LMFDB - Embedded newform 546.2.bi.f.257.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.4
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.f.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.23948 - 1.20983i) q^{3} +1.00000 q^{4} +(1.58996 + 0.917964i) q^{5} +(-1.23948 - 1.20983i) q^{6} +(-0.364289 + 2.62055i) q^{7} +1.00000 q^{8} +(0.0726040 + 2.99912i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.23948 - 1.20983i) q^{3} +1.00000 q^{4} +(1.58996 + 0.917964i) q^{5} +(-1.23948 - 1.20983i) q^{6} +(-0.364289 + 2.62055i) q^{7} +1.00000 q^{8} +(0.0726040 + 2.99912i) q^{9} +(1.58996 + 0.917964i) q^{10} +(-1.69625 + 2.93798i) q^{11} +(-1.23948 - 1.20983i) q^{12} +(3.07128 + 1.88872i) q^{13} +(-0.364289 + 2.62055i) q^{14} +(-0.860135 - 3.06138i) q^{15} +1.00000 q^{16} +3.18506 q^{17} +(0.0726040 + 2.99912i) q^{18} +(-1.01582 - 1.75945i) q^{19} +(1.58996 + 0.917964i) q^{20} +(3.62196 - 2.80738i) q^{21} +(-1.69625 + 2.93798i) q^{22} +2.47560i q^{23} +(-1.23948 - 1.20983i) q^{24} +(-0.814684 - 1.41107i) q^{25} +(3.07128 + 1.88872i) q^{26} +(3.53845 - 3.80518i) q^{27} +(-0.364289 + 2.62055i) q^{28} +(1.81857 - 1.04995i) q^{29} +(-0.860135 - 3.06138i) q^{30} +(-3.14345 - 5.44461i) q^{31} +1.00000 q^{32} +(5.65693 - 1.58939i) q^{33} +3.18506 q^{34} +(-2.98478 + 3.83217i) q^{35} +(0.0726040 + 2.99912i) q^{36} +0.503913i q^{37} +(-1.01582 - 1.75945i) q^{38} +(-1.52175 - 6.05676i) q^{39} +(1.58996 + 0.917964i) q^{40} +(4.35184 - 2.51254i) q^{41} +(3.62196 - 2.80738i) q^{42} +(0.528972 - 0.916206i) q^{43} +(-1.69625 + 2.93798i) q^{44} +(-2.63765 + 4.83513i) q^{45} +2.47560i q^{46} +(10.0977 + 5.82991i) q^{47} +(-1.23948 - 1.20983i) q^{48} +(-6.73459 - 1.90927i) q^{49} +(-0.814684 - 1.41107i) q^{50} +(-3.94781 - 3.85339i) q^{51} +(3.07128 + 1.88872i) q^{52} +(-5.81668 + 3.35826i) q^{53} +(3.53845 - 3.80518i) q^{54} +(-5.39393 + 3.11418i) q^{55} +(-0.364289 + 2.62055i) q^{56} +(-0.869560 + 3.40977i) q^{57} +(1.81857 - 1.04995i) q^{58} +6.20893i q^{59} +(-0.860135 - 3.06138i) q^{60} +(10.1157 - 5.84028i) q^{61} +(-3.14345 - 5.44461i) q^{62} +(-7.88580 - 0.902283i) q^{63} +1.00000 q^{64} +(3.14944 + 5.82231i) q^{65} +(5.65693 - 1.58939i) q^{66} +(-8.59785 - 4.96397i) q^{67} +3.18506 q^{68} +(2.99507 - 3.06845i) q^{69} +(-2.98478 + 3.83217i) q^{70} +(-7.77030 + 13.4586i) q^{71} +(0.0726040 + 2.99912i) q^{72} +(-4.47574 - 7.75221i) q^{73} +0.503913i q^{74} +(-0.697383 + 2.73462i) q^{75} +(-1.01582 - 1.75945i) q^{76} +(-7.08122 - 5.51537i) q^{77} +(-1.52175 - 6.05676i) q^{78} +(3.92399 - 6.79656i) q^{79} +(1.58996 + 0.917964i) q^{80} +(-8.98946 + 0.435496i) q^{81} +(4.35184 - 2.51254i) q^{82} -13.0790i q^{83} +(3.62196 - 2.80738i) q^{84} +(5.06412 + 2.92377i) q^{85} +(0.528972 - 0.916206i) q^{86} +(-3.52435 - 0.898778i) q^{87} +(-1.69625 + 2.93798i) q^{88} +5.33363i q^{89} +(-2.63765 + 4.83513i) q^{90} +(-6.06831 + 7.36041i) q^{91} +2.47560i q^{92} +(-2.69085 + 10.5515i) q^{93} +(10.0977 + 5.82991i) q^{94} -3.72995i q^{95} +(-1.23948 - 1.20983i) q^{96} +(-4.79907 + 8.31223i) q^{97} +(-6.73459 - 1.90927i) q^{98} +(-8.93452 - 4.87394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.23948	−	1.20983i	−0.715612	−	0.698498i
$3$	−1.23948	−	1.20983i	−0.715612	−	0.698498i
$4$	1.00000			0.500000
$5$	1.58996	+	0.917964i	0.711052	+	0.410526i	0.811450	−	0.584421i	$-0.198678\pi$
$5$	1.58996	+	0.917964i	0.711052	+	0.410526i	−0.100398	+	0.994947i	$0.532012\pi$
$6$	−1.23948	−	1.20983i	−0.506014	−	0.493913i
$7$	−0.364289	+	2.62055i	−0.137688	+	0.990476i
$7$	−0.364289	+	2.62055i	−0.137688	+	0.990476i
$8$	1.00000			0.353553
$9$	0.0726040	+	2.99912i	0.0242013	+	0.999707i
$10$	1.58996	+	0.917964i	0.502790	+	0.290286i
$11$	−1.69625	+	2.93798i	−0.511437	+	0.885835i	0.488475	+	0.872578i	$0.337553\pi$
$11$	−1.69625	+	2.93798i	−0.511437	+	0.885835i	−0.999912	+	0.0132573i	$0.995780\pi$
$12$	−1.23948	−	1.20983i	−0.357806	−	0.349249i
$13$	3.07128	+	1.88872i	0.851820	+	0.523835i
$13$	3.07128	+	1.88872i	0.851820	+	0.523835i
$14$	−0.364289	+	2.62055i	−0.0973602	+	0.700372i
$15$	−0.860135	−	3.06138i	−0.222086	−	0.790446i
$16$	1.00000			0.250000
$17$	3.18506			0.772490			0.386245	−	0.922396i	$-0.373772\pi$
$17$	3.18506			0.772490			0.386245	+	0.922396i	$0.373772\pi$
$18$	0.0726040	+	2.99912i	0.0171129	+	0.706900i
$19$	−1.01582	−	1.75945i	−0.233045	−	0.403646i	0.725658	−	0.688056i	$-0.241536\pi$
$19$	−1.01582	−	1.75945i	−0.233045	−	0.403646i	−0.958703	+	0.284410i	$0.908202\pi$
$20$	1.58996	+	0.917964i	0.355526	+	0.205263i
$21$	3.62196	−	2.80738i	0.790376	−	0.612621i
$22$	−1.69625	+	2.93798i	−0.361641	+	0.626380i
$23$			2.47560i			0.516199i	0.966118	+	0.258099i	$0.0830962\pi$
$23$			2.47560i			0.516199i	−0.966118	+	0.258099i	$0.916904\pi$
$24$	−1.23948	−	1.20983i	−0.253007	−	0.246956i
$25$	−0.814684	−	1.41107i	−0.162937	−	0.282215i
$26$	3.07128	+	1.88872i	0.602327	+	0.370407i
$27$	3.53845	−	3.80518i	0.680975	−	0.732307i
$28$	−0.364289	+	2.62055i	−0.0688441	+	0.495238i
$29$	1.81857	−	1.04995i	0.337701	−	0.194971i	−0.321554	−	0.946891i	$-0.604205\pi$
$29$	1.81857	−	1.04995i	0.337701	−	0.194971i	0.659255	+	0.751920i	$0.270872\pi$
$30$	−0.860135	−	3.06138i	−0.157038	−	0.558930i
$31$	−3.14345	−	5.44461i	−0.564580	−	0.977881i	−0.997089	−	0.0762515i	$-0.975705\pi$
$31$	−3.14345	−	5.44461i	−0.564580	−	0.977881i	0.432509	−	0.901630i	$-0.357629\pi$
$32$	1.00000			0.176777
$33$	5.65693	−	1.58939i	0.984745	−	0.276677i
$34$	3.18506			0.546233
$35$	−2.98478	+	3.83217i	−0.504519	+	0.647755i
$36$	0.0726040	+	2.99912i	0.0121007	+	0.499854i
$37$			0.503913i			0.0828428i	0.999142	+	0.0414214i	$0.0131886\pi$
$37$			0.503913i			0.0828428i	−0.999142	+	0.0414214i	$0.986811\pi$
$38$	−1.01582	−	1.75945i	−0.164788	−	0.285421i
$39$	−1.52175	−	6.05676i	−0.243675	−	0.969857i
$40$	1.58996	+	0.917964i	0.251395	+	0.145143i
$41$	4.35184	−	2.51254i	0.679643	−	0.392392i	−0.120077	−	0.992765i	$-0.538314\pi$
$41$	4.35184	−	2.51254i	0.679643	−	0.392392i	0.799721	+	0.600372i	$0.204981\pi$
$42$	3.62196	−	2.80738i	0.558881	−	0.433189i
$43$	0.528972	−	0.916206i	0.0806674	−	0.139720i	−0.822869	−	0.568231i	$-0.807628\pi$
$43$	0.528972	−	0.916206i	0.0806674	−	0.139720i	0.903537	+	0.428511i	$0.140962\pi$
$44$	−1.69625	+	2.93798i	−0.255719	+	0.442918i
$45$	−2.63765	+	4.83513i	−0.393197	+	0.720779i
$46$			2.47560i			0.365008i
$47$	10.0977	+	5.82991i	1.47290	+	0.850380i	0.999535	−	0.0304848i	$-0.00970512\pi$
$47$	10.0977	+	5.82991i	1.47290	+	0.850380i	0.473367	+	0.880865i	$0.343038\pi$
$48$	−1.23948	−	1.20983i	−0.178903	−	0.174624i
$49$	−6.73459	−	1.90927i	−0.962084	−	0.272754i
$50$	−0.814684	−	1.41107i	−0.115214	−	0.199556i
$51$	−3.94781	−	3.85339i	−0.552803	−	0.539583i
$52$	3.07128	+	1.88872i	0.425910	+	0.261918i
$53$	−5.81668	+	3.35826i	−0.798983	+	0.461293i	−0.843115	−	0.537733i	$-0.819281\pi$
$53$	−5.81668	+	3.35826i	−0.798983	+	0.461293i	0.0441326	+	0.999026i	$0.485948\pi$
$54$	3.53845	−	3.80518i	0.481522	−	0.517819i
$55$	−5.39393	+	3.11418i	−0.727317	+	0.419917i
$56$	−0.364289	+	2.62055i	−0.0486801	+	0.350186i
$57$	−0.869560	+	3.40977i	−0.115176	+	0.451636i
$58$	1.81857	−	1.04995i	0.238790	−	0.137866i
$59$			6.20893i			0.808333i	0.914685	+	0.404167i	$0.132438\pi$
$59$			6.20893i			0.808333i	−0.914685	+	0.404167i	$0.867562\pi$
$60$	−0.860135	−	3.06138i	−0.111043	−	0.395223i
$61$	10.1157	−	5.84028i	1.29518	−	0.747771i	0.315610	−	0.948889i	$-0.397791\pi$
$61$	10.1157	−	5.84028i	1.29518	−	0.747771i	0.979567	+	0.201118i	$0.0644575\pi$
$62$	−3.14345	−	5.44461i	−0.399218	−	0.691467i
$63$	−7.88580	−	0.902283i	−0.993518	−	0.113677i
$64$	1.00000			0.125000
$65$	3.14944	+	5.82231i	0.390640	+	0.722168i
$66$	5.65693	−	1.58939i	0.696320	−	0.195640i
$67$	−8.59785	−	4.96397i	−1.05039	−	0.606445i	−0.127634	−	0.991821i	$-0.540738\pi$
$67$	−8.59785	−	4.96397i	−1.05039	−	0.606445i	−0.922760	+	0.385376i	$0.874072\pi$
$68$	3.18506			0.386245
$69$	2.99507	−	3.06845i	0.360564	−	0.369398i
$70$	−2.98478	+	3.83217i	−0.356749	+	0.458032i
$71$	−7.77030	+	13.4586i	−0.922165	+	1.59724i	−0.126108	+	0.992017i	$0.540248\pi$
$71$	−7.77030	+	13.4586i	−0.922165	+	1.59724i	−0.796058	+	0.605221i	$0.793085\pi$
$72$	0.0726040	+	2.99912i	0.00855646	+	0.353450i
$73$	−4.47574	−	7.75221i	−0.523846	−	0.907327i	−0.999615	−	0.0277570i	$-0.991164\pi$
$73$	−4.47574	−	7.75221i	−0.523846	−	0.907327i	0.475769	−	0.879570i	$-0.342170\pi$
$74$			0.503913i			0.0585787i
$75$	−0.697383	+	2.73462i	−0.0805269	+	0.315767i
$76$	−1.01582	−	1.75945i	−0.116523	−	0.201823i
$77$	−7.08122	−	5.51537i	−0.806979	−	0.628535i
$78$	−1.52175	−	6.05676i	−0.172304	−	0.685793i
$79$	3.92399	−	6.79656i	0.441484	−	0.764672i	−0.556316	−	0.830971i	$-0.687786\pi$
$79$	3.92399	−	6.79656i	0.441484	−	0.764672i	0.997800	+	0.0662985i	$0.0211189\pi$
$80$	1.58996	+	0.917964i	0.177763	+	0.102632i
