LMFDB - Embedded newform 666.2.k.a.529.28

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.28
Character	$\chi$	$=$	666.529
Dual form			666.2.k.a.175.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(-0.0457663 + 1.73145i) q^{3} -1.00000 q^{4} +3.78289i q^{5} +(-1.73145 - 0.0457663i) q^{6} +(-1.89981 - 3.29056i) q^{7} -1.00000i q^{8} +(-2.99581 - 0.158484i) q^{9} -3.78289 q^{10} +(1.77832 - 3.08014i) q^{11} +(0.0457663 - 1.73145i) q^{12} +6.52550i q^{13} +(3.29056 - 1.89981i) q^{14} +(-6.54987 - 0.173129i) q^{15} +1.00000 q^{16} +(-4.62329 + 2.66926i) q^{17} +(0.158484 - 2.99581i) q^{18} +(-6.07373 - 3.50667i) q^{19} -3.78289i q^{20} +(5.78438 - 3.13882i) q^{21} +(3.08014 + 1.77832i) q^{22} +(3.59070 - 2.07309i) q^{23} +(1.73145 + 0.0457663i) q^{24} -9.31025 q^{25} -6.52550 q^{26} +(0.411513 - 5.17983i) q^{27} +(1.89981 + 3.29056i) q^{28} +(0.972944 + 0.561729i) q^{29} +(0.173129 - 6.54987i) q^{30} +(-5.60626 + 3.23677i) q^{31} +1.00000i q^{32} +(5.25171 + 3.22003i) q^{33} +(-2.66926 - 4.62329i) q^{34} +(12.4478 - 7.18677i) q^{35} +(2.99581 + 0.158484i) q^{36} +(6.08085 - 0.152657i) q^{37} +(3.50667 - 6.07373i) q^{38} +(-11.2985 - 0.298648i) q^{39} +3.78289 q^{40} +2.48234 q^{41} +(3.13882 + 5.78438i) q^{42} +(7.59704 + 4.38615i) q^{43} +(-1.77832 + 3.08014i) q^{44} +(0.599527 - 11.3328i) q^{45} +(2.07309 + 3.59070i) q^{46} +(-0.437914 + 0.758489i) q^{47} +(-0.0457663 + 1.73145i) q^{48} +(-3.71854 + 6.44071i) q^{49} -9.31025i q^{50} +(-4.41009 - 8.12714i) q^{51} -6.52550i q^{52} +(0.0157288 + 0.0272431i) q^{53} +(5.17983 + 0.411513i) q^{54} +(11.6518 + 6.72718i) q^{55} +(-3.29056 + 1.89981i) q^{56} +(6.34958 - 10.3558i) q^{57} +(-0.561729 + 0.972944i) q^{58} +(2.15572 + 1.24461i) q^{59} +(6.54987 + 0.173129i) q^{60} +(-1.89687 + 1.09516i) q^{61} +(-3.23677 - 5.60626i) q^{62} +(5.16997 + 10.1590i) q^{63} -1.00000 q^{64} -24.6852 q^{65} +(-3.22003 + 5.25171i) q^{66} -9.95292 q^{67} +(4.62329 - 2.66926i) q^{68} +(3.42511 + 6.31197i) q^{69} +(7.18677 + 12.4478i) q^{70} +(-3.85480 + 6.67671i) q^{71} +(-0.158484 + 2.99581i) q^{72} -2.11142 q^{73} +(0.152657 + 6.08085i) q^{74} +(0.426096 - 16.1202i) q^{75} +(6.07373 + 3.50667i) q^{76} -13.5139 q^{77} +(0.298648 - 11.2985i) q^{78} +(-7.55528 + 4.36204i) q^{79} +3.78289i q^{80} +(8.94977 + 0.949575i) q^{81} +2.48234i q^{82} -9.16307 q^{83} +(-5.78438 + 3.13882i) q^{84} +(-10.0975 - 17.4894i) q^{85} +(-4.38615 + 7.59704i) q^{86} +(-1.01713 + 1.65889i) q^{87} +(-3.08014 - 1.77832i) q^{88} +(-3.27769 + 1.89238i) q^{89} +(11.3328 + 0.599527i) q^{90} +(21.4726 - 12.3972i) q^{91} +(-3.59070 + 2.07309i) q^{92} +(-5.34772 - 9.85507i) q^{93} +(-0.758489 - 0.437914i) q^{94} +(13.2653 - 22.9762i) q^{95} +(-1.73145 - 0.0457663i) q^{96} +(6.74841 + 3.89619i) q^{97} +(-6.44071 - 3.71854i) q^{98} +(-5.81566 + 8.94568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.0457663	+	1.73145i	−0.0264232	+	0.999651i
$3$	−0.0457663	+	1.73145i	−0.0264232	+	0.999651i
$4$	−1.00000			−0.500000
$5$			3.78289i			1.69176i	0.533373	+	0.845880i	$0.320924\pi$
$5$			3.78289i			1.69176i	−0.533373	+	0.845880i	$0.679076\pi$
$6$	−1.73145	−	0.0457663i	−0.706860	−	0.0186840i
$7$	−1.89981	−	3.29056i	−0.718060	−	1.24372i	−0.961767	−	0.273868i	$-0.911697\pi$
$7$	−1.89981	−	3.29056i	−0.718060	−	1.24372i	0.243707	−	0.969849i	$-0.421636\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.99581	−	0.158484i	−0.998604	−	0.0528279i
$10$	−3.78289			−1.19625
$11$	1.77832	−	3.08014i	0.536183	−	0.928696i	−0.462922	−	0.886399i	$-0.653199\pi$
$11$	1.77832	−	3.08014i	0.536183	−	0.928696i	0.999105	−	0.0422974i	$-0.0134677\pi$
$12$	0.0457663	−	1.73145i	0.0132116	−	0.499825i
$13$			6.52550i			1.80985i	0.425573	+	0.904924i	$0.360072\pi$
$13$			6.52550i			1.80985i	−0.425573	+	0.904924i	$0.639928\pi$
$14$	3.29056	−	1.89981i	0.879440	−	0.507745i
$15$	−6.54987	−	0.173129i	−1.69117	−	0.0447017i
$16$	1.00000			0.250000
$17$	−4.62329	+	2.66926i	−1.12131	+	0.647391i	−0.941736	−	0.336353i	$-0.890806\pi$
$17$	−4.62329	+	2.66926i	−1.12131	+	0.647391i	−0.179577	+	0.983744i	$0.557473\pi$
$18$	0.158484	−	2.99581i	0.0373550	−	0.706119i
$19$	−6.07373	−	3.50667i	−1.39341	−	0.804485i	−0.399718	−	0.916638i	$-0.630892\pi$
$19$	−6.07373	−	3.50667i	−1.39341	−	0.804485i	−0.993691	+	0.112154i	$0.964225\pi$
$20$		−	3.78289i		−	0.845880i
$21$	5.78438	−	3.13882i	1.26226	−	0.684946i
$22$	3.08014	+	1.77832i	0.656688	+	0.379139i
$23$	3.59070	−	2.07309i	0.748712	−	0.432269i	−0.0765164	−	0.997068i	$-0.524380\pi$
$23$	3.59070	−	2.07309i	0.748712	−	0.432269i	0.825228	+	0.564799i	$0.191046\pi$
$24$	1.73145	+	0.0457663i	0.353430	+	0.00934201i
$25$	−9.31025			−1.86205
$26$	−6.52550			−1.27976
$27$	0.411513	−	5.17983i	0.0791958	−	0.996859i
$28$	1.89981	+	3.29056i	0.359030	+	0.621858i
$29$	0.972944	+	0.561729i	0.180671	+	0.104311i	0.587608	−	0.809146i	$-0.300070\pi$
$29$	0.972944	+	0.561729i	0.180671	+	0.104311i	−0.406937	+	0.913456i	$0.633403\pi$
$30$	0.173129	−	6.54987i	0.0316089	−	1.19584i
$31$	−5.60626	+	3.23677i	−1.00691	+	0.581342i	−0.910286	−	0.413979i	$-0.864139\pi$
$31$	−5.60626	+	3.23677i	−1.00691	+	0.581342i	−0.0966269	+	0.995321i	$0.530805\pi$
$32$			1.00000i			0.176777i
$33$	5.25171	+	3.22003i	0.914205	+	0.560535i
$34$	−2.66926	−	4.62329i	−0.457774	−	0.792888i
$35$	12.4478	−	7.18677i	2.10407	−	1.21479i
$36$	2.99581	+	0.158484i	0.499302	+	0.0264140i
$37$	6.08085	−	0.152657i	0.999685	−	0.0250967i
$37$	6.08085	−	0.152657i	0.999685	−	0.0250967i
$38$	3.50667	−	6.07373i	0.568857	−	0.985289i
$39$	−11.2985	−	0.298648i	−1.80922	−	0.0478220i
$40$	3.78289			0.598127
$41$	2.48234			0.387676			0.193838	−	0.981034i	$-0.437906\pi$
$41$	2.48234			0.387676			0.193838	+	0.981034i	$0.437906\pi$
$42$	3.13882	+	5.78438i	0.484330	+	0.892550i
$43$	7.59704	+	4.38615i	1.15854	+	0.668882i	0.950953	−	0.309335i	$-0.100107\pi$
$43$	7.59704	+	4.38615i	1.15854	+	0.668882i	0.207584	+	0.978217i	$0.433440\pi$
$44$	−1.77832	+	3.08014i	−0.268092	+	0.464348i
$45$	0.599527	−	11.3328i	0.0893722	−	1.68940i
$46$	2.07309	+	3.59070i	0.305660	+	0.529419i
$47$	−0.437914	+	0.758489i	−0.0638763	+	0.110637i	−0.896195	−	0.443660i	$-0.853680\pi$
$47$	−0.437914	+	0.758489i	−0.0638763	+	0.110637i	0.832319	+	0.554297i	$0.187013\pi$
$48$	−0.0457663	+	1.73145i	−0.00660580	+	0.249913i
$49$	−3.71854	+	6.44071i	−0.531220	+	0.920101i
$50$		−	9.31025i		−	1.31667i
$51$	−4.41009	−	8.12714i	−0.617536	−	1.13803i
$52$		−	6.52550i		−	0.904924i
$53$	0.0157288	+	0.0272431i	0.00216052	+	0.00374213i	0.867104	−	0.498128i	$-0.165979\pi$
$53$	0.0157288	+	0.0272431i	0.00216052	+	0.00374213i	−0.864943	+	0.501870i	$0.832646\pi$
$54$	5.17983	+	0.411513i	0.704886	+	0.0559999i
$55$	11.6518	+	6.72718i	1.57113	+	0.907093i
$56$	−3.29056	+	1.89981i	−0.439720	+	0.253873i
$57$	6.34958	−	10.3558i	0.841022	−	1.37166i
$58$	−0.561729	+	0.972944i	−0.0737587	+	0.127754i
$59$	2.15572	+	1.24461i	0.280651	+	0.162034i	0.633718	−	0.773564i	$-0.281528\pi$
$59$	2.15572	+	1.24461i	0.280651	+	0.162034i	−0.353067	+	0.935598i	$0.614861\pi$
$60$	6.54987	+	0.173129i	0.845585	+	0.0223509i
$61$	−1.89687	+	1.09516i	−0.242870	+	0.140221i	−0.616495	−	0.787359i	$-0.711448\pi$
$61$	−1.89687	+	1.09516i	−0.242870	+	0.140221i	0.373625	+	0.927580i	$0.378115\pi$
$62$	−3.23677	−	5.60626i	−0.411071	−	0.711995i
$63$	5.16997	+	10.1590i	0.651354	+	1.27991i
$64$	−1.00000			−0.125000
$65$	−24.6852			−3.06183
$66$	−3.22003	+	5.25171i	−0.396358	+	0.646440i
$67$	−9.95292			−1.21594			−0.607971	−	0.793959i	$-0.708016\pi$
$67$	−9.95292			−1.21594			−0.607971	+	0.793959i	$0.708016\pi$
$68$	4.62329	−	2.66926i	0.560657	−	0.323695i
$69$	3.42511	+	6.31197i	0.412335	+	0.759872i
$70$	7.18677	+	12.4478i	0.858983	+	1.48780i
$71$	−3.85480	+	6.67671i	−0.457481	+	0.792379i	−0.998827	−	0.0484201i	$-0.984581\pi$
$71$	−3.85480	+	6.67671i	−0.457481	+	0.792379i	0.541347	+	0.840800i	$0.317915\pi$
$72$	−0.158484	+	2.99581i	−0.0186775	+	0.353060i
$73$	−2.11142			−0.247123			−0.123562	−	0.992337i	$-0.539432\pi$
$73$	−2.11142			−0.247123			−0.123562	+	0.992337i	$0.539432\pi$
$74$	0.152657	+	6.08085i	0.0177461	+	0.706884i
$75$	0.426096	−	16.1202i	0.0492013	−	1.86140i
$76$	6.07373	+	3.50667i	0.696704	+	0.402242i
$77$	−13.5139			−1.54005
$78$	0.298648	−	11.2985i	0.0338152	−	1.27931i
$79$	−7.55528	+	4.36204i	−0.850035	+	0.490768i	−0.860663	−	0.509175i	$-0.829950\pi$
$79$	−7.55528	+	4.36204i	−0.850035	+	0.490768i	0.0106275	+	0.999944i	$0.496617\pi$
$80$			3.78289i			0.422940i
$81$	8.94977	+	0.949575i	0.994418	+	0.105508i
$82$			2.48234i			0.274128i
$83$	−9.16307			−1.00578			−0.502889	−	0.864351i	$-0.667730\pi$
