LMFDB - Embedded newform 185.2.p.a.103.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(82,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$185 = 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	185.p (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:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.3
Character	$\chi$	$=$	185.103
Dual form			185.2.p.a.97.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16559 - 2.01885i) q^{2} +(0.0549274 + 0.204992i) q^{3} +(-1.71718 + 2.97424i) q^{4} +(-1.83242 + 1.28150i) q^{5} +(0.349826 - 0.349826i) q^{6} +(1.26188 + 4.70941i) q^{7} +3.34372 q^{8} +(2.55907 - 1.47748i) q^{9} +(4.72299 + 2.20570i) q^{10} -0.366430i q^{11} +(-0.704015 - 0.188640i) q^{12} +(-1.46458 + 2.53673i) q^{13} +(8.03678 - 8.03678i) q^{14} +(-0.363346 - 0.305243i) q^{15} +(-0.463041 - 0.802010i) q^{16} +(-4.75903 + 2.74763i) q^{17} +(-5.96563 - 3.44426i) q^{18} +(1.36274 - 0.365145i) q^{19} +(-0.664879 - 7.65061i) q^{20} +(-0.896080 + 0.517352i) q^{21} +(-0.739767 + 0.427105i) q^{22} +4.57650 q^{23} +(0.183662 + 0.685437i) q^{24} +(1.71554 - 4.69648i) q^{25} +6.82838 q^{26} +(0.893629 + 0.893629i) q^{27} +(-16.1738 - 4.33375i) q^{28} +(-4.08509 + 4.08509i) q^{29} +(-0.192728 + 1.08933i) q^{30} +(-0.328846 - 0.328846i) q^{31} +(2.26430 - 3.92188i) q^{32} +(0.0751151 - 0.0201270i) q^{33} +(11.0941 + 6.40518i) q^{34} +(-8.34739 - 7.01253i) q^{35} +10.1484i q^{36} +(5.51420 + 2.56780i) q^{37} +(-2.32556 - 2.32556i) q^{38} +(-0.600455 - 0.160892i) q^{39} +(-6.12711 + 4.28497i) q^{40} +(7.08118 + 4.08832i) q^{41} +(2.08891 + 1.20604i) q^{42} -6.04631 q^{43} +(1.08985 + 0.629224i) q^{44} +(-2.79591 + 5.98681i) q^{45} +(-5.33430 - 9.23928i) q^{46} +(-4.97863 + 4.97863i) q^{47} +(0.138972 - 0.138972i) q^{48} +(-14.5240 + 8.38545i) q^{49} +(-11.4811 + 2.01073i) q^{50} +(-0.824643 - 0.824643i) q^{51} +(-5.02990 - 8.71203i) q^{52} +(1.32960 - 4.96214i) q^{53} +(0.762504 - 2.84570i) q^{54} +(0.469578 + 0.671454i) q^{55} +(4.21939 + 15.7470i) q^{56} +(0.149703 + 0.259294i) q^{57} +(13.0087 + 3.48567i) q^{58} +(2.31870 - 8.65349i) q^{59} +(1.53179 - 0.556523i) q^{60} +(-0.665487 + 0.178317i) q^{61} +(-0.280594 + 1.04719i) q^{62} +(10.1873 + 10.1873i) q^{63} -12.4091 q^{64} +(-0.567076 - 6.52522i) q^{65} +(-0.128187 - 0.128187i) q^{66} +(-4.84572 + 1.29841i) q^{67} -18.8726i q^{68} +(0.251376 + 0.938146i) q^{69} +(-4.42767 + 25.0259i) q^{70} +(5.17637 - 8.96573i) q^{71} +(8.55683 - 4.94029i) q^{72} +(8.94360 - 8.94360i) q^{73} +(-1.24326 - 14.1253i) q^{74} +(1.05697 + 0.0937063i) q^{75} +(-1.25404 + 4.68013i) q^{76} +(1.72567 - 0.462391i) q^{77} +(0.375066 + 1.39976i) q^{78} +(1.85388 - 0.496745i) q^{79} +(1.87626 + 0.876237i) q^{80} +(4.29834 - 7.44494i) q^{81} -19.0612i q^{82} +(-0.386169 + 1.44120i) q^{83} -3.55354i q^{84} +(5.19948 - 11.1335i) q^{85} +(7.04749 + 12.2066i) q^{86} +(-1.06179 - 0.613027i) q^{87} -1.22524i q^{88} +(7.19530 + 1.92798i) q^{89} +(15.3454 - 1.33359i) q^{90} +(-13.7946 - 3.69626i) q^{91} +(-7.85867 + 13.6116i) q^{92} +(0.0493482 - 0.0854735i) q^{93} +(15.8541 + 4.24810i) q^{94} +(-2.02918 + 2.41544i) q^{95} +(0.928326 + 0.248744i) q^{96} -0.442430i q^{97} +(33.8580 + 19.5479i) q^{98} +(-0.541393 - 0.937719i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22}+ \cdots + 32 q^{99}+O(q^{100})$ 68 * q - 4 * q^2 - 8 * q^3 - 30 * q^4 - 10 * q^5 - 8 * q^6 - 2 * q^7 + 12 * q^8 - 6 * q^10 + 14 * q^12 - 6 * q^13 - 8 * q^15 - 26 * q^16 + 12 * q^17 + 18 * q^18 + 4 * q^19 + 48 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 68 * q^27 - 26 * q^28 + 14 * q^29 + 10 * q^30 - 24 * q^31 - 16 * q^32 - 2 * q^33 - 10 * q^35 - 16 * q^37 - 36 * q^38 + 52 * q^39 + 42 * q^40 - 18 * q^41 + 132 * q^42 + 8 * q^43 - 36 * q^44 - 32 * q^45 - 52 * q^46 - 24 * q^47 - 60 * q^48 - 36 * q^49 - 8 * q^50 - 8 * q^51 - 26 * q^52 + 82 * q^53 + 40 * q^54 + 18 * q^55 + 16 * q^56 - 6 * q^57 + 86 * q^58 - 8 * q^59 + 36 * q^60 + 4 * q^61 + 10 * q^62 - 48 * q^63 - 20 * q^64 + 8 * q^65 + 80 * q^66 - 40 * q^67 + 8 * q^69 - 82 * q^70 + 4 * q^71 - 90 * q^72 - 60 * q^73 - 44 * q^74 + 64 * q^75 + 72 * q^76 + 66 * q^77 - 24 * q^78 + 56 * q^79 + 34 * q^80 - 6 * q^81 + 24 * q^83 - 20 * q^85 - 4 * q^86 - 84 * q^87 - 22 * q^89 - 50 * q^90 + 44 * q^91 + 44 * q^92 - 34 * q^93 - 20 * q^94 - 28 * q^95 - 8 * q^96 + 42 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$ .

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	−1.16559	−	2.01885i	−0.824193	−	1.42754i	−0.902534	−	0.430618i	$-0.858296\pi$
$2$	−1.16559	−	2.01885i	−0.824193	−	1.42754i	0.0783413	−	0.996927i	$-0.475038\pi$
$3$	0.0549274	+	0.204992i	0.0317124	+	0.118352i	0.979968	−	0.199157i	$-0.0638203\pi$
$3$	0.0549274	+	0.204992i	0.0317124	+	0.118352i	−0.948255	+	0.317509i	$0.897154\pi$
$4$	−1.71718	+	2.97424i	−0.858589	+	1.48712i
$5$	−1.83242	+	1.28150i	−0.819484	+	0.573102i
$5$	−1.83242	+	1.28150i	−0.819484	+	0.573102i
$6$	0.349826	−	0.349826i	0.142816	−	0.142816i
$7$	1.26188	+	4.70941i	0.476947	+	1.77999i	0.613868	+	0.789408i	$0.289613\pi$
$7$	1.26188	+	4.70941i	0.476947	+	1.77999i	−0.136922	+	0.990582i	$0.543721\pi$
$8$	3.34372			1.18219
$9$	2.55907	−	1.47748i	0.853024	−	0.492494i
$10$	4.72299	+	2.20570i	1.49354	+	0.697503i
$11$		−	0.366430i		−	0.110483i	−0.998473	−	0.0552413i	$-0.982407\pi$
$11$		−	0.366430i		−	0.110483i	0.998473	−	0.0552413i	$-0.0175928\pi$
$12$	−0.704015	−	0.188640i	−0.203232	−	0.0544558i
$13$	−1.46458	+	2.53673i	−0.406202	+	0.703563i	−0.994461	−	0.105110i	$-0.966480\pi$
$13$	−1.46458	+	2.53673i	−0.406202	+	0.703563i	0.588258	+	0.808673i	$0.299814\pi$
$14$	8.03678	−	8.03678i	2.14792	−	2.14792i
$15$	−0.363346	−	0.305243i	−0.0938157	−	0.0788133i
$16$	−0.463041	−	0.802010i	−0.115760	−	0.200503i
$17$	−4.75903	+	2.74763i	−1.15423	+	0.666397i	−0.949915	−	0.312507i	$-0.898831\pi$
$17$	−4.75903	+	2.74763i	−1.15423	+	0.666397i	−0.204319	+	0.978904i	$0.565498\pi$
$18$	−5.96563	−	3.44426i	−1.40611	−	0.811820i
$19$	1.36274	−	0.365145i	0.312634	−	0.0837699i	−0.0990906	−	0.995078i	$-0.531593\pi$
$19$	1.36274	−	0.365145i	0.312634	−	0.0837699i	0.411724	+	0.911308i	$0.364927\pi$
$20$	−0.664879	−	7.65061i	−0.148672	−	1.71073i
$21$	−0.896080	+	0.517352i	−0.195541	+	0.112895i
$22$	−0.739767	+	0.427105i	−0.157719	+	0.0910591i
$23$	4.57650			0.954267			0.477133	−	0.878831i	$-0.341676\pi$
$23$	4.57650			0.954267			0.477133	+	0.878831i	$0.341676\pi$
$24$	0.183662	+	0.685437i	0.0374899	+	0.139914i
$25$	1.71554	−	4.69648i	0.343108	−	0.939296i
$26$	6.82838			1.33916
$27$	0.893629	+	0.893629i	0.171979	+	0.171979i
$28$	−16.1738	−	4.33375i	−3.05656	−	0.819002i
$29$	−4.08509	+	4.08509i	−0.758582	+	0.758582i	−0.976064	−	0.217482i	$-0.930216\pi$
$29$	−4.08509	+	4.08509i	−0.758582	+	0.758582i	0.217482	+	0.976064i	$0.430216\pi$
$30$	−0.192728	+	1.08933i	−0.0351872	+	0.198883i
$31$	−0.328846	−	0.328846i	−0.0590625	−	0.0590625i	0.676959	−	0.736021i	$-0.263298\pi$
$31$	−0.328846	−	0.328846i	−0.0590625	−	0.0590625i	−0.736021	+	0.676959i	$0.763298\pi$
$32$	2.26430	−	3.92188i	0.400275	−	0.693297i
$33$	0.0751151	−	0.0201270i	0.0130759	−	0.00350367i
$34$	11.0941	+	6.40518i	1.90262	+	1.09848i
$35$	−8.34739	−	7.01253i	−1.41097	−	1.18533i
$36$			10.1484i			1.69140i
$37$	5.51420	+	2.56780i	0.906529	+	0.422144i
$37$	5.51420	+	2.56780i	0.906529	+	0.422144i
$38$	−2.32556	−	2.32556i	−0.377256	−	0.377256i
$39$	−0.600455	−	0.160892i	−0.0961498	−	0.0257633i
$40$	−6.12711	+	4.28497i	−0.968782	+	0.677513i
$41$	7.08118	+	4.08832i	1.10590	+	0.638489i	0.937763	−	0.347276i	$-0.112893\pi$
$41$	7.08118	+	4.08832i	1.10590	+	0.638489i	0.168132	+	0.985764i	$0.446226\pi$
$42$	2.08891	+	1.20604i	0.322326	+	0.186095i
$43$	−6.04631			−0.922054			−0.461027	−	0.887386i	$-0.652519\pi$
$43$	−6.04631			−0.922054			−0.461027	+	0.887386i	$0.652519\pi$
$44$	1.08985	+	0.629224i	0.164301	+	0.0948592i
$45$	−2.79591	+	5.98681i	−0.416790	+	0.892460i
$46$	−5.33430	−	9.23928i	−0.786500	−	1.36226i
$47$	−4.97863	+	4.97863i	−0.726208	+	0.726208i	−0.969862	−	0.243654i	$-0.921654\pi$
$47$	−4.97863	+	4.97863i	−0.726208	+	0.726208i	0.243654	+	0.969862i	$0.421654\pi$
$48$	0.138972	−	0.138972i	0.0200589	−	0.0200589i
$49$	−14.5240	+	8.38545i	−2.07486	+	1.19792i
$50$	−11.4811	+	2.01073i	−1.62367	+	0.284360i
$51$	−0.824643	−	0.824643i	−0.115473	−	0.115473i
$52$	−5.02990	−	8.71203i	−0.697521	−	1.20814i
$53$	1.32960	−	4.96214i	0.182635	−	0.681603i	−0.812490	−	0.582976i	$-0.801888\pi$
$53$	1.32960	−	4.96214i	0.182635	−	0.681603i	0.995124	−	0.0986269i	$-0.0314451\pi$
$54$	0.762504	−	2.84570i	0.103764	−	0.387251i
$55$	0.469578	+	0.671454i	0.0633179	+	0.0905388i
$56$	4.21939	+	15.7470i	0.563840	+	2.10428i
$57$	0.149703	+	0.259294i	0.0198287	+	0.0343443i
$58$	13.0087	+	3.48567i	1.70813	+	0.457691i
$59$	2.31870	−	8.65349i	0.301869	−	1.12659i	−0.633739	−	0.773547i	$-0.718481\pi$
