LMFDB - Embedded newform 925.2.t.b.843.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(82,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, 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("925.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.t (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			843.15
Character	$\chi$	$=$	925.843
Dual form			925.2.t.b.282.15

$q$-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} +(0.349826 - 0.349826i) q^{6} +(-1.26188 - 4.70941i) q^{7} -3.34372 q^{8} +(2.55907 - 1.47748i) q^{9} -0.366430i q^{11} +(0.704015 + 0.188640i) q^{12} +(1.46458 - 2.53673i) q^{13} +(8.03678 - 8.03678i) q^{14} +(-0.463041 - 0.802010i) q^{16} +(4.75903 - 2.74763i) q^{17} +(5.96563 + 3.44426i) q^{18} +(1.36274 - 0.365145i) q^{19} +(-0.896080 + 0.517352i) q^{21} +(0.739767 - 0.427105i) q^{22} -4.57650 q^{23} +(0.183662 + 0.685437i) q^{24} +6.82838 q^{26} +(-0.893629 - 0.893629i) q^{27} +(16.1738 + 4.33375i) q^{28} +(-4.08509 + 4.08509i) q^{29} +(-0.328846 - 0.328846i) q^{31} +(-2.26430 + 3.92188i) q^{32} +(-0.0751151 + 0.0201270i) q^{33} +(11.0941 + 6.40518i) q^{34} +10.1484i q^{36} +(-5.51420 - 2.56780i) q^{37} +(2.32556 + 2.32556i) q^{38} +(-0.600455 - 0.160892i) q^{39} +(7.08118 + 4.08832i) q^{41} +(-2.08891 - 1.20604i) q^{42} +6.04631 q^{43} +(1.08985 + 0.629224i) q^{44} +(-5.33430 - 9.23928i) q^{46} +(4.97863 - 4.97863i) q^{47} +(-0.138972 + 0.138972i) q^{48} +(-14.5240 + 8.38545i) q^{49} +(-0.824643 - 0.824643i) q^{51} +(5.02990 + 8.71203i) q^{52} +(-1.32960 + 4.96214i) q^{53} +(0.762504 - 2.84570i) q^{54} +(4.21939 + 15.7470i) q^{56} +(-0.149703 - 0.259294i) q^{57} +(-13.0087 - 3.48567i) q^{58} +(2.31870 - 8.65349i) q^{59} +(-0.665487 + 0.178317i) q^{61} +(0.280594 - 1.04719i) q^{62} +(-10.1873 - 10.1873i) q^{63} -12.4091 q^{64} +(-0.128187 - 0.128187i) q^{66} +(4.84572 - 1.29841i) q^{67} +18.8726i q^{68} +(0.251376 + 0.938146i) q^{69} +(5.17637 - 8.96573i) q^{71} +(-8.55683 + 4.94029i) q^{72} +(-8.94360 + 8.94360i) q^{73} +(-1.24326 - 14.1253i) q^{74} +(-1.25404 + 4.68013i) q^{76} +(-1.72567 + 0.462391i) q^{77} +(-0.375066 - 1.39976i) q^{78} +(1.85388 - 0.496745i) q^{79} +(4.29834 - 7.44494i) q^{81} +19.0612i q^{82} +(0.386169 - 1.44120i) q^{83} -3.55354i q^{84} +(7.04749 + 12.2066i) q^{86} +(1.06179 + 0.613027i) q^{87} +1.22524i q^{88} +(7.19530 + 1.92798i) q^{89} +(-13.7946 - 3.69626i) q^{91} +(7.85867 - 13.6116i) q^{92} +(-0.0493482 + 0.0854735i) q^{93} +(15.8541 + 4.24810i) q^{94} +(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} - 8 q^{6} + 2 q^{7} - 12 q^{8} - 14 q^{12} + 6 q^{13} - 26 q^{16} - 12 q^{17} - 18 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 24 q^{26} + 68 q^{27} + 26 q^{28}+ \cdots + 32 q^{99}+O(q^{100}) $ 68 * q + 4 * q^2 + 8 * q^3 - 30 * q^4 - 8 * q^6 + 2 * q^7 - 12 * q^8 - 14 * q^12 + 6 * q^13 - 26 * q^16 - 12 * q^17 - 18 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 24 * q^26 + 68 * q^27 + 26 * q^28 + 14 * q^29 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 16 * q^37 + 36 * q^38 + 52 * q^39 - 18 * q^41 - 132 * q^42 - 8 * q^43 - 36 * q^44 - 52 * q^46 + 24 * q^47 + 60 * q^48 - 36 * q^49 - 8 * q^51 + 26 * q^52 - 82 * q^53 + 40 * q^54 + 16 * q^56 + 6 * q^57 - 86 * q^58 - 8 * q^59 + 4 * q^61 - 10 * q^62 + 48 * q^63 - 20 * q^64 + 80 * q^66 + 40 * q^67 + 8 * q^69 + 4 * q^71 + 90 * q^72 + 60 * q^73 - 44 * q^74 + 72 * q^76 - 66 * q^77 + 24 * q^78 + 56 * q^79 - 6 * q^81 - 24 * q^83 - 4 * q^86 + 84 * q^87 - 22 * q^89 + 44 * q^91 - 44 * q^92 + 34 * q^93 - 20 * q^94 - 8 * q^96 - 42 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

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	$0.141704\pi$
$2$	1.16559	+	2.01885i	0.824193	+	1.42754i	−0.0783413	+	0.996927i	$0.524962\pi$
$3$	−0.0549274	−	0.204992i	−0.0317124	−	0.118352i	0.948255	−	0.317509i	$-0.102846\pi$
$3$	−0.0549274	−	0.204992i	−0.0317124	−	0.118352i	−0.979968	+	0.199157i	$0.936180\pi$
$4$	−1.71718	+	2.97424i	−0.858589	+	1.48712i
$5$		0			0
$5$		0			0
$6$	0.349826	−	0.349826i	0.142816	−	0.142816i
$7$	−1.26188	−	4.70941i	−0.476947	−	1.77999i	−0.613868	−	0.789408i	$-0.710387\pi$
$7$	−1.26188	−	4.70941i	−0.476947	−	1.77999i	0.136922	−	0.990582i	$-0.456279\pi$
$8$	−3.34372			−1.18219
$9$	2.55907	−	1.47748i	0.853024	−	0.492494i
$10$		0			0
$11$		−	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	−0.588258	−	0.808673i	$-0.700186\pi$
$13$	1.46458	−	2.53673i	0.406202	−	0.703563i	0.994461	+	0.105110i	$0.0335196\pi$
$14$	8.03678	−	8.03678i	2.14792	−	2.14792i
$15$		0			0
$16$	−0.463041	−	0.802010i	−0.115760	−	0.200503i
$17$	4.75903	−	2.74763i	1.15423	−	0.666397i	0.204319	−	0.978904i	$-0.434502\pi$
$17$	4.75903	−	2.74763i	1.15423	−	0.666397i	0.949915	+	0.312507i	$0.101169\pi$
$18$	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			0
$21$	−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	$-0.658324\pi$
$23$	−4.57650			−0.954267			−0.477133	+	0.878831i	$0.658324\pi$