$83$	−9.16307			−1.00578			−0.502889	+	0.864351i	$0.667730\pi$
$84$	−5.78438	+	3.13882i	−0.631128	+	0.342473i
$85$	−10.0975	−	17.4894i	−1.09523	−	1.89699i
$86$	−4.38615	+	7.59704i	−0.472971	+	0.819209i
$87$	−1.01713	+	1.65889i	−0.109048	+	0.177852i
$88$	−3.08014	−	1.77832i	−0.328344	−	0.189569i
$89$	−3.27769	+	1.89238i	−0.347435	+	0.200592i	−0.663555	−	0.748128i	$-0.730953\pi$
$89$	−3.27769	+	1.89238i	−0.347435	+	0.200592i	0.316120	+	0.948719i	$0.397620\pi$
$90$	11.3328	+	0.599527i	1.19458	+	0.0631957i
$91$	21.4726	−	12.3972i	2.25094	−	1.29958i
$92$	−3.59070	+	2.07309i	−0.374356	+	0.216134i
$93$	−5.34772	−	9.85507i	−0.554533	−	1.02192i
$94$	−0.758489	−	0.437914i	−0.0782322	−	0.0451674i
$95$	13.2653	−	22.9762i	1.36099	−	2.35731i
$96$	−1.73145	−	0.0457663i	−0.176715	−	0.00467101i
$97$	6.74841	+	3.89619i	0.685197	+	0.395599i	0.801810	−	0.597579i	$-0.203870\pi$
$97$	6.74841	+	3.89619i	0.685197	+	0.395599i	−0.116613	+	0.993177i	$0.537204\pi$
$98$	−6.44071	−	3.71854i	−0.650609	−	0.375630i
$99$	−5.81566	+	8.94568i	−0.584496	+	0.899074i
$100$	9.31025			0.931025
$101$	−2.50080	+	4.33151i	−0.248839	+	0.431001i	−0.963204	−	0.268772i	$-0.913382\pi$
$101$	−2.50080	+	4.33151i	−0.248839	+	0.431001i	0.714365	+	0.699773i	$0.246716\pi$
$102$	8.12714	−	4.41009i	0.804707	−	0.436664i
$103$	−6.41703	+	3.70487i	−0.632289	+	0.365052i	−0.781638	−	0.623732i	$-0.785616\pi$
$103$	−6.41703	+	3.70487i	−0.632289	+	0.365052i	0.149349	+	0.988785i	$0.452282\pi$
$104$	6.52550			0.639878
$105$	11.8738	+	21.8817i	1.15876	+	2.13543i
$106$	−0.0272431	+	0.0157288i	−0.00264609	+	0.00152772i
$107$	−5.60178	+	9.70257i	−0.541545	+	0.937983i	0.457271	+	0.889327i	$0.348827\pi$
$107$	−5.60178	+	9.70257i	−0.541545	+	0.937983i	−0.998816	+	0.0486553i	$0.984506\pi$
$108$	−0.411513	+	5.17983i	−0.0395979	+	0.498430i
$109$	−5.21732	+	3.01222i	−0.499728	+	0.288518i	−0.728601	−	0.684938i	$-0.759829\pi$
$109$	−5.21732	+	3.01222i	−0.499728	+	0.288518i	0.228873	+	0.973456i	$0.426496\pi$
$110$	−6.72718	+	11.6518i	−0.641412	+	1.11096i
$111$	−0.0139800	+	10.5356i	−0.00132692	+	0.999999i
$112$	−1.89981	−	3.29056i	−0.179515	−	0.310929i
$113$	1.77040	+	1.02214i	0.166545	+	0.0961547i	0.580956	−	0.813935i	$-0.302679\pi$
$113$	1.77040	+	1.02214i	0.166545	+	0.0961547i	−0.414411	+	0.910090i	$0.636012\pi$
$114$	10.3558	+	6.34958i	0.969913	+	0.594692i
$115$	7.84227	+	13.5832i	0.731295	+	1.26664i
$116$	−0.972944	−	0.561729i	−0.0903356	−	0.0521553i
$117$	1.03419	−	19.5492i	0.0956105	−	1.80732i
$118$	−1.24461	+	2.15572i	−0.114575	+	0.198450i
$119$	17.5667	+	10.1422i	1.61034	+	0.929731i
$120$	−0.173129	+	6.54987i	−0.0158044	+	0.597919i
$121$	−0.824832	−	1.42865i	−0.0749847	−	0.129877i
$122$	−1.09516	−	1.89687i	−0.0991512	−	0.171735i
$123$	−0.113607	+	4.29803i	−0.0102436	+	0.387540i
$124$	5.60626	−	3.23677i	0.503457	−	0.290671i
$125$		−	16.3052i		−	1.45838i
$126$	−10.1590	+	5.16997i	−0.905035	+	0.460577i
$127$	3.65273	+	6.32671i	0.324127	+	0.561405i	0.981335	−	0.192304i	$-0.0615961\pi$
$127$	3.65273	+	6.32671i	0.324127	+	0.561405i	−0.657208	+	0.753709i	$0.728263\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−7.94207	+	12.9531i	−0.699260	+	1.14046i
$130$		−	24.6852i		−	2.16504i
$131$	3.59118	+	2.07337i	0.313763	+	0.181151i	0.648609	−	0.761122i	$-0.275351\pi$
$131$	3.59118	+	2.07337i	0.313763	+	0.181151i	−0.334846	+	0.942273i	$0.608684\pi$
$132$	−5.25171	−	3.22003i	−0.457102	−	0.280268i
$133$			26.6480i			2.31067i
$134$		−	9.95292i		−	0.859801i
$135$	19.5947	+	1.55671i	1.68645	+	0.133980i
$136$	2.66926	+	4.62329i	0.228887	+	0.396444i
$137$	6.03331	−	10.4500i	0.515461	−	0.892804i	−0.484378	−	0.874859i	$-0.660954\pi$
$137$	6.03331	−	10.4500i	0.515461	−	0.892804i	0.999839	−	0.0179453i	$-0.00571247\pi$
$138$	−6.31197	+	3.42511i	−0.537311	+	0.291565i
$139$	−6.15945	+	10.6685i	−0.522438	+	0.904889i	0.477221	+	0.878783i	$0.341644\pi$
$139$	−6.15945	+	10.6685i	−0.522438	+	0.904889i	−0.999659	+	0.0261056i	$0.991689\pi$
$140$	−12.4478	+	7.18677i	−1.05203	+	0.607393i
$141$	−1.29324	−	0.792937i	−0.108911	−	0.0667774i
$142$	−6.67671	−	3.85480i	−0.560297	−	0.323488i
$143$	20.0994	+	11.6044i	1.68080	+	0.970410i
$144$	−2.99581	−	0.158484i	−0.249651	−	0.0132070i
$145$	−2.12496	+	3.68054i	−0.176468	+	0.305652i
$146$		−	2.11142i		−	0.174742i
$147$	−10.9815	−	6.73322i	−0.905743	−	0.555347i
$148$	−6.08085	+	0.152657i	−0.499843	+	0.0125484i
$149$	−5.80060	−	10.0469i	−0.475203	−	0.823076i	0.524393	−	0.851476i	$-0.324292\pi$
$149$	−5.80060	−	10.0469i	−0.475203	−	0.823076i	−0.999597	+	0.0283998i	$0.990959\pi$
$150$	16.1202	+	0.426096i	1.31621	+	0.0347906i
$151$	−5.18257	−	8.97647i	−0.421751	−	0.730495i	0.574360	−	0.818603i	$-0.305251\pi$
$151$	−5.18257	−	8.97647i	−0.421751	−	0.730495i	−0.996111	+	0.0881083i	$0.971918\pi$
$152$	−3.50667	+	6.07373i	−0.284428	+	0.492644i
$153$	14.2735	−	7.26388i	1.15395	−	0.587250i
$154$		−	13.5139i		−	1.08898i
$155$	−12.2444	−	21.2078i	−0.983490	−	1.70346i
$156$	11.2985	+	0.298648i	0.904608	+	0.0239110i
$157$	0.940595	−	1.62916i	0.0750676	−	0.130021i	−0.826048	−	0.563600i	$-0.809416\pi$
$157$	0.940595	−	1.62916i	0.0750676	−	0.130021i	0.901116	+	0.433579i	$0.142749\pi$
$158$	−4.36204	−	7.55528i	−0.347025	−	0.601066i
$159$	−0.0478898	+	0.0259868i	−0.00379791	+	0.00206089i
$160$	−3.78289			−0.299064
$161$	−13.6433	−	7.87694i	−1.07524	−	0.620790i
$162$	−0.949575	+	8.94977i	−0.0746057	+	0.703160i
$163$	−7.34906	+	4.24298i	−0.575623	+	0.332336i	−0.759392	−	0.650633i	$-0.774503\pi$
$163$	−7.34906	+	4.24298i	−0.575623	+	0.332336i	0.183769	+	0.982969i	$0.441170\pi$
$164$	−2.48234			−0.193838
$165$	−12.1810	+	19.8666i	−0.948291	+	1.54661i
$166$		−	9.16307i		−	0.711192i
$167$			5.65327i			0.437463i	0.975785	+	0.218732i	$0.0701919\pi$
$167$			5.65327i			0.437463i	−0.975785	+	0.218732i	$0.929808\pi$
$168$	−3.13882	−	5.78438i	−0.242165	−	0.446275i
$169$	−29.5821			−2.27555
$170$	17.4894	−	10.0975i	1.34138	−	0.774444i
$171$	17.6400	+	11.4679i	1.34896	+	0.876972i
$172$	−7.59704	−	4.38615i	−0.579269	−	0.334441i
$173$	21.2223			1.61350			0.806750	−	0.590893i	$-0.201224\pi$
$173$	21.2223			1.61350			0.806750	+	0.590893i	$0.201224\pi$
$174$	−1.65889	−	1.01713i	−0.125760	−	0.0771086i
$175$	17.6877	+	30.6360i	1.33706	+	2.31586i
$176$	1.77832	−	3.08014i	0.134046	−	0.232174i
$177$	−2.25363	+	3.67556i	−0.169393	+	0.276272i
$178$	−1.89238	−	3.27769i	−0.141840	−	0.245674i
$179$		−	16.1183i		−	1.20474i	−0.798217	−	0.602370i	$-0.794223\pi$
$179$		−	16.1183i		−	1.20474i	0.798217	−	0.602370i	$-0.205777\pi$
$180$	−0.599527	+	11.3328i	−0.0446861	+	0.844699i
$181$	−5.95064	+	10.3068i	−0.442307	+	0.766099i	−0.997860	−	0.0653822i	$-0.979173\pi$
$181$	−5.95064	+	10.3068i	−0.442307	+	0.766099i	0.555553	+	0.831481i	$0.312507\pi$
$182$	12.3972	+	21.4726i	0.918941	+	1.59165i
$183$	−1.80940	−	3.33446i	−0.133755	−	0.246490i
$184$	−2.07309	−	3.59070i	−0.152830	−	0.264710i
$185$	0.577486	+	23.0032i	0.0424576	+	1.69123i
$186$	9.85507	−	5.34772i	0.722608	−	0.392114i
$187$			18.9872i			1.38848i
$188$	0.437914	−	0.758489i	0.0319381	−	0.0553185i
$189$	−17.8264	+	8.48658i	−1.29668	+	0.617308i
$190$	22.9762	+	13.2653i	1.66687	+	0.962369i
$191$	13.8276	+	7.98336i	1.00053	+	0.577655i	0.908405	−	0.418092i	$-0.137301\pi$
$191$	13.8276	+	7.98336i	1.00053	+	0.577655i	0.0921238	+	0.995748i	$0.470634\pi$
$192$	0.0457663	−	1.73145i	0.00330290	−	0.124956i
$193$	0.429176	−	0.247785i	0.0308928	−	0.0178359i	−0.484474	−	0.874806i	$-0.660989\pi$
$193$	0.429176	−	0.247785i	0.0308928	−	0.0178359i	0.515367	+	0.856970i	$0.327656\pi$
$194$	−3.89619	+	6.74841i	−0.279730	+	0.484507i
$195$	1.12975	−	42.7412i	0.0809033	−	3.06076i
$196$	3.71854	−	6.44071i	0.265610	−	0.460050i
$197$	1.11213	+	1.92627i	0.0792363	+	0.137241i	0.902921	−	0.429807i	$-0.141419\pi$
$197$	1.11213	+	1.92627i	0.0792363	+	0.137241i	−0.823684	+	0.567049i	$0.808085\pi$
$198$	−8.94568	−	5.81566i	−0.635741	−	0.413301i
$199$		−	1.73848i		−	0.123238i	−0.998100	−	0.0616189i	$-0.980374\pi$
$199$		−	1.73848i		−	0.123238i	0.998100	−	0.0616189i	$-0.0196263\pi$
$200$			9.31025i			0.658334i
$201$	0.455509	−	17.2329i	0.0321291	−	1.21552i
$202$	−4.33151	−	2.50080i	−0.304764	−	0.175955i
$203$		−	4.26871i		−	0.299605i
$204$	4.41009	+	8.12714i	0.308768	+	0.569014i
$205$			9.39040i			0.655854i
$206$	−3.70487	−	6.41703i	−0.258131	−	0.447096i
$207$	−11.0856	+	5.64152i	−0.770502	+	0.392112i
$208$			6.52550i			0.452462i
$209$	−21.6020	+	12.4719i	−1.49424	+	0.862702i
$210$	−21.8817	+	11.8738i	−1.50998	+	0.819370i
$211$	2.55247	+	4.42101i	0.175719	+	0.304355i	0.940410	−	0.340043i	$-0.110442\pi$
$211$	2.55247	+	4.42101i	0.175719	+	0.304355i	−0.764691	+	0.644398i	$0.777108\pi$
