LMFDB - Embedded newform 560.2.cp.a.501.54

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(221,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 0, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.221"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cp (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			501.54
Character	$\chi$	$=$	560.501
Dual form			560.2.cp.a.541.54

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.24777 + 0.665628i) q^{2} +(0.412424 + 1.53919i) q^{3} +(1.11388 + 1.66111i) q^{4} +(-0.258819 + 0.965926i) q^{5} +(-0.509914 + 2.19508i) q^{6} +(-2.59318 + 0.524795i) q^{7} +(0.284191 + 2.81411i) q^{8} +(0.399076 - 0.230407i) q^{9} +(-0.965895 + 1.03298i) q^{10} +(4.57405 - 1.22561i) q^{11} +(-2.09736 + 2.39955i) q^{12} +(-2.24558 + 2.24558i) q^{13} +(-3.58502 - 1.07127i) q^{14} -1.59348 q^{15} +(-1.51855 + 3.70054i) q^{16} +(1.27376 - 2.20622i) q^{17} +(0.651321 - 0.0218593i) q^{18} +(-3.59646 - 0.963667i) q^{19} +(-1.89280 + 0.645999i) q^{20} +(-1.87725 - 3.77495i) q^{21} +(6.52318 + 1.51533i) q^{22} +(-2.29667 + 1.32598i) q^{23} +(-4.21424 + 1.59803i) q^{24} +(-0.866025 - 0.500000i) q^{25} +(-4.29670 + 1.30726i) q^{26} +(3.89951 + 3.89951i) q^{27} +(-3.76023 - 3.72299i) q^{28} +(3.51838 - 3.51838i) q^{29} +(-1.98831 - 1.06067i) q^{30} +(-1.02610 + 1.77726i) q^{31} +(-4.35799 + 3.60665i) q^{32} +(3.77289 + 6.53484i) q^{33} +(3.05789 - 1.90501i) q^{34} +(0.164252 - 2.64065i) q^{35} +(0.827252 + 0.406262i) q^{36} +(0.295647 - 1.10337i) q^{37} +(-3.84612 - 3.59634i) q^{38} +(-4.38250 - 2.53024i) q^{39} +(-2.79178 - 0.453839i) q^{40} -9.11575i q^{41} +(0.170333 - 5.95983i) q^{42} +(3.62164 + 3.62164i) q^{43} +(7.13081 + 6.23279i) q^{44} +(0.119267 + 0.445111i) q^{45} +(-3.74833 + 0.125799i) q^{46} +(-1.07589 - 1.86350i) q^{47} +(-6.32211 - 0.811134i) q^{48} +(6.44918 - 2.72178i) q^{49} +(-0.747790 - 1.20034i) q^{50} +(3.92112 + 1.05066i) q^{51} +(-6.23146 - 1.22884i) q^{52} +(9.43143 - 2.52714i) q^{53} +(2.27009 + 7.46134i) q^{54} +4.73540i q^{55} +(-2.21379 - 7.14837i) q^{56} -5.93305i q^{57} +(6.73207 - 2.04821i) q^{58} +(6.44347 - 1.72652i) q^{59} +(-1.77495 - 2.64694i) q^{60} +(9.92018 + 2.65811i) q^{61} +(-2.46334 + 1.53462i) q^{62} +(-0.913960 + 0.806919i) q^{63} +(-7.83847 + 1.59949i) q^{64} +(-1.58787 - 2.75027i) q^{65} +(0.357944 + 10.6653i) q^{66} +(-3.99156 - 14.8967i) q^{67} +(5.08359 - 0.341610i) q^{68} +(-2.98813 - 2.98813i) q^{69} +(1.96264 - 3.18560i) q^{70} +13.0583i q^{71} +(0.761804 + 1.05757i) q^{72} +(5.41803 + 3.12810i) q^{73} +(1.10333 - 1.17996i) q^{74} +(0.412424 - 1.53919i) q^{75} +(-2.40526 - 7.04750i) q^{76} +(-11.2181 + 5.57867i) q^{77} +(-3.78417 - 6.07428i) q^{78} +(4.54684 + 7.87535i) q^{79} +(-3.18142 - 2.42457i) q^{80} +(-3.70261 + 6.41310i) q^{81} +(6.06770 - 11.3744i) q^{82} +(-12.5062 + 12.5062i) q^{83} +(4.17957 - 7.32314i) q^{84} +(1.80137 + 1.80137i) q^{85} +(2.10832 + 6.92965i) q^{86} +(6.86650 + 3.96438i) q^{87} +(4.74891 + 12.5236i) q^{88} +(-1.45703 + 0.841218i) q^{89} +(-0.147460 + 0.634786i) q^{90} +(4.64473 - 7.00167i) q^{91} +(-4.76081 - 2.33803i) q^{92} +(-3.15873 - 0.846379i) q^{93} +(-0.102073 - 3.04137i) q^{94} +(1.86166 - 3.22449i) q^{95} +(-7.34865 - 5.22028i) q^{96} -10.5610 q^{97} +(9.85881 + 0.896591i) q^{98} +(1.54300 - 1.54300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) $ 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.24777	+	0.665628i	0.882309	+	0.470670i
$2$	1.24777	+	0.665628i	0.882309	+	0.470670i
$3$	0.412424	+	1.53919i	0.238113	+	0.888649i	0.976721	+	0.214514i	$0.0688168\pi$
$3$	0.412424	+	1.53919i	0.238113	+	0.888649i	−0.738608	+	0.674135i	$0.764516\pi$
$4$	1.11388	+	1.66111i	0.556940	+	0.830553i
$5$	−0.258819	+	0.965926i	−0.115747	+	0.431975i
$5$	−0.258819	+	0.965926i	−0.115747	+	0.431975i
$6$	−0.509914	+	2.19508i	−0.208171	+	0.896136i
$7$	−2.59318	+	0.524795i	−0.980130	+	0.198354i
$7$	−2.59318	+	0.524795i	−0.980130	+	0.198354i
$8$	0.284191	+	2.81411i	0.100477	+	0.994939i
$9$	0.399076	−	0.230407i	0.133025	−	0.0768022i
$10$	−0.965895	+	1.03298i	−0.305443	+	0.326657i
$11$	4.57405	−	1.22561i	1.37913	−	0.369536i	0.508323	−	0.861167i	$-0.330266\pi$
$11$	4.57405	−	1.22561i	1.37913	−	0.369536i	0.870804	+	0.491631i	$0.163599\pi$
$12$	−2.09736	+	2.39955i	−0.605456	+	0.692689i
$13$	−2.24558	+	2.24558i	−0.622813	+	0.622813i	−0.946250	−	0.323437i	$-0.895162\pi$
$13$	−2.24558	+	2.24558i	−0.622813	+	0.622813i	0.323437	+	0.946250i	$0.395162\pi$
$14$	−3.58502	−	1.07127i	−0.958138	−	0.286308i
$15$	−1.59348			−0.411435
$16$	−1.51855	+	3.70054i	−0.379637	+	0.925136i
$17$	1.27376	−	2.20622i	0.308933	−	0.535088i	−0.669196	−	0.743086i	$-0.733361\pi$
$17$	1.27376	−	2.20622i	0.308933	−	0.535088i	0.978129	+	0.207998i	$0.0666948\pi$
$18$	0.651321	−	0.0218593i	0.153518	−	0.00515228i
$19$	−3.59646	−	0.963667i	−0.825083	−	0.221080i	−0.178516	−	0.983937i	$-0.557130\pi$
$19$	−3.59646	−	0.963667i	−0.825083	−	0.221080i	−0.646568	+	0.762857i	$0.723796\pi$
$20$	−1.89280	+	0.645999i	−0.423243	+	0.144450i
$21$	−1.87725	−	3.77495i	−0.409649	−	0.823762i
$22$	6.52318	+	1.51533i	1.39075	+	0.323068i
$23$	−2.29667	+	1.32598i	−0.478888	+	0.276486i	−0.719953	−	0.694023i	$-0.755837\pi$
$23$	−2.29667	+	1.32598i	−0.478888	+	0.276486i	0.241065	+	0.970509i	$0.422503\pi$
$24$	−4.21424	+	1.59803i	−0.860228	+	0.326196i
$25$	−0.866025	−	0.500000i	−0.173205	−	0.100000i
$26$	−4.29670	+	1.30726i	−0.842653	+	0.256374i
$27$	3.89951	+	3.89951i	0.750462	+	0.750462i
$28$	−3.76023	−	3.72299i	−0.710617	−	0.703579i
$29$	3.51838	−	3.51838i	0.653346	−	0.653346i	−0.300451	−	0.953797i	$-0.597137\pi$
$29$	3.51838	−	3.51838i	0.653346	−	0.653346i	0.953797	+	0.300451i	$0.0971372\pi$
$30$	−1.98831	−	1.06067i	−0.363013	−	0.193650i
$31$	−1.02610	+	1.77726i	−0.184294	+	0.319206i	−0.943338	−	0.331833i	$-0.892333\pi$
$31$	−1.02610	+	1.77726i	−0.184294	+	0.319206i	0.759045	+	0.651039i	$0.225666\pi$
$32$	−4.35799	+	3.60665i	−0.770390	+	0.637572i
$33$	3.77289	+	6.53484i	0.656776	+	1.13757i
$34$	3.05789	−	1.90501i	0.524424	−	0.326707i
$35$	0.164252	−	2.64065i	0.0277636	−	0.446351i
$36$	0.827252	+	0.406262i	0.137875	+	0.0677104i
$37$	0.295647	−	1.10337i	0.0486041	−	0.181393i	−0.937356	−	0.348372i	$-0.886735\pi$
$37$	0.295647	−	1.10337i	0.0486041	−	0.181393i	0.985960	+	0.166979i	$0.0534013\pi$
$38$	−3.84612	−	3.59634i	−0.623923	−	0.583403i
$39$	−4.38250	−	2.53024i	−0.701762	−	0.405162i
$40$	−2.79178	−	0.453839i	−0.441419	−	0.0717582i
$41$		−	9.11575i		−	1.42364i	−0.702361	−	0.711821i	$-0.747871\pi$
$41$		−	9.11575i		−	1.42364i	0.702361	−	0.711821i	$-0.252129\pi$
$42$	0.170333	−	5.95983i	0.0262829	−	0.919622i
$43$	3.62164	+	3.62164i	0.552294	+	0.552294i	0.927102	−	0.374808i	$-0.122291\pi$
$43$	3.62164	+	3.62164i	0.552294	+	0.552294i	−0.374808	+	0.927102i	$0.622291\pi$
$44$	7.13081	+	6.23279i	1.07501	+	0.939629i
$45$	0.119267	+	0.445111i	0.0177793	+	0.0663533i
$46$	−3.74833	+	0.125799i	−0.552662	+	0.0185481i
$47$	−1.07589	−	1.86350i	−0.156935	−	0.271820i	0.776827	−	0.629714i	$-0.216828\pi$
$47$	−1.07589	−	1.86350i	−0.156935	−	0.271820i	−0.933762	+	0.357895i	$0.883495\pi$
$48$	−6.32211	−	0.811134i	−0.912518	−	0.117077i
$49$	6.44918	−	2.72178i	0.921311	−	0.388825i
$50$	−0.747790	−	1.20034i	−0.105753	−	0.169753i
$51$	3.92112	+	1.05066i	0.549066	+	0.147122i
$52$	−6.23146	−	1.22884i	−0.864148	−	0.170410i
$53$	9.43143	−	2.52714i	1.29551	−	0.347130i	0.455757	−	0.890104i	$-0.349369\pi$
$53$	9.43143	−	2.52714i	1.29551	−	0.347130i	0.839749	+	0.542974i	$0.182702\pi$
$54$	2.27009	+	7.46134i	0.308920	+	1.01536i
$55$			4.73540i			0.638521i
$56$	−2.21379	−	7.14837i	−0.295830	−	0.955240i
$57$		−	5.93305i		−	0.785852i
$58$	6.73207	−	2.04821i	0.883964	−	0.268943i
$59$	6.44347	−	1.72652i	0.838868	−	0.224774i	0.186289	−	0.982495i	$-0.440354\pi$
$59$	6.44347	−	1.72652i	0.838868	−	0.224774i	0.652579	+	0.757721i	$0.273687\pi$
$60$	−1.77495	−	2.64694i	−0.229145	−	0.341719i
$61$	9.92018	+	2.65811i	1.27015	+	0.340336i	0.830088	−	0.557632i	$-0.188290\pi$
$61$	9.92018	+	2.65811i	1.27015	+	0.340336i	0.440061	+	0.897968i	$0.354957\pi$
$62$	−2.46334	+	1.53462i	−0.312845	+	0.194897i
$63$	−0.913960	+	0.806919i	−0.115148	+	0.101662i
$64$	−7.83847	+	1.59949i	−0.979809	+	0.199936i
$65$	−1.58787	−	2.75027i	−0.196951	−	0.341129i
$66$	0.357944	+	10.6653i	0.0440599	+	1.31281i
$67$	−3.99156	−	14.8967i	−0.487646	−	1.81992i	−0.567837	−	0.823141i	$-0.692219\pi$
$67$	−3.99156	−	14.8967i	−0.487646	−	1.81992i	0.0801902	−	0.996780i	$-0.474447\pi$
$68$	5.08359	−	0.341610i	0.616476	−	0.0414263i
$69$	−2.98813	−	2.98813i	−0.359729	−	0.359729i
$70$	1.96264	−	3.18560i	0.234580	−	0.380752i
$71$			13.0583i			1.54974i	0.632123	+	0.774868i	$0.282184\pi$
$71$			13.0583i			1.54974i	−0.632123	+	0.774868i	$0.717816\pi$
$72$	0.761804	+	1.05757i	0.0897795	+	0.124635i
$73$	5.41803	+	3.12810i	0.634133	+	0.366117i	0.782351	−	0.622838i	$-0.214020\pi$
$73$	5.41803	+	3.12810i	0.634133	+	0.366117i	−0.148218	+	0.988955i	$0.547354\pi$
$74$	1.10333	−	1.17996i	0.128260	−	0.137168i
$75$	0.412424	−	1.53919i	0.0476226	−	0.177730i
$76$	−2.40526	−	7.04750i	−0.275903	−	0.808404i