$81$	−8.98946	+	0.435496i	−0.998829	+	0.0483885i
$82$	4.35184	−	2.51254i	0.480580	−	0.277463i
$83$		−	13.0790i		−	1.43561i	−0.696246	−	0.717803i	$-0.745148\pi$
$83$		−	13.0790i		−	1.43561i	0.696246	−	0.717803i	$-0.254852\pi$
$84$	3.62196	−	2.80738i	0.395188	−	0.306311i
$85$	5.06412	+	2.92377i	0.549281	+	0.317127i
$86$	0.528972	−	0.916206i	0.0570405	−	0.0987970i
$87$	−3.52435	−	0.898778i	−0.377850	−	0.0963592i
$88$	−1.69625	+	2.93798i	−0.180820	+	0.313190i
$89$			5.33363i			0.565364i	0.959214	+	0.282682i	$0.0912240\pi$
$89$			5.33363i			0.565364i	−0.959214	+	0.282682i	$0.908776\pi$
$90$	−2.63765	+	4.83513i	−0.278033	+	0.509668i
$91$	−6.06831	+	7.36041i	−0.636132	+	0.771581i
$92$			2.47560i			0.258099i
$93$	−2.69085	+	10.5515i	−0.279028	+	1.09414i
$94$	10.0977	+	5.82991i	1.04150	+	0.601310i
$95$		−	3.72995i		−	0.382684i
$96$	−1.23948	−	1.20983i	−0.126504	−	0.123478i
$97$	−4.79907	+	8.31223i	−0.487272	+	0.843979i	−0.999893	−	0.0146357i	$-0.995341\pi$
$97$	−4.79907	+	8.31223i	−0.487272	+	0.843979i	0.512621	+	0.858615i	$0.328674\pi$
$98$	−6.73459	−	1.90927i	−0.680296	−	0.192866i
$99$	−8.93452	−	4.87394i	−0.897953	−	0.489849i
$100$	−0.814684	−	1.41107i	−0.0814684	−	0.141107i
$101$	4.69535	−	8.13258i	0.467204	−	0.809222i	−0.532094	−	0.846686i	$-0.678595\pi$
$101$	4.69535	−	8.13258i	0.467204	−	0.809222i	0.999298	+	0.0374637i	$0.0119279\pi$
$102$	−3.94781	−	3.85339i	−0.390891	−	0.381543i
$103$	−11.5646	−	6.67680i	−1.13949	−	0.657884i	−0.193185	−	0.981162i	$-0.561882\pi$
$103$	−11.5646	−	6.67680i	−1.13949	−	0.657884i	−0.946304	+	0.323278i	$0.895215\pi$
$104$	3.07128	+	1.88872i	0.301164	+	0.185204i
$105$	8.33585	−	1.13880i	0.813496	−	0.111136i
$106$	−5.81668	+	3.35826i	−0.564966	+	0.326183i
$107$		−	13.3709i		−	1.29262i	−0.763076	−	0.646309i	$-0.776312\pi$
$107$		−	13.3709i		−	1.29262i	0.763076	−	0.646309i	$-0.223688\pi$
$108$	3.53845	−	3.80518i	0.340487	−	0.366154i
$109$	3.82963	−	2.21104i	0.366812	−	0.211779i	−0.305253	−	0.952271i	$-0.598741\pi$
$109$	3.82963	−	2.21104i	0.366812	−	0.211779i	0.672065	+	0.740492i	$0.265408\pi$
$110$	−5.39393	+	3.11418i	−0.514291	+	0.296926i
$111$	0.609651	−	0.624589i	0.0578655	−	0.0592833i
$112$	−0.364289	+	2.62055i	−0.0344220	+	0.247619i
$113$	−13.8390	−	7.98994i	−1.30186	−	0.751631i	−0.321139	−	0.947032i	$-0.604066\pi$
$113$	−13.8390	−	7.98994i	−1.30186	−	0.751631i	−0.980723	+	0.195402i	$0.937399\pi$
$114$	−0.869560	+	3.40977i	−0.0814417	+	0.319355i
$115$	−2.27251	+	3.93611i	−0.211913	+	0.367044i
$116$	1.81857	−	1.04995i	0.168850	−	0.0974857i
$117$	−5.44150	+	9.34827i	−0.503067	+	0.864248i
$118$			6.20893i			0.571578i
$119$	−1.16028	+	8.34661i	−0.106363	+	0.765133i
$120$	−0.860135	−	3.06138i	−0.0785192	−	0.279465i
$121$	−0.254496	−	0.440801i	−0.0231360	−	0.0400728i
$122$	10.1157	−	5.84028i	0.915829	−	0.528754i
$123$	−8.43375	−	2.15077i	−0.760446	−	0.193929i
$124$	−3.14345	−	5.44461i	−0.282290	−	0.488941i
$125$		−	12.1710i		−	1.08861i
$126$	−7.88580	−	0.902283i	−0.702523	−	0.0803818i
$127$	−0.475986	−	0.824432i	−0.0422370	−	0.0731566i	0.844134	−	0.536132i	$-0.180115\pi$
$127$	−0.475986	−	0.824432i	−0.0422370	−	0.0731566i	−0.886371	+	0.462976i	$0.846782\pi$
$128$	1.00000			0.0883883
$129$	−1.76410	+	0.495648i	−0.155321	+	0.0436393i
$130$	3.14944	+	5.82231i	0.276224	+	0.510650i
$131$	−4.95760	+	8.58681i	−0.433147	+	0.750233i	−0.997142	−	0.0755449i	$-0.975930\pi$
$131$	−4.95760	+	8.58681i	−0.433147	+	0.750233i	0.563995	+	0.825778i	$0.309264\pi$
$132$	5.65693	−	1.58939i	0.492372	−	0.138338i
$133$	4.98079	−	2.02106i	0.431889	−	0.175248i
$134$	−8.59785	−	4.96397i	−0.742741	−	0.428822i
$135$	9.11901	−	2.80192i	0.784839	−	0.241151i
$136$	3.18506			0.273117
$137$	3.18307			0.271948			0.135974	−	0.990712i	$-0.456584\pi$
$137$	3.18307			0.271948			0.135974	+	0.990712i	$0.456584\pi$
$138$	2.99507	−	3.06845i	0.254957	−	0.261204i
$139$	0.0981681	+	0.0566774i	0.00832651	+	0.00480731i	0.504157	−	0.863612i	$-0.331803\pi$
$139$	0.0981681	+	0.0566774i	0.00832651	+	0.00480731i	−0.495831	+	0.868419i	$0.665136\pi$
$140$	−2.98478	+	3.83217i	−0.252260	+	0.323878i
$141$	−5.46264	−	19.4426i	−0.460038	−	1.63736i
$142$	−7.77030	+	13.4586i	−0.652069	+	1.12942i
$143$	−10.7587	+	5.81964i	−0.899684	+	0.486663i
$144$	0.0726040	+	2.99912i	0.00605033	+	0.249927i
$145$	3.85528			0.320164
$146$	−4.47574	−	7.75221i	−0.370415	−	0.641577i
$147$	6.03746	+	10.5142i	0.497961	+	0.867199i
$148$			0.503913i			0.0414214i
$149$	10.8563	+	18.8036i	0.889382	+	1.54045i	0.840608	+	0.541644i	$0.182198\pi$
$149$	10.8563	+	18.8036i	0.889382	+	1.54045i	0.0487739	+	0.998810i	$0.484469\pi$
$150$	−0.697383	+	2.73462i	−0.0569411	+	0.223281i
$151$	−4.69698	+	2.71180i	−0.382235	+	0.220684i	−0.678790	−	0.734332i	$-0.737495\pi$
$151$	−4.69698	+	2.71180i	−0.382235	+	0.220684i	0.296555	+	0.955016i	$0.404162\pi$
$152$	−1.01582	−	1.75945i	−0.0823939	−	0.142710i
$153$	0.231248	+	9.55238i	0.0186953	+	0.772264i
$154$	−7.08122	−	5.51537i	−0.570621	−	0.444441i
$155$		−	11.5423i		−	0.927099i
$156$	−1.52175	−	6.05676i	−0.121837	−	0.484929i
$157$	18.4221	−	10.6360i	1.47025	−	0.848848i	0.470805	−	0.882237i	$-0.343964\pi$
$157$	18.4221	−	10.6360i	1.47025	−	0.848848i	0.999442	+	0.0333895i	$0.0106302\pi$
$158$	3.92399	−	6.79656i	0.312176	−	0.540705i
$159$	11.2726	+	2.87473i	0.893974	+	0.227981i
$160$	1.58996	+	0.917964i	0.125697	+	0.0725714i
$161$	−6.48744	−	0.901834i	−0.511282	−	0.0710744i
$162$	−8.98946	+	0.435496i	−0.706278	+	0.0342158i
$163$	8.67648	−	5.00937i	0.679594	−	0.392364i	−0.120108	−	0.992761i	$-0.538324\pi$
$163$	8.67648	−	5.00937i	0.679594	−	0.392364i	0.799702	+	0.600397i	$0.204991\pi$
$164$	4.35184	−	2.51254i	0.339822	−	0.196196i
$165$	10.4533	+	2.66580i	0.813788	+	0.207532i
$166$		−	13.0790i		−	1.01513i
$167$	3.11618	−	1.79913i	0.241137	−	0.139221i	−0.374562	−	0.927202i	$-0.622207\pi$
$167$	3.11618	−	1.79913i	0.241137	−	0.139221i	0.615699	+	0.787981i	$0.288874\pi$
$168$	3.62196	−	2.80738i	0.279440	−	0.216594i
$169$	5.86551	+	11.6015i	0.451193	+	0.892426i
$170$	5.06412	+	2.92377i	0.388400	+	0.224243i
$171$	5.20306	−	3.17431i	0.397888	−	0.242746i
$172$	0.528972	−	0.916206i	0.0403337	−	0.0698600i
$173$	−0.476807	−	0.825853i	−0.0362509	−	0.0627885i	0.847331	−	0.531066i	$-0.178208\pi$
$173$	−0.476807	−	0.825853i	−0.0362509	−	0.0627885i	−0.883582	+	0.468277i	$0.844875\pi$
$174$	−3.52435	−	0.898778i	−0.267180	−	0.0681362i
$175$	3.99457	−	1.62088i	0.301961	−	0.122527i
$176$	−1.69625	+	2.93798i	−0.127859	+	0.221459i
$177$	7.51177	−	7.69582i	0.564619	−	0.578453i
$178$			5.33363i			0.399772i
$179$	15.3789	+	8.87903i	1.14948	+	0.663650i	0.948759	−	0.316000i	$-0.102340\pi$
$179$	15.3789	+	8.87903i	1.14948	+	0.663650i	0.200716	+	0.979649i	$0.435673\pi$
$180$	−2.63765	+	4.83513i	−0.196599	+	0.360389i
$181$		−	5.51564i		−	0.409975i	−0.978765	−	0.204987i	$-0.934285\pi$
$181$		−	5.51564i		−	0.409975i	0.978765	−	0.204987i	$-0.0657153\pi$
$182$	−6.06831	+	7.36041i	−0.449813	+	0.545590i
$183$	−19.6039	−	4.99938i	−1.44916	−	0.369565i
$184$			2.47560i			0.182504i
$185$	−0.462574	+	0.801202i	−0.0340091	+	0.0589056i
$186$	−2.69085	+	10.5515i	−0.197302	+	0.773675i
$187$	−5.40264	+	9.35765i	−0.395080	+	0.684299i
$188$	10.0977	+	5.82991i	0.736451	+	0.425190i
$189$	8.68265	+	10.6589i	0.631570	+	0.775319i
$190$		−	3.72995i		−	0.270599i
$191$	17.4751	−	10.0893i	1.26446	−	0.730034i	0.290523	−	0.956868i	$-0.406171\pi$
$191$	17.4751	−	10.0893i	1.26446	−	0.730034i	0.973933	+	0.226834i	$0.0728374\pi$
$192$	−1.23948	−	1.20983i	−0.0894515	−	0.0873122i
$193$	3.93413	+	2.27137i	0.283185	+	0.163497i	0.634864	−	0.772624i	$-0.281056\pi$
$193$	3.93413	+	2.27137i	0.283185	+	0.163497i	−0.351679	+	0.936121i	$0.614389\pi$
$194$	−4.79907	+	8.31223i	−0.344553	+	0.596783i
$195$	3.14037	−	11.0269i	0.224886	−	0.789654i
$196$	−6.73459	−	1.90927i	−0.481042	−	0.136377i
$197$	5.74363	+	9.94826i	0.409217	+	0.708784i	0.994802	−	0.101826i	$-0.0324687\pi$
$197$	5.74363	+	9.94826i	0.409217	+	0.708784i	−0.585585	+	0.810611i	$0.699135\pi$
$198$	−8.93452	−	4.87394i	−0.634949	−	0.346376i
$199$		−	6.86468i		−	0.486624i	−0.969948	−	0.243312i	$-0.921766\pi$
$199$		−	6.86468i		−	0.486624i	0.969948	−	0.243312i	$-0.0782339\pi$
$200$	−0.814684	−	1.41107i	−0.0576068	−	0.0997780i
$201$	4.65125	+	16.5547i	0.328074	+	1.16768i
$202$	4.69535	−	8.13258i	0.330363	−	0.572206i
$203$	2.08897	+	5.14815i	0.146617	+	0.361329i
$204$	−3.94781	−	3.85339i	−0.276402	−	0.269791i
$205$	9.22567			0.644349
$206$	−11.5646	−	6.67680i	−0.805741	−	0.465195i
$207$	−7.42463	+	0.179738i	−0.516047	+	0.0124927i
$208$	3.07128	+	1.88872i	0.212955	+	0.130959i
$209$	6.89232			0.476752
$210$	8.33585	−	1.13880i	0.575228	−	0.0785847i
$211$	−2.63957	−	4.57187i	−0.181715	−	0.314740i	0.760749	−	0.649046i	$-0.224832\pi$
$211$	−2.63957	−	4.57187i	−0.181715	−	0.314740i	−0.942465	+	0.334305i	$0.891498\pi$