$59$	2.31870	−	8.65349i	0.301869	−	1.12659i	0.935608	−	0.353042i	$-0.114853\pi$
$60$	1.53179	−	0.556523i	0.197754	−	0.0718469i
$61$	−0.665487	+	0.178317i	−0.0852069	+	0.0228311i	−0.301171	−	0.953570i	$-0.597377\pi$
$61$	−0.665487	+	0.178317i	−0.0852069	+	0.0228311i	0.215964	+	0.976401i	$0.430711\pi$
$62$	−0.280594	+	1.04719i	−0.0356355	+	0.132993i
$63$	10.1873	+	10.1873i	1.28348	+	1.28348i
$64$	−12.4091			−1.55114
$65$	−0.567076	−	6.52522i	−0.0703372	−	0.809354i
$66$	−0.128187	−	0.128187i	−0.0157787	−	0.0157787i
$67$	−4.84572	+	1.29841i	−0.591999	+	0.158626i	−0.542367	−	0.840142i	$-0.682472\pi$
$67$	−4.84572	+	1.29841i	−0.591999	+	0.158626i	−0.0496322	+	0.998768i	$0.515805\pi$
$68$		−	18.8726i		−	2.28864i
$69$	0.251376	+	0.938146i	0.0302621	+	0.112940i
$70$	−4.42767	+	25.0259i	−0.529208	+	2.99116i
$71$	5.17637	−	8.96573i	0.614322	−	1.06404i	−0.376181	−	0.926546i	$-0.622763\pi$
$71$	5.17637	−	8.96573i	0.614322	−	1.06404i	0.990503	−	0.137491i	$-0.0439037\pi$
$72$	8.55683	−	4.94029i	1.00843	−	0.582219i
$73$	8.94360	−	8.94360i	1.04677	−	1.04677i	0.0479181	−	0.998851i	$-0.484741\pi$
$73$	8.94360	−	8.94360i	1.04677	−	1.04677i	0.998851	−	0.0479181i	$-0.0152587\pi$
$74$	−1.24326	−	14.1253i	−0.144526	−	1.64204i
$75$	1.05697	+	0.0937063i	0.122048	+	0.0108203i
$76$	−1.25404	+	4.68013i	−0.143848	+	0.536847i
$77$	1.72567	−	0.462391i	0.196658	−	0.0526944i
$78$	0.375066	+	1.39976i	0.0424678	+	0.158492i
$79$	1.85388	−	0.496745i	0.208578	−	0.0558882i	−0.153017	−	0.988224i	$-0.548899\pi$
$79$	1.85388	−	0.496745i	0.208578	−	0.0558882i	0.361595	+	0.932335i	$0.382232\pi$
$80$	1.87626	+	0.876237i	0.209772	+	0.0979662i
$81$	4.29834	−	7.44494i	0.477593	−	0.827216i
$82$		−	19.0612i		−	2.10495i
$83$	−0.386169	+	1.44120i	−0.0423875	+	0.158192i	−0.983876	−	0.178854i	$-0.942761\pi$
$83$	−0.386169	+	1.44120i	−0.0423875	+	0.158192i	0.941488	+	0.337046i	$0.109428\pi$
$84$		−	3.55354i		−	0.387723i
$85$	5.19948	−	11.1335i	0.563962	−	1.20760i
$86$	7.04749	+	12.2066i	0.759951	+	1.31627i
$87$	−1.06179	−	0.613027i	−0.113836	−	0.0657234i
$88$		−	1.22524i		−	0.130611i
$89$	7.19530	+	1.92798i	0.762701	+	0.204365i	0.619144	−	0.785277i	$-0.287480\pi$
$89$	7.19530	+	1.92798i	0.762701	+	0.204365i	0.143556	+	0.989642i	$0.454146\pi$
$90$	15.3454	−	1.33359i	1.61754	−	0.140573i
$91$	−13.7946	−	3.69626i	−1.44607	−	0.387474i
$92$	−7.85867	+	13.6116i	−0.819323	+	1.41911i
$93$	0.0493482	−	0.0854735i	0.00511717	−	0.00886319i
$94$	15.8541	+	4.24810i	1.63523	+	0.438158i
$95$	−2.02918	+	2.41544i	−0.208190	+	0.247819i
$96$	0.928326	+	0.248744i	0.0947468	+	0.0253873i
$97$		−	0.442430i		−	0.0449220i	−0.999748	−	0.0224610i	$-0.992850\pi$
$97$		−	0.442430i		−	0.0449220i	0.999748	−	0.0224610i	$-0.00715016\pi$
$98$	33.8580	+	19.5479i	3.42017	+	1.97464i
$99$	−0.541393	−	0.937719i	−0.0544120	−	0.0942443i
$100$	11.0226	+	13.1671i	1.10226	+	1.31671i
$101$			18.3189i			1.82280i	0.411519	+	0.911401i	$0.364999\pi$
$101$			18.3189i			1.82280i	−0.411519	+	0.911401i	$0.635001\pi$
$102$	−0.703641	+	2.62602i	−0.0696708	+	0.260015i
$103$		−	14.5303i		−	1.43171i	−0.698248	−	0.715856i	$-0.746037\pi$
$103$		−	14.5303i		−	1.43171i	0.698248	−	0.715856i	$-0.253963\pi$
$104$	−4.89716	+	8.48213i	−0.480206	+	0.831741i
$105$	0.979012	−	2.09633i	0.0955418	−	0.204581i
$106$	−11.5676	+	3.09953i	−1.12354	+	0.301053i
$107$	−4.94961	−	18.4722i	−0.478497	−	1.78577i	−0.607712	−	0.794158i	$-0.707912\pi$
$107$	−4.94961	−	18.4722i	−0.478497	−	1.78577i	0.129215	−	0.991617i	$-0.458754\pi$
$108$	−4.19238	+	1.12335i	−0.403412	+	0.108094i
$109$	0.385986	−	1.44052i	0.0369708	−	0.137977i	−0.944974	−	0.327146i	$-0.893913\pi$
$109$	0.385986	−	1.44052i	0.0369708	−	0.137977i	0.981944	+	0.189170i	$0.0605796\pi$
$110$	0.808233	−	1.73064i	0.0770620	−	0.165010i
$111$	−0.223498	+	1.27141i	−0.0212135	+	0.120677i
$112$	3.19269	−	3.19269i	0.301681	−	0.301681i
$113$	−2.42128	+	1.39793i	−0.227775	+	0.131506i	−0.609545	−	0.792751i	$-0.708648\pi$
$113$	−2.42128	+	1.39793i	−0.227775	+	0.131506i	0.381770	+	0.924257i	$0.375315\pi$
$114$	0.348984	−	0.604459i	0.0326854	−	0.0566127i
$115$	−8.38608	+	5.86477i	−0.782006	+	0.546892i
$116$	−5.13521	−	19.1649i	−0.476792	−	1.77941i
$117$			8.65557i			0.800208i
$118$	−20.1728	+	5.40528i	−1.85705	+	0.497596i
$119$	−18.9450	−	18.9450i	−1.73669	−	1.73669i
$120$	−1.21493	−	1.02065i	−0.110907	−	0.0931719i
$121$	10.8657			0.987794
$122$	1.13568	+	1.13568i	0.102819	+	0.102819i
$123$	−0.449122	+	1.67615i	−0.0404960	+	0.151133i
$124$	1.54275	−	0.413380i	0.138543	−	0.0371226i
$125$	2.87492	+	10.8044i	0.257141	+	0.966374i
$126$	8.69250	−	32.4409i	0.774390	−	2.89006i
$127$	13.9871	+	3.74783i	1.24115	+	0.332566i	0.818913	−	0.573918i	$-0.194577\pi$
$127$	13.9871	+	3.74783i	1.24115	+	0.332566i	0.422241	+	0.906484i	$0.361244\pi$
$128$	9.93525	+	17.2084i	0.878161	+	1.52102i
$129$	−0.332108	−	1.23945i	−0.0292405	−	0.109127i
$130$	−12.5125	+	8.75054i	−1.09742	+	0.767473i
$131$	−1.05224	+	3.92700i	−0.0919344	+	0.343104i	−0.996537	−	0.0831524i	$-0.973501\pi$
$131$	−1.05224	+	3.92700i	−0.0919344	+	0.343104i	0.904602	+	0.426256i	$0.140168\pi$
$132$	−0.0691234	+	0.257972i	−0.00601642	+	0.0224536i
$133$	3.43923	+	5.95693i	0.298219	+	0.516531i
$134$	8.26939	+	8.26939i	0.714366	+	0.714366i
$135$	−2.78269	−	0.492324i	−0.239495	−	0.0423725i
$136$	−15.9129	+	9.18731i	−1.36452	+	0.787805i
$137$	−5.83166	+	5.83166i	−0.498233	+	0.498233i	−0.910887	−	0.412655i	$-0.864602\pi$
$137$	−5.83166	+	5.83166i	−0.498233	+	0.498233i	0.412655	+	0.910887i	$0.364602\pi$
$138$	1.60098	−	1.60098i	0.136284	−	0.136284i
$139$	−4.47197	−	7.74568i	−0.379307	−	0.656980i	0.611654	−	0.791125i	$-0.290504\pi$
$139$	−4.47197	−	7.74568i	−0.379307	−	0.656980i	−0.990962	+	0.134146i	$0.957171\pi$
$140$	35.1909	−	12.7854i	2.97417	−	1.08056i
$141$	−1.29404	−	0.747116i	−0.108978	−	0.0629185i
$142$	−24.1340			−2.02528
$143$	0.929533	+	0.536666i	0.0777315	+	0.0448783i
$144$	−2.36991	−	1.36827i	−0.197492	−	0.114022i
$145$	2.25058	−	12.7206i	0.186901	−	1.05639i
$146$	−28.4803	−	7.63128i	−2.35705	−	0.631570i
$147$	−2.51672	−	2.51672i	−0.207575	−	0.207575i
$148$	−17.1061	+	11.9912i	−1.40611	+	0.985668i
$149$			0.433951i			0.0355507i	0.999842	+	0.0177753i	$0.00565836\pi$
$149$			0.433951i			0.0355507i	−0.999842	+	0.0177753i	$0.994342\pi$
$150$	−1.04281	−	2.24309i	−0.0851451	−	0.183148i
$151$	2.72909	+	1.57564i	0.222090	+	0.128224i	0.606918	−	0.794765i	$-0.292406\pi$
$151$	2.72909	+	1.57564i	0.222090	+	0.128224i	−0.384827	+	0.922989i	$0.625739\pi$
$152$	4.55662	−	1.22094i	0.369591	−	0.0990316i
$153$	−8.11913	+	14.0627i	−0.656393	+	1.13691i
$154$	−2.94491	−	2.94491i	−0.237308	−	0.237308i
$155$	1.02400	+	0.181170i	0.0822497	+	0.0145519i
$156$	1.50962	−	1.50962i	0.120866	−	0.120866i
$157$	2.61914	+	0.701796i	0.209030	+	0.0560094i	0.361814	−	0.932250i	$-0.382157\pi$
$157$	2.61914	+	0.701796i	0.209030	+	0.0560094i	−0.152785	+	0.988260i	$0.548824\pi$
$158$	−3.16371	−	3.16371i	−0.251691	−	0.251691i
$159$	1.09023			0.0864609
$160$	0.876720	+	10.0882i	0.0693108	+	0.797544i
$161$	5.77501	+	21.5526i	0.455135	+	1.69859i
$162$	−20.0403			−1.57452
$163$	14.7778	−	8.53197i	1.15749	−	0.668275i	0.206787	−	0.978386i	$-0.433699\pi$
$163$	14.7778	−	8.53197i	1.15749	−	0.668275i	0.950700	+	0.310111i	$0.100366\pi$
$164$	−24.3193	+	14.0408i	−1.89902	+	1.09640i
$165$	−0.111850	+	0.133141i	−0.00870750	+	0.0103650i
$166$	3.35968	−	0.900225i	0.260762	−	0.0698710i
$167$	17.4420	+	10.0702i	1.34970	+	0.779252i	0.988207	−	0.153122i	$-0.0489327\pi$
$167$	17.4420	+	10.0702i	1.34970	+	0.779252i	0.361496	+	0.932374i	$0.382266\pi$
$168$	−2.99624	+	1.72988i	−0.231165	+	0.133463i
$169$	2.21000	+	3.82783i	0.170000	+	0.294448i
$170$	−28.5373	+	2.48004i	−2.18871	+	0.190211i
$171$	2.94785	−	2.94785i	0.225428	−	0.225428i
$172$	10.3826	−	17.9832i	0.791665	−	1.37120i
$173$	−7.46566	−	2.00042i	−0.567604	−	0.152089i	−0.0364063	−	0.999337i	$-0.511591\pi$
$173$	−7.46566	−	2.00042i	−0.567604	−	0.152089i	−0.531197	+	0.847248i	$0.678258\pi$
$174$			2.85814i			0.216675i
$175$	24.2825	+	2.15277i	1.83558	+	0.162734i
$176$	−0.293880	+	0.169672i	−0.0221521	+	0.0127895i
$177$	1.90126			0.142907
$178$	−4.49444	−	16.7735i	−0.336873	−	1.25723i
$179$	1.06842	−	1.06842i	0.0798575	−	0.0798575i	−0.666050	−	0.745907i	$-0.732016\pi$
$179$	1.06842	−	1.06842i	0.0798575	−	0.0798575i	0.745907	+	0.666050i	$0.232016\pi$
$180$	−13.0051	−	18.5961i	−0.969343	−	1.38607i
$181$	−2.22142	+	3.84761i	−0.165117	+	0.285990i	−0.936697	−	0.350142i	$-0.886133\pi$
$181$	−2.22142	+	3.84761i	−0.165117	+	0.285990i	0.771580	+	0.636132i	$0.219467\pi$
$182$	8.61662	+	32.1577i	0.638706	+	2.38368i
$183$	−0.0731070	−	0.126625i	−0.00540423	−	0.00936040i
$184$	15.3026			1.12812
$185$	−13.3950	+	2.36112i	−0.984817	+	0.173593i
$186$	−0.230078			−0.0168701
$187$	1.00681	+	1.74385i	0.0736253	+	0.127523i
