LMFDB - Embedded newform 560.2.cp.a.221.32

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			221.32
Character	$\chi$	$=$	560.221
Dual form			560.2.cp.a.261.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0474363 + 1.41342i) q^{2} +(-1.53919 + 0.412424i) q^{3} +(-1.99550 - 0.134095i) q^{4} +(0.965926 + 0.258819i) 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} +(-0.411639 + 1.35298i) q^{10} +(-1.22561 - 4.57405i) q^{11} +(3.12675 - 0.616595i) q^{12} +(-2.24558 - 2.24558i) q^{13} +(0.618744 + 3.69014i) q^{14} -1.59348 q^{15} +(3.96404 + 0.535172i) q^{16} +(1.27376 - 2.20622i) q^{17} +(-0.306730 - 0.574990i) q^{18} +(0.963667 - 3.59646i) q^{19} +(-1.89280 - 0.645999i) q^{20} +(-3.77495 + 1.87725i) q^{21} +(6.52318 - 1.51533i) q^{22} +(2.29667 - 1.32598i) q^{23} +(0.723184 + 4.44865i) q^{24} +(0.866025 + 0.500000i) q^{25} +(3.28047 - 3.06742i) q^{26} +(3.89951 - 3.89951i) q^{27} +(-5.24506 + 0.699496i) q^{28} +(3.51838 + 3.51838i) q^{29} +(0.0755890 - 2.25226i) q^{30} +(-1.02610 + 1.77726i) q^{31} +(-0.944461 + 5.57745i) q^{32} +(3.77289 + 6.53484i) q^{33} +(3.05789 + 1.90501i) q^{34} +(2.64065 + 0.164252i) q^{35} +(0.827252 - 0.406262i) q^{36} +(-1.10337 - 0.295647i) q^{37} +(5.03758 + 1.53267i) q^{38} +(4.38250 + 2.53024i) q^{39} +(1.00285 - 2.64467i) q^{40} +9.11575i q^{41} +(-2.47426 - 5.42463i) q^{42} +(3.62164 - 3.62164i) q^{43} +(1.83235 + 9.29185i) q^{44} +(-0.445111 + 0.119267i) q^{45} +(1.76522 + 3.30905i) 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} +(-1.05066 + 3.92112i) q^{51} +(4.17994 + 4.78218i) q^{52} +(-2.52714 - 9.43143i) q^{53} +(5.32666 + 5.69662i) q^{54} -4.73540i q^{55} +(-0.739874 - 7.44665i) q^{56} +5.93305i q^{57} +(-5.13984 + 4.80604i) q^{58} +(-1.72652 - 6.44347i) q^{59} +(3.17979 + 0.213678i) q^{60} +(-2.65811 + 9.92018i) 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} +(-9.41542 + 5.02268i) q^{66} +(14.8967 - 3.99156i) q^{67} +(-2.83764 + 4.23171i) q^{68} +(-2.98813 + 2.98813i) q^{69} +(-0.357419 + 3.72455i) q^{70} -13.0583i q^{71} +(0.534976 + 1.18852i) q^{72} +(-5.41803 - 3.12810i) q^{73} +(0.470212 - 1.54550i) q^{74} +(-1.53919 - 0.412424i) q^{75} +(-2.40526 + 7.04750i) q^{76} +(-5.57867 - 11.2181i) q^{77} +(-3.78417 + 6.07428i) q^{78} +(4.54684 + 7.87535i) q^{79} +(3.69045 + 1.54290i) q^{80} +(-3.70261 + 6.41310i) q^{81} +(-12.8844 - 0.432418i) q^{82} +(-12.5062 - 12.5062i) q^{83} +(7.78464 - 3.23984i) q^{84} +(1.80137 - 1.80137i) q^{85} +(4.94709 + 5.29068i) q^{86} +(-6.86650 - 3.96438i) q^{87} +(-13.2202 + 2.14911i) q^{88} +(1.45703 - 0.841218i) q^{89} +(-0.147460 - 0.634786i) q^{90} +(-7.00167 - 4.64473i) q^{91} +(-4.76081 + 2.33803i) q^{92} +(0.846379 - 3.15873i) q^{93} +(2.68494 - 1.43229i) q^{94} +(1.86166 - 3.22449i) q^{95} +(-0.846573 - 8.97426i) q^{96} -10.5610 q^{97} +(3.54108 + 9.24450i) 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 $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.0474363	+	1.41342i	−0.0335426	+	0.999437i
$2$	−0.0474363	+	1.41342i	−0.0335426	+	0.999437i
$3$	−1.53919	+	0.412424i	−0.888649	+	0.238113i	−0.674135	−	0.738608i	$-0.735484\pi$
$3$	−1.53919	+	0.412424i	−0.888649	+	0.238113i	−0.214514	+	0.976721i	$0.568817\pi$
$4$	−1.99550	−	0.134095i	−0.997750	−	0.0670474i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	−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
$10$	−0.411639	+	1.35298i	−0.130172	+	0.427850i
$11$	−1.22561	−	4.57405i	−0.369536	−	1.37913i	−0.861167	−	0.508323i	$-0.830266\pi$
$11$	−1.22561	−	4.57405i	−0.369536	−	1.37913i	0.491631	−	0.870804i	$-0.336401\pi$
$12$	3.12675	−	0.616595i	0.902615	−	0.177996i
$13$	−2.24558	−	2.24558i	−0.622813	−	0.622813i	0.323437	−	0.946250i	$-0.395162\pi$
$13$	−2.24558	−	2.24558i	−0.622813	−	0.622813i	−0.946250	+	0.323437i	$0.895162\pi$
$14$	0.618744	+	3.69014i	0.165366	+	0.986232i
$15$	−1.59348			−0.411435
$16$	3.96404	+	0.535172i	0.991009	+	0.133793i
$17$	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	$0.0666948\pi$
$18$	−0.306730	−	0.574990i	−0.0722970	−	0.135527i
$19$	0.963667	−	3.59646i	0.221080	−	0.825083i	−0.762857	−	0.646568i	$-0.776204\pi$
$19$	0.963667	−	3.59646i	0.221080	−	0.825083i	0.983937	−	0.178516i	$-0.0571295\pi$
$20$	−1.89280	−	0.645999i	−0.423243	−	0.144450i
$21$	−3.77495	+	1.87725i	−0.823762	+	0.409649i
$22$	6.52318	−	1.51533i	1.39075	−	0.323068i
$23$	2.29667	−	1.32598i	0.478888	−	0.276486i	−0.241065	−	0.970509i	$-0.577497\pi$
$23$	2.29667	−	1.32598i	0.478888	−	0.276486i	0.719953	+	0.694023i	$0.244163\pi$
$24$	0.723184	+	4.44865i	0.147619	+	0.908077i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	3.28047	−	3.06742i	0.643353	−	0.601571i
$27$	3.89951	−	3.89951i	0.750462	−	0.750462i
$28$	−5.24506	+	0.699496i	−0.991224	+	0.132192i
$29$	3.51838	+	3.51838i	0.653346	+	0.653346i	0.953797	−	0.300451i	$-0.0971372\pi$
$29$	3.51838	+	3.51838i	0.653346	+	0.653346i	−0.300451	+	0.953797i	$0.597137\pi$
$30$	0.0755890	−	2.25226i	0.0138006	−	0.411204i
$31$	−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	$0.225666\pi$
$32$	−0.944461	+	5.57745i	−0.166959	+	0.985964i
$33$	3.77289	+	6.53484i	0.656776	+	1.13757i
$34$	3.05789	+	1.90501i	0.524424	+	0.326707i
$35$	2.64065	+	0.164252i	0.446351	+	0.0277636i
$36$	0.827252	−	0.406262i	0.137875	−	0.0677104i
$37$	−1.10337	−	0.295647i	−0.181393	−	0.0486041i	0.166979	−	0.985960i	$-0.446599\pi$
$37$	−1.10337	−	0.295647i	−0.181393	−	0.0486041i	−0.348372	+	0.937356i	$0.613265\pi$
$38$	5.03758	+	1.53267i	0.817204	+	0.248631i
$39$	4.38250	+	2.53024i	0.701762	+	0.405162i
$40$	1.00285	−	2.64467i	0.158565	−	0.418159i
$41$			9.11575i			1.42364i	0.702361	+	0.711821i	$0.252129\pi$
$41$			9.11575i			1.42364i	−0.702361	+	0.711821i	$0.747871\pi$
$42$	−2.47426	−	5.42463i	−0.381787	−	0.837039i
$43$	3.62164	−	3.62164i	0.552294	−	0.552294i	−0.374808	−	0.927102i	$-0.622291\pi$
$43$	3.62164	−	3.62164i	0.552294	−	0.552294i	0.927102	+	0.374808i	$0.122291\pi$
$44$	1.83235	+	9.29185i	0.276238	+	1.40080i
$45$	−0.445111	+	0.119267i	−0.0663533	+	0.0177793i
$46$	1.76522	+	3.30905i	0.260268	+	0.487893i
$47$	−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
$51$	−1.05066	+	3.92112i	−0.147122	+	0.549066i
$52$	4.17994	+	4.78218i	0.579653	+	0.663169i
$53$	−2.52714	−	9.43143i	−0.347130	−	1.29551i	−0.890104	−	0.455757i	$-0.849369\pi$
$53$	−2.52714	−	9.43143i	−0.347130	−	1.29551i	0.542974	−	0.839749i	$-0.317298\pi$
$54$	5.32666	+	5.69662i	0.724867	+	0.775212i
$55$		−	4.73540i		−	0.638521i
$56$	−0.739874	−	7.44665i	−0.0988698	−	0.995100i
$57$			5.93305i			0.785852i
$58$	−5.13984	+	4.80604i	−0.674894	+	0.631064i
$59$	−1.72652	−	6.44347i	−0.224774	−	0.838868i	−0.982495	−	0.186289i	$-0.940354\pi$
$59$	−1.72652	−	6.44347i	−0.224774	−	0.838868i	0.757721	−	0.652579i	$-0.226313\pi$
$60$	3.17979	+	0.213678i	0.410510	+	0.0275857i
$61$	−2.65811	+	9.92018i	−0.340336	+	1.27015i	0.557632	+	0.830088i	$0.311710\pi$
$61$	−2.65811	+	9.92018i	−0.340336	+	1.27015i	−0.897968	+	0.440061i	$0.854957\pi$
$62$	−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
$66$	−9.41542	+	5.02268i	−1.15896	+	0.618249i
$67$	14.8967	−	3.99156i	1.81992	−	0.487646i	0.823141	−	0.567837i	$-0.192219\pi$
$67$	14.8967	−	3.99156i	1.81992	−	0.487646i	0.996780	+	0.0801902i	$0.0255528\pi$
$68$	−2.83764	+	4.23171i	−0.344114	+	0.513170i
$69$	−2.98813	+	2.98813i	−0.359729	+	0.359729i
$70$	−0.357419	+	3.72455i	−0.0427197	+	0.445169i
$71$		−	13.0583i		−	1.54974i	−0.632123	−	0.774868i	$-0.717816\pi$
$71$		−	13.0583i		−	1.54974i	0.632123	−	0.774868i	$-0.282184\pi$
$72$	0.534976	+	1.18852i	0.0630476	+	0.140069i
$73$	−5.41803	−	3.12810i	−0.634133	−	0.366117i	0.148218	−	0.988955i	$-0.452646\pi$
$73$	−5.41803	−	3.12810i	−0.634133	−	0.366117i	−0.782351	+	0.622838i	$0.785980\pi$
$74$	0.470212	−	1.54550i	0.0546611	−	0.179660i
$75$	−1.53919	−	0.412424i	−0.177730	−	0.0476226i
$76$	−2.40526	+	7.04750i	−0.275903	+	0.808404i
$77$	−5.57867	−	11.2181i	−0.635748	−	1.27843i
$78$	−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	$0.662401\pi$
$80$	3.69045	+	1.54290i	0.412605	+	0.172502i
$81$	−3.70261	+	6.41310i	−0.411401	+	0.712567i