$212$	−0.0157288	−	0.0272431i	−0.00108026	−	0.00187106i
$213$	−11.3839	−	6.97995i	−0.780015	−	0.478258i
$214$	−9.70257	−	5.60178i	−0.663254	−	0.382930i
$215$	−16.5923	+	28.7387i	−1.13159	+	1.95997i
$216$	−5.17983	−	0.411513i	−0.352443	−	0.0279999i
$217$	21.3016	+	12.2985i	1.44605	+	0.834876i
$218$	−3.01222	−	5.21732i	−0.204013	−	0.353361i
$219$	0.0966320	−	3.65581i	0.00652978	−	0.247037i
$220$	−11.6518	−	6.72718i	−0.785566	−	0.453547i
$221$	−17.4183	−	30.1693i	−1.17168	−	2.02941i
$222$	−10.5356	−	0.0139800i	−0.707106	−	0.000938274i
$223$	4.54804	−	7.87744i	0.304560	−	0.527513i	−0.672604	−	0.740003i	$-0.734824\pi$
$223$	4.54804	−	7.87744i	0.304560	−	0.527513i	0.977163	+	0.212490i	$0.0681574\pi$
$224$	3.29056	−	1.89981i	0.219860	−	0.126936i
$225$	27.8918	+	1.47552i	1.85945	+	0.0983683i
$226$	−1.02214	+	1.77040i	−0.0679916	+	0.117765i
$227$	6.45725	−	3.72810i	0.428583	−	0.247442i	−0.270160	−	0.962815i	$-0.587077\pi$
$227$	6.45725	−	3.72810i	0.428583	−	0.247442i	0.698743	+	0.715373i	$0.253743\pi$
$228$	−6.34958	+	10.3558i	−0.420511	+	0.685832i
$229$	25.1134			1.65954			0.829769	−	0.558106i	$-0.188472\pi$
$229$	25.1134			1.65954			0.829769	+	0.558106i	$0.188472\pi$
$230$	−13.5832	+	7.84227i	−0.895650	+	0.517104i
$231$	0.618479	−	23.3985i	0.0406930	−	1.53951i
$232$	0.561729	−	0.972944i	0.0368793	−	0.0638769i
$233$	22.4357			1.46981			0.734906	−	0.678169i	$-0.237226\pi$
$233$	22.4357			1.46981			0.734906	+	0.678169i	$0.237226\pi$
$234$	19.5492	+	1.03419i	1.27797	+	0.0676069i
$235$	−2.86928	−	1.65658i	−0.187171	−	0.108063i
$236$	−2.15572	−	1.24461i	−0.140326	−	0.0810170i
$237$	−7.20686	−	13.2812i	−0.468136	−	0.862706i
$238$	−10.1422	+	17.5667i	−0.657419	+	1.13868i
$239$	22.0496	+	12.7303i	1.42627	+	0.823457i	0.996824	−	0.0796358i	$-0.0253757\pi$
$239$	22.0496	+	12.7303i	1.42627	+	0.823457i	0.429445	+	0.903093i	$0.358709\pi$
$240$	−6.54987	−	0.173129i	−0.422792	−	0.0111754i
$241$	−17.2958	+	9.98575i	−1.11412	+	0.643238i	−0.939894	−	0.341467i	$-0.889076\pi$
$241$	−17.2958	+	9.98575i	−1.11412	+	0.643238i	−0.174228	+	0.984705i	$0.555743\pi$
$242$	1.42865	−	0.824832i	0.0918371	−	0.0530222i
$243$	−2.05374	+	15.4526i	−0.131747	+	0.991283i
$244$	1.89687	−	1.09516i	0.121435	−	0.0701105i
$245$	−24.3645	−	14.0668i	−1.55659	−	0.898697i
$246$	−4.29803	−	0.113607i	−0.274032	−	0.00724334i
$247$	22.8828	−	39.6341i	1.45599	−	2.52186i
$248$	3.23677	+	5.60626i	0.205535	+	0.355998i
$249$	0.419360	−	15.8654i	0.0265759	−	1.00543i
$250$	16.3052			1.03123
$251$			10.5602i			0.666555i	0.942829	+	0.333278i	$0.108155\pi$
$251$			10.5602i			0.666555i	−0.942829	+	0.333278i	$0.891845\pi$
$252$	−5.16997	−	10.1590i	−0.325677	−	0.639957i
$253$		−	14.7464i		−	0.927101i
$254$	−6.32671	+	3.65273i	−0.396973	+	0.229193i
$255$	30.7441	−	16.6829i	1.92527	−	1.04472i
$256$	1.00000			0.0625000
$257$	2.10324	+	1.21431i	0.131197	+	0.0757465i	0.564162	−	0.825664i	$-0.309199\pi$
$257$	2.10324	+	1.21431i	0.131197	+	0.0757465i	−0.432965	+	0.901411i	$0.642533\pi$
$258$	−12.9531	−	7.94207i	−0.806426	−	0.494452i
$259$	−12.0548	−	19.7194i	−0.749047	−	1.22530i
$260$	24.6852			1.53091
$261$	−2.82573	−	1.83703i	−0.174908	−	0.113709i
$262$	−2.07337	+	3.59118i	−0.128093	+	0.221864i
$263$	−0.928226	−	1.60773i	−0.0572369	−	0.0991372i	0.835987	−	0.548749i	$-0.184896\pi$
$263$	−0.928226	−	1.60773i	−0.0572369	−	0.0991372i	−0.893224	+	0.449612i	$0.851562\pi$
$264$	3.22003	−	5.25171i	0.198179	−	0.323220i
$265$	−0.103058	+	0.0595004i	−0.00633078	+	0.00365508i
$266$	−26.6480			−1.63389
$267$	−3.12654	−	5.76176i	−0.191341	−	0.352614i
$268$	9.95292			0.607971
$269$	23.3816			1.42560			0.712802	−	0.701365i	$-0.247426\pi$
$269$	23.3816			1.42560			0.712802	+	0.701365i	$0.247426\pi$
$270$	−1.55671	+	19.5947i	−0.0947384	+	1.19250i
$271$	−12.5435	−	21.7261i	−0.761966	−	1.31976i	−0.941836	−	0.336074i	$-0.890901\pi$
$271$	−12.5435	−	21.7261i	−0.761966	−	1.31976i	0.179870	−	0.983690i	$-0.442432\pi$
$272$	−4.62329	+	2.66926i	−0.280328	+	0.161848i
$273$	20.4824	+	37.7460i	1.23965	+	2.28449i
$274$	10.4500	+	6.03331i	0.631308	+	0.364486i
$275$	−16.5566	+	28.6769i	−0.998400	+	1.72928i
$276$	−3.42511	−	6.31197i	−0.206167	−	0.379936i
$277$	28.1459	−	16.2500i	1.69112	−	0.976371i	0.737511	−	0.675335i	$-0.236001\pi$
$277$	28.1459	−	16.2500i	1.69112	−	0.976371i	0.953613	−	0.301036i	$-0.0973323\pi$
$278$	−10.6685	−	6.15945i	−0.639853	−	0.369419i
$279$	17.3083	−	8.80826i	1.03622	−	0.527337i
$280$	−7.18677	−	12.4478i	−0.429491	−	0.743901i
$281$			2.54304i			0.151705i	0.997119	+	0.0758526i	$0.0241679\pi$
$281$			2.54304i			0.151705i	−0.997119	+	0.0758526i	$0.975832\pi$
$282$	0.792937	−	1.29324i	0.0472187	−	0.0770114i
$283$		−	21.7227i		−	1.29128i	−0.763642	−	0.645639i	$-0.776591\pi$
$283$		−	21.7227i		−	1.29128i	0.763642	−	0.645639i	$-0.223409\pi$
$284$	3.85480	−	6.67671i	0.228740	−	0.396190i
$285$	39.1750	+	24.0198i	2.32053	+	1.42281i
$286$	−11.6044	+	20.0994i	−0.686183	+	1.18850i
$287$	−4.71596	−	8.16828i	−0.278374	−	0.482159i
$288$	0.158484	−	2.99581i	0.00933875	−	0.176530i
$289$	5.74989	−	9.95911i	0.338229	−	0.585830i
$290$	−3.68054	−	2.12496i	−0.216129	−	0.124782i
$291$	−7.05490	+	11.5062i	−0.413566	+	0.674505i
$292$	2.11142			0.123562
$293$	0.539294			0.0315059			0.0157529	−	0.999876i	$-0.494985\pi$
$293$	0.539294			0.0315059			0.0157529	+	0.999876i	$0.494985\pi$
$294$	6.73322	−	10.9815i	0.392690	−	0.640457i
$295$	−4.70821	+	8.15486i	−0.274123	+	0.474795i
$296$	−0.152657	−	6.08085i	−0.00887303	−	0.353442i
$297$	−15.2228	−	10.4789i	−0.883316	−	0.608048i
$298$	10.0469	−	5.80060i	0.582003	−	0.336020i
$299$	13.5279	+	23.4311i	0.782341	+	1.35505i
$300$	−0.426096	+	16.1202i	−0.0246007	+	0.930700i
$301$		−	33.3314i		−	1.92119i
$302$	8.97647	−	5.18257i	0.516538	−	0.298223i
$303$	−7.38532	−	4.52823i	−0.424275	−	0.260140i
$304$	−6.07373	−	3.50667i	−0.348352	−	0.201121i
$305$	−4.14287	−	7.17566i	−0.237220	−	0.410877i
$306$	7.26388	+	14.2735i	0.415248	+	0.815964i
$307$	−25.1766			−1.43690			−0.718452	−	0.695576i	$-0.755149\pi$
$307$	−25.1766			−1.43690			−0.718452	+	0.695576i	$0.755149\pi$
$308$	13.5139			0.770023
$309$	−6.12111	−	11.2803i	−0.348218	−	0.641714i
$310$	21.2078	−	12.2444i	1.20452	−	0.695433i
$311$	−5.18414	−	2.99307i	−0.293966	−	0.169721i	0.345763	−	0.938322i	$-0.387620\pi$
$311$	−5.18414	−	2.99307i	−0.293966	−	0.169721i	−0.639729	+	0.768601i	$0.720953\pi$
$312$	−0.298648	+	11.2985i	−0.0169076	+	0.639654i
$313$			23.2915i			1.31651i	0.752793	+	0.658257i	$0.228706\pi$
$313$			23.2915i			1.31651i	−0.752793	+	0.658257i	$0.771294\pi$
$314$	1.62916	+	0.940595i	0.0919387	+	0.0530808i
$315$	−38.4304	+	19.5574i	−2.16531	+	1.10194i
$316$	7.55528	−	4.36204i	0.425018	−	0.245384i
$317$	14.9628			0.840394			0.420197	−	0.907433i	$-0.361961\pi$
$317$	14.9628			0.840394			0.420197	+	0.907433i	$0.361961\pi$
$318$	−0.0259868	−	0.0478898i	−0.00145727	−	0.00268553i
$319$	3.46041	−	1.99787i	0.193746	−	0.111859i
$320$		−	3.78289i		−	0.211470i
$321$	−16.5431	−	10.1432i	−0.923346	−	0.566140i
$322$	7.87694	−	13.6433i	0.438965	−	0.760310i
$323$	37.4408			2.08326
$324$	−8.94977	−	0.949575i	−0.497209	−	0.0527542i
$325$		−	60.7541i		−	3.37003i
$326$	−4.24298	−	7.34906i	−0.234997	−	0.407027i
$327$	−4.97672	−	9.17136i	−0.275213	−	0.507178i
$328$		−	2.48234i		−	0.137064i
$329$	3.32781			0.183468
$330$	−19.8666	−	12.1810i	−1.09362	−	0.670543i
$331$			24.0634i			1.32265i	0.750101	+	0.661323i	$0.230005\pi$
$331$			24.0634i			1.32265i	−0.750101	+	0.661323i	$0.769995\pi$
$332$	9.16307			0.502889
$333$	−18.2413	−	0.506383i	−0.999615	−	0.0277496i
$334$	−5.65327			−0.309333
$335$		−	37.6508i		−	2.05708i
$336$	5.78438	−	3.13882i	0.315564	−	0.171237i
$337$	−20.1934			−1.10001			−0.550004	−	0.835162i	$-0.685374\pi$
$337$	−20.1934			−1.10001			−0.550004	+	0.835162i	$0.685374\pi$
$338$		−	29.5821i		−	1.60906i
$339$	−1.85080	+	3.01856i	−0.100522	+	0.163946i
$340$	10.0975	+	17.4894i	0.547615	+	0.948496i
$341$			23.0241i			1.24682i
$342$	−11.4679	+	17.6400i	−0.620113	+	0.953861i
$343$	1.66076			0.0896725
$344$	4.38615	−	7.59704i	0.236485	−	0.409605i
$345$	−23.8775	+	12.9568i	−1.28552	+	0.697571i
$346$			21.2223i			1.14092i
$347$	24.9047	−	14.3788i	1.33696	−	0.771892i	0.350602	−	0.936525i	$-0.385977\pi$
$347$	24.9047	−	14.3788i	1.33696	−	0.771892i	0.986355	+	0.164632i	$0.0526437\pi$
$348$	1.01713	−	1.65889i	0.0545240	−	0.0889259i
$349$	32.3597			1.73218			0.866088	−	0.499891i	$-0.166627\pi$
$349$	32.3597			1.73218			0.866088	+	0.499891i	$0.166627\pi$
$350$	−30.6360	+	17.6877i	−1.63756	+	0.945447i
$351$	33.8010	+	2.68533i	1.80416	+	0.143332i
$352$	3.08014	+	1.77832i	0.164172	+	0.0947847i