$188$	−6.25844	−	23.3568i	−0.456444	−	1.70347i
$189$	−3.08081	+	5.33612i	−0.224096	+	0.388146i
$190$	7.24161	+	1.28121i	0.525361	+	0.0929490i
$191$	3.14026	−	3.14026i	0.227221	−	0.227221i	−0.584310	−	0.811531i	$-0.698635\pi$
$191$	3.14026	−	3.14026i	0.227221	−	0.227221i	0.811531	+	0.584310i	$0.198635\pi$
$192$	−0.681599	−	2.54376i	−0.0491902	−	0.183580i
$193$	17.9118			1.28932			0.644660	−	0.764469i	$-0.276999\pi$
$193$	17.9118			1.28932			0.644660	+	0.764469i	$0.276999\pi$
$194$	−0.893201	+	0.515690i	−0.0641281	+	0.0370244i
$195$	1.30647	−	0.474660i	0.0935582	−	0.0339911i
$196$		−	57.5972i		−	4.11409i
$197$	9.19196	+	2.46298i	0.654900	+	0.175480i	0.570943	−	0.820989i	$-0.306578\pi$
$197$	9.19196	+	2.46298i	0.654900	+	0.175480i	0.0839569	+	0.996469i	$0.473244\pi$
$198$	−1.26208	+	2.18598i	−0.0896920	+	0.155351i
$199$	−2.18010	+	2.18010i	−0.154543	+	0.154543i	−0.780143	−	0.625601i	$-0.784854\pi$
$199$	−2.18010	+	2.18010i	−0.154543	+	0.154543i	0.625601	+	0.780143i	$0.284854\pi$
$200$	5.73629	−	15.7037i	0.405617	−	1.11042i
$201$	−0.532326	−	0.922015i	−0.0375474	−	0.0650339i
$202$	36.9832	−	21.3523i	2.60213	−	1.50234i
$203$	−24.3933	−	14.0835i	−1.71207	−	0.988465i
$204$	3.86874	−	1.03663i	0.270866	−	0.0725783i
$205$	−18.2149	+	1.58297i	−1.27218	+	0.110559i
$206$	−29.3345	+	16.9363i	−2.04383	+	1.18001i
$207$	11.7116	−	6.76169i	0.814012	−	0.469970i
$208$	2.71265			0.188088
$209$	−0.133800	−	0.499348i	−0.00925513	−	0.0345406i
$210$	−5.37330	+	0.466968i	−0.370793	+	0.0322239i
$211$	1.89866			0.130709			0.0653544	−	0.997862i	$-0.479182\pi$
$211$	1.89866			0.130709			0.0653544	+	0.997862i	$0.479182\pi$
$212$	12.4754	+	12.4754i	0.856816	+	0.856816i
$213$	2.12223	+	0.568649i	0.145413	+	0.0389632i
$214$	−31.5234	+	31.5234i	−2.15490	+	2.15490i
$215$	11.0794	−	7.74832i	0.755608	−	0.528431i
$216$	2.98805	+	2.98805i	0.203311	+	0.203311i
$217$	1.13371	−	1.96364i	0.0769610	−	0.133300i
$218$	−3.35810	+	0.899800i	−0.227439	+	0.0609421i
$219$	2.32462	+	1.34212i	0.157083	+	0.0906919i
$220$	−2.80341	+	0.243631i	−0.189006	+	0.0164256i
$221$		−	16.0965i		−	1.08277i
$222$	2.82729	−	1.03073i	0.189756	−	0.0691778i
$223$	−6.21109	−	6.21109i	−0.415925	−	0.415925i	0.467871	−	0.883797i	$-0.345021\pi$
$223$	−6.21109	−	6.21109i	−0.415925	−	0.415925i	−0.883797	+	0.467871i	$0.845021\pi$
$224$	21.3270	+	5.71456i	1.42497	+	0.381820i
$225$	−2.54877	−	14.5533i	−0.169918	−	0.970220i
$226$	5.64442	+	3.25881i	0.375461	+	0.216773i
$227$	−5.91235	−	3.41350i	−0.392417	−	0.226562i	0.290790	−	0.956787i	$-0.406082\pi$
$227$	−5.91235	−	3.41350i	−0.392417	−	0.226562i	−0.683207	+	0.730225i	$0.739415\pi$
$228$	−1.02827			−0.0680988
$229$	−1.40787	−	0.812833i	−0.0930345	−	0.0537135i	0.452761	−	0.891632i	$-0.350439\pi$
$229$	−1.40787	−	0.812833i	−0.0930345	−	0.0537135i	−0.545795	+	0.837918i	$0.683772\pi$
$230$	21.6148	+	10.0944i	1.42524	+	0.665604i
$231$	0.189573	+	0.328350i	0.0124730	+	0.0216038i
$232$	−13.6594	+	13.6594i	−0.896784	+	0.896784i
$233$	−11.5898	+	11.5898i	−0.759276	+	0.759276i	−0.976191	−	0.216915i	$-0.930401\pi$
$233$	−11.5898	+	11.5898i	−0.759276	+	0.759276i	0.216915	+	0.976191i	$0.430401\pi$
$234$	17.4743	−	10.0888i	1.14233	−	0.659526i
$235$	2.74286	−	15.5030i	0.178924	−	1.01131i
$236$	21.7559	+	21.7559i	1.41619	+	1.41619i
$237$	0.203658	+	0.352745i	0.0132290	+	0.0229133i
$238$	−16.1652	+	60.3293i	−1.04783	+	3.91057i
$239$	−1.42895	+	5.33292i	−0.0924313	+	0.344958i	−0.996617	−	0.0821803i	$-0.973812\pi$
$239$	−1.42895	+	5.33292i	−0.0924313	+	0.344958i	0.904186	+	0.427138i	$0.140478\pi$
$240$	−0.0765634	+	0.432747i	−0.00494215	+	0.0279337i
$241$	5.06390	+	18.8987i	0.326194	+	1.21737i	0.913106	+	0.407723i	$0.133677\pi$
$241$	5.06390	+	18.8987i	0.326194	+	1.21737i	−0.586911	+	0.809651i	$0.699656\pi$
$242$	−12.6649	−	21.9363i	−0.814133	−	1.41012i
$243$	5.42441	+	1.45347i	0.347976	+	0.0932399i
$244$	0.612403	−	2.28552i	0.0392051	−	0.146315i
$245$	15.8682	−	33.9782i	1.01378	−	2.17079i
$246$	3.90738	−	1.04698i	0.249126	−	0.0667530i
$247$	−1.06957	+	3.99169i	−0.0680551	+	0.253985i
$248$	−1.09957	−	1.09957i	−0.0698229	−	0.0698229i
$249$	−0.316646			−0.0200666
$250$	18.4615	−	18.3975i	1.16761	−	1.16356i
$251$	−3.50434	−	3.50434i	−0.221192	−	0.221192i	0.587808	−	0.809000i	$-0.299991\pi$
$251$	−3.50434	−	3.50434i	−0.221192	−	0.221192i	−0.809000	+	0.587808i	$0.799991\pi$
$252$	−47.7929	+	12.8061i	−3.01067	+	0.806707i
$253$		−	1.67697i		−	0.105430i
$254$	−8.73683	−	32.6063i	−0.548197	−	2.04590i
$255$	2.56787	+	0.454317i	0.160806	+	0.0284505i
$256$	10.7517	−	18.6225i	0.671980	−	1.16390i
$257$	−6.93002	+	4.00105i	−0.432283	+	0.249579i	−0.700319	−	0.713830i	$-0.746959\pi$
$257$	−6.93002	+	4.00105i	−0.432283	+	0.249579i	0.268036	+	0.963409i	$0.413625\pi$
$258$	−2.11516	+	2.11516i	−0.131684	+	0.131684i
$259$	−5.13456	+	29.2089i	−0.319046	+	1.81495i
$260$	20.3813	+	9.51833i	1.26400	+	0.590302i
$261$	−4.41840	+	16.4897i	−0.273492	+	1.02069i
$262$	9.15452	−	2.45295i	0.565568	−	0.151543i
$263$	4.35453	+	16.2513i	0.268512	+	1.00210i	0.960066	+	0.279775i	$0.0902600\pi$
$263$	4.35453	+	16.2513i	0.268512	+	1.00210i	−0.691553	+	0.722325i	$0.743073\pi$
$264$	0.251164	−	0.0672993i	0.0154581	−	0.00414198i
$265$	3.92257	+	10.7966i	0.240962	+	0.663231i
$266$	8.01744	−	13.8866i	0.491581	−	0.851443i
$267$			1.58088i			0.0967482i
$268$	4.45919	−	16.6419i	0.272388	−	1.01657i
$269$			19.7929i			1.20680i	0.797440	+	0.603398i	$0.206187\pi$
$269$			19.7929i			1.20680i	−0.797440	+	0.603398i	$0.793813\pi$
$270$	2.24953	+	6.19168i	0.136902	+	0.376813i
$271$	−12.7667	−	22.1125i	−0.775519	−	1.34324i	−0.934502	−	0.355958i	$-0.884155\pi$
$271$	−12.7667	−	22.1125i	−0.775519	−	1.34324i	0.158983	−	0.987281i	$-0.449179\pi$
$272$	4.40725	+	2.54453i	0.267229	+	0.154285i
$273$		−	3.03082i		−	0.183433i
$274$	18.5706	+	4.97597i	1.12189	+	0.300609i
$275$	−1.72093	−	0.628624i	−0.103776	−	0.0379075i
$276$	−3.22193	−	0.863313i	−0.193937	−	0.0519653i
$277$	13.2864	−	23.0128i	0.798305	−	1.38270i	−0.122415	−	0.992479i	$-0.539064\pi$
$277$	13.2864	−	23.0128i	0.798305	−	1.38270i	0.920720	−	0.390225i	$-0.127603\pi$
$278$	−10.4249	+	18.0565i	−0.625245	+	1.08296i
$279$	−1.32741	−	0.355677i	−0.0794697	−	0.0212938i
$280$	−27.9114	−	23.4480i	−1.66802	−	1.40128i
$281$	−6.65406	−	1.78295i	−0.396948	−	0.106362i	0.0548223	−	0.998496i	$-0.482541\pi$
$281$	−6.65406	−	1.78295i	−0.396948	−	0.106362i	−0.451771	+	0.892134i	$0.649207\pi$
$282$			3.48331i			0.207428i
$283$	5.34172	+	3.08404i	0.317532	+	0.183327i	0.650292	−	0.759684i	$-0.274646\pi$
$283$	5.34172	+	3.08404i	0.317532	+	0.183327i	−0.332760	+	0.943012i	$0.607980\pi$
$284$	17.7775	+	30.7915i	1.05490	+	1.82714i
$285$	−0.606604	−	0.283292i	−0.0359321	−	0.0167808i
$286$		−	2.50212i		−	0.147954i
$287$	−10.3180	+	38.5072i	−0.609051	+	2.27301i
$288$		−	13.3818i		−	0.788531i
$289$	6.59890	−	11.4296i	0.388171	−	0.672331i
$290$	−28.3043	+	10.2834i	−1.66209	+	0.603861i
$291$	0.0906946	−	0.0243016i	0.00531661	−	0.00142458i
$292$	11.2427	+	41.9582i	0.657926	+	2.45542i
$293$	−14.8916	+	3.99019i	−0.869975	+	0.233109i	−0.666077	−	0.745883i	$-0.732028\pi$
$293$	−14.8916	+	3.99019i	−0.869975	+	0.233109i	−0.203898	+	0.978992i	$0.565361\pi$
$294$	−2.14743	+	8.01433i	−0.125241	+	0.467405i
$295$	6.84058	+	18.8282i	0.398274	+	1.09622i
$296$	18.4380	+	8.58602i	1.07168	+	0.499052i
$297$	0.327452	−	0.327452i	0.0190007	−	0.0190007i
$298$	0.876083	−	0.505807i	0.0507501	−	0.0293006i
$299$	−6.70267	+	11.6094i	−0.387625	+	0.671386i
$300$	−2.09371	+	2.98277i	−0.120880	+	0.172210i
$301$	−7.62974	−	28.4746i	−0.439771	−	1.64125i
$302$		−	7.34618i		−	0.422725i
$303$	−3.75524	+	1.00621i	−0.215733	+	0.0578054i
$304$	−0.923854	−	0.923854i	−0.0529866	−	0.0529866i
$305$	0.990941	−	1.17957i	0.0567411	−	0.0675420i
$306$	37.8541			2.16398
$307$	13.0226	+	13.0226i	0.743237	+	0.743237i	0.973199	−	0.229962i	$-0.0738604\pi$
$307$	13.0226	+	13.0226i	0.743237	+	0.743237i	−0.229962	+	0.973199i	$0.573860\pi$
$308$	−1.58802	+	5.92655i	−0.0904856	+	0.337697i
$309$	2.97859	−	0.798112i	0.169446	−	0.0454030i
$310$	−0.827803	−	2.27847i	−0.0470161	−	0.129409i
$311$	0.130184	−	0.485853i	0.00738205	−	0.0275502i	−0.962137	−	0.272568i	$-0.912127\pi$
$311$	0.130184	−	0.485853i	0.00738205	−	0.0275502i	0.969519	+	0.245018i	$0.0787938\pi$
$312$	−2.00776	−	0.537977i	−0.113667	−	0.0304569i
$313$	8.25875	+	14.3046i	0.466812	+	0.808543i	0.999281	−	0.0379068i	$-0.0120690\pi$
$313$	8.25875	+	14.3046i	0.466812	+	0.808543i	−0.532469	+	0.846450i	$0.678736\pi$
$314$	−1.63601	−	6.10566i	−0.0923251	−	0.344562i
$315$	−31.7224	−	5.61246i	−1.78736	−	0.316226i
$316$	−1.70600	+	6.36688i	−0.0959700	+	0.358165i
$317$	4.96290	−	18.5218i	0.278744	−	1.04029i	−0.674546	−	0.738232i	$-0.735661\pi$
$317$	4.96290	−	18.5218i	0.278744	−	1.04029i	0.953291	−	0.302055i	$-0.0976726\pi$