$212$	−5.81668	+	3.35826i	−0.399491	+	0.230646i
$213$	25.9137	−	7.28079i	1.77558	−	0.498872i
$214$		−	13.3709i		−	0.914019i
$215$	1.68209	−	0.971154i	0.114717	−	0.0662321i
$216$	3.53845	−	3.80518i	0.240761	−	0.258910i
$217$	15.4130	−	6.25416i	1.04630	−	0.424560i
$218$	3.82963	−	2.21104i	0.259375	−	0.149750i
$219$	−3.83131	+	15.0236i	−0.258896	+	1.01520i
$220$	−5.39393	+	3.11418i	−0.363658	+	0.209958i
$221$	9.78221	+	6.01567i	0.658022	+	0.404658i
$222$	0.609651	−	0.624589i	0.0409171	−	0.0419196i
$223$	−14.2982	−	24.7653i	−0.957481	−	1.65841i	−0.728585	−	0.684955i	$-0.759822\pi$
$223$	−14.2982	−	24.7653i	−0.957481	−	1.65841i	−0.228896	−	0.973451i	$-0.573512\pi$
$224$	−0.364289	+	2.62055i	−0.0243401	+	0.175093i
$225$	4.17283	−	2.54578i	0.278189	−	0.169719i
$226$	−13.8390	−	7.98994i	−0.920556	−	0.531483i
$227$		−	6.00983i		−	0.398886i	−0.979909	−	0.199443i	$-0.936087\pi$
$227$		−	6.00983i		−	0.398886i	0.979909	−	0.199443i	$-0.0639133\pi$
$228$	−0.869560	+	3.40977i	−0.0575880	+	0.225818i
$229$	−7.02836	+	12.1735i	−0.464447	+	0.804446i	−0.999176	−	0.0405773i	$-0.987080\pi$
$229$	−7.02836	+	12.1735i	−0.464447	+	0.804446i	0.534729	+	0.845023i	$0.320414\pi$
$230$	−2.27251	+	3.93611i	−0.149845	+	0.259539i
$231$	2.10431	+	15.4033i	0.138454	+	1.01346i
$232$	1.81857	−	1.04995i	0.119395	−	0.0689328i
$233$	−24.0450	−	13.8824i	−1.57524	−	0.909465i	−0.995510	−	0.0946555i	$-0.969825\pi$
$233$	−24.0450	−	13.8824i	−1.57524	−	0.909465i	−0.579729	−	0.814809i	$-0.696842\pi$
$234$	−5.44150	+	9.34827i	−0.355722	+	0.611115i
$235$	10.7033	+	18.5387i	0.698207	+	1.20933i
$236$			6.20893i			0.404167i
$237$	−13.0864	+	3.67679i	−0.850053	+	0.238833i
$238$	−1.16028	+	8.34661i	−0.0752098	+	0.541031i
$239$	5.31347			0.343700			0.171850	−	0.985123i	$-0.445026\pi$
$239$	5.31347			0.343700			0.171850	+	0.985123i	$0.445026\pi$
$240$	−0.860135	−	3.06138i	−0.0555214	−	0.197611i
$241$	−19.2577			−1.24050			−0.620249	−	0.784405i	$-0.712968\pi$
$241$	−19.2577			−1.24050			−0.620249	+	0.784405i	$0.712968\pi$
$242$	−0.254496	−	0.440801i	−0.0163596	−	0.0283357i
$243$	11.6691	+	10.3360i	0.748573	+	0.663052i
$244$	10.1157	−	5.84028i	0.647589	−	0.373885i
$245$	−8.95508	−	9.21778i	−0.572119	−	0.588902i
$246$	−8.43375	−	2.15077i	−0.537716	−	0.137128i
$247$	0.203236	−	7.32236i	0.0129316	−	0.465911i
$248$	−3.14345	−	5.44461i	−0.199609	−	0.345733i
$249$	−15.8234	+	16.2111i	−1.00277	+	1.02734i
$250$		−	12.1710i		−	0.769764i
$251$	−4.75595	+	8.23755i	−0.300193	+	0.519950i	−0.976180	−	0.216964i	$-0.930384\pi$
$251$	−4.75595	+	8.23755i	−0.300193	+	0.519950i	0.675986	+	0.736914i	$0.263718\pi$
$252$	−7.88580	−	0.902283i	−0.496759	−	0.0568385i
$253$	−7.27328	−	4.19923i	−0.457267	−	0.264003i
$254$	−0.475986	−	0.824432i	−0.0298660	−	0.0517295i
$255$	−2.73958	−	9.75069i	−0.171559	−	0.610612i
$256$	1.00000			0.0625000
$257$	−5.26373			−0.328343			−0.164171	−	0.986432i	$-0.552495\pi$
$257$	−5.26373			−0.328343			−0.164171	+	0.986432i	$0.552495\pi$
$258$	−1.76410	+	0.495648i	−0.109828	+	0.0308577i
$259$	−1.32053	−	0.183570i	−0.0820538	−	0.0114065i
$260$	3.14944	+	5.82231i	0.195320	+	0.361084i
$261$	3.28097	+	5.37789i	0.203087	+	0.332883i
$262$	−4.95760	+	8.58681i	−0.306281	+	0.530495i
$263$	9.39641	+	5.42502i	0.579408	+	0.334521i	0.760898	−	0.648872i	$-0.224759\pi$
$263$	9.39641	+	5.42502i	0.579408	+	0.334521i	−0.181490	+	0.983393i	$0.558092\pi$
$264$	5.65693	−	1.58939i	0.348160	−	0.0978199i
$265$	−12.3311			−0.757491
$266$	4.98079	−	2.02106i	0.305392	−	0.123919i
$267$	6.45280	−	6.61091i	0.394905	−	0.404581i
$268$	−8.59785	−	4.96397i	−0.525197	−	0.303223i
$269$	−18.1117			−1.10429			−0.552146	−	0.833747i	$-0.686191\pi$
$269$	−18.1117			−1.10429			−0.552146	+	0.833747i	$0.686191\pi$
$270$	9.11901	−	2.80192i	0.554965	−	0.170519i
$271$	8.67329			0.526865			0.263432	−	0.964678i	$-0.415145\pi$
$271$	8.67329			0.526865			0.263432	+	0.964678i	$0.415145\pi$
$272$	3.18506			0.193123
$273$	16.4264	−	1.78141i	0.994171	−	0.107816i
$274$	3.18307			0.192296
$275$	5.52761			0.333328
$276$	2.99507	−	3.06845i	0.180282	−	0.184699i
$277$	−18.2835			−1.09855			−0.549275	−	0.835642i	$-0.685096\pi$
$277$	−18.2835			−1.09855			−0.549275	+	0.835642i	$0.685096\pi$
$278$	0.0981681	+	0.0566774i	0.00588773	+	0.00339928i
$279$	16.1008	−	9.82288i	0.963931	−	0.588081i
$280$	−2.98478	+	3.83217i	−0.178375	+	0.229016i
$281$	−2.73779			−0.163323			−0.0816614	−	0.996660i	$-0.526023\pi$
$281$	−2.73779			−0.163323			−0.0816614	+	0.996660i	$0.526023\pi$
$282$	−5.46264	−	19.4426i	−0.325296	−	1.15779i
$283$	4.60044	+	2.65607i	0.273468	+	0.157887i	0.630463	−	0.776220i	$-0.282865\pi$
$283$	4.60044	+	2.65607i	0.273468	+	0.157887i	−0.356995	+	0.934106i	$0.616199\pi$
$284$	−7.77030	+	13.4586i	−0.461083	+	0.798619i
$285$	−4.51262	+	4.62318i	−0.267304	+	0.273854i
$286$	−10.7587	+	5.81964i	−0.636173	+	0.344123i
$287$	4.99890	+	12.3195i	0.295076	+	0.727198i
$288$	0.0726040	+	2.99912i	0.00427823	+	0.176725i
$289$	−6.85540			−0.403259
$290$	3.85528			0.226390
$291$	16.0047	−	4.49674i	0.938215	−	0.263603i
$292$	−4.47574	−	7.75221i	−0.261923	−	0.453664i
$293$	−2.86877	−	1.65628i	−0.167595	−	0.0967612i	0.413856	−	0.910342i	$-0.364182\pi$
$293$	−2.86877	−	1.65628i	−0.167595	−	0.0967612i	−0.581451	+	0.813581i	$0.697515\pi$
$294$	6.03746	+	10.5142i	0.352112	+	0.613203i
$295$	−5.69957	+	9.87195i	−0.331842	+	0.574767i
$296$			0.503913i			0.0292894i
$297$	5.17748	+	16.8504i	0.300428	+	0.977760i
$298$	10.8563	+	18.8036i	0.628888	+	1.08927i
$299$	−4.67571	+	7.60326i	−0.270403	+	0.439708i
$300$	−0.697383	+	2.73462i	−0.0402634	+	0.157884i
$301$	2.20827	+	1.71996i	0.127282	+	0.0991369i
$302$	−4.69698	+	2.71180i	−0.270281	+	0.156047i
$303$	−15.6588	+	4.39955i	−0.899577	+	0.252748i
$304$	−1.01582	−	1.75945i	−0.0582613	−	0.100912i
$305$	21.4447			1.22792
$306$	0.231248	+	9.55238i	0.0132196	+	0.546073i
$307$	23.8813			1.36298			0.681490	−	0.731827i	$-0.261332\pi$
$307$	23.8813			1.36298			0.681490	+	0.731827i	$0.261332\pi$
$308$	−7.08122	−	5.51537i	−0.403490	−	0.314268i
$309$	6.25617	+	22.2669i	0.355901	+	1.26672i
$310$		−	11.5423i		−	0.655558i
$311$	−15.8352	−	27.4274i	−0.897934	−	1.55527i	−0.830131	−	0.557569i	$-0.811734\pi$
$311$	−15.8352	−	27.4274i	−0.897934	−	1.55527i	−0.0678034	−	0.997699i	$-0.521599\pi$
$312$	−1.52175	−	6.05676i	−0.0861520	−	0.342896i
$313$	12.5081	+	7.22158i	0.707002	+	0.408188i	0.809950	−	0.586499i	$-0.199494\pi$
$313$	12.5081	+	7.22158i	0.707002	+	0.408188i	−0.102948	+	0.994687i	$0.532828\pi$
$314$	18.4221	−	10.6360i	1.03962	−	0.600226i
$315$	−11.7099	−	8.67348i	−0.659775	−	0.488695i
$316$	3.92399	−	6.79656i	0.220742	−	0.382336i
$317$	12.7938	−	22.1596i	0.718573	−	1.24461i	−0.242992	−	0.970028i	$-0.578129\pi$
$317$	12.7938	−	22.1596i	0.718573	−	1.24461i	0.961565	−	0.274577i	$-0.0885379\pi$
$318$	11.2726	+	2.87473i	0.632135	+	0.161207i
$319$			7.12392i			0.398863i
$320$	1.58996	+	0.917964i	0.0888815	+	0.0513158i
$321$	−16.1766	+	16.5730i	−0.902891	+	0.925013i
$322$	−6.48744	−	0.901834i	−0.361531	−	0.0502572i
$323$	−3.23545	−	5.60396i	−0.180025	−	0.311813i
$324$	−8.98946	+	0.435496i	−0.499414	+	0.0241942i
$325$	0.162995	−	5.87251i	0.00904132	−	0.325748i
$326$	8.67648	−	5.00937i	0.480546	−	0.277443i
$327$	−7.42172	−	1.89269i	−0.410422	−	0.104666i
$328$	4.35184	−	2.51254i	0.240290	−	0.138732i
$329$	−18.9561	+	24.3378i	−1.04508	+	1.34179i
$330$	10.4533	+	2.66580i	0.575435	+	0.146747i
$331$	7.25351	−	4.18782i	0.398689	−	0.230183i	−0.287229	−	0.957862i	$-0.592734\pi$
$331$	7.25351	−	4.18782i	0.398689	−	0.230183i	0.685918	+	0.727679i	$0.259401\pi$
$332$		−	13.0790i		−	0.717803i
$333$	−1.51130	+	0.0365861i	−0.0828186	+	0.00200491i
$334$	3.11618	−	1.79913i	0.170510	−	0.0984438i
$335$	−9.11349	−	15.7850i	−0.497923	−	0.862428i
$336$	3.62196	−	2.80738i	0.197594	−	0.153155i
$337$	−9.14343			−0.498074			−0.249037	−	0.968494i	$-0.580114\pi$
$337$	−9.14343			−0.498074			−0.249037	+	0.968494i	$0.580114\pi$
$338$	5.86551	+	11.6015i	0.319042	+	0.631041i
$339$	7.48659	+	26.6462i	0.406616	+	1.44722i
$340$	5.06412	+	2.92377i	0.274640	+	0.158564i
$341$	21.3282			1.15499
$342$	5.20306	−	3.17431i	0.281349	−	0.171647i
$343$	7.45669	−	16.9528i	0.402623	−	0.915366i
$344$	0.528972	−	0.916206i	0.0285202	−	0.0493985i
$345$	7.57877	−	2.12935i	0.408027	−	0.114640i
$346$	−0.476807	−	0.825853i	−0.0256333	−	0.0443982i
$347$		−	31.0967i		−	1.66936i	−0.550736	−	0.834679i	$-0.685653\pi$
$347$		−	31.0967i		−	1.66936i	0.550736	−	0.834679i	$-0.314347\pi$
$348$	−3.52435	−	0.898778i	−0.188925	−	0.0481796i
$349$	14.0331	+	24.3060i	0.751175	+	1.30107i	0.947254	+	0.320485i	$0.103846\pi$
$349$	14.0331	+	24.3060i	0.751175	+	1.30107i	−0.196079	+	0.980588i	$0.562821\pi$
$350$	3.99457	−	1.62088i	0.213519	−	0.0866398i
$351$	18.0545	−	5.00365i	0.963676	−	0.267075i
