74425	−	9.25806i	−0.224163	−	0.554266i
$280$	5.36515	−	4.52984i	0.320629	−	0.270710i
$281$	−3.91318	+	14.6042i	−0.233441	+	0.871213i	0.745405	+	0.666612i	$0.232256\pi$
$281$	−3.91318	+	14.6042i	−0.233441	+	0.871213i	−0.978846	+	0.204601i	$0.934410\pi$
$282$	−20.9649	−	31.6626i	−1.24844	−	1.88548i
$283$	−9.08155	−	2.43339i	−0.539842	−	0.144650i	−0.0214127	−	0.999771i	$-0.506816\pi$
$283$	−9.08155	−	2.43339i	−0.539842	−	0.144650i	−0.518429	+	0.855121i	$0.673483\pi$
$284$	−30.3793	−	8.14012i	−1.80268	−	0.483027i
$285$	−1.14801	+	1.88701i	−0.0680025	+	0.111777i
$286$	25.5350	+	28.4753i	1.50992	+	1.68378i
$287$	7.73807	−	7.73807i	0.456764	−	0.456764i
$288$	−2.63539	−	21.4019i	−0.155292	−	1.26112i
$289$	14.6605	+	8.46426i	0.862384	+	0.497897i
$290$	−3.28294	+	9.10609i	−0.192781	+	0.534728i
$291$	−2.28835	+	4.59172i	−0.134145	+	0.269171i
$292$			13.7594i			0.805206i
$293$			10.6470i			0.622007i	0.950409	+	0.311003i	$0.100665\pi$
$293$			10.6470i			0.622007i	−0.950409	+	0.311003i	$0.899335\pi$
$294$	8.97241	+	13.5507i	0.523282	+	0.790293i
$295$	0.0315870	+	0.0672028i	0.00183906	+	0.00391270i
$296$	5.93221	+	3.42496i	0.344803	+	0.199072i
$297$	−14.1513	+	20.6134i	−0.821142	+	1.19611i
$298$	−4.20673	+	4.20673i	−0.243689	+	0.243689i
$299$	−8.33918	+	25.4895i	−0.482267	+	1.47410i
$300$	−14.6073	+	20.0018i	−0.843354	+	1.15481i
$301$	−20.2399	−	5.42327i	−1.16661	−	0.312592i
$302$	−18.5557	−	4.97198i	−1.06776	−	0.286105i
$303$	−21.3786	+	1.31131i	−1.22817	+	0.0753328i
$304$	−0.227403	+	0.848679i	−0.0130424	+	0.0486751i
$305$	−5.63575	−	6.67499i	−0.322702	−	0.382209i
$306$	1.75116	+	0.245488i	0.100107	+	0.0140336i
$307$	−7.02494			−0.400935			−0.200467	−	0.979700i	$-0.564246\pi$
$307$	−7.02494			−0.400935			−0.200467	+	0.979700i	$0.564246\pi$
$308$	−22.0186	+	5.89986i	−1.25463	+	0.336176i
$309$	−5.66528	+	1.89667i	−0.322286	+	0.107898i
$310$	−1.38033	+	16.3513i	−0.0783977	+	0.928693i
$311$	10.8300	+	6.25270i	0.614113	+	0.354558i	0.774573	−	0.632484i	$-0.217965\pi$
$311$	10.8300	+	6.25270i	0.614113	+	0.354558i	−0.160461	+	0.987042i	$0.551298\pi$
$312$	0.0813911	+	11.8388i	0.00460787	+	0.670242i
$313$	−2.81600	+	10.5095i	−0.159170	+	0.594030i	0.839542	+	0.543294i	$0.182823\pi$
$313$	−2.81600	+	10.5095i	−0.159170	+	0.594030i	−0.998712	+	0.0507357i	$0.983843\pi$
$314$	1.30606	−	0.349957i	0.0737051	−	0.0197492i
$315$	8.15221	+	7.55045i	0.459325	+	0.425419i
$316$	22.9137	−	13.2293i	1.28900	−	0.744204i
$317$	4.81192	−	2.77816i	0.270264	−	0.156037i	−0.358744	−	0.933436i	$-0.616795\pi$
$317$	4.81192	−	2.77816i	0.270264	−	0.156037i	0.629008	+	0.777399i	$0.283461\pi$
$318$	2.37751	+	2.10270i	0.133324	+	0.117914i
$319$	6.68141	−	6.68141i	0.374087	−	0.374087i
$320$	−9.68031	+	26.8509i	−0.541146	+	1.50101i
$321$	31.2214	−	10.4526i	1.74261	−	0.583406i
$322$	−19.2062	−	19.2062i	−1.07032	−	1.07032i
$323$	−0.132055	−	0.0762420i	−0.00734774	−	0.00424222i
$324$	−24.9706	+	6.24435i	−1.38726	+	0.346908i
$325$	−12.2411	+	13.2346i	−0.679015	+	0.734125i
$326$	5.58979	+	9.68181i	0.309590	+	0.536226i
$327$	−6.44004	+	7.28170i	−0.356135	+	0.402679i
$328$	3.24160	−	12.0978i	0.178988	−	0.667991i
$329$	16.4734			0.908209
$330$	36.0424	−	19.7201i	1.98407	−	1.08556i
$331$	−0.0216613	−	0.0808412i	−0.00119062	−	0.00444344i	0.965328	−	0.261040i	$-0.0840655\pi$
$331$	−0.0216613	−	0.0808412i	−0.00119062	−	0.00444344i	−0.966519	+	0.256597i	$0.917399\pi$
$332$	10.2581	+	17.7676i	0.562989	+	0.975125i
$333$	−4.23196	+	9.97955i	−0.231910	+	0.546876i
$334$	−37.0381	+	21.3839i	−2.02663	+	1.17008i
$335$	−2.69354	−	15.0081i	−0.147164	−	0.819979i
$336$	3.95595	+	1.97150i	0.215815	+	0.107554i
$337$	20.4029	−	5.46694i	1.11142	−	0.297803i	0.344011	−	0.938966i	$-0.388214\pi$
$337$	20.4029	−	5.46694i	1.11142	−	0.297803i	0.767405	+	0.641163i	$0.221548\pi$
$338$	−3.11113	+	28.4895i	−0.169223	+	1.54962i
$339$	23.4712	−	26.5386i	1.27478	−	1.44138i
$340$	−1.40361	−	0.976455i	−0.0761215	−	0.0529557i
$341$	8.00906	−	13.8721i	0.433715	−	0.751216i
$342$	3.73525	+	0.523629i	0.201979	+	0.0283146i
$343$	−18.6451			−1.00674
$344$	−23.1646	+	6.20693i	−1.24895	+	0.334655i
$345$	24.6114	+	14.9730i	1.32503	+	0.806119i
$346$	−8.87635	+	2.37841i	−0.477196	+	0.127864i
$347$	−11.6659	+	11.6659i	−0.626260	+	0.626260i	−0.947125	−	0.320865i	$-0.896026\pi$
$347$	−11.6659	+	11.6659i	−0.626260	+	0.626260i	0.320865	+	0.947125i	$0.396026\pi$
$348$	9.70887	−	0.595517i	0.520450	−	0.0319231i
$349$	13.0370	−	13.0370i	0.697854	−	0.697854i	−0.266094	−	0.963947i	$-0.585733\pi$
$349$	13.0370	−	13.0370i	0.697854	−	0.697854i	0.963947	+	0.266094i	$0.0857330\pi$
$350$	−6.34915	−	17.1186i	−0.339377	−	0.915030i
$351$	−18.5784	+	2.41748i	−0.991640	+	0.129035i
$352$	24.4569	−	24.4569i	1.30356	−	1.30356i
$353$	15.7675			0.839220			0.419610	−	0.907704i	$-0.362167\pi$
$353$	15.7675			0.839220			0.419610	+	0.907704i	$0.362167\pi$
$354$	0.0840043	−	0.0949830i	0.00446478	−	0.00504829i
$355$	−14.0429	+	20.1860i	−0.745318	+	1.07136i
$356$	−7.66091	−	28.5909i	−0.406027	−	1.51532i
$357$	−0.508189	+	0.574605i	−0.0268962	+	0.0304113i
$358$	−3.51612	−	2.03004i	−0.185833	−	0.107291i
$359$	−16.5257	+	16.5257i	−0.872192	+	0.872192i	−0.992711	−	0.120519i	$-0.961544\pi$
$359$	−16.5257	+	16.5257i	−0.872192	+	0.872192i	0.120519	+	0.992711i	$0.461544\pi$
$360$	12.4009	+	2.81864i	0.653587	+	0.148556i
$361$	16.1728	+	9.33737i	0.851200	+	0.491441i
$362$	−22.2463			−1.16924
$363$	−21.0126	+	1.28886i	−1.10288	+	0.0676476i
$364$	−14.3060	−	9.33170i	−0.749839	−	0.489114i
$365$	10.1203	+	3.64857i	0.529718	+	0.190975i
$366$	−6.65393	+	13.3515i	−0.347807	+	0.697896i
$367$	16.8291	−	16.8291i	0.878474	−	0.878474i	−0.114903	−	0.993377i	$-0.536656\pi$
$367$	16.8291	−	16.8291i	0.878474	−	0.878474i	0.993377	+	0.114903i	$0.0366557\pi$
$368$	11.0689	+	2.96590i	0.577007	+	0.154608i
$369$	19.6278	+	2.75154i	1.02178	+	0.143239i
$370$	13.6094	−	11.4905i	0.707520	−	0.597365i
$371$	−1.32996	+	0.356361i	−0.0690479	+	0.0185013i
$372$	15.6367	−	5.23498i	0.810723	−	0.271421i
$373$	−6.80994	−	6.80994i	−0.352605	−	0.352605i	0.508473	−	0.861078i	$-0.330210\pi$
$373$	−6.80994	−	6.80994i	−0.352605	−	0.352605i	−0.861078	+	0.508473i	$0.830210\pi$
$374$	1.41814	+	2.45628i	0.0733301	+	0.127011i
$375$	10.8383	+	16.0478i	0.559685	+	0.828705i