$318$	−1.27076	−	2.20102i	−0.0712605	−	0.123427i
$319$	1.49690	+	1.49690i	0.0838102	+	0.0838102i
$320$	22.7387	−	15.9022i	1.27113	−	0.888959i
$321$	3.51478	−	2.02926i	0.196176	−	0.113262i
$322$	36.7803	−	36.7803i	2.04969	−	2.04969i
$323$	−5.48203	+	5.48203i	−0.305028	+	0.305028i
$324$	14.7620	+	25.5686i	0.820112	+	1.42048i
$325$	9.40116	+	11.2302i	0.521482	+	0.622942i
$326$	−34.4496	−	19.8895i	−1.90799	−	1.10158i
$327$	0.316496			0.0175023
$328$	23.6775	+	13.6702i	1.30737	+	0.754812i
$329$	−29.7289	−	17.1640i	−1.63901	−	0.946280i
$330$	0.399162	+	0.0706214i	0.0219732	+	0.00388758i
$331$	9.44128	+	2.52978i	0.518940	+	0.139049i	0.508776	−	0.860899i	$-0.330098\pi$
$331$	9.44128	+	2.52978i	0.518940	+	0.139049i	0.0101636	+	0.999948i	$0.496765\pi$
$332$	−3.62335	−	3.62335i	−0.198857	−	0.198857i
$333$	17.9051	−	1.57593i	0.981194	−	0.0863607i
$334$		−	46.9505i		−	2.56902i
$335$	7.21550	−	8.58899i	0.394225	−	0.469267i
$336$	0.829843	+	0.479110i	0.0452717	+	0.0261376i
$337$	−31.2631	+	8.37692i	−1.70301	+	0.456320i	−0.973694	−	0.227858i	$-0.926828\pi$
$337$	−31.2631	+	8.37692i	−1.70301	+	0.456320i	−0.729315	+	0.684178i	$0.760161\pi$
$338$	5.15188	−	8.92331i	0.280225	−	0.485364i
$339$	−0.419559	−	0.419559i	−0.0227873	−	0.0227873i
$340$	24.1852	+	34.5826i	1.31163	+	1.87551i
$341$	−0.120499	+	0.120499i	−0.00652539	+	0.00652539i
$342$	−9.38725	−	2.51531i	−0.507604	−	0.136012i
$343$	−33.6855	−	33.6855i	−1.81884	−	1.81884i
$344$	−20.2172			−1.09004
$345$	−1.66286	−	1.39694i	−0.0895252	−	0.0752089i
$346$	4.66331	+	17.4037i	0.250701	+	0.935630i
$347$	4.31321			0.231545			0.115773	−	0.993276i	$-0.463066\pi$
$347$	4.31321			0.231545			0.115773	+	0.993276i	$0.463066\pi$
$348$	3.64658	−	2.10535i	0.195477	−	0.112859i
$349$	11.5422	−	6.66391i	0.617841	−	0.356711i	−0.158187	−	0.987409i	$-0.550565\pi$
$349$	11.5422	−	6.66391i	0.617841	−	0.356711i	0.776028	+	0.630698i	$0.217231\pi$
$350$	−23.9571	−	51.5320i	−1.28056	−	2.75450i
$351$	−3.57569	+	0.958103i	−0.190856	+	0.0511397i
$352$	−1.43709	−	0.829705i	−0.0765973	−	0.0442234i
$353$	17.6672	−	10.2002i	0.940332	−	0.542901i	0.0502677	−	0.998736i	$-0.483993\pi$
$353$	17.6672	−	10.2002i	0.940332	−	0.542901i	0.890064	+	0.455835i	$0.150659\pi$
$354$	−2.21608	−	3.83836i	−0.117783	−	0.204006i
$355$	2.00425	+	23.0625i	0.106375	+	1.22403i
$356$	−18.0899	+	18.0899i	−0.958761	+	0.958761i
$357$	2.84298	−	4.92418i	0.150466	−	0.260615i
$358$	−3.40232	−	0.911649i	−0.179818	−	0.0481821i
$359$		−	34.9558i		−	1.84489i	−0.386123	−	0.922447i	$-0.626186\pi$
$359$		−	34.9558i		−	1.84489i	0.386123	−	0.922447i	$-0.373814\pi$
$360$	−9.34877	+	20.0182i	−0.492723	+	1.05505i
$361$	−14.7308	+	8.50481i	−0.775303	+	0.447621i
$362$	10.3570			0.544352
$363$	0.596827	+	2.22739i	0.0313253	+	0.116908i
$364$	34.6814	−	34.6814i	1.81780	−	1.81780i
$365$	−4.92727	+	27.8496i	−0.257905	+	1.45772i
$366$	−0.170425	+	0.295185i	−0.00890825	+	0.0154295i
$367$	−3.53325	−	13.1863i	−0.184434	−	0.688318i	−0.994751	−	0.102326i	$-0.967372\pi$
$367$	−3.53325	−	13.1863i	−0.184434	−	0.688318i	0.810317	−	0.585992i	$-0.199295\pi$
$368$	−2.11911	−	3.67040i	−0.110466	−	0.191333i
$369$	24.1617			1.25781
$370$	20.3797	+	24.2904i	1.05949	+	1.26280i
$371$	25.0466			1.30035
$372$	0.169479	+	0.293546i	0.00878708	+	0.0152197i
$373$	−9.24926	−	34.5187i	−0.478908	−	1.78731i	−0.606051	−	0.795426i	$-0.707247\pi$
$373$	−9.24926	−	34.5187i	−0.478908	−	1.78731i	0.127143	−	0.991884i	$-0.459419\pi$
$374$	2.34705	−	4.06521i	0.121363	−	0.210207i
$375$	−2.05690	+	1.18279i	−0.106218	+	0.0610792i
$376$	−16.6472	+	16.6472i	−0.858512	+	0.858512i
$377$	−4.37982	−	16.3457i	−0.225572	−	0.841848i
$378$	14.3638			0.738793
$379$	−7.67834	+	4.43309i	−0.394410	+	0.227713i	−0.684069	−	0.729417i	$-0.739791\pi$
$379$	−7.67834	+	4.43309i	−0.394410	+	0.227713i	0.289659	+	0.957130i	$0.406458\pi$
$380$	−3.69964	−	10.1830i	−0.189787	−	0.522377i
$381$			3.07310i			0.157440i
$382$	−9.99996	−	2.67948i	−0.511643	−	0.137094i
$383$	14.5143	−	25.1396i	0.741648	−	1.28457i	−0.210097	−	0.977681i	$-0.567378\pi$
$383$	14.5143	−	25.1396i	0.741648	−	1.28457i	0.951745	−	0.306891i	$-0.0992888\pi$
$384$	−2.98186	+	2.98186i	−0.152167	+	0.152167i
$385$	−2.56960	+	3.05873i	−0.130959	+	0.155887i
$386$	−20.8777	−	36.1613i	−1.06265	−	1.84056i
$387$	−15.4729	+	8.93331i	−0.786534	+	0.454106i
$388$	1.31589	+	0.759731i	0.0668043	+	0.0385695i
$389$	7.17950	−	1.92374i	0.364015	−	0.0975376i	−0.0721752	−	0.997392i	$-0.522994\pi$
$389$	7.17950	−	1.92374i	0.364015	−	0.0975376i	0.436190	+	0.899854i	$0.356327\pi$
$390$	−2.48107	−	2.08431i	−0.125634	−	0.105543i
$391$	−21.7797	+	12.5745i	−1.10145	+	0.635921i
$392$	−48.5644	+	28.0386i	−2.45287	+	1.41617i
$393$	−0.862801			−0.0435226
$394$	−5.74162	−	21.4280i	−0.289259	−	1.07953i
$395$	−2.76051	+	3.28598i	−0.138896	+	0.165336i
$396$	3.71867			0.186870
$397$	−20.5464	−	20.5464i	−1.03119	−	1.03119i	−0.999498	−	0.0316970i	$-0.989909\pi$
$397$	−20.5464	−	20.5464i	−1.03119	−	1.03119i	−0.0316970	−	0.999498i	$-0.510091\pi$
$398$	6.94238	+	1.86020i	0.347990	+	0.0932436i
$399$	−1.03221	+	1.03221i	−0.0516753	+	0.0516753i
$400$	−4.56099	+	0.798782i	−0.228050	+	0.0399391i
$401$	−12.1819	−	12.1819i	−0.608337	−	0.608337i	0.334174	−	0.942511i	$-0.391543\pi$
$401$	−12.1819	−	12.1819i	−0.608337	−	0.608337i	−0.942511	+	0.334174i	$0.891543\pi$
$402$	−1.24094	+	2.14937i	−0.0618926	+	0.107201i
$403$	1.31582	−	0.352572i	0.0655455	−	0.0175629i
$404$	−54.4849	−	31.4569i	−2.71072	−	1.56504i
$405$	1.66429	+	19.1506i	0.0826991	+	0.951600i
$406$			65.6619i			3.25874i
$407$	0.940918	−	2.02057i	0.0466396	−	0.100156i
$408$	−2.75738	−	2.75738i	−0.136511	−	0.136511i
$409$	26.5759	+	7.12099i	1.31409	+	0.352110i	0.846762	−	0.531972i	$-0.178549\pi$
$409$	26.5759	+	7.12099i	1.31409	+	0.352110i	0.467331	+	0.884082i	$0.345216\pi$
$410$	24.4268	+	34.9281i	1.20635	+	1.72498i
$411$	−1.51576	−	0.875126i	−0.0747670	−	0.0431668i
$412$	43.2165	+	24.9511i	2.12913	+	1.22925i
$413$	43.6788			2.14929
$414$	−27.3017	−	15.7627i	−1.34181	−	0.774692i
$415$	−1.13927	−	3.13576i	−0.0559245	−	0.153928i
$416$	6.63250	+	11.4878i	0.325185	+	0.563237i
$417$	1.34217	−	1.34217i	0.0657262	−	0.0657262i
$418$	−0.852154	+	0.852154i	−0.0416802	+	0.0416802i
$419$	−23.1243	+	13.3508i	−1.12969	+	0.652229i	−0.943858	−	0.330352i	$-0.892833\pi$
$419$	−23.1243	+	13.3508i	−1.12969	+	0.652229i	−0.185836	+	0.982581i	$0.559499\pi$
$420$	4.55384	+	6.51158i	0.222205	+	0.317733i
$421$	4.02616	+	4.02616i	0.196223	+	0.196223i	0.798379	−	0.602156i	$-0.205691\pi$
$421$	4.02616	+	4.02616i	0.196223	+	0.196223i	−0.602156	+	0.798379i	$0.705691\pi$
$422$	−2.21304	−	3.83311i	−0.107729	−	0.186593i
$423$	−5.38484	+	20.0965i	−0.261820	+	0.977125i
$424$	4.44582	−	16.5920i	0.215908	−	0.805780i
$425$	4.73987	+	27.0643i	0.229917	+	1.31281i
$426$	−1.32562	−	4.94727i	−0.0642264	−	0.239696i
$427$	−1.67953	−	2.90904i	−0.0812784	−	0.140778i
$428$	63.4401	+	16.9987i	3.06649	+	0.821664i
$429$	−0.0589554	+	0.220025i	−0.00284639	+	0.0106229i
$430$	−28.5567	−	13.3363i	−1.37713	−	0.643135i
$431$	8.13625	−	2.18010i	0.391909	−	0.105012i	−0.0574826	−	0.998347i	$-0.518307\pi$
$431$	8.13625	−	2.18010i	0.391909	−	0.105012i	0.449392	+	0.893335i	$0.351641\pi$
$432$	0.302913	−	1.13049i	0.0145739	−	0.0543905i
$433$	−1.88301	−	1.88301i	−0.0904917	−	0.0904917i	0.660412	−	0.750904i	$-0.270382\pi$
$433$	−1.88301	−	1.88301i	−0.0904917	−	0.0904917i	−0.750904	+	0.660412i	$0.770382\pi$
$434$	−5.28573			−0.253723
$435$	2.73125	−	0.237360i	0.130953	−	0.0113805i
$436$	3.62164	+	3.62164i	0.173445	+	0.173445i
$437$	6.23658	−	1.67109i	0.298336	−	0.0799389i
$438$		−	6.25741i		−	0.298991i
$439$	7.80392	+	29.1246i	0.372461	+	1.39004i	0.857019	+	0.515284i	$0.172314\pi$
$439$	7.80392	+	29.1246i	0.372461	+	1.39004i	−0.484559	+	0.874759i	$0.661020\pi$
$440$	1.57014	+	2.24516i	0.0748534	+	0.107034i
$441$	−24.7787	+	42.9179i	−1.17994	+	2.04371i
$442$	−32.4965	+	18.7618i	−1.54570	+	0.892410i
$443$	−20.2428	+	20.2428i	−0.961764	+	0.961764i	−0.999295	−	0.0375315i	$-0.988051\pi$
$443$	−20.2428	+	20.2428i	−0.961764	+	0.961764i	0.0375315	+	0.999295i	$0.488051\pi$
$444$	−3.39769	−	2.84797i	−0.161247	−	0.135159i
$445$	−15.6555	+	5.68788i	−0.742143	+	0.269632i
$446$	−5.29972	+	19.7788i	−0.250949	+	0.936554i
$447$	−0.0889565	+	0.0238358i	−0.00420750	+	0.00112740i
$448$	−15.6588	−	58.4395i	−0.739810	−	2.76101i
$449$	4.29808	−	1.15167i	0.202839	−	0.0543505i	−0.155969	−	0.987762i	$-0.549850\pi$
$449$	4.29808	−	1.15167i	0.202839	−	0.0543505i	0.358808	+	0.933411i	$0.383183\pi$
$450$	−26.4102	+	22.1087i	−1.24499	+	1.04221i
$451$	1.49808	−	2.59476i	0.0705420	−	0.122182i
$452$		−	9.60196i		−	0.451638i
$453$	−0.173092	+	0.645988i	−0.00813257	+	0.0303512i
$454$			15.9149i			0.746923i
$455$	30.0143	−	10.9047i	1.40709	−	0.511218i
$456$	0.500567	+	0.867008i	0.0234412	+	0.0406014i