$352$	−1.69625	+	2.93798i	−0.0904102	+	0.156595i
$353$	24.5364	+	14.1661i	1.30594	+	0.753984i	0.981416	−	0.191894i	$-0.0614629\pi$
$353$	24.5364	+	14.1661i	1.30594	+	0.753984i	0.324523	+	0.945878i	$0.394796\pi$
$354$	7.51177	−	7.69582i	0.399246	−	0.409028i
$355$	−24.7090	+	14.2657i	−1.31142	+	0.757146i
$356$			5.33363i			0.282682i
$357$	11.5362	−	8.94169i	0.610558	−	0.473244i
$358$	15.3789	+	8.87903i	0.812802	+	0.469271i
$359$	−10.8679	+	18.8238i	−0.573588	+	0.993483i	0.422606	+	0.906314i	$0.361116\pi$
$359$	−10.8679	+	18.8238i	−0.573588	+	0.993483i	−0.996193	+	0.0871698i	$0.972218\pi$
$360$	−2.63765	+	4.83513i	−0.139016	+	0.254834i
$361$	7.43622	−	12.8799i	0.391380	−	0.677890i
$362$		−	5.51564i		−	0.289896i
$363$	−0.217853	+	0.854260i	−0.0114343	+	0.0448370i
$364$	−6.06831	+	7.36041i	−0.318066	+	0.385790i
$365$		−	16.4343i		−	0.860209i
$366$	−19.6039	−	4.99938i	−1.02471	−	0.261322i
$367$	13.6561	+	7.88437i	0.712844	+	0.411561i	0.812113	−	0.583500i	$-0.198317\pi$
$367$	13.6561	+	7.88437i	0.712844	+	0.411561i	−0.0992693	+	0.995061i	$0.531651\pi$
$368$			2.47560i			0.129050i
$369$	7.85136	+	12.8693i	0.408725	+	0.669948i
$370$	−0.462574	+	0.801202i	−0.0240481	+	0.0416525i
$371$	−6.68155	−	16.4663i	−0.346889	−	0.854887i
$372$	−2.69085	+	10.5515i	−0.139514	+	0.547071i
$373$	3.62253	+	6.27441i	0.187568	+	0.324877i	0.944439	−	0.328687i	$-0.106606\pi$
$373$	3.62253	+	6.27441i	0.187568	+	0.324877i	−0.756871	+	0.653564i	$0.773273\pi$
$374$	−5.40264	+	9.35765i	−0.279364	+	0.483873i
$375$	−14.7249	+	15.0857i	−0.760393	+	0.779023i
$376$	10.0977	+	5.82991i	0.520750	+	0.300655i
$377$	7.56841	+	0.210065i	0.389793	+	0.0108189i
$378$	8.68265	+	10.6589i	0.446588	+	0.548233i
$379$	4.24213	−	2.44920i	0.217904	−	0.125807i	−0.387076	−	0.922048i	$-0.626515\pi$
$379$	4.24213	−	2.44920i	0.217904	−	0.125807i	0.604979	+	0.796241i	$0.293181\pi$
$380$		−	3.72995i		−	0.191342i
$381$	−0.407452	+	1.59773i	−0.0208744	+	0.0818541i
$382$	17.4751	−	10.0893i	0.894106	−	0.516212i
$383$	−6.85462	+	3.95752i	−0.350255	+	0.202220i	−0.664797	−	0.747024i	$-0.731482\pi$
$383$	−6.85462	+	3.95752i	−0.350255	+	0.202220i	0.314543	+	0.949243i	$0.398149\pi$
$384$	−1.23948	−	1.20983i	−0.0632518	−	0.0617391i
$385$	−6.19594	−	15.2695i	−0.315774	−	0.778207i
$386$	3.93413	+	2.27137i	0.200242	+	0.115610i
$387$	2.78622	+	1.51993i	0.141631	+	0.0772624i
$388$	−4.79907	+	8.31223i	−0.243636	+	0.421990i
$389$	2.27718	−	1.31473i	0.115458	−	0.0666595i	−0.441159	−	0.897429i	$-0.645433\pi$
$389$	2.27718	−	1.31473i	0.115458	−	0.0666595i	0.556617	+	0.830769i	$0.312099\pi$
$390$	3.14037	−	11.0269i	0.159019	−	0.558369i
$391$			7.88494i			0.398758i
$392$	−6.73459	−	1.90927i	−0.340148	−	0.0964329i
$393$	16.5334	−	4.64528i	0.834002	−	0.234323i
$394$	5.74363	+	9.94826i	0.289360	+	0.501186i
$395$	12.4780	−	7.20417i	0.627836	−	0.362481i
$396$	−8.93452	−	4.87394i	−0.448977	−	0.244925i
$397$	−16.5529	−	28.6705i	−0.830766	−	1.43893i	−0.897432	−	0.441153i	$-0.854569\pi$
$397$	−16.5529	−	28.6705i	−0.830766	−	1.43893i	0.0666658	−	0.997775i	$-0.478764\pi$
$398$		−	6.86468i		−	0.344095i
$399$	−8.61872	−	3.52087i	−0.431476	−	0.176264i
$400$	−0.814684	−	1.41107i	−0.0407342	−	0.0705537i
$401$	6.99738			0.349433			0.174716	−	0.984619i	$-0.444099\pi$
$401$	6.99738			0.349433			0.174716	+	0.984619i	$0.444099\pi$
$402$	4.65125	+	16.5547i	0.231983	+	0.825673i
$403$	0.628914	−	22.6590i	0.0313284	−	1.12873i
$404$	4.69535	−	8.13258i	0.233602	−	0.404611i
$405$	−14.6927	−	7.55958i	−0.730084	−	0.375638i
$406$	2.08897	+	5.14815i	0.103674	+	0.255498i
$407$	−1.48049	−	0.854760i	−0.0733851	−	0.0423689i
$408$	−3.94781	−	3.85339i	−0.195446	−	0.190771i
$409$	−31.8405			−1.57441			−0.787206	−	0.616691i	$-0.788473\pi$
$409$	−31.8405			−1.57441			−0.787206	+	0.616691i	$0.788473\pi$
$410$	9.22567			0.455623
$411$	−3.94534	−	3.85099i	−0.194609	−	0.189955i
$412$	−11.5646	−	6.67680i	−0.569745	−	0.328942i
$413$	−16.2708	−	2.26184i	−0.800634	−	0.111298i
$414$	−7.42463	+	0.179738i	−0.364901	+	0.00883366i
$415$	12.0061	−	20.7951i	0.589354	−	1.02079i
$416$	3.07128	+	1.88872i	0.150582	+	0.0926019i
$417$	−0.0531068	−	0.189017i	−0.00260065	−	0.00925622i
$418$	6.89232			0.337114
$419$	5.19733	+	9.00204i	0.253906	+	0.439778i	0.964598	−	0.263725i	$-0.0849512\pi$
$419$	5.19733	+	9.00204i	0.253906	+	0.439778i	−0.710692	+	0.703504i	$0.751618\pi$
$420$	8.33585	−	1.13880i	0.406748	−	0.0555678i
$421$			0.111490i			0.00543368i	0.999996	+	0.00271684i	$0.000864798\pi$
$421$			0.111490i			0.00543368i	−0.999996	+	0.00271684i	$0.999135\pi$
$422$	−2.63957	−	4.57187i	−0.128492	−	0.222555i
$423$	−16.7515	+	30.7075i	−0.814485	+	1.49305i
$424$	−5.81668	+	3.35826i	−0.282483	+	0.163092i
$425$	−2.59482	−	4.49435i	−0.125867	−	0.218008i
$426$	25.9137	−	7.28079i	1.25552	−	0.352756i
$427$	11.6197	+	28.6362i	0.562318	+	1.38580i
$428$		−	13.3709i		−	0.646309i
$429$	20.3759	+	5.80288i	0.983758	+	0.280166i
$430$	1.68209	−	0.971154i	0.0811175	−	0.0468332i
$431$	19.3138	−	33.4525i	0.930313	−	1.61135i	0.147527	−	0.989058i	$-0.452869\pi$
$431$	19.3138	−	33.4525i	0.930313	−	1.61135i	0.782786	−	0.622291i	$-0.213798\pi$
$432$	3.53845	−	3.80518i	0.170244	−	0.183077i
$433$	−5.30602	−	3.06343i	−0.254991	−	0.147219i	0.367056	−	0.930199i	$-0.380366\pi$
$433$	−5.30602	−	3.06343i	−0.254991	−	0.147219i	−0.622047	+	0.782980i	$0.713699\pi$
$434$	15.4130	−	6.25416i	0.739848	−	0.300209i
$435$	−4.77853	−	4.66425i	−0.229113	−	0.223634i
$436$	3.82963	−	2.21104i	0.183406	−	0.105890i
$437$	4.35570	−	2.51477i	0.208362	−	0.120298i
$438$	−3.83131	+	15.0236i	−0.183067	+	0.717854i
$439$			34.9618i			1.66864i	0.551284	+	0.834318i	$0.314138\pi$
$439$			34.9618i			1.66864i	−0.551284	+	0.834318i	$0.685862\pi$
$440$	−5.39393	+	3.11418i	−0.257145	+	0.148463i
$441$	5.23719	−	20.3365i	0.249390	−	0.968403i
$442$	9.78221	+	6.01567i	0.465292	+	0.286136i
$443$	7.76750	+	4.48457i	0.369045	+	0.213068i	0.673041	−	0.739605i	$-0.264988\pi$
$443$	7.76750	+	4.48457i	0.369045	+	0.213068i	−0.303996	+	0.952673i	$0.598321\pi$
$444$	0.609651	−	0.624589i	0.0289328	−	0.0296417i
$445$	−4.89608	+	8.48026i	−0.232096	+	0.402003i
$446$	−14.2982	−	24.7653i	−0.677042	−	1.17267i
$447$	9.29317	−	36.4410i	0.439552	−	1.72360i
$448$	−0.364289	+	2.62055i	−0.0172110	+	0.123809i
$449$	−9.32220	+	16.1465i	−0.439942	+	0.762002i	−0.997684	−	0.0680121i	$-0.978334\pi$
$449$	−9.32220	+	16.1465i	−0.439942	+	0.762002i	0.557742	+	0.830014i	$0.311668\pi$
$450$	4.17283	−	2.54578i	0.196709	−	0.120009i
$451$			17.0475i			0.802736i
$452$	−13.8390	−	7.98994i	−0.650931	−	0.375815i
$453$	9.10263	+	2.32135i	0.427679	+	0.109067i
$454$		−	6.00983i		−	0.282055i
$455$	−16.4050	+	6.13227i	−0.769077	+	0.287485i
$456$	−0.869560	+	3.40977i	−0.0407209	+	0.159677i
$457$			28.4939i			1.33289i	0.745554	+	0.666445i	$0.232185\pi$
$457$			28.4939i			1.33289i	−0.745554	+	0.666445i	$0.767815\pi$
$458$	−7.02836	+	12.1735i	−0.328414	+	0.568829i
$459$	11.2702	−	12.1197i	0.526046	−	0.565700i
$460$	−2.27251	+	3.93611i	−0.105956	+	0.183522i
$461$	10.2455	+	5.91523i	0.477180	+	0.275500i	0.719240	−	0.694761i	$-0.244490\pi$
$461$	10.2455	+	5.91523i	0.477180	+	0.275500i	−0.242061	+	0.970261i	$0.577823\pi$
$462$	2.10431	+	15.4033i	0.0979016	+	0.716625i
$463$		−	10.9649i		−	0.509582i	−0.966996	−	0.254791i	$-0.917993\pi$
$463$		−	10.9649i		−	0.509582i	0.966996	−	0.254791i	$-0.0820067\pi$
$464$	1.81857	−	1.04995i	0.0844251	−	0.0487429i
$465$	−13.9643	+	14.3064i	−0.647577	+	0.663443i
$466$	−24.0450	−	13.8824i	−1.11386	−	0.643089i
$467$	−10.0288	+	17.3705i	−0.464080	+	0.803810i	−0.999159	−	0.0409918i	$-0.986948\pi$
$467$	−10.0288	+	17.3705i	−0.464080	+	0.803810i	0.535080	+	0.844802i	$0.320282\pi$
$468$	−5.44150	+	9.34827i	−0.251533	+	0.432124i
$469$	16.1404	−	20.7228i	0.745296	−	0.956889i
$470$	10.7033	+	18.5387i	0.493707	+	0.855125i
$471$	−35.7017	−	9.10463i	−1.64505	−	0.419519i
$472$			6.20893i			0.285789i
$473$	1.79453	+	3.10822i	0.0825126	+	0.142916i
$474$	−13.0864	+	3.67679i	−0.601078	+	0.168881i
$475$	−1.65514	+	2.86679i	−0.0759432	+	0.131538i
$476$	−1.16028	+	8.34661i	−0.0531814	+	0.382566i
$477$	−10.4942	−	17.2011i	−0.480494	−	0.787585i
$478$	5.31347			0.243033
$479$	−26.6476	−	15.3850i	−1.21756	−	0.702957i	−0.253163	−	0.967424i	$-0.581471\pi$
$479$	−26.6476	−	15.3850i	−1.21756	−	0.702957i	−0.964395	+	0.264466i	$0.914804\pi$
$480$	−0.860135	−	3.06138i	−0.0392596	−	0.139732i
$481$	−0.951748	+	1.54766i	−0.0433960	+	0.0705671i
$482$	−19.2577			−0.877164
$483$	6.94996	+	8.96653i	0.316234	+	0.407991i
$484$	−0.254496	−	0.440801i	−0.0115680	−	0.0200364i
$485$	−15.2607	+	8.81074i	−0.692951	+	0.400075i
$486$	11.6691	+	10.3360i	0.529321	+	0.468849i
$487$			35.8831i			1.62602i	0.582252	+	0.813009i	$0.302172\pi$
$487$			35.8831i			1.62602i	−0.582252	+	0.813009i	$0.697828\pi$