$82$	−12.8844	−	0.432418i	−1.42284	−	0.0477526i
$83$	−12.5062	−	12.5062i	−1.37273	−	1.37273i	−0.856368	−	0.516366i	$-0.827284\pi$
$83$	−12.5062	−	12.5062i	−1.37273	−	1.37273i	−0.516366	−	0.856368i	$-0.672716\pi$
$84$	7.78464	−	3.23984i	0.849374	−	0.353496i
$85$	1.80137	−	1.80137i	0.195386	−	0.195386i
$86$	4.94709	+	5.29068i	0.533458	+	0.570509i
$87$	−6.86650	−	3.96438i	−0.736166	−	0.425026i
$88$	−13.2202	+	2.14911i	−1.40928	+	0.229096i
$89$	1.45703	−	0.841218i	0.154445	−	0.0891689i	−0.420786	−	0.907160i	$-0.638246\pi$
$89$	1.45703	−	0.841218i	0.154445	−	0.0891689i	0.575231	+	0.817991i	$0.304912\pi$
$90$	−0.147460	−	0.634786i	−0.0155436	−	0.0669123i
$91$	−7.00167	−	4.64473i	−0.733975	−	0.486900i
$92$	−4.76081	+	2.33803i	−0.496349	+	0.243756i
$93$	0.846379	−	3.15873i	0.0877654	−	0.327545i
$94$	2.68494	−	1.43229i	0.276931	−	0.147729i
$95$	1.86166	−	3.22449i	0.191003	−	0.330826i
$96$	−0.846573	−	8.97426i	−0.0864030	−	0.915931i
$97$	−10.5610			−1.07230			−0.536152	−	0.844122i	$-0.680122\pi$
$97$	−10.5610			−1.07230			−0.536152	+	0.844122i	$0.680122\pi$
$98$	3.54108	+	9.24450i	0.357703	+	0.933835i
$99$	1.54300	+	1.54300i	0.155078	+	0.155078i
$100$	−1.66111	−	1.11388i	−0.166111	−	0.111388i
$101$	−0.477932	−	1.78367i	−0.0475561	−	0.177482i	0.938063	−	0.346465i	$-0.112618\pi$
$101$	−0.477932	−	1.78367i	−0.0475561	−	0.177482i	−0.985619	+	0.168984i	$0.945951\pi$
$102$	−5.49234	−	1.67103i	−0.543822	−	0.165456i
$103$	−4.11160	+	2.37383i	−0.405128	+	0.233901i	−0.688694	−	0.725052i	$-0.741816\pi$
$103$	−4.11160	+	2.37383i	−0.405128	+	0.233901i	0.283566	+	0.958953i	$0.408482\pi$
$104$	−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
$107$	−2.31533	−	0.620392i	−0.223832	−	0.0599756i	0.145160	−	0.989408i	$-0.453630\pi$
$107$	−2.31533	−	0.620392i	−0.223832	−	0.0599756i	−0.368992	+	0.929433i	$0.620297\pi$
$108$	−8.30438	+	7.25857i	−0.799090	+	0.698457i
$109$	18.9762	−	5.08466i	1.81759	−	0.487022i	0.821104	−	0.570778i	$-0.193358\pi$
$109$	18.9762	−	5.08466i	1.81759	−	0.487022i	0.996486	+	0.0837561i	$0.0266917\pi$
$110$	6.69310	+	0.224630i	0.638162	+	0.0214176i
$111$	1.82022			0.172768
$112$	10.5603	−	0.692509i	0.997857	−	0.0654360i
$113$	5.53335			0.520533			0.260267	−	0.965537i	$-0.416190\pi$
$113$	5.53335			0.520533			0.260267	+	0.965537i	$0.416190\pi$
$114$	−8.38588	−	0.281442i	−0.785410	−	0.0263595i
$115$	2.56160	−	0.686379i	0.238871	−	0.0640052i
$116$	−6.54912	−	7.49272i	−0.608071	−	0.695681i
$117$	1.41355	+	0.378761i	0.130683	+	0.0350165i
$118$	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
$122$	−13.8953	−	4.22759i	−1.25802	−	0.382748i
$123$	−3.75955	−	14.0308i	−0.338987	−	1.26512i
$124$	2.28591	−	3.40894i	0.205281	−	0.306131i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−1.09716	−	1.33008i	−0.0977427	−	0.118493i
$127$	2.33905			0.207557			0.103778	−	0.994600i	$-0.466907\pi$
$127$	2.33905			0.207557			0.103778	+	0.994600i	$0.466907\pi$
$128$	2.63258	−	11.0032i	0.232689	−	0.972551i
$129$	−4.08072	+	7.06802i	−0.359288	+	0.622305i
$130$	3.96260	−	2.11386i	0.347543	−	0.185398i
$131$	−0.951368	+	3.55056i	−0.0831214	+	0.310213i	−0.994952	−	0.100354i	$-0.968003\pi$
$131$	−0.951368	+	3.55056i	−0.0831214	+	0.310213i	0.911830	+	0.410567i	$0.134669\pi$
$132$	−6.65251	−	13.5462i	−0.579027	−	1.17904i
$133$	0.611562	−	9.83199i	0.0530292	−	0.852542i
$134$	4.93509	+	21.2446i	0.426327	+	1.83525i
$135$	4.77591	−	2.75737i	0.411045	−	0.237317i
$136$	−5.84657	−	4.21150i	−0.501339	−	0.361133i
$137$	10.6399	+	6.14294i	0.909027	+	0.524827i	0.880118	−	0.474755i	$-0.157463\pi$
$137$	10.6399	+	6.14294i	0.909027	+	0.524827i	0.0289092	+	0.999582i	$0.490797\pi$
$138$	−4.08174	−	4.36523i	−0.347460	−	0.371593i
$139$	−15.2519	+	15.2519i	−1.29365	+	1.29365i	−0.361140	+	0.932511i	$0.617612\pi$
$139$	−15.2519	+	15.2519i	−1.29365	+	1.29365i	−0.932511	+	0.361140i	$0.882388\pi$
$140$	−5.24739	−	0.681861i	−0.443485	−	0.0576278i
$141$	2.42455	+	2.42455i	0.204184	+	0.204184i
$142$	18.4569	+	0.619438i	1.54886	+	0.0519821i
$143$	−7.51919	+	13.0236i	−0.628786	+	1.08909i
$144$	−1.70526	+	0.699766i	−0.142105	+	0.0583138i
$145$	2.48787	+	4.30911i	0.206606	+	0.357852i
$146$	4.67833	−	7.50956i	0.387181	−	0.621495i
$147$	−8.80396	+	6.84912i	−0.726139	+	0.564906i
$148$	2.16213	+	0.737919i	0.177726	+	0.0606566i
$149$	−17.1751	−	4.60204i	−1.40704	−	0.377014i	−0.526169	−	0.850380i	$-0.676372\pi$
$149$	−17.1751	−	4.60204i	−1.40704	−	0.377014i	−0.880866	+	0.473366i	$0.843039\pi$
$150$	0.655940	−	2.15595i	0.0535573	−	0.176033i
$151$	15.2634	+	8.81231i	1.24212	+	0.717136i	0.969525	−	0.244994i	$-0.0787861\pi$
$151$	15.2634	+	8.81231i	1.24212	+	0.717136i	0.272591	+	0.962130i	$0.412119\pi$
$152$	−9.84697	−	3.73395i	−0.798695	−	0.302863i
$153$			1.17393i			0.0949069i
$154$	16.1205	−	7.35284i	1.29903	−	0.592509i
$155$	−1.45113	+	1.45113i	−0.116558	+	0.116558i
$156$	−8.40599	−	5.63676i	−0.673018	−	0.451302i
$157$	8.75410	−	2.34565i	0.698653	−	0.187204i	0.108026	−	0.994148i	$-0.465547\pi$
$157$	8.75410	−	2.34565i	0.698653	−	0.187204i	0.590627	+	0.806945i	$0.298880\pi$
$158$	−11.3469	+	6.05300i	−0.902707	+	0.481551i
$159$	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
$163$	−2.58957	+	9.66440i	−0.202831	+	0.756974i	0.787269	+	0.616610i	$0.211494\pi$
$163$	−2.58957	+	9.66440i	−0.202831	+	0.756974i	−0.990100	+	0.140365i	$0.955172\pi$
$164$	1.22237	−	18.1905i	0.0954514	−	1.42044i
$165$	1.95299	+	7.28866i	0.152040	+	0.567422i
$166$	18.2697	−	17.0832i	1.41801	−	1.32592i
$167$		−	7.58164i		−	0.586685i	−0.956007	−	0.293342i	$-0.905232\pi$
$167$		−	7.58164i		−	0.586685i	0.956007	−	0.293342i	$-0.0947676\pi$
$168$	4.20998	+	11.1566i	0.324807	+	0.860753i
$169$		−	2.91471i		−	0.224209i
$170$	2.46064	+	2.63154i	0.188723	+	0.201830i
$171$	0.444070	+	1.65729i	0.0339589	+	0.126736i
$172$	−7.71262	+	6.74133i	−0.588082	+	0.514022i
$173$	3.95675	−	14.7668i	0.300826	−	1.12270i	−0.635653	−	0.771975i	$-0.719269\pi$
$173$	3.95675	−	14.7668i	0.300826	−	1.12270i	0.936479	−	0.350724i	$-0.114064\pi$
$174$	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
$178$	1.11988	+	2.09930i	0.0839383	+	0.157349i
$179$	−17.2531	+	4.62296i	−1.28956	+	0.345536i	−0.837493	−	0.546448i	$-0.815979\pi$
$179$	−17.2531	+	4.62296i	−1.28956	+	0.345536i	−0.452066	+	0.891985i	$0.649313\pi$
$180$	0.904212	−	0.178311i	0.0673960	−	0.0132905i
$181$	−4.33613	+	4.33613i	−0.322302	+	0.322302i	−0.849650	−	0.527347i	$-0.823187\pi$
$181$	−4.33613	+	4.33613i	−0.322302	+	0.322302i	0.527347	+	0.849650i	$0.323187\pi$
$182$	6.89708	−	9.67596i	0.511246	−	0.717230i
$183$		−	16.3653i		−	1.20976i
$184$	−3.07877	−	6.83992i	−0.226970	−	0.504245i
$185$	−0.989254	−	0.571146i	−0.0727314	−	0.0419915i
$186$	4.42446	+	1.34613i	0.324417	+	0.0987027i
$187$	−11.6525	−	3.12228i	−0.852115	−	0.228324i
$188$	1.89706	+	3.86289i	0.138357	+	0.281730i
$189$	8.06570	−	12.1586i	0.586693	−	0.884408i
$190$	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	$0.862754\pi$
$192$	12.7245	−	0.770855i	0.918314	−	0.0556317i
$193$	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	$0.0425958\pi$
$194$	0.500973	−	14.9271i	0.0359678	−	1.07170i
$195$	3.57830	+	3.57830i	0.256247	+	0.256247i
$196$	−13.2343	+	4.56651i	−0.945308	+	0.326179i
$197$	−13.0826	+	13.0826i	−0.932098	+	0.932098i	−0.997837	−	0.0657390i	$-0.979060\pi$
$197$	−13.0826	+	13.0826i	−0.932098	+	0.932098i	0.0657390	+	0.997837i	$0.479060\pi$
$198$	−2.25410	+	2.10771i	−0.160192	+	0.149789i
$199$	7.16485	+	4.13663i	0.507903	+	0.293238i	0.731971	−	0.681335i	$-0.238601\pi$
$199$	7.16485	+	4.13663i	0.507903	+	0.293238i	−0.224068	+	0.974573i	$0.571934\pi$
$200$	1.65317	−	2.29500i	0.116897	−	0.162281i
$201$	−21.2826	+	12.2875i	−1.50116	+	0.866693i
$202$	2.54374	−	0.590908i	0.178977	−	0.0415761i
$203$	10.9702	+	7.27736i	0.769958	+	0.510771i
$204$	2.62239	−	7.68370i	0.183604	−	0.537967i
$205$	−2.35933	+	8.80514i	−0.164783	+	0.614978i
$206$	−3.16018	−	5.92401i	−0.220180	−	0.412745i
$207$	−0.611030	+	1.05833i	−0.0424695	+	0.0735594i
$208$	−7.69980	−	10.1033i	−0.533885	−	0.700541i
$209$	−17.6314			−1.21959
$210$	−0.985957	−	5.88018i	−0.0680375	−	0.405771i