$457$	−21.7236	−	12.5421i	−1.01619	−	0.586696i	−0.103190	−	0.994662i	$-0.532905\pi$
$457$	−21.7236	−	12.5421i	−1.01619	−	0.586696i	−0.912997	+	0.407966i	$0.866238\pi$
$458$			3.78970i			0.177081i
$459$	−6.70816	−	1.79745i	−0.313110	−	0.0838976i
$460$	−3.04282	−	35.0131i	−0.141872	−	1.63249i
$461$	−23.4572	−	6.28532i	−1.09251	−	0.292737i	−0.332798	−	0.942998i	$-0.607993\pi$
$461$	−23.4572	−	6.28532i	−1.09251	−	0.292737i	−0.759711	+	0.650261i	$0.774659\pi$
$462$	0.441927	−	0.765440i	0.0205603	−	0.0356115i
$463$	−17.3725	+	30.0901i	−0.807370	+	1.39841i	0.107309	+	0.994226i	$0.465777\pi$
$463$	−17.3725	+	30.0901i	−0.807370	+	1.39841i	−0.914679	+	0.404181i	$0.867557\pi$
$464$	5.16785	+	1.38472i	0.239911	+	0.0642840i
$465$	0.0191073	+	0.219863i	0.000886079	+	0.0101959i
$466$	36.9071	+	9.88924i	1.70969	+	0.458110i
$467$		−	36.2490i		−	1.67740i	−0.544591	−	0.838702i	$-0.683315\pi$
$467$		−	36.2490i		−	1.67740i	0.544591	−	0.838702i	$-0.316685\pi$
$468$	−25.7437	−	14.8631i	−1.19000	−	0.687049i
$469$	−12.2295	−	21.1820i	−0.564704	−	0.978096i
$470$	−34.4954	+	12.5327i	−1.59115	+	0.578090i
$471$			0.575450i			0.0265153i
$472$	7.75308	−	28.9349i	0.356865	−	1.33184i
$473$			2.21555i			0.101871i
$474$	0.474761	−	0.822310i	0.0218065	−	0.0377699i
$475$	0.622937	−	7.02650i	0.0285823	−	0.322398i
$476$	88.8791	−	23.8151i	4.07376	−	1.09156i
$477$	−3.92892	−	14.6629i	−0.179893	−	0.671370i
$478$	12.4320	−	3.33113i	0.568624	−	0.152362i
$479$	−5.57069	+	20.7901i	−0.254532	+	0.949925i	0.713819	+	0.700330i	$0.246964\pi$
$479$	−5.57069	+	20.7901i	−0.254532	+	0.949925i	−0.968350	+	0.249594i	$0.919703\pi$
$480$	−2.01985	+	0.733841i	−0.0921930	+	0.0334951i
$481$	−14.5898	+	10.2273i	−0.665239	+	0.466324i
$482$	32.2513	−	32.2513i	1.46901	−	1.46901i
$483$	−4.10091	+	2.36766i	−0.186598	+	0.107732i
$484$	−18.6584	+	32.3173i	−0.848108	+	1.46897i
$485$	0.566972	+	0.810719i	0.0257449	+	0.0368128i
$486$	−3.38828	−	12.6452i	−0.153695	−	0.573599i
$487$		−	21.0177i		−	0.952404i	−0.879336	−	0.476202i	$-0.842013\pi$
$487$		−	21.0177i		−	0.952404i	0.879336	−	0.476202i	$-0.157987\pi$
$488$	−2.22521	+	0.596242i	−0.100730	+	0.0269906i
$489$	2.56069	+	2.56069i	0.115799	+	0.115799i
$490$	−87.0927	+	7.56882i	−3.93445	+	0.341924i
$491$	19.3337			0.872519			0.436260	−	0.899821i	$-0.356303\pi$
$491$	19.3337			0.872519			0.436260	+	0.899821i	$0.356303\pi$
$492$	−4.21404	−	4.21404i	−0.189984	−	0.189984i
$493$	8.21676	−	30.6654i	0.370064	−	1.38110i
$494$	9.30530	−	2.49335i	0.418665	−	0.112181i
$495$	2.19374	+	1.02451i	0.0986014	+	0.0460481i
$496$	−0.111469	+	0.416007i	−0.00500510	+	0.0186793i
$497$	48.7553	+	13.0639i	2.18697	+	0.585998i
$498$	0.369078	+	0.639261i	0.0165388	+	0.0286460i
$499$	0.213597	+	0.797157i	0.00956194	+	0.0356856i	0.970542	−	0.240932i	$-0.0774531\pi$
$499$	0.213597	+	0.797157i	0.00956194	+	0.0356856i	−0.960980	+	0.276618i	$0.910786\pi$
$500$	−37.0716	−	10.0023i	−1.65789	−	0.447318i
$501$	−1.10626	+	4.12860i	−0.0494238	+	0.184452i
$502$	−2.99014	+	11.1594i	−0.133456	+	0.498066i
$503$	−11.5673	−	20.0352i	−0.515761	−	0.893324i	−0.999833	−	0.0182956i	$-0.994176\pi$
$503$	−11.5673	−	20.0352i	−0.515761	−	0.893324i	0.484072	−	0.875028i	$-0.339157\pi$
$504$	34.0636	+	34.0636i	1.51731	+	1.51731i
$505$	−23.4756	−	33.5680i	−1.04465	−	1.49376i
$506$	−3.38555	+	1.95465i	−0.150506	+	0.0868946i
$507$	−0.663284	+	0.663284i	−0.0294575	+	0.0294575i
$508$	−35.1652	+	35.1652i	−1.56021	+	1.56021i
$509$	14.9954	+	25.9727i	0.664658	+	1.15122i	0.979378	+	0.202036i	$0.0647559\pi$
$509$	14.9954	+	25.9727i	0.664658	+	1.15122i	−0.314720	+	0.949184i	$0.601911\pi$
$510$	−2.07587	−	5.71369i	−0.0919210	−	0.253007i
$511$	53.4049	+	30.8333i	2.36249	+	1.36399i
$512$	−10.3870			−0.459044
$513$	1.54409	+	0.891478i	0.0681731	+	0.0393597i
$514$	16.1551	+	9.32713i	0.712569	+	0.411402i
$515$	18.6205	+	26.6256i	0.820517	+	1.17327i
$516$	4.25670	+	1.14058i	0.187391	+	0.0502112i
$517$	1.82432	+	1.82432i	0.0802334	+	0.0802334i
$518$	64.9532	−	23.6795i	2.85388	−	1.04042i
$519$		−	1.64028i		−	0.0720002i
$520$	−1.89615	−	21.8185i	−0.0831515	−	0.956806i
$521$	4.56151	+	2.63359i	0.199843	+	0.115380i	0.596582	−	0.802552i	$-0.296525\pi$
$521$	4.56151	+	2.63359i	0.199843	+	0.115380i	−0.396739	+	0.917931i	$0.629858\pi$
$522$	38.4402	−	10.3000i	1.68248	−	0.450820i
$523$	−7.46593	+	12.9314i	−0.326462	+	0.565449i	−0.981807	−	0.189881i	$-0.939190\pi$
$523$	−7.46593	+	12.9314i	−0.326462	+	0.565449i	0.655345	+	0.755330i	$0.272523\pi$
$524$	−9.87297	−	9.87297i	−0.431303	−	0.431303i
$525$	0.892472	+	5.09596i	0.0389507	+	0.222406i
$526$	27.7335	−	27.7335i	1.20924	−	1.20924i
$527$	2.46854	+	0.661442i	0.107531	+	0.0288129i
$528$	−0.0509235	−	0.0509235i	−0.00221616	−	0.00221616i
$529$	−2.05563			−0.0893751
$530$	17.2247	−	20.5035i	0.748193	−	0.890614i
$531$	−6.85166	−	25.5707i	−0.297337	−	1.10968i
$532$	−23.6231			−1.02419
$533$	−20.7420	+	11.9754i	−0.898434	+	0.518711i
$534$	3.19156	−	1.84265i	0.138112	−	0.0797392i
$535$	32.7418	+	27.5059i	1.41555	+	1.18919i
$536$	−16.2027	+	4.34151i	−0.699852	+	0.187525i
$537$	0.277703	+	0.160332i	0.0119838	+	0.00691884i
$538$	39.9590	−	23.0703i	1.72275	−	0.994633i
$539$	3.07268	+	5.32203i	0.132350	+	0.229236i
$540$	6.24265	−	7.43096i	0.268641	−	0.319778i
$541$	−16.9353	+	16.9353i	−0.728105	+	0.728105i	−0.970242	−	0.242137i	$-0.922152\pi$
$541$	−16.9353	+	16.9353i	−0.728105	+	0.728105i	0.242137	+	0.970242i	$0.422152\pi$
$542$	−29.7613	+	51.5480i	−1.27836	+	2.21418i
$543$	−0.910745	−	0.244033i	−0.0390838	−	0.0104725i
$544$			24.8858i			1.06697i
$545$	1.13873	+	3.13428i	0.0487779	+	0.134258i
$546$	−6.11877	+	3.53268i	−0.261859	+	0.151185i
$547$	−0.870417			−0.0372163			−0.0186082	−	0.999827i	$-0.505924\pi$
$547$	−0.870417			−0.0372163			−0.0186082	+	0.999827i	$0.505924\pi$
$548$	−7.33076	−	27.3588i	−0.313154	−	1.16871i
$549$	−1.43957	+	1.43957i	−0.0614394	+	0.0614394i
$550$	0.736789	+	4.20702i	0.0314168	+	0.179388i
$551$	−4.07526	+	7.05856i	−0.173612	+	0.300705i
$552$	0.840531	+	3.13690i	0.0357754	+	0.133515i
$553$	4.67876	+	8.10385i	0.198961	+	0.344611i
$554$	−61.9459			−2.63183
$555$	−1.21976	−	2.61617i	−0.0517760	−	0.111050i
$556$	30.7166			1.30268
$557$	17.1411	+	29.6892i	0.726291	+	1.25797i	0.958440	+	0.285293i	$0.0920911\pi$
$557$	17.1411	+	29.6892i	0.726291	+	1.25797i	−0.232149	+	0.972680i	$0.574576\pi$
$558$	0.829144	+	3.09441i	0.0351005	+	0.130997i
$559$	8.85532	−	15.3379i	0.374540	−	0.648723i
$560$	−1.75894	+	9.94178i	−0.0743288	+	0.420117i
$561$	−0.302173	+	0.302173i	−0.0127578	+	0.0127578i
$562$	4.15636	+	15.5118i	0.175326	+	0.654324i
$563$	−19.7674			−0.833098			−0.416549	−	0.909113i	$-0.636761\pi$
$563$	−19.7674			−0.833098			−0.416549	+	0.909113i	$0.636761\pi$
$564$	4.44420	−	2.56586i	0.187135	−	0.108042i
$565$	2.64537	−	5.66445i	0.111292	−	0.238305i
$566$		−	14.3789i		−	0.604389i
$567$	40.4853	+	10.8480i	1.70022	+	0.455573i
$568$	17.3084	−	29.9789i	0.726242	−	1.25789i
$569$	15.7339	−	15.7339i	0.659600	−	0.659600i	−0.295685	−	0.955285i	$-0.595548\pi$
$569$	15.7339	−	15.7339i	0.659600	−	0.659600i	0.955285	+	0.295685i	$0.0955480\pi$
$570$	0.135124	+	1.55484i	0.00565974	+	0.0651253i
$571$	−23.2159	−	40.2112i	−0.971557	−	1.68279i	−0.690858	−	0.722990i	$-0.742767\pi$
$571$	−23.2159	−	40.2112i	−0.971557	−	1.68279i	−0.280699	−	0.959796i	$-0.590566\pi$
$572$	−3.19235	+	1.84310i	−0.133479	+	0.0770640i
$573$	0.816215	+	0.471242i	0.0340979	+	0.0196864i
$574$	89.7668	−	24.0530i	3.74680	−	1.00395i
$575$	7.85117	−	21.4935i	0.327416	−	0.896339i
$576$	−31.7557	+	18.3342i	−1.32316	+	0.763924i
$577$	−8.06980	+	4.65910i	−0.335950	+	0.193961i	−0.658480	−	0.752598i	$-0.728800\pi$
$577$	−8.06980	+	4.65910i	−0.335950	+	0.193961i	0.322530	+	0.946559i	$0.395467\pi$
$578$	−30.7663			−1.27971
$579$	0.983849	+	3.67178i	0.0408874	+	0.152594i
$580$	33.9695	+	28.5373i	1.41051	+	1.18495i
$581$	−7.27451			−0.301797
$582$	−0.154774	−	0.154774i	−0.00641557	−	0.00641557i
$583$	−1.81828	−	0.487205i	−0.0753053	−	0.0201780i
$584$	29.9049	−	29.9049i	1.23748	−	1.23748i
$585$	−11.0921	−	15.8607i	−0.458601	−	0.655757i
$586$	25.4130	+	25.4130i	1.04980	+	1.04980i
$587$	6.93015	−	12.0034i	0.286038	−	0.495433i	−0.686822	−	0.726825i	$-0.740995\pi$
$587$	6.93015	−	12.0034i	0.286038	−	0.495433i	0.972860	+	0.231393i	$0.0743283\pi$
$588$	11.8070	−	3.16367i	0.486911	−	0.130467i
$589$	−0.568208	−	0.328055i	−0.0234126	−	0.0135173i
$590$	30.0382	−	35.7560i	1.23665	−	1.47205i
$591$			2.01956i			0.0830738i
$592$	−0.493896	−	5.61144i	−0.0202990	−	0.230629i
$593$	8.34054	+	8.34054i	0.342505	+	0.342505i	0.857308	−	0.514803i	$-0.172135\pi$
$593$	8.34054	+	8.34054i	0.342505	+	0.342505i	−0.514803	+	0.857308i	$0.672135\pi$
$594$	−1.04275	−	0.279404i	−0.0427846	−	0.0114641i
$595$	58.9933	+	10.4373i	2.41849	+	0.427889i