$488$	10.1157	−	5.84028i	0.457914	−	0.264377i
$489$	−16.8148	−	4.28811i	−0.760391	−	0.193915i
$490$	−8.95508	−	9.21778i	−0.404549	−	0.416417i
$491$	−32.3384	+	18.6706i	−1.45941	+	0.842592i	−0.998982	−	0.0451043i	$-0.985638\pi$
$491$	−32.3384	+	18.6706i	−1.45941	+	0.842592i	−0.460430	+	0.887696i	$0.652305\pi$
$492$	−8.43375	−	2.15077i	−0.380223	−	0.0969644i
$493$	5.79226	−	3.34416i	0.260870	−	0.150614i
$494$	0.203236	−	7.32236i	0.00914404	−	0.329449i
$495$	−9.73144	−	15.9509i	−0.437396	−	0.716941i
$496$	−3.14345	−	5.44461i	−0.141145	−	0.244470i
$497$	−32.4382	−	25.2653i	−1.45505	−	1.13330i
$498$	−15.8234	+	16.2111i	−0.709064	+	0.726437i
$499$	19.1199	+	11.0389i	0.855925	+	0.494169i	0.862646	−	0.505809i	$-0.168806\pi$
$499$	19.1199	+	11.0389i	0.855925	+	0.494169i	−0.00672032	+	0.999977i	$0.502139\pi$
$500$		−	12.1710i		−	0.544306i
$501$	−6.03907	−	1.54008i	−0.269806	−	0.0688058i
$502$	−4.75595	+	8.23755i	−0.212269	+	0.367660i
$503$	−18.0289	+	31.2270i	−0.803870	+	1.39234i	0.113181	+	0.993574i	$0.463896\pi$
$503$	−18.0289	+	31.2270i	−0.803870	+	1.39234i	−0.917051	+	0.398769i	$0.869437\pi$
$504$	−7.88580	−	0.902283i	−0.351262	−	0.0401909i
$505$	14.9308	−	8.62032i	0.664413	−	0.383599i
$506$	−7.27328	−	4.19923i	−0.323337	−	0.186678i
$507$	6.76578	−	21.4761i	0.300479	−	0.953789i
$508$	−0.475986	−	0.824432i	−0.0211185	−	0.0365783i
$509$		−	27.2107i		−	1.20609i	−0.797705	−	0.603047i	$-0.793953\pi$
$509$		−	27.2107i		−	1.20609i	0.797705	−	0.603047i	$-0.206047\pi$
$510$	−2.73958	−	9.75069i	−0.121311	−	0.431768i
$511$	21.9455	−	8.90487i	0.970813	−	0.393928i
$512$	1.00000			0.0441942
$513$	−10.2895	−	2.36035i	−0.454291	−	0.104212i
$514$	−5.26373			−0.232173
$515$	−12.2581	−	21.2317i	−0.540157	−	0.935580i
$516$	−1.76410	+	0.495648i	−0.0776604	+	0.0218197i
$517$	−34.2564	+	19.7779i	−1.50659	+	0.869832i
$518$	−1.32053	−	0.183570i	−0.0580208	−	0.00806560i
$519$	−0.408155	+	1.60048i	−0.0179160	+	0.0702534i
$520$	3.14944	+	5.82231i	0.138112	+	0.255325i
$521$	−7.90186	−	13.6864i	−0.346187	−	0.599613i	0.639382	−	0.768889i	$-0.279190\pi$
$521$	−7.90186	−	13.6864i	−0.346187	−	0.599613i	−0.985569	+	0.169276i	$0.945857\pi$
$522$	3.28097	+	5.37789i	0.143604	+	0.235384i
$523$		−	1.76412i		−	0.0771397i	−0.999256	−	0.0385698i	$-0.987720\pi$
$523$		−	1.76412i		−	0.0771397i	0.999256	−	0.0385698i	$-0.0122802\pi$
$524$	−4.95760	+	8.58681i	−0.216574	+	0.375117i
$525$	−6.91218	−	2.82372i	−0.301672	−	0.123237i
$526$	9.39641	+	5.42502i	0.409703	+	0.236542i
$527$	−10.0121	−	17.3414i	−0.436133	−	0.755404i
$528$	5.65693	−	1.58939i	0.246186	−	0.0691691i
$529$	16.8714			0.733539
$530$	−12.3311			−0.535627
$531$	−18.6213	+	0.450793i	−0.808097	+	0.0195627i
$532$	4.98079	−	2.02106i	0.215945	−	0.0876241i
$533$	18.1112	+	0.502686i	0.784482	+	0.0217737i
$534$	6.45280	−	6.61091i	0.279240	−	0.286082i
$535$	12.2740	−	21.2593i	0.530653	−	0.919118i
$536$	−8.59785	−	4.96397i	−0.371370	−	0.214411i
$537$	−8.31967	−	29.6113i	−0.359020	−	1.27782i
$538$	−18.1117			−0.780853
$539$	17.0329	−	16.5475i	0.733660	−	0.712752i
$540$	9.11901	−	2.80192i	0.392420	−	0.120575i
$541$	18.1904	+	10.5022i	0.782066	+	0.451526i	0.837162	−	0.546955i	$-0.184213\pi$
$541$	18.1904	+	10.5022i	0.782066	+	0.451526i	−0.0550960	+	0.998481i	$0.517546\pi$
$542$	8.67329			0.372550
$543$	−6.67301	+	6.83651i	−0.286366	+	0.293383i
$544$	3.18506			0.136558
$545$	8.11861			0.347763
$546$	16.4264	−	1.78141i	0.702985	−	0.0762373i
$547$	−37.9155			−1.62115			−0.810575	−	0.585635i	$-0.800845\pi$
$547$	−37.9155			−1.62115			−0.810575	+	0.585635i	$0.800845\pi$
$548$	3.18307			0.135974
$549$	18.2501	+	29.9141i	0.778897	+	1.27670i
$550$	5.52761			0.235698
$551$	−3.69469	−	2.13313i	−0.157399	−	0.0908743i
$552$	2.99507	−	3.06845i	0.127479	−	0.130602i
$553$	16.3813	+	12.7589i	0.696602	+	0.542565i
$554$	−18.2835			−0.776792
$555$	1.54267	−	0.433433i	0.0654828	−	0.0183982i
$556$	0.0981681	+	0.0566774i	0.00416326	+	0.00240366i
$557$	−7.64230	+	13.2369i	−0.323815	+	0.560864i	−0.981272	−	0.192628i	$-0.938299\pi$
$557$	−7.64230	+	13.2369i	−0.323815	+	0.560864i	0.657457	+	0.753492i	$0.271632\pi$
$558$	16.1008	−	9.82288i	0.681602	−	0.415836i
$559$	3.35507	−	1.81485i	0.141904	−	0.0767598i
$560$	−2.98478	+	3.83217i	−0.126130	+	0.161939i
$561$	18.0177	−	5.06229i	0.760706	−	0.213730i
$562$	−2.73779			−0.115487
$563$	−18.7941			−0.792079			−0.396039	−	0.918234i	$-0.629616\pi$
$563$	−18.7941			−0.792079			−0.396039	+	0.918234i	$0.629616\pi$
$564$	−5.46264	−	19.4426i	−0.230019	−	0.818681i
$565$	−14.6690	−	25.4074i	−0.617128	−	1.06890i
$566$	4.60044	+	2.65607i	0.193371	+	0.111643i
$567$	2.13352	−	23.7160i	0.0895993	−	0.995978i
$568$	−7.77030	+	13.4586i	−0.326035	+	0.564709i
$569$		−	21.5237i		−	0.902321i	−0.892443	−	0.451160i	$-0.851010\pi$
$569$		−	21.5237i		−	0.902321i	0.892443	−	0.451160i	$-0.148990\pi$
$570$	−4.51262	+	4.62318i	−0.189013	+	0.193644i
$571$	19.8438	+	34.3705i	0.830438	+	1.43836i	0.897691	+	0.440625i	$0.145243\pi$
$571$	19.8438	+	34.3705i	0.830438	+	1.43836i	−0.0672531	+	0.997736i	$0.521424\pi$
$572$	−10.7587	+	5.81964i	−0.449842	+	0.243331i
$573$	−33.8664	−	8.63659i	−1.41479	−	0.360799i
$574$	4.99890	+	12.3195i	0.208650	+	0.514206i
$575$	3.49326	−	2.01683i	0.145679	−	0.0841077i
$576$	0.0726040	+	2.99912i	0.00302517	+	0.124963i
$577$	−20.4728	−	35.4599i	−0.852293	−	1.47621i	−0.879134	−	0.476575i	$-0.841878\pi$
$577$	−20.4728	−	35.4599i	−0.852293	−	1.47621i	0.0268412	−	0.999640i	$-0.491455\pi$
$578$	−6.85540			−0.285147
$579$	−2.12828	−	7.57496i	−0.0884484	−	0.314805i
$580$	3.85528			0.160082
$581$	34.2742	+	4.76453i	1.42193	+	0.197666i
$582$	16.0047	−	4.49674i	0.663418	−	0.186396i
$583$		−	22.7857i		−	0.943689i
$584$	−4.47574	−	7.75221i	−0.185207	−	0.320789i
$585$	−17.2331	+	9.86828i	−0.712503	+	0.408003i
$586$	−2.86877	−	1.65628i	−0.118508	−	0.0684205i
$587$	32.8994	−	18.9945i	1.35790	−	0.783986i	0.368563	−	0.929603i	$-0.379850\pi$
$587$	32.8994	−	18.9945i	1.35790	−	0.783986i	0.989341	+	0.145616i	$0.0465165\pi$
$588$	6.03746	+	10.5142i	0.248981	+	0.433600i
$589$	−6.38636	+	11.0615i	−0.263145	+	0.455781i
$590$	−5.69957	+	9.87195i	−0.234648	+	0.406422i
$591$	4.91665	−	19.2795i	0.202244	−	0.793052i
$592$			0.503913i			0.0207107i
$593$	−13.8054	−	7.97057i	−0.566921	−	0.327312i	0.188997	−	0.981978i	$-0.439476\pi$
$593$	−13.8054	−	7.97057i	−0.566921	−	0.327312i	−0.755919	+	0.654665i	$0.772810\pi$
$594$	5.17748	+	16.8504i	0.212434	+	0.691381i
$595$	−9.50669	+	12.2057i	−0.389736	+	0.500385i
$596$	10.8563	+	18.8036i	0.444691	+	0.770227i
$597$	−8.30512	+	8.50860i	−0.339906	+	0.348234i
$598$	−4.67571	+	7.60326i	−0.191204	+	0.310921i
$599$	3.66862	−	2.11808i	0.149896	−	0.0865423i	−0.423176	−	0.906047i	$-0.639085\pi$
$599$	3.66862	−	2.11808i	0.149896	−	0.0865423i	0.573072	+	0.819505i	$0.305752\pi$
$600$	−0.697383	+	2.73462i	−0.0284706	+	0.111641i
$601$	−2.17316	+	1.25468i	−0.0886451	+	0.0511793i	−0.543667	−	0.839301i	$-0.682965\pi$
$601$	−2.17316	+	1.25468i	−0.0886451	+	0.0511793i	0.455022	+	0.890480i	$0.349631\pi$
$602$	2.20827	+	1.71996i	0.0900022	+	0.0701004i
$603$	14.2633	−	26.1464i	0.580847	−	1.06476i
$604$	−4.69698	+	2.71180i	−0.191118	+	0.110342i
$605$		−	0.934474i		−	0.0379918i
$606$	−15.6588	+	4.39955i	−0.636097	+	0.178720i
$607$	−37.1080	+	21.4243i	−1.50617	+	0.869586i	−0.506193	+	0.862420i	$0.668948\pi$
$607$	−37.1080	+	21.4243i	−1.50617	+	0.869586i	−0.999974	+	0.00716623i	$0.997719\pi$
$608$	−1.01582	−	1.75945i	−0.0411970	−	0.0713552i
$609$	3.63918	−	8.90832i	0.147467	−	0.360983i
$610$	21.4447			0.868269
$611$	20.0018	+	36.9770i	0.809188	+	1.49593i
$612$	0.231248	+	9.55238i	0.00934764	+	0.386132i
$613$	−18.3170	−	10.5753i	−0.739816	−	0.427133i	0.0821861	−	0.996617i	$-0.473810\pi$
$613$	−18.3170	−	10.5753i	−0.739816	−	0.427133i	−0.822003	+	0.569484i	$0.807143\pi$
$614$	23.8813			0.963773
$615$	−11.4350	−	11.1615i	−0.461104	−	0.450076i
$616$	−7.08122	−	5.51537i	−0.285310	−	0.222221i
$617$	−17.5132	+	30.3337i	−0.705053	+	1.22119i	0.261619	+	0.965171i	$0.415744\pi$
$617$	−17.5132	+	30.3337i	−0.705053	+	1.22119i	−0.966672	+	0.256017i	$0.917590\pi$
$618$	6.25617	+	22.2669i	0.251660	+	0.895707i
$619$	15.4257	+	26.7180i	0.620010	+	1.07389i	0.989483	+	0.144648i	$0.0462048\pi$
$619$	15.4257	+	26.7180i	0.620010	+	1.07389i	−0.369473	+	0.929241i	$0.620462\pi$
$620$		−	11.5423i		−	0.463550i
$621$	9.42011	+	8.75979i	0.378016	+	0.351518i
$622$	−15.8352	−	27.4274i	−0.634935	−	1.09974i
$623$	−13.9771	−	1.94298i	−0.559979	−	0.0778439i
$624$	−1.52175	−	6.05676i	−0.0609186	−	0.242464i
$625$	7.09916	−	12.2961i	0.283967	−	0.491844i
$626$	12.5081	+	7.22158i	0.499926	+	0.288632i
$627$	−8.54287	−	8.33856i	−0.341169	−	0.333010i
$628$	18.4221	−	10.6360i	0.735124	−	0.424424i
$629$			1.60499i			0.0639953i
$630$	−11.7099	−	8.67348i	−0.466532	−	0.345560i