$376$	16.3279	−	9.42692i	0.842047	−	0.486156i
$377$	7.06960	+	0.384866i	0.364103	+	0.0198216i
$378$	6.32444	−	17.8894i	0.325294	−	0.920130i
$379$	−1.23911	+	0.332017i	−0.0636486	+	0.0170546i	−0.290503	−	0.956874i	$-0.593823\pi$
$379$	−1.23911	+	0.332017i	−0.0636486	+	0.0170546i	0.226854	+	0.973929i	$0.427156\pi$
$380$	−2.99392	−	2.08279i	−0.153585	−	0.106845i
$381$	−7.62670	−	22.7806i	−0.390728	−	1.16709i
$382$	31.7486	+	18.3300i	1.62440	+	0.937847i
$383$	−14.5135			−0.741604			−0.370802	−	0.928712i	$-0.620917\pi$
$383$	−14.5135			−0.741604			−0.370802	+	0.928712i	$0.620917\pi$
$384$	23.7957	−	1.45957i	1.21432	−	0.0744832i
$385$	−1.49921	+	17.7595i	−0.0764067	+	0.905108i
$386$	−28.9839	−	50.2016i	−1.47524	−	2.55519i
$387$	−14.2287	−	35.1820i	−0.723286	−	1.78840i
$388$	−7.33625	−	4.23558i	−0.372441	−	0.215029i
$389$	−11.0250	−	19.0959i	−0.558990	−	0.968199i	−0.997581	−	0.0695123i	$-0.977856\pi$
$389$	−11.0250	−	19.0959i	−0.558990	−	0.968199i	0.438591	−	0.898687i	$-0.355478\pi$
$390$	29.0311	+	10.2414i	1.47005	+	0.518591i
$391$	−0.994387	+	1.72233i	−0.0502883	+	0.0871019i
$392$	−6.98790	+	4.03446i	−0.352942	+	0.203771i
$393$	−25.8700	−	12.8927i	−1.30497	−	0.650349i
$394$	24.0441	−	41.6456i	1.21132	−	2.09808i
$395$	−3.65432	−	20.3614i	−0.183869	−	1.02450i
$396$	−32.5422	−	25.4065i	−1.63531	−	1.27672i
$397$	−17.2655	−	29.9046i	−0.866528	−	1.50087i	−0.865522	−	0.500871i	$-0.833013\pi$
$397$	−17.2655	−	29.9046i	−0.866528	−	1.50087i	−0.00100631	−	0.999999i	$-0.500320\pi$
$398$	−0.375825	+	0.216982i	−0.0188384	+	0.0108763i
$399$	−1.08398	+	1.22564i	−0.0542666	+	0.0613588i
$400$	5.93093	+	4.91533i	0.296547	+	0.245766i
$401$	−0.316230	+	1.18018i	−0.0157917	+	0.0589356i	−0.973372	−	0.229231i	$-0.926379\pi$
$401$	−0.316230	+	1.18018i	−0.0157917	+	0.0589356i	0.957580	+	0.288166i	$0.0930456\pi$
$402$	−21.7099	+	14.3749i	−1.08279	+	0.716954i
$403$	11.7451	−	2.47164i	0.585065	−	0.123121i
$404$		−	35.3665i		−	1.75955i
$405$	−2.02861	+	20.0221i	−0.100803	+	0.994906i
$406$	−3.58527	+	6.20987i	−0.177934	+	0.308191i
$407$	−16.7942	+	4.50000i	−0.832459	+	0.223057i
$408$	−0.174882	+	0.860341i	−0.00865796	+	0.0425932i
$409$	2.00360	+	2.00360i	0.0990716	+	0.0990716i	0.754905	−	0.655834i	$-0.227683\pi$
$409$	2.00360	+	2.00360i	0.0990716	+	0.0990716i	−0.655834	+	0.754905i	$0.727683\pi$
$410$	−26.7342	−	18.5982i	−1.32031	−	0.918502i
$411$	−3.64743	−	1.81775i	−0.179914	−	0.0896628i
$412$	−2.55319	−	9.52863i	−0.125787	−	0.469442i
$413$	0.0142368	+	0.0531326i	0.000700548	+	0.00261448i
$414$	6.82944	−	48.7171i	0.335648	−	2.39431i
$415$	15.7885	−	2.83361i	0.775029	−	0.139096i
$416$	25.8778	+	1.40878i	1.26877	+	0.0690711i
$417$	1.96364	−	0.120445i	0.0961599	−	0.00589820i
$418$	3.02491	+	5.23929i	0.147953	+	0.256262i
$419$	−1.88653	+	1.08919i	−0.0921632	+	0.0532104i	−0.545373	−	0.838193i	$-0.683612\pi$
$419$	−1.88653	+	1.08919i	−0.0921632	+	0.0532104i	0.453210	+	0.891404i	$0.350279\pi$
$420$	−13.2679	+	12.6723i	−0.647409	+	0.618347i
$421$	−6.48467	−	1.73756i	−0.316043	−	0.0846836i	0.0973104	−	0.995254i	$-0.468976\pi$
$421$	−6.48467	−	1.73756i	−0.316043	−	0.0846836i	−0.413354	+	0.910571i	$0.635643\pi$
$422$	−35.3547	+	20.4120i	−1.72104	+	0.993642i
$423$	17.9638	+	23.8215i	0.873430	+	1.15824i
$424$	−1.11428	+	1.11428i	−0.0541142	+	0.0541142i
$425$	−1.09039	+	0.773454i	−0.0528919	+	0.0375180i
$426$	41.1492	+	8.36443i	1.99368	+	0.405258i
$427$	−3.23569	−	5.60438i	−0.156586	−	0.271215i
$428$	14.0707	+	52.5124i	0.680131	+	2.53828i
$429$	−21.3944	−	21.1022i	−1.03293	−	1.01882i
$430$	−5.24547	+	62.1374i	−0.252959	+	2.99653i
$431$	−8.59295	−	32.0693i	−0.413908	−	1.54473i	−0.787013	−	0.616936i	$-0.788374\pi$
$431$	−8.59295	−	32.0693i	−0.413908	−	1.54473i	0.373105	−	0.927789i	$-0.378293\pi$
$432$	1.46295	+	7.87039i	0.0703860	+	0.378665i
$433$	5.95909	+	1.59673i	0.286376	+	0.0767341i	0.399147	−	0.916887i	$-0.369306\pi$
$433$	5.95909	+	1.59673i	0.286376	+	0.0767341i	−0.112772	+	0.993621i	$0.535973\pi$
$434$	−3.14613	+	11.7415i	−0.151019	+	0.563611i
$435$	2.13648	−	7.29895i	0.102437	−	0.349958i
$436$	−11.3499	−	11.3499i	−0.543561	−	0.543561i
$437$	−2.12104	+	3.67375i	−0.101463	+	0.175739i
$438$	−1.12468	−	18.3359i	−0.0537391	−	0.876122i
$439$	5.03101			0.240117			0.120059	−	0.992767i	$-0.461692\pi$
$439$	5.03101			0.240117			0.120059	+	0.992767i	$0.461692\pi$
$440$	8.67692	+	18.4605i	0.413656	+	0.880072i
$441$	−7.68801	−	10.1949i	−0.366096	−	0.485474i
$442$	−0.660821	+	2.01986i	−0.0314320	+	0.0960751i
$443$	−0.897963	+	3.35124i	−0.0426635	+	0.159222i	−0.983971	−	0.178327i	$-0.942931\pi$
$443$	−0.897963	+	3.35124i	−0.0426635	+	0.159222i	0.941308	+	0.337550i	$0.109598\pi$
$444$	−16.0194	−	7.98350i	−0.760248	−	0.378880i
$445$	−23.0605	−	1.94671i	−1.09317	−	0.0922827i
$446$		−	59.0605i		−	2.79659i
$447$	3.09659	−	3.50128i	0.146464	−	0.165605i
$448$	−10.5718	+	18.3109i	−0.499470	+	0.865107i
$449$	4.13098	+	1.10689i	0.194953	+	0.0522375i	0.354974	−	0.934876i	$-0.384490\pi$
$449$	4.13098	+	1.10689i	0.194953	+	0.0522375i	−0.160021	+	0.987114i	$0.551156\pi$
$450$	17.8309	−	27.8486i	0.840558	−	1.31280i
$451$	15.8951	+	27.5312i	0.748473	+	1.29639i
$452$	41.3655	+	41.3655i	1.94567	+	1.94567i
$453$	14.7906	+	3.00650i	0.694923	+	0.141258i
$454$	−3.90310	+	6.76036i	−0.183181	+	0.317280i
$455$	−10.6571	+	8.04784i	−0.499615	+	0.377289i
$456$	−0.373026	+	1.83512i	−0.0174686	+	0.0859374i
$457$		−	1.86701i		−	0.0873350i	−0.999046	−	0.0436675i	$-0.986096\pi$
$457$		−	1.86701i		−	0.0873350i	0.999046	−	0.0436675i	$-0.0139042\pi$
$458$	−48.0251	+	12.8683i	−2.24407	+	0.601296i
$459$	−1.38508	−	0.108280i	−0.0646499	−	0.00505407i
$460$	−27.1648	+	39.0483i	−1.26657	+	1.82064i
$461$	0.859116	+	3.20626i	0.0400130	+	0.149331i	0.983042	−	0.183379i	$-0.0587037\pi$
$461$	0.859116	+	3.20626i	0.0400130	+	0.149331i	−0.943029	+	0.332710i	$0.892037\pi$
$462$	28.8599	−	9.66199i	1.34269	−	0.449516i
$463$	−17.6901	−	10.2134i	−0.822131	−	0.474657i	0.0290199	−	0.999579i	$-0.490761\pi$
$463$	−17.6901	−	10.2134i	−0.822131	−	0.474657i	−0.851151	+	0.524921i	$0.824095\pi$
$464$		−	3.02522i		−	0.140442i
$465$	0.295947	−	12.8892i	0.0137242	−	0.597722i
$466$	15.4077	+	15.4077i	0.713750	+	0.713750i
$467$	−11.6246	−	11.6246i	−0.537921	−	0.537921i	0.384997	−	0.922918i	$-0.374202\pi$