$24$	0.183662	+	0.685437i	0.0374899	+	0.139914i
$25$		0			0
$26$	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			0
$31$	−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
$35$		0			0
$36$			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
$40$		0			0
$41$	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	$-0.347481\pi$
$43$	6.04631			0.922054			0.461027	+	0.887386i	$0.347481\pi$
$44$	1.08985	+	0.629224i	0.164301	+	0.0948592i
$45$		0			0
$46$	−5.33430	−	9.23928i	−0.786500	−	1.36226i
$47$	4.97863	−	4.97863i	0.726208	−	0.726208i	−0.243654	−	0.969862i	$-0.578346\pi$
$47$	4.97863	−	4.97863i	0.726208	−	0.726208i	0.969862	+	0.243654i	$0.0783462\pi$
$48$	−0.138972	+	0.138972i	−0.0200589	+	0.0200589i
$49$	−14.5240	+	8.38545i	−2.07486	+	1.19792i
$50$		0			0
$51$	−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	$0.198112\pi$
$53$	−1.32960	+	4.96214i	−0.182635	+	0.681603i	−0.995124	+	0.0986269i	$0.968555\pi$
$54$	0.762504	−	2.84570i	0.103764	−	0.387251i
$55$		0			0
$56$	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	$-0.114853\pi$
$60$		0			0
$61$	−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			0
$66$	−0.128187	−	0.128187i	−0.0157787	−	0.0157787i
$67$	4.84572	−	1.29841i	0.591999	−	0.158626i	0.0496322	−	0.998768i	$-0.484195\pi$
$67$	4.84572	−	1.29841i	0.591999	−	0.158626i	0.542367	+	0.840142i	$0.317528\pi$
$68$			18.8726i			2.28864i
$69$	0.251376	+	0.938146i	0.0302621	+	0.112940i
$70$		0			0
$71$	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	$0.515259\pi$
$73$	−8.94360	+	8.94360i	−1.04677	+	1.04677i	−0.998851	+	0.0479181i	$0.984741\pi$
$74$	−1.24326	−	14.1253i	−0.144526	−	1.64204i
$75$		0			0
$76$	−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	$0.382232\pi$
$80$		0			0
$81$	4.29834	−	7.44494i	0.477593	−	0.827216i
$82$			19.0612i			2.10495i
$83$	0.386169	−	1.44120i	0.0423875	−	0.158192i	−0.941488	−	0.337046i	$-0.890572\pi$
$83$	0.386169	−	1.44120i	0.0423875	−	0.158192i	0.983876	+	0.178854i	$0.0572389\pi$
$84$		−	3.55354i		−	0.387723i
$85$		0			0
$86$	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	$0.454146\pi$
$90$		0			0
$91$	−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
$95$		0			0
$96$	0.928326	+	0.248744i	0.0947468	+	0.0253873i
$97$			0.442430i			0.0449220i	0.999748	+	0.0224610i	$0.00715016\pi$
$97$			0.442430i			0.0449220i	−0.999748	+	0.0224610i	$0.992850\pi$
$98$	−33.8580	−	19.5479i	−3.42017	−	1.97464i
$99$	−0.541393	−	0.937719i	−0.0544120	−	0.0942443i
$100$		0			0
$101$			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	$0.253963\pi$
$103$			14.5303i			1.43171i	−0.698248	+	0.715856i	$0.746037\pi$
$104$	−4.89716	+	8.48213i	−0.480206	+	0.831741i
$105$		0			0
$106$	−11.5676	+	3.09953i	−1.12354	+	0.301053i
$107$	4.94961	+	18.4722i	0.478497	+	1.78577i	0.607712	+	0.794158i	$0.292088\pi$
$107$	4.94961	+	18.4722i	0.478497	+	1.78577i	−0.129215	+	0.991617i	$0.541246\pi$
$108$	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			0
$111$	−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	−0.381770	−	0.924257i	$-0.624685\pi$
$113$	2.42128	−	1.39793i	0.227775	−	0.131506i	0.609545	+	0.792751i	$0.291352\pi$
$114$	0.348984	−	0.604459i	0.0326854	−	0.0566127i
$115$		0			0
$116$	−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
$120$		0			0
$121$	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
$125$		0			0
$126$	8.69250	−	32.4409i	0.774390	−	2.89006i
$127$	−13.9871	−	3.74783i	−1.24115	−	0.332566i	−0.422241	−	0.906484i	$-0.638756\pi$
$127$	−13.9871	−	3.74783i	−1.24115	−	0.332566i	−0.818913	+	0.573918i	$0.805423\pi$
$128$	−9.93525	−	17.2084i	−0.878161	−	1.52102i
$129$	−0.332108	−	1.23945i	−0.0292405	−	0.109127i
$130$		0			0
$131$	−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
$135$		0			0
$136$	−15.9129	+	9.18731i	−1.36452	+	0.787805i
$137$	5.83166	−	5.83166i	0.498233	−	0.498233i	−0.412655	−	0.910887i	$-0.635398\pi$
$137$	5.83166	−	5.83166i	0.498233	−	0.498233i	0.910887	+	0.412655i	$0.135398\pi$
$138$	−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	$0.957171\pi$
$140$		0			0
$141$	−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
$145$		0			0
$146$	−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	$0.994342\pi$
$150$		0			0
$151$	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
$155$		0			0
$156$	1.50962	−	1.50962i	0.120866	−	0.120866i
$157$	−2.61914	−	0.701796i	−0.209030	−	0.0560094i	0.152785	−	0.988260i	$-0.451176\pi$
$157$	−2.61914	−	0.701796i	−0.209030	−	0.0560094i	−0.361814	+	0.932250i	$0.617843\pi$
$158$	3.16371	+	3.16371i	0.251691	+	0.251691i
$159$	1.09023			0.0864609
$160$		0			0
$161$	5.77501	+	21.5526i	0.455135	+	1.69859i
$162$	20.0403			1.57452
$163$	−14.7778	+	8.53197i	−1.15749	+	0.668275i	−0.950700	−	0.310111i	$-0.899634\pi$
$163$	−14.7778	+	8.53197i	−1.15749	+	0.668275i	−0.206787	+	0.978386i	$0.566301\pi$
$164$	−24.3193	+	14.0408i	−1.89902	+	1.09640i
$165$		0			0
$166$	3.35968	−	0.900225i	0.260762	−	0.0698710i