$631$	−13.3366	−	7.69988i	−0.530921	−	0.306527i	0.210470	−	0.977600i	$-0.432500\pi$
$631$	−13.3366	−	7.69988i	−0.530921	−	0.306527i	−0.741391	+	0.671073i	$0.765834\pi$
$632$	3.92399	−	6.79656i	0.156088	−	0.270352i
$633$	−2.25952	+	8.86016i	−0.0898077	+	0.352160i
$634$	12.7938	−	22.1596i	0.508108	−	0.880069i
$635$		−	1.74775i		−	0.0693575i
$636$	11.2726	+	2.87473i	0.446987	+	0.113990i
$637$	−17.0777	−	18.5836i	−0.676644	−	0.736310i
$638$			7.12392i			0.282039i
$639$	−40.9280	−	22.3269i	−1.61909	−	0.883240i
$640$	1.58996	+	0.917964i	0.0628487	+	0.0362857i
$641$		−	9.30710i		−	0.367608i	−0.982963	−	0.183804i	$-0.941159\pi$
$641$		−	9.30710i		−	0.367608i	0.982963	−	0.183804i	$-0.0588412\pi$
$642$	−16.1766	+	16.5730i	−0.638440	+	0.654083i
$643$	−3.03048	+	5.24895i	−0.119511	+	0.206998i	−0.919574	−	0.392917i	$-0.871466\pi$
$643$	−3.03048	+	5.24895i	−0.119511	+	0.206998i	0.800063	+	0.599916i	$0.204799\pi$
$644$	−6.48744	−	0.901834i	−0.255641	−	0.0355372i
$645$	−3.25984	−	0.831325i	−0.128356	−	0.0327334i
$646$	−3.23545	−	5.60396i	−0.127297	−	0.220485i
$647$	5.65052	−	9.78699i	0.222145	−	0.384766i	−0.733314	−	0.679890i	$-0.762027\pi$
$647$	5.65052	−	9.78699i	0.222145	−	0.384766i	0.955459	+	0.295124i	$0.0953608\pi$
$648$	−8.98946	+	0.435496i	−0.353139	+	0.0171079i
$649$	−18.2417	−	10.5319i	−0.716050	−	0.413412i
$650$	0.162995	−	5.87251i	0.00639318	−	0.230339i
$651$	−26.6706	−	10.8953i	−1.04530	−	0.427021i
$652$	8.67648	−	5.00937i	0.339797	−	0.196182i
$653$			35.9225i			1.40576i	0.711311	+	0.702878i	$0.248102\pi$
$653$			35.9225i			1.40576i	−0.711311	+	0.702878i	$0.751898\pi$
$654$	−7.42172	−	1.89269i	−0.290212	−	0.0740099i
$655$	−15.7648	+	9.10179i	−0.615981	+	0.355637i
$656$	4.35184	−	2.51254i	0.169911	−	0.0980980i
$657$	22.9249	−	13.9861i	0.894384	−	0.545651i
$658$	−18.9561	+	24.3378i	−0.738985	+	0.948786i
$659$	14.9107	+	8.60870i	0.580839	+	0.335348i	0.761467	−	0.648204i	$-0.224480\pi$
$659$	14.9107	+	8.60870i	0.580839	+	0.335348i	−0.180628	+	0.983552i	$0.557813\pi$
$660$	10.4533	+	2.66580i	0.406894	+	0.103766i
$661$	2.99584	−	5.18895i	0.116525	−	0.201827i	−0.801863	−	0.597507i	$-0.796158\pi$
$661$	2.99584	−	5.18895i	0.116525	−	0.201827i	0.918388	+	0.395680i	$0.129491\pi$
$662$	7.25351	−	4.18782i	0.281916	−	0.162764i
$663$	−4.84685	−	19.2911i	−0.188236	−	0.749205i
$664$		−	13.0790i		−	0.507564i
$665$	9.77452	+	1.35878i	0.379040	+	0.0526911i
$666$	−1.51130	+	0.0365861i	−0.0585616	+	0.00141768i
$667$	2.59927	+	4.50206i	0.100644	+	0.174321i
$668$	3.11618	−	1.79913i	0.120569	−	0.0696103i
$669$	−12.2395	+	47.9945i	−0.473208	+	1.85557i
$670$	−9.11349	−	15.7850i	−0.352085	−	0.609829i
$671$			39.6262i			1.52975i
$672$	3.62196	−	2.80738i	0.139720	−	0.108297i
$673$	−16.9593	−	29.3743i	−0.653732	−	1.13230i	−0.982210	−	0.187786i	$-0.939869\pi$
$673$	−16.9593	−	29.3743i	−0.653732	−	1.13230i	0.328478	−	0.944512i	$-0.393464\pi$
$674$	−9.14343			−0.352192
$675$	−8.25210	−	1.89299i	−0.317624	−	0.0728613i
$676$	5.86551	+	11.6015i	0.225597	+	0.446213i
$677$	−6.91552	+	11.9780i	−0.265785	+	0.460353i	−0.967769	−	0.251840i	$-0.918964\pi$
$677$	−6.91552	+	11.9780i	−0.265785	+	0.460353i	0.701984	+	0.712193i	$0.252298\pi$
$678$	7.48659	+	26.6462i	0.287521	+	1.02334i
$679$	−20.0344	−	15.6043i	−0.768849	−	0.598836i
$680$	5.06412	+	2.92377i	0.194200	+	0.112121i
$681$	−7.27089	+	7.44904i	−0.278621	+	0.285448i
$682$	21.3282			0.816701
$683$	4.69607			0.179690			0.0898451	−	0.995956i	$-0.471363\pi$
$683$	4.69607			0.179690			0.0898451	+	0.995956i	$0.471363\pi$
$684$	5.20306	−	3.17431i	0.198944	−	0.121373i
$685$	5.06095	+	2.92194i	0.193369	+	0.111642i
$686$	7.45669	−	16.9528i	0.284698	−	0.647261i
$687$	23.4394	−	6.58559i	0.894268	−	0.251256i
$688$	0.528972	−	0.916206i	0.0201669	−	0.0349300i
$689$	−24.2075	−	0.671892i	−0.922231	−	0.0255970i
$690$	7.57877	−	2.12935i	0.288519	−	0.0810630i
$691$	23.8018			0.905465			0.452732	−	0.891646i	$-0.350449\pi$
$691$	23.8018			0.905465			0.452732	+	0.891646i	$0.350449\pi$
$692$	−0.476807	−	0.825853i	−0.0181255	−	0.0313942i
$693$	16.0271	−	21.6379i	0.608821	−	0.821954i
$694$		−	31.0967i		−	1.18042i
$695$	0.104056	+	0.180230i	0.00394705	+	0.00683650i
$696$	−3.52435	−	0.898778i	−0.133590	−	0.0340681i
$697$	13.8609	−	8.00258i	0.525018	−	0.303119i
$698$	14.0331	+	24.3060i	0.531161	+	0.919997i
$699$	13.0078	+	46.2973i	0.492001	+	1.75113i
$700$	3.99457	−	1.62088i	0.150981	−	0.0612636i
$701$			35.3397i			1.33476i	0.744716	+	0.667382i	$0.232585\pi$
$701$			35.3397i			1.33476i	−0.744716	+	0.667382i	$0.767415\pi$
$702$	18.0545	−	5.00365i	0.681422	−	0.188851i
$703$	0.886611	−	0.511885i	0.0334392	−	0.0193061i
$704$	−1.69625	+	2.93798i	−0.0639297	+	0.110729i
$705$	9.16221	−	35.9275i	0.345069	−	1.35311i
$706$	24.5364	+	14.1661i	0.923438	+	0.533147i
$707$	19.6014	+	15.2670i	0.737186	+	0.574175i
$708$	7.51177	−	7.69582i	0.282310	−	0.289227i
$709$	−10.6916	+	6.17279i	−0.401531	+	0.231824i	−0.687144	−	0.726521i	$-0.741136\pi$
$709$	−10.6916	+	6.17279i	−0.401531	+	0.231824i	0.285613	+	0.958345i	$0.407803\pi$
$710$	−24.7090	+	14.2657i	−0.927310	+	0.535383i
$711$	20.6686	+	11.2751i	0.775133	+	0.422848i
$712$			5.33363i			0.199886i
$713$	13.4787	−	7.78193i	0.504781	−	0.291435i
$714$	11.5362	−	8.94169i	0.431730	−	0.334634i
$715$	−22.4481	−	0.623059i	−0.839510	−	0.0233011i
$716$	15.3789	+	8.87903i	0.574738	+	0.331825i
$717$	−6.58592	−	6.42842i	−0.245956	−	0.240074i
$718$	−10.8679	+	18.8238i	−0.405588	+	0.702499i
$719$	1.87992	+	3.25611i	0.0701091	+	0.121433i	0.898949	−	0.438053i	$-0.144332\pi$
$719$	1.87992	+	3.25611i	0.0701091	+	0.121433i	−0.828840	+	0.559486i	$0.810999\pi$
$720$	−2.63765	+	4.83513i	−0.0982994	+	0.180195i
$721$	21.7097	−	27.8732i	0.808513	−	1.03805i
$722$	7.43622	−	12.8799i	0.276747	−	0.479341i
$723$	23.8695	+	23.2986i	0.887715	+	0.866485i
$724$		−	5.51564i		−	0.204987i
$725$	−2.96312	−	1.71076i	−0.110048	−	0.0635360i
$726$	−0.217853	+	0.854260i	−0.00808529	+	0.0317046i
$727$		−	10.4236i		−	0.386592i	−0.981141	−	0.193296i	$-0.938082\pi$
$727$		−	10.4236i		−	0.386592i	0.981141	−	0.193296i	$-0.0619177\pi$
$728$	−6.06831	+	7.36041i	−0.224906	+	0.272795i
$729$	−1.95878	−	26.9289i	−0.0725473	−	0.997365i
$730$		−	16.4343i		−	0.608260i
$731$	1.68481	−	2.91817i	0.0623148	−	0.107932i
$732$	−19.6039	−	4.99938i	−0.724580	−	0.184782i
$733$	17.7435	−	30.7327i	0.655373	−	1.13514i	−0.326428	−	0.945222i	$-0.605845\pi$
$733$	17.7435	−	30.7327i	0.655373	−	1.13514i	0.981800	−	0.189917i	$-0.0608217\pi$
$734$	13.6561	+	7.88437i	0.504057	+	0.291017i
$735$	−0.0523701	+	22.2594i	−0.00193170	+	0.821050i
$736$			2.47560i			0.0912519i
$737$	29.1681	−	16.8402i	1.07442	−	0.620317i
$738$	7.85136	+	12.8693i	0.289013	+	0.473725i
$739$	5.40360	+	3.11977i	0.198775	+	0.114763i	0.596084	−	0.802922i	$-0.296723\pi$
$739$	5.40360	+	3.11977i	0.198775	+	0.114763i	−0.397309	+	0.917685i	$0.630056\pi$
$740$	−0.462574	+	0.801202i	−0.0170046	+	0.0294528i
$741$	−9.11075	+	8.83002i	−0.334692	+	0.324379i
$742$	−6.68155	−	16.4663i	−0.245287	−	0.604497i
$743$	21.5450	+	37.3170i	0.790408	+	1.36903i	0.925714	+	0.378223i	$0.123465\pi$
$743$	21.5450	+	37.3170i	0.790408	+	1.36903i	−0.135306	+	0.990804i	$0.543202\pi$
$744$	−2.69085	+	10.5515i	−0.0986512	+	0.386838i
$745$			39.8627i			1.46046i
$746$	3.62253	+	6.27441i	0.132630	+	0.229723i
$747$	39.2255	−	0.949587i	1.43519	−	0.0347436i
$748$	−5.40264	+	9.35765i	−0.197540	+	0.342150i
$749$	35.0393	+	4.87088i	1.28031	+	0.177978i
$750$	−14.7249	+	15.0857i	−0.537679	+	0.550853i
$751$	−31.3887			−1.14539			−0.572695	−	0.819769i	$-0.694102\pi$
$751$	−31.3887			−1.14539			−0.572695	+	0.819769i	$0.694102\pi$
$752$	10.0977	+	5.82991i	0.368226	+	0.212595i
$753$	15.8610	−	4.45634i	0.578005	−	0.162398i
$754$	7.56841	+	0.210065i	0.275625	+	0.00765013i
$755$	−9.95736			−0.362385
$756$	8.68265	+	10.6589i	0.315785	+	0.387659i
$757$	6.13845	+	10.6321i	0.223106	+	0.386430i	0.955749	−	0.294182i	$-0.0950472\pi$
$757$	6.13845	+	10.6321i	0.223106	+	0.386430i	−0.732644	+	0.680612i	$0.761714\pi$
$758$	4.24213	−	2.44920i	0.154081	−	0.0889588i
$759$	3.93469	+	14.0043i	0.142820	+	0.508324i
$760$		−	3.72995i		−	0.135299i
$761$	14.6878	−	8.48003i	0.532434	−	0.307401i	−0.209573	−	0.977793i	$-0.567207\pi$
$761$	14.6878	−	8.48003i	0.532434	−	0.307401i	0.742007	+	0.670392i	$0.233874\pi$
$762$	−0.407452	+	1.59773i	−0.0147604	+	0.0578796i
$763$	4.39905	+	10.8412i	0.159256	+	0.392478i
$764$	17.4751	−	10.0893i	0.632228	−	0.365017i
$765$	−8.40107	+	15.4002i	−0.303741	+	0.556795i
$766$	−6.85462	+	3.95752i	−0.247668	+	0.142991i
$767$	−11.7269	+	19.0693i	−0.423433	+	0.688554i
$768$	−1.23948	−	1.20983i	−0.0447258	−	0.0436561i
$769$	18.2706	+	31.6457i	0.658856	+	1.14117i	0.980912	+	0.194451i	$0.0622926\pi$
$769$	18.2706	+	31.6457i	0.658856	+	1.14117i	−0.322056	+	0.946720i	$0.604374\pi$