$77$	−11.2181	+	5.57867i	−1.27843	+	0.635748i
$78$	−3.78417	−	6.07428i	−0.428473	−	0.687777i
$79$	4.54684	+	7.87535i	0.511559	+	0.886047i	0.999910	+	0.0133993i	$0.00426525\pi$
$79$	4.54684	+	7.87535i	0.511559	+	0.886047i	−0.488351	+	0.872647i	$0.662401\pi$
$80$	−3.18142	−	2.42457i	−0.355694	−	0.271076i
$81$	−3.70261	+	6.41310i	−0.411401	+	0.712567i
$82$	6.06770	−	11.3744i	0.670065	−	1.25609i
$83$	−12.5062	+	12.5062i	−1.37273	+	1.37273i	−0.516366	+	0.856368i	$0.672716\pi$
$83$	−12.5062	+	12.5062i	−1.37273	+	1.37273i	−0.856368	+	0.516366i	$0.827284\pi$
$84$	4.17957	−	7.32314i	0.456028	−	0.799021i
$85$	1.80137	+	1.80137i	0.195386	+	0.195386i
$86$	2.10832	+	6.92965i	0.227346	+	0.747243i
$87$	6.86650	+	3.96438i	0.736166	+	0.425026i
$88$	4.74891	+	12.5236i	0.506236	+	1.33502i
$89$	−1.45703	+	0.841218i	−0.154445	+	0.0891689i	−0.575231	−	0.817991i	$-0.695088\pi$
$89$	−1.45703	+	0.841218i	−0.154445	+	0.0891689i	0.420786	+	0.907160i	$0.361754\pi$
$90$	−0.147460	+	0.634786i	−0.0155436	+	0.0669123i
$91$	4.64473	−	7.00167i	0.486900	−	0.733975i
$92$	−4.76081	−	2.33803i	−0.496349	−	0.243756i
$93$	−3.15873	−	0.846379i	−0.327545	−	0.0877654i
$94$	−0.102073	−	3.04137i	−0.0105280	−	0.313694i
$95$	1.86166	−	3.22449i	0.191003	−	0.330826i
$96$	−7.34865	−	5.22028i	−0.750018	−	0.532793i
$97$	−10.5610			−1.07230			−0.536152	−	0.844122i	$-0.680122\pi$
$97$	−10.5610			−1.07230			−0.536152	+	0.844122i	$0.680122\pi$
$98$	9.85881	+	0.896591i	0.995890	+	0.0905693i
$99$	1.54300	−	1.54300i	0.155078	−	0.155078i
$100$	−0.134095	−	1.99550i	−0.0134095	−	0.199550i
$101$	1.78367	−	0.477932i	0.177482	−	0.0475561i	−0.168984	−	0.985619i	$-0.554049\pi$
$101$	1.78367	−	0.477932i	0.177482	−	0.0475561i	0.346465	+	0.938063i	$0.387382\pi$
$102$	4.19332	+	3.92099i	0.415200	+	0.388236i
$103$	4.11160	−	2.37383i	0.405128	−	0.233901i	−0.283566	−	0.958953i	$-0.591518\pi$
$103$	4.11160	−	2.37383i	0.405128	−	0.233901i	0.688694	+	0.725052i	$0.258184\pi$
$104$	−6.95750	−	5.68115i	−0.682239	−	0.557083i
$105$	4.13219	−	0.836252i	0.403260	−	0.0816098i
$106$	13.4504	+	3.12452i	1.30642	+	0.303480i
$107$	0.620392	−	2.31533i	0.0599756	−	0.223832i	−0.929433	−	0.368992i	$-0.879703\pi$
$107$	0.620392	−	2.31533i	0.0599756	−	0.223832i	0.989408	+	0.145160i	$0.0463697\pi$
$108$	−2.13392	+	10.8211i	−0.205336	+	1.04126i
$109$	−5.08466	−	18.9762i	−0.487022	−	1.81759i	−0.570778	−	0.821104i	$-0.693358\pi$
$109$	−5.08466	−	18.9762i	−0.487022	−	1.81759i	0.0837561	−	0.996486i	$-0.473308\pi$
$110$	−3.15201	+	5.90871i	−0.300533	+	0.563373i
$111$	1.82022			0.172768
$112$	1.99584	−	10.3931i	0.188589	−	0.982056i
$113$	5.53335			0.520533			0.260267	−	0.965537i	$-0.416190\pi$
$113$	5.53335			0.520533			0.260267	+	0.965537i	$0.416190\pi$
$114$	3.94921	−	7.40311i	0.369877	−	0.693365i
$115$	−0.686379	−	2.56160i	−0.0640052	−	0.238871i
$116$	9.76344	+	1.92535i	0.906513	+	0.178764i
$117$	−0.378761	+	1.41355i	−0.0350165	+	0.130683i
$118$	9.18921	+	2.13464i	0.845935	+	0.196510i
$119$	−2.14528	+	6.38960i	−0.196658	+	0.585734i
$120$	−0.452853	−	4.48424i	−0.0413397	−	0.409353i
$121$	9.89349	−	5.71201i	0.899408	−	0.519273i
$122$	10.6088	+	9.91987i	0.960479	+	0.898102i
$123$	14.0308	−	3.75955i	1.26512	−	0.338987i
$124$	−4.09518	+	0.275190i	−0.367758	+	0.0247128i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	−1.67752	+	0.398495i	−0.149446	+	0.0355008i
$127$	2.33905			0.207557			0.103778	−	0.994600i	$-0.466907\pi$
$127$	2.33905			0.207557			0.103778	+	0.994600i	$0.466907\pi$
$128$	−10.8453	−	3.22170i	−0.958599	−	0.284761i
$129$	−4.08072	+	7.06802i	−0.359288	+	0.622305i
$130$	−0.150645	−	4.48864i	−0.0132125	−	0.393680i
$131$	3.55056	+	0.951368i	0.310213	+	0.0831214i	0.410567	−	0.911830i	$-0.365331\pi$
$131$	3.55056	+	0.951368i	0.310213	+	0.0831214i	−0.100354	+	0.994952i	$0.531997\pi$
$132$	−6.65251	+	13.5462i	−0.579027	+	1.17904i
$133$	9.83199	+	0.611562i	0.852542	+	0.0530292i
$134$	4.93509	−	21.2446i	0.426327	−	1.83525i
$135$	−4.77591	+	2.75737i	−0.411045	+	0.237317i
$136$	6.57055	+	2.95753i	0.563420	+	0.253606i
$137$	−10.6399	−	6.14294i	−0.909027	−	0.524827i	−0.0289092	−	0.999582i	$-0.509203\pi$
$137$	−10.6399	−	6.14294i	−0.909027	−	0.524827i	−0.880118	+	0.474755i	$0.842537\pi$
$138$	−1.73953	−	5.71750i	−0.148079	−	0.486706i
$139$	−15.2519	−	15.2519i	−1.29365	−	1.29365i	−0.932511	−	0.361140i	$-0.882388\pi$
$139$	−15.2519	−	15.2519i	−1.29365	−	1.29365i	−0.361140	−	0.932511i	$-0.617612\pi$
$140$	4.56935	−	2.66852i	0.386181	−	0.225531i
$141$	2.42455	−	2.42455i	0.204184	−	0.204184i
$142$	−8.69198	+	16.2938i	−0.729414	+	1.36735i
$143$	−7.51919	+	13.0236i	−0.628786	+	1.08909i
$144$	0.246614	+	1.82668i	0.0205512	+	0.152223i
$145$	2.48787	+	4.30911i	0.206606	+	0.357852i
$146$	4.67833	+	7.50956i	0.387181	+	0.621495i
$147$	6.84912	+	8.80396i	0.564906	+	0.726139i
$148$	2.16213	−	0.737919i	0.177726	−	0.0606566i
$149$	4.60204	−	17.1751i	0.377014	−	1.40704i	−0.473366	−	0.880866i	$-0.656961\pi$
$149$	4.60204	−	17.1751i	0.377014	−	1.40704i	0.850380	−	0.526169i	$-0.176372\pi$
$150$	1.53914	−	1.64604i	0.125670	−	0.134398i
$151$	−15.2634	−	8.81231i	−1.24212	−	0.717136i	−0.272591	−	0.962130i	$-0.587881\pi$
$151$	−15.2634	−	8.81231i	−1.24212	−	0.717136i	−0.969525	+	0.244994i	$0.921214\pi$
$152$	1.68979	−	10.3947i	0.137060	−	0.843121i
$153$		−	1.17393i		−	0.0949069i
$154$	−17.7110	−	0.506184i	−1.42719	−	0.0407894i
$155$	−1.45113	−	1.45113i	−0.116558	−	0.116558i
$156$	−0.678583	−	10.0982i	−0.0543301	−	0.808501i
$157$	−2.34565	−	8.75410i	−0.187204	−	0.698653i	−0.994148	−	0.108026i	$-0.965547\pi$
$157$	−2.34565	−	8.75410i	−0.187204	−	0.698653i	0.806945	−	0.590627i	$-0.201120\pi$
$158$	0.431371	+	12.8532i	0.0343180	+	1.02254i
$159$	7.77949	+	13.4745i	0.616954	+	1.06859i
$160$	−2.35583	−	5.14296i	−0.186245	−	0.406587i
$161$	5.25981	−	4.64379i	0.414531	−	0.365982i
$162$	−8.88875	+	5.53754i	−0.698366	+	0.435070i
$163$	9.66440	+	2.58957i	0.756974	+	0.202831i	0.616610	−	0.787269i	$-0.288506\pi$
$163$	9.66440	+	2.58957i	0.756974	+	0.202831i	0.140365	+	0.990100i	$0.455172\pi$
$164$	15.1422	−	10.1538i	1.18241	−	0.792882i
$165$	−7.28866	+	1.95299i	−0.567422	+	0.152040i
$166$	−23.9294	+	7.28044i	−1.85728	+	0.565071i
$167$			7.58164i			0.586685i	0.956007	+	0.293342i	$0.0947676\pi$
$167$			7.58164i			0.586685i	−0.956007	+	0.293342i	$0.905232\pi$
$168$	10.0896	−	6.35559i	0.778433	−	0.490345i
$169$			2.91471i			0.224209i
$170$	1.04866	+	3.44675i	0.0804287	+	0.264354i
$171$	−1.65729	+	0.444070i	−0.126736	+	0.0339589i
$172$	−1.98186	+	10.0500i	−0.151115	+	0.766304i
$173$	−14.7668	−	3.95675i	−1.12270	−	0.300826i	−0.350724	−	0.936479i	$-0.614064\pi$
$173$	−14.7668	−	3.95675i	−1.12270	−	0.300826i	−0.771975	+	0.635653i	$0.780731\pi$
$174$	5.92904	+	9.51718i	0.449479	+	0.721495i
$175$	2.50816	+	0.842105i	0.189599	+	0.0636571i
$176$	−2.41047	+	18.7876i	−0.181696	+	1.41617i
$177$	5.31488	+	9.20563i	0.399491	+	0.691938i
$178$	−2.37799	+	0.0798086i	−0.178238	+	0.00598191i
$179$	4.62296	+	17.2531i	0.345536	+	1.28956i	0.891985	+	0.452066i	$0.149313\pi$
$179$	4.62296	+	17.2531i	0.345536	+	1.28956i	−0.546448	+	0.837493i	$0.684021\pi$
$180$	−0.606528	+	0.693916i	−0.0452079	+	0.0517214i
$181$	−4.33613	−	4.33613i	−0.322302	−	0.322302i	0.527347	−	0.849650i	$-0.323187\pi$
$181$	−4.33613	−	4.33613i	−0.322302	−	0.322302i	−0.849650	+	0.527347i	$0.823187\pi$
$182$	10.4561	−	5.64484i	0.775057	−	0.418424i
$183$			16.3653i			1.20976i
$184$	−4.38416	−	6.08625i	−0.323204	−	0.448685i
$185$	0.989254	+	0.571146i	0.0727314	+	0.0419915i
$186$	−3.37801	−	3.15863i	−0.247688	−	0.231602i
$187$	3.12228	−	11.6525i	0.228324	−	0.852115i
$188$	1.89706	−	3.86289i	0.138357	−	0.281730i
$189$	−12.1586	−	8.06570i	−0.884408	−	0.586693i
$190$	4.46925	−	2.78426i	0.324233	−	0.201992i
$191$	−1.27556	−	2.20933i	−0.0922959	−	0.159861i	0.816181	−	0.577796i	$-0.196087\pi$
$191$	−1.27556	−	2.20933i	−0.0922959	−	0.159861i	−0.908477	+	0.417935i	$0.862754\pi$
$192$	−5.69469	−	11.4052i	−0.410979	−	0.823099i
$193$	5.27892	−	9.14336i	0.379985	−	0.658153i	−0.611075	−	0.791573i	$-0.709262\pi$
$193$	5.27892	−	9.14336i	0.379985	−	0.658153i	0.991060	+	0.133420i	$0.0425958\pi$
$194$	−13.1777	−	7.02967i	−0.946103	−	0.504701i
$195$	3.57830	−	3.57830i	0.256247	−	0.256247i
$196$	11.7048	+	7.68104i	0.836055	+	0.548646i
$197$	−13.0826	−	13.0826i	−0.932098	−	0.932098i	0.0657390	−	0.997837i	$-0.479060\pi$
$197$	−13.0826	−	13.0826i	−0.932098	−	0.932098i	−0.997837	+	0.0657390i	$0.979060\pi$
$198$	2.95238	−	0.898252i	0.209817	−	0.0638360i
$199$	−7.16485	−	4.13663i	−0.507903	−	0.293238i	0.224068	−	0.974573i	$-0.428066\pi$
$199$	−7.16485	−	4.13663i	−0.507903	−	0.293238i	−0.731971	+	0.681335i	$0.761399\pi$
$200$	1.16094	−	2.57919i	0.0820909	−	0.182376i
$201$	21.2826	−	12.2875i	1.50116	−	0.866693i
$202$	2.54374	+	0.590908i	0.178977	+	0.0415761i
$203$	−7.27736	+	10.9702i	−0.510771	+	0.769958i
$204$	2.62239	+	7.68370i	0.183604	+	0.537967i
$205$	8.80514	+	2.35933i	0.614978	+	0.164783i
$206$	6.71043	−	0.225212i	0.467538	−	0.0156912i
$207$	−0.611030	+	1.05833i	−0.0424695	+	0.0735594i
$208$	−4.89985	−	11.7199i	−0.339744	−	0.812629i
$209$	−17.6314			−1.21959