$467$	−11.6246	−	11.6246i	−0.537921	−	0.537921i	−0.922918	+	0.384997i	$0.874202\pi$
$468$	−2.10614	−	30.8633i	−0.0973566	−	1.42665i
$469$		−	11.2952i		−	0.521565i
$470$	−8.66019	−	48.2536i	−0.399465	−	2.22577i
$471$	−1.00738	+	0.337261i	−0.0464178	+	0.0155402i
$472$	0.0445162	+	0.0445162i	0.00204902	+	0.00204902i
$473$	30.4356	−	52.7160i	1.39943	−	2.42388i
$474$	−29.4538	+	19.5024i	−1.35286	+	0.895774i
$475$	−2.32583	+	1.64979i	−0.106716	+	0.0756974i
$476$	−0.895630	−	0.895630i	−0.0410511	−	0.0410511i
$477$	−1.96560	−	1.53459i	−0.0899985	−	0.0702640i
$478$	−12.4086	−	46.3097i	−0.567558	−	2.11816i
$479$	10.4768	−	10.4768i	0.478698	−	0.478698i	−0.426017	−	0.904715i	$-0.640084\pi$
$479$	10.4768	−	10.4768i	0.478698	−	0.478698i	0.904715	+	0.426017i	$0.140084\pi$
$480$	7.82047	−	26.7174i	0.356954	−	1.21948i
$481$	−10.9116	−	7.11757i	−0.497528	−	0.324533i
$482$	−4.13104	−	15.4172i	−0.188164	−	0.702236i
$483$	15.9854	+	14.1378i	0.727363	+	0.643291i
$484$		−	34.7610i		−	1.58005i
$485$	−5.06069	+	4.27279i	−0.229794	+	0.194017i
$486$	32.7657	−	10.3624i	1.48628	−	0.470046i
$487$	−6.87207	+	3.96759i	−0.311403	+	0.179789i	−0.647554	−	0.762019i	$-0.724208\pi$
$487$	−6.87207	+	3.96759i	−0.311403	+	0.179789i	0.336151	+	0.941808i	$0.390875\pi$
$488$	−6.41422	−	3.70325i	−0.290358	−	0.167638i
$489$	−4.84925	−	7.32364i	−0.219291	−	0.331187i
$490$	3.70632	+	20.6512i	0.167435	+	0.932927i
$491$	−11.7139	+	6.76302i	−0.528641	+	0.305211i	−0.740463	−	0.672097i	$-0.765394\pi$
$491$	−11.7139	+	6.76302i	−0.528641	+	0.305211i	0.211822	+	0.977308i	$0.432060\pi$
$492$	−6.51897	+	32.0703i	−0.293898	+	1.44584i
$493$	0.507136	+	0.135887i	0.0228403	+	0.00612003i
$494$	−1.40954	+	4.30840i	−0.0634182	+	0.193844i
$495$	−27.3161	+	17.1983i	−1.22777	+	0.773006i
$496$	−1.32734	−	4.95369i	−0.0595992	−	0.222427i
$497$	−12.8805	+	12.8805i	−0.577769	+	0.577769i
$498$	−15.1224	−	22.8388i	−0.677651	−	1.02343i
$499$	−36.2355	+	9.70928i	−1.62212	+	0.434647i	−0.951625	−	0.307263i	$-0.900587\pi$
$499$	−36.2355	+	9.70928i	−1.62212	+	0.434647i	−0.670500	+	0.741910i	$0.733920\pi$
$500$	−27.5439	+	16.2402i	−1.23180	+	0.726284i
$501$	28.0168	−	18.5510i	1.25170	−	0.828796i
$502$	27.3123	+	47.3063i	1.21901	+	2.11138i
$503$	−10.1637	+	37.9313i	−0.453175	+	1.69127i	0.240223	+	0.970718i	$0.422780\pi$
$503$	−10.1637	+	37.9313i	−0.453175	+	1.69127i	−0.693398	+	0.720555i	$0.743887\pi$
$504$	8.67299	+	3.67790i	0.386326	+	0.163827i
$505$	−26.0127	−	9.37812i	−1.15755	−	0.417321i
$506$	68.3335	−	39.4524i	3.03780	−	1.75387i
$507$	1.06939	−	22.4913i	0.0474932	−	0.998872i
$508$	38.3155	−	10.2666i	1.69998	−	0.455508i
$509$	8.63170	−	32.2140i	0.382594	−	1.42786i	−0.459332	−	0.888265i	$-0.651911\pi$
$509$	8.63170	−	32.2140i	0.382594	−	1.42786i	0.841925	−	0.539594i	$-0.181422\pi$
$510$	1.95028	+	1.18650i	0.0863599	+	0.0525393i
$511$	6.90148	+	3.98457i	0.305303	+	0.176267i
$512$		−	16.9149i		−	0.747540i
$513$	−2.95439	−	0.230962i	−0.130440	−	0.0101972i
$514$	−50.3036	−	13.4788i	−2.21879	−	0.594524i
$515$	−7.68550	−	0.648789i	−0.338664	−	0.0285890i
$516$	59.4215	−	19.8937i	2.61589	−	0.875770i
$517$	−12.3859	+	46.2247i	−0.544730	+	2.03296i
$518$	11.4266	−	6.59714i	0.502055	−	0.289862i
$519$	6.84647	−	2.29212i	0.300527	−	0.100613i
$520$	−5.95763	+	14.0753i	−0.261259	+	0.617243i
$521$	−35.0938			−1.53749			−0.768743	−	0.639558i	$-0.779117\pi$
$521$	−35.0938			−1.53749			−0.768743	+	0.639558i	$0.779117\pi$
$522$	−12.8895	+	1.58719i	−0.564156	+	0.0694692i
$523$	−16.3682	+	4.38584i	−0.715730	+	0.191779i	−0.598266	−	0.801298i	$-0.704143\pi$
$523$	−16.3682	+	4.38584i	−0.715730	+	0.191779i	−0.117464	+	0.993077i	$0.537477\pi$
$524$	23.8635	−	41.3328i	1.04248	−	1.80563i
$525$	5.80246	+	13.1191i	0.253240	+	0.572565i
$526$	15.7033	−	15.7033i	0.684697	−	0.684697i
$527$	0.890040			0.0387707
$528$	−8.50643	+	9.61815i	−0.370195	+	0.418576i
$529$	27.9964	+	16.1637i	1.21724	+	0.702771i
$530$	1.74301	+	3.70834i	0.0757116	+	0.161080i
$531$	−0.0613078	+	0.0785268i	−0.00266053	+	0.00340777i
$532$	−1.91039	−	1.91039i	−0.0828260	−	0.0828260i
$533$	−7.40679	+	22.6396i	−0.320824	+	0.980629i
$534$	12.5460	+	37.4743i	0.542918	+	1.62167i
$535$	42.3549	+	3.57548i	1.83116	+	0.154582i
$536$	−6.46370	−	11.1955i	−0.279189	−	0.483570i
$537$	2.85501	+	1.42283i	0.123203	+	0.0613998i
$538$	−16.3211	−	28.2690i	−0.703653	−	1.21876i
$539$	5.30081	−	19.7829i	0.228322	−	0.852110i
$540$	−32.7932	−	5.36737i	−1.41120	−	0.230975i
$541$	−20.8801	−	20.8801i	−0.897705	−	0.897705i	0.0975274	−	0.995233i	$-0.468907\pi$
$541$	−20.8801	−	20.8801i	−0.897705	−	0.897705i	−0.995233	+	0.0975274i	$0.968907\pi$
$542$	9.40742	+	35.1090i	0.404083	+	1.50806i
$543$	17.4457	−	1.07007i	0.748665	−	0.0459212i
$544$	1.85634	+	0.497405i	0.0795900	+	0.0213261i
$545$	−11.3577	+	5.33840i	−0.486510	+	0.228672i
$546$	19.8271	+	11.2662i	0.848522	+	0.482147i
$547$	−24.4240	−	6.54439i	−1.04429	−	0.279818i	−0.304402	−	0.952544i	$-0.598457\pi$
$547$	−24.4240	−	6.54439i	−1.04429	−	0.279818i	−0.739892	+	0.672726i	$0.765123\pi$
$548$	3.36453	−	5.82754i	0.143726	−	0.248940i
$549$	4.57582	−	10.7904i	0.195291	−	0.460523i
$550$	52.8089	−	4.94484i	2.25178	−	0.210849i
$551$	1.08173	+	0.289848i	0.0460832	+	0.0123480i
$552$	23.9346	+	4.86520i	1.01872	+	0.207077i
$553$		−	15.3242i		−	0.651652i
$554$	9.14287	+	34.1217i	0.388443	+	1.44969i
$555$	−10.1199	+	9.66557i	−0.429564	+	0.410281i
$556$			3.24844i			0.137764i
$557$	−2.64158	+	4.57535i	−0.111927	+	0.193864i	−0.916547	−	0.399926i	$-0.869036\pi$
$557$	−2.64158	+	4.57535i	−0.111927	+	0.193864i	0.804620	+	0.593790i	$0.202369\pi$
$558$	−20.4097	+	8.25431i	−0.864010	+	0.349433i
$559$	44.6330	−	9.39257i	1.88778	−	0.397264i
$560$	3.68118	+	4.35999i	0.155558	+	0.184243i
$561$	−1.23026	−	1.85802i	−0.0519416	−	0.0784455i
$562$	32.1954	+	8.62672i	1.35808	+	0.363896i
$563$	1.73316	−	1.73316i	0.0730440	−	0.0730440i	−0.669641	−	0.742685i	$-0.733552\pi$
$563$	1.73316	−	1.73316i	0.0730440	−	0.0730440i	0.742685	+	0.669641i	$0.233552\pi$
$564$	−41.0760	+	27.1979i	−1.72961	+	1.14524i
$565$	41.3938	−	19.4561i	1.74145	−	0.818526i
$566$	−5.36448	+	20.0205i	−0.225486	+	0.841526i
$567$	−4.09916	+	14.3331i	−0.172148	+	0.601935i
$568$	−5.39585	+	20.1376i	−0.226405	+	0.844954i