$770$	−6.19594	−	15.2695i	−0.223286	−	0.550276i
$771$	6.52427	+	6.36824i	0.234966	+	0.229347i
$772$	3.93413	+	2.27137i	0.141593	+	0.0817485i
$773$		−	0.970568i		−	0.0349089i	−0.999848	−	0.0174545i	$-0.994444\pi$
$773$		−	0.970568i		−	0.0349089i	0.999848	−	0.0174545i	$-0.00555621\pi$
$774$	2.78622	+	1.51993i	0.100149	+	0.0546327i
$775$	−5.12183	+	8.87127i	−0.183982	+	0.318666i
$776$	−4.79907	+	8.31223i	−0.172276	+	0.298392i
$777$	1.41468	+	1.82515i	0.0507513	+	0.0654770i
$778$	2.27718	−	1.31473i	0.0816408	−	0.0471354i
$779$	−8.84137	−	5.10457i	−0.316775	−	0.182890i
$780$	3.14037	−	11.0269i	0.112443	−	0.394827i
$781$	−26.3607	−	45.6580i	−0.943259	−	1.63377i
$782$			7.88494i			0.281965i
$783$	2.43966	−	10.6352i	0.0871865	−	0.380071i
$784$	−6.73459	−	1.90927i	−0.240521	−	0.0681884i
$785$	39.0540			1.39390
$786$	16.5334	−	4.64528i	0.589728	−	0.165692i
$787$	23.5083			0.837981			0.418990	−	0.907991i	$-0.362384\pi$
$787$	23.5083			0.837981			0.418990	+	0.907991i	$0.362384\pi$
$788$	5.74363	+	9.94826i	0.204608	+	0.354392i
$789$	−5.08326	−	18.0923i	−0.180969	−	0.644102i
$790$	12.4780	−	7.20417i	0.443947	−	0.256313i
$791$	25.9794	−	33.3551i	0.923723	−	1.18597i
$792$	−8.93452	−	4.87394i	−0.317474	−	0.173188i
$793$	42.0986	+	1.16847i	1.49497	+	0.0414936i
$794$	−16.5529	−	28.6705i	−0.587440	−	1.01748i
$795$	15.2841	+	14.9185i	0.542070	+	0.529106i
$796$		−	6.86468i		−	0.243312i
$797$	−21.5529	+	37.3307i	−0.763443	+	1.32232i	0.177623	+	0.984099i	$0.443159\pi$
$797$	−21.5529	+	37.3307i	−0.763443	+	1.32232i	−0.941066	+	0.338224i	$0.890174\pi$
$798$	−8.61872	−	3.52087i	−0.305099	−	0.124637i
$799$	32.1618	+	18.5686i	1.13780	+	0.656911i
$800$	−0.814684	−	1.41107i	−0.0288034	−	0.0498890i
$801$	−15.9962	+	0.387243i	−0.565198	+	0.0136825i
$802$	6.99738			0.247086
$803$	30.3678			1.07166
$804$	4.65125	+	16.5547i	0.164037	+	0.583839i
$805$	−9.48693	−	7.38912i	−0.334370	−	0.260432i
$806$	0.628914	−	22.6590i	0.0221525	−	0.798129i
$807$	22.4491	+	21.9122i	0.790245	+	0.771346i
$808$	4.69535	−	8.13258i	0.165182	−	0.286103i
$809$	20.1056	+	11.6080i	0.706876	+	0.408115i	0.809903	−	0.586563i	$-0.199519\pi$
$809$	20.1056	+	11.6080i	0.706876	+	0.408115i	−0.103027	+	0.994679i	$0.532853\pi$
$810$	−14.6927	−	7.55958i	−0.516247	−	0.265616i
$811$	14.3001			0.502145			0.251072	−	0.967968i	$-0.419217\pi$
$811$	14.3001			0.502145			0.251072	+	0.967968i	$0.419217\pi$
$812$	2.08897	+	5.14815i	0.0733086	+	0.180665i
$813$	−10.7503	−	10.4932i	−0.377031	−	0.368014i
$814$	−1.48049	−	0.854760i	−0.0518911	−	0.0299593i
$815$	18.3937			0.644303
$816$	−3.94781	−	3.85339i	−0.138201	−	0.134896i
$817$	−2.14936			−0.0751966
$818$	−31.8405			−1.11328
$819$	−22.5153	−	17.6652i	−0.786750	−	0.617272i
$820$	9.22567			0.322174
$821$	−12.0434			−0.420317			−0.210158	−	0.977667i	$-0.567398\pi$
$821$	−12.0434			−0.420317			−0.210158	+	0.977667i	$0.567398\pi$
$822$	−3.94534	−	3.85099i	−0.137610	−	0.134319i
$823$	−37.4655			−1.30597			−0.652983	−	0.757372i	$-0.726483\pi$
$823$	−37.4655			−1.30597			−0.652983	+	0.757372i	$0.726483\pi$
$824$	−11.5646	−	6.67680i	−0.402870	−	0.232597i
$825$	−6.85135	−	6.68749i	−0.238533	−	0.232829i
$826$	−16.2708	−	2.26184i	−0.566134	−	0.0786995i
$827$	12.7766			0.444287			0.222144	−	0.975014i	$-0.428695\pi$
$827$	12.7766			0.444287			0.222144	+	0.975014i	$0.428695\pi$
$828$	−7.42463	+	0.179738i	−0.258024	+	0.00624634i
$829$	−29.2392	−	16.8813i	−1.01552	−	0.586311i	−0.102717	−	0.994711i	$-0.532754\pi$
$829$	−29.2392	−	16.8813i	−1.01552	−	0.586311i	−0.912803	+	0.408400i	$0.866087\pi$
$830$	12.0061	−	20.7951i	0.416736	−	0.721808i
$831$	22.6620	+	22.1200i	0.786135	+	0.767335i
$832$	3.07128	+	1.88872i	0.106477	+	0.0654794i
$833$	−21.4501	−	6.08115i	−0.743201	−	0.210699i
$834$	−0.0531068	−	0.189017i	−0.00183894	−	0.00654514i
$835$	6.60613			0.228615
$836$	6.89232			0.238376
$837$	−31.8407	−	7.30409i	−1.10057	−	0.252466i
$838$	5.19733	+	9.00204i	0.179539	+	0.310970i
$839$	−30.8994	−	17.8398i	−1.06677	−	0.615897i	−0.139469	−	0.990226i	$-0.544540\pi$
$839$	−30.8994	−	17.8398i	−1.06677	−	0.615897i	−0.927296	+	0.374329i	$0.877873\pi$
$840$	8.33585	−	1.13880i	0.287614	−	0.0392923i
$841$	−12.2952	+	21.2959i	−0.423972	+	0.734341i
$842$			0.111490i			0.00384219i
$843$	3.39342	+	3.31227i	0.116876	+	0.114081i
$844$	−2.63957	−	4.57187i	−0.0908577	−	0.157370i
$845$	−1.32387	+	23.8303i	−0.0455424	+	0.819788i
$846$	−16.7515	+	30.7075i	−0.575928	+	1.05575i
$847$	1.24785	−	0.506342i	0.0428767	−	0.0173981i
$848$	−5.81668	+	3.35826i	−0.199746	+	0.115323i
$849$	−2.48874	−	8.85790i	−0.0854133	−	0.304002i
$850$	−2.59482	−	4.49435i	−0.0890014	−	0.154155i
$851$	−1.24749			−0.0427634
$852$	25.9137	−	7.28079i	0.887790	−	0.249436i
$853$	50.6470			1.73412			0.867061	−	0.498202i	$-0.166006\pi$
$853$	50.6470			1.73412			0.867061	+	0.498202i	$0.166006\pi$
$854$	11.6197	+	28.6362i	0.397619	+	0.979909i
$855$	11.1866	−	0.270809i	0.382572	−	0.00926147i
$856$		−	13.3709i		−	0.457009i
$857$	−7.48332	−	12.9615i	−0.255625	−	0.442756i	0.709440	−	0.704766i	$-0.248948\pi$
$857$	−7.48332	−	12.9615i	−0.255625	−	0.442756i	−0.965065	+	0.262010i	$0.915615\pi$
$858$	20.3759	+	5.80288i	0.695622	+	0.198107i
$859$	42.5746	+	24.5804i	1.45263	+	0.838674i	0.998630	−	0.0523306i	$-0.0166650\pi$
$859$	42.5746	+	24.5804i	1.45263	+	0.838674i	0.453995	+	0.891004i	$0.349998\pi$
$860$	1.68209	−	0.971154i	0.0573587	−	0.0331161i
$861$	8.70854	−	21.3176i	0.296786	−	0.726501i
$862$	19.3138	−	33.4525i	0.657830	−	1.13940i
$863$	−25.6886	+	44.4940i	−0.874451	+	1.51459i	−0.0171055	+	0.999854i	$0.505445\pi$
$863$	−25.6886	+	44.4940i	−0.874451	+	1.51459i	−0.857346	+	0.514741i	$0.827888\pi$
$864$	3.53845	−	3.80518i	0.120380	−	0.129455i
$865$		−	1.75077i		−	0.0595278i
$866$	−5.30602	−	3.06343i	−0.180306	−	0.104100i
$867$	8.49710	+	8.29389i	0.288577	+	0.281675i
$868$	15.4130	−	6.25416i	0.523152	−	0.212280i
$869$	13.3121	+	23.0573i	0.451582	+	0.782164i
$870$	−4.77853	−	4.66425i	−0.162007	−	0.158133i
$871$	−17.0309	−	31.4846i	−0.577069	−	1.06682i
$872$	3.82963	−	2.21104i	0.129688	−	0.0748752i
$873$	−25.2778	−	13.7895i	−0.855524	−	0.466703i
$874$	4.35570	−	2.51477i	0.147334	−	0.0850632i
$875$	31.8949	+	4.43377i	1.07824	+	0.149889i
$876$	−3.83131	+	15.0236i	−0.129448	+	0.507600i
$877$	−41.0778	+	23.7163i	−1.38710	+	0.800843i	−0.992987	−	0.118219i	$-0.962281\pi$
$877$	−41.0778	+	23.7163i	−1.38710	+	0.800843i	−0.394113	+	0.919062i	$0.628948\pi$
$878$			34.9618i			1.17990i
$879$	1.55194	+	5.52366i	0.0523457	+	0.186308i
$880$	−5.39393	+	3.11418i	−0.181829	+	0.104979i
$881$	−5.06534	−	8.77342i	−0.170656	−	0.295584i	0.767994	−	0.640457i	$-0.221255\pi$
$881$	−5.06534	−	8.77342i	−0.170656	−	0.295584i	−0.938649	+	0.344873i	$0.887922\pi$
$882$	5.23719	−	20.3365i	0.176345	−	0.684764i
$883$	−12.1164			−0.407751			−0.203875	−	0.978997i	$-0.565354\pi$
$883$	−12.1164			−0.407751			−0.203875	+	0.978997i	$0.565354\pi$
$884$	9.78221	+	6.01567i	0.329011	+	0.202329i
$885$	19.0079	−	5.34051i	0.638944	−	0.179519i
$886$	7.76750	+	4.48457i	0.260954	+	0.150662i
$887$	−4.05982			−0.136315			−0.0681576	−	0.997675i	$-0.521712\pi$
$887$	−4.05982			−0.136315			−0.0681576	+	0.997675i	$0.521712\pi$
$888$	0.609651	−	0.624589i	0.0204586	−	0.0209598i
$889$	2.33386	−	0.947016i	0.0782753	−	0.0317619i
$890$	−4.89608	+	8.48026i	−0.164117	+	0.284259i
$891$	13.9688	−	27.1496i	0.467974	−	0.909545i
$892$	−14.2982	−	24.7653i	−0.478741	−	0.829203i
$893$		−	23.6886i		−	0.792708i
$894$	9.29317	−	36.4410i	0.310810	−	1.21877i
$895$	16.3013	+	28.2346i	0.544891	+	0.943779i
$896$	−0.364289	+	2.62055i	−0.0121700	+	0.0875465i
$897$	14.9941	−	3.76724i	0.500639	−	0.125784i
$898$	−9.32220	+	16.1465i	−0.311086	+	0.538817i
$899$	−11.4332	−	6.60095i	−0.381318	−	0.220154i
$900$	4.17283	−	2.54578i	0.139094	−	0.0848595i
$901$	−18.5265	+	10.6963i	−0.617206	+	0.356344i
$902$			17.0475i			0.567620i
$903$	−0.656227	−	4.80349i	−0.0218379	−	0.159850i
$904$	−13.8390	−	7.98994i	−0.460278	−	0.265742i
$905$	5.06316	−	8.76966i	0.168305	−	0.291513i
$906$	9.10263	+	2.32135i	0.302415	+	0.0771217i
$907$	6.68775	−	11.5835i	0.222063	−	0.384625i	−0.733371	−	0.679828i	$-0.762054\pi$
$907$	6.68775	−	11.5835i	0.222063	−	0.384625i	0.955434	+	0.295204i	$0.0953876\pi$
$908$		−	6.00983i		−	0.199443i
$909$	24.7315	+	13.4915i	0.820292	+	0.447483i
$910$	−16.4050	+	6.13227i	−0.543819	+	0.203283i
$911$			21.8063i			0.722475i	0.932474	+	0.361238i	$0.117646\pi$
$911$			21.8063i			0.722475i	−0.932474	+	0.361238i	$0.882354\pi$
$912$	−0.869560	+	3.40977i	−0.0287940	+	0.112909i
$913$	38.4259	+	22.1852i	1.27171	+	0.734223i
$914$			28.4939i			0.942496i
$915$	−26.5802	−	25.9445i	−0.878713	−	0.857698i
$916$	−7.02836	+	12.1735i	−0.232224	+	0.402223i
$917$	−20.6962	−	16.1197i	−0.683448	−	0.532320i
$918$	11.2702	−	12.1197i	0.371971	−	0.400010i