$210$	5.71267	+	1.70705i	0.394212	+	0.117797i
$211$	−7.86994	+	7.86994i	−0.541789	+	0.541789i	−0.924053	−	0.382264i	$-0.875144\pi$
$211$	−7.86994	+	7.86994i	−0.541789	+	0.541789i	0.382264	+	0.924053i	$0.375144\pi$
$212$	14.7033	+	12.8517i	1.00983	+	0.882656i
$213$	−20.0992	+	5.38556i	−1.37717	+	0.369012i
$214$	2.31526	−	2.47606i	0.158268	−	0.169260i
$215$	−4.43558	+	2.56088i	−0.302504	+	0.174651i
$216$	−9.86547	+	12.0819i	−0.671260	+	0.822068i
$217$	1.72817	−	5.14726i	0.117316	−	0.349419i
$218$	6.28659	−	27.0625i	0.425781	−	1.83290i
$219$	−2.58021	+	9.62946i	−0.174354	+	0.650699i
$220$	−7.86600	+	5.27466i	−0.530326	+	0.355618i
$221$	2.09391	+	7.81460i	0.140852	+	0.525667i
$222$	2.27123	+	1.21159i	0.152435	+	0.0813167i
$223$	18.2726			1.22362			0.611811	−	0.791004i	$-0.290441\pi$
$223$	18.2726			1.22362			0.611811	+	0.791004i	$0.290441\pi$
$224$	9.40830	−	11.6398i	0.628618	−	0.777714i
$225$	−0.460813			−0.0307209
$226$	6.90437	+	3.68315i	0.459272	+	0.244999i
$227$	−0.104069	−	0.388392i	−0.00690733	−	0.0257785i	0.962386	−	0.271685i	$-0.0875810\pi$
$227$	−0.104069	−	0.388392i	−0.00690733	−	0.0257785i	−0.969293	+	0.245907i	$0.920914\pi$
$228$	9.85543	−	6.60870i	0.652692	−	0.437672i
$229$	−3.26463	+	12.1838i	−0.215733	+	0.805126i	0.770175	+	0.637833i	$0.220169\pi$
$229$	−3.26463	+	12.1838i	−0.215733	+	0.805126i	−0.985907	+	0.167292i	$0.946498\pi$
$230$	0.848627	−	3.65317i	0.0559568	−	0.240883i
$231$	−13.2132	−	14.9660i	−0.869367	−	0.984692i
$232$	10.9010	+	8.90122i	0.715686	+	0.584394i
$233$	−0.143430	+	0.0828093i	−0.00939641	+	0.00542502i	−0.504691	−	0.863300i	$-0.668394\pi$
$233$	−0.143430	+	0.0828093i	−0.00939641	+	0.00542502i	0.495294	+	0.868725i	$0.335060\pi$
$234$	−1.41351	+	1.51168i	−0.0924040	+	0.0988218i
$235$	2.07847	−	0.556923i	0.135584	−	0.0363297i
$236$	10.0452	+	8.78014i	0.653885	+	0.571539i
$237$	−10.2464	+	10.2464i	−0.665576	+	0.665576i
$238$	−6.92993	+	6.54482i	−0.449200	+	0.424237i
$239$	−8.91628			−0.576746			−0.288373	−	0.957518i	$-0.593114\pi$
$239$	−8.91628			−0.576746			−0.288373	+	0.957518i	$0.593114\pi$
$240$	2.41978	−	5.89675i	0.156196	−	0.380634i
$241$	−7.14045	+	12.3676i	−0.459957	+	0.796669i	−0.998958	−	0.0456361i	$-0.985469\pi$
$241$	−7.14045	+	12.3676i	−0.459957	+	0.796669i	0.539001	+	0.842305i	$0.318802\pi$
$242$	16.1469	−	0.541913i	1.03796	−	0.0348355i
$243$	4.58251	+	1.22788i	0.293968	+	0.0787685i
$244$	6.63449	+	19.4393i	0.424730	+	1.24447i
$245$	0.959865	+	6.93388i	0.0613235	+	0.442989i
$246$	20.0098	+	4.64825i	1.27578	+	0.296361i
$247$	10.2401	−	5.91214i	0.651564	−	0.376181i
$248$	−5.29303	−	2.38249i	−0.336108	−	0.151288i
$249$	−24.4072	−	14.0915i	−1.54675	−	0.893014i
$250$	1.35298	−	0.411639i	0.0855699	−	0.0260344i
$251$	−18.0689	−	18.0689i	−1.14050	−	1.14050i	−0.988358	−	0.152143i	$-0.951382\pi$
$251$	−18.0689	−	18.0689i	−1.14050	−	1.14050i	−0.152143	−	0.988358i	$-0.548618\pi$
$252$	−2.35842	−	0.619374i	−0.148566	−	0.0390169i
$253$	−8.87993	+	8.87993i	−0.558276	+	0.558276i
$254$	2.91860	+	1.55694i	0.183129	+	0.0976908i
$255$	−2.02972	+	3.51558i	−0.127106	+	0.220154i
$256$	−11.3880	−	11.2389i	−0.711752	−	0.702431i
$257$	6.36378	+	11.0224i	0.396962	+	0.687558i	0.993349	−	0.115139i	$-0.0367312\pi$
$257$	6.36378	+	11.0224i	0.396962	+	0.687558i	−0.596388	+	0.802697i	$0.703398\pi$
$258$	−9.79649	+	6.10305i	−0.609903	+	0.379959i
$259$	−0.187623	+	3.01639i	−0.0116583	+	0.187429i
$260$	2.79979	−	5.70108i	0.173636	−	0.353566i
$261$	0.593442	−	2.21476i	0.0367331	−	0.137090i
$262$	3.79703	+	3.55044i	0.234581	+	0.219347i
$263$	−13.3295	−	7.69581i	−0.821934	−	0.474544i	0.0291486	−	0.999575i	$-0.490720\pi$
$263$	−13.3295	−	7.69581i	−0.821934	−	0.474544i	−0.851083	+	0.525031i	$0.824054\pi$
$264$	−17.3175	+	12.4745i	−1.06582	+	0.767751i
$265$			9.76413i			0.599806i
$266$	11.8610	+	7.30754i	0.727246	+	0.448054i
$267$	−1.89571	−	1.89571i	−0.116015	−	0.116015i
$268$	20.2989	−	23.2235i	1.23995	−	1.41860i
$269$	−0.207789	−	0.775479i	−0.0126691	−	0.0472818i	0.959302	−	0.282382i	$-0.0911247\pi$
$269$	−0.207789	−	0.775479i	−0.0126691	−	0.0472818i	−0.971971	+	0.235101i	$0.924458\pi$
$270$	−7.79464	+	0.261599i	−0.474367	+	0.0159204i
$271$	−9.76645	−	16.9160i	−0.593269	−	1.02757i	−0.993789	−	0.111284i	$-0.964504\pi$
$271$	−9.76645	−	16.9160i	−0.593269	−	1.02757i	0.400519	−	0.916288i	$-0.368830\pi$
$272$	6.22995	+	8.06387i	0.377746	+	0.488944i
$273$	12.6925	+	4.26145i	0.768184	+	0.257915i
$274$	−9.18726	−	14.7472i	−0.555023	−	0.890912i
$275$	−4.57405	−	1.22561i	−0.275825	−	0.0739072i
$276$	1.63519	−	8.29203i	0.0984267	−	0.499121i
$277$	−25.3297	+	6.78707i	−1.52191	+	0.407795i	−0.920371	−	0.391046i	$-0.872113\pi$
$277$	−25.3297	+	6.78707i	−1.52191	+	0.407795i	−0.601542	+	0.798841i	$0.705447\pi$
$278$	−8.87885	−	29.1831i	−0.532518	−	1.75028i
$279$			0.945684i			0.0566166i
$280$	7.47776	−	0.288226i	0.446882	−	0.0172248i
$281$			8.85144i			0.528032i	0.964518	+	0.264016i	$0.0850472\pi$
$281$			8.85144i			0.528032i	−0.964518	+	0.264016i	$0.914953\pi$
$282$	4.63914	−	1.41144i	0.276257	−	0.0840502i
$283$	17.0155	−	4.55928i	1.01146	−	0.271021i	0.285223	−	0.958461i	$-0.407932\pi$
$283$	17.0155	−	4.55928i	1.01146	−	0.271021i	0.726241	+	0.687440i	$0.241266\pi$
$284$	−21.6912	+	14.5454i	−1.28714	+	0.863110i
$285$	5.73089	+	1.53559i	0.339469	+	0.0909603i
$286$	−18.0511	+	11.2455i	−1.06739	+	0.664963i
$287$	4.78390	+	23.6388i	0.282385	+	1.39535i
$288$	−0.908170	+	2.44344i	−0.0535145	+	0.143981i
$289$	5.25505	+	9.10202i	0.309121	+	0.535413i
$290$	0.236031	+	7.03279i	0.0138602	+	0.412980i
$291$	−4.35559	−	16.2553i	−0.255329	−	0.952902i
$292$	0.838924	+	12.4843i	0.0490943	+	0.730586i
$293$	11.0335	+	11.0335i	0.644586	+	0.644586i	0.951679	−	0.307093i	$-0.0993563\pi$
$293$	11.0335	+	11.0335i	0.644586	+	0.644586i	−0.307093	+	0.951679i	$0.599356\pi$
$294$	2.68599	+	15.5443i	0.156650	+	0.906563i
$295$			6.67077i			0.388387i
$296$	3.18903	+	0.518416i	0.185358	+	0.0301323i
$297$	22.6158	+	13.0573i	1.31230	+	0.757659i
$298$	17.1745	−	18.3673i	0.994892	−	1.06399i
$299$	2.17976	−	8.13496i	0.126059	−	0.470457i
$300$	3.01614	−	1.02939i	0.174137	−	0.0594317i
$301$	−11.2922	−	7.49094i	−0.650870	−	0.431771i
$302$	−13.1795	−	21.1555i	−0.758396	−	1.21736i
$303$	1.47125	+	2.54829i	0.0845213	+	0.146395i
$304$	9.02748	−	11.8455i	0.517761	−	0.679384i
$305$	−5.13507	+	8.89419i	−0.294033	+	0.509280i
$306$	0.781403	−	1.46480i	0.0446698	−	0.0837372i
$307$	13.8354	−	13.8354i	0.789631	−	0.789631i	−0.191803	−	0.981433i	$-0.561433\pi$
$307$	13.8354	−	13.8354i	0.789631	−	0.789631i	0.981433	+	0.191803i	$0.0614334\pi$
$308$	−21.7624	−	12.4205i	−1.24003	−	0.707726i
$309$	5.34949	+	5.34949i	0.304322	+	0.304322i
$310$	−0.844770	−	2.77659i	−0.0479797	−	0.157700i
$311$	−9.75762	−	5.63357i	−0.553304	−	0.319450i	0.197149	−	0.980373i	$-0.436832\pi$
$311$	−9.75762	−	5.63357i	−0.553304	−	0.319450i	−0.750454	+	0.660923i	$0.770165\pi$
$312$	5.87491	−	13.0519i	0.332601	−	0.738920i
$313$	−5.24744	+	3.02961i	−0.296603	+	0.171244i	−0.640916	−	0.767611i	$-0.721445\pi$
$313$	−5.24744	+	3.02961i	−0.296603	+	0.171244i	0.344313	+	0.938855i	$0.388112\pi$
$314$	2.90013	−	12.4845i	0.163664	−	0.704539i
$315$	−0.542874	−	1.09166i	−0.0305875	−	0.0615083i
$316$	−8.01717	+	16.3250i	−0.451001	+	0.918351i
$317$	−16.0077	−	4.28924i	−0.899080	−	0.240908i	−0.220459	−	0.975396i	$-0.570755\pi$
$317$	−16.0077	−	4.28924i	−0.899080	−	0.240908i	−0.678621	+	0.734489i	$0.737422\pi$
$318$	0.738061	+	21.9913i	0.0413884	+	1.23321i
$319$	11.7811	−	20.4054i	0.659612	−	1.14248i
$320$	0.483755	−	7.98536i	0.0270427	−	0.446395i
$321$	3.81960			0.213189
$322$	9.65409	−	2.29333i	0.538001	−	0.127802i
$323$	−6.70710	+	6.70710i	−0.373193	+	0.373193i
$324$	−14.7771	+	0.993000i	−0.820950	+	0.0551667i
$325$	3.06752	−	0.821940i	0.170156	−	0.0455930i
$326$	10.3353	+	9.66409i	0.572419	+	0.535245i
$327$	27.1109	−	15.6525i	1.49923	−	0.865584i
$328$	25.6528	−	2.59062i	1.41644	−	0.143043i
$329$	3.76794	+	4.26777i	0.207733	+	0.235290i
$330$	−10.3946	−	2.41464i	−0.572202	−	0.132922i
$331$	−5.06616	+	18.9072i	−0.278461	+	1.03923i	0.675025	+	0.737795i	$0.264133\pi$
$331$	−5.06616	+	18.9072i	−0.278461	+	1.03923i	−0.953486	+	0.301437i	$0.902534\pi$
$332$	−34.7045	−	6.84373i	−1.90466	−	0.375598i
$333$	−0.136238	−	0.508447i	−0.00746580	−	0.0278627i
$334$	−5.04655	+	9.46017i	−0.276135	+	0.517637i
$335$	15.4222			0.842604
$336$	16.8201	−	1.21439i	0.917609	−	0.0662507i
$337$	17.5082			0.953735			0.476867	−	0.878975i	$-0.341772\pi$
$337$	17.5082			0.953735			0.476867	+	0.878975i	$0.341772\pi$
$338$	−1.94012	+	3.63690i	−0.105528	+	0.197822i
$339$	2.28208	+	8.51685i	0.123946	+	0.462572i
$340$	−0.985760	+	4.99878i	−0.0534603	+	0.271097i
$341$	−2.51521	+	9.38689i	−0.136206	+	0.508329i
$342$	−2.36351	−	0.549041i	−0.127804	−	0.0296887i
$343$	−15.2955	+	10.4426i	−0.825880	+	0.563845i
$344$	−9.16246	+	11.2209i	−0.494007	+	0.604992i
$345$	3.65970	−	2.11293i	0.197032	−	0.113756i
$346$	−15.7919	−	14.7663i	−0.848978	−	0.793843i
$347$	−5.14687	+	1.37910i	−0.276298	+	0.0740340i	−0.394307	−	0.918979i	$-0.629016\pi$
$347$	−5.14687	+	1.37910i	−0.276298	+	0.0740340i	0.118009	+	0.993013i	$0.462349\pi$