$167$	−17.4420	−	10.0702i	−1.34970	−	0.779252i	−0.361496	−	0.932374i	$-0.617734\pi$
$167$	−17.4420	−	10.0702i	−1.34970	−	0.779252i	−0.988207	+	0.153122i	$0.951067\pi$
$168$	2.99624	−	1.72988i	0.231165	−	0.133463i
$169$	2.21000	+	3.82783i	0.170000	+	0.294448i
$170$		0			0
$171$	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	0.531197	−	0.847248i	$-0.321742\pi$
$173$	7.46566	+	2.00042i	0.567604	+	0.152089i	0.0364063	+	0.999337i	$0.488409\pi$
$174$			2.85814i			0.216675i
$175$		0			0
$176$	−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	$0.232016\pi$
$180$		0			0
$181$	−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
$185$		0			0
$186$	−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
$190$		0			0
$191$	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	$-0.723001\pi$
$193$	−17.9118			−1.28932			−0.644660	+	0.764469i	$0.723001\pi$
$194$	−0.893201	+	0.515690i	−0.0641281	+	0.0370244i
$195$		0			0
$196$		−	57.5972i		−	4.11409i
$197$	−9.19196	−	2.46298i	−0.654900	−	0.175480i	−0.0839569	−	0.996469i	$-0.526756\pi$
$197$	−9.19196	−	2.46298i	−0.654900	−	0.175480i	−0.570943	+	0.820989i	$0.693422\pi$
$198$	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	$0.284854\pi$
$200$		0			0
$201$	−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
$205$		0			0
$206$	−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
$210$		0			0
$211$	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
$215$		0			0
$216$	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
$220$		0			0
$221$		−	16.0965i		−	1.08277i
$222$	−2.82729	+	1.03073i	−0.189756	+	0.0691778i
$223$	6.21109	+	6.21109i	0.415925	+	0.415925i	0.883797	−	0.467871i	$-0.154979\pi$
$223$	6.21109	+	6.21109i	0.415925	+	0.415925i	−0.467871	+	0.883797i	$0.654979\pi$
$224$	21.3270	+	5.71456i	1.42497	+	0.381820i
$225$		0			0
$226$	5.64442	+	3.25881i	0.375461	+	0.216773i
$227$	5.91235	+	3.41350i	0.392417	+	0.226562i	0.683207	−	0.730225i	$-0.260585\pi$
$227$	5.91235	+	3.41350i	0.392417	+	0.226562i	−0.290790	+	0.956787i	$0.593918\pi$
$228$	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	$0.683772\pi$
$230$		0			0
$231$	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	−0.216915	−	0.976191i	$-0.569599\pi$
$233$	11.5898	−	11.5898i	0.759276	−	0.759276i	0.976191	+	0.216915i	$0.0695993\pi$
$234$	17.4743	−	10.0888i	1.14233	−	0.659526i
$235$		0			0
$236$	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			0
$241$	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
$245$		0			0
$246$	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
$250$		0			0
$251$	−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
$255$		0			0
$256$	10.7517	−	18.6225i	0.671980	−	1.16390i
$257$	6.93002	−	4.00105i	0.432283	−	0.249579i	−0.268036	−	0.963409i	$-0.586375\pi$
$257$	6.93002	−	4.00105i	0.432283	−	0.249579i	0.700319	+	0.713830i	$0.253041\pi$
$258$	2.11516	−	2.11516i	0.131684	−	0.131684i
$259$	−5.13456	+	29.2089i	−0.319046	+	1.81495i
$260$		0			0
$261$	−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	$-0.909740\pi$
$263$	−4.35453	−	16.2513i	−0.268512	−	1.00210i	0.691553	−	0.722325i	$-0.256927\pi$
$264$	0.251164	−	0.0672993i	0.0154581	−	0.00414198i
$265$		0			0
$266$	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	$0.793813\pi$
$270$		0			0
$271$	−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
$275$		0			0
$276$	−3.22193	−	0.863313i	−0.193937	−	0.0519653i
$277$	−13.2864	+	23.0128i	−0.798305	+	1.38270i	0.122415	+	0.992479i	$0.460936\pi$
$277$	−13.2864	+	23.0128i	−0.798305	+	1.38270i	−0.920720	+	0.390225i	$0.872397\pi$
$278$	10.4249	−	18.0565i	0.625245	−	1.08296i
$279$	−1.32741	−	0.355677i	−0.0794697	−	0.0212938i
$280$		0			0
$281$	−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	0.332760	−	0.943012i	$-0.392020\pi$
$283$	−5.34172	−	3.08404i	−0.317532	−	0.183327i	−0.650292	+	0.759684i	$0.725354\pi$
$284$	17.7775	+	30.7915i	1.05490	+	1.82714i
$285$		0			0
$286$		−	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
$290$		0			0
$291$	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	0.203898	−	0.978992i	$-0.434639\pi$
$293$	14.8916	−	3.99019i	0.869975	−	0.233109i	0.666077	+	0.745883i	$0.267972\pi$
$294$	−2.14743	+	8.01433i	−0.125241	+	0.467405i
$295$		0			0
$296$	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
$300$		0			0
$301$	−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			0
$306$	37.8541			2.16398
$307$	−13.0226	−	13.0226i	−0.743237	−	0.743237i	0.229962	−	0.973199i	$-0.426140\pi$
$307$	−13.0226	−	13.0226i	−0.743237	−	0.743237i	−0.973199	+	0.229962i	$0.926140\pi$
$308$	1.58802	−	5.92655i	0.0904856	−	0.337697i
$309$	2.97859	−	0.798112i	0.169446	−	0.0454030i
$310$		0			0
$311$	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	0.532469	−	0.846450i	$-0.321264\pi$
$313$	−8.25875	−	14.3046i	−0.466812	−	0.808543i	−0.999281	+	0.0379068i	$0.987931\pi$
$314$	−1.63601	−	6.10566i	−0.0923251	−	0.344562i
$315$		0			0