$353$			11.4886i			0.611475i	0.952116	+	0.305737i	$0.0989029\pi$
$353$			11.4886i			0.611475i	−0.952116	+	0.305737i	$0.901097\pi$
$354$	−3.67556	−	2.25363i	−0.195354	−	0.119779i
$355$	−25.2573	−	14.5823i	−1.34052	−	0.773947i
$356$	3.27769	−	1.89238i	0.173717	−	0.100296i
$357$	−18.3646	+	29.9517i	−0.971956	+	1.58521i
$358$	16.1183			0.851879
$359$	−19.0920			−1.00764			−0.503819	−	0.863810i	$-0.668072\pi$
$359$	−19.0920			−1.00764			−0.503819	+	0.863810i	$0.668072\pi$
$360$	−11.3328	−	0.599527i	−0.597292	−	0.0315978i
$361$	15.0934	+	26.1426i	0.794391	+	1.37593i
$362$	−10.3068	−	5.95064i	−0.541714	−	0.312759i
$363$	2.51138	−	1.36277i	0.131813	−	0.0715268i
$364$	−21.4726	+	12.3972i	−1.12547	+	0.649790i
$365$		−	7.98727i		−	0.418073i
$366$	3.33446	−	1.80940i	0.174295	−	0.0945788i
$367$	−0.0992612	−	0.171926i	−0.00518139	−	0.00897444i	0.863423	−	0.504481i	$-0.168316\pi$
$367$	−0.0992612	−	0.171926i	−0.00518139	−	0.00897444i	−0.868604	+	0.495506i	$0.834983\pi$
$368$	3.59070	−	2.07309i	0.187178	−	0.108067i
$369$	−7.43661	−	0.393410i	−0.387134	−	0.0204801i
$370$	−23.0032	+	0.577486i	−1.19588	+	0.0300221i
$371$	0.0597635	−	0.103513i	0.00310277	−	0.00537415i
$372$	5.34772	+	9.85507i	0.277266	+	0.510961i
$373$	−30.2414			−1.56584			−0.782919	−	0.622124i	$-0.786270\pi$
$373$	−30.2414			−1.56584			−0.782919	+	0.622124i	$0.786270\pi$
$374$	−18.9872			−0.981803
$375$	28.2316	+	0.746230i	1.45787	+	0.0385351i
$376$	0.758489	+	0.437914i	0.0391161	+	0.0225837i
$377$	−3.66556	+	6.34894i	−0.188786	+	0.326987i
$378$	−8.48658	−	17.8264i	−0.436502	−	0.916889i
$379$	9.39562	+	16.2737i	0.482620	+	0.835923i	0.999801	−	0.0199534i	$-0.00635177\pi$
$379$	9.39562	+	16.2737i	0.482620	+	0.835923i	−0.517181	+	0.855876i	$0.673018\pi$
$380$	−13.2653	+	22.9762i	−0.680497	+	1.17866i
$381$	−11.1215	+	6.03495i	−0.569773	+	0.309180i
$382$	−7.98336	+	13.8276i	−0.408464	+	0.707480i
$383$			25.2608i			1.29076i	0.763860	+	0.645382i	$0.223302\pi$
$383$			25.2608i			1.29076i	−0.763860	+	0.645382i	$0.776698\pi$
$384$	1.73145	+	0.0457663i	0.0883575	+	0.00233550i
$385$		−	51.1214i		−	2.60539i
$386$	0.247785	+	0.429176i	0.0126119	+	0.0218445i
$387$	−22.0641	−	14.3441i	−1.12158	−	0.729151i
$388$	−6.74841	−	3.89619i	−0.342598	−	0.197799i
$389$	−5.76915	+	3.33082i	−0.292508	+	0.168879i	−0.639072	−	0.769147i	$-0.720682\pi$
$389$	−5.76915	+	3.33082i	−0.292508	+	0.168879i	0.346565	+	0.938026i	$0.387348\pi$
$390$	42.7412	+	1.12975i	2.16428	+	0.0572073i
$391$	−11.0672	+	19.1690i	−0.559694	+	0.969418i
$392$	6.44071	+	3.71854i	0.325305	+	0.187815i
$393$	−3.75428	+	6.12304i	−0.189378	+	0.308867i
$394$	−1.92627	+	1.11213i	−0.0970442	+	0.0560285i
$395$	−16.5011	−	28.5808i	−0.830262	−	1.43806i
$396$	5.81566	−	8.94568i	0.292248	−	0.449537i
$397$	5.65104			0.283617			0.141809	−	0.989894i	$-0.454708\pi$
$397$	5.65104			0.283617			0.141809	+	0.989894i	$0.454708\pi$
$398$	1.73848			0.0871423
$399$	−46.1395	−	1.21958i	−2.30987	−	0.0610554i
$400$	−9.31025			−0.465513
$401$	−17.7988	+	10.2761i	−0.888830	+	0.513166i	−0.873560	−	0.486717i	$-0.838194\pi$
$401$	−17.7988	+	10.2761i	−0.888830	+	0.513166i	−0.0152702	+	0.999883i	$0.504861\pi$
$402$	17.2329	+	0.455509i	0.859501	+	0.0227187i
$403$	−21.1216	−	36.5836i	−1.05214	−	1.82236i
$404$	2.50080	−	4.33151i	0.124419	−	0.215501i
$405$	−3.59214	+	33.8560i	−0.178495	+	1.68232i
$406$	4.26871			0.211853
$407$	10.3435	−	19.0013i	0.512707	−	0.941860i
$408$	−8.12714	+	4.41009i	−0.402354	+	0.218332i
$409$	13.4472	+	7.76372i	0.664919	+	0.383891i	0.794149	−	0.607724i	$-0.207917\pi$
$409$	13.4472	+	7.76372i	0.664919	+	0.383891i	−0.129230	+	0.991615i	$0.541250\pi$
$410$	−9.39040			−0.463759
$411$	17.8175	+	10.9246i	0.878872	+	0.538871i
$412$	6.41703	−	3.70487i	0.316144	−	0.182526i
$413$		−	9.45806i		−	0.465401i
$414$	−5.64152	−	11.0856i	−0.277265	−	0.544827i
$415$		−	34.6629i		−	1.70153i
$416$	−6.52550			−0.319939
$417$	−18.1900	−	11.1530i	−0.890768	−	0.546165i
$418$	−12.4719	−	21.6020i	−0.610023	−	1.05659i
$419$	10.9124	−	18.9008i	0.533105	−	0.923366i	−0.466147	−	0.884707i	$-0.654358\pi$
$419$	10.9124	−	18.9008i	0.533105	−	0.923366i	0.999252	−	0.0386584i	$-0.0123084\pi$
$420$	−11.8738	−	21.8817i	−0.579382	−	1.06772i
$421$	−18.9568	−	10.9447i	−0.923896	−	0.533412i	−0.0390200	−	0.999238i	$-0.512424\pi$
$421$	−18.9568	−	10.9447i	−0.923896	−	0.533412i	−0.884876	+	0.465827i	$0.845757\pi$
$422$	−4.42101	+	2.55247i	−0.215211	+	0.124252i
$423$	1.43212	−	2.20289i	0.0696318	−	0.107108i
$424$	0.0272431	−	0.0157288i	0.00132304	−	0.000763859i
$425$	43.0440	−	24.8515i	2.08794	−	1.20547i
$426$	6.97995	−	11.3839i	0.338179	−	0.551554i
$427$	7.20739	+	4.16119i	0.348790	+	0.201374i
$428$	5.60178	−	9.70257i	0.270772	−	0.468991i
$429$	−21.0123	+	34.2700i	−1.01448	+	1.65457i
$430$	−28.7387	−	16.5923i	−1.38591	−	0.800153i
$431$	−23.8853	−	13.7902i	−1.15052	−	0.664251i	−0.201503	−	0.979488i	$-0.564583\pi$
$431$	−23.8853	−	13.7902i	−1.15052	−	0.664251i	−0.949013	+	0.315237i	$0.897916\pi$
$432$	0.411513	−	5.17983i	0.0197990	−	0.249215i
$433$	3.89446			0.187156			0.0935778	−	0.995612i	$-0.470170\pi$
$433$	3.89446			0.187156			0.0935778	+	0.995612i	$0.470170\pi$
$434$	−12.2985	+	21.3016i	−0.590347	+	1.02251i
$435$	−6.27540	−	3.84770i	−0.300883	−	0.184483i
$436$	5.21732	−	3.01222i	0.249864	−	0.144259i
$437$	−29.0785			−1.39102
$438$	3.65581	+	0.0966320i	0.174681	+	0.00461725i
$439$	28.2395	−	16.3041i	1.34780	−	0.778152i	0.359861	−	0.933006i	$-0.382824\pi$
$439$	28.2395	−	16.3041i	1.34780	−	0.778152i	0.987937	+	0.154854i	$0.0494907\pi$
$440$	6.72718	−	11.6518i	0.320706	−	0.555479i
$441$	12.1608	−	18.7058i	0.579086	−	0.890753i
$442$	30.1693	−	17.4183i	1.43501	−	0.828502i
$443$	−7.51220	+	13.0115i	−0.356915	+	0.618195i	−0.987444	−	0.157971i	$-0.949505\pi$
$443$	−7.51220	+	13.0115i	−0.356915	+	0.618195i	0.630529	+	0.776166i	$0.282838\pi$
$444$	0.0139800	−	10.5356i	0.000663460	−	0.500000i
$445$	−7.15866	−	12.3992i	−0.339353	−	0.587776i
$446$	7.87744	+	4.54804i	0.373008	+	0.215356i
$447$	17.6612	−	9.58361i	0.835345	−	0.453289i
$448$	1.89981	+	3.29056i	0.0897575	+	0.155465i
$449$	18.0459	+	10.4188i	0.851640	+	0.491695i	0.861204	−	0.508259i	$-0.169711\pi$
$449$	18.0459	+	10.4188i	0.851640	+	0.491695i	−0.00956360	+	0.999954i	$0.503044\pi$
$450$	−1.47552	+	27.8918i	−0.0695569	+	1.31483i
$451$	4.41438	−	7.64593i	0.207865	−	0.360033i
$452$	−1.77040	−	1.02214i	−0.0832724	−	0.0480773i
$453$	15.7795	−	8.56252i	0.741384	−	0.402302i
$454$	3.72810	+	6.45725i	0.174968	+	0.303054i
$455$	46.8972	+	81.2284i	2.19858	+	3.80805i
$456$	−10.3558	−	6.34958i	−0.484957	−	0.297346i
$457$	−17.9371	+	10.3560i	−0.839062	+	0.484433i	−0.856945	−	0.515407i	$-0.827641\pi$
$457$	−17.9371	+	10.3560i	−0.839062	+	0.484433i	0.0178830	+	0.999840i	$0.494307\pi$
$458$			25.1134i			1.17347i
$459$	11.9238	+	25.0463i	0.556554	+	1.16906i
$460$	−7.84227	−	13.5832i	−0.365648	−	0.633320i
$461$			24.6713i			1.14906i	0.818485	+	0.574528i	$0.194814\pi$
$461$			24.6713i			1.14906i	−0.818485	+	0.574528i	$0.805186\pi$
$462$	23.3985	+	0.618479i	1.08860	+	0.0287743i
$463$		−	22.8695i		−	1.06284i	−0.847110	−	0.531418i	$-0.821660\pi$
$463$		−	22.8695i		−	1.06284i	0.847110	−	0.531418i	$-0.178340\pi$
$464$	0.972944	+	0.561729i	0.0451678	+	0.0260776i
$465$	37.2806	−	20.2298i	1.72885	−	0.938136i
$466$			22.4357i			1.03931i
$467$			7.44344i			0.344441i	0.985058	+	0.172221i	$0.0550942\pi$
$467$			7.44344i			0.344441i	−0.985058	+	0.172221i	$0.944906\pi$
$468$	−1.03419	+	19.5492i	−0.0478053	+	0.903660i
$469$	18.9086	+	32.7507i	0.873120	+	1.51229i
$470$	1.65658	−	2.86928i	0.0764123	−	0.132350i
$471$	2.77775	+	1.70315i	0.127992	+	0.0784770i
$472$	1.24461	−	2.15572i	0.0572877	−	0.0992252i
$473$	27.0199	−	15.5999i	1.24238	−	0.717286i
$474$	13.2812	−	7.20686i	0.610025	−	0.331022i
$475$	56.5479	+	32.6480i	2.59460	+	1.49799i
$476$	−17.5667	−	10.1422i	−0.805170	−	0.464865i
$477$	−0.0428030	−	0.0841080i	−0.00195981	−	0.00385104i
$478$	−12.7303	+	22.0496i	−0.582272	+	1.00852i
$479$		−	28.3050i		−	1.29329i	−0.762792	−	0.646644i	$-0.776172\pi$
$479$		−	28.3050i		−	1.29329i	0.762792	−	0.646644i	$-0.223828\pi$
$480$	0.173129	−	6.54987i	0.00790222	−	0.298959i
$481$	0.996166	+	39.6806i	0.0454212	+	1.80928i
$482$	−9.98575	−	17.2958i	−0.454838	−	0.787803i
$483$	14.2629	−	23.2621i	0.648985	−	1.05846i
$484$	0.824832	+	1.42865i	0.0374924	+	0.0649387i
$485$	−14.7389	+	25.5285i	−0.669258	+	1.15919i
$486$	−15.4526	−	2.05374i	−0.700943	−	0.0931594i
$487$			11.7025i			0.530289i	0.964209	+	0.265144i	$0.0854197\pi$
$487$			11.7025i			0.530289i	−0.964209	+	0.265144i	$0.914580\pi$
$488$	1.09516	+	1.89687i	0.0495756	+	0.0858674i