$348$	1.06320	+	15.8218i	0.0569937	+	0.848138i
$349$	17.7694	−	17.7694i	0.951175	−	0.951175i	−0.0476869	−	0.998862i	$-0.515185\pi$
$349$	17.7694	−	17.7694i	0.951175	−	0.951175i	0.998862	+	0.0476869i	$0.0151850\pi$
$350$	2.56909	+	2.72026i	0.137323	+	0.145404i
$351$	−17.5134			−0.934794
$352$	−15.5133	+	21.8382i	−0.826860	+	1.16398i
$353$	−18.1901	+	31.5061i	−0.968160	+	1.67690i	−0.267285	+	0.963617i	$0.586127\pi$
$353$	−18.1901	+	31.5061i	−0.968160	+	1.67690i	−0.700875	+	0.713284i	$0.747207\pi$
$354$	0.504236	+	15.0243i	0.0267999	+	0.798531i
$355$	−12.6134	−	3.37974i	−0.669448	−	0.179378i
$356$	−3.02031	−	1.48327i	−0.160076	−	0.0786132i
$357$	−10.7195	−	0.666770i	−0.567339	−	0.0352892i
$358$	−5.71575	+	24.6052i	−0.302087	+	1.30042i
$359$	−4.33320	+	2.50177i	−0.228697	+	0.132039i	−0.609971	−	0.792424i	$-0.708819\pi$
$359$	−4.33320	+	2.50177i	−0.228697	+	0.132039i	0.381274	+	0.924462i	$0.375486\pi$
$360$	−1.21870	+	0.462128i	−0.0642311	+	0.0243563i
$361$	−4.44865	−	2.56843i	−0.234139	−	0.135180i
$362$	−2.52426	−	8.29676i	−0.132672	−	0.436068i
$363$	12.8722	+	12.8722i	0.675613	+	0.675613i
$364$	16.8042	−	0.0836262i	0.880779	−	0.00438320i
$365$	−4.42381	+	4.42381i	−0.231553	+	0.231553i
$366$	−10.8932	+	20.4202i	−0.569396	+	1.06738i
$367$	−3.33586	+	5.77787i	−0.174130	+	0.301603i	−0.939860	−	0.341560i	$-0.889045\pi$
$367$	−3.33586	+	5.77787i	−0.174130	+	0.301603i	0.765730	+	0.643163i	$0.222378\pi$
$368$	−1.41926	−	10.5125i	−0.0739839	−	0.548001i
$369$	−2.10033	−	3.63788i	−0.109339	−	0.189380i
$370$	0.854195	+	1.37114i	0.0444075	+	0.0712820i
$371$	−23.1312	+	11.5029i	−1.20091	+	0.597201i
$372$	−2.11252	−	6.18975i	−0.109529	−	0.320924i
$373$	−0.847513	+	3.16296i	−0.0438826	+	0.163772i	−0.984390	−	0.176001i	$-0.943684\pi$
$373$	−0.847513	+	3.16296i	−0.0438826	+	0.163772i	0.940507	+	0.339773i	$0.110350\pi$
$374$	11.6521	−	12.4614i	0.602517	−	0.644364i
$375$	1.38000	+	0.796741i	0.0712627	+	0.0411435i
$376$	4.93835	−	3.55728i	0.254676	−	0.183452i
$377$			15.8016i			0.813825i
$378$	−9.80242	−	18.1573i	−0.504182	−	0.933909i
$379$	−19.5513	−	19.5513i	−1.00428	−	1.00428i	−0.999991	−	0.00429336i	$-0.998633\pi$
$379$	−19.5513	−	19.5513i	−1.00428	−	1.00428i	−0.00429336	−	0.999991i	$-0.501367\pi$
$380$	7.42989	−	0.499278i	0.381145	−	0.0256124i
$381$	0.964679	+	3.60023i	0.0494220	+	0.184445i
$382$	−0.121015	−	3.60578i	−0.00619168	−	0.184488i
$383$	−7.16078	−	12.4028i	−0.365899	−	0.633755i	0.623021	−	0.782205i	$-0.285905\pi$
$383$	−7.16078	−	12.4028i	−0.365899	−	0.633755i	−0.988920	+	0.148450i	$0.952572\pi$
$384$	0.485936	−	18.0216i	0.0247978	−	0.919663i
$385$	−2.48511	−	12.2798i	−0.126653	−	0.625834i
$386$	12.6730	−	7.89505i	0.645037	−	0.401847i
$387$	2.27976	+	0.610859i	0.115887	+	0.0310517i
$388$	−11.7636	−	17.5429i	−0.597208	−	0.890605i
$389$	35.8163	−	9.59695i	1.81596	−	0.486584i	0.819683	−	0.572818i	$-0.194150\pi$
$389$	35.8163	−	9.59695i	1.81596	−	0.486584i	0.996275	+	0.0862331i	$0.0274830\pi$
$390$	6.84672	−	2.08309i	0.346697	−	0.105481i
$391$			6.75595i			0.341663i
$392$	9.49219	+	17.3752i	0.479428	+	0.877581i
$393$			5.85733i			0.295463i
$394$	−7.61599	−	25.0323i	−0.383688	−	1.26111i
$395$	−8.78382	+	2.35362i	−0.441962	+	0.118423i
$396$	4.28181	+	0.844372i	0.215169	+	0.0424313i
$397$	13.2460	+	3.54925i	0.664797	+	0.178132i	0.575410	−	0.817865i	$-0.304843\pi$
$397$	13.2460	+	3.54925i	0.664797	+	0.178132i	0.0893868	+	0.995997i	$0.471509\pi$
$398$	−6.18666	−	9.93071i	−0.310109	−	0.497781i
$399$	3.11364	+	15.3855i	0.155877	+	0.770238i
$400$	3.16537	−	2.44549i	0.158269	−	0.122275i
$401$	12.8321	+	22.2258i	0.640804	+	1.10990i	0.985254	+	0.171100i	$0.0547322\pi$
$401$	12.8321	+	22.2258i	0.640804	+	1.10990i	−0.344450	+	0.938805i	$0.611934\pi$
$402$	34.7347	−	1.16575i	1.73241	−	0.0581422i
$403$	−1.68679	−	6.29520i	−0.0840251	−	0.313586i
$404$	2.78069	+	2.43050i	0.138344	+	0.120922i
$405$	−5.23628	−	5.23628i	−0.260193	−	0.260193i
$406$	−16.3826	+	8.84434i	−0.813054	+	0.438937i
$407$		−	5.40921i		−	0.268125i
$408$	−1.84233	+	11.3331i	−0.0912090	+	0.561070i
$409$	25.8457	+	14.9220i	1.27799	+	0.737846i	0.976478	−	0.215618i	$-0.0691765\pi$
$409$	25.8457	+	14.9220i	1.27799	+	0.737846i	0.301509	+	0.953463i	$0.402510\pi$
$410$	9.41639	+	8.80486i	0.465042	+	0.434841i
$411$	5.06699	−	18.9103i	0.249936	−	0.932775i
$412$	8.52301	+	4.18564i	0.419898	+	0.206212i
$413$	−15.8030	+	7.85868i	−0.777615	+	0.386701i
$414$	−1.46688	+	0.913844i	−0.0720934	+	0.0449130i
$415$	−8.84322	−	15.3169i	−0.434097	−	0.751877i
$416$	1.68718	−	17.8853i	0.0827208	−	0.876897i
$417$	17.1853	−	29.7658i	0.841568	−	1.45764i
$418$	−22.0000	−	11.7360i	−1.07606	−	0.574025i
$419$	6.68782	−	6.68782i	0.326722	−	0.326722i	−0.524617	−	0.851338i	$-0.675791\pi$
$419$	6.68782	−	6.68782i	0.326722	−	0.326722i	0.851338	+	0.524617i	$0.175791\pi$
$420$	5.99186	+	5.93252i	0.292373	+	0.289477i
$421$	4.68780	+	4.68780i	0.228470	+	0.228470i	0.812053	−	0.583584i	$-0.198350\pi$
$421$	4.68780	+	4.68780i	0.228470	+	0.228470i	−0.583584	+	0.812053i	$0.698350\pi$
$422$	−15.0583	+	4.58145i	−0.733029	+	0.223022i
$423$	−0.858726	−	0.495786i	−0.0417527	−	0.0241059i
$424$	9.79200	+	25.8229i	0.475541	+	1.25407i
$425$	−2.20622	+	1.27376i	−0.107018	+	0.0617866i
$426$	−28.6640	−	6.65861i	−1.38878	−	0.322611i
$427$	−27.1198	−	1.68689i	−1.31242	−	0.0816341i
$428$	4.53706	−	1.54847i	0.219307	−	0.0748479i
$429$	−23.1469	−	6.20218i	−1.11754	−	0.299444i
$430$	−7.23920	+	0.242958i	−0.349105	+	0.0117165i
$431$	−5.58365	+	9.67117i	−0.268955	+	0.465844i	−0.968592	−	0.248654i	$-0.920012\pi$
$431$	−5.58365	+	9.67117i	−0.268955	+	0.465844i	0.699637	+	0.714498i	$0.253345\pi$
$432$	−20.3519	+	8.50873i	−0.979182	+	0.409376i
$433$	3.12694			0.150271			0.0751356	−	0.997173i	$-0.476061\pi$
$433$	3.12694			0.150271			0.0751356	+	0.997173i	$0.476061\pi$
$434$	5.58253	−	5.27230i	0.267970	−	0.253078i
$435$	−5.60647	+	5.60647i	−0.268810	+	0.268810i
$436$	25.8578	−	29.5834i	1.23836	−	1.41679i
$437$	9.53767	−	2.55561i	0.456249	−	0.122251i
$438$	−9.62915	+	10.2979i	−0.460099	+	0.492054i
$439$	−18.3783	+	10.6107i	−0.877150	+	0.506423i	−0.869718	−	0.493550i	$-0.835699\pi$
$439$	−18.3783	+	10.6107i	−0.877150	+	0.506423i	−0.00743214	+	0.999972i	$0.502366\pi$
$440$	−13.3260	+	1.34576i	−0.635290	+	0.0641565i
$441$	1.94660	−	2.57213i	0.0926951	−	0.122482i
$442$	−2.58888	+	11.1446i	−0.123141	+	0.530095i
$443$	−7.84107	+	29.2633i	−0.372541	+	1.39034i	0.484364	+	0.874866i	$0.339051\pi$
$443$	−7.84107	+	29.2633i	−0.372541	+	1.39034i	−0.856905	+	0.515474i	$0.827616\pi$
$444$	2.02751	+	3.02358i	0.0962213	+	0.143493i
$445$	−0.435447	−	1.62511i	−0.0206421	−	0.0770375i
$446$	22.8000	+	12.1627i	1.07961	+	0.575922i
$447$	28.3336			1.34013
$448$	19.4872	−	8.26136i	0.920682	−	0.390313i
$449$	−34.7384			−1.63941			−0.819703	−	0.572789i	$-0.805861\pi$
$449$	−34.7384			−1.63941			−0.819703	+	0.572789i	$0.805861\pi$
$450$	−0.574990	−	0.306730i	−0.0271053	−	0.0144594i
$451$	−11.1724	−	41.6959i	−0.526087	−	1.96338i
$452$	6.16348	+	9.19148i	0.289906	+	0.432331i
$453$	7.26881	−	27.1276i	0.341519	−	1.27456i
$454$	0.128670	−	0.553897i	0.00603877	−	0.0259957i
$455$	5.56095	+	6.29863i	0.260702	+	0.295285i
$456$	16.6963	−	1.68612i	0.781875	−	0.0789598i
$457$	1.76391	−	1.01839i	0.0825121	−	0.0476384i	−0.458176	−	0.888861i	$-0.651497\pi$
$457$	1.76391	−	1.01839i	0.0825121	−	0.0476384i	0.540688	+	0.841223i	$0.318164\pi$
$458$	−12.1834	+	13.0295i	−0.569291	+	0.608831i
$459$	13.5703	−	3.63614i	0.633405	−	0.169720i
$460$	3.49055	−	3.99346i	0.162748	−	0.186196i
$461$	4.83006	−	4.83006i	0.224958	−	0.224958i	−0.585624	−	0.810583i	$-0.699151\pi$
$461$	4.83006	−	4.83006i	0.224958	−	0.224958i	0.810583	+	0.585624i	$0.199151\pi$
$462$	−6.52533	−	27.4693i	−0.303586	−	1.27799i
$463$	−26.6776			−1.23981			−0.619906	−	0.784676i	$-0.712829\pi$
$463$	−26.6776			−1.23981			−0.619906	+	0.784676i	$0.712829\pi$
$464$	7.67709	+	18.3627i	0.356400	+	0.852468i
$465$	1.63508	−	2.83204i	0.0758250	−	0.131333i
$466$	−0.234088	+	0.00785634i	−0.0108439	+	0.000363938i
$467$	34.1913	+	9.16154i	1.58219	+	0.423946i	0.939602	−	0.342269i	$-0.111195\pi$
$467$	34.1913	+	9.16154i	1.58219	+	0.423946i	0.642585	+	0.766215i	$0.277862\pi$
$468$	−2.76996	+	0.945367i	−0.128041	+	0.0436996i
$469$	18.1685	+	36.5351i	0.838945	+	1.68703i
$470$	2.96416	+	0.688570i	0.136726	+	0.0317614i
$471$	12.5068	−	7.22079i	0.576282	−	0.332717i
$472$	6.68980	+	17.6420i	0.307923	+	0.812038i
$473$	21.0043	+	12.1268i	0.965776	+	0.557591i
$474$	−19.6055	+	5.96491i	−0.900511	+	0.273977i
$475$	2.63279	+	2.63279i	0.120801	+	0.120801i
$476$	−13.0034	+	3.55370i	−0.596009	+	0.162883i
$477$	3.18158	−	3.18158i	0.145675	−	0.145675i
$478$	−11.1255	−	5.93492i	−0.508868	−	0.271457i
$479$	12.2975	−	21.3000i	0.561889	−	0.973221i	−0.435442	−	0.900217i	$-0.643408\pi$
$479$	12.2975	−	21.3000i	0.561889	−	0.973221i	0.997332	−	0.0730041i	$-0.0232586\pi$
$480$	6.94438	−	5.74714i	0.316966	−	0.262320i
$481$	1.81381	+	3.14161i	0.0827025	+	0.143245i
$482$	−17.1419	+	10.6791i	−0.780793	+	0.486421i
$483$	9.31693	+	6.18062i	0.423935	+	0.281228i
$484$	20.5084	+	10.0716i	0.932200	+	0.457802i