$316$	−1.70600	+	6.36688i	−0.0959700	+	0.358165i
$317$	−4.96290	+	18.5218i	−0.278744	+	1.04029i	0.674546	+	0.738232i	$0.264339\pi$
$317$	−4.96290	+	18.5218i	−0.278744	+	1.04029i	−0.953291	+	0.302055i	$0.902327\pi$
$318$	1.27076	+	2.20102i	0.0712605	+	0.123427i
$319$	1.49690	+	1.49690i	0.0838102	+	0.0838102i
$320$		0			0
$321$	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
$325$		0			0
$326$	−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			0
$331$	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
$335$		0			0
$336$	0.829843	+	0.479110i	0.0452717	+	0.0261376i
$337$	31.2631	−	8.37692i	1.70301	−	0.456320i	0.729315	−	0.684178i	$-0.239839\pi$
$337$	31.2631	−	8.37692i	1.70301	−	0.456320i	0.973694	+	0.227858i	$0.0731723\pi$
$338$	−5.15188	+	8.92331i	−0.280225	+	0.485364i
$339$	−0.419559	−	0.419559i	−0.0227873	−	0.0227873i
$340$		0			0
$341$	−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
$345$		0			0
$346$	4.66331	+	17.4037i	0.250701	+	0.935630i
$347$	−4.31321			−0.231545			−0.115773	−	0.993276i	$-0.536934\pi$
$347$	−4.31321			−0.231545			−0.115773	+	0.993276i	$0.536934\pi$
$348$	−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	$0.217231\pi$
$350$		0			0
$351$	−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	−0.890064	−	0.455835i	$-0.849341\pi$
$353$	−17.6672	+	10.2002i	−0.940332	+	0.542901i	−0.0502677	+	0.998736i	$0.516007\pi$
$354$	−2.21608	−	3.83836i	−0.117783	−	0.204006i
$355$		0			0
$356$	−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	$-0.373814\pi$
$360$		0			0
$361$	−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
$365$		0			0
$366$	−0.170425	+	0.295185i	−0.00890825	+	0.0154295i
$367$	3.53325	+	13.1863i	0.184434	+	0.688318i	0.994751	+	0.102326i	$0.0326285\pi$
$367$	3.53325	+	13.1863i	0.184434	+	0.688318i	−0.810317	+	0.585992i	$0.800705\pi$
$368$	2.11911	+	3.67040i	0.110466	+	0.191333i
$369$	24.1617			1.25781
$370$		0			0
$371$	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	$0.292753\pi$
$373$	9.24926	+	34.5187i	0.478908	+	1.78731i	−0.127143	+	0.991884i	$0.540581\pi$
$374$	2.34705	−	4.06521i	0.121363	−	0.210207i
$375$		0			0
$376$	−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	$0.406458\pi$
$380$		0			0
$381$			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	$0.432622\pi$
$383$	−14.5143	+	25.1396i	−0.741648	+	1.28457i	−0.951745	+	0.306891i	$0.900711\pi$
$384$	−2.98186	+	2.98186i	−0.152167	+	0.152167i
$385$		0			0
$386$	−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	$0.356327\pi$
$390$		0			0
$391$	−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
$395$		0			0
$396$	3.71867			0.186870
$397$	20.5464	+	20.5464i	1.03119	+	1.03119i	0.999498	+	0.0316970i	$0.0100912\pi$
$397$	20.5464	+	20.5464i	1.03119	+	1.03119i	0.0316970	+	0.999498i	$0.489909\pi$
$398$	−6.94238	−	1.86020i	−0.347990	−	0.0932436i
$399$	−1.03221	+	1.03221i	−0.0516753	+	0.0516753i
$400$		0			0
$401$	−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
$405$		0			0
$406$			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	$0.345216\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$	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	$0.559499\pi$
$420$		0			0
$421$	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
$425$		0			0
$426$	−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
$430$		0			0
$431$	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	0.750904	−	0.660412i	$-0.229618\pi$
$433$	1.88301	+	1.88301i	0.0904917	+	0.0904917i	−0.660412	+	0.750904i	$0.729618\pi$
$434$	−5.28573			−0.253723
$435$		0			0
$436$	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	$0.661020\pi$
$440$		0			0
$441$	−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	−0.0375315	−	0.999295i	$-0.511949\pi$
$443$	20.2428	−	20.2428i	0.961764	−	0.961764i	0.999295	+	0.0375315i	$0.0119495\pi$
$444$	−3.39769	−	2.84797i	−0.161247	−	0.135159i
$445$		0			0
$446$	−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	$0.383183\pi$
$450$		0			0
$451$	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
$455$		0			0
$456$	0.500567	+	0.867008i	0.0234412	+	0.0406014i
$457$	21.7236	+	12.5421i	1.01619	+	0.586696i	0.912997	−	0.407966i	$-0.133762\pi$
$457$	21.7236	+	12.5421i	1.01619	+	0.586696i	0.103190	+	0.994662i	$0.467095\pi$
$458$		−	3.78970i		−	0.177081i
$459$	−6.70816	−	1.79745i	−0.313110	−	0.0838976i
$460$		0			0
$461$	−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	$-0.534223\pi$
$463$	17.3725	−	30.0901i	0.807370	−	1.39841i	0.914679	−	0.404181i	$-0.132443\pi$
$464$	5.16785	+	1.38472i	0.239911	+	0.0642840i
$465$		0			0
$466$	36.9071	+	9.88924i	1.70969	+	0.458110i
$467$			36.2490i			1.67740i	0.544591	+	0.838702i	$0.316685\pi$
$467$			36.2490i			1.67740i	−0.544591	+	0.838702i	$0.683315\pi$
$468$	25.7437	+	14.8631i	1.19000	+	0.687049i
$469$	−12.2295	−	21.1820i	−0.564704	−	0.978096i
$470$		0			0
$471$			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			0