$489$	−7.01015	−	12.9187i	−0.317010	−	0.584203i
$490$	14.0668	−	24.3645i	0.635475	−	1.10067i
$491$	−11.4883	−	19.8983i	−0.518458	−	0.897996i	−0.999770	−	0.0214467i	$-0.993173\pi$
$491$	−11.4883	−	19.8983i	−0.518458	−	0.897996i	0.481312	−	0.876550i	$-0.340161\pi$
$492$	0.113607	−	4.29803i	0.00512182	−	0.193770i
$493$	−5.99761			−0.270119
$494$	39.6341	+	22.8828i	1.78322	+	1.02954i
$495$	−33.8405	−	22.0000i	−1.52102	−	0.988826i
$496$	−5.60626	+	3.23677i	−0.251728	+	0.145335i
$497$	29.2935			1.31399
$498$	15.8654	+	0.419360i	0.710944	+	0.0187920i
$499$			0.603810i			0.0270302i	0.999909	+	0.0135151i	$0.00430213\pi$
$499$			0.603810i			0.0270302i	−0.999909	+	0.0135151i	$0.995698\pi$
$500$			16.3052i			0.729192i
$501$	−9.78834	−	0.258729i	−0.437311	−	0.0115592i
$502$	−10.5602			−0.471326
$503$	33.3712	−	19.2668i	1.48795	−	0.859066i	0.488041	−	0.872821i	$-0.337712\pi$
$503$	33.3712	−	19.2668i	1.48795	−	0.859066i	0.999905	+	0.0137548i	$0.00437841\pi$
$504$	10.1590	−	5.16997i	0.452518	−	0.230289i
$505$	−16.3856	−	9.46024i	−0.729150	−	0.420975i
$506$	14.7464			0.655560
$507$	1.35387	−	51.2199i	0.0601273	−	2.27475i
$508$	−3.65273	−	6.32671i	−0.162064	−	0.280702i
$509$	−16.1219	+	27.9239i	−0.714589	+	1.23771i	0.248528	+	0.968625i	$0.420053\pi$
$509$	−16.1219	+	27.9239i	−0.714589	+	1.23771i	−0.963118	+	0.269080i	$0.913280\pi$
$510$	16.6829	+	30.7441i	0.738730	+	1.36137i
$511$	4.01130	+	6.94777i	0.177449	+	0.307351i
$512$			1.00000i			0.0441942i
$513$	−20.6634	+	30.0178i	−0.912310	+	1.32532i
$514$	−1.21431	+	2.10324i	−0.0535608	+	0.0927701i
$515$	−14.0151	−	24.2749i	−0.617581	−	1.06968i
$516$	7.94207	−	12.9531i	0.349630	−	0.570229i
$517$	1.55750	+	2.69767i	0.0684988	+	0.118643i
$518$	19.7194	−	12.0548i	0.866421	−	0.529656i
$519$	−0.971266	+	36.7452i	−0.0426338	+	1.61294i
$520$			24.6852i			1.08252i
$521$	−8.01182	+	13.8769i	−0.351004	+	0.607957i	−0.986426	−	0.164208i	$-0.947493\pi$
$521$	−8.01182	+	13.8769i	−0.351004	+	0.607957i	0.635421	+	0.772166i	$0.280826\pi$
$522$	1.83703	−	2.82573i	0.0804047	−	0.123679i
$523$	−1.06590	−	0.615397i	−0.0466085	−	0.0269094i	0.476515	−	0.879167i	$-0.341900\pi$
$523$	−1.06590	−	0.615397i	−0.0466085	−	0.0269094i	−0.523123	+	0.852257i	$0.675233\pi$
$524$	−3.59118	−	2.07337i	−0.156881	−	0.0905755i
$525$	−53.8541	+	29.2232i	−2.35038	+	1.27541i
$526$	1.60773	−	0.928226i	0.0701006	−	0.0404726i
$527$	17.2796	−	29.9291i	0.752710	−	1.30373i
$528$	5.25171	+	3.22003i	0.228551	+	0.140134i
$529$	−2.90460	+	5.03092i	−0.126287	+	0.218736i
$530$	−0.0595004	−	0.103058i	−0.00258453	−	0.00447654i
$531$	−6.26089	−	4.07026i	−0.271699	−	0.176634i
$532$		−	26.6480i		−	1.15534i
$533$			16.1985i			0.701634i
$534$	5.76176	−	3.12654i	0.249336	−	0.135299i
$535$	−36.7037	−	21.1909i	−1.58684	−	0.916163i
$536$			9.95292i			0.429901i
$537$	27.9080	+	0.737676i	1.20432	+	0.0318331i
$538$			23.3816i			1.00805i
$539$	13.2255	+	22.9072i	0.569663	+	0.986685i
$540$	−19.5947	−	1.55671i	−0.843223	−	0.0669901i
$541$		−	0.0466651i		−	0.00200629i	−0.999999	−	0.00100315i	$-0.999681\pi$
$541$		−	0.0466651i		−	0.00200629i	0.999999	−	0.00100315i	$-0.000319311\pi$
$542$	21.7261	−	12.5435i	0.933214	−	0.538791i
$543$	−17.5733	−	10.7749i	−0.754144	−	0.462396i
$544$	−2.66926	−	4.62329i	−0.114444	−	0.198222i
$545$	−11.3949	−	19.7365i	−0.488104	−	0.845420i
$546$	−37.7460	+	20.4824i	−1.61538	+	0.876564i
$547$	19.4911	+	11.2532i	0.833377	+	0.481151i	0.855008	−	0.518615i	$-0.173552\pi$
$547$	19.4911	+	11.2532i	0.833377	+	0.481151i	−0.0216303	+	0.999766i	$0.506886\pi$
$548$	−6.03331	+	10.4500i	−0.257730	+	0.446402i
$549$	5.85624	−	2.98027i	0.249938	−	0.127195i
$550$	−28.6769	−	16.5566i	−1.22279	−	0.705976i
$551$	−3.93960	−	6.82358i	−0.167832	−	0.290694i
$552$	6.31197	−	3.42511i	0.268655	−	0.145782i
$553$	28.7072	+	16.5741i	1.22075	+	0.704802i
$554$	16.2500	+	28.1459i	0.690398	+	1.19581i
$555$	−39.8552	−	0.0528847i	−1.69176	−	0.00224483i
$556$	6.15945	−	10.6685i	0.261219	−	0.452444i
$557$	−2.02319	+	1.16809i	−0.0857252	+	0.0494934i	−0.542250	−	0.840217i	$-0.682427\pi$
$557$	−2.02319	+	1.16809i	−0.0857252	+	0.0494934i	0.456525	+	0.889711i	$0.349094\pi$
$558$	8.80826	+	17.3083i	0.372883	+	0.732717i
$559$	−28.6218	+	49.5744i	−1.21057	+	2.09678i
$560$	12.4478	−	7.18677i	0.526017	−	0.303696i
$561$	−32.8753	−	0.868973i	−1.38799	−	0.0366881i
$562$	−2.54304			−0.107272
$563$	−6.52429	+	3.76680i	−0.274966	+	0.158752i	−0.631142	−	0.775667i	$-0.717414\pi$
$563$	−6.52429	+	3.76680i	−0.274966	+	0.158752i	0.356176	+	0.934419i	$0.384080\pi$
$564$	1.29324	+	0.792937i	0.0544553	+	0.0333887i
$565$	−3.86664	+	6.69721i	−0.162671	+	0.281754i
$566$	21.7227			0.913072
$567$	−13.8782	−	31.2538i	−0.582830	−	1.31254i
$568$	6.67671	+	3.85480i	0.280148	+	0.161744i
$569$	−11.2405	−	6.48972i	−0.471228	−	0.272063i	0.245526	−	0.969390i	$-0.421039\pi$
$569$	−11.2405	−	6.48972i	−0.471228	−	0.272063i	−0.716753	+	0.697327i	$0.754373\pi$
$570$	−24.0198	+	39.1750i	−1.00608	+	1.64086i
$571$	16.0292	−	27.7633i	0.670800	−	1.16186i	−0.306878	−	0.951749i	$-0.599284\pi$
$571$	16.0292	−	27.7633i	0.670800	−	1.16186i	0.977678	−	0.210110i	$-0.0673824\pi$
$572$	−20.0994	−	11.6044i	−0.840400	−	0.485205i
$573$	−14.4556	+	23.5763i	−0.603891	+	0.984916i
$574$	8.16828	−	4.71596i	0.340938	−	0.196840i
$575$	−33.4303	+	19.3010i	−1.39414	+	0.804907i
$576$	2.99581	+	0.158484i	0.124825	+	0.00660349i
$577$	25.8501	−	14.9246i	1.07615	−	0.621317i	0.146297	−	0.989241i	$-0.453264\pi$
$577$	25.8501	−	14.9246i	1.07615	−	0.621317i	0.929856	+	0.367923i	$0.119931\pi$
$578$	9.95911	+	5.74989i	0.414244	+	0.239164i
$579$	0.409384	+	0.754435i	0.0170134	+	0.0313533i
$580$	2.12496	−	3.68054i	0.0882342	−	0.152826i
$581$	17.4081	+	30.1517i	0.722209	+	1.25090i
$582$	−11.5062	−	7.05490i	−0.476947	−	0.292435i
$583$	0.111883			0.00463374
$584$			2.11142i			0.0873712i
$585$	73.9523	+	3.91221i	3.05755	+	0.161750i
$586$			0.539294i			0.0222780i
$587$	12.4937	−	7.21325i	0.515671	−	0.297723i	−0.219491	−	0.975615i	$-0.570440\pi$
$587$	12.4937	−	7.21325i	0.515671	−	0.297723i	0.735162	+	0.677892i	$0.237106\pi$
$588$	10.9815	+	6.73322i	0.452871	+	0.277673i
$589$	45.4012			1.87072
$590$	−8.15486	−	4.70821i	−0.335730	−	0.193834i
$591$	−3.38614	+	1.83744i	−0.139287	+	0.0755823i
$592$	6.08085	−	0.152657i	0.249921	−	0.00627418i
$593$	32.3548			1.32865			0.664327	−	0.747442i	$-0.268718\pi$
$593$	32.3548			1.32865			0.664327	+	0.747442i	$0.268718\pi$
$594$	10.4789	−	15.2228i	0.429955	−	0.624599i
$595$	−38.3667	+	66.4530i	−1.57288	+	2.72431i
$596$	5.80060	+	10.0469i	0.237602	+	0.411538i
$597$	3.01009	+	0.0795640i	0.123195	+	0.00325634i
$598$	−23.4311	+	13.5279i	−0.958168	+	0.553199i
$599$	35.1674			1.43690			0.718451	−	0.695578i	$-0.244852\pi$
$599$	35.1674			1.43690			0.718451	+	0.695578i	$0.244852\pi$
$600$	−16.1202	−	0.426096i	−0.658105	−	0.0173953i
$601$	−30.9246			−1.26144			−0.630720	−	0.776010i	$-0.717240\pi$
$601$	−30.9246			−1.26144			−0.630720	+	0.776010i	$0.717240\pi$
$602$	33.3314			1.35849
$603$	29.8171	+	1.57738i	1.21424	+	0.0642358i
$604$	5.18257	+	8.97647i	0.210876	+	0.365247i
$605$	5.40443	−	3.12025i	0.219721	−	0.126856i
$606$	4.52823	−	7.38532i	0.183947	−	0.300008i
$607$	−18.2318	−	10.5261i	−0.740007	−	0.427243i	0.0820651	−	0.996627i	$-0.473848\pi$
$607$	−18.2318	−	10.5261i	−0.740007	−	0.427243i	−0.822072	+	0.569384i	$0.807182\pi$
$608$	3.50667	−	6.07373i	0.142214	−	0.246322i
$609$	7.39105	+	0.195363i	0.299500	+	0.00791652i
$610$	7.17566	−	4.14287i	0.290534	−	0.167740i
$611$	−4.94952	−	2.85761i	−0.200236	−	0.115606i
$612$	−14.2735	+	7.26388i	−0.576974	+	0.293625i
$613$	−20.9692	−	36.3198i	−0.846939	−	1.46694i	−0.883927	−	0.467625i	$-0.845110\pi$
$613$	−20.9692	−	36.3198i	−0.846939	−	1.46694i	0.0369878	−	0.999316i	$-0.488224\pi$
$614$		−	25.1766i		−	1.01605i
$615$	−16.2590	−	0.429764i	−0.655625	−	0.0173298i
$616$			13.5139i			0.544489i
$617$	12.5656	−	21.7643i	0.505872	−	0.876197i	−0.494104	−	0.869403i	$-0.664504\pi$
$617$	12.5656	−	21.7643i	0.505872	−	0.876197i	0.999977	−	0.00679422i	$-0.00216268\pi$
$618$	11.2803	−	6.12111i	0.453760	−	0.246227i
$619$	−14.7155	+	25.4881i	−0.591467	+	1.02445i	0.402568	+	0.915390i	$0.368118\pi$
$619$	−14.7155	+	25.4881i	−0.591467	+	1.02445i	−0.994035	+	0.109061i	$0.965216\pi$
$620$	12.2444	+	21.2078i	0.491745	+	0.851728i
$621$	−9.26063	−	19.4523i	−0.371616	−	0.780594i
$622$	2.99307	−	5.18414i	0.120011	−	0.207865i
$623$	12.4540	+	7.19031i	0.498958	+	0.288074i
$624$	−11.2985	−	0.298648i	−0.452304	−	0.0119555i
$625$	15.1296			0.605183
$626$	−23.2915			−0.930917
$627$	−20.6058	−	37.9736i	−0.822918	−	1.51652i
$628$	−0.940595	+	1.62916i	−0.0375338	+	0.0650105i