$485$	2.73338	−	10.2011i	0.124116	−	0.463208i
$486$	4.90062	+	4.58236i	0.222297	+	0.207860i
$487$	12.2723	+	7.08539i	0.556109	+	0.321070i	0.751582	−	0.659639i	$-0.229291\pi$
$487$	12.2723	+	7.08539i	0.556109	+	0.321070i	−0.195473	+	0.980709i	$0.562624\pi$
$488$	−4.66098	+	28.6719i	−0.210993	+	1.29792i
$489$			15.9433i			0.720982i
$490$	−3.41769	+	9.29082i	−0.154395	+	0.419717i
$491$	14.0974	+	14.0974i	0.636206	+	0.636206i	0.949618	−	0.313411i	$-0.101472\pi$
$491$	14.0974	+	14.0974i	0.636206	+	0.636206i	−0.313411	+	0.949618i	$0.601472\pi$
$492$	21.8737	+	19.1190i	0.986142	+	0.861952i
$493$	−3.28074	−	12.2439i	−0.147757	−	0.551438i
$494$	16.7127	−	0.560901i	0.751938	−	0.0252361i
$495$	1.09107	+	1.88978i	0.0490398	+	0.0849395i
$496$	−5.01866	−	6.49600i	−0.225344	−	0.291679i
$497$	−6.85294	−	33.8626i	−0.307396	−	1.51894i
$498$	−21.0750	−	33.8292i	−0.944393	−	1.51592i
$499$	41.3863	+	11.0894i	1.85271	+	0.496431i	0.999677	−	0.0254331i	$-0.00809649\pi$
$499$	41.3863	+	11.0894i	1.85271	+	0.496431i	0.853029	+	0.521864i	$0.174763\pi$
$500$	1.96221	+	0.386948i	0.0877527	+	0.0173048i
$501$	−11.6695	+	3.12685i	−0.521357	+	0.139697i
$502$	−10.5188	−	34.5731i	−0.469475	−	1.54308i
$503$		−	33.3663i		−	1.48773i	−0.668329	−	0.743866i	$-0.732990\pi$
$503$		−	33.3663i		−	1.48773i	0.668329	−	0.743866i	$-0.267010\pi$
$504$	−2.53050	−	2.34267i	−0.112717	−	0.104351i
$505$			1.84659i			0.0821721i
$506$	−16.9909	+	5.16941i	−0.755336	+	0.229808i
$507$	−4.48629	+	1.20210i	−0.199243	+	0.0533870i
$508$	2.60542	+	3.88541i	0.115597	+	0.172387i
$509$	15.3090	+	4.10203i	0.678559	+	0.181819i	0.581607	−	0.813470i	$-0.302424\pi$
$509$	15.3090	+	4.10203i	0.678559	+	0.181819i	0.0969519	+	0.995289i	$0.469091\pi$
$510$	−4.87270	+	3.03561i	−0.215767	+	0.134419i
$511$	−15.6916	−	5.26838i	−0.694154	−	0.233059i
$512$	−6.72877	−	21.6038i	−0.297373	−	0.954761i
$513$	−10.2666	−	17.7823i	−0.453281	−	0.785106i
$514$	0.603749	+	17.9894i	0.0266302	+	0.793477i
$515$	1.22879	+	4.58589i	0.0541468	+	0.202078i
$516$	−16.2862	+	1.09441i	−0.716958	+	0.0481786i
$517$	−7.20511	−	7.20511i	−0.316880	−	0.316880i
$518$	−2.24191	+	3.63889i	−0.0985037	+	0.159884i
$519$		−	24.3607i		−	1.06932i
$520$	7.28830	−	5.25004i	0.319613	−	0.230229i
$521$	10.0284	+	5.78993i	0.439354	+	0.253661i	0.703324	−	0.710870i	$-0.251698\pi$
$521$	10.0284	+	5.78993i	0.439354	+	0.253661i	−0.263969	+	0.964531i	$0.585032\pi$
$522$	2.21469	−	2.36850i	0.0969341	−	0.103667i
$523$	10.1289	−	37.8016i	0.442907	−	1.65295i	−0.278499	−	0.960437i	$-0.589837\pi$
$523$	10.1289	−	37.8016i	0.442907	−	1.65295i	0.721405	−	0.692513i	$-0.243497\pi$
$524$	2.37457	+	6.95756i	0.103733	+	0.303942i
$525$	−0.261732	+	4.20783i	−0.0114229	+	0.183645i
$526$	−11.5097	−	18.4751i	−0.501847	−	0.805555i
$527$	2.61403	+	4.52763i	0.113869	+	0.197227i
$528$	−29.9117	+	4.03829i	−1.30174	+	0.175744i
$529$	−7.98354	+	13.8279i	−0.347111	+	0.601213i
$530$	−6.49928	+	12.1834i	−0.282311	+	0.529214i
$531$	2.17363	−	2.17363i	0.0943275	−	0.0943275i
$532$	9.93578	+	17.0132i	0.430771	+	0.737615i
$533$	20.4702	+	20.4702i	0.886662	+	0.886662i
$534$	−1.10358	−	3.62725i	−0.0477565	−	0.156966i
$535$	2.07587	+	1.19851i	0.0897478	+	0.0518159i
$536$	40.7866	−	15.4662i	1.76171	−	0.668038i
$537$	−24.6491	+	14.2312i	−1.06369	+	0.614121i
$538$	0.256907	−	1.10593i	0.0110760	−	0.0476801i
$539$	26.1630	−	20.3537i	1.12692	−	0.876697i
$540$	−9.90008	−	4.86191i	−0.426031	−	0.209223i
$541$	20.8191	+	5.57847i	0.895084	+	0.239837i	0.676904	−	0.736071i	$-0.263321\pi$
$541$	20.8191	+	5.57847i	0.895084	+	0.239837i	0.218180	+	0.975909i	$0.429988\pi$
$542$	−0.926569	−	27.6081i	−0.0397995	−	1.18587i
$543$	4.88579	−	8.46244i	0.209669	−	0.363158i
$544$	2.40604	+	14.2087i	0.103158	+	0.609194i
$545$	19.6456			0.841526
$546$	13.0008	+	13.7658i	0.556383	+	0.589122i
$547$	−5.07711	+	5.07711i	−0.217082	+	0.217082i	−0.807267	−	0.590186i	$-0.799054\pi$
$547$	−5.07711	+	5.07711i	−0.217082	+	0.217082i	0.590186	+	0.807267i	$0.299054\pi$
$548$	−1.64747	−	24.5165i	−0.0703765	−	1.04729i
$549$	4.57135	−	1.22489i	0.195100	−	0.0522770i
$550$	−4.89157	−	4.57390i	−0.208577	−	0.195032i
$551$	−16.0442	+	9.26314i	−0.683507	+	0.394623i
$552$	7.55975	−	9.25815i	0.321764	−	0.394053i
$553$	−15.9237	−	18.0361i	−0.677146	−	0.766971i
$554$	−36.1234	−	8.39141i	−1.53474	−	0.356517i
$555$	−0.471108	+	1.75820i	−0.0199974	+	0.0746314i
$556$	8.34626	−	42.3239i	0.353960	−	1.79493i
$557$	4.92533	+	18.3816i	0.208693	+	0.778853i	0.988292	+	0.152574i	$0.0487562\pi$
$557$	4.92533	+	18.3816i	0.208693	+	0.778853i	−0.779599	+	0.626279i	$0.784577\pi$
$558$	−0.629474	+	1.18000i	−0.0266477	+	0.0499534i
$559$	−16.2654			−0.687952
$560$	9.52241	+	4.61777i	0.402395	+	0.195136i
$561$	19.2231			0.811599
$562$	−5.89176	+	11.0446i	−0.248529	+	0.465888i
$563$	−2.65434	−	9.90612i	−0.111867	−	0.417493i	0.887166	−	0.461450i	$-0.152670\pi$
$563$	−2.65434	−	9.90612i	−0.111867	−	0.417493i	−0.999033	+	0.0439562i	$0.986004\pi$
$564$	6.72809	+	1.32678i	0.283304	+	0.0558675i
$565$	−1.43214	+	5.34480i	−0.0602504	+	0.224858i
$566$	24.2662	+	5.63701i	1.01999	+	0.236941i
$567$	6.23597	−	18.5734i	0.261886	−	0.780011i
$568$	−36.7476	+	3.71106i	−1.54189	+	0.155712i
$569$	−16.4444	+	9.49419i	−0.689386	+	0.398017i	−0.803382	−	0.595464i	$-0.796968\pi$
$569$	−16.4444	+	9.49419i	−0.689386	+	0.398017i	0.113996	+	0.993481i	$0.463635\pi$
$570$	6.12872	+	5.73070i	0.256704	+	0.240033i
$571$	−7.30536	+	1.95747i	−0.305720	+	0.0819174i	−0.408418	−	0.912795i	$-0.633919\pi$
$571$	−7.30536	+	1.95747i	−0.305720	+	0.0819174i	0.102698	+	0.994713i	$0.467253\pi$
$572$	−30.0091	+	2.01657i	−1.25474	+	0.0843169i
$573$	2.87450	−	2.87450i	0.120084	−	0.120084i
$574$	−9.76542	+	32.6802i	−0.407601	+	1.36404i
$575$	2.65196			0.110595
$576$	−2.75961	+	2.44435i	−0.114984	+	0.101848i
$577$	19.2441	−	33.3318i	0.801143	−	1.38762i	−0.117721	−	0.993047i	$-0.537559\pi$
$577$	19.2441	−	33.3318i	0.801143	−	1.38762i	0.918864	−	0.394574i	$-0.129108\pi$
$578$	0.498561	+	14.8552i	0.0207374	+	0.617894i
$579$	16.2505	+	4.35430i	0.675347	+	0.180959i
$580$	−4.38671	+	8.93245i	−0.182148	+	0.370900i
$581$	25.8677	−	38.9940i	1.07317	−	1.61775i
$582$	5.38518	−	23.1821i	0.223223	−	0.960930i
$583$	40.0425	−	23.1185i	1.65839	−	0.957472i
$584$	−7.26308	+	16.1359i	−0.300548	+	0.667710i
$585$	−1.26736	−	0.731710i	−0.0523988	−	0.0302525i
$586$	6.42313	+	21.1116i	0.265337	+	0.872112i
$587$	−27.7549	−	27.7549i	−1.14557	−	1.14557i	−0.987414	−	0.158154i	$-0.949446\pi$
$587$	−27.7549	−	27.7549i	−1.14557	−	1.14557i	−0.158154	−	0.987414i	$-0.550554\pi$
$588$	−6.99523	+	21.1837i	−0.288478	+	0.873599i
$589$	5.40303	−	5.40303i	0.222628	−	0.222628i
$590$	−4.44025	+	8.32361i	−0.182802	+	0.342678i
$591$	14.7410	−	25.5322i	0.606364	−	1.05025i
$592$	3.63411	+	2.76957i	0.149361	+	0.113829i
$593$	5.57976	+	9.66442i	0.229133	+	0.396870i	0.957551	−	0.288262i	$-0.0930775\pi$
$593$	5.57976	+	9.66442i	0.229133	+	0.396870i	−0.728418	+	0.685133i	$0.759744\pi$
$594$	19.5282	+	31.3462i	0.801251	+	1.28615i
$595$	−5.61664	−	3.72594i	−0.230260	−	0.152748i
$596$	33.6557	−	11.4865i	1.37859	−	0.470504i
$597$	3.41209	−	12.7341i	0.139647	−	0.521172i
$598$	8.13470	−	8.69969i	0.332653	−	0.355757i
$599$	−2.43316	−	1.40478i	−0.0994161	−	0.0573979i	0.449468	−	0.893297i	$-0.351614\pi$
$599$	−2.43316	−	1.40478i	−0.0994161	−	0.0573979i	−0.548884	+	0.835899i	$0.684947\pi$
$600$	4.44865	+	0.723184i	0.181615	+	0.0295239i
$601$		−	29.3301i		−	1.19640i	−0.801347	−	0.598200i	$-0.795883\pi$
$601$		−	29.3301i		−	1.19640i	0.801347	−	0.598200i	$-0.204117\pi$
$602$	−9.10390	−	16.8634i	−0.371047	−	0.687301i
$603$	−5.02523	−	5.02523i	−0.204643	−	0.204643i
$604$	−2.36337	−	35.1699i	−0.0961641	−	1.43104i
$605$	2.95675	+	11.0348i	0.120209	+	0.448626i
$606$	0.139582	+	4.15899i	0.00567012	+	0.168948i
$607$	−4.50787	−	7.80786i	−0.182969	−	0.316911i	0.759921	−	0.650015i	$-0.225237\pi$
$607$	−4.50787	−	7.80786i	−0.182969	−	0.316911i	−0.942890	+	0.333104i	$0.891904\pi$
$608$	19.1489	−	8.77152i	0.776591	−	0.355732i
$609$	−19.8866	−	6.67684i	−0.805844	−	0.270559i
$610$	−12.3276	+	7.67990i	−0.499131	+	0.310950i
$611$	6.60065	+	1.76864i	0.267034	+	0.0715515i
$612$	1.95003	−	1.30762i	0.0788252	−	0.0528574i
$613$	−14.9820	+	4.01441i	−0.605116	+	0.162140i	−0.548353	−	0.836247i	$-0.684745\pi$
$613$	−14.9820	+	4.01441i	−0.605116	+	0.162140i	−0.0567636	+	0.998388i	$0.518078\pi$
$614$	26.4728	−	8.05425i	1.06835	−	0.325043i
$615$			14.5258i			0.585737i
$616$	−18.8871	−	29.9837i	−0.760983	−	1.20808i
$617$			26.7894i			1.07850i	0.842146	+	0.539250i	$0.181292\pi$
$617$			26.7894i			1.07850i	−0.842146	+	0.539250i	$0.818708\pi$
$618$	3.11418	+	10.2357i	0.125271	+	0.411741i
$619$	37.1597	−	9.95690i	1.49357	−	0.400202i	0.582631	−	0.812737i	$-0.302023\pi$
$619$	37.1597	−	9.95690i	1.49357	−	0.400202i	0.910942	+	0.412535i	$0.135357\pi$
$620$	0.794097	−	4.02686i	0.0318917	−	0.161723i
$621$	−14.1266	−	3.78520i	−0.566880	−	0.151895i
$622$	−8.42545	−	13.5244i	−0.337830	−	0.542278i
$623$	3.33688	−	2.94607i	0.133689	−	0.118032i
$624$	16.0183	−	12.3754i	0.641245	−	0.495411i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−8.56421	+	0.287427i	−0.342295	+	0.0114879i