$211$	−7.86994	−	7.86994i	−0.541789	−	0.541789i	0.382264	−	0.924053i	$-0.375144\pi$
$211$	−7.86994	−	7.86994i	−0.541789	−	0.541789i	−0.924053	+	0.382264i	$0.875144\pi$
$212$	3.77821	+	19.1593i	0.259489	+	1.31587i
$213$	5.38556	+	20.0992i	0.369012	+	1.37717i
$214$	0.986704	−	3.24311i	0.0674497	−	0.221694i
$215$	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
$219$	9.62946	+	2.58021i	0.650699	+	0.174354i
$220$	−0.634992	+	9.44949i	−0.0428112	+	0.637084i
$221$	−7.81460	+	2.09391i	−0.525667	+	0.140852i
$222$	−0.0863447	+	2.57274i	−0.00579508	+	0.172671i
$223$	18.2726			1.22362			0.611811	−	0.791004i	$-0.290441\pi$
$223$	18.2726			1.22362			0.611811	+	0.791004i	$0.290441\pi$
$224$	0.477862	+	14.9590i	0.0319285	+	0.999490i
$225$	−0.460813			−0.0307209
$226$	−0.262482	+	7.82093i	−0.0174600	+	0.520241i
$227$	0.388392	−	0.104069i	0.0257785	−	0.00690733i	−0.245907	−	0.969293i	$-0.579086\pi$
$227$	0.388392	−	0.104069i	0.0257785	−	0.00690733i	0.271685	+	0.962386i	$0.412419\pi$
$228$	0.795591	−	11.8394i	0.0526893	−	0.784084i
$229$	12.1838	+	3.26463i	0.805126	+	0.215733i	0.637833	−	0.770175i	$-0.279831\pi$
$229$	12.1838	+	3.26463i	0.805126	+	0.215733i	0.167292	+	0.985907i	$0.446498\pi$
$230$	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	−0.495294	−	0.868725i	$-0.664940\pi$
$233$	0.143430	−	0.0828093i	0.00939641	−	0.00542502i	0.504691	+	0.863300i	$0.331606\pi$
$234$	−0.602401	+	1.97998i	−0.0393802	+	0.129435i
$235$	−0.556923	−	2.07847i	−0.0363297	−	0.135584i
$236$	2.58124	+	13.0895i	0.168024	+	0.852051i
$237$	−10.2464	−	10.2464i	−0.665576	−	0.665576i
$238$	8.92941	+	3.33528i	0.578808	+	0.216194i
$239$	−8.91628			−0.576746			−0.288373	−	0.957518i	$-0.593114\pi$
$239$	−8.91628			−0.576746			−0.288373	+	0.957518i	$0.593114\pi$
$240$	−6.31662	−	0.852787i	−0.407736	−	0.0550472i
$241$	−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	$0.318802\pi$
$242$	−7.60414	−	14.2546i	−0.488813	−	0.916320i
$243$	−1.22788	+	4.58251i	−0.0787685	+	0.293968i
$244$	6.63449	−	19.4393i	0.424730	−	1.24447i
$245$	6.93388	−	0.959865i	0.442989	−	0.0613235i
$246$	20.0098	−	4.64825i	1.27578	−	0.296361i
$247$	−10.2401	+	5.91214i	−0.651564	+	0.376181i
$248$	4.70981	+	3.39266i	0.299073	+	0.215434i
$249$	24.4072	+	14.0915i	1.54675	+	0.893014i
$250$	−1.03298	+	0.965895i	−0.0653314	+	0.0610885i
$251$	−18.0689	+	18.0689i	−1.14050	+	1.14050i	−0.152143	+	0.988358i	$0.548618\pi$
$251$	−18.0689	+	18.0689i	−1.14050	+	1.14050i	−0.988358	+	0.152143i	$0.951382\pi$
$252$	1.93201	−	1.48765i	0.121705	−	0.0937131i
$253$	−8.87993	−	8.87993i	−0.558276	−	0.558276i
$254$	−0.110956	+	3.30605i	−0.00696199	+	0.207440i
$255$	−2.02972	+	3.51558i	−0.127106	+	0.220154i
$256$	15.4272	+	4.24288i	0.964199	+	0.265180i
$257$	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
$259$	−3.01639	−	0.187623i	−0.187429	−	0.0116583i
$260$	2.79979	+	5.70108i	0.173636	+	0.353566i
$261$	−2.21476	−	0.593442i	−0.137090	−	0.0367331i
$262$	−4.97329	−	1.51311i	−0.307251	−	0.0934800i
$263$	13.3295	+	7.69581i	0.821934	+	0.474544i	0.851083	−	0.525031i	$-0.175946\pi$
$263$	13.3295	+	7.69581i	0.821934	+	0.474544i	−0.0291486	+	0.999575i	$0.509280\pi$
$264$	19.4620	−	8.76020i	1.19780	−	0.539153i
$265$		−	9.76413i		−	0.599806i
$266$	13.8677	+	1.33079i	0.850283	+	0.0815957i
$267$	−1.89571	+	1.89571i	−0.116015	+	0.116015i
$268$	−30.2616	+	5.96758i	−1.84852	+	0.364528i
$269$	0.775479	−	0.207789i	0.0472818	−	0.0126691i	−0.235101	−	0.971971i	$-0.575542\pi$
$269$	0.775479	−	0.207789i	0.0472818	−	0.0126691i	0.282382	+	0.959302i	$0.408875\pi$
$270$	3.67077	+	6.88116i	0.223396	+	0.418774i
$271$	−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
$275$	1.22561	−	4.57405i	0.0739072	−	0.275825i
$276$	6.36351	−	5.56213i	0.383038	−	0.334801i
$277$	6.78707	+	25.3297i	0.407795	+	1.52191i	0.798841	+	0.601542i	$0.205447\pi$
$277$	6.78707	+	25.3297i	0.407795	+	1.52191i	−0.391046	+	0.920371i	$0.627887\pi$
$278$	−20.8339	−	22.2808i	−1.24953	−	1.33632i
$279$		−	0.945684i		−	0.0566166i
$280$	1.21267	−	7.38440i	0.0724710	−	0.441303i
$281$		−	8.85144i		−	0.528032i	−0.964518	−	0.264016i	$-0.914953\pi$
$281$		−	8.85144i		−	0.528032i	0.964518	−	0.264016i	$-0.0850472\pi$
$282$	−3.54192	+	3.31189i	−0.210918	+	0.197220i
$283$	−4.55928	−	17.0155i	−0.271021	−	1.01146i	−0.958461	−	0.285223i	$-0.907932\pi$
$283$	−4.55928	−	17.0155i	−0.271021	−	1.01146i	0.687440	−	0.726241i	$-0.258734\pi$
$284$	−1.75105	+	26.0579i	−0.103906	+	1.54625i
$285$	−1.53559	+	5.73089i	−0.0909603	+	0.339469i
$286$	−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
$290$	−6.20859	+	3.31199i	−0.364581	+	0.194487i
$291$	16.2553	−	4.35559i	0.952902	−	0.255329i
$292$	10.3922	+	6.96866i	0.608159	+	0.407810i
$293$	11.0335	−	11.0335i	0.644586	−	0.644586i	−0.307093	−	0.951679i	$-0.599356\pi$
$293$	11.0335	−	11.0335i	0.644586	−	0.644586i	0.951679	+	0.307093i	$0.0993563\pi$
$294$	−9.26304	−	12.7686i	−0.540231	−	0.744678i
$295$		−	6.67077i		−	0.388387i
$296$	−1.14555	+	3.02099i	−0.0665838	+	0.175591i
$297$	−22.6158	−	13.0573i	−1.31230	−	0.757659i
$298$	7.31933	−	24.0572i	0.423997	−	1.39360i
$299$	−8.13496	−	2.17976i	−0.470457	−	0.126059i
$300$	3.01614	+	1.02939i	0.174137	+	0.0594317i
$301$	7.49094	−	11.2922i	0.431771	−	0.650870i
$302$	−13.1795	+	21.1555i	−0.758396	+	1.21736i
$303$	1.47125	+	2.54829i	0.0845213	+	0.146395i
$304$	5.74474	−	13.7408i	0.329483	−	0.788086i
$305$	−5.13507	+	8.89419i	−0.294033	+	0.509280i
$306$	−1.65926	−	0.0556871i	−0.0948535	−	0.00318342i
$307$	13.8354	+	13.8354i	0.789631	+	0.789631i	0.981433	−	0.191803i	$-0.0614334\pi$
$307$	13.8354	+	13.8354i	0.789631	+	0.789631i	−0.191803	+	0.981433i	$0.561433\pi$
$308$	9.62794	+	23.1339i	0.548603	+	1.31817i
$309$	5.34949	−	5.34949i	0.304322	−	0.304322i
$310$	−1.98222	−	2.11989i	−0.112582	−	0.120402i
$311$	9.75762	+	5.63357i	0.553304	+	0.319450i	0.750454	−	0.660923i	$-0.229835\pi$
$311$	9.75762	+	5.63357i	0.553304	+	0.319450i	−0.197149	+	0.980373i	$0.563168\pi$
$312$	8.36585	−	11.6138i	0.473623	−	0.657501i
$313$	5.24744	−	3.02961i	0.296603	−	0.171244i	−0.344313	−	0.938855i	$-0.611888\pi$
$313$	5.24744	−	3.02961i	0.296603	−	0.171244i	0.640916	+	0.767611i	$0.278555\pi$
$314$	2.90013	+	12.4845i	0.163664	+	0.704539i
$315$	−1.09166	+	0.542874i	−0.0615083	+	0.0305875i
$316$	−8.01717	−	16.3250i	−0.451001	−	0.918351i
$317$	4.28924	−	16.0077i	0.240908	−	0.899080i	−0.734489	−	0.678621i	$-0.762578\pi$
$317$	4.28924	−	16.0077i	0.240908	−	0.899080i	0.975396	−	0.220459i	$-0.0707554\pi$
$318$	−19.4141	+	10.3565i	−1.08869	+	0.580763i
$319$	11.7811	−	20.4054i	0.659612	−	1.14248i
$320$	−7.15740	−	3.57374i	−0.400111	−	0.199778i
$321$	3.81960			0.213189
$322$	6.31411	+	7.65459i	0.351872	+	0.426574i
$323$	−6.70710	−	6.70710i	−0.373193	−	0.373193i
$324$	8.24851	−	12.3008i	0.458251	−	0.683380i
$325$	−0.821940	−	3.06752i	−0.0455930	−	0.170156i
$326$	−13.5370	−	4.11859i	−0.749745	−	0.228107i
$327$	−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
$331$	18.9072	+	5.06616i	1.03923	+	0.278461i	0.737795	−	0.675025i	$-0.235867\pi$
$331$	18.9072	+	5.06616i	1.03923	+	0.278461i	0.301437	+	0.953486i	$0.402534\pi$
$332$	23.2791	+	26.6331i	1.27761	+	1.46168i
$333$	0.508447	−	0.136238i	0.0278627	−	0.00746580i
$334$	10.7160	+	0.359645i	0.586354	+	0.0196789i
$335$	15.4222			0.842604
$336$	−15.9687	+	5.42123i	−0.871164	+	0.295752i
$337$	17.5082			0.953735			0.476867	−	0.878975i	$-0.341772\pi$
$337$	17.5082			0.953735			0.476867	+	0.878975i	$0.341772\pi$
$338$	4.11971	+	0.138263i	0.224083	+	0.00752054i
$339$	−8.51685	+	2.28208i	−0.462572	+	0.123946i
$340$	−3.83619	+	3.35309i	−0.208047	+	0.181847i
$341$	9.38689	+	2.51521i	0.508329	+	0.136206i
$342$	−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
$346$	20.6840	+	6.29303i	1.11198	+	0.338315i
$347$	1.37910	+	5.14687i	0.0740340	+	0.276298i	0.993013	−	0.118009i	$-0.0376512\pi$
$347$	1.37910	+	5.14687i	0.0740340	+	0.276298i	−0.918979	+	0.394307i	$0.870984\pi$
$348$	13.1705	+	8.83167i	0.706013	+	0.473427i
$349$	17.7694	+	17.7694i	0.951175	+	0.951175i	0.998862	−	0.0476869i	$-0.0151850\pi$