$629$	−27.7061	+	16.9371i	−1.10471	+	0.675328i
$630$	−19.5574	−	38.4304i	−0.779186	−	1.53110i
$631$	−13.8786	+	8.01280i	−0.552498	+	0.318985i	−0.750129	−	0.661292i	$-0.770009\pi$
$631$	−13.8786	+	8.01280i	−0.552498	+	0.318985i	0.197631	+	0.980276i	$0.436675\pi$
$632$	4.36204	+	7.55528i	0.173513	+	0.300533i
$633$	−7.77156	+	4.21713i	−0.308892	+	0.167616i
$634$			14.9628i			0.594248i
$635$	−23.9333	+	13.8179i	−0.949762	+	0.548345i
$636$	0.0478898	−	0.0259868i	0.00189896	−	0.00103044i
$637$	−42.0288	−	24.2653i	−1.66524	−	0.961428i
$638$	1.99787	+	3.46041i	0.0790963	+	0.136999i
$639$	12.6064	−	19.3912i	0.498701	−	0.767105i
$640$	3.78289			0.149532
$641$	20.7992			0.821521			0.410760	−	0.911743i	$-0.365263\pi$
$641$	20.7992			0.821521			0.410760	+	0.911743i	$0.365263\pi$
$642$	10.1432	−	16.5431i	0.400321	−	0.652904i
$643$	−17.7237	+	10.2328i	−0.698954	+	0.403541i	−0.806958	−	0.590609i	$-0.798887\pi$
$643$	−17.7237	+	10.2328i	−0.698954	+	0.403541i	0.108004	+	0.994150i	$0.465554\pi$
$644$	13.6433	+	7.87694i	0.537620	+	0.310395i
$645$	−49.0002	−	30.0440i	−1.92938	−	1.18298i
$646$			37.4408i			1.47309i
$647$	−9.70849	−	5.60520i	−0.381680	−	0.220363i	0.296869	−	0.954918i	$-0.404058\pi$
$647$	−9.70849	−	5.60520i	−0.381680	−	0.220363i	−0.678549	+	0.734555i	$0.737391\pi$
$648$	0.949575	−	8.94977i	0.0373028	−	0.351580i
$649$	7.66712	−	4.42662i	0.300961	−	0.173760i
$650$	60.7541			2.38297
$651$	−22.2691	+	36.3198i	−0.872794	+	1.42348i
$652$	7.34906	−	4.24298i	0.287811	−	0.166168i
$653$			9.15111i			0.358111i	0.983839	+	0.179055i	$0.0573041\pi$
$653$			9.15111i			0.358111i	−0.983839	+	0.179055i	$0.942696\pi$
$654$	9.17136	−	4.97672i	0.358629	−	0.194605i
$655$	−7.84333	+	13.5850i	−0.306464	+	0.530811i
$656$	2.48234			0.0969189
$657$	6.32542	+	0.334626i	0.246778	+	0.0130550i
$658$			3.32781i			0.129732i
$659$	10.2652	+	17.7798i	0.399875	+	0.692604i	0.993710	−	0.111983i	$-0.0357202\pi$
$659$	10.2652	+	17.7798i	0.399875	+	0.692604i	−0.593835	+	0.804587i	$0.702387\pi$
$660$	12.1810	−	19.8666i	0.474145	−	0.773307i
$661$		−	42.8782i		−	1.66777i	−0.551939	−	0.833884i	$-0.686112\pi$
$661$		−	42.8782i		−	1.66777i	0.551939	−	0.833884i	$-0.313888\pi$
$662$	−24.0634			−0.935252
$663$	53.0337	−	28.7780i	2.05966	−	1.11765i
$664$			9.16307i			0.355596i
$665$	−100.806			−3.90910
$666$	0.506383	−	18.2413i	0.0196220	−	0.706834i
$667$	4.65806			0.180361
$668$		−	5.65327i		−	0.218732i
$669$	13.4312	+	8.23522i	0.519281	+	0.318392i
$670$	37.6508			1.45458
$671$			7.79017i			0.300736i
$672$	3.13882	+	5.78438i	0.121083	+	0.223137i
$673$	19.3048	+	33.4369i	0.744145	+	1.28890i	0.950593	+	0.310440i	$0.100476\pi$
$673$	19.3048	+	33.4369i	0.744145	+	1.28890i	−0.206448	+	0.978458i	$0.566190\pi$
$674$		−	20.1934i		−	0.777822i
$675$	−3.83130	+	48.2256i	−0.147467	+	1.85620i
$676$	29.5821			1.13777
$677$	19.7444	−	34.1984i	0.758840	−	1.31435i	−0.184602	−	0.982813i	$-0.559100\pi$
$677$	19.7444	−	34.1984i	0.758840	−	1.31435i	0.943442	−	0.331536i	$-0.107567\pi$
$678$	−3.01856	−	1.85080i	−0.115927	−	0.0710796i
$679$		−	29.6081i		−	1.13625i
$680$	−17.4894	+	10.0975i	−0.670688	+	0.387222i
$681$	6.15947	+	11.3510i	0.236032	+	0.434972i
$682$	−23.0241			−0.881637
$683$	−18.7351	+	10.8167i	−0.716879	+	0.413890i	−0.813603	−	0.581421i	$-0.802497\pi$
$683$	−18.7351	+	10.8167i	−0.716879	+	0.413890i	0.0967239	+	0.995311i	$0.469164\pi$
$684$	−17.6400	−	11.4679i	−0.674482	−	0.438486i
$685$	39.5312	+	22.8234i	1.51041	+	0.872035i
$686$			1.66076i			0.0634081i
$687$	−1.14935	+	43.4825i	−0.0438503	+	1.65896i
$688$	7.59704	+	4.38615i	0.289634	+	0.167220i
$689$	−0.177775	+	0.102638i	−0.00677268	+	0.00391021i
$690$	−12.9568	−	23.8775i	−0.493257	−	0.909001i
$691$	9.85371			0.374853			0.187426	−	0.982279i	$-0.439985\pi$
$691$	9.85371			0.374853			0.187426	+	0.982279i	$0.439985\pi$
$692$	−21.2223			−0.806750
$693$	40.4850	+	2.14173i	1.53790	+	0.0813575i
$694$	14.3788	+	24.9047i	0.545810	+	0.945371i
$695$	−40.3577	−	23.3005i	−1.53085	−	0.883839i
$696$	1.65889	+	1.01713i	0.0628801	+	0.0385543i
$697$	−11.4766	+	6.62600i	−0.434706	+	0.250978i
$698$			32.3597i			1.22483i
$699$	−1.02680	+	38.8462i	−0.0388371	+	1.46930i
$700$	−17.6877	−	30.6360i	−0.668532	−	1.15793i
$701$	−6.17765	+	3.56667i	−0.233327	+	0.134711i	−0.612106	−	0.790776i	$-0.709677\pi$
$701$	−6.17765	+	3.56667i	−0.233327	+	0.134711i	0.378779	+	0.925487i	$0.376344\pi$
$702$	−2.68533	+	33.8010i	−0.101351	+	1.27574i
$703$	−37.4687	−	20.3963i	−1.41316	−	0.769261i
$704$	−1.77832	+	3.08014i	−0.0670229	+	0.116087i
$705$	2.99959	−	4.89219i	0.112971	−	0.184250i
$706$	−11.4886			−0.432378
$707$	19.0041			0.714724
$708$	2.25363	−	3.67556i	0.0846966	−	0.138136i
$709$	−32.3548	−	18.6801i	−1.21511	−	0.701544i	−0.251242	−	0.967924i	$-0.580839\pi$
$709$	−32.3548	−	18.6801i	−1.21511	−	0.701544i	−0.963868	+	0.266380i	$0.914172\pi$
$710$	14.5823	−	25.2573i	0.547263	−	0.947888i
$711$	23.3255	−	11.8705i	0.874775	−	0.445177i
$712$	1.89238	+	3.27769i	0.0709198	+	0.122837i
$713$	−13.4202	+	23.2445i	−0.502592	+	0.870515i
$714$	−29.9517	−	18.3646i	−1.12091	−	0.687277i
$715$	−43.8982	+	76.0339i	−1.64170	+	2.84351i
$716$			16.1183i			0.602370i
$717$	−23.0510	+	37.5951i	−0.860856	+	1.40401i
$718$		−	19.0920i		−	0.712507i
$719$	23.1626	+	40.1189i	0.863821	+	1.49618i	0.868213	+	0.496191i	$0.165268\pi$
$719$	23.1626	+	40.1189i	0.863821	+	1.49618i	−0.00439274	+	0.999990i	$0.501398\pi$
$720$	0.599527	−	11.3328i	0.0223430	−	0.422349i
$721$	24.3823	+	14.0771i	0.908043	+	0.524259i
$722$	−26.1426	+	15.0934i	−0.972927	+	0.561719i
$723$	−16.4982	−	30.4038i	−0.613575	−	1.13073i
$724$	5.95064	−	10.3068i	0.221154	−	0.383050i
$725$	−9.05836	−	5.22984i	−0.336419	−	0.194232i
$726$	1.36277	+	2.51138i	0.0505771	+	0.0932061i
$727$	8.44005	−	4.87287i	0.313024	−	0.180725i	−0.335255	−	0.942128i	$-0.608822\pi$
$727$	8.44005	−	4.87287i	0.313024	−	0.180725i	0.648279	+	0.761403i	$0.275489\pi$
$728$	−12.3972	−	21.4726i	−0.459471	−	0.795827i
$729$	−26.6613	−	4.26314i	−0.987456	−	0.157894i
$730$	7.98727			0.295622
$731$	−46.8311			−1.73211
$732$	1.80940	+	3.33446i	0.0668773	+	0.123245i
$733$	36.2911			1.34044			0.670222	−	0.742161i	$-0.266199\pi$
$733$	36.2911			1.34044			0.670222	+	0.742161i	$0.266199\pi$
$734$	0.171926	−	0.0992612i	0.00634589	−	0.00366380i
$735$	25.4710	−	41.5420i	0.939514	−	1.53230i
$736$	2.07309	+	3.59070i	0.0764151	+	0.132355i
$737$	−17.6995	+	30.6564i	−0.651968	+	1.12924i
$738$	0.393410	−	7.43661i	0.0144816	−	0.273745i
$739$	−6.64779			−0.244543			−0.122271	−	0.992497i	$-0.539018\pi$
$739$	−6.64779			−0.244543			−0.122271	+	0.992497i	$0.539018\pi$
$740$	−0.577486	−	23.0032i	−0.0212288	−	0.845613i
$741$	67.5770	+	41.4342i	2.48250	+	1.52212i
$742$	0.103513	+	0.0597635i	0.00380010	+	0.00219399i
$743$	38.2095			1.40177			0.700885	−	0.713274i	$-0.252789\pi$
$743$	38.2095			1.40177			0.700885	+	0.713274i	$0.252789\pi$
$744$	−9.85507	+	5.34772i	−0.361304	+	0.196057i
$745$	38.0064	−	21.9430i	1.39245	−	0.803930i
$746$		−	30.2414i		−	1.10721i
$747$	27.4508	+	1.45220i	1.00437	+	0.0531332i
$748$		−	18.9872i		−	0.694240i
$749$	42.5692			1.55545
$750$	−0.746230	+	28.2316i	−0.0272485	+	1.03087i
$751$	11.3824	+	19.7149i	0.415350	+	0.719408i	0.995465	−	0.0951270i	$-0.0303257\pi$
$751$	11.3824	+	19.7149i	0.415350	+	0.719408i	−0.580115	+	0.814535i	$0.696992\pi$
$752$	−0.437914	+	0.758489i	−0.0159691	+	0.0276592i
$753$	−18.2845	−	0.483302i	−0.666322	−	0.0176125i
$754$	−6.34894	−	3.66556i	−0.231215	−	0.133492i
$755$	33.9570	−	19.6051i	1.23582	−	0.713502i
$756$	17.8264	−	8.48658i	0.648339	−	0.308654i
$757$	23.5490	−	13.5960i	0.855903	−	0.494156i	−0.00673510	−	0.999977i	$-0.502144\pi$
$757$	23.5490	−	13.5960i	0.855903	−	0.494156i	0.862638	+	0.505821i	$0.168811\pi$
$758$	−16.2737	+	9.39562i	−0.591087	+	0.341264i
$759$	25.5327	+	0.674891i	0.926778	+	0.0244970i
$760$	−22.9762	−	13.2653i	−0.833436	−	0.481184i
$761$	−18.4541	+	31.9634i	−0.668959	+	1.15867i	0.309236	+	0.950985i	$0.399927\pi$
$761$	−18.4541	+	31.9634i	−0.668959	+	1.15867i	−0.978196	+	0.207686i	$0.933407\pi$
$762$	−6.03495	−	11.1215i	−0.218623	−	0.402891i
$763$	19.8238	+	11.4453i	0.717670	+	0.414347i
$764$	−13.8276	−	7.98336i	−0.500264	−	0.288828i
$765$	27.4785	+	53.9953i	0.993486	+	1.95220i
$766$	−25.2608			−0.912708
$767$	−8.12168	+	14.0672i	−0.293257	+	0.507936i
$768$	−0.0457663	+	1.73145i	−0.00165145	+	0.0624782i
$769$	−7.51741	+	4.34018i	−0.271085	+	0.156511i	−0.629380	−	0.777097i	$-0.716691\pi$
$769$	−7.51741	+	4.34018i	−0.271085	+	0.156511i	0.358296	+	0.933608i	$0.383358\pi$
$770$	51.1214			1.84229
$771$	−2.19877	+	3.58608i	−0.0791867	+	0.129149i