$596$	−1.29067	−	0.745171i	−0.0528681	−	0.0305234i
$597$	−0.566649	−	0.327155i	−0.0231914	−	0.0133896i
$598$	31.2501			1.27791
$599$	6.26237	+	3.61558i	0.255874	+	0.147729i	0.622451	−	0.782659i	$-0.286137\pi$
$599$	6.26237	+	3.61558i	0.255874	+	0.147729i	−0.366577	+	0.930388i	$0.619470\pi$
$600$	3.53422	+	0.313328i	0.144284	+	0.0127916i
$601$	−2.21805	−	3.84178i	−0.0904763	−	0.156709i	0.817235	−	0.576304i	$-0.195506\pi$
$601$	−2.21805	−	3.84178i	−0.0904763	−	0.156709i	−0.907712	+	0.419595i	$0.862172\pi$
$602$	−48.5929	+	48.5929i	−1.98050	+	1.98050i
$603$	−10.4822	+	10.4822i	−0.426867	+	0.426867i
$604$	−9.37267	+	5.41131i	−0.381368	+	0.220183i
$605$	−19.9106	+	13.9244i	−0.809481	+	0.566107i
$606$	6.40844	+	6.40844i	0.260325	+	0.260325i
$607$	12.1001	+	20.9580i	0.491129	+	0.850661i	0.999948	−	0.0102130i	$-0.00325094\pi$
$607$	12.1001	+	20.9580i	0.491129	+	0.850661i	−0.508819	+	0.860874i	$0.669918\pi$
$608$	1.65359	−	6.17129i	0.0670620	−	0.250279i
$609$	1.54714	−	5.77399i	0.0626931	−	0.233974i
$610$	−3.53641	−	0.625675i	−0.143185	−	0.0253328i
$611$	−5.33783	−	19.9211i	−0.215946	−	0.805920i
$612$	−27.8840	−	48.2964i	−1.12714	−	1.95227i
$613$	3.64410	+	0.976435i	0.147184	+	0.0394378i	0.331659	−	0.943399i	$-0.392392\pi$
$613$	3.64410	+	0.976435i	0.147184	+	0.0394378i	−0.184475	+	0.982837i	$0.559058\pi$
$614$	11.1117	−	41.4695i	0.448433	−	1.67357i
$615$	−1.32499	−	3.64696i	−0.0534289	−	0.147059i
$616$	5.77016	−	1.54611i	0.232486	−	0.0622945i
$617$	−3.01209	+	11.2413i	−0.121262	+	0.452556i	−0.999679	−	0.0253391i	$-0.991933\pi$
$617$	−3.01209	+	11.2413i	−0.121262	+	0.452556i	0.878417	+	0.477895i	$0.158600\pi$
$618$	−5.08307	−	5.08307i	−0.204471	−	0.204471i
$619$	26.3769			1.06018			0.530089	−	0.847942i	$-0.322159\pi$
$619$	26.3769			1.06018			0.530089	+	0.847942i	$0.322159\pi$
$620$	−2.29723	+	2.73452i	−0.0922591	+	0.109821i
$621$	4.08969	+	4.08969i	0.164114	+	0.164114i
$622$	−1.13261	+	0.303481i	−0.0454133	+	0.0121685i
$623$			36.3185i			1.45507i
$624$	0.148999	+	0.556071i	0.00596472	+	0.0222606i
$625$	−19.1138	−	16.1140i	−0.764554	−	0.644560i
$626$	19.2526	−	33.3464i	0.769487	−	1.33279i
$627$	0.0950130	−	0.0548558i	0.00379445	−	0.00219073i
$628$	−6.58483	+	6.58483i	−0.262763	+	0.262763i
$629$	−33.2976	+	2.93072i	−1.32766	+	0.116855i
$630$	25.6445	+	70.5848i	1.02170	+	2.81216i
$631$	−2.96939	+	11.0819i	−0.118210	+	0.441164i	−0.999507	−	0.0313980i	$-0.990004\pi$
$631$	−2.96939	+	11.0819i	−0.118210	+	0.441164i	0.881297	+	0.472562i	$0.156671\pi$
$632$	6.19886	−	1.66098i	0.246577	−	0.0660702i
$633$	0.104288	+	0.389209i	0.00414509	+	0.0154697i
$634$	−43.1774	+	11.5694i	−1.71480	+	0.459478i
$635$	−30.4331	+	11.0568i	−1.20770	+	0.438775i
$636$	−1.87212	+	3.24261i	−0.0742344	+	0.128578i
$637$		−	49.1247i		−	1.94639i
$638$	1.27725	−	4.76678i	0.0505670	−	0.188718i
$639$		−	30.5919i		−	1.21020i
$640$	−40.2580	−	18.8010i	−1.59134	−	0.743175i
$641$	−15.1448	−	26.2315i	−0.598183	−	1.03608i	−0.993089	−	0.117362i	$-0.962556\pi$
$641$	−15.1448	−	26.2315i	−0.598183	−	1.03608i	0.394906	−	0.918722i	$-0.370777\pi$
$642$	−8.19356	−	4.73055i	−0.323374	−	0.186700i
$643$		−	32.4250i		−	1.27872i	−0.768909	−	0.639358i	$-0.779200\pi$
$643$		−	32.4250i		−	1.27872i	0.768909	−	0.639358i	$-0.220800\pi$
$644$	−74.0194	−	19.8334i	−2.91677	−	0.781547i
$645$	2.19691	+	1.84559i	0.0865031	+	0.0726701i
$646$	17.4572	+	4.67764i	0.686844	+	0.184039i
$647$	−2.01003	+	3.48147i	−0.0790223	+	0.136871i	−0.902828	−	0.430001i	$-0.858513\pi$
$647$	−2.01003	+	3.48147i	−0.0790223	+	0.136871i	0.823806	+	0.566872i	$0.191847\pi$
$648$	14.3725	−	24.8938i	0.564604	−	0.977922i
$649$	−3.17090	−	0.849639i	−0.124469	−	0.0333512i
$650$	11.7144	−	32.0694i	0.459475	−	1.25786i
$651$	0.464802	+	0.124543i	0.0182170	+	0.00488123i
$652$			58.6036i			2.29509i
$653$	−18.1616	−	10.4856i	−0.710720	−	0.410334i	0.100607	−	0.994926i	$-0.467921\pi$
$653$	−18.1616	−	10.4856i	−0.710720	−	0.410334i	−0.811328	+	0.584592i	$0.801255\pi$
$654$	−0.368903	−	0.638960i	−0.0144253	−	0.0249853i
$655$	−3.10429	−	8.54437i	−0.121295	−	0.333856i
$656$		−	7.57225i		−	0.295647i
$657$	9.67332	−	36.1013i	0.377392	−	1.40845i
$658$			80.0243i			3.11967i
$659$	−13.9788	+	24.2120i	−0.544538	+	0.943167i	0.454098	+	0.890952i	$0.349961\pi$
$659$	−13.9788	+	24.2120i	−0.544538	+	0.943167i	−0.998636	+	0.0522152i	$0.983372\pi$
$660$	−0.203927	−	0.561295i	−0.00793783	−	0.0218484i
$661$	−15.3797	+	4.12099i	−0.598203	+	0.160288i	−0.545199	−	0.838306i	$-0.683546\pi$
$661$	−15.3797	+	4.12099i	−0.598203	+	0.160288i	−0.0530034	+	0.998594i	$0.516879\pi$
$662$	−5.89736	−	22.0092i	−0.229207	−	0.855413i
$663$	3.29965	−	0.884140i	0.128148	−	0.0343371i
$664$	−1.29124	+	4.81898i	−0.0501099	+	0.187013i
$665$	−13.9359	−	6.50824i	−0.540411	−	0.252379i
$666$	−24.0515	−	34.3109i	−0.931977	−	1.32952i
$667$	−18.6954	+	18.6954i	−0.723890	+	0.723890i
$668$	−59.9021	+	34.5845i	−2.31768	+	1.33811i
$669$	0.932064	−	1.61438i	0.0360357	−	0.0624156i
$670$	−25.7502	−	4.55583i	−0.994817	−	0.176007i
$671$	0.0653405	+	0.243854i	0.00252244	+	0.00941389i
$672$			4.68575i			0.180757i
$673$	−2.59711	+	0.695893i	−0.100111	+	0.0268247i	−0.308527	−	0.951216i	$-0.599836\pi$
$673$	−2.59711	+	0.695893i	−0.100111	+	0.0268247i	0.208416	+	0.978040i	$0.433169\pi$
$674$	53.3516	+	53.3516i	2.05503	+	2.05503i
$675$	5.72996	−	2.66385i	0.220546	−	0.102532i
$676$	−15.1798			−0.583839
$677$	21.7292	+	21.7292i	0.835122	+	0.835122i	0.988212	−	0.153090i	$-0.0489225\pi$
$677$	21.7292	+	21.7292i	0.835122	+	0.835122i	−0.153090	+	0.988212i	$0.548922\pi$
$678$	−0.357996	+	1.33606i	−0.0137487	+	0.0513110i
$679$	2.08359	−	0.558295i	0.0799607	−	0.0214254i
$680$	17.3856	−	37.2273i	0.666708	−	1.42760i
$681$	0.374990	−	1.39948i	0.0143696	−	0.0536282i
$682$	0.383722	+	0.102818i	0.0146935	+	0.00393710i
$683$	16.0373	+	27.7774i	0.613650	+	1.06287i	0.990620	+	0.136647i	$0.0436327\pi$
$683$	16.0373	+	27.7774i	0.613650	+	1.06287i	−0.376970	+	0.926225i	$0.623034\pi$
$684$	3.70563	+	13.8296i	0.141688	+	0.528788i
$685$	3.21282	−	18.1593i	0.122755	−	0.693832i
$686$	−28.7427	+	107.269i	−1.09740	+	4.09556i
$687$	0.0892936	−	0.333248i	0.00340677	−	0.0127142i
$688$	2.79969	+	4.84921i	0.106737	+	0.184874i
$689$	10.6403	+	10.6403i	0.405363	+	0.405363i
$690$	−0.882022	+	4.98532i	−0.0335780	+	0.189788i
$691$	21.6651	−	12.5084i	0.824181	−	0.475841i	−0.0276751	−	0.999617i	$-0.508810\pi$
$691$	21.6651	−	12.5084i	0.824181	−	0.475841i	0.851856	+	0.523776i	$0.175477\pi$
$692$	18.7696	−	18.7696i	0.713512	−	0.713512i
$693$	3.73293	−	3.73293i	0.141802	−	0.141802i
$694$	−5.02741	−	8.70773i	−0.190838	−	0.330541i
$695$	18.1206	+	8.46254i	0.687353	+	0.321002i
$696$	−3.55035	−	2.04979i	−0.134576	−	0.0776972i
$697$	−44.9327			−1.70195
$698$	−26.9069	−	15.5347i	−1.01844	−	0.587997i
$699$	−3.01243	−	1.73923i	−0.113940	−	0.0657835i
$700$	−48.1002	+	68.5251i	−1.81802	+	2.59001i
$701$	−19.4813	−	5.22000i	−0.735799	−	0.197157i	−0.128589	−	0.991698i	$-0.541045\pi$
$701$	−19.4813	−	5.22000i	−0.735799	−	0.197157i	−0.607210	+	0.794541i	$0.707711\pi$
$702$	6.10204	+	6.10204i	0.230307	+	0.230307i
$703$	8.45203	+	1.48576i	0.318774	+	0.0560366i
$704$			4.54706i			0.171374i
$705$	3.32866	−	0.289278i	0.125365	−	0.0108948i
$706$	−41.1853	−	23.7784i	−1.55003	−	0.894911i
$707$	−86.2714	+	23.1164i	−3.24457	+	0.869380i
$708$	−3.26479	+	5.65479i	−0.122698	+	0.212520i
$709$	13.2911	+	13.2911i	0.499158	+	0.499158i	0.911176	−	0.412018i	$-0.135176\pi$
$709$	13.2911	+	13.2911i	0.499158	+	0.499158i	−0.412018	+	0.911176i	$0.635176\pi$
$710$	44.2237	−	30.9276i	1.65968	−	1.16069i
$711$	4.01028	−	4.01028i	0.150397	−	0.150397i
$712$	24.0591	+	6.44662i	0.901653	+	0.241597i
$713$	−1.50497	−	1.50497i	−0.0563614	−	0.0563614i
$714$	−13.2549			−0.496053
$715$	−2.39103	+	0.207794i	−0.0894195	+	0.00777104i
$716$	1.34307	+	5.01240i	0.0501929	+	0.187322i
$717$	−1.17170			−0.0437578
$718$	−70.5705	+	40.7439i	−2.63367	+	1.52055i
$719$	31.4778	−	18.1737i	1.17392	−	0.677765i	0.219323	−	0.975652i	$-0.429615\pi$
$719$	31.4778	−	18.1737i	1.17392	−	0.677765i	0.954601	+	0.297887i	$0.0962820\pi$
$720$	6.09610	−	0.529784i	0.227188	−	0.0197439i
$721$	68.4291	−	18.3355i	2.54843	−	0.682851i
$722$	34.3399	+	19.8262i	1.27800	+	0.737853i
$723$	−3.59594	+	2.07612i	−0.133734	+	0.0772116i
$724$	−7.62913	−	13.2140i	−0.283534	−	0.491096i
$725$	12.1774	+	26.1937i	0.452258	+	0.972809i
$726$	3.80111	−	3.80111i	0.141073	−	0.141073i
$727$	4.77979	−	8.27884i	0.177273	−	0.307045i	−0.763673	−	0.645604i	$-0.776606\pi$
$727$	4.77979	−	8.27884i	0.177273	−	0.307045i	0.940945	+	0.338558i	$0.109939\pi$
$728$	−46.1255	−	12.3593i	−1.70952	−	0.458066i
$729$		−	24.5982i		−	0.911046i
$730$	61.9675	−	22.5137i	2.29352	−	0.833269i
$731$	28.7746	−	16.6130i	1.06427	−	0.614454i
$732$	0.502151			0.0185600
$733$	−3.11673	−	11.6318i	−0.115119	−	0.429630i	0.884177	−	0.467153i	$-0.154720\pi$