$349$	17.7694	+	17.7694i	0.951175	+	0.951175i	−0.0476869	+	0.998862i	$0.515185\pi$
$350$	−1.30922	+	3.50513i	−0.0699810	+	0.187357i
$351$	−17.5134			−0.934794
$352$	26.6691	−	2.51579i	1.42147	−	0.134092i
$353$	−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	$0.747207\pi$
$354$	−13.2635	+	7.07546i	−0.704948	+	0.376056i
$355$	3.37974	−	12.6134i	0.179378	−	0.669448i
$356$	−3.02031	+	1.48327i	−0.160076	+	0.0786132i
$357$	−0.666770	+	10.7195i	−0.0352892	+	0.567339i
$358$	−5.71575	−	24.6052i	−0.302087	−	1.30042i
$359$	4.33320	−	2.50177i	0.228697	−	0.132039i	−0.381274	−	0.924462i	$-0.624514\pi$
$359$	4.33320	−	2.50177i	0.228697	−	0.132039i	0.609971	+	0.792424i	$0.291181\pi$
$360$	0.209135	+	1.28649i	0.0110224	+	0.0678039i
$361$	4.44865	+	2.56843i	0.234139	+	0.135180i
$362$	−5.92308	−	6.33446i	−0.311310	−	0.332932i
$363$	12.8722	−	12.8722i	0.675613	−	0.675613i
$364$	13.3490	+	10.2075i	0.699678	+	0.535016i
$365$	−4.42381	−	4.42381i	−0.231553	−	0.231553i
$366$	23.1310	+	0.776309i	1.20908	+	0.0405783i
$367$	−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	$0.222378\pi$
$368$	9.81371	−	4.02713i	0.511575	−	0.209929i
$369$	−2.10033	−	3.63788i	−0.109339	−	0.189380i
$370$	0.854195	−	1.37114i	0.0444075	−	0.0712820i
$371$	−11.5029	−	23.1312i	−0.597201	−	1.20091i
$372$	−2.11252	+	6.18975i	−0.109529	+	0.320924i
$373$	3.16296	+	0.847513i	0.163772	+	0.0438826i	0.339773	−	0.940507i	$-0.389650\pi$
$373$	3.16296	+	0.847513i	0.163772	+	0.0438826i	−0.176001	+	0.984390i	$0.556316\pi$
$374$	4.96584	−	16.3217i	0.256777	−	0.843977i
$375$	−1.38000	−	0.796741i	−0.0712627	−	0.0411435i
$376$	−5.54986	+	2.49809i	−0.286212	+	0.128829i
$377$		−	15.8016i		−	0.813825i
$378$	16.8026	+	11.9770i	0.864231	+	0.616029i
$379$	−19.5513	+	19.5513i	−1.00428	+	1.00428i	−0.00429336	+	0.999991i	$0.501367\pi$
$379$	−19.5513	+	19.5513i	−1.00428	+	1.00428i	−0.999991	+	0.00429336i	$0.998633\pi$
$380$	−4.14733	+	6.18484i	−0.212754	+	0.317275i
$381$	−3.60023	+	0.964679i	−0.184445	+	0.0494220i
$382$	3.18321	−	1.69809i	0.162867	−	0.0868818i
$383$	−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
$387$	−0.610859	+	2.27976i	−0.0310517	+	0.115887i
$388$	21.0744	+	1.41617i	1.06989	+	0.0718951i
$389$	−9.59695	−	35.8163i	−0.486584	−	1.81596i	−0.572818	−	0.819683i	$-0.694150\pi$
$389$	−9.59695	−	35.8163i	−0.486584	−	1.81596i	0.0862331	−	0.996275i	$-0.472517\pi$
$390$	−5.22737	+	4.88789i	−0.264698	+	0.247508i
$391$		−	6.75595i		−	0.341663i
$392$	−5.82659	−	18.9222i	−0.294287	−	0.955717i
$393$		−	5.85733i		−	0.295463i
$394$	−17.8706	−	19.1118i	−0.900308	−	0.962838i
$395$	2.35362	+	8.78382i	0.118423	+	0.441962i
$396$	−2.87215	−	3.28597i	−0.144331	−	0.165126i
$397$	−3.54925	+	13.2460i	−0.178132	+	0.664797i	0.817865	+	0.575410i	$0.195157\pi$
$397$	−3.54925	+	13.2460i	−0.178132	+	0.664797i	−0.995997	+	0.0893868i	$0.971509\pi$
$398$	−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	$0.611934\pi$
$402$	−16.3578	−	30.6640i	−0.815853	−	1.52938i
$403$	6.29520	−	1.68679i	0.313586	−	0.0840251i
$404$	0.714534	+	3.62340i	0.0355494	+	0.180271i
$405$	−5.23628	+	5.23628i	−0.260193	+	0.260193i
$406$	−10.8063	+	15.1603i	−0.536310	+	0.752393i
$407$			5.40921i			0.268125i
$408$	10.7359	+	4.07102i	0.531505	+	0.201546i
$409$	−25.8457	−	14.9220i	−1.27799	−	0.737846i	−0.301509	−	0.953463i	$-0.597490\pi$
$409$	−25.8457	−	14.9220i	−1.27799	−	0.737846i	−0.976478	+	0.215618i	$0.930824\pi$
$410$	−12.3334	−	3.75240i	−0.609105	−	0.185318i
$411$	−18.9103	−	5.06699i	−0.932775	−	0.249936i
$412$	8.52301	−	4.18564i	0.419898	−	0.206212i
$413$	−7.85868	−	15.8030i	−0.386701	−	0.777615i
$414$	−1.46688	−	0.913844i	−0.0720934	−	0.0449130i
$415$	−8.84322	−	15.3169i	−0.434097	−	0.751877i
$416$	14.6455	−	10.4038i	0.718055	−	0.510087i
$417$	17.1853	−	29.7658i	0.841568	−	1.45764i
$418$	0.836371	−	24.9206i	0.0409082	−	1.21891i
$419$	6.68782	+	6.68782i	0.326722	+	0.326722i	0.851338	−	0.524617i	$-0.175791\pi$
$419$	6.68782	+	6.68782i	0.326722	+	0.326722i	−0.524617	+	0.851338i	$0.675791\pi$
$420$	8.35792	−	1.11464i	0.407825	−	0.0543886i
$421$	4.68780	−	4.68780i	0.228470	−	0.228470i	−0.583584	−	0.812053i	$-0.698350\pi$
$421$	4.68780	−	4.68780i	0.228470	−	0.228470i	0.812053	+	0.583584i	$0.198350\pi$
$422$	11.4968	−	10.7502i	0.559657	−	0.523311i
$423$	0.858726	+	0.495786i	0.0417527	+	0.0241059i
$424$	−27.2593	+	4.43134i	−1.32383	+	0.215205i
$425$	2.20622	−	1.27376i	0.107018	−	0.0617866i
$426$	−28.6640	+	6.65861i	−1.38878	+	0.322611i
$427$	−1.68689	+	27.1198i	−0.0816341	+	1.31242i
$428$	4.53706	+	1.54847i	0.219307	+	0.0748479i
$429$	6.20218	−	23.1469i	0.299444	−	1.11754i
$430$	3.40919	+	6.39081i	0.164406	+	0.308192i
$431$	−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	$0.253345\pi$
$432$	17.5447	−	13.3709i	0.844121	−	0.643308i
$433$	3.12694			0.150271			0.0751356	−	0.997173i	$-0.476061\pi$
$433$	3.12694			0.150271			0.0751356	+	0.997173i	$0.476061\pi$
$434$	−7.19325	−	2.68680i	−0.345287	−	0.128971i
$435$	−5.60647	−	5.60647i	−0.268810	−	0.268810i
$436$	−38.5488	+	7.60183i	−1.84615	+	0.364061i
$437$	−2.55561	−	9.53767i	−0.122251	−	0.456249i
$438$	−4.10370	+	13.4881i	−0.196082	+	0.644484i
$439$	18.3783	−	10.6107i	0.877150	−	0.506423i	0.00743214	−	0.999972i	$-0.497634\pi$
$439$	18.3783	−	10.6107i	0.877150	−	0.506423i	0.869718	+	0.493550i	$0.164301\pi$
$440$	−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
$443$	29.2633	+	7.84107i	1.39034	+	0.372541i	0.874866	−	0.484364i	$-0.160949\pi$
$443$	29.2633	+	7.84107i	1.39034	+	0.372541i	0.515474	+	0.856905i	$0.327616\pi$
$444$	−3.63225	−	0.244082i	−0.172379	−	0.0115836i
$445$	1.62511	−	0.435447i	0.0770375	−	0.0206421i
$446$	−0.866783	+	25.8268i	−0.0410434	+	1.22293i
$447$	28.3336			1.34013
$448$	−21.1660	−	0.0341814i	−0.999999	−	0.00161492i
$449$	−34.7384			−1.63941			−0.819703	−	0.572789i	$-0.805861\pi$
$449$	−34.7384			−1.63941			−0.819703	+	0.572789i	$0.805861\pi$
$450$	0.0218593	−	0.651321i	0.00103046	−	0.0307036i
$451$	41.6959	−	11.1724i	1.96338	−	0.526087i
$452$	−11.0418	−	0.741993i	−0.519362	−	0.0349004i
$453$	−27.1276	−	7.26881i	−1.27456	−	0.341519i
$454$	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	−0.540688	−	0.841223i	$-0.681836\pi$
$457$	−1.76391	+	1.01839i	−0.0825121	+	0.0476384i	0.458176	+	0.888861i	$0.348503\pi$
$458$	−5.19224	+	17.0659i	−0.242617	+	0.797436i
$459$	−3.63614	−	13.5703i	−0.169720	−	0.633405i
$460$	−5.20371	+	1.02617i	−0.242624	+	0.0478455i
$461$	4.83006	+	4.83006i	0.224958	+	0.224958i	0.810583	−	0.585624i	$-0.199151\pi$
$461$	4.83006	+	4.83006i	0.224958	+	0.224958i	−0.585624	+	0.810583i	$0.699151\pi$
$462$	−21.7800	+	17.9659i	−1.01330	+	0.835849i
$463$	−26.6776			−1.23981			−0.619906	−	0.784676i	$-0.712829\pi$
$463$	−26.6776			−1.23981			−0.619906	+	0.784676i	$0.712829\pi$
$464$	12.0640	+	15.8299i	0.560059	+	0.734885i
$465$	1.63508	−	2.83204i	0.0758250	−	0.131333i
$466$	0.110240	+	0.206655i	0.00510679	+	0.00957309i
$467$	−9.16154	+	34.1913i	−0.423946	+	1.58219i	0.342269	+	0.939602i	$0.388805\pi$
$467$	−9.16154	+	34.1913i	−0.423946	+	1.58219i	−0.766215	+	0.642585i	$0.777862\pi$
$468$	−2.76996	−	0.945367i	−0.128041	−	0.0436996i
$469$	36.5351	−	18.1685i	1.68703	−	0.838945i
$470$	2.96416	−	0.688570i	0.136726	−	0.0317614i
$471$	−12.5068	+	7.22079i	−0.576282	+	0.332717i
$472$	−18.6233	+	3.02745i	−0.857207	+	0.139350i
$473$	−21.0043	−	12.1268i	−0.965776	−	0.557591i
$474$	14.9685	−	13.9964i	0.687527	−	0.642876i
$475$	2.63279	−	2.63279i	0.120801	−	0.120801i
$476$	−5.13773	+	12.4628i	−0.235487	+	0.571230i
$477$	3.18158	+	3.18158i	0.145675	+	0.145675i
$478$	0.422956	−	12.6024i	0.0193455	−	0.576422i
$479$	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	$-0.0232586\pi$
$480$	1.50498	−	8.88758i	0.0686927	−	0.405660i
$481$	1.81381	+	3.14161i	0.0827025	+	0.143245i
$482$	−17.1419	−	10.6791i	−0.780793	−	0.486421i
$483$	−6.18062	+	9.31693i	−0.281228	+	0.423935i
$484$	20.5084	−	10.0716i	0.932200	−	0.457802i
$485$	−10.2011	−	2.73338i	−0.463208	−	0.124116i
$486$	−6.41875	−	1.95288i	−0.291160	−	0.0885846i
$487$	−12.2723	−	7.08539i	−0.556109	−	0.321070i	0.195473	−	0.980709i	$-0.437376\pi$