$627$	−7.27162	−	27.1381i	−0.290401	−	1.08379i
$628$	11.9287	−	13.6474i	0.476007	−	0.544590i
$629$	−2.05769	−	2.05769i	−0.0820457	−	0.0820457i
$630$	0.0492579	−	1.72350i	0.00196248	−	0.0686659i
$631$		−	26.3247i		−	1.04797i	−0.851728	−	0.523984i	$-0.824445\pi$
$631$		−	26.3247i		−	1.04797i	0.851728	−	0.523984i	$-0.175555\pi$
$632$	−20.8700	+	15.0334i	−0.830163	+	0.597997i
$633$	−15.3590	−	8.86755i	−0.610467	−	0.352453i
$634$	−17.1189	−	16.0071i	−0.679878	−	0.635725i
$635$	−0.605390	+	2.25935i	−0.0240242	+	0.0896594i
$636$	−13.7171	+	27.9315i	−0.543919	+	1.10756i
$637$	−8.37019	+	20.5941i	−0.331639	+	0.815970i
$638$	28.2825	−	17.6195i	1.11971	−	0.697563i
$639$	3.00872	+	5.21126i	0.119023	+	0.206154i
$640$	5.91890	−	9.64192i	0.233965	−	0.381130i
$641$	2.19242	−	3.79739i	0.0865956	−	0.149988i	−0.819474	−	0.573116i	$-0.805735\pi$
$641$	2.19242	−	3.79739i	0.0865956	−	0.149988i	0.906070	+	0.423128i	$0.139068\pi$
$642$	4.76599	+	2.54243i	0.188099	+	0.100342i
$643$	10.2971	−	10.2971i	0.406078	−	0.406078i	−0.474290	−	0.880369i	$-0.657295\pi$
$643$	10.2971	−	10.2971i	0.406078	−	0.406078i	0.880369	+	0.474290i	$0.157295\pi$
$644$	13.5726	+	3.56448i	0.534836	+	0.140460i
$645$	−5.77102	−	5.77102i	−0.227233	−	0.227233i
$646$	−12.8334	+	3.90451i	−0.504922	+	0.153621i
$647$	28.6256	+	16.5270i	1.12539	+	0.649744i	0.942771	−	0.333440i	$-0.108209\pi$
$647$	28.6256	+	16.5270i	1.12539	+	0.649744i	0.182618	+	0.983184i	$0.441543\pi$
$648$	−19.0994	−	8.59701i	−0.750297	−	0.337722i
$649$	27.3567	−	15.7944i	1.07384	−	0.619983i
$650$	4.37468	+	1.01623i	0.171589	+	0.0398599i
$651$	8.63534	+	0.537129i	0.338445	+	0.0210517i
$652$	6.46343	+	18.9381i	0.253127	+	0.741672i
$653$	−37.6877	−	10.0984i	−1.47483	−	0.395181i	−0.570249	−	0.821472i	$-0.693153\pi$
$653$	−37.6877	−	10.0984i	−1.47483	−	0.395181i	−0.904586	+	0.426291i	$0.859820\pi$
$654$	44.2470	−	1.48499i	1.73019	−	0.0580678i
$655$	−1.83790	+	3.18334i	−0.0718128	+	0.124383i
$656$	33.7332	+	13.8427i	1.31706	+	0.540466i
$657$	2.88294			0.112474
$658$	1.86079	+	7.83326i	0.0725412	+	0.305372i
$659$	−13.9371	+	13.9371i	−0.542912	+	0.542912i	−0.924382	−	0.381469i	$-0.875418\pi$
$659$	−13.9371	+	13.9371i	−0.542912	+	0.542912i	0.381469	+	0.924382i	$0.375418\pi$
$660$	−11.3628	−	9.93184i	−0.442297	−	0.386596i
$661$	−18.8048	+	5.03872i	−0.731420	+	0.195983i	−0.605262	−	0.796027i	$-0.706931\pi$
$661$	−18.8048	+	5.03872i	−0.731420	+	0.195983i	−0.126159	+	0.992010i	$0.540265\pi$
$662$	−18.9066	+	20.2197i	−0.734824	+	0.785861i
$663$	−11.1645	+	6.44585i	−0.433595	+	0.250336i
$664$	−38.7480	−	31.6397i	−1.50371	−	1.22786i
$665$	−3.13543	+	9.33869i	−0.121587	+	0.362139i
$666$	0.168442	−	0.725111i	0.00652701	−	0.0280975i
$667$	−3.41524	+	12.7459i	−0.132239	+	0.493521i
$668$	−12.5939	+	8.44503i	−0.487273	+	0.326748i
$669$	7.53604	+	28.1249i	0.291360	+	1.08737i
$670$	19.2434	+	10.2654i	0.743438	+	0.396589i
$671$	48.6332			1.87746
$672$	21.7960	+	9.68061i	0.840797	+	0.373437i
$673$	1.49746			0.0577228			0.0288614	−	0.999583i	$-0.490812\pi$
$673$	1.49746			0.0577228			0.0288614	+	0.999583i	$0.490812\pi$
$674$	21.8463	+	11.6540i	0.841489	+	0.448894i
$675$	−1.42732	−	5.32684i	−0.0549376	−	0.205030i
$676$	−4.84165	+	3.24664i	−0.186217	+	0.124871i
$677$	−12.0081	+	44.8150i	−0.461510	+	1.72238i	0.206697	+	0.978405i	$0.433729\pi$
$677$	−12.0081	+	44.8150i	−0.461510	+	1.72238i	−0.668207	+	0.743975i	$0.732938\pi$
$678$	−2.82153	+	12.1461i	−0.108360	+	0.466469i
$679$	27.3865	−	5.54234i	1.05100	−	0.212696i
$680$	−4.55733	+	5.58120i	−0.174766	+	0.214029i
$681$	0.554887	−	0.320364i	0.0212633	−	0.0122764i
$682$	−9.38659	+	10.0385i	−0.359431	+	0.384395i
$683$	−11.3753	+	3.04802i	−0.435266	+	0.116629i	−0.469797	−	0.882775i	$-0.655673\pi$
$683$	−11.3753	+	3.04802i	−0.435266	+	0.116629i	0.0345313	+	0.999404i	$0.489006\pi$
$684$	−2.58367	−	2.25830i	−0.0987892	−	0.0863482i
$685$	8.68743	−	8.68743i	0.331930	−	0.331930i
$686$	−26.0362	+	2.84883i	−0.994067	+	0.108769i
$687$	−20.0995			−0.766843
$688$	−18.9016	+	7.90240i	−0.720618	+	0.301276i
$689$	−15.5041	+	26.8540i	−0.590661	+	1.02305i
$690$	5.97290	−	0.200459i	0.227385	−	0.00763135i
$691$	−19.0937	−	5.11615i	−0.726360	−	0.194628i	−0.123352	−	0.992363i	$-0.539365\pi$
$691$	−19.0937	−	5.11615i	−0.726360	−	0.194628i	−0.603008	+	0.797735i	$0.706031\pi$
$692$	−9.87585	−	28.9366i	−0.375423	−	1.10000i
$693$	−3.19152	+	4.81104i	−0.121236	+	0.182756i
$694$	−7.34010	−	1.70510i	−0.278626	−	0.0647245i
$695$	18.6797	−	10.7847i	0.708562	−	0.409089i
$696$	−9.20480	+	20.4497i	−0.348907	+	0.775146i
$697$	−20.1114	−	11.6113i	−0.761773	−	0.439810i
$698$	34.0000	−	10.3444i	1.28692	−	0.391541i
$699$	−0.186613	−	0.186613i	−0.00705835	−	0.00705835i
$700$	1.39496	+	5.10432i	0.0527245	+	0.192925i
$701$	27.6467	−	27.6467i	1.04420	−	1.04420i	0.0452255	−	0.998977i	$-0.485599\pi$
$701$	27.6467	−	27.6467i	1.04420	−	1.04420i	0.998977	−	0.0452255i	$-0.0144007\pi$
$702$	−21.8527	−	11.6574i	−0.824778	−	0.439980i
$703$	−2.12656	+	3.68331i	−0.0802048	+	0.138919i
$704$	−33.8932	+	16.9231i	−1.27740	+	0.637812i
$705$	1.71442	+	2.96946i	0.0645687	+	0.111836i
$706$	−43.6684	+	27.2047i	−1.64348	+	1.02386i
$707$	−4.37456	+	2.17543i	−0.164522	+	0.0818153i
$708$	−9.37141	+	19.0825i	−0.352199	+	0.717166i
$709$	2.92328	−	10.9098i	0.109786	−	0.409727i	−0.889058	−	0.457794i	$-0.848640\pi$
$709$	2.92328	−	10.9098i	0.109786	−	0.409727i	0.998844	+	0.0480676i	$0.0153063\pi$
$710$	−13.4890	−	12.6130i	−0.506232	−	0.473356i
$711$	3.62907	+	2.09524i	0.136101	+	0.0785777i
$712$	−2.78136	−	3.86119i	−0.104236	−	0.144704i
$713$		−	5.44238i		−	0.203819i
$714$	−12.9318	−	7.96721i	−0.483959	−	0.298165i
$715$	−10.6337	−	10.6337i	−0.397679	−	0.397679i
$716$	−23.5098	+	26.8971i	−0.878604	+	1.00519i
$717$	−3.67728	−	13.7238i	−0.137331	−	0.512525i
$718$	−7.07210	+	0.237350i	−0.263928	+	0.00885782i
$719$	7.33040	+	12.6966i	0.273378	+	0.473504i	0.969725	−	0.244201i	$-0.0785258\pi$
$719$	7.33040	+	12.6966i	0.273378	+	0.473504i	−0.696347	+	0.717705i	$0.745192\pi$
$720$	−1.82827	−	0.234569i	−0.0681354	−	0.00874185i
$721$	−9.41634	+	8.31352i	−0.350683	+	0.309612i
$722$	−3.84129	−	6.16596i	−0.142958	−	0.229473i
$723$	−21.9810	−	5.88978i	−0.817481	−	0.219043i
$724$	2.37285	−	12.0327i	0.0881862	−	0.447192i
$725$	−4.80619	+	1.28782i	−0.178498	+	0.0478283i
$726$	7.49347	+	24.6296i	0.278109	+	0.914090i
$727$			38.6751i			1.43438i	0.696877	+	0.717190i	$0.254572\pi$
$727$			38.6751i			1.43438i	−0.696877	+	0.717190i	$0.745428\pi$
$728$	21.0235	+	11.0810i	0.779183	+	0.410689i
$729$			29.7754i			1.10279i
$730$	−8.46452	+	2.57530i	−0.313286	+	0.0953162i
$731$	12.6032	−	3.37703i	0.466148	−	0.124904i
$732$	−27.1845	+	18.2289i	−1.00477	+	0.673761i
$733$	38.5025	+	10.3167i	1.42212	+	0.381057i	0.886236	−	0.463233i	$-0.153311\pi$
$733$	38.5025	+	10.3167i	1.42212	+	0.381057i	0.535886	+	0.844290i	$0.319977\pi$
$734$	−8.00831	+	4.98904i	−0.295592	+	0.184149i
$735$	−10.2767	+	4.33711i	−0.379060	+	0.159977i
$736$	5.22649	−	14.0619i	0.192651	−	0.518329i
$737$	−36.5151	−	63.2461i	−1.34505	−	2.32970i
$738$	−0.199264	−	5.93729i	−0.00733500	−	0.218555i
$739$	5.36356	+	20.0171i	0.197302	+	0.736340i	0.991659	+	0.128889i	$0.0411411\pi$
$739$	5.36356	+	20.0171i	0.197302	+	0.736340i	−0.794357	+	0.607451i	$0.792192\pi$
$740$	0.153175	+	2.27944i	0.00563084	+	0.0837940i
$741$	13.3232	+	13.3232i	0.489439	+	0.489439i
$742$	−36.5191	−	1.04372i	−1.34066	−	0.0383163i
$743$			2.03985i			0.0748349i	0.999300	+	0.0374175i	$0.0119131\pi$
$743$			2.03985i			0.0748349i	−0.999300	+	0.0374175i	$0.988087\pi$
$744$	1.48412	−	9.12956i	0.0544106	−	0.334706i
$745$	15.3987	+	8.89046i	0.564166	+	0.325721i
$746$	−3.16286	+	3.38253i	−0.115801	+	0.123843i
$747$	−2.10941	+	7.87243i	−0.0771794	+	0.288037i
$748$	22.8339	−	7.79304i	0.834889	−	0.284942i
$749$	−0.393713	+	6.32966i	−0.0143860	+	0.231281i
$750$	1.19159	+	1.91272i	0.0435107	+	0.0698426i
$751$	4.34437	+	7.52467i	0.158528	+	0.274579i	0.934338	−	0.356388i	$-0.115992\pi$
$751$	4.34437	+	7.52467i	0.158528	+	0.274579i	−0.775810	+	0.630967i	$0.782658\pi$
$752$	8.52976	−	1.15158i	0.311048	−	0.0419936i
$753$	20.3594	−	35.2635i	0.741938	−	1.28507i
$754$	−10.5180	+	19.7168i	−0.383043	+	0.718045i
$755$	12.4625	−	12.4625i	0.453556	−	0.453556i
$756$	−0.145219	−	29.1809i	−0.00528156	−	1.06130i
$757$	19.6906	+	19.6906i	0.715665	+	0.715665i	0.967714	−	0.252049i	$-0.0811044\pi$
$757$	19.6906	+	19.6906i	0.715665	+	0.715665i	−0.252049	+	0.967714i	$0.581104\pi$
$758$	−11.3817	−	37.4095i	−0.413403	−	1.35878i
$759$	−17.3302	−	10.0056i	−0.629045	−	0.363179i
$760$	9.60316	+	4.32256i	0.348343	+	0.156796i
$761$	−41.2663	+	23.8251i	−1.49590	+	0.863660i	−0.999989	−	0.00471237i	$-0.998500\pi$
$761$	−41.2663	+	23.8251i	−1.49590	+	0.863660i	−0.495913	+	0.868372i	$0.665167\pi$
$762$	−1.19271	+	5.13439i	−0.0432074	+	0.185999i
$763$	23.1441	+	46.5403i	0.837871	+	1.68487i
$764$	2.24911	−	4.57975i	0.0813700	−	0.165690i
$765$	1.13393	+	0.303836i	0.0409974	+	0.0109852i
$766$	−0.679362	−	20.2423i	−0.0245464	−	0.731386i
$767$	−10.5923	+	18.3464i	−0.382465	+	0.662450i