$733$	−3.11673	−	11.6318i	−0.115119	−	0.429630i	−0.999296	+	0.0375224i	$0.988053\pi$
$734$	−22.5029	+	22.5029i	−0.830596	+	0.830596i
$735$	7.83685	+	1.38653i	0.289067	+	0.0511428i
$736$	10.3626	−	17.9485i	0.381969	−	0.661590i
$737$	0.475774	+	1.77561i	0.0175254	+	0.0654056i
$738$	−28.1625	−	48.7789i	−1.03668	−	1.79557i
$739$	0.812918			0.0299037			0.0149518	−	0.999888i	$-0.495241\pi$
$739$	0.812918			0.0299037			0.0149518	+	0.999888i	$0.495241\pi$
$740$	15.9790	−	43.8943i	0.587399	−	1.61359i
$741$	−0.877012			−0.0322179
$742$	−29.1939	−	50.5653i	−1.07174	−	1.85631i
$743$	7.48298	+	27.9269i	0.274524	+	1.02454i	0.956160	+	0.292846i	$0.0946023\pi$
$743$	7.48298	+	27.9269i	0.274524	+	1.02454i	−0.681636	+	0.731692i	$0.738731\pi$
$744$	0.165007	−	0.285800i	0.00604944	−	0.0104779i
$745$	−0.556106	−	0.795182i	−0.0203742	−	0.0291332i
$746$	−58.9074	+	58.9074i	−2.15675	+	2.15675i
$747$	1.14111	+	4.25869i	0.0417511	+	0.155817i
$748$	−6.91549			−0.252856
$749$	80.7473	−	46.6195i	2.95044	−	1.70344i
$750$	4.78538	+	2.77393i	0.174737	+	0.101290i
$751$			24.6777i			0.900504i	0.892902	+	0.450252i	$0.148666\pi$
$751$			24.6777i			0.900504i	−0.892902	+	0.450252i	$0.851334\pi$
$752$	6.29822	+	1.68760i	0.229673	+	0.0615406i
$753$	0.525877	−	0.910846i	0.0191640	−	0.0331931i
$754$	−27.8946	+	27.8946i	−1.01586	+	1.01586i
$755$	−7.02003	+	0.610078i	−0.255485	+	0.0222030i
$756$	−10.5806	−	18.3261i	−0.384812	−	0.666515i
$757$	−4.64953	+	2.68441i	−0.168990	+	0.0975664i	−0.582109	−	0.813110i	$-0.697772\pi$
$757$	−4.64953	+	2.68441i	−0.168990	+	0.0975664i	0.413120	+	0.910677i	$0.364439\pi$
$758$	17.8995	+	10.3343i	0.650140	+	0.375358i
$759$	0.343765	−	0.0921114i	0.0124779	−	0.00334343i
$760$	−6.78502	+	8.07657i	−0.246119	+	0.292968i
$761$	2.47876	−	1.43111i	0.0898548	−	0.0518777i	−0.454399	−	0.890798i	$-0.650146\pi$
$761$	2.47876	−	1.43111i	0.0898548	−	0.0518777i	0.544254	+	0.838920i	$0.316813\pi$
$762$	6.20414	−	3.58196i	0.224752	−	0.129761i
$763$	7.27107			0.263231
$764$	3.94750	+	14.7323i	0.142815	+	0.532995i
$765$	−3.14367	−	36.1735i	−0.113660	−	1.30786i
$766$	−67.6708			−2.44504
$767$	18.5557	+	18.5557i	0.670006	+	0.670006i
$768$	4.40802	+	1.18112i	0.159061	+	0.0426202i
$769$	−7.89866	+	7.89866i	−0.284833	+	0.284833i	−0.835033	−	0.550200i	$-0.814552\pi$
$769$	−7.89866	+	7.89866i	−0.284833	+	0.284833i	0.550200	+	0.835033i	$0.314552\pi$
$770$	9.17021	+	1.62243i	0.330472	+	0.0584683i
$771$	−1.20083	−	1.20083i	−0.0432469	−	0.0432469i
$772$	−30.7577	+	53.2740i	−1.10700	+	1.91737i
$773$	−2.70117	+	0.723776i	−0.0971543	+	0.0260324i	−0.307069	−	0.951687i	$-0.599348\pi$
$773$	−2.70117	+	0.723776i	−0.0971543	+	0.0260324i	0.209914	+	0.977720i	$0.432681\pi$
$774$	36.0701	+	20.8251i	1.29651	+	0.748542i
$775$	−2.10857	+	0.980271i	−0.0757420	+	0.0352124i
$776$		−	1.47936i		−	0.0531061i
$777$	−6.26962	+	0.551826i	−0.224921	+	0.0197967i
$778$	−12.2521	−	12.2521i	−0.439258	−	0.439258i
$779$	11.1426	+	2.98566i	0.399226	+	0.106972i
$780$	−0.831689	+	4.70083i	−0.0297792	+	0.168317i
$781$	−3.28531	−	1.89677i	−0.117558	−	0.0678719i
$782$	50.7722	+	29.3133i	1.81561	+	1.04824i
$783$	−7.30110			−0.260920
$784$	13.4504	+	7.76562i	0.480373	+	0.277343i
$785$	−5.69871	+	2.07043i	−0.203396	+	0.0738967i
$786$	1.00567	+	1.74187i	0.0358710	+	0.0621304i
$787$	16.6179	−	16.6179i	0.592366	−	0.592366i	−0.345904	−	0.938270i	$-0.612428\pi$
$787$	16.6179	−	16.6179i	0.592366	−	0.592366i	0.938270	+	0.345904i	$0.112428\pi$
$788$	−23.1097	+	23.1097i	−0.823250	+	0.823250i
$789$	−3.09221	+	1.78529i	−0.110086	+	0.0635580i
$790$	9.85153	+	1.74297i	0.350502	+	0.0620122i
$791$	−9.63879	−	9.63879i	−0.342716	−	0.342716i
$792$	−1.81027	−	3.13548i	−0.0643251	−	0.111414i
$793$	0.522319	−	1.94932i	0.0185481	−	0.0692225i
$794$	−17.5316	+	65.4287i	−0.622173	+	2.32198i
$795$	−1.99776	+	1.39713i	−0.0708534	+	0.0495509i
$796$	−2.74051	−	10.2277i	−0.0971349	−	0.362512i
$797$	10.7864	+	18.6826i	0.382074	+	0.661772i	0.991359	−	0.131180i	$-0.0418765\pi$
$797$	10.7864	+	18.6826i	0.382074	+	0.661772i	−0.609284	+	0.792952i	$0.708543\pi$
$798$	3.28702	+	0.880755i	0.116359	+	0.0311784i
$799$	10.0140	−	37.3729i	0.354271	−	1.32216i
$800$	−14.5345	−	17.3624i	−0.513873	−	0.613852i
$801$	21.2618	−	5.69709i	0.751250	−	0.201297i
$802$	−10.3945	+	38.7926i	−0.367041	+	1.36982i
$803$	−3.27720	−	3.27720i	−0.115650	−	0.115650i
$804$	3.65639			0.128951
$805$	−38.2019	−	32.0929i	−1.34644	−	1.13112i
$806$	−2.24549	−	2.24549i	−0.0790939	−	0.0790939i
$807$	−4.05739	+	1.08717i	−0.142827	+	0.0382704i
$808$			61.2535i			2.15489i
$809$	−6.16251	−	22.9988i	−0.216662	−	0.808595i	−0.985575	−	0.169241i	$-0.945868\pi$
$809$	−6.16251	−	22.9988i	−0.216662	−	0.808595i	0.768912	−	0.639354i	$-0.220798\pi$
$810$	36.7223	−	25.6816i	1.29029	−	0.902359i
$811$	21.2556	−	36.8158i	0.746385	−	1.29278i	−0.203160	−	0.979146i	$-0.565121\pi$
$811$	21.2556	−	36.8158i	0.746385	−	1.29278i	0.949545	−	0.313631i	$-0.101545\pi$
$812$	83.7751	−	48.3676i	2.93993	−	1.69737i
$813$	3.83165	−	3.83165i	0.134382	−	0.134382i
$814$	−5.17594	+	0.455566i	−0.181417	+	0.0159676i
$815$	−16.1455	+	34.5719i	−0.565552	+	1.21100i
$816$	−0.279529	+	1.04322i	−0.00978546	+	0.0365198i
$817$	−8.23954	+	2.20778i	−0.288265	+	0.0772404i
$818$	−16.6002	−	61.9529i	−0.580413	−	2.16613i
$819$	−40.7626	+	10.9223i	−1.42436	+	0.381657i
$820$	26.5701	−	56.8937i	0.927867	−	1.98681i
$821$	11.2509	−	19.4872i	0.392660	−	0.680107i	−0.600140	−	0.799895i	$-0.704888\pi$
$821$	11.2509	−	19.4872i	0.392660	−	0.680107i	0.992799	+	0.119789i	$0.0382217\pi$
$822$			4.08013i			0.142311i
$823$	9.88834	−	36.9038i	0.344686	−	1.28639i	−0.548293	−	0.836286i	$-0.684722\pi$
$823$	9.88834	−	36.9038i	0.344686	−	1.28639i	0.892979	−	0.450099i	$-0.148611\pi$
$824$		−	48.5853i		−	1.69255i
$825$	0.0343367	−	0.387305i	0.00119545	−	0.0134842i
$826$	−50.9113	−	88.1810i	−1.77143	−	3.06821i
$827$	−8.91890	−	5.14933i	−0.310141	−	0.179060i	0.336849	−	0.941559i	$-0.390639\pi$
$827$	−8.91890	−	5.14933i	−0.310141	−	0.179060i	−0.646989	+	0.762499i	$0.723972\pi$
$828$			46.4441i			1.61404i
$829$	−18.0806	−	4.84467i	−0.627964	−	0.168262i	−0.0692181	−	0.997602i	$-0.522050\pi$
$829$	−18.0806	−	4.84467i	−0.627964	−	0.168262i	−0.558745	+	0.829339i	$0.688717\pi$
$830$	−5.00272	+	5.95501i	−0.173647	+	0.206701i
$831$	5.44723	+	1.45958i	0.188962	+	0.0506323i
$832$	18.1741	−	31.4785i	0.630075	−	1.09132i
$833$	46.0802	−	79.8132i	1.59658	−	2.76536i
$834$	−4.27405	−	1.14523i	−0.147998	−	0.0396560i
$835$	−44.8660	+	3.89909i	−1.55265	+	0.134934i
$836$	1.71494	+	0.459516i	0.0593123	+	0.0158927i
$837$		−	0.587733i		−	0.0203150i
$838$	53.9066	+	31.1230i	1.86217	+	1.07513i
$839$	−11.7523	−	20.3556i	−0.405736	−	0.702755i	0.588671	−	0.808373i	$-0.299651\pi$
$839$	−11.7523	−	20.3556i	−0.405736	−	0.702755i	−0.994407	+	0.105618i	$0.966318\pi$
$840$	3.27355	−	7.00954i	0.112948	−	0.241852i
$841$		−	4.37591i		−	0.150893i
$842$	3.43539	−	12.8210i	0.118391	−	0.441843i
$843$		−	1.46196i		−	0.0503527i
$844$	−3.26033	+	5.64705i	−0.112225	+	0.194380i
$845$	−8.95499	−	4.18209i	−0.308061	−	0.143868i
$846$	46.8484	−	12.5530i	1.61068	−	0.431580i
$847$	13.7113	+	51.1712i	0.471125	+	1.75826i
$848$	−4.59535	+	1.23132i	−0.157805	+	0.0422837i
$849$	−0.338797	+	1.26441i	−0.0116275	+	0.0433944i
$850$	49.1142	−	41.1149i	1.68460	−	1.41023i
$851$	25.2357	+	11.7515i	0.865070	+	0.402838i
$852$	−5.33554	+	5.33554i	−0.182793	+	0.182793i
$853$	−45.7978	+	26.4414i	−1.56809	+	0.905336i	−0.571696	+	0.820466i	$0.693714\pi$
$853$	−45.7978	+	26.4414i	−1.56809	+	0.905336i	−0.996392	+	0.0848701i	$0.972952\pi$
$854$	−3.91528	+	6.78146i	−0.133978	+	0.232057i
$855$	−1.62405	+	9.17937i	−0.0555413	+	0.313928i
$856$	−16.5501	−	61.7659i	−0.565672	−	2.11112i
$857$		−	24.7364i		−	0.844979i	−0.906368	−	0.422490i	$-0.861156\pi$
$857$		−	24.7364i		−	0.844979i	0.906368	−	0.422490i	$-0.138844\pi$
$858$	0.512915	−	0.137435i	0.0175106	−	0.00469196i
$859$	−27.6851	−	27.6851i	−0.944602	−	0.944602i	0.0539417	−	0.998544i	$-0.482821\pi$
$859$	−27.6851	−	27.6851i	−0.944602	−	0.944602i	−0.998544	+	0.0539417i	$0.982821\pi$
$860$	4.02007	+	46.2580i	0.137083	+	1.57738i
$861$	−8.46041			−0.288330
$862$	−13.8848	−	13.8848i	−0.472918	−	0.472918i
$863$	−9.42129	+	35.1607i	−0.320705	+	1.19689i	0.597855	+	0.801604i	$0.296020\pi$
$863$	−9.42129	+	35.1607i	−0.320705	+	1.19689i	−0.918560	+	0.395282i	$0.870647\pi$
$864$	5.52814	−	1.48126i	0.188071	−	0.0503935i
$865$	16.2438	−	5.90160i	0.552305	−	0.200660i
$866$	−1.60671	+	5.99633i	−0.0545983	+	0.203763i
$867$	2.70544	+	0.724921i	0.0918817	+	0.0246196i
$868$	3.89355	+	6.74383i	0.132156	+	0.228900i
$869$	−0.182022	−	0.679316i	−0.00617468	−	0.0230442i
$870$	−3.66269	−	5.23732i	−0.124177	−	0.177562i
$871$	3.80325	−	14.1939i	0.128868	−	0.480942i
$872$	1.29063	−	4.81670i	0.0437063	−	0.163114i