$772$	−0.429176	+	0.247785i	−0.0154464	+	0.00891797i
$773$	−14.0144	+	24.2736i	−0.504062	+	0.873062i	0.495927	+	0.868364i	$0.334828\pi$
$773$	−14.0144	+	24.2736i	−0.504062	+	0.873062i	−0.999989	+	0.00469714i	$0.998505\pi$
$774$	14.3441	−	22.0641i	0.515587	−	0.793079i
$775$	52.1957	−	30.1352i	1.87492	−	1.08249i
$776$	3.89619	−	6.74841i	0.139865	−	0.242254i
$777$	34.6948	−	19.9697i	1.24467	−	0.716409i
$778$	−3.33082	−	5.76915i	−0.119416	−	0.206834i
$779$	−15.0770	−	8.70473i	−0.540191	−	0.311879i
$780$	−1.12975	+	42.7412i	−0.0404516	+	1.53038i
$781$	13.7101	+	23.7466i	0.490587	+	0.849721i
$782$	−19.1690	−	11.0672i	−0.685482	−	0.395763i
$783$	3.31004	−	4.80853i	0.118291	−	0.171843i
$784$	−3.71854	+	6.44071i	−0.132805	+	0.230025i
$785$	6.16293	+	3.55817i	0.219964	+	0.126996i
$786$	−6.12304	−	3.75428i	−0.218402	−	0.133911i
$787$	16.2487	+	28.1436i	0.579204	+	1.00321i	0.995571	+	0.0940146i	$0.0299700\pi$
$787$	16.2487	+	28.1436i	0.579204	+	1.00321i	−0.416366	+	0.909197i	$0.636697\pi$
$788$	−1.11213	−	1.92627i	−0.0396181	−	0.0686206i
$789$	2.82619	−	1.53359i	0.100615	−	0.0545974i
$790$	28.5808	−	16.5011i	1.01686	−	0.587084i
$791$		−	7.76747i		−	0.276179i
$792$	8.94568	+	5.81566i	0.317871	+	0.206650i
$793$	−7.14647	−	12.3780i	−0.253778	−	0.439557i
$794$			5.65104i			0.200548i
$795$	−0.0983051	−	0.181162i	−0.00348652	−	0.00642515i
$796$			1.73848i			0.0616189i
$797$	26.2645	+	15.1638i	0.930337	+	0.537130i	0.886918	−	0.461927i	$-0.152842\pi$
$797$	26.2645	+	15.1638i	0.930337	+	0.537130i	0.0434187	+	0.999057i	$0.486175\pi$
$798$	1.21958	−	46.1395i	0.0431727	−	1.63332i
$799$		−	4.67562i		−	0.165412i
$800$		−	9.31025i		−	0.329167i
$801$	10.1193	−	5.14974i	0.357547	−	0.181957i
$802$	−10.2761	−	17.7988i	−0.362863	−	0.628498i
$803$	−3.75478	+	6.50347i	−0.132503	+	0.229502i
$804$	−0.455509	+	17.2329i	−0.0160645	+	0.607759i
$805$	29.7976	−	51.6110i	1.05023	−	1.81905i
$806$	36.5836	−	21.1216i	1.28860	−	0.743975i
$807$	−1.07009	+	40.4840i	−0.0376690	+	1.42511i
$808$	4.33151	+	2.50080i	0.152382	+	0.0879777i
$809$	−26.9739	−	15.5734i	−0.948352	−	0.547531i	−0.0557836	−	0.998443i	$-0.517766\pi$
$809$	−26.9739	−	15.5734i	−0.948352	−	0.547531i	−0.892569	+	0.450911i	$0.851099\pi$
$810$	−33.8560	−	3.59214i	−1.18958	−	0.126215i
$811$	−1.05736	+	1.83140i	−0.0371289	+	0.0643091i	−0.883993	−	0.467501i	$-0.845155\pi$
$811$	−1.05736	+	1.83140i	−0.0371289	+	0.0643091i	0.846864	+	0.531810i	$0.178488\pi$
$812$			4.26871i			0.149802i
$813$	38.1916	−	20.7241i	1.33944	−	0.726828i
$814$	19.0013	+	10.3435i	0.665996	+	0.362539i
$815$	−16.0507	−	27.8007i	−0.562233	−	0.973815i
$816$	−4.41009	−	8.12714i	−0.154384	−	0.284507i
$817$	−30.7615	−	53.2806i	−1.07621	−	1.86405i
$818$	−7.76372	+	13.4472i	−0.271452	+	0.470169i
$819$	−66.2925	+	33.7366i	−2.31645	+	1.17885i
$820$		−	9.39040i		−	0.327927i
$821$	−14.9838	−	25.9527i	−0.522938	−	0.905754i	−0.999644	−	0.0266917i	$-0.991503\pi$
$821$	−14.9838	−	25.9527i	−0.522938	−	0.905754i	0.476706	−	0.879063i	$-0.341831\pi$
$822$	−10.9246	+	17.8175i	−0.381040	+	0.621456i
$823$	−17.7258	+	30.7021i	−0.617884	+	1.07021i	0.371987	+	0.928238i	$0.378676\pi$
$823$	−17.7258	+	30.7021i	−0.617884	+	1.07021i	−0.989871	+	0.141968i	$0.954657\pi$
$824$	3.70487	+	6.41703i	0.129065	+	0.223548i
$825$	−48.8947	−	29.9793i	−1.70230	−	1.04374i
$826$	9.45806			0.329088
$827$	24.0071	+	13.8605i	0.834807	+	0.481976i	0.855496	−	0.517810i	$-0.173253\pi$
$827$	24.0071	+	13.8605i	0.834807	+	0.481976i	−0.0206886	+	0.999786i	$0.506586\pi$
$828$	11.0856	−	5.64152i	0.385251	−	0.196056i
$829$	−4.81083	+	2.77753i	−0.167087	+	0.0964677i	−0.581211	−	0.813753i	$-0.697421\pi$
$829$	−4.81083	+	2.77753i	−0.167087	+	0.0964677i	0.414125	+	0.910220i	$0.364088\pi$
$830$	34.6629			1.20317
$831$	26.8479	+	49.4768i	0.931345	+	1.71633i
$832$		−	6.52550i		−	0.226231i
$833$		−	39.7030i		−	1.37563i
$834$	11.1530	−	18.1900i	0.386197	−	0.629868i
$835$	−21.3857			−0.740083
$836$	21.6020	−	12.4719i	0.747122	−	0.431351i
$837$	14.4589	+	30.3714i	0.499772	+	1.04979i
$838$	18.9008	+	10.9124i	0.652918	+	0.376962i
$839$	−37.7637			−1.30375			−0.651874	−	0.758327i	$-0.726017\pi$
$839$	−37.7637			−1.30375			−0.651874	+	0.758327i	$0.726017\pi$
$840$	21.8817	−	11.8738i	0.754990	−	0.409685i
$841$	−13.8689	−	24.0217i	−0.478239	−	0.828334i
$842$	10.9447	−	18.9568i	0.377179	−	0.653293i
$843$	−4.40314	−	0.116386i	−0.151652	−	0.00400854i
$844$	−2.55247	−	4.42101i	−0.0878597	−	0.152177i
$845$		−	111.906i		−	3.84968i
$846$	2.20289	+	1.43212i	0.0757368	+	0.0492371i
$847$	−3.13404	+	5.42832i	−0.107687	+	0.186519i
$848$	0.0157288	+	0.0272431i	0.000540130	+	0.000935532i
$849$	37.6116	+	0.994167i	1.29083	+	0.0341197i
$850$	24.8515	+	43.0440i	0.852399	+	1.47640i
$851$	21.5180	−	13.1543i	0.737627	−	0.450923i
$852$	11.3839	+	6.97995i	0.390007	+	0.239129i
$853$		−	27.2411i		−	0.932717i	−0.884596	−	0.466358i	$-0.845566\pi$
$853$		−	27.2411i		−	0.932717i	0.884596	−	0.466358i	$-0.154434\pi$
$854$	−4.16119	+	7.20739i	−0.142393	+	0.246632i
$855$	−43.3818	+	66.7301i	−1.48363	+	2.28212i
$856$	9.70257	+	5.60178i	0.331627	+	0.191465i
$857$	−41.8598	−	24.1678i	−1.42990	−	0.825555i	−0.432791	−	0.901494i	$-0.642471\pi$
$857$	−41.8598	−	24.1678i	−1.42990	−	0.825555i	−0.997112	+	0.0759391i	$0.975805\pi$
$858$	−34.2700	−	21.0123i	−1.16996	−	0.717348i
$859$	16.4562	−	9.50100i	0.561479	−	0.324170i	−0.192260	−	0.981344i	$-0.561582\pi$
$859$	16.4562	−	9.50100i	0.561479	−	0.324170i	0.753739	+	0.657174i	$0.228248\pi$
$860$	16.5923	−	28.7387i	0.565794	−	0.979983i
$861$	14.3588	−	7.79160i	0.489346	−	0.265537i
$862$	13.7902	−	23.8853i	0.469696	−	0.813538i
$863$	−3.64869	−	6.31972i	−0.124203	−	0.215126i	0.797218	−	0.603691i	$-0.206304\pi$
$863$	−3.64869	−	6.31972i	−0.124203	−	0.215126i	−0.921421	+	0.388566i	$0.872971\pi$
$864$	5.17983	+	0.411513i	0.176221	+	0.0140000i
$865$			80.2816i			2.72965i
$866$			3.89446i			0.132339i
$867$	16.9805	+	10.4114i	0.576688	+	0.353590i
$868$	−21.3016	−	12.2985i	−0.723024	−	0.417438i
$869$			31.0284i			1.05257i
$870$	3.84770	−	6.27540i	0.130449	−	0.212756i
$871$		−	64.9478i		−	2.20067i
$872$	3.01222	+	5.21732i	0.102007	+	0.176681i
$873$	−19.5995	−	12.7418i	−0.663341	−	0.431244i
$874$		−	29.0785i		−	0.983596i
$875$	−53.6534	+	30.9768i	−1.81382	+	1.04721i
$876$	−0.0966320	+	3.65581i	−0.00326489	+	0.123518i
$877$	−16.7027	−	28.9299i	−0.564010	−	0.976894i	−0.997141	−	0.0755632i	$-0.975925\pi$
$877$	−16.7027	−	28.9299i	−0.564010	−	0.976894i	0.433131	−	0.901331i	$-0.357409\pi$
$878$	16.3041	+	28.2395i	0.550236	+	0.953038i
$879$	−0.0246815	+	0.933758i	−0.000832486	+	0.0314949i
$880$	11.6518	+	6.72718i	0.392783	+	0.226773i
$881$	9.15567	−	15.8581i	0.308462	−	0.534273i	−0.669564	−	0.742755i	$-0.733519\pi$
$881$	9.15567	−	15.8581i	0.308462	−	0.534273i	0.978026	+	0.208482i	$0.0668522\pi$
$882$	18.7058	+	12.1608i	0.629857	+	0.409475i
$883$	3.63619	+	2.09936i	0.122368	+	0.0706490i	0.559934	−	0.828537i	$-0.310826\pi$
$883$	3.63619	+	2.09936i	0.122368	+	0.0706490i	−0.437567	+	0.899186i	$0.644160\pi$
$884$	17.4183	+	30.1693i	0.585839	+	1.01470i
$885$	−13.9042	−	8.52524i	−0.467386	−	0.286573i
$886$	−13.0115	−	7.51220i	−0.437130	−	0.252377i
$887$	0.0626853	+	0.108574i	0.00210477	+	0.00364556i	0.867076	−	0.498176i	$-0.165997\pi$
$887$	0.0626853	+	0.108574i	0.00210477	+	0.00364556i	−0.864971	+	0.501822i	$0.832663\pi$
$888$	10.5356	+	0.0139800i	0.353553	+	0.000469137i
$889$	13.8790	−	24.0391i	0.465486	−	0.806245i
$890$	12.3992	−	7.15866i	0.415621	−	0.239959i
$891$	18.8404	−	25.8779i	0.631176	−	0.866941i
$892$	−4.54804	+	7.87744i	−0.152280	+	0.263756i
$893$	5.31954	−	3.07124i	0.178012	−	0.102775i
$894$	9.58361	+	17.6612i	0.320524	+	0.590678i
$895$	60.9738			2.03813
$896$	−3.29056	+	1.89981i	−0.109930	+	0.0634681i
$897$	−41.1888	+	22.3505i	−1.37525	+	0.746263i
$898$	−10.4188	+	18.0459i	−0.347681	+	0.602201i
$899$	−7.27276			−0.242560
$900$	−27.8918	−	1.47552i	−0.929725	−	0.0491842i
$901$	−0.145438	−	0.0839686i	−0.00484524	−	0.00279740i
$902$	7.64593	+	4.41438i	0.254582	+	0.146983i
$903$	57.7115	+	1.52545i	1.92052	+	0.0507640i
$904$	1.02214	−	1.77040i	0.0339958	−	0.0588825i
$905$	−38.9895	−	22.5106i	−1.29606	−	0.748278i
$906$	8.56252	+	15.7795i	0.284471	+	0.524238i
$907$	−11.1347	+	6.42865i	−0.369723	+	0.213460i	−0.673338	−	0.739335i	$-0.735140\pi$
$907$	−11.1347	+	6.42865i	−0.369723	+	0.213460i	0.303614	+	0.952795i	$0.401807\pi$
$908$	−6.45725	+	3.72810i	−0.214291	+	0.123721i
$909$	8.17839	−	12.5800i	0.271260	−	0.417254i
$910$	−81.2284	+	46.8972i	−2.69269	+	1.55463i
$911$	−28.2128	−	16.2887i	−0.934732	−	0.539668i	−0.0464267	−	0.998922i	$-0.514783\pi$