$476$	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	$0.919703\pi$
$480$		0			0
$481$	−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			0
$486$	−3.38828	−	12.6452i	−0.153695	−	0.573599i
$487$			21.0177i			0.952404i	0.879336	+	0.476202i	$0.157987\pi$
$487$			21.0177i			0.952404i	−0.879336	+	0.476202i	$0.842013\pi$
$488$	2.22521	−	0.596242i	0.100730	−	0.0269906i
$489$	2.56069	+	2.56069i	0.115799	+	0.115799i
$490$		0			0
$491$	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
$495$		0			0
$496$	−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	$0.910786\pi$
$500$		0			0
$501$	−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	$0.00582400\pi$
$503$	11.5673	+	20.0352i	0.515761	+	0.893324i	−0.484072	+	0.875028i	$0.660843\pi$
$504$	34.0636	+	34.0636i	1.51731	+	1.51731i
$505$		0			0
$506$	−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	$0.601911\pi$
$510$		0			0
$511$	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
$515$		0			0
$516$	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
$520$		0			0
$521$	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	−0.655345	−	0.755330i	$-0.727477\pi$
$523$	7.46593	−	12.9314i	0.326462	−	0.565449i	0.981807	+	0.189881i	$0.0608101\pi$
$524$	−9.87297	−	9.87297i	−0.431303	−	0.431303i
$525$		0			0
$526$	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
$530$		0			0
$531$	−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
$535$		0			0
$536$	−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
$540$		0			0
$541$	−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
$545$		0			0
$546$	−6.11877	+	3.53268i	−0.261859	+	0.151185i
$547$	0.870417			0.0372163			0.0186082	−	0.999827i	$-0.494076\pi$
$547$	0.870417			0.0372163			0.0186082	+	0.999827i	$0.494076\pi$
$548$	7.33076	+	27.3588i	0.313154	+	1.16871i
$549$	−1.43957	+	1.43957i	−0.0614394	+	0.0614394i
$550$		0			0
$551$	−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
$555$		0			0
$556$	30.7166			1.30268
$557$	−17.1411	−	29.6892i	−0.726291	−	1.25797i	−0.958440	−	0.285293i	$-0.907909\pi$
$557$	−17.1411	−	29.6892i	−0.726291	−	1.25797i	0.232149	−	0.972680i	$-0.425424\pi$
$558$	−0.829144	−	3.09441i	−0.0351005	−	0.130997i
$559$	8.85532	−	15.3379i	0.374540	−	0.648723i
$560$		0			0
$561$	−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	$-0.363239\pi$
$563$	19.7674			0.833098			0.416549	+	0.909113i	$0.363239\pi$
$564$	4.44420	−	2.56586i	0.187135	−	0.108042i
$565$		0			0
$566$		−	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			0
$571$	−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
$575$		0			0
$576$	−31.7557	+	18.3342i	−1.32316	+	0.763924i
$577$	8.06980	−	4.65910i	0.335950	−	0.193961i	−0.322530	−	0.946559i	$-0.604533\pi$
$577$	8.06980	−	4.65910i	0.335950	−	0.193961i	0.658480	+	0.752598i	$0.271200\pi$
$578$	30.7663			1.27971
$579$	0.983849	+	3.67178i	0.0408874	+	0.152594i
$580$		0			0
$581$	−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
$585$		0			0
$586$	25.4130	+	25.4130i	1.04980	+	1.04980i
$587$	−6.93015	+	12.0034i	−0.286038	+	0.495433i	−0.972860	−	0.231393i	$-0.925672\pi$
$587$	−6.93015	+	12.0034i	−0.286038	+	0.495433i	0.686822	+	0.726825i	$0.259005\pi$
$588$	−11.8070	+	3.16367i	−0.486911	+	0.130467i
$589$	−0.568208	−	0.328055i	−0.0234126	−	0.0135173i
$590$		0			0
$591$			2.01956i			0.0830738i
$592$	0.493896	+	5.61144i	0.0202990	+	0.230629i
$593$	−8.34054	−	8.34054i	−0.342505	−	0.342505i	0.514803	−	0.857308i	$-0.327865\pi$
$593$	−8.34054	−	8.34054i	−0.342505	−	0.342505i	−0.857308	+	0.514803i	$0.827865\pi$
$594$	−1.04275	−	0.279404i	−0.0427846	−	0.0114641i
$595$		0			0
$596$	−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	$0.619470\pi$
$600$		0			0
$601$	−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
$605$		0			0
$606$	6.40844	+	6.40844i	0.260325	+	0.260325i
$607$	−12.1001	−	20.9580i	−0.491129	−	0.850661i	0.508819	−	0.860874i	$-0.330082\pi$
$607$	−12.1001	−	20.9580i	−0.491129	−	0.850661i	−0.999948	+	0.0102130i	$0.996749\pi$
$608$	−1.65359	+	6.17129i	−0.0670620	+	0.250279i
$609$	1.54714	−	5.77399i	0.0626931	−	0.233974i
$610$		0			0
$611$	−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	0.184475	−	0.982837i	$-0.440942\pi$
$613$	−3.64410	−	0.976435i	−0.147184	−	0.0394378i	−0.331659	+	0.943399i	$0.607608\pi$
$614$	11.1117	−	41.4695i	0.448433	−	1.67357i
$615$		0			0
$616$	5.77016	−	1.54611i	0.232486	−	0.0622945i
$617$	3.01209	−	11.2413i	0.121262	−	0.452556i	−0.878417	−	0.477895i	$-0.841400\pi$
$617$	3.01209	−	11.2413i	0.121262	−	0.452556i	0.999679	+	0.0253391i	$0.00806654\pi$
$618$	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	$0.322159\pi$
$620$		0			0
$621$	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
$625$		0			0
$626$	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
$630$		0			0
$631$	−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
$635$		0			0
$636$	−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
$640$		0			0