$487$	−12.2723	−	7.08539i	−0.556109	−	0.321070i	−0.751582	+	0.659639i	$0.770709\pi$
$488$	27.1611	+	10.2994i	1.22953	+	0.466234i
$489$		−	15.9433i		−	0.720982i
$490$	1.02777	+	9.84600i	0.0464300	+	0.444797i
$491$	14.0974	−	14.0974i	0.636206	−	0.636206i	−0.313411	−	0.949618i	$-0.601472\pi$
$491$	14.0974	−	14.0974i	0.636206	−	0.636206i	0.949618	+	0.313411i	$0.101472\pi$
$492$	5.62072	+	28.5027i	0.253402	+	1.28500i
$493$	12.2439	−	3.28074i	0.551438	−	0.147757i
$494$	−7.87057	−	14.7540i	−0.354114	−	0.663816i
$495$	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
$499$	−11.0894	+	41.3863i	−0.496431	+	1.85271i	0.0254331	+	0.999677i	$0.491904\pi$
$499$	−11.0894	+	41.3863i	−0.496431	+	1.85271i	−0.521864	+	0.853029i	$0.674763\pi$
$500$	−1.31621	−	1.50585i	−0.0588628	−	0.0673437i
$501$	3.12685	+	11.6695i	0.139697	+	0.521357i
$502$	−24.6818	−	26.3961i	−1.10160	−	1.17812i
$503$			33.3663i			1.48773i	0.668329	+	0.743866i	$0.267010\pi$
$503$			33.3663i			1.48773i	−0.668329	+	0.743866i	$0.732990\pi$
$504$	2.01102	+	2.80131i	0.0895781	+	0.124780i
$505$		−	1.84659i		−	0.0821721i
$506$	12.9723	−	12.1298i	0.576688	−	0.539236i
$507$	1.20210	+	4.48629i	0.0533870	+	0.199243i
$508$	−4.66757	−	0.313654i	−0.207090	−	0.0139161i
$509$	−4.10203	+	15.3090i	−0.181819	+	0.678559i	0.813470	+	0.581607i	$0.197576\pi$
$509$	−4.10203	+	15.3090i	−0.181819	+	0.678559i	−0.995289	+	0.0969519i	$0.969091\pi$
$510$	−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
$514$	−15.8811	+	8.47182i	−0.700486	+	0.373676i
$515$	−4.58589	+	1.22879i	−0.202078	+	0.0541468i
$516$	9.09087	−	13.5570i	0.400203	−	0.596815i
$517$	−7.20511	+	7.20511i	−0.316880	+	0.316880i
$518$	0.408277	−	4.25452i	0.0179386	−	0.186933i
$519$			24.3607i			1.06932i
$520$	−8.19082	+	3.68684i	−0.359191	+	0.161678i
$521$	−10.0284	−	5.78993i	−0.439354	−	0.253661i	0.263969	−	0.964531i	$-0.414968\pi$
$521$	−10.0284	−	5.78993i	−0.439354	−	0.253661i	−0.703324	+	0.710870i	$0.748302\pi$
$522$	0.943842	−	3.10223i	0.0413108	−	0.135781i
$523$	−37.8016	−	10.1289i	−1.65295	−	0.442907i	−0.692513	−	0.721405i	$-0.743497\pi$
$523$	−37.8016	−	10.1289i	−1.65295	−	0.442907i	−0.960437	+	0.278499i	$0.910163\pi$
$524$	2.37457	−	6.95756i	0.103733	−	0.303942i
$525$	−4.20783	−	0.261732i	−0.183645	−	0.0114229i
$526$	−11.5097	+	18.4751i	−0.501847	+	0.805555i
$527$	2.61403	+	4.52763i	0.113869	+	0.197227i
$528$	11.4586	+	27.9235i	0.498672	+	1.21521i
$529$	−7.98354	+	13.8279i	−0.347111	+	0.601213i
$530$	13.8008	+	0.463175i	0.599468	+	0.0201190i
$531$	2.17363	+	2.17363i	0.0943275	+	0.0943275i
$532$	−2.53879	+	19.5377i	−0.110070	+	0.847068i
$533$	20.4702	−	20.4702i	0.886662	−	0.886662i
$534$	−2.58950	−	2.76935i	−0.112059	−	0.119841i
$535$	−2.07587	−	1.19851i	−0.0897478	−	0.0518159i
$536$	−6.99919	−	43.0554i	−0.302319	−	1.85971i
$537$	24.6491	−	14.2312i	1.06369	−	0.614121i
$538$	0.256907	+	1.10593i	0.0110760	+	0.0476801i
$539$	−20.3537	−	26.1630i	−0.876697	−	1.12692i
$540$	−9.90008	+	4.86191i	−0.426031	+	0.209223i
$541$	−5.57847	+	20.8191i	−0.239837	+	0.895084i	0.736071	+	0.676904i	$0.236679\pi$
$541$	−5.57847	+	20.8191i	−0.239837	+	0.895084i	−0.975909	+	0.218180i	$0.929988\pi$
$542$	24.3726	−	13.0016i	1.04689	−	0.558468i
$543$	4.88579	−	8.46244i	0.209669	−	0.363158i
$544$	11.1021	+	9.18805i	0.475998	+	0.393934i
$545$	19.6456			0.841526
$546$	−6.62530	+	17.7376i	−0.283537	+	0.759100i
$547$	−5.07711	−	5.07711i	−0.217082	−	0.217082i	0.590186	−	0.807267i	$-0.299054\pi$
$547$	−5.07711	−	5.07711i	−0.217082	−	0.217082i	−0.807267	+	0.590186i	$0.799054\pi$
$548$	−20.4082	−	13.6850i	−0.871793	−	0.584594i
$549$	−1.22489	−	4.57135i	−0.0522770	−	0.195100i
$550$	6.40690	+	1.94928i	0.273191	+	0.0831175i
$551$	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
$555$	1.75820	+	0.471108i	0.0746314	+	0.0199974i
$556$	32.4804	−	28.3900i	1.37748	−	1.20400i
$557$	−18.3816	+	4.92533i	−0.778853	+	0.208693i	−0.626279	−	0.779599i	$-0.715423\pi$
$557$	−18.3816	+	4.92533i	−0.778853	+	0.208693i	−0.152574	+	0.988292i	$0.548756\pi$
$558$	1.33665	+	0.0448598i	0.0565848	+	0.00189907i
$559$	−16.2654			−0.687952
$560$	10.3797	+	2.06430i	0.438623	+	0.0872326i
$561$	19.2231			0.811599
$562$	12.5108	+	0.419880i	0.527735	+	0.0177116i
$563$	9.90612	−	2.65434i	0.417493	−	0.111867i	−0.0439562	−	0.999033i	$-0.513996\pi$
$563$	9.90612	−	2.65434i	0.417493	−	0.111867i	0.461450	+	0.887166i	$0.347330\pi$
$564$	−4.51307	−	5.16331i	−0.190035	−	0.217415i
$565$	5.34480	+	1.43214i	0.224858	+	0.0602504i
$566$	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	−0.113996	−	0.993481i	$-0.536365\pi$
$569$	16.4444	−	9.49419i	0.689386	−	0.398017i	0.803382	+	0.595464i	$0.203032\pi$
$570$	−8.02730	−	2.44228i	−0.336227	−	0.102296i
$571$	1.95747	+	7.30536i	0.0819174	+	0.305720i	0.994713	−	0.102698i	$-0.0327474\pi$
$571$	1.95747	+	7.30536i	0.0819174	+	0.305720i	−0.912795	+	0.408418i	$0.866081\pi$
$572$	16.7509	−	24.9803i	0.700392	−	1.04448i
$573$	2.87450	+	2.87450i	0.120084	+	0.120084i
$574$	−33.6384	+	5.64032i	−1.40404	+	0.235422i
$575$	2.65196			0.110595
$576$	3.49668	−	1.16772i	0.145695	−	0.0486549i
$577$	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	$-0.129108\pi$
$578$	−13.1142	+	6.99582i	−0.545480	+	0.290988i
$579$	−4.35430	+	16.2505i	−0.180959	+	0.675347i
$580$	−4.38671	−	8.93245i	−0.182148	−	0.370900i
$581$	−38.9940	−	25.8677i	−1.61775	−	1.07317i
$582$	5.38518	+	23.1821i	0.223223	+	0.960930i
$583$	−40.0425	+	23.1185i	−1.65839	+	0.957472i
$584$	−10.3426	+	14.3580i	−0.427980	+	0.594138i
$585$	1.26736	+	0.731710i	0.0523988	+	0.0302525i
$586$	15.0716	+	16.1184i	0.622603	+	0.665845i
$587$	−27.7549	+	27.7549i	−1.14557	+	1.14557i	−0.158154	+	0.987414i	$0.550554\pi$
$587$	−27.7549	+	27.7549i	−1.14557	+	1.14557i	−0.987414	+	0.158154i	$0.949446\pi$
$588$	18.4867	−	12.4868i	0.762380	−	0.514949i
$589$	5.40303	+	5.40303i	0.222628	+	0.222628i
$590$	9.42858	+	0.316437i	0.388169	+	0.0130275i
$591$	14.7410	−	25.5322i	0.606364	−	1.05025i
$592$	−4.21558	−	1.76245i	−0.173259	−	0.0724362i
$593$	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
$595$	3.72594	−	5.61664i	0.152748	−	0.230260i
$596$	33.6557	+	11.4865i	1.37859	+	0.470504i
$597$	−12.7341	−	3.41209i	−0.521172	−	0.139647i
$598$	3.46680	−	11.3947i	0.141768	−	0.465964i
$599$	2.43316	+	1.40478i	0.0994161	+	0.0573979i	0.548884	−	0.835899i	$-0.315053\pi$
$599$	2.43316	+	1.40478i	0.0994161	+	0.0573979i	−0.449468	+	0.893297i	$0.648386\pi$
$600$	−1.59803	+	4.21424i	−0.0652393	+	0.172046i
$601$			29.3301i			1.19640i	0.801347	+	0.598200i	$0.204117\pi$
$601$			29.3301i			1.19640i	−0.801347	+	0.598200i	$0.795883\pi$
$602$	15.6052	+	11.1235i	0.636021	+	0.453360i
$603$	−5.02523	+	5.02523i	−0.204643	+	0.204643i
$604$	−29.2764	−	19.6317i	−1.19124	−	0.798803i
$605$	−11.0348	+	2.95675i	−0.448626	+	0.120209i
$606$	−3.67158	+	1.95862i	−0.149148	+	0.0795633i
$607$	−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
$611$	−1.76864	+	6.60065i	−0.0715515	+	0.267034i
$612$	0.157418	−	2.34258i	0.00636326	−	0.0946933i
$613$	4.01441	+	14.9820i	0.162140	+	0.605116i	0.998388	+	0.0567636i	$0.0180781\pi$
$613$	4.01441	+	14.9820i	0.162140	+	0.605116i	−0.836247	+	0.548353i	$0.815255\pi$
$614$	−20.2116	+	18.8990i	−0.815673	+	0.762700i
$615$		−	14.5258i		−	0.585737i
$616$	−33.1545	+	12.5109i	−1.33583	+	0.504079i
$617$		−	26.7894i		−	1.07850i	−0.842146	−	0.539250i	$-0.818708\pi$
$617$		−	26.7894i		−	1.07850i	0.842146	−	0.539250i	$-0.181292\pi$
$618$	7.30730	+	7.81482i	0.293943	+	0.314358i
$619$	−9.95690	−	37.1597i	−0.400202	−	1.49357i	−0.812737	−	0.582631i	$-0.802023\pi$
$619$	−9.95690	−	37.1597i	−0.400202	−	1.49357i	0.412535	−	0.910942i	$-0.364643\pi$
$620$	3.09032	−	2.70114i	0.124110	−	0.108480i
$621$	3.78520	−	14.1266i	0.151895	−	0.566880i
$622$	−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
$626$	4.03319	+	7.56054i	0.161199	+	0.302180i
$627$	27.1381	−	7.27162i	1.08379	−	0.290401i
$628$	−17.7833	+	3.50687i	−0.709632	+	0.139939i
$629$	−2.05769	+	2.05769i	−0.0820457	+	0.0820457i
$630$	−0.715523	−	1.56873i	−0.0285071	−	0.0624996i
$631$			26.3247i			1.04797i	0.851728	+	0.523984i	$0.175555\pi$