$768$	12.6020	−	22.1635i	0.454737	−	0.799756i
$769$	−20.8937			−0.753447			−0.376723	−	0.926326i	$-0.622949\pi$
$769$	−20.8937			−0.753447			−0.376723	+	0.926326i	$0.622949\pi$
$770$	5.07288	−	16.9765i	0.182814	−	0.611791i
$771$	−14.3409	+	14.3409i	−0.516476	+	0.516476i
$772$	21.0682	−	1.41575i	0.758260	−	0.0509540i
$773$	7.34154	−	1.96716i	0.264057	−	0.0707538i	−0.124362	−	0.992237i	$-0.539688\pi$
$773$	7.34154	−	1.96716i	0.264057	−	0.0707538i	0.388418	+	0.921483i	$0.373022\pi$
$774$	2.43802	+	2.27968i	0.0876327	+	0.0819415i
$775$	1.77726	−	1.02610i	0.0638412	−	0.0368587i
$776$	−3.00133	−	29.7197i	−0.107741	−	1.06688i
$777$	−4.72017	+	0.955244i	−0.169335	+	0.0342692i
$778$	51.0786	+	11.8655i	1.83126	+	0.425399i
$779$	−8.78455	+	32.7844i	−0.314739	+	1.17462i
$780$	9.92972	+	1.95814i	0.355541	+	0.0701127i
$781$	16.0044	+	59.7293i	0.572683	+	2.13728i
$782$	−4.49695	+	8.42990i	−0.160811	+	0.301453i
$783$	27.4399			0.980623
$784$	0.278677	+	27.9986i	0.00995276	+	0.999950i
$785$	9.06291			0.323469
$786$	−3.89880	+	7.30863i	−0.139066	+	0.260690i
$787$	−10.5310	−	39.3024i	−0.375391	−	1.40098i	−0.852772	−	0.522283i	$-0.825080\pi$
$787$	−10.5310	−	39.3024i	−0.375391	−	1.40098i	0.477381	−	0.878696i	$-0.341586\pi$
$788$	7.15916	−	36.3041i	0.255034	−	1.29328i
$789$	6.34787	−	23.6906i	0.225990	−	0.843407i
$790$	−12.5268	−	2.90997i	−0.445685	−	0.103532i
$791$	−14.3490	+	2.90387i	−0.510191	+	0.103250i
$792$	4.78069	+	3.90368i	0.169874	+	0.138711i
$793$	−28.2456	+	16.3076i	−1.00303	+	0.579100i
$794$	14.1655	+	13.2456i	0.502715	+	0.470067i
$795$	−15.0288	+	4.02696i	−0.533017	+	0.142822i
$796$	−1.10940	−	16.5093i	−0.0393217	−	0.585156i
$797$	0.465157	−	0.465157i	0.0164767	−	0.0164767i	−0.698820	−	0.715297i	$-0.746291\pi$
$797$	0.465157	−	0.465157i	0.0164767	−	0.0164767i	0.715297	+	0.698820i	$0.246291\pi$
$798$	−6.35589	+	21.2701i	−0.224996	+	0.752954i
$799$	−5.48173			−0.193930
$800$	5.57745	−	0.944461i	0.197193	−	0.0333917i
$801$	−0.387644	+	0.671420i	−0.0136967	+	0.0237234i
$802$	1.21741	+	36.2742i	0.0429884	+	1.28089i
$803$	28.6162	+	7.66768i	1.00984	+	0.270587i
$804$	44.1171	+	21.6658i	1.55589	+	0.764094i
$805$	3.12422	+	6.28249i	0.110114	+	0.221429i
$806$	2.08552	−	8.97776i	0.0734594	−	0.316228i
$807$	1.10791	−	0.639652i	0.0390003	−	0.0225168i
$808$	1.85186	+	4.88362i	0.0651482	+	0.171805i
$809$	−44.6151	−	25.7585i	−1.56858	−	0.905622i	−0.996335	−	0.0855420i	$-0.972738\pi$
$809$	−44.6151	−	25.7585i	−1.56858	−	0.905622i	−0.572249	−	0.820080i	$-0.693929\pi$
$810$	−3.04828	−	10.0191i	−0.107106	−	0.352035i
$811$	11.3389	+	11.3389i	0.398162	+	0.398162i	0.877584	−	0.479422i	$-0.159154\pi$
$811$	11.3389	+	11.3389i	0.398162	+	0.398162i	−0.479422	+	0.877584i	$0.659154\pi$
$812$	−26.3288	+	0.131025i	−0.923960	+	0.00459809i
$813$	22.0089	−	22.0089i	0.771887	−	0.771887i
$814$	3.60052	−	6.74947i	0.126198	−	0.236569i
$815$	−5.00266	+	8.66487i	−0.175236	+	0.303517i
$816$	−9.84241	+	12.9148i	−0.344553	+	0.452108i
$817$	−9.53500	−	16.5151i	−0.333587	−	0.577790i
$818$	22.3171	+	35.8229i	0.780298	+	1.25252i
$819$	0.240369	−	3.86438i	0.00839917	−	0.135032i
$820$	5.88877	+	17.2543i	0.205645	+	0.602546i
$821$	−2.80587	+	10.4717i	−0.0979257	+	0.365464i	−0.997447	−	0.0714137i	$-0.977249\pi$
$821$	−2.80587	+	10.4717i	−0.0979257	+	0.365464i	0.899521	+	0.436877i	$0.143916\pi$
$822$	18.9097	−	20.2230i	0.659550	−	0.705358i
$823$	−40.0586	−	23.1278i	−1.39635	−	0.806185i	−0.402346	−	0.915488i	$-0.631805\pi$
$823$	−40.0586	−	23.1278i	−1.39635	−	0.806185i	−0.994009	+	0.109302i	$0.965138\pi$
$824$	7.84871	+	10.8959i	0.273423	+	0.379576i
$825$		−	7.54578i		−	0.262710i
$826$	−24.9495	−	0.713062i	−0.868105	−	0.0248106i
$827$	28.6390	+	28.6390i	0.995876	+	0.995876i	0.999992	−	0.00411544i	$-0.00130999\pi$
$827$	28.6390	+	28.6390i	0.995876	+	0.995876i	−0.00411544	+	0.999992i	$0.501310\pi$
$828$	−2.43862	+	0.163872i	−0.0847479	+	0.00569494i
$829$	0.999220	+	3.72914i	0.0347043	+	0.129518i	0.981105	−	0.193478i	$-0.0619767\pi$
$829$	0.999220	+	3.72914i	0.0347043	+	0.129518i	−0.946400	+	0.322996i	$0.895310\pi$
$830$	−0.838980	−	24.9983i	−0.0291214	−	0.867705i
$831$	−20.8931	−	36.1879i	−0.724774	−	1.25535i
$832$	14.0101	−	21.1937i	0.485714	−	0.734760i
$833$	2.20988	−	17.6952i	0.0765678	−	0.613103i
$834$	41.2563	−	25.7020i	1.42859	−	0.889987i
$835$	−7.32330	−	1.96227i	−0.253433	−	0.0679072i
$836$	−19.6393	−	29.2877i	−0.679239	−	1.01294i
$837$	−10.9318	+	2.92916i	−0.377857	+	0.101247i
$838$	12.7965	−	3.89329i	0.442047	−	0.134491i
$839$			34.3259i			1.18506i	0.805547	+	0.592532i	$0.201871\pi$
$839$			34.3259i			1.18506i	−0.805547	+	0.592532i	$0.798129\pi$
$840$	3.52764	+	11.3908i	0.121715	+	0.393020i
$841$			4.24204i			0.146277i
$842$	2.72899	+	8.96965i	0.0940471	+	0.309115i
$843$	−13.6240	+	3.65054i	−0.469236	+	0.125731i
$844$	−21.8390	−	4.30664i	−0.751728	−	0.148241i
$845$	−2.81540	−	0.754384i	−0.0968526	−	0.0259516i
$846$	−0.741487	−	1.19022i	−0.0254928	−	0.0409206i
$847$	−22.6580	+	20.0043i	−0.778537	+	0.687357i
$848$	−4.97026	+	38.7390i	−0.170679	+	1.33030i
$849$	14.0351	+	24.3096i	0.481685	+	0.834303i
$850$	−3.60072	+	0.120845i	−0.123504	+	0.00414496i
$851$	0.784045	+	2.92610i	0.0268767	+	0.100305i
$852$	−31.3340	−	27.3880i	−1.07349	−	0.938297i
$853$	14.1460	+	14.1460i	0.484348	+	0.484348i	0.906517	−	0.422169i	$-0.138731\pi$
$853$	14.1460	+	14.1460i	0.484348	+	0.484348i	−0.422169	+	0.906517i	$0.638731\pi$
$854$	−32.7165	−	20.1565i	−1.11954	−	0.689743i
$855$		−	1.71576i		−	0.0586776i
$856$	6.69192	+	1.08786i	0.228725	+	0.0371822i
$857$	−29.4317	−	16.9924i	−1.00537	−	0.580449i	−0.0955352	−	0.995426i	$-0.530456\pi$
$857$	−29.4317	−	16.9924i	−1.00537	−	0.580449i	−0.909832	+	0.414977i	$0.863790\pi$
$858$	−24.7537	−	23.1461i	−0.845077	−	0.790195i
$859$	−11.8885	+	44.3685i	−0.405630	+	1.51383i	0.397260	+	0.917706i	$0.369961\pi$
$859$	−11.8885	+	44.3685i	−0.405630	+	1.51383i	−0.802891	+	0.596126i	$0.796706\pi$
$860$	−9.19460	−	4.51545i	−0.313533	−	0.153976i
$861$	−34.4115	+	17.1125i	−1.17274	+	0.583193i
$862$	−13.4045	+	8.35080i	−0.456560	+	0.284429i
$863$	−15.3246	−	26.5430i	−0.521656	−	0.903535i	−0.999683	−	0.0251893i	$-0.991981\pi$
$863$	−15.3246	−	26.5430i	−0.521656	−	0.903535i	0.478027	−	0.878345i	$-0.341352\pi$
$864$	−31.0582	−	2.92983i	−1.05662	−	0.0996749i
$865$	7.64386	−	13.2396i	0.259899	−	0.450158i
$866$	3.90172	+	2.08138i	0.132586	+	0.0707281i
$867$	−11.8424	+	11.8424i	−0.402189	+	0.402189i
$868$	10.4751	−	2.86275i	0.355549	−	0.0971680i
$869$	30.4496	+	30.4496i	1.03293	+	1.03293i
$870$	−10.7274	+	3.26379i	−0.363694	+	0.110653i
$871$	42.4151	+	24.4884i	1.43718	+	0.829757i
$872$	51.9562	−	19.7017i	1.75946	−	0.667183i
$873$	−4.21462	+	2.43331i	−0.142643	+	0.0823552i
$874$	13.6019	+	3.15971i	0.460093	+	0.106879i
$875$	−1.46257	+	2.20474i	−0.0494439	+	0.0745339i
$876$	−18.8696	+	6.44006i	−0.637545	+	0.217590i
$877$	−49.5513	−	13.2772i	−1.67323	−	0.448341i	−0.707251	−	0.706963i	$-0.750065\pi$
$877$	−49.5513	−	13.2772i	−1.67323	−	0.448341i	−0.965979	+	0.258622i	$0.916732\pi$
$878$	−29.9948	+	1.00667i	−1.01228	+	0.0339734i
$879$	−12.4322	+	21.5332i	−0.419327	+	0.726296i
$880$	−17.5236	−	7.19092i	−0.590719	−	0.242406i
$881$	−2.22810			−0.0750668			−0.0375334	−	0.999295i	$-0.511950\pi$
$881$	−2.22810			−0.0750668			−0.0375334	+	0.999295i	$0.511950\pi$
$882$	4.14099	−	1.91373i	0.139434	−	0.0644385i
$883$	8.98791	−	8.98791i	0.302467	−	0.302467i	−0.539511	−	0.841978i	$-0.681391\pi$
$883$	8.98791	−	8.98791i	0.302467	−	0.302467i	0.841978	+	0.539511i	$0.181391\pi$
$884$	−10.6485	+	12.1827i	−0.358148	+	0.409750i
$885$	−10.2676	+	2.75118i	−0.345140	+	0.0924800i
$886$	−29.2623	+	31.2947i	−0.983088	+	1.05137i
$887$	3.46176	−	1.99865i	0.116235	−	0.0671081i	−0.440756	−	0.897627i	$-0.645289\pi$
$887$	3.46176	−	1.99865i	0.116235	−	0.0671081i	0.556990	+	0.830519i	$0.311956\pi$
$888$	0.517291	+	5.12231i	0.0173591	+	0.171894i
$889$	−6.06558	+	1.22752i	−0.203433	+	0.0411697i
$890$	0.538379	−	2.31761i	0.0180465	−	0.0776866i
$891$	−9.07592	+	33.8718i	−0.304055	+	1.13475i
$892$	20.3534	+	30.3527i	0.681483	+	1.01628i
$893$	2.07361	+	7.73880i	0.0693906	+	0.258969i
$894$	35.3539	+	18.8596i	1.18241	+	0.630760i
$895$	−17.8617			−0.597052
$896$	29.8146	+	2.66289i	0.996035	+	0.0889609i
$897$	13.4202			0.448088
$898$	−43.3456	−	23.1228i	−1.44646	−	0.771619i
$899$	2.64287	+	9.86331i	0.0881445	+	0.328960i
$900$	−0.513290	−	0.765459i	−0.0171097	−	0.0255153i
$901$	6.43797	−	24.0268i	0.214480	−	0.800449i
$902$	13.8133	−	59.4637i	0.459934	−	1.97992i
$903$	6.87279	−	20.4702i	0.228712	−	0.681206i
$904$	1.57253	+	15.5715i	0.0523015	+	0.517899i
$905$	5.31066	−	3.06611i	0.176532	−	0.101921i
$906$	27.1267	−	29.0108i	0.901224	−	0.963818i
$907$	1.90400	−	0.510175i	0.0632212	−	0.0169401i	−0.227070	−	0.973878i	$-0.572915\pi$
$907$	1.90400	−	0.510175i	0.0632212	−	0.0169401i	0.290291	+	0.956938i	$0.406248\pi$
$908$	0.529240	−	0.605493i	0.0175635	−	0.0200940i
$909$	0.601700	−	0.601700i	0.0199571	−	0.0199571i
$910$	2.74627	+	11.5608i	0.0910378	+	0.383237i
$911$	−11.6751			−0.386813			−0.193406	−	0.981119i	$-0.561954\pi$