$641$	−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	$0.220800\pi$
$643$			32.4250i			1.27872i	−0.768909	+	0.639358i	$0.779200\pi$
$644$	−74.0194	−	19.8334i	−2.91677	−	0.781547i
$645$		0			0
$646$	17.4572	+	4.67764i	0.686844	+	0.184039i
$647$	2.01003	−	3.48147i	0.0790223	−	0.136871i	−0.823806	−	0.566872i	$-0.808153\pi$
$647$	2.01003	−	3.48147i	0.0790223	−	0.136871i	0.902828	+	0.430001i	$0.141487\pi$
$648$	−14.3725	+	24.8938i	−0.564604	+	0.977922i
$649$	−3.17090	−	0.849639i	−0.124469	−	0.0333512i
$650$		0			0
$651$	0.464802	+	0.124543i	0.0182170	+	0.00488123i
$652$		−	58.6036i		−	2.29509i
$653$	18.1616	+	10.4856i	0.710720	+	0.410334i	0.811328	−	0.584592i	$-0.198745\pi$
$653$	18.1616	+	10.4856i	0.710720	+	0.410334i	−0.100607	+	0.994926i	$0.532079\pi$
$654$	−0.368903	−	0.638960i	−0.0144253	−	0.0249853i
$655$		0			0
$656$		−	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			0
$661$	−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
$665$		0			0
$666$	−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
$670$		0			0
$671$	0.0653405	+	0.243854i	0.00252244	+	0.00941389i
$672$		−	4.68575i		−	0.180757i
$673$	2.59711	−	0.695893i	0.100111	−	0.0268247i	−0.208416	−	0.978040i	$-0.566831\pi$
$673$	2.59711	−	0.695893i	0.100111	−	0.0268247i	0.308527	+	0.951216i	$0.400164\pi$
$674$	53.3516	+	53.3516i	2.05503	+	2.05503i
$675$		0			0
$676$	−15.1798			−0.583839
$677$	−21.7292	−	21.7292i	−0.835122	−	0.835122i	0.153090	−	0.988212i	$-0.451078\pi$
$677$	−21.7292	−	21.7292i	−0.835122	−	0.835122i	−0.988212	+	0.153090i	$0.951078\pi$
$678$	0.357996	−	1.33606i	0.0137487	−	0.0513110i
$679$	2.08359	−	0.558295i	0.0799607	−	0.0214254i
$680$		0			0
$681$	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	$-0.956367\pi$
$683$	−16.0373	−	27.7774i	−0.613650	−	1.06287i	0.376970	−	0.926225i	$-0.376966\pi$
$684$	3.70563	+	13.8296i	0.141688	+	0.528788i
$685$		0			0
$686$	−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			0
$691$	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
$695$		0			0
$696$	−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
$700$		0			0
$701$	−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
$705$		0			0
$706$	−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	$0.635176\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$	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	$0.0962820\pi$
$720$		0			0
$721$	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
$725$		0			0
$726$	3.80111	−	3.80111i	0.141073	−	0.141073i
$727$	−4.77979	+	8.27884i	−0.177273	+	0.307045i	−0.940945	−	0.338558i	$-0.890061\pi$
$727$	−4.77979	+	8.27884i	−0.177273	+	0.307045i	0.763673	+	0.645604i	$0.223394\pi$
$728$	46.1255	+	12.3593i	1.70952	+	0.458066i
$729$		−	24.5982i		−	0.911046i
$730$		0			0
$731$	28.7746	−	16.6130i	1.06427	−	0.614454i
$732$	−0.502151			−0.0185600
$733$	3.11673	+	11.6318i	0.115119	+	0.429630i	0.999296	−	0.0375224i	$-0.0119465\pi$
$733$	3.11673	+	11.6318i	0.115119	+	0.429630i	−0.884177	+	0.467153i	$0.845280\pi$
$734$	−22.5029	+	22.5029i	−0.830596	+	0.830596i
$735$		0			0
$736$	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	$0.495241\pi$
$740$		0			0
$741$	−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	$-0.905398\pi$
$743$	−7.48298	−	27.9269i	−0.274524	−	1.02454i	0.681636	−	0.731692i	$-0.261269\pi$
$744$	0.165007	−	0.285800i	0.00604944	−	0.0104779i
$745$		0			0
$746$	−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
$750$		0			0
$751$			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
$755$		0			0
$756$	−10.5806	−	18.3261i	−0.384812	−	0.666515i
$757$	4.64953	−	2.68441i	0.168990	−	0.0975664i	−0.413120	−	0.910677i	$-0.635561\pi$
$757$	4.64953	−	2.68441i	0.168990	−	0.0975664i	0.582109	+	0.813110i	$0.302228\pi$
$758$	−17.8995	−	10.3343i	−0.650140	−	0.375358i
$759$	0.343765	−	0.0921114i	0.0124779	−	0.00334343i
$760$		0			0
$761$	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
$765$		0			0
$766$	−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	$0.314552\pi$
$770$		0			0
$771$	−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	−0.209914	−	0.977720i	$-0.567319\pi$
$773$	2.70117	−	0.723776i	0.0971543	−	0.0260324i	0.307069	+	0.951687i	$0.400652\pi$
$774$	36.0701	+	20.8251i	1.29651	+	0.748542i
$775$		0			0
$776$		−	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			0
$781$	−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
$785$		0			0
$786$	1.00567	+	1.74187i	0.0358710	+	0.0621304i
$787$	−16.6179	+	16.6179i	−0.592366	+	0.592366i	−0.938270	−	0.345904i	$-0.887572\pi$
$787$	−16.6179	+	16.6179i	−0.592366	+	0.592366i	0.345904	+	0.938270i	$0.387572\pi$
$788$	23.1097	−	23.1097i	0.823250	−	0.823250i
$789$	−3.09221	+	1.78529i	−0.110086	+	0.0635580i
$790$		0			0
$791$	−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
$795$		0			0
$796$	−2.74051	−	10.2277i	−0.0971349	−	0.362512i
$797$	−10.7864	−	18.6826i	−0.382074	−	0.661772i	0.609284	−	0.792952i	$-0.291457\pi$