$569$	−8.99275			−0.376996			−0.188498	−	0.982074i	$-0.560362\pi$
$569$	−8.99275			−0.376996			−0.188498	+	0.982074i	$0.560362\pi$
$570$	4.15998	+	2.53083i	0.174242	+	0.106005i
$571$	−27.1827	−	15.6940i	−1.13756	−	0.656772i	−0.191737	−	0.981446i	$-0.561412\pi$
$571$	−27.1827	−	15.6940i	−1.13756	−	0.656772i	−0.945826	+	0.324674i	$0.894745\pi$
$572$	36.9412	−	33.1267i	1.54459	−	1.38510i
$573$	−25.7791	−	12.8474i	−1.07694	−	0.536707i
$574$	−17.0588	−	17.0588i	−0.712021	−	0.712021i
$575$	21.5174	+	30.3346i	0.897337	+	1.26504i
$576$	−38.0068	+	4.68009i	−1.58362	+	0.195004i
$577$			35.2535i			1.46762i	0.679354	+	0.733811i	$0.262260\pi$
$577$			35.2535i			1.46762i	−0.679354	+	0.733811i	$0.737740\pi$
$578$	18.6597	−	32.3195i	0.776141	−	1.34432i
$579$	25.1441	+	37.9742i	1.04495	+	1.57815i
$580$	11.8134	+	4.25897i	0.490524	+	0.176844i
$581$	11.8826			0.492973
$582$	10.1226	+	5.04473i	0.419594	+	0.209111i
$583$		−	3.99982i		−	0.165655i
$584$	9.12068			0.377417
$585$	−23.2589	−	6.63489i	−0.961639	−	0.274319i
$586$	23.4717			0.969607
$587$			34.9939i			1.44435i	0.691709	+	0.722176i	$0.256858\pi$
$587$			34.9939i			1.44435i	−0.691709	+	0.722176i	$0.743142\pi$
$588$	17.5794	−	11.6400i	0.724962	−	0.480024i
$589$	1.89847			0.0782250
$590$	0.148150	−	0.0696344i	0.00609926	−	0.00286680i
$591$	−16.8523	+	33.8152i	−0.693211	+	1.39097i
$592$	−2.78330	+	4.82082i	−0.114393	+	0.198134i
$593$		−	12.3239i		−	0.506082i	−0.967456	−	0.253041i	$-0.918569\pi$
$593$		−	12.3239i		−	0.506082i	0.967456	−	0.253041i	$-0.0814308\pi$
$594$	45.4427	+	31.1970i	1.86454	+	1.28003i
$595$	−0.896245	+	0.421257i	−0.0367425	+	0.0172699i
$596$	5.45741	+	5.45741i	0.223544	+	0.223544i
$597$	0.284286	−	0.188236i	0.0116351	−	0.00770400i
$598$	56.1924	+	18.3840i	2.29788	+	0.751776i
$599$	35.8857	+	20.7186i	1.46625	+	0.846541i	0.999288	−	0.0377360i	$-0.0120146\pi$
$599$	35.8857	+	20.7186i	1.46625	+	0.846541i	0.466964	+	0.884277i	$0.345348\pi$
$600$	13.2586	+	9.68277i	0.541281	+	0.395297i
$601$	−22.9334			−0.935473			−0.467736	−	0.883868i	$-0.654930\pi$
$601$	−22.9334			−0.935473			−0.467736	+	0.883868i	$0.654930\pi$
$602$	−11.9558	+	44.6195i	−0.487280	+	1.81855i
$603$	16.3335	−	12.3171i	0.665153	−	0.501592i
$604$	−6.45017	+	24.0724i	−0.262454	+	0.979490i
$605$	−25.5673	−	9.21757i	−1.03946	−	0.374747i
$606$	2.89082	+	47.1298i	0.117432	+	1.91452i
$607$	32.8523	−	32.8523i	1.33343	−	1.33343i	0.431159	−	0.902276i	$-0.358105\pi$
$607$	32.8523	−	32.8523i	1.33343	−	1.33343i	0.902276	−	0.431159i	$-0.141895\pi$
$608$	3.95960	+	1.06097i	0.160583	+	0.0430281i
$609$	2.51289	−	5.04227i	0.101827	−	0.204323i
$610$	−14.7152	+	12.4242i	−0.595801	+	0.503040i
$611$	−31.9825	+	16.2144i	−1.29387	+	0.655964i
$612$	0.318472	−	2.27179i	0.0128735	−	0.0918317i
$613$	14.5922	−	25.2744i	0.589372	−	1.02082i	−0.404943	−	0.914342i	$-0.632709\pi$
$613$	14.5922	−	25.2744i	0.589372	−	1.02082i	0.994315	−	0.106480i	$-0.0339581\pi$
$614$			15.4867i			0.624992i
$615$	21.8597	+	13.2989i	0.881466	+	0.536263i
$616$	3.91085	+	14.5955i	0.157572	+	0.588068i
$617$			47.3508i			1.90627i	0.302540	+	0.953137i	$0.402165\pi$
$617$			47.3508i			1.90627i	−0.302540	+	0.953137i	$0.597835\pi$
$618$	4.18127	+	12.4893i	0.168195	+	0.502392i
$619$	−40.5677	−	10.8701i	−1.63055	−	0.436906i	−0.676477	−	0.736464i	$-0.736494\pi$
$619$	−40.5677	−	10.8701i	−1.63055	−	0.436906i	−0.954078	+	0.299558i	$0.903161\pi$
$620$	21.2127	+	1.79071i	0.851921	+	0.0719168i
$621$	−3.01233	+	38.5327i	−0.120881	+	1.54626i
$622$	13.7843	−	23.8750i	0.552698	−	0.957301i
$623$	−16.5593	−	4.43704i	−0.663433	−	0.177766i
$624$	−9.62083	+	0.0661426i	−0.385142	+	0.00264782i
$625$	4.64113	+	24.5654i	0.185645	+	0.982617i
$626$	23.1684	+	6.20796i	0.925996	+	0.248120i
$627$	−2.62416	−	3.96318i	−0.104799	−	0.158274i
$628$	−0.454001	−	1.69435i	−0.0181166	−	0.0676121i
$629$	−0.683124	−	0.683124i	−0.0272379	−	0.0272379i
$630$	16.6452	−	17.9718i	0.663160	−	0.716013i
$631$	4.53759	−	16.9345i	0.180639	−	0.674153i	−0.814883	−	0.579625i	$-0.803199\pi$
$631$	4.53759	−	16.9345i	0.180639	−	0.674153i	0.995522	−	0.0945281i	$-0.0301342\pi$
$632$	−8.76929	−	15.1889i	−0.348824	−	0.604180i
$633$	26.7435	−	17.7078i	1.06296	−	0.703822i
$634$	−6.12454	−	10.6080i	−0.243236	−	0.421298i
$635$	2.60884	−	30.9041i	0.103529	−	1.22639i
$636$	2.72785	−	3.08435i	0.108166	−	0.122303i
$637$	13.6877	−	6.93931i	0.542325	−	0.274946i
$638$	−14.7294	−	14.7294i	−0.583141	−	0.583141i
$639$	−32.6717	−	4.58011i	−1.29247	−	0.181186i
$640$	28.9536	+	10.4384i	1.14449	+	0.412614i
$641$	4.31370	+	2.49051i	0.170381	+	0.0983694i	0.582765	−	0.812640i	$-0.301971\pi$
$641$	4.31370	+	2.49051i	0.170381	+	0.0983694i	−0.412385	+	0.911010i	$0.635304\pi$
$642$	−23.0430	−	68.8285i	−0.909435	−	2.71644i
$643$	−32.1039			−1.26605			−0.633027	−	0.774130i	$-0.718188\pi$
$643$	−32.1039			−1.26605			−0.633027	+	0.774130i	$0.718188\pi$
$644$	−24.9163	+	24.9163i	−0.981840	+	0.981840i
$645$	1.12464	−	48.9808i	0.0442827	−	1.92862i
$646$	−0.168078	+	0.291119i	−0.00661293	+	0.0114539i
$647$	−26.2194	+	7.02546i	−1.03079	+	0.276199i	−0.734292	−	0.678834i	$-0.762486\pi$
$647$	−26.2194	+	7.02546i	−1.03079	+	0.276199i	−0.296498	+	0.955033i	$0.595819\pi$
$648$	4.13920	+	16.5523i	0.162603	+	0.650235i
$649$	−0.159795			−0.00627251
$650$	29.1761	+	26.9859i	1.14438	+	1.05847i
$651$	1.90243	−	9.35909i	0.0745621	−	0.366812i
$652$	12.5603	−	7.25167i	0.491898	−	0.283997i
$653$	3.32521	−	12.4099i	0.130126	−	0.485636i	−0.869845	−	0.493326i	$-0.835781\pi$
$653$	3.32521	−	12.4099i	0.130126	−	0.485636i	0.999970	+	0.00768988i	$0.00244779\pi$
$654$	16.0527	+	14.1973i	0.627711	+	0.555157i
$655$	−24.0731	−	28.5122i	−0.940614	−	1.11406i
$656$	9.83131	+	2.63429i	0.383848	+	0.102852i
$657$	1.76395	+	14.3250i	0.0688183	+	0.558871i
$658$		−	36.3161i		−	1.41575i
$659$	24.8057	+	14.3216i	0.966292	+	0.557889i	0.898104	−	0.439784i	$-0.144945\pi$
$659$	24.8057	+	14.3216i	0.966292	+	0.557889i	0.0681882	+	0.997672i	$0.478278\pi$
$660$	−25.5830	−	46.7580i	−0.995817	−	1.82005i
$661$	1.03386	−	3.85843i	0.0402126	−	0.150076i	−0.942900	−	0.333075i	$-0.891914\pi$
$661$	1.03386	−	3.85843i	0.0402126	−	0.150076i	0.983113	+	0.182999i	$0.0585806\pi$
$662$	−0.178217	+	0.0477530i	−0.00692659	+	0.00185597i