$631$			26.3247i			1.04797i	−0.851728	+	0.523984i	$0.824445\pi$
$632$	23.4543	−	10.5572i	0.932962	−	0.419943i
$633$	15.3590	+	8.86755i	0.610467	+	0.352453i
$634$	22.4220	+	6.82183i	0.890493	+	0.270930i
$635$	2.25935	+	0.605390i	0.0896594	+	0.0240242i
$636$	−13.7171	−	27.9315i	−0.543919	−	1.10756i
$637$	−20.5941	−	8.37019i	−0.815970	−	0.331639i
$638$	28.2825	+	17.6195i	1.11971	+	0.697563i
$639$	3.00872	+	5.21126i	0.119023	+	0.206154i
$640$	5.39070	−	9.94688i	0.213086	−	0.393185i
$641$	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	$0.139068\pi$
$642$	−0.181188	+	5.39868i	−0.00715090	+	0.213069i
$643$	10.2971	+	10.2971i	0.406078	+	0.406078i	0.880369	−	0.474290i	$-0.157295\pi$
$643$	10.2971	+	10.2971i	0.406078	+	0.406078i	−0.474290	+	0.880369i	$0.657295\pi$
$644$	−11.1187	+	8.56137i	−0.438136	+	0.337365i
$645$	−5.77102	+	5.77102i	−0.227233	+	0.227233i
$646$	9.79809	−	9.16177i	0.385501	−	0.360465i
$647$	−28.6256	−	16.5270i	−1.12539	−	0.649744i	−0.182618	−	0.983184i	$-0.558457\pi$
$647$	−28.6256	−	16.5270i	−1.12539	−	0.649744i	−0.942771	+	0.333440i	$0.891791\pi$
$648$	16.9949	+	12.2421i	0.667625	+	0.480915i
$649$	−27.3567	+	15.7944i	−1.07384	+	0.619983i
$650$	4.37468	−	1.01623i	0.171589	−	0.0398599i
$651$	0.537129	−	8.63534i	0.0210517	−	0.338445i
$652$	6.46343	−	18.9381i	0.253127	−	0.741672i
$653$	10.0984	−	37.6877i	0.395181	−	1.47483i	−0.426291	−	0.904586i	$-0.640180\pi$
$653$	10.0984	−	37.6877i	0.395181	−	1.47483i	0.821472	−	0.570249i	$-0.193153\pi$
$654$	−20.8374	−	39.0615i	−0.814808	−	1.52743i
$655$	−1.83790	+	3.18334i	−0.0718128	+	0.124383i
$656$	−4.87850	+	36.1352i	−0.190473	+	1.41084i
$657$	2.88294			0.112474
$658$	6.21088	−	5.12323i	0.242125	−	0.199724i
$659$	−13.9371	−	13.9371i	−0.542912	−	0.542912i	0.381469	−	0.924382i	$-0.375418\pi$
$659$	−13.9371	−	13.9371i	−0.542912	−	0.542912i	−0.924382	+	0.381469i	$0.875418\pi$
$660$	−2.91982	−	14.8064i	−0.113654	−	0.576339i
$661$	5.03872	+	18.8048i	0.195983	+	0.731420i	0.992010	+	0.126159i	$0.0402648\pi$
$661$	5.03872	+	18.8048i	0.195983	+	0.731420i	−0.796027	+	0.605262i	$0.793069\pi$
$662$	−8.05749	+	26.4834i	−0.313163	+	1.02931i
$663$	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
$667$	12.7459	+	3.41524i	0.493521	+	0.132239i
$668$	−1.01666	+	15.1291i	−0.0393356	+	0.585364i
$669$	−28.1249	+	7.53604i	−1.08737	+	0.291360i
$670$	−0.731572	+	21.7980i	−0.0282631	+	0.842130i
$671$	48.6332			1.87746
$672$	−6.90496	−	22.8276i	−0.266365	−	0.880594i
$673$	1.49746			0.0577228			0.0288614	−	0.999583i	$-0.490812\pi$
$673$	1.49746			0.0577228			0.0288614	+	0.999583i	$0.490812\pi$
$674$	−0.830527	+	24.7465i	−0.0319907	+	0.953198i
$675$	5.32684	−	1.42732i	0.205030	−	0.0549376i
$676$	−0.390848	+	5.81631i	−0.0150326	+	0.223704i
$677$	44.8150	+	12.0081i	1.72238	+	0.461510i	0.978405	−	0.206697i	$-0.0662713\pi$
$677$	44.8150	+	12.0081i	1.72238	+	0.461510i	0.743975	+	0.668207i	$0.232938\pi$
$678$	−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
$682$	−4.00032	+	13.1483i	−0.153180	+	0.503474i
$683$	3.04802	+	11.3753i	0.116629	+	0.435266i	0.999404	−	0.0345313i	$-0.0109938\pi$
$683$	3.04802	+	11.3753i	0.116629	+	0.435266i	−0.882775	+	0.469797i	$0.844327\pi$
$684$	−0.663908	−	3.36668i	−0.0253852	−	0.128728i
$685$	8.68743	+	8.68743i	0.331930	+	0.331930i
$686$	14.0341	+	22.1143i	0.535826	+	0.844328i
$687$	−20.0995			−0.766843
$688$	16.2945	−	12.4181i	0.621222	−	0.473436i
$689$	−15.5041	+	26.8540i	−0.590661	+	1.02305i
$690$	−2.81285	−	5.27292i	−0.107083	−	0.200737i
$691$	5.11615	−	19.0937i	0.194628	−	0.726360i	−0.797735	−	0.603008i	$-0.793969\pi$
$691$	5.11615	−	19.0937i	0.194628	−	0.726360i	0.992363	−	0.123352i	$-0.0393646\pi$
$692$	−9.87585	+	28.9366i	−0.375423	+	1.10000i
$693$	4.81104	+	3.19152i	0.182756	+	0.121236i
$694$	−7.34010	+	1.70510i	−0.278626	+	0.0647245i
$695$	−18.6797	+	10.7847i	−0.708562	+	0.409089i
$696$	−13.1076	+	18.1965i	−0.496842	+	0.689735i
$697$	20.1114	+	11.6113i	0.761773	+	0.439810i
$698$	−25.9585	+	24.2727i	−0.982545	+	0.918735i
$699$	−0.186613	+	0.186613i	−0.00705835	+	0.00705835i
$700$	−4.89211	−	2.01675i	−0.184904	−	0.0762260i
$701$	27.6467	+	27.6467i	1.04420	+	1.04420i	0.998977	+	0.0452255i	$0.0144007\pi$
$701$	27.6467	+	27.6467i	1.04420	+	1.04420i	0.0452255	+	0.998977i	$0.485599\pi$
$702$	0.830770	−	24.7537i	0.0313554	−	0.934268i
$703$	−2.12656	+	3.68331i	−0.0802048	+	0.138919i
$704$	2.29077	+	37.8139i	0.0863368	+	1.42516i
$705$	1.71442	+	2.96946i	0.0645687	+	0.111836i
$706$	−43.6684	−	27.2047i	−1.64348	−	1.02386i
$707$	−2.17543	−	4.37456i	−0.0818153	−	0.164522i
$708$	−9.37141	−	19.0825i	−0.352199	−	0.717166i
$709$	−10.9098	−	2.92328i	−0.409727	−	0.109786i	0.0480676	−	0.998844i	$-0.484694\pi$
$709$	−10.9098	−	2.92328i	−0.409727	−	0.109786i	−0.457794	+	0.889058i	$0.651360\pi$
$710$	17.6676	+	5.37532i	0.663054	+	0.201732i
$711$	−3.62907	−	2.09524i	−0.136101	−	0.0785777i
$712$	−1.95321	−	4.33932i	−0.0731996	−	0.162623i
$713$			5.44238i			0.203819i
$714$	−15.1196	−	1.45092i	−0.565836	−	0.0542993i
$715$	−10.6337	+	10.6337i	−0.397679	+	0.397679i
$716$	35.0485	−	6.91156i	1.30982	−	0.258297i
$717$	13.7238	−	3.67728i	0.512525	−	0.137331i
$718$	3.33050	+	6.24329i	0.124293	+	0.232998i
$719$	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
$723$	5.88978	−	21.9810i	0.219043	−	0.817481i
$724$	9.23420	−	8.07130i	0.343186	−	0.299967i
$725$	1.28782	+	4.80619i	0.0478283	+	0.178498i
$726$	17.5831	+	18.8043i	0.652571	+	0.697894i
$727$		−	38.6751i		−	1.43438i	−0.696877	−	0.717190i	$-0.745428\pi$
$727$		−	38.6751i		−	1.43438i	0.696877	−	0.717190i	$-0.254572\pi$
$728$	−15.0606	+	18.3835i	−0.558184	+	0.681338i
$729$		−	29.7754i		−	1.10279i
$730$	6.46253	−	6.04284i	0.239189	−	0.223655i
$731$	−3.37703	−	12.6032i	−0.124904	−	0.466148i
$732$	−2.19450	+	32.6569i	−0.0811109	+	1.20703i
$733$	−10.3167	+	38.5025i	−0.381057	+	1.42212i	0.463233	+	0.886236i	$0.346689\pi$
$733$	−10.3167	+	38.5025i	−0.381057	+	1.42212i	−0.844290	+	0.535886i	$0.819977\pi$
$734$	−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
$738$	5.24147	−	2.79608i	0.192941	−	0.102925i
$739$	−20.0171	+	5.36356i	−0.736340	+	0.197302i	−0.607451	−	0.794357i	$-0.707808\pi$
$739$	−20.0171	+	5.36356i	−0.736340	+	0.197302i	−0.128889	+	0.991659i	$0.541141\pi$
$740$	1.89747	+	1.27238i	0.0697523	+	0.0467735i
$741$	13.3232	−	13.3232i	0.489439	−	0.489439i
$742$	33.2397	−	15.1612i	1.22027	−	0.556584i
$743$		−	2.03985i		−	0.0748349i	−0.999300	−	0.0374175i	$-0.988087\pi$
$743$		−	2.03985i		−	0.0748349i	0.999300	−	0.0374175i	$-0.0119131\pi$
$744$	−8.64849	−	3.27949i	−0.317069	−	0.120232i
$745$	−15.3987	−	8.89046i	−0.564166	−	0.325721i
$746$	−1.34793	+	4.43038i	−0.0493512	+	0.162208i
$747$	7.87243	+	2.10941i	0.288037	+	0.0771794i
$748$	22.8339	+	7.79304i	0.834889	+	0.284942i
$749$	−6.32966	−	0.393713i	−0.231281	−	0.0143860i
$750$	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	$0.782658\pi$
$752$	−3.26759	−	7.96278i	−0.119157	−	0.290373i
$753$	20.3594	−	35.2635i	0.741938	−	1.28507i
$754$	22.3343	+	0.749571i	0.813367	+	0.0272978i
$755$	12.4625	+	12.4625i	0.453556	+	0.453556i
$756$	−17.7255	+	23.1809i	−0.644670	+	0.843081i
$757$	19.6906	−	19.6906i	0.715665	−	0.715665i	−0.252049	−	0.967714i	$-0.581104\pi$
$757$	19.6906	−	19.6906i	0.715665	−	0.715665i	0.967714	+	0.252049i	$0.0811044\pi$
$758$	−26.7067	−	28.5616i	−0.970033	−	1.03741i
$759$	17.3302	+	10.0056i	0.629045	+	0.363179i
$760$	−8.54502	−	6.15530i	−0.309961	−	0.223276i
$761$	41.2663	−	23.8251i	1.49590	−	0.863660i	0.495913	−	0.868372i	$-0.334833\pi$
$761$	41.2663	−	23.8251i	1.49590	−	0.863660i	0.999989	+	0.00471237i	$0.00150000\pi$
$762$	−1.19271	−	5.13439i	−0.0432074	−	0.185999i
$763$	46.5403	−	23.1441i	1.68487	−	0.837871i
$764$	2.24911	+	4.57975i	0.0813700	+	0.165690i
$765$	−0.303836	+	1.13393i	−0.0109852	+	0.0409974i
$766$	17.8701	−	9.53283i	0.645672	−	0.344435i
$767$	−10.5923	+	18.3464i	−0.382465	+	0.662450i
$768$	−25.4952	−	0.168051i	−0.919978	−	0.00606401i
$769$	−20.8937			−0.753447			−0.376723	−	0.926326i	$-0.622949\pi$
$769$	−20.8937			−0.753447			−0.376723	+	0.926326i	$0.622949\pi$