$797$	−10.7864	−	18.6826i	−0.382074	−	0.661772i	−0.991359	+	0.131180i	$0.958124\pi$
$798$	−3.28702	−	0.880755i	−0.116359	−	0.0311784i
$799$	10.0140	−	37.3729i	0.354271	−	1.32216i
$800$		0			0
$801$	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
$805$		0			0
$806$	−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	$-0.220798\pi$
$810$		0			0
$811$	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
$815$		0			0
$816$	−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
$820$		0			0
$821$	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	$0.315278\pi$
$823$	−9.88834	+	36.9038i	−0.344686	+	1.28639i	−0.892979	+	0.450099i	$0.851389\pi$
$824$		−	48.5853i		−	1.69255i
$825$		0			0
$826$	−50.9113	−	88.1810i	−1.77143	−	3.06821i
$827$	8.91890	+	5.14933i	0.310141	+	0.179060i	0.646989	−	0.762499i	$-0.276028\pi$
$827$	8.91890	+	5.14933i	0.310141	+	0.179060i	−0.336849	+	0.941559i	$0.609361\pi$
$828$		−	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	$0.688717\pi$
$830$		0			0
$831$	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
$835$		0			0
$836$	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	$0.966318\pi$
$840$		0			0
$841$		−	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
$845$		0			0
$846$	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
$850$		0			0
$851$	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	$-0.306286\pi$
$853$	45.7978	−	26.4414i	1.56809	−	0.905336i	0.996392	−	0.0848701i	$-0.0270475\pi$
$854$	−3.91528	+	6.78146i	−0.133978	+	0.232057i
$855$		0			0
$856$	−16.5501	−	61.7659i	−0.565672	−	2.11112i
$857$			24.7364i			0.844979i	0.906368	+	0.422490i	$0.138844\pi$
$857$			24.7364i			0.844979i	−0.906368	+	0.422490i	$0.861156\pi$
$858$	−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	$0.982821\pi$
$860$		0			0
$861$	−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	$-0.703980\pi$
$863$	9.42129	−	35.1607i	0.320705	−	1.19689i	0.918560	−	0.395282i	$-0.129353\pi$
$864$	5.52814	−	1.48126i	0.188071	−	0.0503935i
$865$		0			0
$866$	−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
$870$		0			0
$871$	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
$875$		0			0
$876$	−7.98355	+	4.60931i	−0.269739	+	0.155734i
$877$	17.8730	−	17.8730i	0.603529	−	0.603529i	−0.337718	−	0.941247i	$-0.609655\pi$
$877$	17.8730	−	17.8730i	0.603529	−	0.603529i	0.941247	+	0.337718i	$0.109655\pi$
$878$	−49.7022	+	49.7022i	−1.67737	+	1.67737i
$879$	−1.63591	−	2.83348i	−0.0551780	−	0.0955710i
$880$		0			0
$881$	−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	−0.0818490	−	0.996645i	$-0.526083\pi$
$883$	−29.2961	−	16.9141i	−0.985893	−	0.569206i	−0.904044	+	0.427439i	$0.859416\pi$
$884$	47.8748	+	27.6405i	1.61020	+	0.929652i
$885$		0			0
$886$	64.4619	+	17.2725i	2.16564	+	0.580281i
$887$	11.9250	+	11.9250i	0.400402	+	0.400402i	0.878375	−	0.477972i	$-0.158628\pi$
$887$	11.9250	+	11.9250i	0.400402	+	0.400402i	−0.477972	+	0.878375i	$0.658628\pi$
$888$	0.747315	−	4.25124i	0.0250783	−	0.142662i
$889$			70.6003i			2.36786i
$890$		0			0
$891$	−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			0
$896$	−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
$900$		0			0
$901$	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			0
$906$	1.50591	−	0.403507i	0.0500304	−	0.0134056i
$907$	21.4863	+	12.4051i	0.713439	+	0.411904i	0.812333	−	0.583194i	$-0.198197\pi$
$907$	21.4863	+	12.4051i	0.713439	+	0.411904i	−0.0988939	+	0.995098i	$0.531530\pi$
$908$	−20.3051	+	11.7232i	−0.673849	+	0.389047i
$909$	27.0659	+	46.8795i	0.897719	+	1.55489i
$910$		0			0
$911$	−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			0
$916$	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	$0.989232\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$	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			0
$931$	−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
$935$		0			0
$936$			28.9418i			0.945994i
$937$	−12.2443	−	3.28085i	−0.400004	−	0.107181i	0.0532079	−	0.998583i	$-0.483055\pi$
$937$	−12.2443	−	3.28085i	−0.400004	−	0.107181i	−0.453212	+	0.891403i	$0.649722\pi$
$938$	28.5090	−	49.3790i	0.930850	−	1.61228i
$939$	−2.47869	+	2.47869i	−0.0808891	+	0.0808891i
$940$		0			0
$941$	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
$945$		0			0
$946$	4.47286	−	2.58241i	0.145425	−	0.0839614i
$947$	−30.0082	+	17.3253i	−0.975137	+	0.562996i	−0.900798	−	0.434237i	$-0.857018\pi$
$947$	−30.0082	+	17.3253i	−0.975137	+	0.562996i	−0.0743385	+	0.997233i	$0.523685\pi$
$948$	1.39887			0.0454330
$949$	9.58887	+	35.7862i	0.311268	+	1.16167i
$950$		0			0
$951$	4.06942			0.131960
$952$	63.3470	+	63.3470i	2.05309	+	2.05309i
$953$	−46.9523	−	12.5808i	−1.52093	−	0.407533i	−0.600884	−	0.799336i	$-0.705185\pi$
$953$	−46.9523	−	12.5808i	−1.52093	−	0.407533i	−0.920049	+	0.391803i	$0.871852\pi$
$954$	−25.0228	+	25.0228i	−0.810144	+	0.810144i
$955$		0			0
$956$	−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
$960$		0			0