$663$	0.421061	−	1.61577i	0.0163527	−	0.0627514i
$664$	11.7776	−	6.79982i	0.457061	−	0.263884i
$665$	−1.91170	+	0.898548i	−0.0741327	+	0.0348442i
$666$	22.0002	+	9.32948i	0.852490	+	0.361510i
$667$	3.78035	−	14.1085i	0.146376	−	0.546282i
$668$	27.7415	+	48.0497i	1.07335	+	1.85910i
$669$	2.84088	+	46.3155i	0.109835	+	1.79066i
$670$	−33.0858	+	5.93798i	−1.27821	+	0.229404i
$671$	18.1588	−	4.86564i	0.701013	−	0.187836i
$672$	9.19827	−	18.4569i	0.354831	−	0.711991i
$673$	−1.76461	+	1.76461i	−0.0680208	+	0.0680208i	−0.740299	−	0.672278i	$-0.765316\pi$
$673$	−1.76461	+	1.76461i	−0.0680208	+	0.0680208i	0.672278	+	0.740299i	$0.265316\pi$
$674$	−12.0520	−	44.9787i	−0.464226	−	1.73252i
$675$	−12.6436	+	22.6967i	−0.486651	+	0.873597i
$676$	36.9596	+	4.03609i	1.42152	+	0.155234i
$677$	−27.7033	−	7.42307i	−1.06472	−	0.285292i	−0.316400	−	0.948626i	$-0.602474\pi$
$677$	−27.7033	−	7.42307i	−1.06472	−	0.285292i	−0.748324	+	0.663334i	$0.769141\pi$
$678$	−58.5052	−	51.7429i	−2.24688	−	1.98717i
$679$	−4.24900	+	2.45316i	−0.163062	+	0.0941437i
$680$	−0.647263	+	0.930413i	−0.0248214	+	0.0356797i
$681$	2.73565	−	5.48925i	0.104830	−	0.210349i
$682$	−30.5814	−	17.6562i	−1.17102	−	0.676091i
$683$	2.84276	−	1.64127i	0.108775	−	0.0628015i	−0.444625	−	0.895717i	$-0.646663\pi$
$683$	2.84276	−	1.64127i	0.108775	−	0.0628015i	0.553401	+	0.832915i	$0.313330\pi$
$684$	0.679306	−	4.84576i	0.0259739	−	0.185282i
$685$	−3.39408	−	4.01996i	−0.129681	−	0.153595i
$686$			41.1037i			1.56935i
$687$	37.0426	−	12.4014i	1.41326	−	0.473145i
$688$	−5.04407	−	18.8247i	−0.192303	−	0.717686i
$689$	2.23130	−	2.00090i	0.0850059	−	0.0762284i
$690$	33.0084	−	54.2566i	1.25661	−	2.06551i
$691$	−20.9841	+	20.9841i	−0.798274	+	0.798274i	−0.982823	−	0.184550i	$-0.940917\pi$
$691$	−20.9841	+	20.9841i	−0.798274	+	0.798274i	0.184550	+	0.982823i	$0.440917\pi$
$692$	3.08552	+	11.5153i	0.117294	+	0.437747i
$693$	−22.1674	+	8.96518i	−0.842068	+	0.340559i
$694$	25.7179	+	25.7179i	0.976237	+	0.976237i
$695$	2.38928	+	0.861386i	0.0906306	+	0.0326742i
$696$	−0.394751	−	6.43573i	−0.0149630	−	0.243946i
$697$	−0.883207	+	1.52976i	−0.0334538	+	0.0579437i
$698$	−28.7404	−	28.7404i	−1.08784	−	1.08784i
$699$	−12.8240	−	11.3417i	−0.485047	−	0.428982i
$700$	−22.2081	+	8.23679i	−0.839387	+	0.311321i
$701$			19.6387i			0.741742i	0.928684	+	0.370871i	$0.120941\pi$
$701$			19.6387i			0.741742i	−0.928684	+	0.370871i	$0.879059\pi$
$702$	5.32940	+	40.9565i	0.201145	+	1.54581i
$703$	−1.45711	−	1.45711i	−0.0549561	−	0.0549561i
$704$	−43.4320	−	43.4320i	−1.63691	−	1.63691i
$705$	9.11242	+	37.4241i	0.343193	+	1.40947i
$706$		−	34.7599i		−	1.30821i
$707$	−17.7393	−	10.2418i	−0.667154	−	0.385182i
$708$	−0.123222	−	0.108979i	−0.00463096	−	0.00409569i
$709$	4.66533	+	17.4113i	0.175210	+	0.653893i	0.996516	+	0.0834047i	$0.0265794\pi$
$709$	4.66533	+	17.4113i	0.175210	+	0.653893i	−0.821306	+	0.570489i	$0.806754\pi$
$710$	44.5006	+	30.9579i	1.67008	+	1.16183i
$711$	22.1597	−	16.7106i	0.831053	−	0.626697i
$712$	−18.9521	+	5.07819i	−0.710259	+	0.190313i
$713$		−	24.7608i		−	0.927299i
$714$	1.26673	+	1.12032i	0.0474063	+	0.0419268i
$715$	−14.5696	−	35.9551i	−0.544872	−	1.34464i
$716$	−2.63357	+	4.56149i	−0.0984213	+	0.170471i
$717$	11.9585	+	35.7194i	0.446597	+	1.33397i
$718$	36.4313	+	36.4313i	1.35961	+	1.35961i
$719$	0.295439	+	0.511716i	0.0110180	+	0.0190838i	0.871482	−	0.490428i	$-0.163159\pi$
$719$	0.295439	+	0.511716i	0.0110180	+	0.0190838i	−0.860464	+	0.509512i	$0.829826\pi$
$720$	−2.29057	+	10.0776i	−0.0853646	+	0.375571i
$721$	−5.51879	−	1.47875i	−0.205530	−	0.0550717i
$722$	20.5845	−	35.6534i	0.766076	−	1.32688i
$723$	3.98117	+	11.8916i	0.148061	+	0.442252i
$724$			28.8602i			1.07258i
$725$	6.26509	−	7.55959i	0.232680	−	0.280756i
$726$	2.84133	+	46.3229i	0.105452	+	1.71920i
$727$	6.92065	−	25.8282i	0.256673	−	0.957916i	−0.710479	−	0.703718i	$-0.751522\pi$
$727$	6.92065	−	25.8282i	0.256673	−	0.957916i	0.967152	−	0.254198i	$-0.0818115\pi$
$728$	−6.18571	+	9.48304i	−0.229258	+	0.351465i
$729$	−25.1965	+	9.70227i	−0.933205	+	0.359343i
$730$	8.04337	−	22.3104i	0.297698	−	0.825744i
$731$	3.38228			0.125098
$732$	17.3210	+	8.63218i	0.640204	+	0.319054i
$733$	−11.0864	+	19.2022i	−0.409485	+	0.709249i	−0.994832	−	0.101534i	$-0.967625\pi$
$733$	−11.0864	+	19.2022i	−0.409485	+	0.709249i	0.585347	+	0.810783i	$0.300958\pi$
$734$	−37.1003	−	37.1003i	−1.36940	−	1.36940i
$735$	−3.89986	−	16.0165i	−0.143849	−	0.590778i
$736$	13.8378	−	51.6432i	0.510066	−	1.90359i
$737$	31.6946	+	8.49254i	1.16749	+	0.312827i
$738$	6.06585	−	43.2701i	0.223287	−	1.59280i
$739$	7.62415	+	28.4537i	0.280459	+	1.04669i	0.952094	+	0.305805i	$0.0989254\pi$
$739$	7.62415	+	28.4537i	0.280459	+	1.04669i	−0.671636	+	0.740882i	$0.734408\pi$
$740$	−14.9067	−	17.6556i	−0.547983	−	0.649031i
$741$	0.898129	−	3.44647i	0.0329936	−	0.126609i
$742$	0.785607	+	2.93193i	0.0288405	+	0.107634i
$743$	22.8607	+	39.5959i	0.838678	+	1.45263i	0.891000	+	0.454002i	$0.150004\pi$
$743$	22.8607	+	39.5959i	0.838678	+	1.45263i	−0.0523226	+	0.998630i	$0.516662\pi$
$744$	−3.47012	−	10.3651i	−0.127221	−	0.380002i
$745$	5.46116	−	2.56688i	0.200081	−	0.0940432i
$746$	−15.0127	+	15.0127i	−0.549654	+	0.549654i
$747$	12.9576	+	17.1829i	0.474095	+	0.628690i
$748$	3.18655	−	1.83976i	0.116512	−	0.0672681i
$749$	30.4141	+	8.14943i	1.11131	+	0.297774i
$750$	35.3778	−	23.8933i	1.29182	−	0.872458i
$751$	21.3806	−	12.3441i	0.780190	−	0.450443i	−0.0563077	−	0.998413i	$-0.517933\pi$
$751$	21.3806	−	12.3441i	0.780190	−	0.450443i	0.836498	+	0.547971i	$0.184599\pi$
$752$	7.66079	+	13.2689i	0.279360	+	0.483866i
$753$	−23.6939	−	35.7841i	−0.863455	−	1.30404i
$754$	0.848448	−	15.5851i	0.0308987	−	0.567577i
$755$	15.9952	+	11.1275i	0.582126	+	0.404970i
$756$	−23.2080	−	8.20473i	−0.844066	−	0.298403i
$757$	−4.58509	−	17.1118i	−0.166648	−	0.621938i	−0.997824	−	0.0659296i	$-0.978999\pi$
$757$	−4.58509	−	17.1118i	−0.166648	−	0.621938i	0.831176	−	0.556009i	$-0.187668\pi$
$758$	0.731942	+	2.73164i	0.0265853	+	0.0992178i
$759$	−51.6898	+	34.2257i	−1.87622	+	1.24231i
$760$	−1.38062	+	1.98458i	−0.0500804	+	0.0719884i
$761$	−6.40086	−	6.40086i	−0.232031	−	0.232031i	0.581509	−	0.813540i	$-0.302463\pi$
$761$	−6.40086	−	6.40086i	−0.232031	−	0.232031i	−0.813540	+	0.581509i	$0.802463\pi$