$911$	−28.2128	−	16.2887i	−0.934732	−	0.539668i	−0.888305	+	0.459254i	$0.848117\pi$
$912$	6.34958	−	10.3558i	0.210256	−	0.342916i
$913$	−16.2949	+	28.2235i	−0.539281	+	0.934062i
$914$	−10.3560	−	17.9371i	−0.342546	−	0.593307i
$915$	12.6139	−	6.84475i	0.417002	−	0.226281i
$916$	−25.1134			−0.829769
$917$		−	15.7560i		−	0.520309i
$918$	−25.0463	+	11.9238i	−0.826652	+	0.393543i
$919$		−	23.6294i		−	0.779461i	−0.920929	−	0.389731i	$-0.872568\pi$
$919$		−	23.6294i		−	0.779461i	0.920929	−	0.389731i	$-0.127432\pi$
$920$	13.5832	−	7.84227i	0.447825	−	0.258552i
$921$	1.15224	−	43.5919i	0.0379676	−	1.43640i
$922$	−24.6713			−0.812506
$923$	−43.5689	−	25.1545i	−1.43409	−	0.827970i
$924$	−0.618479	+	23.3985i	−0.0203465	+	0.769755i
$925$	−56.6142	+	1.42128i	−1.86146	+	0.0467314i
$926$	22.8695			0.751538
$927$	19.8114	−	10.0821i	0.650691	−	0.331140i
$928$	−0.561729	+	0.972944i	−0.0184397	+	0.0319384i
$929$	8.74712	+	15.1505i	0.286984	+	0.497071i	0.973088	−	0.230432i	$-0.0740141\pi$
$929$	8.74712	+	15.1505i	0.286984	+	0.497071i	−0.686105	+	0.727503i	$0.740681\pi$
$930$	20.2298	+	37.2806i	0.663363	+	1.22248i
$931$	45.1708	−	26.0794i	1.48041	−	0.854717i
$932$	−22.4357			−0.734906
$933$	5.41959	−	8.83908i	0.177430	−	0.289379i
$934$	−7.44344			−0.243557
$935$	−71.8264			−2.34897
$936$	−19.5492	−	1.03419i	−0.638984	−	0.0338034i
$937$	−21.7863	−	37.7351i	−0.711729	−	1.23275i	−0.964208	−	0.265148i	$-0.914579\pi$
$937$	−21.7863	−	37.7351i	−0.711729	−	1.23275i	0.252479	−	0.967602i	$-0.418754\pi$
$938$	−32.7507	+	18.9086i	−1.06935	+	0.617389i
$939$	−40.3280	−	1.06597i	−1.31606	−	0.0347865i
$940$	2.86928	+	1.65658i	0.0935856	+	0.0540317i
$941$	4.85239	−	8.40459i	0.158183	−	0.273982i	−0.776030	−	0.630696i	$-0.782770\pi$
$941$	4.85239	−	8.40459i	0.158183	−	0.273982i	0.934214	+	0.356714i	$0.116103\pi$
$942$	−1.70315	+	2.77775i	−0.0554916	+	0.0905041i
$943$	8.91331	−	5.14610i	0.290257	−	0.167580i
$944$	2.15572	+	1.24461i	0.0701628	+	0.0405085i
$945$	−32.1038	−	67.4352i	−1.04434	−	2.19367i
$946$	15.5999	+	27.0199i	0.507198	+	0.878493i
$947$			24.4430i			0.794291i	0.917756	+	0.397146i	$0.129999\pi$
$947$			24.4430i			0.794291i	−0.917756	+	0.397146i	$0.870001\pi$
$948$	7.20686	+	13.2812i	0.234068	+	0.431353i
$949$		−	13.7781i		−	0.447255i
$950$	−32.6480	+	56.5479i	−1.05924	+	1.83466i
$951$	−0.684792	+	25.9073i	−0.0222059	+	0.840101i
$952$	10.1422	−	17.5667i	0.328709	−	0.569341i
$953$	−25.8223	−	44.7255i	−0.836465	−	1.44880i	−0.892832	−	0.450389i	$-0.851285\pi$
$953$	−25.8223	−	44.7255i	−0.836465	−	1.44880i	0.0563674	−	0.998410i	$-0.482048\pi$
$954$	0.0841080	−	0.0428030i	0.00272310	−	0.00138580i
$955$	−30.2002	+	52.3082i	−0.977254	+	1.69265i
$956$	−22.0496	−	12.7303i	−0.713135	−	0.411729i
$957$	3.30083	+	6.08294i	0.106701	+	0.196634i
$958$	28.3050			0.914493
$959$	−45.8485			−1.48053
$960$	6.54987	+	0.173129i	0.211396	+	0.00558771i
$961$	5.45341	−	9.44558i	0.175916	−	0.304696i
$962$	−39.6806	+	0.996166i	−1.27935	+	0.0321177i
$963$	18.3196	−	28.1793i	0.590340	−	0.908064i
$964$	17.2958	−	9.98575i	0.557061	−	0.321619i
$965$	0.937343	+	1.62353i	0.0301741	+	0.0522631i
$966$	23.2621	+	14.2629i	0.748445	+	0.458901i
$967$			33.6673i			1.08267i	0.840808	+	0.541334i	$0.182080\pi$
$967$			33.6673i			1.08267i	−0.840808	+	0.541334i	$0.817920\pi$
$968$	−1.42865	+	0.824832i	−0.0459186	+	0.0265111i
$969$	−1.71353	+	64.8268i	−0.0550465	+	2.08254i
$970$	−25.5285	−	14.7389i	−0.819670	−	0.473237i
$971$	7.81989	+	13.5445i	0.250952	+	0.434662i	0.963788	−	0.266669i	$-0.0859229\pi$
$971$	7.81989	+	13.5445i	0.250952	+	0.434662i	−0.712836	+	0.701331i	$0.752590\pi$
$972$	2.05374	−	15.4526i	0.0658736	−	0.495642i
$973$	46.8071			1.50057
$974$	−11.7025			−0.374971
$975$	105.192	+	2.78049i	3.36885	+	0.0890469i
$976$	−1.89687	+	1.09516i	−0.0607174	+	0.0350552i
$977$	34.8984	+	20.1486i	1.11650	+	0.644610i	0.940504	−	0.339781i	$-0.110353\pi$
$977$	34.8984	+	20.1486i	1.11650	+	0.644610i	0.175993	+	0.984391i	$0.443686\pi$
$978$	12.9187	−	7.01015i	0.413094	−	0.224160i
$979$			13.4610i			0.430215i
$980$	24.3645	+	14.0668i	0.778295	+	0.449349i
$981$	16.1075	−	8.19718i	0.514272	−	0.261716i
$982$	19.8983	−	11.4883i	0.634979	−	0.366605i
$983$	−34.6400			−1.10484			−0.552422	−	0.833565i	$-0.686296\pi$
$983$	−34.6400			−1.10484			−0.552422	+	0.833565i	$0.686296\pi$
$984$	4.29803	+	0.113607i	0.137016	+	0.00362167i
$985$	−7.28688	+	4.20708i	−0.232179	+	0.134049i
$986$		−	5.99761i		−	0.191003i
$987$	−0.152302	+	5.76192i	−0.00484781	+	0.183404i
$988$	−22.8828	+	39.6341i	−0.727997	+	1.26093i
$989$	36.3715			1.15655
$990$	22.0000	−	33.8405i	0.699206	−	1.07552i
$991$			47.4401i			1.50698i	0.657458	+	0.753492i	$0.271632\pi$
$991$			47.4401i			1.50698i	−0.657458	+	0.753492i	$0.728368\pi$
$992$	−3.23677	−	5.60626i	−0.102768	−	0.177999i
$993$	−41.6645	−	1.10129i	−1.32218	−	0.0349485i
$994$			29.2935i			0.929134i
$995$	6.57649			0.208489
$996$	−0.419360	+	15.8654i	−0.0132879	+	0.502713i
$997$		−	27.7932i		−	0.880221i	−0.897944	−	0.440110i	$-0.854939\pi$
$997$		−	27.7932i		−	0.880221i	0.897944	−	0.440110i	$-0.145061\pi$
$998$	−0.603810			−0.0191133
$999$	1.71161	−	31.5606i	0.0541530	−	0.998533i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.529.28	yes	76
3.2	odd	2		1998.2.k.a.1639.17		76
9.4	even	3		666.2.t.a.85.4	yes	76
9.5	odd	6		1998.2.t.a.307.22		76
37.27	even	6		666.2.t.a.619.4	yes	76
111.101	odd	6		1998.2.t.a.397.22		76
333.175	even	6	inner	666.2.k.a.175.9	✓	76
333.212	odd	6		1998.2.k.a.1063.22		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.9	✓	76	333.175	even	6	inner
666.2.k.a.529.28	yes	76	1.1	even	1	trivial
666.2.t.a.85.4	yes	76	9.4	even	3
666.2.t.a.619.4	yes	76	37.27	even	6
1998.2.k.a.1063.22		76	333.212	odd	6
1998.2.k.a.1639.17		76	3.2	odd	2
1998.2.t.a.307.22		76	9.5	odd	6
1998.2.t.a.397.22		76	111.101	odd	6

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.0457663 + 1.73145i) q^{3} -1.00000 q^{4} +3.78289i q^{5} +(-1.73145 - 0.0457663i) q^{6} +(-1.89981 - 3.29056i) q^{7} -1.00000i q^{8} +(-2.99581 - 0.158484i) q^{9} -3.78289 q^{10} +(1.77832 - 3.08014i) q^{11} +(0.0457663 - 1.73145i) q^{12} +6.52550i q^{13} +(3.29056 - 1.89981i) q^{14} +(-6.54987 - 0.173129i) q^{15} +1.00000 q^{16} +(-4.62329 + 2.66926i) q^{17} +(0.158484 - 2.99581i) q^{18} +(-6.07373 - 3.50667i) q^{19} -3.78289i q^{20} +(5.78438 - 3.13882i) q^{21} +(3.08014 + 1.77832i) q^{22} +(3.59070 - 2.07309i) q^{23} +(1.73145 + 0.0457663i) q^{24} -9.31025 q^{25} -6.52550 q^{26} +(0.411513 - 5.17983i) q^{27} +(1.89981 + 3.29056i) q^{28} +(0.972944 + 0.561729i) q^{29} +(0.173129 - 6.54987i) q^{30} +(-5.60626 + 3.23677i) q^{31} +1.00000i q^{32} +(5.25171 + 3.22003i) q^{33} +(-2.66926 - 4.62329i) q^{34} +(12.4478 - 7.18677i) q^{35} +(2.99581 + 0.158484i) q^{36} +(6.08085 - 0.152657i) q^{37} +(3.50667 - 6.07373i) q^{38} +(-11.2985 - 0.298648i) q^{39} +3.78289 q^{40} +2.48234 q^{41} +(3.13882 + 5.78438i) q^{42} +(7.59704 + 4.38615i) q^{43} +(-1.77832 + 3.08014i) q^{44} +(0.599527 - 11.3328i) q^{45} +(2.07309 + 3.59070i) q^{46} +(-0.437914 + 0.758489i) q^{47} +(-0.0457663 + 1.73145i) q^{48} +(-3.71854 + 6.44071i) q^{49} -9.31025i q^{50} +(-4.41009 - 8.12714i) q^{51} -6.52550i q^{52} +(0.0157288 + 0.0272431i) q^{53} +(5.17983 + 0.411513i) q^{54} +(11.6518 + 6.72718i) q^{55} +(-3.29056 + 1.89981i) q^{56} +(6.34958 - 10.3558i) q^{57} +(-0.561729 + 0.972944i) q^{58} +(2.15572 + 1.24461i) q^{59} +(6.54987 + 0.173129i) q^{60} +(-1.89687 + 1.09516i) q^{61} +(-3.23677 - 5.60626i) q^{62} +(5.16997 + 10.1590i) q^{63} -1.00000 q^{64} -24.6852 q^{65} +(-3.22003 + 5.25171i) q^{66} -9.95292 q^{67} +(4.62329 - 2.66926i) q^{68} +(3.42511 + 6.31197i) q^{69} +(7.18677 + 12.4478i) q^{70} +(-3.85480 + 6.67671i) q^{71} +(-0.158484 + 2.99581i) q^{72} -2.11142 q^{73} +(0.152657 + 6.08085i) q^{74} +(0.426096 - 16.1202i) q^{75} +(6.07373 + 3.50667i) q^{76} -13.5139 q^{77} +(0.298648 - 11.2985i) q^{78} +(-7.55528 + 4.36204i) q^{79} +3.78289i q^{80} +(8.94977 + 0.949575i) q^{81} +2.48234i q^{82} -9.16307 q^{83} +(-5.78438 + 3.13882i) q^{84} +(-10.0975 - 17.4894i) q^{85} +(-4.38615 + 7.59704i) q^{86} +(-1.01713 + 1.65889i) q^{87} +(-3.08014 - 1.77832i) q^{88} +(-3.27769 + 1.89238i) q^{89} +(11.3328 + 0.599527i) q^{90} +(21.4726 - 12.3972i) q^{91} +(-3.59070 + 2.07309i) q^{92} +(-5.34772 - 9.85507i) q^{93} +(-0.758489 - 0.437914i) q^{94} +(13.2653 - 22.9762i) q^{95} +(-1.73145 - 0.0457663i) q^{96} +(6.74841 + 3.89619i) q^{97} +(-6.44071 - 3.71854i) q^{98} +(-5.81566 + 8.94568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Introduction

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