$919$	−4.56863	−	7.91310i	−0.150705	−	0.261029i	0.780782	−	0.624804i	$-0.214821\pi$
$919$	−4.56863	−	7.91310i	−0.150705	−	0.261029i	−0.931487	+	0.363775i	$0.881488\pi$
$920$	−2.27251	+	3.93611i	−0.0749226	+	0.129770i
$921$	−29.6004	−	28.8925i	−0.975365	−	0.952039i
$922$	10.2455	+	5.91523i	0.337417	+	0.194808i
$923$	−49.2842	+	26.6591i	−1.62221	+	0.877495i
$924$	2.10431	+	15.4033i	0.0692269	+	0.506730i
$925$	0.711059	−	0.410530i	0.0233795	−	0.0134981i
$926$		−	10.9649i		−	0.360329i
$927$	19.1849	−	35.1683i	0.630115	−	1.15508i
$928$	1.81857	−	1.04995i	0.0596976	−	0.0344664i
$929$	−11.7550	+	6.78673i	−0.385668	+	0.222665i	−0.680281	−	0.732951i	$-0.738142\pi$
$929$	−11.7550	+	6.78673i	−0.385668	+	0.222665i	0.294614	+	0.955616i	$0.404809\pi$
$930$	−13.9643	+	14.3064i	−0.457906	+	0.469125i
$931$	3.48185	+	13.7887i	0.114113	+	0.451905i
$932$	−24.0450	−	13.8824i	−0.787620	−	0.454732i
$933$	−13.5552	+	53.1537i	−0.443779	+	1.74017i
$934$	−10.0288	+	17.3705i	−0.328154	+	0.568379i
$935$	−17.1800	+	9.91886i	−0.561845	+	0.324382i
$936$	−5.44150	+	9.34827i	−0.177861	+	0.305558i
$937$		−	0.647634i		−	0.0211573i	−0.999944	−	0.0105786i	$-0.996633\pi$
$937$		−	0.647634i		−	0.0211573i	0.999944	−	0.0105786i	$-0.00336735\pi$
$938$	16.1404	−	20.7228i	0.527004	−	0.676623i
$939$	−6.76663	−	24.0837i	−0.220821	−	0.785943i
$940$	10.7033	+	18.5387i	0.349103	+	0.604665i
$941$	−43.1576	+	24.9171i	−1.40690	+	0.812273i	−0.995088	−	0.0989966i	$-0.968437\pi$
$941$	−43.1576	+	24.9171i	−1.40690	+	0.812273i	−0.411810	+	0.911270i	$0.635103\pi$
$942$	−35.7017	−	9.10463i	−1.16322	−	0.296645i
$943$	6.22004	+	10.7734i	0.202552	+	0.350831i
$944$			6.20893i			0.202083i
$945$	4.02062	+	24.9175i	0.130791	+	0.810568i
$946$	1.79453	+	3.10822i	0.0583452	+	0.101057i
$947$	10.8705			0.353243			0.176621	−	0.984279i	$-0.443483\pi$
$947$	10.8705			0.353243			0.176621	+	0.984279i	$0.443483\pi$
$948$	−13.0864	+	3.67679i	−0.425027	+	0.119417i
$949$	0.895466	−	32.2626i	0.0290681	−	1.04729i
$950$	−1.65514	+	2.86679i	−0.0537000	+	0.0930111i
$951$	−42.6671	+	11.9879i	−1.38357	+	0.388733i
$952$	−1.16028	+	8.34661i	−0.0376049	+	0.270515i
$953$	26.6142	+	15.3657i	0.862119	+	0.497744i	0.864721	−	0.502252i	$-0.167495\pi$
$953$	26.6142	+	15.3657i	0.862119	+	0.497744i	−0.00260249	+	0.999997i	$0.500828\pi$
$954$	−10.4942	−	17.2011i	−0.339761	−	0.556907i
$955$	37.0464			1.19879
$956$	5.31347			0.171850
$957$	8.61875	−	8.82993i	0.278605	−	0.285431i
$958$	−26.6476	−	15.3850i	−0.860943	−	0.497066i
$959$	−1.15956	+	8.34140i	−0.0374440	+	0.269358i
$960$	−0.860135	−	3.06138i	−0.0277607	−	0.0988057i
$961$	−4.26254	+	7.38293i	−0.137501	+	0.238159i
$962$	−0.951748	+	1.54766i	−0.0306856	+	0.0498985i
$963$	40.1011	−	0.970783i	1.29224	−	0.0312831i
$964$	−19.2577			−0.620249
$965$	4.17008	+	7.22278i	0.134240	+	0.232510i
$966$	6.94996	+	8.96653i	0.223611	+	0.288493i
$967$			25.4787i			0.819341i	0.912234	+	0.409671i	$0.134356\pi$
$967$			25.4787i			0.819341i	−0.912234	+	0.409671i	$0.865644\pi$
$968$	−0.254496	−	0.440801i	−0.00817982	−	0.0141679i
$969$	−2.76960	+	10.8603i	−0.0889724	+	0.348884i
$970$	−15.2607	+	8.81074i	−0.489990	+	0.282896i
$971$	−9.57391	−	16.5825i	−0.307241	−	0.532157i	0.670517	−	0.741895i	$-0.266073\pi$
$971$	−9.57391	−	16.5825i	−0.307241	−	0.532157i	−0.977758	+	0.209737i	$0.932739\pi$
$972$	11.6691	+	10.3360i	0.374287	+	0.331526i
$973$	−0.184288	+	0.236608i	−0.00590799	+	0.00758530i
$974$			35.8831i			1.14977i
$975$	−7.30678	+	7.08164i	−0.234004	+	0.226794i
$976$	10.1157	−	5.84028i	0.323794	−	0.186943i
$977$	1.43387	−	2.48354i	0.0458736	−	0.0794554i	−0.842177	−	0.539201i	$-0.818726\pi$
$977$	1.43387	−	2.48354i	0.0458736	−	0.0794554i	0.888051	+	0.459746i	$0.152060\pi$
$978$	−16.8148	−	4.28811i	−0.537678	−	0.137119i
$979$	−15.6701	−	9.04714i	−0.500819	−	0.289148i
$980$	−8.95508	−	9.21778i	−0.286060	−	0.294451i
$981$	6.90922	+	11.3250i	0.220594	+	0.361579i
$982$	−32.3384	+	18.6706i	−1.03196	+	0.595802i
$983$	39.2792	−	22.6779i	1.25281	−	0.723312i	0.281146	−	0.959665i	$-0.409285\pi$
$983$	39.2792	−	22.6779i	1.25281	−	0.723312i	0.971667	+	0.236353i	$0.0759521\pi$
$984$	−8.43375	−	2.15077i	−0.268858	−	0.0685642i
$985$			21.0898i			0.671977i
$986$	5.79226	−	3.34416i	0.184463	−	0.106500i
$987$	52.9403	−	7.23243i	1.68511	−	0.230211i
$988$	0.203236	−	7.32236i	0.00646581	−	0.232955i
$989$	2.26816	+	1.30952i	0.0721233	+	0.0416404i
$990$	−9.73144	−	15.9509i	−0.309285	−	0.506954i
$991$	−13.1284	+	22.7390i	−0.417037	+	0.722329i	−0.995640	−	0.0932802i	$-0.970265\pi$
$991$	−13.1284	+	22.7390i	−0.417037	+	0.722329i	0.578603	+	0.815609i	$0.303598\pi$
$992$	−3.14345	−	5.44461i	−0.0998046	−	0.172867i
$993$	−14.0571	−	3.58484i	−0.446089	−	0.113762i
$994$	−32.4382	−	25.2653i	−1.02888	−	0.801366i
$995$	6.30153	−	10.9146i	0.199772	−	0.346015i
$996$	−15.8234	+	16.2111i	−0.501384	+	0.513669i
$997$		−	25.2501i		−	0.799678i	−0.916585	−	0.399839i	$-0.869066\pi$
$997$		−	25.2501i		−	0.799678i	0.916585	−	0.399839i	$-0.130934\pi$
$998$	19.1199	+	11.0389i	0.605231	+	0.349430i
$999$	1.91748	+	1.78307i	0.0606664	+	0.0564139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.f.257.4	yes	34
3.2	odd	2		546.2.bi.e.257.1	yes	34
7.3	odd	6		546.2.bn.e.101.9	yes	34
13.4	even	6		546.2.bn.f.173.9	yes	34
21.17	even	6		546.2.bn.f.101.9	yes	34
39.17	odd	6		546.2.bn.e.173.9	yes	34
91.17	odd	6		546.2.bi.e.17.1	✓	34
273.17	even	6	inner	546.2.bi.f.17.4	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.1	✓	34	91.17	odd	6
546.2.bi.e.257.1	yes	34	3.2	odd	2
546.2.bi.f.17.4	yes	34	273.17	even	6	inner
546.2.bi.f.257.4	yes	34	1.1	even	1	trivial
546.2.bn.e.101.9	yes	34	7.3	odd	6
546.2.bn.e.173.9	yes	34	39.17	odd	6
546.2.bn.f.101.9	yes	34	21.17	even	6
546.2.bn.f.173.9	yes	34	13.4	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.23948 - 1.20983i) q^{3} +1.00000 q^{4} +(1.58996 + 0.917964i) q^{5} +(-1.23948 - 1.20983i) q^{6} +(-0.364289 + 2.62055i) q^{7} +1.00000 q^{8} +(0.0726040 + 2.99912i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.23948 - 1.20983i) q^{3} +1.00000 q^{4} +(1.58996 + 0.917964i) q^{5} +(-1.23948 - 1.20983i) q^{6} +(-0.364289 + 2.62055i) q^{7} +1.00000 q^{8} +(0.0726040 + 2.99912i) q^{9} +(1.58996 + 0.917964i) q^{10} +(-1.69625 + 2.93798i) q^{11} +(-1.23948 - 1.20983i) q^{12} +(3.07128 + 1.88872i) q^{13} +(-0.364289 + 2.62055i) q^{14} +(-0.860135 - 3.06138i) q^{15} +1.00000 q^{16} +3.18506 q^{17} +(0.0726040 + 2.99912i) q^{18} +(-1.01582 - 1.75945i) q^{19} +(1.58996 + 0.917964i) q^{20} +(3.62196 - 2.80738i) q^{21} +(-1.69625 + 2.93798i) q^{22} +2.47560i q^{23} +(-1.23948 - 1.20983i) q^{24} +(-0.814684 - 1.41107i) q^{25} +(3.07128 + 1.88872i) q^{26} +(3.53845 - 3.80518i) q^{27} +(-0.364289 + 2.62055i) q^{28} +(1.81857 - 1.04995i) q^{29} +(-0.860135 - 3.06138i) q^{30} +(-3.14345 - 5.44461i) q^{31} +1.00000 q^{32} +(5.65693 - 1.58939i) q^{33} +3.18506 q^{34} +(-2.98478 + 3.83217i) q^{35} +(0.0726040 + 2.99912i) q^{36} +0.503913i q^{37} +(-1.01582 - 1.75945i) q^{38} +(-1.52175 - 6.05676i) q^{39} +(1.58996 + 0.917964i) q^{40} +(4.35184 - 2.51254i) q^{41} +(3.62196 - 2.80738i) q^{42} +(0.528972 - 0.916206i) q^{43} +(-1.69625 + 2.93798i) q^{44} +(-2.63765 + 4.83513i) q^{45} +2.47560i q^{46} +(10.0977 + 5.82991i) q^{47} +(-1.23948 - 1.20983i) q^{48} +(-6.73459 - 1.90927i) q^{49} +(-0.814684 - 1.41107i) q^{50} +(-3.94781 - 3.85339i) q^{51} +(3.07128 + 1.88872i) q^{52} +(-5.81668 + 3.35826i) q^{53} +(3.53845 - 3.80518i) q^{54} +(-5.39393 + 3.11418i) q^{55} +(-0.364289 + 2.62055i) q^{56} +(-0.869560 + 3.40977i) q^{57} +(1.81857 - 1.04995i) q^{58} +6.20893i q^{59} +(-0.860135 - 3.06138i) q^{60} +(10.1157 - 5.84028i) q^{61} +(-3.14345 - 5.44461i) q^{62} +(-7.88580 - 0.902283i) q^{63} +1.00000 q^{64} +(3.14944 + 5.82231i) q^{65} +(5.65693 - 1.58939i) q^{66} +(-8.59785 - 4.96397i) q^{67} +3.18506 q^{68} +(2.99507 - 3.06845i) q^{69} +(-2.98478 + 3.83217i) q^{70} +(-7.77030 + 13.4586i) q^{71} +(0.0726040 + 2.99912i) q^{72} +(-4.47574 - 7.75221i) q^{73} +0.503913i q^{74} +(-0.697383 + 2.73462i) q^{75} +(-1.01582 - 1.75945i) q^{76} +(-7.08122 - 5.51537i) q^{77} +(-1.52175 - 6.05676i) q^{78} +(3.92399 - 6.79656i) q^{79} +(1.58996 + 0.917964i) q^{80} +(-8.98946 + 0.435496i) q^{81} +(4.35184 - 2.51254i) q^{82} -13.0790i q^{83} +(3.62196 - 2.80738i) q^{84} +(5.06412 + 2.92377i) q^{85} +(0.528972 - 0.916206i) q^{86} +(-3.52435 - 0.898778i) q^{87} +(-1.69625 + 2.93798i) q^{88} +5.33363i q^{89} +(-2.63765 + 4.83513i) q^{90} +(-6.06831 + 7.36041i) q^{91} +2.47560i q^{92} +(-2.69085 + 10.5515i) q^{93} +(10.0977 + 5.82991i) q^{94} -3.72995i q^{95} +(-1.23948 - 1.20983i) q^{96} +(-4.79907 + 8.31223i) q^{97} +(-6.73459 - 1.90927i) q^{98} +(-8.93452 - 4.87394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

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