$762$	−50.2205	+	16.8133i	−1.81930	+	0.609081i
$763$	−8.97974	+	2.40611i	−0.325088	+	0.0871071i
$764$	23.7797	−	41.1876i	0.860318	−	1.49011i
$765$	−1.58649	−	0.836651i	−0.0573597	−	0.0302492i
$766$			31.9954i			1.15604i
$767$	−0.0799373	−	0.0891419i	−0.00288637	−	0.00321873i
$768$	−0.510527	−	8.32326i	−0.0184221	−	0.300340i
$769$	−1.46538	+	5.46885i	−0.0528428	+	0.197212i	−0.987301	−	0.158861i	$-0.949218\pi$
$769$	−1.46538	+	5.46885i	−0.0528428	+	0.197212i	0.934458	+	0.356073i	$0.115885\pi$
$770$	39.1513	+	3.30505i	1.41092	+	0.119106i
$771$	40.0966	+	8.15048i	1.44405	+	0.293532i
$772$	−65.1268	+	37.6010i	−2.34396	+	1.35329i
$773$	−7.73508	−	13.3975i	−0.278211	−	0.481876i	0.692729	−	0.721198i	$-0.256408\pi$
$773$	−7.73508	−	13.3975i	−0.278211	−	0.481876i	−0.970940	+	0.239322i	$0.923075\pi$
$774$	−77.5597	+	31.3676i	−2.78782	+	1.12748i
$775$	6.94205	−	15.1274i	0.249366	−	0.543393i
$776$	−2.80764	+	4.86298i	−0.100789	+	0.174571i
$777$	−8.64345	+	5.72314i	−0.310082	+	0.205316i
$778$	−42.0974	+	24.3049i	−1.50926	+	0.871374i
$779$	−1.88389	+	3.26300i	−0.0674975	+	0.116909i
$780$	13.2862	−	37.6622i	0.475721	−	1.34852i
$781$	−26.4584	−	45.8273i	−0.946757	−	1.63983i
$782$	3.79692	+	2.19216i	0.135778	+	0.0783913i
$783$	10.0316	−	1.86468i	0.358501	−	0.0666381i
$784$	−3.27861	−	5.67872i	−0.117093	−	0.202811i
$785$	−1.36661	−	0.115366i	−0.0487765	−	0.00411758i
$786$	−28.4222	+	57.0311i	−1.01379	+	2.03423i
$787$	−20.7838			−0.740862			−0.370431	−	0.928860i	$-0.620790\pi$
$787$	−20.7838			−0.740862			−0.370431	+	0.928860i	$0.620790\pi$
$788$	−54.0271	−	31.1925i	−1.92463	−	1.11119i
$789$	−11.5593	+	13.0700i	−0.411521	+	0.465303i
$790$	−44.8874	+	8.05605i	−1.59702	+	0.286621i
$791$	32.7272	−	8.76924i	1.16365	−	0.311798i
$792$	−16.8412	+	21.5713i	−0.598426	+	0.766501i
$793$	11.7982	+	7.69589i	0.418967	+	0.273289i
$794$	−65.9256	+	38.0622i	−2.33961	+	1.35078i
$795$	−1.54525	−	2.82426i	−0.0548045	−	0.100166i
$796$	0.281492	+	0.487559i	0.00997723	+	0.0172811i
$797$	−29.9650	−	29.9650i	−1.06141	−	1.06141i	−0.997986	−	0.0634278i	$-0.979797\pi$
$797$	−29.9650	−	29.9650i	−1.06141	−	1.06141i	−0.0634278	−	0.997986i	$-0.520203\pi$
$798$	2.70196	+	2.38965i	0.0956484	+	0.0845928i
$799$	−2.56846	+	0.688216i	−0.0908654	+	0.0243473i
$800$	22.9330	−	27.6714i	0.810804	−	0.978332i
$801$	−11.6412	−	28.7841i	−0.411321	−	1.01704i
$802$	2.60175	+	0.697137i	0.0918710	+	0.0246168i
$803$	−16.3698	+	16.3698i	−0.577677	+	0.577677i
$804$	18.6486	+	28.1643i	0.657686	+	0.993279i
$805$	11.7193	+	24.9334i	0.413052	+	0.878788i
$806$	−5.44879	−	25.8924i	−0.191926	−	0.912020i
$807$	14.1589	+	21.3836i	0.498415	+	0.752738i
$808$	−23.4434			−0.824737
$809$	−18.4469	−	10.6503i	−0.648558	−	0.374445i	0.139346	−	0.990244i	$-0.455500\pi$
$809$	−18.4469	−	10.6503i	−0.648558	−	0.374445i	−0.787904	+	0.615799i	$0.788833\pi$
$810$	44.1393	+	4.47214i	1.55090	+	0.157135i
$811$	−8.20902	+	8.20902i	−0.288258	+	0.288258i	−0.836391	−	0.548133i	$-0.815339\pi$
$811$	−8.20902	+	8.20902i	−0.288258	+	0.288258i	0.548133	+	0.836391i	$0.315339\pi$
$812$	8.05610	+	4.65119i	0.282714	+	0.163225i
$813$	−9.06613	−	27.0801i	−0.317963	−	0.949741i
$814$	9.92038	+	37.0234i	0.347709	+	1.29767i
$815$	−2.00313	−	11.1612i	−0.0701665	−	0.390960i
$816$	−0.699157	−	0.142118i	−0.0244754	−	0.00497513i
$817$	7.21445			0.252402
$818$	4.41699	−	4.41699i	0.154436	−	0.154436i
$819$	−16.0904	−	7.88127i	−0.562245	−	0.275394i
$820$	−24.1276	+	34.6824i	−0.842572	+	1.21116i
$821$	6.63568	−	6.63568i	0.231587	−	0.231587i	−0.581768	−	0.813355i	$-0.697639\pi$
$821$	6.63568	−	6.63568i	0.231587	−	0.231587i	0.813355	+	0.581768i	$0.197639\pi$
$822$	−4.00727	+	8.04085i	−0.139770	+	0.280457i
$823$	−18.8702	+	18.8702i	−0.657773	+	0.657773i	−0.954853	−	0.297080i	$-0.903987\pi$
$823$	−18.8702	+	18.8702i	−0.657773	+	0.657773i	0.297080	+	0.954853i	$0.403987\pi$
$824$	−6.31625	+	1.69244i	−0.220037	+	0.0589588i
$825$	−41.1752	+	6.41794i	−1.43353	+	0.223444i
$826$	0.117132	−	0.0313855i	0.00407555	−	0.00109204i
$827$	−13.4390			−0.467320			−0.233660	−	0.972318i	$-0.575070\pi$
$827$	−13.4390			−0.467320			−0.233660	+	0.972318i	$0.575070\pi$
$828$	−63.2009	−	8.85986i	−2.19638	−	0.307901i
$829$	3.62201	−	6.27351i	0.125798	−	0.217888i	−0.796247	−	0.604972i	$-0.793184\pi$
$829$	3.62201	−	6.27351i	0.125798	−	0.217888i	0.922044	+	0.387084i	$0.126518\pi$
$830$	−6.24677	−	34.8063i	−0.216828	−	1.20814i
$831$	−8.81117	−	26.3186i	−0.305656	−	0.912982i
$832$	2.50179	−	45.9554i	0.0867341	−	1.59322i
$833$	1.09923	−	0.294538i	0.0380860	−	0.0102051i
$834$	−0.265524	−	4.32890i	−0.00919433	−	0.149898i
$835$	42.6976	−	7.66303i	1.47761	−	0.265190i
$836$	6.79696	−	3.92423i	0.235078	−	0.135722i
$837$	15.6083	−	7.45480i	0.539502	−	0.257676i
$838$	2.40115	+	4.15892i	0.0829464	+	0.143667i
$839$	−10.0269	−	37.4208i	−0.346166	−	1.29191i	−0.891244	−	0.453523i	$-0.850167\pi$
$839$	−10.0269	−	37.4208i	−0.346166	−	1.29191i	0.545079	−	0.838385i	$-0.316500\pi$
$840$	8.40012	+	8.79493i	0.289832	+	0.303454i
$841$	25.1440			0.867036
$842$	−3.83050	+	14.2956i	−0.132008	+	0.492660i
$843$	−25.6627	−	5.21648i	−0.883871	−	0.179665i
$844$	26.4806	+	45.8658i	0.911501	+	1.57877i
$845$	12.7692	−	26.1141i	0.439272	−	0.898354i
$846$	52.5152	−	39.6017i	1.80551	−	1.36153i
$847$	−17.4356	−	10.0664i	−0.599094	−	0.345887i
$848$	−0.905521	−	0.905521i	−0.0310957	−	0.0310957i
$849$	3.24384	−	15.9582i	0.111328	−	0.547685i
$850$	1.70510	+	2.40380i	0.0584845	+	0.0824498i
$851$	−19.0044	+	19.0044i	−0.651463	+	0.651463i
$852$	10.8512	−	53.3830i	0.371757	−	1.82887i
$853$	23.1370	−	13.3581i	0.792194	−	0.457374i	−0.0485402	−	0.998821i	$-0.515457\pi$
$853$	23.1370	−	13.3581i	0.792194	−	0.457374i	0.840734	+	0.541448i	$0.182124\pi$
$854$	−12.3550	+	7.13317i	−0.422780	+	0.244092i
$855$	−3.38401	−	1.78459i	−0.115731	−	0.0610317i
$856$	34.8089	−	9.32703i	1.18975	−	0.318791i
$857$	1.04766	−	3.90993i	0.0357875	−	0.133561i	−0.945721	−	0.324980i	$-0.894642\pi$
$857$	1.04766	−	3.90993i	0.0357875	−	0.133561i	0.981508	+	0.191419i	$0.0613090\pi$
$858$	−46.5204	+	47.1645i	−1.58818	+	1.61017i
$859$	40.4234	+	23.3385i	1.37923	+	0.796299i	0.992067	−	0.125713i	$-0.0401218\pi$
$859$	40.4234	+	23.3385i	1.37923	+	0.796299i	0.387163	+	0.922011i	$0.373455\pi$