$911$	−11.6751			−0.386813			−0.193406	+	0.981119i	$0.561954\pi$
$912$	21.9555	+	9.00962i	0.727020	+	0.298338i
$913$	−41.8762	+	72.5317i	−1.38590	+	2.40045i
$914$	2.87883	−	0.0966176i	0.0952232	−	0.00319583i
$915$	−15.8076	−	4.23564i	−0.522585	−	0.140026i
$916$	−23.8749	+	8.14834i	−0.788850	+	0.269229i
$917$	−9.70651	−	0.603757i	−0.320537	−	0.0199378i
$918$	19.3529	+	4.49566i	0.638742	+	0.148379i
$919$	22.3691	−	12.9148i	0.737888	−	0.426020i	−0.0834128	−	0.996515i	$-0.526582\pi$
$919$	22.3691	−	12.9148i	0.737888	−	0.426020i	0.821301	+	0.570495i	$0.193249\pi$
$920$	7.01357	−	2.65953i	0.231231	−	0.0876822i
$921$	27.0014	+	15.5893i	0.889726	+	0.513684i
$922$	9.24185	−	2.81180i	0.304364	−	0.0926017i
$923$	−29.3235	−	29.3235i	−0.965195	−	0.965195i
$924$	10.1422	−	38.6189i	0.333654	−	1.27047i
$925$	−0.807723	+	0.807723i	−0.0265578	+	0.0265578i
$926$	−33.2876	−	17.7573i	−1.09390	−	0.583542i
$927$	1.09389	−	1.89468i	0.0359281	−	0.0622294i
$928$	−2.64347	+	28.0226i	−0.0867762	+	0.919887i
$929$	−12.5345	−	21.7104i	−0.411244	−	0.712296i	0.583782	−	0.811911i	$-0.301572\pi$
$929$	−12.5345	−	21.7104i	−0.411244	−	0.712296i	−0.995026	+	0.0996147i	$0.968239\pi$
$930$	3.92529	−	2.44539i	0.128715	−	0.0801875i
$931$	−25.8171	+	3.57389i	−0.846121	+	0.117129i
$932$	−0.297319	−	0.146013i	−0.00973900	−	0.00478281i
$933$	4.64683	−	17.3422i	0.152130	−	0.567759i
$934$	36.5649	+	34.1902i	1.19644	+	1.11874i
$935$	10.4473	+	6.03178i	0.341665	+	0.197260i
$936$	−4.08554	−	0.664157i	−0.133540	−	0.0217086i
$937$		−	28.4568i		−	0.929642i	−0.885405	−	0.464821i	$-0.846119\pi$
$937$		−	28.4568i		−	0.929642i	0.885405	−	0.464821i	$-0.153881\pi$
$938$	−1.64853	+	57.6810i	−0.0538265	+	1.88335i
$939$	−6.82730	−	6.82730i	−0.222801	−	0.222801i
$940$	3.24027	+	2.83221i	0.105686	+	0.0923764i
$941$	7.05483	+	26.3290i	0.229981	+	0.858300i	0.980348	+	0.197278i	$0.0632102\pi$
$941$	7.05483	+	26.3290i	0.229981	+	0.858300i	−0.750367	+	0.661022i	$0.770123\pi$
$942$	20.4120	−	0.685056i	0.665059	−	0.0223203i
$943$	12.0873	+	20.9359i	0.393618	+	0.681766i
$944$	−3.39563	+	26.4661i	−0.110518	+	0.861399i
$945$	10.9377	−	9.65674i	0.355805	−	0.314134i
$946$	18.1366	+	29.1125i	0.589672	+	0.946530i
$947$	30.4111	+	8.14864i	0.988229	+	0.264795i	0.716506	−	0.697581i	$-0.245740\pi$
$947$	30.4111	+	8.14864i	0.988229	+	0.264795i	0.271722	+	0.962376i	$0.412407\pi$
$948$	−28.4336	−	5.60711i	−0.923482	−	0.182110i
$949$	−19.1911	+	5.14223i	−0.622968	+	0.166924i
$950$	1.53267	+	5.03758i	0.0497263	+	0.163441i
$951$		−	26.4077i		−	0.856330i
$952$	−18.5907	−	4.22121i	−0.602529	−	0.136810i
$953$		−	52.8388i		−	1.71162i	−0.517294	−	0.855808i	$-0.673061\pi$
$953$		−	52.8388i		−	1.71162i	0.517294	−	0.855808i	$-0.326939\pi$
$954$	6.08765	−	1.85215i	0.197095	−	0.0599655i
$955$	2.46418	−	0.660276i	0.0797391	−	0.0213660i
$956$	−9.93166	−	14.8109i	−0.321213	−	0.479018i
$957$	36.2665	+	9.71757i	1.17233	+	0.314124i
$958$	29.5224	−	18.3920i	0.953826	−	0.594217i
$959$	30.8150	+	10.3460i	0.995067	+	0.334090i
$960$	12.4905	−	2.54876i	0.403128	−	0.0822610i
$961$	13.3942	+	23.1995i	0.432072	+	0.748370i
$962$	0.172081	+	5.12734i	0.00554811	+	0.165312i
$963$	−0.285885	−	1.06694i	−0.00921251	−	0.0343815i
$964$	−28.4975	+	1.91499i	−0.917844	+	0.0616778i
$965$	7.46552	+	7.46552i	0.240324	+	0.240324i
$966$	7.51143	+	13.9136i	0.241676	+	0.447663i
$967$			53.1266i			1.70844i	0.519914	+	0.854218i	$0.325964\pi$
$967$			53.1266i			1.70844i	−0.519914	+	0.854218i	$0.674036\pi$
$968$	18.8859	+	26.2181i	0.607015	+	0.842682i
$969$	−13.0896	−	7.55731i	−0.420500	−	0.242776i
$970$	10.2008	−	10.9093i	0.327527	−	0.350275i
$971$	−11.9094	+	44.4466i	−0.382192	+	1.42636i	0.460355	+	0.887735i	$0.347722\pi$
$971$	−11.9094	+	44.4466i	−0.382192	+	1.42636i	−0.842546	+	0.538624i	$0.818944\pi$
$972$	3.06472	+	8.97974i	0.0983010	+	0.288025i
$973$	47.5552	+	31.5469i	1.52455	+	1.01135i
$974$	10.5968	+	17.0097i	0.339542	+	0.545027i
$975$	2.53024	+	4.38250i	0.0810325	+	0.140352i
$976$	−24.9007	+	32.6736i	−0.797052	+	1.04586i
$977$	2.82299	−	4.88956i	0.0903154	−	0.156431i	−0.817328	−	0.576172i	$-0.804546\pi$
$977$	2.82299	−	4.88956i	0.0903154	−	0.156431i	0.907644	+	0.419741i	$0.137879\pi$
$978$	−10.6123	+	19.8936i	−0.339344	+	0.636129i
$979$	−5.63353	+	5.63353i	−0.180048	+	0.180048i
$980$	−10.4487	+	9.31794i	−0.333773	+	0.297651i
$981$	−6.40141	−	6.40141i	−0.204381	−	0.204381i
$982$	8.20674	+	26.9740i	0.261888	+	0.860774i
$983$	−9.13864	−	5.27620i	−0.291477	−	0.168284i	0.347131	−	0.937817i	$-0.387156\pi$
$983$	−9.13864	−	5.27620i	−0.291477	−	0.168284i	−0.638608	+	0.769532i	$0.720489\pi$
$984$	14.5672	+	38.4160i	0.464387	+	1.22466i
$985$	16.0229	−	9.25081i	0.510531	−	0.294755i
$986$	4.05626	−	17.4614i	0.129178	−	0.556084i
$987$	−5.01491	+	7.55969i	−0.159626	+	0.240628i
$988$	21.2270	+	10.4245i	0.675320	+	0.331649i
$989$	−13.1199	−	3.51547i	−0.417189	−	0.111786i
$990$	0.103512	+	3.08427i	0.00328984	+	0.0980245i
$991$	−22.4030	+	38.8032i	−0.711656	+	1.23262i	0.252579	+	0.967576i	$0.418721\pi$
$991$	−22.4030	+	38.8032i	−0.711656	+	1.23262i	−0.964235	+	0.265048i	$0.914612\pi$
$992$	−1.93823	−	11.4461i	−0.0615389	−	0.363414i
$993$	−31.1911			−0.989818
$994$	13.9890	−	46.8143i	0.443703	−	1.48486i
$995$	5.85008	−	5.85008i	0.185460	−	0.185460i
$996$	−3.77920	−	56.2392i	−0.119748	−	1.78201i
$997$	−29.4654	+	7.89523i	−0.933178	+	0.250044i	−0.693209	−	0.720736i	$-0.743804\pi$
$997$	−29.4654	+	7.89523i	−0.933178	+	0.250044i	−0.239969	+	0.970781i	$0.577137\pi$
$998$	44.2593	+	41.3850i	1.40100	+	1.31002i
$999$	5.45548	−	3.14973i	0.172604	−	0.0996529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cp.a.501.54	yes	256
7.2	even	3	inner	560.2.cp.a.261.32	yes	256
16.13	even	4	inner	560.2.cp.a.221.32	✓	256
112.93	even	12	inner	560.2.cp.a.541.54	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cp.a.221.32	✓	256	16.13	even	4	inner
560.2.cp.a.261.32	yes	256	7.2	even	3	inner
560.2.cp.a.501.54	yes	256	1.1	even	1	trivial
560.2.cp.a.541.54	yes	256	112.93	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cp (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24777 + 0.665628i) q^{2} +(0.412424 + 1.53919i) q^{3} +(1.11388 + 1.66111i) q^{4} +(-0.258819 + 0.965926i) q^{5} +(-0.509914 + 2.19508i) q^{6} +(-2.59318 + 0.524795i) q^{7} +(0.284191 + 2.81411i) q^{8} +(0.399076 - 0.230407i) q^{9} +(-0.965895 + 1.03298i) q^{10} +(4.57405 - 1.22561i) q^{11} +(-2.09736 + 2.39955i) q^{12} +(-2.24558 + 2.24558i) q^{13} +(-3.58502 - 1.07127i) q^{14} -1.59348 q^{15} +(-1.51855 + 3.70054i) q^{16} +(1.27376 - 2.20622i) q^{17} +(0.651321 - 0.0218593i) q^{18} +(-3.59646 - 0.963667i) q^{19} +(-1.89280 + 0.645999i) q^{20} +(-1.87725 - 3.77495i) q^{21} +(6.52318 + 1.51533i) q^{22} +(-2.29667 + 1.32598i) q^{23} +(-4.21424 + 1.59803i) q^{24} +(-0.866025 - 0.500000i) q^{25} +(-4.29670 + 1.30726i) q^{26} +(3.89951 + 3.89951i) q^{27} +(-3.76023 - 3.72299i) q^{28} +(3.51838 - 3.51838i) q^{29} +(-1.98831 - 1.06067i) q^{30} +(-1.02610 + 1.77726i) q^{31} +(-4.35799 + 3.60665i) q^{32} +(3.77289 + 6.53484i) q^{33} +(3.05789 - 1.90501i) q^{34} +(0.164252 - 2.64065i) q^{35} +(0.827252 + 0.406262i) q^{36} +(0.295647 - 1.10337i) q^{37} +(-3.84612 - 3.59634i) q^{38} +(-4.38250 - 2.53024i) q^{39} +(-2.79178 - 0.453839i) q^{40} -9.11575i q^{41} +(0.170333 - 5.95983i) q^{42} +(3.62164 + 3.62164i) q^{43} +(7.13081 + 6.23279i) q^{44} +(0.119267 + 0.445111i) q^{45} +(-3.74833 + 0.125799i) q^{46} +(-1.07589 - 1.86350i) q^{47} +(-6.32211 - 0.811134i) q^{48} +(6.44918 - 2.72178i) q^{49} +(-0.747790 - 1.20034i) q^{50} +(3.92112 + 1.05066i) q^{51} +(-6.23146 - 1.22884i) q^{52} +(9.43143 - 2.52714i) q^{53} +(2.27009 + 7.46134i) q^{54} +4.73540i q^{55} +(-2.21379 - 7.14837i) q^{56} -5.93305i q^{57} +(6.73207 - 2.04821i) q^{58} +(6.44347 - 1.72652i) q^{59} +(-1.77495 - 2.64694i) q^{60} +(9.92018 + 2.65811i) q^{61} +(-2.46334 + 1.53462i) q^{62} +(-0.913960 + 0.806919i) q^{63} +(-7.83847 + 1.59949i) q^{64} +(-1.58787 - 2.75027i) q^{65} +(0.357944 + 10.6653i) q^{66} +(-3.99156 - 14.8967i) q^{67} +(5.08359 - 0.341610i) q^{68} +(-2.98813 - 2.98813i) q^{69} +(1.96264 - 3.18560i) q^{70} +13.0583i q^{71} +(0.761804 + 1.05757i) q^{72} +(5.41803 + 3.12810i) q^{73} +(1.10333 - 1.17996i) q^{74} +(0.412424 - 1.53919i) q^{75} +(-2.40526 - 7.04750i) q^{76} +(-11.2181 + 5.57867i) q^{77} +(-3.78417 - 6.07428i) q^{78} +(4.54684 + 7.87535i) q^{79} +(-3.18142 - 2.42457i) q^{80} +(-3.70261 + 6.41310i) q^{81} +(6.06770 - 11.3744i) q^{82} +(-12.5062 + 12.5062i) q^{83} +(4.17957 - 7.32314i) q^{84} +(1.80137 + 1.80137i) q^{85} +(2.10832 + 6.92965i) q^{86} +(6.86650 + 3.96438i) q^{87} +(4.74891 + 12.5236i) q^{88} +(-1.45703 + 0.841218i) q^{89} +(-0.147460 + 0.634786i) q^{90} +(4.64473 - 7.00167i) q^{91} +(-4.76081 - 2.33803i) q^{92} +(-3.15873 - 0.846379i) q^{93} +(-0.102073 - 3.04137i) q^{94} +(1.86166 - 3.22449i) q^{95} +(-7.34865 - 5.22028i) q^{96} -10.5610 q^{97} +(9.85881 + 0.896591i) q^{98} +(1.54300 - 1.54300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) \) 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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