$961$		−	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
$965$		0			0
$966$	9.55992	+	5.51942i	0.307585	+	0.177584i
$967$	−1.82918	−	1.05608i	−0.0588225	−	0.0339612i	0.470300	−	0.882506i	$-0.344146\pi$
$967$	−1.82918	−	1.05608i	−0.0588225	−	0.0339612i	−0.529123	+	0.848545i	$0.677479\pi$
$968$	−36.3320			−1.16775
$969$	−1.42489	−	0.822658i	−0.0457739	−	0.0264276i
$970$		0			0
$971$	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
$975$		0			0
$976$	0.451160	+	0.451160i	0.0144413	+	0.0144413i
$977$	−16.7968	−	29.0930i	−0.537379	−	0.930767i	−0.999044	−	0.0437132i	$-0.986081\pi$
$977$	−16.7968	−	29.0930i	−0.537379	−	0.930767i	0.461665	−	0.887054i	$-0.347252\pi$
$978$	−2.18496	+	8.15436i	−0.0698672	+	0.260748i
$979$	0.706467	−	2.63657i	0.0225788	−	0.0842652i
$980$		0			0
$981$	−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	0.348600	−	0.937272i	$-0.386657\pi$
$983$	5.70185	+	1.52781i	0.181861	+	0.0487295i	−0.166739	+	0.986001i	$0.553324\pi$
$984$	−1.50174	+	5.60457i	−0.0478738	+	0.178667i
$985$		0			0
$986$	−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			0
$991$	−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
$995$		0			0
$996$	0.543737	−	0.941780i	0.0172290	−	0.0298414i
$997$	42.2761	−	24.4081i	1.33890	−	0.773013i	0.352253	−	0.935905i	$-0.385416\pi$
$997$	42.2761	−	24.4081i	1.33890	−	0.773013i	0.986644	+	0.162892i	$0.0520822\pi$
$998$	−1.36038	+	1.36038i	−0.0430619	+	0.0430619i
$999$	2.63299	+	7.22231i	0.0833040	+	0.228504i

Twists

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

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

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16559 + 2.01885i) q^{2} +(-0.0549274 - 0.204992i) q^{3} +(-1.71718 + 2.97424i) q^{4} +(0.349826 - 0.349826i) q^{6} +(-1.26188 - 4.70941i) q^{7} -3.34372 q^{8} +(2.55907 - 1.47748i) q^{9} -0.366430i q^{11} +(0.704015 + 0.188640i) q^{12} +(1.46458 - 2.53673i) q^{13} +(8.03678 - 8.03678i) q^{14} +(-0.463041 - 0.802010i) q^{16} +(4.75903 - 2.74763i) q^{17} +(5.96563 + 3.44426i) q^{18} +(1.36274 - 0.365145i) q^{19} +(-0.896080 + 0.517352i) q^{21} +(0.739767 - 0.427105i) q^{22} -4.57650 q^{23} +(0.183662 + 0.685437i) q^{24} +6.82838 q^{26} +(-0.893629 - 0.893629i) q^{27} +(16.1738 + 4.33375i) q^{28} +(-4.08509 + 4.08509i) q^{29} +(-0.328846 - 0.328846i) q^{31} +(-2.26430 + 3.92188i) q^{32} +(-0.0751151 + 0.0201270i) q^{33} +(11.0941 + 6.40518i) q^{34} +10.1484i q^{36} +(-5.51420 - 2.56780i) q^{37} +(2.32556 + 2.32556i) q^{38} +(-0.600455 - 0.160892i) q^{39} +(7.08118 + 4.08832i) q^{41} +(-2.08891 - 1.20604i) q^{42} +6.04631 q^{43} +(1.08985 + 0.629224i) q^{44} +(-5.33430 - 9.23928i) q^{46} +(4.97863 - 4.97863i) q^{47} +(-0.138972 + 0.138972i) q^{48} +(-14.5240 + 8.38545i) q^{49} +(-0.824643 - 0.824643i) q^{51} +(5.02990 + 8.71203i) q^{52} +(-1.32960 + 4.96214i) q^{53} +(0.762504 - 2.84570i) q^{54} +(4.21939 + 15.7470i) q^{56} +(-0.149703 - 0.259294i) q^{57} +(-13.0087 - 3.48567i) q^{58} +(2.31870 - 8.65349i) q^{59} +(-0.665487 + 0.178317i) q^{61} +(0.280594 - 1.04719i) q^{62} +(-10.1873 - 10.1873i) q^{63} -12.4091 q^{64} +(-0.128187 - 0.128187i) q^{66} +(4.84572 - 1.29841i) q^{67} +18.8726i q^{68} +(0.251376 + 0.938146i) q^{69} +(5.17637 - 8.96573i) q^{71} +(-8.55683 + 4.94029i) q^{72} +(-8.94360 + 8.94360i) q^{73} +(-1.24326 - 14.1253i) q^{74} +(-1.25404 + 4.68013i) q^{76} +(-1.72567 + 0.462391i) q^{77} +(-0.375066 - 1.39976i) q^{78} +(1.85388 - 0.496745i) q^{79} +(4.29834 - 7.44494i) q^{81} +19.0612i q^{82} +(0.386169 - 1.44120i) q^{83} -3.55354i q^{84} +(7.04749 + 12.2066i) q^{86} +(1.06179 + 0.613027i) q^{87} +1.22524i q^{88} +(7.19530 + 1.92798i) q^{89} +(-13.7946 - 3.69626i) q^{91} +(7.85867 - 13.6116i) q^{92} +(-0.0493482 + 0.0854735i) q^{93} +(15.8541 + 4.24810i) q^{94} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{2} + 8 q^{3} - 30 q^{4} - 8 q^{6} + 2 q^{7} - 12 q^{8} - 14 q^{12} + 6 q^{13} - 26 q^{16} - 12 q^{17} - 18 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 24 q^{26} + 68 q^{27} + 26 q^{28}+ \cdots + 32 q^{99}+O(q^{100}) \) 68 * q + 4 * q^2 + 8 * q^3 - 30 * q^4 - 8 * q^6 + 2 * q^7 - 12 * q^8 - 14 * q^12 + 6 * q^13 - 26 * q^16 - 12 * q^17 - 18 * q^18 + 4 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 24 * q^26 + 68 * q^27 + 26 * q^28 + 14 * q^29 - 24 * q^31 + 16 * q^32 + 2 * q^33 + 16 * q^37 + 36 * q^38 + 52 * q^39 - 18 * q^41 - 132 * q^42 - 8 * q^43 - 36 * q^44 - 52 * q^46 + 24 * q^47 + 60 * q^48 - 36 * q^49 - 8 * q^51 + 26 * q^52 - 82 * q^53 + 40 * q^54 + 16 * q^56 + 6 * q^57 - 86 * q^58 - 8 * q^59 + 4 * q^61 - 10 * q^62 + 48 * q^63 - 20 * q^64 + 80 * q^66 + 40 * q^67 + 8 * q^69 + 4 * q^71 + 90 * q^72 + 60 * q^73 - 44 * q^74 + 72 * q^76 - 66 * q^77 + 24 * q^78 + 56 * q^79 - 6 * q^81 - 24 * q^83 - 4 * q^86 + 84 * q^87 - 22 * q^89 + 44 * q^91 - 44 * q^92 + 34 * q^93 - 20 * q^94 - 8 * q^96 - 42 * q^98 + 32 * q^99

Introduction

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