$860$	80.6111	+	6.80497i	2.74882	+	0.232048i
$861$	14.1981	+	12.5570i	0.483871	+	0.427943i
$862$	−70.6978	+	18.9434i	−2.40798	+	0.645215i
$863$	20.7745			0.707173			0.353586	−	0.935402i	$-0.384962\pi$
$863$	20.7745			0.707173			0.353586	+	0.935402i	$0.384962\pi$
$864$	36.7202	−	6.82553i	1.24925	−	0.232209i
$865$	9.28791	+	0.784060i	0.315798	+	0.0266588i
$866$	3.52004	−	13.1370i	0.119616	−	0.446413i
$867$	−13.0784	+	26.2427i	−0.444166	+	0.891248i
$868$	15.2323	+	4.08149i	0.517019	+	0.138535i
$869$	43.0000	+	11.5218i	1.45868	+	0.390851i
$870$	−16.0907	−	4.70994i	−0.545527	−	0.159682i
$871$	11.1176	+	21.9293i	0.376706	+	0.743045i
$872$	−7.52352	+	7.52352i	−0.254778	+	0.254778i
$873$	−8.18082	−	3.46919i	−0.276879	−	0.117414i
$874$	8.09889	+	4.67590i	0.273949	+	0.158165i
$875$	0.169389	+	18.5186i	0.00572641	+	0.626042i
$876$	−23.7872	+	1.45905i	−0.803696	+	0.0492967i
$877$		−	11.5218i		−	0.389064i	−0.980896	−	0.194532i	$-0.937681\pi$
$877$		−	11.5218i		−	0.389064i	0.980896	−	0.194532i	$-0.0623189\pi$
$878$		−	11.0910i		−	0.374303i
$879$	−18.4066	+	1.12902i	−0.620840	+	0.0380807i
$880$	−15.0020	+	7.05130i	−0.505717	+	0.237699i
$881$	42.2672	+	24.4030i	1.42402	+	0.822156i	0.996639	−	0.0819169i	$-0.0261042\pi$
$881$	42.2672	+	24.4030i	1.42402	+	0.822156i	0.427377	+	0.904073i	$0.359438\pi$
$882$	−22.4751	+	16.9484i	−0.756774	+	0.570684i
$883$	−4.14698	+	4.14698i	−0.139557	+	0.139557i	−0.773434	−	0.633877i	$-0.781463\pi$
$883$	−4.14698	+	4.14698i	−0.139557	+	0.139557i	0.633877	+	0.773434i	$0.281463\pi$
$884$	2.62038	+	0.857286i	0.0881329	+	0.0288336i
$885$	−0.112831	+	0.0617338i	−0.00379276	+	0.00207516i
$886$	7.38791	+	1.97959i	0.248202	+	0.0665055i
$887$	42.4913	+	11.3855i	1.42672	+	0.382288i	0.887862	−	0.460109i	$-0.152190\pi$
$887$	42.4913	+	11.3855i	1.42672	+	0.382288i	0.538857	+	0.842397i	$0.318856\pi$
$888$	−5.29203	+	10.6188i	−0.177589	+	0.356344i
$889$	5.94621	−	22.1916i	0.199430	−	0.744281i
$890$	−4.29157	+	50.8376i	−0.143854	+	1.70408i
$891$	−37.1370	−	22.2790i	−1.24414	−	0.746373i
$892$	−76.6194			−2.56541
$893$	−5.47855	+	1.46797i	−0.183333	+	0.0491239i
$894$	−7.71868	−	6.82652i	−0.258151	−	0.228313i
$895$	2.65671	+	3.14661i	0.0888039	+	0.105179i
$896$	19.7449	+	11.3997i	0.659630	+	0.380837i
$897$	−44.9506	−	11.7139i	−1.50086	−	0.391115i
$898$	2.44018	−	9.10686i	0.0814298	−	0.303900i
$899$	−6.31399	+	1.69183i	−0.210583	+	0.0564256i
$900$	−36.1281	−	23.1322i	−1.20427	−	0.771072i
$901$	0.192472	−	0.111124i	0.00641219	−	0.00370208i
$902$	60.6933	−	35.0413i	2.02087	−	1.16675i
$903$	7.22951	−	35.5659i	0.240583	−	1.18356i
$904$	27.4200	−	27.4200i	0.911974	−	0.911974i
$905$	21.2272	+	7.65285i	0.705616	+	0.254389i
$906$	6.62791	−	32.6063i	0.220198	−	1.08327i
$907$	25.9542	+	25.9542i	0.861795	+	0.861795i	0.991547	−	0.129751i	$-0.0414178\pi$
$907$	25.9542	+	25.9542i	0.861795	+	0.861795i	−0.129751	+	0.991547i	$0.541418\pi$
$908$	8.77025	+	5.06351i	0.291051	+	0.168038i
$909$	−4.53399	−	36.8204i	−0.150383	−	1.22125i
$910$	17.7417	+	23.4940i	0.588131	+	0.778818i
$911$	14.9202	+	25.8425i	0.494328	+	0.856201i	0.999979	−	0.00653724i	$-0.00208088\pi$
$911$	14.9202	+	25.8425i	0.494328	+	0.856201i	−0.505651	+	0.862738i	$0.668748\pi$
$912$	−1.49131	−	0.303140i	−0.0493823	−	0.0100380i
$913$	−8.93417	+	33.3428i	−0.295678	+	1.10349i
$914$	−4.11587			−0.136141
$915$	10.9421	−	10.4509i	0.361735	−	0.345497i
$916$	16.6941	+	62.3033i	0.551589	+	2.05856i
$917$	−13.8212	−	23.9391i	−0.456418	−	0.790538i
$918$	−0.238706	+	3.05344i	−0.00787846	+	0.100779i
$919$	−15.3627	+	8.86964i	−0.506767	+	0.292582i	−0.731504	−	0.681837i	$-0.761181\pi$
$919$	−15.3627	+	8.86964i	−0.506767	+	0.292582i	0.224736	+	0.974420i	$0.427848\pi$
$920$	25.8840	+	18.0068i	0.853369	+	0.593666i
$921$	−0.744927	−	12.1447i	−0.0245462	−	0.400183i
$922$	7.06830	−	1.89394i	0.232782	−	0.0623737i
$923$	12.3290	−	37.6850i	0.405816	−	1.24042i
$924$	−12.5345	−	37.4401i	−0.412356	−	1.23169i
$925$	−16.9388	+	6.28244i	−0.556944	+	0.206566i
$926$	−22.5158	+	38.9984i	−0.739914	+	1.28157i
$927$	−3.87972	−	9.59301i	−0.127427	−	0.315076i
$928$	−14.1145			−0.463330
$929$	3.89506	−	1.04368i	0.127793	−	0.0342419i	−0.194356	−	0.980931i	$-0.562262\pi$
$929$	3.89506	−	1.04368i	0.127793	−	0.0342419i	0.322148	+	0.946689i	$0.395595\pi$
$930$	−28.4146	−	0.652423i	−0.931750	−	0.0213938i
$931$	2.34467	−	0.628253i	0.0768435	−	0.0205902i
$932$	19.9885	−	19.9885i	0.654746	−	0.654746i
$933$	−9.66126	+	19.3860i	−0.316296	+	0.634668i
$934$	−25.6267	+	25.6267i	−0.838531	+	0.838531i
$935$	−0.508196	−	2.83161i	−0.0166198	−	0.0926035i
$936$	−20.4584	+	1.39610i	−0.668702	+	0.0456330i
$937$	24.0491	−	24.0491i	0.785650	−	0.785650i	−0.195128	−	0.980778i	$-0.562512\pi$
$937$	24.0491	−	24.0491i	0.785650	−	0.785650i	0.980778	+	0.195128i	$0.0625121\pi$
$938$	−24.9007			−0.813035
$939$	−18.4674	−	3.75388i	−0.602661	−	0.122503i
$940$	−62.5996	+	11.2349i	−2.04178	+	0.366442i
$941$	8.72851	+	32.5752i	0.284541	+	1.06192i	0.949174	+	0.314752i	$0.101921\pi$
$941$	8.72851	+	32.5752i	0.284541	+	1.06192i	−0.664633	+	0.747170i	$0.731412\pi$
$942$	0.743501	+	2.22080i	0.0242246	+	0.0723577i
$943$	42.5577	+	24.5707i	1.38587	+	0.800132i
$944$	−0.0361761	+	0.0361761i	−0.00117743	+	0.00117743i
$945$	−12.1888	+	14.8942i	−0.396500	+	0.484509i
$946$	−116.214	−	67.0961i	−3.77844	−	2.18148i
$947$	20.2545			0.658183			0.329091	−	0.944298i	$-0.393258\pi$
$947$	20.2545			0.658183			0.329091	+	0.944298i	$0.393258\pi$
$948$	25.3005	+	38.2105i	0.821724	+	1.24102i
$949$	−17.3209	−	0.942941i	−0.562259	−	0.0306092i
$950$	3.63700	+	5.12735i	0.118000	+	0.166353i
$951$	5.31315	+	8.02425i	0.172291	+	0.260204i
$952$	−0.593687	+	0.593687i	−0.0192415	+	0.0192415i
$953$	22.6890	+	6.07949i	0.734968	+	0.196934i	0.606841	−	0.794824i	$-0.292437\pi$
$953$	22.6890	+	6.07949i	0.734968	+	0.196934i	0.128128	+	0.991758i	$0.459103\pi$
$954$	−3.38305	+	4.33321i	−0.109530	+	0.140293i
$955$	−23.9885	−	28.4120i	−0.776250	−	0.919392i
$956$	−60.0778	+	16.0978i	−1.94305	+	0.520640i
$957$	12.2593	+	10.8423i	0.396288	+	0.350483i
$958$	−23.0964	−	23.0964i	−0.746211	−	0.746211i
$959$	−1.94867	−	3.37519i	−0.0629257	−	0.108991i
$960$	−47.4463	−	13.8881i	−1.53132	−	0.448235i
$961$	17.2502	−	9.95938i	0.556456	−	0.321270i