$770$	17.4743	−	2.93000i	0.629730	−	0.105590i
$771$	−14.3409	−	14.3409i	−0.516476	−	0.516476i
$772$	−11.7602	+	17.5377i	−0.423257	+	0.631195i
$773$	−1.96716	−	7.34154i	−0.0707538	−	0.264057i	0.921483	−	0.388418i	$-0.126978\pi$
$773$	−1.96716	−	7.34154i	−0.0707538	−	0.264057i	−0.992237	+	0.124362i	$0.960312\pi$
$774$	−3.19327	−	0.971542i	−0.114780	−	0.0349214i
$775$	−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
$779$	32.7844	+	8.78455i	1.17462	+	0.314739i
$780$	−6.66066	−	7.62032i	−0.238490	−	0.272851i
$781$	−59.7293	+	16.0044i	−2.13728	+	0.572683i
$782$	9.54898	+	0.320477i	0.341471	+	0.0114603i
$783$	27.4399			0.980623
$784$	27.0214	−	7.33781i	0.965050	−	0.262065i
$785$	9.06291			0.323469
$786$	8.27886	+	0.277850i	0.295297	+	0.00991059i
$787$	39.3024	−	10.5310i	1.40098	−	0.375391i	0.522283	−	0.852772i	$-0.325080\pi$
$787$	39.3024	−	10.5310i	1.40098	−	0.375391i	0.878696	+	0.477381i	$0.158414\pi$
$788$	27.8607	−	24.3520i	0.992495	−	0.867506i
$789$	−23.6906	−	6.34787i	−0.843407	−	0.225990i
$790$	−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
$794$	−18.5537	−	5.64491i	−0.658448	−	0.200330i
$795$	4.02696	+	15.0288i	0.142822	+	0.533017i
$796$	−13.7428	−	9.21541i	−0.487099	−	0.326632i
$797$	0.465157	+	0.465157i	0.0164767	+	0.0164767i	0.715297	−	0.698820i	$-0.246291\pi$
$797$	0.465157	+	0.465157i	0.0164767	+	0.0164767i	−0.698820	+	0.715297i	$0.746291\pi$
$798$	−21.8938	+	3.67104i	−0.775033	+	0.129953i
$799$	−5.48173			−0.193930
$800$	−3.60665	+	4.35799i	−0.127514	+	0.154078i
$801$	−0.387644	+	0.671420i	−0.0136967	+	0.0237234i
$802$	−32.0231	+	17.0828i	−1.13077	+	0.603214i
$803$	−7.66768	+	28.6162i	−0.270587	+	1.00984i
$804$	44.1171	−	21.6658i	1.55589	−	0.764094i
$805$	6.28249	−	3.12422i	0.221429	−	0.110114i
$806$	2.08552	+	8.97776i	0.0734594	+	0.316228i
$807$	−1.10791	+	0.639652i	−0.0390003	+	0.0225168i
$808$	−5.15527	+	0.838054i	−0.181362	+	0.0294826i
$809$	44.6151	+	25.7585i	1.56858	+	0.905622i	0.996335	+	0.0855420i	$0.0272622\pi$
$809$	44.6151	+	25.7585i	1.56858	+	0.905622i	0.572249	+	0.820080i	$0.306071\pi$
$810$	−7.15266	−	7.64943i	−0.251319	−	0.268774i
$811$	11.3389	−	11.3389i	0.398162	−	0.398162i	−0.479422	−	0.877584i	$-0.659154\pi$
$811$	11.3389	−	11.3389i	0.398162	−	0.398162i	0.877584	+	0.479422i	$0.159154\pi$
$812$	−20.9152	−	15.9930i	−0.733980	−	0.561245i
$813$	22.0089	+	22.0089i	0.771887	+	0.771887i
$814$	−7.64547	−	0.256593i	−0.267974	−	0.00899358i
$815$	−5.00266	+	8.66487i	−0.175236	+	0.303517i
$816$	−6.26333	+	14.9812i	−0.219260	+	0.524446i
$817$	−9.53500	−	16.5151i	−0.333587	−	0.577790i
$818$	22.3171	−	35.8229i	0.780298	−	1.25252i
$819$	3.86438	+	0.240369i	0.135032	+	0.00839917i
$820$	5.88877	−	17.2543i	0.205645	−	0.602546i
$821$	10.4717	+	2.80587i	0.365464	+	0.0979257i	0.436877	−	0.899521i	$-0.356084\pi$
$821$	10.4717	+	2.80587i	0.365464	+	0.0979257i	−0.0714137	+	0.997447i	$0.522751\pi$
$822$	8.05881	−	26.4877i	0.281083	−	0.923866i
$823$	40.0586	+	23.1278i	1.39635	+	0.806185i	0.994009	−	0.109302i	$-0.0348617\pi$
$823$	40.0586	+	23.1278i	1.39635	+	0.806185i	0.402346	+	0.915488i	$0.368195\pi$
$824$	5.51175	+	12.2451i	0.192011	+	0.426579i
$825$			7.54578i			0.262710i
$826$	22.7090	−	10.3580i	0.790149	−	0.360400i
$827$	28.6390	−	28.6390i	0.995876	−	0.995876i	−0.00411544	−	0.999992i	$-0.501310\pi$
$827$	28.6390	−	28.6390i	0.995876	−	0.995876i	0.999992	+	0.00411544i	$0.00130999\pi$
$828$	1.36123	−	2.02997i	0.0473059	−	0.0705464i
$829$	−3.72914	+	0.999220i	−0.129518	+	0.0347043i	−0.322996	−	0.946400i	$-0.604690\pi$
$829$	−3.72914	+	0.999220i	−0.129518	+	0.0347043i	0.193478	+	0.981105i	$0.438023\pi$
$830$	22.0687	−	11.7726i	0.766015	−	0.408632i
$831$	−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
$835$	1.96227	−	7.32330i	0.0679072	−	0.253433i
$836$	35.1835	+	2.36428i	1.21685	+	0.0817704i
$837$	2.92916	+	10.9318i	0.101247	+	0.377857i
$838$	−9.76993	+	9.13544i	−0.337497	+	0.315579i
$839$		−	34.3259i		−	1.18506i	−0.805547	−	0.592532i	$-0.798129\pi$
$839$		−	34.3259i		−	1.18506i	0.805547	−	0.592532i	$-0.201871\pi$
$840$	1.17898	+	11.8661i	0.0406786	+	0.409420i
$841$		−	4.24204i		−	0.146277i
$842$	6.40345	+	6.84820i	0.220678	+	0.236005i
$843$	3.65054	+	13.6240i	0.125731	+	0.469236i
$844$	14.6491	+	16.7598i	0.504244	+	0.576895i
$845$	0.754384	−	2.81540i	0.0259516	−	0.0968526i
$846$	−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
$850$	1.69570	+	3.17874i	0.0581622	+	0.109030i
$851$	−2.92610	+	0.784045i	−0.100305	+	0.0268767i
$852$	−8.05168	−	40.8301i	−0.275846	−	1.39881i
$853$	14.1460	−	14.1460i	0.484348	−	0.484348i	−0.422169	−	0.906517i	$-0.638731\pi$
$853$	14.1460	−	14.1460i	0.484348	−	0.484348i	0.906517	+	0.422169i	$0.138731\pi$
$854$	−38.2516	−	3.67074i	−1.30894	−	0.125610i
$855$			1.71576i			0.0586776i
$856$	−2.40385	+	6.33930i	−0.0821619	+	0.216673i
$857$	29.4317	+	16.9924i	1.00537	+	0.580449i	0.909832	−	0.414977i	$-0.136210\pi$
$857$	29.4317	+	16.9924i	1.00537	+	0.580449i	0.0955352	+	0.995426i	$0.469544\pi$
$858$	32.4220	+	9.86427i	1.10687	+	0.336761i
$859$	44.3685	+	11.8885i	1.51383	+	0.405630i	0.917706	−	0.397260i	$-0.130039\pi$
$859$	44.3685	+	11.8885i	1.51383	+	0.405630i	0.596126	+	0.802891i	$0.296706\pi$
$860$	−9.19460	+	4.51545i	−0.313533	+	0.153976i
$861$	−17.1125	−	34.4115i	−0.583193	−	1.17274i
$862$	−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	$-0.341352\pi$
$864$	18.0664	+	25.4323i	0.614632	+	0.865224i
$865$	7.64386	−	13.2396i	0.259899	−	0.450158i
$866$	−0.148331	+	4.41967i	−0.00504048	+	0.150187i
$867$	−11.8424	−	11.8424i	−0.402189	−	0.402189i
$868$	4.13879	−	10.0396i	0.140480	−	0.340767i
$869$	30.4496	−	30.4496i	1.03293	−	1.03293i
$870$	8.19024	−	7.65834i	0.277675	−	0.259642i
$871$	−42.4151	−	24.4884i	−1.43718	−	0.829757i
$872$	−8.91594	−	54.8462i	−0.301932	−	1.85733i
$873$	4.21462	−	2.43331i	0.142643	−	0.0823552i
$874$	13.6019	−	3.15971i	0.460093	−	0.106879i
$875$	2.20474	+	1.46257i	0.0745339	+	0.0494439i
$876$	−18.8696	−	6.44006i	−0.637545	−	0.217590i
$877$	13.2772	−	49.5513i	0.448341	−	1.67323i	−0.258622	−	0.965979i	$-0.583268\pi$
$877$	13.2772	−	49.5513i	0.448341	−	1.67323i	0.706963	−	0.707251i	$-0.250065\pi$
$878$	14.1256	+	26.4796i	0.476716	+	0.893643i
$879$	−12.4322	+	21.5332i	−0.419327	+	0.726296i
$880$	2.53425	−	18.7713i	0.0854297	−	0.632780i
$881$	−2.22810			−0.0750668			−0.0375334	−	0.999295i	$-0.511950\pi$
$881$	−2.22810			−0.0750668			−0.0375334	+	0.999295i	$0.511950\pi$
$882$	−3.54315	−	2.87337i	−0.119304	−	0.0967513i
$883$	8.98791	+	8.98791i	0.302467	+	0.302467i	0.841978	−	0.539511i	$-0.181391\pi$
$883$	8.98791	+	8.98791i	0.302467	+	0.302467i	−0.539511	+	0.841978i	$0.681391\pi$
$884$	15.8748	−	3.13051i	0.533928	−	0.105290i
$885$	2.75118	+	10.2676i	0.0924800	+	0.345140i
$886$	−12.4709	+	40.9893i	−0.418967	+	1.37706i
$887$	−3.46176	+	1.99865i	−0.116235	+	0.0671081i	−0.556990	−	0.830519i	$-0.688044\pi$
$887$	−3.46176	+	1.99865i	−0.116235	+	0.0671081i	0.440756	+	0.897627i	$0.354711\pi$
$888$	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
$891$	33.8718	+	9.07592i	1.13475	+	0.304055i
$892$	−36.4629	−	2.45025i	−1.22087	−	0.0820406i
$893$	−7.73880	+	2.07361i	−0.258969	+	0.0693906i
$894$	−1.34404	+	40.0472i	−0.0449515	+	1.33938i
$895$	−17.8617			−0.597052
$896$	1.05235	−	29.9148i	0.0351565	−	0.999382i
$897$	13.4202			0.448088
$898$	1.64786	−	49.0999i	0.0549899	−	1.63848i
$899$	−9.86331	+	2.64287i	−0.328960	+	0.0881445i
$900$	0.919552	+	0.0617926i	0.0306517	+	0.00205975i
$901$	−24.0268	−	6.43797i	−0.800449	−	0.214480i
$902$	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
$906$	11.5607	−	37.9978i	0.384079	−	1.26239i
$907$	−0.510175	−	1.90400i	−0.0169401	−	0.0632212i	0.956938	−	0.290291i	$-0.0937521\pi$
$907$	−0.510175	−	1.90400i	−0.0169401	−	0.0632212i	−0.973878	+	0.227070i	$0.927085\pi$
$908$	−0.788992	+	0.155589i	−0.0261836	+	0.00516341i
$909$	0.601700	+	0.601700i	0.0199571	+	0.0199571i
$910$	9.16639	−	7.56117i	0.303863	−	0.250650i
$911$	−11.6751			−0.386813			−0.193406	−	0.981119i	$-0.561954\pi$
$911$	−11.6751			−0.386813			−0.193406	+	0.981119i	$0.561954\pi$