$873$	−0.653682	−	1.13221i	−0.0221238	−	0.0383195i
$874$	−10.6429	−	10.6429i	−0.360003	−	0.360003i
$875$	−47.2545	+	27.1731i	−1.59749	+	0.918618i
$876$	−7.98355	+	4.60931i	−0.269739	+	0.155734i
$877$	−17.8730	+	17.8730i	−0.603529	+	0.603529i	−0.941247	−	0.337718i	$-0.890345\pi$
$877$	−17.8730	+	17.8730i	−0.603529	+	0.603529i	0.337718	+	0.941247i	$0.390345\pi$
$878$	49.7022	−	49.7022i	1.67737	−	1.67737i
$879$	−1.63591	−	2.83348i	−0.0551780	−	0.0955710i
$880$	0.321079	−	0.687517i	0.0108236	−	0.0231762i
$881$	−1.86441	−	1.07642i	−0.0628135	−	0.0362654i	0.468264	−	0.883588i	$-0.344879\pi$
$881$	−1.86441	−	1.07642i	−0.0628135	−	0.0362654i	−0.531078	+	0.847323i	$0.678213\pi$
$882$	115.527			3.88999
$883$	29.2961	+	16.9141i	0.985893	+	0.569206i	0.904044	−	0.427439i	$-0.140584\pi$
$883$	29.2961	+	16.9141i	0.985893	+	0.569206i	0.0818490	+	0.996645i	$0.473917\pi$
$884$	47.8748	+	27.6405i	1.61020	+	0.929652i
$885$	−3.48390	+	2.43645i	−0.117110	+	0.0819004i
$886$	64.4619	+	17.2725i	2.16564	+	0.580281i
$887$	−11.9250	−	11.9250i	−0.400402	−	0.400402i	0.477972	−	0.878375i	$-0.341372\pi$
$887$	−11.9250	−	11.9250i	−0.400402	−	0.400402i	−0.878375	+	0.477972i	$0.841372\pi$
$888$	−0.747315	+	4.25124i	−0.0250783	+	0.142662i
$889$			70.6003i			2.36786i
$890$	29.7308	+	24.9765i	0.996580	+	0.837214i
$891$	−2.72805	−	1.57504i	−0.0913930	−	0.0527658i
$892$	29.1388	−	7.80772i	0.975639	−	0.261422i
$893$	−4.96665	+	8.60249i	−0.166203	+	0.287871i
$894$	0.151807	+	0.151807i	0.00507720	+	0.00507720i
$895$	−0.588621	+	3.32697i	−0.0196754	+	0.111208i
$896$	−68.5041	+	68.5041i	−2.28856	+	2.28856i
$897$	−2.74799	−	0.736320i	−0.0917526	−	0.0245850i
$898$	−7.33482	−	7.33482i	−0.244766	−	0.244766i
$899$	2.68673			0.0896076
$900$	47.6617	+	17.4100i	1.58872	+	0.580332i
$901$	7.30650	+	27.2682i	0.243415	+	0.908436i
$902$	−6.98457			−0.232561
$903$	5.41798	−	3.12807i	0.180299	−	0.104096i
$904$	−8.09610	+	4.67428i	−0.269272	+	0.155464i
$905$	−0.860117	−	9.89717i	−0.0285913	−	0.328993i
$906$	1.50591	−	0.403507i	0.0500304	−	0.0134056i
$907$	−21.4863	−	12.4051i	−0.713439	−	0.411904i	0.0988939	−	0.995098i	$-0.468470\pi$
$907$	−21.4863	−	12.4051i	−0.713439	−	0.411904i	−0.812333	+	0.583194i	$0.801803\pi$
$908$	20.3051	−	11.7232i	0.673849	−	0.389047i
$909$	27.0659	+	46.8795i	0.897719	+	1.55489i
$910$	−56.9992	−	47.8842i	−1.88950	−	1.58735i
$911$	−4.82619	+	4.82619i	−0.159899	+	0.159899i	−0.782522	−	0.622623i	$-0.786067\pi$
$911$	−4.82619	+	4.82619i	−0.159899	+	0.159899i	0.622623	+	0.782522i	$0.286067\pi$
$912$	0.138638	−	0.240128i	0.00459075	−	0.00795142i
$913$	0.528099	+	0.141504i	0.0174775	+	0.00468308i
$914$			58.4757i			1.93420i
$915$	0.296232	+	0.138344i	0.00979314	+	0.00457352i
$916$	4.83512	−	2.79156i	0.159757	−	0.0922356i
$917$	−19.8217			−0.654570
$918$	4.19015	+	15.6379i	0.138296	+	0.516126i
$919$	−31.3230	+	31.3230i	−1.03325	+	1.03325i	−0.0338213	+	0.999428i	$0.510768\pi$
$919$	−31.3230	+	31.3230i	−1.03325	+	1.03325i	−0.999428	+	0.0338213i	$0.989232\pi$
$920$	−28.0408	+	19.6102i	−0.924476	+	0.646528i
$921$	−1.95423	+	3.38482i	−0.0643939	+	0.111534i
$922$	14.6522	+	54.6826i	0.482543	+	1.80088i
$923$	15.1624	+	26.2621i	0.499078	+	0.864428i
$924$	−1.30212			−0.0428367
$925$	21.5195	−	21.4922i	0.707555	−	0.706658i
$926$	80.9967			2.66172
$927$	−21.4682	−	37.1841i	−0.705109	−	1.22128i
$928$	6.77136	+	25.2711i	0.222281	+	0.829564i
$929$	25.2053	−	43.6568i	0.826958	−	1.43233i	−0.0734562	−	0.997298i	$-0.523403\pi$
$929$	25.2053	−	43.6568i	0.826958	−	1.43233i	0.900414	−	0.435034i	$-0.143264\pi$
$930$	0.421600	−	0.294844i	0.0138248	−	0.00966831i
$931$	−16.7306	+	16.7306i	−0.548322	+	0.548322i
$932$	−14.5691	−	54.3728i	−0.477228	−	1.78104i
$933$	0.106747			0.00349473
$934$	−73.1814	+	42.2513i	−2.39457	+	1.38250i
$935$	−4.07964	−	1.90524i	−0.133418	−	0.0623081i
$936$			28.9418i			0.945994i
$937$	12.2443	+	3.28085i	0.400004	+	0.107181i	0.453212	−	0.891403i	$-0.350278\pi$
$937$	12.2443	+	3.28085i	0.400004	+	0.107181i	−0.0532079	+	0.998583i	$0.516945\pi$
$938$	−28.5090	+	49.3790i	−0.930850	+	1.61228i
$939$	−2.47869	+	2.47869i	−0.0808891	+	0.0808891i
$940$	41.3998	+	34.7794i	1.35031	+	1.13438i
$941$	7.75997	+	13.4407i	0.252968	+	0.438153i	0.964342	−	0.264661i	$-0.0852600\pi$
$941$	7.75997	+	13.4407i	0.252968	+	0.438153i	−0.711374	+	0.702814i	$0.751927\pi$
$942$	1.16175	−	0.670736i	0.0378518	−	0.0218538i
$943$	32.4071	+	18.7102i	1.05532	+	0.609289i
$944$	−8.01384	+	2.14730i	−0.260828	+	0.0698888i
$945$	−1.19287	−	13.7261i	−0.0388040	−	0.446509i
$946$	4.47286	−	2.58241i	0.145425	−	0.0839614i
$947$	30.0082	−	17.3253i	0.975137	−	0.562996i	0.0743385	−	0.997233i	$-0.476315\pi$
$947$	30.0082	−	17.3253i	0.975137	−	0.562996i	0.900798	+	0.434237i	$0.142982\pi$
$948$	−1.39887			−0.0454330
$949$	9.58887	+	35.7862i	0.311268	+	1.16167i
$950$	−14.9115	+	6.93236i	−0.483794	+	0.224915i
$951$	4.06942			0.131960
$952$	−63.3470	−	63.3470i	−2.05309	−	2.05309i
$953$	46.9523	+	12.5808i	1.52093	+	0.407533i	0.920049	−	0.391803i	$-0.128148\pi$
$953$	46.9523	+	12.5808i	1.52093	+	0.407533i	0.600884	+	0.799336i	$0.294815\pi$
$954$	−25.0228	+	25.0228i	−0.810144	+	0.810144i
$955$	−1.73005	+	9.77851i	−0.0559832	+	0.316425i
$956$	−13.4076	−	13.4076i	−0.433633	−	0.433633i
$957$	−0.224631	+	0.389073i	−0.00726130	+	0.0125769i
$958$	48.4653	−	12.9862i	1.56584	−	0.419566i
$959$	−34.8226	−	20.1048i	−1.12448	−	0.649219i
$960$	4.50880	+	3.78778i	0.145521	+	0.122250i
$961$		−	30.7837i		−	0.993023i
$962$	37.6531	+	17.5339i	1.21398	+	0.565317i
$963$	−39.9587	−	39.9587i	−1.28765	−	1.28765i
$964$	−64.9049	−	17.3912i	−2.09045	−	0.560134i
$965$	−32.8220	+	22.9539i	−1.05658	+	0.738912i
$966$	9.55992	+	5.51942i	0.307585	+	0.177584i
$967$	1.82918	+	1.05608i	0.0588225	+	0.0339612i	0.529123	−	0.848545i	$-0.322521\pi$
$967$	1.82918	+	1.05608i	0.0588225	+	0.0339612i	−0.470300	+	0.882506i	$0.655854\pi$
$968$	36.3320			1.16775
$969$	−1.42489	−	0.822658i	−0.0457739	−	0.0264276i
$970$	0.975867	−	2.08959i	0.0313332	−	0.0670929i
$971$	5.04155	+	8.73223i	0.161791	+	0.280231i	0.935511	−	0.353297i	$-0.114940\pi$
$971$	5.04155	+	8.73223i	0.161791	+	0.280231i	−0.773720	+	0.633528i	$0.781606\pi$
$972$	−13.6376	+	13.6376i	−0.437427	+	0.437427i
$973$	30.8345	−	30.8345i	0.988508	−	0.988508i
$974$	−42.4317	+	24.4979i	−1.35960	+	0.784965i
$975$	−1.78573	+	2.54401i	−0.0571891	+	0.0814735i
$976$	0.451160	+	0.451160i	0.0144413	+	0.0144413i
$977$	16.7968	+	29.0930i	0.537379	+	0.930767i	0.999044	+	0.0437132i	$0.0139188\pi$
$977$	16.7968	+	29.0930i	0.537379	+	0.930767i	−0.461665	+	0.887054i	$0.652748\pi$
$978$	2.18496	−	8.15436i	0.0698672	−	0.260748i
$979$	0.706467	−	2.63657i	0.0225788	−	0.0842652i
$980$	73.8106	+	105.542i	2.35779	+	3.37143i
$981$	−1.14057	−	4.25668i	−0.0364157	−	0.135905i
$982$	−22.5351	−	39.0320i	−0.719124	−	1.24556i
$983$	−5.70185	−	1.52781i	−0.181861	−	0.0487295i	0.166739	−	0.986001i	$-0.446676\pi$
$983$	−5.70185	−	1.52781i	−0.181861	−	0.0487295i	−0.348600	+	0.937272i	$0.613343\pi$
$984$	−1.50174	+	5.60457i	−0.0478738	+	0.178667i
$985$	−19.9999	+	7.26624i	−0.637248	+	0.231522i
$986$	−71.4862	+	19.1547i	−2.27658	+	0.610009i
$987$	1.88555	−	7.03695i	0.0600176	−	0.223989i
$988$	−10.0356	−	10.0356i	−0.319275	−	0.319275i
$989$	−27.6710			−0.879885
$990$	−0.488668	−	5.62299i	−0.0155309	−	0.178710i
$991$	−38.4778	−	38.4778i	−1.22229	−	1.22229i	−0.966816	−	0.255472i	$-0.917769\pi$
$991$	−38.4778	−	38.4778i	−1.22229	−	1.22229i	−0.255472	−	0.966816i	$-0.582231\pi$
$992$	−2.03430	+	0.545089i	−0.0645891	+	0.0173066i
$993$			2.07434i			0.0658272i
$994$	−30.4543	−	113.657i	−0.965951	−	3.60498i
$995$	1.20107	−	6.78864i	0.0380766	−	0.215214i
$996$	0.543737	−	0.941780i	0.0172290	−	0.0298414i
$997$	−42.2761	+	24.4081i	−1.33890	+	0.773013i	−0.986644	−	0.162892i	$-0.947918\pi$
$997$	−42.2761	+	24.4081i	−1.33890	+	0.773013i	−0.352253	+	0.935905i	$0.614584\pi$
$998$	1.36038	−	1.36038i	0.0430619	−	0.0430619i
$999$	2.63299	+	7.22231i	0.0833040	+	0.228504i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.p.a.103.3	yes	68
5.2	odd	4		185.2.u.a.177.15	yes	68
5.3	odd	4		925.2.y.b.732.3		68
5.4	even	2		925.2.t.b.843.15		68
37.23	odd	12		185.2.u.a.23.15	yes	68
185.23	even	12		925.2.t.b.282.15		68
185.97	even	12	inner	185.2.p.a.97.3	✓	68
185.134	odd	12		925.2.y.b.393.3		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.3	✓	68	185.97	even	12	inner
185.2.p.a.103.3	yes	68	1.1	even	1	trivial
185.2.u.a.23.15	yes	68	37.23	odd	12
185.2.u.a.177.15	yes	68	5.2	odd	4
925.2.t.b.282.15		68	185.23	even	12
925.2.t.b.843.15		68	5.4	even	2
925.2.y.b.393.3		68	185.134	odd	12
925.2.y.b.732.3		68	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	185.2.p.a.103.3

Level	$185$
Weight	$2$
Character	185.103
Analytic conductor	$1.477$
Analytic rank	$0$
Dimension	$68$
Inner twists	$2$