$962$	−15.6909	+	24.0550i	−0.505894	+	0.775564i
$963$	21.3812	+	52.8672i	0.688998	+	1.70362i
$964$	−20.0009	+	5.35922i	−0.644185	+	0.172609i
$965$	10.3865	+	57.8725i	0.334354	+	1.86298i
$966$	31.1671	−	35.2404i	1.00279	−	1.13384i
$967$	−33.7046	−	19.4594i	−1.08387	−	0.625771i	−0.151930	−	0.988391i	$-0.548549\pi$
$967$	−33.7046	−	19.4594i	−1.08387	−	0.625771i	−0.931937	+	0.362620i	$0.881882\pi$
$968$	−23.0421			−0.740601
$969$	0.117804	−	0.236382i	0.00378441	−	0.00759367i
$970$	9.41948	+	11.1564i	0.302441	+	0.358212i
$971$	−15.1156	−	26.1809i	−0.485081	−	0.840185i	0.514772	−	0.857327i	$-0.327877\pi$
$971$	−15.1156	−	26.1809i	−0.485081	−	0.840185i	−0.999853	+	0.0171420i	$0.994543\pi$
$972$	−13.4431	−	42.5071i	−0.431189	−	1.36341i
$973$	1.62936	+	0.940713i	0.0522350	+	0.0301579i
$974$	8.74667	+	15.1497i	0.280261	+	0.485427i
$975$	−24.1781	−	19.7591i	−0.774318	−	0.632796i
$976$	3.00945	−	5.21252i	0.0963301	−	0.166849i
$977$	46.8016	−	27.0209i	1.49732	−	0.864476i	0.497321	−	0.867566i	$-0.334317\pi$
$977$	46.8016	−	27.0209i	1.49732	−	0.864476i	0.999995	+	0.00309032i	$0.000983682\pi$
$978$	−16.1452	+	10.6903i	−0.516266	+	0.341838i
$979$	24.9008	−	43.1295i	0.795834	−	1.37842i
$980$	26.7909	−	4.80823i	0.855805	−	0.153593i
$981$	−13.2715	−	10.3614i	−0.423727	−	0.330814i
$982$	14.9093	+	25.8236i	0.475774	+	0.824064i
$983$	9.24701	−	5.33877i	0.294934	−	0.170280i	−0.345231	−	0.938518i	$-0.612199\pi$
$983$	9.24701	−	5.33877i	0.294934	−	0.170280i	0.640165	+	0.768238i	$0.278866\pi$
$984$	21.2585	+	4.32123i	0.677696	+	0.137756i
$985$	−37.2690	+	31.4665i	−1.18749	+	1.00261i
$986$	0.299566	−	1.11800i	0.00954013	−	0.0356043i
$987$	1.74685	+	28.4793i	0.0556027	+	0.906505i
$988$	5.58931	+	1.82860i	0.177820	+	0.0581756i
$989$		−	94.0946i		−	2.99203i
$990$	37.9141	+	60.2191i	1.20499	+	1.91389i
$991$	−3.14978	+	5.45558i	−0.100056	+	0.173302i	−0.911708	−	0.410840i	$-0.865236\pi$
$991$	−3.14978	+	5.45558i	−0.100056	+	0.173302i	0.811652	+	0.584142i	$0.198569\pi$
$992$	−23.1120	+	6.19283i	−0.733806	+	0.196623i
$993$	0.137461	−	0.0460206i	0.00436221	−	0.00146042i
$994$	28.3954	+	28.3954i	0.900648	+	0.900648i
$995$	0.433251	−	0.0777566i	0.0137350	−	0.00246505i
$996$	−29.6289	+	19.6184i	−0.938828	+	0.621632i
$997$	−6.81926	−	25.4498i	−0.215968	−	0.806004i	−0.985824	−	0.167786i	$-0.946338\pi$
$997$	−6.81926	−	25.4498i	−0.215968	−	0.806004i	0.769855	−	0.638218i	$-0.220328\pi$
$998$	21.4044	+	79.8822i	0.677544	+	2.52863i
$999$	−17.7014	−	6.25799i	−0.560048	−	0.197994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.ca.a.58.11	✓	320
5.2	odd	4		585.2.dv.a.292.70	yes	320
9.7	even	3		585.2.dt.a.448.11	yes	320
13.11	odd	12		585.2.cc.a.193.11	yes	320
45.7	odd	12		585.2.cc.a.97.11	yes	320
65.37	even	12		585.2.dt.a.427.11	yes	320
117.115	odd	12		585.2.dv.a.583.70	yes	320
585.232	even	12	inner	585.2.ca.a.232.70	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.ca.a.58.11	✓	320	1.1	even	1	trivial
585.2.ca.a.232.70	yes	320	585.232	even	12	inner
585.2.cc.a.97.11	yes	320	45.7	odd	12
585.2.cc.a.193.11	yes	320	13.11	odd	12
585.2.dt.a.427.11	yes	320	65.37	even	12
585.2.dt.a.448.11	yes	320	9.7	even	3
585.2.dv.a.292.70	yes	320	5.2	odd	4
585.2.dv.a.583.70	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-2.20453i q^{2} +(0.106040 + 1.72880i) q^{3} -2.85995 q^{4} +(-0.758370 + 2.10354i) q^{5} +(3.81119 - 0.233769i) q^{6} +(-0.828210 + 1.43450i) q^{7} +1.89577i q^{8} +(-2.97751 + 0.366645i) q^{9} +(4.63731 + 1.67185i) q^{10} +(-3.40253 - 3.40253i) q^{11} +(-0.303269 - 4.94428i) q^{12} +(0.195994 - 3.60022i) q^{13} +(3.16240 + 1.82581i) q^{14} +(-3.71702 - 1.08801i) q^{15} -1.54060 q^{16} +(0.0692009 - 0.258261i) q^{17} +(0.808280 + 6.56401i) q^{18} +(0.147606 - 0.550875i) q^{19} +(2.16890 - 6.01601i) q^{20} +(-2.56779 - 1.27970i) q^{21} +(-7.50098 + 7.50098i) q^{22} +(-7.18479 - 1.92516i) q^{23} +(-3.27742 + 0.201028i) q^{24} +(-3.84975 - 3.19052i) q^{25} +(-7.93679 - 0.432075i) q^{26} +(-0.949593 - 5.10865i) q^{27} +(2.36864 - 4.10260i) q^{28} +1.96366i q^{29} +(-2.39855 + 8.19427i) q^{30} +(0.861570 + 3.21542i) q^{31} +7.18785i q^{32} +(5.52150 - 6.24311i) q^{33} +(-0.569344 - 0.152555i) q^{34} +(-2.38944 - 2.83006i) q^{35} +(8.51552 - 1.04859i) q^{36} +(1.80663 - 3.12918i) q^{37} +(-1.21442 - 0.325403i) q^{38} +(6.24485 - 0.0429329i) q^{39} +(-3.98783 - 1.43770i) q^{40} +(-6.38147 - 1.70991i) q^{41} +(-2.82113 + 5.66077i) q^{42} +(3.27409 + 12.2191i) q^{43} +(9.73106 + 9.73106i) q^{44} +(1.48680 - 6.54136i) q^{45} +(-4.24407 + 15.8391i) q^{46} +(-4.97260 - 8.61279i) q^{47} +(-0.163366 - 2.66340i) q^{48} +(2.12814 + 3.68604i) q^{49} +(-7.03360 + 8.48688i) q^{50} +(0.453820 + 0.0922485i) q^{51} +(-0.560533 + 10.2964i) q^{52} +(0.587770 + 0.587770i) q^{53} +(-11.2622 + 2.09341i) q^{54} +(9.73774 - 4.57698i) q^{55} +(-2.71949 - 1.57010i) q^{56} +(0.968005 + 0.196767i) q^{57} +4.32894 q^{58} +(0.0234818 - 0.0234818i) q^{59} +(10.6305 + 3.11166i) q^{60} +(-1.95342 + 3.38343i) q^{61} +(7.08849 - 1.89935i) q^{62} +(1.94005 - 4.57491i) q^{63} +12.7646 q^{64} +(7.42457 + 3.14258i) q^{65} +(-13.7631 - 12.1723i) q^{66} +(-5.90548 + 3.40953i) q^{67} +(-0.197911 + 0.738613i) q^{68} +(2.56634 - 12.6252i) q^{69} +(-6.23894 + 5.26759i) q^{70} +(10.6224 + 2.84625i) q^{71} +(-0.695077 - 5.64469i) q^{72} -4.81106i q^{73} +(-6.89836 - 3.98277i) q^{74} +(5.10755 - 6.99378i) q^{75} +(-0.422146 + 1.57547i) q^{76} +(7.69895 - 2.06293i) q^{77} +(-0.0946469 - 13.7670i) q^{78} +(-8.01195 + 4.62570i) q^{79} +(1.16835 - 3.24072i) q^{80} +(8.73114 - 2.18338i) q^{81} +(-3.76955 + 14.0681i) q^{82} +(-3.58683 - 6.21257i) q^{83} +(7.34375 + 3.65986i) q^{84} +(0.490782 + 0.341424i) q^{85} +(26.9373 - 7.21782i) q^{86} +(-3.39477 + 0.208227i) q^{87} +(6.45043 - 6.45043i) q^{88} +(2.67869 + 9.99701i) q^{89} +(-14.4206 - 3.27770i) q^{90} +(5.00220 + 3.26289i) q^{91} +(20.5481 + 5.50585i) q^{92} +(-5.46747 + 1.83045i) q^{93} +(-18.9871 + 10.9622i) q^{94} +(1.04685 + 0.728263i) q^{95} +(-12.4264 + 0.762202i) q^{96} +(2.56517 + 1.48100i) q^{97} +(8.12598 - 4.69153i) q^{98} +(11.3786 + 8.88355i) 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

Introduction

L-functions

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