$912$	−3.17520	+	23.5188i	−0.105141	+	0.778787i
$913$	−41.8762	+	72.5317i	−1.38590	+	2.40045i
$914$	−1.35574	−	2.54145i	−0.0448439	−	0.0840636i
$915$	4.23564	−	15.8076i	0.140026	−	0.522585i
$916$	−23.8749	−	8.14834i	−0.788850	−	0.269229i
$917$	−0.603757	+	9.70651i	−0.0199378	+	0.320537i
$918$	19.3529	−	4.49566i	0.638742	−	0.148379i
$919$	−22.3691	+	12.9148i	−0.737888	+	0.426020i	−0.821301	−	0.570495i	$-0.806751\pi$
$919$	−22.3691	+	12.9148i	−0.737888	+	0.426020i	0.0834128	+	0.996515i	$0.473418\pi$
$920$	−1.20356	−	7.40370i	−0.0396803	−	0.244093i
$921$	−27.0014	−	15.5893i	−0.889726	−	0.513684i
$922$	−7.05601	+	6.59777i	−0.232377	+	0.217286i
$923$	−29.3235	+	29.3235i	−0.965195	+	0.965195i
$924$	−24.3601	−	31.6365i	−0.801390	−	1.04076i
$925$	−0.807723	−	0.807723i	−0.0265578	−	0.0265578i
$926$	1.26549	−	37.7066i	0.0415865	−	1.23911i
$927$	1.09389	−	1.89468i	0.0359281	−	0.0622294i
$928$	−22.9466	+	16.3006i	−0.753258	+	0.535094i
$929$	−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
$931$	−3.57389	−	25.8171i	−0.117129	−	0.846121i
$932$	−0.297319	+	0.146013i	−0.00973900	+	0.00478281i
$933$	−17.3422	−	4.64683i	−0.567759	−	0.152130i
$934$	−47.8921	−	14.5710i	−1.56708	−	0.476778i
$935$	−10.4473	−	6.03178i	−0.341665	−	0.197260i
$936$	1.46760	−	3.87026i	0.0479699	−	0.126504i
$937$			28.4568i			0.929642i	0.885405	+	0.464821i	$0.153881\pi$
$937$			28.4568i			0.929642i	−0.885405	+	0.464821i	$0.846119\pi$
$938$	23.9467	+	52.5012i	0.781886	+	1.71422i
$939$	−6.82730	+	6.82730i	−0.222801	+	0.222801i
$940$	0.832629	+	4.22226i	0.0271574	+	0.137715i
$941$	−26.3290	+	7.05483i	−0.858300	+	0.229981i	−0.661022	−	0.750367i	$-0.729877\pi$
$941$	−26.3290	+	7.05483i	−0.858300	+	0.229981i	−0.197278	+	0.980348i	$0.563210\pi$
$942$	−9.61272	−	18.0198i	−0.313199	−	0.587118i
$943$	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
$947$	−8.14864	+	30.4111i	−0.264795	+	0.988229i	0.697581	+	0.716506i	$0.254260\pi$
$947$	−8.14864	+	30.4111i	−0.264795	+	0.988229i	−0.962376	+	0.271722i	$0.912407\pi$
$948$	19.0727	+	21.8207i	0.619453	+	0.708703i
$949$	5.14223	+	19.1911i	0.166924	+	0.622968i
$950$	3.59634	+	3.84612i	0.116681	+	0.124785i
$951$			26.4077i			0.856330i
$952$	−17.3714	−	7.85294i	−0.563010	−	0.254515i
$953$			52.8388i			1.71162i	0.517294	+	0.855808i	$0.326939\pi$
$953$			52.8388i			1.71162i	−0.517294	+	0.855808i	$0.673061\pi$
$954$	−4.64783	+	4.34599i	−0.150479	+	0.140706i
$955$	−0.660276	−	2.46418i	−0.0213660	−	0.0797391i
$956$	17.7924	+	1.19563i	0.575448	+	0.0386693i
$957$	−9.71757	+	36.2665i	−0.314124	+	1.17233i
$958$	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
$962$	−4.52644	+	2.41464i	−0.145938	+	0.0778512i
$963$	1.06694	−	0.285885i	0.0343815	−	0.00921251i
$964$	15.9072	−	23.7221i	0.512337	−	0.764037i
$965$	7.46552	−	7.46552i	0.240324	−	0.240324i
$966$	−12.8755	−	9.17775i	−0.414263	−	0.295289i
$967$		−	53.1266i		−	1.70844i	−0.519914	−	0.854218i	$-0.674036\pi$
$967$		−	53.1266i		−	1.70844i	0.519914	−	0.854218i	$-0.325964\pi$
$968$	13.2626	+	29.4647i	0.426276	+	0.947031i
$969$	13.0896	+	7.55731i	0.420500	+	0.242776i
$970$	4.34731	−	14.2888i	0.139584	−	0.458785i
$971$	44.4466	+	11.9094i	1.42636	+	0.382192i	0.887735	−	0.460355i	$-0.152278\pi$
$971$	44.4466	+	11.9094i	1.42636	+	0.382192i	0.538624	+	0.842546i	$0.318944\pi$
$972$	3.06472	−	8.97974i	0.0983010	−	0.288025i
$973$	−31.5469	+	47.5552i	−1.01135	+	1.52455i
$974$	10.5968	−	17.0097i	0.339542	−	0.545027i
$975$	2.53024	+	4.38250i	0.0810325	+	0.140352i
$976$	−15.8458	+	37.9014i	−0.507213	+	1.21320i
$977$	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	$0.137879\pi$
$978$	22.5346	+	0.756292i	0.720576	+	0.0241836i
$979$	−5.63353	−	5.63353i	−0.180048	−	0.180048i
$980$	−13.9653	+	0.985613i	−0.446104	+	0.0314843i
$981$	−6.40141	+	6.40141i	−0.204381	+	0.204381i
$982$	19.2568	+	20.5942i	0.614508	+	0.657188i
$983$	9.13864	+	5.27620i	0.291477	+	0.168284i	0.638608	−	0.769532i	$-0.279511\pi$
$983$	9.13864	+	5.27620i	0.291477	+	0.168284i	−0.347131	+	0.937817i	$0.612844\pi$
$984$	−40.5528	+	6.59237i	−1.29278	+	0.210157i
$985$	−16.0229	+	9.25081i	−0.510531	+	0.294755i
$986$	4.05626	+	17.4614i	0.129178	+	0.556084i
$987$	7.55969	+	5.01491i	0.240628	+	0.159626i
$988$	21.2270	−	10.4245i	0.675320	−	0.331649i
$989$	3.51547	−	13.1199i	0.111786	−	0.417189i
$990$	−2.72281	+	1.45249i	−0.0865366	+	0.0461631i
$991$	−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	$0.914612\pi$
$992$	−8.94349	−	7.40160i	−0.283956	−	0.235001i
$993$	−31.1911			−0.989818
$994$	48.1870	−	8.07975i	1.52840	−	0.256274i
$995$	5.85008	+	5.85008i	0.185460	+	0.185460i
$996$	−46.8150	−	31.3925i	−1.48339	−	0.994709i
$997$	7.89523	+	29.4654i	0.250044	+	0.933178i	0.970781	+	0.239969i	$0.0771372\pi$
$997$	7.89523	+	29.4654i	0.250044	+	0.933178i	−0.720736	+	0.693209i	$0.756196\pi$
$998$	−57.9701	−	17.6372i	−1.83501	−	0.558296i
$999$	−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.221.32	✓	256
7.2	even	3	inner	560.2.cp.a.541.54	yes	256
16.5	even	4	inner	560.2.cp.a.501.54	yes	256
112.37	even	12	inner	560.2.cp.a.261.32	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cp.a.221.32	✓	256	1.1	even	1	trivial
560.2.cp.a.261.32	yes	256	112.37	even	12	inner
560.2.cp.a.501.54	yes	256	16.5	even	4	inner
560.2.cp.a.541.54	yes	256	7.2	even	3	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+(-0.0474363 + 1.41342i) q^{2} +(-1.53919 + 0.412424i) q^{3} +(-1.99550 - 0.134095i) q^{4} +(0.965926 + 0.258819i) 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} +(-0.411639 + 1.35298i) q^{10} +(-1.22561 - 4.57405i) q^{11} +(3.12675 - 0.616595i) q^{12} +(-2.24558 - 2.24558i) q^{13} +(0.618744 + 3.69014i) q^{14} -1.59348 q^{15} +(3.96404 + 0.535172i) q^{16} +(1.27376 - 2.20622i) q^{17} +(-0.306730 - 0.574990i) q^{18} +(0.963667 - 3.59646i) q^{19} +(-1.89280 - 0.645999i) q^{20} +(-3.77495 + 1.87725i) q^{21} +(6.52318 - 1.51533i) q^{22} +(2.29667 - 1.32598i) q^{23} +(0.723184 + 4.44865i) q^{24} +(0.866025 + 0.500000i) q^{25} +(3.28047 - 3.06742i) q^{26} +(3.89951 - 3.89951i) q^{27} +(-5.24506 + 0.699496i) q^{28} +(3.51838 + 3.51838i) q^{29} +(0.0755890 - 2.25226i) q^{30} +(-1.02610 + 1.77726i) q^{31} +(-0.944461 + 5.57745i) q^{32} +(3.77289 + 6.53484i) q^{33} +(3.05789 + 1.90501i) q^{34} +(2.64065 + 0.164252i) q^{35} +(0.827252 - 0.406262i) q^{36} +(-1.10337 - 0.295647i) q^{37} +(5.03758 + 1.53267i) q^{38} +(4.38250 + 2.53024i) q^{39} +(1.00285 - 2.64467i) q^{40} +9.11575i q^{41} +(-2.47426 - 5.42463i) q^{42} +(3.62164 - 3.62164i) q^{43} +(1.83235 + 9.29185i) q^{44} +(-0.445111 + 0.119267i) q^{45} +(1.76522 + 3.30905i) 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} +(-1.05066 + 3.92112i) q^{51} +(4.17994 + 4.78218i) q^{52} +(-2.52714 - 9.43143i) q^{53} +(5.32666 + 5.69662i) q^{54} -4.73540i q^{55} +(-0.739874 - 7.44665i) q^{56} +5.93305i q^{57} +(-5.13984 + 4.80604i) q^{58} +(-1.72652 - 6.44347i) q^{59} +(3.17979 + 0.213678i) q^{60} +(-2.65811 + 9.92018i) 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} +(-9.41542 + 5.02268i) q^{66} +(14.8967 - 3.99156i) q^{67} +(-2.83764 + 4.23171i) q^{68} +(-2.98813 + 2.98813i) q^{69} +(-0.357419 + 3.72455i) q^{70} -13.0583i q^{71} +(0.534976 + 1.18852i) q^{72} +(-5.41803 - 3.12810i) q^{73} +(0.470212 - 1.54550i) q^{74} +(-1.53919 - 0.412424i) q^{75} +(-2.40526 + 7.04750i) q^{76} +(-5.57867 - 11.2181i) q^{77} +(-3.78417 + 6.07428i) q^{78} +(4.54684 + 7.87535i) q^{79} +(3.69045 + 1.54290i) q^{80} +(-3.70261 + 6.41310i) q^{81} +(-12.8844 - 0.432418i) q^{82} +(-12.5062 - 12.5062i) q^{83} +(7.78464 - 3.23984i) q^{84} +(1.80137 - 1.80137i) q^{85} +(4.94709 + 5.29068i) q^{86} +(-6.86650 - 3.96438i) q^{87} +(-13.2202 + 2.14911i) q^{88} +(1.45703 - 0.841218i) q^{89} +(-0.147460 - 0.634786i) q^{90} +(-7.00167 - 4.64473i) q^{91} +(-4.76081 + 2.33803i) q^{92} +(0.846379 - 3.15873i) q^{93} +(2.68494 - 1.43229i) q^{94} +(1.86166 - 3.22449i) q^{95} +(-0.846573 - 8.97426i) q^{96} -10.5610 q^{97} +(3.54108 + 9.24450i) 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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